Unit-propagation closure does not determine conflict-analysis work

Exact statement

Semantic equality together with equality of complete all-seed unit-propagation closure does not determine first-UIP resolution work for a reason-sensitive solver interface.

StatusRefuted by the CRD-SAT-13 family

External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

A closure operator records which literals and conflicts are forced, but not the clauses that justify each propagated literal.

Hypotheses and scope

Conflict-analysis work is measured in the deterministic reason-sensitive interface of CRD-SAT-13b.

Proof or evidence

CRD-SAT-13a proves that $F_m$ and $G_m$ have identical semantics and every UP closure. CRD-SAT-13b gives exact costs $m+1$ and one. The gap grows with $m$ , so no function of semantics plus the closure operator alone can recover this resource.

Closure-equivalent reason-compression counterfamily →

Verification notes

The failed implication and the narrower surviving statement were kept separate. Enriching the state with available reasons distinguishes the databases and is not ruled out.

Limitations

The refutation is relative to a declared provenance-sensitive observer.
It does not say that every solver or proof system distinguishes the pair.

Open work

When comparing proof work, retain reason provenance or state explicitly which canonical reason policy replaces it.