IntelliJ IDEA 12 not finding CodeIgniter classes, throwing errors

I'm using IntelliJ IDEA 12 to develop a PHP web application using the CodeIgniter framework. Due to the way CI instantiates objects and methods, IDEA thinks they don't exist when they're called:

As you can see, I get those annoying orange squigglies under every single CodeIgniter class/method I try to use.

Here's the code for the CI_Controller class, giving some insight into how they're creating the objects:

class CI_Controller {

    private static $instance;

    /**
     * Constructor
     */
    public function __construct()
    {
        self::$instance =& $this;

        // Assign all the class objects that were instantiated by the
        // bootstrap file (CodeIgniter.php) to local class variables
        // so that CI can run as one big super object.
        foreach (is_loaded() as $var => $class)
        {
            $this->$var =& load_class($class);
        }

        $this->load =& load_class('Loader', 'core');

        $this->load->initialize();

        log_message('debug', "Controller Class Initialized");
    }

    public static function &get_instance()
    {
        return self::$instance;
    }
}

Is there any way I can get IntelliJ IDEA to either ignore these errors (but not other errors), or get it to find the objects on its own?

Note: I used to use PHPStorm, a PHP IDE build on the IntelliJ IDEA platform, and it did the same thing when it came to CodeIgniter.