ITPEval Benchmarks Formal Proof Translation Across Theorem Provers

Jiayi Wu, Robert Joseph George, Anima Anandkumar· July 23, 2026 View original

Summary

ITPEval is the first benchmark for evaluating automated formal proof translation across four major Interactive Theorem Provers (ITPs): Lean 4, Rocq, Isabelle, and HOL Light. It reveals significant challenges in translating proofs due to library mismatches and highlights the need for improved semantic fidelity checks.

The field of formal theorem proving, a frontier challenge for machine learning, is currently fragmented. Proofs are often confined to incompatible systems, which limits both the training data available for learning-based provers and the portability of verified results. This fragmentation hinders progress towards a unified ecosystem. To address this, ITPEval has been introduced as the first benchmark specifically designed to evaluate automated formal proof translation across four prominent Interactive Theorem Provers (ITPs): Lean 4, Rocq, Isabelle, and HOL Light. These systems span two distinct logical foundations, making translation particularly challenging. The benchmark includes 1,560 source files and 6,848 theorems, categorized into a "controlled tier" for foundational translation difficulty and an "ecosystem tier" to expose real-world library and proof-style mismatches. Evaluations revealed that statement translation peaks at 29.1% pass@1 and proof translation at 10.5%, with library mismatch being the dominant bottleneck. The study also emphasizes that native type-checking alone can overestimate semantic fidelity, advocating for more robust equivalence checks.

Why it matters

Improving automated translation between formal theorem provers is crucial for accelerating AI research in mathematical reasoning, enabling broader application of formal verification, and fostering collaboration across different proof communities.

How to implement this in your domain

  1. 1Utilize ITPEval to benchmark and improve AI models designed for formal proof translation.
  2. 2Investigate strategies to mitigate library and API mismatches when integrating formal systems.
  3. 3Develop more sophisticated semantic fidelity checks beyond basic type-checking for translated proofs.
  4. 4Promote multi-ITP context training for AI provers to enhance generalization and success rates.

Who benefits

AI DevelopmentSoftware EngineeringCybersecurityResearch & DevelopmentAcademia

Key takeaways

  • Formal theorem proving is fragmented across incompatible systems, limiting AI training and portability.
  • ITPEval is the first benchmark for evaluating automated proof translation across major ITPs.
  • Library and API mismatches are the primary bottlenecks in achieving successful translations.
  • Native type-checking alone can overestimate semantic fidelity, requiring more robust equivalence checks.

Original post by Jiayi Wu, Robert Joseph George, Anima Anandkumar

"arXiv:2607.19407v1 Announce Type: new Abstract: Formal theorem proving has emerged as a frontier challenge for machine learning, yet the ecosystem is fragmented: proofs remain siloed across incompatible systems, limiting both training data for learning-based provers and the porta…"

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Originally posted by Jiayi Wu, Robert Joseph George, Anima Anandkumar on X · view source

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