A lead singer is singing with a band on stage.
A perform sings on stage by herself.
The lead singer, though this singer may be female, is with a band.  The next singer on stage is alone and not with a band.
exists e1 x1 x2 x3 x4.(with(e1,x3) & on(x3,x4) & n_stage(x4) & n_band(x3) & Actor(e1,x1) & v_sing(e1) & n_singer(x1) & of(x1,x2) & n_lead(x2))
exists e1 x1 x2 x3.(by(e1,x1) & n_female(x1) & on(e1,x3) & n_stage(x3) & Theme(e1,x2) & Actor(e1,x1) & v_perform(e1) & n_sing(x2) & n_a(x1))