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With recent advances in large language models (LLMs), formal theorem-proving techniques have made substantial progress on theorem-proving problems, yet formal answer construction remains less studied. This exposes a mismatch between current LLM model families: general LLMs are strong at informal conjecturing but are expensive and unreliable at formal proof generation, whereas prover LLMs are cheap and optimized for formal proofs but weak at mathematical reasoning for proposing candidate answers. Moreover, Lean proof checking alone does not enforce that a constructed witness is a canonical answer: circular or non-closed-form witnesses can eliminate the existential quantifier while failing to constitute an admissible conte","title":"Formally Solving Answer-Construction Problems in Lean","url":"https://arxiv.org/abs/2505.18492","vendor":"arxiv_cs_ai"},"summary":"arXiv:2505.18492v5 Announce Type: replace \nAbstract: Mathematical competition problems fall into two broad types: theorem proving, which asks for a proof of a given statement, and answer construction, which requires constructing a property-satifying object with proofs. With recent advances in large language models (LLMs), formal theorem-proving techniques have made substantial progress on theorem-proving problems, yet formal answer construction remains less studied. This exposes a mismatch between current LLM model families: general LLMs are strong at informal conjecturing but are expensive and unreliable at formal proof generation, whereas prover LLMs are cheap and optimized for formal proofs but weak at mathematical reasoning for proposing candidate answers. 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