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