The AI just tossed a pair of Core Starships my way from a IV planet (Do Not Taunt The Happy Fun Ball(tm)), and it seems they're a mite hard to kill. 4k+ ships, with continual reinforcements (at least 5 ships per second), took about 10 minutes to get one into the red, and one into the yellow. This includes pretty much 100% of my 800/700/550 MkI/II/III fighters.
I'm replacing ships about as fast as they're killing them, but it looks like I'll need at least another 5 minutes to take them down at this rate.
I know I'm at a mite disadvantage since I don't have any IV ships (the map generator apparently doesn't like giving out ARS/Adv Factories on even 15 planet maps of my games), but are these things actually killable in a normal singleplayer game?