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Each step in every SKILL.md now carries labeled Action, Expectation, and Result blocks so the agent can mechanically execute, verify, and branch at each stage. Format chosen after comparing three variants (indented blocks, inline keywords, tables) on a prove-validity simulation; indented blocks scored highest on routing completeness and checkability. Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
2.8 KiB
| name | description |
|---|---|
| prove | Prove validity of logical statements by negation and satisfiability checking. If the negation is unsatisfiable, the original statement is valid. Otherwise a counterexample is returned. |
Given a conjecture (an SMT-LIB2 assertion or a natural language claim), determine whether it holds universally. The method is standard: negate the conjecture and check satisfiability. If the negation is unsatisfiable, the original is valid. If satisfiable, the model is a counterexample.
Step 1: Prepare the negated formula
Action:
Wrap the conjecture in (assert (not ...)) and append
(check-sat)(get-model).
Expectation: A complete SMT-LIB2 formula that negates the original conjecture with all variables declared.
Result: If the negation is well-formed, proceed to Step 2. If the conjecture is natural language, run encode first.
Example: to prove that (> x 3) implies (> x 1):
(declare-const x Int)
(assert (not (=> (> x 3) (> x 1))))
(check-sat)
(get-model)
Step 2: Run the prover
Action: Invoke prove.py with the conjecture and variable declarations.
Expectation:
The script prints valid, invalid (with counterexample), unknown,
or timeout. A run entry is logged to z3agent.db.
Result:
On valid: proceed to explain if the user needs a summary.
On invalid: report the counterexample directly.
On unknown/timeout: try simplify first, or increase the timeout.
python3 scripts/prove.py --conjecture "(=> (> x 3) (> x 1))" --vars "x:Int"
For file input where the file contains the full negated formula:
python3 scripts/prove.py --file negated.smt2
With debug tracing:
python3 scripts/prove.py --conjecture "(=> (> x 3) (> x 1))" --vars "x:Int" --debug
Step 3: Interpret the output
Action: Read the prover output to determine validity of the conjecture.
Expectation:
One of valid, invalid (with counterexample), unknown, or timeout.
Result:
On valid: the conjecture holds universally.
On invalid: the model shows a concrete counterexample.
On unknown/timeout: the conjecture may require auxiliary lemmas or induction.
Parameters
| Parameter | Type | Required | Default | Description |
|---|---|---|---|---|
| conjecture | string | no | the assertion to prove (without negation) | |
| vars | string | no | variable declarations as "name:sort" pairs, comma-separated | |
| file | path | no | .smt2 file with the negated formula | |
| timeout | int | no | 30 | seconds |
| z3 | path | no | auto | path to z3 binary |
| debug | flag | no | off | verbose tracing |
| db | path | no | .z3-agent/z3agent.db | logging database |
Either conjecture (with vars) or file must be provided.