diff --git a/activejob/test/integration/queuing_test.rb b/activejob/test/integration/queuing_test.rb
index e1634972d1..1d1e675435 100644
--- a/activejob/test/integration/queuing_test.rb
+++ b/activejob/test/integration/queuing_test.rb
@@ -59,14 +59,13 @@ class QueuingTest < ActiveSupport::TestCase
   test 'should supply a provider_job_id when available for immediate jobs' do
     skip unless adapter_is?(:delayed_job, :sidekiq, :qu, :que)
     test_job = TestJob.perform_later @id
-    refute test_job.provider_job_id.nil?, 'Provider job id should be set by provider'
+    assert test_job.provider_job_id, 'Provider job id should be set by provider'
   end
 
   test 'should supply a provider_job_id when available for delayed jobs' do
     skip unless adapter_is?(:delayed_job, :sidekiq, :que)
     delayed_test_job = TestJob.set(wait: 1.minute).perform_later @id
-    refute delayed_test_job.provider_job_id.nil?,
-      'Provider job id should by set for delayed jobs by provider'
+    assert delayed_test_job.provider_job_id, 'Provider job id should by set for delayed jobs by provider'
   end
 
   test 'current locale is kept while running perform_later' do
diff --git a/activerecord/test/cases/adapters/mysql/quoting_test.rb b/activerecord/test/cases/adapters/mysql/quoting_test.rb
index 426b088e2f..2024aa36ab 100644
--- a/activerecord/test/cases/adapters/mysql/quoting_test.rb
+++ b/activerecord/test/cases/adapters/mysql/quoting_test.rb
@@ -24,6 +24,6 @@ class MysqlQuotingTest < ActiveRecord::MysqlTestCase
     @conn.stubs(:full_version).returns('5.6.3')
     @conn.remove_instance_variable(:@version) if @conn.instance_variable_defined?(:@version)
     t = Time.now.change(usec: 1)
-    refute_match(/\.000001\z/, @conn.quoted_date(t))
+    assert_no_match(/\.000001\z/, @conn.quoted_date(t))
   end
 end
diff --git a/activerecord/test/cases/adapters/mysql2/quoting_test.rb b/activerecord/test/cases/adapters/mysql2/quoting_test.rb
index 92221e61bf..2de7e1b526 100644
--- a/activerecord/test/cases/adapters/mysql2/quoting_test.rb
+++ b/activerecord/test/cases/adapters/mysql2/quoting_test.rb
@@ -16,6 +16,6 @@ class Mysql2QuotingTest < ActiveRecord::Mysql2TestCase
     @connection.stubs(:full_version).returns('5.6.3')
     @connection.remove_instance_variable(:@version) if @connection.instance_variable_defined?(:@version)
     t = Time.now.change(usec: 1)
-    refute_match(/\.000001\z/, @connection.quoted_date(t))
+    assert_no_match(/\.000001\z/, @connection.quoted_date(t))
   end
 end
diff --git a/activerecord/test/cases/associations/belongs_to_associations_test.rb b/activerecord/test/cases/associations/belongs_to_associations_test.rb
index 73cde05504..e7a269c695 100644
--- a/activerecord/test/cases/associations/belongs_to_associations_test.rb
+++ b/activerecord/test/cases/associations/belongs_to_associations_test.rb
@@ -91,7 +91,7 @@ class BelongsToAssociationsTest < ActiveRecord::TestCase
     end
 
     account = model.new
-    refute account.valid?
+    assert_not account.valid?
     assert_equal [{error: :blank}], account.errors.details[:company]
   ensure
     ActiveRecord::Base.belongs_to_required_by_default = original_value
@@ -108,7 +108,7 @@ class BelongsToAssociationsTest < ActiveRecord::TestCase
     end
 
     account = model.new
-    refute account.valid?
+    assert_not account.valid?
     assert_equal [{error: :blank}], account.errors.details[:company]
   ensure
     ActiveRecord::Base.belongs_to_required_by_default = original_value
diff --git a/activerecord/test/cases/attributes_test.rb b/activerecord/test/cases/attributes_test.rb
index bd74821d87..264b275181 100644
--- a/activerecord/test/cases/attributes_test.rb
+++ b/activerecord/test/cases/attributes_test.rb
@@ -152,7 +152,7 @@ module ActiveRecord
           Type::String.new(limit: 50))
         int_array = ConnectionAdapters::PostgreSQL::OID::Array.new(
           Type::Integer.new)
-        refute_equal string_array, int_array
+        assert_not_equal string_array, int_array
         assert_equal string_array, klass.type_for_attribute("my_array")
         assert_equal int_array, klass.type_for_attribute("my_int_array")
       end
@@ -167,7 +167,7 @@ module ActiveRecord
           Type::String.new(limit: 50))
         int_range = ConnectionAdapters::PostgreSQL::OID::Range.new(
           Type::Integer.new)
-        refute_equal string_range, int_range
+        assert_not_equal string_range, int_range
         assert_equal string_range, klass.type_for_attribute("my_range")
         assert_equal int_range, klass.type_for_attribute("my_int_range")
       end
diff --git a/activerecord/test/cases/enum_test.rb b/activerecord/test/cases/enum_test.rb
index ba23049a92..7c930de97b 100644
--- a/activerecord/test/cases/enum_test.rb
+++ b/activerecord/test/cases/enum_test.rb
@@ -40,43 +40,43 @@ class EnumTest < ActiveRecord::TestCase
     published, written = Book.statuses[:published], Book.statuses[:written]
 
     assert_equal @book, Book.where(status: published).first
-    refute_equal @book, Book.where(status: written).first
+    assert_not_equal @book, Book.where(status: written).first
     assert_equal @book, Book.where(status: [published]).first
-    refute_equal @book, Book.where(status: [written]).first
-    refute_equal @book, Book.where("status <> ?", published).first
+    assert_not_equal @book, Book.where(status: [written]).first
+    assert_not_equal @book, Book.where("status <> ?", published).first
     assert_equal @book, Book.where("status <> ?", written).first
   end
 
   test "find via where with symbols" do
     assert_equal @book, Book.where(status: :published).first
-    refute_equal @book, Book.where(status: :written).first
+    assert_not_equal @book, Book.where(status: :written).first
     assert_equal @book, Book.where(status: [:published]).first
-    refute_equal @book, Book.where(status: [:written]).first
-    refute_equal @book, Book.where.not(status: :published).first
+    assert_not_equal @book, Book.where(status: [:written]).first
+    assert_not_equal @book, Book.where.not(status: :published).first
     assert_equal @book, Book.where.not(status: :written).first
   end
 
   test "find via where with strings" do
     assert_equal @book, Book.where(status: "published").first
-    refute_equal @book, Book.where(status: "written").first
+    assert_not_equal @book, Book.where(status: "written").first
     assert_equal @book, Book.where(status: ["published"]).first
-    refute_equal @book, Book.where(status: ["written"]).first
-    refute_equal @book, Book.where.not(status: "published").first
+    assert_not_equal @book, Book.where(status: ["written"]).first
+    assert_not_equal @book, Book.where.not(status: "published").first
     assert_equal @book, Book.where.not(status: "written").first
   end
 
   test "build from scope" do
     assert Book.written.build.written?
-    refute Book.written.build.proposed?
+    assert_not Book.written.build.proposed?
   end
 
   test "build from where" do
     assert Book.where(status: Book.statuses[:written]).build.written?
-    refute Book.where(status: Book.statuses[:written]).build.proposed?
+    assert_not Book.where(status: Book.statuses[:written]).build.proposed?
     assert Book.where(status: :written).build.written?
-    refute Book.where(status: :written).build.proposed?
+    assert_not Book.where(status: :written).build.proposed?
     assert Book.where(status: "written").build.written?
-    refute Book.where(status: "written").build.proposed?
+    assert_not Book.where(status: "written").build.proposed?
   end
 
   test "update by declaration" do
diff --git a/activerecord/test/cases/touch_later_test.rb b/activerecord/test/cases/touch_later_test.rb
index 49ada22529..b3c42c8e42 100644
--- a/activerecord/test/cases/touch_later_test.rb
+++ b/activerecord/test/cases/touch_later_test.rb
@@ -11,7 +11,7 @@ class TouchLaterTest < ActiveRecord::TestCase
   def test_touch_laster_raise_if_non_persisted
     invoice = Invoice.new
     Invoice.transaction do
-      refute invoice.persisted?
+      assert_not invoice.persisted?
       assert_raises(ActiveRecord::ActiveRecordError) do
         invoice.touch_later
       end
@@ -21,7 +21,7 @@ class TouchLaterTest < ActiveRecord::TestCase
   def test_touch_later_dont_set_dirty_attributes
     invoice = Invoice.create!
     invoice.touch_later
-    refute invoice.changed?
+    assert_not invoice.changed?
   end
 
   def test_touch_later_update_the_attributes