Coming from a C.S. background, as I experiment in search of a replicable result, I don’t see why you wouldn’t prove a negative. A good example would be that you can prove a specific negative claim by providing contradictory evidence. An example of a proof of a rather specific negative claim by contradictory evidence would be if someone were to claim that the one and only watch that you own is in the top drawer of the desk. You make the negative claim that it is not in the drawer and you see it clearly on your wrist. There is no need to look in the drawer.