The negation of 'For all xxx, P(x)P(x)P(x)' is:
For all xxx, not P(x)P(x)P(x)
There exists an xxx such that not P(x)P(x)P(x)
There exists an xxx such that P(x)P(x)P(x)
Not for some xxx, P(x)P(x)P(x)