A Deductive-Complete Constrained Superposition Calculus for Ground Flat Equational Clauses

Abstract

We describe an algorithm that generates prime implicates of equational clause sets without variables and function symbols. The procedure is based on constrained superposition rules, where constraints are used to store literals that are asserted as additional axioms (or hypotheses) during the proof search. This approach is sound and deductive-complete, and it is more efficient than previous algorithms based on conditional paramodulation. It is also more flexible in the sense that it allows one to restrict the search space by imposing additional properties that the generated implicates should satisfy (e.g., to ensure relevance).