diff --git a/pyk/src/pyk/kast/inner.py b/pyk/src/pyk/kast/inner.py
index 957981fd67f..18c3360a6ae 100644
--- a/pyk/src/pyk/kast/inner.py
+++ b/pyk/src/pyk/kast/inner.py
@@ -877,6 +877,22 @@ def _var_occurence(_term: KInner) -> None:
     return _var_occurrences
 
 
+def keep_vars_sorted(occurrences: dict[str, list[KVariable]]) -> dict[str, KVariable]:
+    """Keep the sort of variables from the occurrences dictionary."""
+    occurrences_sorted: dict[str, KVariable] = {}
+    for k, vs in occurrences.items():
+        sort = None
+        for v in vs:
+            if v.sort is not None:
+                if sort is None:
+                    sort = v.sort
+                elif sort != v.sort:
+                    sort = None
+                    break
+        occurrences_sorted[k] = KVariable(k, sort)
+    return occurrences_sorted
+
+
 def collect(callback: Callable[[KInner], None], kinner: KInner) -> None:
     """Collect information about a given term traversing it top-down using a function with side effects.
 
diff --git a/pyk/src/pyk/kast/manip.py b/pyk/src/pyk/kast/manip.py
index 4f4056d703a..dd34a624497 100644
--- a/pyk/src/pyk/kast/manip.py
+++ b/pyk/src/pyk/kast/manip.py
@@ -21,6 +21,7 @@
     bottom_up,
     collect,
     flatten_label,
+    keep_vars_sorted,
     top_down,
     var_occurrences,
 )
@@ -780,23 +781,24 @@ def build_rule(
 
     lhs_vars = free_vars(init_term)
     rhs_vars = free_vars(final_term)
-    var_occurrences = count_vars(
+    occurrences = var_occurrences(
         mlAnd(
             [push_down_rewrites(KRewrite(init_config, final_config))] + init_constraints + final_constraints,
             GENERATED_TOP_CELL,
         )
     )
+    sorted_vars = keep_vars_sorted(occurrences)
     v_subst: dict[str, KVariable] = {}
     vremap_subst: dict[str, KVariable] = {}
-    for v in var_occurrences:
+    for v in occurrences:
         new_v = v
-        if var_occurrences[v] == 1:
+        if len(occurrences[v]) == 1:
             new_v = '_' + new_v
         if v in rhs_vars and v not in lhs_vars:
             new_v = '?' + new_v
         if new_v != v:
-            v_subst[v] = KVariable(new_v)
-            vremap_subst[new_v] = KVariable(v)
+            v_subst[v] = KVariable(new_v, sorted_vars[v].sort)
+            vremap_subst[new_v] = sorted_vars[v]
 
     new_init_config = Subst(v_subst)(init_config)
     new_init_constraints = [Subst(v_subst)(c) for c in init_constraints]
diff --git a/pyk/src/tests/integration/proof/test_refute_node.py b/pyk/src/tests/integration/proof/test_refute_node.py
index 34f99d4977c..7c887322689 100644
--- a/pyk/src/tests/integration/proof/test_refute_node.py
+++ b/pyk/src/tests/integration/proof/test_refute_node.py
@@ -295,7 +295,7 @@ def test_apr_proof_refute_node_to_claim(
         expected = KClaim(
             body=KRewrite(KApply('_<=Int_', KVariable('N', 'Int'), KToken('0', 'Int')), KToken('false', 'Bool')),
             requires=KApply(
-                '_<=Int_', KApply('_+Int_', KVariable('_L', None), KVariable('N', 'Int')), KToken('0', 'Int')
+                '_<=Int_', KApply('_+Int_', KVariable('_L', 'Int'), KVariable('N', 'Int')), KToken('0', 'Int')
             ),
             att=KAtt(entries=[Atts.LABEL('refute-node-claim')]),
         )
diff --git a/pyk/src/tests/unit/kast/test_inner.py b/pyk/src/tests/unit/kast/test_inner.py
index 35c84dbe8ae..d34bc5fd342 100644
--- a/pyk/src/tests/unit/kast/test_inner.py
+++ b/pyk/src/tests/unit/kast/test_inner.py
@@ -5,7 +5,7 @@
 
 import pytest
 
-from pyk.kast.inner import flatten_label
+from pyk.kast.inner import KVariable, flatten_label, keep_vars_sorted
 
 from ..utils import a, f, g, x, y, z
 
@@ -40,3 +40,32 @@ def test_flatten_label(label: str, kast: KInner, expected: list[KInner]) -> None
 
     # Then
     assert actual == expected
+
+
+KEEP_VARS_SORTED_DATA: Final[tuple[tuple[dict[str, list[KVariable]], dict[str, KVariable]], ...]] = (
+    (
+        {'a': [KVariable('a'), KVariable('a')], 'b': [KVariable('b'), KVariable('b')]},
+        {'a': KVariable('a'), 'b': KVariable('b')},
+    ),
+    (
+        {'a': [KVariable('a', 'K'), KVariable('a', 'X')], 'b': [KVariable('b', 'K'), KVariable('b', 'X')]},
+        {'a': KVariable('a'), 'b': KVariable('b')},
+    ),
+    (
+        {'a': [KVariable('a', 'K'), KVariable('a')], 'b': [KVariable('b', 'K'), KVariable('b', 'K')]},
+        {'a': KVariable('a', 'K'), 'b': KVariable('b', 'K')},
+    ),
+    (
+        {'a': [KVariable('a', 'A'), KVariable('a'), KVariable('a', 'B')]},
+        {'a': KVariable('a')},
+    ),
+)
+
+
+@pytest.mark.parametrize('occurrences,expected', KEEP_VARS_SORTED_DATA, ids=count())
+def test_keep_vars_sorted(occurrences: dict[str, list[KVariable]], expected: dict[str, KVariable]) -> None:
+    # When
+    actual = keep_vars_sorted(occurrences)
+
+    # Then
+    assert actual == expected
diff --git a/pyk/src/tests/unit/test_cterm.py b/pyk/src/tests/unit/test_cterm.py
index 50490870d35..82674b677d4 100644
--- a/pyk/src/tests/unit/test_cterm.py
+++ b/pyk/src/tests/unit/test_cterm.py
@@ -103,14 +103,14 @@ def test_cterm_match_with_constraint(t1: CTerm, t2: CTerm) -> None:
 
 BUILD_RULE_TEST_DATA: Final = (
     (
-        T(k(KVariable('K_CELL')), mem(KVariable('MEM_CELL'))),
+        T(k(KVariable('K_CELL', 'K')), mem(KVariable('MEM_CELL'))),
         T(
             k(KVariable('K_CELL')),
             mem(KApply('_[_<-_]', [KVariable('MEM_CELL'), KVariable('KEY'), KVariable('VALUE')])),
         ),
         ['K_CELL'],
         T(
-            k(KVariable('_K_CELL')),
+            k(KVariable('_K_CELL', 'K')),
             mem(
                 KRewrite(
                     KVariable('MEM_CELL'),