Consider the following premises. exists z: U(z) <-> U_1(z). forall z: Q(z) or S_3(z). forall z: S_3(z) -> U_1(z). forall z: Q(z) -> U_1(z). Can we infer forall z: ~U(z) from them?
 From forall z: Q(z) -> U_1(z), forall z: S_3(z) -> U_1(z), forall z: Q(z) or S_3(z) we can infer forall z: U_1(z). From exists z: U(z) <-> U_1(z) we can infer exists z: U_1(z) -> U(z). Finally, from exists z: U_1(z) -> U(z), forall z: U_1(z) we can infer exists z: U(z), which contradicts forall z: ~U(z). Therefore, the answer is no.