Consider the following premises. ~Q_6(c). forall x_8: P_8(x_8) -> Q_8(x_8). forall x_8: ~Q_8(x_8) or R_5(x_8). forall x_8: P_8(x_8). Can we infer ~R_5(c) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) -> Q_8(x_8), forall x_8: P_8(x_8) we can infer forall x_8: Q_8(x_8) via universal modus ponens. From forall x_8: Q_8(x_8) we can infer forall x_8: Q_8(x_8) or Q_6(x_8) via universal addition. From forall x_8: Q_8(x_8) or Q_6(x_8), forall x_8: ~Q_8(x_8) or R_5(x_8) we can infer forall x_8: Q_6(x_8) or R_5(x_8) via universal resolution. From forall x_8: Q_6(x_8) or R_5(x_8) we can infer Q_6(c) or R_5(c) via universal instantiation. Finally, from Q_6(c) or R_5(c), ~Q_6(c) we can infer R_5(c) via disjunctive syllogism, which contradicts ~R_5(c). Therefore, the answer is no.