REAL-Prover: Retrieval Augmented Lean Prover for Mathematical Reasoning

Fuente: arXiv
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Main Authors: Shen, Ziju, Huang, Naohao, Yang, Fanyi, Wang, Yutong, Gao, Guoxiong, Xu, Tianyi, Jiang, Jiedong, He, Wanyi, Yang, Pu, Sun, Mengzhou, Ju, Haocheng, Wu, Peihao, Dai, Bryan, Dong, Bin
Format: Preprint
Published: 2025
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author Shen, Ziju
Huang, Naohao
Yang, Fanyi
Wang, Yutong
Gao, Guoxiong
Xu, Tianyi
Jiang, Jiedong
He, Wanyi
Yang, Pu
Sun, Mengzhou
Ju, Haocheng
Wu, Peihao
Dai, Bryan
Dong, Bin
author_facet Shen, Ziju
Huang, Naohao
Yang, Fanyi
Wang, Yutong
Gao, Guoxiong
Xu, Tianyi
Jiang, Jiedong
He, Wanyi
Yang, Pu
Sun, Mengzhou
Ju, Haocheng
Wu, Peihao
Dai, Bryan
Dong, Bin
contents Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise theorem prover for Lean 4 to push this boundary. This prover, based on our fine-tuned large language model (REAL-Prover-v1) and integrated with a retrieval system (Leansearch-PS), notably boosts performance on solving college-level mathematics problems. To train REAL-Prover-v1, we developed HERALD-AF, a data extraction pipeline that converts natural language math problems into formal statements, and a new open-source Lean 4 interactive environment (Jixia-interactive) to facilitate synthesis data collection. In our experiments, our prover using only supervised fine-tune achieves competitive results with a 23.7% success rate (Pass@64) on the ProofNet dataset-comparable to state-of-the-art (SOTA) models. To further evaluate our approach, we introduce FATE-M, a new benchmark focused on algebraic problems, where our prover achieves a SOTA success rate of 56.7% (Pass@64).
format Preprint
id arxiv_https___arxiv_org_abs_2505_20613
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle REAL-Prover: Retrieval Augmented Lean Prover for Mathematical Reasoning
Shen, Ziju
Huang, Naohao
Yang, Fanyi
Wang, Yutong
Gao, Guoxiong
Xu, Tianyi
Jiang, Jiedong
He, Wanyi
Yang, Pu
Sun, Mengzhou
Ju, Haocheng
Wu, Peihao
Dai, Bryan
Dong, Bin
Computation and Language
Artificial Intelligence
Machine Learning
Logic in Computer Science
Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise theorem prover for Lean 4 to push this boundary. This prover, based on our fine-tuned large language model (REAL-Prover-v1) and integrated with a retrieval system (Leansearch-PS), notably boosts performance on solving college-level mathematics problems. To train REAL-Prover-v1, we developed HERALD-AF, a data extraction pipeline that converts natural language math problems into formal statements, and a new open-source Lean 4 interactive environment (Jixia-interactive) to facilitate synthesis data collection. In our experiments, our prover using only supervised fine-tune achieves competitive results with a 23.7% success rate (Pass@64) on the ProofNet dataset-comparable to state-of-the-art (SOTA) models. To further evaluate our approach, we introduce FATE-M, a new benchmark focused on algebraic problems, where our prover achieves a SOTA success rate of 56.7% (Pass@64).
title REAL-Prover: Retrieval Augmented Lean Prover for Mathematical Reasoning
topic Computation and Language
Artificial Intelligence
Machine Learning
Logic in Computer Science
url https://arxiv.org/abs/2505.20613