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Every super-polynomial proof in purely implicational minimal logic has a polynomially sized proof in classical implicational propositional logic (1505.06506v3)
Published 25 May 2015 in cs.CC and cs.LO
Abstract: In this article we show how any formula A with a proof in minimal implicational logic that is super-polynomially sized has a polynomially-sized proof in classical implicational propositional logic . This fact provides an argument in favor that any classical propositional tautology has short proofs, i.e., NP=CoNP.