Consider the following premises. forall y_2: Q_3(y_2) or S_4(y_2). forall y_2: R(y_2). forall y_2: Q(y_2) <-> Q_3(y_2). exists y_2: ~Q(y_2). Can we infer forall y_2: ~(R(y_2) and S_4(y_2)) from them?
 From forall y_2: Q(y_2) <-> Q_3(y_2), exists y_2: ~Q(y_2) we can infer exists y_2: ~Q_3(y_2). From forall y_2: Q_3(y_2) or S_4(y_2), exists y_2: ~Q_3(y_2) we can infer exists y_2: S_4(y_2). Finally, from forall y_2: R(y_2), exists y_2: S_4(y_2) we can infer exists y_2: R(y_2) and S_4(y_2), which contradicts forall y_2: ~(R(y_2) and S_4(y_2)). Therefore, the answer is no.