# Finite Decision Specifications versus Complete and Sampled Tables

This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.

This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261013-advance-20261018-r06-decision-problem-foundations · 2026-10-13 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [], [[0, No], [1, No], [2, No], [3, No], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [], [[0, No], [1, No], [2, No], [3, No], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0001/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 2. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [0], [[0, Yes], [1, No], [2, No], [3, No], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [[0, Yes], [1, No], [2, No], [3, No], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0002/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 3. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [1], [[0, No], [1, Yes], [2, No], [3, No], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1], [[0, No], [1, Yes], [2, No], [3, No], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0003/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 4. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [0, 1], [[0, Yes], [1, Yes], [2, No], [3, No], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [[0, Yes], [1, Yes], [2, No], [3, No], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0004/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 5. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [2], [[0, No], [1, No], [2, Yes], [3, No], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2], [[0, No], [1, No], [2, Yes], [3, No], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0005/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 6. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [0, 2], [[0, Yes], [1, No], [2, Yes], [3, No], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2], [[0, Yes], [1, No], [2, Yes], [3, No], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0006/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 7. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [1, 2], [[0, No], [1, Yes], [2, Yes], [3, No], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2], [[0, No], [1, Yes], [2, Yes], [3, No], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0007/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 8. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [0, 1, 2], [[0, Yes], [1, Yes], [2, Yes], [3, No], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 2], [[0, Yes], [1, Yes], [2, Yes], [3, No], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0008/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 9. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [3], [[0, No], [1, No], [2, No], [3, Yes], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [3], [[0, No], [1, No], [2, No], [3, Yes], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0009/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 10. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [0, 3], [[0, Yes], [1, No], [2, No], [3, Yes], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3], [[0, Yes], [1, No], [2, No], [3, Yes], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0010/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 11. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [1, 3], [[0, No], [1, Yes], [2, No], [3, Yes], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 3], [[0, No], [1, Yes], [2, No], [3, Yes], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0011/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 12. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [0, 1, 3], [[0, Yes], [1, Yes], [2, No], [3, Yes], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [[0, Yes], [1, Yes], [2, No], [3, Yes], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0012/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 13. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [2, 3], [[0, No], [1, No], [2, Yes], [3, Yes], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 3], [[0, No], [1, No], [2, Yes], [3, Yes], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0013/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 14. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [0, 2, 3], [[0, Yes], [1, No], [2, Yes], [3, Yes], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 3], [[0, Yes], [1, No], [2, Yes], [3, Yes], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0014/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 15. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [1, 2, 3], [[0, No], [1, Yes], [2, Yes], [3, Yes], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 3], [[0, No], [1, Yes], [2, Yes], [3, Yes], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0015/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 16. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [0, 1, 2, 3], [[0, Yes], [1, Yes], [2, Yes], [3, Yes], [4, No], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 2, 3], [[0, Yes], [1, Yes], [2, Yes], [3, Yes], [4, No], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0016/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 17. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [4], [[0, No], [1, No], [2, No], [3, No], [4, Yes], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [4], [[0, No], [1, No], [2, No], [3, No], [4, Yes], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0017/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 18. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [0, 4], [[0, Yes], [1, No], [2, No], [3, No], [4, Yes], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 4], [[0, Yes], [1, No], [2, No], [3, No], [4, Yes], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0018/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 19. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [1, 4], [[0, No], [1, Yes], [2, No], [3, No], [4, Yes], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4], [[0, No], [1, Yes], [2, No], [3, No], [4, Yes], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0019/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 20. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [0, 1, 4], [[0, Yes], [1, Yes], [2, No], [3, No], [4, Yes], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 4], [[0, Yes], [1, Yes], [2, No], [3, No], [4, Yes], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0020/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 21. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [2, 4], [[0, No], [1, No], [2, Yes], [3, No], [4, Yes], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 4], [[0, No], [1, No], [2, Yes], [3, No], [4, Yes], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0021/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 22. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [0, 2, 4], [[0, Yes], [1, No], [2, Yes], [3, No], [4, Yes], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 4], [[0, Yes], [1, No], [2, Yes], [3, No], [4, Yes], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0022/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 23. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [1, 2, 4], [[0, No], [1, Yes], [2, Yes], [3, No], [4, Yes], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 4], [[0, No], [1, Yes], [2, Yes], [3, No], [4, Yes], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0023/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 24. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [0, 1, 2, 4], [[0, Yes], [1, Yes], [2, Yes], [3, No], [4, Yes], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 2, 4], [[0, Yes], [1, Yes], [2, Yes], [3, No], [4, Yes], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0024/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 25. Finite Decision Specification and Complete Truth Table

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

View answer and explanation(6, [3, 4], [[0, No], [1, No], [2, No], [3, Yes], [4, Yes], [5, No]])

Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [3, 4], [[0, No], [1, No], [2, No], [3, Yes], [4, Yes], [5, No]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0025/)

Decision problem · qf-ext18-decision-yes-set-table · candidate





## 26. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [], [No, No, No, No, No, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [], [No, No, No, No, No, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0026/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 27. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [0], [Yes, Yes, No, No, No, No], [1], No)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [Yes, Yes, No, No, No, No], [1], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0027/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 28. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [1], [No, Yes, No, No, No, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1], [No, Yes, No, No, No, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0028/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 29. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, true, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [0, 1], [Yes, Yes, No, Yes, No, No], [3], No)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [Yes, Yes, No, Yes, No, No], [3], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0029/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 30. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [2], [No, No, Yes, No, No, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2], [No, No, Yes, No, No, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0030/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 31. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, false, true]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [0, 2], [Yes, No, Yes, No, No, Yes], [5], No)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2], [Yes, No, Yes, No, No, Yes], [5], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0031/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 32. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [1, 2], [No, Yes, Yes, No, No, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2], [No, Yes, Yes, No, No, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0032/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 33. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [0, 1, 2], [Yes, No, Yes, No, No, No], [1], No)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 2], [Yes, No, Yes, No, No, No], [1], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0033/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 34. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [3], [No, No, No, Yes, No, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [3], [No, No, No, Yes, No, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0034/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 35. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [0, 3], [Yes, No, No, No, No, No], [3], No)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3], [Yes, No, No, No, No, No], [3], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0035/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 36. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, true, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [1, 3], [No, Yes, No, Yes, No, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 3], [No, Yes, No, Yes, No, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0036/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 37. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, true, false, true]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [0, 1, 3], [Yes, Yes, No, Yes, No, Yes], [5], No)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [Yes, Yes, No, Yes, No, Yes], [5], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0037/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 38. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, true, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [2, 3], [No, No, Yes, Yes, No, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 3], [No, No, Yes, Yes, No, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0038/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 39. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, true, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [0, 2, 3], [Yes, Yes, Yes, Yes, No, No], [1], No)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 3], [Yes, Yes, Yes, Yes, No, No], [1], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0039/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 40. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, true, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [1, 2, 3], [No, Yes, Yes, Yes, No, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 3], [No, Yes, Yes, Yes, No, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0040/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 41. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [0, 1, 2, 3], [Yes, Yes, Yes, No, No, No], [3], No)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 2, 3], [Yes, Yes, Yes, No, No, No], [3], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0041/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 42. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, false, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [4], [No, No, No, No, Yes, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [4], [No, No, No, No, Yes, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0042/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 43. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, false, true, true]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [0, 4], [Yes, No, No, No, Yes, Yes], [5], No)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 4], [Yes, No, No, No, Yes, Yes], [5], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0043/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 44. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [1, 4], [No, Yes, No, No, Yes, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4], [No, Yes, No, No, Yes, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0044/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 45. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, false, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [0, 1, 4], [Yes, No, No, No, Yes, No], [1], No)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 4], [Yes, No, No, No, Yes, No], [1], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0045/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 46. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [2, 4], [No, No, Yes, No, Yes, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 4], [No, No, Yes, No, Yes, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0046/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 47. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, true, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [0, 2, 4], [Yes, No, Yes, Yes, Yes, No], [3], No)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 4], [Yes, No, Yes, Yes, Yes, No], [3], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0047/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 48. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, false, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [1, 2, 4], [No, Yes, Yes, No, Yes, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 4], [No, Yes, Yes, No, Yes, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0048/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 49. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, false, true, true]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [0, 1, 2, 4], [Yes, Yes, Yes, No, Yes, Yes], [5], No)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 2, 4], [Yes, Yes, Yes, No, Yes, Yes], [5], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0049/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 50. Whole Finite Decider Table against Its Specification

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

View answer and explanation(6, [3, 4], [No, No, No, Yes, Yes, No], [], Yes)

Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [3, 4], [No, No, No, Yes, Yes, No], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0050/)

Decision problem · qf-ext18-decision-decider-agreement · candidate





## 51. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, false, false], retained subset=[0, 1, 3]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 1, 3], [], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0051/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 52. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, true, false, false], retained subset=[1, 2, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [1, 2, 4], [], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 4], [], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0052/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 53. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, true, false], retained subset=[2, 3, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [2, 3, 5], [], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 3, 5], [], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0053/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 54. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, false, false, true], retained subset=[0, 3, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 3, 4], [0], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3, 4], [0], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0054/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 55. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, false, false], retained subset=[1, 4, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [1, 4, 5], [], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4, 5], [], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0055/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 56. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, false, false, false], retained subset=[0, 2, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 2, 5], [0, 2], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 5], [0, 2], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0056/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 57. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, false, false], retained subset=[0, 1, 3]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 1, 3], [1], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [1], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0057/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 58. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, true, false, false], retained subset=[1, 2, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [1, 2, 4], [1, 2], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 4], [1, 2], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0058/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 59. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, true, false], retained subset=[2, 3, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [2, 3, 5], [3], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 3, 5], [3], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0059/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 60. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, true, false, true], retained subset=[0, 3, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 3, 4], [0, 3], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3, 4], [0, 3], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0060/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 61. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, true, false, false], retained subset=[1, 4, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [1, 4, 5], [1], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4, 5], [1], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0061/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 62. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, true, false, false], retained subset=[0, 2, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 2, 5], [0], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 5], [0], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0062/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 63. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, false, false], retained subset=[0, 1, 3]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 1, 3], [3], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [3], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0063/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 64. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, false, false], retained subset=[1, 2, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [1, 2, 4], [2], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 4], [2], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0064/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 65. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, true, true, false], retained subset=[2, 3, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [2, 3, 5], [2, 3], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 3, 5], [2, 3], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0065/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 66. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, true, false, true], retained subset=[0, 3, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 3, 4], [0, 3], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3, 4], [0, 3], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0066/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 67. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, false, true, false], retained subset=[1, 4, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [1, 4, 5], [4], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4, 5], [4], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0067/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 68. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, false, true, false], retained subset=[0, 2, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 2, 5], [0], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 5], [0], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0068/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 69. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, false, true, false], retained subset=[0, 1, 3]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 1, 3], [1], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [1], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0069/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 70. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, true, true, false], retained subset=[1, 2, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [1, 2, 4], [1, 4], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 4], [1, 4], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0070/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 71. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, false, false], retained subset=[2, 3, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [2, 3, 5], [2], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 3, 5], [2], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0071/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 72. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, true, true], retained subset=[0, 3, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 3, 4], [0, 4], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3, 4], [0, 4], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0072/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 73. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, false, true, false], retained subset=[1, 4, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [1, 4, 5], [1, 4], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4, 5], [1, 4], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0073/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 74. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, true, false], retained subset=[0, 2, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 2, 5], [0, 2], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 5], [0, 2], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0074/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 75. Restricted Decision Domain with Original Input Labels

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, true, true, false], retained subset=[0, 1, 3]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).

View answer and explanation(6, [0, 1, 3], [3], [], Yes)

Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [3], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0075/)

Decision problem · qf-ext18-decision-domain-restriction · candidate





## 76. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, false, false], checked subset=[0, 1]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [], [3], Yes, No, sample-passed-full-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0076/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 77. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, false, true, false], checked subset=[1, 4]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [1, 4], [4], [4], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4], [4], [4], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0077/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 78. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, false, true], checked subset=[0, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 2], [], [5], Yes, No, sample-passed-full-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2], [], [5], Yes, No, sample-passed-full-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0078/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 79. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, false, false], checked subset=[0, 3]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 3], [0], [0], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3], [0], [0], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0079/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 80. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, false, false, false], checked subset=[1, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [1, 2], [1], [1], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2], [1], [1], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0080/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 81. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, false, false, false], checked subset=[2, 5]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [2, 5], [2], [2], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 5], [2], [2], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0081/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 82. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, true, false, false], checked subset=[0, 1]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [], [3], Yes, No, sample-passed-full-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0082/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 83. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, false, true, false], checked subset=[1, 4]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [1, 4], [4], [4], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4], [4], [4], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0083/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 84. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, false, true], checked subset=[0, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 2], [], [5], Yes, No, sample-passed-full-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2], [], [5], Yes, No, sample-passed-full-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0084/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 85. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, false, false], checked subset=[0, 3]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 3], [0], [0], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3], [0], [0], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0085/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 86. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, false, false], checked subset=[1, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [1, 2], [1], [1], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2], [1], [1], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0086/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 87. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, true, false, false], checked subset=[2, 5]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [2, 5], [2], [2], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 5], [2], [2], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0087/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 88. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, false, false], checked subset=[0, 1]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [], [3], Yes, No, sample-passed-full-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0088/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 89. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, true, true, false], checked subset=[1, 4]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [1, 4], [4], [4], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4], [4], [4], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0089/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 90. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, true, false, true], checked subset=[0, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 2], [], [5], Yes, No, sample-passed-full-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2], [], [5], Yes, No, sample-passed-full-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0090/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 91. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, true, false, false], checked subset=[0, 3]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 3], [0], [0], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3], [0], [0], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0091/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 92. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, true, false], checked subset=[1, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [1, 2], [1], [1], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2], [1], [1], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0092/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 93. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, true, false], checked subset=[2, 5]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [2, 5], [2], [2], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 5], [2], [2], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0093/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 94. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, true, true, false], checked subset=[0, 1]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [], [3], Yes, No, sample-passed-full-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0094/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 95. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, false, false, false], checked subset=[1, 4]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [1, 4], [4], [4], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4], [4], [4], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0095/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 96. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, true, true], checked subset=[0, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 2], [], [5], Yes, No, sample-passed-full-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2], [], [5], Yes, No, sample-passed-full-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0096/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 97. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, true, false], checked subset=[0, 3]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 3], [0], [0], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3], [0], [0], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0097/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 98. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, true, false], checked subset=[1, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [1, 2], [1], [1], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2], [1], [1], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0098/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 99. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, false, true, false], checked subset=[2, 5]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [2, 5], [2], [2], No, No, sample-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 5], [2], [2], No, No, sample-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0099/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate





## 100. Sample Agreement Is Not Complete Finite Agreement

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, false, true, false], checked subset=[0, 1]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).

View answer and explanation(6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)

Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [], [3], Yes, No, sample-passed-full-failed).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261018-r06-decision-problem-0100/)

Decision problem · qf-ext18-decision-complete-vs-sample · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261018-r06-decision-problem-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261013-advance-20261018-r06-decision-problem-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261018-r06-decision-problem-foundations/validation-report.json)