Consider the following premises. forall y: W_1(y) -> Q_2(y). forall y: P_4(y) <-> Q_2(y). forall y: ~W_1(y). forall y: Q_2(y) -> W_1(y). Can we infer exists y: P_4(y) from them?
 From forall y: W_1(y) -> Q_2(y), forall y: Q_2(y) -> W_1(y) we can infer forall y: W_1(y) <-> Q_2(y). From forall y: W_1(y) <-> Q_2(y), forall y: ~W_1(y) we can infer forall y: ~Q_2(y). Finally, from forall y: P_4(y) <-> Q_2(y), forall y: ~Q_2(y) we can infer forall y: ~P_4(y), which contradicts exists y: P_4(y). Therefore, the answer is no.