Propositional proof systems, the consistency of first order theories and the complexity of computations

Journal of Symbolic Logic 54 (3):1063-1079 (1989)
We consider the problem about the length of proofs of the sentences $\operatorname{Con}_S(\underline{n})$ saying that there is no proof of contradiction in S whose length is ≤ n. We show the relation of this problem to some problems about propositional proof systems
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    Samuel R. Buss (2012). Towards–Via Proof Complexity and Search. Annals of Pure and Applied Logic 163 (7):906-917.
    Lutz Straßburger (2012). Extension Without Cut. Annals of Pure and Applied Logic 163 (12):1995-2007.
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