Thierry Marianne | Searcharxiv

arXiv2026

Case study: solving P-99 with LPTP and an LLM

Ninety-Nine Prolog Problems (P-99) is a famous set of Prolog exercises. We solved the first thirty three just by prompting an LLM (Large Language Model). We used Claude from Anthropic. By solved we mean: generate the Prolog code and a test file, run the tests and check whether they pass, then formally prove types, groundness, termination, uniqueness, existence and also sometimes functional correctness with LPTP (Logic Program Theorem Prover). Hence our approach is an experiment in vibe-coding/vericoding of P-99. It is a vibe-coding experiment because we started from informal specifications written in English and let Claude generate the Prolog code. It also fits within vericoding because the LLM proved reliability guarantees on the generated Prolog code. Claude wrote 58 logic procedures, 508 tests, 257 lemmas for a total of 11800 proof lines. We manually checked each file generated by the LLM. We checked the Prolog code, ran the tests, examined the logical statements generated by Claude and proof-checked Claude's proofs with LPTP. This paper describes this experiment and provides the main details so that it can be reproduced by the interested reader.

cs.LO↗

arXiv2026

Automated Theorem Proving for Prolog Verification

LPTP (Logic Program Theorem Prover) is an interactive natural-deduction-based theorem prover for pure Prolog programs with negation as failure, unification with the occurs check, and a restricted but extensible set of built-in predicates. With LPTP, one can formally prove termination and partial correctness of such Prolog programs. LPTP was designed in the mid-1990's by Robert F. Staerk. It is written in ISO-Prolog and comes with an Emacs user-interface. From a theoretical point of view, in his publications about LPTP, Staerk associates a set of first-order axioms IND(P) to the considered Prolog program P. IND(P) contains the Clark's equality theory for P, definitions of success, failure and termination for each user-defined logic procedure in P, axioms relating these three points of view, and an axiom schema for proving inductive properties. LPTP is thus a dedicated proof editor where these axioms are hard-wired. We propose to translate these axioms as first-order formulas (FOFs), and apply automated theorem provers to check the property of interest. Using FOF as an intermediary language, we experiment the use of automated theorem provers for Prolog program verification. We evaluate the approach over a benchmark of about 400 properties of Prolog programs from the library available with LPTP. Both the compiler which generates a set of FOF files from a given input Prolog program together with its properties and the benchmark are publicly available.

cs.LO↗