Goedel-Prover: A Frontier Model for Open-Source Automated Theorem
  Proving
Authors: name: Yong Lin, name: Shange Tang, name: Bohan Lyu, name: Jiayun Wu, name: Hongzhou Lin, name: Kaiyu Yang, name: Jia Li, name: Mengzhou Xia, name: Danqi Chen, name: Sanjeev Arora, name: Chi Jin

We introduce Goedel-Prover, an open-source large language model (LLM) that
achieves the state-of-the-art (SOTA) performance in automated formal proof
generation for mathematical problems. The key challenge in this field is the
scarcity of formalized math statements and proofs, which we tackle in the
following ways. We train statement formalizers to translate the natural
language math problems from Numina into formal language (Lean 4), creating a
dataset of 1.64 million formal statements. LLMs are used to check that the
formal statements accurately preserve the content of the original natural
language problems. We then iteratively build a large dataset of formal proofs
by training a series of provers. Each prover succeeds in proving many
statements that the previous ones could not, and these new proofs are added to
the training set for the next prover. The final prover outperforms all existing
open-source models in whole-proof generation. On the miniF2F benchmark, it
achieves a 57.6% success rate (Pass@32), exceeding the previous best
open-source model by 7.6%. On PutnamBench, Goedel-Prover successfully solves 7
problems (Pass@512), ranking first on the leaderboard. Furthermore, it
generates 29.7K formal proofs for Lean Workbook problems, nearly doubling the
15.7K produced by earlier works.