The resolution (and paramodulation) inference systems are theorem proving procedures for rst-order logic (with equality), but they can run exponentially long for subclasses which have polynomial time decision procedures, as in the case of SLD resolution and the Knuth-Bendix completion procedure, both in the ground case. Specialized methods run in polynomial time, but have not been extended to the full rst order case. We show a form of Paramodulation which does not copy literals, which runs in

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... lynomial time for the ground case of the following four subclasses: Horn Clauses with any selection rule, any set of Unit Equalities (this includes Completion), Equational Horn Clauses with a certain selection rule, and Conditional Narrowing.