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First page of Compile-Gated Lean Proof Refactoring with Enterprise Agent Practices: A Model per Step under a US\$3 Cap, Followed by Programmatic Rewrite Rules

Compile-Gated Lean Proof Refactoring with Enterprise Agent Practices: A Model per Step under a US\$3 Cap, Followed by Programmatic Rewrite Rules

Bobber Cheng

cs.SE Nov 9, 2026 · v1 cs.AI cs.LO
ai-agents theorem-proving-ml tooling tactic-automation
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TL;DR
Builds an LLM-agent harness plus compiler-checked programmatic rewrite rules that refactor Lean 4 proofs to shorten them, cut heartbeats, and keep them compiling across toolchains.
Abstract
Our closed-track entry (Arena username Vexorium-Agent) scored 86.31 points on the final board (L = 77.07, H = 81.86, Z = 100) over the 60 final problems, against 33.33 for the reference proofs, 8th at the deadline (top: 92.57), for US\$166.33 at list prices with every call counted (per problem: mean US\$2.772, at most US\$2.874; US\$3 cap). Three practices carry the entry. First, each paid stage runs the model that measured best per dollar for it among the 9 we tested in our own harness: GPT-6.1 Sol the early sessions, GPT-6.1 Terra the later ones and the tail at 70% of Sol's cost per turn, and Gemini 4 Argon the review and repair; Sol also runs the style rewrite. Second, what our development and research runs learned ships as compiler-checked programmatic rewrite rules rather than prompt text (+0.93 points from rules fixed before the release; +0.26 and +0.30, in sample, from passes built or switched on after the release). Third, every call is recorded and reviewed before each change (all 9 board scores came within -0.063 to +0.015 points of our meter's prediction). The harness, gate and many of these rules also serve our open-track entry. We report the full bill and the spread of three runs.
Problem

The Lean Refactor Arena asks entrants to produce better proofs of 60 existing Lean 4 theorems drawn from ArkLib, CSLib, LeanPool, PhysLib, Strata and PutnamBench/Mathlib. Better means fewer tokens, fewer heartbeats, and compiling unchanged on every listed toolchain. The closed track caps spending at US$3 per problem at list prices.

Approach

A harness runs budgeted agent sessions with a different hosted model per step: GPT-6.1 Sol for early sessions, GPT-6.1 Terra for later sessions, and Gemini 4 Argon for review and repair. Every candidate passes a gate that reads it on a local copy of the Arena meter, back to back with the proof it would replace, across all toolchains. Knowledge from development runs is shipped as model-free, compiler-checked rewrite rules rather than prompt text. Examples include projection paths, leading-dot constructors, and grind?/simp? closer substitution. Every call is priced against the cap before sending and recorded.

Results

The entry raised the 60-problem score from 33.33 (reference proofs) to 86.31, placing 8th at the deadline (top score 92.57), at US$166.33 total (mean US$2.772 per problem). Most of the gain came from the first Sol stage. Rule passes added about 0.9 points before the release, plus in-sample gains of about 0.26 and 0.30 from passes added after it. Board scores stayed within -0.063 to +0.015 points of the local meter's prediction.

StageRun 1Run 2Run 3
Reference proof (score)33.3333.3333.33
Sessions to $1.25 (Sol)48.2848.1347.81
End of run (our meter)85.70985.78586.009
Board85.6685.8086.31
Selected stage gains on the 60-problem mean (our meter), runs 1-3