It can be proven false to any reasonable degree of certainty. With experiment, you'd increasingly be looking at an overwhelming probability that it is, or that the universe is actively conspiring against you to fool you on that notion. Which is, frankly, a bad argument.
If something is possible, but has measure zero in the probability space, it's really not worth considering.
If something is possible, but has measure zero in the probability space, it's really not worth considering.