Consider the following premises. Q(a_1). forall y: S_4(y) or ~Q(y). Can we infer exists y: S_4(y) from them?
 From Q(a_1) we can infer exists y: Q(y). From forall y: S_4(y) or ~Q(y) we can infer forall y: Q(y) -> S_4(y). Finally, from forall y: Q(y) -> S_4(y), exists y: Q(y) we can infer exists y: S_4(y). Therefore, the answer is yes.