Consider the following premises. forall x_14: P_14(x_14) or Q_10(x_14). forall x_14: Q_10(x_14) -> T(x_14). forall x_14: ~T(x_14) or P_1(x_14). forall x_14: P_14(x_14) -> Q_14(x_14). exists x_14: Q_14(x_14) -> T(x_14). Can we infer exists x_14: W(x_14) or P_1(x_14) from them? If possible, name the inference rules being used at each step.
 From forall x_14: P_14(x_14) -> Q_14(x_14), exists x_14: Q_14(x_14) -> T(x_14) we can infer exists x_14: P_14(x_14) -> T(x_14) via existential transitivity. From exists x_14: P_14(x_14) -> T(x_14), forall x_14: Q_10(x_14) -> T(x_14), forall x_14: P_14(x_14) or Q_10(x_14) we can infer exists x_14: T(x_14) via existential disjunction elimination. From exists x_14: T(x_14) we can infer exists x_14: T(x_14) or W(x_14) via existential addition. Finally, from exists x_14: T(x_14) or W(x_14), forall x_14: ~T(x_14) or P_1(x_14) we can infer exists x_14: W(x_14) or P_1(x_14) via existential resolution. Therefore, the answer is yes.