Consider the following premises. forall x_18: ~P_18(x_18). forall x_18: Q_13(x_18) -> Q_18(x_18). forall x_18: Q_4(x_18) <-> Q_13(x_18). forall x_18: P_18(x_18) <-> Q_18(x_18). exists x_18: Q_18(x_18) -> Q_13(x_18). Can we infer exists x_18: ~Q_4(x_18) from them?
 From forall x_18: P_18(x_18) <-> Q_18(x_18) we can infer forall x_18: Q_18(x_18) -> P_18(x_18). From exists x_18: Q_18(x_18) -> Q_13(x_18), forall x_18: Q_13(x_18) -> Q_18(x_18) we can infer exists x_18: Q_18(x_18) <-> Q_13(x_18). From forall x_18: Q_18(x_18) -> P_18(x_18), forall x_18: ~P_18(x_18) we can infer forall x_18: ~Q_18(x_18). From exists x_18: Q_18(x_18) <-> Q_13(x_18), forall x_18: ~Q_18(x_18) we can infer exists x_18: ~Q_13(x_18). Finally, from forall x_18: Q_4(x_18) <-> Q_13(x_18), exists x_18: ~Q_13(x_18) we can infer exists x_18: ~Q_4(x_18). Therefore, the answer is yes.