# 第 26065 題：最小頂點覆蓋 [返回所在分頁 131](https://ocme.evemisslab.com/zh-Hant/questions/page/131/) [← 逐題詳解目錄](https://ocme.evemisslab.com/zh-Hant/questions/) · [原題批次](https://ocme.evemisslab.com/zh-Hant/practice/batch-20261015-advance-20261115-r06-minimum-vertex-cover-foundations/#q-20261015-advance-20261115-r06-minimum-vertex-cover-0065) 本頁是已完成第二對話 AI 數理與中英語義覆核的教學詳解，只支持本題明示的模型與前提。沒有人工審查或新 Lean 證明，也不提升原題或 MKO 的 Canonical 真值狀態。 R0051-26065 · q-20261015-advance-20261115-r06-minimum-vertex-cover-0065 ## 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](https://ocme.evemisslab.com/zh-Hant/mko/mko-minimum-vertex-cover/) ## 逐步推導 S001 · implies操作前 source roles = [mincover-minimal-not-minimum] 操作後 derived = [[candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate]] 條件：無 本頁直接列完整來源欄序，不需JavaScript；contract的6/4/6/6與IVT的8/7/8由原mode選，不補欄也不由答案形狀猜。 步驟識別與依賴規則：source_ordered_fields_without_JS · 依賴：G001 S002 · implies操作前 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]] 操作後 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]] 條件：無 非空carrier至多12；端點UTF16排序後edge族English排序，loop/反向duplicate拒絕。未提供candidate時保持null，不擅補空candidate。 步驟識別與依賴規則：Mincover_complete_simple_graph_UTF16_English_and_optional_candidate · 依賴：G001, S001 S003 · implies操作前 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] 操作後 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, 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[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], 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[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, 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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]]] 條件：無 逐全部mask核所有edges；每個失敗mask保首uncovered edge index反例，通過者全列source順序。較小size計數0給下界，實際最小解給上界；全部ties依numeric mask保留，不改English/大小序。 步驟識別與依賴規則：Mincover_ALL_masks_acceptance_refutations_ALLcovers_ALLminimizers · 依賴：G001, S002 S004 · implies操作前 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]]] 操作後 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]] 條件：無 先核candidate真cover；較小解取完整source清單的首minimum，不用任意小集合代替。 步驟識別與依賴規則：Mincover_actual_candidate_complete_cover_and_smaller_witness · 依賴：G001, S003 S005 · implies操作前 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]]] 操作後 derived = [是, 2, [c0, c1], 否] 條件：無 逐刪都失cover，所以inclusion-minimal；但完整枚舉已有嚴格更小cover，所以不是minimum。cover對superset單調使逐刪可驗全部proper subset責任，不等同最大／最優大小。 步驟識別與依賴規則：Mincover_ALL_single_deletions_minimal_BUT_smaller_cover_exists · 依賴：G001, S004 ## 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。 來源雜湊與覆核憑證 - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: 40afcd6a2e597c3c9a12857bee87d548988bf49933f34814988f277cb5f5ff7e - candidate record SHA-256: 15e991755cbab6e503668bfa4a0d46dbfedf75ac7edce6ba8a503ad99e28b847 - semantic review receipt SHA-256: 90df1e889242e9afdf01e068788ee8500ef366ffcfc0496e30a6800de32631c3 - question-first witness SHA-256: ae1e849608590ca856c9f3b6911ba58e3bf53c608eb7369606192a770f48bd5c - Lean: NOT_RUN · human review: NOT_PERFORMED [同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0065.json)