Update README.md

README.md

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----
-license: cc-by-4.0
----
+---
+language:
+  - en
+  - code
+license: cc-by-4.0
+task_categories:
+  - translation
+tags:
+  - formal-verification
+  - theorem-proving
+  - interactive-theorem-provers
+  - lean4
+  - rocq
+  - coq
+  - isabelle
+  - hol-light
+  - code-translation
+pretty_name: ITPEval
+size_categories:
+  - 1K<n<10K
+---
+
+# ITPEval: Benchmarking Formal Translation Across Interactive Theorem Provers
+
+ITPEval is a benchmark for evaluating automated formal proof translation across four major interactive theorem provers (ITPs) spanning two logical foundations. It accompanies the NeurIPS 2026 paper *ITPEval: Benchmarking Formal Translation Across Interactive Theorem Provers*.
+
+## Dataset Summary
+
+The benchmark comprises **390 aligned files** spanning over 1,700 theorems and lemmas, each formalized in all four ITPs:
+
+| ITP | Foundation | File Extension |
+|---|---|---|
+| Lean 4 | Calculus of Inductive Constructions | `.lean` |
+| Rocq (Coq) | Calculus of Inductive Constructions | `.v` |
+| Isabelle/HOL | Higher-order logic | `.thy` |
+| HOL Light | Higher-order logic | `.ml` |
+
+Every theorem is present in all four ITPs (4-way intersection), yielding **12 balanced directed translation pairs** per file.
+
+## Data Files
+
+| File | Records | Description |
+|---|---|---|
+| `stmts.json` | 1,560 | Sorry-stripped theorem statements (390 theorems × 4 ITPs) |
+| `proofs.json` | 296 | Full proof files (74 theorems × 4 ITPs) |
+
+## Record Schema
+
+Each record is a JSON object with the following fields:
+
+| Field | Type | Description |
+|---|---|---|
+| `theorem_id` | int | Globally unique theorem identifier (1–390) |
+| `title` | string | Theorem name (e.g., `"circle_average"`, `"aime_1983_p1"`) |
+| `source` | string | Benchmark source: `"babel-formal"`, `"hundred-theorems"`, or `"minif2f"` |
+| `tier` | string | `"a"` (controlled/axiomatized) or `"b"` (ecosystem/library-dependent) |
+| `prover` | string | ITP system: `"lean4"`, `"rocq"`, `"isabelle"`, or `"hol-light"` |
+| `content` | string | Full file text (statement-only for `stmts.json`, complete proof for `proofs.json`) |
+| `split` | string | *(miniF2F only)* `"test"` or `"valid"` |
+
+## Benchmark Structure
+
+The benchmark is organized into two tiers:
+
+| Tier | Source | Files | Lemmas | Description |
+|---|---|---|---|---|
+| A (Controlled) | Babel-formal | 16 | 165 | Self-contained, axiomatized theorems. Isolates foundational translation difficulty. |
+| B (Ecosystem) | Hundred Theorems | 58 | 1,231 | Classical theorems from real ITP libraries. Tests library API and tactic translation. |
+| B (Ecosystem) | miniF2F | 316 | 316 | Competition math statements. Tests pure statement translation. |
+
+**Translation modes:**
+
+- **Statement translation** (`stmts.json`): All 390 files. Source file has proof bodies replaced by placeholders (`sorry`, `Admitted`, etc.). Yields 4,680 directed pairs per model (390 × 12 directions).
+- **Proof translation** (`proofs.json`): Babel-formal + Hundred Theorems (74 files). Source file contains the complete proof. Yields 888 directed pairs per model (74 × 12 directions).
+
+## Usage
+
+```python
+import json
+
+# Load data
+stmts  = json.load(open("stmts.json"))   # 1,560 records
+proofs = json.load(open("proofs.json"))   # 296 records
+
+# All Lean 4 statements
+lean4_stmts = [r for r in stmts if r["prover"] == "lean4"]
+
+# All 4 ITP variants of one theorem
+theorem_1 = [r for r in stmts if r["theorem_id"] == 1]
+
+# Generate all directed translation pairs for a theorem
+def translation_pairs(records, theorem_id):
+    variants = [r for r in records if r["theorem_id"] == theorem_id]
+    pairs = []
+    for src in variants:
+        for tgt in variants:
+            if src["prover"] != tgt["prover"]:
+                pairs.append({"src": src, "tgt_prover": tgt["prover"]})
+    return pairs
+
+# Tier A only (controlled)
+tier_a = [r for r in stmts if r["tier"] == "a"]
+
+# miniF2F test split
+minif2f_test = [r for r in stmts if r["source"] == "minif2f" and r.get("split") == "test"]
+```
+
+## Evaluation Protocol
+
+For each (source file, target ITP) pair:
+
+1. Prompt an LLM with the source file and the target ITP name
+2. The LLM generates a complete file in the target ITP
+3. Run the generated file through the target ITP binary
+4. Mark as **verified** if and only if the ITP exits with code 0 (no errors, no partial credit)
+
+Per-prover timeouts: Lean 4 and Rocq at 60s, Isabelle at 120s, HOL Light at 300s.
+
+## Key Results
+
+With five LLMs (GPT-5.5, Claude Sonnet 4.6, Gemini 3.1 Pro, DeepSeek-V4-Pro, Qwen3-235B), evaluated zero-shot at temperature 0:
+
+- Statement translation peaks at **29.1%** pass@1; proof translation peaks at **10.5%**
+- Tier A (controlled) reaches **29.7%** proof pass@1 vs. **5.2%** for Tier B (ecosystem)
+- Translation direction matters sharply: e.g., Lean 4 → Isabelle (19.8%) vs. Isabelle → Lean 4 (1.9%)
+
+
+## License
+
+This dataset is released under [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). Individual formalizations may inherit licenses from their upstream sources (Mathlib, Archive of Formal Proofs, HOL Light core, MathComp, miniF2F).