第 26065 題：最小頂點覆蓋

原題與已知條件

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","c1","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5"],"edges":[["c0","l0_0"],["c0","l0_1"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"],["c1","l1_3"],["c1","l1_4"],["c1","l1_5"]],"candidate":["l0_0","l0_1","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","c1","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5"],"edges":[["c0","l0_0"],["c0","l0_1"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"],["c1","l1_3"],["c1","l1_4"],["c1","l1_5"]],"candidate":["l0_0","l0_1","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5"]}。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-minimum-vertex-cover

逐步推導

source roles = [mincover-minimal-not-minimum]

derived = [[candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate]]

source roles = [[c0, l0_0, l0_1, c1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [[c0, l0_0], [c0, l0_1], [c1, l1_0], [c1, l1_1], [c1, l1_2], [c1, l1_3], [c1, l1_4], [c1, l1_5]], [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5]]

derived = [[c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [[c0, l0_0], [c0, l0_1], [c1, l1_0], [c1, l1_1], [c1, l1_2], [c1, l1_3], [c1, l1_4], [c1, l1_5]], [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5]]

source roles = [[c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [[c0, l0_0], [c0, l0_1], [c1, l1_0], [c1, l1_1], [c1, l1_2], [c1, l1_3], [c1, l1_4], [c1, l1_5]], 1024]

derived = [[3, 7, 11, 14, 15, 19, 23, 27, 30, 31, 35, 39, 43, 46, 47, 51, 55, 59, 62, 63, 67, 71, 75, 78, 79, 83, 87, 91, 94, 95, 99, 103, 107, 110, 111, 115, 119, 123, 126, 127, 131, 135, 139, 142, 143, 147, 151, 155, 158, 159, 163, 167, 171, 174, 175, 179, 183, 187, 190, 191, 195, 199, 203, 206, 207, 211, 215, 219, 222, 223, 227, 231, 235, 238, 239, 243, 247, 251, 254, 255, 259, 263, 267, 270, 271, 275, 279, 283, 286, 287, 291, 295, 299, 302, 303, 307, 311, 315, 318, 319, 323, 327, 331, 334, 335, 339, 343, 347, 350, 351, 355, 359, 363, 366, 367, 371, 375, 379, 382, 383, 387, 391, 395, 398, 399, 403, 407, 411, 414, 415, 419, 423, 427, 430, 431, 435, 439, 443, 446, 447, 451, 455, 459, 462, 463, 467, 471, 475, 478, 479, 483, 487, 491, 494, 495, 499, 503, 507, 510, 511, 515, 519, 523, 526, 527, 531, 535, 539, 542, 543, 547, 551, 555, 558, 559, 563, 567, 571, 574, 575, 579, 583, 587, 590, 591, 595, 599, 603, 606, 607, 611, 615, 619, 622, 623, 627, 631, 635, 638, 639, 643, 647, 651, 654, 655, 659, 663, 667, 670, 671, 675, 679, 683, 686, 687, 691, 695, 699, 702, 703, 707, 711, 715, 718, 719, 723, 727, 731, 734, 735, 739, 743, 747, 750, 751, 755, 759, 763, 766, 767, 771, 775, 779, 782, 783, 787, 791, 795, 798, 799, 803, 807, 811, 814, 815, 819, 823, 827, 830, 831, 835, 839, 843, 846, 847, 851, 855, 859, 862, 863, 867, 871, 875, 878, 879, 883, 887, 891, 894, 895, 899, 903, 907, 910, 911, 915, 919, 923, 926, 927, 931, 935, 939, 942, 943, 947, 951, 955, 958, 959, 963, 967, 971, 974, 975, 979, 983, 987, 990, 991, 995, 999, 1003, 1006, 1007, 1009, 1011, 1013, 1015, 1017, 1019, 1020, 1021, 1022, 1023], [[0, 0], [1, 2], [2, 0], [4, 1], [5, 2], [6, 1], [8, 0], [9, 2], [10, 0], [12, 2], [13, 2], [16, 0], [17, 3], [18, 0], [20, 1], [21, 3], [22, 1], [24, 0], [25, 3], [26, 0], [28, 3], [29, 3], [32, 0], [33, 2], [34, 0], [36, 1], [37, 2], [38, 1], [40, 0], [41, 2], [42, 0], [44, 2], [45, 2], [48, 0], [49, 4], [50, 0], [52, 1], [53, 4], [54, 1], [56, 0], [57, 4], [58, 0], [60, 4], [61, 4], [64, 0], [65, 2], [66, 0], [68, 1], [69, 2], [70, 1], [72, 0], [73, 2], [74, 0], [76, 2], [77, 2], [80, 0], [81, 3], [82, 0], [84, 1], [85, 3], [86, 1], [88, 0], [89, 3], [90, 0], [92, 3], [93, 3], [96, 0], [97, 2], [98, 0], [100, 1], [101, 2], [102, 1], [104, 0], [105, 2], [106, 0], [108, 2], [109, 2], [112, 0], [113, 5], [114, 0], [116, 1], [117, 5], [118, 1], [120, 0], [121, 5], [122, 0], [124, 5], [125, 5], [128, 0], [129, 2], [130, 0], [132, 1], [133, 2], [134, 1], [136, 0], [137, 2], [138, 0], [140, 2], [141, 2], [144, 0], [145, 3], [146, 0], [148, 1], [149, 3], [150, 1], [152, 0], [153, 3], [154, 0], [156, 3], [157, 3], [160, 0], [161, 2], [162, 0], [164, 1], [165, 2], [166, 1], [168, 0], [169, 2], [170, 0], [172, 2], [173, 2], [176, 0], [177, 4], [178, 0], [180, 1], [181, 4], [182, 1], [184, 0], [185, 4], [186, 0], [188, 4], [189, 4], [192, 0], [193, 2], [194, 0], [196, 1], [197, 2], [198, 1], [200, 0], [201, 2], [202, 0], [204, 2], [205, 2], [208, 0], [209, 3], [210, 0], [212, 1], [213, 3], [214, 1], [216, 0], [217, 3], [218, 0], [220, 3], [221, 3], [224, 0], [225, 2], [226, 0], [228, 1], [229, 2], [230, 1], [232, 0], [233, 2], [234, 0], [236, 2], [237, 2], [240, 0], [241, 6], [242, 0], [244, 1], [245, 6], [246, 1], [248, 0], [249, 6], [250, 0], [252, 6], [253, 6], [256, 0], [257, 2], [258, 0], [260, 1], [261, 2], [262, 1], [264, 0], [265, 2], [266, 0], [268, 2], [269, 2], [272, 0], [273, 3], [274, 0], [276, 1], [277, 3], [278, 1], [280, 0], [281, 3], [282, 0], [284, 3], [285, 3], [288, 0], [289, 2], [290, 0], [292, 1], [293, 2], [294, 1], [296, 0], [297, 2], [298, 0], [300, 2], [301, 2], [304, 0], [305, 4], [306, 0], [308, 1], [309, 4], [310, 1], [312, 0], [313, 4], [314, 0], [316, 4], [317, 4], [320, 0], [321, 2], [322, 0], [324, 1], [325, 2], [326, 1], [328, 0], [329, 2], [330, 0], [332, 2], [333, 2], [336, 0], [337, 3], [338, 0], [340, 1], [341, 3], [342, 1], [344, 0], [345, 3], [346, 0], [348, 3], [349, 3], [352, 0], [353, 2], [354, 0], [356, 1], [357, 2], [358, 1], [360, 0], [361, 2], [362, 0], [364, 2], [365, 2], [368, 0], [369, 5], [370, 0], [372, 1], [373, 5], [374, 1], [376, 0], [377, 5], [378, 0], [380, 5], [381, 5], [384, 0], [385, 2], [386, 0], [388, 1], [389, 2], [390, 1], [392, 0], [393, 2], [394, 0], [396, 2], [397, 2], [400, 0], [401, 3], [402, 0], [404, 1], [405, 3], [406, 1], [408, 0], [409, 3], [410, 0], [412, 3], [413, 3], [416, 0], [417, 2], [418, 0], [420, 1], [421, 2], [422, 1], [424, 0], [425, 2], [426, 0], [428, 2], [429, 2], [432, 0], [433, 4], [434, 0], [436, 1], [437, 4], [438, 1], [440, 0], [441, 4], [442, 0], [444, 4], [445, 4], [448, 0], [449, 2], [450, 0], [452, 1], [453, 2], [454, 1], [456, 0], [457, 2], [458, 0], [460, 2], [461, 2], [464, 0], [465, 3], [466, 0], [468, 1], [469, 3], [470, 1], [472, 0], [473, 3], [474, 0], [476, 3], [477, 3], [480, 0], [481, 2], [482, 0], [484, 1], [485, 2], [486, 1], [488, 0], [489, 2], [490, 0], [492, 2], [493, 2], [496, 0], [497, 7], [498, 0], [500, 1], [501, 7], [502, 1], [504, 0], [505, 7], [506, 0], [508, 7], [509, 7], [512, 0], [513, 2], [514, 0], [516, 1], [517, 2], [518, 1], [520, 0], [521, 2], [522, 0], [524, 2], [525, 2], [528, 0], [529, 3], [530, 0], [532, 1], [533, 3], [534, 1], [536, 0], [537, 3], [538, 0], [540, 3], [541, 3], [544, 0], [545, 2], [546, 0], [548, 1], [549, 2], [550, 1], [552, 0], [553, 2], [554, 0], [556, 2], [557, 2], [560, 0], [561, 4], [562, 0], [564, 1], [565, 4], [566, 1], [568, 0], [569, 4], [570, 0], [572, 4], [573, 4], [576, 0], [577, 2], [578, 0], [580, 1], [581, 2], [582, 1], [584, 0], [585, 2], [586, 0], [588, 2], [589, 2], [592, 0], [593, 3], [594, 0], [596, 1], [597, 3], [598, 1], [600, 0], [601, 3], [602, 0], [604, 3], [605, 3], [608, 0], [609, 2], [610, 0], [612, 1], [613, 2], [614, 1], [616, 0], [617, 2], [618, 0], [620, 2], [621, 2], [624, 0], [625, 5], [626, 0], [628, 1], [629, 5], [630, 1], [632, 0], [633, 5], [634, 0], [636, 5], [637, 5], [640, 0], [641, 2], [642, 0], [644, 1], [645, 2], [646, 1], [648, 0], [649, 2], [650, 0], [652, 2], [653, 2], [656, 0], [657, 3], [658, 0], [660, 1], [661, 3], [662, 1], [664, 0], [665, 3], [666, 0], [668, 3], [669, 3], [672, 0], [673, 2], [674, 0], [676, 1], [677, 2], [678, 1], [680, 0], [681, 2], [682, 0], [684, 2], [685, 2], [688, 0], [689, 4], [690, 0], [692, 1], [693, 4], [694, 1], [696, 0], [697, 4], [698, 0], [700, 4], [701, 4], [704, 0], [705, 2], [706, 0], [708, 1], [709, 2], [710, 1], [712, 0], [713, 2], [714, 0], [716, 2], [717, 2], [720, 0], [721, 3], [722, 0], [724, 1], [725, 3], [726, 1], [728, 0], [729, 3], [730, 0], [732, 3], [733, 3], [736, 0], [737, 2], [738, 0], [740, 1], [741, 2], [742, 1], [744, 0], [745, 2], [746, 0], [748, 2], [749, 2], [752, 0], [753, 6], [754, 0], [756, 1], [757, 6], [758, 1], [760, 0], [761, 6], [762, 0], [764, 6], [765, 6], [768, 0], [769, 2], [770, 0], [772, 1], [773, 2], [774, 1], [776, 0], [777, 2], [778, 0], [780, 2], [781, 2], [784, 0], [785, 3], [786, 0], [788, 1], [789, 3], [790, 1], [792, 0], [793, 3], [794, 0], [796, 3], [797, 3], [800, 0], [801, 2], [802, 0], [804, 1], [805, 2], [806, 1], [808, 0], [809, 2], [810, 0], [812, 2], [813, 2], [816, 0], [817, 4], [818, 0], [820, 1], [821, 4], [822, 1], [824, 0], [825, 4], [826, 0], [828, 4], [829, 4], [832, 0], [833, 2], [834, 0], [836, 1], [837, 2], [838, 1], [840, 0], [841, 2], [842, 0], [844, 2], [845, 2], [848, 0], [849, 3], [850, 0], [852, 1], [853, 3], [854, 1], [856, 0], [857, 3], [858, 0], [860, 3], [861, 3], [864, 0], [865, 2], [866, 0], [868, 1], [869, 2], [870, 1], [872, 0], [873, 2], [874, 0], [876, 2], [877, 2], [880, 0], [881, 5], [882, 0], [884, 1], [885, 5], [886, 1], [888, 0], [889, 5], [890, 0], [892, 5], [893, 5], [896, 0], [897, 2], [898, 0], [900, 1], [901, 2], [902, 1], [904, 0], [905, 2], [906, 0], [908, 2], [909, 2], [912, 0], [913, 3], [914, 0], [916, 1], [917, 3], [918, 1], [920, 0], [921, 3], [922, 0], [924, 3], [925, 3], [928, 0], [929, 2], [930, 0], [932, 1], [933, 2], [934, 1], [936, 0], [937, 2], [938, 0], [940, 2], [941, 2], [944, 0], [945, 4], [946, 0], [948, 1], [949, 4], [950, 1], [952, 0], [953, 4], [954, 0], [956, 4], [957, 4], [960, 0], [961, 2], [962, 0], [964, 1], [965, 2], [966, 1], [968, 0], [969, 2], [970, 0], [972, 2], [973, 2], [976, 0], [977, 3], [978, 0], [980, 1], [981, 3], [982, 1], [984, 0], [985, 3], [986, 0], [988, 3], [989, 3], [992, 0], [993, 2], [994, 0], [996, 1], [997, 2], [998, 1], [1000, 0], [1001, 2], [1002, 0], [1004, 2], [1005, 2], [1008, 0], [1010, 0], [1012, 1], [1014, 1], [1016, 0], [1018, 0]], [[c0, c1], [c0, c1, l0_0], [c0, c1, l0_1], [c1, l0_0, l0_1], [c0, c1, l0_0, l0_1], [c0, c1, l1_0], [c0, c1, l0_0, l1_0], [c0, c1, l0_1, l1_0], [c1, l0_0, l0_1, l1_0], [c0, c1, l0_0, l0_1, l1_0], [c0, c1, l1_1], [c0, c1, l0_0, l1_1], [c0, c1, l0_1, l1_1], [c1, l0_0, l0_1, l1_1], [c0, c1, l0_0, l0_1, l1_1], [c0, c1, l1_0, l1_1], [c0, c1, l0_0, l1_0, l1_1], [c0, c1, l0_1, l1_0, l1_1], [c1, l0_0, l0_1, l1_0, l1_1], [c0, c1, l0_0, l0_1, l1_0, l1_1], [c0, c1, l1_2], [c0, c1, l0_0, l1_2], [c0, c1, l0_1, l1_2], [c1, l0_0, l0_1, l1_2], [c0, c1, l0_0, l0_1, l1_2], [c0, c1, l1_0, l1_2], [c0, c1, l0_0, l1_0, l1_2], [c0, c1, l0_1, l1_0, l1_2], [c1, l0_0, l0_1, l1_0, l1_2], [c0, c1, l0_0, l0_1, l1_0, l1_2], [c0, c1, l1_1, l1_2], [c0, c1, l0_0, l1_1, l1_2], [c0, c1, l0_1, l1_1, l1_2], [c1, l0_0, l0_1, l1_1, l1_2], [c0, c1, l0_0, l0_1, l1_1, l1_2], [c0, c1, l1_0, l1_1, l1_2], [c0, c1, l0_0, l1_0, l1_1, l1_2], [c0, c1, l0_1, l1_0, l1_1, l1_2], [c1, l0_0, l0_1, l1_0, l1_1, l1_2], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2], [c0, c1, l1_3], [c0, c1, l0_0, l1_3], [c0, c1, l0_1, l1_3], [c1, l0_0, l0_1, l1_3], [c0, c1, l0_0, l0_1, l1_3], [c0, c1, l1_0, l1_3], [c0, c1, l0_0, l1_0, l1_3], [c0, c1, l0_1, l1_0, l1_3], [c1, l0_0, l0_1, l1_0, l1_3], [c0, c1, l0_0, l0_1, l1_0, l1_3], [c0, c1, l1_1, l1_3], [c0, c1, l0_0, l1_1, l1_3], [c0, c1, l0_1, l1_1, l1_3], [c1, l0_0, l0_1, l1_1, l1_3], [c0, c1, l0_0, l0_1, l1_1, l1_3], [c0, c1, l1_0, l1_1, l1_3], [c0, c1, l0_0, l1_0, l1_1, l1_3], [c0, c1, l0_1, l1_0, l1_1, l1_3], [c1, l0_0, l0_1, l1_0, l1_1, l1_3], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3], [c0, c1, l1_2, l1_3], [c0, c1, l0_0, l1_2, l1_3], [c0, c1, l0_1, l1_2, l1_3], [c1, l0_0, l0_1, l1_2, l1_3], [c0, c1, l0_0, l0_1, l1_2, l1_3], [c0, c1, l1_0, l1_2, l1_3], [c0, c1, l0_0, l1_0, l1_2, l1_3], [c0, c1, l0_1, l1_0, l1_2, l1_3], [c1, l0_0, l0_1, l1_0, l1_2, l1_3], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3], [c0, c1, l1_1, l1_2, l1_3], [c0, c1, l0_0, l1_1, l1_2, l1_3], [c0, c1, l0_1, l1_1, l1_2, l1_3], [c1, l0_0, l0_1, l1_1, l1_2, l1_3], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3], [c0, c1, l1_0, l1_1, l1_2, l1_3], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3], [c0, c1, l1_4], [c0, c1, l0_0, l1_4], [c0, c1, l0_1, l1_4], [c1, l0_0, l0_1, l1_4], [c0, c1, l0_0, l0_1, l1_4], [c0, c1, l1_0, l1_4], [c0, c1, l0_0, l1_0, l1_4], [c0, c1, l0_1, l1_0, l1_4], [c1, l0_0, l0_1, l1_0, l1_4], [c0, c1, l0_0, l0_1, l1_0, l1_4], [c0, c1, l1_1, l1_4], [c0, c1, l0_0, l1_1, l1_4], [c0, c1, l0_1, l1_1, l1_4], [c1, l0_0, l0_1, l1_1, l1_4], [c0, c1, l0_0, l0_1, l1_1, l1_4], [c0, c1, l1_0, l1_1, l1_4], [c0, c1, l0_0, l1_0, l1_1, l1_4], [c0, c1, l0_1, l1_0, l1_1, l1_4], [c1, l0_0, l0_1, l1_0, l1_1, l1_4], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_4], [c0, c1, l1_2, l1_4], [c0, c1, l0_0, l1_2, l1_4], [c0, c1, l0_1, l1_2, l1_4], [c1, l0_0, l0_1, l1_2, l1_4], [c0, c1, l0_0, l0_1, l1_2, l1_4], [c0, c1, l1_0, l1_2, l1_4], [c0, c1, l0_0, l1_0, l1_2, l1_4], [c0, c1, l0_1, l1_0, l1_2, l1_4], [c1, l0_0, l0_1, l1_0, l1_2, l1_4], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_4], [c0, c1, l1_1, l1_2, l1_4], [c0, c1, l0_0, l1_1, l1_2, l1_4], [c0, c1, l0_1, l1_1, l1_2, l1_4], [c1, l0_0, l0_1, l1_1, l1_2, l1_4], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_4], [c0, c1, l1_0, l1_1, l1_2, l1_4], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_4], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_4], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4], [c0, c1, l1_3, l1_4], [c0, c1, l0_0, l1_3, l1_4], [c0, c1, l0_1, l1_3, l1_4], [c1, l0_0, l0_1, l1_3, l1_4], [c0, c1, l0_0, l0_1, l1_3, l1_4], [c0, c1, l1_0, l1_3, l1_4], [c0, c1, l0_0, l1_0, l1_3, l1_4], [c0, c1, l0_1, l1_0, l1_3, l1_4], [c1, l0_0, l0_1, l1_0, l1_3, l1_4], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_4], [c0, c1, l1_1, l1_3, l1_4], [c0, c1, l0_0, l1_1, l1_3, l1_4], [c0, c1, l0_1, l1_1, l1_3, l1_4], [c1, l0_0, l0_1, l1_1, l1_3, l1_4], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_4], [c0, c1, l1_0, l1_1, l1_3, l1_4], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_4], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_4], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4], [c0, c1, l1_2, l1_3, l1_4], [c0, c1, l0_0, l1_2, l1_3, l1_4], [c0, c1, l0_1, l1_2, l1_3, l1_4], [c1, l0_0, l0_1, l1_2, l1_3, l1_4], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_4], [c0, c1, l1_0, l1_2, l1_3, l1_4], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_4], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_4], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4], [c0, c1, l1_1, l1_2, l1_3, l1_4], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_4], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_4], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_4], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_4], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], [c0, c1, l1_5], [c0, c1, l0_0, l1_5], [c0, c1, l0_1, l1_5], [c1, l0_0, l0_1, l1_5], [c0, c1, l0_0, l0_1, l1_5], [c0, c1, l1_0, l1_5], [c0, c1, l0_0, l1_0, l1_5], [c0, c1, l0_1, l1_0, l1_5], [c1, l0_0, l0_1, l1_0, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_5], [c0, c1, l1_1, l1_5], [c0, c1, l0_0, l1_1, l1_5], [c0, c1, l0_1, l1_1, l1_5], [c1, l0_0, l0_1, l1_1, l1_5], [c0, c1, l0_0, l0_1, l1_1, l1_5], [c0, c1, l1_0, l1_1, l1_5], [c0, c1, l0_0, l1_0, l1_1, l1_5], [c0, c1, l0_1, l1_0, l1_1, l1_5], [c1, l0_0, l0_1, l1_0, l1_1, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_5], [c0, c1, l1_2, l1_5], [c0, c1, l0_0, l1_2, l1_5], [c0, c1, l0_1, l1_2, l1_5], [c1, l0_0, l0_1, l1_2, l1_5], [c0, c1, l0_0, l0_1, l1_2, l1_5], [c0, c1, l1_0, l1_2, l1_5], [c0, c1, l0_0, l1_0, l1_2, l1_5], [c0, c1, l0_1, l1_0, l1_2, l1_5], [c1, l0_0, l0_1, l1_0, l1_2, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_5], [c0, c1, l1_1, l1_2, l1_5], [c0, c1, l0_0, l1_1, l1_2, l1_5], [c0, c1, l0_1, l1_1, l1_2, l1_5], [c1, l0_0, l0_1, l1_1, l1_2, l1_5], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_5], [c0, c1, l1_0, l1_1, l1_2, l1_5], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_5], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_5], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_5], [c0, c1, l1_3, l1_5], [c0, c1, l0_0, l1_3, l1_5], [c0, c1, l0_1, l1_3, l1_5], [c1, l0_0, l0_1, l1_3, l1_5], [c0, c1, l0_0, l0_1, l1_3, l1_5], [c0, c1, l1_0, l1_3, l1_5], [c0, c1, l0_0, l1_0, l1_3, l1_5], [c0, c1, l0_1, l1_0, l1_3, l1_5], [c1, l0_0, l0_1, l1_0, l1_3, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_5], [c0, c1, l1_1, l1_3, l1_5], [c0, c1, l0_0, l1_1, l1_3, l1_5], [c0, c1, l0_1, l1_1, l1_3, l1_5], [c1, l0_0, l0_1, l1_1, l1_3, l1_5], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_5], [c0, c1, l1_0, l1_1, l1_3, l1_5], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_5], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_5], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_5], [c0, c1, l1_2, l1_3, l1_5], [c0, c1, l0_0, l1_2, l1_3, l1_5], [c0, c1, l0_1, l1_2, l1_3, l1_5], [c1, l0_0, l0_1, l1_2, l1_3, l1_5], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_5], [c0, c1, l1_0, l1_2, l1_3, l1_5], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_5], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_5], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_5], [c0, c1, l1_1, l1_2, l1_3, l1_5], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_5], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_5], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_5], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_5], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_5], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_5], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5], [c0, c1, l1_4, l1_5], [c0, c1, l0_0, l1_4, l1_5], [c0, c1, l0_1, l1_4, l1_5], [c1, l0_0, l0_1, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_4, l1_5], [c0, c1, l1_0, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_4, l1_5], [c0, c1, l1_1, l1_4, l1_5], [c0, c1, l0_0, l1_1, l1_4, l1_5], [c0, c1, l0_1, l1_1, l1_4, l1_5], [c1, l0_0, l0_1, l1_1, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_1, l1_4, l1_5], [c0, c1, l1_0, l1_1, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_1, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_1, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_5], [c0, c1, l1_2, l1_4, l1_5], [c0, c1, l0_0, l1_2, l1_4, l1_5], [c0, c1, l0_1, l1_2, l1_4, l1_5], [c1, l0_0, l0_1, l1_2, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_2, l1_4, l1_5], [c0, c1, l1_0, l1_2, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_2, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_2, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_5], [c0, c1, l1_1, l1_2, l1_4, l1_5], [c0, c1, l0_0, l1_1, l1_2, l1_4, l1_5], [c0, c1, l0_1, l1_1, l1_2, l1_4, l1_5], [c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_5], [c0, c1, l1_0, l1_1, l1_2, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5], [c0, c1, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_3, l1_4, l1_5], [c0, c1, l1_0, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_5], [c0, c1, l1_1, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_1, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_1, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_5], [c0, c1, l1_0, l1_1, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5], [c0, c1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_2, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l1_0, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5], [c0, c1, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5]], [0, 0, 1, 9, 34, 71, 90, 72, 37, 10, 1], 2, [[c0, c1]]]

source roles = [[l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [[c0, l0_0], [c0, l0_1], [c1, l1_0], [c1, l1_1], [c1, l1_2], [c1, l1_3], [c1, l1_4], [c1, l1_5]]]

derived = [[[[c0, l0_0], 是], [[c0, l0_1], 是], [[c1, l1_0], 是], [[c1, l1_1], 是], [[c1, l1_2], 是], [[c1, l1_3], 是], [[c1, l1_4], 是], [[c1, l1_5], 是]], 8, 2, [c0, c1]]

source roles = [[l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5], 否], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5], 否], [l1_4, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5], 否], [l1_5, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], 否]]]

derived = [是, 2, [c0, c1], 否]

逐步反向核對

• 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

([l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5], 否], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5], 否], [l1_4, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5], 否], [l1_5, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

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。