Towards Solving More Challenging IMO Problems via Decoupled Reasoning and Proving

TL;DR

This paper introduces a decoupled reasoning and proving framework using specialized models to improve automated theorem proving on difficult IMO problems, achieving success where previous methods failed.

Contribution

It proposes a novel modular approach that separates high-level reasoning from low-level proof generation, enabling more effective tackling of complex mathematical problems.

Findings

Successfully solved 5 challenging IMO problems with the new framework

Demonstrated significant improvement over existing open-source provers on difficult benchmarks

Released a dataset of generated and verified lemmas for future research

Abstract

Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and their weak formal proving performance. Recent studies show that the informal accuracy exceeds 80% while formal success remains below 8% on benchmarks like PutnamBench. We argue this gap persists because current state-of-the-art provers, by tightly coupling reasoning and proving, are trained with paradigms that inadvertently punish deep reasoning in favor of shallow, tactic-based strategies. To bridge this fundamental gap, we propose a novel framework that decouples high-level reasoning from low-level proof generation. Our approach utilizes two distinct, specialized models: a powerful, general-purpose Reasoner to generate diverse, strategic subgoal lemmas, and an efficient Prover to rigorously verify them. This modular design liberates the model's full reasoning potential and bypasses the pitfalls of end-to-end training. We evaluate our method on a challenging set of post-2000 IMO problems, a problem set on which no prior open-source prover has reported success. Our decoupled framework successfully solves 5 of these problems, demonstrating a significant step towards automated reasoning on exceptionally difficult mathematical challenges. To foster future research, we release our full dataset of generated and verified lemmas for a wide range of IMO problems, available at https://tencent-imo.github.io/ .