We show a quadratic separation between resolution and cut-free sequent calculus width. We use this gap to get, for the first time, first, a super-polynomial separation between resolution and cut-free sequent calculus for refuting CNF formulas, and secondly, a quadratic separation between resolution width and monomial space in polynomial calculus ... more >>>

We identify two new big clusters of proof complexity measures equivalent up to
polynomial and $\log n$ factors. The first cluster contains, among others,
the logarithm of tree-like resolution size, regularized (that is, multiplied
by the logarithm of proof length) clause and monomial space, and clause
space, both ordinary and ... more >>>