Consider the following premises. ~R_12(a_12). forall x_12: R_12(x_12) or S_12(x_12). u_2 -> ~S_12(a_12). Can we infer ~u_2 from them? If possible, name the inference rules being used at each step.
 From forall x_12: R_12(x_12) or S_12(x_12) we can infer R_12(a_12) or S_12(a_12) via universal instantiation. From R_12(a_12) or S_12(a_12), ~R_12(a_12) we can infer S_12(a_12) via disjunctive syllogism. Finally, from u_2 -> ~S_12(a_12), S_12(a_12) we can infer ~u_2 via modus tollens. Therefore, the answer is yes.