Consider the following premises. forall x: ~T_2(x) or U(x). Q_1(a_8) -> ~q_2. forall x: T_2(x) or Q_1(x). q_2. Can we infer ~U(a_8) from them? If possible, name the inference rules being used at each step.
 From forall x: T_2(x) or Q_1(x), forall x: ~T_2(x) or U(x) we can infer forall x: Q_1(x) or U(x) via universal resolution. From forall x: Q_1(x) or U(x) we can infer Q_1(a_8) or U(a_8) via universal instantiation. From Q_1(a_8) -> ~q_2, q_2 we can infer ~Q_1(a_8) via modus tollens. Finally, from Q_1(a_8) or U(a_8), ~Q_1(a_8) we can infer U(a_8) via disjunctive syllogism, which contradicts ~U(a_8). Therefore, the answer is no.