Indeed. The file should be located at
www.yourdomain.com/robot.txt . Right in your root assuming that you have that access. That is where Google, as well as other well behaved bots will look for it. It gets more complicated if you are on a shared server through a provider that gives you a default address such as
www.sharedservercompany.com/yourusername or something similar. In that situation, you would require you host to assist if they are able.
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Curiously,
Within your code you do not have a "forums/" prefix on your items. That would be required if your forum was located within a forums folder in the root, correct?