@inproceedings{xin-etal-2025-bfs,
title = "{BFS}-Prover: Scalable Best-First Tree Search for {LLM}-based Automatic Theorem Proving",
author = "Xin, Ran and
Xi, Chenguang and
Yang, Jie and
Chen, Feng and
Wu, Hang and
Xiao, Xia and
Sun, Yifan and
Zheng, Shen and
Ding, Ming",
editor = "Che, Wanxiang and
Nabende, Joyce and
Shutova, Ekaterina and
Pilehvar, Mohammad Taher",
booktitle = "Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)",
month = jul,
year = "2025",
address = "Vienna, Austria",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2025.acl-long.1565/",
doi = "10.18653/v1/2025.acl-long.1565",
pages = "32588--32599",
ISBN = "979-8-89176-251-0",
abstract = "Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating the underlying large proof search spaces. While the existing approaches primarily rely on value functions and/or Monte Carlo Tree Search (MCTS), the potential of simpler methods like Best-First Tree Search (BFS) remains underexplored. In this paper, we investigate whether BFS can achieve competitive performance in large-scale theorem proving tasks. We present BFS-Prover, a scalable expert iteration framework, featuring three key innovations. First, we implement strategic data filtering at each expert iteration round, excluding problems solvable via beam search node expansion to focus on harder cases. Second, we improve the sample efficiency of BFS through Direct Preference Optimization (DPO) applied to state-tactic pairs automatically annotated with compiler error feedback, refining the LLM{'}s policy to prioritize productive expansions. Third, we employ length normalization in BFS to encourage exploration of deeper proof paths. BFS-Prover achieves a state-of-the-art score of 72.95 on the MiniF2F test set and therefore challenges the perceived necessity of complex tree search methods, demonstrating that BFS can achieve competitive performance when properly scaled."
}<?xml version="1.0" encoding="UTF-8"?>
<modsCollection xmlns="http://www.loc.gov/mods/v3">
<mods ID="xin-etal-2025-bfs">
<titleInfo>
<title>BFS-Prover: Scalable Best-First Tree Search for LLM-based Automatic Theorem Proving</title>
</titleInfo>
<name type="personal">
<namePart type="given">Ran</namePart>
<namePart type="family">Xin</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Chenguang</namePart>
<namePart type="family">Xi</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Jie</namePart>
<namePart type="family">Yang</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Feng</namePart>
<namePart type="family">Chen</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Hang</namePart>
<namePart type="family">Wu</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Xia</namePart>
<namePart type="family">Xiao</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Yifan</namePart>
<namePart type="family">Sun</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Shen</namePart>
<namePart type="family">Zheng</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Ming</namePart>
<namePart type="family">Ding</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<originInfo>
<dateIssued>2025-07</dateIssued>
</originInfo>
<typeOfResource>text</typeOfResource>
<relatedItem type="host">
<titleInfo>
<title>Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)</title>
</titleInfo>
<name type="personal">
<namePart type="given">Wanxiang</namePart>
<namePart type="family">Che</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Joyce</namePart>
<namePart type="family">Nabende</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Ekaterina</namePart>
<namePart type="family">Shutova</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Mohammad</namePart>
<namePart type="given">Taher</namePart>
<namePart type="family">Pilehvar</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<originInfo>
<publisher>Association for Computational Linguistics</publisher>
<place>
<placeTerm type="text">Vienna, Austria</placeTerm>
</place>
</originInfo>
<genre authority="marcgt">conference publication</genre>
<identifier type="isbn">979-8-89176-251-0</identifier>
</relatedItem>
<abstract>Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating the underlying large proof search spaces. While the existing approaches primarily rely on value functions and/or Monte Carlo Tree Search (MCTS), the potential of simpler methods like Best-First Tree Search (BFS) remains underexplored. In this paper, we investigate whether BFS can achieve competitive performance in large-scale theorem proving tasks. We present BFS-Prover, a scalable expert iteration framework, featuring three key innovations. First, we implement strategic data filtering at each expert iteration round, excluding problems solvable via beam search node expansion to focus on harder cases. Second, we improve the sample efficiency of BFS through Direct Preference Optimization (DPO) applied to state-tactic pairs automatically annotated with compiler error feedback, refining the LLM’s policy to prioritize productive expansions. Third, we employ length normalization in BFS to encourage exploration of deeper proof paths. BFS-Prover achieves a state-of-the-art score of 72.95 on the MiniF2F test set and therefore challenges the perceived necessity of complex tree search methods, demonstrating that BFS can achieve competitive performance when properly scaled.</abstract>
<identifier type="citekey">xin-etal-2025-bfs</identifier>
<identifier type="doi">10.18653/v1/2025.acl-long.1565</identifier>
<location>
<url>https://aclanthology.org/2025.acl-long.1565/</url>
</location>
<part>
<date>2025-07</date>
<extent unit="page">
<start>32588</start>
<end>32599</end>
</extent>
</part>
</mods>
</modsCollection>
%0 Conference Proceedings
%T BFS-Prover: Scalable Best-First Tree Search for LLM-based Automatic Theorem Proving
%A Xin, Ran
%A Xi, Chenguang
%A Yang, Jie
%A Chen, Feng
%A Wu, Hang
%A Xiao, Xia
%A Sun, Yifan
%A Zheng, Shen
%A Ding, Ming
%Y Che, Wanxiang
%Y Nabende, Joyce
%Y Shutova, Ekaterina
%Y Pilehvar, Mohammad Taher
%S Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2025
%8 July
%I Association for Computational Linguistics
%C Vienna, Austria
%@ 979-8-89176-251-0
%F xin-etal-2025-bfs
%X Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating the underlying large proof search spaces. While the existing approaches primarily rely on value functions and/or Monte Carlo Tree Search (MCTS), the potential of simpler methods like Best-First Tree Search (BFS) remains underexplored. In this paper, we investigate whether BFS can achieve competitive performance in large-scale theorem proving tasks. We present BFS-Prover, a scalable expert iteration framework, featuring three key innovations. First, we implement strategic data filtering at each expert iteration round, excluding problems solvable via beam search node expansion to focus on harder cases. Second, we improve the sample efficiency of BFS through Direct Preference Optimization (DPO) applied to state-tactic pairs automatically annotated with compiler error feedback, refining the LLM’s policy to prioritize productive expansions. Third, we employ length normalization in BFS to encourage exploration of deeper proof paths. BFS-Prover achieves a state-of-the-art score of 72.95 on the MiniF2F test set and therefore challenges the perceived necessity of complex tree search methods, demonstrating that BFS can achieve competitive performance when properly scaled.
%R 10.18653/v1/2025.acl-long.1565
%U https://aclanthology.org/2025.acl-long.1565/
%U https://doi.org/10.18653/v1/2025.acl-long.1565
%P 32588-32599
Markdown (Informal)
[BFS-Prover: Scalable Best-First Tree Search for LLM-based Automatic Theorem Proving](https://aclanthology.org/2025.acl-long.1565/) (Xin et al., ACL 2025)
ACL
- Ran Xin, Chenguang Xi, Jie Yang, Feng Chen, Hang Wu, Xia Xiao, Yifan Sun, Shen Zheng, and Ming Ding. 2025. BFS-Prover: Scalable Best-First Tree Search for LLM-based Automatic Theorem Proving. In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 32588–32599, Vienna, Austria. Association for Computational Linguistics.