Abstract : P versus NP is one of the most important and unsolved problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? This incognita was first mentioned in a letter written by Kurt Gödel to John von Neumann in 1956. However, the precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in a seminal paper. Under the assumption of P = NP, we show that P = EXP is also hold. Since P is not equal to EXP, we prove that P is not equal to NP by the Reductio ad absurdum rule.