Consider the following premises. forall x_10: ~Q_10(x_10). forall x_10: S(x_10) <-> P_10(x_10). forall x_10: P_10(x_10) -> Q_10(x_10). forall x_10: S(x_10) -> Q_9(x_10). forall x_10: Q_9(x_10) -> S(x_10). forall x_10: Q_10(x_10) -> P_10(x_10). Can we infer forall x_10: P_10(x_10) -> Q_10(x_10) from them? If possible, name the inference rules being used at each step.
That is one of the premises. Therefore, the answer is yes.