Consider the following premises. forall x_7: ~Q_7(x_7) or R_5(x_7). ~R_7(a_3). forall x_7: ~P_7(x_7) or R_7(x_7). forall x_7: P_7(x_7) or Q_7(x_7). Can we infer ~R_5(a_3) from them? If possible, name the inference rules being used at each step.
 From forall x_7: P_7(x_7) or Q_7(x_7), forall x_7: ~P_7(x_7) or R_7(x_7) we can infer forall x_7: Q_7(x_7) or R_7(x_7) via universal resolution. From forall x_7: Q_7(x_7) or R_7(x_7), forall x_7: ~Q_7(x_7) or R_5(x_7) we can infer forall x_7: R_7(x_7) or R_5(x_7) via universal resolution. From forall x_7: R_7(x_7) or R_5(x_7) we can infer R_7(a_3) or R_5(a_3) via universal instantiation. Finally, from R_7(a_3) or R_5(a_3), ~R_7(a_3) we can infer R_5(a_3) via disjunctive syllogism, which contradicts ~R_5(a_3). Therefore, the answer is no.