Consider the following premises. forall z: S(z) -> R(z). forall z: R(z) -> ~P_3(z). exists z: R(z) -> S(z). forall z: P_2(z) -> P_3(z). forall z: U_2(z) or P_2(z). forall z: U_2(z) -> P_3(z). Can we infer forall z: S(z) from them?
 From forall z: U_2(z) -> P_3(z), forall z: P_2(z) -> P_3(z), forall z: U_2(z) or P_2(z) we can infer forall z: P_3(z). From exists z: R(z) -> S(z), forall z: S(z) -> R(z) we can infer exists z: R(z) <-> S(z). From forall z: R(z) -> ~P_3(z), forall z: P_3(z) we can infer forall z: ~R(z). Finally, from exists z: R(z) <-> S(z), forall z: ~R(z) we can infer exists z: ~S(z), which contradicts forall z: S(z). Therefore, the answer is no.