We prove that any Resolution proof for the weak pigeon hole principle,
with n holes and any number of pigeons, is of length
\Omega(2^{n^{\epsilon}}), (for some global constant \epsilon > 0).
One corollary is that a certain propositional formulation of
the statement NP \not \subset P/poly does not have short Resolution proofs.

We prove that any Resolution proof for the weak
pigeon hole principle, with n holes and any number of
pigeons, is of length \Omega(2^{n^{\epsilon}}),
(for some global constant \epsilon > 0).