I think the "Using a computer program with board games" and the 3.16 rule contradict themselves.

Quoting the two rules:

Using a computer to decide your moves in a board game (specifically chess, checkers, reversi, gomoku, nine men's morris, go, four in a row, pente and backgammon) on FlyOrDie is allowed.
FlyOrDie members have the right to know if they are playing against a computer. Therefore FlyOrDie uses a system to detect suspected program use, which will be indicated on the concerned players' info screen with a small icon. 

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The following are not tolerated: 
3.16 Using, developing, promoting, or communicating the existence of a program that grants the user unnatural or unintended benefits in game or that alters performance of the game.

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In my opinion any kind of non-human activity in the games should be a bannable offense.