定理基准:评估大语言模型在形式化数学定理证明中的表现 / TheoremBench: Evaluating LLMs on Theorem Proving in Formal Mathematics
1️⃣ 一句话总结
本文提出了一个名为TheoremBench的Lean4形式化数学基准测试,通过包含经典定理及其子定理的结构化任务,更细致地评估大语言模型的定理证明能力,并揭示了现有模型偏向于解决简单子问题、依赖冗长策略而非高效证明计划的问题。
LLMs have recently achieved strong results on formal proving benchmarks. However, existing evaluations remain heavily concentrated on competition-style problems and often fail to capture how models behave on longer, more dependency-rich mathematical developments. We introduce TheoremBench, a Lean4 benchmark designed to evaluate theorem provers beyond contest settings. The benchmark is built from nearly one hundred classical theorems and is released in two complementary forms: a plain main version containing one target theorem per instance, and a premised version that expands each theorem into a structured family of related proving tasks consisting of the main theorem together with automatically extracted supporting subtheorems. This design enables evaluation of not only whether the final theorem was proved from scratch, but also of partial progress through the internal proof structure of a theorem. Our experiments show that explicit premises substantially improve performance for Lean4-capable prover models. To provide a comprehensive evaluation, we introduce theorem-level coverage and token-efficiency metrics that expose qualitative differences in proof behavior. The results show that current provers remain strongly biased toward easy subtheorems and often solve theorems through long and inefficient tactic traces rather than compact proof plans. TheoremBench therefore provides a more fine-grained view of formal reasoning ability and highlights the importance of structural benchmark design for evaluating Lean4 theorem provers.
定理基准:评估大语言模型在形式化数学定理证明中的表现 / TheoremBench: Evaluating LLMs on Theorem Proving in Formal Mathematics
本文提出了一个名为TheoremBench的Lean4形式化数学基准测试,通过包含经典定理及其子定理的结构化任务,更细致地评估大语言模型的定理证明能力,并揭示了现有模型偏向于解决简单子问题、依赖冗长策略而非高效证明计划的问题。
源自 arXiv: 2606.09450