Are we talking about Justice League? Cause this sounds like Justice League.
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So, Superman is even more confusing than I thought? Superman isn't even the proper Superman for his world; that Superman died and he just decided "Fuck it, I'm Superman here now". And Batman is all #NotMySuperman in JL and Trinity. But then, if Superman died and left his world without a Superman, thus leading to Luthorman, Supergirl, New Superman, and Superwoman to fill in the gap of a missing Superman, who the fuck is Superman filling in for? What the fuck is happening? Who fucking approved this? Bring me their hands.
Pre-Flashpoint Superman is filling in for New 52 Superman. There will always be a Superman. It's basically a new "Reign of Supermen."