Mathesis: Towards Formal Theorem Proving from Natural Languages

TL;DR

Mathesis presents an end-to-end pipeline that automates formal theorem proving from natural language problem statements, combining autoformalization and proof generation, and demonstrates strong results on real-world exam problems.

Contribution

It introduces the first autoformalizer using reinforcement learning and a comprehensive theorem proving pipeline capable of handling informal natural language inputs.

Findings

Autoformalizer outperforms baselines by 22% in pass-rate on Gaokao-Formal.

Achieves 64% accuracy on MiniF2F with pass@32.

Attains 18% state-of-the-art accuracy on Gaokao-Formal.

Abstract

Recent advances in large language models show strong promise for formal reasoning. However, most LLM-based theorem provers have long been constrained by the need for expert-written formal statements as inputs, limiting their applicability to real-world problems expressed in natural language. We tackle this gap with Mathesis, the first end-to-end theorem proving pipeline processing informal problem statements. It contributes Mathesis-Autoformalizer, the first autoformalizer using reinforcement learning to enhance the formalization ability of natural language problems, aided by our novel LeanScorer framework for nuanced formalization quality assessment. It also proposes a Mathesis-Prover, which generates formal proofs from the formalized statements. To evaluate the real-world applicability of end-to-end formal theorem proving, we introduce Gaokao-Formal, a benchmark of 488 complex problems from China's national college entrance exam. Our approach is carefully designed, with a thorough study of each component. Experiments demonstrate Mathesis's effectiveness, with the autoformalizer outperforming the best baseline by 22% in pass-rate on Gaokao-Formal. The full system surpasses other model combinations, achieving 64% accuracy on MiniF2F with pass@32 and a state-of-the-art 18% on Gaokao-Formal.