> It is impossible to prove a negative
Since this statement is itself a negative, you've presented a paradox, because if it were proven true it would then be false.
Since this statement is itself a negative, you've presented a paradox, because if it were proven true it would then be false.
It is easier to prove a positive since it requires only the "smoking gun" to be made apparent. It is much harder to disprove a negative because it requires hypothetical smoking gun that could have caused the effect (Han's beating of Magnus) to be disproven. Since we don't have a record of every electromagnetic and sonic wave which passed through the room the day Hans beat Magnus, disproving the cheating claim is likely impossible.
If we're being pedantic, which your initial response struck me as, there are again true statements with no proof, and this isn't a paradox, it's Gödel's first incompleteness theorem (which is specifically different from the liar's paradox you mentioned, precisely in the difference between what is true and what is provable).