Consider the following premises. forall x_9: P_7(x_9) or Q_7(x_9). forall x_9: P_7(x_9) -> R(x_9). forall x_9: ~P_9(x_9). forall x_9: Q_7(x_9) -> R(x_9). forall x_9: P_9(x_9) or Q_9(x_9). Can we infer ~R(b) from them? If possible, name the inference rules being used at each step.
 From forall x_9: P_9(x_9) or Q_9(x_9), forall x_9: ~P_9(x_9) we can infer forall x_9: Q_9(x_9) via universal disjunctive syllogism. Finally, from forall x_9: P_7(x_9) -> R(x_9), forall x_9: Q_7(x_9) -> R(x_9), forall x_9: P_7(x_9) or Q_7(x_9) we can infer forall x_9: R(x_9) via universal disjunction elimination, which contradicts ~R(b). Therefore, the answer is no.