Consider the following premises. exists x_8: ~Q_8(x_8). forall x_8: P(x_8) <-> Q_8(x_8). forall x_8: P(x_8) or Q(x_8). Can we infer forall x_8: ~Q(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P(x_8) <-> Q_8(x_8), exists x_8: ~Q_8(x_8) we can infer exists x_8: ~P(x_8) via existential biconditional elimination. Finally, from forall x_8: P(x_8) or Q(x_8), exists x_8: ~P(x_8) we can infer exists x_8: Q(x_8) via existential disjunctive syllogism, which contradicts forall x_8: ~Q(x_8). Therefore, the answer is no.