ENIGMAWatch: ProofWatch Meets ENIGMA

Abstract

In this work we describe a new learning-based proof guidance – ENIGMAWatch – for saturation-style first-order theorem provers. ENIGMAWatch combines two guiding approaches for the given-clause selection implemented for the E ATP system: ProofWatch and ENIGMA. ProofWatch is motivated by the watchlist (hints) method and based on symbolic matching of multiple related proofs, while ENIGMA is based on statistical machine learning. The two methods are combined by using the evolving information about symbolic proof matching as additional characterization of the saturation-style proof search for the statistical learning methods. The new system is evaluated on a large set of problems from the Mizar library. We show that the added proof-matching information is considered important by the statistical machine learners, and that it leads to improved performance over ProofWatch and ENIGMA.