M. Ajtai, The complexity of the pigeonhole principle, in*Proc. 29th Ann. IEEE Symp. Foundations of Computer Science*, 1988, 346–355.

M. Ajtai, 138-1 on finite structures,*Annals of Pure and Applied Logic*,**24** (1983), 1–48.

P. Beame, Lower bounds for recognizing small cliques on CRCW PRAM's,*Discrete Applied Mathematics*,**29** (1990), 3–20.

P. Beame, J. Håstad, Optimal bounds for decision problems on the CRCW PRAM,*Journal of the ACM*,**36** (1989), 643–670.

P. Beame, R. Implagiazzo, J. Krajíček, T. Pitassi, P. Pudlák, A. Woods, Exponential lower bounds for the pigeonhole principle,*Proc. 24th Ann. ACM Symp. Theory of Computing* 1992, 200–220.

S. Bellantoni, T. Pitassi, A. Urquhart, Approximation and small-depth Frege proofs,*SIAM Journal of Computing*,**21** (1992), 1161–1179.

M. Bonet and S. Buss, The deduction rule and linear and near-linear proof simulations, preprint 1992.

S. Buss, Polynomial size proofs of the propositional pigeonhole principle,*Journal of Symbolic Logic*,**52** (1987), 916–927.

S. Buss, Personal communication, 1993.

S. A. Cook andR. Reckhow. The relative efficiency of propositional proof systems,*Journal of Symbolic Logic*,**44** (1979), 36–50.

M. Furst, J. Saxe, M. Sipser, Parity, circuits and the polynomial time hierarchy,*Mathematical Systems Theory*,**17** (1984) 13–27.

A. Haken, The intractability of Resolution,*Theoretical Computer Science*
**39** (1985) 297–308.

J. Håstad,*Computational limitations of small-depth circuits*, The MIT Press, Cambridge, Massachusetts, 1987.

J. Krajíček, Lower bounds to the size of constant-depth propositional proofs, preprint (1991).

J. Krajíček, P. Pudlák, A. Woods, Exponential lower bounds to the size of bounded-depth Frege proofs of the pigeonhole principle, preprint (1991).

J. Lynch, A depth-size tradeoff for Boolean circuits with unbounded fan-in,*Lecture Notes in Computer Science*
**223** (1986), 234–248.

J. Paris, A. Wilkie, A. Woods, Provability of the pigeonhole principle and the existence of infinitely many primes,*Journal of Symbolic Logic*,**53** Number 4 (1988).

T. Pitassi, P. Beame, R. Impagliazzo, Exponential lower bounds for the pigeonhole principle, University of Toronto TR 257/91 (1991).

G. S. Tseitin, On the complexity of derivation in the propositional calculus,*Studies in Constructive Mathematics and Mathematical Logic*, Part II, A.O. Slisenko, 1968.

A. Urquhart, Hard examples for Resolution,*JACM*,**34** (1987), 209–219.

A. C. Yao, Separating the polynomial-time hierarchy by oracles,*Proc. 26th Ann. IEEE Symp. Foundations of Computer Science*, 1985, 1–10.