Consider the following premises. forall x_1: Q_2(x_1) or ~T_1(x_1). forall x_1: ~Q_2(x_1). exists x_1: S(x_1) -> T_1(x_1). Can we infer exists x_1: ~S(x_1) from them?
 From forall x_1: Q_2(x_1) or ~T_1(x_1) we can infer forall x_1: T_1(x_1) -> Q_2(x_1). From forall x_1: T_1(x_1) -> Q_2(x_1), forall x_1: ~Q_2(x_1) we can infer forall x_1: ~T_1(x_1). Finally, from exists x_1: S(x_1) -> T_1(x_1), forall x_1: ~T_1(x_1) we can infer exists x_1: ~S(x_1). Therefore, the answer is yes.