We consider the proof complexity of the minimal complete fragment, KS, of
standard deep inference systems for propositional logic. To examine the size of
proofs we employ atomic flows, diagrams that trace structural changes through a
proof but ignore logical information. As results we obtain a polynomial
simulation of versions of Resolution, along with some extensions. We also show
that these systems, as well as bounded-depth Frege systems, cannot polynomially
simulate KS, by giving polynomial-size proofs of certain variants of the
propositional pigeonhole principle in KS.Comment: 27 pages, 2 figures, full version of conference pape