DeepSeek-Prover-V2: recursively building Lean-checked proof-search training

What is recorded here?

DeepSeek-Prover-V2 used recursive subgoal decomposition and Lean-checked training traces for formal proof search, reporting 217/244 miniF2F test problems at 8192 samples and 47 PutnamBench problems in the selected corrected v2 evaluation. A long formal proof can be split into smaller lemmas that are easier to solve and check. DeepSeek-Prover-V2 uses DeepSeek-V3 to propose subgoals, a smaller prover to solve them, and composed Lean-checked proofs to build training examples for reinforcement learning. The671B prover reports 217/244 miniF2F test problems, 88.9%, when allowed 8192 samples per problem; this is not a single-attempt success rate. The selected July2025v2 paper reports 47 PutnamBench problems after excluding two incorrectly formalized statements from an initial 49. It advertises 658 problems but actually attempted 649 compatible with Lean4.9.0-rc2. The live arXiv abstract still displays 49; the figures here follow the selected PDF version. The authors disclose buggy7B proofs and vacuous proofs of misformulated benchmarks, illustrating why compiler success and correspondence to the intended question must be checked separately. Its 15-task formal AIME subset supplies the correct answers and excludes geometry/combinatorics, so the reported 6/15 proof result cannot be ranked directly against an informal answer-finding model. The Lean proofs and large-model benchmark have not been independently replayed here.

Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.

Scientific scope

The target is arXiv 2504.21801v2. Lean proof search is evaluated on specified formal statements and sampling budgets; it does not establish autonomous resolution of an unrelated open mathematical problem. The final Putnam result retains 47 accepted problems after two misformalizations were removed from the earlier 49. The 649 compatible problems used in the filtered dataset differ from the advertised 658. MiniF2F and FormalAIME results have separate denominators and budgets; supplied answers in FormalAIME matter. The paper discloses a Lean 4.9 release-candidate bug affecting the 7B experiment. Statement vacuity and kernel/environment correctness must be checked separately. WRS has not independently rerun the benchmarks.

Read the original work

• Ren et al., DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition — arXiv2504.21801v2

This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.

People and systems

Z.Z. Ren; Zhihong Shao; Junxiao Song; Huajian Xin; Haocheng Wang; Wanjia Zhao; Liyue Zhang; Zhe Fu; Qihao Zhu; Dejian Yang; Z.F. Wu; Zhibin Gou; Shirong Ma; Hongxuan Tang; Yuxuan Liu; Wenjun Gao; Daya Guo; Chong Ruan

Source-listed contributors to this scoped work. Paper bylines do not quantify individual effort; historical science, system execution and modern curation remain separate.

DeepSeek-Prover-V2 · DeepSeek-AI · DeepSeek-Prover-V2-671B
Formal proof generation on the reported corrected benchmark with explicit sample budgets.. Source-reported attribution; provider attestation is unavailable.

DeepSeek-V3 · DeepSeek-AI · DeepSeek-V3
Proposed subgoal decompositions and informal/formal plans for the reported cold-start training pipeline.. Source-reported attribution; provider attestation is unavailable.