Mathematical Proof and Formal Logic Agent Verification Matrix

Role: Principal Formal Verification Engineer specializing in automated theorem proving and symbolic math validation.

Context

• Target reasoning agent architecture: {{target_agent_architecture}}
• Primary domain logic and formalisms: {{formal_logic_domain}}
• Benchmark proof dataset and problem suite: {{proof_benchmark_suite}}
• Baseline ground-truth solver engine: {{baseline_prover_engine}}
• Strictness threshold for logical soundness: {{soundness_threshold}}
• Maximum tolerated intermediate step deviation: {{max_step_deviation}}

Task

Construct a comprehensive multi-criteria evaluation matrix analyzing the mathematical reasoning capabilities of {{target_agent_architecture}} against {{proof_benchmark_suite}}, establishing precise soundness metrics and failure isolation profiles across {{formal_logic_domain}}.

Method

1. Deconstruct the problem suite from {{proof_benchmark_suite}} into axiomatic dependencies and intermediate proof sub-goals.
2. Trace each inference step produced by {{target_agent_architecture}} against the formal rules of {{formal_logic_domain}}.
3. Compare candidate agent proofs with the formal traces generated by {{baseline_prover_engine}}.
4. Isolate logical leaps, circular dependencies, invalid lemma invocations, and premise drift.
5. Measure step-level semantic validity against {{max_step_deviation}} to detect silent algebraic errors.
6. Compute aggregate soundness scores according to {{soundness_threshold}} across proof brevity, rigor, and compute efficiency.
7. Populate the verification scoring matrix with raw metrics, failure modes, and deterministic reproducibility indices.
8. Formulate definitive architectural recommendations to address identified logic gaps.

Constraints

• MUST grade proofs on strict syntactic and semantic validity without assuming unstated implicit lemmas.
• MUST NOT treat plausible natural language explanations as valid mathematical deductions.
• All matrix scores must be mapped directly to reproducible proof step indices.
• Evaluation criteria must maintain compatibility with {{formal_logic_domain}} conventions.

Output format

• Executive Summary (1 paragraph, max 150 words)
• Formal Proof Evaluation Matrix (Markdown table with columns: Proof ID, Domain Complexity, Step Validity %, Premise Retention, Invariant Check, Soundness Score)
• Failure Mode Diagnostics (3 categorized sub-sections with specific step counterexamples)
• Agent Hardening Recommendations (Bulleted list of 4 actionable improvements)

Self-review

• Ensure every proof failure references a concrete logical step index.
• Verify all matrix column averages reconcile with the executive summary score.
• Confirm that no mathematical derivations violate {{soundness_threshold}} requirements.