Detecting Non-Provable Goals

In this paper we present a method to detect non-provable goals. The general idea, adopted from cycle unification, is to determine in advance how terms may be modified during a derivation. Since a complete predetermination is obviously not possible, we analyze how terms may be changed by, roughly speaking, adding and deleting function symbols. Such changes of a term are encoded by an efficiently decidable clause set. The satisfiability of such a set ensures that the goal containing the term under consideration cannot contribute to a successful derivation.

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