Consider the following premises. forall x_13: Q_13(x_13) -> P_13(x_13). forall x_13: P_13(x_13) -> Q_13(x_13). P_13(c) or ~Q_13(c). Can we infer ~(Q_13(c) <-> P_13(c)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.