Consider the following premises. exists x_12: Q_1(x_12) -> P_12(x_12). forall x_12: P_12(x_12) <-> Q_12(x_12). forall x_12: Q_1(x_12) or ~Q(x_12). Can we infer forall x_12: ~(Q(x_12) -> Q_12(x_12)) from them?
That contradicts the premises. Therefore the answer is no.