第 25333 題：有限商群

原題與已知條件

完整有限群、subgroup與全部coset partition及代表元責任。操作=quotient-nonnormal-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[1,2,3,4,5,6,7,8,9,0,11,12,13,14,15,16,17,18,19,10],[2,3,4,5,6,7,8,9,0,1,12,13,14,15,16,17,18,19,10,11],[3,4,5,6,7,8,9,0,1,2,13,14,15,16,17,18,19,10,11,12],[4,5,6,7,8,9,0,1,2,3,14,15,16,17,18,19,10,11,12,13],[5,6,7,8,9,0,1,2,3,4,15,16,17,18,19,10,11,12,13,14],[6,7,8,9,0,1,2,3,4,5,16,17,18,19,10,11,12,13,14,15],[7,8,9,0,1,2,3,4,5,6,17,18,19,10,11,12,13,14,15,16],[8,9,0,1,2,3,4,5,6,7,18,19,10,11,12,13,14,15,16,17],[9,0,1,2,3,4,5,6,7,8,19,10,11,12,13,14,15,16,17,18],[10,19,18,17,16,15,14,13,12,11,0,9,8,7,6,5,4,3,2,1],[11,10,19,18,17,16,15,14,13,12,1,0,9,8,7,6,5,4,3,2],[12,11,10,19,18,17,16,15,14,13,2,1,0,9,8,7,6,5,4,3],[13,12,11,10,19,18,17,16,15,14,3,2,1,0,9,8,7,6,5,4],[14,13,12,11,10,19,18,17,16,15,4,3,2,1,0,9,8,7,6,5],[15,14,13,12,11,10,19,18,17,16,5,4,3,2,1,0,9,8,7,6],[16,15,14,13,12,11,10,19,18,17,6,5,4,3,2,1,0,9,8,7],[17,16,15,14,13,12,11,10,19,18,7,6,5,4,3,2,1,0,9,8],[18,17,16,15,14,13,12,11,10,19,8,7,6,5,4,3,2,1,0,9],[19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"subset":[0,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 完整有限群、subgroup與全部coset partition及代表元責任。操作=quotient-nonnormal-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[1,2,3,4,5,6,7,8,9,0,11,12,13,14,15,16,17,18,19,10],[2,3,4,5,6,7,8,9,0,1,12,13,14,15,16,17,18,19,10,11],[3,4,5,6,7,8,9,0,1,2,13,14,15,16,17,18,19,10,11,12],[4,5,6,7,8,9,0,1,2,3,14,15,16,17,18,19,10,11,12,13],[5,6,7,8,9,0,1,2,3,4,15,16,17,18,19,10,11,12,13,14],[6,7,8,9,0,1,2,3,4,5,16,17,18,19,10,11,12,13,14,15],[7,8,9,0,1,2,3,4,5,6,17,18,19,10,11,12,13,14,15,16],[8,9,0,1,2,3,4,5,6,7,18,19,10,11,12,13,14,15,16,17],[9,0,1,2,3,4,5,6,7,8,19,10,11,12,13,14,15,16,17,18],[10,19,18,17,16,15,14,13,12,11,0,9,8,7,6,5,4,3,2,1],[11,10,19,18,17,16,15,14,13,12,1,0,9,8,7,6,5,4,3,2],[12,11,10,19,18,17,16,15,14,13,2,1,0,9,8,7,6,5,4,3],[13,12,11,10,19,18,17,16,15,14,3,2,1,0,9,8,7,6,5,4],[14,13,12,11,10,19,18,17,16,15,4,3,2,1,0,9,8,7,6,5],[15,14,13,12,11,10,19,18,17,16,5,4,3,2,1,0,9,8,7,6],[16,15,14,13,12,11,10,19,18,17,6,5,4,3,2,1,0,9,8,7],[17,16,15,14,13,12,11,10,19,18,7,6,5,4,3,2,1,0,9,8],[18,17,16,15,14,13,12,11,10,19,8,7,6,5,4,3,2,1,0,9],[19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"subset":[0,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-finite-quotient-group

逐步推導

source roles = [quotient-nonnormal-boundary]

derived = [[subgroup, normal, cosets, representative_counterexample, well_defined, quotient_group_certificate, boundary]]

source roles = [[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10], [2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 13, 14, 15, 16, 17, 18, 19, 10, 11, 12], [4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 15, 16, 17, 18, 19, 10, 11, 12, 13, 14], [6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 17, 18, 19, 10, 11, 12, 13, 14, 15, 16], [8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 19, 10, 11, 12, 13, 14, 15, 16, 17, 18], [10, 19, 18, 17, 16, 15, 14, 13, 12, 11, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1], [11, 10, 19, 18, 17, 16, 15, 14, 13, 12, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2], [12, 11, 10, 19, 18, 17, 16, 15, 14, 13, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3], [13, 12, 11, 10, 19, 18, 17, 16, 15, 14, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4], [14, 13, 12, 11, 10, 19, 18, 17, 16, 15, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5], [15, 14, 13, 12, 11, 10, 19, 18, 17, 16, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6], [16, 15, 14, 13, 12, 11, 10, 19, 18, 17, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7], [17, 16, 15, 14, 13, 12, 11, 10, 19, 18, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8], [18, 17, 16, 15, 14, 13, 12, 11, 10, 19, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9], [19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]], 0]

derived = [20, [[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3], [4, 4, 4, 4], [5, 5, 5, 5], [6, 6, 6, 6], [7, 7, 7, 7], [8, 8, 8, 8], [9, 9, 9, 9], [10, 10, 10, 10], [11, 11, 11, 11], [12, 12, 12, 12], [13, 13, 13, 13], [14, 14, 14, 14], [15, 15, 15, 15], [16, 16, 16, 16], [17, 17, 17, 17], [18, 18, 18, 18], [19, 19, 19, 19]], 是]

source roles = [20, 0]

derived = [[[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 8000, [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]]

source roles = [0, [0, 10]]

derived = [[[0, 0, 0, 是], [0, 10, 10, 是], [10, 0, 10, 是], [10, 10, 0, 是]], [[0, 0, 是], [10, 10, 是]], 是, [[0, [0, 10]], [1, [0, 12]], [2, [0, 14]], [3, [0, 16]], [4, [0, 18]], [5, [0, 10]], [6, [0, 12]], [7, [0, 14]], [8, [0, 16]], [9, [0, 18]], [10, [0, 10]], [11, [0, 12]], [12, [0, 14]], [13, [0, 16]], [14, [0, 18]], [15, [0, 10]], [16, [0, 12]], [17, [0, 14]], [18, [0, 16]], [19, [0, 18]]], 否]

source roles = [[0, 10], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]]

derived = [[[0, 10], [1, 11], [2, 12], [3, 13], [4, 14], [5, 15], [6, 16], [7, 17], [8, 18], [9, 19]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]

source roles = [0, 0, [0, 10], [0, 10]]

derived = [[[0, 0, 0, 0], [0, 10, 10, 0], [10, 0, 10, 0], [10, 10, 0, 0]], [0], 是]

source roles = [0, 1, [0, 10], [1, 11]]

derived = [[[0, 1, 1, 1], [0, 11, 11, 1], [10, 1, 19, 9], [10, 11, 9, 9]], [1, 9], 否]

source roles = [0, 2, [0, 10], [2, 12]]

derived = [[[0, 2, 2, 2], [0, 12, 12, 2], [10, 2, 18, 8], [10, 12, 8, 8]], [2, 8], 否]

source roles = [0, 3, [0, 10], [3, 13]]

derived = [[[0, 3, 3, 3], [0, 13, 13, 3], [10, 3, 17, 7], [10, 13, 7, 7]], [3, 7], 否]

source roles = [0, 4, [0, 10], [4, 14]]

derived = [[[0, 4, 4, 4], [0, 14, 14, 4], [10, 4, 16, 6], [10, 14, 6, 6]], [4, 6], 否]

source roles = [0, 5, [0, 10], [5, 15]]

derived = [[[0, 5, 5, 5], [0, 15, 15, 5], [10, 5, 15, 5], [10, 15, 5, 5]], [5], 是]

source roles = [0, 6, [0, 10], [6, 16]]

derived = [[[0, 6, 6, 6], [0, 16, 16, 6], [10, 6, 14, 4], [10, 16, 4, 4]], [4, 6], 否]

source roles = [0, 7, [0, 10], [7, 17]]

derived = [[[0, 7, 7, 7], [0, 17, 17, 7], [10, 7, 13, 3], [10, 17, 3, 3]], [3, 7], 否]

source roles = [0, 8, [0, 10], [8, 18]]

derived = [[[0, 8, 8, 8], [0, 18, 18, 8], [10, 8, 12, 2], [10, 18, 2, 2]], [2, 8], 否]

source roles = [0, 9, [0, 10], [9, 19]]

derived = [[[0, 9, 9, 9], [0, 19, 19, 9], [10, 9, 11, 1], [10, 19, 1, 1]], [1, 9], 否]

source roles = [1, 0, [1, 11], [0, 10]]

derived = [[[1, 0, 1, 1], [1, 10, 11, 1], [11, 0, 11, 1], [11, 10, 1, 1]], [1], 是]

source roles = [1, 1, [1, 11], [1, 11]]

derived = [[[1, 1, 2, 2], [1, 11, 12, 2], [11, 1, 10, 0], [11, 11, 0, 0]], [0, 2], 否]

source roles = [1, 2, [1, 11], [2, 12]]

derived = [[[1, 2, 3, 3], [1, 12, 13, 3], [11, 2, 19, 9], [11, 12, 9, 9]], [3, 9], 否]

source roles = [1, 3, [1, 11], [3, 13]]

derived = [[[1, 3, 4, 4], [1, 13, 14, 4], [11, 3, 18, 8], [11, 13, 8, 8]], [4, 8], 否]

source roles = [1, 4, [1, 11], [4, 14]]

derived = [[[1, 4, 5, 5], [1, 14, 15, 5], [11, 4, 17, 7], [11, 14, 7, 7]], [5, 7], 否]

source roles = [1, 5, [1, 11], [5, 15]]

derived = [[[1, 5, 6, 6], [1, 15, 16, 6], [11, 5, 16, 6], [11, 15, 6, 6]], [6], 是]

source roles = [1, 6, [1, 11], [6, 16]]

derived = [[[1, 6, 7, 7], [1, 16, 17, 7], [11, 6, 15, 5], [11, 16, 5, 5]], [5, 7], 否]

source roles = [1, 7, [1, 11], [7, 17]]

derived = [[[1, 7, 8, 8], [1, 17, 18, 8], [11, 7, 14, 4], [11, 17, 4, 4]], [4, 8], 否]

source roles = [1, 8, [1, 11], [8, 18]]

derived = [[[1, 8, 9, 9], [1, 18, 19, 9], [11, 8, 13, 3], [11, 18, 3, 3]], [3, 9], 否]

source roles = [1, 9, [1, 11], [9, 19]]

derived = [[[1, 9, 0, 0], [1, 19, 10, 0], [11, 9, 12, 2], [11, 19, 2, 2]], [0, 2], 否]

source roles = [2, 0, [2, 12], [0, 10]]

derived = [[[2, 0, 2, 2], [2, 10, 12, 2], [12, 0, 12, 2], [12, 10, 2, 2]], [2], 是]

source roles = [2, 1, [2, 12], [1, 11]]

derived = [[[2, 1, 3, 3], [2, 11, 13, 3], [12, 1, 11, 1], [12, 11, 1, 1]], [1, 3], 否]

source roles = [2, 2, [2, 12], [2, 12]]

derived = [[[2, 2, 4, 4], [2, 12, 14, 4], [12, 2, 10, 0], [12, 12, 0, 0]], [0, 4], 否]

source roles = [2, 3, [2, 12], [3, 13]]

derived = [[[2, 3, 5, 5], [2, 13, 15, 5], [12, 3, 19, 9], [12, 13, 9, 9]], [5, 9], 否]

source roles = [2, 4, [2, 12], [4, 14]]

derived = [[[2, 4, 6, 6], [2, 14, 16, 6], [12, 4, 18, 8], [12, 14, 8, 8]], [6, 8], 否]

source roles = [2, 5, [2, 12], [5, 15]]

derived = [[[2, 5, 7, 7], [2, 15, 17, 7], [12, 5, 17, 7], [12, 15, 7, 7]], [7], 是]

source roles = [2, 6, [2, 12], [6, 16]]

derived = [[[2, 6, 8, 8], [2, 16, 18, 8], [12, 6, 16, 6], [12, 16, 6, 6]], [6, 8], 否]

source roles = [2, 7, [2, 12], [7, 17]]

derived = [[[2, 7, 9, 9], [2, 17, 19, 9], [12, 7, 15, 5], [12, 17, 5, 5]], [5, 9], 否]

source roles = [2, 8, [2, 12], [8, 18]]

derived = [[[2, 8, 0, 0], [2, 18, 10, 0], [12, 8, 14, 4], [12, 18, 4, 4]], [0, 4], 否]

source roles = [2, 9, [2, 12], [9, 19]]

derived = [[[2, 9, 1, 1], [2, 19, 11, 1], [12, 9, 13, 3], [12, 19, 3, 3]], [1, 3], 否]

source roles = [3, 0, [3, 13], [0, 10]]

derived = [[[3, 0, 3, 3], [3, 10, 13, 3], [13, 0, 13, 3], [13, 10, 3, 3]], [3], 是]

source roles = [3, 1, [3, 13], [1, 11]]

derived = [[[3, 1, 4, 4], [3, 11, 14, 4], [13, 1, 12, 2], [13, 11, 2, 2]], [2, 4], 否]

source roles = [3, 2, [3, 13], [2, 12]]

derived = [[[3, 2, 5, 5], [3, 12, 15, 5], [13, 2, 11, 1], [13, 12, 1, 1]], [1, 5], 否]

source roles = [3, 3, [3, 13], [3, 13]]

derived = [[[3, 3, 6, 6], [3, 13, 16, 6], [13, 3, 10, 0], [13, 13, 0, 0]], [0, 6], 否]

source roles = [3, 4, [3, 13], [4, 14]]

derived = [[[3, 4, 7, 7], [3, 14, 17, 7], [13, 4, 19, 9], [13, 14, 9, 9]], [7, 9], 否]

source roles = [3, 5, [3, 13], [5, 15]]

derived = [[[3, 5, 8, 8], [3, 15, 18, 8], [13, 5, 18, 8], [13, 15, 8, 8]], [8], 是]

source roles = [3, 6, [3, 13], [6, 16]]

derived = [[[3, 6, 9, 9], [3, 16, 19, 9], [13, 6, 17, 7], [13, 16, 7, 7]], [7, 9], 否]

source roles = [3, 7, [3, 13], [7, 17]]

derived = [[[3, 7, 0, 0], [3, 17, 10, 0], [13, 7, 16, 6], [13, 17, 6, 6]], [0, 6], 否]

source roles = [3, 8, [3, 13], [8, 18]]

derived = [[[3, 8, 1, 1], [3, 18, 11, 1], [13, 8, 15, 5], [13, 18, 5, 5]], [1, 5], 否]

source roles = [3, 9, [3, 13], [9, 19]]

derived = [[[3, 9, 2, 2], [3, 19, 12, 2], [13, 9, 14, 4], [13, 19, 4, 4]], [2, 4], 否]

source roles = [4, 0, [4, 14], [0, 10]]

derived = [[[4, 0, 4, 4], [4, 10, 14, 4], [14, 0, 14, 4], [14, 10, 4, 4]], [4], 是]

source roles = [4, 1, [4, 14], [1, 11]]

derived = [[[4, 1, 5, 5], [4, 11, 15, 5], [14, 1, 13, 3], [14, 11, 3, 3]], [3, 5], 否]

source roles = [4, 2, [4, 14], [2, 12]]

derived = [[[4, 2, 6, 6], [4, 12, 16, 6], [14, 2, 12, 2], [14, 12, 2, 2]], [2, 6], 否]

source roles = [4, 3, [4, 14], [3, 13]]

derived = [[[4, 3, 7, 7], [4, 13, 17, 7], [14, 3, 11, 1], [14, 13, 1, 1]], [1, 7], 否]

source roles = [4, 4, [4, 14], [4, 14]]

derived = [[[4, 4, 8, 8], [4, 14, 18, 8], [14, 4, 10, 0], [14, 14, 0, 0]], [0, 8], 否]

source roles = [4, 5, [4, 14], [5, 15]]

derived = [[[4, 5, 9, 9], [4, 15, 19, 9], [14, 5, 19, 9], [14, 15, 9, 9]], [9], 是]

source roles = [4, 6, [4, 14], [6, 16]]

derived = [[[4, 6, 0, 0], [4, 16, 10, 0], [14, 6, 18, 8], [14, 16, 8, 8]], [0, 8], 否]

source roles = [4, 7, [4, 14], [7, 17]]

derived = [[[4, 7, 1, 1], [4, 17, 11, 1], [14, 7, 17, 7], [14, 17, 7, 7]], [1, 7], 否]

source roles = [4, 8, [4, 14], [8, 18]]

derived = [[[4, 8, 2, 2], [4, 18, 12, 2], [14, 8, 16, 6], [14, 18, 6, 6]], [2, 6], 否]

source roles = [4, 9, [4, 14], [9, 19]]

derived = [[[4, 9, 3, 3], [4, 19, 13, 3], [14, 9, 15, 5], [14, 19, 5, 5]], [3, 5], 否]

source roles = [5, 0, [5, 15], [0, 10]]

derived = [[[5, 0, 5, 5], [5, 10, 15, 5], [15, 0, 15, 5], [15, 10, 5, 5]], [5], 是]

source roles = [5, 1, [5, 15], [1, 11]]

derived = [[[5, 1, 6, 6], [5, 11, 16, 6], [15, 1, 14, 4], [15, 11, 4, 4]], [4, 6], 否]

source roles = [5, 2, [5, 15], [2, 12]]

derived = [[[5, 2, 7, 7], [5, 12, 17, 7], [15, 2, 13, 3], [15, 12, 3, 3]], [3, 7], 否]

source roles = [5, 3, [5, 15], [3, 13]]

derived = [[[5, 3, 8, 8], [5, 13, 18, 8], [15, 3, 12, 2], [15, 13, 2, 2]], [2, 8], 否]

source roles = [5, 4, [5, 15], [4, 14]]

derived = [[[5, 4, 9, 9], [5, 14, 19, 9], [15, 4, 11, 1], [15, 14, 1, 1]], [1, 9], 否]

source roles = [5, 5, [5, 15], [5, 15]]

derived = [[[5, 5, 0, 0], [5, 15, 10, 0], [15, 5, 10, 0], [15, 15, 0, 0]], [0], 是]

source roles = [5, 6, [5, 15], [6, 16]]

derived = [[[5, 6, 1, 1], [5, 16, 11, 1], [15, 6, 19, 9], [15, 16, 9, 9]], [1, 9], 否]

source roles = [5, 7, [5, 15], [7, 17]]

derived = [[[5, 7, 2, 2], [5, 17, 12, 2], [15, 7, 18, 8], [15, 17, 8, 8]], [2, 8], 否]

source roles = [5, 8, [5, 15], [8, 18]]

derived = [[[5, 8, 3, 3], [5, 18, 13, 3], [15, 8, 17, 7], [15, 18, 7, 7]], [3, 7], 否]

source roles = [5, 9, [5, 15], [9, 19]]

derived = [[[5, 9, 4, 4], [5, 19, 14, 4], [15, 9, 16, 6], [15, 19, 6, 6]], [4, 6], 否]

source roles = [6, 0, [6, 16], [0, 10]]

derived = [[[6, 0, 6, 6], [6, 10, 16, 6], [16, 0, 16, 6], [16, 10, 6, 6]], [6], 是]

source roles = [6, 1, [6, 16], [1, 11]]

derived = [[[6, 1, 7, 7], [6, 11, 17, 7], [16, 1, 15, 5], [16, 11, 5, 5]], [5, 7], 否]

source roles = [6, 2, [6, 16], [2, 12]]

derived = [[[6, 2, 8, 8], [6, 12, 18, 8], [16, 2, 14, 4], [16, 12, 4, 4]], [4, 8], 否]

source roles = [6, 3, [6, 16], [3, 13]]

derived = [[[6, 3, 9, 9], [6, 13, 19, 9], [16, 3, 13, 3], [16, 13, 3, 3]], [3, 9], 否]

source roles = [6, 4, [6, 16], [4, 14]]

derived = [[[6, 4, 0, 0], [6, 14, 10, 0], [16, 4, 12, 2], [16, 14, 2, 2]], [0, 2], 否]

source roles = [6, 5, [6, 16], [5, 15]]

derived = [[[6, 5, 1, 1], [6, 15, 11, 1], [16, 5, 11, 1], [16, 15, 1, 1]], [1], 是]

source roles = [6, 6, [6, 16], [6, 16]]

derived = [[[6, 6, 2, 2], [6, 16, 12, 2], [16, 6, 10, 0], [16, 16, 0, 0]], [0, 2], 否]

source roles = [6, 7, [6, 16], [7, 17]]

derived = [[[6, 7, 3, 3], [6, 17, 13, 3], [16, 7, 19, 9], [16, 17, 9, 9]], [3, 9], 否]

source roles = [6, 8, [6, 16], [8, 18]]

derived = [[[6, 8, 4, 4], [6, 18, 14, 4], [16, 8, 18, 8], [16, 18, 8, 8]], [4, 8], 否]

source roles = [6, 9, [6, 16], [9, 19]]

derived = [[[6, 9, 5, 5], [6, 19, 15, 5], [16, 9, 17, 7], [16, 19, 7, 7]], [5, 7], 否]

source roles = [7, 0, [7, 17], [0, 10]]

derived = [[[7, 0, 7, 7], [7, 10, 17, 7], [17, 0, 17, 7], [17, 10, 7, 7]], [7], 是]

source roles = [7, 1, [7, 17], [1, 11]]

derived = [[[7, 1, 8, 8], [7, 11, 18, 8], [17, 1, 16, 6], [17, 11, 6, 6]], [6, 8], 否]

source roles = [7, 2, [7, 17], [2, 12]]

derived = [[[7, 2, 9, 9], [7, 12, 19, 9], [17, 2, 15, 5], [17, 12, 5, 5]], [5, 9], 否]

source roles = [7, 3, [7, 17], [3, 13]]

derived = [[[7, 3, 0, 0], [7, 13, 10, 0], [17, 3, 14, 4], [17, 13, 4, 4]], [0, 4], 否]

source roles = [7, 4, [7, 17], [4, 14]]

derived = [[[7, 4, 1, 1], [7, 14, 11, 1], [17, 4, 13, 3], [17, 14, 3, 3]], [1, 3], 否]

source roles = [7, 5, [7, 17], [5, 15]]

derived = [[[7, 5, 2, 2], [7, 15, 12, 2], [17, 5, 12, 2], [17, 15, 2, 2]], [2], 是]

source roles = [7, 6, [7, 17], [6, 16]]

derived = [[[7, 6, 3, 3], [7, 16, 13, 3], [17, 6, 11, 1], [17, 16, 1, 1]], [1, 3], 否]

source roles = [7, 7, [7, 17], [7, 17]]

derived = [[[7, 7, 4, 4], [7, 17, 14, 4], [17, 7, 10, 0], [17, 17, 0, 0]], [0, 4], 否]

source roles = [7, 8, [7, 17], [8, 18]]

derived = [[[7, 8, 5, 5], [7, 18, 15, 5], [17, 8, 19, 9], [17, 18, 9, 9]], [5, 9], 否]

source roles = [7, 9, [7, 17], [9, 19]]

derived = [[[7, 9, 6, 6], [7, 19, 16, 6], [17, 9, 18, 8], [17, 19, 8, 8]], [6, 8], 否]

source roles = [8, 0, [8, 18], [0, 10]]

derived = [[[8, 0, 8, 8], [8, 10, 18, 8], [18, 0, 18, 8], [18, 10, 8, 8]], [8], 是]

source roles = [8, 1, [8, 18], [1, 11]]

derived = [[[8, 1, 9, 9], [8, 11, 19, 9], [18, 1, 17, 7], [18, 11, 7, 7]], [7, 9], 否]

source roles = [8, 2, [8, 18], [2, 12]]

derived = [[[8, 2, 0, 0], [8, 12, 10, 0], [18, 2, 16, 6], [18, 12, 6, 6]], [0, 6], 否]

source roles = [8, 3, [8, 18], [3, 13]]

derived = [[[8, 3, 1, 1], [8, 13, 11, 1], [18, 3, 15, 5], [18, 13, 5, 5]], [1, 5], 否]

source roles = [8, 4, [8, 18], [4, 14]]

derived = [[[8, 4, 2, 2], [8, 14, 12, 2], [18, 4, 14, 4], [18, 14, 4, 4]], [2, 4], 否]

source roles = [8, 5, [8, 18], [5, 15]]

derived = [[[8, 5, 3, 3], [8, 15, 13, 3], [18, 5, 13, 3], [18, 15, 3, 3]], [3], 是]

source roles = [8, 6, [8, 18], [6, 16]]

derived = [[[8, 6, 4, 4], [8, 16, 14, 4], [18, 6, 12, 2], [18, 16, 2, 2]], [2, 4], 否]

source roles = [8, 7, [8, 18], [7, 17]]

derived = [[[8, 7, 5, 5], [8, 17, 15, 5], [18, 7, 11, 1], [18, 17, 1, 1]], [1, 5], 否]

source roles = [8, 8, [8, 18], [8, 18]]

derived = [[[8, 8, 6, 6], [8, 18, 16, 6], [18, 8, 10, 0], [18, 18, 0, 0]], [0, 6], 否]

source roles = [8, 9, [8, 18], [9, 19]]

derived = [[[8, 9, 7, 7], [8, 19, 17, 7], [18, 9, 19, 9], [18, 19, 9, 9]], [7, 9], 否]

source roles = [9, 0, [9, 19], [0, 10]]

derived = [[[9, 0, 9, 9], [9, 10, 19, 9], [19, 0, 19, 9], [19, 10, 9, 9]], [9], 是]

source roles = [9, 1, [9, 19], [1, 11]]

derived = [[[9, 1, 0, 0], [9, 11, 10, 0], [19, 1, 18, 8], [19, 11, 8, 8]], [0, 8], 否]

source roles = [9, 2, [9, 19], [2, 12]]

derived = [[[9, 2, 1, 1], [9, 12, 11, 1], [19, 2, 17, 7], [19, 12, 7, 7]], [1, 7], 否]

source roles = [9, 3, [9, 19], [3, 13]]

derived = [[[9, 3, 2, 2], [9, 13, 12, 2], [19, 3, 16, 6], [19, 13, 6, 6]], [2, 6], 否]

source roles = [9, 4, [9, 19], [4, 14]]

derived = [[[9, 4, 3, 3], [9, 14, 13, 3], [19, 4, 15, 5], [19, 14, 5, 5]], [3, 5], 否]

source roles = [9, 5, [9, 19], [5, 15]]

derived = [[[9, 5, 4, 4], [9, 15, 14, 4], [19, 5, 14, 4], [19, 15, 4, 4]], [4], 是]

source roles = [9, 6, [9, 19], [6, 16]]

derived = [[[9, 6, 5, 5], [9, 16, 15, 5], [19, 6, 13, 3], [19, 16, 3, 3]], [3, 5], 否]

source roles = [9, 7, [9, 19], [7, 17]]

derived = [[[9, 7, 6, 6], [9, 17, 16, 6], [19, 7, 12, 2], [19, 17, 2, 2]], [2, 6], 否]

source roles = [9, 8, [9, 19], [8, 18]]

derived = [[[9, 8, 7, 7], [9, 18, 17, 7], [19, 8, 11, 1], [19, 18, 1, 1]], [1, 7], 否]

source roles = [9, 9, [9, 19], [9, 19]]

derived = [[[9, 9, 8, 8], [9, 19, 18, 8], [19, 9, 10, 0], [19, 19, 0, 0]], [0, 8], 否]

source roles = [[0, 1, [1, 9], 否], [0, 10], [1, 11]]

derived = [[0, 1, 0, 1, 1, 10, 1, 9], 否, 否]

逐步反向核對

• S106 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S105 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S104 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S103 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S102 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S101 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S100 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S099 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S098 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S097 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S096 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S095 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S094 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S093 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S092 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S091 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S090 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S089 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S088 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S087 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S086 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S085 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S084 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S083 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S082 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S081 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S080 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S079 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S078 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S077 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S076 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S075 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S074 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S073 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S072 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S071 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S070 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S069 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S068 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S067 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S066 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S065 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S064 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S063 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S062 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S061 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S060 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S059 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S058 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S057 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S056 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S055 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S054 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S053 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S052 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S051 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S050 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S049 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S048 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S047 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S046 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S045 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S044 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S043 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S042 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S041 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S040 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S039 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S038 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S037 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S036 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S035 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S034 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S033 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S032 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S031 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S030 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S029 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S028 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S027 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S026 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S025 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S024 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S023 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S022 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S021 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S020 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S019 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S018 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S017 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S016 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S015 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S014 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S013 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S012 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S011 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S010 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S009 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S008 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S007 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S006 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S005 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S004 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。

結論

([0, 10], 否, [[0, 10], [1, 11], [2, 12], [3, 13], [4, 14], [5, 15], [6, 16], [7, 17], [8, 18], [9, 19]], [0, 1, 0, 1, 1, 10, 1, 9], 否, 否, explicit_representative_dependence_blocks_quotient_group_multiplication)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。