SAT is not in P, is true and provable in a simply consistent extension B' of
a first order theory B of computing, with a single finite axiom characterizing
a universal Turing machine. Therefore, P is not equal to NP, is true and
provable in a simply consistent extension B" of B.Comment: In the 2nd printing the proof, in the 1st printing, of theorem 1 is
divided into three parts a new lemma 4, a new corollary 8, and the remaining
part of the original proof. The 2nd printing contains some simplifications,
more explanations, but no error has been correcte