Consider the following premises. forall x_10: Q_10(x_10). exists x_10: P_7(x_10) <-> P_10(x_10). forall x_10: P_10(x_10) -> ~Q_10(x_10). forall x_10: T_3(x_10) <-> P_7(x_10). Can we infer forall x_10: T_3(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> ~Q_10(x_10), forall x_10: Q_10(x_10) we can infer forall x_10: ~P_10(x_10) via universal modus tollens. From exists x_10: P_7(x_10) <-> P_10(x_10), forall x_10: ~P_10(x_10) we can infer exists x_10: ~P_7(x_10) via existential biconditional elimination. Finally, from forall x_10: T_3(x_10) <-> P_7(x_10), exists x_10: ~P_7(x_10) we can infer exists x_10: ~T_3(x_10) via existential biconditional elimination, which contradicts forall x_10: T_3(x_10). Therefore, the answer is no.