I am not greatly interested in automated proofs, but rather in tools to assist humans in developing proofs and studying them - I'm talking more about distributed databases and user interfaces than about anything from AI, and about using strict validation techniques to replace the need for a trust model such as peer review.
In respect of the even/odd thing, I may have misremembered what I was trying to prove: I'd have to find back my notes from my teenage years. I'm sure the problem revolved around proving a negation, and was intended to be a stepping stone to playing with prime numbers; I suspect it was less to do with the axioms as P1 .. P5, and more to do with the axioms as (P1 .. P5 plus the permitted rules of logic as described by Hofstadter).
Hugo
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