Consider the following premises. forall z: W(z) or U_2(z). forall z: S_2(z) -> T(z). forall z: T_2(z) -> S_2(z). forall z: U_2(z) -> T(z). forall z: ~W(z) or T_2(z). Can we infer exists z: ~T(z) from them? If possible, name the inference rules being used at each step.
 From forall z: W(z) or U_2(z), forall z: ~W(z) or T_2(z) we can infer forall z: U_2(z) or T_2(z) via universal resolution. From forall z: T_2(z) -> S_2(z), forall z: S_2(z) -> T(z) we can infer forall z: T_2(z) -> T(z) via universal transitivity. Finally, from forall z: U_2(z) -> T(z), forall z: T_2(z) -> T(z), forall z: U_2(z) or T_2(z) we can infer forall z: T(z) via universal disjunction elimination, which contradicts exists z: ~T(z). Therefore, the answer is no.