EKSTRAKTO A tool to reconstruct Dedukti proofs from TSTP files (extended abstract)

TL;DR

This paper presents a versatile tool that reconstructs complete Dedukti proofs from TSTP proof traces, enabling better proof checking and reuse across various proof assistants by integrating automated theorem provers.

Contribution

The authors developed a generic tool that extracts TPTP subproblems and reconstructs Dedukti proofs using different automated provers, improving proof completeness and reusability.

Findings

Successfully reconstructed proofs for a large proportion of TPTP CNF problems.

Significantly increased the number of Dedukti proofs obtainable from automated theorem prover traces.

The tool is proof calculus agnostic and compatible with multiple provers.

Abstract

Proof assistants often call automated theorem provers to prove subgoals. However, each prover has its own proof calculus and the proof traces that it produces often lack many details to build a complete proof. Hence these traces are hard to check and reuse in proof assistants. Dedukti is a proof checker whose proofs can be translated to various proof assistants: Coq, HOL, Lean, Matita, PVS. We implemented a tool that extracts TPTP subproblems from a TSTP file and reconstructs complete proofs in Dedukti using automated provers able to generate Dedukti proofs like ZenonModulo or ArchSAT. This tool is generic: it assumes nothing about the proof calculus of the prover producing the trace, and it can use different provers to produce the Dedukti proof. We applied our tool on traces produced by automated theorem provers on the CNF problems of the TPTP library and we were able to reconstruct a proof for a large proportion of them, significantly increasing the number of Dedukti proofs that could be obtained for those problems.