ATP cross-verification of the Mizar MPTP challenge problems

Authors:
Josef Urban;Geoff Sutcliffe
Affiliations:
Dep't of Theoretical Computer Science, Charles University in Prague;Dep't of Computer Science, University of Miami
Venue:
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Year:
2007

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Abstract

Mizar is a proof assistant used for formalization and mechanical verification of mathematics. The main use of Mizar is in the development of the Mizar Mathematical Library (MML), in which proofs are verified by the Mizar proof checker. The Mizar proof checker has a quite complex implementation, and also lacks the ability to print out detailed atomic proof steps in a format that is easy to verify by an independent proof-checking tool. This can raise concerns about the correctness of the MML. This paper describes how a Mizar-to-ATP translation (the MPTP system), ATP verification tools (the GDV system), and Automated Theorem Proving (ATP) systems, have been used for an independent crossverification of a part of the MML.