Consider the following premises. exists x_7: U_2(x_7). forall x_7: Q(x_7). forall x_7: Q(x_7) <-> W_4(x_7). Can we infer exists x_7: U_2(x_7) and W_4(x_7) from them?
 From forall x_7: Q(x_7) <-> W_4(x_7) we can infer forall x_7: Q(x_7) -> W_4(x_7). From forall x_7: Q(x_7) -> W_4(x_7), forall x_7: Q(x_7) we can infer forall x_7: W_4(x_7). Finally, from exists x_7: U_2(x_7), forall x_7: W_4(x_7) we can infer exists x_7: U_2(x_7) and W_4(x_7). Therefore, the answer is yes.