Consider the following premises. forall x: T(x) or ~Q(x). exists x: T(x) <-> P(x). Can we infer forall x: ~(Q(x) -> P(x)) from them?
 From exists x: T(x) <-> P(x) we can infer exists x: T(x) -> P(x). Finally, from forall x: T(x) or ~Q(x) we can infer forall x: Q(x) -> T(x), which contradicts forall x: ~(Q(x) -> P(x)). Therefore, the answer is no.