Consider the following premises. forall y: W(y) <-> U_2(y). forall y: ~Q(y). forall y: U_4(y) <-> U_2(y). forall y: Q(y) <-> U_4(y). Can we infer exists y: W(y) from them?
 From forall y: Q(y) <-> U_4(y), forall y: ~Q(y) we can infer forall y: ~U_4(y). From forall y: U_4(y) <-> U_2(y), forall y: ~U_4(y) we can infer forall y: ~U_2(y). Finally, from forall y: W(y) <-> U_2(y), forall y: ~U_2(y) we can infer forall y: ~W(y), which contradicts exists y: W(y). Therefore, the answer is no.