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Datasets:
nph4rd
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eleusis-rules

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Tags:
eleusis
induction
reasoning
rules
card-games
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pandas
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(value % 5 != prev_value % 5) and (value != min(values))
(value % 2 != prev_value % 2) or (value % 2 == n % 2)
(color == prev_color) and (abs(value - prev_value) != 3)
(color != prev_color) and (value % 6 == prev_value % 6)
(value % 6 != prev_value % 6) or (value >= max(values))
(color != prev_color) or (value >= max(values))
(abs(value - prev_value) == 5) or (value > min(values))
(value < prev_value) or (value == prev_value + 3)
(value % 3 == prev_value % 3) and (value <= min(values))
(value > max(values)) or (value < min(values))
(abs(value - prev_value) < 1) or (abs(value - prev_value) > 7)
(suit != prev_suit) and (abs(value - prev_value) == 2)
(abs(value - prev_value) == 6) or (value % 5 == n % 5)
(abs(value - prev_value) <= 7) or (value % 4 == n % 4)
(abs(value - prev_value) > 7) or (value == prev_value + 2)
(abs(value - prev_value) != 5) and (value >= min(values))
(abs(value - prev_value) < 5) and (value == min(values))
value > prev_value if suit == prev_suit else value < prev_value
(value % 6 == prev_value % 6) or (abs(value - prev_value) < 5)
(value % 5 == prev_value % 5) or (abs(value - prev_value) < 3)
value < prev_value if color == prev_color else value > prev_value
(abs(value - prev_value) > 6) or (value == prev_value + 2)
(value != prev_value) and (abs(value - prev_value) != 4)
(abs(value - prev_value) == 6) or (value > min(values))
(value == max(values)) or (value == prev_value + 1)
(value % 4 == prev_value % 4) or (value == min(values))
(abs(value - prev_value) > 7) or (value != min(values))
(abs(value - prev_value) <= 7) or (value != max(values))
(value >= max(values)) or (value < min(values))
(abs(value - prev_value) == 5) or (value < max(values))
(value <= prev_value) and (abs(value - prev_value) != 1)
(suit != prev_suit) or (value == prev_value + 1)
(abs(value - prev_value) > 3) or (value != max(values))
(value != prev_value) and (abs(value - prev_value) < 4)
(color == prev_color) and (value % 2 != prev_value % 2)
(abs(value - prev_value) == 5) or (value != min(values))
(abs(value - prev_value) != 3) and (abs(value - prev_value) <= 7)
(abs(value - prev_value) != 7) and (value <= max(values))
(abs(value - prev_value) != 6) or (value <= min(values))
(value < prev_value) or (value >= prev_value + 3)
(color == prev_color) and (abs(value - prev_value) < 4)
(color != prev_color) or (value % 5 == prev_value % 5)
(abs(value - prev_value) == 6) or (value % 4 == n % 4)
(suit != prev_suit) or (value == prev_value + 2)
(value != prev_value) and (abs(value - prev_value) != 3)
value > prev_value if suit == prev_suit else color != prev_color
(suit == prev_suit) or (value % 3 != prev_value % 3)
(value % 3 != prev_value % 3) and (abs(value - prev_value) > 2)
(abs(value - prev_value) < 4) or (value > min(values))
(suit != prev_suit) or (value >= min(values))
(value == prev_value + 2) or (value <= prev_value - 3)
(abs(value - prev_value) != 7) or (value % 2 == n % 2)
value >= prev_value if color == prev_color else value < prev_value
value % 2 == n % 2
(abs(value - prev_value) > 5) or (value < min(values))
(abs(value - prev_value) != 3) or (value >= min(values))
(abs(value - prev_value) != 1) or (value == max(values))
(abs(value - prev_value) > 2) and (abs(value - prev_value) != 6)
(color == prev_color) or (abs(value - prev_value) < 5)
(abs(value - prev_value) != 5) and (value <= min(values))
(suit == prev_suit) and (value % 2 == prev_value % 2)
(abs(value - prev_value) != 1) and (value >= max(values))
(color == prev_color) and (abs(value - prev_value) < 3)
(abs(value - prev_value) == 5) and (value >= min(values))
(abs(value - prev_value) > 1) and (abs(value - prev_value) <= 7)
(value < prev_value) or (value % 6 != prev_value % 6)
(value % 2 != prev_value % 2) or (value > min(values))
(value <= prev_value - 2) or (value == prev_value + 3)
(abs(value - prev_value) > 5) or (value % 3 == n % 3)
(value > min(values)) or (value < max(values))
(abs(value - prev_value) == 6) or (value < min(values))
(value + prev_value) % 5 == 2
(value % 2 != prev_value % 2) and (value % 5 != prev_value % 5)
(value % 6 == prev_value % 6) or (value <= prev_value - 2)
value % 4 == prev_value % 4
(suit == prev_suit) or (value != max(values))
(value >= prev_value) and (abs(value - prev_value) < 4)
(value % 3 != prev_value % 3) or (abs(value - prev_value) < 7)
(value % 3 != prev_value % 3) or (abs(value - prev_value) > 7)
(abs(value - prev_value) == 6) or (value >= max(values))
(abs(value - prev_value) < 4) or (abs(value - prev_value) > 6)
(suit == prev_suit) or (abs(value - prev_value) == 2)
(abs(value - prev_value) != 4) or (value == max(values))
(value % 3 != prev_value % 3) and (value % 5 != prev_value % 5)
(value != max(values)) or (value % 3 == n % 3)
(value % 5 != prev_value % 5) or (value > min(values))
(value < prev_value) or (value % 5 != prev_value % 5)
(value < prev_value) or (value == prev_value + 1)
(abs(value - prev_value) < 6) or (value % 3 == n % 3)
(value % 5 != prev_value % 5) and (abs(value - prev_value) != 6)
(color != prev_color) or (value % 5 == n % 5)
(abs(value - prev_value) != 6) or (value < min(values))
value >= prev_value if color != prev_color else value % 2 != prev_value % 2
(value <= prev_value) or (value % 6 != prev_value % 6)
(value != prev_value) and (abs(value - prev_value) < 6)
(abs(value - prev_value) > 3) or (value >= prev_value + 2)
(abs(value - prev_value) < 5) or (value % 3 == n % 3)
(value >= prev_value) and (value % 3 == n % 3)
(suit == prev_suit) or (value % 6 == prev_value % 6)
(value % 4 == prev_value % 4) and (abs(value - prev_value) != 4)
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Eleusis Rules

Secret induction rules for the eleusis single-agent environment — a faithful, full 52-card implementation of the card game Eleusis Express, where a model discovers a hidden card-sequence rule by playing (with mainline/sideline, No-Play, rule-guessing, and authentic scoring). This dataset is the rule bank the environment draws its secret rules from.

Each row is one rule over a standard 52-card deck: suits C/D/H/S × ranks 1–13 (A=1, J=11, Q=12, K=13), with color derived from suit (D,H = Red; C,S = Black).

Splits

split rows
train 1873
test 465

An 80/20 stratified split: rules are bucketed by a label-free structural signature (which card attributes and operator classes they use — suit/color, modular, absolute-difference, history aggregates, boolean compounds, conditionals) and each bucket is split 80/20, so train and test share the same structural distribution (per-bucket shares match within ~0.1%).

Schema

column type description
rule string a Python boolean expression deciding whether a card may legally follow the previous card 
from datasets import load_dataset
train = load_dataset("nph4rd/eleusis-rules", split="train")
test  = load_dataset("nph4rd/eleusis-rules", split="test")
test[0]   # {'rule': 'suit != prev_suit'}

The rule DSL

A rule is a sandboxed boolean Python expression over a fixed namespace describing the candidate card, the legal sequence so far, and the previous card:

value (=rank), rank, suit, color, prev_value, prev_rank, prev_suit, prev_color, values, ranks, suits, colors, n (plus abs/len/min/max/sum). Examples:

suit != prev_suit
color != prev_color
value >= prev_value
value % 3 == prev_value % 3
abs(value - prev_value) <= 3
value == prev_value if color != prev_color else value > prev_value

How the rules were produced

  1. Enumerate a broad space of relational rule expressions over the 52-card DSL (suit/color patterns, order, parity/modular, absolute-difference, products, history aggregates, boolean compounds, conditionals).
  2. Validate each against the faithfulness guard: every card in the deck must be legal in some reachable sequence state (no card permanently excluded, no terminating condition) and the rule must discriminate (reject some card in some state) — Express's "the rule should at some point encompass every card, with no condition that terminates the sequence". Impossible and purely card-intrinsic rules are removed; only genuinely sequence-dependent rules survive.
  3. Deduplicate by behavioral signature (legality over a fixed probe set of histories), so functionally-identical surface forms collapse to a single canonical entry.

The result is 2338 functionally-distinct, guaranteed-playable rules. Difficulty coverage is emergent — from trivial suit/color alternation to compound conditional and history-dependent rules — with no manual difficulty/family labels.

Related

  • nph4rd/eleusis-small-rules — the analogous bank on an abstract 16-card deck, used as a single-agent induction benchmark.
  • Used by the eleusis verifiers environment; see its README for the full game protocol (play / No-Play / guess), the draw-from-stock mechanic, and the authentic 12 − cards_left + 6·guess + 3·empty scoring.
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Number of rows:
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Total file size:
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