Consider the following premises. forall z: S_4(z). forall z: S_4(z) <-> T(z). exists z: Q(z). Can we infer forall z: ~(Q(z) and T(z)) from them?
 From forall z: S_4(z) <-> T(z) we can infer forall z: S_4(z) -> T(z). From forall z: S_4(z) -> T(z), forall z: S_4(z) we can infer forall z: T(z). Finally, from exists z: Q(z), forall z: T(z) we can infer exists z: Q(z) and T(z), which contradicts forall z: ~(Q(z) and T(z)). Therefore, the answer is no.