Consider the following premises. forall x_12: P_4(x_12) and Q_7(x_12). forall x_12: W_3(x_12) <-> P_4(x_12). exists x_12: T(x_12). Can we infer exists x_12: T(x_12) and W_3(x_12) from them?
 From forall x_12: W_3(x_12) <-> P_4(x_12) we can infer forall x_12: P_4(x_12) -> W_3(x_12). From forall x_12: P_4(x_12) and Q_7(x_12) we can infer forall x_12: P_4(x_12). From forall x_12: P_4(x_12) -> W_3(x_12), forall x_12: P_4(x_12) we can infer forall x_12: W_3(x_12). Finally, from exists x_12: T(x_12), forall x_12: W_3(x_12) we can infer exists x_12: T(x_12) and W_3(x_12). Therefore, the answer is yes.