Consider the following premises. forall x_16: Q_1(x_16) -> Q(x_16). exists x_16: ~P_2(x_16). forall x_16: P_15(x_16) or P_2(x_16). forall x_16: Q(x_16) -> Q_1(x_16). forall x_16: ~P_15(x_16) or Q(x_16). Can we infer forall x_16: ~Q_1(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: Q(x_16) -> Q_1(x_16), forall x_16: Q_1(x_16) -> Q(x_16) we can infer forall x_16: Q(x_16) <-> Q_1(x_16) via universal biconditional introduction. From forall x_16: P_15(x_16) or P_2(x_16), forall x_16: ~P_15(x_16) or Q(x_16) we can infer forall x_16: P_2(x_16) or Q(x_16) via universal resolution. From forall x_16: P_2(x_16) or Q(x_16), exists x_16: ~P_2(x_16) we can infer exists x_16: Q(x_16) via existential disjunctive syllogism. From forall x_16: Q(x_16) <-> Q_1(x_16) we can infer forall x_16: Q(x_16) -> Q_1(x_16) via universal biconditional elimination. Finally, from forall x_16: Q(x_16) -> Q_1(x_16), exists x_16: Q(x_16) we can infer exists x_16: Q_1(x_16) via existential modus ponens, which contradicts forall x_16: ~Q_1(x_16). Therefore, the answer is no.