Consider the following premises. forall x_9: P_9(x_9) -> R_1(x_9). exists x_9: P(x_9) -> Q_9(x_9). forall x_9: Q_9(x_9) -> P_9(x_9). forall x_9: P_9(x_9) -> Q_9(x_9). Can we infer forall x_9: ~(P(x_9) -> R_1(x_9)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.