diff --git a/src/Analyser/TypeSpecifier.php b/src/Analyser/TypeSpecifier.php
index 718eb63e3c9..6f8731e5ad1 100644
--- a/src/Analyser/TypeSpecifier.php
+++ b/src/Analyser/TypeSpecifier.php
@@ -1584,6 +1584,15 @@ private function getConditionalSpecifiedTypes(
 		$ifType = $conditionalType->getIf();
 		$elseType = $conditionalType->getElse();
 
+		if (
+			(
+				$argumentExpr instanceof Node\Scalar
+				|| ($argumentExpr instanceof ConstFetch && in_array(strtolower($argumentExpr->name->toString()), ['true', 'false', 'null'], true))
+			) && ($ifType instanceof NeverType || $elseType instanceof NeverType)
+		) {
+			return null;
+		}
+
 		if ($leftType->isSuperTypeOf($ifType)->yes() && $rightType->isSuperTypeOf($elseType)->yes()) {
 			$context = $conditionalType->isNegated() ? TypeSpecifierContext::createFalse() : TypeSpecifierContext::createTrue();
 		} elseif ($leftType->isSuperTypeOf($elseType)->yes() && $rightType->isSuperTypeOf($ifType)->yes()) {
diff --git a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeFunctionCallRuleTest.php b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeFunctionCallRuleTest.php
index 0a399fdc3c6..f67114ce681 100644
--- a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeFunctionCallRuleTest.php
+++ b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeFunctionCallRuleTest.php
@@ -1179,4 +1179,19 @@ public function testBug14177(): void
 		$this->analyse([__DIR__ . '/data/bug-14177.php'], []);
 	}
 
+	public function testBug13566(): void
+	{
+		$this->treatPhpDocTypesAsCertain = true;
+		$this->analyse([__DIR__ . '/data/bug-13566.php'], [
+			[
+				'Call to function is_numeric() with 123 will always evaluate to true.',
+				199,
+			],
+			[
+				'Call to function assertIsInt() with int will always evaluate to true.',
+				204,
+			],
+		]);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeMethodCallRuleTest.php b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeMethodCallRuleTest.php
index fb64511afff..91371852a16 100644
--- a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeMethodCallRuleTest.php
+++ b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeMethodCallRuleTest.php
@@ -290,6 +290,18 @@ public function testBug12087b(): void
 		]);
 	}
 
+	public function testBug13566(): void
+	{
+		$this->treatPhpDocTypesAsCertain = true;
+		$this->analyse([__DIR__ . '/data/bug-13566.php'], []);
+	}
+
+	public function testBug10337(): void
+	{
+		$this->treatPhpDocTypesAsCertain = true;
+		$this->analyse([__DIR__ . '/data/bug-10337.php'], []);
+	}
+
 	public static function getAdditionalConfigFiles(): array
 	{
 		return [
diff --git a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeStaticMethodCallRuleTest.php b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeStaticMethodCallRuleTest.php
index 8a680853799..efd534dda7e 100644
--- a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeStaticMethodCallRuleTest.php
+++ b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeStaticMethodCallRuleTest.php
@@ -161,6 +161,12 @@ public function testBug12087b(): void
 		]);
 	}
 
+	public function testBug13566(): void
+	{
+		$this->treatPhpDocTypesAsCertain = true;
+		$this->analyse([__DIR__ . '/data/bug-13566.php'], []);
+	}
+
 	public static function getAdditionalConfigFiles(): array
 	{
 		return [
diff --git a/tests/PHPStan/Rules/Comparison/data/bug-10337.php b/tests/PHPStan/Rules/Comparison/data/bug-10337.php
new file mode 100644
index 00000000000..a0efb9ca9a5
--- /dev/null
+++ b/tests/PHPStan/Rules/Comparison/data/bug-10337.php
@@ -0,0 +1,62 @@
+<?php declare(strict_types=1);
+
+namespace Bug10337;
+
+use function PHPStan\Testing\assertType;
+
+class App
+{
+	/**
+	 * @return ($calledFromShutdownHandler is true ? void : never)
+	 */
+	public function callExit(bool $calledFromShutdownHandler = false): void
+	{
+		// run before shutdown code here
+
+		if (!$calledFromShutdownHandler) {
+			exit;
+		}
+	}
+
+	public function testOnlyVoid(): void
+	{
+		(new App())->callExit(true);
+	}
+
+	/**
+	 * @return never
+	 */
+	public function testVoidAndNever(): void
+	{
+		$app = new App();
+		assertType('null', $app->callExit(true));
+		assertType('never', $app->callExit(false));
+	}
+
+	/**
+	 * @return never
+	 */
+	public function testVoidAndNever2(): void
+	{
+		$app = new class() extends App {
+		};
+		assertType('null', $app->callExit(true));
+		assertType('never', $app->callExit(false));
+	}
+
+	/**
+	 * @return never
+	 */
+	public function testVoidAndNever3(): void
+	{
+		$app = new class() extends App {
+			#[\Override]
+			public function callExit(bool $calledFromShutdownHandler = false): void
+			{
+				parent::callExit($calledFromShutdownHandler);
+			}
+		};
+		assertType('null', $app->callExit(true));
+		assertType('never', $app->callExit(false));
+	}
+}
diff --git a/tests/PHPStan/Rules/Comparison/data/bug-13566.php b/tests/PHPStan/Rules/Comparison/data/bug-13566.php
new file mode 100644
index 00000000000..0f0ac5a4b4d
--- /dev/null
+++ b/tests/PHPStan/Rules/Comparison/data/bug-13566.php
@@ -0,0 +1,212 @@
+<?php // lint >= 8.0
+
+declare(strict_types = 1);
+
+namespace Bug13566;
+
+use LogicException;
+
+class ReturnViaBool
+{
+	/** @return ($exit is true ? never : void) */
+	public static function notFound(bool $exit = true): void
+	{
+		header('HTTP/1.1 404 Not Found', true, 404);
+
+		if ($exit) {
+			echo '404 Not Found';
+			exit;
+		}
+	}
+
+	public function test(): void
+	{
+		// send 404 header without exiting
+		self::notFound(false);
+	}
+}
+
+class ReturnViaInt
+{
+	/** @return ($exit is 1 ? never : void) */
+	public static function notFound(int $exit = 1): void
+	{
+		header('HTTP/1.1 404 Not Found', true, 404);
+
+		if ($exit == 1) {
+			echo '404 Not Found';
+			exit;
+		}
+	}
+
+	public function test(): void
+	{
+		// send 404 header
+		self::notFound(0);
+	}
+}
+
+class ReturnViaString
+{
+	/** @return ($exit is '1' ? never : void) */
+	public static function notFound(string $exit = '1'): void
+	{
+		header('HTTP/1.1 404 Not Found', true, 404);
+
+		if ($exit == '1') {
+			echo '404 Not Found';
+			exit;
+		}
+	}
+
+	public function test(): void
+	{
+		// send 404 header
+		self::notFound('0');
+	}
+}
+
+class ReturnViaIntNonNative
+{
+	/** @return ($exit is 1 ? never : void) */
+	public static function notFound(int $exit = 1)
+	{
+		header('HTTP/1.1 404 Not Found', true, 404);
+
+		if ($exit == 1) {
+			echo '404 Not Found';
+			exit;
+		}
+	}
+
+	public function test(): void
+	{
+		// send 404 header
+		self::notFound(0);
+	}
+}
+
+class ReturnsMaybeNever
+{
+	/** @return ($exit is true ? never : 1) */
+	public static function notFound(bool $exit = true)
+	{
+		header('HTTP/1.1 404 Not Found', true, 404);
+
+		if ($exit) {
+			echo '404 Not Found';
+			exit;
+		}
+		return 1;
+	}
+
+	public function test(): void
+	{
+		// send 404 header
+		self::notFound(false);
+
+	}
+}
+
+class ReturnsMaybeVoid
+{
+	/** @return ($exit is true ? void : 1) */
+	public static function notFound(bool $exit = true)
+	{
+		header('HTTP/1.1 404 Not Found', true, 404);
+
+		if ($exit) {
+			echo '404 Not Found';
+			return;
+		}
+		return 1;
+	}
+
+	public function test(): void
+	{
+		// send 404 header
+		self::notFound(false);
+
+	}
+}
+
+
+
+class ReturnsWithInstanceMethod
+{
+	/** @return ($exit is true ? never-return : void) */
+	public function notFound(bool $exit = true): void
+	{
+		header('HTTP/1.1 404 Not Found', true, 404);
+
+		if ($exit) {
+			echo '404 Not Found';
+			exit;
+		}
+	}
+
+
+	public function test(): void
+	{
+		// send 404 header
+		$this->notFound(false);
+
+	}
+}
+
+/** @return ($exit is true ? never-return : void) */
+function notFound(bool $exit = true): void
+{
+	header('HTTP/1.1 404 Not Found', true, 404);
+
+	if ($exit) {
+		echo '404 Not Found';
+		exit;
+	}
+}
+
+function test(): void
+{
+	// send 404 header
+	notFound(false);
+}
+
+
+class ReturnViaUnion
+{
+	/**
+	 * @return ($exit is int ? void : never)
+	 */
+	public static function notFound(int|string $exit = 'hello world'): void
+	{
+		header('HTTP/1.1 404 Not Found', true, 404);
+
+		if (!is_int($exit)) {
+			echo '404 Not Found';
+			exit;
+		}
+	}
+
+	public function test(): void
+	{
+		// send 404 header
+		self::notFound(0);
+	}
+}
+
+
+$x = 123;
+if (is_numeric($x)) {
+}
+
+function doFoo($mixed) {
+	assertIsInt($mixed);
+	assertIsInt($mixed);
+}
+
+/** @phpstan-assert int $i */
+function assertIsInt($i):void {
+	if (!is_int($i)) {
+		throw new \LogicException();
+	}
+}