Consider the following premises. forall x_7: ~P_7(x_7). ~Q(a_3) or r. forall x_7: P_7(x_7) or Q(x_7). Can we infer Q_4(a_3) or r from them?
 From forall x_7: P_7(x_7) or Q(x_7), forall x_7: ~P_7(x_7) we can infer forall x_7: Q(x_7). From forall x_7: Q(x_7) we can infer forall x_7: Q(x_7) or Q_4(x_7). From forall x_7: Q(x_7) or Q_4(x_7) we can infer Q(a_3) or Q_4(a_3). Finally, from Q(a_3) or Q_4(a_3), ~Q(a_3) or r we can infer Q_4(a_3) or r. Therefore, the answer is yes.