Consider the following premises. forall z_1: S(z_1) -> U_2(z_1). exists z_1: U_2(z_1) -> S(z_1). Can we infer exists z_1: S(z_1) -> U_2(z_1) from them?
 From forall z_1: S(z_1) -> U_2(z_1), exists z_1: U_2(z_1) -> S(z_1) we can infer exists z_1: S(z_1) <-> U_2(z_1). Finally, from exists z_1: S(z_1) <-> U_2(z_1) we can infer exists z_1: S(z_1) -> U_2(z_1). Therefore, the answer is yes.