"There is only" in first order logic

Question

I'm trying to translate the statement "There is only three things that are not small" into first order logic. I'm using some software to verify my sentences, but I feel like I don't understand what "There is only" is meant to claim.

I interpreted it as "There are at most", and used the answer here, in particular method 2 for "At most $n$".

The sentence I've produced with this is:

$$\exists x \exists y \exists z \forall w \, (\lnot \text{Small}(w) \to (w = x \lor w = y \lor w = z))$$

Which I understand to mean that there exists up to 3 objects, which, for all objects $w$, if it is not small, it is one of the 3 objects.

This passes 3 of the 4 test worlds for the software, but fails on the last one.

I was hoping someone could help me clarify what is meant by "only". I've spent a decent amount of time Googling, but most results lead to explanations of the biconditional.

Thanks!

Answer 1

Thanks to Bram28 for advising me to check the conditions of the test worlds. His suggestion that the English translated effectively to "Exactly 3 things are not small" was the correct solution.