Consider the following premises. u_3 <-> R_19(a_19). forall x_19: R_19(x_19) -> S_19(x_19). w -> u_3. ~S_19(a_19). Can we infer w 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 R_19(a_19) -> S_19(a_19), ~S_19(a_19) we can infer ~R_19(a_19) via modus tollens. From u_3 <-> R_19(a_19), ~R_19(a_19) we can infer ~u_3 via biconditional elimination. Finally, from w -> u_3, ~u_3 we can infer ~w via modus tollens, which contradicts w. Therefore, the answer is no.