Consider the following premises. forall z_4: Q_4(z_4) -> Q(z_4). forall z_4: T_2(z_4) -> T_1(z_4). exists z_4: T_1(z_4) <-> Q(z_4). forall z_4: ~Q_4(z_4). forall z_4: T_1(z_4) -> T_2(z_4). forall z_4: Q(z_4) -> Q_4(z_4). Can we infer exists z_4: ~T_2(z_4) from them?
 From forall z_4: Q_4(z_4) -> Q(z_4), forall z_4: Q(z_4) -> Q_4(z_4) we can infer forall z_4: Q_4(z_4) <-> Q(z_4). From forall z_4: Q_4(z_4) <-> Q(z_4), forall z_4: ~Q_4(z_4) we can infer forall z_4: ~Q(z_4). From forall z_4: T_1(z_4) -> T_2(z_4), forall z_4: T_2(z_4) -> T_1(z_4) we can infer forall z_4: T_1(z_4) <-> T_2(z_4). From exists z_4: T_1(z_4) <-> Q(z_4), forall z_4: ~Q(z_4) we can infer exists z_4: ~T_1(z_4). Finally, from forall z_4: T_1(z_4) <-> T_2(z_4), exists z_4: ~T_1(z_4) we can infer exists z_4: ~T_2(z_4). Therefore, the answer is yes.