# Towards Solving More Challenging IMO Problems via Decoupled Reasoning and Proving

arXiv: https://arxiv.org/abs/2507.06804 · HTML: https://mlsanity.com/paper/2507.06804/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 14 of its 18 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 14 of 14)

- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving](https://mlsanity.com/paper/2502.07640/) (2025)
- [Baldur: Whole-Proof Generation and Repair with Large Language Models](https://mlsanity.com/paper/2303.04910/) (2023)
- [LEGO-Prover: Neural Theorem Proving with Growing Libraries](https://mlsanity.com/paper/2310.00656/) (2023)
- [BFS-Prover: Scalable Best-First Tree Search for LLM-based Automatic Theorem Proving](https://mlsanity.com/paper/2502.03438/) (2025)
- [HunyuanProver: A Scalable Data Synthesis Framework and Guided Tree Search for Automated Theorem Proving](https://mlsanity.com/paper/2412.20735/) (2024)
- [The Open Proof Corpus: A Large-Scale Study of LLM-Generated Mathematical Proofs](https://mlsanity.com/paper/2506.21621/) (2025)
- [Proving Theorems Recursively](https://mlsanity.com/paper/2405.14414/) (2024)
- [Reviving DSP for Advanced Theorem Proving in the Era of Reasoning Models](https://mlsanity.com/paper/2506.11487/) (2025)
- [MPS-Prover: Advancing Stepwise Theorem Proving by Multi-Perspective Search and Data Curation](https://mlsanity.com/paper/2505.10962/) (2025)

## Built on by (most cited first, 7 of 7)

- [Hilbert: Recursively Building Formal Proofs with Informal Reasoning](https://mlsanity.com/paper/2509.22819/) (2025)
- [ProofFlow: A Dependency Graph Approach to Faithful Proof Autoformalization](https://mlsanity.com/paper/2510.15981/) (2025)
- [Reasoning Shift: How Context Silently Shortens LLM Reasoning](https://mlsanity.com/paper/2604.01161/) (2026)
- [V-Math: An Agentic Approach to the Vietnamese National High School Graduation Mathematics Exams](https://mlsanity.com/paper/2509.12251/) (2025)
- [EconProver: Towards More Economical Test-Time Scaling for Automated Theorem Proving](https://mlsanity.com/paper/2509.12603/) (2025)
- [From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier](https://mlsanity.com/paper/2607.07779/) (2026)
- [Reliable Use of Lemmas via Eligibility Reasoning and Section-Aware Reinforcement Learning](https://mlsanity.com/paper/2602.00998/) (2026)

## Abstract (arXiv)

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/ .