%---------------- SGGS v1.0 (IJCAR 2020 submission) ----------------%

------ Parsing...successful


------ Proving...
use I-
not ground preserving

Gamma_0: (extend-no-conflict)
  0: difference(X0,X1,X2), [member(k(X0,X1,X2),
X2)], member(k(X0,X1,X2),X0)

Gamma_1: (extend-no-conflict)
  0: difference(X0,X1,X2), [member(k(X0,X1,X2),
X2)], member(k(X0,X1,X2),X0)
  1: difference(X0,X1,X0), ~(member(k(X0,X1,X0),X0)), [member(k(X0,X1,X0),
X1)]

Gamma_2: (right-split)
  0: difference(X0,X1,X2), [member(k(X0,X1,X2),
X2)], member(k(X0,X1,X2),X0)
  1: X0 != X1 | difference(X0,X1,X0), ~(member(k(X0,X1,X0),X0)), [member(
k(X0,X1,X0),X1)]

Gamma_3: (extend-no-conflict)
  0: difference(X0,X1,X2), [member(k(X0,X1,X2),
X2)], member(k(X0,X1,X2),X0)
  1: X0 != X1 | difference(X0,X1,X0), ~(member(k(X0,X1,X0),X0)), [member(
k(X0,X1,X0),X1)]
  2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1)

Gamma_4: (extend-no-conflict)
  0: difference(X0,X1,X2), [member(k(X0,X1,X2),
X2)], member(k(X0,X1,X2),X0)
  1: X0 != X1 | difference(X0,X1,X0), ~(member(k(X0,X1,X0),X0)), [member(
k(X0,X1,X0),X1)]
  2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1)
  3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)]

Gamma_5: (extend-no-conflict)
  0: difference(X0,X1,X2), [member(k(X0,X1,X2),
X2)], member(k(X0,X1,X2),X0)
  1: X0 != X1 | difference(X0,X1,X0), ~(member(k(X0,X1,X0),X0)), [member(
k(X0,X1,X0),X1)]
  2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1)
  3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)]
  4: [equal_sets(X0,X0)], ~(subset(X0,X0))
  0: difference(X0,X1,X2), [member(k(X0,X1,X2),X2)], member(k(X0,X1,X2),
X0)
  1: X0 != X1 | difference(X0,X1,X0), ~(member(k(X0,X1,X0),X0)), [member(
k(X0,X1,X0),X1)]
  2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1)
  3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)]
  4: [equal_sets(X0,X0)], ~(subset(X0,X0))

SZS status Satisfiable