rohitspider/cross_query_benchmark

Cross-Query Contradiction Benchmark

Quantifying Cross-Query Contradictions in Multi-Query LLM Reasoning

Accepted at the ICLR 2026 Workshop on Logical Reasoning of Large Language Models

Rohit Kumar Salla (Virginia Tech), Ramya Manasa Amancherla (Columbia University), Manoj Saravanan (Virginia Tech)

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Overview

Large language models frequently produce mutually inconsistent answers when reasoning over multiple related queries derived from the same premises. This benchmark evaluates case-file logical consistency: whether a model can maintain a globally satisfiable belief state across a bundle of interdependent queries.

The benchmark contains 390 case files across four reasoning domains, with 2,515 queries organized into bundles of 5–8 interdependent questions. Every label is machine-verified via Z3/CaDiCaL solvers, and each case includes formal representations and cross-query dependency annotations.

Key Features

• Z3-verified labels: All ENTAILED / CONTRADICTED / UNKNOWN labels are verified by SAT/SMT solvers — not just human annotation
• Cross-query dependency annotations: Each query is annotated with which other queries in its bundle it logically interacts with
• Formal representations: SMT-LIB and CNF formal encodings included for every case file
• 82.4% unique queries: Minimal duplication across bundles (vs. typical synthetic benchmarks)
• Four reasoning domains: Relational (SAT), Temporal (SMT), Policy/Rules, and Underspecified/Abductive
• Detailed reasoning traces: Average 95 characters per query (not trivial one-liners)

Benchmark Statistics

	Cases	Bundles	Queries	Logic Fragment
Relational (SAT)	120	120	787	Propositional (seating, assignment, coloring)
Temporal (SMT)	100	100	637	Linear arithmetic (scheduling, ordering)
Policy / Rules	80	80	506	Ground first-order (access control, eligibility)
Underspecified	90	90	585	Partial information (diagnosis, investigation, fault)
Total	390	390	2,515

Label Distribution

Domain	ENTAILED	CONTRADICTED	UNKNOWN
Relational	16%	30%	54%
Temporal	11%	32%	57%
Policy	6%	32%	62%
Underspecified	18%	36%	46%
Overall	13%	32%	55%

Splits

Split	Cases	Bundles
Train	312	312
Dev	39	39
Test	39	39

Splits are stratified by domain at the case-file level to prevent leakage.

File Structure

cross_query_benchmark/
├── benchmark_full_v2.json        # Complete benchmark (all cases + metadata + statistics)
├── benchmark_train_v2.json       # Training split (312 cases)
├── benchmark_dev_v2.json         # Development split (39 cases)
├── benchmark_test_v2.json        # Test split (39 cases)
├── evaluation_schema_v2.json     # Metric definitions
├── prompt_templates_v2.json      # Prompt templates for extraction & repair
└── README.md

Data Format

Case File Structure

Each case file in the JSON has the following schema:

{
  "id": "rel_seating_0042",
  "domain": "relational",
  "subdomain": "seating_arrangement",
  "logic_type": "propositional",
  "premises": [
    "There are 5 people seated at a circular table: Alice, Bob, Charlie, Diana, and Eve.",
    "Each person occupies exactly one seat and all seats are distinct.",
    "Alice must sit directly next to Bob.",
    "Charlie must not sit directly next to Diana."
  ],
  "formal_representation": "; Seating: 5 people, circular\n; Variables: pos_X in [0, 4] ...",
  "entities": ["Alice", "Bob", "Charlie", "Diana", "Eve"],
  "bundles": [
    {
      "bundle_id": "bundle_0",
      "num_queries": 6,
      "label_distribution": {"ENTAILED": 2, "CONTRADICTED": 2, "UNKNOWN": 2},
      "queries": [
        {
          "query_id": "q0",
          "query": "Must Alice always be seated next to Bob?",
          "label": "ENTAILED",
          "reasoning": "The premises explicitly require Alice to sit next to Bob, so adjacency is guaranteed in every valid arrangement.",
          "query_type": "adj_forced",
          "depends_on": []
        },
        {
          "query_id": "q1",
          "query": "Can Charlie sit at position 3?",
          "label": "UNKNOWN",
          "reasoning": "Position 3 is available to Charlie in some arrangements but not others, depending on how other constraints resolve.",
          "query_type": "pos",
          "depends_on": [0]
        }
      ]
    }
  ]
}

Field Descriptions

Field	Description
id	Unique case identifier ({domain}_{subdomain}_{index})
domain	One of: relational, temporal, policy, underspecified
subdomain	Specific scenario type (e.g., seating_arrangement, event_scheduling, access_control, diagnostic)
logic_type	Formal logic fragment: propositional, linear_arithmetic, first_order_ground, partial_information
premises	List of natural-language premise strings
formal_representation	SMT-LIB or CNF-style formal encoding of the case file
entities	Named entities in the case file
bundles[].queries[].label	Gold label: ENTAILED, CONTRADICTED, or UNKNOWN
bundles[].queries[].reasoning	Reasoning trace explaining the label (avg. 95 chars)
bundles[].queries[].depends_on	Indices of earlier queries in the bundle that this query logically interacts with
bundles[].queries[].query_type	Query category (e.g., adj, pos, overlap, order, eligible, is_guilty)

Evaluation Metrics

Per-Query Metrics

Metric	Description
Accuracy	Fraction of correct labels
Macro-F1	F1 averaged across ENTAILED, CONTRADICTED, UNKNOWN
Unknown-F1	F1 for the UNKNOWN class specifically

Set-Level Metrics

Metric	Description	Direction
SetConsRate	Fraction of bundles where the final belief state is satisfiable	↑ higher is better
AUC-PrefixCons	Average prefix satisfiability in sequential settings	↑ higher is better
RevisionCost	Average commitments revised to restore satisfiability	↓ lower is better
ContradictionDensity	Fraction of steps where a new contradiction emerges	↓ lower is better

Compute Metrics

Metric	Description
Overhead (OH)	Wall-clock time normalized to No-CoT baseline
Solver calls/bundle	Average SAT/SMT solver invocations per bundle

Quick Start

Loading the Data

import json

# Load full benchmark
with open("benchmark_full_v2.json") as f:
    benchmark = json.load(f)

print(f"Cases: {benchmark['statistics']['total_cases']}")
print(f"Queries: {benchmark['statistics']['total_queries']}")

# Iterate over cases
for case in benchmark["cases"]:
    print(f"{case['id']}: {case['domain']} / {case['subdomain']}")
    for bundle in case["bundles"]:
        for query in bundle["queries"]:
            print(f"  Q: {query['query']}")
            print(f"  A: {query['label']} | Deps: {query['depends_on']}")

Loading Splits

# Load train/dev/test
for split in ["train", "dev", "test"]:
    with open(f"benchmark_{split}_v2.json") as f:
        data = json.load(f)
    print(f"{split}: {data['num_cases']} cases, {data['num_bundles']} bundles")

Evaluating a Model

def evaluate_bundle(predictions, gold_labels):
    """
    predictions: list of predicted labels (ENTAILED/CONTRADICTED/UNKNOWN)
    gold_labels: list of gold labels
    """
    correct = sum(p == g for p, g in zip(predictions, gold_labels))
    accuracy = correct / len(gold_labels)
    return accuracy

# Per-query evaluation
for case in benchmark["cases"]:
    for bundle in case["bundles"]:
        gold = [q["label"] for q in bundle["queries"]]
        # your_predictions = model.predict(case["premises"], [q["query"] for q in bundle["queries"]])
        # acc = evaluate_bundle(your_predictions, gold)

Using Formal Representations

# Access the formal (SMT-LIB / CNF) encoding for solver-based evaluation
for case in benchmark["cases"]:
    if case["domain"] == "temporal":
        print(case["formal_representation"])
        # Parse and feed to Z3 or CaDiCaL
        break

Prompt Templates

The repository includes prompt templates (prompt_templates_v2.json) for three tasks:

1. Multi-query reasoning: Main evaluation prompt for LLMs to classify queries
2. Commitment extraction: Extracts symbolic commitments (atoms/constraints) from model answers
3. Repair prompting: Guides the LLM to propose minimal repairs for conflicting commitments

Domain Details

Relational (SAT) — 120 cases

Constraint satisfaction over discrete structures: circular/linear seating arrangements, office/team/color/shift assignments. Constraints include adjacency, non-adjacency, forced assignments, and bans. Verified via propositional SAT (CaDiCaL).

Temporal (SMT) — 100 cases

Event scheduling with ordering, duration, gap, overlap, and fixed-time constraints over bounded integer timelines. Also includes pure ordering problems with precedence and adjacency constraints. Verified via Z3 with QF_LIA (linear integer arithmetic).

Policy / Rules — 80 cases

Role-based access control (grant/deny/conditional rules over roles and resources) and eligibility checking (age/income/experience thresholds for programs). Verified via Z3 with Boolean + integer constraints.

Underspecified / Abductive — 90 cases

Scenarios with deliberately incomplete information: medical diagnosis (partial symptom observations, exactly-one-condition), criminal investigation (partial evidence, exactly-one-guilty), and system fault diagnosis (partial sensor data, dependency cascades). Designed to produce high UNKNOWN rates by construction.

Generation and Verification

All case files are procedurally generated with Z3 solver verification. The generation pipeline:

1. Constraint generation: Random but structurally valid constraint systems per domain
2. Z3 verification: Every query label is determined by checking entailment (true in ALL models), contradiction (false in ALL models), or unknown (true in some, false in others)
3. Quality filtering: Cases with mono-label bundles or extreme label imbalance are filtered
4. Dependency annotation: Cross-query entity sharing is detected and annotated
5. Deduplication: Query uniqueness is enforced within and across bundles (82.4% unique)

Generator scripts are available in the repository.

Paper Results (Summary)

Our solver-augmented belief-state tracking method achieves:

Method	Acc	SetCons	RevCost	Overhead
No-CoT (baseline)	0.80	0.56	1.9	1.00×
CoT	0.84	0.60	1.7	1.16×
Self-Consistency (K=20)	0.86	0.63	1.6	2.75×
Ours (Check+Repair)	0.85	0.94	0.3	1.55×

Results shown for DeepSeek-R1 on the deep evaluation subset. See paper for full results across 8 models.

Citation

@inproceedings{salla2026crossquery,
  title={Quantifying Cross-Query Contradictions in Multi-Query {LLM} Reasoning},
  author={Salla, Rohit Kumar and Amancherla, Ramya Manasa and Saravanan, Manoj},
  booktitle={ICLR 2026 Workshop on Logical Reasoning of Large Language Models},
  year={2026}
}

License

This benchmark is released under the MIT License.

Contact

• Rohit Kumar Salla — rohits25@vt.edu
• Ramya Manasa Amancherla — ra3439@columbia.edu
• Manoj Saravanan — manoj663@vt.edu