The undecidability of simultaneous rigid E-unification

AbstractSimultaneous rigid E-unification was introduced in 1987 by Gallier, Raatz and Snyder. It is used in the area of automated reasoning with equality in extension procedures, like the tableau method or the connection method. Many articles in this area assumed the existence of an algorithm for the simultaneous rigid E-unification problem. There were several faulty proofs of the decidability of this problem. In this paper we prove that simultaneous rigid E-unification is undecidable. As a consequence, we obtain the undecidability of the ℶ∗-fragment of intuitionistic logic with equality