Towards Solving More Challenging IMO Problems via Decoupled Reasoning
  and Proving
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/ .
686f1f4dd938c25d68441b24
Zhenwen Liang
686f1f4dd938c25d68441b25
Linfeng Song
claimed_verified
2025-07-11T08:03:43.665Z
64c94eddcb2f1bf0e7db5a4d
/avatars/f7e2532d3c85d5e5b5a02c579ea68c3a.svg
Linfeng Song
user
freesunshine0316
686f1f4dd938c25d68441b26
Yang Li
686f1f4dd938c25d68441b27
Tao Yang
686f1f4dd938c25d68441b28
Feng Zhang
686f1f4dd938c25d68441b29
Haitao Mi
686f1f4dd938c25d68441b2a
Dong Yu
Towards Solving More Challenging IMO Problems via Decoupled Reasoning
  and Proving
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/ .
A novel framework decouples high-level reasoning from low-level proof generation to improve automated theorem proving performance on challenging mathematical problems.
Automated Theorem Proving Large Language Models formal proving PutnamBench subgoal lemmas Reasoner Prover IMO problems