Prolog “or” operator, query

you can ‘invoke’ alternative bindings on Y this way:

...registered(X, Y), (Y=ct101; Y=ct102; Y=ct103).

Note the parenthesis are required to keep the correct execution control flow. The ;/2 it’s the general or operator. For your restricted use you could as well choice the more idiomatic

...registered(X, Y), member(Y, [ct101,ct102,ct103]).

that on backtracking binds Y to each member of the list.

edit I understood with a delay your last requirement. If you want that Y match all 3 values the or is inappropriate, use instead

...registered(X, ct101), registered(X, ct102), registered(X, ct103).

or the more compact

...findall(Y, registered(X, Y), L), sort(L, [ct101,ct102,ct103]).

findall/3 build the list in the very same order that registered/2 succeeds. Then I use sort to ensure the matching.

...setof(Y, registered(X, Y), [ct101,ct102,ct103]).

setof/3 also sorts the result list

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