Consider the following premises. forall x_3: R_3(x_3) or S_3(x_3). ~R_3(a_3). Can we infer ~S_3(a_3) from them? If possible, name the inference rules being used at each step.
 From forall x_3: R_3(x_3) or S_3(x_3) we can infer R_3(a_3) or S_3(a_3) via universal instantiation. Finally, from R_3(a_3) or S_3(a_3), ~R_3(a_3) we can infer S_3(a_3) via disjunctive syllogism, which contradicts ~S_3(a_3). Therefore, the answer is no.