Consider the following premises. P_17(a_17). forall x_17: Q_14(x_17) -> T(x_17). forall x_17: P_17(x_17) <-> T(x_17). Can we infer exists x_17: T(x_17) or Q(x_17) from them? If possible, name the inference rules being used at each step.
 From P_17(a_17) we can infer exists x_17: P_17(x_17) via existential generalization. From exists x_17: P_17(x_17) we can infer exists x_17: P_17(x_17) or Q_14(x_17) via existential addition. From forall x_17: P_17(x_17) <-> T(x_17) we can infer forall x_17: P_17(x_17) -> T(x_17) via universal biconditional elimination. From forall x_17: P_17(x_17) -> T(x_17), forall x_17: Q_14(x_17) -> T(x_17), exists x_17: P_17(x_17) or Q_14(x_17) we can infer exists x_17: T(x_17) via existential disjunction elimination. Finally, from exists x_17: T(x_17) we can infer exists x_17: T(x_17) or Q(x_17) via existential addition. Therefore, the answer is yes.