Consider the following premises. forall x: W(x) <-> W_2(x). exists x: R(x) -> W(x). forall x: Q(x) or W_2(x). forall x: ~Q(x) or R(x). Can we infer exists x: W(x) from them? If possible, name the inference rules being used at each step.
 From forall x: W(x) <-> W_2(x) we can infer forall x: W_2(x) -> W(x) via universal biconditional elimination. From forall x: Q(x) or W_2(x), forall x: ~Q(x) or R(x) we can infer forall x: W_2(x) or R(x) via universal resolution. Finally, from forall x: W_2(x) -> W(x), exists x: R(x) -> W(x), forall x: W_2(x) or R(x) we can infer exists x: W(x) via existential disjunction elimination. Therefore, the answer is yes.