Consider the following premises. forall x_6: U_1(x_6) <-> Q(x_6). exists x_6: ~P_6(x_6). forall x_6: P_6(x_6) <-> U_1(x_6). Can we infer exists x_6: ~Q(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) <-> U_1(x_6), exists x_6: ~P_6(x_6) we can infer exists x_6: ~U_1(x_6) via existential biconditional elimination. Finally, from forall x_6: U_1(x_6) <-> Q(x_6), exists x_6: ~U_1(x_6) we can infer exists x_6: ~Q(x_6) via existential biconditional elimination. Therefore, the answer is yes.