Rigid E-unification is NP-complete

Rigid E-unification is a restricted kind of unification modulo equational theories, or E-unification, that arises naturally in extending P. Andrews' (1981) theorem-proving method of mating to first-order languages with equality. 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 discussed.<
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