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We study the complexity of the following "resolution width problem": Does a given 3-CNF have a resolution refutation of width k? We prove that the problem cannot be decided in time O(n^((k-3)/12)). This lower bound is unconditional and does not rely on any unproven complexity theoretic assumptions. The lower bound is matched by a trivial upper bound of n^O(k). We also prove that the resolution width problem is EXPTIME-complete (if k is part of the input). This confirms a conjecture by Vardi,arXiv:1204.0775v2 fatcat:nuwbzqnmgren5nzlg3s2dx7ihu