Consider the following premises. forall x_12: Q_12(x_12) -> W_2(x_12). forall x_12: W_2(x_12) <-> Q_12(x_12). forall x_12: W_2(x_12) <-> Q_8(x_12). exists x_12: ~Q_8(x_12). Can we infer exists x_12: ~Q_12(x_12) from them?
 From forall x_12: W_2(x_12) <-> Q_12(x_12) we can infer forall x_12: W_2(x_12) -> Q_12(x_12). From forall x_12: W_2(x_12) -> Q_12(x_12), forall x_12: Q_12(x_12) -> W_2(x_12) we can infer forall x_12: W_2(x_12) <-> Q_12(x_12). From forall x_12: W_2(x_12) <-> Q_8(x_12), exists x_12: ~Q_8(x_12) we can infer exists x_12: ~W_2(x_12). Finally, from forall x_12: W_2(x_12) <-> Q_12(x_12), exists x_12: ~W_2(x_12) we can infer exists x_12: ~Q_12(x_12). Therefore, the answer is yes.