Consider the following premises. exists x: S_4(x) or R_3(x). forall x: U_3(x) -> Q_2(x). forall x: Q_2(x) <-> S_4(x). forall x: R_3(x) -> U_3(x). Can we infer exists x: Q_2(x) from them?
 From forall x: Q_2(x) <-> S_4(x) we can infer forall x: S_4(x) -> Q_2(x). From forall x: R_3(x) -> U_3(x), forall x: U_3(x) -> Q_2(x) we can infer forall x: R_3(x) -> Q_2(x). Finally, from forall x: S_4(x) -> Q_2(x), forall x: R_3(x) -> Q_2(x), exists x: S_4(x) or R_3(x) we can infer exists x: Q_2(x). Therefore, the answer is yes.