Men ride on horses while carrying flags.
The men are carrying French flags.
Men ride on horses while carrying flags does not indicate that they are carrying French flags.
(x)
exists e1 s1 x1 x2.(n_man(x1) & Theme(e1,x2) & Actor(e1,x1) & v_carry(e1) & n_flag(x2) & a_french(s1) & Theme(s1,x2))