  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.
