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