Consider the following premises. forall x_12: W(x_12). exists x_12: P(x_12) -> P_2(x_12). forall x_12: P(x_12) and Q_12(x_12). Can we infer forall x_12: ~(P_2(x_12) and W(x_12)) from them?
That contradicts the premises. Therefore the answer is no.