Abstract
We prove exponential lower bounds on the resolution proofs of some tautologies, based on rectangular grid graphs. More specifically, we show a 2^{\Omega (n)} lower bound for any resolution proof of the mutilated chessboard problem on a 2n × 2n chessboard as well as for the Tseitin tautology based on the n × n rectangular grid graph. The former result answers a 35 year old conjecture by McCarthy.

