{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0001","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[]、B=[1]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[]","explanation_zh":"全部阻擋元素=[]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115001,"parameters":{"A":[],"B":[1],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0002","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-1]、B=[]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-1]","explanation_zh":"全部阻擋元素=[-1]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115002,"parameters":{"A":[-1],"B":[],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-1]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0003","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-2, 2, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-2, 2]","explanation_zh":"全部阻擋元素=[-2, 2]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115003,"parameters":{"A":[-2,2,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-2,2]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0004","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-3, 3, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-3, 3]","explanation_zh":"全部阻擋元素=[-3, 3]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115004,"parameters":{"A":[-3,3,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-3,3]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0005","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-4, 4, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-4, 4]","explanation_zh":"全部阻擋元素=[-4, 4]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115005,"parameters":{"A":[-4,4,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-4,4]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0006","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-5, 5, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-5, 5]","explanation_zh":"全部阻擋元素=[-5, 5]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115006,"parameters":{"A":[-5,5,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-5,5]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0007","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-6, 6, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-6, 6]","explanation_zh":"全部阻擋元素=[-6, 6]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115007,"parameters":{"A":[-6,6,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-6,6]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0008","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-7, 7, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-7, 7]","explanation_zh":"全部阻擋元素=[-7, 7]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115008,"parameters":{"A":[-7,7,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-7,7]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0009","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-8, 8, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-8, 8]","explanation_zh":"全部阻擋元素=[-8, 8]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115009,"parameters":{"A":[-8,8,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-8,8]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0010","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-9, 9, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-9, 9]","explanation_zh":"全部阻擋元素=[-9, 9]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115010,"parameters":{"A":[-9,9,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-9,9]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0011","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-10, 10, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-10, 10]","explanation_zh":"全部阻擋元素=[-10, 10]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115011,"parameters":{"A":[-10,10,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-10,10]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0012","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-11, 11, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-11, 11]","explanation_zh":"全部阻擋元素=[-11, 11]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115012,"parameters":{"A":[-11,11,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-11,11]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0013","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-12, 12, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-12, 12]","explanation_zh":"全部阻擋元素=[-12, 12]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115013,"parameters":{"A":[-12,12,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-12,12]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0014","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-13, 13, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-13, 13]","explanation_zh":"全部阻擋元素=[-13, 13]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115014,"parameters":{"A":[-13,13,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0015","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-14, 14, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-14, 14]","explanation_zh":"全部阻擋元素=[-14, 14]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115015,"parameters":{"A":[-14,14,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-14,14]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0016","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-15, 15, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-15, 15]","explanation_zh":"全部阻擋元素=[-15, 15]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115016,"parameters":{"A":[-15,15,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-15,15]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0017","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-16, 16, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-16, 16]","explanation_zh":"全部阻擋元素=[-16, 16]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115017,"parameters":{"A":[-16,16,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-16,16]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0018","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-17, 17, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-17, 17]","explanation_zh":"全部阻擋元素=[-17, 17]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115018,"parameters":{"A":[-17,17,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-17,17]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0019","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-18, 18, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-18, 18]","explanation_zh":"全部阻擋元素=[-18, 18]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115019,"parameters":{"A":[-18,18,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-18,18]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0020","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-19, 19, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-19, 19]","explanation_zh":"全部阻擋元素=[-19, 19]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115020,"parameters":{"A":[-19,19,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-19,19]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0021","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-20, 20, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-20, 20]","explanation_zh":"全部阻擋元素=[-20, 20]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115021,"parameters":{"A":[-20,20,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-20,20]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0022","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-21, 21, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-21, 21]","explanation_zh":"全部阻擋元素=[-21, 21]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115022,"parameters":{"A":[-21,21,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-21,21]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0023","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-22, 22, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-22, 22]","explanation_zh":"全部阻擋元素=[-22, 22]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115023,"parameters":{"A":[-22,22,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-22,22]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0024","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-23, 23, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-23, 23]","explanation_zh":"全部阻擋元素=[-23, 23]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115024,"parameters":{"A":[-23,23,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-23,23]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0025","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格包含的全部阻擋元素","stem_zh":"有限整數集合；同一整數型別；A=[-24, 24, 0]、B=[0]。完整列A⊆B的阻擋元素，即所有屬A但不屬B者，遞增且去重。","answer":{"kind":"expression","value":"[-24, 24]","explanation_zh":"全部阻擋元素=[-24, 24]。阻擋者正是A\\B；沒有阻擋才通過包含，空A不產生反例。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格包含的全部阻擋元素"]},"variant":{"family_id":"qf-density11-subset-obstruction-list","seed":202610115025,"parameters":{"A":[-24,24,0],"B":[0],"operation":"density11_subset_obstruction_list","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-obstruction-list/[-24,24]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0026","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[0]、B=[0]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(是, 否, [], [])","explanation_zh":"非嚴格嚴格資格與見證=(是, 否, [], [])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115026,"parameters":{"A":[0],"B":[0],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[],[]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0027","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[]、B=[-1]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(是, 是, [], [-1])","explanation_zh":"非嚴格嚴格資格與見證=(是, 是, [], [-1])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115027,"parameters":{"A":[],"B":[-1],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[],[-1]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0028","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-2]、B=[]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-2], [])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-2], [])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115028,"parameters":{"A":[-2],"B":[],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-2],[]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0029","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[0]、B=[0, 3]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(是, 是, [], [3])","explanation_zh":"非嚴格嚴格資格與見證=(是, 是, [], [3])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115029,"parameters":{"A":[0],"B":[0,3],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[],[3]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0030","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-4, 0]、B=[0]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-4], [])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-4], [])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115030,"parameters":{"A":[-4,0],"B":[0],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-4],[]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0031","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-5, 0]、B=[0, 5]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-5], [5])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-5], [5])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115031,"parameters":{"A":[-5,0],"B":[0,5],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-5],[5]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0032","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[0]、B=[0, 6]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(是, 是, [], [6])","explanation_zh":"非嚴格嚴格資格與見證=(是, 是, [], [6])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115032,"parameters":{"A":[0],"B":[0,6],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[],[6]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0033","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-7, 0]、B=[0]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-7], [])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-7], [])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115033,"parameters":{"A":[-7,0],"B":[0],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-7],[]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0034","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-8, 0]、B=[0, 8]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-8], [8])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-8], [8])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115034,"parameters":{"A":[-8,0],"B":[0,8],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-8],[8]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0035","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[0]、B=[0, 9]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(是, 是, [], [9])","explanation_zh":"非嚴格嚴格資格與見證=(是, 是, [], [9])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115035,"parameters":{"A":[0],"B":[0,9],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[],[9]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0036","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-10, 0]、B=[0]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-10], [])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-10], [])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115036,"parameters":{"A":[-10,0],"B":[0],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-10],[]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0037","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-11, 0]、B=[0, 11]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-11], [11])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-11], [11])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115037,"parameters":{"A":[-11,0],"B":[0,11],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-11],[11]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0038","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[0]、B=[0, 12]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(是, 是, [], [12])","explanation_zh":"非嚴格嚴格資格與見證=(是, 是, [], [12])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115038,"parameters":{"A":[0],"B":[0,12],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[],[12]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0039","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-13, 0]、B=[0]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-13], [])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-13], [])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115039,"parameters":{"A":[-13,0],"B":[0],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0040","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-14, 0]、B=[0, 14]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-14], [14])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-14], [14])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115040,"parameters":{"A":[-14,0],"B":[0,14],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-14],[14]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0041","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[0]、B=[0, 15]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(是, 是, [], [15])","explanation_zh":"非嚴格嚴格資格與見證=(是, 是, [], [15])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115041,"parameters":{"A":[0],"B":[0,15],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[],[15]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0042","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-16, 0]、B=[0]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-16], [])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-16], [])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115042,"parameters":{"A":[-16,0],"B":[0],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-16],[]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0043","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-17, 0]、B=[0, 17]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-17], [17])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-17], [17])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115043,"parameters":{"A":[-17,0],"B":[0,17],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-17],[17]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0044","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[0]、B=[0, 18]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(是, 是, [], [18])","explanation_zh":"非嚴格嚴格資格與見證=(是, 是, [], [18])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115044,"parameters":{"A":[0],"B":[0,18],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[],[18]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0045","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-19, 0]、B=[0]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-19], [])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-19], [])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115045,"parameters":{"A":[-19,0],"B":[0],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-19],[]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0046","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-20, 0]、B=[0, 20]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-20], [20])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-20], [20])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115046,"parameters":{"A":[-20,0],"B":[0,20],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-20],[20]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0047","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[0]、B=[0, 21]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(是, 是, [], [21])","explanation_zh":"非嚴格嚴格資格與見證=(是, 是, [], [21])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115047,"parameters":{"A":[0],"B":[0,21],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[],[21]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0048","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-22, 0]、B=[0]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-22], [])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-22], [])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115048,"parameters":{"A":[-22,0],"B":[0],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-22],[]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0049","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[-23, 0]、B=[0, 23]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(否, 否, [-23], [23])","explanation_zh":"非嚴格嚴格資格與見證=(否, 否, [-23], [23])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115049,"parameters":{"A":[-23,0],"B":[0,23],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[-23],[23]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0050","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"非嚴格與嚴格包含的資格見證","stem_zh":"有限整數集合；同一整數型別；A=[0]、B=[0, 24]。依序答 (A⊆B是否, A⊊B是否, A\\B, B\\A)，兩個見證集遞增。","answer":{"kind":"expression","value":"(是, 是, [], [24])","explanation_zh":"非嚴格嚴格資格與見證=(是, 是, [], [24])。左差空才非嚴格包含，再要求右差非空才嚴格；集合相等只通過非嚴格欄。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非嚴格與嚴格包含的資格見證"]},"variant":{"family_id":"qf-density11-subset-strict-witnesses","seed":202610115050,"parameters":{"A":[0],"B":[0,24],"operation":"density11_subset_strict_witnesses","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-strict-witnesses/[[],[24]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0051","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=[]、B=[0]、C=[0, 1]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([], [], [])","explanation_zh":"三段包含阻擋=([], [], [])。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":1,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115051,"parameters":{"A":[],"B":[0],"C":[0,1],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[],[],[]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0052","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=[1]、B=[]、C=[1]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([1], [], [])","explanation_zh":"三段包含阻擋=([1], [], [])。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":1,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115052,"parameters":{"A":[1],"B":[],"C":[1],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[1],[],[]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0053","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=[0]、B=[0, 2]、C=[0]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([], [2], [])","explanation_zh":"三段包含阻擋=([], [2], [])。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":1,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115053,"parameters":{"A":[0],"B":[0,2],"C":[0],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[],[2],[]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0054","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=[-3, 0]、B=[0, 3]、C=[0, 4]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-3], [3], [-3])","explanation_zh":"三段包含阻擋=([-3], [3], [-3])。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":1,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115054,"parameters":{"A":[-3,0],"B":[0,3],"C":[0,4],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-3],[3],[-3]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0055","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=[-4, 0]、B=[0, 4]、C=[0, 5]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-4], [4], [-4])","explanation_zh":"三段包含阻擋=([-4], [4], [-4])。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":1,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115055,"parameters":{"A":[-4,0],"B":[0,4],"C":[0,5],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-4],[4],[-4]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0056","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=[-5, 0]、B=[0, 5]、C=[0, 6]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-5], [5], [-5])","explanation_zh":"三段包含阻擋=([-5], [5], [-5])。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":1,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115056,"parameters":{"A":[-5,0],"B":[0,5],"C":[0,6],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-5],[5],[-5]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0057","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=[-6, 0]、B=[0, 6]、C=[0, 7]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-6], [6], [-6])","explanation_zh":"三段包含阻擋=([-6], [6], [-6])。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":1,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115057,"parameters":{"A":[-6,0],"B":[0,6],"C":[0,7],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-6],[6],[-6]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0058","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=[-7, 0]、B=[0, 7]、C=[0, 8]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-7], [7], [-7])","explanation_zh":"三段包含阻擋=([-7], [7], [-7])。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":1,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115058,"parameters":{"A":[-7,0],"B":[0,7],"C":[0,8],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-7],[7],[-7]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0059","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=[-8, 0]、B=[0, 8]、C=[0, 9]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-8], [8], [-8])","explanation_zh":"三段包含阻擋=([-8], [8], [-8])。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":202610115059,"parameters":{"A":[-8,0],"B":[0,8],"C":[0,9],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-8],[8],[-8]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0060","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=[-9, 0]、B=[0, 9]、C=[0, 10]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-9], [9], [-9])","explanation_zh":"三段包含阻擋=([-9], [9], [-9])。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":202610115060,"parameters":{"A":[-9,0],"B":[0,9],"C":[0,10],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-9],[9],[-9]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0061","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=[-10, 0]、B=[0, 10]、C=[0, 11]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-10], [10], [-10])","explanation_zh":"三段包含阻擋=([-10], [10], [-10])。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":202610115061,"parameters":{"A":[-10,0],"B":[0,10],"C":[0,11],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-10],[10],[-10]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0062","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=[-11, 0]、B=[0, 11]、C=[0, 12]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-11], [11], [-11])","explanation_zh":"三段包含阻擋=([-11], [11], [-11])。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":202610115062,"parameters":{"A":[-11,0],"B":[0,11],"C":[0,12],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-11],[11],[-11]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0063","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=[-12, 0]、B=[0, 12]、C=[0, 13]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-12], [12], [-12])","explanation_zh":"三段包含阻擋=([-12], [12], [-12])。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":202610115063,"parameters":{"A":[-12,0],"B":[0,12],"C":[0,13],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-12],[12],[-12]]"}},"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"}}
{"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0065","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=[-14, 0]、B=[0, 14]、C=[0, 15]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-14], [14], [-14])","explanation_zh":"三段包含阻擋=([-14], [14], [-14])。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":202610115065,"parameters":{"A":[-14,0],"B":[0,14],"C":[0,15],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-14],[14],[-14]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0066","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=[-15, 0]、B=[0, 15]、C=[0, 16]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-15], [15], [-15])","explanation_zh":"三段包含阻擋=([-15], [15], [-15])。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":202610115066,"parameters":{"A":[-15,0],"B":[0,15],"C":[0,16],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-15],[15],[-15]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0067","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=[-16, 0]、B=[0, 16]、C=[0, 17]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-16], [16], [-16])","explanation_zh":"三段包含阻擋=([-16], [16], [-16])。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":202610115067,"parameters":{"A":[-16,0],"B":[0,16],"C":[0,17],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-16],[16],[-16]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0068","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=[-17, 0]、B=[0, 17]、C=[0, 18]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-17], [17], [-17])","explanation_zh":"三段包含阻擋=([-17], [17], [-17])。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":3,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115068,"parameters":{"A":[-17,0],"B":[0,17],"C":[0,18],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-17],[17],[-17]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0069","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=[-18, 0]、B=[0, 18]、C=[0, 19]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-18], [18], [-18])","explanation_zh":"三段包含阻擋=([-18], [18], [-18])。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":3,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115069,"parameters":{"A":[-18,0],"B":[0,18],"C":[0,19],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-18],[18],[-18]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0070","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=[-19, 0]、B=[0, 19]、C=[0, 20]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-19], [19], [-19])","explanation_zh":"三段包含阻擋=([-19], [19], [-19])。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":3,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115070,"parameters":{"A":[-19,0],"B":[0,19],"C":[0,20],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-19],[19],[-19]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0071","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=[-20, 0]、B=[0, 20]、C=[0, 21]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-20], [20], [-20])","explanation_zh":"三段包含阻擋=([-20], [20], [-20])。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":3,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115071,"parameters":{"A":[-20,0],"B":[0,20],"C":[0,21],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-20],[20],[-20]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0072","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=[-21, 0]、B=[0, 21]、C=[0, 22]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-21], [21], [-21])","explanation_zh":"三段包含阻擋=([-21], [21], [-21])。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":3,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115072,"parameters":{"A":[-21,0],"B":[0,21],"C":[0,22],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-21],[21],[-21]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0073","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=[-22, 0]、B=[0, 22]、C=[0, 23]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-22], [22], [-22])","explanation_zh":"三段包含阻擋=([-22], [22], [-22])。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":3,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115073,"parameters":{"A":[-22,0],"B":[0,22],"C":[0,23],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-22],[22],[-22]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0074","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=[-23, 0]、B=[0, 23]、C=[0, 24]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-23], [23], [-23])","explanation_zh":"三段包含阻擋=([-23], [23], [-23])。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":3,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115074,"parameters":{"A":[-23,0],"B":[0,23],"C":[0,24],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-23],[23],[-23]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0075","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=[-24, 0]、B=[0, 24]、C=[0, 25]。依序列 (A\\B, B\\C, A\\C)，各遞增，保留空段。","answer":{"kind":"expression","value":"([-24], [24], [-24])","explanation_zh":"三段包含阻擋=([-24], [24], [-24])。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":3,"skills":["三段包含的有序阻擋集"]},"variant":{"family_id":"qf-density11-subset-chain-obstructions","seed":202610115075,"parameters":{"A":[-24,0],"B":[0,24],"C":[0,25],"operation":"density11_subset_chain_obstructions","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-chain-obstructions/[[-24],[24],[-24]]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0076","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[]、B=[]、有序候選=[100, 101, 102]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 否, 否]","explanation_zh":"包含反例候選資格=[否, 否, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115076,"parameters":{"A":[],"B":[],"candidates":[100,101,102],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"outside_A\",\"outside_A\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0077","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[-1, 101, 102]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[是, 否, 否]","explanation_zh":"包含反例候選資格=[是, 否, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115077,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[-1,101,102],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"outside_A\",\"outside_A\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0078","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[1, 2, 102]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 否, 否]","explanation_zh":"包含反例候選資格=[否, 否, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115078,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[1,2,102],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"shared\",\"outside_A\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0079","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[-1, 2, 102]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[是, 否, 否]","explanation_zh":"包含反例候選資格=[是, 否, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115079,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[-1,2,102],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"shared\",\"outside_A\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0080","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[100, -2, 102]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 是, 否]","explanation_zh":"包含反例候選資格=[否, 是, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115080,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[100,-2,102],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"obstructs\",\"outside_A\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0081","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[1, -2, 102]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 是, 否]","explanation_zh":"包含反例候選資格=[否, 是, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115081,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[1,-2,102],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"obstructs\",\"outside_A\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0082","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[-1, -2, 102]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[是, 是, 否]","explanation_zh":"包含反例候選資格=[是, 是, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115082,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[-1,-2,102],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"obstructs\",\"outside_A\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0083","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[100, 101, 3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 否, 否]","explanation_zh":"包含反例候選資格=[否, 否, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115083,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[100,101,3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"outside_A\",\"shared\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0084","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[1, 101, 3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 否, 否]","explanation_zh":"包含反例候選資格=[否, 否, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115084,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[1,101,3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"outside_A\",\"shared\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0085","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[-1, 101, 3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[是, 否, 否]","explanation_zh":"包含反例候選資格=[是, 否, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115085,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[-1,101,3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"outside_A\",\"shared\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0086","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[100, 2, 3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 否, 否]","explanation_zh":"包含反例候選資格=[否, 否, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115086,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[100,2,3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"shared\",\"shared\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0087","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[1, 2, 3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 否, 否]","explanation_zh":"包含反例候選資格=[否, 否, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115087,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[1,2,3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"shared\",\"shared\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0088","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[-1, 2, 3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[是, 否, 否]","explanation_zh":"包含反例候選資格=[是, 否, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115088,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[-1,2,3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"shared\",\"shared\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0089","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[100, -2, 3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 是, 否]","explanation_zh":"包含反例候選資格=[否, 是, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115089,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[100,-2,3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"obstructs\",\"shared\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0090","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[1, -2, 3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 是, 否]","explanation_zh":"包含反例候選資格=[否, 是, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115090,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[1,-2,3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"obstructs\",\"shared\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0091","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[-1, -2, 3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[是, 是, 否]","explanation_zh":"包含反例候選資格=[是, 是, 否]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115091,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[-1,-2,3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"obstructs\",\"shared\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0092","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[100, 101, -3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 否, 是]","explanation_zh":"包含反例候選資格=[否, 否, 是]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115092,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[100,101,-3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"outside_A\",\"obstructs\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0093","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[1, 101, -3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 否, 是]","explanation_zh":"包含反例候選資格=[否, 否, 是]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115093,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[1,101,-3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"outside_A\",\"obstructs\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0094","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[-1, 101, -3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[是, 否, 是]","explanation_zh":"包含反例候選資格=[是, 否, 是]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115094,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[-1,101,-3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"outside_A\",\"obstructs\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0095","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[100, 2, -3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 否, 是]","explanation_zh":"包含反例候選資格=[否, 否, 是]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115095,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[100,2,-3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"shared\",\"obstructs\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0096","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[1, 2, -3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 否, 是]","explanation_zh":"包含反例候選資格=[否, 否, 是]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115096,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[1,2,-3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"shared\",\"obstructs\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0097","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[-1, 2, -3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[是, 否, 是]","explanation_zh":"包含反例候選資格=[是, 否, 是]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115097,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[-1,2,-3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"shared\",\"obstructs\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0098","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[100, -2, -3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 是, 是]","explanation_zh":"包含反例候選資格=[否, 是, 是]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115098,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[100,-2,-3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"obstructs\",\"obstructs\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0099","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[1, 2, 3]、有序候選=[1, -2, -3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[否, 是, 是]","explanation_zh":"包含反例候選資格=[否, 是, 是]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115099,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[1,2,3],"candidates":[1,-2,-3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"obstructs\",\"obstructs\"]"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261011-r05-subset-0100","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-subset"],"title_zh":"三個候選的包含反例資格","stem_zh":"有限整數集合；同一整數型別；A=[-3, -2, -1, 1, 2, 3]、B=[]、有序候選=[-1, -2, -3]。逐項答是否c∈A且c∉B，域外A的候選不算阻擋見證。","answer":{"kind":"expression","value":"[是, 是, 是]","explanation_zh":"包含反例候選資格=[是, 是, 是]。先要求屬A，再排除屬B；共有元素與A外元素都不是反例，不只看候選未進B。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["三個候選的包含反例資格"]},"variant":{"family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115100,"parameters":{"A":[-3,-2,-1,1,2,3],"B":[],"candidates":[-1,-2,-3],"operation":"density11_subset_candidate_witness_mask","domain":"finite_integer_set_slice","semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"obstructs\",\"obstructs\"]"}},"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"}}