Consider the following premises. u or ~T(a_8). S(a_8) -> u. forall x_2: T(x_2) or S(x_2). Can we infer ~u from them? If possible, name the inference rules being used at each step.
 From forall x_2: T(x_2) or S(x_2) we can infer T(a_8) or S(a_8) via universal instantiation. From u or ~T(a_8) we can infer T(a_8) -> u via rewriting. Finally, from T(a_8) -> u, S(a_8) -> u, T(a_8) or S(a_8) we can infer u via disjunction elimination, which contradicts ~u. Therefore, the answer is no.