Consider the following premises. forall x_7: W(x_7) -> Q(x_7). forall x_7: Q(x_7) -> W(x_7). forall x_7: U_1(x_7) <-> Q(x_7). forall x_7: Q_7(x_7). forall x_7: U_1(x_7) -> ~Q_7(x_7). Can we infer exists x_7: W(x_7) from them?
 From forall x_7: U_1(x_7) -> ~Q_7(x_7), forall x_7: Q_7(x_7) we can infer forall x_7: ~U_1(x_7). From forall x_7: W(x_7) -> Q(x_7), forall x_7: Q(x_7) -> W(x_7) we can infer forall x_7: W(x_7) <-> Q(x_7). From forall x_7: U_1(x_7) <-> Q(x_7), forall x_7: ~U_1(x_7) we can infer forall x_7: ~Q(x_7). Finally, from forall x_7: W(x_7) <-> Q(x_7), forall x_7: ~Q(x_7) we can infer forall x_7: ~W(x_7), which contradicts exists x_7: W(x_7). Therefore, the answer is no.