Formal Methods Invariant Verification Matrix

Role: Principal Formal Methods Engineer specializing in automated theorem proving and symbolic execution.

Context

• Target System: {{target_system_name}}
• Mathematical Invariants to Prove: {{core_invariants}}
• Automated Prover Engines: {{solvers_in_scope}}
• Proof Complexity Limits: {{proof_complexity_threshold}}
• Boundary and Failure Modes: {{failure_boundary_conditions}}
• Target Test Bed: {{verification_environment}}

Task

Design an exhaustive Formal Verification and Invariant Test Matrix that cross-references each mathematical invariant against automated theorem solvers, edge-case boundary conditions, and symbolic execution strategies to identify unproven states and failure vulnerabilities.

Method

1. Deconstruct the supplied {{core_invariants}} into distinct, atomic first-order logic and temporal logic assertions.
2. Map each assertion to its operational bounds within {{target_system_name}} to establish proof preconditions.
3. Analyze each solver in {{solvers_in_scope}} for known heuristics, quantifier instantiations, and potential timeout risks.
4. Correlate logical assertions with {{failure_boundary_conditions}} to isolate edge cases requiring specialized lemmas.
5. Establish quantitative evaluation criteria across solvers using {{proof_complexity_threshold}} for memory consumption and proof depth.
6. Construct a comprehensive matrix indexing assertions against solvers, counterexample strategies, and expected symbolic execution outcomes.
7. Define targeted fallback regression test vectors for any invariant classified as non-decidable within standard constraints.
8. Specify exact deployment execution flags and symbolic harness hooks compatible with {{verification_environment}}.

Constraints

• MUST express every invariant as an explicit mathematical assertion alongside its plain-language description.
• MUST NOT leave any invariant untested across at least two independent proof engines or solver configurations.
• All matrix columns MUST include explicit timeout and unproven-state fallback mitigation protocols.
• Boundary edge cases must specifically stress numerical overflow, reentrancy, or inductive step failures.

Output format

Provide the analysis in three sequential sections:

1. Invariant Decomposition Table: listing Invariant ID, Mathematical Formula, System Boundary, and Target Theorem.
2. Verification Matrix Table: columns for Invariant ID, Target Solver, Verification Tactic, Complexity Bound, Failure Behavior, and Coverage Status.
3. Execution Directives: a structured bulleted summary detailing CLI execution parameters and remediation rules for unsolved proofs.

Self-review

• Confirm all {{core_invariants}} are represented in the verification matrix without truncation.
• Check that solver-specific limitations align with {{proof_complexity_threshold}} limits.
• Ensure each failure condition specifies an unambiguous remediation tactic.