Alright! I'm back with proof that Superman was indeed knocked out, thus beaten in a fight.
Doomday/Braniac(DD): As always, you fight valiantly, Kryptonian. Shall we see WHO you are so intent on protecting? [walks over to ventilator]
Supes: [wiping mouth] Back OFF.
DD: [holding ventilator] Interesting. An erratic heartbeat, irregular breathing... The whelp is barely alive. [panel shows Supes leaping at DD from behind] Tell me, Kryptonian. This life you struggle so hard to preserve? Your own progeny?
DD: [elbowing Supes in the stomach] Unlikely. [grabbing Supes by the cape] Perhaps the child of someone close to you. Or even more likely-- [slams Supes into the side of a cliff] --The child of a complete stranger. [Throwing Supes into the sky] A typically weak, unaccomplished type on whose behalf you posture effectively.
*three pages later after DD/Braniac puts the baby in a new ventilator and monologues to a captured JLA*
Supes: *thinking* It's the wind that wakes me up. No. Not the wind exactly... I'm MOVING! How long was I out? Seconds? Minutes? [panel shows Supes headed toward plane] Have to figure out where I am. Wanna stop, but body feels like jelly. Head's still spinning, so groggy... Can't-- [Supes goes through plane] A PLANE?! NO!
[panel shows plane falling and a firey trail leading to Supes]
Supes: *thinking* Braniac WANTED this! Saw far enough to see the plane-- And plotted the course. No time to waste, Clark! Get your act together-- [Supes flying toward falling plane] --And MOVE! [panel shows Supes holding onto bottom of the plane's wing trying to stop its descent] Feels like I'm... Watching someone else do this. Like I'm... Detached. Must have a concussion. At least I can blow out the fire.
And there you go. Doomsday/Brainiac knocked Supes out (possibly giving him a concussion) and threw him through a plane. Thus proves that Superman CAN be beaten. ^.^