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.
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)
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
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.
| 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.