Consider the following premises. forall x_22: P_22(x_22) or Q_22(x_22). forall x_22: Q_22(x_22) -> Q_14(x_22). exists x_22: ~P_22(x_22). forall x_22: Q_14(x_22) -> Q(x_22). forall x_22: Q(x_22) <-> U(x_22). Can we infer forall x_22: ~U(x_22) from them? If possible, name the inference rules being used at each step.
 From forall x_22: P_22(x_22) or Q_22(x_22), exists x_22: ~P_22(x_22) we can infer exists x_22: Q_22(x_22) via existential disjunctive syllogism. From forall x_22: Q_22(x_22) -> Q_14(x_22), forall x_22: Q_14(x_22) -> Q(x_22) we can infer forall x_22: Q_22(x_22) -> Q(x_22) via universal transitivity. From forall x_22: Q(x_22) <-> U(x_22) we can infer forall x_22: Q(x_22) -> U(x_22) via universal biconditional elimination. From forall x_22: Q_22(x_22) -> Q(x_22), exists x_22: Q_22(x_22) we can infer exists x_22: Q(x_22) via existential modus ponens. Finally, from forall x_22: Q(x_22) -> U(x_22), exists x_22: Q(x_22) we can infer exists x_22: U(x_22) via existential modus ponens, which contradicts forall x_22: ~U(x_22). Therefore, the answer is no.