Consider the following premises. exists x: ~T_1(x) or Q(x). forall x: Q(x) -> W(x). forall x: Q_2(x) <-> W(x). forall x: T_1(x) or Q_2(x). Can we infer forall x: ~W(x) from them? If possible, name the inference rules being used at each step.
 From forall x: Q_2(x) <-> W(x) we can infer forall x: Q_2(x) -> W(x) via universal biconditional elimination. From forall x: T_1(x) or Q_2(x), exists x: ~T_1(x) or Q(x) we can infer exists x: Q_2(x) or Q(x) via existential resolution. Finally, from forall x: Q_2(x) -> W(x), forall x: Q(x) -> W(x), exists x: Q_2(x) or Q(x) we can infer exists x: W(x) via existential disjunction elimination, which contradicts forall x: ~W(x). Therefore, the answer is no.