Formal Specification Lemma and Invariant Proof Checklist

Role: Principal Formal Methods Architect specializing in symbolic execution and automated theorem proving test suites.

Context

• Target System: {{system_under_proof}}
• SMT/Solver Backend: {{solver_backend}}
• Foundational Axioms: {{axiom_definitions}}
• Core State Invariants: {{invariant_properties}}
• State Space Parameter Constraints: {{state_space_constraints}}
• Recursion and Unrolling Bounds: {{recursion_depth_limit}}

Task

Author a formal verification and proof-validation checklist to test the soundness, completeness, and solver termination guarantees for {{system_under_proof}} using {{solver_backend}} against the specified {{invariant_properties}}.

Method

1. Review the foundational soundness of {{axiom_definitions}} to detect circular dependencies or contradictory premises.
2. Map {{invariant_properties}} to inductive invariant test steps, ensuring inductive base cases and step transitions are independently checked.
3. Formulate sanity checks for {{solver_backend}} quantifier handling, trigger selection, and timeout profiles under {{state_space_constraints}}.
4. Define counterexample validation tests to ensure the harness rejects deliberately injected invalid states.
5. Construct boundary checklist items targeting induction unrolling up to {{recursion_depth_limit}}.
6. Draft regression checks for proof stability against solver version updates or heuristic changes.
7. Assign verification evidence standards (e.g., proof certificates, unsat cores) to every checklist line item.

Constraints

• Check items MUST require concrete proof artifacts (e.g., unsat-core inspection or model extraction) for sign-off.
• MUST NOT accept solver silence or basic timeout without explicit validation of proof convergence.
• The checklist must specifically test inductive step stability within {{state_space_constraints}}.
• Induction loop limits must strictly enforce {{recursion_depth_limit}}.

Output format

Structured markdown checklist divided into:

1. Axiom Soundness & Consistency Checks (4-5 items)
2. Inductive Invariant Proof Validation (5-6 items with proof tactics)
3. Solver Mechanics & Timeout Guards (4-5 items referencing {{solver_backend}})
4. Proof Failure & Counterexample Triage (3 items with failure modes)

Self-review

• Are base cases and inductive steps explicitly separated across {{invariant_properties}}?
• Does every item demand verifiable evidence from {{solver_backend}} rather than binary test completion?
• Are bounded model checking edge conditions properly bounded by {{recursion_depth_limit}}?