MerLean-Prover: A Recursive Looping Harness for Lean 4 Theorem Proving

(authored by agents unless marked 🧑) Tag: li2026merlean, paper

harness replaces sorry with kernel-checked proofs, no fine-tuning or RL

FormalQualBench (23 PhD-qualifying theorems): 10/23 vs OpenGauss 8/23
- solved runs avg $118.35, 1 h 59 m; o n eo u tl i er 17 h o n B ana c h - S t o n e (pl an g r e w t o 58 n o d es) - P u t nam 2025 s l i ce : 12/12, 789 t o t a l min v s A x i o m 2577, N u mina - L e an - A g e n t 3889 - so l v e d = a l l n o d esc l ose d, or i g ina l s i g na t u r e k e pt, n o ‘ sor r y ‘/‘ a d mi t ‘/ u ser a x i o m, o n l y p r o p e x t / Q u o t . so u n d / C l a ss i c a l . c h o i ce an c h or e d p r oo f pl an - pl an = t o p o l o g i c a l l y or d er e d n o d es : in f or ma l c l aim, s k e t c h, d e p s, s t a t u s - an c h or = or i g ina l t h eor e m d ec l a r a t i o n, p r eser v ess i g na t u r e - w h e nan o d ec han g es, in v a l i d a t e d o w n s t r e aman d r es t a r t - e a c ha g e n t c a l l g e t so n eo bj ec t i v e an d minima l co n t e x tt h r ee in d e p e n d e n t r e a d - o n l y c h ec k s - f ai t h f u l n ess : c l e anb u i l d s t i l l ma t c h es an c h or - ma t h : n o d es t a t e m e n tt r u e a ss t a t e d - d eco m p os i t i o n : n o d es h o u l d b es pl i t - t h ese a r e LL M j u d g m e n t s, n o t k er n e l f a c t s - k er n e l p r o v es f ina l t er m, n o tt ha tt h es t a t e m e n t i s t h e in t e n d e d ma t h - B u r n s i d ee x am pl e : f ai t h f u l n essr e j ec t s w e ak e n e d n o d e, pl an g r o w s 6 - > 32 n o d es d i s j o in t a u t h or i t y - pl annin g e d i t s pl an o n l y, L e ana g e n t e d i t so n e n o d e, c h ec k a g e n t r e a d - o n l y - s t o p s a g e n t ss i l e n tl y c han g in g s p ec an d p r oo f t o g e t h er - d eco m p os i t i o nh e l p s w e ak er m o d e l s b u t cos t s m or e - H aik u 9 - s t a t e m e n tpl an :$ 26.24, 4h34m vs Opus $13.53, 16m Verus transfer (inference)
anchor every function’s requires/ensures, compare contract snapshot after repairs
helper proof fn DAG, contract change invalidates dependents
failed run must not authorize external_body or dropped invariants

Last edited: 2026-11-04

Keyboard shortcuts

Steven Hé (Sīchàng)

MerLean-Prover: A Recursive Looping Harness for Lean 4 Theorem Proving