Can Haskell express negative class constraint (such as two types are _not_ the same)?

Question

One can express (a ~ b), but can one write something like (a !~ b)?

My hunch is that no, since in a handwawy way constraint resolution is analogous to search, and one can't conclusively say there's no result of a search, only that so far no result was found.

But maybe I'm wrong and there's some way?