Internal Guidance for Satallax

TL;DR

This paper introduces an internal guidance technique for Satallax, a higher-order logic theorem prover, using Naive Bayesian classification with positive and negative examples to improve proof search efficiency.

Contribution

It presents a novel internal guidance method based on Bayesian classification that incorporates negative examples, enhancing theorem prover performance.

Findings

Solves 26% more problems with guidance

Efficient Bayesian classification scheme implemented

Improved proof search in higher-order logic

Abstract

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.