In this paper we will study the properties of writing a 3CNFSAT formula, this will enable us to instore a set of constraints which we’ll follow to deduce an optimal writing form of 3CNFSAT that fulfills the property of maximum complexity of satisfiability. By solving this signature writing we can result to the cap polynomial time siffucient to prove the satisfiability of all remaining writing possibilities of the formula that use the number of literals figuring in the signature writing or less. The proof of SAT to be an NP-complete problem by the Cook-Levin theorem allows us to reduce every decision problem in the complexity class NP to the SAT problem for CNF formulas (CNFSAT), and the reduction of the unrestricted SAT problem to a conjunctive normal form with each clause containing at most three literals (3CNFSAT) allows us to deduce that determining the satisfiability of 3CNFSAT formulas is also NP-complete. By increasing the length of the signature formula through conjucting n of it’s duplications while introducing new literals for each duplication, we can study the evolution of the cap polynomial time in function of n, thus resulting to a solution for P vs NP.