@godcentral,
It's ok someone already answered this at philosophy forums here:
http://forums.philosophyforums.com/threads/contradictory-of-x-y-axy-by-65457.html
If all sevens are after all sixes then all sixes are black.
It is false that if all sevens are after all sixes then all sixes are black.
So we just move the negation through the equation:
~(Vx) (Vy) (Axy -> By)
(3x)~ (Vy) (Axy -> By)
(3x)(3y) ~(Axy -> By)
(3x)(3y) ~(~Axy v By)
Now use De Morgan
(3x)(3y)(Axy & ~By)
Some sevens are after some sixes and it is false that some sixes are black.
I don't like the question because they mix a relation and a predicate.