Consider the following premises. forall x_6: ~P_6(x_6) or R_5(x_6). forall x_6: P_6(x_6). ~Q_6(a_3). Can we infer ~R_5(a_3) from them?
 From forall x_6: P_6(x_6) we can infer forall x_6: P_6(x_6) or Q_6(x_6). From forall x_6: P_6(x_6) or Q_6(x_6), forall x_6: ~P_6(x_6) or R_5(x_6) we can infer forall x_6: Q_6(x_6) or R_5(x_6). From forall x_6: Q_6(x_6) or R_5(x_6) we can infer Q_6(a_3) or R_5(a_3). Finally, from Q_6(a_3) or R_5(a_3), ~Q_6(a_3) we can infer R_5(a_3), which contradicts ~R_5(a_3). Therefore, the answer is no.