Specifically, what is the result of:
6.F.14. TEST CASE, SIMPLE CONVOY PARADOX

The most common paradox is when the attacked unit supports an attack on one of the convoying fleets.

England:
F London Supports F Wales - English Channel
F Wales - English Channel

France:
A Brest - London
F English Channel Convoys A Brest - London

IIRC Szykman is actually the name of a method of resolving any convoy paradox. We follow the Szykman method of cancelling any moves involved in the smallest convoy paradox chain which can be found.

To look up how our adjudicator handles individual test cases you can check http://phpdiplomacy.net/datc.php

(In this case: http://phpdiplomacy.net/datc/maps/614-largemap.png )

Interesting that you would read it that way, considering that the resolutions to the paradox is usually either

- the convoyed army moves but the dislodged fleet's support is not cut
OR
- the convoyed army just holds, and all other orders are carried out.

Neither of which matches your reading of the Adjudicator

I remember reading that in the software, paradoxes were resolved somehow, but I don't remember how.

Obviously, kestas is the VOA. :-)

Thanks to Szykman it's pretty simple;
- Find the smallest chain of moves which cannot be resolved.
- This chain will either be a chain of moves (A move to B, B move to C, C move to A), or a convoy paradox.
- If it's a chain of moves, all units move.
- If not it's a convoy paradox; all moves in the chain fail (this is the Szykman method of handling convoy paradoxes).


There are alternative methods to Szykman that are still used, since some adjudicators have trouble finding the shortest possible paradox chain. Our adjudicator makes finding the shortest chain particularly easy, so Szykman is perfect (plus the DATC recommends it)

Maybe we'll get lucky and Kruijswijk will show up to clarify things / show where I'm wrong

Yes, I show up.

Little mistake, only the convoying armies fail. A moving fleet could succeed and dislodge a convoying fleet (dependent on the situation).

For really deep information, look in my article of the Pouch:

http://www.diplom.org/Zine/S2009M/Kruijswijk/DipMath_Chp1.htm

The Szykman rule can be formulated in different ways. Currently I prefer to say, that the convoying fleet(s) part of the paradox, fail to participate in the convoy, while other orders are adjudicated as normal (it is formulated that way in the article, but on in the DATC). As consequence of this failure, the convoying army will not move or cut support.

I prefer this, because as I explain in the article, the resolution (not the existence) of the convoying army is not part of the paradox.

For other resolutions, see section 4.A.2. of the DATC. In early times, the 1982 rules was preferred, because it was easier to implement. After I published the DATC, most new adjudicators use the Szykman rule (which is better if one does not consider the ease of implementation).

Regards,

Lucas

So, in short, the convoy fails and the convoying fleet is dislodged. Oddly, I'd never actually encountered the situation in a game until yesterday.