第 24965 題：有限群同態的核

原題與已知條件

完整來源／目標Cayley table與complete total map逐對同態核對。操作=kernel-normal-subgroup-audit；資料={"source_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],[26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],[28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],[30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]],"source_identity":0,"target_table":[[0,1],[1,0]],"target_identity":0,"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 完整來源／目標Cayley table與complete total map逐對同態核對。操作=kernel-normal-subgroup-audit；資料={"source_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[23,24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[24,25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[25,26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],[26,27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[27,28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],[28,29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[29,30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],[30,31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[31,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]],"source_identity":0,"target_table":[[0,1],[1,0]],"target_identity":0,"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。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-group-homomorphism-kernel

逐步推導

source roles = [kernel-normal-subgroup-audit]

derived = [[kernel, contains_identity, product_closed, inverse_closed, conjugate_rows, subgroup, normal, certificate]]

source roles = [Kernel ORIGINAL SOURCE group, 64, [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]], 0]

derived = [32, [[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], [20, 20, 20, 20], [21, 21, 21, 21], [22, 22, 22, 22], [23, 23, 23, 23], [24, 24, 24, 24], [25, 25, 25, 25], [26, 26, 26, 26], [27, 27, 27, 27], [28, 28, 28, 28], [29, 29, 29, 29], [30, 30, 30, 30], [31, 31, 31, 31]], 是]

source roles = [Kernel ORIGINAL SOURCE group, 32, FOR EVERY x,y,z in0..n-1]

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, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 32768, 是]

source roles = [Kernel ORIGINAL SOURCE group, 0]

derived = [[0, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [[0, 0, 0, 0], [1, 31, 0, 0], [2, 30, 0, 0], [3, 29, 0, 0], [4, 28, 0, 0], [5, 27, 0, 0], [6, 26, 0, 0], [7, 25, 0, 0], [8, 24, 0, 0], [9, 23, 0, 0], [10, 22, 0, 0], [11, 21, 0, 0], [12, 20, 0, 0], [13, 19, 0, 0], [14, 18, 0, 0], [15, 17, 0, 0], [16, 16, 0, 0], [17, 15, 0, 0], [18, 14, 0, 0], [19, 13, 0, 0], [20, 12, 0, 0], [21, 11, 0, 0], [22, 10, 0, 0], [23, 9, 0, 0], [24, 8, 0, 0], [25, 7, 0, 0], [26, 6, 0, 0], [27, 5, 0, 0], [28, 4, 0, 0], [29, 3, 0, 0], [30, 2, 0, 0], [31, 1, 0, 0]], 是]

source roles = [Kernel ORIGINAL TARGET group, 64, [[0, 1], [1, 0]], 0]

derived = [2, [[0, 0, 0, 0], [1, 1, 1, 1]], 是]

source roles = [Kernel ORIGINAL TARGET group, 2, FOR EVERY x,y,z in0..n-1]

derived = [[[是, 是], [是, 是]], 8, 是]

source roles = [Kernel ORIGINAL TARGET group, 0]

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

source roles = [[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]], [[0, 1], [1, 0]], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]]

derived = [[[0, 0, 0, 0, 是], [0, 1, 1, 1, 是], [0, 2, 0, 0, 是], [0, 3, 1, 1, 是], [0, 4, 0, 0, 是], [0, 5, 1, 1, 是], [0, 6, 0, 0, 是], [0, 7, 1, 1, 是], [0, 8, 0, 0, 是], [0, 9, 1, 1, 是], [0, 10, 0, 0, 是], [0, 11, 1, 1, 是], [0, 12, 0, 0, 是], [0, 13, 1, 1, 是], [0, 14, 0, 0, 是], [0, 15, 1, 1, 是], [0, 16, 0, 0, 是], [0, 17, 1, 1, 是], [0, 18, 0, 0, 是], [0, 19, 1, 1, 是], [0, 20, 0, 0, 是], [0, 21, 1, 1, 是], [0, 22, 0, 0, 是], [0, 23, 1, 1, 是], [0, 24, 0, 0, 是], [0, 25, 1, 1, 是], [0, 26, 0, 0, 是], [0, 27, 1, 1, 是], [0, 28, 0, 0, 是], [0, 29, 1, 1, 是], [0, 30, 0, 0, 是], [0, 31, 1, 1, 是], [1, 0, 1, 1, 是], [1, 1, 0, 0, 是], [1, 2, 1, 1, 是], [1, 3, 0, 0, 是], [1, 4, 1, 1, 是], [1, 5, 0, 0, 是], [1, 6, 1, 1, 是], [1, 7, 0, 0, 是], [1, 8, 1, 1, 是], [1, 9, 0, 0, 是], [1, 10, 1, 1, 是], [1, 11, 0, 0, 是], [1, 12, 1, 1, 是], [1, 13, 0, 0, 是], [1, 14, 1, 1, 是], [1, 15, 0, 0, 是], [1, 16, 1, 1, 是], [1, 17, 0, 0, 是], [1, 18, 1, 1, 是], [1, 19, 0, 0, 是], [1, 20, 1, 1, 是], [1, 21, 0, 0, 是], [1, 22, 1, 1, 是], [1, 23, 0, 0, 是], 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[22, 8, 0, 0, 是], [22, 9, 1, 1, 是], [22, 10, 0, 0, 是], [22, 11, 1, 1, 是], [22, 12, 0, 0, 是], [22, 13, 1, 1, 是], [22, 14, 0, 0, 是], [22, 15, 1, 1, 是], [22, 16, 0, 0, 是], [22, 17, 1, 1, 是], [22, 18, 0, 0, 是], [22, 19, 1, 1, 是], [22, 20, 0, 0, 是], [22, 21, 1, 1, 是], [22, 22, 0, 0, 是], [22, 23, 1, 1, 是], [22, 24, 0, 0, 是], [22, 25, 1, 1, 是], [22, 26, 0, 0, 是], [22, 27, 1, 1, 是], [22, 28, 0, 0, 是], [22, 29, 1, 1, 是], [22, 30, 0, 0, 是], [22, 31, 1, 1, 是], [23, 0, 1, 1, 是], [23, 1, 0, 0, 是], [23, 2, 1, 1, 是], [23, 3, 0, 0, 是], [23, 4, 1, 1, 是], [23, 5, 0, 0, 是], [23, 6, 1, 1, 是], [23, 7, 0, 0, 是], [23, 8, 1, 1, 是], [23, 9, 0, 0, 是], [23, 10, 1, 1, 是], [23, 11, 0, 0, 是], [23, 12, 1, 1, 是], [23, 13, 0, 0, 是], [23, 14, 1, 1, 是], [23, 15, 0, 0, 是], [23, 16, 1, 1, 是], [23, 17, 0, 0, 是], [23, 18, 1, 1, 是], [23, 19, 0, 0, 是], [23, 20, 1, 1, 是], [23, 21, 0, 0, 是], [23, 22, 1, 1, 是], [23, 23, 0, 0, 是], [23, 24, 1, 1, 是], [23, 25, 0, 0, 是], [23, 26, 1, 1, 是], [23, 27, 0, 0, 是], [23, 28, 1, 1, 是], [23, 29, 0, 0, 是], [23, 30, 1, 1, 是], [23, 31, 0, 0, 是], [24, 0, 0, 0, 是], [24, 1, 1, 1, 是], [24, 2, 0, 0, 是], [24, 3, 1, 1, 是], [24, 4, 0, 0, 是], [24, 5, 1, 1, 是], [24, 6, 0, 0, 是], [24, 7, 1, 1, 是], [24, 8, 0, 0, 是], [24, 9, 1, 1, 是], [24, 10, 0, 0, 是], [24, 11, 1, 1, 是], [24, 12, 0, 0, 是], [24, 13, 1, 1, 是], [24, 14, 0, 0, 是], [24, 15, 1, 1, 是], [24, 16, 0, 0, 是], [24, 17, 1, 1, 是], [24, 18, 0, 0, 是], [24, 19, 1, 1, 是], [24, 20, 0, 0, 是], [24, 21, 1, 1, 是], [24, 22, 0, 0, 是], [24, 23, 1, 1, 是], [24, 24, 0, 0, 是], [24, 25, 1, 1, 是], [24, 26, 0, 0, 是], [24, 27, 1, 1, 是], [24, 28, 0, 0, 是], [24, 29, 1, 1, 是], [24, 30, 0, 0, 是], [24, 31, 1, 1, 是], [25, 0, 1, 1, 是], [25, 1, 0, 0, 是], [25, 2, 1, 1, 是], [25, 3, 0, 0, 是], [25, 4, 1, 1, 是], [25, 5, 0, 0, 是], [25, 6, 1, 1, 是], [25, 7, 0, 0, 是], [25, 8, 1, 1, 是], [25, 9, 0, 0, 是], [25, 10, 1, 1, 是], [25, 11, 0, 0, 是], [25, 12, 1, 1, 是], [25, 13, 0, 0, 是], [25, 14, 1, 1, 是], [25, 15, 0, 0, 是], [25, 16, 1, 1, 是], [25, 17, 0, 0, 是], [25, 18, 1, 1, 是], [25, 19, 0, 0, 是], [25, 20, 1, 1, 是], [25, 21, 0, 0, 是], [25, 22, 1, 1, 是], [25, 23, 0, 0, 是], [25, 24, 1, 1, 是], [25, 25, 0, 0, 是], [25, 26, 1, 1, 是], [25, 27, 0, 0, 是], [25, 28, 1, 1, 是], [25, 29, 0, 0, 是], [25, 30, 1, 1, 是], [25, 31, 0, 0, 是], [26, 0, 0, 0, 是], [26, 1, 1, 1, 是], [26, 2, 0, 0, 是], [26, 3, 1, 1, 是], [26, 4, 0, 0, 是], [26, 5, 1, 1, 是], [26, 6, 0, 0, 是], [26, 7, 1, 1, 是], [26, 8, 0, 0, 是], [26, 9, 1, 1, 是], [26, 10, 0, 0, 是], [26, 11, 1, 1, 是], [26, 12, 0, 0, 是], [26, 13, 1, 1, 是], [26, 14, 0, 0, 是], [26, 15, 1, 1, 是], [26, 16, 0, 0, 是], [26, 17, 1, 1, 是], [26, 18, 0, 0, 是], [26, 19, 1, 1, 是], [26, 20, 0, 0, 是], [26, 21, 1, 1, 是], [26, 22, 0, 0, 是], [26, 23, 1, 1, 是], [26, 24, 0, 0, 是], [26, 25, 1, 1, 是], [26, 26, 0, 0, 是], [26, 27, 1, 1, 是], [26, 28, 0, 0, 是], [26, 29, 1, 1, 是], [26, 30, 0, 0, 是], [26, 31, 1, 1, 是], [27, 0, 1, 1, 是], [27, 1, 0, 0, 是], [27, 2, 1, 1, 是], [27, 3, 0, 0, 是], [27, 4, 1, 1, 是], [27, 5, 0, 0, 是], [27, 6, 1, 1, 是], [27, 7, 0, 0, 是], [27, 8, 1, 1, 是], [27, 9, 0, 0, 是], [27, 10, 1, 1, 是], [27, 11, 0, 0, 是], [27, 12, 1, 1, 是], [27, 13, 0, 0, 是], [27, 14, 1, 1, 是], [27, 15, 0, 0, 是], [27, 16, 1, 1, 是], [27, 17, 0, 0, 是], [27, 18, 1, 1, 是], [27, 19, 0, 0, 是], [27, 20, 1, 1, 是], [27, 21, 0, 0, 是], [27, 22, 1, 1, 是], [27, 23, 0, 0, 是], [27, 24, 1, 1, 是], [27, 25, 0, 0, 是], [27, 26, 1, 1, 是], [27, 27, 0, 0, 是], [27, 28, 1, 1, 是], [27, 29, 0, 0, 是], [27, 30, 1, 1, 是], [27, 31, 0, 0, 是], [28, 0, 0, 0, 是], [28, 1, 1, 1, 是], [28, 2, 0, 0, 是], [28, 3, 1, 1, 是], [28, 4, 0, 0, 是], [28, 5, 1, 1, 是], [28, 6, 0, 0, 是], [28, 7, 1, 1, 是], [28, 8, 0, 0, 是], [28, 9, 1, 1, 是], [28, 10, 0, 0, 是], [28, 11, 1, 1, 是], [28, 12, 0, 0, 是], [28, 13, 1, 1, 是], [28, 14, 0, 0, 是], [28, 15, 1, 1, 是], [28, 16, 0, 0, 是], [28, 17, 1, 1, 是], [28, 18, 0, 0, 是], [28, 19, 1, 1, 是], [28, 20, 0, 0, 是], [28, 21, 1, 1, 是], [28, 22, 0, 0, 是], [28, 23, 1, 1, 是], [28, 24, 0, 0, 是], [28, 25, 1, 1, 是], [28, 26, 0, 0, 是], [28, 27, 1, 1, 是], [28, 28, 0, 0, 是], [28, 29, 1, 1, 是], [28, 30, 0, 0, 是], [28, 31, 1, 1, 是], [29, 0, 1, 1, 是], [29, 1, 0, 0, 是], [29, 2, 1, 1, 是], [29, 3, 0, 0, 是], [29, 4, 1, 1, 是], [29, 5, 0, 0, 是], [29, 6, 1, 1, 是], [29, 7, 0, 0, 是], [29, 8, 1, 1, 是], [29, 9, 0, 0, 是], [29, 10, 1, 1, 是], [29, 11, 0, 0, 是], [29, 12, 1, 1, 是], [29, 13, 0, 0, 是], [29, 14, 1, 1, 是], [29, 15, 0, 0, 是], [29, 16, 1, 1, 是], [29, 17, 0, 0, 是], [29, 18, 1, 1, 是], [29, 19, 0, 0, 是], [29, 20, 1, 1, 是], [29, 21, 0, 0, 是], [29, 22, 1, 1, 是], [29, 23, 0, 0, 是], [29, 24, 1, 1, 是], [29, 25, 0, 0, 是], [29, 26, 1, 1, 是], [29, 27, 0, 0, 是], [29, 28, 1, 1, 是], [29, 29, 0, 0, 是], [29, 30, 1, 1, 是], [29, 31, 0, 0, 是], [30, 0, 0, 0, 是], [30, 1, 1, 1, 是], [30, 2, 0, 0, 是], [30, 3, 1, 1, 是], [30, 4, 0, 0, 是], [30, 5, 1, 1, 是], [30, 6, 0, 0, 是], [30, 7, 1, 1, 是], [30, 8, 0, 0, 是], [30, 9, 1, 1, 是], [30, 10, 0, 0, 是], [30, 11, 1, 1, 是], [30, 12, 0, 0, 是], [30, 13, 1, 1, 是], [30, 14, 0, 0, 是], [30, 15, 1, 1, 是], [30, 16, 0, 0, 是], [30, 17, 1, 1, 是], [30, 18, 0, 0, 是], [30, 19, 1, 1, 是], [30, 20, 0, 0, 是], [30, 21, 1, 1, 是], [30, 22, 0, 0, 是], [30, 23, 1, 1, 是], [30, 24, 0, 0, 是], [30, 25, 1, 1, 是], [30, 26, 0, 0, 是], [30, 27, 1, 1, 是], [30, 28, 0, 0, 是], [30, 29, 1, 1, 是], [30, 30, 0, 0, 是], [30, 31, 1, 1, 是], [31, 0, 1, 1, 是], [31, 1, 0, 0, 是], [31, 2, 1, 1, 是], [31, 3, 0, 0, 是], [31, 4, 1, 1, 是], [31, 5, 0, 0, 是], [31, 6, 1, 1, 是], [31, 7, 0, 0, 是], [31, 8, 1, 1, 是], [31, 9, 0, 0, 是], [31, 10, 1, 1, 是], [31, 11, 0, 0, 是], [31, 12, 1, 1, 是], [31, 13, 0, 0, 是], [31, 14, 1, 1, 是], [31, 15, 0, 0, 是], [31, 16, 1, 1, 是], [31, 17, 0, 0, 是], [31, 18, 1, 1, 是], [31, 19, 0, 0, 是], [31, 20, 1, 1, 是], [31, 21, 0, 0, 是], [31, 22, 1, 1, 是], [31, 23, 0, 0, 是], [31, 24, 1, 1, 是], [31, 25, 0, 0, 是], [31, 26, 1, 1, 是], [31, 27, 0, 0, 是], [31, 28, 1, 1, 是], [31, 29, 0, 0, 是], [31, 30, 1, 1, 是], [31, 31, 0, 0, 是]], 是, null]

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

derived = [[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 0, 0]

source roles = [Kernel ACTUAL identity preimage, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 0]

derived = [是, [[0, 0, 0, 是], [0, 2, 2, 是], [0, 4, 4, 是], [0, 6, 6, 是], [0, 8, 8, 是], [0, 10, 10, 是], [0, 12, 12, 是], [0, 14, 14, 是], [0, 16, 16, 是], [0, 18, 18, 是], [0, 20, 20, 是], [0, 22, 22, 是], [0, 24, 24, 是], [0, 26, 26, 是], [0, 28, 28, 是], [0, 30, 30, 是], [2, 0, 2, 是], [2, 2, 4, 是], [2, 4, 6, 是], [2, 6, 8, 是], [2, 8, 10, 是], [2, 10, 12, 是], [2, 12, 14, 是], [2, 14, 16, 是], [2, 16, 18, 是], [2, 18, 20, 是], [2, 20, 22, 是], [2, 22, 24, 是], [2, 24, 26, 是], [2, 26, 28, 是], [2, 28, 30, 是], [2, 30, 0, 是], [4, 0, 4, 是], [4, 2, 6, 是], [4, 4, 8, 是], [4, 6, 10, 是], [4, 8, 12, 是], [4, 10, 14, 是], [4, 12, 16, 是], [4, 14, 18, 是], [4, 16, 20, 是], [4, 18, 22, 是], [4, 20, 24, 是], [4, 22, 26, 是], [4, 24, 28, 是], [4, 26, 30, 是], [4, 28, 0, 是], [4, 30, 2, 是], [6, 0, 6, 是], [6, 2, 8, 是], [6, 4, 10, 是], [6, 6, 12, 是], [6, 8, 14, 是], [6, 10, 16, 是], [6, 12, 18, 是], [6, 14, 20, 是], [6, 16, 22, 是], [6, 18, 24, 是], [6, 20, 26, 是], [6, 22, 28, 是], [6, 24, 30, 是], [6, 26, 0, 是], [6, 28, 2, 是], [6, 30, 4, 是], [8, 0, 8, 是], [8, 2, 10, 是], [8, 4, 12, 是], [8, 6, 14, 是], [8, 8, 16, 是], [8, 10, 18, 是], [8, 12, 20, 是], [8, 14, 22, 是], [8, 16, 24, 是], [8, 18, 26, 是], [8, 20, 28, 是], [8, 22, 30, 是], [8, 24, 0, 是], [8, 26, 2, 是], [8, 28, 4, 是], [8, 30, 6, 是], [10, 0, 10, 是], [10, 2, 12, 是], [10, 4, 14, 是], [10, 6, 16, 是], [10, 8, 18, 是], [10, 10, 20, 是], [10, 12, 22, 是], [10, 14, 24, 是], [10, 16, 26, 是], [10, 18, 28, 是], [10, 20, 30, 是], [10, 22, 0, 是], [10, 24, 2, 是], [10, 26, 4, 是], [10, 28, 6, 是], [10, 30, 8, 是], [12, 0, 12, 是], [12, 2, 14, 是], [12, 4, 16, 是], [12, 6, 18, 是], [12, 8, 20, 是], [12, 10, 22, 是], [12, 12, 24, 是], [12, 14, 26, 是], [12, 16, 28, 是], [12, 18, 30, 是], [12, 20, 0, 是], [12, 22, 2, 是], [12, 24, 4, 是], [12, 26, 6, 是], [12, 28, 8, 是], [12, 30, 10, 是], [14, 0, 14, 是], [14, 2, 16, 是], [14, 4, 18, 是], [14, 6, 20, 是], [14, 8, 22, 是], [14, 10, 24, 是], [14, 12, 26, 是], [14, 14, 28, 是], [14, 16, 30, 是], [14, 18, 0, 是], [14, 20, 2, 是], [14, 22, 4, 是], [14, 24, 6, 是], [14, 26, 8, 是], [14, 28, 10, 是], [14, 30, 12, 是], [16, 0, 16, 是], [16, 2, 18, 是], [16, 4, 20, 是], [16, 6, 22, 是], [16, 8, 24, 是], [16, 10, 26, 是], [16, 12, 28, 是], [16, 14, 30, 是], [16, 16, 0, 是], [16, 18, 2, 是], [16, 20, 4, 是], [16, 22, 6, 是], [16, 24, 8, 是], [16, 26, 10, 是], [16, 28, 12, 是], [16, 30, 14, 是], [18, 0, 18, 是], [18, 2, 20, 是], [18, 4, 22, 是], [18, 6, 24, 是], [18, 8, 26, 是], [18, 10, 28, 是], [18, 12, 30, 是], [18, 14, 0, 是], [18, 16, 2, 是], [18, 18, 4, 是], [18, 20, 6, 是], [18, 22, 8, 是], [18, 24, 10, 是], [18, 26, 12, 是], [18, 28, 14, 是], [18, 30, 16, 是], [20, 0, 20, 是], [20, 2, 22, 是], [20, 4, 24, 是], [20, 6, 26, 是], [20, 8, 28, 是], [20, 10, 30, 是], [20, 12, 0, 是], [20, 14, 2, 是], [20, 16, 4, 是], [20, 18, 6, 是], [20, 20, 8, 是], [20, 22, 10, 是], [20, 24, 12, 是], [20, 26, 14, 是], [20, 28, 16, 是], [20, 30, 18, 是], [22, 0, 22, 是], [22, 2, 24, 是], [22, 4, 26, 是], [22, 6, 28, 是], [22, 8, 30, 是], [22, 10, 0, 是], [22, 12, 2, 是], [22, 14, 4, 是], [22, 16, 6, 是], [22, 18, 8, 是], [22, 20, 10, 是], [22, 22, 12, 是], [22, 24, 14, 是], [22, 26, 16, 是], [22, 28, 18, 是], [22, 30, 20, 是], [24, 0, 24, 是], [24, 2, 26, 是], [24, 4, 28, 是], [24, 6, 30, 是], [24, 8, 0, 是], [24, 10, 2, 是], [24, 12, 4, 是], [24, 14, 6, 是], [24, 16, 8, 是], [24, 18, 10, 是], [24, 20, 12, 是], [24, 22, 14, 是], [24, 24, 16, 是], [24, 26, 18, 是], [24, 28, 20, 是], [24, 30, 22, 是], [26, 0, 26, 是], [26, 2, 28, 是], [26, 4, 30, 是], [26, 6, 0, 是], [26, 8, 2, 是], [26, 10, 4, 是], [26, 12, 6, 是], [26, 14, 8, 是], [26, 16, 10, 是], [26, 18, 12, 是], [26, 20, 14, 是], [26, 22, 16, 是], [26, 24, 18, 是], [26, 26, 20, 是], [26, 28, 22, 是], [26, 30, 24, 是], [28, 0, 28, 是], [28, 2, 30, 是], [28, 4, 0, 是], [28, 6, 2, 是], [28, 8, 4, 是], [28, 10, 6, 是], [28, 12, 8, 是], [28, 14, 10, 是], [28, 16, 12, 是], [28, 18, 14, 是], [28, 20, 16, 是], [28, 22, 18, 是], [28, 24, 20, 是], [28, 26, 22, 是], [28, 28, 24, 是], [28, 30, 26, 是], [30, 0, 30, 是], [30, 2, 0, 是], [30, 4, 2, 是], [30, 6, 4, 是], [30, 8, 6, 是], [30, 10, 8, 是], [30, 12, 10, 是], [30, 14, 12, 是], [30, 16, 14, 是], [30, 18, 16, 是], [30, 20, 18, 是], [30, 22, 20, 是], [30, 24, 22, 是], [30, 26, 24, 是], [30, 28, 26, 是], [30, 30, 28, 是]], 是, [[0, 0, 是], [2, 30, 是], [4, 28, 是], [6, 26, 是], [8, 24, 是], [10, 22, 是], [12, 20, 是], [14, 18, 是], [16, 16, 是], [18, 14, 是], [20, 12, 是], [22, 10, 是], [24, 8, 是], [26, 6, 是], [28, 4, 是], [30, 2, 是]], 是, 是]

source roles = [Kernel ACTUAL identity preimage, 0, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 0]

derived = [[[0, 0, 0, 0], [2, 2, 0, 2], [4, 4, 0, 4], [6, 6, 0, 6], [8, 8, 0, 8], [10, 10, 0, 10], [12, 12, 0, 12], [14, 14, 0, 14], [16, 16, 0, 16], [18, 18, 0, 18], [20, 20, 0, 20], [22, 22, 0, 22], [24, 24, 0, 24], [26, 26, 0, 26], [28, 28, 0, 28], [30, 30, 0, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 1, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 31]

derived = [[[0, 1, 31, 0], [2, 3, 31, 2], [4, 5, 31, 4], [6, 7, 31, 6], [8, 9, 31, 8], [10, 11, 31, 10], [12, 13, 31, 12], [14, 15, 31, 14], [16, 17, 31, 16], [18, 19, 31, 18], [20, 21, 31, 20], [22, 23, 31, 22], [24, 25, 31, 24], [26, 27, 31, 26], [28, 29, 31, 28], [30, 31, 31, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 2, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 30]

derived = [[[0, 2, 30, 0], [2, 4, 30, 2], [4, 6, 30, 4], [6, 8, 30, 6], [8, 10, 30, 8], [10, 12, 30, 10], [12, 14, 30, 12], [14, 16, 30, 14], [16, 18, 30, 16], [18, 20, 30, 18], [20, 22, 30, 20], [22, 24, 30, 22], [24, 26, 30, 24], [26, 28, 30, 26], [28, 30, 30, 28], [30, 0, 30, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 3, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 29]

derived = [[[0, 3, 29, 0], [2, 5, 29, 2], [4, 7, 29, 4], [6, 9, 29, 6], [8, 11, 29, 8], [10, 13, 29, 10], [12, 15, 29, 12], [14, 17, 29, 14], [16, 19, 29, 16], [18, 21, 29, 18], [20, 23, 29, 20], [22, 25, 29, 22], [24, 27, 29, 24], [26, 29, 29, 26], [28, 31, 29, 28], [30, 1, 29, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 4, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 28]

derived = [[[0, 4, 28, 0], [2, 6, 28, 2], [4, 8, 28, 4], [6, 10, 28, 6], [8, 12, 28, 8], [10, 14, 28, 10], [12, 16, 28, 12], [14, 18, 28, 14], [16, 20, 28, 16], [18, 22, 28, 18], [20, 24, 28, 20], [22, 26, 28, 22], [24, 28, 28, 24], [26, 30, 28, 26], [28, 0, 28, 28], [30, 2, 28, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 5, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 27]

derived = [[[0, 5, 27, 0], [2, 7, 27, 2], [4, 9, 27, 4], [6, 11, 27, 6], [8, 13, 27, 8], [10, 15, 27, 10], [12, 17, 27, 12], [14, 19, 27, 14], [16, 21, 27, 16], [18, 23, 27, 18], [20, 25, 27, 20], [22, 27, 27, 22], [24, 29, 27, 24], [26, 31, 27, 26], [28, 1, 27, 28], [30, 3, 27, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 6, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 26]

derived = [[[0, 6, 26, 0], [2, 8, 26, 2], [4, 10, 26, 4], [6, 12, 26, 6], [8, 14, 26, 8], [10, 16, 26, 10], [12, 18, 26, 12], [14, 20, 26, 14], [16, 22, 26, 16], [18, 24, 26, 18], [20, 26, 26, 20], [22, 28, 26, 22], [24, 30, 26, 24], [26, 0, 26, 26], [28, 2, 26, 28], [30, 4, 26, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 7, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 25]

derived = [[[0, 7, 25, 0], [2, 9, 25, 2], [4, 11, 25, 4], [6, 13, 25, 6], [8, 15, 25, 8], [10, 17, 25, 10], [12, 19, 25, 12], [14, 21, 25, 14], [16, 23, 25, 16], [18, 25, 25, 18], [20, 27, 25, 20], [22, 29, 25, 22], [24, 31, 25, 24], [26, 1, 25, 26], [28, 3, 25, 28], [30, 5, 25, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 8, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 24]

derived = [[[0, 8, 24, 0], [2, 10, 24, 2], [4, 12, 24, 4], [6, 14, 24, 6], [8, 16, 24, 8], [10, 18, 24, 10], [12, 20, 24, 12], [14, 22, 24, 14], [16, 24, 24, 16], [18, 26, 24, 18], [20, 28, 24, 20], [22, 30, 24, 22], [24, 0, 24, 24], [26, 2, 24, 26], [28, 4, 24, 28], [30, 6, 24, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 9, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 23]

derived = [[[0, 9, 23, 0], [2, 11, 23, 2], [4, 13, 23, 4], [6, 15, 23, 6], [8, 17, 23, 8], [10, 19, 23, 10], [12, 21, 23, 12], [14, 23, 23, 14], [16, 25, 23, 16], [18, 27, 23, 18], [20, 29, 23, 20], [22, 31, 23, 22], [24, 1, 23, 24], [26, 3, 23, 26], [28, 5, 23, 28], [30, 7, 23, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 10, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 22]

derived = [[[0, 10, 22, 0], [2, 12, 22, 2], [4, 14, 22, 4], [6, 16, 22, 6], [8, 18, 22, 8], [10, 20, 22, 10], [12, 22, 22, 12], [14, 24, 22, 14], [16, 26, 22, 16], [18, 28, 22, 18], [20, 30, 22, 20], [22, 0, 22, 22], [24, 2, 22, 24], [26, 4, 22, 26], [28, 6, 22, 28], [30, 8, 22, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 11, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 21]

derived = [[[0, 11, 21, 0], [2, 13, 21, 2], [4, 15, 21, 4], [6, 17, 21, 6], [8, 19, 21, 8], [10, 21, 21, 10], [12, 23, 21, 12], [14, 25, 21, 14], [16, 27, 21, 16], [18, 29, 21, 18], [20, 31, 21, 20], [22, 1, 21, 22], [24, 3, 21, 24], [26, 5, 21, 26], [28, 7, 21, 28], [30, 9, 21, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 12, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 20]

derived = [[[0, 12, 20, 0], [2, 14, 20, 2], [4, 16, 20, 4], [6, 18, 20, 6], [8, 20, 20, 8], [10, 22, 20, 10], [12, 24, 20, 12], [14, 26, 20, 14], [16, 28, 20, 16], [18, 30, 20, 18], [20, 0, 20, 20], [22, 2, 20, 22], [24, 4, 20, 24], [26, 6, 20, 26], [28, 8, 20, 28], [30, 10, 20, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 13, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 19]

derived = [[[0, 13, 19, 0], [2, 15, 19, 2], [4, 17, 19, 4], [6, 19, 19, 6], [8, 21, 19, 8], [10, 23, 19, 10], [12, 25, 19, 12], [14, 27, 19, 14], [16, 29, 19, 16], [18, 31, 19, 18], [20, 1, 19, 20], [22, 3, 19, 22], [24, 5, 19, 24], [26, 7, 19, 26], [28, 9, 19, 28], [30, 11, 19, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 14, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 18]

derived = [[[0, 14, 18, 0], [2, 16, 18, 2], [4, 18, 18, 4], [6, 20, 18, 6], [8, 22, 18, 8], [10, 24, 18, 10], [12, 26, 18, 12], [14, 28, 18, 14], [16, 30, 18, 16], [18, 0, 18, 18], [20, 2, 18, 20], [22, 4, 18, 22], [24, 6, 18, 24], [26, 8, 18, 26], [28, 10, 18, 28], [30, 12, 18, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 15, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 17]

derived = [[[0, 15, 17, 0], [2, 17, 17, 2], [4, 19, 17, 4], [6, 21, 17, 6], [8, 23, 17, 8], [10, 25, 17, 10], [12, 27, 17, 12], [14, 29, 17, 14], [16, 31, 17, 16], [18, 1, 17, 18], [20, 3, 17, 20], [22, 5, 17, 22], [24, 7, 17, 24], [26, 9, 17, 26], [28, 11, 17, 28], [30, 13, 17, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 16, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 16]

derived = [[[0, 16, 16, 0], [2, 18, 16, 2], [4, 20, 16, 4], [6, 22, 16, 6], [8, 24, 16, 8], [10, 26, 16, 10], [12, 28, 16, 12], [14, 30, 16, 14], [16, 0, 16, 16], [18, 2, 16, 18], [20, 4, 16, 20], [22, 6, 16, 22], [24, 8, 16, 24], [26, 10, 16, 26], [28, 12, 16, 28], [30, 14, 16, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 17, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 15]

derived = [[[0, 17, 15, 0], [2, 19, 15, 2], [4, 21, 15, 4], [6, 23, 15, 6], [8, 25, 15, 8], [10, 27, 15, 10], [12, 29, 15, 12], [14, 31, 15, 14], [16, 1, 15, 16], [18, 3, 15, 18], [20, 5, 15, 20], [22, 7, 15, 22], [24, 9, 15, 24], [26, 11, 15, 26], [28, 13, 15, 28], [30, 15, 15, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 18, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 14]

derived = [[[0, 18, 14, 0], [2, 20, 14, 2], [4, 22, 14, 4], [6, 24, 14, 6], [8, 26, 14, 8], [10, 28, 14, 10], [12, 30, 14, 12], [14, 0, 14, 14], [16, 2, 14, 16], [18, 4, 14, 18], [20, 6, 14, 20], [22, 8, 14, 22], [24, 10, 14, 24], [26, 12, 14, 26], [28, 14, 14, 28], [30, 16, 14, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 19, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 13]

derived = [[[0, 19, 13, 0], [2, 21, 13, 2], [4, 23, 13, 4], [6, 25, 13, 6], [8, 27, 13, 8], [10, 29, 13, 10], [12, 31, 13, 12], [14, 1, 13, 14], [16, 3, 13, 16], [18, 5, 13, 18], [20, 7, 13, 20], [22, 9, 13, 22], [24, 11, 13, 24], [26, 13, 13, 26], [28, 15, 13, 28], [30, 17, 13, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 20, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 12]

derived = [[[0, 20, 12, 0], [2, 22, 12, 2], [4, 24, 12, 4], [6, 26, 12, 6], [8, 28, 12, 8], [10, 30, 12, 10], [12, 0, 12, 12], [14, 2, 12, 14], [16, 4, 12, 16], [18, 6, 12, 18], [20, 8, 12, 20], [22, 10, 12, 22], [24, 12, 12, 24], [26, 14, 12, 26], [28, 16, 12, 28], [30, 18, 12, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 21, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 11]

derived = [[[0, 21, 11, 0], [2, 23, 11, 2], [4, 25, 11, 4], [6, 27, 11, 6], [8, 29, 11, 8], [10, 31, 11, 10], [12, 1, 11, 12], [14, 3, 11, 14], [16, 5, 11, 16], [18, 7, 11, 18], [20, 9, 11, 20], [22, 11, 11, 22], [24, 13, 11, 24], [26, 15, 11, 26], [28, 17, 11, 28], [30, 19, 11, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 22, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 10]

derived = [[[0, 22, 10, 0], [2, 24, 10, 2], [4, 26, 10, 4], [6, 28, 10, 6], [8, 30, 10, 8], [10, 0, 10, 10], [12, 2, 10, 12], [14, 4, 10, 14], [16, 6, 10, 16], [18, 8, 10, 18], [20, 10, 10, 20], [22, 12, 10, 22], [24, 14, 10, 24], [26, 16, 10, 26], [28, 18, 10, 28], [30, 20, 10, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 23, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 9]

derived = [[[0, 23, 9, 0], [2, 25, 9, 2], [4, 27, 9, 4], [6, 29, 9, 6], [8, 31, 9, 8], [10, 1, 9, 10], [12, 3, 9, 12], [14, 5, 9, 14], [16, 7, 9, 16], [18, 9, 9, 18], [20, 11, 9, 20], [22, 13, 9, 22], [24, 15, 9, 24], [26, 17, 9, 26], [28, 19, 9, 28], [30, 21, 9, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 24, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 8]

derived = [[[0, 24, 8, 0], [2, 26, 8, 2], [4, 28, 8, 4], [6, 30, 8, 6], [8, 0, 8, 8], [10, 2, 8, 10], [12, 4, 8, 12], [14, 6, 8, 14], [16, 8, 8, 16], [18, 10, 8, 18], [20, 12, 8, 20], [22, 14, 8, 22], [24, 16, 8, 24], [26, 18, 8, 26], [28, 20, 8, 28], [30, 22, 8, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 25, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 7]

derived = [[[0, 25, 7, 0], [2, 27, 7, 2], [4, 29, 7, 4], [6, 31, 7, 6], [8, 1, 7, 8], [10, 3, 7, 10], [12, 5, 7, 12], [14, 7, 7, 14], [16, 9, 7, 16], [18, 11, 7, 18], [20, 13, 7, 20], [22, 15, 7, 22], [24, 17, 7, 24], [26, 19, 7, 26], [28, 21, 7, 28], [30, 23, 7, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 26, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 6]

derived = [[[0, 26, 6, 0], [2, 28, 6, 2], [4, 30, 6, 4], [6, 0, 6, 6], [8, 2, 6, 8], [10, 4, 6, 10], [12, 6, 6, 12], [14, 8, 6, 14], [16, 10, 6, 16], [18, 12, 6, 18], [20, 14, 6, 20], [22, 16, 6, 22], [24, 18, 6, 24], [26, 20, 6, 26], [28, 22, 6, 28], [30, 24, 6, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 27, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 5]

derived = [[[0, 27, 5, 0], [2, 29, 5, 2], [4, 31, 5, 4], [6, 1, 5, 6], [8, 3, 5, 8], [10, 5, 5, 10], [12, 7, 5, 12], [14, 9, 5, 14], [16, 11, 5, 16], [18, 13, 5, 18], [20, 15, 5, 20], [22, 17, 5, 22], [24, 19, 5, 24], [26, 21, 5, 26], [28, 23, 5, 28], [30, 25, 5, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 28, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 4]

derived = [[[0, 28, 4, 0], [2, 30, 4, 2], [4, 0, 4, 4], [6, 2, 4, 6], [8, 4, 4, 8], [10, 6, 4, 10], [12, 8, 4, 12], [14, 10, 4, 14], [16, 12, 4, 16], [18, 14, 4, 18], [20, 16, 4, 20], [22, 18, 4, 22], [24, 20, 4, 24], [26, 22, 4, 26], [28, 24, 4, 28], [30, 26, 4, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 29, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 3]

derived = [[[0, 29, 3, 0], [2, 31, 3, 2], [4, 1, 3, 4], [6, 3, 3, 6], [8, 5, 3, 8], [10, 7, 3, 10], [12, 9, 3, 12], [14, 11, 3, 14], [16, 13, 3, 16], [18, 15, 3, 18], [20, 17, 3, 20], [22, 19, 3, 22], [24, 21, 3, 24], [26, 23, 3, 26], [28, 25, 3, 28], [30, 27, 3, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 30, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 2]

derived = [[[0, 30, 2, 0], [2, 0, 2, 2], [4, 2, 2, 4], [6, 4, 2, 6], [8, 6, 2, 8], [10, 8, 2, 10], [12, 10, 2, 12], [14, 12, 2, 14], [16, 14, 2, 16], [18, 16, 2, 18], [20, 18, 2, 20], [22, 20, 2, 22], [24, 22, 2, 24], [26, 24, 2, 26], [28, 26, 2, 28], [30, 28, 2, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [Kernel ACTUAL identity preimage, 31, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 1]

derived = [[[0, 31, 1, 0], [2, 1, 1, 2], [4, 3, 1, 4], [6, 5, 1, 6], [8, 7, 1, 8], [10, 9, 1, 10], [12, 11, 1, 12], [14, 13, 1, 14], [16, 15, 1, 16], [18, 17, 1, 18], [20, 19, 1, 20], [22, 21, 1, 22], [24, 23, 1, 24], [26, 25, 1, 26], [28, 27, 1, 28], [30, 29, 1, 30]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]

source roles = [[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是, 0]

derived = [f(kl)=f(k)f(l)=e, f(k^-1)=f(k)^-1=e, f(gkg^-1)=f(g)e*f(g)^-1=e]

逐步反向核對

• 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, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是, 是, 是, [[0, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [1, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [2, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [3, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [4, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [5, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [6, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [7, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [8, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [9, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [10, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [11, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [12, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [13, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [14, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [15, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [16, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [17, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [18, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [19, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [20, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [21, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [22, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [23, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [24, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [25, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [26, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [27, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [28, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [29, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [30, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是], [31, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], 是]], 是, 是, identity_preimage_is_a_normal_subgroup_by_complete_audit)

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。