Mathesis: Towards Formal Theorem Proving from Natural Languages
Authors: name: Yu Xuejun, name: Jianyuan Zhong, name: Zijin Feng, name: Pengyi Zhai, name: Roozbeh Yousefzadeh, name: Wei Chong Ng, name: Haoxiong Liu, name: Ziyi Shou, name: Jing Xiong, name: Yudong Zhou, name: Claudia Beth Ong, name: Austen Jeremy Sugiarto, name: Yaoxi Zhang, name: Wai Ming Tai, name: Huan Cao, name: Dongcai Lu, name: Jiacheng Sun, name: Qiang Xu, name: Shen Xin, name: Zhenguo Li

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.