Consider the following premises. exists x_10: P(x_10) -> P_10(x_10). forall x_10: P(x_10) -> P_10(x_10). forall x_10: P_10(x_10) <-> P(x_10). Can we infer forall x_10: ~(P_10(x_10) -> P(x_10)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.