Consider the following premises. exists x: W(x) or ~Q(x). forall x: U_2(x) -> U_4(x). forall x: U_4(x) -> Q(x). Can we infer exists x: U_2(x) -> W(x) from them? If possible, name the inference rules being used at each step.
 From exists x: W(x) or ~Q(x) we can infer exists x: Q(x) -> W(x) via existential rewriting. From forall x: U_4(x) -> Q(x), exists x: Q(x) -> W(x) we can infer exists x: U_4(x) -> W(x) via existential transitivity. Finally, from forall x: U_2(x) -> U_4(x), exists x: U_4(x) -> W(x) we can infer exists x: U_2(x) -> W(x) via existential transitivity. Therefore, the answer is yes.