I have to find an infinite domain where the statement is true and another infinite domain where it is false:
$$(\forall x)(\exists y)[x < y \wedge FILL(x, y)],$$
where $FILL(x, y) = x \geq y \vee (\forall z)[(x \geq z) \vee (z \geq y)]$.
Since the $FILL$ is an OR statement I can cross out the contradiction $x \geq y$ and look at the rest...
I have come up with the naturals being true and negative integers being false. Any thoughts?