Consider the following premises. forall y: U(y) -> Q_1(y). forall y: Q_1(y) -> U(y). forall y: Q_1(y) -> U(y). forall y: Q_1(y) -> ~Q(y). forall y: Q(y). Can we infer forall y: ~U(y) from them?
 From forall y: Q_1(y) -> ~Q(y), forall y: Q(y) we can infer forall y: ~Q_1(y). From forall y: Q_1(y) -> U(y), forall y: U(y) -> Q_1(y) we can infer forall y: Q_1(y) <-> U(y). From forall y: Q_1(y) <-> U(y) we can infer forall y: U(y) -> Q_1(y). From forall y: U(y) -> Q_1(y), forall y: Q_1(y) -> U(y) we can infer forall y: U(y) <-> Q_1(y). Finally, from forall y: U(y) <-> Q_1(y), forall y: ~Q_1(y) we can infer forall y: ~U(y). Therefore, the answer is yes.