This paper gives two distinct proofs of an exponential separation
between regular resolution and unrestricted resolution.
The previous best known separation between these systems was
quasi-polynomial.

Using a notion of real communication complexity recently
introduced by J. Krajicek, we prove a lower bound on the depth of
monotone real circuits and the size of monotone real formulas for
st-connectivity. This implies a super-polynomial speed-up of dag-like
over tree-like Cutting Planes proofs.