Consider the following premises. forall x_6: Q_4(x_6) -> P_1(x_6). forall x_6: P_4(x_6) -> P_1(x_6). forall x_6: P_4(x_6) or Q_4(x_6). forall x_6: P_6(x_6). exists x_6: P_6(x_6) -> Q_3(x_6). Can we infer exists x_6: Q_3(x_6) and P_1(x_6) from them?
 From exists x_6: P_6(x_6) -> Q_3(x_6), forall x_6: P_6(x_6) we can infer exists x_6: Q_3(x_6). From forall x_6: P_4(x_6) -> P_1(x_6), forall x_6: Q_4(x_6) -> P_1(x_6), forall x_6: P_4(x_6) or Q_4(x_6) we can infer forall x_6: P_1(x_6). Finally, from exists x_6: Q_3(x_6), forall x_6: P_1(x_6) we can infer exists x_6: Q_3(x_6) and P_1(x_6). Therefore, the answer is yes.