Consider the following premises. exists x_3: P(x_3) <-> Q(x_3). forall x_3: ~P_3(x_3). forall x_3: P_3(x_3) <-> P(x_3). Can we infer forall x_3: Q(x_3) from them? If possible, name the inference rules being used at each step.
 From forall x_3: P_3(x_3) <-> P(x_3), forall x_3: ~P_3(x_3) we can infer forall x_3: ~P(x_3) via universal biconditional elimination. Finally, from exists x_3: P(x_3) <-> Q(x_3), forall x_3: ~P(x_3) we can infer exists x_3: ~Q(x_3) via existential biconditional elimination, which contradicts forall x_3: Q(x_3). Therefore, the answer is no.