IDEF-GeoBench

IDEF-GeoBench is a small, curated benchmark (n = 40) for Euclidean geometry reasoning and structured solution generation under a strict, machine-checkable input/output (I/O) format designed for programmatic checking and API-based evaluation.

• Dataset (Hugging Face): https://huggingface.co/datasets/sabakublashvili/idef-geobench
• API key / developer access: https://idef-mathematics.com/api

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Overview

Many Euclidean geometry problems can be expressed as formal constraints (incidence, perpendicularity, parallelism, equal lengths, cyclicity, tangency, ratios, etc.). In algebraic methods, these constraints translate to polynomial relations over coordinates; proving a goal becomes a stepwise derivation (e.g., coordinate model → generators → goal polynomial(s) → reductions + non-degeneracy conditions).

IDEF-GeoBench is designed to evaluate systems that can:

1. solve Euclidean geometry problems, and
2. return results in a structured format that can be parsed and validated automatically.

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What “strict I/O format” means

• Input (I): each problem is provided in a formal DSL encoding (entities + constraints + goal), not only as free-form natural language.
• Output (O): a solver is expected to return a structured final answer and/or an auditable reasoning trace that conforms to a required schema (e.g., JSON or a defined trace format).

This benchmark therefore measures both mathematical correctness and format compliance (machine-checkability).

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Dataset design

• Style: IMO-inspired Euclidean geometry problems (emphasis on formal structure).
• Scale: intentionally small (n = 40). Full IMO-level instances can be expensive to solve and verify end-to-end; this release is a public, sanity-checkable benchmark slice.
• Difficulty note: problems are “IMO-inspired” and may be simplified to fit practical compute constraints while preserving Olympiad-like structure.

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Data fields

Each dataset record includes (edit field names below to match your actual schema exactly):

• id (string): unique problem identifier
• description (string, optional): human-readable statement (when available)
• formal (string): the formal DSL text containing GIVEN: constraints and GOAL:
• meta (object, optional): tags such as difficulty, topic, source, etc.

If your dataset uses different key names (e.g., problem, goal, given, dsl), update this section to match the exact keys.

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Formal DSL (input)

Problems are represented using a constraint language with sections such as:

• GIVEN: entities and constraints
• GOAL: target property

Minimal semantics (core predicates)

The following interpretation is assumed (adjust if your DSL differs):

• POINTS A,B,C,... declares point symbols.
• COL A B C means points A, B, C are collinear.
• EQLEN A B C D means segment length |AB| equals |CD|.
• PERP A B C D means line AB is perpendicular to line CD.
  (If your DSL uses a different convention, document it here.)

If you support additional predicates (e.g., PARA, CIRC, TANG, MIDP, RATIO), list them with one-line semantics for reproducibility.

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Example formal instance (illustrative)

GIVEN:
POINTS A,B,C,O,T,L,T_A,L_A,T_B,L_B,T_C,L_C,M_TA,M_LA,M_TB,M_LB,M_TC,M_LC,P_A,P_B,P_C,M_PAB,M_PBC,O2,K
EQLEN O A O B
EQLEN O B O C
EQLEN O T O A
PERP O T T L
COL B C M_TA
EQLEN T M_TA M_TA T_A
PERP B C T T_A
COL B C M_LA
EQLEN L M_LA M_LA L_A
PERP B C L L_A
COL C A M_TB
EQLEN T M_TB M_TB T_B
PERP C A T T_B
COL C A M_LB
EQLEN L M_LB M_LB L_B
PERP C A L L_B
COL A B M_TC
EQLEN T M_TC M_TC T_C
PERP A B T T_C
COL A B M_LC
EQLEN L M_LC M_LC L_C
PERP A B L L_C
COL T_B L_B P_A
COL T_C L_C P_A
COL T_C L_C P_B
COL T_A L_A P_B
COL T_A L_A P_C
COL T_B L_B P_C
COL P_A P_B M_PAB
EQLEN P_A M_PAB M_PAB P_B
COL P_B P_C M_PBC
EQLEN P_B M_PBC M_PBC P_C
PERP P_A P_B M_PAB O2
PERP P_B P_C M_PBC O2
GOAL:
EQLEN O K O A
EQLEN O2 K O2 P_A
COL O O2 K