Learning to Disprove: Formal Counterexample Generation with Large Language Models
Mathematical reasoning demands two critical, complementary skills: constructing rigorous proofs for true statements and discovering counterexamples that disprove false ones. However, current AI efforts in mathematics focus almost exclusively on proof construction, often neglecting the equally important task of finding counterexamples. In this paper, we address this gap by fine-tuning large language models (LLMs) to reason about and generate counterexamples. We formalize this task as formal counterexample generation, which requires LLMs not only to propose candidate counterexamples but also to produce formal proofs that can be automatically verified in the Lean 4 theorem prover. To enable ...
| Authors | Zenan Li, Zhaoyu Li, Kaiyu Yang et al. |
|---|---|
| Primary category | cs.AI |
| Published | 19 March 2026 |
| Last updated at source | 14 October 2026 |
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