Solved demos

Each picture is a committed corpus record, solved when this site was built and drawn on the same canvas the editor extension uses -- nothing is a screenshot or retyped, and if the engine stopped answering a record the way it says, this page would not build. A puzzle demonstrates the inference, not the intended application.

Every one of the 61 checks these 22 records answer arrives with a reason.

temporalknights-knavesplantedcategoricalquantitiesdimensionalpigeonholesatisfaction

The baton changes handsThe flight puzzleA negative offsetOne given removedFour checks, three verdictsFive in a chainThree in a chainNot bounded by the typeTravelling twiceAn unconstrained departure

cleo.cleo_0920 — Derived in 21 steps over 21 facts, from 10 of the record's givens.
cleo.bram_0920 — Answered from 15 of the record's givens, and the step names which of them were needed rather than why they force it.
cleo.anna_0830 — Derived in 24 steps over 24 facts, from 7 of the record's givens.
cleo.esme_0959 — Answered from 7 of the record's givens, and the step names which of them were needed rather than why they force it.
cleo.cleo_0916 — Derived in 21 steps over 21 facts, from 10 of the record's givens.
cleo.bram_at_handoff — Two worlds satisfy every statement and disagree about cleo.bram_at_handoff: holds_at(HOLDS(holder=bram), occurrence.bram_to_cleo) is true in one and false in the other. Nothing the record states rules either out, so the givens do not decide it.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

UNKNOWN does not mean the solver gave up. Two worlds satisfy every statement and disagree about this check, so the givens genuinely do not decide it.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`

avery.A — Two worlds satisfy every statement and disagree about avery.A: occurrence.avery_departs is {"num": 380, "den": 1} in one and {"num": 4, "den": 1} in the other. Nothing the record states rules either out, so the givens do not decide it.
blake.B — Two worlds satisfy every statement and disagree about blake.B: occurrence.avery_departs is {"num": 510, "den": 1} in one and {"num": 4, "den": 1} in the other. Nothing the record states rules either out, so the givens do not decide it.
blake.C — Derived in 5 steps over 6 facts, from 2 of the record's givens.
blake.D — Two worlds satisfy every statement and disagree about blake.D: occurrence.avery_departs is {"num": 0, "den": 1} in one and {"num": 510, "den": 1} in the other. Nothing the record states rules either out, so the givens do not decide it.
casey.E — Two worlds satisfy every statement and disagree about casey.E: occurrence.casey_departs is {"num": 0, "den": 1} in one and {"num": 441, "den": 1} in the other. Nothing the record states rules either out, so the givens do not decide it.

UNKNOWN does not mean the solver gave up. Two worlds satisfy every statement and disagree about this check, so the givens genuinely do not decide it.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`

alice.alice_actual — The check is one of the facts already established: the step identifies it, from 1 of the record's givens.
alice.alice_wrong — Answered from 1 of the record's givens, and the step names which of them were needed rather than why they force it.
bob.bob_actual — Derived in 5 steps over 6 facts, from 2 of the record's givens.
carol.carol_actual — Derived in 8 steps over 10 facts, from 3 of the record's givens.
carol.carol_after_alice — Derived in 10 steps over 9 facts, from 2 of the record's givens.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`
Generator	`guardrail_gamut.cases.generated_temporal:ChainScenario`
alice_minutes	`430`
bob_offset	`95`
carol_offset	`-20`
carol_stated	`1`

alice.alice_actual — The check is one of the facts already established: the step identifies it, from 1 of the record's givens.
alice.alice_wrong — Answered from 1 of the record's givens, and the step names which of them were needed rather than why they force it.
bob.bob_actual — Derived in 5 steps over 6 facts, from 2 of the record's givens.
carol.carol_actual — Two worlds satisfy every statement and disagree about carol.carol_actual: occurrence.carol_departs is {"num": 505, "den": 1} in one and {"num": 4, "den": 1} in the other. Nothing the record states rules either out, so the givens do not decide it.
carol.carol_after_alice — Two worlds satisfy every statement and disagree about carol.carol_after_alice: occurrence.carol_departs is {"num": 431, "den": 1} in one and {"num": 0, "den": 1} in the other. Nothing the record states rules either out, so the givens do not decide it.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

UNKNOWN does not mean the solver gave up. Two worlds satisfy every statement and disagree about this check, so the givens genuinely do not decide it.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`
Generator	`guardrail_gamut.cases.generated_temporal:ChainScenario`
alice_minutes	`430`
bob_offset	`95`
carol_offset	`-20`
carol_stated	`0`

blake.B — Answered from 3 of the record's givens, and the step names which of them were needed rather than why they force it.
blake.C — Derived in 5 steps over 6 facts, from 2 of the record's givens.
blake.D — Derived in 6 steps over 7 facts, from 3 of the record's givens.
casey.E — Two worlds satisfy every statement and disagree about casey.E: occurrence.casey_departs is {"num": 0, "den": 1} in one and {"num": 441, "den": 1} in the other. Nothing the record states rules either out, so the givens do not decide it.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

UNKNOWN does not mean the solver gave up. Two worlds satisfy every statement and disagree about this check, so the givens genuinely do not decide it.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`

bram.bram_on_time — Derived in 5 steps over 6 facts, from 2 of the record's givens.
cleo.cleo_on_time — Derived in 8 steps over 10 facts, from 3 of the record's givens.
dimi.dimi_on_time — Derived in 11 steps over 13 facts, from 4 of the record's givens.
esme.esme_on_time — Derived in 14 steps over 16 facts, from 5 of the record's givens.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`

bob.bob_at_1030 — Derived in 5 steps over 6 facts, from 2 of the record's givens.
carol.carol_at_1100 — Answered from 3 of the record's givens, and the step names which of them were needed rather than why they force it.
carol.carol_after_alice — Derived in 10 steps over 9 facts, from 2 of the record's givens.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`

carol.carol_within_the_day — Two worlds satisfy every statement and disagree about carol.carol_within_the_day: occurrence.carol_departs is {"num": 0, "den": 1} in one and {"num": -1, "den": 1} in the other. Nothing the record states rules either out, so the givens do not decide it.

UNKNOWN does not mean the solver gave up. Two worlds satisfy every statement and disagree about this check, so the givens genuinely do not decide it.

Provenance

Field	Value
Origin	`authored`

alice.alice_at_0900 — The conflict is drawn: 1 of the record's givens cannot all hold, and nothing is derived about the check from them.

INCONSISTENT_BASE is a statement about the givens, not about the check beside it. Nothing is being claimed about the check; the premises are being refused, because no world satisfies them all.

Provenance

Field	Value
Origin	`authored`

carol.carol_at_1115 — Two worlds satisfy every statement and disagree about carol.carol_at_1115: occurrence.carol_departs is {"num": 675, "den": 1} in one and {"num": 4, "den": 1} in the other. Nothing the record states rules either out, so the givens do not decide it.

UNKNOWN does not mean the solver gave up. Two worlds satisfy every statement and disagree about this check, so the givens genuinely do not decide it.

Provenance

Field	Value
Origin	`authored`

More than one solutionOne solution

The same island, with claims that leave one islander undetermined: two assignments satisfy every statement and disagree about Daniel.

jacob_is_a_knight — Answered from 1 of the record's givens, and the step names which of them were needed rather than why they force it.
daniel_is_a_knight — Two worlds satisfy every statement and disagree about daniel_is_a_knight: daniel.kind is knight in one and knave in the other. Nothing the record states rules either out, so the givens do not decide it.
victoria_is_a_knight — The check is one of the facts already established: the step identifies it, from 2 of the record's givens.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

UNKNOWN does not mean the solver gave up. Two worlds satisfy every statement and disagree about this check, so the givens genuinely do not decide it.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`reasoning-gym`
Licence	`Apache-2.0`
Revision	`reasoning-gym 0.1.25`
Generator	`reasoning_gym.logic.knights_knaves:KKProblemSampler,KKProblemFormatter`
depth_constraint	`2`
formatter_seed	`1`
index	`0`
n_people	`3`
n_problems	`1`
rand_seed	`1`
skip_multiple_solutions	`0`
skip_no_solution	`1`
width_constraint	`2`

Three islanders, each a knight who only tells the truth or a knave who only lies, each making a claim about the others.

aurora_is_a_knight — Answered from 2 of the record's givens, and the step names which of them were needed rather than why they force it.
sebastian_is_a_knight — Answered from 2 of the record's givens, and the step names which of them were needed rather than why they force it.
grace_is_a_knight — Answered from 2 of the record's givens, and the step names which of them were needed rather than why they force it.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`reasoning-gym`
Licence	`Apache-2.0`
Revision	`reasoning-gym 0.1.25`
Generator	`reasoning_gym.logic.knights_knaves:KKProblemSampler,KKProblemFormatter`
depth_constraint	`2`
formatter_seed	`7`
index	`0`
n_people	`3`
n_problems	`1`
rand_seed	`7`
skip_multiple_solutions	`1`
skip_no_solution	`1`
width_constraint	`2`

A planted solutionPlanted, with no range statedA planted contradiction

in_range — Answered from 1 of the record's givens, and the step names which of them were needed rather than why they force it.
below_range — Answered from 1 of the record's givens, and the step names which of them were needed rather than why they force it.
at_witness — Two worlds satisfy every statement and disagree about at_witness: s_0 is 1 in one and 0 in the other. Nothing the record states rules either out, so the givens do not decide it.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

UNKNOWN does not mean the solver gave up. Two worlds satisfy every statement and disagree about this check, so the givens genuinely do not decide it.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`
Generator	`guardrail_gamut.generation:plant`
high	`4`
low	`0`
slots	`2`
witness_s_0	`1`
witness_s_1	`3`

in_declared_range — None of the record's own givens was needed: a declared range decides this, and the declared range is drawn as its premise.
below_declared_range — None of the record's own givens was needed: a declared range decides this, and the declared range is drawn as its premise.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`
Generator	`guardrail_gamut.generation:plant_declared`
slots	`2`
witness_d_0	`1`
witness_d_1	`2`

in_range — The conflict is drawn: 2 of the record's givens cannot all hold, and nothing is derived about the check from them.

INCONSISTENT_BASE is a statement about the givens, not about the check beside it. Nothing is being claimed about the check; the premises are being refused, because no world satisfies them all.

Provenance

Field	Value
Origin	`authored`
Generator	`guardrail_gamut.generation:contradict`
conflict_slot	`0`
high	`4`
low	`0`
slots	`2`
witness_s_0	`1`
witness_s_1	`3`

Three seats, one arrangementA small zebra puzzle

blake_in_seat_2 — Answered from 6 of the record's givens, and the step names which of them were needed rather than why they force it.
casey_in_seat_2 — Answered from 2 of the record's givens, and the step names which of them were needed rather than why they force it.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`

ben_in_house_3 — Answered from 3 of the record's givens, and the step names which of them were needed rather than why they force it.
cai_drinks_milk — Answered from 2 of the record's givens, and the step names which of them were needed rather than why they force it.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`

At exactly the threshold

claim.amount_meets_threshold — Answered from 1 of the record's givens, and the step names which of them were needed rather than why they force it.
claim.amount_exceeds_threshold — Answered from 1 of the record's givens, and the step names which of them were needed rather than why they force it.
claim.suspicion_over_referral — Answered from 1 of the record's givens, and the step names which of them were needed rather than why they force it.
claim.suspicion_certain — Answered from 1 of the record's givens, and the step names which of them were needed rather than why they force it.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`

Hours into minutes

late.late_at_1100 — Derived in 5 steps over 6 facts, from 2 of the record's givens.
late.late_at_0902 — Answered from 2 of the record's givens, and the step names which of them were needed rather than why they force it.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

VERIFIED means the givens entail the check. Where a core is shown it names which statements were needed, which is not the same as why they force the answer.

Provenance

Field	Value
Origin	`authored`

Room for every pigeonGivens that cannot all hold

pigeon_0_in_hole_0 — Two worlds satisfy every statement and disagree about pigeon_0_in_hole_0: pigeon_0.hole is 0 in one and 1 in the other. Nothing the record states rules either out, so the givens do not decide it.

UNKNOWN does not mean the solver gave up. Two worlds satisfy every statement and disagree about this check, so the givens genuinely do not decide it.

Provenance

Field	Value
Origin	`authored`
Generator	`packages/guardrail-gamut/tools/hard_puzzle.py:declared_pigeonhole_request`

Three pigeons, two holes, and no two pigeons sharing one -- the pigeonhole principle, stated as givens that cannot all hold.

pigeon_0_in_hole_0 — The conflict is drawn: 1 of the record's givens cannot all hold, and nothing is derived about the check from them.

INCONSISTENT_BASE is a statement about the givens, not about the check beside it. Nothing is being claimed about the check; the premises are being refused, because no world satisfies them all.

Provenance

Field	Value
Origin	`authored`
Generator	`packages/guardrail-gamut/tools/hard_puzzle.py:declared_pigeonhole_request`

Four queens, two boards

row_0_in_column_1 — Two worlds satisfy every statement and disagree about row_0_in_column_1: queen_0.column is 1 in one and 2 in the other. Nothing the record states rules either out, so the givens do not decide it.
row_0_in_column_0 — Answered from 2 of the record's givens, and the step names which of them were needed rather than why they force it.

FALSIFIED means the givens rule the check out, and the witness is a world in which every statement holds and the check does not.

UNKNOWN does not mean the solver gave up. Two worlds satisfy every statement and disagree about this check, so the givens genuinely do not decide it.

Provenance

Field	Value
Origin	`authored`