We present a simple proof of the bounded-depth Frege lower bounds of
Pitassi et. al. and Krajicek et. al. for the pigeonhole
principle. Our method uses the interpretation of proofs as two player
games given by Pudlak and Buss. Our lower bound is conceptually
simpler than previous ones, and relies on tools and intuition that are
well-known in the context of computational complexity. This makes the
lower bound of Pitassi et. al. and Krajicek
et. al. accessible to the general computational complexity audience.
We hope this new view will open new directions for research in proof
complexity.