Consider the following premises. forall x_13: P_7(x_13) -> Q_7(x_13). forall x_13: ~P_6(x_13) or P_7(x_13). forall x_13: Q_7(x_13) -> Q_13(x_13). forall x_13: Q_6(x_13) -> P_13(x_13). forall x_13: P_13(x_13) <-> Q_13(x_13). forall x_13: P_6(x_13) or Q_6(x_13). Can we infer forall x_13: Q_13(x_13) from them?
 From forall x_13: P_13(x_13) <-> Q_13(x_13) we can infer forall x_13: P_13(x_13) -> Q_13(x_13). From forall x_13: P_7(x_13) -> Q_7(x_13), forall x_13: Q_7(x_13) -> Q_13(x_13) we can infer forall x_13: P_7(x_13) -> Q_13(x_13). From forall x_13: P_6(x_13) or Q_6(x_13), forall x_13: ~P_6(x_13) or P_7(x_13) we can infer forall x_13: Q_6(x_13) or P_7(x_13). From forall x_13: Q_6(x_13) -> P_13(x_13), forall x_13: P_13(x_13) -> Q_13(x_13) we can infer forall x_13: Q_6(x_13) -> Q_13(x_13). Finally, from forall x_13: Q_6(x_13) -> Q_13(x_13), forall x_13: P_7(x_13) -> Q_13(x_13), forall x_13: Q_6(x_13) or P_7(x_13) we can infer forall x_13: Q_13(x_13). Therefore, the answer is yes.