Consider the following premises. forall z: W(z). exists z: U(z) -> U_1(z). forall z: P_3(z) -> U(z). forall z: R_1(z) or P_3(z). forall z: R_1(z) -> U(z). Can we infer exists z: U_1(z) and W(z) from them?
 From forall z: R_1(z) -> U(z), forall z: P_3(z) -> U(z), forall z: R_1(z) or P_3(z) we can infer forall z: U(z). From exists z: U(z) -> U_1(z), forall z: U(z) we can infer exists z: U_1(z). Finally, from exists z: U_1(z), forall z: W(z) we can infer exists z: U_1(z) and W(z). Therefore, the answer is yes.