Consider the following premises. forall x_9: P_9(x_9) -> Q_9(x_9). forall x_9: ~Q_9(x_9). forall x_9: Q_9(x_9) -> P_9(x_9). forall x_9: Q(x_9) <-> P_9(x_9). Can we infer forall x_9: ~Q_9(x_9) from them?
That is one of the premises. Therefore, the answer is yes.