Consider the following premises. forall x_5: Q_5(x_5) -> W(x_5). forall x_5: P_5(x_5). forall x_5: P_5(x_5) -> W(x_5). exists x_5: T_1(x_5) -> ~W(x_5). Can we infer forall x_5: T_1(x_5) from them? If possible, name the inference rules being used at each step.
 From forall x_5: P_5(x_5) we can infer forall x_5: P_5(x_5) or Q_5(x_5) via universal addition. From forall x_5: P_5(x_5) -> W(x_5), forall x_5: Q_5(x_5) -> W(x_5), forall x_5: P_5(x_5) or Q_5(x_5) we can infer forall x_5: W(x_5) via universal disjunction elimination. Finally, from exists x_5: T_1(x_5) -> ~W(x_5), forall x_5: W(x_5) we can infer exists x_5: ~T_1(x_5) via existential modus tollens, which contradicts forall x_5: T_1(x_5). Therefore, the answer is no.