Consider the following premises. forall y_4: W(y_4) or Q_4(y_4). forall y_4: W(y_4) -> R_2(y_4). forall y_4: R_2(y_4) -> W(y_4). forall y_4: R_2(y_4) <-> Q_4(y_4). Can we infer exists y_4: ~R_2(y_4) from them?
 From forall y_4: W(y_4) -> R_2(y_4), forall y_4: R_2(y_4) -> W(y_4) we can infer forall y_4: W(y_4) <-> R_2(y_4). From forall y_4: R_2(y_4) <-> Q_4(y_4) we can infer forall y_4: Q_4(y_4) -> R_2(y_4). From forall y_4: W(y_4) <-> R_2(y_4) we can infer forall y_4: W(y_4) -> R_2(y_4). Finally, from forall y_4: W(y_4) -> R_2(y_4), forall y_4: Q_4(y_4) -> R_2(y_4), forall y_4: W(y_4) or Q_4(y_4) we can infer forall y_4: R_2(y_4), which contradicts exists y_4: ~R_2(y_4). Therefore, the answer is no.