Proving that P is not equal to NP and that P is not equal to the intersection of NP and co-NP
<|reference_start|>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.<|reference_end|>
@article{cohen2005proving,
    title={Proving that P is not equal to NP and that P is not equal to the
  intersection of NP and co-NP},
    author={R. A. Cohen},
    journal={arXiv preprint arXiv:cs/0511085},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0511085},
    primaryClass={cs.CC}
}