Consider the following premises. forall x_12: P_6(x_12) -> P_12(x_12). forall x_12: P_12(x_12) <-> Q_12(x_12). Q_12(f) -> P_6(f). Can we infer ~(P_6(f) <-> Q_12(f)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.