Discover and Prove: An Open-source Agentic Framework for Hard Mode Automated Theorem Proving in Lean 4
Chengwu Liu, Yichun Yin Huawei Noah's Ark Lab, Ye Yuan, Jiaxuan Xie Peking University, Botao Li, Siqi Li, Jianhao Shen, Yan Xu Tencent 等 10 位作者
Most ATP benchmarks embed the final answer within the formal statement — a convention we call “Easy Mode” — a design that simplifies the task relative to what human competitors face and may lead to optimistic estimates of model capability.We call the stricter, more realistic setting “Hard Mode”: the system must independently discover the answer before constructing a formal proof.To enable Hard Mode research, we make two contributions.First, we release MiniF2F-Hard and FIMO-Hard, expert-reannotated Hard Mode variants of two widely-used ATP benchmarks.Second, we introduce Discover And Prove (DAP), an agentic framework that uses LLM natural-language reasoning with explicit self-reflection to discover answers, then rewrites Hard Mode statements into Easy Mode ones for existing ATP provers.DAP sets the state of the art: on CombiBench it raises solved problems from 7 (previous SOTA, Pass@16) to 10; on PutnamBench it is the first system to formally prove 36 theorems in Hard Mode — while simultaneously revealing that state-of-the-art LLMs exceed 80% answer accuracy on the same problems where formal provers manage under 10%, exposing a substantial gap that Hard Mode benchmarks are uniquely suited to measure.
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Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表