Consider the following premises. exists x_11: ~P_11(x_11) or Q_3(x_11). forall x_11: W_1(x_11) or ~Q_3(x_11). forall x_11: W_1(x_11) <-> P(x_11). forall x_11: P_11(x_11) or P(x_11). Can we infer exists x_11: W_1(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) or P(x_11), exists x_11: ~P_11(x_11) or Q_3(x_11) we can infer exists x_11: P(x_11) or Q_3(x_11) via existential resolution. From forall x_11: W_1(x_11) <-> P(x_11) we can infer forall x_11: P(x_11) -> W_1(x_11) via universal biconditional elimination. From forall x_11: W_1(x_11) or ~Q_3(x_11) we can infer forall x_11: Q_3(x_11) -> W_1(x_11) via universal rewriting. Finally, from forall x_11: P(x_11) -> W_1(x_11), forall x_11: Q_3(x_11) -> W_1(x_11), exists x_11: P(x_11) or Q_3(x_11) we can infer exists x_11: W_1(x_11) via existential disjunction elimination. Therefore, the answer is yes.