Consider the following premises. ~p. p -> R_10(a_10). R_10(a_10) -> p. 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 R_10(a_10) -> p, p -> R_10(a_10) we can infer R_10(a_10) <-> p via biconditional introduction. From R_10(a_10) <-> p, ~p 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, which contradicts ~S_10(a_10). Therefore, the answer is no.