Consider the following premises. exists z_3: U_1(z_3) -> S_2(z_3). forall z_3: U_1(z_3) or ~S_2(z_3). Can we infer exists z_3: S_2(z_3) <-> U_1(z_3) from them?
 From forall z_3: U_1(z_3) or ~S_2(z_3) we can infer forall z_3: S_2(z_3) -> U_1(z_3). Finally, from forall z_3: S_2(z_3) -> U_1(z_3), exists z_3: U_1(z_3) -> S_2(z_3) we can infer exists z_3: S_2(z_3) <-> U_1(z_3). Therefore, the answer is yes.