% Started on gyro.thornwood at Wed Dec 3 18:09:56 CST 2003. % Here is the mace head file head.r9. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % op(450, infix_right, +). % ring sum % op(400, infix_right, *). % ring product % op(350, prefix, -). % ring minus % % set(print_models_portable). % assign(domain_size, 4). % assign(iterate_up_to, 9). % % % The following fixes [+,-,*] as the ring of integers (mod domain_size). % % set(integer_ring). % % clauses(theory). % % g(x) = M * x. % f(x,y) = (H * x) + (K * y). % % % denial of group % % f(f(X,Y),Z) != f(X,f(Y,Z)) | f(f(g(X),X),Y) != Y | f(g(X),X) != f(g(Y),Y). % % end_of_list. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % g(f(f(f(y,g(z)),z),f(g(f(f(x,z),y)),x))) = z. % candidate 1 interpretation( 7, [ function(M, [3]), function(H, [6]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,3,6,2,5,1,4, 6,2,5,1,4,0,3, 5,1,4,0,3,6,2, 4,0,3,6,2,5,1, 3,6,2,5,1,4,0, 2,5,1,4,0,3,6, 1,4,0,3,6,2,5]) ]). % f(f(f(y,z),g(z)),f(g(f(f(x,g(z)),y)),x)) = z. % candidate 2 interpretation( 9, [ function(M, [2]), function(H, [1]), function(K, [7]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,8,1,3,5,7]), function(+(_,_), [0,1,2,3,4,5,6,7,8, 1,2,3,4,5,6,7,8,0, 2,3,4,5,6,7,8,0,1, 3,4,5,6,7,8,0,1,2, 4,5,6,7,8,0,1,2,3, 5,6,7,8,0,1,2,3,4, 6,7,8,0,1,2,3,4,5, 7,8,0,1,2,3,4,5,6, 8,0,1,2,3,4,5,6,7]), function(*(_,_), [0,0,0,0,0,0,0,0,0, 0,1,2,3,4,5,6,7,8, 0,2,4,6,8,1,3,5,7, 0,3,6,0,3,6,0,3,6, 0,4,8,3,7,2,6,1,5, 0,5,1,6,2,7,3,8,4, 0,6,3,0,6,3,0,6,3, 0,7,5,3,1,8,6,4,2, 0,8,7,6,5,4,3,2,1]), function(f(_,_), [0,7,5,3,1,8,6,4,2, 1,8,6,4,2,0,7,5,3, 2,0,7,5,3,1,8,6,4, 3,1,8,6,4,2,0,7,5, 4,2,0,7,5,3,1,8,6, 5,3,1,8,6,4,2,0,7, 6,4,2,0,7,5,3,1,8, 7,5,3,1,8,6,4,2,0, 8,6,4,2,0,7,5,3,1]) ]). % g(f(f(g(f(y,z)),x),f(f(g(f(z,x)),z),y))) = z. % candidate 3 interpretation( 9, [ function(M, [2]), function(H, [1]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,8,1,3,5,7]), function(+(_,_), [0,1,2,3,4,5,6,7,8, 1,2,3,4,5,6,7,8,0, 2,3,4,5,6,7,8,0,1, 3,4,5,6,7,8,0,1,2, 4,5,6,7,8,0,1,2,3, 5,6,7,8,0,1,2,3,4, 6,7,8,0,1,2,3,4,5, 7,8,0,1,2,3,4,5,6, 8,0,1,2,3,4,5,6,7]), function(*(_,_), [0,0,0,0,0,0,0,0,0, 0,1,2,3,4,5,6,7,8, 0,2,4,6,8,1,3,5,7, 0,3,6,0,3,6,0,3,6, 0,4,8,3,7,2,6,1,5, 0,5,1,6,2,7,3,8,4, 0,6,3,0,6,3,0,6,3, 0,7,5,3,1,8,6,4,2, 0,8,7,6,5,4,3,2,1]), function(f(_,_), [0,4,8,3,7,2,6,1,5, 1,5,0,4,8,3,7,2,6, 2,6,1,5,0,4,8,3,7, 3,7,2,6,1,5,0,4,8, 4,8,3,7,2,6,1,5,0, 5,0,4,8,3,7,2,6,1, 6,1,5,0,4,8,3,7,2, 7,2,6,1,5,0,4,8,3, 8,3,7,2,6,1,5,0,4]) ]). % g(f(g(f(f(y,x),z)),f(f(f(g(z),z),y),x))) = z. % candidate 5 interpretation( 4, [ function(M, [3]), function(H, [3]), function(K, [1]), function(X, [0]), function(Y, [1]), function(Z, [0]), function(g(_), [0,3,2,1]), function(+(_,_), [0,1,2,3, 1,2,3,0, 2,3,0,1, 3,0,1,2]), function(*(_,_), [0,0,0,0, 0,1,2,3, 0,2,0,2, 0,3,2,1]), function(f(_,_), [0,1,2,3, 3,0,1,2, 2,3,0,1, 1,2,3,0]) ]). % g(f(f(g(f(y,z)),x),f(f(g(f(x,x)),x),y))) = z. % candidate 7 interpretation( 5, [ function(M, [3]), function(H, [2]), function(K, [1]), function(X, [0]), function(Y, [1]), function(Z, [0]), function(g(_), [0,3,1,4,2]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,1,2,3,4, 2,3,4,0,1, 4,0,1,2,3, 1,2,3,4,0, 3,4,0,1,2]) ]). % g(f(g(f(f(y,x),z)),f(f(f(g(x),x),y),x))) = z. % candidate 9 interpretation( 7, [ function(M, [3]), function(H, [3]), function(K, [6]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,6,5,4,3,2,1, 3,2,1,0,6,5,4, 6,5,4,3,2,1,0, 2,1,0,6,5,4,3, 5,4,3,2,1,0,6, 1,0,6,5,4,3,2, 4,3,2,1,0,6,5]) ]). % g(f(g(f(f(y,x),z)),f(f(f(x,g(x)),y),x))) = z. % candidate 11 interpretation( 5, [ function(M, [4]), function(H, [2]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,3,2,1]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,3,1,4,2, 2,0,3,1,4, 4,2,0,3,1, 1,4,2,0,3, 3,1,4,2,0]) ]). % g(f(f(g(f(x,z)),y),f(f(g(f(x,y)),x),x))) = z. % candidate 15 interpretation( 5, [ function(M, [2]), function(H, [2]), function(K, [1]), function(X, [1]), function(Y, [0]), function(Z, [0]), function(g(_), [0,2,4,1,3]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,1,2,3,4, 2,3,4,0,1, 4,0,1,2,3, 1,2,3,4,0, 3,4,0,1,2]) ]). % g(f(f(g(f(y,z)),y),f(f(z,g(f(x,z))),x))) = z. % candidate 19 interpretation( 5, [ function(M, [1]), function(H, [3]), function(K, [1]), function(X, [0]), function(Y, [1]), function(Z, [0]), function(g(_), [0,1,2,3,4]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,1,2,3,4, 3,4,0,1,2, 1,2,3,4,0, 4,0,1,2,3, 2,3,4,0,1]) ]). % f(g(f(f(y,x),g(z))),f(f(y,f(z,g(z))),x)) = z. % candidate 26 interpretation( 5, [ function(M, [3]), function(H, [1]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,1,4,2]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,2,4,1,3, 1,3,0,2,4, 2,4,1,3,0, 3,0,2,4,1, 4,1,3,0,2]) ]). % g(f(f(g(f(y,z)),y),f(f(x,g(f(x,x))),x))) = z. % candidate 27 interpretation( 5, [ function(M, [4]), function(H, [2]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,3,2,1]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,4,3,2,1, 2,1,0,4,3, 4,3,2,1,0, 1,0,4,3,2, 3,2,1,0,4]) ]). % g(f(f(g(f(x,z)),x),f(f(x,g(f(y,x))),y))) = z. % candidate 37 interpretation( 5, [ function(M, [1]), function(H, [2]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3,4]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,4,3,2,1, 2,1,0,4,3, 4,3,2,1,0, 1,0,4,3,2, 3,2,1,0,4]) ]). % g(f(f(g(f(x,y)),x),f(f(y,g(f(x,z))),x))) = z. % candidate 40 interpretation( 5, [ function(M, [4]), function(H, [3]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,3,2,1]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,3,1,4,2, 3,1,4,2,0, 1,4,2,0,3, 4,2,0,3,1, 2,0,3,1,4]) ]). % g(f(f(f(x,g(x)),y),f(g(f(x,f(z,y))),x))) = z. % candidate 42 interpretation( 4, [ function(M, [3]), function(H, [1]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,2,1]), function(+(_,_), [0,1,2,3, 1,2,3,0, 2,3,0,1, 3,0,1,2]), function(*(_,_), [0,0,0,0, 0,1,2,3, 0,2,0,2, 0,3,2,1]), function(f(_,_), [0,3,2,1, 1,0,3,2, 2,1,0,3, 3,2,1,0]) ]). % g(f(f(g(f(y,z)),x),f(g(f(z,x)),f(z,y)))) = z. % candidate 55 interpretation( 5, [ function(M, [3]), function(H, [1]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,1,4,2]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,3,1,4,2, 1,4,2,0,3, 2,0,3,1,4, 3,1,4,2,0, 4,2,0,3,1]) ]). % f(f(g(f(y,g(z))),x),f(g(f(z,x)),f(z,y))) = z. % candidate 56 interpretation( 5, [ function(M, [2]), function(H, [1]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,1,3]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,2,4,1,3, 1,3,0,2,4, 2,4,1,3,0, 3,0,2,4,1, 4,1,3,0,2]) ]). % g(f(f(f(y,z),x),f(g(f(z,x)),g(f(z,y))))) = z. % candidate 57 interpretation( 5, [ function(M, [2]), function(H, [4]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,1,3]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,2,4,1,3, 4,1,3,0,2, 3,0,2,4,1, 2,4,1,3,0, 1,3,0,2,4]) ]). % f(f(f(y,z),x),f(g(f(z,x)),g(f(g(z),y)))) = z. % candidate 58 interpretation( 5, [ function(M, [3]), function(H, [4]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,1,4,2]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,3,1,4,2, 4,2,0,3,1, 3,1,4,2,0, 2,0,3,1,4, 1,4,2,0,3]) ]). % f(f(f(g(y),z),x),g(f(g(f(y,z)),f(z,x)))) = z. % candidate 59 interpretation( 7, [ function(M, [3]), function(H, [4]), function(K, [1]), function(X, [0]), function(Y, [1]), function(Z, [0]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,1,2,3,4,5,6, 4,5,6,0,1,2,3, 1,2,3,4,5,6,0, 5,6,0,1,2,3,4, 2,3,4,5,6,0,1, 6,0,1,2,3,4,5, 3,4,5,6,0,1,2]) ]). % f(f(f(y,g(y)),x),g(f(g(f(z,z)),f(z,x)))) = z. % candidate 62 interpretation( 7, [ function(M, [4]), function(H, [3]), function(K, [1]), function(X, [0]), function(Y, [1]), function(Z, [0]), function(g(_), [0,4,1,5,2,6,3]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,1,2,3,4,5,6, 3,4,5,6,0,1,2, 6,0,1,2,3,4,5, 2,3,4,5,6,0,1, 5,6,0,1,2,3,4, 1,2,3,4,5,6,0, 4,5,6,0,1,2,3]) ]). % f(f(f(y,g(x)),x),g(f(g(f(z,z)),f(z,y)))) = z. % candidate 63 interpretation( 7, [ function(M, [1]), function(H, [6]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3,4,5,6]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,2,4,6,1,3,5, 6,1,3,5,0,2,4, 5,0,2,4,6,1,3, 4,6,1,3,5,0,2, 3,5,0,2,4,6,1, 2,4,6,1,3,5,0, 1,3,5,0,2,4,6]) ]). % g(f(f(g(f(y,z)),x),f(g(f(x,x)),f(x,y)))) = z. % candidate 65 interpretation( 5, [ function(M, [2]), function(H, [3]), function(K, [1]), function(X, [0]), function(Y, [1]), function(Z, [0]), function(g(_), [0,2,4,1,3]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,1,2,3,4, 3,4,0,1,2, 1,2,3,4,0, 4,0,1,2,3, 2,3,4,0,1]) ]). % f(f(g(f(y,x)),y),f(f(x,z),g(f(g(x),x)))) = z. % candidate 67 interpretation( 7, [ function(M, [4]), function(H, [2]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,1,5,2,6,3]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 2,0,5,3,1,6,4, 4,2,0,5,3,1,6, 6,4,2,0,5,3,1, 1,6,4,2,0,5,3, 3,1,6,4,2,0,5, 5,3,1,6,4,2,0]) ]). % f(f(g(f(y,x)),y),f(f(x,z),g(f(x,g(x))))) = z. % candidate 68 interpretation( 9, [ function(M, [2]), function(H, [4]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,8,1,3,5,7]), function(+(_,_), [0,1,2,3,4,5,6,7,8, 1,2,3,4,5,6,7,8,0, 2,3,4,5,6,7,8,0,1, 3,4,5,6,7,8,0,1,2, 4,5,6,7,8,0,1,2,3, 5,6,7,8,0,1,2,3,4, 6,7,8,0,1,2,3,4,5, 7,8,0,1,2,3,4,5,6, 8,0,1,2,3,4,5,6,7]), function(*(_,_), [0,0,0,0,0,0,0,0,0, 0,1,2,3,4,5,6,7,8, 0,2,4,6,8,1,3,5,7, 0,3,6,0,3,6,0,3,6, 0,4,8,3,7,2,6,1,5, 0,5,1,6,2,7,3,8,4, 0,6,3,0,6,3,0,6,3, 0,7,5,3,1,8,6,4,2, 0,8,7,6,5,4,3,2,1]), function(f(_,_), [0,4,8,3,7,2,6,1,5, 4,8,3,7,2,6,1,5,0, 8,3,7,2,6,1,5,0,4, 3,7,2,6,1,5,0,4,8, 7,2,6,1,5,0,4,8,3, 2,6,1,5,0,4,8,3,7, 6,1,5,0,4,8,3,7,2, 1,5,0,4,8,3,7,2,6, 5,0,4,8,3,7,2,6,1]) ]). % g(f(f(f(y,x),x),f(g(f(x,x)),g(f(z,y))))) = z. % candidate 79 interpretation( 5, [ function(M, [2]), function(H, [1]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,1,3]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,3,1,4,2, 1,4,2,0,3, 2,0,3,1,4, 3,1,4,2,0, 4,2,0,3,1]) ]). % g(f(f(g(f(y,z)),z),f(x,f(g(f(z,x)),y)))) = z. % candidate 104 interpretation( 9, [ function(M, [8]), function(H, [4]), function(K, [1]), function(X, [0]), function(Y, [1]), function(Z, [0]), function(g(_), [0,8,7,6,5,4,3,2,1]), function(+(_,_), [0,1,2,3,4,5,6,7,8, 1,2,3,4,5,6,7,8,0, 2,3,4,5,6,7,8,0,1, 3,4,5,6,7,8,0,1,2, 4,5,6,7,8,0,1,2,3, 5,6,7,8,0,1,2,3,4, 6,7,8,0,1,2,3,4,5, 7,8,0,1,2,3,4,5,6, 8,0,1,2,3,4,5,6,7]), function(*(_,_), [0,0,0,0,0,0,0,0,0, 0,1,2,3,4,5,6,7,8, 0,2,4,6,8,1,3,5,7, 0,3,6,0,3,6,0,3,6, 0,4,8,3,7,2,6,1,5, 0,5,1,6,2,7,3,8,4, 0,6,3,0,6,3,0,6,3, 0,7,5,3,1,8,6,4,2, 0,8,7,6,5,4,3,2,1]), function(f(_,_), [0,1,2,3,4,5,6,7,8, 4,5,6,7,8,0,1,2,3, 8,0,1,2,3,4,5,6,7, 3,4,5,6,7,8,0,1,2, 7,8,0,1,2,3,4,5,6, 2,3,4,5,6,7,8,0,1, 6,7,8,0,1,2,3,4,5, 1,2,3,4,5,6,7,8,0, 5,6,7,8,0,1,2,3,4]) ]). % f(f(g(f(y,g(z))),z),f(x,f(g(f(z,x)),y))) = z. % candidate 105 interpretation( 7, [ function(M, [6]), function(H, [5]), function(K, [6]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,6,5,4,3,2,1]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,6,5,4,3,2,1, 5,4,3,2,1,0,6, 3,2,1,0,6,5,4, 1,0,6,5,4,3,2, 6,5,4,3,2,1,0, 4,3,2,1,0,6,5, 2,1,0,6,5,4,3]) ]). % f(f(f(y,g(z)),z),g(f(x,f(g(f(z,x)),y)))) = z. % candidate 106 interpretation( 7, [ function(M, [6]), function(H, [3]), function(K, [6]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,6,5,4,3,2,1]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,6,5,4,3,2,1, 3,2,1,0,6,5,4, 6,5,4,3,2,1,0, 2,1,0,6,5,4,3, 5,4,3,2,1,0,6, 1,0,6,5,4,3,2, 4,3,2,1,0,6,5]) ]). % g(f(f(g(f(y,z)),x),f(z,f(g(f(x,z)),y)))) = z. % candidate 107 interpretation( 4, [ function(M, [1]), function(H, [1]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3]), function(+(_,_), [0,1,2,3, 1,2,3,0, 2,3,0,1, 3,0,1,2]), function(*(_,_), [0,0,0,0, 0,1,2,3, 0,2,0,2, 0,3,2,1]), function(f(_,_), [0,3,2,1, 1,0,3,2, 2,1,0,3, 3,2,1,0]) ]). % f(f(f(g(y),y),x),g(f(z,f(g(f(z,z)),x)))) = z. % candidate 108 interpretation( 7, [ function(M, [2]), function(H, [6]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,1,3,5]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,2,4,6,1,3,5, 6,1,3,5,0,2,4, 5,0,2,4,6,1,3, 4,6,1,3,5,0,2, 3,5,0,2,4,6,1, 2,4,6,1,3,5,0, 1,3,5,0,2,4,6]) ]). % g(f(f(f(y,z),g(z)),f(x,g(f(z,f(y,x)))))) = z. % candidate 137 interpretation( 7, [ function(M, [1]), function(H, [1]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3,4,5,6]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,3,6,2,5,1,4, 1,4,0,3,6,2,5, 2,5,1,4,0,3,6, 3,6,2,5,1,4,0, 4,0,3,6,2,5,1, 5,1,4,0,3,6,2, 6,2,5,1,4,0,3]) ]). % f(f(g(f(y,x)),y),f(x,f(z,g(f(g(x),x))))) = z. % candidate 143 interpretation( 5, [ function(M, [3]), function(H, [4]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,1,4,2]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,2,4,1,3, 4,1,3,0,2, 3,0,2,4,1, 2,4,1,3,0, 1,3,0,2,4]) ]). % g(f(f(g(y),f(y,z)),f(g(f(f(x,z),z)),x))) = z. % candidate 185 interpretation( 7, [ function(M, [1]), function(H, [2]), function(K, [6]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3,4,5,6]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,6,5,4,3,2,1, 2,1,0,6,5,4,3, 4,3,2,1,0,6,5, 6,5,4,3,2,1,0, 1,0,6,5,4,3,2, 3,2,1,0,6,5,4, 5,4,3,2,1,0,6]) ]). % g(f(g(f(y,f(x,z))),f(f(f(y,g(z)),z),x))) = z. % candidate 191 interpretation( 7, [ function(M, [2]), function(H, [4]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,1,3,5]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,3,6,2,5,1,4, 4,0,3,6,2,5,1, 1,4,0,3,6,2,5, 5,1,4,0,3,6,2, 2,5,1,4,0,3,6, 6,2,5,1,4,0,3, 3,6,2,5,1,4,0]) ]). % f(f(y,f(g(x),x)),g(f(f(g(f(z,z)),z),y))) = z. % candidate 195 interpretation( 9, [ function(M, [2]), function(H, [7]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,8,1,3,5,7]), function(+(_,_), [0,1,2,3,4,5,6,7,8, 1,2,3,4,5,6,7,8,0, 2,3,4,5,6,7,8,0,1, 3,4,5,6,7,8,0,1,2, 4,5,6,7,8,0,1,2,3, 5,6,7,8,0,1,2,3,4, 6,7,8,0,1,2,3,4,5, 7,8,0,1,2,3,4,5,6, 8,0,1,2,3,4,5,6,7]), function(*(_,_), [0,0,0,0,0,0,0,0,0, 0,1,2,3,4,5,6,7,8, 0,2,4,6,8,1,3,5,7, 0,3,6,0,3,6,0,3,6, 0,4,8,3,7,2,6,1,5, 0,5,1,6,2,7,3,8,4, 0,6,3,0,6,3,0,6,3, 0,7,5,3,1,8,6,4,2, 0,8,7,6,5,4,3,2,1]), function(f(_,_), [0,4,8,3,7,2,6,1,5, 7,2,6,1,5,0,4,8,3, 5,0,4,8,3,7,2,6,1, 3,7,2,6,1,5,0,4,8, 1,5,0,4,8,3,7,2,6, 8,3,7,2,6,1,5,0,4, 6,1,5,0,4,8,3,7,2, 4,8,3,7,2,6,1,5,0, 2,6,1,5,0,4,8,3,7]) ]). % g(f(g(f(y,f(x,z))),f(f(f(y,x),x),g(x)))) = z. % candidate 201 interpretation( 7, [ function(M, [2]), function(H, [2]), function(K, [6]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,1,3,5]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,6,5,4,3,2,1, 2,1,0,6,5,4,3, 4,3,2,1,0,6,5, 6,5,4,3,2,1,0, 1,0,6,5,4,3,2, 3,2,1,0,6,5,4, 5,4,3,2,1,0,6]) ]). % f(f(y,f(x,x)),g(f(g(f(g(f(y,x)),z)),x))) = z. % candidate 205 interpretation( 7, [ function(M, [2]), function(H, [4]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,1,3,5]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 4,2,0,5,3,1,6, 1,6,4,2,0,5,3, 5,3,1,6,4,2,0, 2,0,5,3,1,6,4, 6,4,2,0,5,3,1, 3,1,6,4,2,0,5]) ]). % g(f(g(f(x,f(y,z))),f(f(f(x,y),x),g(x)))) = z. % candidate 215 interpretation( 9, [ function(M, [2]), function(H, [4]), function(K, [7]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,8,1,3,5,7]), function(+(_,_), [0,1,2,3,4,5,6,7,8, 1,2,3,4,5,6,7,8,0, 2,3,4,5,6,7,8,0,1, 3,4,5,6,7,8,0,1,2, 4,5,6,7,8,0,1,2,3, 5,6,7,8,0,1,2,3,4, 6,7,8,0,1,2,3,4,5, 7,8,0,1,2,3,4,5,6, 8,0,1,2,3,4,5,6,7]), function(*(_,_), [0,0,0,0,0,0,0,0,0, 0,1,2,3,4,5,6,7,8, 0,2,4,6,8,1,3,5,7, 0,3,6,0,3,6,0,3,6, 0,4,8,3,7,2,6,1,5, 0,5,1,6,2,7,3,8,4, 0,6,3,0,6,3,0,6,3, 0,7,5,3,1,8,6,4,2, 0,8,7,6,5,4,3,2,1]), function(f(_,_), [0,7,5,3,1,8,6,4,2, 4,2,0,7,5,3,1,8,6, 8,6,4,2,0,7,5,3,1, 3,1,8,6,4,2,0,7,5, 7,5,3,1,8,6,4,2,0, 2,0,7,5,3,1,8,6,4, 6,4,2,0,7,5,3,1,8, 1,8,6,4,2,0,7,5,3, 5,3,1,8,6,4,2,0,7]) ]). % f(f(x,f(g(x),z)),f(g(f(f(y,g(x)),x)),y)) = z. % candidate 228 interpretation( 9, [ function(M, [2]), function(H, [7]), function(K, [7]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,8,1,3,5,7]), function(+(_,_), [0,1,2,3,4,5,6,7,8, 1,2,3,4,5,6,7,8,0, 2,3,4,5,6,7,8,0,1, 3,4,5,6,7,8,0,1,2, 4,5,6,7,8,0,1,2,3, 5,6,7,8,0,1,2,3,4, 6,7,8,0,1,2,3,4,5, 7,8,0,1,2,3,4,5,6, 8,0,1,2,3,4,5,6,7]), function(*(_,_), [0,0,0,0,0,0,0,0,0, 0,1,2,3,4,5,6,7,8, 0,2,4,6,8,1,3,5,7, 0,3,6,0,3,6,0,3,6, 0,4,8,3,7,2,6,1,5, 0,5,1,6,2,7,3,8,4, 0,6,3,0,6,3,0,6,3, 0,7,5,3,1,8,6,4,2, 0,8,7,6,5,4,3,2,1]), function(f(_,_), [0,7,5,3,1,8,6,4,2, 7,5,3,1,8,6,4,2,0, 5,3,1,8,6,4,2,0,7, 3,1,8,6,4,2,0,7,5, 1,8,6,4,2,0,7,5,3, 8,6,4,2,0,7,5,3,1, 6,4,2,0,7,5,3,1,8, 4,2,0,7,5,3,1,8,6, 2,0,7,5,3,1,8,6,4]) ]). % f(f(y,f(g(z),z)),g(f(f(x,g(f(z,x))),y))) = z. % candidate 235 interpretation( 5, [ function(M, [1]), function(H, [1]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3,4]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,3,1,4,2, 1,4,2,0,3, 2,0,3,1,4, 3,1,4,2,0, 4,2,0,3,1]) ]). % g(f(g(f(y,f(x,z))),f(f(g(x),x),f(y,x)))) = z. % candidate 279 interpretation( 5, [ function(M, [4]), function(H, [4]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,3,2,1]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,2,4,1,3, 4,1,3,0,2, 3,0,2,4,1, 2,4,1,3,0, 1,3,0,2,4]) ]). % g(f(f(y,g(f(x,y))),f(f(x,x),g(f(z,x))))) = z. % candidate 285 interpretation( 7, [ function(M, [3]), function(H, [4]), function(K, [6]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,6,5,4,3,2,1, 4,3,2,1,0,6,5, 1,0,6,5,4,3,2, 5,4,3,2,1,0,6, 2,1,0,6,5,4,3, 6,5,4,3,2,1,0, 3,2,1,0,6,5,4]) ]). % f(f(g(y),f(y,x)),g(f(z,f(g(f(z,z)),x)))) = z. % candidate 311 interpretation( 7, [ function(M, [4]), function(H, [2]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,1,5,2,6,3]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,3,6,2,5,1,4, 2,5,1,4,0,3,6, 4,0,3,6,2,5,1, 6,2,5,1,4,0,3, 1,4,0,3,6,2,5, 3,6,2,5,1,4,0, 5,1,4,0,3,6,2]) ]). % g(f(g(f(y,f(x,z))),f(g(z),f(f(z,y),x)))) = z. % candidate 313 interpretation( 7, [ function(M, [5]), function(H, [3]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,5,3,1,6,4,2]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 3,1,6,4,2,0,5, 6,4,2,0,5,3,1, 2,0,5,3,1,6,4, 5,3,1,6,4,2,0, 1,6,4,2,0,5,3, 4,2,0,5,3,1,6]) ]). % g(f(f(y,f(x,g(z))),f(z,g(f(f(z,y),x))))) = z. % candidate 315 interpretation( 7, [ function(M, [3]), function(H, [3]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 3,1,6,4,2,0,5, 6,4,2,0,5,3,1, 2,0,5,3,1,6,4, 5,3,1,6,4,2,0, 1,6,4,2,0,5,3, 4,2,0,5,3,1,6]) ]). % g(f(g(f(y,f(x,z))),f(y,f(f(g(z),z),x)))) = z. % candidate 321 interpretation( 7, [ function(M, [6]), function(H, [2]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,6,5,4,3,2,1]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,2,4,6,1,3,5, 2,4,6,1,3,5,0, 4,6,1,3,5,0,2, 6,1,3,5,0,2,4, 1,3,5,0,2,4,6, 3,5,0,2,4,6,1, 5,0,2,4,6,1,3]) ]). % f(f(y,g(f(x,z))),f(x,f(z,g(f(g(z),y))))) = z. % candidate 367 interpretation( 7, [ function(M, [5]), function(H, [4]), function(K, [6]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,5,3,1,6,4,2]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,6,5,4,3,2,1, 4,3,2,1,0,6,5, 1,0,6,5,4,3,2, 5,4,3,2,1,0,6, 2,1,0,6,5,4,3, 6,5,4,3,2,1,0, 3,2,1,0,6,5,4]) ]). % f(f(x,g(f(y,x))),f(y,f(z,g(f(g(x),x))))) = z. % candidate 381 interpretation( 5, [ function(M, [1]), function(H, [4]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3,4]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,2,4,1,3, 4,1,3,0,2, 3,0,2,4,1, 2,4,1,3,0, 1,3,0,2,4]) ]). % f(f(y,x),f(g(f(f(g(f(z,g(x))),y),x)),x)) = z. % candidate 398 interpretation( 7, [ function(M, [5]), function(H, [6]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,5,3,1,6,4,2]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,2,4,6,1,3,5, 6,1,3,5,0,2,4, 5,0,2,4,6,1,3, 4,6,1,3,5,0,2, 3,5,0,2,4,6,1, 2,4,6,1,3,5,0, 1,3,5,0,2,4,6]) ]). % f(f(x,y),f(g(f(f(g(f(z,x)),x),y)),g(x))) = z. % candidate 403 interpretation( 7, [ function(M, [3]), function(H, [5]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,2,4,6,1,3,5, 5,0,2,4,6,1,3, 3,5,0,2,4,6,1, 1,3,5,0,2,4,6, 6,1,3,5,0,2,4, 4,6,1,3,5,0,2, 2,4,6,1,3,5,0]) ]). % g(f(f(g(y),y),f(f(g(f(z,f(x,z))),z),x))) = z. % candidate 413 interpretation( 7, [ function(M, [1]), function(H, [5]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3,4,5,6]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,2,4,6,1,3,5, 5,0,2,4,6,1,3, 3,5,0,2,4,6,1, 1,3,5,0,2,4,6, 6,1,3,5,0,2,4, 4,6,1,3,5,0,2, 2,4,6,1,3,5,0]) ]). % g(f(f(y,x),g(f(f(f(x,f(g(x),z)),y),x)))) = z. % candidate 455 interpretation( 7, [ function(M, [2]), function(H, [3]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,1,3,5]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,4,1,5,2,6,3, 3,0,4,1,5,2,6, 6,3,0,4,1,5,2, 2,6,3,0,4,1,5, 5,2,6,3,0,4,1, 1,5,2,6,3,0,4, 4,1,5,2,6,3,0]) ]). % g(f(f(x,y),g(f(f(f(g(x),f(x,z)),x),y)))) = z. % candidate 471 interpretation( 7, [ function(M, [4]), function(H, [5]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,1,5,2,6,3]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,4,1,5,2,6,3, 5,2,6,3,0,4,1, 3,0,4,1,5,2,6, 1,5,2,6,3,0,4, 6,3,0,4,1,5,2, 4,1,5,2,6,3,0, 2,6,3,0,4,1,5]) ]). % f(g(f(g(x),x)),f(f(f(z,g(f(y,x))),y),x)) = z. % candidate 479 interpretation( 5, [ function(M, [1]), function(H, [3]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3,4]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,3,1,4,2, 3,1,4,2,0, 1,4,2,0,3, 4,2,0,3,1, 2,0,3,1,4]) ]). % f(f(x,y),f(g(f(x,f(g(f(g(x),z)),y))),x)) = z. % candidate 509 interpretation( 7, [ function(M, [3]), function(H, [5]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,4,1,5,2,6,3, 5,2,6,3,0,4,1, 3,0,4,1,5,2,6, 1,5,2,6,3,0,4, 6,3,0,4,1,5,2, 4,1,5,2,6,3,0, 2,6,3,0,4,1,5]) ]). % f(f(y,z),g(f(f(g(z),f(y,f(z,x))),g(x)))) = z. % candidate 524 interpretation( 7, [ function(M, [5]), function(H, [4]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,5,3,1,6,4,2]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 4,2,0,5,3,1,6, 1,6,4,2,0,5,3, 5,3,1,6,4,2,0, 2,0,5,3,1,6,4, 6,4,2,0,5,3,1, 3,1,6,4,2,0,5]) ]). % g(f(f(y,x),g(f(f(z,f(g(z),f(z,y))),x)))) = z. % candidate 533 interpretation( 7, [ function(M, [2]), function(H, [5]), function(K, [1]), function(X, [0]), function(Y, [1]), function(Z, [0]), function(g(_), [0,2,4,6,1,3,5]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,1,2,3,4,5,6, 5,6,0,1,2,3,4, 3,4,5,6,0,1,2, 1,2,3,4,5,6,0, 6,0,1,2,3,4,5, 4,5,6,0,1,2,3, 2,3,4,5,6,0,1]) ]). % f(f(y,x),g(f(f(z,f(g(z),f(g(z),y))),x))) = z. % candidate 537 interpretation( 9, [ function(M, [8]), function(H, [4]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,8,7,6,5,4,3,2,1]), function(+(_,_), [0,1,2,3,4,5,6,7,8, 1,2,3,4,5,6,7,8,0, 2,3,4,5,6,7,8,0,1, 3,4,5,6,7,8,0,1,2, 4,5,6,7,8,0,1,2,3, 5,6,7,8,0,1,2,3,4, 6,7,8,0,1,2,3,4,5, 7,8,0,1,2,3,4,5,6, 8,0,1,2,3,4,5,6,7]), function(*(_,_), [0,0,0,0,0,0,0,0,0, 0,1,2,3,4,5,6,7,8, 0,2,4,6,8,1,3,5,7, 0,3,6,0,3,6,0,3,6, 0,4,8,3,7,2,6,1,5, 0,5,1,6,2,7,3,8,4, 0,6,3,0,6,3,0,6,3, 0,7,5,3,1,8,6,4,2, 0,8,7,6,5,4,3,2,1]), function(f(_,_), [0,4,8,3,7,2,6,1,5, 4,8,3,7,2,6,1,5,0, 8,3,7,2,6,1,5,0,4, 3,7,2,6,1,5,0,4,8, 7,2,6,1,5,0,4,8,3, 2,6,1,5,0,4,8,3,7, 6,1,5,0,4,8,3,7,2, 1,5,0,4,8,3,7,2,6, 5,0,4,8,3,7,2,6,1]) ]). % f(g(f(x,y)),f(f(x,g(f(x,g(f(y,z))))),x)) = z. % candidate 596 interpretation( 7, [ function(M, [3]), function(H, [1]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,3,6,2,5,1,4, 1,4,0,3,6,2,5, 2,5,1,4,0,3,6, 3,6,2,5,1,4,0, 4,0,3,6,2,5,1, 5,1,4,0,3,6,2, 6,2,5,1,4,0,3]) ]). % f(f(g(x),x),f(f(z,g(f(x,f(g(x),y)))),y)) = z. % candidate 602 interpretation( 5, [ function(M, [3]), function(H, [3]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,1,4,2]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,4,3,2,1, 3,2,1,0,4, 1,0,4,3,2, 4,3,2,1,0, 2,1,0,4,3]) ]). % g(f(f(y,x),f(f(z,g(f(x,z))),g(f(z,y))))) = z. % candidate 667 interpretation( 9, [ function(M, [2]), function(H, [4]), function(K, [1]), function(X, [1]), function(Y, [0]), function(Z, [0]), function(g(_), [0,2,4,6,8,1,3,5,7]), function(+(_,_), [0,1,2,3,4,5,6,7,8, 1,2,3,4,5,6,7,8,0, 2,3,4,5,6,7,8,0,1, 3,4,5,6,7,8,0,1,2, 4,5,6,7,8,0,1,2,3, 5,6,7,8,0,1,2,3,4, 6,7,8,0,1,2,3,4,5, 7,8,0,1,2,3,4,5,6, 8,0,1,2,3,4,5,6,7]), function(*(_,_), [0,0,0,0,0,0,0,0,0, 0,1,2,3,4,5,6,7,8, 0,2,4,6,8,1,3,5,7, 0,3,6,0,3,6,0,3,6, 0,4,8,3,7,2,6,1,5, 0,5,1,6,2,7,3,8,4, 0,6,3,0,6,3,0,6,3, 0,7,5,3,1,8,6,4,2, 0,8,7,6,5,4,3,2,1]), function(f(_,_), [0,1,2,3,4,5,6,7,8, 4,5,6,7,8,0,1,2,3, 8,0,1,2,3,4,5,6,7, 3,4,5,6,7,8,0,1,2, 7,8,0,1,2,3,4,5,6, 2,3,4,5,6,7,8,0,1, 6,7,8,0,1,2,3,4,5, 1,2,3,4,5,6,7,8,0, 5,6,7,8,0,1,2,3,4]) ]). % f(g(f(x,g(x))),f(f(z,x),f(y,g(f(x,y))))) = z. % candidate 764 interpretation( 5, [ function(M, [3]), function(H, [2]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,1,4,2]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,4,3,2,1, 2,1,0,4,3, 4,3,2,1,0, 1,0,4,3,2, 3,2,1,0,4]) ]). % f(f(g(y),y),f(x,g(f(f(g(f(z,z)),z),x)))) = z. % candidate 784 interpretation( 5, [ function(M, [2]), function(H, [3]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,1,3]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,4,3,2,1, 3,2,1,0,4, 1,0,4,3,2, 4,3,2,1,0, 2,1,0,4,3]) ]). % g(f(f(x,y),g(f(g(x),f(f(f(x,z),x),y))))) = z. % candidate 826 interpretation( 7, [ function(M, [4]), function(H, [5]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,1,5,2,6,3]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,2,4,6,1,3,5, 5,0,2,4,6,1,3, 3,5,0,2,4,6,1, 1,3,5,0,2,4,6, 6,1,3,5,0,2,4, 4,6,1,3,5,0,2, 2,4,6,1,3,5,0]) ]). % f(f(y,x),g(f(x,f(g(f(g(y),f(z,x))),x)))) = z. % candidate 870 interpretation( 7, [ function(M, [5]), function(H, [3]), function(K, [1]), function(X, [0]), function(Y, [1]), function(Z, [0]), function(g(_), [0,5,3,1,6,4,2]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,1,2,3,4,5,6, 3,4,5,6,0,1,2, 6,0,1,2,3,4,5, 2,3,4,5,6,0,1, 5,6,0,1,2,3,4, 1,2,3,4,5,6,0, 4,5,6,0,1,2,3]) ]). % g(f(f(x,g(y)),f(y,f(g(f(x,f(z,x))),x)))) = z. % candidate 875 interpretation( 7, [ function(M, [6]), function(H, [6]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,6,5,4,3,2,1]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,2,4,6,1,3,5, 6,1,3,5,0,2,4, 5,0,2,4,6,1,3, 4,6,1,3,5,0,2, 3,5,0,2,4,6,1, 2,4,6,1,3,5,0, 1,3,5,0,2,4,6]) ]). % f(f(y,x),f(g(z),f(z,g(f(f(g(z),y),x))))) = z. % candidate 914 interpretation( 9, [ function(M, [2]), function(H, [7]), function(K, [1]), function(X, [0]), function(Y, [1]), function(Z, [0]), function(g(_), [0,2,4,6,8,1,3,5,7]), function(+(_,_), [0,1,2,3,4,5,6,7,8, 1,2,3,4,5,6,7,8,0, 2,3,4,5,6,7,8,0,1, 3,4,5,6,7,8,0,1,2, 4,5,6,7,8,0,1,2,3, 5,6,7,8,0,1,2,3,4, 6,7,8,0,1,2,3,4,5, 7,8,0,1,2,3,4,5,6, 8,0,1,2,3,4,5,6,7]), function(*(_,_), [0,0,0,0,0,0,0,0,0, 0,1,2,3,4,5,6,7,8, 0,2,4,6,8,1,3,5,7, 0,3,6,0,3,6,0,3,6, 0,4,8,3,7,2,6,1,5, 0,5,1,6,2,7,3,8,4, 0,6,3,0,6,3,0,6,3, 0,7,5,3,1,8,6,4,2, 0,8,7,6,5,4,3,2,1]), function(f(_,_), [0,1,2,3,4,5,6,7,8, 7,8,0,1,2,3,4,5,6, 5,6,7,8,0,1,2,3,4, 3,4,5,6,7,8,0,1,2, 1,2,3,4,5,6,7,8,0, 8,0,1,2,3,4,5,6,7, 6,7,8,0,1,2,3,4,5, 4,5,6,7,8,0,1,2,3, 2,3,4,5,6,7,8,0,1]) ]). % f(g(f(y,z)),f(y,f(z,f(z,g(f(x,g(x))))))) = z. % candidate 978 interpretation( 4, [ function(M, [1]), function(H, [3]), function(K, [1]), function(X, [1]), function(Y, [0]), function(Z, [0]), function(g(_), [0,1,2,3]), function(+(_,_), [0,1,2,3, 1,2,3,0, 2,3,0,1, 3,0,1,2]), function(*(_,_), [0,0,0,0, 0,1,2,3, 0,2,0,2, 0,3,2,1]), function(f(_,_), [0,1,2,3, 3,0,1,2, 2,3,0,1, 1,2,3,0]) ]). % f(g(f(y,x)),f(y,g(f(x,g(f(x,f(z,x))))))) = z. % candidate 987 interpretation( 7, [ function(M, [4]), function(H, [1]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,1,5,2,6,3]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,3,6,2,5,1,4, 1,4,0,3,6,2,5, 2,5,1,4,0,3,6, 3,6,2,5,1,4,0, 4,0,3,6,2,5,1, 5,1,4,0,3,6,2, 6,2,5,1,4,0,3]) ]). % f(y,g(f(f(g(f(f(f(g(z),z),x),z)),x),y))) = z. % candidate 1026 interpretation( 5, [ function(M, [4]), function(H, [4]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,3,2,1]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,3,1,4,2, 4,2,0,3,1, 3,1,4,2,0, 2,0,3,1,4, 1,4,2,0,3]) ]). % g(f(y,f(f(f(g(f(f(x,z),y)),g(z)),z),x))) = z. % candidate 1038 interpretation( 7, [ function(M, [5]), function(H, [3]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,5,3,1,6,4,2]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,3,6,2,5,1,4, 3,6,2,5,1,4,0, 6,2,5,1,4,0,3, 2,5,1,4,0,3,6, 5,1,4,0,3,6,2, 1,4,0,3,6,2,5, 4,0,3,6,2,5,1]) ]). % f(x,f(g(f(g(f(f(z,g(f(y,x))),y)),x)),x)) = z. % candidate 1119 interpretation( 7, [ function(M, [3]), function(H, [3]), function(K, [1]), function(X, [0]), function(Y, [1]), function(Z, [0]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,1,2,3,4,5,6, 3,4,5,6,0,1,2, 6,0,1,2,3,4,5, 2,3,4,5,6,0,1, 5,6,0,1,2,3,4, 1,2,3,4,5,6,0, 4,5,6,0,1,2,3]) ]). % f(y,g(f(f(f(g(f(z,z)),f(z,g(x))),x),y))) = z. % candidate 1130 interpretation( 7, [ function(M, [6]), function(H, [2]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,6,5,4,3,2,1]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,4,1,5,2,6,3, 2,6,3,0,4,1,5, 4,1,5,2,6,3,0, 6,3,0,4,1,5,2, 1,5,2,6,3,0,4, 3,0,4,1,5,2,6, 5,2,6,3,0,4,1]) ]). % f(x,f(f(g(f(g(f(y,z)),f(y,x))),x),g(x))) = z. % candidate 1202 interpretation( 7, [ function(M, [4]), function(H, [4]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,1,5,2,6,3]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 4,2,0,5,3,1,6, 1,6,4,2,0,5,3, 5,3,1,6,4,2,0, 2,0,5,3,1,6,4, 6,4,2,0,5,3,1, 3,1,6,4,2,0,5]) ]). % f(y,f(g(f(g(f(z,f(g(f(z,x)),z))),y)),x)) = z. % candidate 1270 interpretation( 5, [ function(M, [1]), function(H, [2]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3,4]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,3,1,4,2, 2,0,3,1,4, 4,2,0,3,1, 1,4,2,0,3, 3,1,4,2,0]) ]). % g(f(y,g(f(f(f(x,f(g(f(z,x)),z)),z),y)))) = z. % candidate 1287 interpretation( 5, [ function(M, [1]), function(H, [1]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3,4]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,2,4,1,3, 1,3,0,2,4, 2,4,1,3,0, 3,0,2,4,1, 4,1,3,0,2]) ]). % g(f(y,f(g(f(f(g(z),f(z,f(x,z))),y)),x))) = z. % candidate 1351 interpretation( 5, [ function(M, [1]), function(H, [3]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3,4]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,2,4,1,3, 3,0,2,4,1, 1,3,0,2,4, 4,1,3,0,2, 2,4,1,3,0]) ]). % f(g(y),f(g(f(f(x,g(f(z,f(y,z)))),z)),x)) = z. % candidate 1374 interpretation( 7, [ function(M, [2]), function(H, [2]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,1,3,5]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 2,0,5,3,1,6,4, 4,2,0,5,3,1,6, 6,4,2,0,5,3,1, 1,6,4,2,0,5,3, 3,1,6,4,2,0,5, 5,3,1,6,4,2,0]) ]). % f(y,g(f(f(f(x,g(f(z,x))),f(y,x)),g(x)))) = z. % candidate 1540 interpretation( 7, [ function(M, [3]), function(H, [4]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 4,2,0,5,3,1,6, 1,6,4,2,0,5,3, 5,3,1,6,4,2,0, 2,0,5,3,1,6,4, 6,4,2,0,5,3,1, 3,1,6,4,2,0,5]) ]). % f(y,f(g(f(f(x,g(z)),f(f(y,z),g(z)))),x)) = z. % candidate 1565 interpretation( 7, [ function(M, [5]), function(H, [6]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,5,3,1,6,4,2]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 6,4,2,0,5,3,1, 5,3,1,6,4,2,0, 4,2,0,5,3,1,6, 3,1,6,4,2,0,5, 2,0,5,3,1,6,4, 1,6,4,2,0,5,3]) ]). % g(f(y,f(f(z,f(g(f(f(z,y),z)),g(x))),x))) = z. % candidate 1684 interpretation( 7, [ function(M, [4]), function(H, [4]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,1,5,2,6,3]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,3,6,2,5,1,4, 4,0,3,6,2,5,1, 1,4,0,3,6,2,5, 5,1,4,0,3,6,2, 2,5,1,4,0,3,6, 6,2,5,1,4,0,3, 3,6,2,5,1,4,0]) ]). % g(f(y,f(g(f(z,f(f(g(z),x),f(z,y)))),x))) = z. % candidate 1761 interpretation( 7, [ function(M, [5]), function(H, [6]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,5,3,1,6,4,2]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,4,1,5,2,6,3, 6,3,0,4,1,5,2, 5,2,6,3,0,4,1, 4,1,5,2,6,3,0, 3,0,4,1,5,2,6, 2,6,3,0,4,1,5, 1,5,2,6,3,0,4]) ]). % f(y,f(g(f(g(z),f(f(z,x),f(g(z),y)))),x)) = z. % candidate 1762 interpretation( 7, [ function(M, [3]), function(H, [6]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,2,4,6,1,3,5, 6,1,3,5,0,2,4, 5,0,2,4,6,1,3, 4,6,1,3,5,0,2, 3,5,0,2,4,6,1, 2,4,6,1,3,5,0, 1,3,5,0,2,4,6]) ]). % f(y,g(f(f(x,f(g(f(z,x)),f(g(z),z))),y))) = z. % candidate 1779 interpretation( 7, [ function(M, [5]), function(H, [1]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,5,3,1,6,4,2]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 1,6,4,2,0,5,3, 2,0,5,3,1,6,4, 3,1,6,4,2,0,5, 4,2,0,5,3,1,6, 5,3,1,6,4,2,0, 6,4,2,0,5,3,1]) ]). % f(x,g(f(f(x,f(g(f(z,x)),f(x,y))),g(y)))) = z. % candidate 1827 interpretation( 7, [ function(M, [5]), function(H, [1]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,5,3,1,6,4,2]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,3,6,2,5,1,4, 1,4,0,3,6,2,5, 2,5,1,4,0,3,6, 3,6,2,5,1,4,0, 4,0,3,6,2,5,1, 5,1,4,0,3,6,2, 6,2,5,1,4,0,3]) ]). % f(y,g(f(f(z,g(f(z,f(z,f(g(x),x))))),y))) = z. % candidate 1878 interpretation( 7, [ function(M, [4]), function(H, [6]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,1,5,2,6,3]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,4,1,5,2,6,3, 6,3,0,4,1,5,2, 5,2,6,3,0,4,1, 4,1,5,2,6,3,0, 3,0,4,1,5,2,6, 2,6,3,0,4,1,5, 1,5,2,6,3,0,4]) ]). % f(g(y),g(f(f(z,g(f(x,f(y,f(z,z))))),x))) = z. % candidate 1885 interpretation( 7, [ function(M, [6]), function(H, [6]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,6,5,4,3,2,1]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 6,4,2,0,5,3,1, 5,3,1,6,4,2,0, 4,2,0,5,3,1,6, 3,1,6,4,2,0,5, 2,0,5,3,1,6,4, 1,6,4,2,0,5,3]) ]). % f(y,g(f(f(f(g(f(z,z)),z),g(x)),f(x,y)))) = z. % candidate 1910 interpretation( 4, [ function(M, [3]), function(H, [3]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,2,1]), function(+(_,_), [0,1,2,3, 1,2,3,0, 2,3,0,1, 3,0,1,2]), function(*(_,_), [0,0,0,0, 0,1,2,3, 0,2,0,2, 0,3,2,1]), function(f(_,_), [0,3,2,1, 3,2,1,0, 2,1,0,3, 1,0,3,2]) ]). % f(y,f(f(g(f(z,y)),f(z,z)),g(f(x,g(x))))) = z. % candidate 2067 interpretation( 5, [ function(M, [2]), function(H, [2]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,1,3]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,4,3,2,1, 2,1,0,4,3, 4,3,2,1,0, 1,0,4,3,2, 3,2,1,0,4]) ]). % f(y,g(f(g(f(f(z,g(x)),f(x,z))),f(z,y)))) = z. % candidate 2068 interpretation( 5, [ function(M, [4]), function(H, [3]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,3,2,1]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,2,4,1,3, 3,0,2,4,1, 1,3,0,2,4, 4,1,3,0,2, 2,4,1,3,0]) ]). % g(f(x,f(f(g(x),g(f(y,f(x,z)))),f(y,x)))) = z. % candidate 2169 interpretation( 7, [ function(M, [3]), function(H, [2]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 2,0,5,3,1,6,4, 4,2,0,5,3,1,6, 6,4,2,0,5,3,1, 1,6,4,2,0,5,3, 3,1,6,4,2,0,5, 5,3,1,6,4,2,0]) ]). % g(f(g(x),f(f(x,g(f(x,f(y,z)))),f(x,y)))) = z. % candidate 2176 interpretation( 7, [ function(M, [5]), function(H, [2]), function(K, [6]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,5,3,1,6,4,2]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,6,5,4,3,2,1, 2,1,0,6,5,4,3, 4,3,2,1,0,6,5, 6,5,4,3,2,1,0, 1,0,6,5,4,3,2, 3,2,1,0,6,5,4, 5,4,3,2,1,0,6]) ]). % g(f(y,g(f(f(f(z,x),z),f(g(f(x,z)),y))))) = z. % candidate 2190 interpretation( 7, [ function(M, [6]), function(H, [6]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,6,5,4,3,2,1]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,3,6,2,5,1,4, 6,2,5,1,4,0,3, 5,1,4,0,3,6,2, 4,0,3,6,2,5,1, 3,6,2,5,1,4,0, 2,5,1,4,0,3,6, 1,4,0,3,6,2,5]) ]). % g(f(x,g(f(f(z,f(x,x)),f(g(f(y,x)),y))))) = z. % candidate 2307 interpretation( 7, [ function(M, [3]), function(H, [6]), function(K, [4]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,3,6,2,5,1,4]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,4,1,5,2,6,3, 6,3,0,4,1,5,2, 5,2,6,3,0,4,1, 4,1,5,2,6,3,0, 3,0,4,1,5,2,6, 2,6,3,0,4,1,5, 1,5,2,6,3,0,4]) ]). % f(y,f(x,g(f(f(g(z),f(f(z,g(z)),y)),x)))) = z. % candidate 2988 interpretation( 7, [ function(M, [5]), function(H, [4]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,5,3,1,6,4,2]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,3,6,2,5,1,4, 4,0,3,6,2,5,1, 1,4,0,3,6,2,5, 5,1,4,0,3,6,2, 2,5,1,4,0,3,6, 6,2,5,1,4,0,3, 3,6,2,5,1,4,0]) ]). % f(y,g(f(z,f(g(f(x,f(g(y),f(z,z)))),x)))) = z. % candidate 3022 interpretation( 5, [ function(M, [2]), function(H, [4]), function(K, [3]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,1,3]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,3,1,4,2, 4,2,0,3,1, 3,1,4,2,0, 2,0,3,1,4, 1,4,2,0,3]) ]). % f(y,g(f(z,f(g(f(z,z)),f(g(x),f(x,y)))))) = z. % candidate 3239 interpretation( 7, [ function(M, [2]), function(H, [1]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,2,4,6,1,3,5]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 1,6,4,2,0,5,3, 2,0,5,3,1,6,4, 3,1,6,4,2,0,5, 4,2,0,5,3,1,6, 5,3,1,6,4,2,0, 6,4,2,0,5,3,1]) ]). % f(y,g(f(x,g(f(z,f(f(g(f(y,z)),z),x)))))) = z. % candidate 3330 interpretation( 7, [ function(M, [1]), function(H, [1]), function(K, [5]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,1,2,3,4,5,6]), function(+(_,_), [0,1,2,3,4,5,6, 1,2,3,4,5,6,0, 2,3,4,5,6,0,1, 3,4,5,6,0,1,2, 4,5,6,0,1,2,3, 5,6,0,1,2,3,4, 6,0,1,2,3,4,5]), function(*(_,_), [0,0,0,0,0,0,0, 0,1,2,3,4,5,6, 0,2,4,6,1,3,5, 0,3,6,2,5,1,4, 0,4,1,5,2,6,3, 0,5,3,1,6,4,2, 0,6,5,4,3,2,1]), function(f(_,_), [0,5,3,1,6,4,2, 1,6,4,2,0,5,3, 2,0,5,3,1,6,4, 3,1,6,4,2,0,5, 4,2,0,5,3,1,6, 5,3,1,6,4,2,0, 6,4,2,0,5,3,1]) ]). % f(y,f(x,g(f(g(z),f(f(g(z),z),f(y,x)))))) = z. % candidate 3416 interpretation( 5, [ function(M, [4]), function(H, [1]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,3,2,1]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,2,4,1,3, 1,3,0,2,4, 2,4,1,3,0, 3,0,2,4,1, 4,1,3,0,2]) ]). % f(y,g(f(x,f(g(z),f(z,f(g(f(z,x)),y)))))) = z. % candidate 3476 interpretation( 5, [ function(M, [4]), function(H, [2]), function(K, [2]), function(X, [0]), function(Y, [0]), function(Z, [1]), function(g(_), [0,4,3,2,1]), function(+(_,_), [0,1,2,3,4, 1,2,3,4,0, 2,3,4,0,1, 3,4,0,1,2, 4,0,1,2,3]), function(*(_,_), [0,0,0,0,0, 0,1,2,3,4, 0,2,4,1,3, 0,3,1,4,2, 0,4,3,2,1]), function(f(_,_), [0,2,4,1,3, 2,4,1,3,0, 4,1,3,0,2, 1,3,0,2,4, 3,0,2,4,1]) ]). % Checked 3541, passed 896, new_interps 100. % Finished Wed Dec 3 18:19:43 CST 2003.