Do we need to waste our time proving that unicorns do not exist?

Do we need to prove that unicorns, tooth fairies, hobbits and so on do not exist? The question is not just funny, insofar as an upholder of the existence of ghosts and the like could easily claim that there are no evidences of their non-existence. In Indian epistemology, this amounts to say that there are no bādhakas 'invalidating cognitions' telling us that the existence of ghosts, etc. is invalid.
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