Consider the following premises. forall x_14: T_2(x_14). exists x_14: ~Q_14(x_14). forall x_14: Q_14(x_14) -> T_2(x_14). forall x_14: T_2(x_14) <-> Q_14(x_14). Can we infer exists x_14: S_4(x_14) from them?
 From forall x_14: T_2(x_14) <-> Q_14(x_14) we can infer forall x_14: T_2(x_14) -> Q_14(x_14). From forall x_14: Q_14(x_14) -> T_2(x_14), forall x_14: T_2(x_14) -> Q_14(x_14) we can infer forall x_14: Q_14(x_14) <-> T_2(x_14). From forall x_14: Q_14(x_14) <-> T_2(x_14), exists x_14: ~Q_14(x_14) we can infer exists x_14: ~T_2(x_14). From forall x_14: T_2(x_14) we can infer forall x_14: T_2(x_14) or S_4(x_14). Finally, from forall x_14: T_2(x_14) or S_4(x_14), exists x_14: ~T_2(x_14) we can infer exists x_14: S_4(x_14). Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.