If you have truly resigned you will not read this but it's worth a run out anyway. There is a school of thought that says:
When you get right down to it, the statement “you cannot prove a negative” is really just a different way of saying “You can’t prove me wrong because I don’t even know what I’m talking about.”
Apart from that check out Professor Stephen Hales.
Whether academics can prove a negative in an abstract way or not doesn't really alter mundane situations in which people can end up on death row because they can't prove an alibi, don't have the means to disprove an "expert" in court or whatever other concrete situation people may find themselves in.
Re an alibi: Christopher Jeffries didn't have one either and he was under suspicion due to false testimony from the real one.
If someone had stated that I was lurking in PdL that night, the way in which the PT system appears to have worked (in criminal trials) is that I would have had to have provided counter proof that I wasn't.
My use of a phone, Internet or bank card doesn't prove that I wasn't there.
If I had a clear recollection of someone I'd met and who could testify for me or CCTV showing me clearly elsewhere should... but otherwise, what practical proof could I have provided?