Consider the following premises. exists z: U_3(z) <-> U_1(z). forall z: R(z) or U_3(z). forall z: U_1(z) or ~R(z). Can we infer exists z: U_1(z) from them?
 From forall z: U_1(z) or ~R(z) we can infer forall z: R(z) -> U_1(z). From exists z: U_3(z) <-> U_1(z) we can infer exists z: U_3(z) -> U_1(z). Finally, from forall z: R(z) -> U_1(z), exists z: U_3(z) -> U_1(z), forall z: R(z) or U_3(z) we can infer exists z: U_1(z). Therefore, the answer is yes.