added the released Stage 1 final evaluation subsets: evaluation_normal, evaluation_hard, evaluation_extra_hard, and evaluation_order5
added metadata files for the new evaluation subsets
updated the README and metadata to reflect the current released subsets

Update (March 24, 2026)

This dataset was updated on March 24, 2026.

Main changes:

added eq1_id and eq2_id to all released subsets
added the hard3 subset
updated the README to reflect the current released subsets

This dataset contains selected problem subsets for the Mathematics Distillation Challenge: Equational Theories, including public training subsets and released Stage 1 evaluation subsets.

This dataset is intended for Stage 1 of the Mathematics Distillation Challenge: Equational Theories competition.

Competition page:

https://competition.sair.foundation/competitions/mathematics-distillation-challenge-equational-theories-stage1/overview

The full raw implication dataset contains 4694 laws, which yields 4694 * (4694 - 1) = 22,028,942 ordered implications.

The full raw implications table can be downloaded from the Equational Theories Project implications page by selecting Download raw implications table:

https://teorth.github.io/equational_theories/implications/

The full list of all 4694 equations is available here:

equations.txt

Because the full raw dataset is very large, the competition organizers selected public subsets to make testing and experimentation more practical for participants.

Subsets

normal: 1000 selected problems, chosen programmatically, with 500 ground-truth TRUE labels and 500 ground-truth FALSE labels
hard: 200 selected problems co-curated by human mathematicians and AI, with 74 ground-truth TRUE labels and 126 ground-truth FALSE labels
hard1: a deduplicated version of the 200-problem hard subset, containing 69 unique problems total, with 24 ground-truth TRUE labels and 45 ground-truth FALSE labels
hard2: 200 selected problems co-curated by human mathematicians and AI, with 100 ground-truth TRUE labels and 100 ground-truth FALSE labels
hard3: 400 selected problems with 195 ground-truth TRUE labels and 205 ground-truth FALSE labels
evaluation_normal: 200 Stage 1 final evaluation problems, with 100 ground-truth TRUE labels and 100 ground-truth FALSE labels
evaluation_hard: 200 Stage 1 final evaluation problems, with 100 ground-truth TRUE labels and 100 ground-truth FALSE labels
evaluation_extra_hard: 200 Stage 1 final evaluation problems, with 100 ground-truth TRUE labels and 100 ground-truth FALSE labels
evaluation_order5: 200 order-5 evaluation problems, with 100 ground-truth TRUE labels and 100 ground-truth FALSE labels

All subsets are exposed as the train split in this repository. The evaluation_* subsets are released Stage 1 evaluation subsets.

Data Schema

Each record has the following fields:

id: stable identifier such as normal_0001, hard_0001, hard3_0001, or evaluation_normal_0001
index: 1-based index within the subset
difficulty: subset difficulty label such as normal, hard, extra_hard, or order5_normal
eq1_id: 1-based equation identifier for equation1; for the order-4-and-below subsets, this refers to the full 4694-law equation list
eq2_id: 1-based equation identifier for equation2; for the order-4-and-below subsets, this refers to the full 4694-law equation list
equation1: Equation 1
equation2: Equation 2
answer: whether Equation 1 implies Equation 2 over all magmas

Subset Metadata

Subset-level metadata for the official released subsets is stored under metadata/.

Each metadata file contains:

subset_name: subset identifier
source: release source, such as official
curators: list of named curators, if provided
difficulty: subset difficulty label
problem_count: total number of problems in the subset
true_count: number of ground-truth TRUE labels
false_count: number of ground-truth FALSE labels
selection_method: high-level selection method such as programmatic, human, or human_ai
derived_from: parent subset name if the subset is derived from another subset
notes: optional explanatory notes

Records in hard1, hard2, and hard3 use subset-specific IDs and keep difficulty: hard. Records in evaluation_order5 use order-5 equation identifiers.

Usage

from datasets import load_dataset

normal = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "normal",
    split="train",
)

hard = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "hard",
    split="train",
)

hard1 = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "hard1",
    split="train",
)

hard2 = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "hard2",
    split="train",
)

hard3 = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "hard3",
    split="train",
)

evaluation_normal = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "evaluation_normal",
    split="train",
)

evaluation_hard = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "evaluation_hard",
    split="train",
)

evaluation_extra_hard = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "evaluation_extra_hard",
    split="train",
)

evaluation_order5 = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "evaluation_order5",
    split="train",
)

Files

data/normal.jsonl
data/hard.jsonl
data/hard1.jsonl
data/hard2.jsonl
data/hard3.jsonl
data/evaluation_normal.jsonl
data/evaluation_hard.jsonl
data/evaluation_extra_hard.jsonl
data/evaluation_order5.jsonl
metadata/normal.json
metadata/hard.json
metadata/hard1.json
metadata/hard2.json
metadata/hard3.json
metadata/evaluation_normal.json
metadata/evaluation_hard.json
metadata/evaluation_extra_hard.json
metadata/evaluation_order5.json

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