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

------ Parsing...successful


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

Gamma_0: (extend-no-conflict)
  0: [greater(e_2,e_1)]

Gamma_1: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]

Gamma_2: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]

Gamma_3: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))

Gamma_4: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]

Gamma_5: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]

Gamma_6: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))

Gamma_7: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  7: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]

Gamma_8: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  7: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_1,
e_2)]

Gamma_9: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  7: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_1,
e_2)]
  9: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_2,
e_1)]

Gamma_10: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  7: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_1,
e_2)]
  9: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_2,
e_1)]
  10: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))

Gamma_11: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  7: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_1,
e_2)]
  9: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_2,
e_1)]
  10: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  11: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))

Gamma_12: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  7: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_1,
e_2)]
  9: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_2,
e_1)]
  10: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  11: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))
  12: [~(equalish(e_2,e_1))]

Gamma_13: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  7: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_1,
e_2)]
  9: [~(equalish(e_2,e_1))]
  10: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_2,
e_1)]
  11: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  12: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))

Gamma_14: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  7: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_1,
e_2)]
  9: [~(equalish(e_2,e_1))]
  10: [~(product(e_2,e_2,e_2))], ~(product(e_2,e_1,e_2))
  11: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  12: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))

Gamma_15: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  7: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_1,
e_2)]
  9: [~(equalish(e_2,e_1))]
  10: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  11: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  12: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))

Gamma_16: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  9: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_1,
e_2)]
  10: [~(equalish(e_2,e_1))]
  11: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  12: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))

Gamma_17: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))

Gamma_18: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))

Gamma_19: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))
  11: ~(product(e_2,e_1,e_1)), ~(product(e_1,e_1,e_2)), [equalish(e_1,
e_1)]

Gamma_20: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))
  11: ~(product(e_2,e_1,e_1)), ~(product(e_1,e_1,e_2)), [equalish(e_1,
e_1)]
  12: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_2))], equalish(
e_2,e_1)

Gamma_21: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_2))], equalish(
e_2,e_1)
  11: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))
  12: ~(product(e_2,e_1,e_1)), ~(product(e_1,e_1,e_2)), [equalish(e_1,
e_1)]

Gamma_22: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [product(e_1,
e_1,e_1)], equalish(e_2,e_1), ~(group_element(e_1))

Gamma_23: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [product(e_1,
e_1,e_1)], equalish(e_2,e_1), ~(group_element(e_1))

Gamma_24: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [product(e_1,
e_1,e_1)], equalish(e_2,e_1), ~(group_element(e_1))
  12: ~(product(e_1,e_1,e_1)), [equalish(e_1,e_1)]

Gamma_25: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [product(e_1,
e_1,e_1)], equalish(e_2,e_1), ~(group_element(e_1))
  12: ~(product(e_1,e_1,e_1)), [equalish(e_1,e_1)]
  13: ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_1))], equalish(e_2,
e_1)

Gamma_26: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_1))], equalish(e_2,
e_1)
  12: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [product(e_1,
e_1,e_1)], equalish(e_2,e_1), ~(group_element(e_1))
  13: ~(product(e_1,e_1,e_1)), [equalish(e_1,e_1)]

Gamma_27: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_1))], equalish(e_2,
e_1)
  12: [~(product(e_2,e_2,e_2))], ~(product(e_2,e_1,e_1)), equalish(e_2,
e_1), ~(group_element(e_1))

Gamma_28: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_1))], equalish(e_2,
e_1)
  12: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [equalish(e_2,
e_1)], ~(group_element(e_1))

Gamma_29: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_1))], equalish(e_2,
e_1)
  12: [~(product(e_2,e_2,e_2))], ~(product(e_2,e_1,e_1)), ~(group_element(e_1))

Gamma_30: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  8: [~(equalish(e_2,e_1))]
  9: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_1))], equalish(e_2,
e_1)
  12: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_1))], ~(group_element(e_1))

Gamma_31: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_1))], ~(group_element(e_1))
  8: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  9: [~(equalish(e_2,e_1))]
  10: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  11: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_2))], equalish(
e_2,e_1)
  12: ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_1))], equalish(e_2,
e_1)

Gamma_32: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_1))], ~(group_element(e_1))
  8: [~(product(e_2,e_2,e_2))], ~(group_element(e_2)), ~(group_element(e_1))
  9: [~(equalish(e_2,e_1))]
  10: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))

Gamma_33: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: [group_element(e_1)]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  7: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_1))], ~(group_element(e_1))
  8: ~(product(e_2,e_2,e_2)), ~(group_element(e_2)), [~(group_element(e_1))]
  9: [~(equalish(e_2,e_1))]
  10: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))

Gamma_34: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_2)), ~(group_element(e_2)), [~(group_element(e_1))]
  6: [group_element(e_1)]
  7: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  8: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_1))], ~(group_element(e_1))
  9: [~(equalish(e_2,e_1))]
  10: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))

Gamma_35: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_2)), ~(group_element(e_2)), [~(group_element(e_1))]
  6: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  7: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  8: [~(equalish(e_2,e_1))]

Gamma_36: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  4: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_2)), ~(group_element(e_2)), [~(group_element(e_1))]
  6: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  7: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  8: [~(equalish(e_2,e_1))]

Gamma_37: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  5: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  6: ~(product(e_2,e_2,e_2)), ~(group_element(e_2)), [~(group_element(e_1))]
  7: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  8: [~(equalish(e_2,e_1))]

Gamma_38: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]

Gamma_39: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]

Gamma_40: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]

Gamma_41: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]

Gamma_42: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]

Gamma_43: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))

Gamma_44: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))

Gamma_45: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  11: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), ~(product(e_1,e_2,e_2)), [equalish(
e_1,e_2)]

Gamma_46: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  11: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), ~(product(e_1,e_2,e_2)), [equalish(
e_1,e_2)]
  12: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)

Gamma_47: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  11: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  12: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), ~(product(e_1,e_2,e_2)), [equalish(
e_1,e_2)]

Gamma_48: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [product(e_1,
e_2,e_1)], equalish(e_2,e_1), ~(group_element(e_2)), ~(group_element(e_1))

Gamma_49: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [product(e_1,
e_2,e_1)], equalish(e_2,e_1), ~(group_element(e_2)), ~(group_element(e_1))

Gamma_50: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [product(e_1,
e_2,e_1)], equalish(e_2,e_1), ~(group_element(e_2)), ~(group_element(e_1))
  12: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_51: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)
  12: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [product(e_1,
e_2,e_1)], equalish(e_2,e_1), ~(group_element(e_2)), ~(group_element(e_1))

Gamma_52: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)
  12: [~(product(e_2,e_2,e_1))], ~(product(e_2,e_1,e_2)), equalish(e_2,
e_1), ~(group_element(e_2)), ~(group_element(e_1))

Gamma_53: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  11: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)
  12: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_2))], equalish(e_2,
e_1), ~(group_element(e_2)), ~(group_element(e_1))

Gamma_54: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_2))], equalish(e_2,
e_1), ~(group_element(e_2)), ~(group_element(e_1))
  10: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  11: ~(product(e_2,e_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  12: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_55: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_2))], equalish(e_2,
e_1), ~(group_element(e_2)), ~(group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), [product(e_2,e_1,e_1)], equalish(e_2,e_1), ~(
group_element(e_2)), ~(group_element(e_1))
  11: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_56: (extend-no-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_2))], equalish(e_2,
e_1), ~(group_element(e_2)), ~(group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), [product(e_2,e_1,e_1)], equalish(e_2,e_1), ~(
group_element(e_2)), ~(group_element(e_1))
  11: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_57: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_2))], equalish(e_2,
e_1), ~(group_element(e_2)), ~(group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), [product(e_2,e_1,e_1)], equalish(e_2,e_1), ~(
group_element(e_2)), ~(group_element(e_1))
  11: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)
  12: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)

Gamma_58: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_2))], equalish(e_2,
e_1), ~(group_element(e_2)), ~(group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  11: ~(product(e_2,e_2,e_1)), [product(e_2,e_1,e_1)], equalish(e_2,e_1), ~(
group_element(e_2)), ~(group_element(e_1))
  12: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_59: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_2))], equalish(e_2,
e_1), ~(group_element(e_2)), ~(group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  11: [~(product(e_2,e_2,e_1))], equalish(e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  12: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_60: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: [group_element(e_1)]
  9: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_2))], equalish(e_2,
e_1), ~(group_element(e_2)), ~(group_element(e_1))
  10: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  11: ~(product(e_2,e_2,e_1)), equalish(e_2,e_1), ~(group_element(e_2)), [~(
group_element(e_1))]
  12: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_61: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_1)), equalish(e_2,e_1), ~(group_element(e_2)), [~(
group_element(e_1))]
  9: [group_element(e_1)]
  10: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_2))], equalish(e_2,
e_1), ~(group_element(e_2)), ~(group_element(e_1))
  11: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  12: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_62: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_1)), equalish(e_2,e_1), ~(group_element(e_2)), [~(
group_element(e_1))]
  9: [~(product(e_2,e_2,e_1))], equalish(e_2,e_1), ~(group_element(e_2))
  10: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  11: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_63: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_1)), equalish(e_2,e_1), ~(group_element(e_2)), [~(
group_element(e_1))]
  9: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_1)], ~(group_element(e_2))
  10: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  11: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_64: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_1)), equalish(e_2,e_1), ~(group_element(e_2)), [~(
group_element(e_1))]
  9: [~(product(e_2,e_2,e_1))], ~(group_element(e_2))
  10: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  11: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_65: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  5: [~(equalish(e_2,e_1))]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  8: ~(product(e_2,e_2,e_1)), equalish(e_2,e_1), ~(group_element(e_2)), [~(
group_element(e_1))]
  9: [~(product(e_2,e_2,e_1))], ~(group_element(e_2))
  10: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  11: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_66: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [~(product(e_2,e_2,e_1))], ~(group_element(e_2))
  5: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  6: [~(equalish(e_2,e_1))]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  8: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  9: ~(product(e_2,e_2,e_1)), equalish(e_2,e_1), ~(group_element(e_2)), [~(
group_element(e_1))]
  10: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  11: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_67: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [~(product(e_2,e_2,e_1))], ~(group_element(e_2))
  5: [~(group_element(e_2))]
  6: [~(equalish(e_2,e_1))]

Gamma_68: (extend-conflict)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [group_element(e_2)]
  3: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  4: [~(product(e_2,e_2,e_1))], ~(group_element(e_2))
  5: [~(group_element(e_2))]
  6: [~(equalish(e_2,e_1))]

Gamma_69: (move)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [~(group_element(e_2))]
  3: [group_element(e_2)]
  4: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  5: [~(product(e_2,e_2,e_1))], ~(group_element(e_2))
  6: [~(equalish(e_2,e_1))]

Gamma_70: (resolve)
  0: [greater(e_2,e_1)]
  1: [next(e_1,e_2)]
  2: [~(group_element(e_2))]
  3: []
  4: [~(equalish(e_2,e_1))]

SZS status Unsatisfiable