Spacer QE: avoid assertion on extended arithmetic model values and add #3845 regression (#10096)

Spacer crashed in quantifier-elimination projection on certain HORN
inputs when model evaluation produced arithmetic expressions that were
not plain numerals. The failure was an assertion in
`spacer_qe_project.cpp` during sign/offset computation for projected
literals.

- **Projection robustness in Spacer arithmetic QE**
- Updated numeral extraction in `src/muz/spacer/spacer_qe_project.cpp`
from `is_numeral` to `is_extended_numeral` at all model-evaluation sites
used by projection.
- This covers evaluated arithmetic forms (e.g., normalized arithmetic
expressions) that are semantically numeric but not syntactic numerals,
preventing assertion failures in disequality/equality handling and bound
selection.

- **Regression coverage for the crashing HORN shape**
- Added a focused regression in `src/test/api_datalog.cpp` that
evaluates the reported Spacer/HORN input pattern through
`Z3_eval_smtlib2_string`.
- The test exercises the exact QE/projection path that previously
triggered the assertion.

```cpp
// Before
VERIFY(a.is_numeral(val, r));

// After
VERIFY(a.is_extended_numeral(val, r));
```

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>

src/muz/spacer/spacer_qe_project.cpp

@@ -367,7 +367,7 @@ class arith_project_util {
                         cx = mk_mul(c, m_var->x());
                         cxt = mk_add(cx, t);
                         val = mdl(cxt);
-                        VERIFY(a.is_numeral(val, r));
+                        VERIFY(a.is_extended_numeral(val, r));
                         SASSERT(r > rational::zero() || r < rational::zero());
                         if (r > rational::zero()) {
                             c = -c;
@@ -473,7 +473,7 @@ class arith_project_util {
                 cx = mk_mul(c, m_var->x());
                 cxt = mk_add(cx, t);
                 val = mdl(cxt);
-                VERIFY(a.is_numeral(val, r));
+                VERIFY(a.is_extended_numeral(val, r));
 
                 if (is_eq) {
                     TRACE(qe, tout << "equality term\n";);
@@ -711,7 +711,7 @@ class arith_project_util {
             cx = mk_mul(m_coeffs[max_t], m_var->x());
             cxt = mk_add(cx, m_terms.get(max_t));
             val = mdl(cxt);
-            VERIFY(a.is_numeral(val, r));
+            VERIFY(a.is_extended_numeral(val, r));
 
             // get the offset from the smallest/largest possible value for x
             // literal      smallest/largest val of x
@@ -771,13 +771,13 @@ class arith_project_util {
         // evaluate x in mdl
         rational r_x;
         val = mdl(m_var->x());
-        VERIFY(a.is_numeral(val, r_x));
+        VERIFY(a.is_extended_numeral(val, r_x));
 
         for (unsigned i = 0; i < m_terms.size(); ++i) {
             rational const &ac = m_coeffs[i];
             if (!m_eq[i] && ac.is_pos() == do_pos) {
                 val = mdl(m_terms.get(i));
-                VERIFY(a.is_numeral(val, r));
+                VERIFY(a.is_extended_numeral(val, r));
                 r /= abs(ac);
                 // skip the literal if false in the model
                 if (do_pos) {