Proving that P is not equal to NP and that P is not equal to the   intersection of NP and co-NP
  The open question, P=NP?, was presented by Cook (1971). In this paper, a proof that P is not equal to NP is presented. In addition, it is shown that P is not equal to the intersection of NP and co-NP. Finally, the exact inclusion relationships between the classes P, NP and co-NP are presented. 
R. A. Cohen