A Syntactico-Semantical Bi-Polar Disorder FLP Paradox Implies SAT is NOT NP-complete, P vs. NP does not exist, and ZFC is Inconsistent!
Rafee Ebrahim Kamouna · arXiv (Cornell University) · 2008
After examining the {\bf P} versus {\bf NP} problem against the Kleene-Rosser paradox of the $\lambda$-calculus [94], it was found that it represents a counter-example to NP-completeness. We prove that it contradicts the proof of Cook's theorem. A logical formalization of the liar's paradox leads to the same result. This formalization of the liar's paradox into a computable form is a 2-valued instance of a fuzzy logic programming paradox discovered in the system of [90]. Three proofs that show that {\bf SAT} is (NOT) NP-complete are presented. The counter-example classes to NP-completeness are also counter-examples to Fagin's theorem [36] and the Immermann-Vardi theorem [89,110], the fundamental results of descriptive complexity. All these results show that {\bf ZF$ ot$C} is inconsistent.