Evaluation of Automated Theorem Proving on the Mizar Mathematical Library

  • Josef Urban
  • Krystof Hoder
  • Andrei Voronkov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)


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.


Theorem Prover Automate Theorem Mizar Mathematical Library Included Axiom Obvious Inference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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