Claim Verification: "The binary operator eml is defined by the expression \(\text{eml}(a, b) = \exp(a) - \ln(b)\) (where exp is the exponential function and ln is the principal branch of the natural logarithm). For every real \(x > 0\), the nested expression \(\text{eml}(1, \text{eml}(\text{eml}(1, x), 1))\) equals the natural logarithm \(\ln(x)\)." — Proved

Automated fact-verification of the claim: "The binary operator eml is defined by the expression \(\text{eml}(a, b) = \exp(a) - \ln(b)\) (where exp is the exponential function and ln is the principal branch of the natural logarithm). For every real \(x > 0\), the nested expression \(\text{eml}(1, \text{eml}(\text{eml}(1, x), 1))\) equals the natural logarithm \(\ln(x)\)." Verdict: PROVED Files proof.py — Re-runnable Python verification script proof.md — Structured proof report proof_audit.md — Full verification audit trail proof_narrative.md — Plain-language summary proof.json — Machine-readable structured data Generated by Proof Engine v1.18.0.针对下述断言的自动化事实核查：二元运算符`eml`由表达式$ ext{eml}(a, b) = exp(a) - ln(b)$定义（其中$exp$为指数函数，$ln$为自然对数的主分支）。对于任意正实数$x$，嵌套表达式$ ext{eml}(1, ext{eml}( ext{eml}(1, x), 1))$恒等于自然对数$ln(x)$。 判定结果：已证明。 相关文件： `proof.py` — 可重复运行的Python验证脚本 `proof.md` — 结构化证明报告 `proof_audit.md` — 完整验证审核追踪记录 `proof_narrative.md` — 通俗语言总结 `proof.json` — 机器可读结构化数据 本内容由Proof Engine v1.18.0生成。