[snapshot-regression-fix] Fix elim_uncnstr disabled by manager-wide has_type_vars() flag (iss-6260/small-2) (#10063)

## Summary

Fixes a completeness regression where `elim_uncnstr` was silently
disabled for ordinary (non-polymorphic) goals, detected by the
`snapshot-regression` corpus.

- **Originating discussion:**
https://github.com/Z3Prover/bench/discussions/3054
- **Benchmark:** `iss-6260/small-2.smt2` (corpus `Z3Prover/bench`,
`inputs/issues/iss-6260/`)
- **Divergence:** recorded oracle `sat` → current z3 produces `unknown`

### Divergence diff

```diff
--- small-2.expected.out (expected)
+++ produced (current z3)
@@ -1,3 +1,3 @@
-sat
+unknown
 (error "line 17 column 0: unexpected character")
 (error "line 17 column 1: unexpected character")
```

(The `(error ...)` lines are expected: the benchmark contains a stray
```` ``` ```` fence on line 17. Only the `sat` → `unknown` change is the
regression.)

## Root cause

`git bisect` over the regression window pins the flip to commit
`208cc5686` ("fix build"), which added `|| m().has_type_vars()` to the
`elim_uncnstr_tactic` guard and an equivalent `if (m.has_type_vars())
return;` to the `elim_unconstrained` simplifier.

`ast_manager::has_type_vars()` is a **manager-wide, sticky** flag: it is
set to `true` as soon as *any* type variable is created, and is never
reset. In particular `finite_set_decl_plugin::init()` creates type
variables `A`/`B` to define its polymorphic signatures. Those type
variables never occur in the user's assertions, but once the finite_set
plugin is initialized — which happens while processing this benchmark —
the flag is globally `true` (confirmed by instrumenting `mk_type_var`:
the only type vars created for this benchmark are the finite_set
signature vars `A` and `B`).

As a result `elim_uncnstr` bails out for goals that contain **no**
polymorphic terms at all, i.e. it is effectively disabled. Unconstrained
subterms that used to be eliminated now reach the theory solvers.

For this benchmark the (single) assertion is `(not (xor (>= x 0) (>= x1
0) (>= x 0) x4 (str.contains ...)))`. The duplicated `(>= x 0)` cancels
(`a xor a = false`), and the free Boolean `x4` can fix the parity
regardless of the value of the `str.contains` term, so the goal is
trivially `sat`. That `str.contains`/`str.replace_re` subterm is
unconstrained and was previously removed by `elim_uncnstr`; without that
elimination it reaches `theory_seq`, which marks `str.replace_re` as
unhandled and gives up in `final_check` → `unknown` (`incomplete (theory
seq)`).

## Fix

Make the guard precise. Keep `has_type_vars()` as a cheap pre-filter
(matching existing usage in `ast_translation.cpp` and
`ast_manager::has_type_var`), but only bail out when the goal / asserted
formulas **actually** contain type-variable typed terms, using the
existing `polymorphism::util::has_type_vars(expr*)`.

This preserves the polymorphism crash-protection (goals with genuine
type-variable terms still skip `elim_uncnstr`) while restoring
`elim_uncnstr` for the vast majority of goals that merely triggered a
polymorphic-plugin initialization. Both twin guards (the `elim_uncnstr`
tactic and the `elim_unconstrained` simplifier) are fixed consistently.

## Validation

Built this checkout and re-ran the benchmark (step 5 of the fixer
workflow):

- `./configure && make -C build -j$(nproc)` — Z3 version 4.17.0.
- Unpatched master reproduced the divergence: `z3 -T:20
iss-6260/small-2.smt2` → `unknown`.
- After the fix, `z3 -T:20 inputs/issues/iss-6260/small-2.smt2` produces
**exactly** the recorded oracle:

```
sat
(error "line 17 column 0: unexpected character")
(error "line 17 column 1: unexpected character")
(error "line 17 column 2: unexpected character")
```

- Regression sanity checks: sibling `iss-6260/small.smt2` unchanged
(`sat`); plain arithmetic unconstrained goals unchanged; polymorphic
goals with genuine type-variable terms (including `declare-type-var` and
forcing `(check-sat-using (then elim-uncnstr smt))`) still solve without
crashing — the guard still fires for those.

Opened as a **draft** for human review.




> Generated by [Fix a Z3 snapshot-regression
divergence](https://github.com/Z3Prover/bench/actions/runs/28844840657)
· 861.2 AIC · ⌖ 45.8 AIC · ⊞ 8.9K ·
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Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

src/ast/simplifiers/elim_unconstrained.cpp

@@ -116,6 +116,7 @@ eliminate:
 #include "ast/ast_ll_pp.h"
 #include "ast/ast_pp.h"
 #include "ast/recfun_decl_plugin.h"
+#include "ast/polymorphism_util.h"
 #include "ast/simplifiers/elim_unconstrained.h"
 
 elim_unconstrained::elim_unconstrained(ast_manager& m, dependent_expr_state& fmls) :
@@ -425,8 +426,18 @@ void elim_unconstrained::update_model_trail(generic_model_converter& mc, vector<
 void elim_unconstrained::reduce() {
     if (!m_config.m_enabled)
         return;
-    if (m.has_type_vars())
-        return;
+    // has_type_vars() is a manager-wide flag that is set as soon as any type variable is
+    // created, including the ones used to define polymorphic signatures of builtin plugins
+    // (e.g. finite_set) that never occur in the asserted formulas. Only bail out when the
+    // formulas actually contain type-variable typed terms, which this simplifier cannot invert.
+    if (m.has_type_vars()) {
+        polymorphism::util u(m);
+        for (unsigned i : indices()) {
+            auto [f, p, d] = m_fmls[i]();
+            if (u.has_type_vars(f))
+                return;
+        }
+    }
     generic_model_converter_ref mc = alloc(generic_model_converter, m, "elim-unconstrained");
     m_inverter.set_model_converter(mc.get());
     m_created_compound = true;

src/tactic/core/elim_uncnstr_tactic.cpp

@@ -27,6 +27,7 @@ Notes:
 #include "ast/datatype_decl_plugin.h"
 #include "ast/seq_decl_plugin.h"
 #include "ast/for_each_expr.h"
+#include "ast/polymorphism_util.h"
 #include "tactic/core/collect_occs.h"
 #include "ast/ast_smt2_pp.h"
 #include "ast/ast_ll_pp.h"
@@ -936,6 +937,21 @@ class elim_uncnstr_tactic : public tactic {
         m_rw = alloc(rw, m(), produce_proofs, m_vars, m_nonvars, m_disabled, m_mc.get(), m_max_memory, m_max_steps);            
     }
 
+    // The manager-wide has_type_vars() flag is a coarse over-approximation: it becomes
+    // true as soon as any type variable is created, including the type variables used to
+    // define the polymorphic signatures of builtin plugins (e.g. finite_set). Those never
+    // occur in the actual goal, so relying on the global flag needlessly disables this
+    // tactic. Check whether the goal itself contains type-variable typed terms instead.
+    bool goal_has_type_vars(goal_ref const & g) {
+        if (!m().has_type_vars())
+            return false;
+        polymorphism::util u(m());
+        for (unsigned i = 0; i < g->size(); ++i)
+            if (u.has_type_vars(g->form(i)))
+                return true;
+        return false;
+    }
+
     void run(goal_ref const & g, goal_ref_buffer & result) {
         bool produce_proofs = g->proofs_enabled();
         TRACE(goal, g->display(tout););
@@ -945,7 +961,7 @@ class elim_uncnstr_tactic : public tactic {
         collect_occs p;
         p(*g, m_vars);
         disable_quantified(g);
-        if (m_vars.empty() || recfun::util(m()).has_rec_defs() || m().has_type_vars()) {
+        if (m_vars.empty() || recfun::util(m()).has_rec_defs() || goal_has_type_vars(g)) {
             result.push_back(g.get());
             // did not increase depth since it didn't do anything.
             return;