Formal Logic Model Counterexample Solver Script

Role: Director of Formal Epistemology and Automated Mathematical Reasoning.

Context

• Formal Model Title: {{economic_model_name}}
• Set of Fundamental Axioms: {{core_propositions}}
• Theoretical Boundary Constraints: {{boundary_assumptions}}
• Target Claim to Validate: {{target_theorem}}
• Target Verification Language: {{solver_language}}
• Search Space Boundaries: {{counterexample_bounds}}

Task

Generate an automated formal solver script using {{solver_language}} that translates the analytical foundations of {{economic_model_name}} into first-order logical constraints, verifies the logical validity of {{target_theorem}}, and searches for falsifying counterexamples.

Method

1. Translate {{core_propositions}} into explicit symbolic logic declarations and arithmetic assertions within {{solver_language}}.
2. Model {{boundary_assumptions}} as active solver constraints defining state spaces, parameter domains, and agent behaviors.
3. Formulate the negation of {{target_theorem}} as the target objective to prove claim invalidity via satisfiability search.
4. Configure solver optimization heuristics and parameter domains according to {{counterexample_bounds}}.
5. Implement an automated solver invocation pipeline that checks for SAT (claim falsified by counterexample) versus UNSAT (claim logically entails from axioms).
6. Script a parsing routine that prints detailed variable assignments for any detected counterexample state.
7. Construct validation assertions that verify model consistency by ensuring the underlying axioms themselves do not contain hidden contradictions.

Constraints

• MUST produce fully syntactically valid code matching the conventions of {{solver_language}} (e.g., Z3 Python API, SMT-LIB2, or Lean).
• MUST NOT allow unconstrained real variables without explicit bounds defined in {{counterexample_bounds}}.
• Axiom satisfiability MUST be proven independently before evaluating the target theorem.
• The script MUST output explicit diagnostic messages explaining whether the theorem is proven or refuted.

Output format

1. Solver Initialization & Symbol Declarations: Variable, constant, and function definitions.
2. Axiom & Constraint Encodings: Symbolic definitions of {{core_propositions}} and {{boundary_assumptions}}.
3. Axiomatic Consistency Check: Isolated solver execution ensuring axioms are non-contradictory.
4. Theorem Verification & Negation Assertion: Target proof encoding.
5. Counterexample Extraction Routine: Formatting and printing discovered edge cases.

Self-review

• Ensure all 6 variables are referenced correctly with {{variable}} syntax.
• Confirm the logic inversion correctly targets the negation of {{target_theorem}}.
• Verify syntax is error-free according to {{solver_language}} specifications.
• Check that counterexample bounds are strictly enforced to prevent solver divergence.