Consider the following premises. forall x_1: T(x_1) -> T_4(x_1). forall x_1: T_4(x_1) or Q_3(x_1). forall x_1: T_4(x_1) -> T(x_1). forall x_1: Q_2(x_1). exists x_1: ~T(x_1). Can we infer exists x_1: Q_3(x_1) and Q_2(x_1) from them?
 From forall x_1: T(x_1) -> T_4(x_1), forall x_1: T_4(x_1) -> T(x_1) we can infer forall x_1: T(x_1) <-> T_4(x_1). From forall x_1: T(x_1) <-> T_4(x_1), exists x_1: ~T(x_1) we can infer exists x_1: ~T_4(x_1). From forall x_1: T_4(x_1) or Q_3(x_1), exists x_1: ~T_4(x_1) we can infer exists x_1: Q_3(x_1). Finally, from exists x_1: Q_3(x_1), forall x_1: Q_2(x_1) we can infer exists x_1: Q_3(x_1) and Q_2(x_1). Therefore, the answer is yes.