Consider the following premises. forall x_11: Q(x_11) <-> Q_11(x_11). forall x_11: P_4(x_11) -> Q_11(x_11). forall x_11: Q(x_11) -> P_4(x_11). Can we infer ~(Q(a_2) -> P_4(a_2)) from them?
That contradicts the premises. Therefore the answer is no.