Metamath

A structured dataset of formally verified theorems and axioms from Metamath, one of the largest collections of rigorously verified mathematics in the world.

Source

• Repository: https://github.com/metamath/set.mm
• Commit: 160dfc7e4ec5f201f5bae4ca5a5eeb67242902b5
• Files: 5
• License: cc0-1.0

Schema

Column	Type	Description
statement	string	Declaration signature/claim with the leading keyword removed (verbatim slice); the full declaration minus its proof
proof	string	Verbatim proof/body, empty if the declaration has none
type	string	Declaration keyword
symbolic_name	string	Declaration identifier
library	string	Sub-library
filename	string	Repository-relative source path
imports	list[string]	File-level Require/Import modules
deps	list[string]	Intra-corpus identifiers referenced
docstring	string	Preceding documentation comment, empty if absent
source_url	string	Upstream repository
commit	string	Upstream commit extracted

Statistics

• Entries: 63,141
• With proof: 59,651 (94.5%)
• With docstring: 63,141 (100.0%)
• Libraries: 5

By type

Type	Count
$p	59,651
$a	3,490

Example

eqcomx |- R |= ( ( = B ) A )
$=
      ( ke kc ax-cb1 ax-refl a1i hb ht weq ax-ceq syl2anc wc ax-eqmp ) HBIZBIZH
      CIZBIZDUADTCIZDGJZABEKLZHUAIUCIDHTIUBIZUAUGDHHIHIZUDUHDUEAAMNZNHAOZKLGAUI
      BCHHUJUJEFPQUFAMBBTUBAUIHBUJERAUIHCUJFREEPQS $.

• type: $p | symbolic_name: eqcomx | hol.mm

Use

Each declaration is split into a statement (signature/claim) and a proof (body) that are disjoint and together form the complete declaration, for proof modeling, autoformalization, retrieval, and dependency analysis via deps.

Citation

@misc{metamath_dataset,
  title  = {Metamath},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/metamath/set.mm, commit 160dfc7e4ec5},
  url    = {https://huggingface.co/datasets/phanerozoic/Metamath}
}