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