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I've heard that if they say "You cannot enter this competition" it means that they have banned you from these competitions for whatever reason. I can't say for sure, but that's what I think happened for you.
I finished 1726 with 24-6 and 12th/1209 place in the world, but I'm in Junior Division so it's not impressive -w-
I ended up getting matched up with way too many low-ranking players, so I didn't get very many high-quality battles. I didn't really see that many of the Top 12 Pokemon either...
Actually that is probably not the case; Pure Power in Japanese is "Yoga Power" according to Bulbapedia. That also explains why a thing like Medicham has Pure Power.
I guess Alakazam went to the gym?
Ability with move compatibility needs to be considered when checking if a pokemon is legal. Since Gen IV introduced the Ability Capsule, new combinations (in my case, HA Lickilicky with Gen III event move Wish) can be made.