# Proof Sketch Refinement

HybridProver joins whole-proof synthesis and stepwise tactic generation in one pipeline: a whole-proof model drafts candidate proofs, and candidates that fail Isabelle's checker are abstracted into proof sketches that keep the high-level structure, then filled subgoal by subgoal by a tactic model and Sledgehammer. On the 244 test problems of the Isabelle version of miniF2F, the pipeline reaches a 73.8% success rate, above the previous best Isabelle result of 61.9%. Both 7B-scale models are trained with supervised fine-tuning and reinforcement learning rewarded by Isabelle verification, indicating that lightweight models can generate Isabelle/HOL proofs.

HybridProver joins whole-proof synthesis and stepwise tactic generation in one pipeline: a whole-proof model drafts candidate proofs, and candidates that fail Isabelle's checker are abstracted into proof sketches that keep the high-level structure, then filled subgoal by subgoal by a tactic model and Sledgehammer. On the 244 test problems of the Isabelle version of miniF2F, the pipeline reaches a 73.8% success rate, above the previous best Isabelle result of 61.9%. Both 7B-scale models are trained with supervised fine-tuning and reinforcement learning rewarded by Isabelle verification, indicating that lightweight models can generate Isabelle/HOL proofs.