For a proof system P we introduce the complexity class DNPP(P)
of all disjoint NP-pairs for which the disjointness of the pair is
efficiently provable in the proof system P.
We exhibit structural properties of proof systems which make the
previously defined canonical NP-pairs of these proof systems hard or
complete for DNPP(P).
Moreover we demonstrate that non-equivalent proof systems can have
equivalent canonical pairs and that depending on the properties of the
proof systems different scenarios for DNPP(P) and the reductions between
the canonical pairs exist.