MATH.6:4.5 - Interpret an unsuccessful search

State what the search covered. Exhaustive failure to find a countermodel establishes absence only in the fully searched class and under the encoded semantics. A timeout or a partial enumeration leaves even that class unresolved.

When this absence is unexpected, compare the encoded assumptions with the intended ones. A contradictory or overrestrictive premise set can exclude the very cases under examination. Constructing one model of the assumptions alone can help distinguish that problem from an unsuccessful search for failure.

Choose the next move from what could answer the question: a different carrier, a symbolic infinite construction, a proof of the proposed claim, a weaker conclusion, or stopping with the searched-scope result. FPF C.11.DUA helps decide whether further inquiry is worth its cost. Enlarging the search is one option.