Bound Variable and Free Variable, A Questions and one Example?

Question

I see a Local Contest Question as :

for statement $ \forall x [ \exists y ( x<y+z) \to \exists z (x < y+z)] $ two following axiom is True:

I) $ y, z$ is free and $x$ is bounded.

II) $x,y,z$ is bounded.

I think just (I) is True. Who can inspect it very carefully with complete proof?

Answer 1

The first $z$ is free and the second $y$ is free. The rest are bounded.

So it's neither because one instance of "z" is bounded and another isn't. If statement I read "There are variables called $x$ and $y$ which are unbounded" or statement II read "There are variables called $x$, $y$ and $z$ which are bounded", then it would be unambiguous. I don't see how you can choose between statements I and II.