Polynomial size proofs of the propositional pigeonhole principle

Journal of Symbolic Logic 52 (4):916-927 (1987)
Abstract
Cook and Reckhow defined a propositional formulation of the pigeonhole principle. This paper shows that there are Frege proofs of this propositional pigeonhole principle of polynomial size. This together with a result of Haken gives another proof of Urquhart's theorem that Frege systems have an exponential speedup over resolution. We also discuss connections to provability in theories of bounded arithmetic
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Pavel Hrubeš (2009). On Lengths of Proofs in Non-Classical Logics. Annals of Pure and Applied Logic 157 (2):194-205.
Emil Jeřábek (2012). Proofs with Monotone Cuts. Mathematical Logic Quarterly 58 (3):177-187.

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