Consider the following premises. forall z: W(z) -> T(z). forall z: ~U_4(z). forall z: W(z) -> U_4(z). forall z: T(z) -> W(z). forall z: U_4(z) -> W(z). Can we infer forall z: ~T(z) from them? If possible, name the inference rules being used at each step.
 From forall z: W(z) -> U_4(z), forall z: U_4(z) -> W(z) we can infer forall z: W(z) <-> U_4(z) via universal biconditional introduction. From forall z: W(z) <-> U_4(z), forall z: ~U_4(z) we can infer forall z: ~W(z) via universal biconditional elimination. From forall z: W(z) -> T(z), forall z: T(z) -> W(z) we can infer forall z: W(z) <-> T(z) via universal biconditional introduction. Finally, from forall z: W(z) <-> T(z), forall z: ~W(z) we can infer forall z: ~T(z) via universal biconditional elimination. Therefore, the answer is yes.