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… CONTINUE READING