P does not equal NP
Proof by contradiction. Assume P = NP. Let y be a proof that P = NP.
The proof y can be verified in polynomial time by a
competent computer scientist, the existence of which we assert.
However, since P = NP, the proof y can be generated in polynomial
time by such computer scientists. Since this generation has not yet
occurred (despite attempts by such computer scientists to produce a proof),
we have a contradiction.