Consider the following premises. forall z: U_3(z) or ~S_2(z). exists z: S_2(z) <-> U_3(z). Can we infer exists z: U_3(z) <-> S_2(z) from them?
 From forall z: U_3(z) or ~S_2(z) we can infer forall z: S_2(z) -> U_3(z). From exists z: S_2(z) <-> U_3(z) we can infer exists z: U_3(z) -> S_2(z). Finally, from exists z: U_3(z) -> S_2(z), forall z: S_2(z) -> U_3(z) we can infer exists z: U_3(z) <-> S_2(z). Therefore, the answer is yes.