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FormalProofBench: Can Models Write Graduate Level Math Proofs That Are Formally Verified?

Nikil Ravi, Kexing Ying, Vasilii Nesterov, Rayan Krishnan, Elif Uskuplu, Bingyu Xia, Janitha Aswedige, Langston Nashold · Mar 27, 2026 · Citations: 0

Automatic Metrics
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How to use this page

Low trust

Use this as background context only. Do not make protocol decisions from this page alone.

Best use

Background context only

What to verify

Validate the evaluation procedure and quality controls in the full paper before operational use.

Evidence quality

Low

Derived from extracted protocol signals and abstract evidence.

Abstract

We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level. Each task pairs a natural-language problem with a Lean~4 formal statement, and a model must output a Lean proof accepted by the Lean 4 checker. FormalProofBench targets advanced undergraduate and graduate mathematics, with problems drawn from qualifying exams and standard textbooks across topics including analysis, algebra, probability, and logic. We evaluate a range of frontier models with an agentic harness, and find that the best-performing foundation model achieves 33.5% accuracy, with performance dropping rapidly after that. In addition to the accuracy numbers, we also provide empirical analysis of tool-use, failure modes, cost and latency, thereby providing a thorough evaluation of the formal-theorem proving abilities of frontier models.

Abstract-only analysis — low confidence

All signals on this page are inferred from the abstract only and may be inaccurate. Do not use this page as a primary protocol reference.

  • This paper looks adjacent to evaluation work, but not like a strong protocol reference.
  • The available metadata is too thin to trust this as a primary source.
Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub

Should You Rely On This Paper?

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

A benchmark-and-metrics comparison anchor.

Main weakness

This paper looks adjacent to evaluation work, but not like a strong protocol reference.

Trust level

Low

Usefulness score

5/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Detected

Usefulness for eval research

Adjacent candidate

Extraction confidence 45%

If you are doing eval pipeline work, start here:

Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub Tool-Use Eval Hub

What We Could Verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

missing

None explicit

No explicit feedback protocol extracted.

"We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level."

Evaluation Modes

partial

Automatic Metrics

Includes extracted eval setup.

"We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level."

Quality Controls

missing

Not reported

No explicit QC controls found.

"We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level."

Benchmarks / Datasets

partial

Formalproofbench

Useful for quick benchmark comparison.

"We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level."

Reported Metrics

partial

Accuracy

Useful for evaluation criteria comparison.

"We evaluate a range of frontier models with an agentic harness, and find that the best-performing foundation model achieves 33.5% accuracy, with performance dropping rapidly after that."

Human Feedback Details

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Not reported
  • Expertise required: Math

Evaluation Details

  • Evaluation modes: Automatic Metrics
  • Agentic eval: None
  • Quality controls: Not reported
  • Evidence quality: Low
  • Use this page as: Background context only

Protocol And Measurement Signals

Benchmarks / Datasets

Formalproofbench

Reported Metrics

accuracy

Research Brief

Metadata summary

We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key Takeaways

  • We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level.
  • Each task pairs a natural-language problem with a Lean~4 formal statement, and a model must output a Lean proof accepted by the Lean 4 checker.
  • FormalProofBench targets advanced undergraduate and graduate mathematics, with problems drawn from qualifying exams and standard textbooks across topics including analysis, algebra, probability, and logic.

Researcher Actions

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • Validate inferred eval signals (Automatic metrics) against the full paper.
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

Accuracy

Research Summary

Contribution Summary

  • We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level.
  • We evaluate a range of frontier models with an agentic harness, and find that the best-performing foundation model achieves 33.5% accuracy, with performance dropping rapidly after that.
  • In addition to the accuracy numbers, we also provide empirical analysis of tool-use, failure modes, cost and latency, thereby providing a thorough evaluation of the formal-theorem proving abilities of frontier models.

Why It Matters For Eval

  • We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level.
  • We evaluate a range of frontier models with an agentic harness, and find that the best-performing foundation model achieves 33.5% accuracy, with performance dropping rapidly after that.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Pass: Evaluation mode is explicit

    Detected: Automatic Metrics

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Pass: Benchmark or dataset anchors are present

    Detected: Formalproofbench

  • Pass: Metric reporting is present

    Detected: accuracy

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