Consider the following premises. exists x_17: ~Q_17(x_17). forall x_17: P_17(x_17) or W(x_17). forall x_17: P_17(x_17) <-> Q_17(x_17). Can we infer exists x_17: W(x_17) or R_4(x_17) from them? If possible, name the inference rules being used at each step.
 From forall x_17: P_17(x_17) <-> Q_17(x_17), exists x_17: ~Q_17(x_17) we can infer exists x_17: ~P_17(x_17) via existential biconditional elimination. From forall x_17: P_17(x_17) or W(x_17), exists x_17: ~P_17(x_17) we can infer exists x_17: W(x_17) via existential disjunctive syllogism. Finally, from exists x_17: W(x_17) we can infer exists x_17: W(x_17) or R_4(x_17) via existential addition. Therefore, the answer is yes.