Definition ZWitness := Psatz Z.Definition ZWeakChecker := check_normalised_formulas 0 1 Z.add Z.mul Zeq_bool Z.leb.

Lemma ZWeakChecker_sound : forall (l : list (NFormula Z)) (cm : ZWitness), ZWeakChecker l cm = true -> forall env, make_impl (eval_nformula env) l False.