Consider the following premises. forall x_3: P_3(x_3) and Q_3(x_3). forall x_3: Q(x_3). Can we infer exists x_3: ~(Q(x_3) and P_3(x_3)) from them?
 From forall x_3: P_3(x_3) and Q_3(x_3) we can infer forall x_3: P_3(x_3). Finally, from forall x_3: Q(x_3), forall x_3: P_3(x_3) we can infer forall x_3: Q(x_3) and P_3(x_3), which contradicts exists x_3: ~(Q(x_3) and P_3(x_3)). Therefore, the answer is no.