Consider the following premises. exists x_11: P_7(x_11) <-> P(x_11). forall x_11: P_11(x_11). forall x_11: P_11(x_11) -> P(x_11). forall x_11: ~P_7(x_11). Can we infer exists x_11: Q_1(x_11) from them?
 From forall x_11: P_11(x_11) -> P(x_11), forall x_11: P_11(x_11) we can infer forall x_11: P(x_11). From exists x_11: P_7(x_11) <-> P(x_11), forall x_11: ~P_7(x_11) we can infer exists x_11: ~P(x_11). From forall x_11: P(x_11) we can infer forall x_11: P(x_11) or Q_1(x_11). Finally, from forall x_11: P(x_11) or Q_1(x_11), exists x_11: ~P(x_11) we can infer exists x_11: Q_1(x_11). Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.