Implication of Clauses is Undecidable

Abstract Clause implication, A ⇒ B of two clauses A and B , is shown to be undecidable using the undecidability of finitely generated stable transitive relations on free terms. Clause implication is undecidable even in the case where A consists of four literals. The decision problem of clause implication is equivalent to the decision problem of clause sets that consist of one clause and some ground units, hence the undecidability results hold also for these clause sets. Clause implication is an important problem in Automated Deduction Systems, as it can be used advantageously to reduce the search space.

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