Consider the following premises. forall x_12: Q(x_12) <-> Q_12(x_12). Q_2(g) -> r_4. forall x_12: Q_12(x_12) -> Q_2(x_12). Can we infer ~(Q(g) -> r_4) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.