Prolog code for generating pairs.

pair.pl

 use_module(library(clpfd)).
:- use_module(library(lists)).

ingroup(1, 1).
ingroup(2, 1).
ingroup(3, 1).
ingroup(5, 1).
ingroup(3, 2).
ingroup(4, 2).
ingroup(5, 2).
ingroup(6, 2).
ingroup(7, 2).

pair(P, Q, Prev) :- ingroup(P, G), ingroup(Q, G), P > Q,
\+member([P,Q],Prev).

all_pairs_([[P, Q] | R], Acc) :-
   pair(P, Q, Acc),
   Acc_ = [[P, Q] | Acc],
   all_pairs(R, Acc_).

all_pairs_([[P]], Prev) :- ingroup(P, _).
all_pairs_([], Prev).

all_pairs(L, Prev) :- all_pairs_(L, Prev), flatten(L, M),
all_different(M).

groupings(S1, S2, Prev, Acc) :-
   copy_term(S1, S2),
   all_pairs(S1, Prev),
   append(S1, Prev, Acc).

% S1 = [[A, B], [C, D], [E, F], [G]], groupings(S1, S2, [], Prev),
groupings(S2, S3, Prev, Prev_), groupings(S3, S4, Prev_, Prev__).