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Question 35367: Uncovered Codomain Targets

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0069-35367 · q-20261004-advance-20261005-r02-surjective-0042

Original question and givens

The declared total function f:A→B has A={-4, -3, -2, -1, 0}, B={-6, -5, -4, -3, -2, -1}, and table {(-4, -1), (-3, -1), (-2, -2), (-1, -2), (0, -3)}. List the uncovered targets B∖f[A] in increasing order, using ∅ for the empty set.

  • G001 — The declared total function f:A→B has A={-4, -3, -2, -1, 0}, B={-6, -5, -4, -3, -2, -1}, and table {(-4, -1), (-3, -1), (-2, -2), (-1, -2), (0, -3)}. List the uncovered targets B∖f[A] in increasing order, using ∅ for the empty set.

Definition and scope

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.

Step-by-step derivation

S001 · implies

Before

source roles = [qf-surjective-missing-targets, [A, B, operation, pairs]]

After

derived = [missing_targets, no-invented-domain]

Conditions: none

Keep EACH bank’s keys/operation/domain distinct:LDL/PULSE/function legacy table underscores,TREE full tree_* with its declared domain,and permissive BASE signed without invented op/domain.All arithmetic respects the binary-primitive contract.

Step identifiers and dependencies

Rule: R69_SOURCE_specific_keys_operation_domain_AND_binary_contract · Uses: G001

S002 · implies

Before

source roles = [function ORIGINAL A, 100, [-4, -3, -2, -1, 0]]

After

derived = [[-4, -3, -2, -1, 0]]

Conditions: none

Type EVERY RAW SAFE label,distinctness and THIS bank’s cardinality bound;empty is allowed.Sort ONLY the derived representation,not original JSON.Do not exchange TREE and LDL limits.

Step identifiers and dependencies

Rule: Finite_RAW_ALL_SAFE_distinct_labels_then_derived_sort · Uses: G001, S001

S003 · implies

Before

source roles = [function ORIGINAL B, 100, [-6, -5, -4, -3, -2, -1]]

After

derived = [[-6, -5, -4, -3, -2, -1]]

Conditions: none

Type EVERY RAW SAFE label,distinctness and THIS bank’s cardinality bound;empty is allowed.Sort ONLY the derived representation,not original JSON.Do not exchange TREE and LDL limits.

Step identifiers and dependencies

Rule: Finite_RAW_ALL_SAFE_distinct_labels_then_derived_sort · Uses: G001, S002

S004 · implies

Before

source roles = [function ORIGINAL table, 0, [-4, -1]]

After

derived = [[-4, -1]]

Conditions: none

BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.

Step identifiers and dependencies

Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S003

S005 · implies

Before

source roles = [function ORIGINAL table, 1, [-3, -1]]

After

derived = [[-3, -1]]

Conditions: none

BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.

Step identifiers and dependencies

Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S004

S006 · implies

Before

source roles = [function ORIGINAL table, 2, [-2, -2]]

After

derived = [[-2, -2]]

Conditions: none

BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.

Step identifiers and dependencies

Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S005

S007 · implies

Before

source roles = [function ORIGINAL table, 3, [-1, -2]]

After

derived = [[-1, -2]]

Conditions: none

BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.

Step identifiers and dependencies

Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S006

S008 · implies

Before

source roles = [function ORIGINAL table, 4, [0, -3]]

After

derived = [[0, -3]]

Conditions: none

BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.

Step identifiers and dependencies

Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S007

S009 · implies

Before

source roles = [[-4, -3, -2, -1, 0], [-6, -5, -4, -3, -2, -1], [[-4, -1], [-3, -1], [-2, -2], [-1, -2], [0, -3]]]

After

derived = [Yes]

Conditions: none

FIRST qualify the WHOLE total function A→B:EXACTLY one output for EVERY A and all pairs in A×B.Identical repeated rows normalize in THIS legacy bank,unlike a different PULSE table rule.Qualify ORIGINAL B even for later codomain changes.

Step identifiers and dependencies

Rule: Function_WHOLE_qualified_total_AtoB_before_SURJECTIVE_claim · Uses: G001, S008

S010 · implies

Before

source roles = [ORIGINAL B, -4, -1, -6]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S009

S011 · implies

Before

source roles = [ORIGINAL B, -3, -1, -6]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S010

S012 · implies

Before

source roles = [ORIGINAL B, -2, -2, -6]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S011

S013 · implies

Before

source roles = [ORIGINAL B, -1, -2, -6]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S012

S014 · implies

Before

source roles = [ORIGINAL B, 0, -3, -6]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S013

S015 · implies

Before

source roles = [ORIGINAL B, -4, -1, -5]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S014

S016 · implies

Before

source roles = [ORIGINAL B, -3, -1, -5]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S015

S017 · implies

Before

source roles = [ORIGINAL B, -2, -2, -5]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S016

S018 · implies

Before

source roles = [ORIGINAL B, -1, -2, -5]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S017

S019 · implies

Before

source roles = [ORIGINAL B, 0, -3, -5]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S018

S020 · implies

Before

source roles = [ORIGINAL B, -4, -1, -4]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S019

S021 · implies

Before

source roles = [ORIGINAL B, -3, -1, -4]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S020

S022 · implies

Before

source roles = [ORIGINAL B, -2, -2, -4]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S021

S023 · implies

Before

source roles = [ORIGINAL B, -1, -2, -4]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S022

S024 · implies

Before

source roles = [ORIGINAL B, 0, -3, -4]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S023

S025 · implies

Before

source roles = [ORIGINAL B, -4, -1, -3]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S024

S026 · implies

Before

source roles = [ORIGINAL B, -3, -1, -3]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S025

S027 · implies

Before

source roles = [ORIGINAL B, -2, -2, -3]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S026

S028 · implies

Before

source roles = [ORIGINAL B, -1, -2, -3]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S027

S029 · implies

Before

source roles = [ORIGINAL B, 0, -3, -3]

After

derived = [Yes]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S028

S030 · implies

Before

source roles = [ORIGINAL B, -4, -1, -2]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S029

S031 · implies

Before

source roles = [ORIGINAL B, -3, -1, -2]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S030

S032 · implies

Before

source roles = [ORIGINAL B, -2, -2, -2]

After

derived = [Yes]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S031

S033 · implies

Before

source roles = [ORIGINAL B, -1, -2, -2]

After

derived = [Yes]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S032

S034 · implies

Before

source roles = [ORIGINAL B, 0, -3, -2]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S033

S035 · implies

Before

source roles = [ORIGINAL B, -4, -1, -1]

After

derived = [Yes]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S034

S036 · implies

Before

source roles = [ORIGINAL B, -3, -1, -1]

After

derived = [Yes]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S035

S037 · implies

Before

source roles = [ORIGINAL B, -2, -2, -1]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S036

S038 · implies

Before

source roles = [ORIGINAL B, -1, -2, -1]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S037

S039 · implies

Before

source roles = [ORIGINAL B, 0, -3, -1]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S038

S040 · implies

Before

source roles = [[-4, -3, -2, -1, 0], [-6, -5, -4, -3, -2, -1], [[-6, []], [-5, []], [-4, []], [-3, [0]], [-2, [-2, -1]], [-1, [-4, -3]]]]

After

derived = [[-6, -5, -4], No]

Conditions: none

Surjectivity requires a preimage for EVERY declared target;multiple preimages are allowed.For a QUALIFIED empty function,the empty-codomain condition is vacuous.The missing set is B(or B2)minus range,not a replacement of the ORIGINAL codomain.

Step identifiers and dependencies

Rule: Surjective_ALL_codomain_targets_covered_including_EMPTY_vacuity · Uses: G001, S039

Reverse checks

  • S040 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S039 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S038 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S037 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S036 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S035 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S034 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S033 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S032 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S031 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S030 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S029 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S028 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S027 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S026 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S025 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S024 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S023 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S022 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S021 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S020 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S019 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S018 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S017 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S016 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S015 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S014 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S013 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S012 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S011 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S010 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S009 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S008 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S007 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S006 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S005 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S004 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S003 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S002 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
  • S001 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.

Result

{-6, -5, -4}

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

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.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: b0113d23b8c6631e785c65491e12e33f046387995cba6e84c137f2d79f7c120c
  • candidate record SHA-256: a7e55f202af5e5289c172ae4ad21892075f0395c91079b2245cff4eda9dd8420
  • semantic review receipt SHA-256: ccf93c72638d6abf6a412514da5838d55ecb09b71d0e4fdec2b559dc9fdee14b
  • question-first witness SHA-256: 11af9a338b5a610342b2cfb2ee295683131b3139ac402dd19b1ba1725976d518
  • Lean: NOT_RUN · human review: NOT_PERFORMED
Same-source full JSON