Towards Solving More Challenging IMO Problems via Decoupled Reasoning
  and Proving
Authors: name: Zhenwen Liang; name: Linfeng Song; name: Yang Li; name: Tao Yang; name: Feng Zhang; name: Haitao Mi; name: Dong Yu
Published: 2025-07-07 22:38:49

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/ .