Consider the following premises. forall x_4: Q(x_4) or ~Q_4(x_4). exists x_4: Q(x_4) -> Q_4(x_4). Can we infer forall x_4: ~(Q_4(x_4) -> Q(x_4)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.