There are trees with no leaves in the background.
There are trees
The tree with no leaves
exists p1 x1 x4.(n_background(x4) & exists x2.(-exists x3.((x1 = x2) & with(x2,x3) & in(x3,x4) & n_leaf(x3)) & n_tree(x2)))
exists p1 x1 x2.((x1 = x2) & n_tree(x2))