  The purpose of this article is to examine and limit the conditions in which
the P complexity class could be equivalent to the NP complexity class. Proof is
provided by demonstrating that as the number of clauses in a NP-complete
problem approaches infinity, the number of input sets processed per computation
performed also approaches infinity when solved by a polynomial time solution.
It is then possible to determine that the only deterministic optimization of a
NP-complete problem that could prove P = NP would be one that examines no more
than a polynomial number of input sets for a given problem.
  It is then shown that subdividing the set of all possible input sets into a
representative polynomial search partition is a problem in the FEXP complexity
class. The findings of this article are combined with the findings of other
articles in this series of 4 articles. The final conclusion will be
demonstrated that P =/= NP.
