In Philosophy, there's the concept of Russell's Teapot: an example which acts on the example of "disproving the existence of a tea kettle floating around Saturn"
It's a reference to the fact that some things that are ridiculously unlikely but are also ridiculously hard to prove.
The thing is, though, that this doesn't mean they are impossible to prove.
However, there are two ways I'm aware of to disprove Russell's Teapot, and a third way that doesn't apply to the teapot itself, but some similar claims.
The first is the long way - to disprove at each possible instance. In the case of a tea kettle, take the space of a tea kettle, and simultaneously search a grid of the entire orbit around Saturn with a grid resolution of that size, and if there are no tea kettles, then it is disproven.
The second is the induced way... to find some claim about about the subject in question that doesn't match what is possible, and it requires some impossible aspect of the claim. In the case of the tea kettle, it would be specifically designating a tea-kettle as a human-made object, and going through all human space flights to show that none have put a kettle in orbit around Saturn. Although not as absolute, it's still pretty solid proof.
The third way is if the definition of the "teapot" itself is somehow fully accessible by definition. For example, if instead of a Teapot, Russell's proof said, "a magical lamp that instantly creates a copy of itself in the hands of anyone who dons cream colored pants and a hat." At which point you could disprove the existence of this particular lamp that floats around Saturn using any person that puts on cream colored pants and a hat and seeing that the kettle doesn't suddenly appear in their hands.
All cases of a "Russell's teapot" scenario require at least one full coverage in some aspect to prove or disprove...
- Full coverage of Saturn in the first example (Coverage of affected)
- Full coverage of teapots in space second example (Coverage of concept)
- The Definition including a disprovable full coverage in the third (Coverage of Definition)
Each case, however, will require having a very firm definition of the subject matter. If you're trying to philosophically debate someone on the topic of the supernatural or paranormal, unless it's a purely academic philosophical debate (such as an online religion debate), they're likely going to be highly resistant to actually making a concrete definition and following it to its logical conclusions.
However, for a philosophical debate, the above proofs should be sufficient, even if 1 & 2 are generally impractical for most debates.
In non-philosophical debates, sadly, the solid philosophical proof usually doesn't "prove to people" (in no small part because many people don't fully grasp logic), and frequently people just want to be right without going through the effort to become right.
The times I've had this particular debate in regards to the paranormal with someone, the best I got was "whatever the definition is in the dictionary"... this was an "easy" philosophical solution, as the dictionary I looked it called the supernatural 'outside of what is natural', and then I looked up natural and it was 'not man-made', thereby meaning all man-made things are supernatural by definition... this did not sit well with the person I was debating with.
However, not a philosophical proof against the supernatural, but a physics one making use of full coverage (proof method 2), is CERN's experiments with particle physics. If you consider the supernatural being active non-physical things that influence the physical world, CERN has tracked every particle capable of interacting with fermions (basically, what we're made of), so we are fully aware of all physical interactions with humans - something a soul or ghost would have to do... aannnndd... none of them were potential methods for human interactions by ghosts/souls/etc.
Another argument is that, if you consider humans natural, as "in nature or deriving from nature" is another definition of natural, then anything that exists is, by definition, natural. Therefore, by definition, the supernatural simply doesn't exist, as supernatural becomes a synonym for imaginary or non-existing.