Consider the following premises. forall x_7: ~Q_7(x_7). exists x_7: P_7(x_7) or Q_7(x_7). forall x_7: ~P_7(x_7). Can we infer exists x_7: Q_1(x_7) from them?
 From exists x_7: P_7(x_7) or Q_7(x_7), forall x_7: ~P_7(x_7) we can infer exists x_7: Q_7(x_7). From exists x_7: Q_7(x_7) we can infer exists x_7: Q_7(x_7) or Q_1(x_7). Finally, from exists x_7: Q_7(x_7) or Q_1(x_7), forall x_7: ~Q_7(x_7) we can infer exists x_7: Q_1(x_7). Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.