title: Simplifying a 9 variable boolean expression
body: <p>I am trying to create a tic-tac-toe program as a mental exercise and I have the board states stored as booleans like so:</p>
  
  <p><a href="http://i.imgur.com/xBiuoAO.png" rel="noreferrer">http://i.imgur.com/xBiuoAO.png</a></p>
  
  <p>I would like to simplify this boolean expression...</p>
  
  <pre><code>(a&amp;b&amp;c) | (d&amp;e&amp;f) | (g&amp;h&amp;i) | (a&amp;d&amp;g) | (b&amp;e&amp;h) | (c&amp;f&amp;i) | (a&amp;e&amp;i) | (g&amp;e&amp;c)
  </code></pre>
  
  <p>My first thoughts were to use a <a href="http://en.wikipedia.org/wiki/Karnaugh_map" rel="noreferrer">Karnaugh Map</a> but there were no solvers online that supported 9 variables.</p>
  
  <p>and heres the question:</p>
  
  <p>First of all, how would I know if a boolean condition is already as simple as possible?</p>
  
  <p>and second: What is the above boolean condition simplified?</p>