P != NP Proof (0907.3965v80)

Abstract: This paper demonstrates that P \not= NP. The way was to generalize the traditional definitions of the classes P and NP, to construct an artificial problem (a generalization to SAT: The XG-SAT, much more difficult than the former) and then to demonstrate that it is in NP but not in P (where the classes P and NP are generalized and called too simply P and NP in this paper, and then it is explained why the traditional classes P and NP should be fixed and replaced by these generalized ones into Theory of Computer Science). The demonstration consists of: 1. Definition of Restricted Type X Program; 2. Definition of the General Extended Problem of Satisfiability of a Boolean Formula - XG-SAT; 3. Generalization to classes P and NP; 4. Demonstration that the XG-SAT is in NP; 5. Demonstration that the XG-SAT is not in P; 6. Demonstration that the Baker-Gill-Solovay Theorem does not refute the proof; 7. Demonstration that the Razborov-Rudich Theorem does not refute the proof; 8. Demonstration that the Aaronson-Wigderson Theorem does not refute the proof.