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

------ Parsing...successful


------ Proving...
use I+

Gamma_0: (extend-no-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]

Gamma_1: (extend-no-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [~(well_founded_relation(inclusion_relation(esk2_0)))], ~(connected(inclusion_relation(esk2_0))), well_ordering(
inclusion_relation(esk2_0)), ~(antisymmetric(inclusion_relation(esk2_0))), ~(
transitive(inclusion_relation(esk2_0))), ~(reflexive(inclusion_relation(esk2_0))), ~(
relation(inclusion_relation(esk2_0)))

Gamma_2: (extend-no-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [~(well_founded_relation(inclusion_relation(esk2_0)))], ~(connected(inclusion_relation(esk2_0))), well_ordering(
inclusion_relation(esk2_0)), ~(antisymmetric(inclusion_relation(esk2_0))), ~(
transitive(inclusion_relation(esk2_0))), ~(reflexive(inclusion_relation(esk2_0))), ~(
relation(inclusion_relation(esk2_0)))
  2: well_founded_relation(inclusion_relation(esk2_0)), [~(ordinal(esk2_0))]

Gamma_3: (extend-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [~(well_founded_relation(inclusion_relation(esk2_0)))], ~(connected(inclusion_relation(esk2_0))), well_ordering(
inclusion_relation(esk2_0)), ~(antisymmetric(inclusion_relation(esk2_0))), ~(
transitive(inclusion_relation(esk2_0))), ~(reflexive(inclusion_relation(esk2_0))), ~(
relation(inclusion_relation(esk2_0)))
  2: well_founded_relation(inclusion_relation(esk2_0)), [~(ordinal(esk2_0))]
  3: [ordinal(esk2_0)]

Gamma_4: (move)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [~(well_founded_relation(inclusion_relation(esk2_0)))], ~(connected(inclusion_relation(esk2_0))), well_ordering(
inclusion_relation(esk2_0)), ~(antisymmetric(inclusion_relation(esk2_0))), ~(
transitive(inclusion_relation(esk2_0))), ~(reflexive(inclusion_relation(esk2_0))), ~(
relation(inclusion_relation(esk2_0)))
  2: [ordinal(esk2_0)]
  3: well_founded_relation(inclusion_relation(esk2_0)), [~(ordinal(esk2_0))]

Gamma_5: (resolve)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [~(well_founded_relation(inclusion_relation(esk2_0)))], ~(connected(inclusion_relation(esk2_0))), well_ordering(
inclusion_relation(esk2_0)), ~(antisymmetric(inclusion_relation(esk2_0))), ~(
transitive(inclusion_relation(esk2_0))), ~(reflexive(inclusion_relation(esk2_0))), ~(
relation(inclusion_relation(esk2_0)))
  2: [ordinal(esk2_0)]
  3: [well_founded_relation(inclusion_relation(esk2_0))]

Gamma_6: (extend-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [~(well_founded_relation(inclusion_relation(esk2_0)))], ~(connected(inclusion_relation(esk2_0))), well_ordering(
inclusion_relation(esk2_0)), ~(antisymmetric(inclusion_relation(esk2_0))), ~(
transitive(inclusion_relation(esk2_0))), ~(reflexive(inclusion_relation(esk2_0))), ~(
relation(inclusion_relation(esk2_0)))
  2: [ordinal(esk2_0)]
  3: [well_founded_relation(inclusion_relation(esk2_0))]

Gamma_7: (move)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [~(well_founded_relation(inclusion_relation(esk2_0)))], ~(connected(inclusion_relation(esk2_0))), well_ordering(
inclusion_relation(esk2_0)), ~(antisymmetric(inclusion_relation(esk2_0))), ~(
transitive(inclusion_relation(esk2_0))), ~(reflexive(inclusion_relation(esk2_0))), ~(
relation(inclusion_relation(esk2_0)))
  3: [ordinal(esk2_0)]

Gamma_8: (resolve)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [~(connected(inclusion_relation(esk2_0)))], well_ordering(inclusion_relation(esk2_0)), ~(
antisymmetric(inclusion_relation(esk2_0))), ~(transitive(inclusion_relation(esk2_0))), ~(
reflexive(inclusion_relation(esk2_0))), ~(relation(inclusion_relation(esk2_0)))
  3: [ordinal(esk2_0)]

Gamma_9: (extend-no-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [~(connected(inclusion_relation(esk2_0)))], well_ordering(inclusion_relation(esk2_0)), ~(
antisymmetric(inclusion_relation(esk2_0))), ~(transitive(inclusion_relation(esk2_0))), ~(
reflexive(inclusion_relation(esk2_0))), ~(relation(inclusion_relation(esk2_0)))
  3: [ordinal(esk2_0)]

Gamma_10: (extend-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [~(connected(inclusion_relation(esk2_0)))], well_ordering(inclusion_relation(esk2_0)), ~(
antisymmetric(inclusion_relation(esk2_0))), ~(transitive(inclusion_relation(esk2_0))), ~(
reflexive(inclusion_relation(esk2_0))), ~(relation(inclusion_relation(esk2_0)))
  3: [ordinal(esk2_0)]
  4: connected(inclusion_relation(esk2_0)), [~(ordinal(esk2_0))]

Gamma_11: (resolve)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [~(connected(inclusion_relation(esk2_0)))], well_ordering(inclusion_relation(esk2_0)), ~(
antisymmetric(inclusion_relation(esk2_0))), ~(transitive(inclusion_relation(esk2_0))), ~(
reflexive(inclusion_relation(esk2_0))), ~(relation(inclusion_relation(esk2_0)))
  3: [ordinal(esk2_0)]
  4: [connected(inclusion_relation(esk2_0))]

Gamma_12: (extend-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [~(connected(inclusion_relation(esk2_0)))], well_ordering(inclusion_relation(esk2_0)), ~(
antisymmetric(inclusion_relation(esk2_0))), ~(transitive(inclusion_relation(esk2_0))), ~(
reflexive(inclusion_relation(esk2_0))), ~(relation(inclusion_relation(esk2_0)))
  3: [ordinal(esk2_0)]
  4: [connected(inclusion_relation(esk2_0))]

Gamma_13: (move)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [~(connected(inclusion_relation(esk2_0)))], well_ordering(inclusion_relation(esk2_0)), ~(
antisymmetric(inclusion_relation(esk2_0))), ~(transitive(inclusion_relation(esk2_0))), ~(
reflexive(inclusion_relation(esk2_0))), ~(relation(inclusion_relation(esk2_0)))
  4: [ordinal(esk2_0)]

Gamma_14: (resolve)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [well_ordering(inclusion_relation(esk2_0))], ~(antisymmetric(inclusion_relation(esk2_0))), ~(
transitive(inclusion_relation(esk2_0))), ~(reflexive(inclusion_relation(esk2_0))), ~(
relation(inclusion_relation(esk2_0)))
  4: [ordinal(esk2_0)]

Gamma_15: (extend-no-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: well_ordering(inclusion_relation(esk2_0)), [~(antisymmetric(inclusion_relation(esk2_0)))], ~(
transitive(inclusion_relation(esk2_0))), ~(reflexive(inclusion_relation(esk2_0))), ~(
relation(inclusion_relation(esk2_0)))
  4: [ordinal(esk2_0)]

Gamma_16: (extend-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: well_ordering(inclusion_relation(esk2_0)), [~(antisymmetric(inclusion_relation(esk2_0)))], ~(
transitive(inclusion_relation(esk2_0))), ~(reflexive(inclusion_relation(esk2_0))), ~(
relation(inclusion_relation(esk2_0)))
  4: [ordinal(esk2_0)]
  5: [antisymmetric(inclusion_relation(esk2_0))]

Gamma_17: (move)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: well_ordering(inclusion_relation(esk2_0)), [~(antisymmetric(inclusion_relation(esk2_0)))], ~(
transitive(inclusion_relation(esk2_0))), ~(reflexive(inclusion_relation(esk2_0))), ~(
relation(inclusion_relation(esk2_0)))
  5: [ordinal(esk2_0)]

Gamma_18: (resolve)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: [well_ordering(inclusion_relation(esk2_0))], ~(transitive(inclusion_relation(esk2_0))), ~(
reflexive(inclusion_relation(esk2_0))), ~(relation(inclusion_relation(esk2_0)))
  5: [ordinal(esk2_0)]

Gamma_19: (extend-no-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: well_ordering(inclusion_relation(esk2_0)), [~(transitive(inclusion_relation(esk2_0)))], ~(
reflexive(inclusion_relation(esk2_0))), ~(relation(inclusion_relation(esk2_0)))
  5: [ordinal(esk2_0)]

Gamma_20: (extend-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: well_ordering(inclusion_relation(esk2_0)), [~(transitive(inclusion_relation(esk2_0)))], ~(
reflexive(inclusion_relation(esk2_0))), ~(relation(inclusion_relation(esk2_0)))
  5: [ordinal(esk2_0)]
  6: [transitive(inclusion_relation(esk2_0))]

Gamma_21: (move)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: [transitive(inclusion_relation(esk2_0))]
  5: well_ordering(inclusion_relation(esk2_0)), [~(transitive(inclusion_relation(esk2_0)))], ~(
reflexive(inclusion_relation(esk2_0))), ~(relation(inclusion_relation(esk2_0)))
  6: [ordinal(esk2_0)]

Gamma_22: (resolve)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: [transitive(inclusion_relation(esk2_0))]
  5: [well_ordering(inclusion_relation(esk2_0))], ~(reflexive(inclusion_relation(esk2_0))), ~(
relation(inclusion_relation(esk2_0)))
  6: [ordinal(esk2_0)]

Gamma_23: (extend-no-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: [transitive(inclusion_relation(esk2_0))]
  5: well_ordering(inclusion_relation(esk2_0)), [~(reflexive(inclusion_relation(esk2_0)))], ~(
relation(inclusion_relation(esk2_0)))
  6: [ordinal(esk2_0)]

Gamma_24: (extend-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: [transitive(inclusion_relation(esk2_0))]
  5: well_ordering(inclusion_relation(esk2_0)), [~(reflexive(inclusion_relation(esk2_0)))], ~(
relation(inclusion_relation(esk2_0)))
  6: [ordinal(esk2_0)]
  7: [reflexive(inclusion_relation(esk2_0))]

Gamma_25: (move)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: [transitive(inclusion_relation(esk2_0))]
  5: [reflexive(inclusion_relation(esk2_0))]
  6: well_ordering(inclusion_relation(esk2_0)), [~(reflexive(inclusion_relation(esk2_0)))], ~(
relation(inclusion_relation(esk2_0)))
  7: [ordinal(esk2_0)]

Gamma_26: (resolve)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: [transitive(inclusion_relation(esk2_0))]
  5: [reflexive(inclusion_relation(esk2_0))]
  6: [well_ordering(inclusion_relation(esk2_0))], ~(relation(inclusion_relation(esk2_0)))
  7: [ordinal(esk2_0)]

Gamma_27: (extend-no-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: [transitive(inclusion_relation(esk2_0))]
  5: [reflexive(inclusion_relation(esk2_0))]
  6: well_ordering(inclusion_relation(esk2_0)), [~(relation(inclusion_relation(esk2_0)))]
  7: [ordinal(esk2_0)]

Gamma_28: (extend-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: [transitive(inclusion_relation(esk2_0))]
  5: [reflexive(inclusion_relation(esk2_0))]
  6: well_ordering(inclusion_relation(esk2_0)), [~(relation(inclusion_relation(esk2_0)))]
  7: [ordinal(esk2_0)]
  8: [relation(inclusion_relation(esk2_0))]

Gamma_29: (move)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: [transitive(inclusion_relation(esk2_0))]
  5: [reflexive(inclusion_relation(esk2_0))]
  6: [relation(inclusion_relation(esk2_0))]
  7: well_ordering(inclusion_relation(esk2_0)), [~(relation(inclusion_relation(esk2_0)))]
  8: [ordinal(esk2_0)]

Gamma_30: (resolve)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: [transitive(inclusion_relation(esk2_0))]
  5: [reflexive(inclusion_relation(esk2_0))]
  6: [relation(inclusion_relation(esk2_0))]
  7: [well_ordering(inclusion_relation(esk2_0))]
  8: [ordinal(esk2_0)]

Gamma_31: (extend-conflict)
  0: [~(well_ordering(inclusion_relation(esk2_0)))]
  1: [well_founded_relation(inclusion_relation(esk2_0))]
  2: [connected(inclusion_relation(esk2_0))]
  3: [antisymmetric(inclusion_relation(esk2_0))]
  4: [transitive(inclusion_relation(esk2_0))]
  5: [reflexive(inclusion_relation(esk2_0))]
  6: [relation(inclusion_relation(esk2_0))]
  7: [well_ordering(inclusion_relation(esk2_0))]
  8: [ordinal(esk2_0)]

Gamma_32: (move)
  0: [well_ordering(inclusion_relation(esk2_0))]
  1: [~(well_ordering(inclusion_relation(esk2_0)))]
  2: [well_founded_relation(inclusion_relation(esk2_0))]
  3: [connected(inclusion_relation(esk2_0))]
  4: [antisymmetric(inclusion_relation(esk2_0))]
  5: [transitive(inclusion_relation(esk2_0))]
  6: [reflexive(inclusion_relation(esk2_0))]
  7: [relation(inclusion_relation(esk2_0))]
  8: [ordinal(esk2_0)]

Gamma_33: (resolve)
  0: [well_ordering(inclusion_relation(esk2_0))]
  1: []
  2: [well_founded_relation(inclusion_relation(esk2_0))]
  3: [connected(inclusion_relation(esk2_0))]
  4: [antisymmetric(inclusion_relation(esk2_0))]
  5: [transitive(inclusion_relation(esk2_0))]
  6: [reflexive(inclusion_relation(esk2_0))]
  7: [relation(inclusion_relation(esk2_0))]
  8: [ordinal(esk2_0)]

SZS status Unsatisfiable