Set of Support for Theory Reasoning

Abstract

This paper describes initial experiments using the set of support strategy to improve how a saturation-based theorem prover performs theory reasoning with explicit theory axioms. When dealing with theories such as arithmetic, modern automated theorem provers often resort to adding explicit theory axioms, for example, x+y = y+x. Reasoning with such axioms can be explosive. However, little has been done to explore methods that mitigate the negative impact of theory axioms on saturation-based reasoning. The set of support strategy requires that all inferences involve a premise with an ancestor in a so-called set of support,initially taken to be a subset of the input clauses, usually those corresponding to the goal. This leads to completely goal orientated reasoning but is incomplete for practical reasoning (e.g. in the presence of ordering constraints). The idea of this paper is to apply the set of support strategy to theory axioms only, and then to explore the effect of allowing some limited reasoning within this set. The suggested approach is implemented and evaluated within the VAMPIRE theorem prover.