{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/real-prover-retrieval-augmented-lean-prover","title":"REAL-Prover: Retrieval Augmented Lean Prover for Mathematical Reasoning","arxiv_id":"2505.20613","date":"2025-05-27","proceeding":null,"authors":["Ziju Shen","Naohao Huang","Fanyi Yang","Yutong Wang","Guoxiong Gao","Tianyi Xu","Jiedong Jiang","Wanyi He","Pu Yang","Mengzhou Sun","Haocheng Ju","Peihao Wu","Bryan Dai","Bin Dong"],"abstract":"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).","url_abs":"https://arxiv.org/abs/2505.20613v2","url_pdf":"https://arxiv.org/pdf/2505.20613v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"real-prover-retrieval-augmented-lean-prover","repo_url":"https://github.com/frenzymath/REAL-Prover","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"language-modeling","task_name":"Language Modeling"},{"task_slug":"language-modelling","task_name":"Language Modelling"},{"task_slug":"large-language-model","task_name":"Large Language Model"},{"task_slug":"math","task_name":"Math"},{"task_slug":"mathematical-reasoning","task_name":"Mathematical Reasoning"},{"task_slug":"retrieval","task_name":"Retrieval"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2505.20613","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}