It's also true that he can't possibly take the entire year off as PTO, because he'd be fired before it's allowed to happen. So taking a full year PTO is already a contradiction.

Then in classicial logic, a contradiction can imply anything: https://en.m.wikipedia.org/wiki/Principle_of_explosion Therefore he can be fired 0,1,2,10,100,1000 times, with all those possibilities being true simultaneously.