The He† Refutation Method
In order to generalize the results of the previous section to the first-order case, we will need the notion of unification modulo a set of equations, or E-unification. The concept of E-unification comes up naturally when we apply the Skolem-Herbrand-Gödel theorem to a set of universal Horn clauses with equality, in order to reduce unsatisfiability in the first-order case to unsatisfiability in the ground case. Recall that this theorem states that a set of universal prenex sentences is unsatisfiable if and only if some set of ground substitution instances of the matrices of these sentences is unsatisfiable.
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