Not really. Math uses no physical observation, only axioms. Nothing can "prove" or "disprove" axioms. If observation supports the axiomatic theory, then we use the theory for physical prediction. If observation doesn't, then we don't use the theory. Does that count as "disproof"?

In practice, infinite sets never exist as enumerations of every element, but as ways to generate more elements along with descriptions for which elements to include. Infinite set theories allow for equivocating a finite description with the infinite enumeration. In contrast, programming languages usually make a distinction between data (always finite) and data generation (possibly infinite). I would think that already counts as a "disproof" in a way.

It's a very interesting idea; if you want to learn more about it, look up "ultrafinitism".