Consider the following premises. R_10(i_4) -> p. forall x_10: R_10(x_10) or S_10(x_10). ~p. p -> R_10(i_4). Can we infer ~S_10(i_4) 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(i_4) or S_10(i_4) via universal instantiation. From p -> R_10(i_4), R_10(i_4) -> p we can infer p <-> R_10(i_4) via biconditional introduction. From p <-> R_10(i_4), ~p we can infer ~R_10(i_4) via biconditional elimination. Finally, from R_10(i_4) or S_10(i_4), ~R_10(i_4) we can infer S_10(i_4) via disjunctive syllogism, which contradicts ~S_10(i_4). Therefore, the answer is no.