jableable/metamath-proof-graphs

Metamath Proof Graphs (10k)

This repository provides a PyTorch Geometric dataset designed for the TAG-DS TopoBench challenge.
It contains 20,000 graphs total: 10,000 theorem-only DAGs and 10,000 full proof DAGs drawn from the first 10k theorems in the Metamath [1] database.

Contents

• data.pt
  A preprocessed PyG dataset containing:
  • data — global collated storage of all nodes, edges, and labels
  • slices — pointers for reconstructing individual graphs
  • train_idx, val_idx, test_idx — fixed graph-level splits

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Dataset Structure

1. Theorem Graphs (indices 0–9,999)

Each theorem is represented as a small DAG consisting only of:

• its hypothesis nodes
• its conclusion node
• no proof steps

These encode the statement only, not the derivation.

2. Proof Graphs (indices 10,000–19,999)

For each of the same theorems, the full proof DAG is included, containing:

• hypothesis nodes
• intermediate proof steps
• the same conclusion node

Thus each theorem appears twice:

1. once as a theorem-only graph
2. once as the complete proof of that theorem

This pairing enables:

• learning from theorem statements
• evaluating on masked proof conclusions
• consistent label space across both halves

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Additional Details

• Total graphs: 20,000
• Node embeddings: 768-dimensional CodeBERT vectors
• Graph type: directed acyclic graphs (DAGs)
• Label space: 3,557 justification labels, where all labels with <5 training occurrences are collapsed into UNK
• Conclusion masking: the conclusion node’s embedding is zeroed out; the model must infer its label from the structure and other nodes
• Monotonicity constraint: in Metamath, proofs only use theorems with index <= the current theorem, so later theorems never appear in earlier graphs
• Theorem-only graphs are included in training as prior knowledge for downstream proof prediction.

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Basic Usage

import torch

obj = torch.load("data.pt", weights_only=False)

data      = obj["data"]
slices    = obj["slices"]
train_idx = obj["train_idx"]
val_idx   = obj["val_idx"]
test_idx  = obj["test_idx"]

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Acknowledgements

Thanks to the Erdős Institute for providing the project-based, collaborative environment where key components of the preprocessing pipeline were first developed.

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References

[1] Metamath Official Site — https://us.metamath.org/index.html