[class.spaceship]

The synthesized three-way comparison of type R ([cmp.categories]) of glvalues a and b of the same type is defined as follows:

(1.1)
If a <=> b is usable ([class.compare.default]) and can be explicitly converted to R using static_cast, static_cast<R>(a <=> b).
(1.2)
Otherwise, if a <=> b is usable or overload resolution for a <=> b is performed and finds at least one viable candidate, the synthesized three-way comparison is not defined.
(1.3)
Otherwise, if R is not a comparison category type, or either the expression a == b or the expression a < b is not usable, the synthesized three-way comparison is not defined.
(1.4)
Otherwise, if R is strong_ordering, then a == b ? strong_ordering::equal : a < b ? strong_ordering::less : strong_ordering::greater
(1.5)
Otherwise, if R is weak_ordering, then a == b ? weak_ordering::equivalent : a < b ? weak_ordering::less : weak_ordering::greater
(1.6)
Otherwise (when R is partial_ordering), a == b ? partial_ordering::equivalent : a < b ? partial_ordering::less : b < a ? partial_ordering::greater : partial_ordering::unordered

[Note 1:

A synthesized three-way comparison is ill-formed if overload resolution finds usable candidates that do not otherwise meet the requirements implied by the defined expression.

— end note]

Let R be the declared return type of a defaulted three-way comparison operator function, and let

x {i be the elements of the expanded list of subobjects for an object x of type C .}_{i be the elements of the expanded list of subobjects for an object x of type C .}

(2.1)
If R is auto, then let $c v {i R {i be the type of the expression x {i <=> x {i .}_{i .}}_{i <=> x {i .}_{i .}}}_{i be the type of the expression x {i <=> x {i .}_{i .}}_{i <=> x {i .}_{i .}}}}_{i R {i be the type of the expression x {i <=> x {i .}_{i .}}_{i <=> x {i .}_{i .}}}_{i be the type of the expression x {i <=> x {i .}_{i .}}_{i <=> x {i .}_{i .}}}}$

The operator function is defined as deleted if that expression is not usable or if $R {i is not a comparison category type ([cmp. categories. pre]) for any i .}_{i is not a comparison category type ([cmp. categories. pre]) for any i .}$

The return type is deduced as the common comparison type (see below) of $R {0, R {1, \dots, R {n - 1 .}_{n - 1 .}}_{1, \dots, R {n - 1 .}_{n - 1 .}}}_{0, R {1, \dots, R {n - 1 .}_{n - 1 .}}_{1, \dots, R {n - 1 .}_{n - 1 .}}}$
(2.2)
Otherwise, R shall not contain a placeholder type.

If the synthesized three-way comparison of type R between any objects $x {i and x {i is not defined, the operator function is defined as deleted .}_{i is not defined, the operator function is defined as deleted .}}_{i and x {i is not defined, the operator function is defined as deleted .}_{i is not defined, the operator function is defined as deleted .}}$

The return value of type R of the defaulted three-way comparison operator function with parameters x and y of the same type is determined by comparing corresponding elements

x {i and y {i in the expanded lists of subobjects for x and y (in increasing index order) until the first index i where the synthesized three-way comparison of type R between x {i and y {i yields a result value v {i where}_{i where v}}_{i yields a result value v {i where v}_{i where v}}}_{i and y {i yields a result value v {i where v}_{i where v}}_{i yields a result value v {i where v}_{i where v_{i}}}}}_{i in the expanded lists of subobjects for x and y (in increasing index order) until the first index i where the synthesized three-way comparison of type R between x {i and y {i yields a result value v {i where v}_{i where v}}_{i yields a result value v {i where v}_{i where v_{i}}}}_{i and y {i yields a result value v {i where v}_{i where v_{i}}}_{i yields a result value v {i where v_{i}}_{i where v i_{i}}}}}}_{i and y {i in the expanded lists of subobjects for x and y (in increasing index order) until the first index i where the synthesized three-way comparison of type R between x {i and y {i yields a result value v {i where v}_{i where v}}_{i yields a result value v {i where v}_{i where v_{i}}}}_{i and y {i yields a result value v {i where v}_{i where v_{i}}}_{i yields a result value v {i where v_{i}}_{i where v i_{i}}}}}_{i in the expanded lists of subobjects for x and y (in increasing index order) until the first index i where the synthesized three-way comparison of type R between x {i and y {i yields a result value v {i where v}_{i where v_{i}}}_{i yields a result value v {i where v_{i}}_{i where v i_{i}}}}_{i and y {i yields a result value v {i where v_{i}}_{i where v i_{i}}}_{i yields a result value v {i where v i_{i}}_{i where v i_{i}}}}}}

The return value is a copy of

v {i if such an index exists and static_cast < R > (std ​::​ strong_ordering ​::​ equal) otherwise .}_{i if such an index exists and static_cast < R > (std ​::​ strong_ordering ​::​ equal) otherwise .}

The common comparison type U of a possibly-empty list of n comparison category types