Consider the following premises. exists y: Q_1(y) -> R(y). forall y: R(y) -> Q(y). forall y: ~Q_1(y). forall y: T_1(y) -> R(y). forall y: Q(y) -> T_1(y). forall y: R(y) -> Q_1(y). Can we infer exists y: ~T_1(y) from them?
 From forall y: R(y) -> Q(y), forall y: Q(y) -> T_1(y) we can infer forall y: R(y) -> T_1(y). From forall y: R(y) -> Q_1(y), exists y: Q_1(y) -> R(y) we can infer exists y: R(y) <-> Q_1(y). From forall y: T_1(y) -> R(y), forall y: R(y) -> T_1(y) we can infer forall y: T_1(y) <-> R(y). From exists y: R(y) <-> Q_1(y), forall y: ~Q_1(y) we can infer exists y: ~R(y). Finally, from forall y: T_1(y) <-> R(y), exists y: ~R(y) we can infer exists y: ~T_1(y). Therefore, the answer is yes.