Consider the following premises. forall x_3: Q(x_3) -> W(x_3). forall x_3: T_4(x_3) -> Q(x_3). exists x_3: W(x_3) or T_4(x_3). forall x_3: W(x_3) -> Q(x_3). forall x_3: Q(x_3) -> T_4(x_3). Can we infer forall x_3: ~Q(x_3) from them? If possible, name the inference rules being used at each step.
 From forall x_3: W(x_3) -> Q(x_3), forall x_3: Q(x_3) -> W(x_3) we can infer forall x_3: W(x_3) <-> Q(x_3) via universal biconditional introduction. From forall x_3: Q(x_3) -> T_4(x_3), forall x_3: T_4(x_3) -> Q(x_3) we can infer forall x_3: Q(x_3) <-> T_4(x_3) via universal biconditional introduction. From forall x_3: W(x_3) <-> Q(x_3) we can infer forall x_3: W(x_3) -> Q(x_3) via universal biconditional elimination. From forall x_3: Q(x_3) <-> T_4(x_3) we can infer forall x_3: T_4(x_3) -> Q(x_3) via universal biconditional elimination. Finally, from forall x_3: W(x_3) -> Q(x_3), forall x_3: T_4(x_3) -> Q(x_3), exists x_3: W(x_3) or T_4(x_3) we can infer exists x_3: Q(x_3) via existential disjunction elimination, which contradicts forall x_3: ~Q(x_3). Therefore, the answer is no.