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Handbook of Automated Reasoning by Andrei Voronkov, Alan J.A. Robinson

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5.3 Refutational Completeness

We establish the refutational completeness of general ordered resolution by showing that the calculus has the reduction property for counterexamples. We essentially use the model functor I from Definition 3.14, but applied to general clauses and with an additional restriction on productive clauses.

Let N be a set of general clauses and image002 be an admissible ordering. We use induction on image002 to define, for each clause C , a Herbrand interpretation I C and a set ε C as follows.

5.2

Definition

Take I C to be ...

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