Consider the following premises. forall x_4: T(x_4). exists x_4: T(x_4) -> T_3(x_4). Can we infer exists x_4: T_3(x_4) or S(x_4) from them?
 From exists x_4: T(x_4) -> T_3(x_4), forall x_4: T(x_4) we can infer exists x_4: T_3(x_4). Finally, from exists x_4: T_3(x_4) we can infer exists x_4: T_3(x_4) or S(x_4). Therefore, the answer is yes.