Consider the following premises. exists x_10: Q(x_10) -> P_10(x_10). forall x_10: Q_10(x_10) -> Q(x_10). forall x_10: P_10(x_10) <-> Q_10(x_10). Can we infer forall x_10: ~(Q_10(x_10) -> Q(x_10)) from them?
That contradicts the premises. Therefore the answer is no.