第 9931 題：合成證明項判定

原題與已知條件

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。

• G001 — 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。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-lean-proof-term

逐步推導

synthetic proposition/term calculus or supplied synthetic receipt

no actual Lean build,source-digest check or kernel acceptance

environment ID="env-5";statement ID="";term hash text="0000000000000000000000000000000000000000000000000000000000000005";type hash text="0000000000000000000000000000000000000000000000000000000000000069"

IDs nonempty=否;term lexical shape=是;type lexical shape=是

IDs and shapes qualified=否;supplied kernel flag=否;axioms recorded=是

synthetic qualified=否;status=合成receipt仍不完整

逐步反向核對

• S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。

結論

(env-5, 缺, 是, 是, 否, 是, 否, 合成receipt仍不完整)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。