{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261011-r05-subset-0064",
  "pilot_number": "R0009-05139",
  "number": 5139,
  "family_id": "qf-density11-subset-chain-obstructions",
  "title": {
    "zh-Hant": "第 5139 題：三段包含的有序阻擋集",
    "en": "Question 5139: Three Ordered Inclusion Obstructions"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261011-r05-subset-0064",
    "batch_id": "batch-20261008-advance-20261011-r05-subset-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-subset"
    ],
    "title_zh": "三段包含的有序阻擋集",
    "stem_zh": "有限整數集合；同一整數型別；A=[-13, 0]、B=[0, 13]、C=[0, 14]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。",
    "answer": {
      "kind": "expression",
      "value": "([-13], [13], [-13])",
      "explanation_zh": "三段包含阻擋=([-13], [13], [-13])。分別枚舉三段隸屬條件；某一鏈節失敗不自動決定另一段，三段不能互相替代。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 2,
      "skills": [
        "三段包含的有序阻擋集"
      ]
    },
    "variant": {
      "family_id": "qf-density11-subset-chain-obstructions",
      "seed": 202610115064,
      "parameters": {
        "A": [
          -13,
          0
        ],
        "B": [
          0,
          13
        ],
        "C": [
          0,
          14
        ],
        "operation": "density11_subset_chain_obstructions",
        "domain": "finite_integer_set_slice",
        "semantic_template": "qf-density11-subset-chain-obstructions/[[-13],[13],[-13]]"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_integer_rational_arithmetic",
        "producer_finite_enumeration",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-08",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261008-advance-20261011-r05-subset-0064",
    "batch_id": "batch-20261008-advance-20261011-r05-subset-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "207eff31550c56aff7ffd733c6a36b2b30af56e38ad03b5d253cef9a75dadc4b",
      "family_id": "qf-density11-subset-chain-obstructions",
      "seed": 202610115064,
      "semantic_template": "qf-density11-subset-chain-obstructions/[[-13],[13],[-13]]"
    },
    "fields": {
      "title": "Three Ordered Inclusion Obstructions",
      "stem": "Finite integer sets A=[-13, 0] and B=[0, 13]; repeated elements count once. C=[0, 14] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.",
      "answer": {
        "kind": "expression",
        "value": "([-13], [13], [-13])",
        "explanation": "Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-13], [13], [-13])."
      },
      "skills": [
        "Three Ordered Inclusion Obstructions"
      ],
      "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."
    }
  },
  "givens": [
    {
      "id": "G001",
      "text": {
        "zh-Hant": "有限整數集合；同一整數型別；A=[-13, 0]、B=[0, 13]、C=[0, 14]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。",
        "en": "Finite integer sets A=[-13, 0] and B=[0, 13]; repeated elements count once. C=[0, 14] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "A=[-13, 0];B=[0, 13];same integer type",
      "after": "A⊆B means every A-element belongs to B",
      "relation": "implies",
      "rule_id": "set_inclusion_definition",
      "conditions": [],
      "explanation": {
        "zh-Hant": "包含的反例必須屬A且不屬B；域外A的數字不是見證，空A不產生阻擋。",
        "en": "An inclusion obstruction must belong to A but not B;an element outside A is no witness,and empty A gives no obstruction."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "A\\B:source element=-13;target=[0, 13]",
      "after": "obstruction=是",
      "relation": "implies",
      "rule_id": "inclusion_obstruction_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐一核對來源集合的全部元素，目標集合不含才列為阻擋。",
        "en": "Audit every source-set element;list it as an obstruction exactly when the target omits it."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "A\\B:source element=0;target=[0, 13]",
      "after": "obstruction=否",
      "relation": "implies",
      "rule_id": "inclusion_obstruction_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐一核對來源集合的全部元素，目標集合不含才列為阻擋。",
        "en": "Audit every source-set element;list it as an obstruction exactly when the target omits it."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "B\\C:source element=0;target=[0, 14]",
      "after": "obstruction=否",
      "relation": "implies",
      "rule_id": "inclusion_obstruction_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐一核對來源集合的全部元素，目標集合不含才列為阻擋。",
        "en": "Audit every source-set element;list it as an obstruction exactly when the target omits it."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "B\\C:source element=13;target=[0, 14]",
      "after": "obstruction=是",
      "relation": "implies",
      "rule_id": "inclusion_obstruction_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐一核對來源集合的全部元素，目標集合不含才列為阻擋。",
        "en": "Audit every source-set element;list it as an obstruction exactly when the target omits it."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "A\\C:source element=-13;target=[0, 14]",
      "after": "obstruction=是",
      "relation": "implies",
      "rule_id": "inclusion_obstruction_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐一核對來源集合的全部元素，目標集合不含才列為阻擋。",
        "en": "Audit every source-set element;list it as an obstruction exactly when the target omits it."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "A\\C:source element=0;target=[0, 14]",
      "after": "obstruction=否",
      "relation": "implies",
      "rule_id": "inclusion_obstruction_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐一核對來源集合的全部元素，目標集合不含才列為阻擋。",
        "en": "Audit every source-set element;list it as an obstruction exactly when the target omits it."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "([-13], [13], [-13])",
      "after": "three independently audited directional differences",
      "relation": "implies",
      "rule_id": "inclusion_chain_scope",
      "conditions": [],
      "explanation": {
        "zh-Hant": "前兩包含若都成立可推出第三包含；但某一鏈節有阻擋時，不能直接猜第三段的阻擋，仍按明示集合核對。",
        "en": "If both first inclusions hold,the third follows.But a failed link does not determine the third obstruction set;use the explicit sets to audit it."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": [
      [
        -13
      ],
      [
        13
      ],
      [
        -13
      ]
    ]
  },
  "conclusion": {
    "canonical_value": "([-13], [13], [-13])",
    "explanation": {
      "zh-Hant": "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。",
      "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged."
    }
  },
  "definition_note": {
    "zh-Hant": "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。",
    "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate."
  },
  "source": {
    "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db",
    "question_binding": {
      "batch_id": "batch-20261008-advance-20261011-r05-subset-foundations",
      "batch_path": "public/data/questions/batches/batch-20261008-advance-20261011-r05-subset-foundations/questions.jsonl",
      "batch_sha256": "faef8ba0762c4b1138b5f3bb62aed94757b8580fef3c3b9df5518b48ec561db7",
      "original_line": 64,
      "original_line_sha256": "5fabb8de1dc7972d040e3aa26b4f29014797ae6eb20160228a4488773db69fd2",
      "question_compact_sha256": "207eff31550c56aff7ffd733c6a36b2b30af56e38ad03b5d253cef9a75dadc4b",
      "english_row_compact_sha256": "2f5a0badfe124c693084229cf70ee247f908d48871372614d11f4cfb0f8f8acf",
      "english_manifest_path": "public/data/i18n/editions/batch-20261008-advance-20261011-r05-subset-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261008-advance-20261011-r05-subset-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-subset": {
        "sha256": "984a77e67dc9322e36b869843513f1cb76f9527912202782848120c123ce99b3",
        "english_sha256": "af2446cfbbb6eff0aba71545b87591295e79df30d0992a5085cf44be4170d534",
        "original_path": "public/data/mko/subset.json",
        "english_path": "public/data/i18n/editions/mko-subset.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "3132b1200be7a5de38191badc52fb1727d4dd9d4c2f26818de2e8a76426d2d3f",
    "original_candidate_sha256": "cf2156a04e07533b4cbda73385d15a6f1b17a551e0055240848500c68b558f91",
    "original_candidate_line_sha256": "cf2156a04e07533b4cbda73385d15a6f1b17a551e0055240848500c68b558f91"
  },
  "historical_source_state": {
    "review_state": {
      "derivation": "candidate_authored_and_locally_checked",
      "source_question_state": "candidate",
      "independent_AI_or_human_review": "NOT_PERFORMED",
      "formalization": "not_formalized",
      "Lean": "NOT_RUN"
    },
    "scope_note": {
      "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。",
      "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged."
    },
    "label": "Frozen producer metadata; current per-question review is separate below."
  },
  "revision": {
    "id": "review-20261026-005-p10",
    "review_date": "2026-10-26",
    "owner_authorized_reader_publication": true,
    "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.",
    "review_receipts": {
      "semantic_review_sha256": "71e7db519df31f3a164533e472e293cb64f001b475a8d002b4a5c2740a237b56",
      "question_first_witness_sha256": "5a43f4f81b6256281f8d139a4010bbde127be803c528e5878857269c8f854462"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 8,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "827d6e5228e445767a638977d1bc658e04db2b6e5ddd79b84c6927e30e7bb6b7",
      "arithmetic_steps": 0
    },
    "uses_answer_as_premise": false,
    "human_review": "NOT_PERFORMED",
    "formalization": "not_formalized",
    "Lean": "NOT_RUN",
    "Canonical_truth_promotion": false,
    "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged."
  }
}