This is a specific case that (maybe) proves the general claim that P != NP.
Proving an inequality is "easy", because only requires a single counterexample: if there is one problem in NP that is not in P (I.e. an NP problem not solvable in polynomial time), then NP can't possible equal P.
Fukuyama is proposing that CLIQUE is such a counter-example.
(Proving the inequality doesn't actually require the special property of NP-completeness which others are talking about; that is only useable in a proof P = NP.)
> Proving an inequality is "easy", because only requires a single counterexample:
Proving an equality isn't exactly "harder" (no NP-hard pun intended) - all you have to do is show that a single NP-complete problem can be reduced to a problem within P in polynomial time.
Proving an inequality is "easy", because only requires a single counterexample: if there is one problem in NP that is not in P (I.e. an NP problem not solvable in polynomial time), then NP can't possible equal P.
Fukuyama is proposing that CLIQUE is such a counter-example.
(Proving the inequality doesn't actually require the special property of NP-completeness which others are talking about; that is only useable in a proof P = NP.)