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R0009-05023 · q-20261008-advance-20261011-r04-set-0073
Finite integer set A=[-22, 0]; raw candidates=[-22, 22, 0, 22] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.
G001 — Finite integer set A=[-22, 0]; raw candidates=[-22, 22, 0, 22] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
raw integer list=[-22, 0]
After
extensional set=[-22, 0]
Conditions: none
A set depends on its elements;deduplication and numeric ordering do not change membership.The original list is retained as source.
Rule: set_extensionality_normalization · Uses: G001
Before
candidate=-22;A=[-22, 0]
After
in A=Yes
Conditions: none
Partition only candidate set C;do not add A-elements that were not candidates.
Rule: candidate_set_partition_row · Uses: G001, S001
Before
candidate=0;A=[-22, 0]
After
in A=Yes
Conditions: none
Partition only candidate set C;do not add A-elements that were not candidates.
Rule: candidate_set_partition_row · Uses: G001, S002
Before
candidate=22;A=[-22, 0]
After
in A=No
Conditions: none
Partition only candidate set C;do not add A-elements that were not candidates.
Rule: candidate_set_partition_row · Uses: G001, S003
Before
[-22, 0, 22]
After
([-22, 0], [22])
Conditions: none
The two parts are disjoint and cover the deduplicated candidate set;list members of A before nonmembers.
Rule: candidate_set_partition_complete · Uses: G001, S004
S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.([-22, 0], [22])
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: ebb11176efd463b7bab42943ec7e9eeeb729068af0f8315a321cb450fb0651cfcandidate record SHA-256: 6c1ee54961f79cc02dd7c1fd4098943d3e6ed57c3a969a9e0e811647e71ff226semantic review receipt SHA-256: 71e7db519df31f3a164533e472e293cb64f001b475a8d002b4a5c2740a237b56question-first witness SHA-256: 5a43f4f81b6256281f8d139a4010bbde127be803c528e5878857269c8f854462Lean: NOT_RUN · human review: NOT_PERFORMED