Consider the following premises. forall y: P(y). forall y: S(y) or W(y). forall y: W(y) -> R(y). forall y: ~S(y) or Q_1(y). forall y: R(y) or ~Q_1(y). Can we infer exists y: ~(R(y) and P(y)) from them?
 From forall y: R(y) or ~Q_1(y) we can infer forall y: Q_1(y) -> R(y). From forall y: S(y) or W(y), forall y: ~S(y) or Q_1(y) we can infer forall y: W(y) or Q_1(y). From forall y: W(y) -> R(y), forall y: Q_1(y) -> R(y), forall y: W(y) or Q_1(y) we can infer forall y: R(y). Finally, from forall y: R(y), forall y: P(y) we can infer forall y: R(y) and P(y), which contradicts exists y: ~(R(y) and P(y)). Therefore, the answer is no.