{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0001","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h0\",\"type\":\"P0\"}],\"term\":{\"kind\":\"var\",\"name\":\"h0\"},\"claimed_type\":\"P0\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P0, P0, 是)","explanation_zh":"第二批擴展核對=(P0, P0, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197001,"parameters":{"context":[{"name":"h0","type":"P0"}],"term":{"kind":"var","name":"h0"},"claimed_type":"P0","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P0\",\"context\":[{\"name\":\"h0\",\"type\":\"P0\"}],\"term\":{\"kind\":\"var\",\"name\":\"h0\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0002","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[],\"term\":{\"kind\":\"lam\",\"name\":\"x1\",\"var_type\":\"P1\",\"body\":{\"kind\":\"var\",\"name\":\"x1\"}},\"claimed_type\":[\"imp\",\"P1\",\"P1\"]}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"([imp, P1, P1], [imp, P1, P1], 是)","explanation_zh":"第二批擴展核對=([imp, P1, P1], [imp, P1, P1], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197002,"parameters":{"context":[],"term":{"kind":"lam","name":"x1","var_type":"P1","body":{"kind":"var","name":"x1"}},"claimed_type":["imp","P1","P1"],"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":[\"imp\",\"P1\",\"P1\"],\"context\":[],\"term\":{\"body\":{\"kind\":\"var\",\"name\":\"x1\"},\"kind\":\"lam\",\"name\":\"x1\",\"var_type\":\"P1\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0003","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h2\",\"type\":\"P2\"},{\"name\":\"q2\",\"type\":\"Q2\"}],\"term\":{\"kind\":\"pair\",\"left\":{\"kind\":\"var\",\"name\":\"h2\"},\"right\":{\"kind\":\"var\",\"name\":\"q2\"}},\"claimed_type\":[\"and\",\"P2\",\"Q2\"]}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"([and, P2, Q2], [and, P2, Q2], 是)","explanation_zh":"第二批擴展核對=([and, P2, Q2], [and, P2, Q2], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197003,"parameters":{"context":[{"name":"h2","type":"P2"},{"name":"q2","type":"Q2"}],"term":{"kind":"pair","left":{"kind":"var","name":"h2"},"right":{"kind":"var","name":"q2"}},"claimed_type":["and","P2","Q2"],"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":[\"and\",\"P2\",\"Q2\"],\"context\":[{\"name\":\"h2\",\"type\":\"P2\"},{\"name\":\"q2\",\"type\":\"Q2\"}],\"term\":{\"kind\":\"pair\",\"left\":{\"kind\":\"var\",\"name\":\"h2\"},\"right\":{\"kind\":\"var\",\"name\":\"q2\"}}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0004","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"pair3\",\"type\":[\"and\",\"P3\",\"Q3\"]}],\"term\":{\"kind\":\"fst\",\"pair\":{\"kind\":\"var\",\"name\":\"pair3\"}},\"claimed_type\":\"P3\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P3, P3, 是)","explanation_zh":"第二批擴展核對=(P3, P3, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197004,"parameters":{"context":[{"name":"pair3","type":["and","P3","Q3"]}],"term":{"kind":"fst","pair":{"kind":"var","name":"pair3"}},"claimed_type":"P3","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P3\",\"context\":[{\"name\":\"pair3\",\"type\":[\"and\",\"P3\",\"Q3\"]}],\"term\":{\"kind\":\"fst\",\"pair\":{\"kind\":\"var\",\"name\":\"pair3\"}}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0005","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h4\",\"type\":\"P4\"}],\"term\":{\"kind\":\"var\",\"name\":\"h4\"},\"claimed_type\":\"P4\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P4, P4, 是)","explanation_zh":"第二批擴展核對=(P4, P4, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197005,"parameters":{"context":[{"name":"h4","type":"P4"}],"term":{"kind":"var","name":"h4"},"claimed_type":"P4","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P4\",\"context\":[{\"name\":\"h4\",\"type\":\"P4\"}],\"term\":{\"kind\":\"var\",\"name\":\"h4\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0006","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[],\"term\":{\"kind\":\"lam\",\"name\":\"x5\",\"var_type\":\"P5\",\"body\":{\"kind\":\"var\",\"name\":\"x5\"}},\"claimed_type\":[\"imp\",\"P5\",\"P5\"]}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"([imp, P5, P5], [imp, P5, P5], 是)","explanation_zh":"第二批擴展核對=([imp, P5, P5], [imp, P5, P5], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197006,"parameters":{"context":[],"term":{"kind":"lam","name":"x5","var_type":"P5","body":{"kind":"var","name":"x5"}},"claimed_type":["imp","P5","P5"],"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":[\"imp\",\"P5\",\"P5\"],\"context\":[],\"term\":{\"body\":{\"kind\":\"var\",\"name\":\"x5\"},\"kind\":\"lam\",\"name\":\"x5\",\"var_type\":\"P5\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0007","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h6\",\"type\":\"P6\"},{\"name\":\"q6\",\"type\":\"Q6\"}],\"term\":{\"kind\":\"pair\",\"left\":{\"kind\":\"var\",\"name\":\"h6\"},\"right\":{\"kind\":\"var\",\"name\":\"q6\"}},\"claimed_type\":[\"and\",\"P6\",\"Q6\"]}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"([and, P6, Q6], [and, P6, Q6], 是)","explanation_zh":"第二批擴展核對=([and, P6, Q6], [and, P6, Q6], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197007,"parameters":{"context":[{"name":"h6","type":"P6"},{"name":"q6","type":"Q6"}],"term":{"kind":"pair","left":{"kind":"var","name":"h6"},"right":{"kind":"var","name":"q6"}},"claimed_type":["and","P6","Q6"],"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":[\"and\",\"P6\",\"Q6\"],\"context\":[{\"name\":\"h6\",\"type\":\"P6\"},{\"name\":\"q6\",\"type\":\"Q6\"}],\"term\":{\"kind\":\"pair\",\"left\":{\"kind\":\"var\",\"name\":\"h6\"},\"right\":{\"kind\":\"var\",\"name\":\"q6\"}}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0008","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"pair7\",\"type\":[\"and\",\"P7\",\"Q7\"]}],\"term\":{\"kind\":\"fst\",\"pair\":{\"kind\":\"var\",\"name\":\"pair7\"}},\"claimed_type\":\"P7\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P7, P7, 是)","explanation_zh":"第二批擴展核對=(P7, P7, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197008,"parameters":{"context":[{"name":"pair7","type":["and","P7","Q7"]}],"term":{"kind":"fst","pair":{"kind":"var","name":"pair7"}},"claimed_type":"P7","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P7\",\"context\":[{\"name\":\"pair7\",\"type\":[\"and\",\"P7\",\"Q7\"]}],\"term\":{\"kind\":\"fst\",\"pair\":{\"kind\":\"var\",\"name\":\"pair7\"}}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0009","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h8\",\"type\":\"P8\"}],\"term\":{\"kind\":\"var\",\"name\":\"h8\"},\"claimed_type\":\"P8\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P8, P8, 是)","explanation_zh":"第二批擴展核對=(P8, P8, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197009,"parameters":{"context":[{"name":"h8","type":"P8"}],"term":{"kind":"var","name":"h8"},"claimed_type":"P8","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P8\",\"context\":[{\"name\":\"h8\",\"type\":\"P8\"}],\"term\":{\"kind\":\"var\",\"name\":\"h8\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0010","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[],\"term\":{\"kind\":\"lam\",\"name\":\"x9\",\"var_type\":\"P9\",\"body\":{\"kind\":\"var\",\"name\":\"x9\"}},\"claimed_type\":[\"imp\",\"P9\",\"P9\"]}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"([imp, P9, P9], [imp, P9, P9], 是)","explanation_zh":"第二批擴展核對=([imp, P9, P9], [imp, P9, P9], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197010,"parameters":{"context":[],"term":{"kind":"lam","name":"x9","var_type":"P9","body":{"kind":"var","name":"x9"}},"claimed_type":["imp","P9","P9"],"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":[\"imp\",\"P9\",\"P9\"],\"context\":[],\"term\":{\"body\":{\"kind\":\"var\",\"name\":\"x9\"},\"kind\":\"lam\",\"name\":\"x9\",\"var_type\":\"P9\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0011","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h10\",\"type\":\"P10\"},{\"name\":\"q10\",\"type\":\"Q10\"}],\"term\":{\"kind\":\"pair\",\"left\":{\"kind\":\"var\",\"name\":\"h10\"},\"right\":{\"kind\":\"var\",\"name\":\"q10\"}},\"claimed_type\":[\"and\",\"P10\",\"Q10\"]}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"([and, P10, Q10], [and, P10, Q10], 是)","explanation_zh":"第二批擴展核對=([and, P10, Q10], [and, P10, Q10], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197011,"parameters":{"context":[{"name":"h10","type":"P10"},{"name":"q10","type":"Q10"}],"term":{"kind":"pair","left":{"kind":"var","name":"h10"},"right":{"kind":"var","name":"q10"}},"claimed_type":["and","P10","Q10"],"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":[\"and\",\"P10\",\"Q10\"],\"context\":[{\"name\":\"h10\",\"type\":\"P10\"},{\"name\":\"q10\",\"type\":\"Q10\"}],\"term\":{\"kind\":\"pair\",\"left\":{\"kind\":\"var\",\"name\":\"h10\"},\"right\":{\"kind\":\"var\",\"name\":\"q10\"}}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0012","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"pair11\",\"type\":[\"and\",\"P11\",\"Q11\"]}],\"term\":{\"kind\":\"fst\",\"pair\":{\"kind\":\"var\",\"name\":\"pair11\"}},\"claimed_type\":\"P11\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P11, P11, 是)","explanation_zh":"第二批擴展核對=(P11, P11, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197012,"parameters":{"context":[{"name":"pair11","type":["and","P11","Q11"]}],"term":{"kind":"fst","pair":{"kind":"var","name":"pair11"}},"claimed_type":"P11","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P11\",\"context\":[{\"name\":\"pair11\",\"type\":[\"and\",\"P11\",\"Q11\"]}],\"term\":{\"kind\":\"fst\",\"pair\":{\"kind\":\"var\",\"name\":\"pair11\"}}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0013","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h12\",\"type\":\"P12\"}],\"term\":{\"kind\":\"var\",\"name\":\"h12\"},\"claimed_type\":\"P12\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P12, P12, 是)","explanation_zh":"第二批擴展核對=(P12, P12, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197013,"parameters":{"context":[{"name":"h12","type":"P12"}],"term":{"kind":"var","name":"h12"},"claimed_type":"P12","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P12\",\"context\":[{\"name\":\"h12\",\"type\":\"P12\"}],\"term\":{\"kind\":\"var\",\"name\":\"h12\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0014","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[],\"term\":{\"kind\":\"lam\",\"name\":\"x13\",\"var_type\":\"P13\",\"body\":{\"kind\":\"var\",\"name\":\"x13\"}},\"claimed_type\":[\"imp\",\"P13\",\"P13\"]}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"([imp, P13, P13], [imp, P13, P13], 是)","explanation_zh":"第二批擴展核對=([imp, P13, P13], [imp, P13, P13], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197014,"parameters":{"context":[],"term":{"kind":"lam","name":"x13","var_type":"P13","body":{"kind":"var","name":"x13"}},"claimed_type":["imp","P13","P13"],"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":[\"imp\",\"P13\",\"P13\"],\"context\":[],\"term\":{\"body\":{\"kind\":\"var\",\"name\":\"x13\"},\"kind\":\"lam\",\"name\":\"x13\",\"var_type\":\"P13\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0015","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h14\",\"type\":\"P14\"},{\"name\":\"q14\",\"type\":\"Q14\"}],\"term\":{\"kind\":\"pair\",\"left\":{\"kind\":\"var\",\"name\":\"h14\"},\"right\":{\"kind\":\"var\",\"name\":\"q14\"}},\"claimed_type\":[\"and\",\"P14\",\"Q14\"]}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"([and, P14, Q14], [and, P14, Q14], 是)","explanation_zh":"第二批擴展核對=([and, P14, Q14], [and, P14, Q14], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197015,"parameters":{"context":[{"name":"h14","type":"P14"},{"name":"q14","type":"Q14"}],"term":{"kind":"pair","left":{"kind":"var","name":"h14"},"right":{"kind":"var","name":"q14"}},"claimed_type":["and","P14","Q14"],"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":[\"and\",\"P14\",\"Q14\"],\"context\":[{\"name\":\"h14\",\"type\":\"P14\"},{\"name\":\"q14\",\"type\":\"Q14\"}],\"term\":{\"kind\":\"pair\",\"left\":{\"kind\":\"var\",\"name\":\"h14\"},\"right\":{\"kind\":\"var\",\"name\":\"q14\"}}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0016","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"pair15\",\"type\":[\"and\",\"P15\",\"Q15\"]}],\"term\":{\"kind\":\"fst\",\"pair\":{\"kind\":\"var\",\"name\":\"pair15\"}},\"claimed_type\":\"P15\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P15, P15, 是)","explanation_zh":"第二批擴展核對=(P15, P15, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197016,"parameters":{"context":[{"name":"pair15","type":["and","P15","Q15"]}],"term":{"kind":"fst","pair":{"kind":"var","name":"pair15"}},"claimed_type":"P15","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P15\",\"context\":[{\"name\":\"pair15\",\"type\":[\"and\",\"P15\",\"Q15\"]}],\"term\":{\"kind\":\"fst\",\"pair\":{\"kind\":\"var\",\"name\":\"pair15\"}}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0017","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h16\",\"type\":\"P16\"}],\"term\":{\"kind\":\"var\",\"name\":\"h16\"},\"claimed_type\":\"P16\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P16, P16, 是)","explanation_zh":"第二批擴展核對=(P16, P16, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197017,"parameters":{"context":[{"name":"h16","type":"P16"}],"term":{"kind":"var","name":"h16"},"claimed_type":"P16","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P16\",\"context\":[{\"name\":\"h16\",\"type\":\"P16\"}],\"term\":{\"kind\":\"var\",\"name\":\"h16\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0018","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[],\"term\":{\"kind\":\"lam\",\"name\":\"x17\",\"var_type\":\"P17\",\"body\":{\"kind\":\"var\",\"name\":\"x17\"}},\"claimed_type\":[\"imp\",\"P17\",\"P17\"]}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"([imp, P17, P17], [imp, P17, P17], 是)","explanation_zh":"第二批擴展核對=([imp, P17, P17], [imp, P17, P17], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197018,"parameters":{"context":[],"term":{"kind":"lam","name":"x17","var_type":"P17","body":{"kind":"var","name":"x17"}},"claimed_type":["imp","P17","P17"],"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":[\"imp\",\"P17\",\"P17\"],\"context\":[],\"term\":{\"body\":{\"kind\":\"var\",\"name\":\"x17\"},\"kind\":\"lam\",\"name\":\"x17\",\"var_type\":\"P17\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0019","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h18\",\"type\":\"P18\"},{\"name\":\"q18\",\"type\":\"Q18\"}],\"term\":{\"kind\":\"pair\",\"left\":{\"kind\":\"var\",\"name\":\"h18\"},\"right\":{\"kind\":\"var\",\"name\":\"q18\"}},\"claimed_type\":[\"and\",\"P18\",\"Q18\"]}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"([and, P18, Q18], [and, P18, Q18], 是)","explanation_zh":"第二批擴展核對=([and, P18, Q18], [and, P18, Q18], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197019,"parameters":{"context":[{"name":"h18","type":"P18"},{"name":"q18","type":"Q18"}],"term":{"kind":"pair","left":{"kind":"var","name":"h18"},"right":{"kind":"var","name":"q18"}},"claimed_type":["and","P18","Q18"],"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":[\"and\",\"P18\",\"Q18\"],\"context\":[{\"name\":\"h18\",\"type\":\"P18\"},{\"name\":\"q18\",\"type\":\"Q18\"}],\"term\":{\"kind\":\"pair\",\"left\":{\"kind\":\"var\",\"name\":\"h18\"},\"right\":{\"kind\":\"var\",\"name\":\"q18\"}}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0020","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"pair19\",\"type\":[\"and\",\"P19\",\"Q19\"]}],\"term\":{\"kind\":\"fst\",\"pair\":{\"kind\":\"var\",\"name\":\"pair19\"}},\"claimed_type\":\"P19\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P19, P19, 是)","explanation_zh":"第二批擴展核對=(P19, P19, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197020,"parameters":{"context":[{"name":"pair19","type":["and","P19","Q19"]}],"term":{"kind":"fst","pair":{"kind":"var","name":"pair19"}},"claimed_type":"P19","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P19\",\"context\":[{\"name\":\"pair19\",\"type\":[\"and\",\"P19\",\"Q19\"]}],\"term\":{\"kind\":\"fst\",\"pair\":{\"kind\":\"var\",\"name\":\"pair19\"}}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0021","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h20\",\"type\":\"P20\"}],\"term\":{\"kind\":\"var\",\"name\":\"h20\"},\"claimed_type\":\"P20\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P20, P20, 是)","explanation_zh":"第二批擴展核對=(P20, P20, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197021,"parameters":{"context":[{"name":"h20","type":"P20"}],"term":{"kind":"var","name":"h20"},"claimed_type":"P20","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P20\",\"context\":[{\"name\":\"h20\",\"type\":\"P20\"}],\"term\":{\"kind\":\"var\",\"name\":\"h20\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0022","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[],\"term\":{\"kind\":\"lam\",\"name\":\"x21\",\"var_type\":\"P21\",\"body\":{\"kind\":\"var\",\"name\":\"x21\"}},\"claimed_type\":[\"imp\",\"P21\",\"P21\"]}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"([imp, P21, P21], [imp, P21, P21], 是)","explanation_zh":"第二批擴展核對=([imp, P21, P21], [imp, P21, P21], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197022,"parameters":{"context":[],"term":{"kind":"lam","name":"x21","var_type":"P21","body":{"kind":"var","name":"x21"}},"claimed_type":["imp","P21","P21"],"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":[\"imp\",\"P21\",\"P21\"],\"context\":[],\"term\":{\"body\":{\"kind\":\"var\",\"name\":\"x21\"},\"kind\":\"lam\",\"name\":\"x21\",\"var_type\":\"P21\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0023","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h22\",\"type\":\"P22\"},{\"name\":\"q22\",\"type\":\"Q22\"}],\"term\":{\"kind\":\"pair\",\"left\":{\"kind\":\"var\",\"name\":\"h22\"},\"right\":{\"kind\":\"var\",\"name\":\"q22\"}},\"claimed_type\":[\"and\",\"P22\",\"Q22\"]}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"([and, P22, Q22], [and, P22, Q22], 是)","explanation_zh":"第二批擴展核對=([and, P22, Q22], [and, P22, Q22], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197023,"parameters":{"context":[{"name":"h22","type":"P22"},{"name":"q22","type":"Q22"}],"term":{"kind":"pair","left":{"kind":"var","name":"h22"},"right":{"kind":"var","name":"q22"}},"claimed_type":["and","P22","Q22"],"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":[\"and\",\"P22\",\"Q22\"],\"context\":[{\"name\":\"h22\",\"type\":\"P22\"},{\"name\":\"q22\",\"type\":\"Q22\"}],\"term\":{\"kind\":\"pair\",\"left\":{\"kind\":\"var\",\"name\":\"h22\"},\"right\":{\"kind\":\"var\",\"name\":\"q22\"}}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0024","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"pair23\",\"type\":[\"and\",\"P23\",\"Q23\"]}],\"term\":{\"kind\":\"fst\",\"pair\":{\"kind\":\"var\",\"name\":\"pair23\"}},\"claimed_type\":\"P23\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P23, P23, 是)","explanation_zh":"第二批擴展核對=(P23, P23, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197024,"parameters":{"context":[{"name":"pair23","type":["and","P23","Q23"]}],"term":{"kind":"fst","pair":{"kind":"var","name":"pair23"}},"claimed_type":"P23","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P23\",\"context\":[{\"name\":\"pair23\",\"type\":[\"and\",\"P23\",\"Q23\"]}],\"term\":{\"kind\":\"fst\",\"pair\":{\"kind\":\"var\",\"name\":\"pair23\"}}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0025","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-small-calculus；資料={\"context\":[{\"name\":\"h24\",\"type\":\"P24\"}],\"term\":{\"kind\":\"var\",\"name\":\"h24\"},\"claimed_type\":\"P24\"}。請依 [inferred_type,claimed_type,matches] 欄序回答。","answer":{"kind":"expression","value":"(P24, P24, 是)","explanation_zh":"第二批擴展核對=(P24, P24, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-small-calculus","seed":202610197025,"parameters":{"context":[{"name":"h24","type":"P24"}],"term":{"kind":"var","name":"h24"},"claimed_type":"P24","domain":"Synthetic_typed_proof_calculus","operation":"proofterm-small-calculus","semantic_template":"qf-ext19-proofterm-small-calculus/{\"claimed_type\":\"P24\",\"context\":[{\"name\":\"h24\",\"type\":\"P24\"}],\"term\":{\"kind\":\"var\",\"name\":\"h24\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0026","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h0\",\"type\":\"P0\"}],\"term\":{\"kind\":\"var\",\"name\":\"h0\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h0], [h0], [], P0, 是)","explanation_zh":"第二批擴展核對=([h0], [h0], [], P0, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197026,"parameters":{"context":[{"name":"h0","type":"P0"}],"term":{"kind":"var","name":"h0"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h0\",\"type\":\"P0\"}],\"term\":{\"kind\":\"var\",\"name\":\"h0\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0027","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h1\",\"type\":\"P1\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing1\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([missing1], [h1], [missing1], 不求值, 否)","explanation_zh":"第二批擴展核對=([missing1], [h1], [missing1], 不求值, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197027,"parameters":{"context":[{"name":"h1","type":"P1"}],"term":{"kind":"var","name":"missing1"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h1\",\"type\":\"P1\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing1\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0028","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h2\",\"type\":\"P2\"}],\"term\":{\"kind\":\"var\",\"name\":\"h2\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h2], [h2], [], P2, 是)","explanation_zh":"第二批擴展核對=([h2], [h2], [], P2, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197028,"parameters":{"context":[{"name":"h2","type":"P2"}],"term":{"kind":"var","name":"h2"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h2\",\"type\":\"P2\"}],\"term\":{\"kind\":\"var\",\"name\":\"h2\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0029","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h3\",\"type\":\"P3\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing3\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([missing3], [h3], [missing3], 不求值, 否)","explanation_zh":"第二批擴展核對=([missing3], [h3], [missing3], 不求值, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197029,"parameters":{"context":[{"name":"h3","type":"P3"}],"term":{"kind":"var","name":"missing3"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h3\",\"type\":\"P3\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing3\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0030","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h4\",\"type\":\"P4\"}],\"term\":{\"kind\":\"var\",\"name\":\"h4\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h4], [h4], [], P4, 是)","explanation_zh":"第二批擴展核對=([h4], [h4], [], P4, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197030,"parameters":{"context":[{"name":"h4","type":"P4"}],"term":{"kind":"var","name":"h4"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h4\",\"type\":\"P4\"}],\"term\":{\"kind\":\"var\",\"name\":\"h4\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0031","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h5\",\"type\":\"P5\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing5\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([missing5], [h5], [missing5], 不求值, 否)","explanation_zh":"第二批擴展核對=([missing5], [h5], [missing5], 不求值, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197031,"parameters":{"context":[{"name":"h5","type":"P5"}],"term":{"kind":"var","name":"missing5"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h5\",\"type\":\"P5\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing5\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0032","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h6\",\"type\":\"P6\"}],\"term\":{\"kind\":\"var\",\"name\":\"h6\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h6], [h6], [], P6, 是)","explanation_zh":"第二批擴展核對=([h6], [h6], [], P6, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197032,"parameters":{"context":[{"name":"h6","type":"P6"}],"term":{"kind":"var","name":"h6"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h6\",\"type\":\"P6\"}],\"term\":{\"kind\":\"var\",\"name\":\"h6\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0033","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h7\",\"type\":\"P7\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing7\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([missing7], [h7], [missing7], 不求值, 否)","explanation_zh":"第二批擴展核對=([missing7], [h7], [missing7], 不求值, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197033,"parameters":{"context":[{"name":"h7","type":"P7"}],"term":{"kind":"var","name":"missing7"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h7\",\"type\":\"P7\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing7\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0034","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h8\",\"type\":\"P8\"}],\"term\":{\"kind\":\"var\",\"name\":\"h8\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h8], [h8], [], P8, 是)","explanation_zh":"第二批擴展核對=([h8], [h8], [], P8, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197034,"parameters":{"context":[{"name":"h8","type":"P8"}],"term":{"kind":"var","name":"h8"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h8\",\"type\":\"P8\"}],\"term\":{\"kind\":\"var\",\"name\":\"h8\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0035","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h9\",\"type\":\"P9\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing9\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([missing9], [h9], [missing9], 不求值, 否)","explanation_zh":"第二批擴展核對=([missing9], [h9], [missing9], 不求值, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197035,"parameters":{"context":[{"name":"h9","type":"P9"}],"term":{"kind":"var","name":"missing9"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h9\",\"type\":\"P9\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing9\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0036","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h10\",\"type\":\"P10\"}],\"term\":{\"kind\":\"var\",\"name\":\"h10\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h10], [h10], [], P10, 是)","explanation_zh":"第二批擴展核對=([h10], [h10], [], P10, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197036,"parameters":{"context":[{"name":"h10","type":"P10"}],"term":{"kind":"var","name":"h10"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h10\",\"type\":\"P10\"}],\"term\":{\"kind\":\"var\",\"name\":\"h10\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0037","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h11\",\"type\":\"P11\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing11\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([missing11], [h11], [missing11], 不求值, 否)","explanation_zh":"第二批擴展核對=([missing11], [h11], [missing11], 不求值, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197037,"parameters":{"context":[{"name":"h11","type":"P11"}],"term":{"kind":"var","name":"missing11"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h11\",\"type\":\"P11\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing11\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0038","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h12\",\"type\":\"P12\"}],\"term\":{\"kind\":\"var\",\"name\":\"h12\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h12], [h12], [], P12, 是)","explanation_zh":"第二批擴展核對=([h12], [h12], [], P12, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197038,"parameters":{"context":[{"name":"h12","type":"P12"}],"term":{"kind":"var","name":"h12"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h12\",\"type\":\"P12\"}],\"term\":{\"kind\":\"var\",\"name\":\"h12\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0039","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h13\",\"type\":\"P13\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing13\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([missing13], [h13], [missing13], 不求值, 否)","explanation_zh":"第二批擴展核對=([missing13], [h13], [missing13], 不求值, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197039,"parameters":{"context":[{"name":"h13","type":"P13"}],"term":{"kind":"var","name":"missing13"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h13\",\"type\":\"P13\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing13\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0040","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h14\",\"type\":\"P14\"}],\"term\":{\"kind\":\"var\",\"name\":\"h14\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h14], [h14], [], P14, 是)","explanation_zh":"第二批擴展核對=([h14], [h14], [], P14, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197040,"parameters":{"context":[{"name":"h14","type":"P14"}],"term":{"kind":"var","name":"h14"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h14\",\"type\":\"P14\"}],\"term\":{\"kind\":\"var\",\"name\":\"h14\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0041","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h15\",\"type\":\"P15\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing15\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([missing15], [h15], [missing15], 不求值, 否)","explanation_zh":"第二批擴展核對=([missing15], [h15], [missing15], 不求值, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197041,"parameters":{"context":[{"name":"h15","type":"P15"}],"term":{"kind":"var","name":"missing15"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h15\",\"type\":\"P15\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing15\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0042","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h16\",\"type\":\"P16\"}],\"term\":{\"kind\":\"var\",\"name\":\"h16\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h16], [h16], [], P16, 是)","explanation_zh":"第二批擴展核對=([h16], [h16], [], P16, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197042,"parameters":{"context":[{"name":"h16","type":"P16"}],"term":{"kind":"var","name":"h16"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h16\",\"type\":\"P16\"}],\"term\":{\"kind\":\"var\",\"name\":\"h16\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0043","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h17\",\"type\":\"P17\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing17\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([missing17], [h17], [missing17], 不求值, 否)","explanation_zh":"第二批擴展核對=([missing17], [h17], [missing17], 不求值, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197043,"parameters":{"context":[{"name":"h17","type":"P17"}],"term":{"kind":"var","name":"missing17"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h17\",\"type\":\"P17\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing17\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0044","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h18\",\"type\":\"P18\"}],\"term\":{\"kind\":\"var\",\"name\":\"h18\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h18], [h18], [], P18, 是)","explanation_zh":"第二批擴展核對=([h18], [h18], [], P18, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197044,"parameters":{"context":[{"name":"h18","type":"P18"}],"term":{"kind":"var","name":"h18"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h18\",\"type\":\"P18\"}],\"term\":{\"kind\":\"var\",\"name\":\"h18\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0045","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h19\",\"type\":\"P19\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing19\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([missing19], [h19], [missing19], 不求值, 否)","explanation_zh":"第二批擴展核對=([missing19], [h19], [missing19], 不求值, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197045,"parameters":{"context":[{"name":"h19","type":"P19"}],"term":{"kind":"var","name":"missing19"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h19\",\"type\":\"P19\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing19\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0046","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h20\",\"type\":\"P20\"}],\"term\":{\"kind\":\"var\",\"name\":\"h20\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h20], [h20], [], P20, 是)","explanation_zh":"第二批擴展核對=([h20], [h20], [], P20, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197046,"parameters":{"context":[{"name":"h20","type":"P20"}],"term":{"kind":"var","name":"h20"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h20\",\"type\":\"P20\"}],\"term\":{\"kind\":\"var\",\"name\":\"h20\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0047","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h21\",\"type\":\"P21\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing21\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([missing21], [h21], [missing21], 不求值, 否)","explanation_zh":"第二批擴展核對=([missing21], [h21], [missing21], 不求值, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197047,"parameters":{"context":[{"name":"h21","type":"P21"}],"term":{"kind":"var","name":"missing21"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h21\",\"type\":\"P21\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing21\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0048","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h22\",\"type\":\"P22\"}],\"term\":{\"kind\":\"var\",\"name\":\"h22\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h22], [h22], [], P22, 是)","explanation_zh":"第二批擴展核對=([h22], [h22], [], P22, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197048,"parameters":{"context":[{"name":"h22","type":"P22"}],"term":{"kind":"var","name":"h22"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h22\",\"type\":\"P22\"}],\"term\":{\"kind\":\"var\",\"name\":\"h22\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0049","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h23\",\"type\":\"P23\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing23\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([missing23], [h23], [missing23], 不求值, 否)","explanation_zh":"第二批擴展核對=([missing23], [h23], [missing23], 不求值, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197049,"parameters":{"context":[{"name":"h23","type":"P23"}],"term":{"kind":"var","name":"missing23"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h23\",\"type\":\"P23\"}],\"term\":{\"kind\":\"var\",\"name\":\"missing23\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0050","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-context-use；資料={\"context\":[{\"name\":\"h24\",\"type\":\"P24\"}],\"term\":{\"kind\":\"var\",\"name\":\"h24\"}}。請依 [free_variables,context_names,missing,inferred_or_不求值,context_complete] 欄序回答。","answer":{"kind":"expression","value":"([h24], [h24], [], P24, 是)","explanation_zh":"第二批擴展核對=([h24], [h24], [], P24, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-context-use","seed":202610197050,"parameters":{"context":[{"name":"h24","type":"P24"}],"term":{"kind":"var","name":"h24"},"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-context-use","semantic_template":"qf-ext19-proofterm-context-use/{\"context\":[{\"name\":\"h24\",\"type\":\"P24\"}],\"term\":{\"kind\":\"var\",\"name\":\"h24\"}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0051","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":false,\"tactic_finished\":false,\"term_present\":false,\"unresolved_goals\":0}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(否, 否, 否, 0, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(否, 否, 否, 0, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197051,"parameters":{"statement_ready":false,"tactic_finished":false,"term_present":false,"unresolved_goals":0,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":false,\"tactic_finished\":false,\"term_present\":false,\"unresolved_goals\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0052","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":1}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 1, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 是, 1, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197052,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":true,"unresolved_goals":1,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0053","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":2}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 2, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 是, 2, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197053,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":true,"unresolved_goals":2,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0054","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":false,\"unresolved_goals\":3}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 否, 3, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 否, 3, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197054,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":false,"unresolved_goals":3,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":false,\"unresolved_goals\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0055","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":false,\"term_present\":true,\"unresolved_goals\":4}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 是, 4, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 否, 是, 4, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197055,"parameters":{"statement_ready":true,"tactic_finished":false,"term_present":true,"unresolved_goals":4,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":false,\"term_present\":true,\"unresolved_goals\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0056","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":false,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":5}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, 是, 5, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(否, 是, 是, 5, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197056,"parameters":{"statement_ready":false,"tactic_finished":true,"term_present":true,"unresolved_goals":5,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":false,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0057","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":false,\"unresolved_goals\":6}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 否, 6, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 否, 6, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197057,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":false,"unresolved_goals":6,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":false,\"unresolved_goals\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0058","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":7}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 7, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 是, 7, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197058,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":true,"unresolved_goals":7,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0059","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":false,\"term_present\":true,\"unresolved_goals\":8}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 是, 8, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 否, 是, 8, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197059,"parameters":{"statement_ready":true,"tactic_finished":false,"term_present":true,"unresolved_goals":8,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":false,\"term_present\":true,\"unresolved_goals\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0060","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":false,\"unresolved_goals\":9}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 否, 9, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 否, 9, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197060,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":false,"unresolved_goals":9,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":false,\"unresolved_goals\":9}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0061","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":false,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":10}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, 是, 10, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(否, 是, 是, 10, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197061,"parameters":{"statement_ready":false,"tactic_finished":true,"term_present":true,"unresolved_goals":10,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":false,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":10}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0062","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":11}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 11, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 是, 11, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197062,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":true,"unresolved_goals":11,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":11}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0063","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":false,\"term_present\":false,\"unresolved_goals\":12}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 12, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 否, 否, 12, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197063,"parameters":{"statement_ready":true,"tactic_finished":false,"term_present":false,"unresolved_goals":12,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":false,\"term_present\":false,\"unresolved_goals\":12}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0064","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":13}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 13, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 是, 13, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197064,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":true,"unresolved_goals":13,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":13}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0065","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":14}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 14, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 是, 14, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197065,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":true,"unresolved_goals":14,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":14}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0066","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":false,\"tactic_finished\":true,\"term_present\":false,\"unresolved_goals\":15}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, 否, 15, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(否, 是, 否, 15, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197066,"parameters":{"statement_ready":false,"tactic_finished":true,"term_present":false,"unresolved_goals":15,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":false,\"tactic_finished\":true,\"term_present\":false,\"unresolved_goals\":15}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0067","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":false,\"term_present\":true,\"unresolved_goals\":16}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 是, 16, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 否, 是, 16, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197067,"parameters":{"statement_ready":true,"tactic_finished":false,"term_present":true,"unresolved_goals":16,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":false,\"term_present\":true,\"unresolved_goals\":16}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0068","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":17}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 17, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 是, 17, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197068,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":true,"unresolved_goals":17,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":17}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0069","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":false,\"unresolved_goals\":18}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 否, 18, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 否, 18, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197069,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":false,"unresolved_goals":18,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":false,\"unresolved_goals\":18}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0070","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":19}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 19, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 是, 19, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197070,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":true,"unresolved_goals":19,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":19}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0071","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":false,\"tactic_finished\":false,\"term_present\":true,\"unresolved_goals\":20}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(否, 否, 是, 20, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(否, 否, 是, 20, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197071,"parameters":{"statement_ready":false,"tactic_finished":false,"term_present":true,"unresolved_goals":20,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":false,\"tactic_finished\":false,\"term_present\":true,\"unresolved_goals\":20}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0072","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":false,\"unresolved_goals\":21}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 否, 21, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 否, 21, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197072,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":false,"unresolved_goals":21,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":false,\"unresolved_goals\":21}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0073","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":22}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 22, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 是, 22, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197073,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":true,"unresolved_goals":22,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":22}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0074","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":23}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 23, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 是, 是, 23, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197074,"parameters":{"statement_ready":true,"tactic_finished":true,"term_present":true,"unresolved_goals":23,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":23}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0075","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-tactic-vs-term；資料={\"statement_ready\":true,\"tactic_finished\":false,\"term_present\":false,\"unresolved_goals\":24}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 24, 否, 否, 否, 尚無kernel receipt)","explanation_zh":"第二批擴展核對=(是, 否, 否, 24, 否, 否, 否, 尚無kernel receipt)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-tactic-vs-term","seed":202610197075,"parameters":{"statement_ready":true,"tactic_finished":false,"term_present":false,"unresolved_goals":24,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-tactic-vs-term","semantic_template":"qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":true,\"tactic_finished\":false,\"term_present\":false,\"unresolved_goals\":24}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0076","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"\",\"statement_id\":\"\",\"term_sha256\":\"bad\",\"type_sha256\":\"bad\",\"kernel_checked\":true,\"axioms_recorded\":false}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(缺, 缺, 否, 否, 是, 否, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(缺, 缺, 否, 否, 是, 否, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197076,"parameters":{"environment_id":"","statement_id":"","term_sha256":"bad","type_sha256":"bad","kernel_checked":true,"axioms_recorded":false,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":false,\"environment_id\":\"\",\"kernel_checked\":true,\"statement_id\":\"\",\"term_sha256\":\"bad\",\"type_sha256\":\"bad\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0077","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-1\",\"statement_id\":\"thm-1\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000001\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000065\",\"kernel_checked\":false,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-1, thm-1, 是, 是, 否, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-1, thm-1, 是, 是, 否, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197077,"parameters":{"environment_id":"env-1","statement_id":"thm-1","term_sha256":"0000000000000000000000000000000000000000000000000000000000000001","type_sha256":"0000000000000000000000000000000000000000000000000000000000000065","kernel_checked":false,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-1\",\"kernel_checked\":false,\"statement_id\":\"thm-1\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000001\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000065\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0078","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-2\",\"statement_id\":\"thm-2\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000002\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000066\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-2, thm-2, 是, 是, 是, 是, 是, 合成receipt欄位完整)","explanation_zh":"第二批擴展核對=(env-2, thm-2, 是, 是, 是, 是, 是, 合成receipt欄位完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197078,"parameters":{"environment_id":"env-2","statement_id":"thm-2","term_sha256":"0000000000000000000000000000000000000000000000000000000000000002","type_sha256":"0000000000000000000000000000000000000000000000000000000000000066","kernel_checked":true,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-2\",\"kernel_checked\":true,\"statement_id\":\"thm-2\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000002\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000066\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0079","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-3\",\"statement_id\":\"thm-3\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000003\",\"type_sha256\":\"bad\",\"kernel_checked\":false,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-3, thm-3, 是, 否, 否, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-3, thm-3, 是, 否, 否, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197079,"parameters":{"environment_id":"env-3","statement_id":"thm-3","term_sha256":"0000000000000000000000000000000000000000000000000000000000000003","type_sha256":"bad","kernel_checked":false,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-3\",\"kernel_checked\":false,\"statement_id\":\"thm-3\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000003\",\"type_sha256\":\"bad\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0080","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-4\",\"statement_id\":\"thm-4\",\"term_sha256\":\"bad\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000068\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-4, thm-4, 否, 是, 是, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-4, thm-4, 否, 是, 是, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197080,"parameters":{"environment_id":"env-4","statement_id":"thm-4","term_sha256":"bad","type_sha256":"0000000000000000000000000000000000000000000000000000000000000068","kernel_checked":true,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-4\",\"kernel_checked\":true,\"statement_id\":\"thm-4\",\"term_sha256\":\"bad\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000068\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0081","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-5\",\"statement_id\":\"\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000005\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000069\",\"kernel_checked\":false,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-5, 缺, 是, 是, 否, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-5, 缺, 是, 是, 否, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197081,"parameters":{"environment_id":"env-5","statement_id":"","term_sha256":"0000000000000000000000000000000000000000000000000000000000000005","type_sha256":"0000000000000000000000000000000000000000000000000000000000000069","kernel_checked":false,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-5\",\"kernel_checked\":false,\"statement_id\":\"\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000005\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000069\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0082","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"\",\"statement_id\":\"thm-6\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000006\",\"type_sha256\":\"bad\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(缺, thm-6, 是, 否, 是, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(缺, thm-6, 是, 否, 是, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197082,"parameters":{"environment_id":"","statement_id":"thm-6","term_sha256":"0000000000000000000000000000000000000000000000000000000000000006","type_sha256":"bad","kernel_checked":true,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"\",\"kernel_checked\":true,\"statement_id\":\"thm-6\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000006\",\"type_sha256\":\"bad\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0083","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-7\",\"statement_id\":\"thm-7\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000007\",\"type_sha256\":\"000000000000000000000000000000000000000000000000000000000000006b\",\"kernel_checked\":false,\"axioms_recorded\":false}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-7, thm-7, 是, 是, 否, 否, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-7, thm-7, 是, 是, 否, 否, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197083,"parameters":{"environment_id":"env-7","statement_id":"thm-7","term_sha256":"0000000000000000000000000000000000000000000000000000000000000007","type_sha256":"000000000000000000000000000000000000000000000000000000000000006b","kernel_checked":false,"axioms_recorded":false,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":false,\"environment_id\":\"env-7\",\"kernel_checked\":false,\"statement_id\":\"thm-7\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000007\",\"type_sha256\":\"000000000000000000000000000000000000000000000000000000000000006b\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0084","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-8\",\"statement_id\":\"thm-8\",\"term_sha256\":\"bad\",\"type_sha256\":\"000000000000000000000000000000000000000000000000000000000000006c\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-8, thm-8, 否, 是, 是, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-8, thm-8, 否, 是, 是, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197084,"parameters":{"environment_id":"env-8","statement_id":"thm-8","term_sha256":"bad","type_sha256":"000000000000000000000000000000000000000000000000000000000000006c","kernel_checked":true,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-8\",\"kernel_checked\":true,\"statement_id\":\"thm-8\",\"term_sha256\":\"bad\",\"type_sha256\":\"000000000000000000000000000000000000000000000000000000000000006c\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0085","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-9\",\"statement_id\":\"thm-9\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000009\",\"type_sha256\":\"bad\",\"kernel_checked\":false,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-9, thm-9, 是, 否, 否, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-9, thm-9, 是, 否, 否, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197085,"parameters":{"environment_id":"env-9","statement_id":"thm-9","term_sha256":"0000000000000000000000000000000000000000000000000000000000000009","type_sha256":"bad","kernel_checked":false,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-9\",\"kernel_checked\":false,\"statement_id\":\"thm-9\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000009\",\"type_sha256\":\"bad\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0086","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-10\",\"statement_id\":\"\",\"term_sha256\":\"000000000000000000000000000000000000000000000000000000000000000a\",\"type_sha256\":\"000000000000000000000000000000000000000000000000000000000000006e\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-10, 缺, 是, 是, 是, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-10, 缺, 是, 是, 是, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197086,"parameters":{"environment_id":"env-10","statement_id":"","term_sha256":"000000000000000000000000000000000000000000000000000000000000000a","type_sha256":"000000000000000000000000000000000000000000000000000000000000006e","kernel_checked":true,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-10\",\"kernel_checked\":true,\"statement_id\":\"\",\"term_sha256\":\"000000000000000000000000000000000000000000000000000000000000000a\",\"type_sha256\":\"000000000000000000000000000000000000000000000000000000000000006e\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0087","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-11\",\"statement_id\":\"thm-11\",\"term_sha256\":\"000000000000000000000000000000000000000000000000000000000000000b\",\"type_sha256\":\"000000000000000000000000000000000000000000000000000000000000006f\",\"kernel_checked\":false,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-11, thm-11, 是, 是, 否, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-11, thm-11, 是, 是, 否, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197087,"parameters":{"environment_id":"env-11","statement_id":"thm-11","term_sha256":"000000000000000000000000000000000000000000000000000000000000000b","type_sha256":"000000000000000000000000000000000000000000000000000000000000006f","kernel_checked":false,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-11\",\"kernel_checked\":false,\"statement_id\":\"thm-11\",\"term_sha256\":\"000000000000000000000000000000000000000000000000000000000000000b\",\"type_sha256\":\"000000000000000000000000000000000000000000000000000000000000006f\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0088","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"\",\"statement_id\":\"thm-12\",\"term_sha256\":\"bad\",\"type_sha256\":\"bad\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(缺, thm-12, 否, 否, 是, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(缺, thm-12, 否, 否, 是, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197088,"parameters":{"environment_id":"","statement_id":"thm-12","term_sha256":"bad","type_sha256":"bad","kernel_checked":true,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"\",\"kernel_checked\":true,\"statement_id\":\"thm-12\",\"term_sha256\":\"bad\",\"type_sha256\":\"bad\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0089","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-13\",\"statement_id\":\"thm-13\",\"term_sha256\":\"000000000000000000000000000000000000000000000000000000000000000d\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000071\",\"kernel_checked\":false,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-13, thm-13, 是, 是, 否, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-13, thm-13, 是, 是, 否, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197089,"parameters":{"environment_id":"env-13","statement_id":"thm-13","term_sha256":"000000000000000000000000000000000000000000000000000000000000000d","type_sha256":"0000000000000000000000000000000000000000000000000000000000000071","kernel_checked":false,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-13\",\"kernel_checked\":false,\"statement_id\":\"thm-13\",\"term_sha256\":\"000000000000000000000000000000000000000000000000000000000000000d\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000071\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0090","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-14\",\"statement_id\":\"thm-14\",\"term_sha256\":\"000000000000000000000000000000000000000000000000000000000000000e\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000072\",\"kernel_checked\":true,\"axioms_recorded\":false}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-14, thm-14, 是, 是, 是, 否, 是, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-14, thm-14, 是, 是, 是, 否, 是, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197090,"parameters":{"environment_id":"env-14","statement_id":"thm-14","term_sha256":"000000000000000000000000000000000000000000000000000000000000000e","type_sha256":"0000000000000000000000000000000000000000000000000000000000000072","kernel_checked":true,"axioms_recorded":false,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":false,\"environment_id\":\"env-14\",\"kernel_checked\":true,\"statement_id\":\"thm-14\",\"term_sha256\":\"000000000000000000000000000000000000000000000000000000000000000e\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000072\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0091","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-15\",\"statement_id\":\"\",\"term_sha256\":\"000000000000000000000000000000000000000000000000000000000000000f\",\"type_sha256\":\"bad\",\"kernel_checked\":false,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-15, 缺, 是, 否, 否, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-15, 缺, 是, 否, 否, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197091,"parameters":{"environment_id":"env-15","statement_id":"","term_sha256":"000000000000000000000000000000000000000000000000000000000000000f","type_sha256":"bad","kernel_checked":false,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-15\",\"kernel_checked\":false,\"statement_id\":\"\",\"term_sha256\":\"000000000000000000000000000000000000000000000000000000000000000f\",\"type_sha256\":\"bad\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0092","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-16\",\"statement_id\":\"thm-16\",\"term_sha256\":\"bad\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000074\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-16, thm-16, 否, 是, 是, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-16, thm-16, 否, 是, 是, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197092,"parameters":{"environment_id":"env-16","statement_id":"thm-16","term_sha256":"bad","type_sha256":"0000000000000000000000000000000000000000000000000000000000000074","kernel_checked":true,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-16\",\"kernel_checked\":true,\"statement_id\":\"thm-16\",\"term_sha256\":\"bad\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000074\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0093","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-17\",\"statement_id\":\"thm-17\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000011\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000075\",\"kernel_checked\":false,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-17, thm-17, 是, 是, 否, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-17, thm-17, 是, 是, 否, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197093,"parameters":{"environment_id":"env-17","statement_id":"thm-17","term_sha256":"0000000000000000000000000000000000000000000000000000000000000011","type_sha256":"0000000000000000000000000000000000000000000000000000000000000075","kernel_checked":false,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-17\",\"kernel_checked\":false,\"statement_id\":\"thm-17\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000011\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000075\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0094","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"\",\"statement_id\":\"thm-18\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000012\",\"type_sha256\":\"bad\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(缺, thm-18, 是, 否, 是, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(缺, thm-18, 是, 否, 是, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197094,"parameters":{"environment_id":"","statement_id":"thm-18","term_sha256":"0000000000000000000000000000000000000000000000000000000000000012","type_sha256":"bad","kernel_checked":true,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"\",\"kernel_checked\":true,\"statement_id\":\"thm-18\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000012\",\"type_sha256\":\"bad\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0095","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-19\",\"statement_id\":\"thm-19\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000013\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000077\",\"kernel_checked\":false,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-19, thm-19, 是, 是, 否, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-19, thm-19, 是, 是, 否, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197095,"parameters":{"environment_id":"env-19","statement_id":"thm-19","term_sha256":"0000000000000000000000000000000000000000000000000000000000000013","type_sha256":"0000000000000000000000000000000000000000000000000000000000000077","kernel_checked":false,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-19\",\"kernel_checked\":false,\"statement_id\":\"thm-19\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000013\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000077\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0096","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-20\",\"statement_id\":\"\",\"term_sha256\":\"bad\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000078\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-20, 缺, 否, 是, 是, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-20, 缺, 否, 是, 是, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197096,"parameters":{"environment_id":"env-20","statement_id":"","term_sha256":"bad","type_sha256":"0000000000000000000000000000000000000000000000000000000000000078","kernel_checked":true,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-20\",\"kernel_checked\":true,\"statement_id\":\"\",\"term_sha256\":\"bad\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000078\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0097","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-21\",\"statement_id\":\"thm-21\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000015\",\"type_sha256\":\"bad\",\"kernel_checked\":false,\"axioms_recorded\":false}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-21, thm-21, 是, 否, 否, 否, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-21, thm-21, 是, 否, 否, 否, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197097,"parameters":{"environment_id":"env-21","statement_id":"thm-21","term_sha256":"0000000000000000000000000000000000000000000000000000000000000015","type_sha256":"bad","kernel_checked":false,"axioms_recorded":false,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":false,\"environment_id\":\"env-21\",\"kernel_checked\":false,\"statement_id\":\"thm-21\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000015\",\"type_sha256\":\"bad\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0098","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-22\",\"statement_id\":\"thm-22\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000016\",\"type_sha256\":\"000000000000000000000000000000000000000000000000000000000000007a\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-22, thm-22, 是, 是, 是, 是, 是, 合成receipt欄位完整)","explanation_zh":"第二批擴展核對=(env-22, thm-22, 是, 是, 是, 是, 是, 合成receipt欄位完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197098,"parameters":{"environment_id":"env-22","statement_id":"thm-22","term_sha256":"0000000000000000000000000000000000000000000000000000000000000016","type_sha256":"000000000000000000000000000000000000000000000000000000000000007a","kernel_checked":true,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-22\",\"kernel_checked\":true,\"statement_id\":\"thm-22\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000016\",\"type_sha256\":\"000000000000000000000000000000000000000000000000000000000000007a\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0099","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-23\",\"statement_id\":\"thm-23\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000017\",\"type_sha256\":\"000000000000000000000000000000000000000000000000000000000000007b\",\"kernel_checked\":false,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(env-23, thm-23, 是, 是, 否, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(env-23, thm-23, 是, 是, 否, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197099,"parameters":{"environment_id":"env-23","statement_id":"thm-23","term_sha256":"0000000000000000000000000000000000000000000000000000000000000017","type_sha256":"000000000000000000000000000000000000000000000000000000000000007b","kernel_checked":false,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-23\",\"kernel_checked\":false,\"statement_id\":\"thm-23\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000017\",\"type_sha256\":\"000000000000000000000000000000000000000000000000000000000000007b\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r07-lean-proof-term-0100","batch_id":"batch-20261013-advance-20261019-r07-lean-proof-term-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-proof-term"],"title_zh":"合成證明項判定","stem_zh":"合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"\",\"statement_id\":\"thm-24\",\"term_sha256\":\"bad\",\"type_sha256\":\"bad\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。","answer":{"kind":"expression","value":"(缺, thm-24, 否, 否, 是, 是, 否, 合成receipt仍不完整)","explanation_zh":"第二批擴展核對=(缺, thm-24, 否, 否, 是, 是, 否, 合成receipt仍不完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["合成證明項判定"]},"variant":{"family_id":"qf-ext19-proofterm-kernel-receipt","seed":202610197100,"parameters":{"environment_id":"","statement_id":"thm-24","term_sha256":"bad","type_sha256":"bad","kernel_checked":true,"axioms_recorded":true,"domain":"Synthetic_typed_proof_calculus","operation":"proofterm-kernel-receipt","semantic_template":"qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"\",\"kernel_checked\":true,\"statement_id\":\"thm-24\",\"term_sha256\":\"bad\",\"type_sha256\":\"bad\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}