Consider the following premises. forall y_3: W_1(y_3) -> W_2(y_3). forall y_3: P(y_3) or U(y_3). forall y_3: U(y_3) <-> W_2(y_3). exists y_3: ~P(y_3) or W_1(y_3). Can we infer exists y_3: W_2(y_3) from them? If possible, name the inference rules being used at each step.
 From forall y_3: P(y_3) or U(y_3), exists y_3: ~P(y_3) or W_1(y_3) we can infer exists y_3: U(y_3) or W_1(y_3) via existential resolution. From forall y_3: U(y_3) <-> W_2(y_3) we can infer forall y_3: U(y_3) -> W_2(y_3) via universal biconditional elimination. Finally, from forall y_3: U(y_3) -> W_2(y_3), forall y_3: W_1(y_3) -> W_2(y_3), exists y_3: U(y_3) or W_1(y_3) we can infer exists y_3: W_2(y_3) via existential disjunction elimination. Therefore, the answer is yes.