NanoProof: Open and Efficient Automated Theorem Proving in Lean 4

2026-10-08

AI Summary

This study addresses the reproducibility challenges in Lean 4 automated theorem proving arising from opaque training pipelines and prohibitive computational requirements. To this end, it proposes the first end-to-end open-source factorized execution-guided theorem prover. Methodologically, the approach employs a factorized execution-guided architecture integrated with Lean 4 formal verification tools and an efficient training pipeline, achieving full reproducibility from raw data to model weights. The primary contributions include the release of a structured proof tree dataset alongside its extraction utilities, the reconstruction of the system using minimal compute—ranging from one-tenth to one-thousandth of that required by comparable systems—and the attainment of a pass@16 accuracy of 50.8% on the MiniF2F benchmark, surpassing existing state-of-the-art systems.

Abstract

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.

Problem

• Automated Theorem Proving
• Lean 4
• Reproducibility
• Compute Efficiency
• Open-source

Innovation

• Automated Theorem Proving
• Lean 4
• Execution-Guided
• Compute Efficiency
• Open-Source Reproducibility