It would be interesting if the idea isn't to disprove the existance of the witches, but to prove they didn't commit the crimes. These could be mutually exclusive. The witches could exist and yet not have had anything to do with the murders.
Sort of like in a way that Higurashi provides the source of the mystery eventually, disproving that the supernatural had anything to do with the incidents, but not disproving the existance of the supernatural. (Hanyuu and the timeloops for example).
Just a thought.
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