Consider the following premises. exists x_4: Q_4(x_4). forall x_4: S(x_4) or Q(x_4). forall x_4: S(x_4) -> ~Q_4(x_4). Can we infer forall x_4: ~Q(x_4) from them? If possible, name the inference rules being used at each step.
 From forall x_4: S(x_4) -> ~Q_4(x_4), exists x_4: Q_4(x_4) we can infer exists x_4: ~S(x_4) via existential modus tollens. Finally, from forall x_4: S(x_4) or Q(x_4), exists x_4: ~S(x_4) we can infer exists x_4: Q(x_4) via existential disjunctive syllogism, which contradicts forall x_4: ~Q(x_4). Therefore, the answer is no.