A Tough Nut for Tree Resolution

Abstract

One of the earliest proposed hard problems for theorem provers is<br />a propositional version of the Mutilated Chessboard problem. It is well<br />known from recreational mathematics: Given a chessboard having two<br />diagonally opposite squares removed, prove that it cannot be covered with<br />dominoes. In Proof Complexity, we consider not ordinary, but 2n * 2n<br />mutilated chessboard. In the paper, we show a 2^Omega(n) lower bound for tree resolution.