Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation

Computer Science > Artificial Intelligence [Submitted on 10 Jun 2026] Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation Joshua Ong Jun Leang, Zheng Zhao, Mihaela Cătălina Stoian, Qiyuan Xu, Haonan Li, Wenda Li, Shay B. Cohen, Eleonora Giunchiglia Modern Lean theorem provers achieve strong performance only with substantial training and inference compute, driven in part by scarce verified proof data and the long reasoning traces of formal proof search, making both supervised fine-tuning (SFT) and sampling expensive. We introduce Pythagoras-Prover, a compute-efficient open-source family of Lean theorem provers built for practical compute budgets. The family spans two generation paradigms: autoregressive models at 4B and 32B parameters, and a first proof-of-concept diffusion-based prover (4B) that iteratively refines Lean proofs at inference time. For training efficiency, we build a Lean-verified corpus stratified into easy, medium, and hard problems for curriculum SFT, so models acquire proof skills progressively from shorter, simpler proofs to longer, harder ones. During SFT, a dynamic proof-reasoning filtering scheme preserves informative proof traces while keeping each instance within an 8k-token context budget. We also introduce Augmented Lean Formalisation (ALF), which expands scarce verified corpora into variants of formal statements, populated via self-distillation for extra training signal without formally verifying every mutated instance. By perturbing known problems while preserving their formal character, ALF reduces reliance on any statement's surface form. Empirically, Pythagoras-Prover-4B surpasses DeepSeek-Prover-V2-671B at pass@32 on MiniF2F-Test (86.1% vs 82.4%) with ~167x fewer parameters, while Pythagoras-Prover-32B sets the open-source state of the art at 93.0% on MiniF2F-Test and solves 93 of 672 PutnamBench problems. We release MiniF2F-ALF, an ALF-mutated contamination-sensitive benchmark on which every evaluated model loses accuracy; here our 32B remains strongest and our 4B matches the prior state of the art, Goedel-Prover-V2-32B. Comments: Pythagoras-Prover: Technical Report Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2606.12594 [cs.AI]   (or arXiv:2606.12594v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2606.12594 Focus to learn more Submission history From: Joshua Jun Leang Ong [view email] [v1] Wed, 10 Jun 2026 18:43:11 UTC (1,138 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-06 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)