(Suppose my initials were DC.)
If I (DC) win the game, then nobody can truthfully think to themselves 'I win the game iff DC wins the game'. (Here, 'the game' is defined so that whoever thinks about the game loses.)
Apparently the argument that proves this is 'ingenious'. Yep, even though it leaps out at you within a split-second.
[Yeah, OK, so I'm a bitter, twisted, failure of a human being. I know that already, and I'm sure it comes through very clearly. But damn - something's going wrong somewhere if trivialities like this constitute publishable research.]