These people are demonstrating for their leader.
People are marching with signs.
Demonstrating for their leader does not mean that they are marching with signs.
exists e1 x1 x2.(n_leader(x2) & of(x2,x1) & n_thing(x1) & n_people(x1) & for(e1,x2) & Actor(e1,x1) & v_demonstrate(e1))
exists e1 x1 x2.(with(e1,x2) & n_sign(x2) & Actor(e1,x1) & v_march(e1) & n_people(x1))