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