Consider the following premises. forall x_7: P_7(x_7) or Q_7(x_7). forall x_7: Q_7(x_7) -> W(x_7). forall x_7: Q(x_7). exists x_7: P_7(x_7) -> W(x_7). Can we infer exists x_7: W(x_7) and Q(x_7) from them?
 From exists x_7: P_7(x_7) -> W(x_7), forall x_7: Q_7(x_7) -> W(x_7), forall x_7: P_7(x_7) or Q_7(x_7) we can infer exists x_7: W(x_7). Finally, from exists x_7: W(x_7), forall x_7: Q(x_7) we can infer exists x_7: W(x_7) and Q(x_7). Therefore, the answer is yes.