Maybe I'm just being snarky or missing the real meaning of the term, but I think of "supernatural" as something that is beyond any capacity to test or prove. Anything that can be proven would fall under my definition of "natural", even if it's beyond my capacity to explain or understand.

By definition, I'd consider any sort of gods, demons, ghosts, or whatever to be either nonexistent or something that exists (which would imply that it's something natural and operates in some currently unknown way).