Consider the following premises. S_8(a_8) -> p_2. forall x_8: T(x_8) or S_8(x_8). p_2 or ~T(a_8). Can we infer ~p_2 from them? If possible, name the inference rules being used at each step.
 From forall x_8: T(x_8) or S_8(x_8) we can infer T(a_8) or S_8(a_8) via universal instantiation. From p_2 or ~T(a_8) we can infer T(a_8) -> p_2 via rewriting. Finally, from T(a_8) -> p_2, S_8(a_8) -> p_2, T(a_8) or S_8(a_8) we can infer p_2 via disjunction elimination, which contradicts ~p_2. Therefore, the answer is no.