Consider the following premises. exists x_6: S(x_6) -> Q_6(x_6). forall x_6: ~Q_5(x_6). forall x_6: Q_5(x_6) -> S(x_6). forall x_6: S(x_6) -> Q_5(x_6). forall x_6: Q_6(x_6) -> S(x_6). Can we infer exists x_6: ~Q_6(x_6) from them?
 From exists x_6: S(x_6) -> Q_6(x_6), forall x_6: Q_6(x_6) -> S(x_6) we can infer exists x_6: S(x_6) <-> Q_6(x_6). From forall x_6: S(x_6) -> Q_5(x_6), forall x_6: Q_5(x_6) -> S(x_6) we can infer forall x_6: S(x_6) <-> Q_5(x_6). From forall x_6: S(x_6) <-> Q_5(x_6), forall x_6: ~Q_5(x_6) we can infer forall x_6: ~S(x_6). Finally, from exists x_6: S(x_6) <-> Q_6(x_6), forall x_6: ~S(x_6) we can infer exists x_6: ~Q_6(x_6). Therefore, the answer is yes.