第 26084 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-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v10"],["v10","v11"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"]}。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-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v10"],["v10","v11"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"]}。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-nonminimum-witness]

derived = [[candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate]]

source roles = [[v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9], [v9, v10], [v10, v11]], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11]]

derived = [[v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v1, v2], [v10, v11], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9]]

source roles = [[v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v1, v2], [v10, v11], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], 4096]

derived = [[1365, 1366, 1367, 1373, 1374, 1375, 1382, 1383, 1390, 1391, 1397, 1398, 1399, 1405, 1406, 1407, 1446, 1447, 1454, 1455, 1461, 1462, 1463, 1469, 1470, 1471, 1493, 1494, 1495, 1501, 1502, 1503, 1510, 1511, 1518, 1519, 1525, 1526, 1527, 1533, 1534, 1535, 1702, 1703, 1710, 1711, 1717, 1718, 1719, 1725, 1726, 1727, 1749, 1750, 1751, 1757, 1758, 1759, 1766, 1767, 1774, 1775, 1781, 1782, 1783, 1789, 1790, 1791, 1877, 1878, 1879, 1885, 1886, 1887, 1894, 1895, 1902, 1903, 1909, 1910, 1911, 1917, 1918, 1919, 1958, 1959, 1966, 1967, 1973, 1974, 1975, 1981, 1982, 1983, 2005, 2006, 2007, 2013, 2014, 2015, 2022, 2023, 2030, 2031, 2037, 2038, 2039, 2045, 2046, 2047, 2726, 2727, 2730, 2731, 2734, 2735, 2741, 2742, 2743, 2745, 2746, 2747, 2749, 2750, 2751, 2773, 2774, 2775, 2777, 2778, 2779, 2781, 2782, 2783, 2790, 2791, 2794, 2795, 2798, 2799, 2805, 2806, 2807, 2809, 2810, 2811, 2813, 2814, 2815, 2901, 2902, 2903, 2905, 2906, 2907, 2909, 2910, 2911, 2918, 2919, 2922, 2923, 2926, 2927, 2933, 2934, 2935, 2937, 2938, 2939, 2941, 2942, 2943, 2982, 2983, 2986, 2987, 2990, 2991, 2997, 2998, 2999, 3001, 3002, 3003, 3005, 3006, 3007, 3029, 3030, 3031, 3033, 3034, 3035, 3037, 3038, 3039, 3046, 3047, 3050, 3051, 3054, 3055, 3061, 3062, 3063, 3065, 3066, 3067, 3069, 3070, 3071, 3413, 3414, 3415, 3417, 3418, 3419, 3421, 3422, 3423, 3430, 3431, 3434, 3435, 3438, 3439, 3445, 3446, 3447, 3449, 3450, 3451, 3453, 3454, 3455, 3494, 3495, 3498, 3499, 3502, 3503, 3509, 3510, 3511, 3513, 3514, 3515, 3517, 3518, 3519, 3541, 3542, 3543, 3545, 3546, 3547, 3549, 3550, 3551, 3558, 3559, 3562, 3563, 3566, 3567, 3573, 3574, 3575, 3577, 3578, 3579, 3581, 3582, 3583, 3750, 3751, 3754, 3755, 3758, 3759, 3765, 3766, 3767, 3769, 3770, 3771, 3773, 3774, 3775, 3797, 3798, 3799, 3801, 3802, 3803, 3805, 3806, 3807, 3814, 3815, 3818, 3819, 3822, 3823, 3829, 3830, 3831, 3833, 3834, 3835, 3837, 3838, 3839, 3925, 3926, 3927, 3929, 3930, 3931, 3933, 3934, 3935, 3942, 3943, 3946, 3947, 3950, 3951, 3957, 3958, 3959, 3961, 3962, 3963, 3965, 3966, 3967, 4006, 4007, 4010, 4011, 4014, 4015, 4021, 4022, 4023, 4025, 4026, 4027, 4029, 4030, 4031, 4053, 4054, 4055, 4057, 4058, 4059, 4061, 4062, 4063, 4070, 4071, 4074, 4075, 4078, 4079, 4085, 4086, 4087, 4089, 4090, 4091, 4093, 4094, 4095], [[0, 0], [1, 1], [2, 2], [3, 2], [4, 0], [5, 1], [6, 4], [7, 4], [8, 0], [9, 1], [10, 3], [11, 3], [12, 0], [13, 1], [14, 4], [15, 4], [16, 0], [17, 2], [18, 2], [19, 2], [20, 0], [21, 5], [22, 5], [23, 5], [24, 0], [25, 3], [26, 3], [27, 3], [28, 0], [29, 5], [30, 5], [31, 5], [32, 0], [33, 1], [34, 2], [35, 2], [36, 0], [37, 1], [38, 6], [39, 6], [40, 0], [41, 1], [42, 3], [43, 3], [44, 0], [45, 1], [46, 6], [47, 6], [48, 0], [49, 2], [50, 2], [51, 2], [52, 0], [53, 6], [54, 6], [55, 6], [56, 0], [57, 3], [58, 3], [59, 3], [60, 0], [61, 6], [62, 6], [63, 6], [64, 0], [65, 1], [66, 2], [67, 2], [68, 0], [69, 1], [70, 4], [71, 4], [72, 0], [73, 1], [74, 3], [75, 3], [76, 0], [77, 1], [78, 4], [79, 4], [80, 0], [81, 2], [82, 2], [83, 2], [84, 0], [85, 7], [86, 7], [87, 7], [88, 0], [89, 3], [90, 3], [91, 3], [92, 0], [93, 7], [94, 7], [95, 7], [96, 0], [97, 1], [98, 2], [99, 2], [100, 0], [101, 1], [102, 7], [103, 7], [104, 0], [105, 1], [106, 3], [107, 3], [108, 0], [109, 1], [110, 7], [111, 7], [112, 0], [113, 2], [114, 2], [115, 2], [116, 0], [117, 7], [118, 7], [119, 7], [120, 0], [121, 3], [122, 3], [123, 3], [124, 0], [125, 7], [126, 7], [127, 7], [128, 0], [129, 1], [130, 2], [131, 2], [132, 0], [133, 1], [134, 4], [135, 4], [136, 0], [137, 1], [138, 3], [139, 3], [140, 0], [141, 1], [142, 4], [143, 4], [144, 0], [145, 2], [146, 2], [147, 2], [148, 0], [149, 5], [150, 5], [151, 5], [152, 0], [153, 3], [154, 3], [155, 3], [156, 0], [157, 5], [158, 5], [159, 5], [160, 0], [161, 1], [162, 2], [163, 2], [164, 0], [165, 1], [166, 8], [167, 8], [168, 0], [169, 1], [170, 3], [171, 3], [172, 0], [173, 1], [174, 8], [175, 8], [176, 0], [177, 2], [178, 2], [179, 2], [180, 0], [181, 8], [182, 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[682, 3], [683, 3], [684, 0], [685, 1], [686, 10], [687, 10], [688, 0], [689, 2], [690, 2], [691, 2], [692, 0], [693, 10], [694, 10], [695, 10], [696, 0], [697, 3], [698, 3], [699, 3], [700, 0], [701, 10], [702, 10], [703, 10], [704, 0], [705, 1], [706, 2], [707, 2], [708, 0], [709, 1], [710, 4], [711, 4], [712, 0], [713, 1], [714, 3], [715, 3], [716, 0], [717, 1], [718, 4], [719, 4], [720, 0], [721, 2], [722, 2], [723, 2], [724, 0], [725, 10], [726, 10], [727, 10], [728, 0], [729, 3], [730, 3], [731, 3], [732, 0], [733, 10], [734, 10], [735, 10], [736, 0], [737, 1], [738, 2], [739, 2], [740, 0], [741, 1], [742, 10], [743, 10], [744, 0], [745, 1], [746, 3], [747, 3], [748, 0], [749, 1], [750, 10], [751, 10], [752, 0], [753, 2], [754, 2], [755, 2], [756, 0], [757, 10], [758, 10], [759, 10], [760, 0], [761, 3], [762, 3], [763, 3], [764, 0], [765, 10], [766, 10], [767, 10], [768, 0], [769, 1], [770, 2], [771, 2], [772, 0], [773, 1], [774, 4], [775, 4], [776, 0], [777, 1], [778, 3], [779, 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[v1, v10, v2, v3, v4, v6, v7, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v9], [v0, v11, v2, v3, v4, v6, v7, v9], [v1, v11, v2, v3, v4, v6, v7, v9], [v0, v1, v11, v2, v3, v4, v6, v7, v9], [v0, v10, v11, v2, v3, v4, v6, v7, v9], [v1, v10, v11, v2, v3, v4, v6, v7, v9], [v0, v1, v10, v11, v2, v3, v4, v6, v7, v9], [v1, v10, v3, v5, v6, v7, v9], [v0, v1, v10, v3, v5, v6, v7, v9], [v1, v11, v3, v5, v6, v7, v9], [v0, v1, v11, v3, v5, v6, v7, v9], [v1, v10, v11, v3, v5, v6, v7, v9], [v0, v1, v10, v11, v3, v5, v6, v7, v9], [v0, v10, v2, v3, v5, v6, v7, v9], [v1, v10, v2, v3, v5, v6, v7, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v9], [v0, v11, v2, v3, v5, v6, v7, v9], [v1, v11, v2, v3, v5, v6, v7, v9], [v0, v1, v11, v2, v3, v5, v6, v7, v9], [v0, v10, v11, v2, v3, v5, v6, v7, v9], [v1, v10, v11, v2, v3, v5, v6, v7, v9], [v0, v1, v10, v11, v2, v3, v5, v6, v7, v9], [v0, v10, v2, v4, v5, v6, v7, v9], [v1, v10, v2, v4, v5, v6, v7, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v9], [v0, v11, v2, v4, v5, v6, v7, v9], [v1, v11, v2, v4, v5, v6, v7, v9], [v0, v1, v11, v2, v4, v5, v6, v7, v9], [v0, v10, v11, v2, v4, v5, v6, v7, v9], [v1, v10, v11, v2, v4, v5, v6, v7, v9], [v0, v1, v10, v11, v2, v4, v5, v6, v7, v9], [v1, v10, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v9], [v1, v11, v3, v4, v5, v6, v7, v9], [v0, v1, v11, v3, v4, v5, v6, v7, v9], [v1, v10, v11, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v11, v3, v4, v5, v6, v7, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v9], [v1, v10, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v9], [v0, v11, v2, v3, v4, v5, v6, v7, v9], [v1, v11, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v11, v2, v3, v4, v5, v6, v7, v9], [v0, v10, v11, v2, v3, v4, v5, v6, v7, v9], [v1, v10, v11, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v9], [v0, v10, v2, v4, v6, v8, v9], [v1, v10, v2, v4, v6, v8, v9], [v0, v1, v10, v2, v4, v6, v8, v9], [v0, v11, v2, v4, v6, v8, v9], [v1, v11, v2, v4, v6, v8, v9], [v0, v1, v11, v2, v4, v6, v8, v9], [v0, v10, v11, v2, v4, v6, v8, v9], [v1, v10, v11, v2, v4, v6, v8, v9], [v0, v1, v10, v11, v2, v4, v6, v8, v9], [v1, v10, v3, v4, v6, v8, v9], [v0, v1, v10, v3, v4, v6, v8, v9], [v1, v11, v3, v4, v6, v8, v9], [v0, v1, v11, v3, v4, v6, v8, v9], [v1, v10, v11, v3, v4, v6, v8, v9], [v0, v1, v10, v11, v3, v4, v6, v8, v9], [v0, v10, v2, v3, v4, v6, v8, v9], [v1, v10, v2, v3, v4, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v8, v9], [v0, v11, v2, v3, v4, v6, v8, v9], [v1, v11, v2, v3, v4, v6, v8, v9], [v0, v1, v11, v2, v3, v4, v6, v8, v9], [v0, v10, v11, v2, v3, v4, v6, v8, v9], [v1, v10, v11, v2, v3, v4, v6, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v6, v8, v9], [v1, v10, v3, v5, v6, v8, v9], [v0, v1, v10, v3, v5, v6, v8, v9], [v1, v11, v3, v5, v6, v8, v9], [v0, v1, v11, v3, v5, v6, v8, v9], [v1, v10, v11, v3, v5, v6, v8, v9], [v0, v1, v10, v11, v3, v5, v6, v8, v9], [v0, v10, v2, v3, v5, v6, v8, v9], [v1, v10, v2, v3, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v8, v9], [v0, v11, v2, v3, v5, v6, v8, v9], [v1, v11, v2, v3, v5, v6, v8, v9], [v0, v1, v11, v2, v3, v5, v6, v8, v9], [v0, v10, v11, v2, v3, v5, v6, v8, v9], [v1, v10, v11, v2, v3, v5, v6, v8, v9], [v0, v1, v10, v11, v2, v3, v5, v6, v8, v9], [v0, v10, v2, v4, v5, v6, v8, v9], [v1, v10, v2, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v8, v9], [v0, v11, v2, v4, v5, v6, v8, v9], [v1, v11, v2, v4, v5, v6, v8, v9], [v0, v1, v11, v2, v4, v5, v6, v8, v9], [v0, v10, v11, v2, v4, v5, v6, v8, v9], [v1, v10, v11, v2, v4, v5, v6, v8, v9], [v0, v1, v10, v11, v2, v4, v5, v6, v8, v9], [v1, v10, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v8, v9], [v1, v11, v3, v4, v5, v6, v8, v9], [v0, v1, v11, v3, v4, v5, v6, v8, v9], [v1, v10, v11, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v11, v3, v4, v5, v6, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v8, v9], [v0, v11, v2, v3, v4, v5, v6, v8, v9], [v1, v11, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v11, v2, v3, v4, v5, v6, v8, v9], [v0, v10, v11, v2, v3, v4, v5, v6, v8, v9], [v1, v10, v11, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v8, v9], [v1, v10, v3, v5, v7, v8, v9], [v0, v1, v10, v3, v5, v7, v8, v9], [v1, v11, v3, v5, v7, v8, v9], [v0, v1, v11, v3, v5, v7, v8, v9], [v1, v10, v11, v3, v5, v7, v8, v9], [v0, v1, v10, v11, v3, v5, v7, v8, v9], [v0, v10, v2, v3, v5, v7, v8, v9], [v1, v10, v2, v3, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v7, v8, v9], [v0, v11, v2, v3, v5, v7, v8, v9], [v1, v11, v2, v3, v5, v7, v8, v9], [v0, v1, v11, v2, v3, v5, v7, v8, v9], [v0, v10, v11, v2, v3, v5, v7, v8, v9], [v1, v10, v11, v2, v3, v5, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v5, v7, v8, v9], [v0, v10, v2, v4, v5, v7, v8, v9], [v1, v10, v2, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v7, v8, v9], [v0, v11, v2, v4, v5, v7, v8, v9], [v1, v11, v2, v4, v5, v7, v8, v9], [v0, v1, v11, v2, v4, v5, v7, v8, v9], [v0, v10, v11, v2, v4, v5, v7, v8, v9], [v1, v10, v11, v2, v4, v5, v7, v8, v9], [v0, v1, v10, v11, v2, v4, v5, v7, v8, v9], [v1, v10, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v7, v8, v9], [v1, v11, v3, v4, v5, v7, v8, v9], [v0, v1, v11, v3, v4, v5, v7, v8, v9], [v1, v10, v11, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v11, v3, v4, v5, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v11, v2, v3, v4, v5, v7, v8, v9], [v1, v11, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v11, v2, v3, v4, v5, v7, v8, v9], [v0, v10, v11, v2, v3, v4, v5, v7, v8, v9], [v1, v10, v11, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v7, v8, v9], [v0, v10, v2, v4, v6, v7, v8, v9], [v1, v10, v2, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v6, v7, v8, v9], [v0, v11, v2, v4, v6, v7, v8, v9], [v1, v11, v2, v4, v6, v7, v8, v9], [v0, v1, v11, v2, v4, v6, v7, v8, v9], [v0, v10, v11, v2, v4, v6, v7, v8, v9], [v1, v10, v11, v2, v4, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v4, v6, v7, v8, v9], [v1, v10, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v6, v7, v8, v9], [v1, v11, v3, v4, v6, v7, v8, v9], [v0, v1, v11, v3, v4, v6, v7, v8, v9], [v1, v10, v11, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v4, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v11, v2, v3, v4, v6, v7, v8, v9], [v1, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v5, v6, v7, v8, v9], [v1, v11, v3, v5, v6, v7, v8, v9], [v0, v1, v11, v3, v5, v6, v7, v8, v9], [v1, v10, v11, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v11, v2, v3, v5, v6, v7, v8, v9], [v1, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v8, v9], [v1, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9]], [0, 0, 0, 0, 0, 0, 7, 56, 126, 120, 55, 12, 1], 6, [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v1, v10, v3, v5, v7, v9], [v1, v11, v3, v5, v7, v9]]]

source roles = [[v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v1, v2], [v10, v11], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]]]

derived = [[[[v0, v1], 是], [[v1, v2], 是], [[v10, v11], 是], [[v10, v9], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 12, 6, [v0, v10, v2, v4, v6, v8]]

逐步反向核對

• 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

([v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], 是, 12, 6, [v0, v10, v2, v4, v6, v8], 否, explicit_smaller_cover_refutes_minimum_status)

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。