Z3 could return `sat` for an unsatisfiable QF_ABV formula equating two
store chains over distinct constant arrays. The rewrite path for array
equalities was missing a necessary base-value constraint in
finite-domain cases where stores cannot cover all indices.
- **Root cause**
- In `array_rewriter::mk_eq_core`, equality rewriting for nested stores
over const-array bases did not enforce equality of the underlying const
values when the index domain size exceeds the number of updated indices.
- **Rewriter fix**
- Added a sound rewrite branch for:
- `store* ((as const ...) v)` vs `store* ((as const ...) w)`
- When `|domain| > (#stores_lhs + #stores_rhs)`, rewrite now includes:
- select equalities for touched indices (existing behavior)
- **and** base-value equality `v = w` (new requirement)
- This prevents spurious models where only updated indices are
constrained.
- **Regression coverage**
- Added a focused regression in `src/test/mod_factor.cpp` that asserts
`unsat` for a minimized constant-array/store-chain BV case with
`(distinct x y)` and one store per side.
```cpp
(assert (distinct x y))
(assert (= (store A0 i0 e0) (store A1 i1 e1)))
(check-sat) ; expected: unsat
```
---------
Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
The is_mod handler in theory_lra called ensure_nla(), which
unnecessarily created the NLA solver for pure linear problems, causing
the optimizer to return a finite value instead of -infinity.
Fix: check `m_nla` instead of calling `ensure_nla()`, matching the
pattern used by the is_idiv handler. The mod division is only registered
when NLA is already active due to nonlinear terms.
Update mod_factor tests to use QF_NIA logic and assert the mul term
before the mod term so that internalize_mul triggers ensure_nla() before
mod internalization.
Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
When a monic x*y has a factor x with mod(x, p) = 0 (fixed), propagate
mod(x*y, p) = 0. This enables Z3 to prove divisibility properties like
x mod p = 0 => (x*y) mod p = 0, which previously timed out even for
p = 2. The lemma fires in the NLA divisions check and allows Gröbner
basis and LIA to subsequently derive distributivity of div over addition.
Extends division tuples from (q, x, y) to (q, x, y, r) to track the
mod lpvar. Also registers bounded divisions from the mod internalization
path in theory_lra, not just the idiv path.
Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
