Associative-commutative superposition

Abstract

We present an associative-commutative paramodulation calculus that generalizes the associative-commutative completion procedure to firstorder clauses. The calculus is parametrized by a selection function (on negative literats) and a well-founded ordering on terms. It is compatible with an "abstract notion of redundancy that covers such simplification techniques as tautology deletion, subsumption, and simplification by (associative-commutative) rewriting. The proof of refutational completeness of the calculus is comparatively simple, and the techniques employed may be of independent interest.