Consider the following premises. forall x_7: P_7(x_7) <-> Q_7(x_7). forall x_7: P_1(x_7) -> P_7(x_7). exists x_7: Q_3(x_7) -> P_1(x_7). Can we infer forall x_7: ~(Q_3(x_7) -> Q_7(x_7)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.