Internal Guidance for Satallax
This work addresses the efficiency of automated theorem provers for higher-order logic, offering a domain-specific incremental improvement.
The authors tackled the problem of automated theorem proving by developing an internal guidance method that uses both positive and negative examples from previous proofs to influence clause selection, resulting in a 26% increase in solved problems on a higher-order logic benchmark compared to the baseline.
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.