Consider the following premises. forall x_12: P_12(x_12) <-> Q_12(x_12). forall x_12: W_3(x_12) -> P_5(x_12). forall x_12: P_5(x_12) -> Q_12(x_12). forall x_12: ~P_12(x_12). Can we infer forall x_12: ~W_3(x_12) from them?
 From forall x_12: P_12(x_12) <-> Q_12(x_12) we can infer forall x_12: Q_12(x_12) -> P_12(x_12). From forall x_12: P_5(x_12) -> Q_12(x_12), forall x_12: Q_12(x_12) -> P_12(x_12) we can infer forall x_12: P_5(x_12) -> P_12(x_12). From forall x_12: W_3(x_12) -> P_5(x_12), forall x_12: P_5(x_12) -> P_12(x_12) we can infer forall x_12: W_3(x_12) -> P_12(x_12). Finally, from forall x_12: W_3(x_12) -> P_12(x_12), forall x_12: ~P_12(x_12) we can infer forall x_12: ~W_3(x_12). Therefore, the answer is yes.