Consider the following premises. exists x_5: Q(x_5). forall x_5: P(x_5) and Q_5(x_5). Can we infer forall x_5: ~Q(x_5) from them? If possible, name the inference rules being used at each step.
 From forall x_5: P(x_5) and Q_5(x_5) we can infer forall x_5: P(x_5) via universal simplification. From forall x_5: P(x_5), exists x_5: Q(x_5) we can infer exists x_5: P(x_5) and Q(x_5) via existential conjunction. Finally, from exists x_5: P(x_5) and Q(x_5) we can infer exists x_5: P(x_5) via existential simplification, which contradicts forall x_5: ~Q(x_5). Therefore, the answer is no.