Pigeon hole ���
true ��pigeon(1), pigeon(2), pigeon(3) , pigeon(4) , pigeon (5) , pigeon(6) , pigeon (7) , pigeon (8) , pigeon (9) , pigeon (10) , pigeon (11).
pigeon(M) ��hole(M, 1); hole(M, 2); hole(M, 3); hole(M, 4); hole(M, 5); hole(M, 6); hole(M, 7); hole(M, 8); hole(M, 9); hole(M, 10).
hole(M1, N), hole(M2, N), M1 ~ M2 ��false. 
Bennett 's quasigroups 
true �� dom( 1) , dom(2) , dom(3) , dom(4) , dom(5) , dom(6) , dom(7) , dom(8) , dom(9) , dom(10) , dom(11) . 
dom(M), dom(N) ��
p(M, N, 1) ; p(M, N, 2) ; p(M, N, 3) ; p(M, N, 4) ; p(M, N, 5); p(M, N, 6) ; p(M, N, 7) ; p(M, N, 8); p(M, N, 9); p(M, N, 10) ; p(M, N, 11). 
p(X, 11, Y),Y + �P< X ��false. 
p(E, X, Y), p(Y, E, Z), p(Z, E, U), X ~ U ��false. 
p(X, X, U), X ~ U �� false. 
p(X,Y, U),p(X, Y1, U),Y ~ Y1 �� false. 
p(X, Y, U),p(X1, Y, U), X ~ X1 �� false. 
�藝5 
true �� p(i(i(i(X, Y) , Z), i(i(Z, X) , i(U, X)))) . 
p(X),p(i(X, Y)) - p(Y). 
p(i(i(a, b), i(i(b, c), i(a, c)))) ��false' 
�藝7 
true �� p(i(X, i(Y, X))). true �� p(i(i(X, Y), i(i(Y, Z), i(X, Z)))). 
true ��p(i(i(n(X), n(Y)) i(Y X))). true ��p(i(i(i(X,Y),Y),i(i(Y,X),X))). 
p(X),p(i(X, Y)) - p(Y). 
p(i(i(a, b), i(n(b), b(a)))) �� false.