Decoupling Reasoning from Proving: A New Framework for Tackling Olympiad-Level Mathematics

Zhenwen Liang, Linfeng Song, Yang Li, TAO YANG, feng zhang, Haitao Mi, Dong Yu

Keywords: theorem proving, IMO, LLM

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 \emph{Reasoner} to generate diverse, strategic subgoal lemmas, and an efficient \emph{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 will release our full dataset of generated and verified lemmas for a wide range of IMO problems, after the paper acceptance.

Submission Number: 47