P != NP Proof

This paper demonstrates that P ≠ 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 Extended General 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 The paper demonstrates three new revolutionary ideas in the foundations of Computational Complexity Theory, against the established theory in the area: 1. Language Incompleteness: There are computational decision problems that are not languages (cannot be modeled as string acceptance testing to languages); 2. NP-Completeness Incompleteness: The Cook-Levin Theorem and the concept of NP-Completeness are false, whence it cannot in general be applied on an instance of the XG-SAT to reduce it to one of the SAT; and 3. SAT's weakness: The complexity class of the SAT maybe does not decide P versus NP question (if SAT is not in P then NP ≠ P; on the other hand, SAT in P doesn’t imply NP = P). The objective of the paper is just help the complexity theorists about their main question: If I am right, then the P versus NP Clay Mathematics Institute Prize must be canceled and replaced by the correct problem intended by them: "Is SAT in P?" Mathematics Subject Classification (2009). Primary 68Q15; Secondary 68Q17.