Consider the following premises. forall x_14: Q_14(x_14). forall x_14: U(x_14) and P(x_14). exists x_14: Q(x_14). Can we infer exists x_14: Q(x_14) and U(x_14) from them? If possible, name the inference rules being used at each step.
 From exists x_14: Q(x_14), forall x_14: Q_14(x_14) we can infer exists x_14: Q(x_14) and Q_14(x_14) via existential conjunction. From exists x_14: Q(x_14) and Q_14(x_14) we can infer exists x_14: Q(x_14) via existential simplification. From forall x_14: U(x_14) and P(x_14) we can infer forall x_14: U(x_14) via universal simplification. Finally, from exists x_14: Q(x_14), forall x_14: U(x_14) we can infer exists x_14: Q(x_14) and U(x_14) via existential conjunction. Therefore, the answer is yes.