Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data
  Synthesis and Self-Correction
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.
6892cb908da45ffb0a2b2490
Yong Lin
6892cb908da45ffb0a2b2491
Shange Tang
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Bohan Lyu
6892cb908da45ffb0a2b2493
Ziran Yang
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Jui-Hui Chung
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Haoyu Zhao
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Lai Jiang
6892cb908da45ffb0a2b2497
Yihan Geng
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Jiawei Ge
6892cb908da45ffb0a2b2499
Jingruo Sun
6892cb908da45ffb0a2b249a
Jiayun Wu
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Jiri Gesi
6892cb908da45ffb0a2b249c
Ximing Lu
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David Acuna
6892cb908da45ffb0a2b249e
Kaiyu Yang
6892cb908da45ffb0a2b249f
Hongzhou Lin
6892cb908da45ffb0a2b24a0
Yejin Choi
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Danqi Chen
6892cb908da45ffb0a2b24a2
Sanjeev Arora
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Chi Jin
Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data
  Synthesis and Self-Correction
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.
Goedel-Prover-V2, a series of open-source language models, achieves state-of-the-art performance in automated theorem proving through scaffolded data synthesis, verifier-guided self-correction, and model averaging.
scaffolded data synthesis verifier-guided self-correction model averaging automated theorem proving MiniF2F PutnamBench pass@32 pass@184 pass@1024