Consider the following premises. forall x_2: ~P_2(x_2) or R_2(x_2). forall x_2: ~Q_2(x_2) or R(x_2). forall x_2: P_2(x_2) or Q_2(x_2). Can we infer exists x_2: ~(R_2(x_2) or R(x_2)) from them?
 From forall x_2: P_2(x_2) or Q_2(x_2), forall x_2: ~P_2(x_2) or R_2(x_2) we can infer forall x_2: Q_2(x_2) or R_2(x_2). Finally, from forall x_2: Q_2(x_2) or R_2(x_2), forall x_2: ~Q_2(x_2) or R(x_2) we can infer forall x_2: R_2(x_2) or R(x_2), which contradicts exists x_2: ~(R_2(x_2) or R(x_2)). Therefore, the answer is no.