Consider the following premises. forall y: Q_3(y) <-> R_4(y). forall y: P(y) -> U(y). forall y: ~W_4(y) or P(y). exists y: U(y) -> R_4(y). forall y: W_4(y) or Q_3(y). Can we infer forall y: ~R_4(y) from them?
 From forall y: P(y) -> U(y), exists y: U(y) -> R_4(y) we can infer exists y: P(y) -> R_4(y). From forall y: W_4(y) or Q_3(y), forall y: ~W_4(y) or P(y) we can infer forall y: Q_3(y) or P(y). From forall y: Q_3(y) <-> R_4(y) we can infer forall y: Q_3(y) -> R_4(y). Finally, from forall y: Q_3(y) -> R_4(y), exists y: P(y) -> R_4(y), forall y: Q_3(y) or P(y) we can infer exists y: R_4(y), which contradicts forall y: ~R_4(y). Therefore, the answer is no.