The dog leaps to catch the Frisbee.
A dog is competing in a dog show.
There is no evidence in sentence one that the dog catching the Frisbee was competing in a dog show.  The dog could have been on the beach or in his backyard.
exists e1 p1 x1 x2.(ne_geo_frisbee(x2) & n_dog(x1) & Topic(e1,p1) & Actor(e1,x1) & v_leap(e1) & exists e2.(Theme(e2,x2) & Actor(e2,x1) & v_catch(e2)))
exists e1 x1 x2 x3.(in(e1,x2) & n_show(x2) & of(x2,x3) & n_dog(x3) & Actor(e1,x1) & v_compete(e1) & n_dog(x1))