Consider the following premises. forall x_7: P_7(x_7) -> Q_7(x_7). forall x_7: P_7(x_7) <-> Q_7(x_7). Can we infer ~(P_7(a_2) -> Q_7(a_2)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.