David believed that Olivia offered the crystal to a girl .
* crystal ( x _ 6 ) ; believe . agent ( x _ 1 , David ) AND believe . ccomp ( x _ 1 , x _ 4 ) AND offer . agent ( x _ 4 , Olivia ) AND offer . theme ( x _ 4 , x _ 6 ) AND offer . recipient ( x _ 4 , x _ 9 ) AND girl ( x _ 9 )