"Supernatural" is a mistake of a concept. It is misapplied to phenomenon whose physics are currently beyond our understanding. Either it involves an area of physics we do not yet know, or is sufficiently complex such that it prevents us from accurately predicting outcomes. More stubborn versions assert AROUND the complex physics issue and state that such events are UNCAUSED (except by - surprise! - a deity). But this of course assumes it is always unnatural for an event to be uncaused, or indeed what might be, er, the CAUSE (i.e. the principal or "law" in physics which permits acausality) of uncaused events.

AT BEST we can only ever state that we simply do not understand a particular baffling phenomenon. How could we ever "prove" such a thing were "supernatural"? What TEST would allow us to conclude that what was happening operated outside the laws of physics?