Consider the following premises. forall x_14: T(x_14) -> Q_11(x_14). forall x_14: P_14(x_14) or T(x_14). forall x_14: P_11(x_14) <-> Q_11(x_14). forall x_14: ~P_14(x_14) or S_1(x_14). forall x_14: S_1(x_14) <-> P_11(x_14). Can we infer exists x_14: ~Q_11(x_14) from them?
 From forall x_14: P_14(x_14) or T(x_14), forall x_14: ~P_14(x_14) or S_1(x_14) we can infer forall x_14: T(x_14) or S_1(x_14). From forall x_14: P_11(x_14) <-> Q_11(x_14) we can infer forall x_14: P_11(x_14) -> Q_11(x_14). From forall x_14: S_1(x_14) <-> P_11(x_14) we can infer forall x_14: S_1(x_14) -> P_11(x_14). From forall x_14: S_1(x_14) -> P_11(x_14), forall x_14: P_11(x_14) -> Q_11(x_14) we can infer forall x_14: S_1(x_14) -> Q_11(x_14). Finally, from forall x_14: T(x_14) -> Q_11(x_14), forall x_14: S_1(x_14) -> Q_11(x_14), forall x_14: T(x_14) or S_1(x_14) we can infer forall x_14: Q_11(x_14), which contradicts exists x_14: ~Q_11(x_14). Therefore, the answer is no.