The Undecidability of Simultaneous Rigid E-Unification

Abstract Simultaneous 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.

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