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In this paper we develop a connection between optimal propositional proof systems and structural complexity theory--specifically, there exists an optimal propositional proof system if and only if there is a suitable recursive presentation of the class of all easy (polynomial time recognizable) subsets of TAUT. As a corollary we obtain the result that if there does not exist an optimal propositional proof system, then for every theory T there exists an easy subset of TAUT which is not T-provably easy.