Consider the following premises. Q_12(a_5) -> R(a_5). forall x_12: P_12(x_12) <-> Q_12(x_12). forall x_12: R(x_12) -> P_12(x_12). Can we infer ~(R(a_5) <-> Q_12(a_5)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.