I am not sure about it, but does theses two equalities holds ?
$$ \lnot (\forall x, mov(x)) = \forall x,(\lnot mov(x)) $$
$$ \lnot (\exists x, mov(x)) = \forall x, (\lnot mov(x)) $$
Thank you
Aymeric
p.s: mov is just a predicate that stands for movable (mov(x) <=> "x is movable")