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 systems of linear inequalities over the reals [6,4]. These methods have been recently extended to combine linear inequalities with uninterpreted function symbols, and to deal with integer models [5]. One key aspect of these procedures is that the yield quantifier-free interpolants when the premises A and B are quantifier-free.
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