Evaluation of Automated Theorem Proving on the Mizar Mathematical Library

摘要

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.