arXiv:2606.29493cs.AI2026-06中稿 · ICML被引 4

发现数学证明基准数据集存在398个可验证缺陷,影响AI模型评估可靠性。

Faults in Our Formal Benchmarking: Dataset Defects and Evaluation Failures in Lean Theorem Proving

论文配图:Faults in Our Formal Benchmarking: Dataset Defects and Evaluation Failures in Lean Theorem Proving
图 1 · 摘自论文原文
  • 用静态检查器审计5个主流基准,发现4833处问题
  • 398个经机器验证的错误包括反例、空真定理等
  • 适合研究形式化数学与可信评估的研究者

大型语言模型辅助的Lean定理证明基准常被视为内在可靠,因每个解题实例均有机器可验证的证明。然而,内核仅验证证明是否成立形式命题,不确保命题忠实表达原始非形式问题,也不检测评估工具对平凡或对抗性解法的鲁棒性。我们对五个广泛使用的Lean定理证明基准及其变体进行审计,使用大规模静态检查器发现4833项问题,其中包括398个机械认证的严重缺陷,如反例、空真定理和无意义公理。还识别出语义缺陷:缺少假设、问题简化、翻译不全或错误,以及Lean特有的规范陷阱。除数据集构建外,我们调查评估阶段的失败模式,并在修正子集上显示缺陷可导致评分虚高或虚低。本文提出故障分类法、一套自动化检查器及面向召回率的语义审计提示,发布标准以指导形式数学数据集构建,提升评估的可重现性与可信度。检查器、审计提示及修正数据快照已开源:https://github.com/Shashi456/atp-checkers。

原文摘要 · Abstract (English)

Benchmarks for LLM-assisted theorem proving in Lean are often treated as intrinsically reliable because every solved instance comes with a machine-checked proof. However, the kernel only checks that a proof establishes a \emph{formal} statement; it does not verify that the statement faithfully encodes the intended informal problem, nor that evaluation harnesses are robust to trivial or adversarial solutions. We audit five widely used Lean theorem-proving benchmarks and their forks, using corpus-scale static checkers to surface 4,833 findings, including 398 mechanically certified issues such as counterexamples, vacuous theorems, and unsound axioms. We also document semantic defects such as missing hypotheses, problem simplification, incomplete or incorrect translations, and Lean-specific specification hazards. Beyond dataset construction, we survey evaluation-time failure modes and show, on corrected subsets, that defects can both inflate and deflate reported prover scores. We propose a fault taxonomy, a suite of automated checkers and recall-oriented semantic audit prompts, and release standards to guide the creation of formal math datasets and to make evaluation more reproducible and trustworthy. Our checkers, audit prompts, and corrected dataset snapshots are available at https://github.com/Shashi456/atp-checkers.

形式化数学基准测试漏洞审计

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