Abstract
Rigid E -unification is a restricted kind of unification modulo equational theories, or E -unification, that arises naturally in extending Andrew's theorem proving method of matings to first-order languages with equality. This extension was first presented by J. H. Gallier, S. Raatz, and W. Snyder, who conjectured that rigid E -unification is decidable. In this paper, it is shown that rigid E -unification is NP-complete and that finite complete sets of rigid E -unifiers always exist. As a consequence, deciding whether a family of mated sets is an equational mating is an NP-complete problem. Some implications of this result regarding the complexity of theorem proving in first-order logic with equality are also discussed.
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