Question 5800: Candidate Truth Reports Checked Independently

Original question and givens

In a classical integer context, ordered pairs=[[12, 0], [-23, 2], [-1, 0]]. P_i means a_i≤b_i. Candidate reported=[0, 0, 0], with 1 reporting True and 0 False. Give (actual truth values, report-match Yes/No values, signed a_i−b_i values).

• G001 — In a classical integer context, ordered pairs=[[12, 0], [-23, 2], [-1, 0]]. P_i means a_i≤b_i. Candidate reported=[0, 0, 0], with 1 reporting True and 0 False. Give (actual truth values, report-match Yes/No values, signed a_i−b_i values).

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-proposition

Step-by-step derivation

classical integer formulas with explicit binding/data

a truth verdict is not a delivered general proof object

integer comparison difference0 := sub(12, 0)

integer comparison difference0 = 12

row=0;a=12;b=0;a−b=12

statement=a≤b;truth=False

integer comparison difference1 := sub(-23, 2)

integer comparison difference1 = -25

row=1;a=-23;b=2;a−b=-25

statement=a≤b;truth=True

integer comparison difference2 := sub(-1, 0)

integer comparison difference2 = -1

row=2;a=-1;b=0;a−b=-1

statement=a≤b;truth=True

row=0;reported bit=0;independently computed truth=False

report matches=Yes

row=1;reported bit=0;independently computed truth=True

report matches=No

row=2;reported bit=0;independently computed truth=True

report matches=No

Reverse checks

• S010 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S009 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S006 · premise_and_result_audit — Recompute integer comparison difference2 with exact rational arithmetic, not rounded decimals.
• 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 — Recompute integer comparison difference1 with exact rational arithmetic, not rounded decimals.
• 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 — Recompute integer comparison difference0 with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

([False, True, True], [Yes, No, No], [12, -25, -1])

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.