Consider the following premises. forall x_6: ~P_6(x_6). forall x_6: P_6(x_6) <-> Q(x_6). exists x_6: ~P_3(x_6) or R_3(x_6). forall x_6: P_3(x_6) or Q(x_6). Can we infer forall x_6: ~R_3(x_6) from them?
 From forall x_6: P_6(x_6) <-> Q(x_6), forall x_6: ~P_6(x_6) we can infer forall x_6: ~Q(x_6). From forall x_6: P_3(x_6) or Q(x_6), exists x_6: ~P_3(x_6) or R_3(x_6) we can infer exists x_6: Q(x_6) or R_3(x_6). Finally, from exists x_6: Q(x_6) or R_3(x_6), forall x_6: ~Q(x_6) we can infer exists x_6: R_3(x_6), which contradicts forall x_6: ~R_3(x_6). Therefore, the answer is no.