Consider the following premises. S_19(a_19) <-> w_2. forall x_19: R_19(x_19) -> S_19(x_19). ~w_2. Can we infer ~R_19(a_19) or u from them? If possible, name the inference rules being used at each step.
 From forall x_19: R_19(x_19) -> S_19(x_19) we can infer R_19(a_19) -> S_19(a_19) via universal instantiation. From S_19(a_19) <-> w_2, ~w_2 we can infer ~S_19(a_19) via biconditional elimination. From R_19(a_19) -> S_19(a_19), ~S_19(a_19) we can infer ~R_19(a_19) via modus tollens. Finally, from ~R_19(a_19) we can infer ~R_19(a_19) or u via addition. Therefore, the answer is yes.