% *****************************************************************
% AIM:  Commutativity + imord2 L => aa1
%
%    L(L(x,y,z),y,z) = x # label("imord2 L").
% *****************************************************************

assign(order, kbo).
set(lex_order_vars).

clear(back_demod).
set(restrict_denials).

set(para_from_small).

clear(cac_redundancy).

assign(max_weight,5).

formulas(assumptions).

   % loop axioms
   1 * x = x.
   x * 1 = x.
   x \ (x * y) = y.
   x * (x \ y) = y.
   (x * y) / y = x.
   (x / y) * y = x.

   % associator (right associated * a = left associated)
   (x * (y * z)) \ ((x * y) * z) = a(x,y,z) # label("associator").

   % commutator ( (x * y) * K(y,x) = y * x )
   (x * y) \ (y * x) = K(y,x) # label("commutator").

   % inner mappings
   (y * x) \ (y * (x * u)) = L(u,x,y).
   ((u * x) * y) / (x * y) = R(u,x,y).
   x \ (u * x) = T(u,x).

   % abelian inner mapping group
   T(T(u,x),y) = T(T(u,y),x).
   T(L(u,x,y),z) = L(T(u,z),x,y).
   T(R(u,x,y),z) = R(T(u,z),x,y).
   L(R(u,x,y),z,w) = R(L(u,z,w),x,y).
   L(L(u,x,y),z,w) = L(L(u,z,w),x,y).
   R(R(u,x,y),z,w) = R(R(u,z,w),x,y).

   % extra assumption for this case
   x * y = y * x # label("Commutativity").
   L(L(x,y,z),y,z) = x # label("imord2 L").

end_of_list.

formulas(goals).

   a(a(x,y,z),u,w) = 1 # label("aa1").

end_of_list.

% *********************
% AIM: Auxiliary Lemmas
% *********************

formulas(assumptions).

   % cancellation laws (long form)

   x * y != u | x * z != u | y = z # label("*-Cancellation 1").
   y * x != u | z * x != u | y = z # label("*-Cancellation 2").

   x / y != u | x / z != u | y = z # label("/-Cancellation 1").
   y / x != u | z / x != u | y = z # label("/-Cancellation 2").

   x \ y != u | x \ z != u | y = z # label("\-Cancellation 1").
   y \ x != u | z \ x != u | y = z # label("\-Cancellation 2").

   T(x,y) != u | T(z,y) != u | x = z # label("T-Cancellation 1").
   L(z,x,y) != u | L(w,x,y) != u | z = w # label("L-Cancellation 1").
   R(z,x,y) != u | R(w,x,y) != u | z = w # label("R-Cancellation 1").

   % cancellation laws (short form)

   x * y != x * z | y = z # label("*-Cancellation 3").
   y * x != z * x | y = z # label("*-Cancellation 4").

   x / y != x / z | y = z # label("/-Cancellation 3").
   y / x != z / x | y = z # label("/-Cancellation 4").

   x \ y != x \ z | y = z # label("\-Cancellation 3").
   y \ x != z \ x | y = z # label("\-Cancellation 4").

   T(x,y) != T(z,y) | x = z # label("T-Cancellation 2").
   L(z,x,y) != L(w,x,y) | z = w # label("L-Cancellation 2").
   R(z,x,y) != R(w,x,y) | z = w # label("R-Cancellation 2").

   % compatibility

   a(x,y,z) != 1 | L(z,y,x) = z # label("Compat 1").
   L(x,y,z) != x | a(z,y,x) = 1 # label("Compat 2").
   T(x,y) != x | T(y,x) = y # label("Compat 3").
   T(x,y) != x | K(x,y) = 1 # label("Compat 4").
   K(x,y) != 1 | T(x,y) = x # label("Compat 5").

   % sometimes helpful for demodulation-free proofs

   x != y | x * z = y * z # label("Aux 1").
   x != y | z * x = z * y # label("Aux 2").
   x != y | x / z = y / z # label("Aux 3").
   x != y | z / x = z / y # label("Aux 4").
   x != y | x \ z = y \ z # label("Aux 5").
   x != y | z \ x = z \ y # label("Aux 6").

   x != y | y != z | x = z # label("Transitivity =").

end_of_list.

%
% Hints extracted from previously found proofs.
%

formulas(hints).

a(a(x,y,z),u,w) = 1.
1 * x = x.
x * 1 = x.
x \ (x * y) = y.
x * (x \ y) = y.
(x / y) * y = x.
(x * (y * z)) \ ((x * y) * z) = a(x,y,z).
(x * y) \ (x * (y * z)) = L(z,y,x).
((x * y) * z) / (y * z) = R(x,y,z).
x \ (y * x) = T(y,x).
L(L(x,y,z),u,w) = L(L(x,u,w),y,z).
x * y = y * x.
L(L(x,y,z),y,z) = x.
x * y != z | x * u != z | y = u.
x * y != z | u * y != z | x = u.
x \ y != z | x \ u != z | y = u.
x \ y != z | u \ y != z | x = u.
T(x,y) != z | T(u,y) != z | x = u.
L(x,y,z) != u | L(w,y,z) != u | x = w.
x * y != x * z | y = z.
x * y != z * y | x = z.
x \ y != x \ z | y = z.
x \ y != z \ y | x = z.
L(x,y,z) != L(u,y,z) | x = u.
a(x,y,z) != 1 | L(z,y,x) = z.
L(x,y,z) != x | a(z,y,x) = 1.
T(x,y) != x | K(x,y) = 1.
x != y | x * z = y * z.
x != y | z * x = z * y.
x != y | x \ z = y \ z.
x != y | z \ x = z \ y.
x != y | y != z | x = z.
a(a(c1,c2,c3),c4,c5) != 1.
1 \ x = x.
x \ x = 1.
(x * y) * L(z,y,x) = x * (y * z).
x \ (y * ((y \ x) * z)) = L(z,y \ x,y).
L(x \ y,x,z) = (z * x) \ (z * y).
R(x,y,z) * (y * z) = (x * y) * z.
L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),y,z),u,w).
x \ (y * x) = y.
(x \ y) * x = y.
(x * (y * z)) \ (z * (x * y)) = a(x,y,z).
(x * y) \ (y * (x * z)) = L(z,x,y).
(x * y) \ (x * (z * y)) = L(z,y,x).
L(L(L(x,y,z),u,w),y,z) = L(x,u,w).
x * y != z | y * u != z | x = u.
1 * x != y | x = y.
x * y != z | x \ z = y.
x * 1 != y | x = y.
x \ y != z | x * z = y.
L(L(x,y,z),u,w) != L(v5,y,z) | L(x,u,w) = v5.
L(x,y,z) != u | L(u,y,z) = x.
(x * y) * z = (y * x) * z.
x * (y * z) = x * (z * y).
(x * y) \ z = (y * x) \ z.
x \ (y * z) = x \ (z * y).
x * (x \ (y * z)) = z * y.
x \ (x * (y * z)) = z * y.
(x * y) \ (x * (y * z)) = u * (u \ L(z,y,x)).
x * (x \ y) = y * 1.
T(x,y) = x.
x \ (y * x) = y * 1.
(x \ y) \ y = x.
x \ y != z | z * x = y.
K(x,y) = 1.
x != y | T(z,u) != y | x = z.
L(x,y,x) = x.
L(x \ y,x,z) = (x * z) \ (z * y).
(x * y) \ (y * (z * x)) = L(z,x,y).
(x * y) \ ((x * z) * y) = L(z,x,y).
(x * y) \ (y * (z * x)) = R(z,x,y).
x \ y != z * 1 | z * x = y.
x \ (y * x) != z | y = z.
(x \ y) \ y != z | x = z.
x \ (x * y) != z | y = z.
x \ (y * z) != u | x \ (z * y) = u.
(x * y) * L(z,x,y) = y * (z * x).
L(x,y,z) * (y * z) = z * (x * y).
x \ (x * (y * 1)) = L(y,1,x).
(x * y) \ ((z * x) * y) = L(z,x,y).
(x * y) \ (y * (z * x)) != u | L(z,x,y) = u.
(x * y) \ (x * (z * y)) != u | L(z,y,x) = u.
(x * y) \ (y * (x * z)) != u | L(z,x,y) = u.
(x * y) \ ((z * x) * y) != u | L(z,x,y) = u.
R(x,y,z) = L(x,y,z).
(x * y) \ (y * (x * z)) = R(z,x,y).
L(x,y,z) * (y * z) = (x * y) * z.
x \ (1 * (x * y)) = R(y,x,1).
x \ (x * y) = R(y,x,1).
R(x,y,1) = x.
L(x,y,1) = x.
a(1,x,y) = 1.
a(K(x,y),z,u) = 1.
(x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)).
(x * y) * z != x * (y * u) | L(u,y,x) = z.
(x \ y) * x = (z \ y) * z.
x * ((y \ (x \ z)) * y) = z.
x * y != z | y \ z = x.
(x * y) \ (y * z) != u | L(x \ z,x,y) = u.
x * L(y,z,z \ x) = (z \ x) * (z * y).
(x * (y * z)) \ (y * (x * z)) = a(x,z,y).
x * (x \ y) != z | y = z.
(x * (y * z)) \ (y * (z * x)) = a(x,z,y).
L(x,x \ y,z) = ((x \ y) * z) \ (y * z).
(x * L(y,x,z)) \ (z * (x * y)) = L(z,x,L(y,x,z)).
L(x \ y,x,z) = (x * z) \ (y * z).
L(x \ 1,x,y) = (x * y) \ y.
L(x \ y,x,x \ z) = z \ (y * (x \ z)).
L(x \ y,x,y \ z) = (x * (y \ z)) \ z.
L(x \ (y \ z),x,y) = (x * y) \ z.
L(x \ ((y * z) \ (z * (x * y))),x,y * z) = a(x,y,z).
L((x * y) \ z,x,y) = x \ (y \ z).
L(x \ (y \ z),x,y) = (y * x) \ z.
L((x * y) \ z,y,x) = y \ (x \ z).
L(x \ y,z \ x,z) = (z \ x) \ (z \ y).
x \ (y \ (z * (y * x))) = L(z,x,y).
x \ (y \ (x * (y * z))) = L(L(z,y,x),x,y).
x \ (y \ (x * (z * y))) = L(L(z,y,x),x,y).
L(x \ y,z,z \ x) = z \ ((z \ x) \ y).
(x * y) \ (z \ (y * (z * x))) = L(a(z,x,y),x * y,z).
L(L(x \ y,x,z),z,x) = z \ (x \ (y * z)).
x \ (y * (x * z)) = z * L(y,z,x).
x \ (y \ (z * (x * y))) = L(z,x,y).
x \ ((x \ y) \ (z * y)) = L(z,x,x \ y).
x * (y * L(z,y,x)) = z * (x * y).
(x \ y) * L(z,x \ y,x) = x \ (z * y).
x \ (y * (z * x)) = z * L(y,z,x).
x \ (y \ (z * (y * x))) != u | L(z,x,y) = u.
L(x \ L(y,z,u),x,z) = (x * z) \ (u \ (y * (z * u))).
x * (y * L(z,y,x)) = z * (y * x).
x \ ((y \ z) * (y * x)) = y * ((y * x) \ (z * x)).
(x * (y * z)) \ ((y * z) * L(x,z,y)) = a(y,z,L(x,z,y)).
(x * y) * L(L(z,x,y),u,w) = y * (x * L(z,u,w)).
(x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w)).
(x * L(y,x,z)) \ (y * (x * z)) = z.
(x * (y * z)) \ (y * (z * L(x,y,z))) = a(z,L(x,y,z),y).
(x * y) * L(z,y,x) != u | x * (y * z) = u.
(x \ y) * x != z | y = z.
x * y != z | y * x = z.
x * L(y,z,z \ x) != u | (z \ x) * (z * y) = u.
x * (y * L(z,x,y)) = y * (x * L(z,y,x)).
(x * (y * L(z,y,x))) \ (x * (y * L(z,x,y))) = a(x,L(z,y,x),y).
(x * (y * z)) \ (y * (z * L(x,y,z))) = a(y,L(x,z,y),z).
a(x,L(y,z,x),z) = a(z,L(y,x,z),x).
a(x,L(L(y,x,z),z,x),z) = a(z,y,x).
a(x,y,K(z,u)) = 1.
L(K(x,y),z,u) = K(x,y).
L(x \ 1,x,y) = (y * x) \ y.
L((x \ y) \ z,x \ y,x) = y \ (x * z).
(x * (y * z)) \ (x * (z * (y * u))) = L(L(u,y,z),y * z,x).
(x * y) * L(L(L(z,y,x),u,w),v5,v6) != v7 | x * (y * L(L(z,u,w),v5,v6)) = v7.
(x * (y * z)) \ ((x * y) * (u * L(z,y,x))) = L(u,L(z,y,x),x * y).
L(L((x * y) \ z,u,w),x,y) = L(x \ (y \ z),u,w).
x \ y != z * u | x * (u * z) = y.
((x * y) \ z) \ z = y * x.
x * (y * z) != u | x * (z * y) = u.
L(x,y,y \ (x \ z)) = y \ ((y \ (x \ z)) \ z).
(x \ (y \ z)) \ z = x * L(y,x,x \ (y \ z)).
((x \ y) \ y) \ z = x \ z.
x \ y != z | z \ y = x.
x != y | z != y | x = z.
x \ y != z * u | (u * z) \ y = x.
(x * y) \ z != u | (y * x) \ z = u.
((x \ y) \ y) \ (x * z) = z.
x \ ((y * z) * (y \ x)) = L(z,y,y \ x).
((x * y) * L(z,y,x)) \ ((x * u) * (y * z)) = L(u,x,y * z).
L(x,y,L(x,z,u)) = x.
L(L(x,y,z),u,x) = L(x,y,z).
L(L(L(x,y,z),u,w),v5,x) = L(L(x,y,z),u,w).
(x * y) * L((x * y) \ (y * z),u,w) = y * (x * L(x \ z,u,w)).
x * (y * z) != u * (z * x) | L(y,z,x) = u.
L(L(x,y,z) \ u,L(x,y,z),y * z) = (z * (x * y)) \ (u * (y * z)).
x \ (x * y) = L(y,1,x).
(x * y) \ ((x * z) * y) != u | L(z,x,y) = u.
x \ ((y * z) * (y \ x)) != u | L(z,y,y \ x) = u.
(x \ y) \ ((z \ y) * z) = x.
L(x,y,L(L(x,z,u),w,v5)) = x.
L(L(x,y,z),u,L(x,w,v5)) = L(x,y,z).
(x * L(y,z,u)) * L(y,w,v5) = L(y,z,u) * (x * L(y,w,v5)).
L(x,y,z) * (x * u) = x * (u * L(x,y,z)).
L(x,x \ y,z) = (z * (x \ y)) \ (y * z).
L(L(x,x \ y,z),z,x \ y) = z \ ((x \ y) \ (y * z)).
L(x,x \ y,z) \ (y * z) = z * (x \ y).
L(x \ 1,x,y) \ y = x * y.
L(x \ 1,x,x \ y) = y \ (x \ y).
L(L(x \ 1,y,z),x,u) = L((x * u) \ u,y,z).
L(x \ y,x,x \ 1) = y * (x \ 1).
L((x \ y) \ z,x \ y,x) = y \ (z * ((x \ y) \ y)).
L(x \ L(x,y,z),x,y * z) = a(x,y,z).
L((x \ y) \ 1,x \ y,y) = L(y \ x,y,x \ y).
L(x,x \ 1,y) = (y * (x \ 1)) \ y.
(x \ y) \ (x \ (y * z)) = L(z,x \ y,x).
(x \ 1) \ (x \ y) = L(y,x \ 1,x).
(x * y) \ (z \ (y * (x * z))) = L(a(z,x,y),x * y,z).
L(a(x,y,z),y * z,x) = (y * z) \ (y * L(z,y,x)).
x * L(L(y,z,x),x,z) = z \ (x * (z * y)).
x \ ((x \ y) \ (y * z)) = L(z,x,x \ y).
x \ ((x \ 1) \ y) = L(y,x,x \ 1).
(x * y) \ (z \ (x * (y * z))) = L(a(z,y,x),y * x,z).
L(x \ L(x,y,y \ z),x,z) = a(x,y,y \ z).
L(L(x \ L(x,y,z),u,w),x,y * z) = L(a(x,y,z),u,w).
x \ L(x,y,y \ 1) = a(x,y,y \ 1).
L((x * y) \ (x * L(y,z,u)),y,z * u) = L(a(y,z,u),y,x).
L(x \ (L(y,z,u) * (y \ x)),y,z * u) = L(a(y,z,u),y,y \ x).
L((x \ y) \ (x \ L(y,z,u)),y,z * u) = L(a(y,z,u),x \ y,x).
x * L(L(y,x,z),z,x) = z \ (x * (z * y)).
x * L(L(L(y,z,x),x,z),u,w) = z \ (x * (z * L(y,u,w))).
x * L(L(y,x,z),z,x) = z \ (x * (y * z)).
x \ (y * (x * (y \ z))) = y * (x \ (y \ (z * x))).
x \ (y * (L(z,y,x) * x)) = y * L(z,x,y).
(x * (L(x,y,z) \ u)) \ (u * x) = L(x,y,z).
L(x,x \ 1,y) \ y = y * (x \ 1).
L(x,x \ y,y \ z) \ z = (y \ z) * (x \ y).
L(L(x,L(x,y,z) \ u,w),y,z) \ (u * w) = w * (L(x,y,z) \ u).
x \ (y * L(x,z,u)) = L(x,z,u) * (x \ y).
L(x,y,z) \ (u * x) = x * (L(x,y,z) \ u).
L(x,y,z) \ (u * L(x,w,v5)) = L(x,w,v5) * (L(x,y,z) \ u).
L(L(x,y,x \ z),x \ z,y) = y \ ((x \ z) \ (z * y)).
L(x,x \ 1,y) \ y = (x \ 1) * y.
x \ y != y * (z \ 1) | L(z,z \ 1,y) = x.
L(x,x \ 1,y) \ z = ((y * (x \ 1)) \ y) \ z.
L(x,y,z) * (x \ 1) = x \ L(x,y,z).
x * (L(x,y,z) \ 1) = L(x,y,z) \ x.
L(x,y,z) * (L(x,u,w) \ 1) = L(x,u,w) \ L(x,y,z).
(x \ y) * (L(x \ y,z,u) \ x) = L(x \ y,z,u) \ y.
L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u).
x * (L(x,y,z) \ u) != w | L(x,y,z) \ (x * u) = w.
x * ((x \ y) * L(x,z,u)) = y * L(x,z,u).
x * (L(x,y,z) * (x \ u)) = u * L(x,y,z).
L(x,y,z) * (x \ (y * z)) = x \ (z * (x * y)).
L(x \ (y * (L(y,z,u) \ w)),x,L(y,z,u)) = (x * L(y,z,u)) \ (y * w).
L(x,y,z) \ (u * x) != w | x * (L(x,y,z) \ u) = w.
(x * (y * (x \ 1))) \ (y * x) = L(x,x \ 1,y).
x \ (L(x,y,z) \ x) = L(x,y,z) \ 1.
x \ (y * L(x,z,u)) != w | L(x,z,u) * (x \ y) = w.
(x \ 1) * L(x,y,z) = x \ L(x,y,z).
(x \ L(x,y,z)) * L(u,L(x,y,z),x \ 1) = (x \ 1) * (u * L(x,y,z)).
L(a(x,y,z),y * z,x) = L(z \ L(z,y,x),z,y).
L(L(a(x,y,z),y * z,x),z,y) = z \ L(z,y,x).
(x \ y) * L(z,x \ y,x) = x \ (y * z).
(x \ 1) * (x * y) = L(y,x,x \ 1).
(x \ 1) * (x * y) != z | L(y,x,x \ 1) = z.
(x * (x \ ((x \ 1) \ y))) \ (x \ ((x \ 1) \ y)) = x \ ((x \ ((x \ 1) \ y)) \ y).
(x * L(y,x,x \ (y \ z))) \ z = x \ (y \ z).
(x \ (y \ z)) \ z != x * u | L(y,x,x \ (y \ z)) = u.
x \ (y * (x * (y \ z))) = y * (x \ (y \ (x * z))).
x \ (y * (x * (y \ (y * z)))) = y * (x \ (z * L(x,z,y))).
x * (y \ (z * L(y,z,x))) = y \ (x * (y * z)).
x * (L(y,z,x) * (y \ z)) = y \ (x * (y * z)).
x * ((y \ z) * L(y,z,x)) = y \ (x * (y * z)).
L(L(x,y,z),z,y) = (z \ x) * L(z,x,y).
L(L(x,y,z),z,y) = (y \ x) * L(y,x,z).
L((x \ y) * L(x,y,z),x,z) = L(y,z,x).
x \ (y \ (x * (y * z))) = (x \ z) * L(x,z,y).
L(L(L(x,y,z),u,w),z,y) = (y \ L(x,u,w)) * L(y,L(x,u,w),z).
(x \ y) \ L(L(y,z,x),x,z) = L(x,y,z).
(x \ L(y,z,x)) * L(x,L(y,z,x),z) = L(y,x,z).
L(L(L(x,y,z),u,w),z,y) = L((y \ x) * L(y,x,z),u,w).
L((x \ y) * L(x,y,z),z,x) = L(y,x,z).
(x \ y) \ L(L(y,x,z),z,x) = L(x,y,z).
L(L(x,L(y,x,z),z),z,L(y,x,z)) = (L(y,x,z) \ x) * y.
x \ L(L(y,z,u),u,z) = x \ (L(z,y,u) * (z \ y)).
L(L(x,y \ x,z),z,y \ x) = y * L(y \ x,x,z).
x \ ((y \ (x \ z)) \ z) = (x \ y) * L(x,y,y \ (x \ z)).
(x \ y) \ ((z \ y) * L(z,y,x)) = L(x,y,z).
(x \ L(y,z,u)) * L(x,L(y,z,u),w) = L((x \ y) * L(x,y,w),z,u).
L(L(x,L(y,x,z),z),z,L(y,x,z)) = y * (L(y,x,z) \ x).
L(x \ L(x,y,z),x,x \ y) = y \ L(L(y,x,z),z,x).
x \ L(L(y,z,u),u,z) != w | x \ ((z \ y) * L(z,y,u)) = w.
(x \ 1) \ L(x \ 1,y,z) = x * L(x \ 1,y,z).
(x \ 1) \ L(L(x \ 1,y,z),u,w) = x * L(L(x \ 1,y,z),u,w).
(x * (x \ y)) * L(y \ (x \ y),z,u) = (x \ y) * (x * L(x \ 1,z,u)).
L(L(x \ 1,x * y,z),x,y) = ((x * y) * z) \ (y * z).
(x \ 1) * L(L(x,y,z),u,w) = x \ L(L(x,y,z),u,w).
(x \ 1) \ ((x * y) \ y) = x * L(x \ 1,x,y).
L((x * (y \ 1)) \ x,z,L(y,u,w)) = L(y,y \ 1,x).
L((x * (y \ 1)) \ x,x,y \ 1) = ((y \ 1) \ y) * L(y \ 1,y,x).
L(L(x,x * (y \ 1),z),z,x * (y \ 1)) = L(y,y \ 1,x) * L(x * (y \ 1),x,z).
L(x \ 1,x,L(y \ L(y,x,z),y,y \ x)) = L(L(x,y,z),z,y) \ (x \ L(L(x,y,z),z,y)).
L(x * (y \ 1),y,y \ 1) = y \ x.
(x * y) * (x \ 1) = L(y,x,x \ 1).
(x * y) * (y \ 1) = L(x,y,y \ 1).
L(L(x,y,z),u,w) \ (x \ L(L(x,y,z),u,w)) = x \ 1.
x * ((y \ z) \ z) = y * x.
L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w).
L((x \ 1) * y,x,x \ 1) = x \ y.
(x * (y \ 1)) \ ((y \ 1) * ((x * (y \ 1)) * y)) = (y \ 1) * ((y \ x) * ((x * (y \ 1)) \ y)).
(x * y) \ L(y,x,x \ 1) = x \ 1.
L(x,y,y \ 1) \ (y * x) = L(y,y \ 1,y * x).
(x \ 1) * (y * x) = L(y,x,x \ 1).
(x \ 1) \ L(y,x,x \ 1) = y * x.
(x \ y) * ((x * y) * (y \ 1)) = L(L(y,y \ 1,x),x,y \ 1).
L(x * y,x \ 1,x) = (x \ 1) \ y.
x \ (y \ L(y,x,x \ 1)) = L(x \ 1,x,y).
L(L(x,y,z) \ 1,x,x \ 1) = (x \ 1) * (L(x,y,z) \ x).
L((x \ y) * L(x,z,u),x,x \ 1) = (x \ 1) * (y * L(x,z,u)).
L(x,y,z) \ 1 != x \ u | L(x,y,z) \ x = u.
L((L(x,y,z) \ x) \ (L(x,u,w) * (L(x,y,z) \ 1)),x,u * w) = L(a(x,u,w),x,x \ (L(x,y,z) \ x)).
x * ((y \ z) \ z) != u | y * x = u.
(x \ 1) \ L(x \ 1,y,z) != u | x * L(x \ 1,y,z) = u.
L(x,1,y) = x.
L(x,1,y) != z | x = z.
L(x,1,y) = z \ (z * x).
(x * (y * z)) \ (z * (x * L(y,z,x))) = a(L(y,z,x),x,z).
(x * a(x,y,z)) \ L(1 \ (L(x,y,z) * (x \ 1)),x,y * z) = x \ 1.
L(x,y,y \ 1) \ (x * (y * (y \ 1))) = a(y \ 1,y,x).
L(x \ 1,x,L(y,x,x \ 1)) = x \ (L(y,x,x \ 1) \ y).
x * L(y,x,x \ 1) = (x \ 1) \ y.
x * (y * (x \ 1)) = L(y,x \ 1,x).
(x * (x \ ((x \ 1) \ y))) \ (x \ ((x \ 1) \ y)) = x \ (L(y,x,x \ 1) \ y).
(x * (y \ 1)) \ ((y \ 1) * (y * (x * (y \ 1)))) = (y \ 1) * ((y \ x) * ((x * (y \ 1)) \ y)).
((x * y) * L(z,x,y)) * L((y * (z * x)) \ (u * (x * y)),w,v5) = (x * y) * (L(z,x,y) * L(L(z,x,y) \ u,w,v5)).
(x \ y) * (x * L(x \ 1,z,u)) = y * L(y \ (x \ y),z,u).
L(x \ 1,x,y) != z | (y * x) \ y = z.
x \ (y * (x * L(x \ z,u,w))) = y * L(L((y * x) \ (y * z),y,x),u,w).
x \ (y * (x * L(x \ z,u,w))) = y * L(y \ (x \ (y * z)),u,w).
(x \ y) \ (y * z) = x * L(z,x,x \ y).
(x \ 1) * ((((x \ 1) \ y) * (x \ 1)) \ ((x \ 1) \ y)) = ((x \ 1) \ y) \ (y * x).
x * L(L(y,x,x \ 1),z,u) = (x \ 1) \ L(y,z,u).
x \ ((y \ 1) \ x) = ((y \ 1) \ y) * L(y \ 1,y,x).
(x \ 1) * ((((x \ 1) \ y) * (x \ 1)) \ ((x \ 1) \ y)) = ((x \ 1) \ y) \ (x * y).
(x * (y * z)) \ (y * (z * x)) = a(y,z,L(x,z,y)).
a(x,y,L(z,y,x)) = a(z,y,x).
a((x \ y) \ z,x \ y,x) = a(x,x \ y,y \ (x * z)).
(x * a(x,y,z)) \ L(1 \ (x \ L(x,y,z)),x,y * z) = x \ 1.
L(x \ (y \ z),y,x) = L(y \ (x \ z),x,y).
L(x \ (y \ (x * L(y,z,u))),y,z * u) = L(L(a(y,z,u),y,x),x,y).
L(x \ (L(y,z,u) * (y \ x)),y,z * u) = L(L(a(y,z,u),y,x),x,y).
L(L(a(x,y,z),x,u),u,x) = L(a(x,y,z),x,x \ u).
L(L(a(x,y,z),u,x),x,u) = L(a(x,y,z),x,x \ u).
(x \ a(x,y,z)) * L(x,a(x,y,z),u) = L(a(x,y,z),x,x \ u).
L(a(x,y,z),x,x \ u) != L(w,x,u) | L(a(x,y,z),u,x) = w.
x * L(a(y,z,u),y,y \ x) = y \ (x * (y * a(y,z,u))).
(x \ a(x,y,z)) \ L(a(x,y,z),x,x \ u) = L(x,a(x,y,z),u).
L(L(a(x,y,z),u,z),z,u) = L(a(z,y,L(x,y,z)),z,z \ u).
a(x,y,z) * L(x,a(x,y,z),u) = x * L(a(x,y,z),x,x \ u).
x \ (y * (x * a(x,z,u))) = (x \ y) * (x * a(x,z,u)).
x \ (y * (x * a(x,z,u))) != w | (x \ y) * (x * a(x,z,u)) = w.
L(L(a(x,y,z),u,z),z,u) = L(a(x,y,z),z,z \ u).
a(x,y,z) * L(u,a(x,y,z),x) = (x \ u) * (x * a(x,y,z)).
(x \ a(x,y,z)) \ L(a(x,y,z),x,u) = L(x,a(x,y,z),x * u).
a(x,y,z) \ (x * L(a(x,y,z),x,x \ u)) = L(x,a(x,y,z),u).
(a(x,y,z) \ x) * L(a(x,y,z),x,x \ u) = L(x,a(x,y,z),u).
(((x * (L(x,y,z) \ u)) * (x \ 1)) * L(x,y,z)) \ (x * u) = L(x,x \ 1,x * (L(x,y,z) \ u)).
a(x,y,z) \ ((x \ u) \ (u * a(x,y,z))) = L(x,a(x,y,z),u).
(a(x,y,z) \ x) * L(a(x,y,z),x,u) = L(x,a(x,y,z),x * u).
L(L(x,y,a(x,z,u)),a(x,z,u),y) = L(x,a(x,z,u),x * y).
(x \ y) * L(x,y,a(y,z,u)) = L(y,a(y,z,u),y * x).
x \ (L(y,z,z \ 1) * (x * z)) = (z \ 1) \ L(y,z,x).
(x \ 1) \ L(y * (x \ 1),z,u) = x * L(x \ y,z,u).
L((L(x,y,z) \ x) \ (L(x,y,z) \ L(x,u,w)),x,u * w) = L(a(x,u,w),x,x \ (L(x,y,z) \ x)).
x \ L(y,x \ 1,x) = y * (x \ 1).
(x \ 1) \ L(y,x \ 1,x) = y * L(x,y,x \ 1).
x \ L(y,x \ 1,x) = (x \ 1) * y.
L(x,y \ 1,y) \ (x * (y \ 1)) = L(y \ 1,y,x * (y \ 1)).
L((x \ 1) \ y,z,u) * (x \ 1) = x \ L(1 \ (x * y),z,u).
x * ((x \ 1) * y) != z | L(y,x \ 1,x) = z.
L((x \ 1) \ y,z,u) * (x \ 1) = x \ L(x * y,z,u).
(x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u).
x \ L(x * L(y,(x \ 1) \ 1,x \ 1),z,u) = (x \ 1) * L(y * ((x \ 1) \ 1),z,u).
x \ L(x * L(y,(x \ 1) \ 1,x \ 1),z,u) = (x \ 1) * L(y * x,z,u).
x \ L(x * L(y,(x \ 1) \ 1,x \ 1),z,u) = (x \ 1) * L(x * y,z,u).
((x * y) * L(z,y,x)) \ ((x * u) * (y * z)) = L(u,x,z * y).
L(x,y,z * u) = L(x,y,u * z).
(x \ y) * L(x,L(y,z,y),u) = L((x \ y) * L(x,y,u),z,y).
L((x \ y) * L(x,y,z),u,y) = (x \ y) * L(x,y,z).
L(L(x \ 1,x * y,z),x,y) = (z * (x * y)) \ (y * z).
L(L(x \ 1,x,y),x * y,z) = (z * (x * y)) \ (y * z).
x \ L(L(y \ 1,y,z),y * z,u) = x \ ((u * (y * z)) \ (z * u)).
L(x \ 1,x,L(y \ L(y,x,z),y,y \ x)) = x \ 1.
L(x,y,z) \ (x * u) != w | x * (L(x,y,z) \ u) = w.
L(x,y \ 1,y) \ (x * y) = L(y,y \ 1,x).
x * (L(x,y \ 1,y) \ y) = L(y,y \ 1,x).
L(a(x,y,y \ (z \ y)),y * (y \ (z \ y)),x) = (y * (y \ (z \ y))) \ ((z \ y) * (z * L(z \ 1,y,x))).
L(a(x,y,y \ (z \ y)),z \ y,x) = (y * (y \ (z \ y))) \ ((z \ y) * (z * L(z \ 1,y,x))).
L(a(x,y,y \ (z \ y)),z \ y,x) = (z \ y) \ ((z \ y) * (z * L(z \ 1,y,x))).
L(a(x,y,y \ (z \ y)),z \ y,x) != u | z * L(z \ 1,y,x) = u.
x \ ((y \ z) * y) != u | u \ z = x.
(x \ y) \ ((y * (z \ 1)) * L(L(z,z \ 1,y),y,x)) = L(x,y,L(z,z \ 1,y)).
(x \ y) \ ((z * y) * L(L(z \ 1,z,y),y,x)) = L(x,y,L(z \ 1,z,y)).
(x \ L(y,z,u)) \ L((w \ y) * L(w,y,x),z,u) = L(x,L(y,z,u),w).
(x \ y) \ (y * (z * L(z \ 1,y,x))) = L(x,y,L(z \ 1,z,y)).
(x \ y) \ (y * ((z \ 1) * L(z,y,x))) = L(x,y,L(z,z \ 1,y)).
(a(x,y,z) \ L(x,u,w)) \ L(L(x,a(x,y,z),x * v5),u,w) = L(a(x,y,z),L(x,u,w),v5).
L(((x * y) \ y) \ 1,(x * y) \ y,y) = L(y \ (x * y),y,L(x \ 1,x,y)).
L(x \ (y * x),x,L(y \ 1,y,x)) = L(x \ (y * x),x,(y * x) \ x).
L(x \ (y * x),x,L(y \ 1,y,x)) = L(y,x,(y * x) \ x).
L(x,y,L(x \ 1,x,y)) = L(x,y,(x * y) \ y).
L(L(x,y,(x * y) \ y),L(x \ 1,x,y),y) = (L(x \ 1,x,y) \ x) * L(L(x \ 1,x,y),x,y).
L(x \ 1,x,y) * L(L(L(x,y,(x * y) \ y),L(x \ 1,x,y),y),z,u) = y \ (L(x \ 1,x,y) * (y * L(x,z,u))).
L(L(x,y,(x * y) \ y),L(x \ 1,x,y),y) = (L(x \ 1,x,y) \ x) * (x \ 1).
L(L(x,y,(x * y) \ y),L(x \ 1,x,y),y) = (x \ 1) * (L(x \ 1,x,y) \ x).
L(L(x,y,(x * y) \ y),L(x \ 1,x,y),y) = L(x \ 1,x,y) \ 1.
L(L(x \ 1,x,y) \ 1,L(x \ 1,x,y),y) = L(x,y,(x * y) \ y).
x \ (L(y \ 1,y,x) * (x * L(y,z,u))) = L(y \ 1,y,x) * L(L(y \ 1,y,x) \ 1,z,u).
L(L(x \ 1,x,y) \ 1,L(x \ 1,x,y),y) = L(x,y,(y * x) \ y).
L(x,y,(y * x) \ y) != z | (y * L(x \ 1,x,y)) \ y = z.
L(x \ 1,x,y * (x \ 1)) != z | y * (L(y,x \ 1,x) \ (x \ 1)) = z.
(x * a(x,y,z)) \ L(x \ L(x,y,z),x,y * z) = x \ 1.
(x * a(x,y,z)) \ a(x,y,z) = x \ 1.
(x \ 1) \ a(x,y,z) = x * a(x,y,z).
L(x \ 1,x,a(x,y,z)) = x \ 1.
L(a(x,y,z),x,x \ 1) = a(x,y,z).
(x \ 1) * a(x \ 1,y,z) = x \ a(x \ 1,y,z).
x \ a(x \ 1,y,L(z,y,x \ 1)) = (x \ 1) * a(z,y,x \ 1).
(x \ 1) * a(y,z,x \ 1) = x \ a(y,z,x \ 1).
a(x,y,z \ 1) \ (z \ a(x,y,z \ 1)) = z \ 1.
(x \ 1) * a(y,z,x \ 1) != u | x \ a(y,z,x \ 1) = u.
L(x,y,y \ 1) \ (x * 1) = a(y \ 1,y,x).
L(x,y,y \ 1) \ x = a(y \ 1,y,x).
(x * (x \ ((x \ 1) \ y))) \ (x \ ((x \ 1) \ y)) = x \ a(x \ 1,x,y).
L(x \ 1,x,L(y,x,x \ 1)) = x \ a(x \ 1,x,y).
((x \ 1) \ y) \ (x \ ((x \ 1) \ y)) = x \ a(x \ 1,x,y).
(x \ 1) \ ((x \ 1) \ ((x * y) \ y)) = L(x \ 1,x,y) * ((x \ 1) \ x).
(x * (y * z)) * L((x * (y * z)) \ (u * (z * x)),w,v5) = (z * x) * (L(y,z,x) * L(L(y,z,x) \ u,w,v5)).
(x * (y * z)) * L((x * (z * y)) \ (u * (y * x)),w,v5) = (y * x) * (L(z,y,x) * L(L(z,y,x) \ u,w,v5)).
(x * (y * z)) * L((x * (y * z)) \ (u * (y * x)),w,v5) = (y * x) * (L(z,y,x) * L(L(z,y,x) \ u,w,v5)).
x * ((y * z) * L((y * z) \ (x \ (u * (y * x))),w,v5)) = (y * x) * (L(z,y,x) * L(L(z,y,x) \ u,w,v5)).
x * (y * (z * L(z \ (y \ (x \ (u * (y * x)))),w,v5))) = (y * x) * (L(z,y,x) * L(L(z,y,x) \ u,w,v5)).
(x * y) * (L(z,x,y) * L(L(z,x,y) \ u,w,v5)) = y * (x * (z * L(z \ L(u,x,y),w,v5))).
(x * y) \ (y * (x * (z * L(z \ L(u,x,y),w,v5)))) = L(z,x,y) * L(L(z,x,y) \ u,w,v5).
L(x,y,z) * L(L(x,y,z) \ u,w,v5) = L(x * L(x \ L(u,y,z),w,v5),y,z).
L((x \ 1) * L((x \ 1) \ L(1,x,y),z,u),x,y) = y \ (L(x \ 1,x,y) * (y * L(x,z,u))).
L(x * L(x \ L(y,x \ 1,y),z,u),x \ 1,y) = L(x,x \ 1,y) * L(y * (x \ 1),z,u).
L(x,x \ 1,y) * L(y * (x \ 1),z,u) = L(x * L(x \ y,z,u),x \ 1,y).
L(L(x,x * (y \ 1),z),z,x * (y \ 1)) = L(y * L(y \ x,x,z),y \ 1,x).
L(L(x,x * (y \ 1),z),z,x * (y \ 1)) = y * L(y \ x,x,z).
x * a(x,y,y \ 1) = L(x,y,y \ 1).
x \ a(y,x,x \ 1) = L(x \ 1,x,y).
(x * (y \ 1)) * a(x * (y \ 1),y,y \ 1) = y \ x.
x * L(x \ 1,x,y) = a(y,x,x \ 1).
(x \ 1) \ ((x * y) \ y) = a(y,x,x \ 1).
x * ((x * y) \ y) = a(y,x,x \ 1).
x * ((y * x) \ y) = a(y,x,x \ 1).
a(x \ y,x,x \ 1) = x * (y \ (x \ y)).
a(x,x \ y,(x \ y) \ 1) = (x \ y) * (y \ x).
x * ((L(x,y,z) * (x * u)) \ (u * L(x,y,z))) = a(u * L(x,y,z),x,x \ 1).
(x \ 1) \ ((x \ 1) \ ((x * y) \ y)) = ((x \ 1) \ x) * L(x \ 1,x,y).
((x \ 1) \ x) * L(x \ 1,x,y) = (x \ 1) \ a(y,x,x \ 1).
(x \ 1) \ a(y,x,x \ 1) = y \ ((x \ 1) \ y).
(x \ 1) \ L(a(x,y,z),x,u) = u \ (a(x,y,z) * (u * x)).
L(x * y,z,u) = L(y * x,z,u).
(x * (y \ 1)) \ ((y \ 1) * L(x,y \ 1,y)) = (y \ 1) * ((y \ x) * ((x * (y \ 1)) \ y)).
(x \ 1) * ((x \ y) * ((y * (x \ 1)) \ x)) = (y * (x \ 1)) \ (x \ (y * 1)).
(x \ 1) * ((x \ y) * ((y * (x \ 1)) \ x)) = (y * (x \ 1)) \ (x \ y).
(x \ y) * ((x * y) * (y \ 1)) = x \ ((y \ 1) \ (1 * x)).
(x \ 1) * (y \ ((x \ 1) \ y)) = ((x \ 1) \ y) \ (x * y).
(x \ y) \ (y * (z \ L(z,y,x))) = L(x,y,L(z,z \ 1,y)).
L(x \ L(x,y,z),z,z \ y) = z \ L(z,y,L(x,x \ 1,y)).
L(x,y,y \ z) != y \ L(y,z,L(u,u \ 1,z)) | u \ L(u,z,y) = x.
L(L(x,y,x \ z),x \ z,y) = y \ ((x \ z) \ (y * z)).
(x \ y) * L(x,y,L(z,y,x)) = z * (L(z,y,x) \ y).
(x \ y) * z != u * (L(u,y,x) \ y) | L(x,y,L(u,y,x)) = z.
((x \ y) * L(x,y,L(z,y,x))) \ (y * z) = L(z,y,x).
((x \ y) * L(x,y,L(z,y,x))) \ (z * y) = L(z,y,x).
(x \ y) * ((x * y) * (y \ 1)) = x \ ((y \ 1) \ x).
(x \ y) * L(x,y,y \ 1) = x \ ((y \ 1) \ x).
(x * (y \ 1)) \ ((y \ 1) \ (x * (y \ 1))) = ((x * (y \ 1)) \ y) * (y \ x).
((x * (y \ 1)) \ y) * (y \ x) = (x * (y \ 1)) \ x.
(x \ y) * ((y * (x \ 1)) \ x) = (y * (x \ 1)) \ y.
(x \ 1) * ((y * (x \ 1)) \ y) = (y * (x \ 1)) \ (x \ y).
a(x,y \ 1,(y \ 1) \ 1) = (x * (y \ 1)) \ (y \ x).
(x * (y \ 1)) \ (y \ x) = a(x,y \ 1,y).
(x * (y \ 1)) * a(x,y \ 1,y) = y \ x.
a(x * (y \ 1),y,y \ 1) = a(x,y \ 1,y).
(x * y) * a(x,(y \ 1) \ 1,y \ 1) = (y \ 1) \ x.
a((x \ 1) \ y,x \ 1,x) = a(y,x,x \ 1).
L(x \ 1,x,y * (x \ 1)) = x \ a(y,x \ 1,x).
(x * y) * a(x,y,y \ 1) = (y \ 1) \ x.
a(x,x \ 1,1 \ (x * y)) = a(y,x,x \ 1).
x * (L(x,y \ 1,y) \ (y \ 1)) = y \ a(x,y \ 1,y).
x * a(y,y \ x,(y \ x) \ 1) = ((y \ x) \ 1) \ y.
x * ((y \ x) * (x \ y)) = ((y \ x) \ 1) \ y.
x * ((x \ y) * (y \ x)) = ((y \ x) \ 1) \ y.
L(x \ y,y \ x,y) = x \ (((x \ y) \ 1) \ x).
(x \ y) \ (x \ x) = y \ (((y \ x) \ 1) \ y).
x \ (((x \ y) \ 1) \ x) = (y \ x) \ 1.
((x \ y) \ 1) \ x = x * ((y \ x) \ 1).
((x * y) \ x) \ 1 = x \ ((y \ 1) \ x).
L(x \ y,(x \ y) \ 1,y) = (y \ x) \ 1.
L(L(x,x * ((y \ x) \ 1),z),z,((x \ y) \ 1) \ x) = ((x \ y) \ 1) * L(((x \ y) \ 1) \ x,x,z).
((x \ y) \ 1) * L(x * ((y \ x) \ 1),z,u) = (x \ y) \ L((x \ y) * x,z,u).
(x \ ((y \ 1) \ x)) \ 1 = (x * y) \ x.
L(x \ 1,x,y) \ 1 = y \ ((x \ 1) \ y).
L(x \ (x * (y \ 1)),(x \ (x * (y \ 1))) \ 1,x * (y \ 1)) = L(y,y \ 1,x) \ 1.
L(a(x,y,z),((x * (y * z)) \ (z * (x * y))) \ 1,z * (x * y)) = ((z * (x * y)) \ (x * (y * z))) \ 1.
L(x \ 1,((x * y) \ L(y,x,x \ 1)) \ 1,L(y,x,x \ 1)) = (L(y,x,x \ 1) \ (x * y)) \ 1.
L(L(x,x * ((y \ x) \ 1),z),z,x * ((y \ x) \ 1)) = ((x \ y) \ 1) * L(((x \ y) \ 1) \ x,x,z).
((x \ y) \ 1) * L(x * ((y \ x) \ 1),z,u) = (x \ y) \ L(y,z,u).
((x \ y) \ 1) * L(((x \ y) \ 1) \ x,x,z) = (y \ x) * L((y \ x) \ x,x,z).
((x \ y) \ 1) * L(((x \ y) \ 1) \ x,x,z) = (y \ x) * L(y,x,z).
((x \ y) \ 1) * L(x * ((y \ x) \ 1),x,z) = (y \ x) * L(y,x,z).
(x \ y) \ L(y,x,z) = (y \ x) * L(y,x,z).
(x \ y) * ((y \ x) * L(y,x,z)) = L(y,x,z).
(L(x,y,z) \ y) * L(L(x,y,z),y,z) = (y \ L(x,y,z)) \ x.
(x \ y) * L(L(x,y,z),z,y) = L(y,x,z).
(x \ y) * (y \ ((x \ 1) \ y)) = L(y,x,x \ 1).
(x \ L(y,x,z)) \ y = (L(y,x,z) \ x) * y.
(L(x,y,z) \ y) * L(x,z,y) = L(y,L(x,y,z),z).
((x \ y) \ x) * (z \ (x \ (y * z))) = L(x,x \ y,z).
(x * (y \ 1)) * L(L(L(y,y \ 1,x),x,z),z,x) = L(x,L(y,y \ 1,x),z).
(((x \ y) \ 1) * (x \ y)) \ (y * ((x \ y) \ 1)) = ((x \ y) \ x) * (x \ (((x \ y) \ 1) \ x)).
L(x \ 1,(y \ (y * (x \ 1))) \ 1,y * (x \ 1)) = L(x,x \ 1,y) \ 1.
L(a(x,y,z),a(x,y,z) \ 1,z * (x * y)) = ((z * (x * y)) \ (x * (y * z))) \ 1.
L(x \ 1,(x \ 1) \ 1,L(y,x,x \ 1)) = (L(y,x,x \ 1) \ (x * y)) \ 1.
(x \ (y \ x)) \ 1 = (x * (y \ 1)) \ x.
(x \ 1) \ a(y,x,x \ 1) = L(x \ 1,x,y) \ 1.
x * (L(y \ 1,y,x) \ 1) = (y \ 1) \ x.
x \ ((L(y \ 1,y,x) \ 1) \ x) = L(y \ 1,x,x \ ((y \ 1) \ x)).
((x \ 1) \ y) * ((x \ 1) * L((x \ 1) \ 1,z,u)) = y * L(L(x \ 1,x,y) \ 1,z,u).
L(x,x \ 1,y) = (y \ (x \ y)) \ 1.
L(x,x \ 1,y) \ 1 = y \ (x \ y).
L(x \ 1,x,x \ y) \ 1 = L(x,x \ 1,y).
x * (L(y,y \ 1,z) \ 1) = x * (z \ (y \ z)).
x * (L(y,y \ 1,x) \ 1) = y \ x.
L(x,x \ 1,y * (x * z)) \ 1 = (y * (x * z)) \ (z * L(y,z,x)).
(x * L(y,z,u)) \ (L(y,z,u) * (y \ x)) = L(y,y \ 1,x * L(y,z,u)) \ 1.
((x \ 1) \ (((x \ 1) \ y) \ (x * y))) \ 1 = ((x \ 1) \ y) \ (x \ ((x \ 1) \ y)).
x \ (((y \ x) * L(y,x,z)) \ x) = ((y \ x) * L(y,x,z)) \ 1.
L(L(x,x \ 1,y),L(x,x \ 1,y) \ 1,y) = x.
L(x \ (y \ x),x,L(y,z,u)) = L(y,y \ 1,x * L(y,z,u)) \ 1.
L(x,x \ 1,L(x,y,z) * (x * u)) \ 1 = (L(x,y,z) * (x * u)) \ (u * L(x,y,z)).
(x * L(y,x,L(z \ 1,z,x) \ 1)) \ (y * ((z \ 1) \ x)) = L(z \ 1,z,x) \ 1.
L(L(x \ 1,x,y) \ 1,L(x \ 1,x,y),y) \ 1 = L(x \ 1,y,y \ ((x \ 1) \ y)).
((x \ 1) \ y) * ((x \ 1) * L(x,z,u)) = y * L(L(x \ 1,x,y) \ 1,z,u).
(x * (L(x,y,z) \ y)) \ x = y \ L(x,y,z).
(x * (L(x,y \ 1,y) \ (y \ 1))) \ x = x * L(y,x,y \ 1).
L(x,y,z) * (L(x,z,y) \ z) = L(z,L(x,z,y),y).
(x \ (y \ (z * x))) \ L(y,y \ z,x) = (y \ z) \ y.
x * ((y \ 1) * L(L(y,x,z),z,x)) = L(x,L(y,y \ 1,x),z).
x * (y \ L(L(y,x,z),z,x)) = L(x,L(y,y \ 1,x),z).
L(x \ 1,x,L(y,x,x \ 1)) = (L(y,x,x \ 1) \ (x * y)) \ 1.
(L(x,y,y \ 1) \ (y * x)) \ 1 = y \ a(y \ 1,y,x).
L(x,x \ 1,x * y) \ 1 = x \ a(x \ 1,x,y).
L(L(x,y,z),L(x,x \ 1,u) \ 1,u) = L(L(x,x \ 1,u),y,z).
x \ (L(y,z,u) * (x * (L(y,y \ 1,x) \ 1))) = (L(y,y \ 1,x) \ 1) * L(L(y,y \ 1,x),z,u).
(L(x,x \ 1,y) \ 1) * L(L(x,x \ 1,y),z,u) = y \ (L(x,z,u) * (x \ y)).
L(x,x \ 1,y) \ L(L(x,x \ 1,y),z,u) = y \ (L(x,z,u) * (x \ y)).
L(x \ 1,x,y) \ L(L(x \ 1,(x \ 1) \ 1,y),z,u) = y \ (L(x \ 1,z,u) * ((x \ 1) \ y)).
L(x \ y,(x \ y) \ 1,y) \ L(L(x \ y,(x \ y) \ 1,y),z,u) = y \ (L(x \ y,z,u) * x).
L(x \ 1,x,y) \ L(L(x \ 1,x,y),z,u) = y \ (L(x \ 1,z,u) * ((x \ 1) \ y)).
((x \ y) \ 1) \ L(L(y \ x,(y \ x) \ 1,x),z,u) = x \ (L(y \ x,z,u) * y).
((x \ y) \ 1) \ L((x \ y) \ 1,z,u) = x \ (L(y \ x,z,u) * y).
(x \ y) * L((x \ y) \ 1,z,u) = x \ (L(y \ x,z,u) * y).
(x \ y) * L((x \ y) \ 1,z,u) != w | x \ (y * L(y \ x,z,u)) = w.
L(x \ 1,x,y) \ ((z * (x * y)) \ (y * z)) = y \ (L(x \ 1,x * y,z) * ((x \ 1) \ y)).
L(x \ 1,x,y) \ ((z * (x * y)) \ (y * z)) != u | y \ (((x \ 1) \ y) * L(x \ 1,x * y,z)) = u.
L(a(x,y,z),a(x,y,z) \ 1,z * (x * y)) = a(z,y,x) \ 1.
L(a(x,y,z),u,a(z,y,x) \ 1) = a(x,y,z).
((x \ y) \ (z \ y)) \ L(z,z \ x,x \ y) = (z \ x) \ z.
((x \ y) \ 1) \ L(y,y \ x,x \ y) = (y \ x) \ y.
((x \ 1) \ y) * (x \ L(x,z,u)) = y * L(L(x \ 1,x,y) \ 1,z,u).
(x \ L(x,y,z)) * ((x \ 1) \ u) = u * L(L(x \ 1,x,u) \ 1,y,z).
L(x \ 1,(x \ 1) \ 1,y * (x \ 1)) = L(x,x \ 1,y) \ 1.
L(x \ 1,x,y * (x \ 1)) = L(x,x \ 1,y) \ 1.
L(x,x \ 1,y) \ 1 = x \ a(y,x \ 1,x).
(x \ a(y,x \ 1,x)) \ 1 = L(x,x \ 1,y).
x \ a(y,x \ 1,x) = L(x \ 1,x,x \ y).
x * (L(x,y \ 1,y) \ (y \ 1)) = L(y \ 1,y,y \ x).
a(x \ y,x,x \ 1) = a(y,x \ 1,x).
L(x \ 1,x,x \ y) \ y = y * L(x,y,x \ 1).
x * (y \ (x \ y)) = a(y,x \ 1,x).
(x \ (y \ x)) \ x = x * L(y,x,y \ 1).
L(x,y,y \ (x \ y)) = L(x,y,x \ 1).
a(x,(y \ 1) \ 1,y \ 1) = ((y \ 1) \ x) \ (y * x).
((x \ 1) \ y) \ (x * y) = a(y,x,x \ 1).
((x \ 1) \ y) \ (x \ ((x \ 1) \ y)) = ((x \ 1) \ a(y,x,x \ 1)) \ 1.
((x \ 1) \ y) \ (x \ ((x \ 1) \ y)) = (L(x \ 1,x,y) \ 1) \ 1.
((x \ 1) \ y) \ (x \ ((x \ 1) \ y)) = L(x \ 1,x,y).
x \ a(x \ 1,x,y) = L(x \ 1,x,y).
L(x,x \ 1,x * y) \ 1 = L(x \ 1,x,y).
(((x \ y) \ 1) * (x \ y)) \ (y * ((x \ y) \ 1)) = ((x \ y) \ x) * ((y \ x) \ 1).
((x \ y) \ x) * ((y \ x) \ 1) = 1 \ (y * ((x \ y) \ 1)).
((x \ y) \ x) * ((y \ x) \ 1) = y * ((x \ y) \ 1).
((x \ y) \ 1) \ (x * ((y \ x) \ 1)) = (y \ x) \ y.
L(x,x \ y,y \ x) = y * ((x \ y) \ 1).
L(x \ 1,y,y \ ((x \ 1) \ y)) = L(x,y,(x * y) \ y) \ 1.
(L(L(x,y,z) \ u,x,x \ 1) * L(x,y,z)) \ (x * u) = L(x,x \ 1,x * (L(x,y,z) \ u)).
(L(x,y,z) * L(L(x,y,z) \ u,x,x \ 1)) \ (x * u) = L(x,x \ 1,x * (L(x,y,z) \ u)).
L(x * L(x \ L(y,z,u),x,x \ 1),z,u) \ (x * y) = L(x,x \ 1,x * (L(x,z,u) \ y)).
L(x,x \ 1,x * (L(x,y,z) \ u)) = L(x * (L(u,y,z) * (x \ 1)),y,z) \ (x * u).
L(x,x \ 1,x * (L(x,y,z) \ u)) = L(L(L(u,y,z),x \ 1,x),y,z) \ (x * u).
L(x,x \ 1,x * (L(x,y,z) \ u)) = L(u,x \ 1,x) \ (x * u).
L(x,x \ 1,x * (L(x,y,z) \ u)) = u * (L(u,x \ 1,x) \ x).
L(x,x \ 1,x * (L(x,y,z) \ u)) = L(x,x \ 1,u).
L(x,x \ 1,L(x,y,z) * u) = L(x,x \ 1,x * u).
L(x \ (y \ x),x,L(y,z,u)) = L(y,y \ 1,y * (L(y,w,v5) \ (x * L(y,z,u)))) \ 1.
L(x \ (y \ x),x,L(y,z,u)) = L(y,y \ 1,y * (L(y,z,u) * (L(y,w,v5) \ x))) \ 1.
L(x \ (y \ x),x,L(y,z,u)) = L(y \ 1,y,L(y,z,u) * (L(y,w,v5) \ x)).
L(x \ (y \ x),x,L(y,z,u)) = L(y \ 1,y,x).
L(x,y,z) * (u * (u \ (x \ u))) = (L(x,y,z) * u) * L(x \ 1,x,u).
L(x,y,z) * (u * (u \ (x \ u))) = (u * L(x,y,z)) * L(x \ 1,x,u).
(x * L(y,z,u)) * L(y \ 1,y,x) = L(y,z,u) * (y \ x).
(a(x,y,z) * L(x,u,w)) * (x \ 1) = L(x,u,w) * (x \ a(x,y,z)).
(x \ 1) * (a(x,y,z) * L(x,u,w)) = L(x,u,w) * (x \ a(x,y,z)).
(a(x,y,z) \ L(x,u,w)) \ L(L(x,a(x,y,z),v5),u,w) = L(a(x,y,z),L(x,u,w),x \ v5).
(x \ (a(x,y,z) \ u)) \ ((a(x,y,z) \ u) * a(x,y,z)) = (a(x,y,z) \ u) \ (x * u).
(x \ (a(x,y,z) \ u)) \ u = (a(x,y,z) \ u) \ (x * u).
L((L(x,y,z) \ x) \ (L(x,y,z) \ L(x,u,w)),x,u * w) = L(a(x,u,w),x,L(x,y,z) \ 1).
L(a(x,y,z),L(x,u,w) \ x,L(x,u,w)) = L(a(x,y,z),x,L(x,u,w) \ 1).
x \ (L(y,z \ 1,z) * (z \ x)) != u | L(y * (z \ 1),z,z \ x) = u.
L(x,x \ 1,x * (x * y)) \ 1 = (L(x,z,u) * (x * y)) \ (y * L(x,z,u)).
(L(x,y,z) * (x * u)) \ (u * L(x,y,z)) = L(x \ 1,x,x * u).
a(x * L(y,z,u),y,y \ 1) = y * L(y \ 1,y,y * x).
a(x * L(y,z,u),y,y \ 1) = a(y * x,y,y \ 1).
(x * y) \ (x * ((x * y) * L((x * y) \ (y * z),u,w))) = x * L(x \ L(z,y,x),u,w).
(x * y) \ (x * (y * (x * L(x \ z,u,w)))) = x * L(x \ L(z,y,x),u,w).
x \ L(x * L(x \ y,z,u),w,x) = L(x \ L(y,w,x),z,u).
x \ L(x * L(y,z,u),w,x) = L(x \ L(x * y,w,x),z,u).
x * L(L((x \ 1) * L(y,z,u),x,x \ 1),w,x \ 1) = L((x \ 1) \ L((x \ 1) * y,w,x \ 1),z,u).
L((x \ 1) \ L((x \ 1) * y,z,x \ 1),u,w) = x * L(x \ L(y,u,w),z,x \ 1).
L((x \ 1) \ L(y * (x \ 1),z,x \ 1),u,w) = x * L(x \ L(y,u,w),z,x \ 1).
x * L(x \ L(y,z,u),w,x \ 1) = L(x * L(x \ y,w,x \ 1),z,u).
L(1,x,y) = K(z,u).
L(1,x,y) = 1.
L((x \ 1) * L((x \ 1) \ 1,y,z),x,u) = u \ (L(x \ 1,x,u) * (u * L(x,y,z))).
x \ (L(y \ 1,y,x) * (x * L(y,z,u))) = L((y \ 1) * L(y,z,u),y,x).
x \ (L(y \ 1,y,x) * (x * L(y,z,u))) = L(y \ L(y,z,u),y,x).
x \ ((x * L(y,z,u)) * L(y \ 1,y,x)) = L(y \ L(y,z,u),y,x).
L(x \ L(x,y,z),x,u) = u \ (L(x,y,z) * (x \ u)).
L(x \ L(x,y,z),x,x \ u) = L(x \ L(x,y,z),x,u).
(x * y) \ (L(z,x,y) * (z \ (x * y))) = a(z,x,y).
(x * y) \ (z \ (x * (y * z))) = y \ (L(x,y,z) * (x \ y)).
L(x \ (L(y,z,u) * (y \ x)),y,z * u) = L(a(y,z,u),y,x).
L(x \ 1,x,L(y \ L(y,x,z),y,x)) = x \ 1.
(x * y) \ (z \ (x * (y * z))) = y \ ((x \ y) * L(x,y,z)).
(x * y) \ (z \ (y * (z * x))) = a(z,x,y).
L(a(x,y,z),x,x \ u) = L(a(x,y,z),x,u).
L(a(x,y,z),y * z,x) = a(x,y,z).
L(x \ L(x,y,z),x,y) = a(z,y,x).
L(a(x,y,z),z,y) = z \ L(z,y,x).
L(x * L(x \ 1,y,z),x \ 1,y) = a(z,y,x \ 1).
L(a(x,y,z),y * z,x) = y \ ((z \ y) * L(z,y,x)).
x \ ((y \ x) * L(y,x,z)) = a(z,x,y).
(x \ y) * L(x,y,z) = y * a(z,y,x).
x \ L(L(x,y,z),z,y) = a(y,x,z).
L(x,y,z) \ L(x,z,y) = a(y,L(x,y,z),z).
L(L(x,y,z),z,y) = x * a(y,x,z).
L(x * a(y,x,z),z,y) = L(x,y,z).
L(x * a(y,x,z),y,z) = L(x,z,y).
(x \ y) \ (y * a(x,y,z)) = L(x,y,z).
(x \ L(y,z,u)) \ L(y * a(x,y,w),z,u) = L(x,L(y,z,u),w).
x \ ((y \ x) * L(y,x,z)) = a(y,x,z).
x * L(L(x \ 1,y,z),z,y) = a(y,x \ 1,z).
L(x,y,z) \ L(x,z,y) = a(z,L(x,y,z),y).
(x * y) \ (y * L(L(x,z,u),u,z)) = L(a(z,x,u),x,y).
L(x,L(y,y \ 1,x),z) = x * a(x,y,z).
(x \ y) * L(x,y,z) = y * a(x,y,z).
a(x,y,z) = a(z,y,x).
(x \ y) \ L(L(y,z,u),u,z) = x * L(a(z,y,u),x,x \ y).
(x \ y) * (x * a(y,x,z)) = L(y,x,z).
x \ (x * a(y,z \ 1,u)) = z * L(L(z \ 1,y,u),u,y).
(x * a(y,x,z)) \ (a(y,x,z) * L(L(x,y,z),z,y)) = a(y,x,z).
L(x,L(y \ 1,y,x),z) = x * a(x,y \ 1,z).
L(x,L(y,y \ 1,x),z) \ L(x,u,w) = L(x,u,w) * ((x * a(x,y,z)) \ 1).
x \ ((y \ (x \ z)) \ z) = y * a(x,y,y \ (x \ z)).
(x \ y) * L(x,y,z) = y * (u \ (u * a(x,y,z))).
x * (y * a(x,y,z)) = y * L(x,y,z).
(x * a(y,x,L(z,x,y))) \ (z * x) = L(z,x,y).
((x \ y) * L(x,y,z)) \ 1 = y \ ((y * a(x,y,z)) \ y).
a(x,y,L(z,y,x)) = a(x,y,z).
(x * (y * z)) \ (z * (x * L(y,z,x))) = a(z,x,L(y,z,x)).
a(x,L(L(y,x,z),z,x),z) = a(x,y,z).
a(x,x \ y,(x \ y) \ z) = a(x,x \ y,y \ (x * z)).
x \ a(y,z,u) = x \ a(u,z,y).
x * a(y,z,u) = x * a(u,z,y).
a(x,y,z) * u = a(z,y,x) * u.
L(a(x,y,z),u,a(x,y,z) \ 1) = a(x,y,z).
L(a(x,y,z),x,y) = x \ L(x,y,z).
L(a(x,y,z),x,x \ y) = x \ L(x,y,z).
(x * ((y \ x) \ (x * a(y,x,L(z \ 1,z,x) \ 1)))) \ (y * ((z \ 1) \ x)) = L(z \ 1,z,x) \ 1.
a(x,y,L(L(z,y,x),u,w)) = a(x,y,L(z,u,w)).
a(x,y,z * a(x,z,y)) = a(x,y,L(z,x,y)).
a(x,y,z) * u = u * a(z,y,x).
a(x,y,z) \ (u * a(z,y,x)) = u.
x \ (y * a(z,u,w)) = x \ (y * a(w,u,z)).
a(x,y,z) * u != w | u * a(z,y,x) = w.
x * (y \ L(y,L(x,x \ 1,y),z)) = (y \ x) * L(y,x,z).
((x \ y) * L(x,z,u)) * (x * a((x \ y) * L(x,z,u),x,x \ 1)) = x * ((x \ 1) * (y * L(x,z,u))).
(x \ (y \ z)) * a(x,x \ (y \ z),y) = y \ (x \ z).
L(L(x,y,z),z,y) * a(y,L(L(x,y,z),z,y),z) = x.
L(x * a(y,x,z),y,L(z,x,y)) = L(x,L(z,x,y),y).
((x * a(y,x,z)) \ z) * L(x,y,z) = z * a(x * a(y,x,z),z,y).
(x * a(y,x,z)) \ (z * x) = L(z,x,y).
x \ ((x * a(y,x,z)) \ x) = (x * a(y,x,z)) \ 1.
L(L(x,y,z),z,y) * a(y,x,z) = x.
x * a(y,z,u) != w | x * a(u,z,y) = w.
a(x,y,z) * u != w | a(z,y,x) * u = w.
a(x,y,z) != u | a(z,y,x) = u.
L(a(x,y,z),u,x) = a(x,y,z).
(x * L(a(x,y,z),x,a(x,y,z) \ u)) \ u = x \ (a(x,y,z) \ u).
(x \ a(x,y,z)) \ L(a(x,y,z),x,u) = L(x,a(x,y,z),u).
a(x,y,y \ (z \ y)) = z * L(z \ 1,y,x).
L(a(x,y,z),u,x) = a(z,y,x).
L(L(a(x,y,z),u,w),v5,x) = L(a(x,y,z),u,w).
a(x,y,z) * (x * u) = x * (u * a(x,y,z)).
a(x,y,z) * (u * x) = x * (u * a(x,y,z)).
a(x,y,z) * (x \ 1) = x \ a(x,y,z).
L(a(x,y,z),u,z) = a(z,y,x).
L(x,a(x,y,z),x * u) = L(x,a(x,y,z),u).
(x * a(x,y,z)) \ 1 = x \ (a(x,y,z) \ 1).
L(x * L(x \ L(1,y,z),u,w),y,z) = a(w,u,u \ (L(x,y,z) \ u)).
(x \ (y \ x)) * L((x \ (y \ x)) \ 1,x,z) = a(z,x,L(y,x,x \ (y \ x))).
L(L(x \ 1,y,z),x,x \ 1) = (x \ 1) * a(z,y,y \ (x \ y)).
L(x,y,L(z \ 1,z,y)) = (x \ y) \ (y * a(x,y,y \ (z \ y))).
a(x,y,z) * (u * x) = x * (u * a(z,y,x)).
L(a(x,y,z),u,z) = a(x,y,z).
L(a(x,y,z),x,a(x,y,z) \ u) = x \ ((a(x,y,z) \ u) \ (x * u)).
(x * L(a(y,z,u),w,v5)) \ (L(a(y,z,u),w,v5) * (x * y)) = y.
x \ (y * L(a(x,z,u),w,v5)) = (x \ y) * L(a(x,z,u),w,v5).
x \ (L(a(x,y,z),u,w) \ x) = L(a(x,y,z),u,w) \ 1.
L(x,y,a(x,z,u)) = x.
L((x \ 1) \ y,x \ 1,a(x,z,u)) = (x \ a(x,z,u)) \ (a(x,z,u) * y).
(x \ 1) \ L(a(x,y,z),x,u) = u \ (x * (u * a(x,y,z))).
L((x \ 1) \ y,x \ 1,a(x,z,u)) = (x \ a(x,z,u)) \ (y * a(x,z,u)).
L((x \ 1) \ y,x \ 1,a(x,z,u)) != (x \ a(x,z,u)) \ w | a(x,z,u) * y = w.
L((x \ 1) \ y,x \ 1,a(x,z,u)) != (x \ a(x,z,u)) \ w | y * a(x,z,u) = w.
L(x * L(x \ 1,y,z),u,w) = a(z,y,y \ (L(x,u,w) \ y)).
(x \ (y \ x)) * L((x \ (y \ x)) \ 1,x,z) = a(z,x,L(y,x,y \ 1)).
(x \ 1) * a(y,z,z \ (x \ z)) = L(x \ 1,z,y).
L(x,y,L(z \ 1,z,y)) = L(x,y,y \ (z \ y)).
x \ ((y \ x) * L((y \ x) \ x,x,z)) = a(z,x,L(y,x,y \ 1)).
x \ ((y \ x) * L(y,x,z)) = a(z,x,L(y,x,y \ 1)).
a(x,y,L(z,y,z \ 1)) = a(x,y,z).
L(x * a(y,x,z),y,L(z,x,z \ 1)) = L(x,L(z,x,z \ 1),y).
(a(x,y,z) \ L(x,u,w)) \ L(L(x,a(x,y,z),v5),u,w) = L(a(x,y,z),L(x,u,w),v5).
L(L(x,y,z),u,a(x,w,v5)) = L(x,y,z).
L(x,y,a(z,u,x)) = x.
x \ (y * a(x,z,u)) = a(x,z,u) * (x \ y).
L(x,y,z) \ (u * a(x,w,v5)) = a(x,w,v5) * (L(x,y,z) \ u).
x * L(a(x,y,z),x,a(x,y,z) \ 1) = (a(x,y,z) \ 1) \ x.
L(a(x,y,z),L(x,u,w),x \ v5) = L(a(x,y,z),L(x,u,w),v5).
(x * L(y,z,u)) \ (L(y,z,u) * (x * a(y,w,v5))) = a(y,w,v5).
(a(x,y,z) \ 1) * L(x,u,w) = a(x,y,z) \ L(x,u,w).
(x \ 1) * a(y,z,x) = x \ a(y,z,x).
x * L(a(y,z,x),x,a(y,z,x) \ 1) = (a(y,z,x) \ 1) \ x.
(a(x,y,z) \ 1) \ x = x * a(x,y,z).
a(x,y,z) * (L(x,u,w) \ x) = x * (L(x,u,w) \ a(x,y,z)).
x * L(a(x,y,z),x,y) = L(x,y,z).
a(x,y,y \ L(y,x,z)) = a(x,y,a(y,x,z)).
L(a(x,y,z),u,x) != w | a(z,y,x) = w.
L(a(x,y,z),u,x) != w | a(x,y,z) = w.
L(a(x,y,z),u,z) != w | a(x,y,z) = w.
x * (y * L(a(y,z,u),y,x)) = y * (x * a(u,z,y)).
L(a(x,y,z),z,z \ u) = L(a(x,y,z),z,u).
a(x,y,L(z,z \ 1,y)) = z \ L(z,y,x).
x \ L(x,L(y \ 1,y,x),z) = y * L(L(y \ 1,x,z),z,x).
L(x,y,z) * ((x * a(x,u,w)) \ 1) = (x * a(x,u,w)) \ L(x,y,z).
x \ L(x,(x * y) \ x,z) = y * L(L(y \ 1,x,z),z,x).
x \ L(x,(x * y) \ x,z) = a(x,y \ 1,z).
L(x,y,(x * y) \ y) = L(x,y,y \ (x \ y)).
L(x,y,(y * z) \ y) = L(x,y,y \ (z \ y)).
L(x \ 1,y,y \ ((x \ 1) \ y)) = L(x,y,y \ (x \ y)) \ 1.
(x * L(y \ 1,y,x)) \ x = L(y,x,x \ (y \ x)).
(x * L(y \ 1,y,x)) \ x = L(y,x,y \ 1).
a(x,L(y \ 1,y,x) \ 1,z) = x \ L(x,L(y,x,y \ 1),z).
x * a(x,L(y \ 1,y,x) \ 1,z) = L(x,L(y,x,y \ 1),z).
a(x,y,z) * L(L(y,x,z),z,x) = y.
L(x,y,z) * a(y,L(x,z,y),z) = L(x,z,y).
(x * a(y,x,z)) \ x = a(y,x,z).
L(L(x,y,z),L(x,z,y) \ 1,L(x,z,y)) = (L(x,z,y) \ 1) \ a(z,L(x,y,z),y).
a(x,y,z) \ y = y * a(x,y,z).
(x * a(y,x,z)) \ 1 = x \ a(y,x,z).
(a(x,y,z) * L(y,u,w)) * L(y \ 1,y,a(x,y,z)) = L(y,u,w) * ((y * a(x,y,z)) \ 1).
L(L(x,y,z),z,y) \ 1 = x \ a(y,x,z).
L(x \ 1,x,a(y,x,z)) = x \ 1.
(a(x,y,z) * L(y,u,w)) * (y \ 1) = L(y,u,w) * ((y * a(x,y,z)) \ 1).
L(x,y,z) * ((x * a(u,x,w)) \ 1) = (x \ 1) * (a(u,x,w) * L(x,y,z)).
L((x \ 1) * L(x,y,z),u,w) = a(z,y,y \ (L(x \ 1,u,w) \ y)).
L(x \ L(x,y,z),u,w) = a(z,y,y \ (L(x \ 1,u,w) \ y)).
L(x,y,L(a(x,z,u),w,v5)) = x.
x * a(x,x \ 1,y) = L(x,x \ 1,y).
(L(x,y,z) \ 1) \ a(y,L(x,z,y),z) = L(x,z,y).
(L(x,y,z) \ 1) \ a(z,L(x,z,y),y) = L(x,z,y).
L(L(x,y,z),u,L(a(x,w,v5),v6,v7)) = L(x,y,z).
L(x,y,x \ L(x,z,u)) = x.
L(L(x,y,z),y,z) = L(x,u,x \ L(x,w,v5)).
x \ L(x,x \ L(x,y,z),u) = a(u,x,x \ L(x,y,z)).
L(L(x,y,z),y,z) != u | x = u.
x \ L(x,y,L(z,z \ 1,y)) = L(z \ L(z,y,x),x,y).
a(x,y,z) \ L(a(x,y,z),z,u) = a(u,z,a(x,y,z)).
(L(x,y,z) \ x) * a(x,u,w) = x * (L(x,y,z) \ a(x,u,w)).
x * (y * a(y,z,x)) = y * (x * a(y,z,x)).
x \ (y * (x * a(y,z,x))) = y * a(y,z,x).
x \ (y * (x * a(x,z,y))) = y * a(y,z,x).
(x \ y) * (x * a(x,z,y)) = y * a(y,z,x).
(x \ y) * (x * a(x,z,y)) = y * a(x,z,y).
(x * a(y,x,z)) \ (x * z) = L(z,x,y).
(x * a(y,x,x \ z)) \ z = L(x \ z,x,y).
(x \ y) * a(z,x \ y,x) = L(x,x \ y,z) \ y.
x * (L(x,y,z) \ y) = y * a(z,y,x).
((x \ y) * a(x,x \ y,(x \ y) \ z)) \ z = y \ (x * z).
x * a(y,x,x \ 1) = L(x,x \ 1,x * y).
(x \ y) * a(x,x \ y,z) = L(x,x \ y,z) \ y.
(x \ y) * L(x,y,z) = z * (L(z,y,x) \ y).
x \ (y * a(z,y,x)) = L(x,y,z) \ y.
(x * a(y,x,z)) \ z = x \ L(z,x,y).
L(x,x \ (y \ z),y) \ (y \ z) = y \ (x \ z).
L(x \ (y \ z),x,y) \ (y \ z) = y \ ((x \ (y \ z)) \ z).
a(x,y,z) \ (x \ u) = x \ (a(x,y,z) \ u).
((x * y) \ z) \ (x \ z) = x \ ((y \ (x \ z)) \ z).
a(x,y,z) \ (x \ (u * (x * a(x,y,z)))) = L(u,x,a(x,y,z)).
L(x,a(y,z,u),y) = L(x,y,a(y,z,u)).
a(x,y,z) \ ((x \ u) * (x * a(x,y,z))) = L(u,x,a(x,y,z)).
a(x,y,z) * L(u,x,a(x,y,z)) = (x \ u) * (x * a(x,y,z)).
x * ((x * a(x,y,z)) \ (u * a(x,y,z))) = L(u,x,a(x,y,z)).
L(a(x,y,z) \ u,x,a(x,y,z)) = x * ((x * a(x,y,z)) \ u).
L(x,y,z) * (x \ (a(x,u,w) \ 1)) = (x * a(x,u,w)) \ L(x,y,z).
L(a(x,y,z),u,L(x,w,v5)) = a(x,y,z).
L(x \ 1,y,(x \ 1) \ 1) = L(x,y,y \ (x \ y)) \ 1.
L(x,y,y \ (x \ y)) \ 1 = L(x \ 1,y,x).
L(x,y,x \ 1) \ 1 = L(x \ 1,y,x).
L(x \ 1,y,x) \ 1 = L(x,y,x \ 1).
L((x \ 1) * L((x \ 1) \ L(1,y,x),z,u),y,x) = L(x \ 1,y,x) * L(L(x,y,x \ 1),z,u).
L(L(x \ 1,y,x) * L(L(x,y,x \ 1),z,u),L(x \ 1,y,x) \ 1,z) = a(u,z,L(x \ 1,y,x) \ 1).
L(x \ 1,y,x) * L(L(x,y,x \ 1),z,u) = L((x \ 1) * L((x \ 1) \ 1,z,u),y,x).
L(x \ 1,y,x) * L(L(x,y,x \ 1),z,u) = L((x \ 1) * L(x,z,u),y,x).
L(x \ 1,y,x) * L(L(x,y,x \ 1),z,u) = L(x \ L(x,z,u),y,x).
L(x,y,a(x,z,u)) != w | x = w.
(a(x,y,z) \ 1) \ z = z * a(x,y,z).
L(x,a(y,z,x),u) * (x \ (a(y,z,x) * u)) = x \ (u * ((a(y,z,x) \ 1) \ x)).
L(x,a(x,y,z),u) * (x \ (a(z,y,x) * u)) = x \ (u * ((a(z,y,x) \ 1) \ x)).
L(x,a(x,y,z),u) * (x \ (u * a(x,y,z))) = x \ (u * ((a(z,y,x) \ 1) \ x)).
L(x,a(x,y,z),u) * (a(x,y,z) * (x \ u)) = x \ (u * ((a(z,y,x) \ 1) \ x)).
L(x,a(x,y,z),u) * (a(x,y,z) * (x \ u)) = x \ (u * ((a(x,y,z) \ 1) \ x)).
L(x,a(x,y,z),u) * (a(x,y,z) * (x \ u)) = x \ (u * (x * a(x,y,z))).
L(x,a(x,y,z),u) * (a(x,y,z) * (x \ u)) = (x \ u) * (x * a(x,y,z)).
L(x,y,L(z,y,x)) = L(x,y,z).
(x \ L(y,x,z)) * L(x,z,y) = y * a(x * a(z,x,y),y,z).
L(L(x,y,z),y,L(z,y,x)) = x.
(x * L(y,x,z)) \ (z * (x * y)) = L(z,x,y).
x \ L(L(x,y,z),L(z,y,x),y) = a(y,x,L(z,y,x)).
L(x,L(y,z,x),z) * a(z,L(x,z,y),L(y,z,x)) = L(x,z,y).
(x \ (y * (x * z))) \ (x * (z * y)) = L(x,z,y).
(x \ (y * (x * z))) \ (x * (y * z)) = L(x,z,y).
L(a(x,y,z),x,L(x,u,w) \ 1) = a(x,y,z).
((L(x,y,z) \ 1) \ L(x,u,w)) \ L((a(x,v5,v6) \ x) * a(x,v5,v6),u,w) = L(L(x,y,z) \ 1,L(x,u,w),a(x,v5,v6)).
L(L(x,y,z) \ 1,L(x,u,w),a(x,v5,v6)) = ((L(x,y,z) \ 1) \ L(x,u,w)) \ L(x,u,w).
L(L(x,y,z) \ 1,L(x,u,w),a(x,v5,v6)) = L(x,y,z) \ 1.
(L(x,y,z) \ 1) \ a(x,u,w) = L(x,y,z) * a(x,u,w).
L(x \ y,(x \ y) \ 1,y) * a(x \ y,z,u) = (((y \ x) \ 1) \ 1) \ a(x \ y,z,u).
L(x \ y,(x \ y) \ 1,y) * a(x \ y,z,u) = (y \ x) \ a(x \ y,z,u).
L(x \ y,(x \ y) \ 1,y) * a(x \ y,z,u) = (y \ x) \ a(u,z,x \ y).
((x \ y) \ 1) * a(y \ x,z,u) = (x \ y) \ a(u,z,y \ x).
((x \ y) \ 1) * a(z,u,y \ x) = (x \ y) \ a(z,u,y \ x).
((x * (y \ 1)) \ x) * a(z,u,(y \ x) \ x) = (x \ (y \ x)) \ a(z,u,(y \ x) \ x).
((L(x,y,z) \ u) \ u) \ L(x * L(x \ 1,u,w),y,z) = (((L(x,y,z) \ u) \ u) \ 1) * a(w,u,u \ (L(x,y,z) \ u)).
(x \ (y \ x)) \ a(z,u,(y \ x) \ x) = ((x * (y \ 1)) \ x) * a(z,u,y).
((L(x,y,z) \ u) \ u) \ L(x * L(x \ 1,u,w),y,z) = (L(x,y,z) \ 1) * a(w,u,u \ (L(x,y,z) \ u)).
a(x,y,(z \ u) \ u) = a(x,y,z).
a(x,y,(z \ u) \ u) = a(z,y,x).
a(x,y,z \ (z * u)) = a(x,y,u).
a(x,y,z * u) = a(x,y,u * z).
a(x,y,(z \ u) \ u) != w | a(z,y,x) = w.
a(x,y,a(z,u,w)) = a(x,y,a(w,u,z)).
((L(x,y,z) \ u) \ u) \ L(x * L(x \ 1,u,w),y,z) = L(L(x,y,z) \ 1,u,w).
L(x,y,z) \ L(x * L(x \ 1,u,w),y,z) = L(L(x,y,z) \ 1,u,w).
L(L(x,y,z) \ 1,u,x \ 1) = L(x,y,z) \ L(x * (x \ 1),y,z).
L(x * L(x \ L(L(x * L(x \ 1,y,z),u,w),u,w),v5,v6),u,w) = L(x,u,w) * L(L(L(x,u,w) \ 1,y,z),v5,v6).
L(L(x,y,z) \ 1,u,x \ 1) = L(x,y,z) \ L(1,y,z).
L(x * L(x \ (x * L(x \ 1,y,z)),u,w),v5,v6) = L(x,v5,v6) * L(L(L(x,v5,v6) \ 1,y,z),u,w).
L(x,y,z) * L(L(L(x,y,z) \ 1,u,w),v5,v6) = L(x * L(L(x \ 1,u,w),v5,v6),y,z).
L(x * L(L(x \ 1,y,z),z,y),u,w) = a(y,L(x,u,w) \ 1,z).
L(a(x,y \ 1,z),u,w) = a(x,L(y,u,w) \ 1,z).
a(x,L(y,z,x) \ 1,u) = a(x,y \ 1,u).
a(x,L(y \ 1,z,u) \ 1,w) = L(a(x,y,w),z,u).
a(x,L(y \ 1,y * x,z) \ 1,u) = a(x,((z * (y * x)) \ (x * z)) \ 1,u).
L(x,L(y,x,y \ 1),z) = x * a(x,(y \ 1) \ 1,z).
L(a(x,y,z),u,y \ 1) = a(x,(y \ 1) \ 1,z).
L(a(x,y,z),y,u) = a(x,u \ ((y \ 1) \ u),z).
a(x,L(y,z,y \ 1),u) = L(a(x,y,u),z,y).
a(x,L(L(y \ 1,z,u),w,v5) \ 1,v6) = L(L(a(x,y,v6),z,u),w,v5).
a(x,L(y \ 1,y * x,z) \ 1,u) = a(x,((z * (x * y)) \ (x * z)) \ 1,u).
L(x,L(y,x,y \ 1),z) = x * a(x,y,z).
L(x * a(y,x,z),y,L(z,x,z \ 1)) = x * a(x,z,y).
L(a(x,y,z),u,y \ 1) = a(x,y,z).
L(L(a(x,y,z),u,w),w,u) = a(x,(y \ 1) \ a(u,y \ 1,w),z).
(x \ 1) * (a(y,x,z) \ x) = a(y,x,z) \ 1.
(x \ 1) * (a(y,x,z) * L(x,u,w)) = (x \ L(x,u,w)) * a(y,x,z).
L(x,y,z) * ((x * a(u,x,w)) \ 1) = (x \ L(x,y,z)) * a(u,x,w).
(x \ 1) * (x * a(y,x,z)) = a(y,x,z) \ 1.
(x \ L(x,y,z)) * a(u,x,w) = L(x,y,z) * (x \ a(u,x,w)).
L(a(x,y,z),y,y \ 1) = a(x,y,z) \ 1.
a(x,y,z) \ 1 = a(x,y,z).
a(x,y,z) \ 1 = a(z,y,x).
a(x,y,z) * a(x,y,z) = 1.
a(x,y,z) \ x = x * a(x,y,z).
(x * a(x,y,z)) \ 1 = x \ a(x,y,z).
(x * a(x,y,z)) \ L(x,u,w) = L(x,u,w) * (x \ a(x,y,z)).
a(x,y,z) \ L(x,u,w) = a(x,y,z) * L(x,u,w).
1 * L(L(x,a(y,z,u),a(y,z,u)),w,v5) = a(y,z,u) * (a(y,z,u) * L(x,w,v5)).
L(a(x,a(y,z,u),w),a(y,z,u),a(y,z,u)) = 1 \ (a(y,z,u) * L(L(a(y,z,u),x,w),w,x)).
a(x,y,z) * (x \ a(x,y,z)) = x \ 1.
x * a(x,L(y \ 1,z,u) \ 1,w) = L(a(x,y,w),z,u) \ x.
(x \ L(x,y,z)) * L(a(x,u,w),L(x,y,z),x \ 1) = (x \ 1) * (a(x,u,w) \ L(x,y,z)).
a(x,L(y \ 1,z,u) \ 1,w) * L(x,v5,v6) = L(a(x,y,w),z,u) \ L(x,v5,v6).
a(x,y,z) * (a(x,y,z) * L(u,w,v5)) = L(L(u,a(x,y,z),a(x,y,z)),w,v5).
L(a(x,a(y,z,u),w),a(y,z,u),a(y,z,u)) = a(y,z,u) * L(L(a(y,z,u),x,w),w,x).
L((x \ 1) \ y,x \ a(x,z,u),a(x,z,u)) = (x \ a(x,z,u)) \ (a(x,z,u) \ y).
(x \ 1) \ (a(x,y,z) * (u * (x \ a(x,y,z)))) = L(u,x \ a(x,y,z),a(x,y,z)).
(x \ 1) \ (y * ((x \ a(x,z,u)) * L(a(x,z,u),x \ a(x,z,u),y))) = L(y,x \ a(x,z,u),a(x,z,u)).
a(x,y,z) * (a(x,y,z) * L(a(x,y,z),u,w)) = L(a(x,y,z),u,w).
a(x,L(y \ 1,x * y,z) \ 1,u) = a(x,((z * (x * y)) \ (x * z)) \ 1,u).
L(a(x,y,z),x * y,u) = a(x,((u * (x * y)) \ (x * u)) \ 1,z).
(x \ L(x,y,z)) * L(a(x,u,w),L(x,y,z),1) = (x \ 1) * (a(x,u,w) \ L(x,y,z)).
L(a(x,y,z),u,w) \ L(x,v5,v6) = L(a(x,y,z),u,w) * L(x,v5,v6).
L(L(x,y,z) \ 1,u,x \ 1) = L(x,y,z) \ 1.
(x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1.
(x \ 1) \ (y * (L(x,z,u) \ 1)) = ((x \ 1) \ y) * (L(x,z,u) \ 1).
L(a(x,L(y,z,u),w),v5,y \ 1) = a(x,(L(y,z,u) \ 1) \ 1,w).
(x \ 1) \ (y * (L(x,z,u) \ 1)) = (L(x,z,u) \ 1) * ((x \ 1) \ y).
(x \ 1) \ (y * (L(x,z,u) \ 1)) != w | (L(x,z,u) \ 1) * ((x \ 1) \ y) = w.
L(a(x,L(y,z,u),w),v5,y \ 1) = a(x,L(y,z,u),w).
L(a(x,y,z),u,L(y,w,v5) \ 1) = a(x,L(L(y,w,v5),w,v5),z).
L(a(x,y,z),u,L(y,w,v5) \ 1) = a(x,y,z).
(L(x,y,z) \ 1) \ a(u,x,w) = a(u,x,w) * L(x,y,z).
L(a(x,y,z),u,w) \ x = x * L(a(x,y,z),u,w).
x \ (x * L(a(x,y,z),u,w)) = L(a(x,y,z),u,w) \ 1.
L(a(x,y,z),u,w) \ 1 = L(a(x,y,z),u,w).
(x \ 1) * (a(x,y,z) \ L(x,u,w)) = (x \ L(x,u,w)) * a(x,y,z).
x \ L(x,L(y,y \ 1,x),z) = y \ ((x \ y) * L(x,y,z)).
L(x,x \ 1,y) \ ((y \ L(x,x \ 1,y)) * L(y,L(x,x \ 1,y),z)) = y \ L(y,x,z).
a(x,L(y,y \ 1,x),z) = x \ L(x,y,z).
L(a(x,L(y,y \ 1,x),z),u,L(x,w,v5)) = x \ L(x,y,z).
L(x \ L(x,y,z),u,L(x,w,v5)) = x \ L(x,y,z).
L(x \ L(x,y,z),u,x) = x \ L(x,y,z).
L(x \ 1,y,x) * L(L(x,y,x \ 1),z,u) = x \ L(x,z,u).
L(x \ L(x,y,z),L(x \ 1,u,x) \ 1,y) = a(z,y,L(x \ 1,u,x) \ 1).
L(x \ L(x,y,z),L(x,u,x \ 1),y) = a(z,y,L(x \ 1,u,x) \ 1).
L(x \ L(x,y,z),L(x,u,x \ 1),y) = a(z,y,L(x,u,x \ 1)).
L(a(x,y,L(z,u,z \ 1)),y,L(z,u,z \ 1)) = (z \ L(z,y,x)) * a(L(z,u,z \ 1),z \ L(z,y,x),y).
L(a(x,y,z) \ L(a(x,y,z),z,u),L(a(x,y,z),w,a(x,y,z) \ 1),z) = a(z \ u,z,L(a(x,y,z),w,a(x,y,z) \ 1)).
L(a(x,y,y \ L(y,z,u)),L(y,w,y \ 1),y \ L(y,z,u)) = a(x,y \ L(y,z,u),L(y,w,y \ 1)).
(x \ L(x,y,z)) * a(L(x,u,x \ 1),x \ L(x,y,z),y) = a(z,y,L(x,u,x \ 1)).
a(x,y \ L(y,z,u),L(y,w,y \ 1)) = a(x,y,y \ L(y,z,u)).
L(a(x,y,a(z,u,y)),L(a(z,u,y),w,a(z,u,y) \ 1),y) = a(y \ x,y,L(a(z,u,y),w,a(z,u,y) \ 1)).
(x \ L(x,y,z)) * a(y,x \ L(x,y,z),L(x,u,x \ 1)) = a(z,y,L(x,u,x \ 1)).
a(x,y,L(z,u,z \ 1)) = (z \ L(z,y,x)) * a(y,z,z \ L(z,y,x)).
a(x,y,L(z,u,z \ 1)) = (z \ L(z,y,x)) * a(y,z,a(z,y,x)).
a(x,y,L(z,u,z \ 1)) = (z \ L(z,y,x)) * a(y,z,a(x,y,z)).
a(x,y,L(z,u,z \ 1)) = L(z,y,x) * (z \ a(y,z,a(x,y,z))).
L(x,y,z) * (x \ a(y,x,a(z,y,x))) = a(z,y,x).
a(x,y,L(z,u,z \ 1)) = a(x,y,z).
L(x * a(y,x,z),y,L(z,u,z \ 1)) = L(x,L(z,u,z \ 1),y).
L(x,y,L(z,u,z \ 1)) = (y \ x) * (y * a(x,y,z)).
L(x,y,L(z,u,z \ 1)) = L(x,y,z).
L(x * a(y,x,z),y,z) = L(x,L(z,u,z \ 1),y).
L(x * a(y,x,z),y,z) = x * a(x,z,y).
x * a(x,y,z) = L(x,y,z).
x * a(y,z,x) = L(x,z,y).
a(x,y,z) * x = L(x,y,z).
x \ L(x,y,z) = a(x,y,z).
x \ L(x,y,z) != u | a(x,y,z) = u.
L(L(a(x,y,z),x,u),x * u,w) = (w * (x * u)) \ (w * (u * L(x,y,z))).
(x \ y) \ (x \ L(y,z,u)) = L(a(y,z,u),x \ y,x).
(x \ y) * L(x,z,y) = y * a(x,z,y).
a(x,y,z) * L(u,x,a(x,y,z)) = (x \ u) * L(x,y,z).
L(a(x,y,z) \ u,x,a(x,y,z)) = x * (L(x,y,z) \ u).
L(x,y,z) \ 1 = x \ a(x,y,z).
x \ a(y,z,x \ 1) = L(x \ 1,z,y).
a(x,y,z) * L(a(x,y,z),u,w) = a(w,u,a(x,y,z)).
a(x,y,y \ (z \ y)) = a(x,y,z \ 1).
x \ (L(x,y,z) * a(y,L(z,y,x),L(x,y,z))) = a(y,x,L(z,y,x)).
x \ L(x,y,z * u) = a(x,y,u * z).
x \ (L(y \ 1,z,u) * ((y \ 1) \ x)) = a(L(y \ 1,y,x),z,u).
L(x,y,z) \ L(L(x,u,w),y,z) = a(L(x,y,z),u,w).
a(x,y,z) * (L(x \ L(x,y,z),u,w) \ x) = L(x \ L(x,y,z),u,w) \ L(x,y,z).
L(x,y,z) * L(L(x,y,z) \ x,u,w) = L(x * L(a(x,y,z),u,w),y,z).
x * L(L(y \ 1,y,x) \ 1,z,u) = a(y,z,u) * ((y \ 1) \ x).
x \ (L(y,z,u) * (y \ x)) = L(a(y,z,u),y,x).
L(L(a(x,y,z),x,z),x * z,y) = (y * (x * z)) \ (z * (y * L(x,z,y))).
(x \ y) * L(x,z,y) = L(y,z,x).
L(x,y,z) \ x = a(x,y,z).
L(x,y,z) \ 1 = x \ a(z,y,x).
x * (L(x,y,z) \ 1) = a(x,y,z).
L(a(x,y \ 1,z),u,w) = a(x,y \ a(y,u,w),z).
a(x,y,z * u) != w | a(x,y,u * z) = w.
x \ (L(y \ 1,z,u) * ((y \ 1) \ x)) = a(u,z,L(y \ 1,y,x)).
x \ L(L(y,z,u),w,v5) != a(L(y,w,v5),z,u) | L(y,w,v5) = x.
L(x \ L(x,y,z),u,w) \ L(x,y,z) = a(x,y,z) * (L(a(x,y,z),u,w) \ x).
a(x,y,1 \ z) * L(L(z \ 1,z,a(x,y,1 \ z)) \ 1,u,w) = a(z,u,w) * (((z \ 1) \ 1) * a(x,y,1 \ z)).
L(L(x,y,z),u,w \ (L(x,v5,v6) * (x \ w))) = L(x,y,z).
x * L(x \ 1,y,z) = a(z,y,x \ 1).
(x * y) \ (y * a(z,u,x \ 1)) = L(L(x \ 1,u,z),x,y).
(x \ a(x,y,z)) * L(a(x,y,z),u,w) = x \ a(w,u,a(x,y,z)).
L(x \ L(x,y,z),u,w) = a(z,y,L(x \ 1,u,w) \ 1).
L(x,y,z) \ L(z,y,x) = x \ z.
x * L(y,z,x) = y * L(x,z,y).
x \ (y * L(x,z,y)) = L(y,z,x).
x \ (y * L(y \ x,z,u)) = a(u,z,(x \ y) \ 1).
(x * y) \ (y * a(z,u,x \ 1)) != w | L(L(x \ 1,u,z),x,y) = w.
L(x,L(y,z,y \ 1),u) = L(x,y,u).
L(x,L(y \ 1,z,y),u) = L(x,y \ 1,u).
L(x,y \ (y * z),u) = L(x,z,u).
a(x,L(y,z,y \ 1),u) = x \ L(x,y,u).
L(x,a(y,z,u),w) = L(x,a(u,z,y),w).
a(x,L(y,z,y \ 1),u) = a(x,y,u).
L(x,L(y,z,x),z) \ L(x,z,y) = a(z,L(x,z,y),L(y,z,x)).
L(x,y,z) \ x = x \ L(x,y,z).
x * (L(x,y,z) \ a(x,u,w)) = a(x,u,w) * a(x,y,z).
L(x,y,z) * L(a(x,y,z),u,w) = L(x * L(a(x,y,z),u,w),y,z).
(x \ 1) * a(y,z,x) = L(x,z,y) \ 1.
(x \ L(x,y,z)) \ x = L(x,y,z).
L(x \ L(x,y,z),u \ L(x,y,z),u) = (u \ L(x,y,z)) \ (u \ x).
L(x \ 1,x,y) \ L(L(x \ 1,x,y),x * y,z) = ((z * (x * y)) \ (y * z)) \ L(x \ 1,x,y).
(x \ L(x,y,z)) * a(x,u,w) = x * (L(x,y,z) \ a(x,u,w)).
(x \ 1) * (x \ L(x,y,z)) = L(x,y,z) \ 1.
x * (L(x,y,z) \ a(x,u,w)) != v5 | a(x,y,z) * a(x,u,w) = v5.
L(x \ 1,y,z) \ 1 = x * a(z,y,x \ 1).
L(x \ L(x,y,z),z,y) \ z = L(z,y,L(x,x \ 1,y)).
(L(x,y,z) \ L(x,u,w)) \ (L(x,y,z) \ x) = x \ L(x,u,w).
L(x \ 1,x,y) \ L(L(x \ 1,x,y),x * y,z) = ((z * (x * y)) \ (z * y)) \ L(x \ 1,x,y).
(x \ 1) * (a(x,y,z) \ L(x,u,w)) = x * (L(x,u,w) \ a(x,y,z)).
L(x,y,L(z,z \ 1,y)) = L(a(z,y,x),x,y) \ x.
L(x,y,z) * a(u,L(x,y,z),w) = L(x * a(u,x,w),y,z).
((x \ y) * L(x,z,u)) * (x * a(x * (x \ y),x,x \ 1)) = x * ((x \ 1) * (y * L(x,z,u))).
a(x,y,L(z \ 1,u,w) \ 1) = L(a(z,y,x),u,w).
x \ L(y * L(y \ L(x,z,u),w,v5),z,u) = a(v5,w,(x \ L(y,z,u)) \ 1).
a(x,y * a(z,u,y \ 1),w) = L(a(x,y,w),u,z).
L(a(x,y,z),u,y) = a(x,y,z).
a(x,y \ (y * z),u) = a(x,z,u).
a(x,y,z) * L(L(a(x,y,z),u,w),w,u) = a(u,a(x,y,z),w).
a(x,y,a(z,x,u)) = 1.
a(x,y,L(z \ 1,u,y) \ 1) = z \ L(z,y,x).
(x \ 1) \ a(y,x \ 1,z) = x * a(y,x \ 1,z).
L(a(x,y,z),u,y) != w | a(z,y,x) = w.
L(a(x,y,z),u,y) != w | a(x,y,z) = w.
a(x,y * z,u) = a(x,z * y,u).
a(a(x,y,z),u,y) = 1.
L(L(a(x,y,z),u,w),w,u) = a(x,y * a(u,y \ 1,w),z).
L(x,y,a(z,x,u)) = x.
L(x,y,a(z,x,u)) != w | x = w.
((x \ y) * a(x,x \ y,y \ (x * z))) \ z = y \ (x * z).
(x \ y) * L(x,x \ 1,x * y) = L(y,x,x \ 1).
a(x,y * z,L(L(y \ 1,y,z) \ 1,u,y * z) \ 1) = L(y \ 1,y,z) \ ((x * (y * z)) \ (z * x)).
(x * ((y \ x) \ (x * (z \ L(z,x,y))))) \ (y * ((z \ 1) \ x)) = L(z \ 1,z,x) \ 1.
L(a(x,y,z),x,u) = a(z,y,u \ ((x \ 1) \ u)).
a(x,y,L(z \ 1,u,w) \ 1) = L(a(x,y,z),u,w).
L(a(x,y,z),z,u) = a(x,y,u \ ((z \ 1) \ u)).
(x \ 1) \ a(y,z,u \ ((x \ 1) \ u)) = u \ (x * (u * a(x,z,y))).
L(a(x,y,z),u,w) = L(a(z,y,x),u,w).
L(a(x,y,z \ 1),u,w) = a(x,y,L(z,u,w) \ 1).
a(x,y,L(a(z,u,w),v5,v6) \ 1) = L(a(x,y,a(z,u,w)),v5,v6).
a(x,y,L(z,u,x) \ 1) = a(x,y,z \ 1).
L(a(x,y,z \ 1),u,z) = a(x,y,z \ 1).
L(a(x,y,a(z,u,w)),v5,v6) = a(x,y,L(a(z,u,w),v5,v6)).
a(x,y,z \ 1) * (z * u) = z * (u * a(x,y,z \ 1)).
(x \ 1) \ (y * (x \ a(y,x \ a(x,z,u),a(x,z,u)))) = L(y,x \ a(x,z,u),a(x,z,u)).
(x * (y * z)) \ (z * (x * L(y,z,x))) = L(a(y,x,z),y * z,x).
(x * (y * z)) \ (z * (x * L(y,z,x))) = a(y,x,z).
L(L(x \ L(x,y,z),x \ 1,u),u,x \ 1) = u \ ((x \ 1) \ (u * (L(x,y,z) \ 1))).
L(x,y,L(z,z \ 1,y)) = (x \ L(x,y,z)) \ x.
L(x,y,L(z,z \ 1,y)) = L(x,y,z).
L(x,y,L(z \ 1,z,y)) = L(x,y,z \ 1).
L(x,y * a(z,u,y \ 1),w) = x * L(a(x,y,w),u,z).
a(x,y,L(z,x,y)) = a(z,y,x).
a(x,y,L(z,x,y)) = a(x,y,z).
a(x,y \ a(y,z,u),a(w,v5,v6)) = a(x,y \ 1,L(a(w,v5,v6),z,u)).
L(x,y,a(z,u,x \ 1)) = x.
(x * L(a(y,z,x \ 1),x,u)) \ (x * (u * a(y,z,x \ 1))) = u.
L(x,y,a(z,u,L(x,w,v5) \ 1)) = x.
L(x \ 1,y,a(z,u,x)) = x \ 1.
L(x \ 1,y,a(x,z,u)) = x \ 1.
a(x,y,z) \ ((x \ 1) * (u * a(x,y,z))) = u * (x \ 1).
((x \ 1) * y) * a(x,z,u) = (x \ 1) * (y * a(x,z,u)).
L(x,y,a(z,u,w \ (x \ w))) = x.
L(x,y * a(z,u,y \ 1),w \ 1) = x * a(x,y,L(w,u,z) \ 1).
L(x,a(y,z,u),y \ 1) = L(x,y \ 1,a(y,z,u)).
L(x,a(x,y,z),x \ 1) = x.
L(x,(y \ 1) \ 1,a(y \ 1,z,u)) = L(x,a(y \ 1,z,u),y).
a(x,y,z) \ (L(u,x \ 1,(x \ 1) \ 1) * (a(x,y,z) * (x \ 1))) = ((x \ 1) \ 1) \ L(u,a(x,y,z),x \ 1).
x \ L(x,y \ 1,a(y,z,u)) = a(x,a(y,z,u),y \ 1).
L(x,a(x,y,z),x \ 1) = (x \ u) \ u.
L(x,y,(z \ u) \ u) = L(x,y,z).
a(x,(y \ z) \ z,u) = x \ L(x,y,u).
L(x,y,a(z,u,w) \ 1) = L(x,y,a(z,u,w)).
x * a(x,(y \ z) \ z,u) = L(x,y,u).
L(x,y,a(z,u,w)) = L(x,y,a(w,u,z)).
L(a(x,y,z),u,x \ 1) = a(x,y,z).
L(a(x \ 1,y,z),u,x) = a(x \ 1,y,z).
L(L(a(x,y,z),u,w),v5,x \ 1) = L(a(x,y,z),u,w).
a(x \ 1,y,L(z,u,x) \ 1) = a(x \ 1,y,z \ 1).
L(L(x \ L(x,y,z),u,w),v5,x \ 1) = L(a(x,L(y,y \ 1,x),z),u,w).
a(x \ 1,y,x \ (z \ x)) = a(x \ 1,y,z \ 1).
a(x \ 1,y,(z \ x) \ 1) = a(x \ 1,y,x \ z).
a(L(x,y,z) \ 1,u,L(x,y,z) \ (z \ x)) = a(L(x,y,z) \ 1,u,L(z,y,x) \ 1).
a(x,a(y,z,u),y \ 1) = a(x,y \ 1,a(y,z,u)).
x \ a(y,x \ 1,a(x,z,u)) = L(x \ 1,a(x,z,u),y).
L(L(a(x,y,z),u,y),y,u) = a(x,L(y,y \ 1,u),z).
a(x,y,z) * a(x,y * a(u,y \ 1,w),z) = a(u,a(x,y,z),w).
a(x,L(y,y \ 1,z),u) = L(a(x,y,u),y,z).
L(a(x,y \ z,u),y \ z,z) = a(x,(z \ y) \ 1,u).
(L(x,x \ y,y \ (x * z)) \ y) \ z = y \ (x * z).
(L(x,y,z) \ u) \ (x \ u) = u \ (L(x,y,z) * (x \ u)).
x \ (L(y,L(z,z \ 1,y),u) * (y \ x)) = ((y * a(y,z,u)) \ x) \ (y \ x).
L(x,y,z) * (x \ L(z,x,y)) = z * a(x * a(y,x,z),z,y).
(x * a(y,z,L(x,x,u) \ 1)) \ (x * (u * a(y,z,x \ 1))) = u.
L(x,(y \ 1) \ 1,a(y \ 1,z,u)) = L(x,a(u,z,y \ 1),y).
a(x,y,z) \ (L(u,x \ 1,x) * (a(x,y,z) * (x \ 1))) = ((x \ 1) \ 1) \ L(u,a(x,y,z),x \ 1).
((x * (y * z)) \ (x * z)) \ L(y \ 1,y,z) = z \ (L(y \ 1,y * z,x) * ((y \ 1) \ z)).
((x * (y * z)) \ (x * z)) \ L(y \ 1,y,z) = z \ (((y \ 1) \ z) * L(y \ 1,y * z,x)).
a(x,y \ a(y,z,u),a(w,v5,u)) = a(x,y \ 1,a(w,v5,u)).
L(x,y \ a(y,z,u),a(y,z,u)) = (y \ 1) \ (x * (y \ a(x,y \ 1,a(y,z,u)))).
L(x,y \ a(y,z,u),a(y,z,u)) = (y \ 1) \ (x * L(y \ 1,a(y,z,u),x)).
L(x,y \ a(y,z,u),a(y,z,u)) = L(x,a(y,z,u),y \ 1).
L(x,y \ a(y,z,u),a(y,z,u)) = L(x,y \ 1,a(y,z,u)).
L((x \ 1) \ y,x \ 1,a(x,z,u)) = (x \ a(x,z,u)) \ (a(x,z,u) \ y).
a(x,y,z) \ u = u * a(x,y,z).
a(x,y,z) \ u = a(x,y,z) * u.
(x * a(y,z,u)) * a(y,z,u) = x.
L((x \ y) * a(z,u,w),a(z,u,w),x) = (x * a(z,u,w)) \ y.
L(x * a(y,z,u),y,a(y,z,u)) = y * (L(y,z,u) \ x).
a(x,y,z) * (u \ (w * (u * a(x,y,z)))) = L(w,a(x,y,z),u).
a(x,y,z) * u != w | a(x,y,z) * w = u.
x \ (a(y,z,u) * (w * (x * a(y,z,u)))) = L(w,x,a(y,z,u)).
L(x,x \ 1,a(y,z,u)) = (a(y,z,u) * (x \ a(y,z,u))) \ 1.
x \ (a(y,z,u) * (w * (x * a(y,z,u)))) = L(w,x * a(y,z,u),a(y,z,u)).
a(x \ y,x,L(a(z,u,x),w,a(z,u,x) \ 1)) = a(y,x,a(z,u,x)).
a(x \ y,x,a(z,u,x)) = a(y,x,a(z,u,x)).
a(x,y,z) * L(L(z \ 1,z,a(x,y,1 \ z)) \ 1,u,w) = a(z,u,w) * (((z \ 1) \ 1) * a(x,y,1 \ z)).
a(x,y,z) * L(L(z \ 1,z,a(x,y,z)) \ 1,u,w) = a(z,u,w) * (((z \ 1) \ 1) * a(x,y,1 \ z)).
a(x,y,z) * (((x \ 1) \ 1) * a(u,w,1 \ x)) = a(u,w,x) * L((x \ 1) \ 1,y,z).
a(x,y,z) * (((x \ 1) \ 1) * a(u,w,1 \ x)) = a(u,w,x) * L(x,y,z).
a(x,y,z) * (x * a(u,w,1 \ x)) = a(u,w,x) * L(x,y,z).
a(x,y,z) * (x * a(u,w,x)) = a(u,w,x) * L(x,y,z).
a(x,y,z) * L(z,u,w) = a(z,u,w) * L(z,y,x).
L(x,y,z) * a(x,u,w) = a(x,y,z) * L(x,u,w).
L(x,y,z) * a(u,w,x) = a(x,y,z) * L(x,w,u).
a(x,y,z \ ((u \ 1) \ z)) * ((u \ 1) \ a(x,y,z \ ((u \ 1) \ z))) = u.
a(x,y,z \ ((u \ 1) \ z)) * (z \ (u * (z * a(u,y,x)))) = u.
a(x,y,z \ ((u \ 1) \ z)) * (z \ (u * (z * a(x,y,u)))) = u.
(x \ 1) * (a(x,y,z) * L(x,u,w)) = x * (L(x,u,w) \ a(x,y,z)).
L(x,y,z) * (x \ a(x,u,w)) = x * (L(x,y,z) \ a(x,u,w)).
(x * a(x,y,z)) \ L(x,u,w) = x * (L(x,u,w) \ a(x,y,z)).
L(x,y,z) * (x \ a(x,u,w)) != v5 | a(x,y,z) * a(x,u,w) = v5.
x * (L(x,y,z) \ a(x,u,w)) = L(x,u,w) \ L(x,y,z).
L(x,y,z) \ L(x,u,w) = a(x,u,w) * a(x,y,z).
a(x,y,z) * a(x,z,y) = a(z,L(x,z,y),y).
a(x,a(y,z,u),w) * a(x,L(y,a(y,z,u) \ 1,v5) \ L(y,z,u),w) = a(y,a(x,a(y,z,u),w),v5).
a(x,y,z) * a(x,z,y) = a(y,L(x,y,z),z).
a(x,a(y,z,u),w) * a(x,L(y,a(y,z,u),v5) \ L(y,z,u),w) = a(y,a(x,a(y,z,u),w),v5).
a(x,y,z) * a(x,z,y) = a(z,L(x,y,z),y).
a(x,y,z) * a(x,z,y) != u | a(y,L(x,y,z),z) = u.
L(x,a(y,z,u \ 1),u) = L(x,u,a(u \ 1,z,y)).
L(x,a(y,z,u \ 1),u) = L(x,u,a(y,z,u \ 1)).
a(x,y * z,((z * ((y \ 1) * y)) \ (1 * (y * z))) \ 1) = L(y \ 1,y,z) \ ((x * (y * z)) \ (z * x)).
(x * L(y,x,L(z,z \ 1,x))) \ (y * ((z \ 1) \ x)) = L(z \ 1,z,x) \ 1.
a(x,y * z,((z * 1) \ (1 * (y * z))) \ 1) = L(y \ 1,y,z) \ ((x * (y * z)) \ (z * x)).
L(x \ 1,x,y) \ ((z * (x * y)) \ (y * z)) = a(z,x * y,(y \ (1 * (x * y))) \ 1).
L(x \ 1,x,y) \ ((z * (x * y)) \ (y * z)) = a(z,x * y,(y \ (x * y)) \ 1).
L(x \ 1,x,y) \ ((z * (x * y)) \ (y * z)) = a(z,x * y,x \ 1).
x \ (((y \ 1) \ x) * L(y \ 1,y * x,z)) = a(z,y * x,y \ 1).
((x * (y * z)) \ (x * z)) \ L(y \ 1,y,z) = a(x,y * z,y \ 1).
L(a(x,y,z) \ 1,a(x,y,z),u) \ 1 = (u * x) \ (x * ((a(x,y,z) \ 1) \ u)).
(x * L(y,x,z)) \ (y * ((z \ 1) \ x)) = L(z \ 1,z,x) \ 1.
L(a(x,y,z) \ 1,a(x,y,z),u) \ 1 = (u * x) \ (x * (a(x,y,z) \ u)).
L(a(x,y,z),a(x,y,z),u) \ 1 = (u * x) \ (x * (a(x,y,z) \ u)).
L(a(x,y,z),a(x,y,z),u) = (u * x) \ (x * (a(x,y,z) \ u)).
L(a(x,y,z),a(x,y,z),u) = (x * u) \ (x * (a(x,y,z) \ u)).
L(a(x,y,z),a(x,y,z),u) = (x * u) \ (x * (u * a(x,y,z))).
L(a(x,y,z),a(x,y,z),u) = L(a(x,y,z),u,x).
L(a(x,y,z),a(x,y,z),u) = a(x,y,z).
L(a(x,y,z),a(x,y,z),u) \ w = w * a(x,y,z).
L(x \ L(x,y,z),u,w) \ L(x,y,z) = a(x,y,z) * (x * L(a(x,y,z),u,w)).
L(x \ L(x,y,z),u,w) \ L(x,y,z) = x * (L(a(x,y,z),u,w) * a(x,y,z)).
L(x \ L(x,y,z),u,w) \ L(x,y,z) = x * (a(x,y,z) * L(a(x,y,z),u,w)).
L(x \ L(x,y,z),u,w) \ L(x,y,z) = x * a(w,u,a(x,y,z)).
L(a(x,y,z),u,w) \ L(x,y,z) = x * a(w,u,a(x,y,z)).
L(a(x,y,z),u,w) * L(x,y,z) = x * a(w,u,a(x,y,z)).
L(x,y,z) * L(a(x,y,z),u,w) = x * a(w,u,a(x,y,z)).
L(x * L(a(x,y,z),u,w),y,z) = x * a(w,u,a(x,y,z)).
L(x * L(a(x,y,z \ 1),u,w),y,L(z \ 1,z,y)) = x * a(w,u,a(x,y,z \ 1)).
L(x * a(x,y,L(z,u,w) \ 1),y,L(z \ 1,z,y)) = x * a(w,u,a(x,y,z \ 1)).
L(L(x,y,L(z,u,w) \ 1),y,L(z \ 1,z,y)) = x * a(w,u,a(x,y,z \ 1)).
L(L(x,y,L(z,u,w) \ 1),y,z \ 1) = x * a(w,u,a(x,y,z \ 1)).
L(L(x,y,z \ 1),y,L(z,u,w) \ 1) = x * a(w,u,a(x,y,z \ 1)).
L(L(x,y,z),y,L(z \ 1,u,w) \ 1) = x * a(w,u,a(x,y,(z \ 1) \ 1)).
L(L(x,y,z),y,L(z \ 1,u,w) \ 1) = x * a(w,u,a(x,y,z)).
x \ L(L(x,y,z),y,L(z \ 1,u,w) \ 1) = a(w,u,a(x,y,z)).
x * a(y,z,a(x,u,w)) != v5 | L(L(x,u,w),u,L(w \ 1,z,y) \ 1) = v5.
(x \ y) \ L(y * (x \ 1),x,L((x \ 1) \ 1,z,u) \ 1) = a(u,z,a(x \ y,x,x \ 1)).
x \ L(L(x,y,z),y,L(z,z \ 1,u)) = a(z \ u,z,a(x,y,z)).
(x \ y) \ L(y * (x \ 1),x,L(x,z,u) \ 1) = a(u,z,a(x \ y,x,x \ 1)).
x \ L(L(x,y,z),y,L(z,z \ 1,u)) = a(u,z,a(x,y,z)).
a(x,y,z) * a(x,L(z,y,x),y) = a(y,L(x,y,z),L(z,y,x)).
L(x,y * a(z,u,y \ 1),w \ 1) = L(x,y,L(w,u,z) \ 1).
L(x,y * a(z,u,y \ 1),w) = L(x,y,L(w \ 1,u,z) \ 1).
a(x \ 1,y * a(z,u,y \ 1),w \ 1) = w * L(w \ 1,y,L(x,u,z) \ 1).
L(x,L(y \ 1,z,u) \ 1,w) = L(x,y,L(w \ 1,z,u) \ 1).
a(x \ 1,y * a(z,u,y \ 1),w \ 1) = a(L(x,u,z) \ 1,y,w \ 1).
L(x,y \ 1,L(z \ 1,u,w) \ 1) = L(x,L(y,u,w) \ 1,z).
a(x,L(y,z,x),z) \ (L(y,z,x) \ y) = y \ L(y,x,z).
a(x,L(y,z,x),z) \ a(y,z,x) = y \ L(y,x,z).
a(x,L(y,z,x),z) \ a(x,z,y) = y \ L(y,x,z).
a(x,y,z) * a(x,L(z,y,x),y) = z \ L(z,x,y).
a(x,L(y,x,z),L(z,x,y)) = z \ L(z,y,x).
a(x,L(y,x,z),L(z,x,y)) = a(z,y,x).
x \ (L(x,y,z) * a(x,z,y)) = a(y,x,L(z,y,x)).
x \ (a(x,y,z) * L(x,z,y)) = a(z,x,L(y,z,x)).
L(x,y,z) * (x \ a(x,z,y)) = a(y,x,L(z,y,x)).
a(x,y,z) * a(x,z,y) = a(y,x,L(z,y,x)).
a(x,L(y,x,z),z) = a(x,y,L(z,x,y)).
a(x,L(y,x,z),z) = a(z,y,x).
(L(x,y,z) \ 1) \ a(y,x,z) = L(x,z,y).
a(x,y,z) * L(y,x,z) = L(y,z,x).
a(x,y,z) * L(y,z,x) = L(y,x,z).
a(x,(x \ y) * a(z,u,w),a(z,u,w)) * ((x * a(z,u,w)) \ y) = L((x \ y) * a(z,u,w),x,a(z,u,w)).
L(L(x \ L(x,y,z),u,w),v5,x \ 1) = L(x \ L(x,y,z),u,w).
L(x \ L(x,y,z),x \ 1,u) = u \ ((x \ 1) \ (u * (L(x,y,z) \ 1))).
L(x \ L(x,y,z),x \ 1,u) = u \ ((L(x,y,z) \ 1) * ((x \ 1) \ u)).
x \ ((L(y,z,u) \ 1) * ((y \ 1) \ x)) = L(a(y,z,u),y \ 1,x).
L(a(x \ 1,y,z),x \ 1,u) = a(z,y,L(x \ 1,x,u)).
L(a(x,y,z \ 1),z \ 1,u) = a(x,y,L(z \ 1,z,u)).
L(a(x \ 1,y,z \ 1),u,w) = a(L(x,u,w) \ 1,y,z \ 1).
a(L(x,y,z) \ 1,u,w \ 1) = a(x \ 1,u,L(w,y,z) \ 1).
a(L(x,y,z) \ 1,u,L(x,y,z) \ (z \ x)) = a(x \ 1,u,L(L(z,y,x),y,z) \ 1).
a(L(x,y,z) \ 1,u,L(x,y,z) \ (z \ x)) = a(x \ 1,u,L(z,y,x) \ 1).
a(L(x,y,z) \ 1,u,L(x,y,z) \ (z \ x)) = a(x \ 1,u,z \ 1).
a(x,y,z) \ (L(u,x \ 1,x) * (x \ a(x,y,z))) = ((x \ 1) \ 1) \ L(u,a(x,y,z),x \ 1).
L(x * (y \ 1),y,y \ a(y,z,u)) = ((y \ 1) \ 1) \ L(x,a(y,z,u),y \ 1).
L(x * (y \ 1),y,y \ a(y,z,u)) = y \ L(x,a(y,z,u),y \ 1).
L(x * (y \ 1),y,y \ a(y,z,u)) = y \ L(x,y \ 1,a(y,z,u)).
L(x * ((y \ 1) \ 1),L(y \ 1,z,y),(y \ 1) \ a(y \ 1,u,w)) = (y \ 1) \ L(x,(y \ 1) \ 1,a(y \ 1,u,w)).
L(x * (y \ 1),y,L(y,z,u) \ 1) = y \ L(x,y \ 1,a(y,z,u)).
L(x * ((y \ 1) \ 1),L(y \ 1,z,y),(y \ 1) \ a(y \ 1,u,w)) = (y \ 1) \ L(x,y,a(y \ 1,u,w)).
(x \ y) \ (x \ L(y,x \ 1,a(x,z,u))) = a(u,z,a(x \ y,x,x \ 1)).
L(x * ((y \ 1) \ 1),L(y \ 1,z,y),(y \ 1) \ a(y \ 1,u,w)) = (y \ 1) \ L(x,y,a(w,u,y \ 1)).
L(x * y,L(x \ 1,z,x),(x \ 1) \ a(x \ 1,u,w)) = (x \ 1) \ L(y,x,a(w,u,x \ 1)).
L(x * y,L(x \ 1,z,x),L(x \ 1,u,w) \ 1) = (x \ 1) \ L(y,x,a(w,u,x \ 1)).
L(x * y,x \ 1,L(x \ 1,z,u) \ 1) = (x \ 1) \ L(y,x,a(u,z,x \ 1)).
(x \ 1) \ L(y,x,a(z,u,x \ 1)) = L(x * y,L(x,u,z) \ 1,x).
L(a(x,y \ 1,a(y,z,u)),y \ x,y) = a(u,z,a(y \ x,y,y \ 1)).
a(x,y \ 1,L(a(y,z,u),y \ x,y)) = a(u,z,a(y \ x,y,y \ 1)).
a(x,y,a(z \ u,z,z \ 1)) = a(u,z \ 1,a(z,y,x)).
a(x,y \ 1,a(y,z,u)) = a(u,z,a(x,y \ 1,y)).
x \ L(L(y * L(y \ x,z,y \ 1),u,w),u,w) = a(y \ 1,z,(x \ L(y,u,w)) \ 1).
((x \ y) * L(x,z,u)) * (x * a(y,x,x \ 1)) = x * ((x \ 1) * (y * L(x,z,u))).
((x \ y) * L(x,z,u)) * L(x,x \ 1,x * y) = x * ((x \ 1) * (y * L(x,z,u))).
L(x,y,z) * ((x \ u) * L(x,x \ 1,x * u)) = x * ((x \ 1) * (u * L(x,y,z))).
x * ((x \ 1) * (y * L(x,z,u))) = L(x,z,u) * L(y,x,x \ 1).
L(x,y,z) * L(u,x,x \ 1) = L(u * L(x,y,z),x \ 1,x).
L((x \ y) * L(x,z,u),x \ 1,x) = L(x,z,u) * (y * (x \ 1)).
L(x,y * a(z,u,w),a(z,u,w)) = L(x,y,a(z,u,w)).
a(x,y * a(z,u,w),a(z,u,w)) = x \ L(x,y,a(z,u,w)).
a(x,y * a(z,u,w),a(z,u,w)) = a(x,y,a(z,u,w)).
a(x,x \ y,a(z,u,w)) * ((x * a(z,u,w)) \ y) = L((x \ y) * a(z,u,w),x,a(z,u,w)).
((x * a(y,z,u)) \ w) * a(x,x \ w,a(y,z,u)) = L((x \ w) * a(y,z,u),x,a(y,z,u)).
x \ (L(y,L(z,z \ 1,y),u) * (y \ x)) = y \ ((a(y,z,u) \ (y \ x)) \ x).
x \ (L(y,L(z,z \ 1,y),u) * (y \ x)) = y \ ((y \ (a(y,z,u) \ x)) \ x).
x \ (L(y,L(z,z \ 1,y),u) * (y \ x)) = y \ ((a(y,z,u) \ x) \ (y * x)).
x \ ((a(x,y,z) \ u) \ (x * u)) = u \ ((x * a(x,y,z)) * (x \ u)).
x \ ((a(x,y,z) \ u) \ (x * u)) = L(a(x,y,z),x,x \ u).
x \ ((a(x,y,z) \ u) \ (x * u)) = L(a(x,y,z),x,u).
L(a(x,y,z),x,a(x,y,z) \ u) = L(a(x,y,z),x,u).
L(a(x,y,z),x,u * a(x,y,z)) = L(a(x,y,z),x,u).
(x \ a(x,y,z)) \ L(a(x,y,z),x,u) = L(x,a(x,y,z),u * a(x,y,z)).
L(x,a(x,y,z),u * a(x,y,z)) = L(x,a(x,y,z),u).
L(x,a(x,y,z),u) * (L(x,u * a(x,y,z),a(x,y,z)) \ (u * a(x,y,z))) = L(u * a(x,y,z),L(x,u * a(x,y,z),a(x,y,z)),a(x,y,z)).
L(x * a(y,z,u),L(y,x * a(y,z,u),a(y,z,u)),a(y,z,u)) = L(y,a(y,z,u),x) * (y \ (x * a(y,z,u))).
L(x * a(y,z,u),L(y,x * a(y,z,u),a(y,z,u)),a(y,z,u)) = L(y,a(y,z,u),x) * (a(y,z,u) * (y \ x)).
L(x * a(y,z,u),L(y,x * a(y,z,u),a(y,z,u)),a(y,z,u)) = (y \ x) * (y * a(y,z,u)).
L(x * a(y,z,u),y,a(y,z,u)) = (y \ x) * (y * a(y,z,u)).
L(x * a(y,z,u),y,a(y,z,u)) = (y \ x) * L(y,z,u).
(x \ y) * L(x,z,u) = x * (L(x,z,u) \ y).
a(x,y,z) * L(u,x,a(x,y,z)) = x * (L(x,y,z) \ u).
L(x * (L(x,y,z) \ u),x \ 1,x) = L(x,y,z) * (u * (x \ 1)).
(x \ 1) \ (L(x,y,z) \ u) = L(x,y,z) * (u * (x \ 1)).
L(L(x,y,z),y,z) * (u * (L(x,y,z) \ 1)) = (L(x,y,z) \ 1) \ (x \ u).
(L(x,y,z) \ 1) \ (x \ u) = x * (u * (L(x,y,z) \ 1)).
L(x * (y * (L(x,z,u) \ 1)),L(x,z,u) \ 1,x) = (x * (L(x,z,u) \ 1)) \ y.
L(x * (y * (L(x,z,u) \ 1)),L(x,z,u) \ 1,x) = a(x,z,u) \ y.
L(x * (y * (L(x,z,u) \ 1)),L(x,z,u) \ 1,x) = y * a(x,z,u).
L(x,y,z) * (x \ L(z,x,y)) = z * a(y,z,x * a(y,x,z)).
L(x,y,z) * (x \ L(z,x,y)) = z * a(y,z,L(x,y,z)).
x * (y * a(z,y,L(x,z,y))) = L(y,x,z) * L(x,z,y).
L(x,y,z) * a(y,L(x,y,z),L(z,y,L(x,y,z))) = L(z,y,L(x,y,z)) * (z \ (x * a(y,x,z))).
L(x,y,z) * L(y,z,x) = y * (x * a(y,x,z)).
L(x,y,z) * a(y,L(x,y,z),L(z,y,L(x,y,z))) = L(z,y,x) * (z \ (x * a(y,x,z))).
L(x,y,z) * L(y,z,x) = x * L(y,x,z).
L(x,y,z) * a(y,L(x,y,z),L(z,y,L(x,y,z))) = L(z,y,x) * (L(z,x,y) \ x).
L(x,y,z) * a(y,L(x,y,z),L(z,y,L(x,y,z))) = L(x,L(z,x,y),y).
L(x,y,z) * a(y,L(x,y,z),L(z,y,x)) = L(x,L(z,x,y),y).
L(x * a(y,x,L(z,y,x)),y,z) = L(x,L(z,x,y),y).
L(x * a(y,x,L(L(z,x,y),y,x)),y,L(z,x,y)) = L(x,z,y).
L(x * a(y,x,L(z,y,x)),y,L(z,x,y)) = L(x,z,y).
L(x * a(y,x,z),y,L(z,x,y)) = L(x,z,y).
L(x,L(y,x,z),z) = L(x,y,z).
(x \ (y * (x * L(z,x,y)))) \ (x * (y * L(z,x,y))) = L(x,z,y).
(x \ (y * (x * z))) \ (x * (z * L(y,x,z))) = L(x,y,z).
a(x \ 1,y,(z \ L(x,u,w)) \ 1) = z \ (x * L(x \ z,y,x \ 1)).
a(x \ 1,y,(z \ L(x,u,w)) \ 1) = a(x \ 1,y,(z \ x) \ 1).
a(x \ 1,y,(z \ L(x,u,w)) \ 1) = a(x \ 1,y,x \ z).
a(L(x,y,z) \ 1,u,L(x,y,z) \ (z \ x)) = a(L(x,y,z) \ 1,u,L(z,x,y) \ 1).
a(L(x,y,z) \ 1,u,L(x,y,z) \ (z \ x)) = a(x \ 1,u,L(L(z,x,y),y,z) \ 1).
a(L(x,y,z) \ 1,u,L(x,y,z) \ (z \ x)) = a(x \ 1,u,L(z,x,y) \ 1).
a(x \ 1,y,L(z,x,u) \ 1) = a(x \ 1,y,z \ 1).
L(a(x,y,z \ 1),z,u) = a(z \ 1,y,(x \ 1) \ 1).
a(x \ 1,y,(z \ 1) \ 1) = a(z,y,L(x,x,u) \ 1).
a(x,y,L(z,z,u) \ 1) = a(x,y,z \ 1).
(x * a(y,z,x \ 1)) \ (x * (u * a(y,z,x \ 1))) = u.
L(x,a(y,z,u \ 1),u) = x.
L(x,y,a(z,u,y \ 1)) = x.
L(x * y,L(x,z,u) \ 1,x) = (x \ 1) \ y.
(x \ 1) \ (y * (L(x,z,u) \ 1)) = y * a(x,z,u).
(L(x,y,z) \ 1) * ((x \ 1) \ u) = u * a(x,y,z).
(x \ 1) * (y * a(x,z,u)) = y * (L(x,z,u) \ 1).
L(a(x,y,z),x \ 1,u) = u \ (u * a(x,y,z)).
L(a(x,y,z),x \ 1,u) = a(x,y,z).
a(x,y \ 1,a(y,z,u)) = 1.
a(x,y,a(z,u \ 1,u)) = 1.
a(x,y,a(z,u,u \ 1)) = 1.
a(x,y,a(z,u \ 1,u)) = a(w,v5,a(v6,v7,v7 \ 1)).
L(a(x,y,y \ 1),z,u) = a(x,y,y \ 1).
a(x,y,a(z,u \ 1,u)) = w \ L(w,v5,a(v6,v7,v7 \ 1)).
L(x,y,a(z,u \ 1,u)) = L(x,w,a(v5,v6,v6 \ 1)).
L(x,y,a(z,u,u \ 1)) = x.
((x * a(y,z,z \ 1)) \ u) * a(x,x \ u,a(y,z,z \ 1)) = (x \ u) * a(y,z,z \ 1).
L(x,y,a(z,z \ 1,u)) = x.
((x * a(y,z,z \ 1)) \ u) * 1 = (x \ u) * a(y,z,z \ 1).
(x \ (y * (x * a(z,z \ 1,u)))) \ (x * (a(z,z \ 1,u) * L(y,x,a(z,z \ 1,u)))) = x.
a(x,x \ 1,y) * (z * u) = u * (z * a(x,x \ 1,y)).
(x \ (y * (x * a(z,z \ 1,u)))) \ (x * (a(z,z \ 1,u) * y)) = x.
(x * a(y,y \ 1,z)) * L(u * w,a(y,y \ 1,z),x) = x * (w * (u * a(y,y \ 1,z))).
L((x * (y * a(z,z \ 1,u))) \ w,y * x,a(z,z \ 1,u)) = (y * x) \ (a(z,z \ 1,u) \ w).
a(x,x \ 1,y) \ (z * (u * (w * a(x,x \ 1,y)))) = (w * u) * L(z,w * u,a(x,x \ 1,y)).
(x * (y * a(z,z \ 1,u))) \ w = (y * x) \ (a(z,z \ 1,u) \ w).
a(x,x \ 1,y) * (z * (u * (w * a(x,x \ 1,y)))) = (w * u) * L(z,w * u,a(x,x \ 1,y)).
L(x,a(y,y \ 1,z),u) = x.
(x * (a(y,y \ 1,z) * u)) \ ((x * a(y,y \ 1,z)) * (w * u)) = L(w,L(u,a(y,y \ 1,z),x),x * a(y,y \ 1,z)).
(x * a(y,y \ 1,z)) * (u * w) = x * (w * (u * a(y,y \ 1,z))).
(x * (y * a(z,z \ 1,u))) \ ((x * a(z,z \ 1,u)) * (w * y)) = L(w,L(y,a(z,z \ 1,u),x),x * a(z,z \ 1,u)).
(x * (y * a(z,z \ 1,u))) \ ((x * a(z,z \ 1,u)) * (y * w)) = L(w,L(y,a(z,z \ 1,u),x),x * a(z,z \ 1,u)).
(x * (y * a(z,z \ 1,u))) \ ((x * a(z,z \ 1,u)) * (y * w)) = L(w,y,x * a(z,z \ 1,u)).
(x * (y * a(z,z \ 1,u))) \ (x * (w * (y * a(z,z \ 1,u)))) = L(w,y,x * a(z,z \ 1,u)).
L(x,y * a(z,z \ 1,u),w) = L(x,y,w * a(z,z \ 1,u)).
x \ L(x,y,z * a(u,u \ 1,w)) = a(x,y * a(u,u \ 1,w),z).
a(x,y * a(z,z \ 1,u),w) = a(x,y,w * a(z,z \ 1,u)).
a(x,x \ 1,y) * (z * (u * (w * a(x,x \ 1,y)))) = (u * w) * L(z,w * u,a(x,x \ 1,y)).
a(x,x \ 1,y) * (z * (u * (w * a(x,x \ 1,y)))) = (u * w) * z.
a(x,x \ 1,y) * (z * (u * (w * a(x,x \ 1,y)))) = z * (u * w).
(x * (y * a(z,z \ 1,u))) \ w = (x * y) \ (a(z,z \ 1,u) \ w).
(x * (y * a(z,z \ 1,u))) \ w = (x * y) \ (w * a(z,z \ 1,u)).
(x * y) \ ((x * (z * (y * a(u,u \ 1,w)))) * a(u,u \ 1,w)) = L(z,y,x * a(u,u \ 1,w)).
(x * y) \ (a(z,z \ 1,u) * (x * (w * (y * a(z,z \ 1,u))))) = L(w,y,x * a(z,z \ 1,u)).
L(x,y,z * a(u,u \ 1,w)) = (z * y) \ (z * (x * y)).
L(x,y,z * a(u,u \ 1,w)) = L(x,y,z).
L(x,y * a(z,z \ 1,u),w) = L(x,y,w).
L(x,y,L(z,z \ 1,u)) = L(x,y,z).
L(x,y,L(z \ 1,z,u)) = L(x,y,z \ 1).
L(x,L(y,y \ 1,z),u) = L(x,y,u).
a(x,y * a(z,z \ 1,u),a(w,v5,v6)) = a(w,v5,v6) * L(a(w,v5,v6),y,x).
L(x,y,(z \ u) \ 1) = L(x,y,u \ z).
a(x,y,a(z,u,y)) = z \ L(L(z,u,y),u,y).
L(x,y,((z * a(u,w,z \ 1)) \ 1) * L(a((z * a(u,w,z \ 1)) \ 1,z,v5),w,u)) = L(x,y,(z * a(u,w,z \ 1)) \ 1).
L(x,(y \ z) \ 1,u) = L(x,z \ y,u).
a(x,y * a(z,z \ 1,u),a(w,v5,v6)) = a(x,y,a(w,v5,v6)).
a(x,y,a(z,u,w) * a(v5,v5 \ 1,v6)) = a(x,y,a(z,u,w)).
a(x,y,a(z,u,w) * a(v5,v6,v6 \ 1)) = a(x,y,a(z,u,w)).
a(x,y,a(z,u,u \ 1) * a(w,v5,v6)) = a(x,y,a(w,v5,v6)).
L(x,y,L(L(z \ 1,z * u,w),z,u)) = L(x,y,((u * w) \ (w * (z * u))) \ 1).
a(x,y,a(z,u,y)) = z \ z.
a(x,y,a(z,u,y)) = 1.
L(a(x,y,z),z,u) = a(x,y,z).
L(a(x,y,z),x,u) = a(z,y,x).
a(x,y,L(z \ 1,z,u)) = a(x,y,z \ 1).
a(x,y,z \ ((u \ 1) \ z)) = a(x,y,u).
L(a(x,y,z),x,u) = a(x,y,z).
(x * (y * z)) \ ((x * y) * (a(L(z,y,x),u,w) * L(z,y,x))) = a(w,u,L(z,y,x)).
a(x,y,z) * L(u,x,a(x,y,z)) = u * a(z,y,x).
L(x \ 1,x,y) \ a(z,u,x \ 1) = L(L(x \ 1,x,y),u,z) \ 1.
a(x,y,z) * (u \ (z * (u * a(x,y,z)))) = z.
(x * (y * z)) \ (x * (z * L(y,u,w))) = L(a(y,u,w),y * z,x).
(x * (y * z)) \ ((x * z) * (a(L(y,z,x),u,w) * L(y,z,x))) = a(w,u,L(y,z,x)).
x * (L(x,y,z) \ u) = u * a(z,y,x).
x * (L(x,y,z) \ u) = u * a(x,y,z).
(x * a(y,z,u)) \ (x * u) = L(u,z,y).
L(x,y,z) \ (x * u) = u * a(x,y,z).
(x \ y) * L(x,z,u) = y * a(x,z,u).
(x \ L(y,z,u)) * a(y,z,u) = y * (L(x,x \ 1,L(y,z,u)) \ 1).
x * L(a(y,z,u),z,w) = y * (L(y,w \ ((z \ 1) \ w),u) \ x).
(x * a(y,z,L(z \ 1,u,w))) \ (x * L(z \ 1,u,w)) = (z * y) \ (y * a(w,u,z \ 1)).
(x * a(y,z,x \ u)) \ u = L(x \ u,z,y).
(x * a(y,z,u)) \ (y * x) = L(y,z,u).
(x * y) * a(x,z,u) = y * L(x,z,u).
(x * y) * a(y,z,u) = x * L(y,z,u).
x * (y * a(x,z,u)) = y * L(x,z,u).
L(x \ 1,y,z) * L(x,u,w) = a(z,y,x \ 1) * a(x,u,w).
a(x,y,z) * (u \ L(x,y,z)) = x * (L(u,u \ 1,L(x,y,z)) \ 1).
L(x,y,z * L(u,u \ 1,w)) = L(x,y,u * z).
(x * L(y,z,u)) \ (((x * y) * w) * a(y,z,u)) = L(w,x * y,a(y,z,u)).
L(x,a(y,z,x),u) = x.
L(x,a(x,y,z),u) = x.
a(x,a(y,a(x,z,u),w),v5) = a(y,a(x,z,u),w) * a(y,x \ L(x,z,u),w).
a(x,a(y,a(x,z,u),w),v5) = a(y,a(x,z,u),w) * a(y,a(x,z,u),w).
a(x,a(y,a(x,z,u),w),v5) = 1.
x \ ((a(y,a(x,z,u),w) \ (x \ v5)) \ v5) = a(y,a(x,z,u),w) * 1.
x \ (((x \ y) * a(z,a(x,u,w),v5)) \ y) = a(z,a(x,u,w),v5) * 1.
((x \ y) * a(z,a(x,u,w),v5)) \ y = a(z,a(x,u,w),v5) * x.
(x * a(y,a(x,z,u),w)) \ v5 = (x \ v5) * a(y,a(x,z,u),w).
L(x,y,L(L(z \ 1,z * u,w),z,u)) = L(x,y,L(z,u,w) \ 1).
(x * (y * z)) \ ((z * x) * (a(L(y,z,x),u,w) * L(y,z,x))) = a(w,u,L(y,z,x)).
(x * (y * z)) \ ((z * x) * L(L(y,z,x),u,w)) = a(w,u,L(y,z,x)).
(x * (y * z)) \ (x * (z * L(y,u,w))) = a(w,u,L(y,z,x)).
L(a(x,y,z),x * u,w) = a(z,y,L(x,u,w)).
a(x,y,L(z,u,y)) = a(x,y,z).
L(a(x,y,L(z,u,w)),z * u,w) = a(z,y,x).
a(x,((y * (x * z)) \ (x * y)) \ 1,u) = a(u,z,L(x,z,y)).
a(x,y,a(z,u,L(w,v5,x)) \ 1) = a(x,y,a(w,u,z) \ 1).
L(x * a(y,z,L(x,u,w)),z,y) = x * a(w,x * u,a(x,z,y)).
a(x,y,L(L(z,u,y),w,v5)) = a(x,y,L(z,w,v5)).
L(a(x,y,L(z,u,w)),z * u,w) = a(x,y,z).
x \ (y * a(z,y * u,a(y,x \ 1,x))) = (y * a(x,x \ 1,L(y,u,z))) * (x \ 1).
a(x,y,a(z,u,L(w,v5,x))) = a(x,y,a(w,u,z) \ 1).
(x * L(y,z,u)) \ ((y * (w * x)) * a(y,z,u)) = L(L(w,x,y),x * y,a(y,z,u)).
L(L(x,y,z),y * z,a(z,u,w)) = (y * L(z,u,w)) \ ((x * y) * L(z,u,w)).
L(L(x,y,z),y * z,a(z,u,w)) = L(x,y,L(z,u,w)).
L(x,y,L(z,u,u \ 1)) = L(x,y,z).
L(L(x,y,z),y,L(z,u,w)) = L(x,y * z,a(z,u,w)).
L(x,y,z * (u \ 1)) = L(x,y,u \ z).
L(x,y,(z \ (u \ z)) \ w) = L(x,y,w * L(u,u \ 1,z)).
L(x,y,(z \ (u \ z)) \ w) = L(x,y,u * w).
(x * a(y,y \ 1,L(x,z,u))) * (y \ 1) = y \ (x * 1).
(x * a(y,y \ 1,L(x,z,u))) * (y \ 1) = y \ x.
(x \ 1) * (y * a(x,x \ 1,L(y,z,u))) = x \ y.
x * (L(y,y \ 1,L(x,z,u)) \ 1) = y \ x.
a(x,y,z) * (u \ L(x,y,z)) = u \ x.
a(x,y,z) * (u \ x) = u \ L(x,y,z).
(x \ y) \ L(y,z,u) = x * a(y,z,u).
x \ L(y,z,u) != w | a(u,z,y) * (x \ y) = w.
L(x,y \ (z \ y),u) = L(x,z \ 1,u).
x * L(a(y,z,u),z,w) = y * (L(y,(z \ 1) \ 1,u) \ x).
x * L(a(y,z,u),z,w) = y * (L(y,z,u) \ x).
L(a(x,y,z),y,u) = a(x,y,z).
a(x,(y \ z) \ 1,u) = a(x,z \ y,u).
a(x,(x * y) \ (y * (x * z)),u) = a(u,z,L(x,z,y)).
a(x,y \ (z \ y),u) = a(x,z \ 1,u).
a(x,L(y,x,z),u) = a(u,y,L(x,y,z)).
a(x,L(y \ 1,y,z) \ a(u,y * z,y \ 1),w) = a(x,((u * (y * z)) \ (u * z)) \ 1,w).
L(x,y,z) * a(x,L(y,x,z),u) = L(L(x,y,z),y,u).
a(x,y,z) * L(x,L(y,x,z),u) = L(L(x,y,z),y,u).
L(x,y,(z \ u) \ w) = L(x,y,(u \ z) * w).
L(x,y,(z \ u) \ w) = L(x,y,w * (u \ z)).
x \ L(x,y,z * (u \ w)) = a(x,y,(w \ u) \ z).
a(x,y,(z \ u) \ w) = a(x,y,w * (u \ z)).
a(x,y,z * (u \ 1)) = a(x,y,u \ z).
a(x,y,L(z \ 1,z,u) * ((w * u) \ (w * (z * u)))) = a(x,y,a(w,z * u,z \ 1)).
a(x,y,z \ u) * L(y,x,u * (z \ 1)) = L(y,u * (z \ 1),x).
a(x,y,L(z \ 1,z,u) * L(z,u,w)) = a(x,y,a(w,z * u,z \ 1)).
a(x,y,a(z,u,u \ 1) * a(u,z,w)) = a(x,y,a(w,u * z,u \ 1)).
a(x,y,a(z,u,u \ 1) * a(w,z,u)) = a(x,y,a(w,u * z,u \ 1)).
a(x,y,a(z,u * w,u \ 1)) = a(x,y,a(z,w,u)).
L(x,y,a(z,u * w,u \ 1)) = x * a(x,y,a(z,w,u)).
L(x,y,a(z,u * w,u \ 1)) = L(x,y,a(z,w,u)).
L(x * y,z,a(u,y,x)) = x * y.
L(x,y,a(z,u * w,w \ 1)) = L(x,y,a(z,u,w)).
L(x * y,z,a(x,y,u)) = x * y.
L(x,y,a(z,u * (z \ 1),w)) = L(x,y,a(w,u,z \ 1)).
a(x,y,z \ u) * L(y,x,z \ u) = L(y,u * (z \ 1),x).
L(x,y * (z \ 1),u) = L(x,z \ y,u).
a(x,y * (z \ 1),u) = x \ L(x,z \ y,u).
a(x,y * (z \ 1),u) = a(x,z \ y,u).
a(x,(y \ 1) \ z,u) = a(x,z * y,u).
L(x,y,a(z,z \ u,w)) = L(x,y,a(w,u,z \ 1)).
L((x * y) * a(z,x * y,a(x,y,u)),a(x,y,u),z) = x * y.
a(x,y,z) * (u * (x * y)) = (x * y) * (u * a(x,y,z)).
a(x,y,z) * (u * L(x * y,a(x,y,z),u)) = u * (a(x,y,z) * (x * y)).
L(a(x,y,z) \ 1,a(x,y,z),u) \ 1 = (u * (x * y)) \ ((x * y) * ((a(x,y,z) \ 1) \ u)).
a(x,y,z) * (u * L(x * y,a(x,y,z),u)) = u * ((x * y) * a(x,y,z)).
L(a(x,y,z) \ 1,a(x,y,z),u) \ 1 = (u * (x * y)) \ ((x * y) * (a(x,y,z) \ u)).
L(a(x,y,z) \ 1,a(x,y,z),u) \ 1 = (u * (x * y)) \ ((x * y) * (u * a(x,y,z))).
a(x,y,z) * (u * L(x * y,a(x,y,z),u)) = u * (y * L(x,y,z)).
a(x,y,L(y \ 1,z,u)) = a(x,y,y \ 1).
L(x * a(x,y,z),y,L(z,u,w)) = x * a(w,z * u,a(x,y,L(z,u,w))).
L(L(x,y,z),y,L(z,u,w)) = x * a(w,z * u,a(x,y,L(z,u,w))).
(x * a(y,z,z \ 1)) \ u = (x \ u) * a(y,z,z \ 1).
(x * a(y,z,z \ 1)) \ (x * L(z \ 1,u,w)) = (z * y) \ (y * a(w,u,z \ 1)).
(x * y) \ (y * a(z,u,x \ 1)) = (w \ (w * L(x \ 1,u,z))) * a(y,x,x \ 1).
(x * y) \ (y * a(z,u,x \ 1)) = L(x \ 1,u,z) * a(y,x,x \ 1).
(x * y) \ (y * a(z,u,x \ 1)) = a(x \ 1,u,z) * L(x \ 1,x,y).
(x * y) \ (y * a(z,u,x \ 1)) = a(z,u,x \ 1) * L(x \ 1,x,y).
a(x,y,z \ 1) * L(z \ 1,z,u) = L(L(z \ 1,y,x),z,u).
L(x,y,L(z \ 1,u,w) * L(a((z * a(w,u,z \ 1)) \ 1,z,v5),u,w)) = L(x,y,(z * a(w,u,z \ 1)) \ 1).
L(x,y,L(z \ 1,u,w) * L(a(L(z \ 1,u,w),z,v5),u,w)) = L(x,y,(z * a(w,u,z \ 1)) \ 1).
L(x,y,L(z \ 1,u,w) * L(a(v5,z,L(z \ 1,u,w)),u,w)) = L(x,y,(z * a(w,u,z \ 1)) \ 1).
L(x,y,L(z \ 1,u,w) * L(a(v5,z,z \ 1),u,w)) = L(x,y,(z * a(w,u,z \ 1)) \ 1).
L(x,y,L(z \ 1,u,w) * a(v5,z,z \ 1)) = L(x,y,(z * a(w,u,z \ 1)) \ 1).
L(x,y,a(z \ 1,u,w) * L(z \ 1,z,v5)) = L(x,y,(z * a(w,u,z \ 1)) \ 1).
L(x,y,a(z,u,w \ 1) * L(w \ 1,w,v5)) = L(x,y,(w * a(z,u,w \ 1)) \ 1).
L(x,y,L(L(z \ 1,u,w),z,v5)) = L(x,y,(z * a(w,u,z \ 1)) \ 1).
L(x,y,L(L(z \ 1,u,w),z,v5)) = L(x,y,L(z \ 1,u,w)).
L(x,y,L(z \ 1,z * u,w)) = L(x,y,L(z,u,w) \ 1).
L(L(x,y,z \ 1),y,L(z,u,w) \ 1) = L(x,y * (z \ 1),a(z \ 1,z * u,w)).
L(x,y,L(z,z \ u,w) \ 1) = L(x,y,L(z \ 1,u,w)).
L(L(x,y,z \ 1),y,L(z,u,w) \ 1) = L(x,y * (z \ 1),a(w,z * u,z \ 1)).
L(L(x,y,z \ 1),y,L(z,u,w) \ 1) = L(x,z \ y,a(w,z * u,z \ 1)).
L(L(x,y * z,y \ 1),y * z,L(y,u,w) \ 1) = L(x,z,a(w,y * u,y \ 1)).
x * a(y,z,a(x,u * w,u \ 1)) = L(x,w,a(y,u * z,u \ 1)).
x * a(y,z,a(x,u * w,w \ 1)) = L(x,u,a(y,w * z,w \ 1)).
a(x,y,a(z,u * w,w \ 1)) = a(z,u,a(x,y,w)).
L(x,y,a(z,u,a(x,w,v5))) = x.
L(x,y,a(z,u * w,w \ 1)) = x * a(z,u,a(x,y,w)).
L(x,a(y,z,a(x,u,w)),v5) = x.
a(x,y,a(z,u,w)) * (v5 * z) = z * (v5 * a(x,y,a(z,u,w))).
a(x,y,a(z,u,w)) * (v5 * L(z,a(x,y,a(z,u,w)),v5)) = v5 * (a(x,y,a(z,u,w)) * z).
a(x,y,a(z,u,w)) * (z * v5) = z * (v5 * a(x,y,a(z,u,w))).
x * a(y,z,a(x,u,w)) = L(x,u,a(y,z,w)).
L(L(x,y,z),y,L(z \ 1,u,w) \ 1) = L(x,y,a(w,u,z)).
L(L(x,y,z),y,L(z \ 1,u,w) \ 1) = L(x,y,a(z,u,w)).
L(L(x,y,z),y,L((z \ 1) \ 1,u,w)) = L(x,y,a(z,(z \ 1) \ u,w)).
x \ L(x,y,a(z,u,w)) = a(w,u,a(x,y,z)).
a(x,y,a(z,u,w)) = a(w,u,a(x,y,z)).
x * (y * a(z,u,a(x,w,v5))) != v6 | (x * y) * a(z,u,a(x,w,v5)) = v6.
a(x,y,a(z,u,w)) * (v5 * L(z,a(x,y,a(z,u,w)),v5)) = v5 * (z * a(x,y,a(z,u,w))).
a(x,L(L(y \ 1,y,z),y * z,u) \ 1,w) = a(x,((u * (y * z)) \ (u * z)) \ 1,w).
L(L(a(x,y,z),y,u),y * u,w) = a(x,((w * (y * u)) \ (w * u)) \ 1,z).
L(a(x,y,z),y * u,w) = a(x,((w * (y * u)) \ (w * u)) \ 1,z).
L(a(x,y,z),y * u,w) = a(x,((w * (y * u)) \ (u * w)) \ 1,z).
L(a(x,y,z),y * u,w) = a(x,(u * w) \ (w * (y * u)),z).
L(a(x,y,z),y * u,w) = a(x,L(y,u,w),z).
a(x,L(y,z,x),u) = a(u,y,x).
L(a(x,y,z),y * (y \ u),u \ y) = a(x,u * ((y \ u) \ 1),z).
L(a(x,y,z),u,u \ y) = a(x,u * ((y \ u) \ 1),z).
L(a(x,y,z),u,u \ y) = a(x,(y \ u) \ u,z).
L(a(x,y,z),u,u \ y) = a(x,y,z).
(x \ y) * (x * a(z,y,u)) = y * a(z,y,u).
(x \ y) \ L(L(y,z,u),u,z) = x * a(z,y,u).
L(x,y,a(z,x * y,u)) = y \ (x * y).
a(x,y,L(z,x,y)) * ((u \ z) \ L(z,x,y)) = u * a(x,z,y).
a(x,y,z) * ((u \ z) \ L(z,x,y)) = u * a(x,z,y).
a(x,y,z) * (u * a(z,x,y)) = u * a(x,z,y).
L((x * a(y,z,u)) \ w,x * a(y,z,u),a(z,u,y)) = (x * a(z,y,u)) \ (a(z,u,y) * w).
a(x,y,z) * (u * a(y,x,z)) = u * a(x,z,y).
L((x * a(y,z,u)) \ w,x * a(y,z,u),a(y,u,z)) = (x * a(z,y,u)) \ (a(z,u,y) * w).
a(x,y,z) * (u * a(x,z,y)) = u * a(y,x,z).
a(x,y,a(z,u,w)) * L(z,u,a(y,x,w)) = z * a(x,a(z,u,w),y).
L(x,y,a(z,u,w)) \ (x * a(u,a(x,y,w),z)) = a(u,z,a(x,y,w)).
a(x,y,a(z,u,w)) * L(x,y,a(u,w,z)) = x * a(w,a(x,y,z),u).
L(x,y,a(z,u,w)) \ (x * a(z,a(x,y,w),u)) = a(u,z,a(x,y,w)).
a(x,y,a(z,u,w)) * L(x,y,a(z,w,u)) = x * a(w,a(x,y,z),u).
a(x,a(y,z,u),w) * a(y,z,a(x,w,u)) = a(w,x,a(y,z,u)).
a(x,y,a(z,u,w)) * a(z,a(x,y,w),u) = a(u,z,a(x,y,w)).
L((x * a(y,z,u)) \ w,x * a(y,z,u),a(y,u,z)) = (x * a(z,y,u)) \ (w * a(y,u,z)).
L(x,y,a(z,x * y,u)) = x.
a(x,y,a(z,u,L(w,v5,x))) = a(x,y,a(z,u,w)).
L(L(x,y,z),y,L(z,u,w)) = x * a(w,z * u,a(x,y,z)).
x * a(y,z * u,a(x,w,z)) = L(x,w * z,a(z,u,y)).
a(x,y * z,a(u,w,y)) = a(u,w * y,a(y,z,x)).
a(x,y * z,a(u,w,y)) = a(u,y * w,a(y,z,x)).
a(x,L(y,z,u) * w,a(v5,L(u,y,z),L(y,z,u))) = a(v5,u * L(y,u,z),a(L(y,z,u),w,x)).
a(x,y * z,a(y,u,w)) = a(x,z,a(y,y * u,w)).
a(x,y * L(z,u,w),a(v5,L(w,z,u),L(z,u,w))) = a(v5,w * L(z,w,u),a(L(z,u,w),y,x)).
L(L(x,y,z),y,L(z,u,w)) = L(x,y,a(z,(z \ 1) \ u,w)).
L(x,y,a(z,(z \ 1) \ u,w)) = L(x,y * z,a(z,u,w)).
L(x,y * z,a(z,u,w)) = L(x,y,a(z,u * z,w)).
L(x,y * (z \ 1),a(z \ 1,z * u,w)) = L(x,y,a(z \ 1,L(u,z,z \ 1),w)).
L(x,y * (z \ 1),a(u,z * w,z \ 1)) = L(x,y,a(z \ 1,L(w,z,z \ 1),u)).
L(x,y,a(z \ 1,L(u,z,z \ 1),w)) = L(x,y * (z \ 1),a(w,u,z)).
L(x,y,a(z \ 1,L(u,z,z \ 1),w)) = L(x,y * (z \ 1),a(z,u,w)).
L(x,y,a(z \ 1,L(u,z,z \ 1),w)) = L(x,z \ y,a(z,u,w)).
L(x,y \ z,a(y,u,w)) = L(x,z,a(w,u,y \ 1)).
L(x,y \ z,a(y,u,w)) = L(x,z,a(y,y \ u,w)).
a(x,y,a(z,u,w)) * (v5 * z) = v5 * (z * a(x,y,a(z,u,w))).
x * (y * a(z,u,a(y,w,v5))) = y * (x * a(z,u,a(y,w,v5))).
x * (y * a(z,u,a(x,w,v5))) = y * L(x,w,a(z,u,v5)).
(x * y) * a(z,u,a(x,w,v5)) = y * L(x,w,a(z,u,v5)).
L(x * L(y,x,a(z,y * x,u)),a(y,x,u),z) = y * x.
L(x * y,a(y,x,z),u) = y * x.
L(x * y,a(x,y,z),u) = x * y.
a(x,y,z) * (u * (x * y)) = u * (y * L(x,y,z)).
(x * y) * (z * a(x,y,u)) = z * (y * L(x,y,u)).
L(a(x,y,z) \ 1,a(x,y,z),u) \ 1 = (u * (x * y)) \ (u * (y * L(x,y,z))).
L(a(x,y,z) \ 1,a(x,y,z),u) \ 1 = a(z,y,L(x,y,u)).
L(a(x,y,z),a(x,y,z),u) \ 1 = a(z,y,L(x,y,u)).
a(x,y,L(z,y,u)) = 1 * a(z,y,x).
a(x,y,L(z,y,u)) = a(z,y,x).
a(x,L(y,x,z),u) = a(x,y,u).
L(x,L(y,x,z),u) = x * a(x,y,u).
a(x,L(y,z,u),L(z,w,v5)) = L(a(z,y,x),z * w,v5).
L(x,L(y,x,z),u) = L(x,y,u).
a(x,L(y,z,u),L(z,w,v5)) = a(x,y,L(z,w,v5)).
a(x,y,z) * L(x,y,u) = L(L(x,y,z),y,u).
a(x,y,z) * L(x,y,L(z,u,w)) = x * a(w,z * u,a(x,y,z)).
L(L(x,y,a(z,u,w)),y,a(z,w,u)) = x * a(w,a(x,y,z),u).
a(x,y,z) * a(x,y,L(z,u,w)) = a(w,z * u,a(x,y,z)).
L(L(x,y,a(z,u,w)),y,a(z,w,u)) = x * a(u,a(x,y,z),w).
a(x,y * L(z,u,w),a(v5,w,L(z,u,w))) = a(v5,w * L(z,w,u),a(L(z,u,w),y,x)).
a(x,y * L(z,u,w),a(v5,w,L(z,u,w))) = a(v5,w * L(z,w,u),a(x,y,L(z,u,w))).
a(x,y * L(z,y,u),a(L(z,u,y),w,v5)) = a(v5,w * L(z,u,y),a(x,y,z)).
a(x,y * L(z,y,u),a(L(z,u,y),w,v5)) = a(v5,w * L(z,u,y),a(z,y,x)).
a(x,y * L(z,y,u),a(w,v5,L(z,u,y))) = a(w,v5 * L(z,u,y),a(z,y,x)).
a(x,L(y,z,u) * w,a(v5,u,L(y,z,u))) = a(v5,u,y) * a(v5,u,L(L(y,z,u),w,x)).
a(x,L(y,z,u) * w,a(v5,u,L(y,z,u))) = a(v5,u,y) * a(v5,u,L(y,w,x)).
a(x,L(y,z,u) * w,a(v5,u,L(y,z,u))) = a(x,y * w,a(v5,u,y)).
a(x,y * L(z,u,w),a(v5,w,L(z,u,w))) = a(x,z * y,a(v5,w,z)).
a(x,y * L(z,y,u),a(w,v5,L(z,u,y))) = a(w,z * v5,a(x,y,z)).
a(x,y * L(z,u,w),a(z,w,v5)) = a(x,z * y,a(v5,w,z)).
a(x,y * L(z,u,w),a(z,w,v5)) = a(x,z * y,a(z,w,v5)).
a(x,y * L(z,u,w),a(z,w,v5)) = a(x,y,a(z,z * w,v5)).
L(x,y * L(z,u,w),a(z,w,v5)) = (v6 * a(x,y,a(z,z * w,v5))) \ (x * v6).
L(x,y * L(z,u,w),a(z,w,v5)) = L(x,y,a(z,z * w,v5)).
L(x,(y \ z) * L(y,u,w),a(y,w,v5)) = L(x,z,a(y,y \ (y * w),v5)).
L(x,y * a(z,u,w),a(z,w,v5)) = L(x,y,a(z,z \ (z * w),v5)).
L(x,y * a(z,u,w),a(z,w,v5)) = L(x,y,a(z,w,v5)).
L((x * a(y,z,u)) \ w,x,a(y,u,z)) = (x * a(z,y,u)) \ (w * a(y,u,z)).
(x * a(y,z,u)) \ (((w * x) * a(z,y,u)) * a(z,u,y)) = L(L(w,x,a(z,y,u)),x,a(z,u,y)).
(x * a(y,z,u)) \ (a(z,u,y) * ((w * x) * a(z,y,u))) = L(L(w,x,a(z,y,u)),x,a(z,u,y)).
(x * a(y,z,u)) \ ((w * x) * a(u,z,y)) = L(L(w,x,a(z,y,u)),x,a(z,u,y)).
(x * a(y,z,u)) \ ((w * x) * a(y,z,u)) = L(L(w,x,a(z,y,u)),x,a(z,u,y)).
L(L(x,y,a(z,u,w)),y,a(z,w,u)) = L(x,y,a(u,z,w)).
x * a(y,a(x,z,u),w) = L(x,z,a(y,u,w)).
a(x,a(y,z,u),w) = a(x,u,a(y,z,w)).
(x \ y) * a(z,a(x,u,w),v5) = L(x,u,a(z,w,v5)) \ y.
a(x,a(y,z,u),w) = a(x,y,a(u,z,w)).
(x \ L(x,y,a(z,u,w))) * a(z,a(x,y,u),w) = 1.
a(x,y,a(z,u,w)) * a(z,x,a(w,y,u)) = a(u,z,a(x,y,w)).
a(x,y,a(z,u,w)) * a(z,x,a(u,y,w)) = a(u,z,a(x,y,w)).
a(x,y,a(z,u,w)) * a(z,a(x,y,u),w) = 1.
a(x,y,a(z,u,w)) * a(z,x,a(u,y,w)) = 1.
a(x,y,a(z,u,w)) = 1.

end_of_list.
