1. Introduction We introduce DeepSeek Prover V2, an open source large language model designed for formal theorem proving in Lean 4, with initialization data collected through a recursive theorem proving pipeline powered by DeepSeek V3. The cold start training procedure begins by prompting DeepSeek V3 to decompose complex problems into a series of subgoals. The proofs of resolved subgoals are synthesized into a chain of thought process, combined with DeepSeek V3's step by step reasoning, to create an initial cold start for reinforcement learning. This process enables us to integrate both informal and formal mathematical reasoning into a unified model. 2. Model Summary Synthesize Cold Start Reasoning Data through Recursive Proof Search To construct the cold start dataset, we develop a simple yet effective pipeline for recursive theorem proving, utilizing DeepSeek V3 as a unified tool for both subgoal decomposition and formalization. We prompt DeepSeek V3 to decompose theorems into high level proof sketches while simultaneously formalizing these proof steps in Lean 4, resulting in a sequence of subgoals. We use a smaller 7B model to handle the proof search for each subgoal, thereby re…
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