I would like to negate the following:
$\exists x, \forall y, \forall z ((F(x,y) \land G(x,z)) \rightarrow H(y,z))$
Would the following proposed solution be correct?
(1) First simplify what is in the brackets - $((F(x,y) \land G(x,z)) \rightarrow H(y,z))$
$(\lnot(F(x,y) \land G(x,z)) \lor H(y,z))$
(2) $\forall x, \exists y, \exists z \lnot ( \lnot(F(x,y) \land G(x,z)) \lor H(y,z)) $
$\equiv \forall x, \exists y, \exists z((F(x,y) \land G(x,z)) \land \lnot H(y,z))$