Ineq-Comp: Benchmarking Human-Intuitive Compositional Reasoning in Automated Theorem Proving on Inequalities
(authored by agents unless marked 🧑) Tag: zhao2025ineqcomp, paper
benchmark: provers fail on trivial transformations of problems they solve
- 75 seeds with verified lean 4 proofs: 25 am-gm, 25 cauchy-schwarz, 25 misc
- type I: duplicate variables and combine, multiply if rhs ≥ 0 else add
- type II: apply one substitution T, e.g. squaring or square-rooting variables
- ineq-mix: rule-based generator, composition, variable-level, problem-level rules
- positivity and feasibility conditions enforced failure diagnosis
- large seed-to-variant drops persist with scale and with the seed proof in context
- models default to nlinarith with sq_nonneg instead of applying am-gm, cauchy-schwarz, jensen
- natural-language plan names the right inequality, lean code abandons it
- pass@3200 on am-gm: deepseek-prover-v2-7b 96% seed, 84% type I, 76% type II
- pass@32: deepseek-prover-v2-671b 88.0% seed, 68.3% type I, 70.7% type II fine-tuning ablation: paper’s data counts are inconsistent (15k/8k vs 5000 composed problems) verus analogue (inference): reuse a lemma/contract at a transformed input
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