A young boy smiles while holding a tube of toothpaste.
A kid likes to play with toothpaste in the bathroom.
Playing with toothpaste implies smearing it or using it in any capacity, not just holding the tube. The bathroom was not mentioned in the first sentence.
exists e2 e1 s1 x1 x2 x3.(while(e1,e2) & Theme(e2,x2) & Actor(e2,x1) & v_hold(e2) & of(x2,x3) & n_toothpaste(x3) & n_tube(x2) & Actor(e1,x1) & v_smile(e1) & n_boy(x1) & a_young(s1) & Theme(s1,x1))
exists e1 p1 x1 x3.(n_bathroom(x3) & Topic(e1,p1) & Actor(e1,x1) & v_like(e1) & exists e2 x2.(in(e2,x3) & with(e2,x2) & n_toothpaste(x2) & Actor(e2,x1) & v_play(e2)) & n_kid(x1))