Automated mathematical proof generation with built-in A/B review loop. Given a theorem statement, spawns Agent A to produce a proof and Agent B to review it. If B rejects, A revises — loop continues until B accepts or a configurable retry limit is reached.
Activate when the user asks to prove a mathematical statement (theorem, proposition, lemma). Trigger keywords: "证明", "求证", "prove", "proof", "定理", "theorem", "推导", "demonstrate".
User: "prove that the medians of a triangle are concurrent"
┌─────────────────────────────────────────────────────────┐
│ 1. Ask user for configurations (feedback mode, refs) │
│ 2. Agent A produces a proof (spawned as subagent) │
│ 3. Agent B reviews the proof (spawned as subagent) │
│ 4. If B rejects → send feedback to A → revise │
│ 5. If B accepts → present final proof to user │
│ 6. Loop up to configurable max retries (default: 50) │
└─────────────────────────────────────────────────────────┘
Before spawning the first agent, ask the user for the following:
| Mode | Description |
|---|---|
| ------ | ------------- |
| 🔍 Hint-only | Only pass direction-level hints to A (e.g., "Step 3 was rejected because it assumed what needs to be proved"). A must figure out the fix independently. |
| 📝 With history | Direction hint + A's own previous proof text. A can base revisions on what it wrote before instead of starting from scratch. |
| 📋 Full disclosure | Direction hint + A's previous proof + B's complete review (error locations, suggestions, fix directions). Most informative for A. |
Default: Hint-only. If user doesn't specify, use hint-only.
Ask: "Do you want A and B to reference any local files or folders? (e.g., textbook chapters, lecture notes, theorem references)"
If yes, the user specifies a path (file or folder). Its contents will be included in every spawn prompt sent to both A and B as context/reference material.
The user may supply constraints that must be passed to both A and B:
These constraints must be included verbatim in every spawn prompt sent to both A and B.
{
"mode": "run",
"task": "请严格证明以下定理：\n\n[定理陈述]\n\n[参考材料（如有）]\n\n要求：\n[用户约束，逐条列出]\n\n用 LaTeX 格式输出完整证明。"
}
{
"mode": "run",
"task": "请严格审查以下证明。\n\n[证明全文]\n\n[参考材料（如有）]\n\n请逐行检查：\n1. 每一步的推理是否正确？\n2. 有没有逻辑漏洞或循环论证？\n3. 有没有违反用户要求的约束（[约束列表]）？\n4. 整体逻辑链是否完整？\n5. 评价：通过 / 需要修改（说明理由）"
}
Hint-only mode (默认):
{
"mode": "run",
"task": "请重新证明以下定理。之前的版本被驳回，需要修改。\n\n[定理陈述]\n\n[参考材料（如有）]\n\n你上一轮写的证明原文：\n[A上一轮的完整证明]\n\n提示：上一轮被驳回的原因是[方向性提示，不包含B的完整审查]。\n\n要求：\n[用户约束，逐条列出]\n\n用 LaTeX 格式输出完整证明。"
}
With-history mode:
{
"mode": "run",
"task": "请重新证明以下定理。之前的版本被驳回，需要修改。\n\n[定理陈述]\n\n[参考材料（如有）]\n\n你上一轮写的证明原文：\n[A上一轮的完整证明]\n\n提示：上一轮被驳回的原因是[方向性提示]。你可以参考自己之前写的证明进行修改。\n\n要求：\n[用户约束，逐条列出]\n\n用 LaTeX 格式输出完整证明。"
}
Full disclosure mode:
{
"mode": "run",
"task": "请重新证明以下定理。之前的版本被驳回，需要根据审查意见修改。\n\n[定理陈述]\n\n[参考材料（如有）]\n\n你上一轮写的证明原文：\n[A上一轮的完整证明]\n\n审查意见原文：\n[B的完整审查结果]\n\n要求：\n[用户约束，逐条列出]\n\n用 LaTeX 格式输出完整证明。"
}
🎉 证明通过！
[完整证明文本]
😿 已达到最大重试次数（N次），证明未能通过审查。
最后一份证明的问题：[概述]
> 三角形的三条中线交于一点（重心定理）
| Round | A Action | B Action | Result |
|---|---|---|---|
| ------- | ---------- | ---------- | -------- |
| 1 | 向量法证明 | B审查 | ❌ 违反约束（用了向量） |
| 2 | 综合法，相似三角形 | B审查 | ❌ 第三步逻辑漏洞 |
| 3 | 修正第三步 | B审查 | ❌ 循环论证 |
| 4 | 平行四边形构造 | B审查 | ❌ 未定义符号 |
| 5 | 新思路尝试 | B审查 | ❌ 方向错误 |
| 6 | 平行四边形+比例 | B审查 | ❌ 共线未证明 |
| 7 | 相似+唯一性 | B审查 | ❌ 论证不完整 |
| 8 | 修正表述 | B审查 | ❌ 根本逻辑问题 |
| 9 | 倍长中线法 | B审查 | ✅ 通过 |
共 1 个版本