Consider the following premises. exists z: P_4(z) -> T(z). forall z: T(z) -> U(z). forall z: R(z) <-> P_4(z). Can we infer exists z: R(z) -> U(z) from them?
 From exists z: P_4(z) -> T(z), forall z: T(z) -> U(z) we can infer exists z: P_4(z) -> U(z). From forall z: R(z) <-> P_4(z) we can infer forall z: R(z) -> P_4(z). Finally, from forall z: R(z) -> P_4(z), exists z: P_4(z) -> U(z) we can infer exists z: R(z) -> U(z). Therefore, the answer is yes.