Consider the following premises. forall x_5: R_5(x_5) -> S_5(x_5). q or R_5(a_5). q -> S_5(a_5). Can we infer ~S_5(a_5) from them? If possible, name the inference rules being used at each step.
 From forall x_5: R_5(x_5) -> S_5(x_5) we can infer R_5(a_5) -> S_5(a_5) via universal instantiation. Finally, from q -> S_5(a_5), R_5(a_5) -> S_5(a_5), q or R_5(a_5) we can infer S_5(a_5) via disjunction elimination, which contradicts ~S_5(a_5). Therefore, the answer is no.