diff --git a/src/Type/ObjectType.php b/src/Type/ObjectType.php
index 25ee53d4e9..78e4473410 100644
--- a/src/Type/ObjectType.php
+++ b/src/Type/ObjectType.php
@@ -1228,14 +1228,14 @@ public function hasOffsetValueType(Type $offsetType): TrinaryLogic
 
 	public function getOffsetValueType(Type $offsetType): Type
 	{
-		if (!$this->isExtraOffsetAccessibleClass()->no()) {
-			return new MixedType();
-		}
-
 		if ($this->isInstanceOf(ArrayAccess::class)->yes()) {
 			return RecursionGuard::run($this, fn (): Type => $this->getMethod('offsetGet', new OutOfClassScope())->getOnlyVariant()->getReturnType());
 		}
 
+		if (!$this->isExtraOffsetAccessibleClass()->no()) {
+			return new MixedType();
+		}
+
 		return new ErrorType();
 	}
 
diff --git a/tests/PHPStan/Analyser/nsrt/bug-12125.php b/tests/PHPStan/Analyser/nsrt/bug-12125.php
new file mode 100644
index 0000000000..815e3cb701
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-12125.php
@@ -0,0 +1,37 @@
+<?php declare(strict_types = 1);
+
+namespace Bug12125;
+
+use ArrayAccess;
+use Exception;
+use stdClass;
+
+use function PHPStan\Testing\assertType;
+
+/** @var ArrayAccess<array-key, stdClass>|array<array-key, stdClass> $bug */
+$bug = [];
+
+assertType('stdClass|null', $bug['key'] ?? null);
+
+interface MyInterface {
+	/** @return array<string, string> | ArrayAccess<string, string> */
+	public function getStrings(): array | ArrayAccess;
+}
+
+function myFunction(MyInterface $container): string {
+	$strings = $container->getStrings();
+	assertType('array<string, string>|ArrayAccess<string, string>', $strings);
+	assertType('string|null', $strings['test']);
+	return $strings['test'];
+}
+
+function myOtherFunction(MyInterface $container): string {
+	$strings = $container->getStrings();
+	assertType('array<string, string>|ArrayAccess<string, string>', $strings);
+	if (isset($strings['test'])) {
+		assertType('string', $strings['test']);
+		return $strings['test'];
+	} else {
+		throw new Exception();
+	}
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-13144.php b/tests/PHPStan/Analyser/nsrt/bug-13144.php
new file mode 100644
index 0000000000..fb47f4d862
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-13144.php
@@ -0,0 +1,23 @@
+<?php
+
+namespace Bug13144;
+
+use ArrayObject;
+
+use function PHPStan\Testing\assertType;
+
+$arr = new ArrayObject(['a' => 1, 'b' => 2]);
+
+assertType('ArrayObject<string, int>', $arr); // correctly inferred as `ArrayObject<string, int>`
+
+$a = $arr['a']; // ok
+$b = $arr['b']; // ok
+
+assertType('int|null', $a); // correctly inferred as `int|null`
+assertType('int|null', $b); // correctly inferred as `int|null`
+
+
+['a' => $a, 'b' => $b] = $arr; // ok
+
+assertType('int|null', $a); // incorrectly inferred as `mixed`
+assertType('int|null', $b); // incorrectly inferred as `mixed`
diff --git a/tests/PHPStan/Analyser/nsrt/bug-9456.php b/tests/PHPStan/Analyser/nsrt/bug-9456.php
new file mode 100644
index 0000000000..22b5e4dad8
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-9456.php
@@ -0,0 +1,71 @@
+<?php // lint >= 8.0
+
+namespace Bug9456;
+
+use ArrayAccess;
+
+use function PHPStan\Testing\assertType;
+
+/**
+ * @template TKey of array-key
+ * @template TValue of mixed
+ *
+ * @implements ArrayAccess<TKey, TValue>
+ */
+class Collection implements ArrayAccess {
+	/**
+	 * @param (callable(TValue, TKey): bool)|TValue|string $key
+	 * @param TValue|string|null $operator
+	 * @param TValue|null $value
+	 * @return static<int<0, 1>, static<TKey, TValue>>
+	 */
+	public function partition($key, $operator = null, $value = null) {} // @phpstan-ignore-line
+
+	/**
+	 * @param TKey $key
+	 * @return TValue
+	 */
+	public function offsetGet($key): mixed { return null; } // @phpstan-ignore-line
+
+	/**
+	 * @param TKey $key
+	 * @return bool
+	 */
+	public function offsetExists($key): bool { return true; }
+
+	/**
+	 * @param TKey|null $key
+	 * @param TValue $value
+	 * @return void
+	 */
+	public function offsetSet($key, $value): void {}
+
+	/**
+	 * @param TKey $key
+	 * @return void
+	 */
+	public function offsetUnset($key): void {}
+}
+
+class HelloWorld
+{
+	/**
+	 * @param Collection<int, string> $collection
+	 */
+	public function sayHello(Collection $collection): void
+	{
+		$result = $collection->partition('key');
+
+		assertType(
+			'Bug9456\Collection<int<0, 1>, Bug9456\Collection<int, string>>',
+			$result
+		);
+		assertType('Bug9456\Collection<int, string>', $result[0]);
+		assertType('Bug9456\Collection<int, string>', $result[1]);
+
+		[$one, $two] = $collection->partition('key');
+
+		assertType('Bug9456\Collection<int, string>', $one);
+		assertType('Bug9456\Collection<int, string>', $two);
+	}
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-9575.php b/tests/PHPStan/Analyser/nsrt/bug-9575.php
new file mode 100644
index 0000000000..fb19202e4f
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-9575.php
@@ -0,0 +1,22 @@
+<?php
+
+namespace Bug9575;
+
+use SimpleXMLElement;
+use function PHPStan\Testing\assertType;
+
+$string = <<<XML
+<a>
+ <foo name="one" game="lonely">1</foo>
+</a>
+XML;
+
+$xml = new SimpleXMLElement($string);
+foreach($xml->foo[0]->attributes() as $a => $b) {
+	echo $a,'="',$b,"\"\n";
+}
+
+assertType('(SimpleXMLElement|null)', $xml->foo);
+assertType('(SimpleXMLElement|null)', $xml->foo[0]);
+assertType('(SimpleXMLElement|null)', $xml->foobar);
+assertType('(SimpleXMLElement|null)', $xml->foo->attributes());