A baby sits in a smiling woman's lap.
There is a woman with a child.
To say a there is a woman with a child implies a close physical relationship, as would be the case if a baby sits on the woman's lap. A child implies someone of a young age, such as a baby.
exists e2 e1 x1 x2 x3.(in(e1,x3) & n_lap(x3) & of(x3,x2) & n_woman(x2) & Actor(e2,x2) & v_smile(e2) & Actor(e1,x1) & v_sit(e1) & n_baby(x1))
exists p1 x1 x2 x3.((x1 = x2) & with(x2,x3) & n_child(x3) & n_woman(x2))