Consider the following premises. forall x_11: S(x_11) -> ~Q_3(x_11). forall x_11: Q_3(x_11) and Q_7(x_11). forall x_11: P_11(x_11) or S(x_11). exists x_11: ~P_11(x_11) or P(x_11). Can we infer exists x_11: P(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) or S(x_11), exists x_11: ~P_11(x_11) or P(x_11) we can infer exists x_11: S(x_11) or P(x_11) via existential resolution. From forall x_11: Q_3(x_11) and Q_7(x_11) we can infer forall x_11: Q_3(x_11) via universal simplification. From forall x_11: S(x_11) -> ~Q_3(x_11), forall x_11: Q_3(x_11) we can infer forall x_11: ~S(x_11) via universal modus tollens. Finally, from exists x_11: S(x_11) or P(x_11), forall x_11: ~S(x_11) we can infer exists x_11: P(x_11) via existential disjunctive syllogism. Therefore, the answer is yes.