Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data
  Synthesis and Self-Correction
Authors: name: Yong Lin, name: Shange Tang, name: Bohan Lyu, name: Ziran Yang, name: Jui-Hui Chung, name: Haoyu Zhao, name: Lai Jiang, name: Yihan Geng, name: Jiawei Ge, name: Jingruo Sun, name: Jiayun Wu, name: Jiri Gesi, name: Ximing Lu, name: David Acuna, name: Kaiyu Yang, name: Hongzhou Lin, name: Yejin Choi, name: Danqi Chen, name: Sanjeev Arora, name: Chi Jin

We introduce Goedel-Prover-V2, a series of open-source language models that
set a new state-of-the-art in automated theorem proving. Built on the standard
expert iteration and reinforcement learning pipeline, our approach incorporates
three key innovations: (1) Scaffolded data synthesis: We generate synthetic
tasks of increasing difficulty to train the model to master increasingly
complex theorems; (2) Verifier-guided self-correction: We enable the model to
iteratively revise its proofs by leveraging feedback from the Lean compiler;
(3) Model averaging: We merge model checkpoints to mitigate the decrease in
model output diversity in later stages of training. Our small model,
Goedel-Prover-V2-8B, reaches 84.6% pass@32 on MiniF2F and outperforms
DeepSeek-Prover-V2-671B under the same metric, despite being 80X smaller. Our
flagship model, Goedel-Prover-V2-32B, achieves 88.1% on MiniF2F at pass@32 in
standard mode and 90.4% in self-correction mode, outperforming prior SOTA by a
large margin. Additionally, our flagship model solves 86 problems on
PutnamBench at pass@184, securing the first place among open-source models on
the leaderboard, surpassing DeepSeek-Prover-V2-671B's record of solving 47
problems by pass@1024 with a significantly smaller model size and compute
budget. At the time of its release (July-August 2025), Goedel-Prover-V2
achieves the strongest overall performance among all open-source theorem
provers. It also ranks among the top-performing models--including closed-source
systems with publicly reported performance--under a constrained test-time
compute budget. Our models, code, and data are released at
https://github.com/Goedel-LM/Goedel-Prover-V2.