第 26524 題：拓撲連通分支

原題與已知條件

subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"cardinality_not_definition","model":{"points":[0,1,2,3,4,5,6,7],"topology":[[],[0,1,2,3,4,5,6,7],[0],[1,2,3,4,5,6,7]],"basepoint":0}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"cardinality_not_definition","model":{"points":[0,1,2,3,4,5,6,7],"topology":[[],[0,1,2,3,4,5,6,7],[0],[1,2,3,4,5,6,7]],"basepoint":0}}。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-topological-connected-component

逐步推導

source roles = [component-boundary]

derived = [[mode, basepoint, own_component, larger_component, own_size, larger_size, global_maximum_definition, certificate]]

source roles = [component ORIGINAL space, [0, 1, 2, 3, 4, 5, 6, 7], [[], [0, 1, 2, 3, 4, 5, 6, 7], [0], [1, 2, 3, 4, 5, 6, 7]], 否]

derived = [[0, 1, 2, 3, 4, 5, 6, 7], [[], [0, 1, 2, 3, 4, 5, 6, 7], [0], [1, 2, 3, 4, 5, 6, 7]], [[0, 0, 0, 0, 是, 是], [0, 1, 255, 0, 是, 是], [0, 2, 1, 0, 是, 是], [0, 3, 254, 0, 是, 是], [1, 0, 255, 0, 是, 是], [1, 1, 255, 255, 是, 是], [1, 2, 255, 1, 是, 是], [1, 3, 255, 254, 是, 是], [2, 0, 1, 0, 是, 是], [2, 1, 255, 1, 是, 是], [2, 2, 1, 1, 是, 是], [2, 3, 255, 0, 是, 是], [3, 0, 254, 0, 是, 是], [3, 1, 255, 254, 是, 是], [3, 2, 255, 0, 是, 是], [3, 3, 254, 254, 是, 是]]]

source roles = [[0, 1, 2, 3, 4, 5, 6, 7], [[], [0, 1, 2, 3, 4, 5, 6, 7], [0], [1, 2, 3, 4, 5, 6, 7]]]

derived = [[[1, [0], [[], [0]], null, 是], [2, [1], [[], [1]], null, 是], [3, [0, 1], [[], [0, 1], [0], [1]], [0], 否], [4, [2], [[], [2]], null, 是], [5, [0, 2], [[], [0, 2], [0], [2]], [0], 否], [6, [1, 2], [[], [1, 2]], null, 是], [7, [0, 1, 2], [[], [0, 1, 2], [0], [1, 2]], [0], 否], [8, [3], [[], [3]], null, 是], [9, [0, 3], [[], [0, 3], [0], [3]], [0], 否], [10, [1, 3], [[], [1, 3]], null, 是], [11, [0, 1, 3], [[], [0, 1, 3], [0], [1, 3]], [0], 否], [12, [2, 3], [[], [2, 3]], null, 是], [13, [0, 2, 3], [[], [0, 2, 3], [0], [2, 3]], [0], 否], [14, [1, 2, 3], [[], [1, 2, 3]], null, 是], [15, [0, 1, 2, 3], [[], [0, 1, 2, 3], [0], [1, 2, 3]], [0], 否], [16, [4], [[], [4]], null, 是], [17, [0, 4], [[], [0, 4], [0], [4]], [0], 否], [18, [1, 4], [[], [1, 4]], null, 是], [19, [0, 1, 4], [[], [0, 1, 4], [0], [1, 4]], [0], 否], [20, [2, 4], [[], [2, 4]], null, 是], [21, [0, 2, 4], [[], [0, 2, 4], [0], [2, 4]], [0], 否], [22, [1, 2, 4], [[], [1, 2, 4]], null, 是], [23, [0, 1, 2, 4], [[], [0, 1, 2, 4], [0], [1, 2, 4]], [0], 否], [24, [3, 4], [[], [3, 4]], null, 是], [25, [0, 3, 4], [[], [0, 3, 4], [0], [3, 4]], [0], 否], [26, [1, 3, 4], [[], [1, 3, 4]], null, 是], [27, [0, 1, 3, 4], [[], [0, 1, 3, 4], [0], [1, 3, 4]], [0], 否], [28, [2, 3, 4], [[], [2, 3, 4]], null, 是], [29, [0, 2, 3, 4], [[], [0, 2, 3, 4], [0], [2, 3, 4]], [0], 否], [30, [1, 2, 3, 4], [[], [1, 2, 3, 4]], null, 是], [31, [0, 1, 2, 3, 4], [[], [0, 1, 2, 3, 4], [0], [1, 2, 3, 4]], [0], 否], [32, [5], [[], [5]], null, 是], [33, [0, 5], [[], [0, 5], [0], [5]], [0], 否], [34, [1, 5], [[], [1, 5]], null, 是], [35, [0, 1, 5], [[], [0, 1, 5], [0], [1, 5]], [0], 否], [36, [2, 5], [[], [2, 5]], null, 是], [37, [0, 2, 5], [[], [0, 2, 5], [0], [2, 5]], [0], 否], [38, [1, 2, 5], [[], [1, 2, 5]], null, 是], [39, [0, 1, 2, 5], [[], [0, 1, 2, 5], [0], [1, 2, 5]], [0], 否], [40, [3, 5], [[], [3, 5]], null, 是], [41, [0, 3, 5], [[], [0, 3, 5], [0], [3, 5]], [0], 否], [42, [1, 3, 5], [[], [1, 3, 5]], null, 是], [43, [0, 1, 3, 5], [[], [0, 1, 3, 5], [0], [1, 3, 5]], [0], 否], [44, [2, 3, 5], [[], [2, 3, 5]], null, 是], [45, [0, 2, 3, 5], [[], [0, 2, 3, 5], [0], [2, 3, 5]], [0], 否], [46, [1, 2, 3, 5], [[], [1, 2, 3, 5]], null, 是], [47, [0, 1, 2, 3, 5], [[], [0, 1, 2, 3, 5], [0], [1, 2, 3, 5]], [0], 否], [48, [4, 5], [[], [4, 5]], null, 是], [49, [0, 4, 5], [[], [0, 4, 5], [0], [4, 5]], [0], 否], [50, [1, 4, 5], [[], [1, 4, 5]], null, 是], [51, [0, 1, 4, 5], [[], [0, 1, 4, 5], [0], [1, 4, 5]], [0], 否], [52, [2, 4, 5], [[], [2, 4, 5]], null, 是], [53, [0, 2, 4, 5], [[], [0, 2, 4, 5], [0], [2, 4, 5]], [0], 否], [54, [1, 2, 4, 5], [[], [1, 2, 4, 5]], null, 是], [55, [0, 1, 2, 4, 5], [[], [0, 1, 2, 4, 5], [0], [1, 2, 4, 5]], [0], 否], [56, [3, 4, 5], [[], [3, 4, 5]], null, 是], [57, [0, 3, 4, 5], [[], [0, 3, 4, 5], [0], [3, 4, 5]], [0], 否], [58, [1, 3, 4, 5], [[], [1, 3, 4, 5]], null, 是], [59, [0, 1, 3, 4, 5], [[], [0, 1, 3, 4, 5], [0], [1, 3, 4, 5]], [0], 否], [60, [2, 3, 4, 5], [[], [2, 3, 4, 5]], null, 是], [61, [0, 2, 3, 4, 5], [[], [0, 2, 3, 4, 5], [0], [2, 3, 4, 5]], [0], 否], [62, [1, 2, 3, 4, 5], [[], [1, 2, 3, 4, 5]], null, 是], [63, [0, 1, 2, 3, 4, 5], [[], [0, 1, 2, 3, 4, 5], [0], [1, 2, 3, 4, 5]], [0], 否], [64, [6], [[], [6]], null, 是], [65, [0, 6], [[], [0, 6], [0], [6]], [0], 否], [66, [1, 6], [[], [1, 6]], null, 是], [67, [0, 1, 6], [[], [0, 1, 6], [0], [1, 6]], [0], 否], [68, [2, 6], [[], [2, 6]], null, 是], [69, [0, 2, 6], [[], [0, 2, 6], [0], [2, 6]], [0], 否], [70, [1, 2, 6], [[], [1, 2, 6]], null, 是], [71, [0, 1, 2, 6], [[], [0, 1, 2, 6], [0], [1, 2, 6]], [0], 否], [72, [3, 6], [[], [3, 6]], null, 是], [73, [0, 3, 6], [[], [0, 3, 6], [0], [3, 6]], [0], 否], [74, [1, 3, 6], [[], [1, 3, 6]], null, 是], [75, [0, 1, 3, 6], [[], [0, 1, 3, 6], [0], [1, 3, 6]], [0], 否], [76, [2, 3, 6], [[], [2, 3, 6]], null, 是], [77, [0, 2, 3, 6], [[], [0, 2, 3, 6], [0], [2, 3, 6]], [0], 否], [78, [1, 2, 3, 6], [[], [1, 2, 3, 6]], null, 是], [79, [0, 1, 2, 3, 6], [[], [0, 1, 2, 3, 6], [0], [1, 2, 3, 6]], [0], 否], [80, [4, 6], [[], [4, 6]], null, 是], [81, [0, 4, 6], [[], [0, 4, 6], [0], [4, 6]], [0], 否], [82, [1, 4, 6], [[], [1, 4, 6]], null, 是], [83, [0, 1, 4, 6], [[], [0, 1, 4, 6], [0], [1, 4, 6]], [0], 否], [84, [2, 4, 6], [[], [2, 4, 6]], null, 是], [85, [0, 2, 4, 6], [[], [0, 2, 4, 6], [0], [2, 4, 6]], [0], 否], [86, [1, 2, 4, 6], [[], [1, 2, 4, 6]], null, 是], [87, [0, 1, 2, 4, 6], [[], [0, 1, 2, 4, 6], [0], [1, 2, 4, 6]], [0], 否], [88, [3, 4, 6], [[], [3, 4, 6]], null, 是], [89, [0, 3, 4, 6], [[], [0, 3, 4, 6], [0], [3, 4, 6]], [0], 否], [90, [1, 3, 4, 6], [[], [1, 3, 4, 6]], null, 是], [91, [0, 1, 3, 4, 6], [[], [0, 1, 3, 4, 6], [0], [1, 3, 4, 6]], [0], 否], [92, [2, 3, 4, 6], [[], [2, 3, 4, 6]], null, 是], [93, [0, 2, 3, 4, 6], [[], [0, 2, 3, 4, 6], [0], [2, 3, 4, 6]], [0], 否], [94, [1, 2, 3, 4, 6], [[], [1, 2, 3, 4, 6]], null, 是], [95, [0, 1, 2, 3, 4, 6], [[], [0, 1, 2, 3, 4, 6], [0], [1, 2, 3, 4, 6]], [0], 否], [96, [5, 6], [[], [5, 6]], null, 是], [97, [0, 5, 6], [[], [0, 5, 6], [0], [5, 6]], [0], 否], [98, [1, 5, 6], [[], [1, 5, 6]], null, 是], [99, [0, 1, 5, 6], [[], [0, 1, 5, 6], [0], [1, 5, 6]], [0], 否], [100, [2, 5, 6], [[], [2, 5, 6]], null, 是], [101, [0, 2, 5, 6], [[], [0, 2, 5, 6], [0], [2, 5, 6]], [0], 否], [102, [1, 2, 5, 6], [[], [1, 2, 5, 6]], null, 是], [103, [0, 1, 2, 5, 6], [[], [0, 1, 2, 5, 6], [0], [1, 2, 5, 6]], [0], 否], [104, [3, 5, 6], [[], [3, 5, 6]], null, 是], [105, [0, 3, 5, 6], [[], [0, 3, 5, 6], [0], [3, 5, 6]], [0], 否], [106, [1, 3, 5, 6], [[], [1, 3, 5, 6]], null, 是], [107, [0, 1, 3, 5, 6], [[], [0, 1, 3, 5, 6], [0], [1, 3, 5, 6]], [0], 否], [108, [2, 3, 5, 6], [[], [2, 3, 5, 6]], null, 是], [109, [0, 2, 3, 5, 6], [[], [0, 2, 3, 5, 6], [0], [2, 3, 5, 6]], [0], 否], [110, [1, 2, 3, 5, 6], [[], [1, 2, 3, 5, 6]], null, 是], [111, [0, 1, 2, 3, 5, 6], [[], [0, 1, 2, 3, 5, 6], [0], [1, 2, 3, 5, 6]], [0], 否], [112, [4, 5, 6], [[], [4, 5, 6]], null, 是], [113, [0, 4, 5, 6], [[], [0, 4, 5, 6], [0], [4, 5, 6]], [0], 否], [114, [1, 4, 5, 6], [[], [1, 4, 5, 6]], null, 是], [115, [0, 1, 4, 5, 6], [[], [0, 1, 4, 5, 6], [0], [1, 4, 5, 6]], [0], 否], [116, [2, 4, 5, 6], [[], [2, 4, 5, 6]], null, 是], [117, [0, 2, 4, 5, 6], [[], [0, 2, 4, 5, 6], [0], [2, 4, 5, 6]], [0], 否], [118, [1, 2, 4, 5, 6], [[], [1, 2, 4, 5, 6]], null, 是], [119, [0, 1, 2, 4, 5, 6], [[], [0, 1, 2, 4, 5, 6], [0], [1, 2, 4, 5, 6]], [0], 否], [120, [3, 4, 5, 6], [[], [3, 4, 5, 6]], null, 是], [121, [0, 3, 4, 5, 6], [[], [0, 3, 4, 5, 6], [0], [3, 4, 5, 6]], [0], 否], [122, [1, 3, 4, 5, 6], [[], [1, 3, 4, 5, 6]], null, 是], [123, [0, 1, 3, 4, 5, 6], [[], [0, 1, 3, 4, 5, 6], [0], [1, 3, 4, 5, 6]], [0], 否], [124, [2, 3, 4, 5, 6], [[], [2, 3, 4, 5, 6]], null, 是], [125, [0, 2, 3, 4, 5, 6], [[], [0, 2, 3, 4, 5, 6], [0], [2, 3, 4, 5, 6]], [0], 否], [126, [1, 2, 3, 4, 5, 6], [[], [1, 2, 3, 4, 5, 6]], null, 是], [127, [0, 1, 2, 3, 4, 5, 6], [[], [0, 1, 2, 3, 4, 5, 6], [0], [1, 2, 3, 4, 5, 6]], [0], 否], [128, [7], [[], [7]], null, 是], [129, [0, 7], [[], [0, 7], [0], [7]], [0], 否], [130, [1, 7], [[], [1, 7]], null, 是], [131, [0, 1, 7], [[], [0, 1, 7], [0], [1, 7]], [0], 否], [132, [2, 7], [[], [2, 7]], null, 是], [133, [0, 2, 7], [[], [0, 2, 7], [0], [2, 7]], [0], 否], [134, [1, 2, 7], [[], [1, 2, 7]], null, 是], [135, [0, 1, 2, 7], [[], [0, 1, 2, 7], [0], [1, 2, 7]], [0], 否], [136, [3, 7], [[], [3, 7]], null, 是], [137, [0, 3, 7], [[], [0, 3, 7], [0], [3, 7]], [0], 否], [138, [1, 3, 7], [[], [1, 3, 7]], null, 是], [139, [0, 1, 3, 7], [[], [0, 1, 3, 7], [0], [1, 3, 7]], [0], 否], [140, [2, 3, 7], [[], [2, 3, 7]], null, 是], [141, [0, 2, 3, 7], [[], [0, 2, 3, 7], [0], [2, 3, 7]], [0], 否], [142, [1, 2, 3, 7], [[], [1, 2, 3, 7]], null, 是], [143, [0, 1, 2, 3, 7], [[], [0, 1, 2, 3, 7], [0], [1, 2, 3, 7]], [0], 否], [144, [4, 7], [[], [4, 7]], null, 是], [145, [0, 4, 7], [[], [0, 4, 7], [0], [4, 7]], [0], 否], [146, [1, 4, 7], [[], [1, 4, 7]], null, 是], [147, [0, 1, 4, 7], [[], [0, 1, 4, 7], [0], [1, 4, 7]], [0], 否], [148, [2, 4, 7], [[], [2, 4, 7]], null, 是], [149, [0, 2, 4, 7], [[], [0, 2, 4, 7], [0], [2, 4, 7]], [0], 否], [150, [1, 2, 4, 7], [[], [1, 2, 4, 7]], null, 是], [151, [0, 1, 2, 4, 7], [[], [0, 1, 2, 4, 7], [0], [1, 2, 4, 7]], [0], 否], [152, [3, 4, 7], [[], [3, 4, 7]], null, 是], [153, [0, 3, 4, 7], [[], [0, 3, 4, 7], [0], [3, 4, 7]], [0], 否], [154, [1, 3, 4, 7], [[], [1, 3, 4, 7]], null, 是], [155, [0, 1, 3, 4, 7], [[], [0, 1, 3, 4, 7], [0], [1, 3, 4, 7]], [0], 否], [156, [2, 3, 4, 7], [[], [2, 3, 4, 7]], null, 是], [157, [0, 2, 3, 4, 7], [[], [0, 2, 3, 4, 7], [0], [2, 3, 4, 7]], [0], 否], [158, [1, 2, 3, 4, 7], [[], [1, 2, 3, 4, 7]], null, 是], [159, [0, 1, 2, 3, 4, 7], [[], [0, 1, 2, 3, 4, 7], [0], [1, 2, 3, 4, 7]], [0], 否], [160, [5, 7], [[], [5, 7]], null, 是], [161, [0, 5, 7], [[], [0, 5, 7], [0], [5, 7]], [0], 否], [162, [1, 5, 7], [[], [1, 5, 7]], null, 是], [163, [0, 1, 5, 7], [[], [0, 1, 5, 7], [0], [1, 5, 7]], [0], 否], [164, [2, 5, 7], [[], [2, 5, 7]], null, 是], [165, [0, 2, 5, 7], [[], [0, 2, 5, 7], [0], [2, 5, 7]], [0], 否], [166, [1, 2, 5, 7], [[], [1, 2, 5, 7]], null, 是], [167, [0, 1, 2, 5, 7], [[], [0, 1, 2, 5, 7], [0], [1, 2, 5, 7]], [0], 否], [168, [3, 5, 7], [[], [3, 5, 7]], null, 是], [169, [0, 3, 5, 7], [[], [0, 3, 5, 7], [0], [3, 5, 7]], [0], 否], [170, [1, 3, 5, 7], [[], [1, 3, 5, 7]], null, 是], [171, [0, 1, 3, 5, 7], [[], [0, 1, 3, 5, 7], [0], [1, 3, 5, 7]], [0], 否], [172, [2, 3, 5, 7], [[], [2, 3, 5, 7]], null, 是], [173, [0, 2, 3, 5, 7], [[], [0, 2, 3, 5, 7], [0], [2, 3, 5, 7]], [0], 否], [174, [1, 2, 3, 5, 7], [[], [1, 2, 3, 5, 7]], null, 是], [175, [0, 1, 2, 3, 5, 7], [[], [0, 1, 2, 3, 5, 7], [0], [1, 2, 3, 5, 7]], [0], 否], [176, [4, 5, 7], [[], [4, 5, 7]], null, 是], [177, [0, 4, 5, 7], [[], [0, 4, 5, 7], [0], [4, 5, 7]], [0], 否], [178, [1, 4, 5, 7], [[], [1, 4, 5, 7]], null, 是], [179, [0, 1, 4, 5, 7], [[], [0, 1, 4, 5, 7], [0], [1, 4, 5, 7]], [0], 否], [180, [2, 4, 5, 7], [[], [2, 4, 5, 7]], null, 是], [181, [0, 2, 4, 5, 7], [[], [0, 2, 4, 5, 7], [0], [2, 4, 5, 7]], [0], 否], [182, [1, 2, 4, 5, 7], [[], [1, 2, 4, 5, 7]], null, 是], [183, [0, 1, 2, 4, 5, 7], [[], [0, 1, 2, 4, 5, 7], [0], [1, 2, 4, 5, 7]], [0], 否], [184, [3, 4, 5, 7], [[], [3, 4, 5, 7]], null, 是], [185, [0, 3, 4, 5, 7], [[], [0, 3, 4, 5, 7], [0], [3, 4, 5, 7]], [0], 否], [186, [1, 3, 4, 5, 7], [[], [1, 3, 4, 5, 7]], null, 是], [187, [0, 1, 3, 4, 5, 7], [[], [0, 1, 3, 4, 5, 7], [0], [1, 3, 4, 5, 7]], [0], 否], [188, [2, 3, 4, 5, 7], [[], [2, 3, 4, 5, 7]], null, 是], [189, [0, 2, 3, 4, 5, 7], [[], [0, 2, 3, 4, 5, 7], [0], [2, 3, 4, 5, 7]], [0], 否], [190, [1, 2, 3, 4, 5, 7], [[], [1, 2, 3, 4, 5, 7]], null, 是], [191, [0, 1, 2, 3, 4, 5, 7], [[], [0, 1, 2, 3, 4, 5, 7], [0], [1, 2, 3, 4, 5, 7]], [0], 否], [192, [6, 7], [[], [6, 7]], null, 是], [193, [0, 6, 7], [[], [0, 6, 7], [0], [6, 7]], [0], 否], [194, [1, 6, 7], [[], [1, 6, 7]], null, 是], [195, [0, 1, 6, 7], [[], [0, 1, 6, 7], [0], [1, 6, 7]], [0], 否], [196, [2, 6, 7], [[], [2, 6, 7]], null, 是], [197, [0, 2, 6, 7], [[], [0, 2, 6, 7], [0], [2, 6, 7]], [0], 否], [198, [1, 2, 6, 7], [[], [1, 2, 6, 7]], null, 是], [199, [0, 1, 2, 6, 7], [[], [0, 1, 2, 6, 7], [0], [1, 2, 6, 7]], [0], 否], [200, [3, 6, 7], [[], [3, 6, 7]], null, 是], [201, [0, 3, 6, 7], [[], [0, 3, 6, 7], [0], [3, 6, 7]], [0], 否], [202, [1, 3, 6, 7], [[], [1, 3, 6, 7]], null, 是], [203, [0, 1, 3, 6, 7], [[], [0, 1, 3, 6, 7], [0], [1, 3, 6, 7]], [0], 否], [204, [2, 3, 6, 7], [[], [2, 3, 6, 7]], null, 是], [205, [0, 2, 3, 6, 7], [[], [0, 2, 3, 6, 7], [0], [2, 3, 6, 7]], [0], 否], [206, [1, 2, 3, 6, 7], [[], [1, 2, 3, 6, 7]], null, 是], [207, [0, 1, 2, 3, 6, 7], [[], [0, 1, 2, 3, 6, 7], [0], [1, 2, 3, 6, 7]], [0], 否], [208, [4, 6, 7], [[], [4, 6, 7]], null, 是], [209, [0, 4, 6, 7], [[], [0, 4, 6, 7], [0], [4, 6, 7]], [0], 否], [210, [1, 4, 6, 7], [[], [1, 4, 6, 7]], null, 是], [211, [0, 1, 4, 6, 7], [[], [0, 1, 4, 6, 7], [0], [1, 4, 6, 7]], [0], 否], [212, [2, 4, 6, 7], [[], [2, 4, 6, 7]], null, 是], [213, [0, 2, 4, 6, 7], [[], [0, 2, 4, 6, 7], [0], [2, 4, 6, 7]], [0], 否], [214, [1, 2, 4, 6, 7], [[], [1, 2, 4, 6, 7]], null, 是], [215, [0, 1, 2, 4, 6, 7], [[], [0, 1, 2, 4, 6, 7], [0], [1, 2, 4, 6, 7]], [0], 否], [216, [3, 4, 6, 7], [[], [3, 4, 6, 7]], null, 是], [217, [0, 3, 4, 6, 7], [[], [0, 3, 4, 6, 7], [0], [3, 4, 6, 7]], [0], 否], [218, [1, 3, 4, 6, 7], [[], [1, 3, 4, 6, 7]], null, 是], [219, [0, 1, 3, 4, 6, 7], [[], [0, 1, 3, 4, 6, 7], [0], [1, 3, 4, 6, 7]], [0], 否], [220, [2, 3, 4, 6, 7], [[], [2, 3, 4, 6, 7]], null, 是], [221, [0, 2, 3, 4, 6, 7], [[], [0, 2, 3, 4, 6, 7], [0], [2, 3, 4, 6, 7]], [0], 否], [222, [1, 2, 3, 4, 6, 7], [[], [1, 2, 3, 4, 6, 7]], null, 是], [223, [0, 1, 2, 3, 4, 6, 7], [[], [0, 1, 2, 3, 4, 6, 7], [0], [1, 2, 3, 4, 6, 7]], [0], 否], [224, [5, 6, 7], [[], [5, 6, 7]], null, 是], [225, [0, 5, 6, 7], [[], [0, 5, 6, 7], [0], [5, 6, 7]], [0], 否], [226, [1, 5, 6, 7], [[], [1, 5, 6, 7]], null, 是], [227, [0, 1, 5, 6, 7], [[], [0, 1, 5, 6, 7], [0], [1, 5, 6, 7]], [0], 否], [228, [2, 5, 6, 7], [[], [2, 5, 6, 7]], null, 是], [229, [0, 2, 5, 6, 7], [[], [0, 2, 5, 6, 7], [0], [2, 5, 6, 7]], [0], 否], [230, [1, 2, 5, 6, 7], [[], [1, 2, 5, 6, 7]], null, 是], [231, [0, 1, 2, 5, 6, 7], [[], [0, 1, 2, 5, 6, 7], [0], [1, 2, 5, 6, 7]], [0], 否], [232, [3, 5, 6, 7], [[], [3, 5, 6, 7]], null, 是], [233, [0, 3, 5, 6, 7], [[], [0, 3, 5, 6, 7], [0], [3, 5, 6, 7]], [0], 否], [234, [1, 3, 5, 6, 7], [[], [1, 3, 5, 6, 7]], null, 是], [235, [0, 1, 3, 5, 6, 7], [[], [0, 1, 3, 5, 6, 7], [0], [1, 3, 5, 6, 7]], [0], 否], [236, [2, 3, 5, 6, 7], [[], [2, 3, 5, 6, 7]], null, 是], [237, [0, 2, 3, 5, 6, 7], [[], [0, 2, 3, 5, 6, 7], [0], [2, 3, 5, 6, 7]], [0], 否], [238, [1, 2, 3, 5, 6, 7], [[], [1, 2, 3, 5, 6, 7]], null, 是], [239, [0, 1, 2, 3, 5, 6, 7], [[], [0, 1, 2, 3, 5, 6, 7], [0], [1, 2, 3, 5, 6, 7]], [0], 否], [240, [4, 5, 6, 7], [[], [4, 5, 6, 7]], null, 是], [241, [0, 4, 5, 6, 7], [[], [0, 4, 5, 6, 7], [0], [4, 5, 6, 7]], [0], 否], [242, [1, 4, 5, 6, 7], [[], [1, 4, 5, 6, 7]], null, 是], [243, [0, 1, 4, 5, 6, 7], [[], [0, 1, 4, 5, 6, 7], [0], [1, 4, 5, 6, 7]], [0], 否], [244, [2, 4, 5, 6, 7], [[], [2, 4, 5, 6, 7]], null, 是], [245, [0, 2, 4, 5, 6, 7], [[], [0, 2, 4, 5, 6, 7], [0], [2, 4, 5, 6, 7]], [0], 否], [246, [1, 2, 4, 5, 6, 7], [[], [1, 2, 4, 5, 6, 7]], null, 是], [247, [0, 1, 2, 4, 5, 6, 7], [[], [0, 1, 2, 4, 5, 6, 7], [0], [1, 2, 4, 5, 6, 7]], [0], 否], [248, [3, 4, 5, 6, 7], [[], [3, 4, 5, 6, 7]], null, 是], [249, [0, 3, 4, 5, 6, 7], [[], [0, 3, 4, 5, 6, 7], [0], [3, 4, 5, 6, 7]], [0], 否], [250, [1, 3, 4, 5, 6, 7], [[], [1, 3, 4, 5, 6, 7]], null, 是], [251, [0, 1, 3, 4, 5, 6, 7], [[], [0, 1, 3, 4, 5, 6, 7], [0], [1, 3, 4, 5, 6, 7]], [0], 否], [252, [2, 3, 4, 5, 6, 7], [[], [2, 3, 4, 5, 6, 7]], null, 是], [253, [0, 2, 3, 4, 5, 6, 7], [[], [0, 2, 3, 4, 5, 6, 7], [0], [2, 3, 4, 5, 6, 7]], [0], 否], [254, [1, 2, 3, 4, 5, 6, 7], [[], [1, 2, 3, 4, 5, 6, 7]], null, 是], [255, [0, 1, 2, 3, 4, 5, 6, 7], [[], [0, 1, 2, 3, 4, 5, 6, 7], [0], [1, 2, 3, 4, 5, 6, 7]], [0], 否]], [[0], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3], [4], [1, 4], [2, 4], [1, 2, 4], [3, 4], [1, 3, 4], [2, 3, 4], [1, 2, 3, 4], [5], [1, 5], [2, 5], [1, 2, 5], [3, 5], [1, 3, 5], [2, 3, 5], [1, 2, 3, 5], [4, 5], [1, 4, 5], [2, 4, 5], [1, 2, 4, 5], [3, 4, 5], [1, 3, 4, 5], [2, 3, 4, 5], [1, 2, 3, 4, 5], [6], [1, 6], [2, 6], [1, 2, 6], [3, 6], [1, 3, 6], [2, 3, 6], [1, 2, 3, 6], [4, 6], [1, 4, 6], [2, 4, 6], [1, 2, 4, 6], [3, 4, 6], [1, 3, 4, 6], [2, 3, 4, 6], [1, 2, 3, 4, 6], [5, 6], [1, 5, 6], [2, 5, 6], [1, 2, 5, 6], [3, 5, 6], [1, 3, 5, 6], [2, 3, 5, 6], [1, 2, 3, 5, 6], [4, 5, 6], [1, 4, 5, 6], [2, 4, 5, 6], [1, 2, 4, 5, 6], [3, 4, 5, 6], [1, 3, 4, 5, 6], [2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6], [7], [1, 7], [2, 7], [1, 2, 7], [3, 7], [1, 3, 7], [2, 3, 7], [1, 2, 3, 7], [4, 7], [1, 4, 7], [2, 4, 7], [1, 2, 4, 7], [3, 4, 7], [1, 3, 4, 7], [2, 3, 4, 7], [1, 2, 3, 4, 7], [5, 7], [1, 5, 7], [2, 5, 7], [1, 2, 5, 7], [3, 5, 7], [1, 3, 5, 7], [2, 3, 5, 7], [1, 2, 3, 5, 7], [4, 5, 7], [1, 4, 5, 7], [2, 4, 5, 7], [1, 2, 4, 5, 7], [3, 4, 5, 7], [1, 3, 4, 5, 7], [2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 7], [6, 7], [1, 6, 7], [2, 6, 7], [1, 2, 6, 7], [3, 6, 7], [1, 3, 6, 7], [2, 3, 6, 7], [1, 2, 3, 6, 7], [4, 6, 7], [1, 4, 6, 7], [2, 4, 6, 7], [1, 2, 4, 6, 7], [3, 4, 6, 7], [1, 3, 4, 6, 7], [2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 7], [5, 6, 7], [1, 5, 6, 7], [2, 5, 6, 7], [1, 2, 5, 6, 7], [3, 5, 6, 7], [1, 3, 5, 6, 7], [2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 7], [4, 5, 6, 7], [1, 4, 5, 6, 7], [2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 7], [3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7]]]

source roles = [[[0], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3], [4], [1, 4], [2, 4], [1, 2, 4], [3, 4], [1, 3, 4], [2, 3, 4], [1, 2, 3, 4], [5], [1, 5], [2, 5], [1, 2, 5], [3, 5], [1, 3, 5], [2, 3, 5], [1, 2, 3, 5], [4, 5], [1, 4, 5], [2, 4, 5], [1, 2, 4, 5], [3, 4, 5], [1, 3, 4, 5], [2, 3, 4, 5], [1, 2, 3, 4, 5], [6], [1, 6], [2, 6], [1, 2, 6], [3, 6], [1, 3, 6], [2, 3, 6], [1, 2, 3, 6], [4, 6], [1, 4, 6], [2, 4, 6], [1, 2, 4, 6], [3, 4, 6], [1, 3, 4, 6], [2, 3, 4, 6], [1, 2, 3, 4, 6], [5, 6], [1, 5, 6], [2, 5, 6], [1, 2, 5, 6], [3, 5, 6], [1, 3, 5, 6], [2, 3, 5, 6], [1, 2, 3, 5, 6], [4, 5, 6], [1, 4, 5, 6], [2, 4, 5, 6], [1, 2, 4, 5, 6], [3, 4, 5, 6], [1, 3, 4, 5, 6], [2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6], [7], [1, 7], [2, 7], [1, 2, 7], [3, 7], [1, 3, 7], [2, 3, 7], [1, 2, 3, 7], [4, 7], [1, 4, 7], [2, 4, 7], [1, 2, 4, 7], [3, 4, 7], [1, 3, 4, 7], [2, 3, 4, 7], [1, 2, 3, 4, 7], [5, 7], [1, 5, 7], [2, 5, 7], [1, 2, 5, 7], [3, 5, 7], [1, 3, 5, 7], [2, 3, 5, 7], [1, 2, 3, 5, 7], [4, 5, 7], [1, 4, 5, 7], [2, 4, 5, 7], [1, 2, 4, 5, 7], [3, 4, 5, 7], [1, 3, 4, 5, 7], [2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 7], [6, 7], [1, 6, 7], [2, 6, 7], [1, 2, 6, 7], [3, 6, 7], [1, 3, 6, 7], [2, 3, 6, 7], [1, 2, 3, 6, 7], [4, 6, 7], [1, 4, 6, 7], [2, 4, 6, 7], [1, 2, 4, 6, 7], [3, 4, 6, 7], [1, 3, 4, 6, 7], [2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 7], [5, 6, 7], [1, 5, 6, 7], [2, 5, 6, 7], [1, 2, 5, 6, 7], [3, 5, 6, 7], [1, 3, 5, 6, 7], [2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 7], [4, 5, 6, 7], [1, 4, 5, 6, 7], [2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 7], [3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7]]]

derived = [[[0], [1, 2, 3, 4, 5, 6, 7]], 是, 是, [是, 是], [是, 是]]

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

derived = [[0], [0], 是, 是]

source roles = [0, [0], [[0], [1, 2, 3, 4, 5, 6, 7]]]

derived = [[1, 2, 3, 4, 5, 6, 7], 1, 7, 否]

逐步反向核對

• S006 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S005 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S004 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S003 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S002 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S001 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。

結論

(cardinality_not_definition, 0, [0], [1, 2, 3, 4, 5, 6, 7], 1, 7, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)

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。