Efficient Proof Generation for Lean Statements with Multiple Candidate Answers

Pengzhen Lin, Ke Zhang, Maziar Raissi, Zhouxing Shi

In formal systems such as Lean 4, efficiently finding answers to mathematical problems and generating verifiable proofs is an important task in automated mathematical reasoning. In the traditional way where an upstream solver provides multiple candidate answers, the common workflow requires searching for proofs for each candidate separately, incurring redundant computational cost. To this end, we propose a joint proof framework that integrates candidate answer selection, answer supplementation, and formal proof generation into a unified reasoning process. At its core is a trained prover that selects given or proposes new answers and generates a proof for at least one answer in a single call. Joint proof can also reuse generated proofs to check for faithfulness errors. For problems with a unique answer, if two distinct answers both obtain verifiable proofs under the same formal statement, this confirms the statement does not faithfully preserve the original problem semantics. On MATH-500, AMC 2023, and AIME 2024/2025/2026, our framework achieves the same formal proof success rate as per-candidate proof generation with about one sixth of the token cost, and identifies at least 6.1%…