Processing error with processing-arduino examples
Note: I am testing this on OS X, so my paths may differ slightly from yours.


I have managed to reproduce your issue, by incorrectly copying the arduino directory, from the unzipped processing2-arduino.zip package, to the libraries directory under the Arduino directory in my home directory, thus 

/Users/user/Documents/Arduino/libraries/arduino


Then opening the Arduino IDE and running the arduino_output example, via the menu, File -&gt; Sketchbook -&gt; Libraries -&gt; Arduino -&gt; arduino_output. When I hit the compile button, in the Arduino IDE, the compiler throws up the exact same errors that you describe in your question.

However this is not the correct usage of this package. This package is intended to be used in conjunction with the Processing application, not the Arduino IDE. You should download Processing and then follow the instructions again:


  
  Unzip the library and copy the "arduino" folder into the "libraries" sub-folder of your Processing Sketchbook. (You can find
  the location of your Sketchbook by opening the Processing Preferences.
  If you haven't made a "libraries" sub-folder, create one.)
  


Thus, on OS X, the path should now be 

/Users/user/Documents/Processing/libraries/arduino


However, as usual, the documentation on the Arduino website leaves a lot to be desired. Pay careful attention to the following paragraph if you are running OS X or Linux:


  Note: if you run Linux, you need to change Arduino.jar into
  arduino.jar, because Linux is case sensitive and it does not work if
  you don't change this letter (Arduino.jar is in the folder "library"
  of this Processing Library).


So, 

/Users/user/Documents/Arduino/libraries/arduino/library/Arduino.jar


becomes

/Users/user/Documents/Arduino/libraries/arduino/library/arduino.jar


Relaunch the Processing application. File -&gt; Examples..., opens up a window, scroll down to Contributed Libraries, open that, open Arduino (Firmata), open the arduino_output example. Hit the Run button, and after compiling you should see the window below:



HTH.