prove

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)`: ```smtlib (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. ```bash python3 scripts/prove.py --conjecture "(=> (> x 3) (> x 1))" --vars "x:Int" ``` For file input where the file contains the full negated formula: ```bash python3 scripts/prove.py --file negated.smt2 ``` With debug tracing: ```bash 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.