Consider the following premises. forall x_14: Q_14(x_14). forall x_14: Q_10(x_14) -> Q(x_14). forall x_14: U_1(x_14). exists x_14: Q(x_14) or ~Q_14(x_14). Can we infer exists x_14: U_1(x_14) and Q(x_14) from them? If possible, name the inference rules being used at each step.
 From exists x_14: Q(x_14) or ~Q_14(x_14) we can infer exists x_14: Q_14(x_14) -> Q(x_14) via existential rewriting. From forall x_14: Q_14(x_14) we can infer forall x_14: Q_14(x_14) or Q_10(x_14) via universal addition. From exists x_14: Q_14(x_14) -> Q(x_14), forall x_14: Q_10(x_14) -> Q(x_14), forall x_14: Q_14(x_14) or Q_10(x_14) we can infer exists x_14: Q(x_14) via existential disjunction elimination. Finally, from forall x_14: U_1(x_14), exists x_14: Q(x_14) we can infer exists x_14: U_1(x_14) and Q(x_14) via existential conjunction. Therefore, the answer is yes.