two dancers dance together.
Two dancers perform together during a competition.
Just because two dancers dance doesn't mean they are in a competition.
exists e1 p1 x1.(exists s1.(Theme(s1,x1) & a_together(s1)) & Topic(e1,p1) & Actor(e1,x1) & v_dance(e1) & n_dancer(x1) & card_eq_2(x1))
exists e1 s1 x1 x2.(during(e1,x2) & n_competition(x2) & a_together(s1) & Manner(e1,s1) & Actor(e1,x1) & v_perform(e1) & n_dancer(x1) & card_eq_2(x1))