Using FOL
The set domain:
n s Set(s) (s = {} ) (x,s2 Set(s2) s = {x|s2})
n x,s {x|s} = {}
n x,s x s s = {x|s}
n x,s x s [ y,s2} (s = {y|s2} (x = y x s2))]
n s1,s2 s1 s2 (x x s1 x s2)
n s1,s2 (s1 = s2) (s1 s2 s2 s1)
n x,s1,s2 x (s1 s2) (x s1 x s2)
n x,s1,s2 x (s1 s2) (x s1 x s2)