diff --git a/core/modules/system/tests/modules/system_incompatible_core_version_dependencies_test/system_incompatible_core_version_dependencies_test.info.yml b/core/modules/system/tests/modules/system_incompatible_core_version_dependencies_test/system_incompatible_core_version_dependencies_test.info.yml
index f429775dd3..35dd9d8948 100644
--- a/core/modules/system/tests/modules/system_incompatible_core_version_dependencies_test/system_incompatible_core_version_dependencies_test.info.yml
+++ b/core/modules/system/tests/modules/system_incompatible_core_version_dependencies_test/system_incompatible_core_version_dependencies_test.info.yml
@@ -4,4 +4,4 @@ description: 'Support module for testing system dependencies.'
 package: Testing
 version: VERSION
 dependencies:
-  - drupal:system_incompatible_core_version_test
+  - drupal:system_core_incompatible_semver_test
diff --git a/core/modules/system/tests/modules/system_incompatible_core_version_test/system_incompatible_core_version_test.info.yml b/core/modules/system/tests/modules/system_incompatible_core_version_test/system_incompatible_core_version_test.info.yml
deleted file mode 100644
index 7f671a15e4..0000000000
--- a/core/modules/system/tests/modules/system_incompatible_core_version_test/system_incompatible_core_version_test.info.yml
+++ /dev/null
@@ -1,6 +0,0 @@
-name: 'System incompatible core version test'
-type: module
-description: 'Support module for testing system dependencies.'
-package: Testing
-version: VERSION
-core: 8.x
diff --git a/core/modules/system/tests/modules/system_test/system_test.module b/core/modules/system/tests/modules/system_test/system_test.module
index 4fed070ec5..0e6f41352d 100644
--- a/core/modules/system/tests/modules/system_test/system_test.module
+++ b/core/modules/system/tests/modules/system_test/system_test.module
@@ -70,7 +70,6 @@ function system_test_system_info_alter(&$info, Extension $file, $type) {
     'system_incompatible_module_version_dependencies_test',
     'system_incompatible_core_version_dependencies_test',
     'system_incompatible_module_version_test',
-    'system_incompatible_core_version_test',
   ])) {
     $info['hidden'] = FALSE;
   }
diff --git a/core/modules/system/tests/src/Functional/Module/DependencyTest.php b/core/modules/system/tests/src/Functional/Module/DependencyTest.php
index fae801f459..c5027c37fd 100644
--- a/core/modules/system/tests/src/Functional/Module/DependencyTest.php
+++ b/core/modules/system/tests/src/Functional/Module/DependencyTest.php
@@ -91,7 +91,7 @@ public function testIncompatibleCoreVersionDependency() {
     // marked as having an incompatible dependency.
     $this->drupalGet('admin/modules');
     $this->assertRaw(t('@module (<span class="admin-missing">incompatible with</span> this version of Drupal core)', [
-      '@module' => 'System incompatible core version test',
+      '@module' => 'System core incompatible semver test',
     ]), 'A module that depends on a module with an incompatible core version is marked as such.');
     $checkbox = $this->xpath('//input[@type="checkbox" and @disabled="disabled" and @name="modules[system_incompatible_core_version_dependencies_test][enable]"]');
     $this->assert(count($checkbox) == 1, 'Checkbox for the module is disabled.');
@@ -115,7 +115,6 @@ public function testCoreCompatibility() {
 
     // Test incompatible 'core_version_requirement'.
     $this->drupalGet('admin/modules');
-    $assert_session->fieldDisabled('modules[system_incompatible_core_version_test][enable]');
     $assert_session->fieldDisabled('modules[system_core_incompatible_semver_test][enable]');
 
     // Test compatible 'core_version_requirement' and compatible 'core'.
diff --git a/core/modules/system/tests/src/Functional/System/ThemeTest.php b/core/modules/system/tests/src/Functional/System/ThemeTest.php
index 2a7b5f898c..db473afc7a 100644
--- a/core/modules/system/tests/src/Functional/System/ThemeTest.php
+++ b/core/modules/system/tests/src/Functional/System/ThemeTest.php
@@ -376,7 +376,6 @@ public function testInvalidTheme() {
     // Check for the error text of a theme with the wrong core version
     // using 7.x and ^7.
     $incompatible_core_message = 'This theme is not compatible with Drupal ' . \Drupal::VERSION . ". Check that the .info.yml file contains a compatible 'core' or 'core_version_requirement' value.";
-    $this->assertThemeIncompatibleText('Theme test with invalid core version', $incompatible_core_message);
     $this->assertThemeIncompatibleText('Theme test with invalid semver core version', $incompatible_core_message);
     // Check for the error text of a theme without a content region.
     $this->assertText("This theme is missing a 'content' region.");
diff --git a/core/modules/system/tests/themes/test_invalid_core/test_invalid_core.info.yml b/core/modules/system/tests/themes/test_invalid_core/test_invalid_core.info.yml
deleted file mode 100644
index 9651b62df3..0000000000
--- a/core/modules/system/tests/themes/test_invalid_core/test_invalid_core.info.yml
+++ /dev/null
@@ -1,7 +0,0 @@
-name: 'Theme test with invalid core version'
-type: theme
-base theme: stable
-description: 'Test theme which has an invalid core version.'
-version: VERSION
-package: Testing
-core: 8.x
diff --git a/core/tests/Drupal/KernelTests/Core/Extension/ModuleInstallerTest.php b/core/tests/Drupal/KernelTests/Core/Extension/ModuleInstallerTest.php
index 24b3261a7e..696a4f798b 100644
--- a/core/tests/Drupal/KernelTests/Core/Extension/ModuleInstallerTest.php
+++ b/core/tests/Drupal/KernelTests/Core/Extension/ModuleInstallerTest.php
@@ -103,14 +103,6 @@ public function testInvalidCoreInstall($module_name, $install_dependencies) {
    */
   public function providerTestInvalidCoreInstall() {
     return [
-      'no dependencies system_incompatible_core_version_test' => [
-        'system_incompatible_core_version_test',
-        FALSE,
-      ],
-      'install_dependencies system_incompatible_core_version_test' => [
-        'system_incompatible_core_version_test',
-        TRUE,
-      ],
       'no dependencies system_core_incompatible_semver_test' => [
         'system_core_incompatible_semver_test',
         FALSE,
@@ -129,7 +121,7 @@ public function providerTestInvalidCoreInstall() {
    */
   public function testDependencyInvalidCoreInstall() {
     $this->expectException(MissingDependencyException::class);
-    $this->expectExceptionMessage("Unable to install modules: module 'system_incompatible_core_version_dependencies_test'. Its dependency module 'system_incompatible_core_version_test' is incompatible with this version of Drupal core.");
+    $this->expectExceptionMessage("Unable to install modules: module 'system_incompatible_core_version_dependencies_test'. Its dependency module 'system_core_incompatible_semver_test' is incompatible with this version of Drupal core.");
     $this->container->get('module_installer')->install(['system_incompatible_core_version_dependencies_test']);
   }