Consider the following premises. forall y_2: T(y_2). exists y_2: ~S_2(y_2). forall y_2: S_2(y_2) or P_3(y_2). Can we infer forall y_2: ~(P_3(y_2) and T(y_2)) from them?
 From forall y_2: S_2(y_2) or P_3(y_2), exists y_2: ~S_2(y_2) we can infer exists y_2: P_3(y_2). Finally, from exists y_2: P_3(y_2), forall y_2: T(y_2) we can infer exists y_2: P_3(y_2) and T(y_2), which contradicts forall y_2: ~(P_3(y_2) and T(y_2)). Therefore, the answer is no.