diff --git a/libcxx/include/CMakeLists.txt b/libcxx/include/CMakeLists.txt
--- a/libcxx/include/CMakeLists.txt
+++ b/libcxx/include/CMakeLists.txt
@@ -99,6 +99,7 @@
   __bsd_locale_fallbacks.h
   __compare/common_comparison_category.h
   __compare/ordering.h
+  __compare/three_way_comparable.h
   __concepts/arithmetic.h
   __concepts/assignable.h
   __concepts/boolean_testable.h
diff --git a/libcxx/include/__compare/three_way_comparable.h b/libcxx/include/__compare/three_way_comparable.h
new file mode 100644
--- /dev/null
+++ b/libcxx/include/__compare/three_way_comparable.h
@@ -0,0 +1,58 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP___COMPARE_THREE_WAY_COMPARABLE_H
+#define _LIBCPP___COMPARE_THREE_WAY_COMPARABLE_H
+
+#include <__compare/common_comparison_category.h>
+#include <__compare/ordering.h>
+#include <__concepts/common_reference_with.h>
+#include <__concepts/equality_comparable.h>
+#include <__concepts/same_as.h>
+#include <__concepts/totally_ordered.h>
+#include <__config>
+#include <type_traits>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_SPACESHIP_OPERATOR) && !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+template<class _Tp, class _Cat>
+concept __compares_as =
+  same_as<common_comparison_category_t<_Tp, _Cat>, _Cat>;
+
+template<class _Tp, class _Cat = partial_ordering>
+concept three_way_comparable =
+  __weakly_equality_comparable_with<_Tp, _Tp> &&
+  __partially_ordered_with<_Tp, _Tp> &&
+  requires(__make_const_lvalue_ref<_Tp> __a, __make_const_lvalue_ref<_Tp> __b) {
+    { __a <=> __b } -> __compares_as<_Cat>;
+  };
+
+template<class _Tp, class _Up, class _Cat = partial_ordering>
+concept three_way_comparable_with =
+  three_way_comparable<_Tp, _Cat> &&
+  three_way_comparable<_Up, _Cat> &&
+  common_reference_with<__make_const_lvalue_ref<_Tp>, __make_const_lvalue_ref<_Up>> &&
+  three_way_comparable<common_reference_t<__make_const_lvalue_ref<_Tp>, __make_const_lvalue_ref<_Up>>, _Cat> &&
+  __weakly_equality_comparable_with<_Tp, _Up> &&
+  __partially_ordered_with<_Tp, _Up> &&
+  requires(__make_const_lvalue_ref<_Tp> __t, __make_const_lvalue_ref<_Up> __u) {
+    { __t <=> __u } -> __compares_as<_Cat>;
+    { __u <=> __t } -> __compares_as<_Cat>;
+  };
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_SPACESHIP_OPERATOR) && !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif // _LIBCPP___COMPARE_THREE_WAY_COMPARABLE_H
diff --git a/libcxx/include/compare b/libcxx/include/compare
--- a/libcxx/include/compare
+++ b/libcxx/include/compare
@@ -35,6 +35,12 @@
   template<class... Ts>
     using common_comparison_category_t = typename common_comparison_category<Ts...>::type;
 
+  // [cmp.concept], concept three_way_comparable
+  template<class T, class Cat = partial_ordering>
+    concept three_way_comparable = see below;
+  template<class T, class U, class Cat = partial_ordering>
+    concept three_way_comparable_with = see below;
+
   // [cmp.alg], comparison algorithms
   template<class T> constexpr strong_ordering strong_order(const T& a, const T& b);
   template<class T> constexpr weak_ordering weak_order(const T& a, const T& b);
@@ -122,6 +128,7 @@
 
 #include <__compare/common_comparison_category.h>
 #include <__compare/ordering.h>
+#include <__compare/three_way_comparable.h>
 #include <__config>
 #include <type_traits>
 
diff --git a/libcxx/include/module.modulemap b/libcxx/include/module.modulemap
--- a/libcxx/include/module.modulemap
+++ b/libcxx/include/module.modulemap
@@ -362,6 +362,7 @@
     module __compare {
       module common_comparison_category { private header "__compare/common_comparison_category.h" }
       module ordering                   { private header "__compare/ordering.h"                   }
+      module three_way_comparable       { private header "__compare/three_way_comparable.h"       }
     }
   }
   module complex {
diff --git a/libcxx/test/libcxx/diagnostics/detail.headers/compare/three_way_comparable.module.verify.cpp b/libcxx/test/libcxx/diagnostics/detail.headers/compare/three_way_comparable.module.verify.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/libcxx/diagnostics/detail.headers/compare/three_way_comparable.module.verify.cpp
@@ -0,0 +1,16 @@
+// -*- C++ -*-
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// REQUIRES: modules-build
+
+// WARNING: This test was generated by 'generate_private_header_tests.py'
+// and should not be edited manually.
+
+// expected-error@*:* {{use of private header from outside its module: '__compare/three_way_comparable.h'}}
+#include <__compare/three_way_comparable.h>
diff --git a/libcxx/test/std/language.support/cmp/cmp.concept/three_way_comparable.compile.pass.cpp b/libcxx/test/std/language.support/cmp/cmp.concept/three_way_comparable.compile.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/language.support/cmp/cmp.concept/three_way_comparable.compile.pass.cpp
@@ -0,0 +1,226 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-no-concepts
+
+// template<class T, class Cat = partial_ordering>
+// concept three_way_comparable = // see below
+
+#include <compare>
+
+#include "compare_types.h"
+
+namespace fundamentals {
+// with default ordering
+static_assert(std::three_way_comparable<int>);
+static_assert(std::three_way_comparable<double>);
+static_assert(std::three_way_comparable<void*>);
+static_assert(std::three_way_comparable<char*>);
+static_assert(std::three_way_comparable<char const*>);
+static_assert(std::three_way_comparable<char volatile*>);
+static_assert(std::three_way_comparable<char const volatile*>);
+static_assert(std::three_way_comparable<wchar_t&>);
+#ifndef _LIBCPP_HAS_NO_CHAR8_T
+static_assert(std::three_way_comparable<char8_t const&>);
+#endif
+#ifndef _LIBCPP_HAS_NO_UNICODE_CHARS
+static_assert(std::three_way_comparable<char16_t volatile&>);
+static_assert(std::three_way_comparable<char32_t const volatile&>);
+#endif
+#ifndef _LIBCPP_HAS_NO_INT128
+static_assert(std::three_way_comparable<__int128_t const&>);
+static_assert(std::three_way_comparable<__uint128_t const&>);
+#endif
+static_assert(std::three_way_comparable<unsigned char&&>);
+static_assert(std::three_way_comparable<unsigned short const&&>);
+static_assert(std::three_way_comparable<unsigned int volatile&&>);
+static_assert(std::three_way_comparable<unsigned long const volatile&&>);
+
+// with explicit ordering
+static_assert(std::three_way_comparable<int, std::strong_ordering>);
+static_assert(std::three_way_comparable<int, std::weak_ordering>);
+static_assert(std::three_way_comparable<double, std::partial_ordering>);
+static_assert(!std::three_way_comparable<double, std::weak_ordering>);
+static_assert(std::three_way_comparable<void*, std::strong_ordering>);
+static_assert(std::three_way_comparable<void*, std::weak_ordering>);
+static_assert(std::three_way_comparable<char*, std::strong_ordering>);
+static_assert(std::three_way_comparable<char*, std::weak_ordering>);
+static_assert(std::three_way_comparable<char const*, std::strong_ordering>);
+static_assert(std::three_way_comparable<char const*, std::weak_ordering>);
+static_assert(std::three_way_comparable<char volatile*, std::strong_ordering>);
+static_assert(std::three_way_comparable<char volatile*, std::weak_ordering>);
+static_assert(std::three_way_comparable<char const volatile*, std::strong_ordering>);
+static_assert(std::three_way_comparable<char const volatile*, std::weak_ordering>);
+static_assert(std::three_way_comparable<wchar_t&, std::strong_ordering>);
+static_assert(std::three_way_comparable<wchar_t&, std::weak_ordering>);
+static_assert(std::three_way_comparable<char8_t const&, std::strong_ordering>);
+static_assert(std::three_way_comparable<char8_t const&, std::weak_ordering>);
+static_assert(std::three_way_comparable<char16_t volatile&, std::strong_ordering>);
+static_assert(std::three_way_comparable<char16_t volatile&, std::weak_ordering>);
+static_assert(std::three_way_comparable<char32_t const volatile&, std::strong_ordering>);
+static_assert(std::three_way_comparable<char32_t const volatile&, std::weak_ordering>);
+static_assert(std::three_way_comparable<unsigned char&&, std::strong_ordering>);
+static_assert(std::three_way_comparable<unsigned char&&, std::weak_ordering>);
+static_assert(std::three_way_comparable<unsigned short const&&, std::strong_ordering>);
+static_assert(std::three_way_comparable<unsigned short const&&, std::weak_ordering>);
+static_assert(std::three_way_comparable<unsigned int volatile&&, std::strong_ordering>);
+static_assert(std::three_way_comparable<unsigned int volatile&&, std::weak_ordering>);
+static_assert(std::three_way_comparable<unsigned long const volatile&&, std::strong_ordering>);
+static_assert(std::three_way_comparable<unsigned long const volatile&&, std::weak_ordering>);
+
+static_assert(!std::three_way_comparable<int[5]>);
+static_assert(!std::three_way_comparable<int (*)(int)>);
+static_assert(!std::three_way_comparable<int (&)(int)>);
+static_assert(!std::three_way_comparable<int (*)(int) noexcept>);
+static_assert(!std::three_way_comparable<int (&)(int) noexcept>);
+static_assert(!std::three_way_comparable<std::nullptr_t>);
+static_assert(!std::three_way_comparable<void>);
+
+struct S {};
+static_assert(!std::three_way_comparable<int S::*>);
+static_assert(!std::three_way_comparable<int (S::*)()>);
+static_assert(!std::three_way_comparable<int (S::*)() noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() &>);
+static_assert(!std::three_way_comparable<int (S::*)() & noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() &&>);
+static_assert(!std::three_way_comparable<int (S::*)() && noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() const>);
+static_assert(!std::three_way_comparable<int (S::*)() const noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() const&>);
+static_assert(!std::three_way_comparable<int (S::*)() const & noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() const&&>);
+static_assert(!std::three_way_comparable<int (S::*)() const && noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() volatile>);
+static_assert(!std::three_way_comparable<int (S::*)() volatile noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() volatile&>);
+static_assert(!std::three_way_comparable<int (S::*)() volatile & noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() volatile&&>);
+static_assert(!std::three_way_comparable<int (S::*)() volatile && noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() const volatile>);
+static_assert(!std::three_way_comparable<int (S::*)() const volatile noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() const volatile&>);
+static_assert(!std::three_way_comparable<int (S::*)() const volatile & noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() const volatile&&>);
+static_assert(!std::three_way_comparable<int (S::*)() const volatile && noexcept>);
+} // namespace fundamentals
+
+namespace user_defined {
+
+struct S {
+    auto operator<=>(const S&) const = default;
+};
+
+static_assert(std::three_way_comparable<S>);
+static_assert(std::three_way_comparable<S, std::strong_ordering>);
+static_assert(std::three_way_comparable<S, std::partial_ordering>);
+
+struct SpaceshipNotDeclared {
+};
+
+static_assert(!std::three_way_comparable<SpaceshipNotDeclared>);
+
+struct SpaceshipDeleted {
+    auto operator<=>(const SpaceshipDeleted&) const = delete;
+};
+
+static_assert(!std::three_way_comparable<SpaceshipDeleted>);
+
+struct SpaceshipWithoutEqualityOperator {
+    auto operator<=>(const SpaceshipWithoutEqualityOperator&) const;
+};
+
+static_assert(!std::three_way_comparable<SpaceshipWithoutEqualityOperator>);
+
+struct EqualityOperatorDeleted {
+    bool operator==(const EqualityOperatorDeleted&) const = delete;
+};
+
+static_assert(!std::three_way_comparable<EqualityOperatorDeleted>);
+
+struct EqualityOperatorOnly {
+    bool operator==(const EqualityOperatorOnly&) const = default;
+};
+
+static_assert(!std::three_way_comparable<EqualityOperatorOnly>);
+
+struct SpaceshipDeclaredEqualityOperatorDeleted {
+    bool operator==(const SpaceshipDeclaredEqualityOperatorDeleted&) const = delete;
+    auto operator<=>(const SpaceshipDeclaredEqualityOperatorDeleted&) const = default;
+};
+
+static_assert(!std::three_way_comparable<SpaceshipDeclaredEqualityOperatorDeleted>);
+
+struct AllInequalityOperators {
+    bool operator<(const AllInequalityOperators&) const;
+    bool operator<=(const AllInequalityOperators&) const;
+    bool operator>(const AllInequalityOperators&) const;
+    bool operator>=(const AllInequalityOperators&) const;
+    bool operator!=(const AllInequalityOperators&) const;
+};
+
+static_assert(!std::three_way_comparable<AllInequalityOperators>);
+
+struct AllComparisonOperators {
+    bool operator<(const AllComparisonOperators&) const;
+    bool operator<=(const AllComparisonOperators&) const;
+    bool operator>(const AllComparisonOperators&) const;
+    bool operator>=(const AllComparisonOperators&) const;
+    bool operator!=(const AllComparisonOperators&) const;
+    bool operator==(const AllComparisonOperators&) const;
+};
+
+static_assert(!std::three_way_comparable<AllComparisonOperators>);
+
+struct AllButOneInequalityOperators {
+    bool operator<(const AllButOneInequalityOperators&) const;
+    bool operator<=(const AllButOneInequalityOperators&) const;
+    bool operator>(const AllButOneInequalityOperators&) const;
+    bool operator!=(const AllButOneInequalityOperators&) const;
+};
+
+static_assert(!std::three_way_comparable<AllButOneInequalityOperators>);
+
+struct AllInequalityOperatorsOneDeleted {
+    bool operator<(const AllInequalityOperatorsOneDeleted&) const;
+    bool operator<=(const AllInequalityOperatorsOneDeleted&) const;
+    bool operator>(const AllInequalityOperatorsOneDeleted&) const;
+    bool operator>=(const AllInequalityOperatorsOneDeleted&) const = delete;
+    bool operator!=(const AllInequalityOperatorsOneDeleted&) const;
+};
+
+static_assert(!std::three_way_comparable<AllInequalityOperatorsOneDeleted>);
+
+struct EqualityOperatorWrongReturnType {
+    int operator==(const EqualityOperatorWrongReturnType&);
+    auto operator<=>(const EqualityOperatorWrongReturnType&) const = default;
+};
+
+static_assert(!std::three_way_comparable<EqualityOperatorWrongReturnType>);
+
+struct SpaceshipWrongReturnType {
+    bool operator==(const SpaceshipWrongReturnType&) const = default;
+    int operator<=>(const SpaceshipWrongReturnType&);
+};
+
+static_assert(!std::three_way_comparable<SpaceshipWrongReturnType>);
+
+struct EqualityOperatorNonConstArgument {
+    bool operator==(EqualityOperatorNonConstArgument&);
+    auto operator<=>(const EqualityOperatorNonConstArgument&) const = default;
+};
+
+static_assert(!std::three_way_comparable<EqualityOperatorNonConstArgument>);
+
+struct SpaceshipNonConstArgument {
+    bool operator==(const SpaceshipNonConstArgument&) const = default;
+    auto operator<=>(SpaceshipNonConstArgument&);
+};
+
+static_assert(!std::three_way_comparable<SpaceshipNonConstArgument>);
+} // namespace user_defined
diff --git a/libcxx/test/std/language.support/cmp/cmp.concept/three_way_comparable_with.compile.pass.cpp b/libcxx/test/std/language.support/cmp/cmp.concept/three_way_comparable_with.compile.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/language.support/cmp/cmp.concept/three_way_comparable_with.compile.pass.cpp
@@ -0,0 +1,227 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-no-concepts
+
+// template<class T, class U, class Cat = partial_ordering>
+// concept three_way_comparable_with = // see below
+
+#include <compare>
+
+#include "compare_types.h"
+
+template <class T, class U = T, typename Cat = std::partial_ordering>
+constexpr bool check_three_way_comparable_with() {
+  constexpr bool result = std::three_way_comparable_with<T, U, Cat>;
+  static_assert(std::three_way_comparable_with<U, T, Cat> == result);
+  static_assert(std::three_way_comparable_with<T, U const, Cat> == result);
+  static_assert(std::three_way_comparable_with<T const, U const, Cat> == result);
+  static_assert(std::three_way_comparable_with<T, U const&, Cat> == result);
+  static_assert(std::three_way_comparable_with<T const, U const&, Cat> == result);
+  static_assert(std::three_way_comparable_with<T, U const&&, Cat> == result);
+  static_assert(std::three_way_comparable_with<T const, U const&&, Cat> == result);
+  if constexpr (!std::is_void_v<T>) {
+    static_assert(std::three_way_comparable_with<T&, U const, Cat> == result);
+    static_assert(std::three_way_comparable_with<T const&, U const, Cat> == result);
+    static_assert(std::three_way_comparable_with<T&, U const&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T const&, U const&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T&, U const&&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T const&, U const&&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T&&, U const, Cat> == result);
+    static_assert(std::three_way_comparable_with<T const&&, U const, Cat> == result);
+    static_assert(std::three_way_comparable_with<T&&, U const&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T const&&, U const&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T&&, U const&&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T const&&, U const&&, Cat> == result);
+  }
+  return result;
+}
+
+namespace fundamentals {
+static_assert(check_three_way_comparable_with<int, int>());
+static_assert(check_three_way_comparable_with<int, char>());
+static_assert(!check_three_way_comparable_with<int, unsigned int>());
+static_assert(check_three_way_comparable_with<int, double>());
+static_assert(check_three_way_comparable_with<int*, int*>());
+
+static_assert(check_three_way_comparable_with<int, int, std::strong_ordering>());
+static_assert(check_three_way_comparable_with<int, char, std::strong_ordering>());
+static_assert(check_three_way_comparable_with<int, short, std::strong_ordering>());
+
+static_assert(check_three_way_comparable_with<int, int, std::weak_ordering>());
+static_assert(check_three_way_comparable_with<int, char, std::weak_ordering>());
+static_assert(!check_three_way_comparable_with<int, unsigned int, std::weak_ordering>());
+
+static_assert(!check_three_way_comparable_with<int, bool>());
+static_assert(!check_three_way_comparable_with<int, int*>());
+static_assert(!check_three_way_comparable_with<int, int[5]>());
+static_assert(!check_three_way_comparable_with<int, int (*)()>());
+static_assert(!check_three_way_comparable_with<int, int (&)()>());
+struct S {};
+static_assert(!check_three_way_comparable_with<int, int S::*>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)()>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() volatile>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() volatile noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const volatile>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const volatile noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() &>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() & noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const&>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const & noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() volatile&>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() volatile & noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const volatile&>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const volatile & noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() &&>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() && noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const&&>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const&& noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() volatile&&>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() volatile&& noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const volatile&&>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const volatile&& noexcept>());
+static_assert(!check_three_way_comparable_with<int*, int[5]>());
+static_assert(!check_three_way_comparable_with<int[5], int[5]>());
+static_assert(!check_three_way_comparable_with<std::nullptr_t, int>());
+static_assert(!check_three_way_comparable_with<std::nullptr_t, int*>());
+static_assert(!check_three_way_comparable_with<std::nullptr_t, int[5]>());
+static_assert(!check_three_way_comparable_with<std::nullptr_t, int (*)()>());
+static_assert(!check_three_way_comparable_with<std::nullptr_t, int (&)()>());
+static_assert(!check_three_way_comparable_with<std::nullptr_t, int (S::*)()>());
+static_assert(!check_three_way_comparable_with<void, int>());
+static_assert(!check_three_way_comparable_with<void, int*>());
+static_assert(!check_three_way_comparable_with<void, std::nullptr_t>());
+static_assert(!check_three_way_comparable_with<void, int[5]>());
+static_assert(!check_three_way_comparable_with<void, int (*)()>());
+static_assert(!check_three_way_comparable_with<void, int (&)()>());
+static_assert(!check_three_way_comparable_with<void, int S::*>());
+static_assert(!check_three_way_comparable_with<void, int (S::*)()>());
+} // namespace fundamentals
+
+namespace user_defined {
+struct S {
+    bool operator==(int) const;
+    std::strong_ordering operator<=>(int) const;
+    operator int() const;
+
+    bool operator==(const S&) const = default;
+    auto operator<=>(const S&) const = default;
+};
+
+static_assert(check_three_way_comparable_with<S, int>());
+static_assert(check_three_way_comparable_with<S, int, std::strong_ordering>());
+static_assert(check_three_way_comparable_with<S, int, std::weak_ordering>());
+
+struct SpaceshipNotDeclared {
+};
+
+static_assert(!check_three_way_comparable_with<SpaceshipNotDeclared>());
+
+struct SpaceshipDeleted {
+    auto operator<=>(const SpaceshipDeleted&) const = delete;
+};
+
+static_assert(!check_three_way_comparable_with<SpaceshipDeleted>());
+
+struct SpaceshipWithoutEqualityOperator {
+    auto operator<=>(const SpaceshipWithoutEqualityOperator&) const;
+};
+
+static_assert(!check_three_way_comparable_with<SpaceshipWithoutEqualityOperator>());
+
+struct EqualityOperatorDeleted {
+    bool operator==(const EqualityOperatorDeleted&) const = delete;
+};
+
+static_assert(!check_three_way_comparable_with<EqualityOperatorDeleted>());
+
+struct EqualityOperatorOnly {
+    bool operator==(const EqualityOperatorOnly&) const = default;
+};
+
+static_assert(!check_three_way_comparable_with<EqualityOperatorOnly>());
+
+struct SpaceshipDeclaredEqualityOperatorDeleted {
+    bool operator==(const SpaceshipDeclaredEqualityOperatorDeleted&) const = delete;
+    auto operator<=>(const SpaceshipDeclaredEqualityOperatorDeleted&) const = default;
+};
+
+static_assert(!check_three_way_comparable_with<SpaceshipDeclaredEqualityOperatorDeleted>());
+
+struct AllInequalityOperators {
+    bool operator<(const AllInequalityOperators&) const;
+    bool operator<=(const AllInequalityOperators&) const;
+    bool operator>(const AllInequalityOperators&) const;
+    bool operator>=(const AllInequalityOperators&) const;
+    bool operator!=(const AllInequalityOperators&) const;
+};
+
+static_assert(!check_three_way_comparable_with<AllInequalityOperators>());
+
+struct AllComparisonOperators {
+    bool operator<(const AllComparisonOperators&) const;
+    bool operator<=(const AllComparisonOperators&) const;
+    bool operator>(const AllComparisonOperators&) const;
+    bool operator>=(const AllComparisonOperators&) const;
+    bool operator!=(const AllComparisonOperators&) const;
+    bool operator==(const AllComparisonOperators&) const;
+};
+
+static_assert(!check_three_way_comparable_with<AllComparisonOperators>());
+
+struct AllButOneInequalityOperators {
+    bool operator<(const AllButOneInequalityOperators&) const;
+    bool operator<=(const AllButOneInequalityOperators&) const;
+    bool operator>(const AllButOneInequalityOperators&) const;
+    bool operator!=(const AllButOneInequalityOperators&) const;
+};
+
+static_assert(!check_three_way_comparable_with<AllButOneInequalityOperators>());
+
+struct AllInequalityOperatorsOneDeleted {
+    bool operator<(const AllInequalityOperatorsOneDeleted&) const;
+    bool operator<=(const AllInequalityOperatorsOneDeleted&) const;
+    bool operator>(const AllInequalityOperatorsOneDeleted&) const;
+    bool operator>=(const AllInequalityOperatorsOneDeleted&) const = delete;
+    bool operator!=(const AllInequalityOperatorsOneDeleted&) const;
+};
+
+static_assert(!check_three_way_comparable_with<AllInequalityOperatorsOneDeleted>());
+
+struct EqualityOperatorWrongReturnType {
+    int operator==(const EqualityOperatorWrongReturnType&);
+    auto operator<=>(const EqualityOperatorWrongReturnType&) const = default;
+};
+
+static_assert(!check_three_way_comparable_with<EqualityOperatorWrongReturnType>());
+
+struct SpaceshipWrongReturnType {
+    bool operator==(const SpaceshipWrongReturnType&) const = default;
+    int operator<=>(const SpaceshipWrongReturnType&);
+};
+
+static_assert(!check_three_way_comparable_with<SpaceshipWrongReturnType>());
+
+struct EqualityOperatorNonConstArgument {
+    bool operator==(EqualityOperatorNonConstArgument&);
+    auto operator<=>(const EqualityOperatorNonConstArgument&) const = default;
+};
+
+static_assert(!check_three_way_comparable_with<EqualityOperatorNonConstArgument>());
+
+struct SpaceshipNonConstArgument {
+    bool operator==(const SpaceshipNonConstArgument&) const = default;
+    auto operator<=>(SpaceshipNonConstArgument&);
+};
+
+static_assert(!check_three_way_comparable_with<SpaceshipNonConstArgument>());
+} // namespace user_defined