> And if P neq NP, then SAT might not be P. Small correction: If P != NP, then SAT definitely isn't in P. That's because SAT is NP-complete, so if it was in P,

> And if P neq NP, then SAT might not be P. Small correction: If P != NP, then SAT definitely isn't in P. That's because SAT is NP-complete, so if it was in P, every other NP problem could be polynomially reduced to it and would hence also be in P.