Consider the following premises. R_10(a_10) -> u. u -> R_10(a_10). ~u. forall x_10: R_10(x_10) or S_10(x_10). Can we infer S_10(a_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: R_10(x_10) or S_10(x_10) we can infer R_10(a_10) or S_10(a_10) via universal instantiation. From u -> R_10(a_10), R_10(a_10) -> u we can infer u <-> R_10(a_10) via biconditional introduction. From u <-> R_10(a_10), ~u we can infer ~R_10(a_10) via biconditional elimination. Finally, from R_10(a_10) or S_10(a_10), ~R_10(a_10) we can infer S_10(a_10) via disjunctive syllogism. Therefore, the answer is yes.