Internal Guidance for Satallax
We propose a new internal guidance method for automated theorem provers based on the given-clause algorithm. Our method influences the choice of unprocessed clauses using positive and negative examples from previous proofs. To this end, we present an efficient scheme for Naive Bayesian classification by generalising label occurrences to types with monoid structure. This makes it possible to extend existing fast classifiers, which consider only positive examples, with negative ones. We implement the method in the higher-order logic prover Satallax, where we modify the delay with which propositions are processed. We evaluated our method on a simply-typed higher-order logic version of the Flyspeck project, where it solves 26 % more problems than Satallax without internal guidance.
We would like to thank Sebastian Joosten and Cezary Kaliszyk for reading initial drafts of the paper, and especially Josef Urban for inspiring discussions and inviting the authors to Prague. Furthermore, we would like to thank the anonymous IJCAR referees for their valuable comments.
This work has been supported by the Austrian Science Fund (FWF) grant P26201 as well as by the European Research Council (ERC) grant AI4REASON.
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