Consider the following premises. forall x_10: P_10(x_10) or Q_5(x_10). forall x_10: Q(x_10). forall x_10: ~Q_10(x_10). exists x_10: P_10(x_10) -> Q_10(x_10). Can we infer forall x_10: ~(Q_5(x_10) and Q(x_10)) from them? If possible, name the inference rules being used at each step.
 From exists x_10: P_10(x_10) -> Q_10(x_10), forall x_10: ~Q_10(x_10) we can infer exists x_10: ~P_10(x_10) via existential modus tollens. From forall x_10: P_10(x_10) or Q_5(x_10), exists x_10: ~P_10(x_10) we can infer exists x_10: Q_5(x_10) via existential disjunctive syllogism. Finally, from exists x_10: Q_5(x_10), forall x_10: Q(x_10) we can infer exists x_10: Q_5(x_10) and Q(x_10) via existential conjunction, which contradicts forall x_10: ~(Q_5(x_10) and Q(x_10)). Therefore, the answer is no.