Claim Verification: "The binary operator eml is defined by the expression \(\text{eml}(a, b) = \exp(a) - \ln(b)\). There exists a finite binary tree consisting solely of eml operations, whose 10 leaves are drawn from \(\{1, x, y\}\), such that the tree evaluates exactly to \(x + y\). The tree has K = 19 tokens (9 eml operations and 10 leaves), and the identity holds for all real \(x\) and \(y\) (and formally for all complex \(x, y\) in the algebraic setting where \(\ln \circ \exp\) is the identity)." — Proved

Automated fact-verification of the claim: "The binary operator eml is defined by the expression \(\text{eml}(a, b) = \exp(a) - \ln(b)\). There exists a finite binary tree consisting solely of eml operations, whose 10 leaves are drawn from \(\{1, x, y\}\), such that the tree evaluates exactly to \(x + y\). The tree has K = 19 tokens (9 eml operations and 10 leaves), and the identity holds for all real \(x\) and \(y\) (and formally for all complex \(x, y\) in the algebraic setting where \(\ln \circ \exp\) is the identity)." 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。存在一棵仅由`eml`运算构成的有限二叉树，其10个叶节点取自集合({1, x, y})，使得该树的求值结果恰好为(x + y)。该树包含K=19个Token（9个`eml`运算与10个叶节点），且该恒等式对所有实数(x,y)均成立（在代数语境下形式上对所有满足(ln circ exp)为恒等映射的复数(x,y)亦成立）。 判定结果：已证明（PROVED） 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` — 完整验证审计追踪 - `proof_narrative.md` — 通俗语言总结 - `proof.json` — 机器可读结构化数据 本结果由Proof Engine v1.18.0生成。