SC-TPTP: An Extension of the TPTP Derivation Format for Sequent-Based Calculus

TL;DR

This paper introduces SC-TPTP, an extended proof format for first-order logic that facilitates proof transfer between systems, supports multiple proof strategies, and integrates with proof assistants and theorem provers.

Contribution

It extends the TPTP proof format to include sequent calculus proofs, enabling better interoperability and detailed proof descriptions across various proof tools.

Findings

Successfully implemented parsing, printing, and checking of SC-TPTP proofs.

Enabled proof queries from the Lisa proof assistant to the G"odeland theorem prover.

Exported proofs into Coq and reconstructed low-level proof steps.

Abstract

Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe proofs in first-order logic: SC-TPTP. To avoid multiplication of standards, our proposed format over-specifies the TPTP derivation format by focusing on sequent formalisms. By doing so, it provides a high level of detail, is faithful to mathematical tradition, and cover multiple existing tools and in particular tableaux-based strategies. We make use of this format to allow the Lisa proof assistant to query the Go\'eland automated theorem prover, and implement a library of tools able to parse, print and check SC-TPTP proofs, export them into Coq files, and rebuild low-level proof steps from advanced ones.