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

------ Parsing...successful


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

Gamma_0: (extend-no-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]

Gamma_1: (extend-no-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))

Gamma_2: (extend-no-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]

Gamma_3: (extend-no-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]

Gamma_4: (extend-no-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]

Gamma_5: (extend-no-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))

Gamma_6: (extend-no-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))
  6: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]

Gamma_7: (extend-no-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))
  6: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]
  7: [subset(b,bb)], ~(equal_sets(b,bb))

Gamma_8: (extend-no-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))
  6: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]
  7: [subset(b,bb)], ~(equal_sets(b,bb))
  8: ~(subset(bb,b)), ~(subset(b,bb)), [equal_sets(bb,b)]

Gamma_9: (extend-no-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))
  6: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]
  7: [subset(b,bb)], ~(equal_sets(b,bb))
  8: ~(subset(bb,b)), ~(subset(b,bb)), [equal_sets(bb,b)]
  9: ~(subset(b,bb)), [member(member_of_1_not_of_2(b,X0),bb)], ~(member(member_of_1_not_of_2(b,X0),b))

Gamma_10: (extend-no-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))
  6: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]
  7: [subset(b,bb)], ~(equal_sets(b,bb))
  8: ~(subset(bb,b)), ~(subset(b,bb)), [equal_sets(bb,b)]
  9: ~(subset(b,bb)), [member(member_of_1_not_of_2(b,X0),bb)], ~(member(member_of_1_not_of_2(b,X0),b))
  10: ~(subset(b,bb)), [member(element_of_b,bb)], ~(member(element_of_b,b))

Gamma_11: (extend-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))
  6: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]
  7: [subset(b,bb)], ~(equal_sets(b,bb))
  8: ~(subset(bb,b)), ~(subset(b,bb)), [equal_sets(bb,b)]
  9: ~(subset(b,bb)), [member(member_of_1_not_of_2(b,X0),bb)], ~(member(member_of_1_not_of_2(b,X0),b))
  10: ~(subset(b,bb)), [member(element_of_b,bb)], ~(member(element_of_b,b))
  11: [~(member(element_of_b,bb))]

Gamma_12: (move)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))
  6: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]
  7: [subset(b,bb)], ~(equal_sets(b,bb))
  8: ~(subset(bb,b)), ~(subset(b,bb)), [equal_sets(bb,b)]
  9: ~(subset(b,bb)), [member(member_of_1_not_of_2(b,X0),bb)], ~(member(member_of_1_not_of_2(b,X0),b))
  10: [~(member(element_of_b,bb))]
  11: ~(subset(b,bb)), [member(element_of_b,bb)], ~(member(element_of_b,b))

Gamma_13: (resolve)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))
  6: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]
  7: [subset(b,bb)], ~(equal_sets(b,bb))
  8: ~(subset(bb,b)), ~(subset(b,bb)), [equal_sets(bb,b)]
  9: ~(subset(b,bb)), [member(member_of_1_not_of_2(b,X0),bb)], ~(member(member_of_1_not_of_2(b,X0),b))
  10: [~(member(element_of_b,bb))]
  11: [~(subset(b,bb))], ~(member(element_of_b,b))

Gamma_14: (extend-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))
  6: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]
  7: [subset(b,bb)], ~(equal_sets(b,bb))
  8: ~(subset(bb,b)), ~(subset(b,bb)), [equal_sets(bb,b)]
  9: ~(subset(b,bb)), [member(member_of_1_not_of_2(b,X0),bb)], ~(member(member_of_1_not_of_2(b,X0),b))
  10: [~(member(element_of_b,bb))]
  11: [~(subset(b,bb))], ~(member(element_of_b,b))

Gamma_15: (move)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))
  6: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]
  7: [~(subset(b,bb))], ~(member(element_of_b,b))
  8: [subset(b,bb)], ~(equal_sets(b,bb))
  9: ~(subset(bb,b)), ~(subset(b,bb)), [equal_sets(bb,b)]
  10: ~(subset(b,bb)), [member(member_of_1_not_of_2(b,X0),bb)], ~(member(member_of_1_not_of_2(b,X0),b))
  11: [~(member(element_of_b,bb))]

Gamma_16: (resolve)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))
  6: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]
  7: [~(subset(b,bb))], ~(member(element_of_b,b))
  8: ~(member(element_of_b,b)), [~(equal_sets(b,bb))]
  9: [~(member(element_of_b,bb))]

Gamma_17: (extend-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: [equal_sets(b,bb)]
  5: [subset(bb,b)], ~(equal_sets(b,bb))
  6: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]
  7: [~(subset(b,bb))], ~(member(element_of_b,b))
  8: ~(member(element_of_b,b)), [~(equal_sets(b,bb))]
  9: [~(member(element_of_b,bb))]

Gamma_18: (move)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: ~(member(element_of_b,b)), [~(equal_sets(b,bb))]
  5: [equal_sets(b,bb)]
  6: [subset(bb,b)], ~(equal_sets(b,bb))
  7: ~(subset(bb,b)), ~(member(member_of_1_not_of_2(bb,X0),bb)), [member(
member_of_1_not_of_2(bb,X0),b)]
  8: [~(subset(b,bb))], ~(member(element_of_b,b))
  9: [~(member(element_of_b,bb))]

Gamma_19: (resolve)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: ~(member(element_of_b,b)), [~(equal_sets(b,bb))]
  5: [~(member(element_of_b,b))]
  6: [~(subset(b,bb))], ~(member(element_of_b,b))
  7: [~(member(element_of_b,bb))]

Gamma_20: (extend-conflict)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [member(element_of_b,b)]
  4: ~(member(element_of_b,b)), [~(equal_sets(b,bb))]
  5: [~(member(element_of_b,b))]
  6: [~(subset(b,bb))], ~(member(element_of_b,b))
  7: [~(member(element_of_b,bb))]

Gamma_21: (move)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [~(member(element_of_b,b))]
  4: [member(element_of_b,b)]
  5: ~(member(element_of_b,b)), [~(equal_sets(b,bb))]
  6: [~(subset(b,bb))], ~(member(element_of_b,b))
  7: [~(member(element_of_b,bb))]

Gamma_22: (resolve)
  0: subset(X0,X1), [member(member_of_1_not_of_2(X0,X1),
X0)]
  1: [subset(X0,X0)], ~(member(member_of_1_not_of_2(X0,X0),X0))
  2: ~(subset(X0,X0)), [equal_sets(X0,X0)]
  3: [~(member(element_of_b,b))]
  4: []
  5: [~(member(element_of_b,bb))]

SZS status Unsatisfiable