A Polynomial Time Algorithm for 3SAT

By creating new concepts and methods—the checking tree, long unit path, direct contradiction unit pair, indirect contradiction unit pair, additional contradiction unit pair, two-unit layer and three-unit layer—we successfully transform solving a 3SAT problem to solving 2SAT problems in polynomial time. Each time, we add only one layer of the three-unit layers to the two-unit layers to calculate 2SAT paths, respectively. The key is as follows: in each 2SAT path, any two units cannot be a direct contradiction unit pair and cannot be an indirect contradiction unit pair and additional contradiction unit pair. This guarantees that all of the 2SAT paths we got, respectively, can shape at least one long path without contradictions. Thus, we proved that NP = P.