Consider the following premises. forall x_17: ~P_11(x_17). exists x_17: Q_11(x_17) -> T(x_17). forall x_17: W(x_17) <-> T(x_17). forall x_17: P_11(x_17) or Q_11(x_17). Can we infer exists x_17: W(x_17) from them? If possible, name the inference rules being used at each step.
 From forall x_17: W(x_17) <-> T(x_17) we can infer forall x_17: T(x_17) -> W(x_17) via universal biconditional elimination. From forall x_17: P_11(x_17) or Q_11(x_17), forall x_17: ~P_11(x_17) we can infer forall x_17: Q_11(x_17) via universal disjunctive syllogism. From exists x_17: Q_11(x_17) -> T(x_17), forall x_17: Q_11(x_17) we can infer exists x_17: T(x_17) via existential modus ponens. Finally, from forall x_17: T(x_17) -> W(x_17), exists x_17: T(x_17) we can infer exists x_17: W(x_17) via existential modus ponens. Therefore, the answer is yes.