Abstract
A Craig interpolant [1] for a mutually inconsistent pair of formulas (A,B) is a formula that is (1) implied by A, (2) inconsistent with B, and (3) expressed over the common variables of A and B. It is known that a Craig interpolant can be efficiently derived from a refutation of A ∧ B, for certain theories and proof systems. For example, interpolants can be derived from resolution proofs in propositional logic, and for “cutting planes” proofs for systems of linear inequalities over the reals [5,3]. These methods have been extended to the theory of linear inequalities with uninterpreted function symbols [4].
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