Consider the following premises. exists z_4: T(z_4) <-> S(z_4). forall z_4: S(z_4) -> Q(z_4). forall z_4: Q(z_4) <-> T(z_4). Can we infer forall z_4: ~(T(z_4) <-> S(z_4)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.