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 $\epsilon > 0$).