arXiv:2606.06468cs.AI2026-06被引 4

用蓝图生成与迭代优化,让AI高效证明数学定理。

Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement

论文配图:Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement
图 1 · 摘自论文原文
  • 构建定理依赖蓝图,分步生成并验证数学命题
  • 在MiniF2F上达99.2%通过率,PutnamBench达88.8%
  • 适合想低成本实现高精度数学证明的开发者

我们提出Goedel-Architect,一个基于蓝图生成与迭代优化的代理框架,用于在Lean 4中进行形式化定理证明。蓝图是定义与引理构成的依赖图,逐步推导出主定理。首先,系统生成包含形式化定义与引理及其依赖关系的蓝图,可由自然语言证明引导。随后,配备工具的Lean证明组件并行闭合每个开放引理节点,失败的引理则驱动全局蓝图的优化。该策略不同于主流的递归引理分解,避免无效循环。采用深度求索-视觉-闪速(DeepSeek-V4-Flash,284B-A13B)作为核心模型,Goedel-Architect在MiniF2F-test上达到99.2% pass@1,在PutnamBench上达75.6%。若以自然语言证明引导更难问题的初始蓝图,可解决余下两个MiniF2F测试题(达100%),将PutnamBench提升至88.8%(597/672),并在IMO 2025中解决4/6、Putnam 2025中解决11/12、USAMO 2026中解决3/6。该开源系统性能达当前最优,成本仅为同类方案的1/500。

原文摘要 · Abstract (English)

We introduce Goedel-Architect, an agentic framework for formal theorem proving in Lean 4 centered on blueprint generation and refinement. A blueprint is a dependency graph of definitions and lemmas that builds up to the main theorem. First, Goedel-Architect generates a blueprint of formally stated definitions and lemmas, along with declared dependencies. This blueprint is optionally guided by a natural language proof. Then, a tool-equipped Lean prover component closes each open lemma node in parallel using relevant dependencies. Failed lemmas in turn drive refinement of the global blueprint. This strategy contrasts with other mainstream approaches which use recursive lemma decomposition, and can inefficiently loop on dead-end strategies. Using the open-weight DeepSeek-V4-Flash (284B-A13B) as the backbone, Goedel-Architect attains 99.2% pass@1 on MiniF2F-test and 75.6% pass@1 on PutnamBench. With an optional natural-language proof seeding the initial blueprint on the harder problems, we additionally close the remaining two MiniF2F-test problems (reaching 100%), lift PutnamBench to 88.8% (597/672), and solve 4/6 on IMO 2025, 11/12 on Putnam 2025, and 3/6 on USAMO 2026. This represents state-of-the-art performance for an open-source pipeline at a price point up to 500x less than comparable open-source pipelines.

形式化证明数学定理蓝图生成Lean 4

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