Discovering New Theorems via LLMs with In-Context Proof Learning in Lean
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915982535032832 |
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| author | Kasaura, Kazumi Onda, Naoto Oriike, Yuta Taniguchi, Masaya Sannai, Akiyoshi Sonoda, Sho |
| author_facet | Kasaura, Kazumi Onda, Naoto Oriike, Yuta Taniguchi, Masaya Sannai, Akiyoshi Sonoda, Sho |
| contents | Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called \textit{Conjecturing-Proving Loop} (CPL), which iteratively generates mathematical conjectures and attempts to prove them in Lean 4. A key feature of CPL is that each iteration conditions the LLM on previously generated theorems and their formal proofs, enabling parameter-free improvement of proof strategies via in-context learning. We provide both theoretical and experimental evidence that CPL increases the discovery rate of hard-to-prove theorems compared to frameworks that generate statements and proofs simultaneously. Moreover, our experiments show that reusing the LLM's own formally verified outputs as context consistently improves subsequent proof success, demonstrating the effectiveness of self-generated in-context learning for neural theorem proving. The source code is available at https://github.com/auto-res/ConjecturingProvingLoop. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14274 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discovering New Theorems via LLMs with In-Context Proof Learning in Lean Kasaura, Kazumi Onda, Naoto Oriike, Yuta Taniguchi, Masaya Sannai, Akiyoshi Sonoda, Sho Machine Learning Artificial Intelligence Logic in Computer Science Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called \textit{Conjecturing-Proving Loop} (CPL), which iteratively generates mathematical conjectures and attempts to prove them in Lean 4. A key feature of CPL is that each iteration conditions the LLM on previously generated theorems and their formal proofs, enabling parameter-free improvement of proof strategies via in-context learning. We provide both theoretical and experimental evidence that CPL increases the discovery rate of hard-to-prove theorems compared to frameworks that generate statements and proofs simultaneously. Moreover, our experiments show that reusing the LLM's own formally verified outputs as context consistently improves subsequent proof success, demonstrating the effectiveness of self-generated in-context learning for neural theorem proving. The source code is available at https://github.com/auto-res/ConjecturingProvingLoop. |
| title | Discovering New Theorems via LLMs with In-Context Proof Learning in Lean |
| topic | Machine Learning Artificial Intelligence Logic in Computer Science |
| url | https://arxiv.org/abs/2509.14274 |