CONJECTURE EXTRACTION FOR PROOF AUTOFORMALIZATION USING LARGE LANGUAGE MODELS AND AUTOMATED THEOREM PROVERS

MathAI 2026 Conference Submission102 Authors

Keywords: automated theorem prover, large language models, conjecture extraction

Abstract: Autoformalization and ATP have each advanced the mechanization of mathematics, yet the translation of informal proofs into fully formalized counterparts remains an open challenge: especially for interactive theorem provers beyond Isabelle. We introduce conjecture extraction, a novel proof autoformalization pipeline tailored to Lean 4 that decomposes an informal proof into individual lemmas (conjectures), formalizes and proves each in isolation, and then reassembles them to recover the original argument. Unlike prior sketch-based methods, our approach is compatible with end-to-end proof generation models and leverages repeated conjecture refinement to incrementally improve performance. We implement an open-source system that integrates off-the-shelf autoformalization LLMs, automated theorem provers, and an online reinforcement-learning loop to optimize both conjecture generation and proof search. On the MiniF2F benchmark, conjecture extraction achieves an absolute improvement of 11.2 percentage points in pass@1 over the Draft, Sketch, and Prove port (DSP) for Lean 4, demonstrating the efficacy of proof decomposition and recomposition. Our results suggest that conjecture extraction not only bridges a gap in proof autoformalization for Lean but also offers a general framework for scaling formalization efforts across diverse proof assistants. We release our code and models to foster further research in large-scale formalized mathematics.

Submission Number: 102