Consider the following premises. forall y: Q_1(y) -> ~P(y). forall y: P(y). exists y: Q_1(y) or ~S(y). Can we infer forall y: S(y) from them?
 From forall y: Q_1(y) -> ~P(y), forall y: P(y) we can infer forall y: ~Q_1(y). From exists y: Q_1(y) or ~S(y) we can infer exists y: S(y) -> Q_1(y). Finally, from exists y: S(y) -> Q_1(y), forall y: ~Q_1(y) we can infer exists y: ~S(y), which contradicts forall y: S(y). Therefore, the answer is no.