Consider the following premises. forall x_3: Q_3(x_3) -> P_2(x_3). exists x_3: P_2(x_3) -> P(x_3). forall x_3: P(x_3) -> Q_3(x_3). Can we infer forall x_3: ~(P_2(x_3) -> P(x_3)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.