Evaluation of Automated Theorem Proving on the Mizar Mathematical Library

  • Josef Urban
  • Krystof Hoder
  • Andrei Voronkov
Conference paper

DOI: 10.1007/978-3-642-15582-6_30

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)
Cite this paper as:
Urban J., Hoder K., Voronkov A. (2010) Evaluation of Automated Theorem Proving on the Mizar Mathematical Library. In: Fukuda K., Hoeven J..., Joswig M., Takayama N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Josef Urban
    • 1
  • Krystof Hoder
    • 2
  • Andrei Voronkov
    • 2
  1. 1.Radboud UniversityNijmegen
  2. 2.University of Manchester 

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