Consider the following premises. exists x_2: R_4(x_2) -> P_2(x_2). forall x_2: R_4(x_2) <-> P_2(x_2). Can we infer forall x_2: ~(P_2(x_2) -> R_4(x_2)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.