A girl imagined that the cake was given to Liam .
* cake ( x _ 5 ) ; girl ( x _ 1 ) AND imagine . agent ( x _ 2 , x _ 1 ) AND imagine . ccomp ( x _ 2 , x _ 7 ) AND give . theme ( x _ 7 , x _ 5 ) AND give . recipient ( x _ 7 , Liam )