Consider the following premises. exists z_1: S(z_1) -> T_1(z_1). forall z_1: S(z_1) <-> T_1(z_1). Can we infer forall z_1: ~(T_1(z_1) -> S(z_1)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.