Consider the following premises. forall x_19: T(x_19) -> S_19(x_19). T(a_19) or q_4. ~S_19(a_19). Can we infer ~q_4 from them? If possible, name the inference rules being used at each step.
 From forall x_19: T(x_19) -> S_19(x_19) we can infer T(a_19) -> S_19(a_19) via universal instantiation. From T(a_19) -> S_19(a_19), ~S_19(a_19) we can infer ~T(a_19) via modus tollens. Finally, from T(a_19) or q_4, ~T(a_19) we can infer q_4 via disjunctive syllogism, which contradicts ~q_4. Therefore, the answer is no.