A man is barrel racing on a brown horse.
The man is racing on a horse
"Is barrel racing on a brown horse" is a rephrasing of "is racing on a horse".
exists p1 x1.(exists s1 x2 x3 x4.((x1 = x2) & on(x2,x4) & n_horse(x4) & a_brown(s1) & Theme(s1,x4) & n_racing(x2) & of(x2,x3) & n_barrel(x3)) & n_man(x1))
exists e1 x1 x2.(n_man(x1) & on(e1,x2) & n_horse(x2) & Actor(e1,x1) & v_race(e1))