# NanoProof: Open and Efficient Automated Theorem Proving in Lean 4

arXiv: https://arxiv.org/abs/2610.11605 · HTML: https://mlsanity.com/paper/2610.11605/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 50 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 24 of 24)

- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [ByT5: Towards a token-free future with pre-trained byte-to-byte models](https://mlsanity.com/paper/2105.13626/) (2021)
- [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)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction](https://mlsanity.com/paper/2508.03613/) (2025)
- [Stop Regressing: Training Value Functions via Classification for Scalable Deep RL](https://mlsanity.com/paper/2403.03950/) (2024)
- [Proof Artifact Co-training for Theorem Proving with Language Models](https://mlsanity.com/paper/2102.06203/) (2021)
- [Lean Workbook: A large-scale Lean problem set formalized from natural language math problems](https://mlsanity.com/paper/2406.03847/) (2024)
- [InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning](https://mlsanity.com/paper/2402.06332/) (2024)
- [Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving](https://mlsanity.com/paper/2507.23726/) (2025)
- [Nemotron-CC-Math: A 133 Billion-Token-Scale High Quality Math Pretraining Dataset](https://mlsanity.com/paper/2508.15096/) (2025)
- [InternLM2.5-StepProver: Advancing Automated Theorem Proving via Critic-Guided Search](https://mlsanity.com/paper/2410.15700/) (2024)
- [Holophrasm: a neural Automated Theorem Prover for higher-order logic](https://mlsanity.com/paper/1608.02644/) (2016)
- [LeanReasoner: Boosting Complex Logical Reasoning with Lean](https://mlsanity.com/paper/2403.13312/) (2024)
- [Scaling up Multi-Turn Off-Policy RL and Multi-Agent Tree Search for LLM Step-Provers](https://mlsanity.com/paper/2509.06493/) (2025)
- [LEAN-GitHub: Compiling GitHub LEAN repositories for a versatile LEAN prover](https://mlsanity.com/paper/2407.17227/) (2024)
- [Pantograph: A Machine-to-Machine Interaction Interface for Advanced Theorem Proving, High Level Reasoning, and Data Extraction in Lean 4](https://mlsanity.com/paper/2410.16429/) (2024)
- [The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale](https://mlsanity.com/paper/2512.07087/) (2025)
- [Formalization of physics index notation in Lean 4](https://mlsanity.com/paper/2411.07667/) (2024)
- [LeanTree: Accelerating White-Box Proof Search with Factorized States in Lean 4](https://mlsanity.com/paper/2507.14722/) (2025)

## Abstract (arXiv)

We introduce NanoProof, to our knowledge the first factorized execution-guided theorem prover in Lean 4 whose training data, extraction tooling, training pipeline, and weights are all released, making it end-to-end reproducible using open-source resources. To this end, we build and release a dataset of structured proof trees, as well as a tool for programmatic interaction and data extraction within the Lean 4 formal verifier. To support sustainable research, we focus on compute efficiency to facilitate accessible training and evaluation. NanoProof achieves 50.8% pass@16 on MiniF2F-Test, exceeding the two closest systems of its class, HyperTree Proof Search and ABEL, at roughly 90x and 7x less compute, and using more than four orders of magnitude less compute than AlphaProof. Stronger open-weight provers exist, but they are fine-tuned from large pretrained language models and release neither training data nor pipeline; NanoProof shows that the factorized execution-guided class of provers can be rebuilt from scratch with modest resources.