Consider the following premises. exists x_16: Q_11(x_16) -> W(x_16). forall x_16: W(x_16) or ~Q_16(x_16). forall x_16: P_11(x_16) -> Q_11(x_16). forall x_16: P_11(x_16) or Q_16(x_16). Can we infer exists x_16: W(x_16) or Q(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: W(x_16) or ~Q_16(x_16) we can infer forall x_16: Q_16(x_16) -> W(x_16) via universal rewriting. From forall x_16: P_11(x_16) -> Q_11(x_16), exists x_16: Q_11(x_16) -> W(x_16) we can infer exists x_16: P_11(x_16) -> W(x_16) via existential transitivity. From exists x_16: P_11(x_16) -> W(x_16), forall x_16: Q_16(x_16) -> W(x_16), forall x_16: P_11(x_16) or Q_16(x_16) we can infer exists x_16: W(x_16) via existential disjunction elimination. Finally, from exists x_16: W(x_16) we can infer exists x_16: W(x_16) or Q(x_16) via existential addition. Therefore, the answer is yes.