Consider the following premises. forall z_2: W(z_2) -> U_3(z_2). forall z_2: S(z_2) <-> W(z_2). exists z_2: U_3(z_2) -> S(z_2). Can we infer forall z_2: ~(W(z_2) <-> S(z_2)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.