Consider the following premises. exists x_7: T(x_7). forall x_7: P_7(x_7) <-> P(x_7). forall x_7: P_7(x_7). Can we infer forall x_7: ~(P(x_7) and T(x_7)) from them? If possible, name the inference rules being used at each step.
 From forall x_7: P_7(x_7) <-> P(x_7) we can infer forall x_7: P_7(x_7) -> P(x_7) via universal biconditional elimination. From forall x_7: P_7(x_7) -> P(x_7), forall x_7: P_7(x_7) we can infer forall x_7: P(x_7) via universal modus ponens. Finally, from forall x_7: P(x_7), exists x_7: T(x_7) we can infer exists x_7: P(x_7) and T(x_7) via existential conjunction, which contradicts forall x_7: ~(P(x_7) and T(x_7)). Therefore, the answer is no.