Consider the following premises. exists z: U(z) -> R_3(z). forall z: R_3(z) -> U(z). forall z: U_3(z) -> R_3(z). forall z: U(z) -> U_3(z). Can we infer exists z: R_3(z) -> U(z) from them?
 From exists z: U(z) -> R_3(z), forall z: R_3(z) -> U(z) we can infer exists z: U(z) <-> R_3(z). Finally, from exists z: U(z) <-> R_3(z) we can infer exists z: R_3(z) -> U(z). Therefore, the answer is yes.