Well the anti-life equation allows darkseid to control the will of any sentient being. So...seeing as Hal has the strongest will around....they'll just end up grunting DBZ style at each other for all eternity.
Well, Jack Kirby originally intended for it to control will. DC writers can make it into a bunch of things, but all it's other abilities still pale in comparison to what parallax can do. Recreating the universe is pretty much as high as you get before divine level. The control of the will is the best DS has going for him. I don't know if it's absolute and automatic though. I imagine someone on Hal's level could fight it.
i still dont think parallax could beat a enemy of the source who is multiversal seriously the guy was trying to kill the tree upon which the entire DCU was on
a) not protected by the Source
b) not protected by the Presence
c) not protected by something on the order of the Odinpower or vast magical might or the Power Cosmic.
d) not universally important.
seeing how it would not be hal jordons will power it would try to take over it would be the paricite parallax i think this would be hard to call now if hal jordon had control of the parallax then he might be able to do so its hard to say
but then again parallax could simply know that doomsday was gonna fight him so he could have a version of him self from the past pervent him from getting the anti life equation