AI-assisted theorem proving

AI-Assisted Theorem Proving in Lean 4: Aristotle API Case Study on IMO 2009 Problem 6

This paper presents a case study of using the Aristotle API for AI-assisted formal theorem proving in Lean 4, targeting the Grasshopper problem (IMO 2009 Problem 6). The generated artifact verifies four helper lemmas but leaves the main theorem unresolved via a 'sorry' placeholder, exposing a key limitation: local proof search can succeed while global combinatorial bookkeeping remains unsolved. The study provides a reproducible Lean artifact and precise analysis distinguishing verified from unverified proof content, offering a concrete benchmark for evaluating AI formalization capabilities.