In many textbooks, a proof is provided where the work output of a super-efficient heat engine is provided to a carnot refrigerator, with the net result that a spontaneous heat transfer occurs from the cold reservoir to a hot reservoir. Let's use some numbers, TH = 600 K and TL = 300 K, so that means the carnot efficiency is 50% and the carnot COP is 1. Between these temperatures, By connecting a heat engine of efficiency 60% to the carnot fridge of COP = 1, then one can show that the impossible occurs. But, between these temperatures (TH = 600 K and TL = 300K) what if we connect a super-efficient heat engine of efficiency 60% to a fridge of COP = 0.5? Though a super-efficient heat engine can't exist, coupling the two together gives a net heat transfer from the hot reservoir to the cold reservoir, which could occur. What is wrong with this line of argument?