# Question 6201: Sequential Candidate Trace and First Rejected Row

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0011-06201 · q-20261009-advance-20261013-r04-proof-0051



## Original question and givens

Given facts and single-premise MP only: Fin(0)=∅, facts=[], rules=[], where [i,j] means i→j. Facts have depth 0 and each MP adds one. Ordered trace=[]. Each row may use only facts and earlier accepted rows for a single MP. Give (row-eligibility mask, first invalid row’s zero-based index or none). Continue auditing; invalid rows do not become premises.


- G001 — Given facts and single-premise MP only: Fin(0)=∅, facts=[], rules=[], where [i,j] means i→j. Facts have depth 0 and each MP adds one. Ordered trace=[]. Each row may use only facts and earlier accepted rows for a single MP. Give (row-eligibility mask, first invalid row’s zero-based index or none). Continue auditing; invalid rows do not become premises.





## 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.


- [mko-proof](https://ocme.evemisslab.com/en/mko/mko-proof/)





## Step-by-step derivation

S001 · impliesBefore

n=0;given facts=[];original indexed rules=[]

After

use only given facts and single-premise MP;not-derived does not mean False

Conditions: none

Atoms use0-based indices and a rule i→j requires an already derived i.A cycle without facts cannot generate conclusions.Not-derived is not False,and this finite check is not general logical completeness.

Step identifiers and dependenciesRule: given_unary_MP_scope · Uses: G001





S002 · impliesBefore

given facts=[]

After

initial accepted atoms=[]

Conditions: none

Candidate lines may use only the given facts and preceding legal lines;globally reachable conclusions are not automatically accepted prefix premises.

Step identifiers and dependenciesRule: candidate_trace_given_facts · Uses: G001, S001





S003 · impliesBefore

line validity=[];final accepted=[]

After

first invalid line=none

Conditions: none

The first error is a0-based trace position.Continue auditing after an error without accepting invalid lines.An empty sequence has no bad line but does not thereby prove a target.

Step identifiers and dependenciesRule: horn_candidate_trace_boundary · Uses: G001, S002









## Reverse checks


- 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.





## Result

([], none)

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: 9cd56d597c6c2ddf59f215cc3659c6b515e66c397571f5690bb93bf61e25cdd1
- candidate record SHA-256: 26a45ca7c42a859313650d532b01906031c24397b1263f2d084c20c3633854d1
- semantic review receipt SHA-256: b9bbc1c947f477a9c4bb5a579368ac5265f2da4572ce612c30f3633ecaf4ae80
- question-first witness SHA-256: 93f720df3ab3af13a792a3e6b443728e3c2a56276df839911f36569333236c55
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261009-advance-20261013-r04-proof-0051.json)