Evaluation of automated theorem proving on the Mizar mathematical library

Authors:
Josef Urban;Krystof Hoder;Andrei Voronkov
Affiliations:
Radboud University, Nijmegen;University of Manchester;University of Manchester
Venue:
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Year:
2010

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Abstract

This paper investigates the strength of first-order automatic theorem provers (ATPs) in proving theorems and lemmas from the Mizar proof assistant's formal mathematical library. Several Mizar use-cases are described and evaluated, as well as various ATP systems and strategies. The new version of the leading Vampire ATP system is included in the evaluation, experiments with Mizar-specific strategy-selection are performed with E the prover, and the SInE axiom selection is evaluated on large Mizar problems with both E and Vampire. A rough mathematical division of the Mizar library is introduced, and the ATP performance is evaluated on it.