A Formally Verified Checker for First-Order Proofs

Author Seulkee Baek

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Seulkee Baek
  • Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA, USA


I'd like to thank Jeremy Avigad and the anonymous referees for their careful proofreading of drafts and advice for improvements.

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Seulkee Baek. A Formally Verified Checker for First-Order Proofs. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


The Verified TESC Verifier (VTV) is a formally verified checker for the new Theory-Extensible Sequent Calculus (TESC) proof format for first-order ATPs. VTV accepts a TPTP problem and a TESC proof as input, and uses the latter to verify the unsatisfiability of the former. VTV is written in Agda, and the soundness of its proof-checking kernel is verified in respect to a first-order semantics formalized in Agda. VTV shows robust performance in a comprehensive test using all eligible problems from the TPTP problem library, successfully verifying all but the largest 5 of 12296 proofs, with >97% of the proofs verified in less than 1 second.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Theorem proving algorithms
  • TESC
  • TPTP
  • TSTP
  • ATP


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