# MA-LoT: Model-Collaboration Lean-based Long Chain-of-Thought Reasoning enhances Formal Theorem Proving

arXiv: https://arxiv.org/abs/2503.03205 · HTML: https://mlsanity.com/paper/2503.03205/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 48 references that are in the map.
- First posted on arXiv 5 Mar 2025.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [A Generalist Agent](https://mlsanity.com/paper/2205.06175/) (2022)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [AgentBoard: An Analytical Evaluation Board of Multi-turn LLM Agents](https://mlsanity.com/paper/2401.13178/) (2024)
- [ScienceWorld: Is your Agent Smarter than a 5th Grader?](https://mlsanity.com/paper/2203.07540/) (2022)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [Auto-GPT for Online Decision Making: Benchmarks and Additional Opinions](https://mlsanity.com/paper/2306.02224/) (2023)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [Formal Mathematics Statement Curriculum Learning](https://mlsanity.com/paper/2202.01344/) (2022)
- [OpenAgents: An Open Platform for Language Agents in the Wild](https://mlsanity.com/paper/2310.10634/) (2023)
- [Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving](https://mlsanity.com/paper/2502.07640/) (2025)
- [Lean Workbook: A large-scale Lean problem set formalized from natural language math problems](https://mlsanity.com/paper/2406.03847/) (2024)
- [Formal Mathematical Reasoning: A New Frontier in AI](https://mlsanity.com/paper/2412.16075/) (2024)
- [Lean-STaR: Learning to Interleave Thinking and Proving](https://mlsanity.com/paper/2407.10040/) (2024)
- [TheoremLlama: Transforming General-Purpose LLMs into Lean4 Experts](https://mlsanity.com/paper/2407.03203/) (2024)
- [CEM-RL: Combining evolutionary and gradient-based methods for policy search](https://mlsanity.com/paper/1810.01222/) (2018)
- [LeanAgent: Lifelong Learning for Formal Theorem Proving](https://mlsanity.com/paper/2410.06209/) (2024)
- [Let's Synthesize Step by Step: Iterative Dataset Synthesis with Large Language Models by Extrapolating Errors from Small Models](https://mlsanity.com/paper/2310.13671/) (2023)
- [LEAN-GitHub: Compiling GitHub LEAN repositories for a versatile LEAN prover](https://mlsanity.com/paper/2407.17227/) (2024)
- [Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning](https://mlsanity.com/paper/2412.15184/) (2024)

## Built on by (most cited first, 24 of 24)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Leanabell-Prover: Posttraining Scaling in Formal Reasoning](https://mlsanity.com/paper/2504.06122/) (2025)
- [Solving Inequality Proofs with Large Language Models](https://mlsanity.com/paper/2506.07927/) (2025)
- [Mathematical Proof as a Litmus Test: Revealing Failure Modes of Advanced Large Reasoning Models](https://mlsanity.com/paper/2506.17114/) (2025)
- [A Minimal Agent for Automated Theorem Proving](https://mlsanity.com/paper/2602.24273/) (2026)
- [Let's Reason Formally: Natural-Formal Hybrid Reasoning Enhances LLM's Math Capability](https://mlsanity.com/paper/2505.23703/) (2025)
- [SorryDB: Can AI Provers Complete Real-World Lean Theorems?](https://mlsanity.com/paper/2603.02668/) (2026)
- [GAR: Generative Adversarial Reinforcement Learning for Formal Theorem Proving](https://mlsanity.com/paper/2510.11769/) (2025)
- [How Well Do Large Reasoning Models Translate? A Comprehensive Evaluation for Multi-Domain Machine Translation](https://mlsanity.com/paper/2505.19987/) (2025)
- [Lean4Physics: Comprehensive Reasoning Framework for College-level Physics in Lean4](https://mlsanity.com/paper/2510.26094/) (2025)
- [Reasoning Models Reason Well, Until They Don't](https://mlsanity.com/paper/2510.22371/) (2025)
- [Inductive Deductive Synthesis: Enabling AI to Generate Formally Verified Systems](https://mlsanity.com/paper/2605.23109/) (2026)
- [Typed Chain-of-Thought: A Curry-Howard Framework for Verifying LLM Reasoning](https://mlsanity.com/paper/2510.01069/) (2025)
- [PhysProver: Advancing Automatic Theorem Proving for Physics](https://mlsanity.com/paper/2601.15737/) (2026)
- [Clarifying Before Reasoning: A Coq Prover with Structural Context](https://mlsanity.com/paper/2507.02541/) (2025)
- [Multi-agent Autoformalization of Tensor Network Theory](https://mlsanity.com/paper/2607.07857/) (2026)
- [LLM-based Automated Theorem Proving Hinges on Scalable Synthetic Data Generation](https://mlsanity.com/paper/2505.12031/) (2025)
- [Lean4Agent: Formal Modeling and Verification for Agent Workflow and Trajectory](https://mlsanity.com/paper/2606.06523/) (2026)
- [Hypothesis-Disciplined Multi-Agent Automated Formalization of Asymptotic Statistical Theory](https://mlsanity.com/paper/2606.20642/) (2026)
- [Automated Formal Proofs of Combinatorial Identities via Wilf-Zeilberger Guidance and LLMs](https://mlsanity.com/paper/2605.04472/) (2026)
- [Diffusion-Proof: Recipe for Formal Theorem Proving Beyond Auto-Regressive Generation](https://mlsanity.com/paper/2606.19315/) (2026)
- [MathAdv: What Theorem Provers Know, Reason, Formalize, and Generalize](https://mlsanity.com/paper/2608.25449/) (2026)
- [Making Grid Beam Search Less Greedy](https://mlsanity.com/paper/2609.39368/) (2026)

## Abstract (arXiv)

Solving mathematical problems using computer-verifiable languages like Lean has significantly impacted the mathematical and computer science communities. State-of-the-art methods utilize a single Large Language Model (LLM) to generate complete proof or perform tree search, but they fail to balance these tasks. We propose **MA-LoT**: *Model-CollAboration Lean-based Long Chain-of-Thought*, a comprehensive framework for Lean4 theorem proving to solve this issue. It separates the cognition tasks of general NL for whole-proof generation and error analysis for proof correction using the model-collaboration method. We achieve this by structured interaction of the LLM and Lean4 verifier in Long CoT. To implement the framework, we propose the novel *LoT-Transfer Learning* training-inference pipeline, which enables the Long CoT thinking capability to LLMs without special data annotation. Extensive experiment shows that our framework achieves a **61.07%** accuracy rate on the Lean4 version of the MiniF2F-Test dataset, largely outperforming DeepSeek-V3 (33.61%), single-model tree search (InternLM-Step-Prover, 50.70%), and whole-proof generation (Godel-Prover, 55.33%) baselines. Furthermore, our findings highlight the potential of combining Long CoT with formal verification for a more insightful generation in a broader perspective.