Consider the following premises. forall x_12: T(x_12) <-> R(x_12). exists x_12: ~T(x_12). forall x_12: R(x_12) <-> P(x_12). Can we infer exists x_12: ~P(x_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: T(x_12) <-> R(x_12) we can infer forall x_12: R(x_12) -> T(x_12) via universal biconditional elimination. From forall x_12: R(x_12) -> T(x_12), exists x_12: ~T(x_12) we can infer exists x_12: ~R(x_12) via existential modus tollens. Finally, from forall x_12: R(x_12) <-> P(x_12), exists x_12: ~R(x_12) we can infer exists x_12: ~P(x_12) via existential biconditional elimination. Therefore, the answer is yes.