  We present and study a framework in which one can present alternation-based
lower bounds on proof length in proof systems for quantified Boolean formulas.
A key notion in this framework is that of proof system ensemble, which is
(essentially) a sequence of proof systems where, for each, proof checking can
be performed in the polynomial hierarchy. We introduce a proof system ensemble
called relaxing QU-res which is based on the established proof system
QU-resolution. Our main results include an exponential separation of the
tree-like and general versions of relaxing QU-res, and an exponential lower
bound for relaxing QU-res; these are analogs of classical results in
propositional proof complexity.
