Consider the following premises. exists x_2: W(x_2) -> P(x_2). forall x_2: ~W(x_2). forall x_2: P(x_2) -> W(x_2). forall x_2: P(x_2) or U(x_2). Can we infer exists x_2: U(x_2) from them? If possible, name the inference rules being used at each step.
 From exists x_2: W(x_2) -> P(x_2), forall x_2: P(x_2) -> W(x_2) we can infer exists x_2: W(x_2) <-> P(x_2) via existential biconditional introduction. From exists x_2: W(x_2) <-> P(x_2), forall x_2: ~W(x_2) we can infer exists x_2: ~P(x_2) via existential biconditional elimination. Finally, from forall x_2: P(x_2) or U(x_2), exists x_2: ~P(x_2) we can infer exists x_2: U(x_2) via existential disjunctive syllogism. Therefore, the answer is yes.