Consider the following premises. R_10(i) <-> r_2. Q_2(i) -> r_2. forall x_10: P_10(x_10) or Q_2(x_10). forall x_10: ~P_10(x_10) or R_10(x_10). Can we infer ~r_2 from them?
 From forall x_10: P_10(x_10) or Q_2(x_10), forall x_10: ~P_10(x_10) or R_10(x_10) we can infer forall x_10: Q_2(x_10) or R_10(x_10). From forall x_10: Q_2(x_10) or R_10(x_10) we can infer Q_2(i) or R_10(i). From R_10(i) <-> r_2 we can infer R_10(i) -> r_2. Finally, from Q_2(i) -> r_2, R_10(i) -> r_2, Q_2(i) or R_10(i) we can infer r_2, which contradicts ~r_2. Therefore, the answer is no.