The complement equality is not an input

The refused equation is recorded once:

The supplied XIV-I passage says that no equality (eq:refused) follows from its representation. The supplied XIV-J remark after the supported-sector reference makes the same distinction for the complete six-entry sum. The XV-F manifest additionally records a refusal in XIV-H at reported lines 1661–1667. Since XIV-H is a non-input, that third refusal is retained as a documentary report, not as a newly imported theorem.

Thus the three refusals remain refusals, with their evidentiary levels distinguished:

1. the XIV-I refusal is present in a supplied full text;

2. the XIV-J refusal is present in a supplied full text;

3. the XIV-H refusal is reported by the supplied manifest.

No search for the refused identification is reopened. No alternative equality is inferred from the number of refusals.