Consider the following premises. forall x_8: Q_6(x_8). forall x_8: P_8(x_8) or Q_8(x_8). forall x_8: ~P_8(x_8). Can we infer exists y: Q_8(y) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) or Q_8(x_8), forall x_8: ~P_8(x_8) we can infer forall x_8: Q_8(x_8) via universal disjunctive syllogism. From forall x_8: Q_8(x_8), forall x_8: Q_6(x_8) we can infer forall x_8: Q_8(x_8) and Q_6(x_8) via universal conjunction. From forall x_8: Q_8(x_8) and Q_6(x_8) we can infer forall x_8: Q_8(x_8) via universal simplification. From forall x_8: Q_8(x_8) we can infer Q_8(a_1) via universal instantiation. Finally, from Q_8(a_1) we can infer exists y: Q_8(y) via existential generalization. Therefore, the answer is yes.