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.
All cases require full coverage to prove... either full coverage of teapots in the second example, full coverage of Saturn in the first example, or full coverage of accessibility in the third.
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, they're likely going to be highly resistant to actually making a concrete definition.
This is in philosophical debate. However, in non-philosophical debate, this usually doesn't convince people (in no small part because many people don't fully grasp logic).
The few times I've had that 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, 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 fermion (basically, the type of matter we're made of), so we are fully aware of all physical interactions with humans... 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.