Consider the following premises. forall x_13: P_13(x_13) -> Q_6(x_13). forall x_13: ~P_13(x_13). forall x_13: P_13(x_13) <-> Q_13(x_13). exists x_13: W(x_13) <-> Q_13(x_13). forall x_13: Q_6(x_13) -> Q_13(x_13). Can we infer exists x_13: ~W(x_13) from them?
 From forall x_13: P_13(x_13) <-> Q_13(x_13) we can infer forall x_13: Q_13(x_13) -> P_13(x_13). From forall x_13: P_13(x_13) -> Q_6(x_13), forall x_13: Q_6(x_13) -> Q_13(x_13) we can infer forall x_13: P_13(x_13) -> Q_13(x_13). From forall x_13: Q_13(x_13) -> P_13(x_13), forall x_13: P_13(x_13) -> Q_13(x_13) we can infer forall x_13: Q_13(x_13) <-> P_13(x_13). From forall x_13: Q_13(x_13) <-> P_13(x_13), forall x_13: ~P_13(x_13) we can infer forall x_13: ~Q_13(x_13). Finally, from exists x_13: W(x_13) <-> Q_13(x_13), forall x_13: ~Q_13(x_13) we can infer exists x_13: ~W(x_13). Therefore, the answer is yes.