Consider the following premises. forall z: U_4(z) -> P_4(z). exists z: U_4(z) or ~S(z). forall z: R_4(z) -> S(z). Can we infer exists z: R_4(z) -> P_4(z) from them?
 From exists z: U_4(z) or ~S(z) we can infer exists z: S(z) -> U_4(z). From exists z: S(z) -> U_4(z), forall z: U_4(z) -> P_4(z) we can infer exists z: S(z) -> P_4(z). Finally, from forall z: R_4(z) -> S(z), exists z: S(z) -> P_4(z) we can infer exists z: R_4(z) -> P_4(z). Therefore, the answer is yes.