Consider the following premises. Q_11(a_1). forall x: S(x) or ~Q_11(x). Can we infer exists x: S(x) from them?
 From forall x: S(x) or ~Q_11(x) we can infer forall x: Q_11(x) -> S(x). From Q_11(a_1) we can infer exists x: Q_11(x). Finally, from forall x: Q_11(x) -> S(x), exists x: Q_11(x) we can infer exists x: S(x). Therefore, the answer is yes.