Consider the following premises. exists x_12: Q_12(x_12) -> P_8(x_12). forall x_12: P_8(x_12) <-> Q_3(x_12). forall x_12: Q_3(x_12) <-> Q_12(x_12). Can we infer forall x_12: ~(Q_3(x_12) <-> P_8(x_12)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.