Journal of Symbolic Logic 52 (4):916-927 (1987)

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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DOI 10.2307/2273826
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A Lower Bound for Intuitionistic Logic.Pavel Hrubeš - 2007 - Annals of Pure and Applied Logic 146 (1):72-90.
On Lengths of Proofs in Non-Classical Logics.Pavel Hrubeš - 2009 - Annals of Pure and Applied Logic 157 (2-3):194-205.
Some More Curious Inferences.Jeffrey Ketland - 2005 - Analysis 65 (1):18–24.

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