Consider the following premises. forall x_8: S(x_8). forall x_8: P_8(x_8) -> Q_8(x_8). forall x_8: P_8(x_8) or Q_5(x_8). forall x_8: ~Q_8(x_8). Can we infer ~Q_5(a_2) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) -> Q_8(x_8), forall x_8: ~Q_8(x_8) we can infer forall x_8: ~P_8(x_8) via universal modus tollens. Finally, from forall x_8: P_8(x_8) or Q_5(x_8), forall x_8: ~P_8(x_8) we can infer forall x_8: Q_5(x_8) via universal disjunctive syllogism, which contradicts ~Q_5(a_2). Therefore, the answer is no.