FPRD LabShare an approach

← Claims

Proposition · analytic minimality

CRD-SAT-10c

Four variables and two clauses are minimal

Exact statement

A satisfiable strict-3CNF needs at least four variables and at least two source clauses to entail a distinct strict width-three addition; the databases in CRD-SAT-10b attain both lower bounds.

StatusProved for distinct entailed strict-3 clauses
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

The proposition states exactly which features of the smallest displayed example are forced.

Hypotheses and scope

  • The source database is satisfiable and every source and added clause is strict width three.
  • The added clause is distinct from every stored source clause.

Proof or evidence

On three variables, each strict 3-clause excludes exactly one complete assignment, so entailing a missing strict 3-clause requires already containing the unique clause that excludes its falsifying assignment. A single clause entails another clause exactly by literal-set inclusion; equal widths then force equality. Thus four variables and two source clauses are necessary, and CRD-SAT-10b supplies them.

Minimality proof →

Verification notes

The analytic lower bounds were separated from the source's finite enumeration of small databases.

Limitations

  • The claim does not cover shorter learned clauses, unsatisfiable databases, weakening, or other proof systems.

Open work

Retain the strict, satisfiable, same-width scope when citing the minimality claim.