Fixpoint cnf_checker (f : cnf) (l : list Witness)  {struct f}: bool :=
    match f with
    | nil => true
    | e::f => match l with
              | nil => false
              | c::l => match checker e c with
                        | true => cnf_checker f l
                        |   _  => false
                        end
              end
    end.

Lemma cnf_checker_sound : forall t w, cnf_checker t w = true -> forall env, eval_cnf env t.