let me tick the list:
most likely false, because, as Scott Aaronson said "If P = NP, then the world would be a profoundly different place than we usually assume it to be."
yes, it's The Open Problem in computational complexity theory
...
it's important, again quoting Scott because if it would be true, "there would be no special value in "creative leaps," no fundamental gap between solving a problem and recognizing the solution once it's found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss..."
it's an equality rather than a negation