Bohan Lyu

Yong Lin, Shange Tang, Bohan Lyu et al.

We introduce Goedel-Prover, an open-source language model that achieves state-of-the-art (as of April 5 2025) performance in automated formal proof generation for mathematical problems. A key challenge in this field is the scarcity of formalized mathematical statements and proofs, which we address through the following approaches. First, we train LLMs to convert natural language math problems from the Numina dataset to equivalent formal statements in Lean 4. This process creates the dataset Goedel-Pset-v1, which includes 1.64 million formal statements. Next, we develop a large dataset of formal proofs by training a series of provers. Each new prover can prove many statements that previous ones could not, and these new proofs are added to the training set for the next prover. Finally, we obtain the dataset Goedel-Pset-v1-solved, which contains proofs for over 800K statements from Goedel-Pset-v1. Supervised fine-tuning (SFT) of DeepSeek-Prover-V1.5-Base on Goedel-Pset-v1-solved (i.e., no RL) yields a Goedel-Prover-SFT that achieves a success rate of 57.6% (Pass@32) on miniF2F, surpassing the previous leader DeepSeek-Prover-V1.5-RL (trained using SFT + RL on a proprietary dataset) by 7.6%. On PutnamBench, Goedel-Prover-SFT successfully solves 7 problems (Pass@512), ranking first on the leaderboard. We provide extensive discussion of our training methodology, highlighting the key design choices that contribute to Goedel-Prover's strong performance. Further RL training (including DPO) improves Goedel-Prover-SFT's success rate to over 60% (Pass@32) on miniF2F. To aid future research, we provide extensive discussion of our training methodology and design choices. We also fully open-source our codes, models, and datasets. Additionally, we open-source formal proofs for 29.7K problems in Lean Workbook, nearly doubling the 15.7K solved by prior provers.

Haoyu Zhao, Yihan Geng, Shange Tang et al.

LLM-based formal proof assistants (e.g., in Lean) hold great promise for automating mathematical discovery. But beyond syntactic correctness, do these systems truly understand mathematical structure as humans do? We investigate this question in context of mathematical inequalities -- specifically the prover's ability to recognize that the given problem simplifies by applying a known inequality such as AM/GM. Specifically, we are interested in their ability to do this in a compositional setting where multiple inequalities must be applied as part of a solution. We introduce Ineq-Comp, a benchmark built from elementary inequalities through systematic transformations, including variable duplication, algebraic rewriting, and multi-step composition. Although these problems remain easy for humans, we find that most provers -- including Goedel, STP, and Kimina-7B -- struggle significantly. DeepSeek-Prover-V2-7B shows relative robustness, but still suffers a 20% performance drop (pass@32). Even for DeepSeek-Prover-V2-671B model, the gap between compositional variants and seed problems exists, implying that simply scaling up the model size alone does not fully solve the compositional weakness. Strikingly, performance remains poor for all models even when formal proofs of the constituent parts are provided in context, revealing that the source of weakness is indeed in compositional reasoning. Our results expose a persisting gap between the generalization behavior of current AI provers and human mathematical intuition. All data and evaluation code can be found at https://github.com/haoyuzhao123/LeanIneqComp.