Consider the following premises. forall x_5: Q_5(x_5) -> P_5(x_5). exists x_5: Q(x_5) -> P_5(x_5). forall x_5: P_5(x_5) -> Q_5(x_5). Can we infer forall x_5: ~(Q(x_5) -> Q_5(x_5)) from them?
That contradicts the premises. Therefore the answer is no.