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