A soccer game or a football game
Both soccer and football are popular.
The soccer and football game might not be popular. It can't be implied.
(exists x1 x2.(a_topic(x1) & n_game(x1) & of(x1,x2) & n_soccer(x2)) | exists x3 x4.(a_topic(x3) & n_game(x3) & of(x3,x4) & n_football(x4)))
exists s1 x1 x2 x3.(n_football(x3) & n_soccer(x2) & subset_of(x3,x1) & subset_of(x2,x1) & Theme(s1,x1) & a_popular(s1))