@inproceedings{kasaura-etal-2026-discovering,
    title = "Discovering New Theorems via {LLM}s with In-Context Proof Learning in Lean",
    author = "Kasaura, Kazumi  and
      Onda, Naoto  and
      Oriike, Yuta  and
      Taniguchi, Masaya  and
      Sannai, Akiyoshi  and
      Sonoda, Sho",
    editor = "Yanaka, Hitomi  and
      Abzianidze, Lasha",
    booktitle = "Proceedings of the 6th Workshop on Natural Language Meets Logic and Machine Learning ({NALOMA})",
    month = aug,
    year = "2026",
    address = "Prague, Czechia",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-naloma/2026.naloma-1.5/",
    pages = "40--49",
    ISBN = "979-8-89176-389-0",
    abstract = "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 *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."
}