Consider the following premises. forall y: ~U(y). forall y: W_4(y) -> Q_2(y). forall y: U(y) -> W_4(y). forall y: W_4(y) -> U(y). exists y: Q_2(y) -> W_4(y). Can we infer exists y: ~Q_2(y) from them?
 From forall y: W_4(y) -> U(y), forall y: U(y) -> W_4(y) we can infer forall y: W_4(y) <-> U(y). From forall y: W_4(y) -> Q_2(y), exists y: Q_2(y) -> W_4(y) we can infer exists y: W_4(y) <-> Q_2(y). From forall y: W_4(y) <-> U(y), forall y: ~U(y) we can infer forall y: ~W_4(y). Finally, from exists y: W_4(y) <-> Q_2(y), forall y: ~W_4(y) we can infer exists y: ~Q_2(y). Therefore, the answer is yes.