Consider the following premises. R(a_4) and s. forall y: ~R(y). Can we infer r_2 from them? If possible, name the inference rules being used at each step.
 From forall y: ~R(y) we can infer ~R(a_4) via universal instantiation. From R(a_4) and s we can infer R(a_4) via simplification. From R(a_4) we can infer R(a_4) or r_2 via addition. Finally, from R(a_4) or r_2, ~R(a_4) we can infer r_2 via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.