diff --git a/src/Analyser/TypeSpecifier.php b/src/Analyser/TypeSpecifier.php
index c094bbd0c4..8f786167e6 100644
--- a/src/Analyser/TypeSpecifier.php
+++ b/src/Analyser/TypeSpecifier.php
@@ -259,63 +259,76 @@ public function specifyTypesInCondition(
 				);
 			}
 
-			if ($context->true()) {
-				$type = TypeCombinator::intersect($scope->getType($expr->right), $scope->getType($expr->left));
-				$leftTypes = $this->create($expr->left, $type, $context, false, $scope);
-				$rightTypes = $this->create($expr->right, $type, $context, false, $scope);
+			$exprLeftType = $scope->getType($expr->left);
+			$exprRightType = $scope->getType($expr->right);
+
+			$identicalType = $scope->getType($expr);
+			if ($identicalType instanceof ConstantBooleanType && !$context->null()) {
+				$never = new NeverType();
+				$contextForTypes = $identicalType->getValue() ? $context->negate() : $context;
+				$leftTypes = $this->create($expr->left, $never, $contextForTypes, false, $scope);
+				$rightTypes = $this->create($expr->right, $never, $contextForTypes, false, $scope);
 				return $leftTypes->unionWith($rightTypes);
+			}
 
-			} elseif ($context->false()) {
-				$identicalType = $scope->getType($expr);
-				if ($identicalType instanceof ConstantBooleanType) {
-					$never = new NeverType();
-					$contextForTypes = $identicalType->getValue() ? $context->negate() : $context;
-					$leftTypes = $this->create($expr->left, $never, $contextForTypes, false, $scope);
-					$rightTypes = $this->create($expr->right, $never, $contextForTypes, false, $scope);
-					return $leftTypes->unionWith($rightTypes);
-				}
+			$types = null;
 
-				$exprLeftType = $scope->getType($expr->left);
-				$exprRightType = $scope->getType($expr->right);
+			if (
+				(
+					$exprLeftType instanceof ConstantType
+					&& !$expr->right instanceof Node\Scalar
+				) || $exprLeftType instanceof EnumCaseObjectType
+			) {
+				$types = $this->create(
+					$expr->right,
+					$exprLeftType,
+					$context,
+					false,
+					$scope,
+				);
+			}
+			if (
+				(
+					$exprRightType instanceof ConstantType
+					&& !$expr->left instanceof Node\Scalar
+				) || $exprRightType instanceof EnumCaseObjectType
+			) {
+				$leftType = $this->create(
+					$expr->left,
+					$exprRightType,
+					$context,
+					false,
+					$scope,
+				);
+				if ($types !== null) {
+					$types = $types->unionWith($leftType);
+				} else {
+					$types = $leftType;
+				}
+			}
 
-				$types = null;
+			if ($types !== null) {
+				return $types;
+			}
 
-				if (
-					(
-						$exprLeftType instanceof ConstantType
-						&& !$expr->right instanceof Node\Scalar
-					) || $exprLeftType instanceof EnumCaseObjectType
-				) {
-					$types = $this->create(
-						$expr->right,
-						$exprLeftType,
-						$context,
-						false,
-						$scope,
-					);
+			$furtherSpecificationPossible = static function (Expr $expr) use (&$furtherSpecificationPossible): bool {
+				if ($expr instanceof Expr\Variable) {
+					return true;
 				}
-				if (
-					(
-						$exprRightType instanceof ConstantType
-						&& !$expr->left instanceof Node\Scalar
-					) || $exprRightType instanceof EnumCaseObjectType
-				) {
-					$leftType = $this->create(
-						$expr->left,
-						$exprRightType,
-						$context,
-						false,
-						$scope,
-					);
-					if ($types !== null) {
-						$types = $types->unionWith($leftType);
-					} else {
-						$types = $leftType;
-					}
+
+				if ($expr instanceof ArrayDimFetch) {
+					return $furtherSpecificationPossible($expr->var);
 				}
 
-				if ($types !== null) {
-					return $types;
+				return false;
+			};
+
+			if ($furtherSpecificationPossible($expr->left) || $furtherSpecificationPossible($expr->right)) {
+				if ($context->true()) {
+					$type = TypeCombinator::intersect($scope->getType($expr->right), $scope->getType($expr->left));
+					$leftTypes = $this->create($expr->left, $type, $context, false, $scope);
+					$rightTypes = $this->create($expr->right, $type, $context, false, $scope);
+					return $leftTypes->unionWith($rightTypes);
 				}
 
 				return $this->create($expr->left, $exprLeftType, $context, false, $scope)->normalize($scope)
diff --git a/tests/PHPStan/Analyser/TypeSpecifierTest.php b/tests/PHPStan/Analyser/TypeSpecifierTest.php
index 9ea86aedaf..43af6df355 100644
--- a/tests/PHPStan/Analyser/TypeSpecifierTest.php
+++ b/tests/PHPStan/Analyser/TypeSpecifierTest.php
@@ -554,7 +554,6 @@ public function dataCondition(): array
 				),
 				[
 					'$foo' => '123',
-					123 => '123',
 				],
 				['$foo' => '~123'],
 			],
diff --git a/tests/PHPStan/Analyser/data/equal.php b/tests/PHPStan/Analyser/data/equal.php
index 113d2868b2..6fb7929cc1 100644
--- a/tests/PHPStan/Analyser/data/equal.php
+++ b/tests/PHPStan/Analyser/data/equal.php
@@ -99,4 +99,14 @@ public function stdClass(\stdClass $a, \stdClass $b): void
 		assertType('stdClass', $b);
 	}
 
+	/**
+	 * @param array{a: string, b: array{c: string|null}} $a
+	 */
+	public function arrayOffset(array $a): void
+	{
+		if (strlen($a['a']) > 0 && $a['a'] === $a['b']['c']) {
+			assertType('array{a: non-empty-string, b: array{c: non-empty-string}}', $a);
+		}
+	}
+
 }
diff --git a/tests/PHPStan/Analyser/data/identical.php b/tests/PHPStan/Analyser/data/identical.php
index 26602e2918..f46c675214 100644
--- a/tests/PHPStan/Analyser/data/identical.php
+++ b/tests/PHPStan/Analyser/data/identical.php
@@ -41,4 +41,14 @@ public function foo(\stdClass $a, \stdClass $b): void
 		assertType('stdClass', $b);
 	}
 
+	/**
+	 * @param array{a: string, b: array{c: string|null}} $a
+	 */
+	public function arrayOffset(array $a): void
+	{
+		if (strlen($a['a']) > 0 && $a['a'] === $a['b']['c']) {
+			assertType('array{a: non-empty-string, b: array{c: non-empty-string}}', $a);
+		}
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Arrays/NonexistentOffsetInArrayDimFetchRuleTest.php b/tests/PHPStan/Rules/Arrays/NonexistentOffsetInArrayDimFetchRuleTest.php
index ccaacd8b11..5621266e40 100644
--- a/tests/PHPStan/Rules/Arrays/NonexistentOffsetInArrayDimFetchRuleTest.php
+++ b/tests/PHPStan/Rules/Arrays/NonexistentOffsetInArrayDimFetchRuleTest.php
@@ -163,6 +163,10 @@ public function testRule(): void
 				'Cannot access offset \'foo\' on array|int.',
 				443,
 			],
+			[
+				'Offset \'feature_pretty…\' does not exist on array{version: non-empty-string, commit: string|null, pretty_version: string|null, feature_version: non-empty-string, feature_pretty_version?: string|null}.',
+				504,
+			],
 		]);
 	}
 
diff --git a/tests/PHPStan/Rules/Arrays/data/nonexistent-offset.php b/tests/PHPStan/Rules/Arrays/data/nonexistent-offset.php
index d74ee08af5..065d636722 100644
--- a/tests/PHPStan/Rules/Arrays/data/nonexistent-offset.php
+++ b/tests/PHPStan/Rules/Arrays/data/nonexistent-offset.php
@@ -485,3 +485,26 @@ function test($array): void {
 	}
 
 }
+
+/**
+ * @phpstan-type Version array{version: string, commit: string|null, pretty_version: string|null, feature_version?: string|null, feature_pretty_version?: string|null}
+ */
+class VersionGuesser
+{
+	/**
+	 * @param array $versionData
+	 *
+	 * @phpstan-param Version $versionData
+	 *
+	 * @return array
+	 * @phpstan-return Version
+	 */
+	private function postprocess(array $versionData): array
+	{
+		if (!empty($versionData['feature_version']) && $versionData['feature_version'] === $versionData['version'] && $versionData['feature_pretty_version'] === $versionData['pretty_version']) {
+			unset($versionData['feature_version'], $versionData['feature_pretty_version']);
+		}
+
+		return $versionData;
+	}
+}
diff --git a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeMethodCallRuleTest.php b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeMethodCallRuleTest.php
index 31d32db056..86128a9bd5 100644
--- a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeMethodCallRuleTest.php
+++ b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeMethodCallRuleTest.php
@@ -80,6 +80,54 @@ public function testRule(): void
 				'Call to method ImpossibleMethodCall\Foo::isSame() with *NEVER* and stdClass will always evaluate to false.',
 				84,
 			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isSame() with \'foo\' and \'foo\' will always evaluate to true.',
+				101,
+			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isNotSame() with \'foo\' and \'foo\' will always evaluate to false.',
+				104,
+			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isSame() with array{} and array{} will always evaluate to true.',
+				113,
+			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isNotSame() with array{} and array{} will always evaluate to false.',
+				116,
+			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isSame() with array{1, 3} and array{1, 3} will always evaluate to true.',
+				119,
+			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isNotSame() with array{1, 3} and array{1, 3} will always evaluate to false.',
+				122,
+			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isSame() with 1 and stdClass will always evaluate to false.',
+				126,
+			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isNotSame() with 1 and stdClass will always evaluate to true.',
+				130,
+			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isSame() with \'1\' and stdClass will always evaluate to false.',
+				133,
+			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isNotSame() with \'1\' and stdClass will always evaluate to true.',
+				136,
+			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isSame() with array{\'a\', \'b\'} and array{1, 2} will always evaluate to false.',
+				139,
+			],
+			[
+				'Call to method ImpossibleMethodCall\Foo::isNotSame() with array{\'a\', \'b\'} and array{1, 2} will always evaluate to true.',
+				142,
+			],
 		]);
 	}
 
diff --git a/tests/PHPStan/Rules/Comparison/data/impossible-method-call.php b/tests/PHPStan/Rules/Comparison/data/impossible-method-call.php
index c213bfb8d5..14564e2912 100644
--- a/tests/PHPStan/Rules/Comparison/data/impossible-method-call.php
+++ b/tests/PHPStan/Rules/Comparison/data/impossible-method-call.php
@@ -92,6 +92,56 @@ public function doDolor(\stdClass $std1, \stdClass $std2)
 
 			}
 		}
+		if ($this->isSame(self::createStdClass('a'), self::createStdClass('a'))) {
+
+		}
+		if ($this->isNotSame(self::createStdClass('b'), self::createStdClass('b'))) {
+
+		}
+		if ($this->isSame(self::returnFoo('a'), self::returnFoo('a'))) {
+
+		}
+		if ($this->isNotSame(self::returnFoo('b'), self::returnFoo('b'))) {
+
+		}
+		if ($this->isSame(self::createStdClass('a')->foo, self::createStdClass('a')->foo)) {
+
+		}
+		if ($this->isNotSame(self::createStdClass('b')->foo, self::createStdClass('b')->foo)) {
+
+		}
+		if ($this->isSame([], [])) {
+
+		}
+		if ($this->isNotSame([], [])) {
+
+		}
+		if ($this->isSame([1, 3], [1, 3])) {
+
+		}
+		if ($this->isNotSame([1, 3], [1, 3])) {
+
+		}
+		$std3 = new \stdClass();
+		if ($this->isSame(1, $std3)) {
+
+		}
+		$std4 = new \stdClass();
+		if ($this->isNotSame(1, $std4)) {
+
+		}
+		if ($this->isSame('1', new \stdClass())) {
+
+		}
+		if ($this->isNotSame('1', new \stdClass())) {
+
+		}
+		if ($this->isSame(['a', 'b'], [1, 2])) {
+
+		}
+		if ($this->isNotSame(['a', 'b'], [1, 2])) {
+
+		}
 	}
 
 	public function nullableInt(): ?int
@@ -99,4 +149,17 @@ public function nullableInt(): ?int
 
 	}
 
+	public static function createStdClass(string $foo): \stdClass
+	{
+		return new \stdClass();
+	}
+
+	/**
+	 * @return 'foo'
+	 */
+	public static function returnFoo(string $foo): string
+	{
+		return 'foo';
+	}
+
 }