  We introduce the NP-complete problem 3SAT_N and extend Tovey's results to a
classification theorem for this problem. This theorem leads us to generalize
the concept of truth assignments for SAT to aggressive truth assignments for
3SAT_N. We introduce the concept of a set compatible with the P and NP problem,
and prove that all aggressive truth assignments are pseudo-algorithms. We
combine algorithm, pseudo-algorithm and diagonalization method to study the
complexity of 3SAT_N and the P versus NP problem. The main result is P != NP.
