Consider the following premises. exists x: Q(x). forall x: S_4(x) <-> U_2(x). forall x: S_4(x) <-> Q(x). Can we infer exists x: U_2(x) from them?
 From forall x: S_4(x) <-> Q(x) we can infer forall x: Q(x) -> S_4(x). From forall x: S_4(x) <-> U_2(x) we can infer forall x: S_4(x) -> U_2(x). From forall x: Q(x) -> S_4(x), forall x: S_4(x) -> U_2(x) we can infer forall x: Q(x) -> U_2(x). Finally, from forall x: Q(x) -> U_2(x), exists x: Q(x) we can infer exists x: U_2(x). Therefore, the answer is yes.