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

------ Parsing...successful


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

Gamma_0: (extend-no-conflict)
  0: [group_element(e_2)]

Gamma_1: (extend-no-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))

Gamma_2: (extend-no-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]

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

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

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

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

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

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

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

Gamma_10: (extend-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  5: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  6: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_2,
e_1)]
  7: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_1,
e_2)]
  8: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  9: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))
  10: [~(equalish(e_2,e_1))]

Gamma_11: (move)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  5: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  6: [~(equalish(e_2,e_1))]
  7: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_2)), [equalish(e_2,
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_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_12: (resolve)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  5: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  6: [~(equalish(e_2,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_2)), [equalish(e_1,
e_2)]
  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_13: (extend-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  5: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  6: [~(equalish(e_2,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_2)), [equalish(e_1,
e_2)]
  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_14: (move)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: [product(e_2,e_1,e_2)], product(e_2,e_1,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  6: ~(product(e_2,e_1,e_2)), [equalish(e_1,e_1)]
  7: [~(equalish(e_2,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_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_15: (resolve)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  6: [~(equalish(e_2,e_1))]
  7: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))

Gamma_16: (extend-no-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  6: [~(equalish(e_2,e_1))]
  7: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))

Gamma_17: (extend-no-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  6: [~(equalish(e_2,e_1))]
  7: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))
  9: ~(product(e_2,e_1,e_1)), ~(product(e_1,e_1,e_2)), [equalish(e_1,
e_1)]

Gamma_18: (extend-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  6: [~(equalish(e_2,e_1))]
  7: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))
  9: ~(product(e_2,e_1,e_1)), ~(product(e_1,e_1,e_2)), [equalish(e_1,
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)

Gamma_19: (move)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  6: [~(equalish(e_2,e_1))]
  7: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: ~(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)
  9: [product(e_1,e_1,e_2)], product(e_1,e_1,e_1), ~(group_element(e_1))
  10: ~(product(e_2,e_1,e_1)), ~(product(e_1,e_1,e_2)), [equalish(e_1,
e_1)]

Gamma_20: (resolve)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  6: [~(equalish(e_2,e_1))]
  7: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: ~(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)
  9: ~(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_21: (extend-no-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  6: [~(equalish(e_2,e_1))]
  7: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: ~(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)
  9: ~(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_22: (extend-no-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  6: [~(equalish(e_2,e_1))]
  7: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: ~(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)
  9: ~(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))
  10: ~(product(e_1,e_1,e_1)), [equalish(e_1,e_1)]

Gamma_23: (extend-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  6: [~(equalish(e_2,e_1))]
  7: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: ~(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)
  9: ~(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))
  10: ~(product(e_1,e_1,e_1)), [equalish(e_1,e_1)]
  11: ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_1))], equalish(e_2,
e_1)

Gamma_24: (move)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  6: [~(equalish(e_2,e_1))]
  7: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: ~(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)
  9: ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_1))], equalish(e_2,
e_1)
  10: ~(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))
  11: ~(product(e_1,e_1,e_1)), [equalish(e_1,e_1)]

Gamma_25: (resolve)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  6: [~(equalish(e_2,e_1))]
  7: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: ~(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)
  9: ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_1))], equalish(e_2,
e_1)
  10: [~(product(e_2,e_2,e_2))], ~(product(e_2,e_1,e_1)), equalish(e_2,
e_1), ~(group_element(e_1))

Gamma_26: (extend-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [product(e_2,e_1,e_1)], ~(group_element(e_2)), ~(
group_element(e_1))
  6: [~(equalish(e_2,e_1))]
  7: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  8: ~(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)
  9: ~(product(e_2,e_1,e_1)), [~(product(e_1,e_1,e_1))], equalish(e_2,
e_1)
  10: ~(product(e_2,e_2,e_2)), ~(product(e_2,e_1,e_1)), [equalish(e_2,
e_1)], ~(group_element(e_1))

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

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

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

Gamma_30: (resolve)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_1))], ~(group_element(e_1))
  6: [~(product(e_2,e_2,e_2))], ~(group_element(e_2)), ~(group_element(e_1))
  7: [~(equalish(e_2,e_1))]
  8: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))

Gamma_31: (extend-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: [group_element(e_1)]
  4: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  5: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_1))], ~(group_element(e_1))
  6: ~(product(e_2,e_2,e_2)), ~(group_element(e_2)), [~(group_element(e_1))]
  7: [~(equalish(e_2,e_1))]
  8: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))

Gamma_32: (move)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: ~(product(e_2,e_2,e_2)), ~(group_element(e_2)), [~(group_element(e_1))]
  4: [group_element(e_1)]
  5: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  6: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_1))], ~(group_element(e_1))
  7: [~(equalish(e_2,e_1))]
  8: [product(e_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))

Gamma_33: (resolve)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: ~(product(e_2,e_2,e_2)), ~(group_element(e_2)), [~(group_element(e_1))]
  4: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  5: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  6: [~(equalish(e_2,e_1))]

Gamma_34: (extend-conflict)
  0: [group_element(e_2)]
  1: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  2: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  3: ~(product(e_2,e_2,e_2)), ~(group_element(e_2)), [~(group_element(e_1))]
  4: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  5: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  6: [~(equalish(e_2,e_1))]

Gamma_35: (move)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_2)], product(e_2,e_2,e_1), ~(group_element(e_2))
  3: ~(product(e_2,e_2,e_2)), [equalish(e_2,e_2)]
  4: ~(product(e_2,e_2,e_2)), ~(group_element(e_2)), [~(group_element(e_1))]
  5: ~(product(e_2,e_2,e_2)), [~(product(e_2,e_1,e_2))]
  6: [~(equalish(e_2,e_1))]

Gamma_36: (resolve)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]

Gamma_37: (extend-no-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]

Gamma_38: (extend-no-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]

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

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

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

Gamma_42: (extend-no-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  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_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))

Gamma_43: (extend-no-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  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_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  9: ~(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_44: (extend-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  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_1,e_2,e_2)], product(e_1,e_2,e_1), ~(group_element(e_2)), ~(
group_element(e_1))
  9: ~(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)]
  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)

Gamma_45: (move)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  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_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], 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_1)), ~(product(e_2,e_1,e_2)), ~(product(e_1,e_2,e_2)), [equalish(
e_1,e_2)]

Gamma_46: (resolve)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  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_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  9: ~(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_47: (extend-no-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  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_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  9: ~(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_48: (extend-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  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_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  9: ~(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))
  10: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_49: (move)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  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_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  9: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)
  10: ~(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: (resolve)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  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_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  9: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
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))

Gamma_51: (extend-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  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_2,e_1)), ~(product(e_2,e_1,e_2)), [~(product(e_1,e_2,e_2))], equalish(
e_2,e_1)
  9: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
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))

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

Gamma_53: (resolve)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  7: ~(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))
  8: ~(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))
  9: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_54: (extend-no-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  7: ~(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))
  8: ~(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))
  9: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_55: (extend-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  7: ~(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))
  8: ~(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))
  9: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)
  10: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)

Gamma_56: (move)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  7: ~(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))
  8: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  9: ~(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))
  10: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_57: (resolve)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  7: ~(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))
  8: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
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_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_58: (extend-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: [group_element(e_1)]
  7: ~(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))
  8: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
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_1,e_2,e_1))], equalish(e_2,
e_1)

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

Gamma_60: (resolve)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: ~(product(e_2,e_2,e_1)), equalish(e_2,e_1), ~(group_element(e_2)), [~(
group_element(e_1))]
  7: [~(product(e_2,e_2,e_1))], equalish(e_2,e_1), ~(group_element(e_2))
  8: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  9: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_61: (extend-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  3: [~(equalish(e_2,e_1))]
  4: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  6: ~(product(e_2,e_2,e_1)), equalish(e_2,e_1), ~(group_element(e_2)), [~(
group_element(e_1))]
  7: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_1)], ~(group_element(e_2))
  8: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  9: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

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

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

Gamma_64: (move)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [~(product(e_2,e_2,e_1))], ~(group_element(e_2))
  3: [product(e_2,e_2,e_1)], ~(group_element(e_2))
  4: [~(equalish(e_2,e_1))]
  5: ~(product(e_2,e_2,e_1)), [equalish(e_2,e_2)]
  6: ~(product(e_2,e_2,e_1)), [equalish(e_1,e_1)]
  7: ~(product(e_2,e_2,e_1)), equalish(e_2,e_1), ~(group_element(e_2)), [~(
group_element(e_1))]
  8: ~(product(e_2,e_2,e_1)), [~(product(e_2,e_1,e_1))], equalish(e_2,
e_1)
  9: ~(product(e_2,e_2,e_1)), [~(product(e_1,e_2,e_1))], equalish(e_2,
e_1)

Gamma_65: (resolve)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [~(product(e_2,e_2,e_1))], ~(group_element(e_2))
  3: [~(group_element(e_2))]
  4: [~(equalish(e_2,e_1))]

Gamma_66: (extend-conflict)
  0: [group_element(e_2)]
  1: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  2: [~(product(e_2,e_2,e_1))], ~(group_element(e_2))
  3: [~(group_element(e_2))]
  4: [~(equalish(e_2,e_1))]

Gamma_67: (move)
  0: [~(group_element(e_2))]
  1: [group_element(e_2)]
  2: [~(product(e_2,e_2,e_2))], ~(group_element(e_2))
  3: [~(product(e_2,e_2,e_1))], ~(group_element(e_2))
  4: [~(equalish(e_2,e_1))]

Gamma_68: (resolve)
  0: [~(group_element(e_2))]
  1: []
  2: [~(equalish(e_2,e_1))]

SZS status Unsatisfiable