Consider the following premises. forall x_11: ~P_5(x_11). forall x_11: P_11(x_11) or Q_11(x_11). forall x_11: Q_11(x_11) -> P(x_11). forall x_11: P_5(x_11) or Q_5(x_11). forall x_11: P_11(x_11) -> P(x_11). Can we infer ~Q_5(a_2) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) -> P(x_11), forall x_11: Q_11(x_11) -> P(x_11), forall x_11: P_11(x_11) or Q_11(x_11) we can infer forall x_11: P(x_11) via universal disjunction elimination. Finally, from forall x_11: P_5(x_11) or Q_5(x_11), forall x_11: ~P_5(x_11) we can infer forall x_11: Q_5(x_11) via universal disjunctive syllogism, which contradicts ~Q_5(a_2). Therefore, the answer is no.