"Therefore, P is not equal to NP, is true and provable in a simply consistent extension B" of B"

does not necessarily imply P \neq NP (the caveat being the B" and B stuff). I'm not really a complexity theory guy, but I would say WHP that this either

(a) does not apply to the most general forms of computation (e.g., what people mean when they ask P =? NP)

(b) is wrong

Although amusingly, I heard that Cornell was sued for not allowing creationists to post their physics theories there.