Using Aristotle API for AI-Assisted Theorem Proving in Lean 4: A Formalisation Case Study of the Grasshopper Problem
The article discusses a case study on using the Aristotle API for AI-assisted theorem proving in Lean 4, focusing on the Grasshopper problem. It highlights the limitations of local proof search in AI-assisted formalization, where local components may be verified while the overall theorem remains unresolved. The study provides a reproducible Lean artifact and a detailed analysis of verified and unverified proof content.
- ▪The paper presents a formalization case study of the Grasshopper problem using the Aristotle API in Lean 4.
- ▪It identifies a limitation in AI-assisted theorem proving, where local proofs can succeed while global combinatorial aspects remain unresolved.
- ▪The study includes a Lean artifact that demonstrates both verified and unverified components of the proof.
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| Original publisher | arXiv cs.AI |
| Canonical URL | https://arxiv.org/abs/2605.20120 |
| Publication time | Wed, 20 May 2026 00:00:00 -0400 |
| Retrieval time | 2026-05-20T04:04:59.484Z |
| Last seen | 2026-05-20T04:04:59.484Z |
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| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
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| Cluster | u3BghgdwsuvS |
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| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
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| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
Opening excerpt (first ~120 words) tap to expand
Computer Science > Artificial Intelligence arXiv:2605.20120 (cs) [Submitted on 19 May 2026] Title:Using Aristotle API for AI-Assisted Theorem Proving in Lean 4: A Formalisation Case Study of the Grasshopper Problem Authors:Gabriel Rongyang Lau View a PDF of the paper titled Using Aristotle API for AI-Assisted Theorem Proving in Lean 4: A Formalisation Case Study of the Grasshopper Problem, by Gabriel Rongyang Lau View PDF HTML (experimental) Abstract:AI-assisted theorem proving can now generate substantial Lean developments for olympiad-level mathematics, but the evidential status of such developments depends on which declarations are actually verified.
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