diff --git a/array_api_tests/hypothesis_helpers.py b/array_api_tests/hypothesis_helpers.py
index d9fdabd5..0b633ce7 100644
--- a/array_api_tests/hypothesis_helpers.py
+++ b/array_api_tests/hypothesis_helpers.py
@@ -10,7 +10,7 @@
 from hypothesis import assume, reject
 from hypothesis.strategies import (SearchStrategy, booleans, composite, floats,
                                    integers, just, lists, none, one_of,
-                                   sampled_from, shared, builds)
+                                   sampled_from, shared, builds, permutations)
 
 from . import _array_module as xp, api_version
 from . import array_helpers as ah
@@ -148,6 +148,25 @@ def mutually_promotable_dtypes(
     return one_of(strats).map(tuple)
 
 
+@composite
+def mutually_non_promotable_dtypes(
+    draw,
+    max_size: Optional[int] = 2,
+) -> Sequence[Tuple[DataType, ...]]:
+    """Generate a pair of dtypes which cannot be promoted."""
+    assert max_size == 2
+
+    _categories = [
+        (xp.bool,),
+        dh.uint_dtypes + dh.int_dtypes,
+        dh.real_float_dtypes + dh.complex_dtypes
+    ]
+    cat_st = permutations(_categories).map(lambda s: s[:2])
+    cat_from, cat_to = draw(cat_st)
+    from_, to = draw(sampled_from(cat_from)), draw(sampled_from(cat_to))
+    return from_, to
+
+
 class OnewayPromotableDtypes(NamedTuple):
     input_dtype: DataType
     result_dtype: DataType
diff --git a/array_api_tests/test_data_type_functions.py b/array_api_tests/test_data_type_functions.py
index 34c40024..2ae98329 100644
--- a/array_api_tests/test_data_type_functions.py
+++ b/array_api_tests/test_data_type_functions.py
@@ -204,3 +204,13 @@ def test_isdtype(dtype, kind):
 def test_result_type(dtypes):
     out = xp.result_type(*dtypes)
     ph.assert_dtype("result_type", in_dtype=dtypes, out_dtype=out, repr_name="out")
+
+
+@given(hh.mutually_non_promotable_dtypes(2))
+def test_result_type_false(dtypes):
+    """Test _very_ strict promotion rules according to the spec.
+       Conforming array libraries may extend the promotion rules, and
+       then they'll need to xfail this test.
+    """
+    with pytest.raises(TypeError):
+        xp.result_type(*dtypes)