{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0001","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1dd63ec7c3aa1769f74025d6952e89c34f75a9738980cdc091a92b9efe2abfe7","family_id":"qf-density11-subset-obstruction-list","seed":202610115001,"semantic_template":"qf-density11-subset-obstruction-list/[]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[] and B=[1]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is []."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0002","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9dd9436a95c26cf3894fbdbc3230866cab3a0de0772d4f07deed838fb6be3ac1","family_id":"qf-density11-subset-obstruction-list","seed":202610115002,"semantic_template":"qf-density11-subset-obstruction-list/[-1]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-1] and B=[]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-1]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-1]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0003","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7eba7bd6c1590bf9f3b363050d3b7f6dd1836637bec2cac63007899bb16a65f4","family_id":"qf-density11-subset-obstruction-list","seed":202610115003,"semantic_template":"qf-density11-subset-obstruction-list/[-2,2]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-2, 2, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-2, 2]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-2, 2]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0004","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a1fc15331a53fb2f4736096c873d22493aafc72711ea98d02f2c644b75c805ef","family_id":"qf-density11-subset-obstruction-list","seed":202610115004,"semantic_template":"qf-density11-subset-obstruction-list/[-3,3]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-3, 3, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-3, 3]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-3, 3]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0005","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b0d0609b36fc5d634dc75b53b174a3f265f270a3ac2d8eb312b48375831f1bf4","family_id":"qf-density11-subset-obstruction-list","seed":202610115005,"semantic_template":"qf-density11-subset-obstruction-list/[-4,4]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-4, 4, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-4, 4]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-4, 4]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0006","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"32b0ad0dccfefca7cc49e67d3c934769e2e3af1cdc416420924aa1bb269ae2db","family_id":"qf-density11-subset-obstruction-list","seed":202610115006,"semantic_template":"qf-density11-subset-obstruction-list/[-5,5]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-5, 5, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-5, 5]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-5, 5]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0007","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4529f0e1476a58c5b2416a1255a690bf41b3e510d11ba7ae903de693dcf5a5af","family_id":"qf-density11-subset-obstruction-list","seed":202610115007,"semantic_template":"qf-density11-subset-obstruction-list/[-6,6]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-6, 6, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-6, 6]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-6, 6]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0008","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"de8ca1001ccf02c4875c52e373b62a882fd708297a5f76115868f8c1a701674e","family_id":"qf-density11-subset-obstruction-list","seed":202610115008,"semantic_template":"qf-density11-subset-obstruction-list/[-7,7]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-7, 7, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-7, 7]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-7, 7]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0009","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d94c05a7df794f3b5dbb9efe3f6e45b824480e69d656468ec2483df97661fa68","family_id":"qf-density11-subset-obstruction-list","seed":202610115009,"semantic_template":"qf-density11-subset-obstruction-list/[-8,8]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-8, 8, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-8, 8]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-8, 8]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0010","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c281493c3fa78f20a2479802b14228f3c4352297ddd30fbf9677a38ba1bd685d","family_id":"qf-density11-subset-obstruction-list","seed":202610115010,"semantic_template":"qf-density11-subset-obstruction-list/[-9,9]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-9, 9, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-9, 9]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-9, 9]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0011","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"608aa1409a12a8a25236c13eb8218038a50ef30b3ee3e8b020db116064cf7bbd","family_id":"qf-density11-subset-obstruction-list","seed":202610115011,"semantic_template":"qf-density11-subset-obstruction-list/[-10,10]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-10, 10, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-10, 10]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-10, 10]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0012","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f97c5ebb6005edb005fd718d02aea1586d7dc845b1504093f937f999c6058cdd","family_id":"qf-density11-subset-obstruction-list","seed":202610115012,"semantic_template":"qf-density11-subset-obstruction-list/[-11,11]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-11, 11, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-11, 11]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-11, 11]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0013","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1f5603972f682d5eceaa74b9fc30085caf8b8e8b3fa79c15dda198891c7c3bb","family_id":"qf-density11-subset-obstruction-list","seed":202610115013,"semantic_template":"qf-density11-subset-obstruction-list/[-12,12]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-12, 12, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-12, 12]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-12, 12]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0014","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64626daa1ec8185a80db4c6d86e795d96c2a7f4bc4f64429d385f945cb822142","family_id":"qf-density11-subset-obstruction-list","seed":202610115014,"semantic_template":"qf-density11-subset-obstruction-list/[-13,13]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-13, 13, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-13, 13]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-13, 13]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0015","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"358dbc7f2cbfcd87ec3b71c912c0f8acf7d010b5f70d43428525819d26fcb589","family_id":"qf-density11-subset-obstruction-list","seed":202610115015,"semantic_template":"qf-density11-subset-obstruction-list/[-14,14]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-14, 14, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-14, 14]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-14, 14]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0016","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bbc8689c2a63b48a288edc7783d2727c857092b0a4bfbcff55c3070cbbba4f39","family_id":"qf-density11-subset-obstruction-list","seed":202610115016,"semantic_template":"qf-density11-subset-obstruction-list/[-15,15]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-15, 15, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-15, 15]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-15, 15]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0017","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aa1bc61b1bf5157573e8fa996ca16a1c3b3fa8d7d02111a7c532faea1599e0ed","family_id":"qf-density11-subset-obstruction-list","seed":202610115017,"semantic_template":"qf-density11-subset-obstruction-list/[-16,16]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-16, 16, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-16, 16]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-16, 16]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0018","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3a8dddcbeb80596b7b94d05c747b48ebfbe826e729b6c23474f6f8c0cebda680","family_id":"qf-density11-subset-obstruction-list","seed":202610115018,"semantic_template":"qf-density11-subset-obstruction-list/[-17,17]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-17, 17, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-17, 17]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-17, 17]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0019","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b77bfd4b3d18061e5e772aee3aca0133137ff56773f9db6899e1681b19d5369","family_id":"qf-density11-subset-obstruction-list","seed":202610115019,"semantic_template":"qf-density11-subset-obstruction-list/[-18,18]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-18, 18, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-18, 18]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-18, 18]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0020","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d9204b682ad832e79ce7368b60b82ba196fba67cd8c45589e40ed5d0f6d3bd95","family_id":"qf-density11-subset-obstruction-list","seed":202610115020,"semantic_template":"qf-density11-subset-obstruction-list/[-19,19]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-19, 19, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-19, 19]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-19, 19]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0021","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1f14154680a371a3e6223c853313cfd723d8a183b6029cd7f1cc2d5c8b00e6e9","family_id":"qf-density11-subset-obstruction-list","seed":202610115021,"semantic_template":"qf-density11-subset-obstruction-list/[-20,20]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-20, 20, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-20, 20]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-20, 20]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0022","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3383f538935d06830012c2876062a0bb8ee947537226afe30162b7968eabaeda","family_id":"qf-density11-subset-obstruction-list","seed":202610115022,"semantic_template":"qf-density11-subset-obstruction-list/[-21,21]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-21, 21, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-21, 21]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-21, 21]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0023","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6de89a1ba458e80b487962d5d113e2a87837b8b5985d8ce552229517c6b6d00d","family_id":"qf-density11-subset-obstruction-list","seed":202610115023,"semantic_template":"qf-density11-subset-obstruction-list/[-22,22]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-22, 22, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-22, 22]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-22, 22]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0024","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9f69aad2432414831b5f0b48666f9b434a3620daf0e22f894fa471f1784e7372","family_id":"qf-density11-subset-obstruction-list","seed":202610115024,"semantic_template":"qf-density11-subset-obstruction-list/[-23,23]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-23, 23, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-23, 23]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-23, 23]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0025","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee84a46229e34e1102dcd88f1a344c2cb1c4da5a09670c44ba97c8ec33ca1acf","family_id":"qf-density11-subset-obstruction-list","seed":202610115025,"semantic_template":"qf-density11-subset-obstruction-list/[-24,24]"},"fields":{"title":"Complete Inclusion Obstruction Set","stem":"Finite integer sets A=[-24, 24, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.","answer":{"kind":"expression","value":"[-24, 24]","explanation":"The obstruction set is A\\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-24, 24]."},"skills":["Complete Inclusion Obstruction Set"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0026","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e4c2020fa34945d6f35807df857530e8be9dc7064f5ca6b9a863215147d49f1c","family_id":"qf-density11-subset-strict-witnesses","seed":202610115026,"semantic_template":"qf-density11-subset-strict-witnesses/[[],[]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(Yes, No, [], [])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, No, [], [])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0027","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"34d61bb3c472584bf6aec05e58a2577ffb67e8b7388e21d5a8e0686ddc6f83a9","family_id":"qf-density11-subset-strict-witnesses","seed":202610115027,"semantic_template":"qf-density11-subset-strict-witnesses/[[],[-1]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[] and B=[-1]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(Yes, Yes, [], [-1])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [-1])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0028","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d14ef5b48c162a7320d43ee214a9cbab57c74be5730ccd9ec45f2068f7685ed7","family_id":"qf-density11-subset-strict-witnesses","seed":202610115028,"semantic_template":"qf-density11-subset-strict-witnesses/[[-2],[]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-2] and B=[]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-2], [])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-2], [])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0029","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e857711e802adf0ad1633e73adeb238b9ffeb56489e9d343c794d1406db6ab98","family_id":"qf-density11-subset-strict-witnesses","seed":202610115029,"semantic_template":"qf-density11-subset-strict-witnesses/[[],[3]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[0] and B=[0, 3]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(Yes, Yes, [], [3])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [3])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0030","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dac1aa4c34c83f0166eddc5a06cbfb5adcb73daeedd6b063eacfb400600e965e","family_id":"qf-density11-subset-strict-witnesses","seed":202610115030,"semantic_template":"qf-density11-subset-strict-witnesses/[[-4],[]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-4, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-4], [])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-4], [])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0031","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d69059d77730fd7452cc817ce152d7581c835a44e8b023313c0a103d08337055","family_id":"qf-density11-subset-strict-witnesses","seed":202610115031,"semantic_template":"qf-density11-subset-strict-witnesses/[[-5],[5]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-5, 0] and B=[0, 5]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-5], [5])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-5], [5])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0032","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dce5aceb09fd9b482dd6a617ff1606c09f100dda700fa545774ae4a5d66aecd2","family_id":"qf-density11-subset-strict-witnesses","seed":202610115032,"semantic_template":"qf-density11-subset-strict-witnesses/[[],[6]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[0] and B=[0, 6]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(Yes, Yes, [], [6])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [6])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0033","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c627fa5d2651da957d836965f24f8302e1f4fe0934a9b442aff0a7f9b40474f","family_id":"qf-density11-subset-strict-witnesses","seed":202610115033,"semantic_template":"qf-density11-subset-strict-witnesses/[[-7],[]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-7, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-7], [])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-7], [])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0034","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9dd4b7233f7b6d4856b93e2404cb67a1bd7d786d3516a449c5f817a2b8b73021","family_id":"qf-density11-subset-strict-witnesses","seed":202610115034,"semantic_template":"qf-density11-subset-strict-witnesses/[[-8],[8]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-8, 0] and B=[0, 8]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-8], [8])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-8], [8])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0035","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fffb4808c99e2a8ec2451a9a80d1b059ba264fe3a6eb626987b84940ee3078a3","family_id":"qf-density11-subset-strict-witnesses","seed":202610115035,"semantic_template":"qf-density11-subset-strict-witnesses/[[],[9]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[0] and B=[0, 9]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(Yes, Yes, [], [9])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [9])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0036","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e0b20d52759741d88645768e90ea4b8ddb9231c37675f8b86d2b1c6070b619a2","family_id":"qf-density11-subset-strict-witnesses","seed":202610115036,"semantic_template":"qf-density11-subset-strict-witnesses/[[-10],[]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-10, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-10], [])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-10], [])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0037","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"95fd7968ebe8be6ac65891e21938724789fa33307f4b9844d31b42fab7f023bd","family_id":"qf-density11-subset-strict-witnesses","seed":202610115037,"semantic_template":"qf-density11-subset-strict-witnesses/[[-11],[11]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-11, 0] and B=[0, 11]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-11], [11])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-11], [11])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0038","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"551c4ccc9fc588e167710b78b82bebec6d678f28438a12bb34dbd21f04df4bff","family_id":"qf-density11-subset-strict-witnesses","seed":202610115038,"semantic_template":"qf-density11-subset-strict-witnesses/[[],[12]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[0] and B=[0, 12]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(Yes, Yes, [], [12])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [12])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0039","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5a430fac7b44f257f6ce545feec761b1c6eb273d674cde0c4d17f283f5ad7dcf","family_id":"qf-density11-subset-strict-witnesses","seed":202610115039,"semantic_template":"qf-density11-subset-strict-witnesses/[[-13],[]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-13, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-13], [])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-13], [])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0040","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2f43624dae7e0733553c658950dbe20b22a0a08820ffeeb0ce05ad4d1159f01e","family_id":"qf-density11-subset-strict-witnesses","seed":202610115040,"semantic_template":"qf-density11-subset-strict-witnesses/[[-14],[14]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-14, 0] and B=[0, 14]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-14], [14])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-14], [14])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0041","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b5a5f31f2b7583608f8940ca1dc7e9ed588dcf49c7f722de46de631a7c49bd89","family_id":"qf-density11-subset-strict-witnesses","seed":202610115041,"semantic_template":"qf-density11-subset-strict-witnesses/[[],[15]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[0] and B=[0, 15]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(Yes, Yes, [], [15])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [15])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0042","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6acce5472a6417a0897d14a4e6651b5884ce4d7d2011bf5ccf2fe6c8d0bf08ad","family_id":"qf-density11-subset-strict-witnesses","seed":202610115042,"semantic_template":"qf-density11-subset-strict-witnesses/[[-16],[]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-16, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-16], [])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-16], [])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0043","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"714626c04614eef06b5e45fe887b0816b003aad446df83d678ef9ac48cf28775","family_id":"qf-density11-subset-strict-witnesses","seed":202610115043,"semantic_template":"qf-density11-subset-strict-witnesses/[[-17],[17]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-17, 0] and B=[0, 17]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-17], [17])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-17], [17])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0044","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a61b740507593714e603374cb2e731a2ee0e5a7afd6eb9e6f84fcfbbf8e965fa","family_id":"qf-density11-subset-strict-witnesses","seed":202610115044,"semantic_template":"qf-density11-subset-strict-witnesses/[[],[18]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[0] and B=[0, 18]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(Yes, Yes, [], [18])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [18])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0045","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6ad45c0976d25dff8f55a196c8714209ef95c13ffc2981d984fc50cc7588e9e6","family_id":"qf-density11-subset-strict-witnesses","seed":202610115045,"semantic_template":"qf-density11-subset-strict-witnesses/[[-19],[]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-19, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-19], [])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-19], [])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0046","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ffaaf3019b2944defedbf1ea19d1a06a9fe48f73ff7d73b8ff273c0e38a72d4c","family_id":"qf-density11-subset-strict-witnesses","seed":202610115046,"semantic_template":"qf-density11-subset-strict-witnesses/[[-20],[20]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-20, 0] and B=[0, 20]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-20], [20])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-20], [20])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0047","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e743fb29b1015d1e9008f0e4127f76e90e3d6a0d7dd810860627fb2a97438dff","family_id":"qf-density11-subset-strict-witnesses","seed":202610115047,"semantic_template":"qf-density11-subset-strict-witnesses/[[],[21]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[0] and B=[0, 21]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(Yes, Yes, [], [21])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [21])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0048","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87050846d2d63987bcc76006c6a1a8c07db3495506c96792d09d727c3b9c8c32","family_id":"qf-density11-subset-strict-witnesses","seed":202610115048,"semantic_template":"qf-density11-subset-strict-witnesses/[[-22],[]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-22, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-22], [])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-22], [])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0049","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"41d7b0273aef2e8edd3345f4b0750948176ae9f10bbcd415fbf4c590f3d34aae","family_id":"qf-density11-subset-strict-witnesses","seed":202610115049,"semantic_template":"qf-density11-subset-strict-witnesses/[[-23],[23]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[-23, 0] and B=[0, 23]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(No, No, [-23], [23])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-23], [23])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0050","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c28d01656e682b906b563b26addedf0bd1eea760e97e4c6abf3aef12e37a77c","family_id":"qf-density11-subset-strict-witnesses","seed":202610115050,"semantic_template":"qf-density11-subset-strict-witnesses/[[],[24]]"},"fields":{"title":"Non-Strict and Strict Inclusion Witnesses","stem":"Finite integer sets A=[0] and B=[0, 24]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\\B, B\\A), with both witness sets increasing.","answer":{"kind":"expression","value":"(Yes, Yes, [], [24])","explanation":"An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [24])."},"skills":["Non-Strict and Strict Inclusion Witnesses"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0051","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"68facfc72ecee0a530281f09183f55d9826021898a26da5c52dc1241c7a0b692","family_id":"qf-density11-subset-chain-obstructions","seed":202610115051,"semantic_template":"qf-density11-subset-chain-obstructions/[[],[],[]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[] and B=[0]; repeated elements count once. C=[0, 1] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([], [], [])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([], [], [])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0052","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6bac1a155052a6375c74e75251d42e5ba3ebca45285301d35b1f1e26928fc855","family_id":"qf-density11-subset-chain-obstructions","seed":202610115052,"semantic_template":"qf-density11-subset-chain-obstructions/[[1],[],[]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[1] and B=[]; repeated elements count once. C=[1] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([1], [], [])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([1], [], [])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0053","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dc12046b94c2c63e1e16931ea884be75b9c0000e2e56b441fe7ea5555a3a2597","family_id":"qf-density11-subset-chain-obstructions","seed":202610115053,"semantic_template":"qf-density11-subset-chain-obstructions/[[],[2],[]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[0] and B=[0, 2]; repeated elements count once. C=[0] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([], [2], [])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([], [2], [])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0054","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8326e83ec9f4a039bec46988604585d509a1ab76fa4f82a51e9f60690682b836","family_id":"qf-density11-subset-chain-obstructions","seed":202610115054,"semantic_template":"qf-density11-subset-chain-obstructions/[[-3],[3],[-3]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-3, 0] and B=[0, 3]; repeated elements count once. C=[0, 4] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-3], [3], [-3])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-3], [3], [-3])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0055","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4920a27cdade4696926a276e617834f0026afecc862cf11daad0ccc59ec0f80c","family_id":"qf-density11-subset-chain-obstructions","seed":202610115055,"semantic_template":"qf-density11-subset-chain-obstructions/[[-4],[4],[-4]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-4, 0] and B=[0, 4]; repeated elements count once. C=[0, 5] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-4], [4], [-4])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-4], [4], [-4])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0056","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6c2c79a074b9b2b56731adb4daad05b18353cda196f68c173634781d1a0a40ef","family_id":"qf-density11-subset-chain-obstructions","seed":202610115056,"semantic_template":"qf-density11-subset-chain-obstructions/[[-5],[5],[-5]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-5, 0] and B=[0, 5]; repeated elements count once. C=[0, 6] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-5], [5], [-5])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-5], [5], [-5])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0057","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12c3970d7c14dea59c6fa0fd886fa4ce71a65a53636cb365a1d164ca80589f90","family_id":"qf-density11-subset-chain-obstructions","seed":202610115057,"semantic_template":"qf-density11-subset-chain-obstructions/[[-6],[6],[-6]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-6, 0] and B=[0, 6]; repeated elements count once. C=[0, 7] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-6], [6], [-6])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-6], [6], [-6])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0058","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e23c547b7a0c98abc21632cbad68f0a0edbc93fbc0fe2a95ab11639afe1141ab","family_id":"qf-density11-subset-chain-obstructions","seed":202610115058,"semantic_template":"qf-density11-subset-chain-obstructions/[[-7],[7],[-7]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-7, 0] and B=[0, 7]; repeated elements count once. C=[0, 8] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-7], [7], [-7])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-7], [7], [-7])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0059","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d98e8117153ff5302cae8fbed93d7750bb8ac10650f1459edd6171d91e030030","family_id":"qf-density11-subset-chain-obstructions","seed":202610115059,"semantic_template":"qf-density11-subset-chain-obstructions/[[-8],[8],[-8]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-8, 0] and B=[0, 8]; repeated elements count once. C=[0, 9] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-8], [8], [-8])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-8], [8], [-8])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0060","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e2d60514c089ecc1a30c16cf8970732f243fdb856d732c1d73f8238f16d0c204","family_id":"qf-density11-subset-chain-obstructions","seed":202610115060,"semantic_template":"qf-density11-subset-chain-obstructions/[[-9],[9],[-9]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-9, 0] and B=[0, 9]; repeated elements count once. C=[0, 10] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-9], [9], [-9])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-9], [9], [-9])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0061","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e7a5aafeb561e4e364e0233b1733bdba32759ae28d7aca5b4297007d69b9f0de","family_id":"qf-density11-subset-chain-obstructions","seed":202610115061,"semantic_template":"qf-density11-subset-chain-obstructions/[[-10],[10],[-10]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-10, 0] and B=[0, 10]; repeated elements count once. C=[0, 11] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-10], [10], [-10])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-10], [10], [-10])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0062","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8fe216a907c71bfeabe02f153c95d2fe27cec8d292027aac2c7b8561b7bed20a","family_id":"qf-density11-subset-chain-obstructions","seed":202610115062,"semantic_template":"qf-density11-subset-chain-obstructions/[[-11],[11],[-11]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-11, 0] and B=[0, 11]; repeated elements count once. C=[0, 12] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-11], [11], [-11])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-11], [11], [-11])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0063","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d3d7aa175ac5c66350177135d248f3337c3bac1d8fe42432aaf2ef5420be73e8","family_id":"qf-density11-subset-chain-obstructions","seed":202610115063,"semantic_template":"qf-density11-subset-chain-obstructions/[[-12],[12],[-12]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-12, 0] and B=[0, 12]; repeated elements count once. C=[0, 13] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-12], [12], [-12])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-12], [12], [-12])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0064","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"207eff31550c56aff7ffd733c6a36b2b30af56e38ad03b5d253cef9a75dadc4b","family_id":"qf-density11-subset-chain-obstructions","seed":202610115064,"semantic_template":"qf-density11-subset-chain-obstructions/[[-13],[13],[-13]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-13, 0] and B=[0, 13]; repeated elements count once. C=[0, 14] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-13], [13], [-13])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-13], [13], [-13])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0065","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54ea842261bfb3b920162416495be5ab1db6a25208ffea3633c248785daaadda","family_id":"qf-density11-subset-chain-obstructions","seed":202610115065,"semantic_template":"qf-density11-subset-chain-obstructions/[[-14],[14],[-14]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-14, 0] and B=[0, 14]; repeated elements count once. C=[0, 15] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-14], [14], [-14])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-14], [14], [-14])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0066","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29a6850635fdd9dc126bddf18d15f3b9fb6e9a418ce32a1541f4c2604194d53b","family_id":"qf-density11-subset-chain-obstructions","seed":202610115066,"semantic_template":"qf-density11-subset-chain-obstructions/[[-15],[15],[-15]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-15, 0] and B=[0, 15]; repeated elements count once. C=[0, 16] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-15], [15], [-15])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-15], [15], [-15])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0067","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"692a96ffe335c71c97b7a98cde69ba832d635845ac3e22d1d1934e1c6cd923ee","family_id":"qf-density11-subset-chain-obstructions","seed":202610115067,"semantic_template":"qf-density11-subset-chain-obstructions/[[-16],[16],[-16]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-16, 0] and B=[0, 16]; repeated elements count once. C=[0, 17] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-16], [16], [-16])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-16], [16], [-16])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0068","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f46f99a8f2035ceea43dda673141fe62ed318cf8beac1b6b399173bf142cacf6","family_id":"qf-density11-subset-chain-obstructions","seed":202610115068,"semantic_template":"qf-density11-subset-chain-obstructions/[[-17],[17],[-17]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-17, 0] and B=[0, 17]; repeated elements count once. C=[0, 18] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-17], [17], [-17])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-17], [17], [-17])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0069","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5c271b4802409971be85ae6eb7516c53cdadfc18d2f96318e5e0d268162b6633","family_id":"qf-density11-subset-chain-obstructions","seed":202610115069,"semantic_template":"qf-density11-subset-chain-obstructions/[[-18],[18],[-18]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-18, 0] and B=[0, 18]; repeated elements count once. C=[0, 19] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-18], [18], [-18])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-18], [18], [-18])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0070","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5e9bf0e1c43ffc9c549d3cd992edc6e65c75d007b07e9c93beeb882ce71cf42c","family_id":"qf-density11-subset-chain-obstructions","seed":202610115070,"semantic_template":"qf-density11-subset-chain-obstructions/[[-19],[19],[-19]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-19, 0] and B=[0, 19]; repeated elements count once. C=[0, 20] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-19], [19], [-19])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-19], [19], [-19])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0071","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2d43dcfdd1e4926eef8ad08400ff03e88252dce2f7dc303a63e4e8765383e5c4","family_id":"qf-density11-subset-chain-obstructions","seed":202610115071,"semantic_template":"qf-density11-subset-chain-obstructions/[[-20],[20],[-20]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-20, 0] and B=[0, 20]; repeated elements count once. C=[0, 21] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-20], [20], [-20])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-20], [20], [-20])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0072","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"743d81e925dd82d9be5ca31a786f610c2293136b6a4dbfb37fbab4e9bf6913d9","family_id":"qf-density11-subset-chain-obstructions","seed":202610115072,"semantic_template":"qf-density11-subset-chain-obstructions/[[-21],[21],[-21]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-21, 0] and B=[0, 21]; repeated elements count once. C=[0, 22] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-21], [21], [-21])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-21], [21], [-21])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0073","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c49e5ed907129d0959ef84db82e472923097edf82d5de759f306cae74af8fe83","family_id":"qf-density11-subset-chain-obstructions","seed":202610115073,"semantic_template":"qf-density11-subset-chain-obstructions/[[-22],[22],[-22]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-22, 0] and B=[0, 22]; repeated elements count once. C=[0, 23] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-22], [22], [-22])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-22], [22], [-22])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0074","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"88b4d3d3cd87221455fb94dbfd69cb86856718c14e3d185eccf4fc8195dee84a","family_id":"qf-density11-subset-chain-obstructions","seed":202610115074,"semantic_template":"qf-density11-subset-chain-obstructions/[[-23],[23],[-23]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-23, 0] and B=[0, 23]; repeated elements count once. C=[0, 24] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-23], [23], [-23])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-23], [23], [-23])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0075","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"24523df9e67ec9a81e6e371c557195b8e81ff10f7e73158470f9ff676e05fd72","family_id":"qf-density11-subset-chain-obstructions","seed":202610115075,"semantic_template":"qf-density11-subset-chain-obstructions/[[-24],[24],[-24]]"},"fields":{"title":"Three Ordered Inclusion Obstructions","stem":"Finite integer sets A=[-24, 0] and B=[0, 24]; repeated elements count once. C=[0, 25] uses the same integer type. Give (A\\B, B\\C, A\\C), each increasing, retaining empty parts.","answer":{"kind":"expression","value":"([-24], [24], [-24])","explanation":"Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-24], [24], [-24])."},"skills":["Three Ordered Inclusion Obstructions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0076","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"19aa0abd981ce3a9584889d4c53f1af3f62ea1e71108be850157242a23c940c8","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115076,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"outside_A\",\"outside_A\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[] and B=[]; repeated elements count once. Ordered candidates=[100, 101, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, No, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0077","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ff228f3035eb69fb3eb07c369e2432ede4fc0af4c771c80ac1dadee2d5f97406","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115077,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"outside_A\",\"outside_A\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 101, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[Yes, No, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, No, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0078","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"41eb600f73c5a9018de10429454410961337997faf49cd791876d185550ee041","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115078,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"shared\",\"outside_A\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, 2, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, No, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0079","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1136fd6127271ea5ef4b7d49fbdeaedff13fafe19c3099e4693b186b91420cd","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115079,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"shared\",\"outside_A\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 2, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[Yes, No, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, No, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0080","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"28d8cc28911df630d32db1fa919696f697697db8896699a554c153fb202b5e3d","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115080,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"obstructs\",\"outside_A\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, -2, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, Yes, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, Yes, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0081","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4be57bf38fcc7658b20a9510f207741a75df191397ed0886c6b7c5d84e4de19d","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115081,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"obstructs\",\"outside_A\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, -2, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, Yes, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, Yes, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0082","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4d716dd4b6fcd4fee92874038598f14cddf33bef7b552a1d0532e6023942cd2e","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115082,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"obstructs\",\"outside_A\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, -2, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[Yes, Yes, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, Yes, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0083","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"941df7ef308333637f623000a7ba3caccbb12ccdc5322cb958c242f83af887ff","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115083,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"outside_A\",\"shared\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, 101, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, No, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0084","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"23c9c877d1ca5b39645a342e3914c0ad0b232862f2dbaa9bd63e6bbb1c6cee31","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115084,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"outside_A\",\"shared\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, 101, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, No, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0085","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d987e91b7266378302421b6aef495a3b59f87b99c401ba978001ae33d0398a61","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115085,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"outside_A\",\"shared\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 101, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[Yes, No, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, No, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0086","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fe1bab46111f00e80104e560c0f35d6bfd983b5ddfcb2107459f80afdabbe391","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115086,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"shared\",\"shared\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, 2, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, No, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0087","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b3d630b1a04c13dc3bfd832d06d32a7ce4ad7c3073ac4070624e75d3baf7002e","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115087,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"shared\",\"shared\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, 2, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, No, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0088","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"33b070017df5423c8ecd7f1189a8cda67c8285925b0d010434fdfe6ddc417a26","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115088,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"shared\",\"shared\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 2, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[Yes, No, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, No, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0089","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"03b70cf798902d6a961dcb947750032596fb2948238bf6d2a4cf3056ee904ec0","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115089,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"obstructs\",\"shared\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, -2, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, Yes, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, Yes, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0090","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5c8347e2895d0ef3fb796bc12415808b1b3976f0483efece0734500190c5cc5a","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115090,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"obstructs\",\"shared\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, -2, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, Yes, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, Yes, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0091","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"600fe93f18303a71f72cf877874ee0751af326f2ce9e34585c1542f2af9edc73","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115091,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"obstructs\",\"shared\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, -2, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[Yes, Yes, No]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, Yes, No]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0092","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fa175fb7edef7d1f837ae9d9fa6a3f4e150207592149265aeb894a01a3119862","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115092,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"outside_A\",\"obstructs\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, 101, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, No, Yes]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, Yes]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0093","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ba775a658618306e3a9b6ff86ae8377bc84279701a76dcf98d78ffdebe25a6a4","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115093,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"outside_A\",\"obstructs\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, 101, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, No, Yes]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, Yes]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0094","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a05c876dae79581ddeb8354ea2684618d14fdbf132d4e317e48c0bf9fbd79e2b","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115094,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"outside_A\",\"obstructs\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 101, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[Yes, No, Yes]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, No, Yes]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0095","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c2d3c2a75d6d7603df4f6cc5b4e74b1496fe8224abfdd2c153658122ccdc817e","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115095,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"shared\",\"obstructs\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, 2, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, No, Yes]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, Yes]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0096","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a0cfb78277ec2a59c5b037e707ea6d03a82a021b99c531c323ce40ba9fcdc567","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115096,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"shared\",\"obstructs\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, 2, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, No, Yes]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, Yes]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0097","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8005076ccf1e9c5745ebc2ed5b89509485e4d5ec68f0c51ae8aca61e1e331e76","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115097,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"shared\",\"obstructs\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 2, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[Yes, No, Yes]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, No, Yes]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0098","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"84b1684601a639d05499a253f39e0b56552a88ed3a8ec8522aca482e78258265","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115098,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"outside_A\",\"obstructs\",\"obstructs\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, -2, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, Yes, Yes]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, Yes, Yes]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0099","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5bc56685892df7aab389f9faf87738e203de650eca001489cb9c692cccd650a4","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115099,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"shared\",\"obstructs\",\"obstructs\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, -2, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[No, Yes, Yes]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, Yes, Yes]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r05-subset-0100","batch_id":"batch-20261008-advance-20261011-r05-subset-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4e4be9be2f781460c19f9451722bfb8f226cb7cb5f8e12fc30cd5bc5ba5159ad","family_id":"qf-density11-subset-candidate-witness-mask","seed":202610115100,"semantic_template":"qf-density11-subset-candidate-witness-mask/[\"obstructs\",\"obstructs\",\"obstructs\"]"},"fields":{"title":"Candidate Inclusion-Counterexample Mask","stem":"Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[]; repeated elements count once. Ordered candidates=[-1, -2, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.","answer":{"kind":"expression","value":"[Yes, Yes, Yes]","explanation":"Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, Yes, Yes]."},"skills":["Candidate Inclusion-Counterexample Mask"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}