The spectators wear hats
The game goers were wearing hats.
Spectators would be game goers.
exists e1 x1 x2.(n_spectator(x1) & Theme(e1,x2) & Actor(e1,x1) & v_wear(e1) & n_hat(x2))
exists e1 x1 x2 x3.(n_goer(x1) & of(x1,x2) & n_game(x2) & Theme(e1,x3) & Actor(e1,x1) & v_wear(e1) & n_hat(x3))