Consider the following premises. forall x: T_4(x) -> Q_4(x). forall x: ~Q(x). forall x: Q_4(x) -> T_4(x). forall x: T_4(x) -> Q(x). forall x: Q(x) -> T_4(x). Can we infer forall x: ~Q_4(x) from them? If possible, name the inference rules being used at each step.
 From forall x: T_4(x) -> Q(x), forall x: Q(x) -> T_4(x) we can infer forall x: T_4(x) <-> Q(x) via universal biconditional introduction. From forall x: T_4(x) -> Q_4(x), forall x: Q_4(x) -> T_4(x) we can infer forall x: T_4(x) <-> Q_4(x) via universal biconditional introduction. From forall x: T_4(x) <-> Q(x), forall x: ~Q(x) we can infer forall x: ~T_4(x) via universal biconditional elimination. Finally, from forall x: T_4(x) <-> Q_4(x), forall x: ~T_4(x) we can infer forall x: ~Q_4(x) via universal biconditional elimination. Therefore, the answer is yes.