After concluding the discussion and properties of the lexicographic path ordering, we show it may be used to strongly restrict paramodulation inferences. The resulting calculus is called (ground) superposition
On first-order Horn clauses, (ground) superposition can be applied by introducing a new constant true and replacing every atomic predicate P by an equation P = true. This is related to the notion of analytic cut (cut with subformulas of a goal sequent) which may be employed in the inverse method.