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University of Namur

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Representative Papers

Case study: proving sqrt(2) irrational with LPTP and an LLM

Jul 23, 2026

This work formalizes a proof of the irrationality of √2 within a logic programming framework and investigates the feasibility of leveraging large language models (LLMs) to assist in constructing machine-verifiable mathematical proofs. By integrating the LPTP logic program theorem prover with an LLM, the study develops a complete formal proof from basic predicates in a natural-deduction style. It presents the first successful collaboration between an LLM and LPTP to generate a human-readable yet fully machine-verifiable proof of the irrationality of √2, which has been rigorously validated by LPTP. The results demonstrate the effectiveness of human–AI cooperation in formal mathematics and offer a novel pathway toward AI-assisted theorem proving.

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Latest Papers

Case study: proving sqrt(2) irrational with LPTP and an LLM

Jul 23, 2026

This work formalizes a proof of the irrationality of √2 within a logic programming framework and investigates the feasibility of leveraging large language models (LLMs) to assist in constructing machine-verifiable mathematical proofs. By integrating the LPTP logic program theorem prover with an LLM, the study develops a complete formal proof from basic predicates in a natural-deduction style. It presents the first successful collaboration between an LLM and LPTP to generate a human-readable yet fully machine-verifiable proof of the irrationality of √2, which has been rigorously validated by LPTP. The results demonstrate the effectiveness of human–AI cooperation in formal mathematics and offer a novel pathway toward AI-assisted theorem proving.

0 citationsRead paper