Consider the following premises. forall x_8: P_8(x_8) -> R_8(x_8). exists x_8: U(x_8) or Q(x_8). forall x_8: P_8(x_8) or Q_8(x_8). forall x_8: Q_8(x_8) -> R_8(x_8). forall x_8: U(x_8) -> ~R_8(x_8). Can we infer exists x_8: Q(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) -> R_8(x_8), forall x_8: Q_8(x_8) -> R_8(x_8), forall x_8: P_8(x_8) or Q_8(x_8) we can infer forall x_8: R_8(x_8) via universal disjunction elimination. From forall x_8: U(x_8) -> ~R_8(x_8), forall x_8: R_8(x_8) we can infer forall x_8: ~U(x_8) via universal modus tollens. Finally, from exists x_8: U(x_8) or Q(x_8), forall x_8: ~U(x_8) we can infer exists x_8: Q(x_8) via existential disjunctive syllogism. Therefore, the answer is yes.