Still, Cyprian and Stephen were in conflict over a points of doctrine, (whether or not heretics must be re-baptized, and whether or not bishops who had apostatized could still exercise episcopal authority and confect sacraments once they had returned to the Church).  Cyprian called 3 separate councils to decide these very issues, not to, as you falsely claim, to "deny his (Pope Stephen's) bogus claims of authority."  Cyprian was actually incorrect as we know from how all these things were eventually ironed out.  As far as the papacy is concerned, Cyprian certainly supported the teaching of the Church, and his own words prove your assertion is completely bogus: