Consider the following premises. forall y: Q_2(y) -> U(y). exists y: ~S(y). forall y: U(y) -> Q_2(y). forall y: S(y) <-> Q_2(y). Can we infer forall y: U(y) from them?
 From forall y: S(y) <-> Q_2(y), exists y: ~S(y) we can infer exists y: ~Q_2(y). From forall y: Q_2(y) -> U(y), forall y: U(y) -> Q_2(y) we can infer forall y: Q_2(y) <-> U(y). Finally, from forall y: Q_2(y) <-> U(y), exists y: ~Q_2(y) we can infer exists y: ~U(y), which contradicts forall y: U(y). Therefore, the answer is no.