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I'd say that the two objects cannot coexist. You have an object that can move anything, and an object that can't be moved by anything, basically. One of these objects would have to give in to the other, which it is doesn't matter, but one of them is not real. If the irrisistable force moves the immovable object, then the immovable object wasn't immovable. If the immovable object stands it's ground against the irrisistable force, then the irrisistable force wasn't irrisistable.
Think of it like a tournament, where these two objects faced off on every object except each other, and now it's the final championship to determine who is the ultimate entity.
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