Consider the following premises. forall x_9: W(x_9). exists x_9: S(x_9) or Q_9(x_9). forall x_9: Q_9(x_9) -> Q_1(x_9). forall x_9: S(x_9) -> Q_1(x_9). Can we infer forall x_9: ~(Q_1(x_9) and W(x_9)) from them? If possible, name the inference rules being used at each step.
 From forall x_9: S(x_9) -> Q_1(x_9), forall x_9: Q_9(x_9) -> Q_1(x_9), exists x_9: S(x_9) or Q_9(x_9) we can infer exists x_9: Q_1(x_9) via existential disjunction elimination. Finally, from exists x_9: Q_1(x_9), forall x_9: W(x_9) we can infer exists x_9: Q_1(x_9) and W(x_9) via existential conjunction, which contradicts forall x_9: ~(Q_1(x_9) and W(x_9)). Therefore, the answer is no.