We prove an exponential lower bound for tree-like Cutting Planes
refutations of a set of clauses which has polynomial size resolution
refutations. This implies an exponential separation between tree-like
and dag-like proofs for both Cutting Planes and resolution; in both
cases only superpolynomial separations were known before.
In order to ... more >>>

We show that is hard to find regular or even ordered (also known as Davis-Putnam) Resolution proofs, extending the breakthrough result for general Resolution from Atserias and Müller to these restricted forms. Namely, regular and ordered Resolution are automatable if and only if P = NP. Specifically, for a CNF ... more >>>