Consider the following premises. forall z_3: S(z_3) <-> W(z_3). forall z_3: U_1(z_3) -> W(z_3). forall z_3: ~S(z_3). forall z_3: W(z_3) -> U_1(z_3). Can we infer forall z_3: S(z_3) <-> W(z_3) from them?
That is one of the premises. Therefore, the answer is yes.