code: def _check_satisfiability(self, extra_constraints=(), solver=None, model_callback=None):
          
          return 'SAT' if self.satisfiable(extra_constraints=extra_constraints, solver=solver, model_callback=model_callback) else 'UNSAT'
docs: This function does a constraint check and returns the solvers state
  
          :param solver:              The backend solver object.
          :param extra_constraints:   Extra constraints (as ASTs) to add to s for this solve
          :param model_callback:      a function that will be executed with recovered models (if any)
          :return:                    'SAT', 'UNSAT', or 'UNKNOWN'