EvolProver: Advancing Automated Theorem Proving by Evolving Formalized
  Problems via Symmetry and Difficulty
Authors: name: Yuchen Tian; name: Ruiyuan Huang; name: Xuanwu Wang; name: Jing Ma; name: Zengfeng Huang; name: Ziyang Luo; name: Hongzhan Lin; name: Da Zheng; name: Lun Du
Published: 2025-10-01 10:15:27

Abstract: Large Language Models (LLMs) for formal theorem proving have shown
significant promise, yet they often lack generalizability and are fragile to
even minor transformations of problem statements. To address this limitation,
we introduce a novel data augmentation pipeline designed to enhance model
robustness from two perspectives: symmetry and difficulty. From the symmetry
perspective, we propose two complementary methods: EvolAST, an Abstract Syntax
Tree (AST) based approach that targets syntactic symmetry to generate
semantically equivalent problem variants, and EvolDomain, which leverages LLMs
to address semantic symmetry by translating theorems across mathematical
domains. From the difficulty perspective, we propose EvolDifficulty, which uses
carefully designed evolutionary instructions to guide LLMs in generating new
theorems with a wider range of difficulty. We then use the evolved data to
train EvolProver, a 7B-parameter non-reasoning theorem prover. EvolProver
establishes a new state-of-the-art (SOTA) on FormalMATH-Lite with a 53.8%
pass@32 rate, surpassing all models of comparable size, including
reasoning-based models. It also sets new SOTA records for non-reasoning models
on MiniF2F-Test (69.8% pass@32), Ineq-Comp-Seed (52.2% pass@32), and
Ineq-Comp-Transformed (34.0% pass@32). Ablation studies further confirm our
data augmentation pipeline's effectiveness across multiple benchmarks.