Consider the following premises. forall x_11: P_11(x_11) -> S(x_11). forall x_11: ~S(x_11) or R(x_11). exists x_11: Q_11(x_11) -> S(x_11). forall x_11: P_11(x_11) or Q_11(x_11). Can we infer exists x_11: W(x_11) or R(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) -> S(x_11), exists x_11: Q_11(x_11) -> S(x_11), forall x_11: P_11(x_11) or Q_11(x_11) we can infer exists x_11: S(x_11) via existential disjunction elimination. From exists x_11: S(x_11) we can infer exists x_11: S(x_11) or W(x_11) via existential addition. Finally, from exists x_11: S(x_11) or W(x_11), forall x_11: ~S(x_11) or R(x_11) we can infer exists x_11: W(x_11) or R(x_11) via existential resolution. Therefore, the answer is yes.