Consider the following premises. forall z: ~Q(z). exists z: T_4(z) -> Q(z). forall z: Q(z) <-> T_4(z). Can we infer forall z: T_4(z) from them? If possible, name the inference rules being used at each step.
 From forall z: Q(z) <-> T_4(z) we can infer forall z: Q(z) -> T_4(z) via universal biconditional elimination. From forall z: Q(z) -> T_4(z), exists z: T_4(z) -> Q(z) we can infer exists z: Q(z) <-> T_4(z) via existential biconditional introduction. Finally, from exists z: Q(z) <-> T_4(z), forall z: ~Q(z) we can infer exists z: ~T_4(z) via existential biconditional elimination, which contradicts forall z: T_4(z). Therefore, the answer is no.