Consider the following premises. forall x_5: ~Q_1(x_5). forall x_5: T(x_5). forall x_5: T(x_5) -> Q_1(x_5). Can we infer forall x_5: S(x_5) from them?
 From forall x_5: T(x_5) we can infer forall x_5: T(x_5) or S(x_5). From forall x_5: T(x_5) -> Q_1(x_5), forall x_5: ~Q_1(x_5) we can infer forall x_5: ~T(x_5). Finally, from forall x_5: T(x_5) or S(x_5), forall x_5: ~T(x_5) we can infer forall x_5: S(x_5). Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.