Narrow proofs may be maximally long
We prove that there are 3-conjunctive normal form formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size nΩ(w). This shows that the simple counting argument that any formula refutable in width w must have a proof in size nO(w) is essentially tight. Moreover, our lower bound generalizes to polynomial calculus resolution and Sherali-Adams, implyi
