Consider the following premises. forall x_10: R_10(x_10) -> S_10(x_10). R_10(a_10) or s_2. s_2 <-> S_10(a_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) -> S_10(x_10) we can infer R_10(a_10) -> S_10(a_10) via universal instantiation. From s_2 <-> S_10(a_10) we can infer s_2 -> S_10(a_10) via biconditional elimination. Finally, from R_10(a_10) -> S_10(a_10), s_2 -> S_10(a_10), R_10(a_10) or s_2 we can infer S_10(a_10) via disjunction elimination, which contradicts ~S_10(a_10). Therefore, the answer is no.