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Datasets:
phanerozoic
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Mizar

Tasks:
Text Generation
Feature Extraction
Modalities:
Text
Formats:
parquet
Languages:
English
Size:
10K - 100K
Tags:
theorem-proving
formal-methods
mizar
set-theory
mathematics
Libraries:
Datasets
pandas
Polars
License:
Dataset card Data Studio Files
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 Community
Mizar / README.md
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License: reflect MML dual-license (GPL-3.0 or CC-BY-SA-3.0)
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metadata 
license:
  - gpl-3.0
  - cc-by-sa-3.0
tags:
  - theorem-proving
  - formal-methods
  - mizar
  - set-theory
  - mathematics
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
size_categories:
  - 10K<n<100K

Mizar

A structured dataset of theorems and schemes from the Mizar Mathematical Library (MML), one of the largest libraries of formalized mathematics.

Source

Statistics

Property Value
Total Entries 31,246
Theorems 30,606
Schemes 640
Articles 1,153
Docstring Coverage 100%

Schema

Column Type Description
fact string Theorem statement in Mizar syntax
type string "theorem" or "scheme"
library string Article name
imports list[string] Environ section (vocabularies, notations, etc.)
filename string Source .miz file
symbolic_name string Article:Label identifier
docstring string Article title

About Mizar

Mizar is known for:

  • Natural language-like proof style
  • Tarski-Grothendieck set theory foundation
  • Extensive library covering algebra, topology, analysis
  • Named results: Hahn-Banach, Jordan curve theorem, etc.

Mizar Syntax

  • for x holds P[x] - universal quantification
  • ex x st P[x] - existential quantification
  • x in X - set membership
  • X c= Y - subset relation
  • iff - biconditional

Creator

Charles Norton (phanerozoic)