The Mathematician learns if the Lunatic attacks a different player(s) than the real Demon attacked.
If the Storyteller is executed and the Atheist is in play: eliminate the Atheist, all other characters who died by execution this game are not eliminated.
If the game ends due to the Mayor's ability and no other characters were eliminated: retire the Mayor.
If the game ends due to the Slayer's ability and no other characters were eliminated: retire the Slayer.