Consider the following premises. ~u_1. u_1 <-> R(a_19). forall x: R(x) <-> S(x). Can we infer S(a_19) from them? If possible, name the inference rules being used at each step.
 From forall x: R(x) <-> S(x) we can infer forall x: S(x) -> R(x) via universal biconditional elimination. From forall x: S(x) -> R(x) we can infer S(a_19) -> R(a_19) via universal instantiation. From u_1 <-> R(a_19), ~u_1 we can infer ~R(a_19) via biconditional elimination. Finally, from S(a_19) -> R(a_19), ~R(a_19) we can infer ~S(a_19) via modus tollens, which contradicts S(a_19). Therefore, the answer is no.