% ********************************************************* % AIM: generalized Moufang => aa1 % ********************************************************* assign(order, kbo). set(lex_order_vars). clear(back_demod). set(restrict_denials). set(para_from_small). 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. % cancellation laws x * y = u & x * z = u -> y = z. y * x = u & z * x = u -> y = z. % other form x * y = x * z -> y = z. y * x = z * x -> y = z. % useful in demodulation free runs x != y | z * x = z * y. x != y | x * z = y * z. % 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 % L(u,x,y) = u L(x) L(y) L(yx)^{-1} (y * x) \ (y * (x * u)) = L(u,x,y). % R(u,x,y) = u R(x) R(y) R(xy)^{-1} ((u * x) * y) / (x * y) = R(u,x,y). % T(u,x) = u R(x) L(x)^{-1} x \ (u * x) = T(u,x). % obvious compatibility a(x,y,z) = 1 -> L(z,y,x) = z. L(x,y,z) = x -> a(z,y,x) = 1. T(x,y) = x -> T(y,x) = y. T(x,y) = x -> K(x,y) = 1. K(x,y) = 1 -> T(x,y) = 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 assumptions for this special case (generalized Moufang) ((1 / x) \ y) * (z * x) = x * ((y * z) * x) # label("Osborn"). x * ((y * x) \ 1) = y \ 1 # label("WIP"). end_of_list. formulas(goals). a(a(x,y,z),u,w) = 1 # label("aa1"). 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) * y = x. x * y != z | x * u != z | u = y. x * y != z | u * y != z | u = x. x * y != x * z | y = z. x * y != z * y | x = z. x != y | z * x = z * y. x != y | x * z = y * z. (x * (y * z)) \ ((x * y) * z) = a(x,y,z). a(x,y,z) = (x * (y * z)) \ ((x * y) * z). (x * y) \ (y * x) = K(y,x). K(x,y) = (y * x) \ (x * y). (x * y) \ (x * (y * z)) = L(z,y,x). L(x,y,z) = (z * y) \ (z * (y * x)). ((x * y) * z) / (y * z) = R(x,y,z). R(x,y,z) = ((x * y) * z) / (y * z). x \ (y * x) = T(y,x). T(x,y) = y \ (x * y). a(x,y,z) != 1 | L(z,y,x) = z. L(x,y,z) != x | a(z,y,x) = 1. T(x,y) != x | T(y,x) = y. T(x,y) != x | K(x,y) = 1. K(x,y) != 1 | T(x,y) = x. T(T(x,y),z) = T(T(x,z),y). T(L(x,y,z),u) = L(T(x,u),y,z). L(T(x,y),z,u) = T(L(x,z,u),y). T(R(x,y,z),u) = R(T(x,u),y,z). R(T(x,y),z,u) = T(R(x,z,u),y). L(R(x,y,z),u,w) = R(L(x,u,w),y,z). R(L(x,y,z),u,w) = L(R(x,u,w),y,z). L(L(x,y,z),u,w) = L(L(x,u,w),y,z). R(R(x,y,z),u,w) = R(R(x,u,w),y,z). ((1 / x) \ y) * (z * x) = x * ((y * z) * x). x * ((y * x) \ 1) = y \ 1. a(a(c1,c2,c3),c4,c5) != 1. 1 \ x = x. x \ (1 * (x * y)) = y. x \ x = 1. x \ (x * (y \ (y * z))) = z. (x * (x \ 1)) * y = y. x * (x \ (1 * y)) = y. x * (y * (y \ 1)) = x. x \ (y * (y \ (x * z))) = z. x * (y * (y \ (x \ z))) = z. x / x = 1. x / 1 = x. x * (((x \ y) * z) / z) = y. x / (y \ x) = y. ((1 / x) * x) * y = y. x * ((1 / y) * y) = x. (x / y) \ x = y. (x \ (x * (y / z))) * z = y. ((x * (x \ y)) / z) * z = y. (((x * y) / z) * z) / y = x. (((x / y) / z) * z) * y = x. x != y | 1 * z != y | z = x. x != y | x * z != y | z = 1. x != y | x * z != y | 1 = z. x != y | z * u != y | u = z \ x. x != y | z * u != y | z \ x = u. x != y | z * u != y | z = x / u. x != y | z * u != y | x / u = z. x != 1 * y | x = y. 1 * x != y | y = x. 1 * x != y | x = y. x * y != (x * z) * 1 | y = z. (x * y) * 1 != x * z | z = y. x != y * z | y \ x = z. x * y != z | x \ z = y. x * y != z * (z \ (x * u)) | y = u. x * (x \ (y * z)) != y * u | u = z. x != y * 1 | x = y. x * 1 != y | y = x. x * 1 != y | x = y. x * y != z \ (z * (u * y)) | x = u. x \ (x * (y * z)) != u * z | u = y. x * (y \ z) != z | x = y. x != y * z | x / z = y. x * y != z | z / y = x. x * (y * (y \ z)) = x * z. ((x / y) * y) * z = x * z. (x * (x \ y)) * z = y * z. (x * (y * z)) * a(x,y,z) = (x * y) * z. a(x,x \ y,z) = (x * ((x \ y) * z)) \ (y * z). (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z). a(x,y,(x * y) \ z) = (x * (y * ((x * y) \ z))) \ z. (x * (y * ((x * y) \ z))) \ z = a(x,y,(x * y) \ z). (x * y) * K(y,x) = y * x. K(x \ y,x) = y \ ((x \ y) * x). x \ ((y \ x) * y) = K(y \ x,y). K(x,x \ y) = ((x \ y) * x) \ y. ((x \ y) * x) \ y = K(x,x \ y). K(x,y / x) = y \ (x * (y / x)). x \ (y * (x / y)) = K(y,x / y). K(x / y,y) = (y * (x / y)) \ x. (x * (y / x)) \ y = K(y / x,x). L(x,y,1) = y \ (1 * (y * x)). x \ (1 * (x * y)) = L(y,x,1). L(x,1,y) = (y * 1) \ (y * x). (x * 1) \ (x * y) = L(y,1,x). L(1,x,y) = (y * x) \ (y * x). (x * y) \ (x * y) = L(1,y,x). (x * y) * L(z,y,x) = x * (y * z). L(x,y \ z,y) = z \ (y * ((y \ z) * x)). x \ (y * ((y \ x) * z)) = L(z,y \ x,y). L(x \ y,x,z) = (z * x) \ (z * y). L(x,y,z / y) = z \ ((z / y) * (y * x)). x \ ((x / y) * (y * z)) = L(z,y,x / y). L(x,y / x,z) = (z * (y / x)) \ (z * y). R(x,1,y) = ((x * 1) * y) / y. ((x * 1) * y) / y = R(x,1,y). R(x,y,1) = (x * y) / (y * 1). (x * y) / (y * 1) = R(x,y,1). R(x,x \ y,z) = (y * z) / ((x \ y) * z). R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)). R(x,y,z) * (y * z) = (x * y) * z. R(x / y,y,z) = (x * z) / (y * z). R(x,y / z,z) = ((x * (y / z)) * z) / y. ((x * (y / z)) * z) / y = R(x,y / z,z). T(x,x) = x. x * T(y,x) = y * x. T(x,x \ y) = (x \ y) \ y. T(x / y,y) = y \ x. T(T(T(x,y),z),u) = T(T(T(x,z),u),y). T(T(T(x,y),z),u) = T(T(T(x,u),y),z). T(R(T(x,y),z,u),w) = T(T(R(x,z,u),w),y). T(T(R(x,y,z),u),w) = T(R(T(x,w),y,z),u). x * y != z | x = z / y. (1 / x) \ y = (x * ((y * z) * x)) / (z * x). (x * ((y * z) * x)) / (z * x) = (1 / x) \ y. ((1 / x) \ y) * x = x * ((y * 1) * x). x * (y * z) = z * ((((1 / z) * x) * y) * z). x * ((((1 / x) * y) * z) * x) = y * (z * x). ((1 / x) \ y) * z = x * ((y * (z / x)) * x). x * ((y * (z / x)) * x) = ((1 / x) \ y) * z. x * y != z | y = x \ z. (x * y) \ 1 = y \ (x \ 1). (x \ y) * (y \ 1) = x \ 1. x * (y \ 1) = (y / x) \ 1. (x / y) \ 1 = y * (x \ 1). (x * (x \ 1)) \ y = y. T(x,1) = x * 1. K(x,x) = 1. x / (y * (y \ 1)) = x. x / ((1 / y) * y) = x. T(x,y) = T(T(x,y),x). T(T(x,y),x) = T(x,y). L(x,y,z) = T(L(x,y,z),x). T(L(x,y,z),x) = L(x,y,z). (x / (y \ x)) * z = y * z. ((x * y) * z) / a(x,y,z) = x * (y * z). (x * y) / K(x,y) = y * x. (x * (y * z)) / L(z,y,x) = x * y. (x * y) / T(x,y) = y. (x \ y) * (z * (x \ 1)) = (x \ 1) * ((y * z) * (x \ 1)). (x \ 1) * ((y * z) * (x \ 1)) = (x \ y) * (z * (x \ 1)). x / (y / ((z \ x) \ y)) = z. ((x / y) \ x) * z = y * z. x * ((y / (x \ z)) \ y) = z. R(x,y,z) \ ((x * y) * z) = y * z. ((x / (y / z)) \ x) \ y = z. x = T(x,1). T(x,1) = x. K(x,1) = 1. T(1,x) = 1. K(1,x) = 1. (x * (x \ 1)) * y != z | y = z. ((1 / x) * x) * y != z | y = z. x * (y * (y \ 1)) != z | z = x. T(x,1) != y | y = x. x * ((1 / y) * y) != z | x = z. x * (y \ y) != z | x = z. R(x,x \ 1,y) = y / ((x \ 1) * y). L(x \ 1,x,y) = (y * x) \ y. R(1 / x,x,y) = y / (x * y). a(x,1 / y,y) = x \ ((x * (1 / y)) * y). x \ ((x * (1 / y)) * y) = a(x,1 / y,y). L(x,1 / x,y) = (y * (1 / x)) \ y. x * y != ((x * z) / u) * u | y = z. T((x * y) / x,x) = y. x = (y * T(x,y)) / y. (x * T(y,x)) / x = y. x = y \ (x * T(y,x)). x \ (y * T(x,y)) = y. (x \ y) * T(x,x \ y) = y. x * (y * (y \ T(z,x))) = z * x. x * T(y / x,x) = y. x * y != z | y * u != z | u = T(x,y). x * y != z | y * u != z | T(x,y) = u. x * y != y * z | T(x,y) = z. x * y != z * x | T(z,x) = y. x * y != z * T(x,z) | y = z. x * T(y,x) != y * z | z = x. x * y != y * T(z,y) | x = z. x * T(y,x) != z * x | z = y. a(x,y,T(z,y)) = (x * (z * y)) \ ((x * y) * T(z,y)). (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z)). a(x,T(y,x),z) = (x * (T(y,x) * z)) \ ((y * x) * z). (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z). L(x,T(y,z),z) = (y * z) \ (z * (T(y,z) * x)). (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y). L(T(x,y),y,z) = (z * y) \ (z * (x * y)). (x * y) \ (x * (z * y)) = L(T(z,y),y,x). R(x,y,T(z,y)) = ((x * y) * T(z,y)) / (z * y). ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y)). x * T(T(y,x),z) = T(y,z) * x. x * L(T(y,x),z,u) = L(y,z,u) * x. x * R(T(y,x),z,u) = R(y,z,u) * x. T(x \ y,z) = T(T(y / x,z),x). T(T(x / y,z),y) = T(y \ x,z). L(x \ y,z,u) = T(L(y / x,z,u),x). T(L(x / y,z,u),y) = L(y \ x,z,u). R(x \ y,z,u) = T(R(y / x,z,u),x). T(R(x / y,z,u),y) = R(y \ x,z,u). T(x / (x / y),x / y) = y. K(x \ 1,x) = (x \ 1) * x. L(x,y \ 1,y) = y * ((y \ 1) * x). x * ((x \ 1) * y) = L(y,x \ 1,x). R(x,y,y \ 1) = (x * y) * (y \ 1). (x * y) * (y \ 1) = R(x,y,y \ 1). R(x,1 / y,y) = (x * (1 / y)) * y. (x * (1 / y)) * y = R(x,1 / y,y). T(x,T(x,y)) = x. x * T(x,y) = T(x,y) * x. T(x,y) * x = x * T(x,y). T(x,y) = T(T(x,y),T(x,z)). T(T(x,y),T(x,z)) = T(x,y). T(x / y,y \ x) = x / y. x / T(y,y \ x) = y \ x. T(x,y) = T(T((z * x) / z,y),z). T(T((x * y) / x,z),x) = T(y,z). T((x * y) / x,y) = (x * y) / x. (x * T(T(y,x),z)) / x = T(y,z). L(x,y,z) \ (u * L(T(x,u),y,z)) = u. x != y * z | T(x / y,y) = z. x * y != z | T(z / x,x) = y. x * y != z | y \ z = T(x,y). x * y != z | T(x,y) = y \ z. x \ x != y | 1 = y. x \ (y * (y \ x)) = 1. (x / y) \ (z * (z \ x)) = y. x * 1 = y * (y \ x). x * (x \ y) = y * 1. x * 1 != y * z | y \ x = z. (x / y) * y = x * 1. x * (x \ y) != z | z = y. x * 1 != y * z | x / z = y. (x / y) * y != z | z = x. x * (x \ y) = (y / z) * z. (x / y) * y = z * (z \ x). (x * y) * L(z,y,x) != u | u = x * (y * z). (x * y) * L(z,y,x) != u | x * (y * z) = u. x * T(y,x) != z | z = y * x. x * T(y,x) != z | y * x = z. (x * (x \ 1)) \ y != z | z = y. ((1 / x) * x) \ y != z | z = y. x * y != z | z = y * T(x,y). x * y != z | y * T(x,y) = z. x / 1 != y | y = x. R(x,y,z) * (y * z) != u | u = (x * y) * z. R(x,y,z) * (y * z) != u | (x * y) * z = u. x / (y * (y \ 1)) != z | z = x. L(x \ (y \ z),x,y) = (y * x) \ z. ((x * (x \ y)) / z) \ y = z. (x / y) * y = 1 * x. (1 * x) / y = x / y. ((1 * x) / y) \ x = y. ((x / y) * y) / z = x / z. (((x / y) * y) / z) \ x = z. R((x / y) / z,z,y) = x / (z * y). x != y | z != y | z = x. x != y | x = (z / y) \ z. x * (x \ y) = (z / y) \ z. (x / y) \ x = z * (z \ y). x != y | x = z / (y \ z). (x / y) * y = z / (x \ z). x / (y \ x) = (y / z) * z. (x * y) / y = z / (x \ z). x * (x \ y) = z / (y \ z). x / (y \ x) = z * (z \ y). x != y | x = (y / z) * z. (x * y) / y = (x / z) * z. x != y | x = z * (z \ y). x \ (x * y) = z * (z \ y). (x / (y * (y \ z))) * z = x. K(x,1 / x) = x * (1 / x). x != (y * (y \ z)) * u | x = z * u. (x \ y) * x = y * K(x \ y,x). x * K(y \ x,y) = (y \ x) * y. x != ((y / z) * z) * u | x = y * u. x * (y / x) = y * K(x,y / x). x * K(y,x / y) = y * (x / y). x * y != (y * x) * z | K(x,y) = z. (x * y) * z != y * x | K(y,x) = z. L(x,K(y,z),z * y) = (y * z) \ ((z * y) * (K(y,z) * x)). (x * y) \ ((y * x) * (K(x,y) * z)) = L(z,K(x,y),y * x). L(K(x,y),y * x,z) = (z * (y * x)) \ (z * (x * y)). (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x). R(x,y,K(y,x)) = (y * x) / (y * K(y,x)). (x * y) / (x * K(x,y)) = R(y,x,K(x,y)). (x * y) / T(y * x,K(x,y)) = K(x,y). T(x,x \ y) * z = ((x \ y) \ y) * z. x * T(y,y \ z) = x * ((y \ z) \ z). (x \ y) \ y = z * (z \ T(x,x \ y)). L((x \ y) \ y,z,u) = T(L(x,z,u),x \ y). T(L(x,y,z),x \ u) = L((x \ u) \ u,y,z). (x * y) * (y \ (x \ 1)) = 1. x \ 1 = (y \ x) \ (y \ 1). (x \ y) \ (x \ 1) = y \ 1. ((1 / x) * y) \ 1 = y \ x. (x * y) \ 1 = T(x,y) \ (y \ 1). T(x,y) \ (y \ 1) = (x * y) \ 1. T(x * y,y \ (x \ 1)) = ((x * y) \ 1) \ 1. (x \ 1) / (y \ 1) = x \ y. x \ 1 != y * (z \ 1) | x \ z = y. a(x,y,z) * (((x * y) * z) \ 1) = (x * (y * z)) \ 1. (x \ 1) * ((y \ 1) \ 1) = (y \ x) \ 1. 1 / ((x \ y) * (y \ 1)) = x. (x \ (1 / y)) * y = x \ 1. (x \ 1) \ 1 = (y \ 1) \ ((x \ y) \ 1). (x \ 1) \ ((y \ x) \ 1) = (y \ 1) \ 1. (x / y) * (y * (x \ 1)) = 1. R(x,y,z) \ 1 = (y * z) * (((x * y) * z) \ 1). (x * y) * (((z * x) * y) \ 1) = R(z,x,y) \ 1. 1 / (x * (y \ 1)) = y / x. T(x,L(x,y,z)) = x. x * L(x,y,z) = L(x,y,z) * x. L(x,y,z) * x = x * L(x,y,z). x != y * (y \ z) | x = z. ((x / y) \ x) * (y \ z) = z. x * (((y / x) \ y) \ z) = z. (x / y) * ((z / y) \ z) = x. x != (y \ x) * z | T(y,y \ x) = z. (x \ y) * z != y | T(x,x \ y) = z. T(x / (x / y),(z / (x / y)) \ z) = y. x != y * z | x = z * T(y,z). K(x \ 1,x) = x * T(x \ 1,x). x * T(x \ 1,x) = K(x \ 1,x). K(x \ 1,x) / x = x \ 1. (x \ 1) \ K(x \ 1,x) = x. T(x,y) * z != x * T(x,y) | z = x. (x \ y) * (y / x) = (y / x) * (x \ y). (x / y) * (y \ x) = (y \ x) * (x / y). x * y != z * (z \ u) | x = u / y. z * (z \ u) != x * y | x = u / y. x * (x \ y) != z * u | y / u = z. x * ((y / (z \ u)) \ y) != u | x = z. x / (y \ ((x / z) * z)) = y. (x / y) * y != z * u | z \ x = u. (x \ y) * z != x \ 1 | z = y \ 1. ((1 / x) \ y) \ x = y \ 1. (x / y) \ x != z * u | z \ y = u. (x / y) \ x != z | z = y. x \ (x * y) != z | z = y. x \ (y * x) != z | z = T(y,x). x \ (y * x) != z | T(y,x) = z. (x * y) \ (y * x) != z | z = K(y,x). (x * y) \ (y * x) != z | K(y,x) = z. (x \ y) \ y != z | z = T(x,x \ y). (x \ y) \ y != z | T(x,x \ y) = z. T(x,x) != y | y = x. x \ (y \ 1) != z | z = (y * x) \ 1. x \ (y \ 1) != z | (y * x) \ 1 = z. T((x * y) / x,x) != z | z = y. (x \ y) \ (x \ 1) != z | z = y \ 1. (x \ y) \ (x \ 1) != z | y \ 1 = z. x / (y \ x) != z | z = y. (x * y) / y != z | z = x. ((x * y) * z) / a(x,y,z) != u | u = x * (y * z). ((x * y) * z) / a(x,y,z) != u | x * (y * z) = u. (x * (y * z)) / L(z,y,x) != u | u = x * y. (x * (y * z)) / L(z,y,x) != u | x * y = u. x / x != y | y = 1. x / x != y | 1 = y. (x * T(y,x)) / x != z | z = y. 1 / (x * (y \ 1)) != z | z = y / x. 1 / (x * (y \ 1)) != z | y / x = z. (1 * x) / y != z | z = x / y. (1 * x) / y != z | x / y = z. (x \ 1) / (y \ 1) != z | z = x \ y. (x \ 1) / (y \ 1) != z | x \ y = z. (x / (y \ x)) * z != u | u = y * z. (x / (y \ x)) * z != u | y * z = u. x / (y \ x) != z * u | z \ y = u. (x * (x \ y)) \ z = y \ z. (x * y) / y != z * u | x / u = z. ((x / y) * y) * z != u | u = x * z. ((x / y) * y) * z != u | x * z = u. x \ (x * y) != z * u | z \ y = u. x * (y * (y \ z)) != u | u = x * z. x * (y * (y \ z)) != u | x * z = u. R(x,y,y \ z) * z = (x * y) * (y \ z). L(x,1 / y,y) = K(y,1 / y) \ (y * ((1 / y) * x)). K(x,1 / x) \ (x * ((1 / x) * y)) = L(y,1 / x,x). (x * y) \ 1 != z | z = y \ (x \ 1). (x * y) \ 1 != z | y \ (x \ 1) = z. (x \ y) * (y \ 1) != z | z = x \ 1. (x \ y) * (y \ 1) != z | x \ 1 = z. 1 / (x \ y) = (1 / y) * x. (((1 / x) * y) * z) \ 1 = z \ (y \ x). (x \ ((1 / y) * z)) * (z \ y) = x \ 1. 1 / (x \ y) != z | z = (1 / y) * x. 1 / (x \ y) != z | (1 / y) * x = z. x / (y \ 1) = (1 / x) \ y. (x \ 1) / y = x \ (1 / y). x != (y / z) \ 1 | x = z * (y \ 1). ((x / y) \ (1 / z)) * z = y * (x \ 1). x * ((y \ 1) \ 1) = (y \ (1 / x)) \ 1. (x \ (1 / y)) \ 1 = y * ((x \ 1) \ 1). (x \ 1) / y != z | z = x \ (1 / y). (x \ 1) / y != z | x \ (1 / y) = z. R(x,y / z,z * (y \ 1)) = ((x * (y / z)) * (z * (y \ 1))) / 1. ((x * (y / z)) * (z * (y \ 1))) / 1 = R(x,y / z,z * (y \ 1)). ((1 / (x * (y \ 1))) \ z) * 1 = (x * (y \ 1)) * ((z * (y / x)) * (x * (y \ 1))). (x * (y \ 1)) * ((z * (y / x)) * (x * (y \ 1))) = ((1 / (x * (y \ 1))) \ z) * 1. (x / y) \ 1 != z | z = y * (x \ 1). (x / y) \ 1 != z | y * (x \ 1) = z. 1 / (x * y) = (1 / y) / x. (1 / x) / y = 1 / (y * x). 1 / (x * (y \ (z \ 1))) = (z * y) / x. 1 / (x * (y * (z \ 1))) = (z / y) / x. 1 / (x * (y \ z)) = ((1 / z) * y) / x. ((1 / x) * y) / z = 1 / (z * (y \ x)). ((x \ y) \ y) * (T(x,x \ y) \ z) = z. x != y * ((z / u) \ z) | x / u = y. x * ((y / z) \ y) != u | u / z = x. (x \ 1) * x != y | y = K(x \ 1,x). (x \ 1) * x != y | K(x \ 1,x) = y. x != (y * z) \ 1 | x = z \ (y \ 1). ((1 / x) \ (y * z)) \ x = z \ (y \ 1). (x \ 1) * (y \ 1) = ((1 / y) \ x) \ 1. ((1 / x) \ y) \ 1 = (y \ 1) * (x \ 1). x / (y \ 1) != z | z = (1 / x) \ y. x / (y \ 1) != z | (1 / x) \ y = z. 1 / x = (1 / (y * x)) * y. (1 / (x * y)) * x = 1 / y. 1 / T(x,y) = (1 / (x * y)) * y. (1 / (x * y)) * y = 1 / T(x,y). 1 / x = (1 / y) * (y / x). (1 / x) * (x / y) = 1 / y. ((1 / x) * y) \ 1 != z | z = y \ x. ((1 / x) * y) \ 1 != z | y \ x = z. x / y = (1 / x) \ (1 / y). (1 / x) \ (1 / y) = x / y. x / (y \ (z \ 1)) = (1 / x) \ (z * y). x / (y * (z \ 1)) = (1 / x) \ (z / y). x / (y \ z) = (1 / x) \ ((1 / z) * y). (1 / x) \ ((1 / y) * z) = x / (z \ y). (x \ (y \ 1)) / z = (y * x) \ (1 / z). (x \ y) / z = ((1 / y) * x) \ (1 / z). ((1 / x) * y) \ (1 / z) = (y \ x) / z. x != y / (z \ 1) | x = (1 / y) \ z. 1 / ((x \ 1) * y) = (1 / (1 / y)) \ x. T(1 / (x * y),x) = x \ (1 / y). (1 / (x * y)) * x != z | z = 1 / y. (1 / (x * y)) * x != z | 1 / y = z. (1 / x) / y != z | z = 1 / (y * x). (1 / x) / y != z | 1 / (y * x) = z. (1 / x) \ (1 / y) != z | z = x / y. (1 / x) \ (1 / y) != z | x / y = z. (1 / (1 / x)) * (1 / y) = 1 / (y / x). (x / y) * (z * x) = x * (((1 / y) * z) * x). x * (((1 / y) * z) * x) = (x / y) * (z * x). x * y != x * z | z = y. x != y \ (1 * (y * z)) | x = z. L(x,y,1) = x. x != y | x = y / 1. L(x,y,1) = x / 1. L(x,y,1) != z | z = x. x \ (x * y) = L(y,1,x). L(x,1,y) = x. L(x,1,y) != z | z = x. 1 = L(1,x,y). L(1,x,y) = 1. a(x,y,1) = 1. a(x,y,K(z,z)) = 1. (x * y) / y = R(x,1,y). R(x,1,y) = x. (x * y) / y = R(x,y,1). R(x,y,1) = x. R(x,y,1) != z | z = x. x != (y * (y \ z)) \ u | x = z \ u. L((x \ y) \ 1,x \ y,x) = y \ x. L(x \ 1,x,y) * z = ((y * x) \ y) * z. x * L(y \ 1,y,z) = x * ((z * y) \ z). (x * y) * L(y \ 1,y,x) = x. L(x \ 1,x,y / x) = y \ (y / x). L(T(x \ 1,y),x,z) = T((z * x) \ z,y). T((x * y) \ x,z) = L(T(y \ 1,z),y,x). R((x * y) \ x,z,u) = L(R(y \ 1,z,u),y,x). L((x * y) \ x,z,u) = L(L(y \ 1,z,u),y,x). L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z). x / L(y \ 1,y,x) = x * y. R(1 / x,x,y) * z = (y / (x * y)) * z. R(1 / x,x,x \ y) = (x \ y) / y. R(1 / (x / y),x / y,y) = y / x. R(T(1 / x,y),x,z) = T(z / (x * z),y). T(x / (y * x),z) = R(T(1 / y,z),y,x). R(1 / x,x,y) \ y = x * y. T(x,y) * z != x * y | T(y,T(x,y)) = z. x * T(T(y,x),z) != u * x | u = T(y,z). x * T(T(y,x),z) != u * x | T(y,z) = u. x * (x \ y) != z * u | z \ y = u. (x / y) * y != z * u | x / u = z. x * T(T(y,x),z) != u | T(y,z) * x = u. x * L(T(y,x),z,u) != w | L(y,z,u) * x = w. x * R(T(y,x),z,u) != w | R(y,z,u) * x = w. L(x,y,z) * x != u | x * L(x,y,z) = u. L(x,y \ 1,y) != z | z = y * ((y \ 1) * x). L(x,y \ 1,y) != z | y * ((y \ 1) * x) = z. L(x \ 1,x,1 / x) = 1 / x. L(x,y,1 / y) = (1 / y) * (y * x). (1 / x) * (x * y) = L(y,x,1 / x). K(x,1 / x) != y | y = x * (1 / x). K(x,1 / x) != y | x * (1 / x) = y. L(x,y,1 / y) != z | z = (1 / y) * (y * x). L(x,y,1 / y) != z | (1 / y) * (y * x) = z. R(x,y,y \ 1) != z | z = (x * y) * (y \ 1). R(x,y,y \ 1) != z | (x * y) * (y \ 1) = z. (x \ 1) \ (y \ 1) != z | T(y \ x,x \ 1) = z. x \ (y \ 1) != z | T(y \ (1 / x),x) = z. T(x / y,y) != z | z = y \ x. T(x / y,y) != z | y \ x = z. ((x / y) * y) / z != u | x / z = u. (x * y) \ x != z | z = L(y \ 1,y,x). (x * y) \ x != z | L(y \ 1,y,x) = z. x / L(y,1 / y,x) = x * (1 / y). ((x * y) \ x) * (L(y \ 1,y,x) \ z) = z. L(x \ 1,x,y) * (((y * x) \ y) \ z) = z. R(x,x \ 1,y) \ y = (x \ 1) * y. x / (y * x) != z | z = R(1 / y,y,x). x / (y * x) != z | R(1 / y,y,x) = z. T(x,x \ y) != z | (x \ y) \ y = z. T(x * y,K(y,x)) != z | K(y,x) \ (y * x) = z. x * y != (z \ u) \ u | x \ T(z,z \ u) = y. x \ T(y,y \ z) = x \ ((y \ z) \ z). x * y != (z * u) \ (z * (u * w)) | x \ L(w,u,z) = y. x \ L(y,x \ 1,x) = (x \ 1) * y. x != y | z * u != y | u \ x = T(z,u). x != y | z * u != y | T(z,u) = u \ x. x * y != ((z * u) * w) / (u * w) | R(z,u,w) / y = x. R(x,y,y \ 1) / (y \ 1) = x * y. (x * y) \ ((x \ (x * y)) * x) = K(y,x). K(x,y) = (y * x) \ ((y \ (y * x)) * y). x \ (y * T(y \ x,y)) = K(y \ x,y). x * K(x,x \ 1) = (x \ 1) \ 1. K(x \ 1,x) \ 1 = K(x,x \ 1). L(x \ T(y,z),x,z) = (z * x) \ (y * z). x * T(x \ (y * x),z) = T(y,z) * x. x * T(T(T(y,x),z),u) = T(T(y,z),u) * x. x * T(x \ y,z) = T(y / x,z) * x. T(x / y,z) * y = y * T(y \ x,z). x * T(y,z) = T((x * y) / x,z) * x. T((x * y) / x,z) * x = x * T(y,z). (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y). (x * T(x \ y,z)) / x = T(y / x,z). (x * T(y,z)) / x = T((x * y) / x,z). T((((x * y) / x) \ z) \ z,x) = T(y,((x * y) / x) \ z). T(x,(y * x) / y) = x. T(x,y) * z != u | u = z * T(T(x,z),y). T(x,y) * z != u | z * T(T(x,z),y) = u. T(T(x,y),z) != u | u = T(T(x,z),y). T(T(x,y),z) != u | T(T(x,z),y) = u. (x \ y) * x != y * z | K(x \ y,x) = z. L(K(x \ y,x),y,z) = (z * y) \ (z * ((x \ y) * x)). (x * y) \ (x * ((z \ y) * z)) = L(K(z \ y,z),y,x). x \ ((y \ x) * y) != z | z = K(y \ x,y). x \ ((y \ x) * y) != z | K(y \ x,y) = z. K(x \ y,x) * z != (x \ y) * x | T(y,K(x \ y,x)) = z. x \ (y * (x / y)) != z | z = K(y,x / y). x \ (y * (x / y)) != z | K(y,x / y) = z. T(x,y) \ (y \ 1) = y \ (x \ 1). x \ (L(x,y,z) \ 1) = (x * L(x,y,z)) \ 1. (x * L(x,y,z)) \ 1 = x \ (L(x,y,z) \ 1). x * (y \ 1) = 1 / T(x \ y,y \ 1). 1 / T(x \ y,y \ 1) = x * (y \ 1). x != (y \ z) \ z | x = T(y,y \ z). x * K(x,x \ 1) = T(x,x \ 1). (x * y) * K(x * y,y \ (x \ 1)) = ((x * y) \ 1) \ 1. x \ ((x \ 1) \ 1) != y | y = K(x,x \ 1). x \ ((x \ 1) \ 1) != y | K(x,x \ 1) = y. x * y != K(z \ 1,z) \ 1 | x \ K(z,z \ 1) = y. x \ K(y,y \ 1) = (K(y \ 1,y) * x) \ 1. (K(x \ 1,x) * y) \ 1 = y \ K(x,x \ 1). T(T(x,y),z) \ (y \ 1) = y \ (T(x,z) \ 1). (x * y) * L(z,y,x) != x * u | u = y * z. (x * y) * L(z,y,x) != x * u | y * z = u. x * y != z * u | u = z \ (x * y). x * y != z * u | z \ (x * y) = u. x \ (x * y) != z * u | z = y / u. x \ (x * y) != z * u | y / u = z. x * y != z * (u * (u \ w)) | (z * w) / y = x. (x * y) / L(z \ y,z,x) = x * z. x * y != z * (u * (u \ (z \ (x * w)))) | y = w. L(x \ (y \ ((y * x) * z)),x,y) = z. x * ((x \ y) * z) = y * L(z,x \ y,x). x * L(y,z \ x,z) = z * ((z \ x) * y). (x / y) * (y * z) = x * L(z,y,x / y). x * L(y,z,x / z) = (x / z) * (z * y). x * y != (z * u) * L(w,u,z) | (z * (u * w)) / y = x. (x * (y * z)) / T(x * y,L(z,y,x)) = L(z,y,x). x * (y * z) != (x * y) * u | L(z,y,x) = u. (x * y) * z != x * (y * u) | L(u,y,x) = z. L(x,L(y,z,u),u * z) = (u * (z * y)) \ ((u * z) * (L(y,z,u) * x)). (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y). L(L(x,y,z),z * y,u) = (u * (z * y)) \ (u * (z * (y * x))). (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). R(x * y,L(z,y,x),u) = ((x * (y * z)) * u) / (L(z,y,x) * u). ((x * (y * z)) * u) / (L(z,y,x) * u) = R(x * y,L(z,y,x),u). (x * y) * T(L(z,y,x),u) = x * (y * T(z,u)). (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w)). (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)). (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z). (x * (y * z)) * K(L(z,y,x),x * y) = L(z,y,x) * (x * y). K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y). (x * y) \ (x * (y * z)) != u | u = L(z,y,x). (x * y) \ (x * (y * z)) != u | L(z,y,x) = u. x * ((x \ 1) * y) != z | L(y,x \ 1,x) = z. (1 / x) * (x * y) != z | L(y,x,1 / x) = z. T(x,x \ 1) * L(y,K(x,x \ 1),x) = x * (K(x,x \ 1) * y). L((x \ y) \ z,x \ y,x) = y \ (x * z). x != (y * (y \ 1)) \ z | x = z. L((x \ 1) \ y,x \ 1,x) = x * y. L(x \ y,x,1 / x) = (1 / x) * y. L(x \ y,x,z / x) = z \ ((z / x) * y). L(x \ y,x,z / y) = ((z / y) * x) \ z. L(a(x,y,z),x * (y * z),u) = (u * (x * (y * z))) \ (u * ((x * y) * z)). (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),y * (z * u),x). L(T(x \ y,z),x,u) = T((u * x) \ (u * y),z). T((x * y) \ (x * z),u) = L(T(y \ z,u),y,x). L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z). L(x \ (y / z),x,1 / y) = ((1 / y) * x) \ (1 / z). L((x \ 1) \ y,x \ 1,x) != z | z = x * y. L((x \ 1) \ y,x \ 1,x) != z | x * y = z. L(L(x,y,z) \ u,L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * u). L(x \ L(y,z,u),x,u * z) = ((u * z) * x) \ (u * (z * y)). x * y != (z * (z \ u)) * w | x \ (u * w) = y. R(x,x \ y,z) \ (y * z) = (x \ y) * z. x * y != ((z / u) * u) * w | x \ (z * w) = y. R(x / y,y,z) \ (x * z) = y * z. x * y != R(z,u,w) * (u * w) | x \ ((z * u) * w) = y. (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z)). R(x,y / z,z) * y = (x * (y / z)) * z. (x * y) * z != u * (y * z) | R(x,y,z) = u. K(x * y,R(z,x,y)) = ((z * x) * y) \ ((x * y) * R(z,x,y)). ((x * y) * z) \ ((y * z) * R(x,y,z)) = K(y * z,R(x,y,z)). R(R(x,y,z),y * z,u) = (((x * y) * z) * u) / ((y * z) * u). (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u). R(x,R(y,z,u),z * u) = ((x * R(y,z,u)) * (z * u)) / ((y * z) * u). ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u). T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z. L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y). ((x * y) * z) * K(y * z,R(x,y,z)) = (y * z) * R(x,y,z). R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y. ((x * y) * z) / (y * z) != u | u = R(x,y,z). ((x * y) * z) / (y * z) != u | R(x,y,z) = u. (R(x,y,z) * (y * z)) / z != u | u = x * y. (R(x,y,z) * (y * z)) / z != u | x * y = u. (x * y) * (y \ 1) != z | z = R(x,y,y \ 1). (x * y) * (y \ 1) != z | R(x,y,y \ 1) = z. R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u). x != y / ((1 / z) * z) | x = y. R(x / (1 / y),1 / y,y) = x * y. x != y / (z * (z \ 1)) | x = y. R(x / y,y,y \ 1) = x * (y \ 1). R(x / y,y,x \ z) = z / (y * (x \ z)). R(x / (y / z),y / z,z) = (x * z) / y. T(R(x / y,y,z),y * z) = (y * z) \ (x * z). R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z)). R(x / y,y,x \ z) \ z = y * (x \ z). R(R(1 / x,x,y),x * y,z) = (y * z) / ((x * y) * z). R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z)). R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u). R(R(x / y,y,z),y * z,u) = ((x * z) * u) / ((y * z) * u). (x * y) / L(z,y / z,x) = x * (y / z). (x * (y * z)) / L(T(y,z),z,x) = x * z. (x * (y * z)) / L(K(y,z),z * y,x) = x * (z * y). R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z. R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z. R(x,K(y \ x,y),z) \ (((y \ x) * y) * z) = K(y \ x,y) * z. R(x,x \ 1,x) = x / K(x \ 1,x). x / K(x \ 1,x) = R(x,x \ 1,x). L(x,1 / x,x) = K(x,1 / x) \ x. K(x,1 / x) \ x = L(x,1 / x,x). x * y != L(L(z,u,w),v5,v6) | x \ L(L(z,v5,v6),u,w) = y. x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u). x * y != L(R(z,u,w),v5,v6) | x \ R(L(z,v5,v6),u,w) = y. x \ R(L(y,x \ 1,x),z,u) = (x \ 1) * R(y,z,u). x * y != L(T(z,u),w,v5) | x \ T(L(z,w,v5),u) = y. x \ T(L(y,x \ 1,x),z) = (x \ 1) * T(y,z). x * (y * (x \ 1)) = L(T(y,x \ 1),x \ 1,x). L(T(x,y \ 1),y \ 1,y) = y * (x * (y \ 1)). x * y != R(L(z,u,w),v5,v6) | L(R(z,v5,v6),u,w) / y = x. L(R(x,y,y \ 1),z,u) / (y \ 1) = L(x,z,u) * y. x * y != R(R(z,u,w),v5,v6) | R(R(z,v5,v6),u,w) / y = x. R(R(x,1 / y,y),z,u) / y = R(x,z,u) * (1 / y). x * y != R(T(z,u),w,v5) | T(R(z,w,v5),u) / y = x. T(R(x,1 / y,y),z) / y = T(x,z) * (1 / y). L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u). R((x * y) \ z,u,w) = L(R(y \ (x \ z),u,w),y,x). L(R(x \ (y \ z),u,w),x,y) = R((y * x) \ z,u,w). L((x * y) \ z,u,w) = L(L(y \ (x \ z),u,w),y,x). L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w). L(x,(y \ z) / x,y) = (y * ((y \ z) / x)) \ z. x * (y * (y \ z)) != u * w | (x * z) / w = u. ((x / y) * y) * z != u * w | u \ (x * z) = w. (x * y) / y != z * u | z \ x = u. (x \ y) * (y \ 1) != z * u | z \ (x \ 1) = u. R(x,y,z) \ ((x * y) * z) != u * w | u \ (y * z) = w. (x * y) \ (x * (y * z)) != u * w | u \ L(z,y,x) = w. 1 / (x * y) != z | (1 / y) / x = z. (x * (x \ y)) * z != u | y * z = u. (x * T(y,x)) / x != z * u | z \ y = u. (((x * y) / z) * z) / y != u * w | x / w = u. x \ (y * (y \ (x * z))) != u * w | u \ z = w. x \ 1 != y | (z \ x) \ (z \ 1) = y. (x \ 1) * ((y \ 1) \ 1) != z | (y \ x) \ 1 = z. (x \ (y \ 1)) / z != u | (y * x) \ (1 / z) = u. (x * (y \ 1)) / z != u | (y / x) \ (1 / z) = u. (x \ y) \ 1 != z | (y \ 1) * ((x \ 1) \ 1) = z. x / (y \ (z \ 1)) != u | (1 / x) \ (z * y) = u. x / (y * (z \ 1)) != u | (1 / x) \ (z / y) = u. (1 / x) * y != z | 1 / (y \ x) = z. ((1 / x) * y) / z != u | 1 / (z * (y \ x)) = u. (1 / x) \ y != z | x / (y \ 1) = z. ((1 / x) * y) \ (1 / z) != u | (y \ x) / z = u. (1 / x) \ ((1 / y) * z) != u | x / (z \ y) = u. L(T(x \ 1,y),x,z / x) = T(z \ (z / x),y). T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y). R(T(1 / x,y),x,x \ z) = T((x \ z) / z,y). T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y). R(R(1 / x,x,x \ y),y,z) = ((x \ y) * z) / (y * z). x * (y * (y \ (x \ z))) != u * w | u \ z = w. x * (y * (y \ z)) != u * w | u \ (x * z) = w. (((x / y) / z) * z) * y != u * w | x / w = u. ((x / y) * y) * z != u * w | (x * z) / w = u. (1 / x) \ L(L(y,x,1 / x),z,u) = x * L(y,z,u). (1 / x) * (y * x) = L(T(y,x),x,1 / x). L(T(x,y),y,1 / y) = (1 / y) * (x * y). (1 / x) \ L(y,x,1 / x) != z | z = x * y. (1 / x) \ L(y,x,1 / x) != z | x * y = z. R((x / y) / z,z,y) != u | x / (z * y) = u. R(T(x,R(x,y,z) \ u),y,z) != w | (R(x,y,z) \ u) \ u = w. T(x \ y,T(x,x \ y)) != z | ((x \ y) \ y) \ y = z. (x * (x \ y)) * z != u * w | u \ (y * z) = w. (x * y) \ x != z * u | L(y \ 1,y,x) / u = z. x != (y \ 1) * y | x = K(y \ 1,y). ((x \ 1) * y) / L(x \ y,x,x \ 1) = K(x \ 1,x). (x * y) \ (x * z) != u | u = L(y \ z,y,x). (x * y) \ (x * z) != u | L(y \ z,y,x) = u. L(T((x \ 1) \ y,z),x \ 1,x) = T(x * y,z). L(T(x \ y,z),x,1 / x) = T((1 / x) * y,z). R((1 / x) * y,z,u) = L(R(x \ y,z,u),x,1 / x). L(R(x \ y,z,u),x,1 / x) = R((1 / x) * y,z,u). L((1 / x) * y,z,u) = L(L(x \ y,z,u),x,1 / x). L(L(x \ y,z,u),x,1 / x) = L((1 / x) * y,z,u). R(T(x / (1 / y),z),1 / y,y) = T(x * y,z). R(T(x / y,z),y,y \ 1) = T(x * (y \ 1),z). R(x * (y \ 1),z,u) = R(R(x / y,z,u),y,y \ 1). R(R(x / y,z,u),y,y \ 1) = R(x * (y \ 1),z,u). K(x,1 / x) * L(x,1 / x,x) = x. ((x / y) \ x) * z != u | y * z = u. ((1 / x) \ y) * x = x * (y * x). (x * (y * x)) / x = (1 / x) \ y. T((1 / x) \ y,x) = y * x. (((1 / x) * y) \ z) * (y \ x) = (y \ x) * (z * (y \ x)). (x / y) * x = x * ((1 / y) * x). x * ((1 / y) * x) = (x / y) * x. T(x,y) = ((1 / y) * x) * y. T(x \ y,x \ 1) = y * (x \ 1). T(((1 / x) * y) \ z,y \ x) = z * (y \ x). T(x / (y \ 1),x) = y * x. T(x / y,x) = (1 / y) * x. x * (y * x) != z | ((1 / x) \ y) * x = z. x * y != ((1 / z) * u) * z | T(u,z) / y = x. T(x,y) / y = (1 / y) * x. x * y != T(z,L(z,u,w)) | z / y = x. x / L(x,y,z) = (1 / L(x,y,z)) * x. (1 / L(x,y,z)) * x = x / L(x,y,z). x * y != T(T(z,u),T(z,w)) | T(z,u) / y = x. T(x,y) / T(x,z) = (1 / T(x,z)) * T(x,y). (1 / T(x,y)) * T(x,z) = T(x,z) / T(x,y). x * y != T(z,T(z,u)) | z / y = x. x / T(x,y) = (1 / T(x,y)) * x. (1 / T(x,y)) * x = x / T(x,y). x * y != T(L(z,u,w),z) | L(z,u,w) / y = x. L(x,y,z) / x = (1 / x) * L(x,y,z). (1 / x) * L(x,y,z) = L(x,y,z) / x. x * y != T(T(z,u),z) | T(z,u) / y = x. T(x,y) / x = (1 / x) * T(x,y). (1 / x) * T(x,y) = T(x,y) / x. x * y != T(z / u,u) | (u \ z) / y = x. (x \ y) / x = (1 / x) * (y / x). (1 / x) * (y / x) = (x \ y) / x. T(x,y \ 1) = (y * x) * (y \ 1). (x * y) * (x \ 1) = T(y,x \ 1). T(x,x * y) = (1 / y) * (x * y). T((1 / x) \ y,x) != z | y * x = z. x != (1 / y) * z | x = 1 / (z \ y). T(x / y,x) = 1 / (x \ y). T(x / y,x) * z = ((1 / y) * x) * z. T(x / y,x) \ 1 = x \ y. x * T((1 / y) * x,z) = T(x / y,z) * x. T(x / y,x) != z * u | z \ ((1 / y) * x) = u. T(x,y) = T(x / y,x) * y. T(x / y,x) * y = T(x,y). x != (1 / y) * z | x = T(z / y,z). T(x,y) / y = T(x / y,x). T(x / y,x) = T(x,y) / y. x != (y / (z \ y)) * u | x = z * u. T(x,y \ 1) / (y \ 1) = y * x. x * (T(y,z) / z) = x * ((1 / z) * y). T(T((1 / x) * y,z),x) = T(x \ T(y,x),z). T(x / y,x) != z | (1 / y) * x = z. T(x,y) \ 1 = y \ (x \ y). T(x,x * y) * y = T(x * y,y). T(x / y,x) * y != z | z = T(x,y). T(x / y,x) * y != z | T(x,y) = z. x * (T(y,x) \ 1) = y \ x. (x \ y) \ 1 = x \ ((y / x) \ x). x \ ((y / x) \ x) = (x \ y) \ 1. T(x,y) \ 1 = x \ (T(x,y) \ x). x \ (T(x,y) \ x) = T(x,y) \ 1. x * ((x \ y) \ 1) = (y / x) \ x. x * (T(x,y) \ 1) = T(x,y) \ x. T(x,y) * (x \ 1) = x \ T(x,y). x * (y \ 1) = ((x * y) / x) \ x. ((x * y) / x) \ x = x * (y \ 1). x * (L(x,y,z) \ 1) = L(x,y,z) \ x. L(x,y,z) * (x \ 1) = x \ L(x,y,z). T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y). x * (((y * x) / y) \ 1) = ((y * x) / y) \ x. ((x * y) / x) * (y \ 1) = y \ ((x * y) / x). x * ((x \ (1 / y)) \ 1) = (1 / (x * y)) \ x. (x * y) / x = (1 / x) \ (y / x). (1 / x) \ (y / x) = (x * y) / x. ((1 / x) \ y) * x != z | z = x * (y * x). ((1 / x) \ y) * x != z | x * (y * x) = z. x * (((1 / y) * z) * x) = (x / (z \ y)) * x. x * (1 / y) = (x / (x * y)) * x. (x / (x * y)) * x = x * (1 / y). T(a(x,y,z),(x * (y * z)) \ 1) = ((x * y) * z) * ((x * (y * z)) \ 1). ((x * y) * z) * ((x * (y * z)) \ 1) = T(a(x,y,z),(x * (y * z)) \ 1). T(L(x,y,z),(z * y) \ 1) = (z * (y * x)) * ((z * y) \ 1). (x * (y * z)) * ((x * y) \ 1) = T(L(z,y,x),(x * y) \ 1). T(T(x,y),y \ 1) = (x * y) * (y \ 1). x * (1 / x) = T(x,1 / x) / x. T(x,1 / x) / x = x * (1 / x). T(1 / x,T(x,y)) = T(x,y) \ (T(x,y) / x). T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y)). T(x \ 1,y) / (x \ 1) != z | x * T(x \ 1,y) = z. x != T(L(y,z,u),y) | x = L(y,z,u). (x * L(x \ 1,y,z)) * (x \ 1) = L(x \ 1,y,z). T(x * y,x \ 1) = (x \ 1) \ T(y,x \ 1). (x \ 1) \ T(y,x \ 1) = T(x * y,x \ 1). x * y != T((z * u) / z,u) | ((z * u) / z) / y = x. ((x * (y \ 1)) / x) / (y \ 1) = y * ((x * (y \ 1)) / x). L(x \ 1,y,z) / (x \ 1) = x * L(x \ 1,y,z). 1 / T(x,y \ 1) = y / (y * x). T(x \ y,x \ 1) != z | y * (x \ 1) = z. (1 / T(x,y \ 1)) \ y = y * x. (x * y) * (x \ 1) != z | z = T(y,x \ 1). (x * y) * (x \ 1) != z | T(y,x \ 1) = z. x * ((x \ y) \ 1) != z | z = (y / x) \ x. x * ((x \ y) \ 1) != z | (y / x) \ x = z. x != y * (z \ 1) | x = T(z \ y,z \ 1). x \ T(x,y) = T(x \ T(x,y),x \ 1). T(x \ T(x,y),x \ 1) = x \ T(x,y). (x \ T(x,y)) \ 1 = (x \ 1) \ (T(x,y) \ 1). (x \ 1) \ (T(x,y) \ 1) = (x \ T(x,y)) \ 1. x / (x * (y \ 1)) = (x * y) / x. (x * (1 / y)) / x = x / (x * y). (x * (1 / y)) / x != z * u | z \ (x / (x * y)) = u. x != y * (1 / y) | x = K(y,1 / y). T(x,1 / x) / x = K(x,1 / x). (1 / x) \ (y / (y * z)) != u | x / T(z,y \ 1) = u. (1 / T(x,y \ (z \ 1))) \ (z * y) = (z * y) * x. (x \ 1) \ x = x * x. (x \ y) \ ((1 / y) * x) = ((1 / y) * x) * ((1 / y) * x). ((1 / x) * y) * ((1 / x) * y) = (y \ x) \ ((1 / x) * y). ((x * y) / x) \ x != z | z = x * (y \ 1). ((x * y) / x) \ x != z | x * (y \ 1) = z. x / (x * (y \ z)) = (x * ((1 / z) * y)) / x. (x * ((1 / y) * z)) / x = x / (x * (z \ y)). ((x / y) \ x) * z != u | T(u / y,(x / y) \ x) = z. T(x / y,(z / y) \ z) = y \ x. (x * y) * z != (u * x) * L(y,x,u) | T(u,x * y) = z. T((x * y) / x,x * y) = L(y,x,(x * y) / x). x != (y * z) * L(u,z,y) | x = y * (z * u). L(x,y,z) * (z * y) = z * (y * T(x,z * y)). x * (y * T(z,x * y)) = L(z,y,x) * (x * y). x * L(x \ (y * x),z,u) = L(y,z,u) * x. x * L(R(T(y,x),z,u),w,v5) = L(R(y,z,u),w,v5) * x. x * L(x \ y,z,u) = L(y / x,z,u) * x. L(x / y,z,u) * y = y * L(y \ x,z,u). x * L(T(x,y),z,u) = L(T(x,y),z,u) * x. L(T(x,y),z,u) * x = x * L(T(x,y),z,u). x * L(y,z,u) = L((x * y) / x,z,u) * x. L((x * y) / x,z,u) * x = x * L(y,z,u). (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y). x != R(y,z,u) * (z * u) | x = (y * z) * u. (x * y) * R(T(z,x * y),x,y) = (z * x) * y. (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). R(x,y,z) * u != u * w | R(T(x,u),y,z) = w. x * R(x,y,z) = R(x,y,z) * x. R(x,y,z) * x = x * R(x,y,z). x * R(x \ y,z,u) = R(y / x,z,u) * x. R(x / y,z,u) * y = y * R(y \ x,z,u). x * R(T(x,y),z,u) = R(T(x,y),z,u) * x. R(T(x,y),z,u) * x = x * R(T(x,y),z,u). x * R(y,z,u) = R((x * y) / x,z,u) * x. R((x * y) / x,z,u) * x = x * R(y,z,u). (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). (x / y) * R(y,z,u) = R(x / (x / y),z,u) * (x / y). R(x / (x / y),z,u) * (x / y) = (x / y) * R(y,z,u). T(x,R(x,y,z)) = x. (x * R(x,y,z)) * u != R(x,y,z) * x | 1 = u. 1 = K(R(x,y,z),x). K(R(x,y,z),x) = 1. x * y != T(z,R(z,u,w)) | z / y = x. x / R(x,y,z) = (1 / R(x,y,z)) * x. (1 / R(x,y,z)) * x = x / R(x,y,z). x \ 1 = R(x,y,z) \ (x \ R(x,y,z)). R(x,y,z) \ (x \ R(x,y,z)) = x \ 1. R(x,y,z) * (x \ 1) = x \ R(x,y,z). x * K(R(y,z,u),y) = x. x * y != T(L(z / u,w,v5),u) | L(u \ z,w,v5) / y = x. L(x \ y,z,u) / x = (1 / x) * L(y / x,z,u). (1 / x) * L(y / x,z,u) = L(x \ y,z,u) / x. (x * L(x \ y,z,u)) / x = L(y / x,z,u). (x * R(x \ y,z,u)) / x = R(y / x,z,u). T(x / (y * x),y) = R(y \ 1,y,x). T((x * y) / (z * y),z) = R(z \ x,z,y). T(x / (y * z),y) = R(y \ (x / z),y,z). R(x \ (y / z),x,z) = T(y / (x * z),x). ((x \ y) \ y) \ z = T(x,x \ y) \ z. T(x,x \ y) \ z = ((x \ y) \ y) \ z. K(x,(y \ z) \ z) = (T(y,y \ z) * x) \ (x * ((y \ z) \ z)). (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,(x \ y) \ y). L(x,y,(z \ u) \ u) = (T(z,z \ u) * y) \ (((z \ u) \ u) * (y * x)). (T(x,x \ y) * z) \ (((x \ y) \ y) * (z * u)) = L(u,z,(x \ y) \ y). x != (y / z) * z | x = y. (x / ((y \ z) \ z)) * T(y,y \ z) = x. x * y != z * T(u,u \ w) | x \ (z * ((u \ w) \ w)) = y. (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,T(x,x \ y)). x * ((y \ z) \ z) != u | x * T(y,y \ z) = u. x != y * ((z \ u) \ u) | x = y * T(z,z \ u). (x \ y) \ 1 = (y \ 1) * T(x,x \ 1). (x \ 1) * T(y,y \ 1) = (y \ x) \ 1. R(x,y \ 1,(z \ 1) \ 1) = ((x * (y \ 1)) * ((z \ 1) \ 1)) / ((z \ y) \ 1). ((x * (y \ 1)) * ((z \ 1) \ 1)) / ((z \ y) \ 1) = R(x,y \ 1,(z \ 1) \ 1). (x \ 1) * ((y \ (z \ 1)) \ 1) = ((z * y) \ x) \ 1. (x * (y \ 1)) * ((z \ 1) \ 1) = (z \ (y / x)) \ 1. (x \ y) * ((z \ 1) \ 1) = (z \ ((1 / y) * x)) \ 1. (x \ ((1 / y) * z)) \ 1 = (z \ y) * ((x \ 1) \ 1). (x \ 1) * ((y \ z) \ 1) = (((1 / z) * y) \ x) \ 1. (((1 / x) * y) \ z) \ 1 = (z \ 1) * ((y \ x) \ 1). 1 / (x * (y \ (z \ u))) = (((1 / u) * z) * y) / x. (((1 / x) * y) * z) / u = 1 / (u * (z \ (y \ x))). x / (y \ (z \ u)) = (1 / x) \ (((1 / u) * z) * y). (1 / x) \ (((1 / y) * z) * u) = x / (u \ (z \ y)). x * y != ((1 / z) * u) \ 1 | (u \ z) / y = x. (x \ y) / (z \ u) = ((1 / y) * x) \ ((1 / u) * z). ((1 / x) * y) \ ((1 / z) * u) = (y \ x) / (u \ z). x * y != 1 / (z * (u * (w \ 1))) | x \ ((w / u) / z) = y. (1 / x) \ ((y / z) / u) = x / (u * (z * (y \ 1))). x / (y * (z * (u \ 1))) = (1 / x) \ ((u / z) / y). x / (y \ (z \ (u \ 1))) = (1 / x) \ ((u * z) * y). x != ((y * z) * u) / (z * u) | x = R(y,z,u). (1 / ((x * y) * (z \ 1))) \ (z / y) = R(x,y,z \ 1). x / ((y / z) \ z) = (1 / x) \ ((z \ y) / z). (1 / x) \ ((y \ z) / y) = x / ((z / y) \ y). K(x \ 1,x) \ (x \ 1) != y | L(x \ 1,x,x \ 1) = y. T(x,y) / (x * y) != z | R(1 / y,y,T(x,y)) = z. ((x \ y) \ y) / T(z,z \ T(x,x \ y)) = z \ ((x \ y) \ y). x != y \ ((z \ y) * z) | x = K(z \ y,z). K(x,y) = K(y \ (y * x),y). K(x \ (x * y),x) = K(y,x). K(x,y) = K(z \ (z * x),y). K(x \ (x * y),z) = K(y,z). K((x / y) \ x,z) = K(y,z). K(x \ (y \ 1),z) = K((y * x) \ 1,z). K((x * y) \ 1,z) = K(y \ (x \ 1),z). T(x,y) = y * T(y \ x,x). x * T(x \ y,y) = T(y,x). x * y != T(z / u,z) * u | x \ T(z,u) = y. x \ T(y,x) = T(x \ y,y). T(x \ y,y) = x \ T(y,x). T(x,y * T(y \ x,x)) = x. T(x / y,z) * y != u | u = y * T(y \ x,z). T(x / y,z) * y != u | y * T(y \ x,z) = u. T(T(x / y,z),y) != u | u = T(y \ x,z). T(T(x / y,z),y) != u | T(y \ x,z) = u. x * ((y * T(z,x)) / y) = ((y * z) / y) * x. (x * (y \ z)) / x = T((x * (z / y)) / x,y). T((x * (y / z)) / x,z) = (x * (z \ y)) / x. T((x * y) / x,z) * x != u | u = x * T(y,z). T((x * y) / x,z) * x != u | x * T(y,z) = u. x != 1 / T(y,z \ 1) | x = z / (z * y). x * (y \ 1) = y / (y * (x \ y)). x / (x * (y \ x)) = y * (x \ 1). (x * (y \ 1)) \ y = y * (x \ y). x / (x * y) = (x / y) * (x \ 1). (x / y) * (x \ 1) = x / (x * y). (x * y) \ (1 / y) = (1 / y) * (x \ (1 / y)). (1 / x) * (y \ (1 / x)) = (y * x) \ (1 / x). (x \ 1) \ y = y * ((x \ y) \ y). x * ((y \ x) \ x) = (y \ 1) \ x. (x \ T(x,y)) \ x = x * (T(x,y) \ x). x \ ((y \ 1) \ x) = (y \ x) \ x. x * y != z \ x | y = T(z,x) \ 1. (x \ y) \ y = T(x \ 1,y) \ 1. T(x \ 1,y) \ 1 = (x \ y) \ y. (x \ 1) \ y = y * T(x,x \ y). x * T(y,y \ x) = (y \ 1) \ x. (x \ 1) \ y != y * z | (x \ y) \ y = z. x \ (y \ x) = ((1 / y) \ x) \ x. ((1 / x) \ y) \ y = y \ (x \ y). x * ((y \ x) \ x) != z | z = (y \ 1) \ x. x * ((y \ x) \ x) != z | (y \ 1) \ x = z. 1 / ((x \ y) \ y) = T(x \ 1,y). x / (x \ (y \ x)) = (1 / y) \ x. (1 / x) * (y \ x) = T(y \ 1,x). 1 / T(x,x \ y) = T(x \ 1,y). x / (x \ y) = (1 / (x / y)) \ x. (1 / (x / y)) \ x = x / (x \ y). x / (T(y,x) \ 1) = (1 / y) \ x. 1 / x = T(x \ 1,x). T(x \ 1,x) = 1 / x. T(x \ 1,x) != y | 1 / x = y. x * (1 / x) = (x \ 1) * x. (x \ 1) * x = x * (1 / x). x * T(1 / x,y) = T(x \ 1,y) * x. T(x \ 1,y) * x = x * T(1 / x,y). 1 / T(x,y) = T(x \ 1,x * y). T(x \ 1,x * y) = 1 / T(x,y). 1 / (x / (x \ y)) = (1 / x) * (1 / (x / y)). (1 / x) * (1 / (x / y)) = 1 / (x / (x \ y)). (1 / x) \ T(y,x) = (1 / y) \ x. T((1 / x) \ y,y) = T(x,y) * y. (1 / x) \ L(x,y,z) = (1 / L(x,y,z)) \ x. (1 / L(x,y,z)) \ x = (1 / x) \ L(x,y,z). x * (y \ 1) != T(z,y \ 1) | x = y * z. T(x,y \ 1) = y * ((1 / x) \ (y \ 1)). x * ((1 / y) \ (x \ 1)) = T(y,x \ 1). T(x * y,x) = T(T(y,x \ 1),x) * x. T(T(x,y \ 1),y) * y = T(y * x,y). (x / L(x,y,z)) / x = 1 / L(x,y,z). (L(x,y,z) / x) / L(x,y,z) = 1 / x. L(L(x,y,z) \ u,L(x,y,z),1 / x) = (L(x,y,z) / x) \ ((1 / x) * u). x != (y * z) * (z \ 1) | x = R(y,z,z \ 1). T(T(x,y),y \ 1) = R(x,y,y \ 1). T(T(x,y / z),z * (y \ 1)) = R(x,y / z,(y / z) \ 1). (x \ R(x,y,z)) * K(x \ 1,R(x,y,z)) = (x \ 1) * R(x,y,z). (x \ R(x,y,z)) \ 1 != u | (x \ 1) \ (R(x,y,z) \ 1) = u. T(T(x,y),y \ 1) * y = T(y * x,y). (1 / L(x,y,z)) * x != u | u = x / L(x,y,z). (1 / L(x,y,z)) * x != u | x / L(x,y,z) = u. x * y != T(z,y) | x = (1 / y) * z. T(T(x,y),y \ 1) = (1 / y) * (y * x). R(x,y,y \ 1) * y = T(y * x,y). x * y != (z * (z \ u)) * w | (u * w) / y = x. (x * y) / a(z,z \ x,y) = z * ((z \ x) * y). (x * y) * a(x,y / z,z) = (x * (y / z)) * z. (x * (y * z)) \ ((x * y) * z) != u | u = a(x,y,z). (x * (y * z)) \ ((x * y) * z) != u | a(x,y,z) = u. ((x * y) * z) * a(R(x,y,z),y,z) = (R(x,y,z) * y) * z. R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z. x \ R(x,1 / y,y) = a(x,1 / y,y). T(x,x * y) = L(T(x,y),y,x). L(T(x,y),y,x) = T(x,x * y). L(T(x,y),y,x) != z | T(x,x * y) = z. (R(x,y,z) * z) \ ((x * y) * z) = L(T(y,z),z,R(x,y,z)). x != L(T(y,z),u,w) | x = T(L(y,u,w),z). T(x,x * y) = T(L(x,y,x),y). T(L(x,y,x),y) = T(x,x * y). L(T(T(x,y),z),y,x) = T(T(x,x * y),z). R(T(x,x * y),z,u) = L(R(T(x,y),z,u),y,x). L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u). L(T(x,x * y),z,u) = L(L(T(x,y),z,u),y,x). L(L(T(x,y),z,u),y,x) = L(T(x,x * y),z,u). x * T(y,y * x) = L(y,x,y) * x. (x * y) * R(L(T(x,y),y,x),z,u) = R(x,z,u) * (x * y). (x * T(y,y * x)) / x = L(y,x,y). x * y != y * T(z,u) | x = T((y * z) / y,u). L(x,y,x) = T((y * x) / y,x * y). T((x * y) / x,y * x) = L(y,x,y). (x \ y) * T(x,y) = L(x,x \ y,x) * (x \ y). L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). T(x,y) * T(y,x * y) = L(y,T(x,y),y) * T(x,y). L(x,T(y,x),x) * T(y,x) = T(y,x) * T(x,y * x). T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x). T(L(x,y,x),z) = T(T((y * x) / y,z),x * y). T(T((x * y) / x,z),y * x) = T(L(y,x,y),z). T((L(x,y,z) * (1 / x)) / L(x,y,z),L(x,y,z) / x) = L(1 / x,L(x,y,z),1 / x). T(R(x,y,K(y,x)),z) * (y * K(y,x)) = (y * K(y,x)) * T((y * K(y,x)) \ (y * x),z). (x * K(x,y)) * T((x * K(x,y)) \ (x * y),z) = T(R(y,x,K(x,y)),z) * (x * K(x,y)). L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z). (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). (x / (y * x)) * (R(1 / y,y,x) \ z) = z. (x * y) \ y = R(T(1 / x,x * y),x,y). R(T(1 / x,x * y),x,y) = (x * y) \ y. (x / y) * T(y,z) != u * (x / y) | T(x / (x / y),z) = u. x * T(x \ (y * x),z) != u | T(y,z) * x = u. L(x \ 1,x,y) != z | (y * x) \ y = z. x != (y * z) \ (z * y) | x = K(z,y). L(x \ T(x,y),x,y) = K(x,y). K(x,y) = L(x \ T(x,y),x,y). L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u). L(x \ T(x,y),x,y) != z | K(x,y) = z. x \ (y * T(y \ x,y)) != z | K(y \ x,y) = z. x != y * L(T(z,y),u,w) | x = L(z,u,w) * y. x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y. x * ((x \ y) * z) != y * u | L(z,x \ y,x) = u. x * L(L(y,z \ x,z),u,w) = z * ((z \ x) * L(y,u,w)). x \ (y * ((y \ x) * z)) != u | u = L(z,y \ x,y). x \ (y * ((y \ x) * z)) != u | L(z,y \ x,y) = u. x * L(L(y,z,x / z),u,w) = (x / z) * (z * L(y,u,w)). L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u). R(x \ (y * z),u,w) = L(R((y \ x) \ z,u,w),y \ x,y). L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w). (x * y) / ((z \ x) * y) != u | u = R(z,z \ x,y). (x * y) / ((z \ x) * y) != u | R(z,z \ x,y) = u. R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u). R((x * y) / z,u,w) = R(R(x / (z / y),u,w),z / y,y). R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w). T((x * y) / z,z / y) = R((z / y) \ x,z / y,y). R((x / y) \ z,x / y,y) = T((z * y) / x,x / y). (x * y) \ (x * (z * y)) != u | u = L(T(z,y),y,x). (x * y) \ (x * (z * y)) != u | L(T(z,y),y,x) = u. T(x,y \ 1) != z | (y * x) * (y \ 1) = z. T(((x * y) * z) / (x * z),x) = R(y,x,z). R(x,y,z) = T(((y * x) * z) / (y * z),y). T((x * (y \ z)) / z,y) = R(y \ x,y,y \ z). T(x / (y * (y \ z)),y) * z = ((y \ (x / (y \ z))) * y) * (y \ z). ((x \ (y / (x \ z))) * x) * (x \ z) = T(y / (x * (x \ z)),x) * z. T(R(x \ y,x,z),x * z) != u | T((x * z) \ (y * z),x) = u. x * T(y,y \ x) != z | (y \ 1) \ x = z. (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z)). ((x \ y) / y) * (R(1 / x,x,x \ y) \ z) = z. x * R(y,x,z) = (((x * y) * z) / (x * z)) * x. (((x * y) * z) / (x * z)) * x = x * R(y,x,z). T(R(x,y,x),y * x) = T(x,y). R(x,y,x) * (y * x) = (y * x) * T(x,y). x != T(R(y,z,u),w) | x = R(T(y,w),z,u). T(x,y) = R(T(x,y * x),y,x). R(T(x,y * x),y,x) = T(x,y). (x * y) * L(T(y,x),z,u) = L(R(y,x,y),z,u) * (x * y). L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u). (x * y) * R(T(y,x),z,u) = R(R(y,x,y),z,u) * (x * y). R(R(x,y,x),z,u) * (y * x) = (y * x) * R(T(x,y),z,u). R(T(x,y),y / x,x) = T(x,y / x). R(x,1 / x,x) = T(x,1 / x). (x * y) * T(y,x) = (y * x) * y. R(x,y,x) * (y * x) = (x * T(y,x)) * T(x,y). (x * T(y,x)) * T(x,y) = R(x,y,x) * (y * x). x * T(y,x / y) = (y * (x / y)) * y. (x * (y / x)) * x = y * T(x,y / x). x * y != (z * u) * T(u,z) | x \ ((u * z) * u) = y. (T(x,y) * (y * x)) \ ((x * y) * x) = K(y * x,T(x,y)). T(T(R(x,y,z),u),w) = R(T(T(x,w),u),y,z). R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y). (x * (y * x)) / (z * x) = (1 / x) \ (y / z). x \ (y * (z * x)) = (((1 / x) * y) * z) * x. (((1 / x) * y) * z) * x = x \ (y * (z * x)). x \ (y * (z * x)) != u * x | u = ((1 / x) * y) * z. x \ (y * (z * x)) != u * x | ((1 / x) * y) * z = u. x * (T(y,x) * x) = y * (x * x). x * T((1 / y) \ x,x) = y * (x * x). ((1 / x) \ y) * y = x * (y * y). x * y != (z / u) * u | z / y = x. x / y = (1 / (x / (y * y))) \ y. (1 / (x / (y * y))) \ y = x / y. x * y != ((1 / x) \ z) * (u * x) | y = (z * u) * x. (x * y) * (x * y) = ((x * y) * x) * y. ((x * y) * x) * y = (x * y) * (x * y). (x \ y) * y = (x \ 1) * (y * y). (x \ 1) * (y * y) = (x \ y) * y. (x / y) * (y \ 1) = (1 / (x / (y * y))) \ 1. (1 / (x / (y * y))) \ 1 = (x / y) * (y \ 1). ((x * y) * (x * y)) * z != ((x * y) * x) * y | 1 = z. 1 = a(x * y,x,y). a(x * y,x,y) = 1. T((((1 / x) \ y) * z) / x,x) = (y * (z / x)) * x. x \ (((1 / x) \ y) * z) = (y * (z / x)) * x. x * y != ((1 / x) \ z) * z | y = z * z. (x * (x / y)) * y = x * x. x \ (((1 / x) \ y) * z) != u | u = (y * (z / x)) * x. x \ (((1 / x) \ y) * z) != u | (y * (z / x)) * x = u. (x * x) / y = x * (x / y). (x * y) * (y \ x) = x * x. x * y != z * z | T(z * (z / x),x) = y. x * (y \ (x / y)) = (x / y) * (x / y). (x / y) * (x / y) = x * (y \ (x / y)). (x * y) * R(L(z,y,x),u,w) != v5 | x * (y * R(z,u,w)) = v5. (x * y) * L(L(z,y,x),u,w) != v5 | x * (y * L(z,u,w)) = v5. x * x = (x / y) * (y * x). (x / y) * (y * x) = x * x. x * ((x \ y) * y) = y * y. x * y != z * z | x = z * (z / y). x / y = x * (x / (y * x)). x * (x / (y * x)) = x / y. x * y != (z / u) * (u * z) | x \ (z * z) = y. x \ (y * y) = (x \ y) * y. x * (y * (x * y)) = (x * y) * (x * y). (x * y) * (x * y) = x * (y * (x * y)). (x * y) * ((x \ 1) * T(y,x \ 1)) = T(y,x \ 1) * T(y,x \ 1). T(x * (x / y),y) = (y \ x) * x. x != (y / z) * (y / z) | x = y * (z \ (y / z)). x * ((x \ (y / z)) * (y / z)) = y * (z \ (y / z)). (x * y) * z != x * x | z = y \ x. ((x * y) \ x) * x = y \ x. x * y != z * ((z \ x) * u) | y = L(u,z \ x,z). x = L(x,y \ x,y). L(x,y \ x,y) = x. (1 / (x * x)) * y = 1 / ((y \ x) * x). 1 / ((x \ y) * y) = (1 / (y * y)) * x. L(x * y,y,x) = x * y. L(T(x,y),z \ x,z) = T(x,y). (x * y) * (x * y) != z | x * (y * (x * y)) = z. x \ (x / y) = x / (y * x). x / (y * x) = x \ (x / y). x * y != z / (u \ z) | x \ u = y. x \ y = x / ((y \ x) * x). x / ((y \ x) * x) = x \ y. (x \ y) * ((x \ y) / y) = (x \ y) / x. x * (x / y) = x / (y / x). x / (y / x) = x * (x / y). (x \ (x / y)) * (y * x) = x. x \ (x / y) != z | z = x / (y * x). x \ (x / y) != z | x / (y * x) = z. x != ((1 / y) \ z) * z | x = y * (z * z). (1 / x) \ (y * y) = x * (y * y). T((x * y) \ x,x) = x \ (y \ x). (x \ y) / y = (y * x) \ y. x * y != (z / u) \ z | u / y = x. x / y = (y * (y / x)) \ y. (x * (x / y)) \ x = y / x. x * y != z \ (z * u) | u / y = x. x / (y * x) = ((y * x) * y) \ (y * x). ((x * y) * x) \ (x * y) = y / (x * y). (x \ y) * y = (y \ x) \ y. (x \ y) \ x = (y \ x) * x. x \ y != z * y | (y * x) \ y = z. x * ((y \ x) \ 1) = ((x * y) \ x) \ 1. ((x * y) \ x) \ 1 = x * ((y \ x) \ 1). (x \ y) / y != z | z = (y * x) \ y. (x \ y) / y != z | (y * x) \ y = z. ((x \ y) / y) * (1 / y) = x \ (1 / y). (x \ (x / y)) \ 1 = (y * x) * (x \ 1). (1 / x) * (x \ y) = 1 / ((y \ x) * x). 1 / ((x \ y) * y) = (1 / y) * (y \ x). (x * (x / y)) \ x != z | z = y / x. (x * (x / y)) \ x != z | y / x = z. x / (y * x) != z | z = x \ (x / y). x / (y * x) != z | x \ (x / y) = z. x * y != (x \ z) \ x | T(z \ x,x) = y. T(x \ y,y) = T(y \ x,y) \ 1. T(x \ y,x) \ 1 = T(y \ x,x). (x \ y) \ x != z * x | y \ x = z. (x / ((y \ z) \ x)) \ y = (z \ y) * y. (x \ ((1 / x) \ y)) \ x = (y \ 1) * x. 1 / ((x \ y) * y) != z | (1 / y) * (y \ x) = z. x * T(x,y) = z * ((z \ x) * T(x,y)). x * ((x \ y) * T(y,z)) = y * T(y,z). x != (1 / y) \ (z * u) | x = y / (u \ (z \ 1)). x * (y * y) = x / (y \ (y \ 1)). x / (y \ (y \ 1)) = x * (y * y). (x * (y * y)) \ x = y \ (y \ 1). 1 / T(x \ y,y) = T(y \ x,y). x / (y * y) = x * (y \ (y \ 1)). x * (y \ (y \ 1)) = x / (y * y). x * y != z / z | 1 / y = x. 1 / (x * x) = x \ (x \ 1). (1 / x) / x = x \ (x \ 1). x \ (x / (y * y)) = y \ (y \ 1). (x \ (x \ 1)) * y = (x * x) \ y. 1 / T(x,y) = T(y \ (y / x),y). T(x \ (x / y),x) = 1 / T(y,x). x * y != z \ (z * u) | x \ u = y. (x \ (x \ 1)) \ y = (x * x) * y. (((1 / x) * y) \ (((1 / x) * y) \ 1)) \ z = (T(y / x,y) * ((1 / x) * y)) * z. (x / (y \ z)) / ((1 / z) * y) != u | (((1 / z) * y) * (1 / x)) \ ((1 / z) * y) = u. ((x * y) * x) \ (x * y) != z | y / (x * y) = z. ((x \ y) \ 1) * ((y \ 1) * ((x \ 1) \ 1)) = (y \ 1) * (((x \ 1) \ 1) * ((y \ 1) * ((x \ 1) \ 1))). (x \ 1) * (((y \ 1) \ 1) * ((x \ 1) * ((y \ 1) \ 1))) = ((y \ x) \ 1) * ((x \ 1) * ((y \ 1) \ 1)). x \ (x / (y * (z * (y * z)))) = (y * z) \ ((y * z) \ 1). 1 / ((x \ y) * y) = (y \ (y \ 1)) * x. (x \ y) * ((y * x) \ y) = (x \ y) / x. x != y / (z * y) | x = y \ (y / z). ((x * y) * x) \ (x * y) = y \ (y / x). ((x * y) * x) \ (x * y) != z | y \ (y / x) = z. (x / y) * (1 / y) = (y / x) \ (1 / y). (x / y) \ (1 / x) = (y / x) * (1 / x). ((x * y) \ x) * (1 / x) = y \ (1 / x). x * (y * y) != (1 / z) \ (y * y) | x = z. x \ (y * y) = ((y * y) \ x) \ 1. ((x * x) \ y) \ 1 = y \ (x * x). x != y \ (z * z) | x = (y \ z) * z. ((x * x) \ y) \ 1 = (y \ x) * x. 1 / ((x \ y) * y) = (y * y) \ x. x != 1 / ((y \ z) * z) | x = (1 / z) * (z \ y). (x * x) \ y = (1 / x) * (x \ y). (1 / x) * (x \ y) = (x * x) \ y. 1 / (x * (y * x)) = ((y * x) * (y * x)) \ y. ((x * y) * (x * y)) \ x = 1 / (y * (x * y)). 1 / (x * y) = (y * y) \ (y / x). (x * x) \ (x / y) = 1 / (y * x). 1 / (x * (y * y)) = (y * y) \ (1 / x). x * ((x \ 1) \ y) = ((x \ 1) * (x \ 1)) \ y. ((x \ 1) * (x \ 1)) \ y = x * ((x \ 1) \ y). (1 / x) * (x \ 1) = x \ (x \ 1). (1 / x) \ y = x \ ((x * x) * y). x \ ((x * x) * y) = (1 / x) \ y. (1 / x) * y = (x * x) \ (x * y). (x * x) \ (x * y) = (1 / x) * y. (x * x) \ (x \ (x / y)) = 1 / ((y * x) * x). (1 / (x * y)) * (y \ (x \ 1)) = (x * y) \ ((x * y) \ 1). x * ((1 / x) \ y) = (x * x) * y. x != (y * z) \ (y * u) | x = L(z \ u,z,y). (1 / x) * y = L(x \ y,x,x). L(x \ y,x,x) = (1 / x) * y. x != (y * z) \ (y * (z * u)) | x = L(u,z,y). (1 / x) * (x * y) = L(y,x,x). L(a(x,y,z),x * (y * z),x * (y * z)) = (1 / (x * (y * z))) * ((x * y) * z). x != (1 / y) * (y * z) | x = T(T(z,y),y \ 1). L(x,y,y) = T(T(x,y),y \ 1). T(T(x,y),y \ 1) = L(x,y,y). x != (1 / y) * (y * z) | x = L(z,y,1 / y). L(x,y,y) = L(x,y,1 / y). L(x,y,1 / y) = L(x,y,y). L(x,y,y) \ 1 = (y * x) \ y. (1 / x) \ L(y,z,z) = x / ((z * y) \ z). x != T(T(y,z),z \ 1) | x = R(y,z,z \ 1). L(x,y,y) = R(x,y,y \ 1). R(x,y,y \ 1) = L(x,y,y). x != T(T(y,z),z \ 1) | x = (y * z) * (z \ 1). L(x,y,y) = (x * y) * (y \ 1). (x * y) * (y \ 1) = L(x,y,y). T(x,x \ 1) = L(x,x,x). x != R(y / z,z,z \ 1) | x = y * (z \ 1). L(x / y,y,y) = x * (y \ 1). x != (y * z) * (z \ 1) | x = (z \ (z / y)) \ 1. L(x,y,y) = (y \ (y / x)) \ 1. (x \ (x / y)) \ 1 = L(y,x,x). (x * (y * z)) * (z \ (y \ 1)) = L(x,y * z,y * z). 1 / L(x,y,y) = y \ (y / x). (x \ y) \ 1 = L(y \ x,x,x). L(x \ y,y,y) = (y \ x) \ 1. 1 / L(x,y,y) != z | z = y \ (y / x). 1 / L(x,y,y) != z | y \ (y / x) = z. 1 / (x * L(y,z,z)) = (z \ (z / y)) / x. (x \ (x / y)) \ 1 != z | z = L(y,x,x). (x \ (x / y)) \ 1 != z | L(y,x,x) = z. x != L(y,z,z) | x = L(y,z,1 / z). (x \ y) \ 1 = L(y \ x,x,1 / x). L(x \ y,y,1 / y) = (y \ x) \ 1. x * y != z * ((1 / z) \ u) | x \ ((z * z) * u) = y. T(x / y,x) \ ((((1 / y) * x) * ((1 / y) * x)) * z) = (1 / ((1 / y) * x)) \ z. x * (x / y) = (x * x) * (1 / y). (x * x) * (1 / y) = x * (x / y). x * ((x * y) / x) = (x * x) * (y / x). (x * x) * (y / x) = x * ((x * y) / x). L(x,y * x,1 / (y * x)) = ((y * x) \ y) \ 1. ((x \ 1) \ 1) \ x = (x \ 1) * x. ((x \ 1) \ 1) \ x = K(x \ 1,x). x != ((y \ z) \ z) \ u | x = T(y,y \ z) \ u. (x \ 1) * x = T(x,x \ 1) \ x. T(x,x \ 1) \ x = (x \ 1) * x. ((x \ 1) \ 1) \ x != y | K(x \ 1,x) = y. ((x \ 1) \ 1) * K(x \ 1,x) = x. x / K(x \ 1,x) = (x \ 1) \ 1. x * y != T(x,x \ 1) \ x | T(x \ 1,x) = y. T(x \ 1,x) = T(x,x \ 1) \ 1. T(x,x \ 1) \ 1 = T(x \ 1,x). x != ((y \ z) \ z) * u | x = T(y,y \ z) * u. x = T(x,x \ 1) * K(x \ 1,x). T(x,x \ 1) * K(x \ 1,x) = x. x != y / K(y \ 1,y) | x = R(y,y \ 1,y). (x \ 1) \ 1 = R(x,x \ 1,x). R(x,x \ 1,x) = (x \ 1) \ 1. R(x,x \ 1,x) = T(x,x \ 1). x != T(y \ 1,y) | x = 1 / y. T(x,x \ 1) \ 1 = 1 / x. x / L(T(y \ 1,y),T(y,y \ 1),x) = x * T(y,y \ 1). (x \ 1) \ 1 = T((1 / x) \ 1,1 / x). T((1 / x) \ 1,1 / x) = (x \ 1) \ 1. x != T(y,y \ z) \ u | x = ((y \ z) \ z) \ u. 1 / x = ((x \ 1) \ 1) \ 1. ((x \ 1) \ 1) \ 1 = 1 / x. (x \ 1) \ 1 = 1 / (1 / x). 1 / (1 / x) = (x \ 1) \ 1. x != 1 / T(y,z) | x = T(y \ 1,y * z). ((T(x,y) \ 1) \ 1) \ 1 = T(x \ 1,x * y). T(x \ 1,x * y) = ((T(x,y) \ 1) \ 1) \ 1. x != 1 / (y \ z) | x = (1 / z) * y. (((x \ y) \ 1) \ 1) \ 1 = (1 / y) * x. x * y != ((z \ 1) \ 1) \ 1 | (1 / z) / y = x. (1 / x) / y = ((x \ 1) \ 1) \ (1 / y). ((x \ 1) \ 1) \ (1 / y) = (1 / x) / y. ((x \ (y \ 1)) \ 1) \ 1 = 1 / (y * x). 1 / (1 / x) != y | y = (x \ 1) \ 1. 1 / (1 / x) != y | (x \ 1) \ 1 = y. ((x \ y) \ 1) \ 1 = 1 / ((1 / y) * x). 1 / ((1 / x) * y) = ((y \ x) \ 1) \ 1. 1 / (x * (1 / y)) = ((y \ 1) \ 1) / x. ((x \ 1) \ 1) / y = 1 / (y * (1 / x)). x / (1 / y) = (1 / x) \ ((y \ 1) \ 1). (1 / x) \ ((y \ 1) \ 1) = x / (1 / y). ((x \ (y \ x)) \ 1) \ 1 = 1 / T(y,x). x / (x * (1 / y)) = (x * ((y \ 1) \ 1)) / x. (x * ((y \ 1) \ 1)) / x = x / (x * (1 / y)). (1 / x) * ((y \ 1) \ 1) = (y \ ((x \ 1) \ 1)) \ 1. (x \ ((y \ 1) \ 1)) \ 1 = (1 / y) * ((x \ 1) \ 1). (x \ 1) * (1 / y) = ((y \ 1) \ x) \ 1. ((x \ 1) \ y) \ 1 = (y \ 1) * (1 / x). ((x \ (y \ z)) \ 1) \ 1 = 1 / (((1 / z) * y) * x). 1 / (((1 / x) * y) * z) = ((z \ (y \ x)) \ 1) \ 1. 1 / (x * (y \ (1 / z))) = (((z \ 1) \ 1) * y) / x. (((x \ 1) \ 1) * y) / z = 1 / (z * (y \ (1 / x))). 1 / (1 / (x * y)) = (y \ (x \ 1)) \ 1. x / (1 / (1 / y)) = (1 / x) \ (y \ 1). x / (1 / (1 / y)) != z | (1 / x) \ (y \ 1) = z. x * (((y \ 1) \ 1) * x) = (x / (1 / y)) * x. 1 / ((x \ 1) * y) = ((y \ 1) \ 1) \ x. ((x \ 1) \ 1) * (1 / y) = 1 / (y / x). (T(x,y) \ x) * T(x,y) = x. x \ (y * T(y,z)) = (x \ y) * T(y,z). x * (y * T(x * y,z)) = (x * y) * T(x * y,z). (x * y) * T(x * y,z) = x * (y * T(x * y,z)). x / T(x,y) = T(x,y) \ x. (T(x,y) \ x) \ x = T(x,y). x != T(y,z) \ y | x = y * (T(y,z) \ 1). x / T(x,y) = x * (T(x,y) \ 1). x * (T(x,y) \ 1) = x / T(x,y). x != y / T(y,z) | x = (1 / T(y,z)) * y. T(x,y) \ x = (1 / T(x,y)) * x. (1 / T(x,y)) * x = T(x,y) \ x. x * y != z / T(z,u) | (T(z,u) \ z) / y = x. (T(x,y) \ x) / x = 1 / T(x,y). (x * x) / T(x,y) = x * (T(x,y) \ x). x * y != x / T(x,z) | T(1 / T(x,z),x) = y. T(1 / T(x,y),x) = T(x,y) \ 1. 1 / (x \ T(x,y)) = T(x,y) \ x. (T(x,y) \ x) \ 1 = x \ T(x,y). ((T(x,y) \ x) / x) \ 1 = T(x,y). (x * (T(y,z) \ y)) * (y \ T(y,z)) = R(x,T(y,z) \ y,(T(y,z) \ y) \ 1). R(x,T(y,z) \ y,(T(y,z) \ y) \ 1) = (x * (T(y,z) \ y)) * (y \ T(y,z)). (x \ y) \ ((x \ y) / x) = (y * x) \ y. x * y != (1 / z) \ (1 / u) | (z / u) / y = x. (x / y) / (1 / y) = (y * (1 / x)) \ y. (x \ y) * (1 / y) = (y \ x) \ (1 / y). (x \ y) \ (1 / x) = (y \ x) * (1 / x). x \ (1 / y) != z * (1 / y) | (y * x) \ y = z. ((x * y) \ y) * (1 / y) = T(x,y) \ (1 / y). ((x * (y * z)) \ (x * y)) * (1 / (x * y)) = L(z,y,x) \ (1 / (x * y)). (x * y) * (y \ 1) != z | L(x,y,y) = z. T(x,1 / x) = (x \ 1) \ 1. (x \ 1) \ 1 != y | 1 / (1 / x) = y. T(x,1 / x) = T(x,x \ 1). ((x \ 1) \ 1) / x = K(x,1 / x). x != T(y,1 / y) | x = R(y,1 / y,y). T(x,x \ 1) = R(x,1 / x,x). R(x,1 / x,x) = T(x,x \ 1). T(x,x \ 1) / x = K(x,1 / x). L(T(x,x \ 1),1 / x,x) = T(x,x * (1 / x)). R(T(x,x \ 1),y,z) = R(R(x,y,z),1 / x,x). R(R(x,y,z),1 / x,x) = R(T(x,x \ 1),y,z). (x \ 1) \ (1 / x) = K(x,1 / x). (x \ 1) / (1 / x) = K(1 / x,1 / (1 / x)). K(1 / x,1 / (1 / x)) = (x \ 1) / (1 / x). (x \ 1) * K(x,1 / x) = 1 / x. x != (1 / y) / z | x = 1 / (z * y). ((x \ 1) \ 1) \ (1 / y) = 1 / (y * x). ((x \ 1) \ 1) \ (1 / y) != z | 1 / (y * x) = z. (1 / (x * y)) * ((z \ 1) \ 1) = (z \ ((y \ (x \ 1)) \ 1)) \ 1. (x \ ((y \ (z \ 1)) \ 1)) \ 1 = (1 / (z * y)) * ((x \ 1) \ 1). (x \ 1) \ (1 / y) = 1 / (y * (1 / x)). 1 / (x * (1 / y)) = (y \ 1) \ (1 / x). 1 / (x * (1 / y)) != z | (y \ 1) \ (1 / x) = z. x * y != ((z \ 1) \ u) \ 1 | ((u \ 1) * (1 / z)) / y = x. ((x \ 1) * (1 / y)) / z = ((y \ 1) \ x) \ (1 / z). ((x * (y \ 1)) \ z) \ 1 = (z \ 1) * (1 / (y / x)). (x \ 1) * ((y \ 1) * (1 / x)) = (y / (x \ 1)) \ (x \ 1). x != 1 / ((y \ 1) * z) | x = (1 / (1 / z)) \ y. ((x \ 1) \ 1) \ y = (1 / (1 / x)) \ y. (1 / (1 / x)) \ y = ((x \ 1) \ 1) \ y. x * y != 1 / ((z \ 1) * u) | x \ (((u \ 1) \ 1) \ z) = y. (1 / x) \ (((y \ 1) \ 1) \ z) = x / ((z \ 1) * y). 1 / ((x \ (y \ 1)) * z) = ((z \ 1) \ 1) \ (y * x). (x \ 1) * (1 / y) = 1 / (y / (1 / x)). 1 / (x / (1 / y)) = (y \ 1) * (1 / x). ((x \ y) \ 1) * (1 / z) = 1 / (z / ((1 / y) * x)). 1 / (x / ((1 / y) * z)) = ((z \ y) \ 1) * (1 / x). ((x \ 1) \ 1) * ((1 / y) * z) = 1 / ((z \ y) / x). (x * (T(x,y) \ x)) \ (x * x) = T(x,y). x / (1 / y) = (y * (1 / (x * y))) \ y. (x * (1 / (y * x))) \ x = y / (1 / x). (x * ((y \ 1) \ 1)) \ (1 / (y \ (1 / x))) = (1 \ (y \ (1 / x))) * (1 / (y \ (1 / x))). R(x,y,y \ 1) != z | L(x,y,y) = z. T(T(x,y),y \ 1) != z | L(x,y,y) = z. ((x \ (y \ 1)) \ 1) \ (1 / z) = 1 / (z * (y * x)). ((x \ y) \ 1) \ (1 / z) = 1 / (z * ((1 / y) * x)). 1 / (x * ((1 / y) * z)) = ((z \ y) \ 1) \ (1 / x). x != (y \ 1) * (1 / z) | x = ((z \ 1) \ y) \ 1. 1 / (x / (1 / y)) = ((x \ 1) \ y) \ 1. x / (y / (1 / x)) = x * (1 / (y * x)). 1 / (x / (1 / y)) = (1 / y) * (y * (1 / (x * y))). (1 / x) * (x * (1 / (y * x))) = 1 / (y / (1 / x)). (x / (1 / y)) * y = (1 / (x * y)) \ y. (1 / (x * y)) \ y = (x / (1 / y)) * y. T(T(x,y * z),z \ (y \ 1)) != u | L(x,y * z,y * z) = u. (1 / x) * (x * y) != z | L(y,x,x) = z. x * y != 1 / (z / (1 / u)) | x \ (((z \ 1) \ u) \ 1) = y. (1 / x) \ (((y \ 1) \ z) \ 1) = x / (y / (1 / z)). x / (1 / (1 / x)) = x * (1 / x). x / (1 / (1 / x)) = K(x,1 / x). K(x,1 / x) * (1 / (1 / x)) = x. K(x,1 / x) * y != x | y = L(x,1 / x,x). 1 / (1 / x) = L(x,1 / x,x). L(x,1 / x,x) = 1 / (1 / x). L(T(x,y),1 / x,x) = T(1 / (1 / x),y). L(x,y,1 / y) != z | L(x,y,y) = z. L(x,y,y) != z | (1 / y) * (y * x) = z. (x * y) * z != (y * x) * (K(x,y) * u) | L(u,K(x,y),y * x) = z. (x * y) * (K(y,x) * z) != (y * x) * u | L(z,K(y,x),x * y) = u. (x * y) \ (y * (T(x,y) * z)) != u | L(z,T(x,y),y) = u. (x * (y * z)) \ (x * (y * (z * u))) != w | L(L(u,z,y),y * z,x) = w. (T(x,x \ y) * z) \ (((x \ y) \ y) * (z * u)) != w | L(u,z,T(x,x \ y)) = w. (x * (y * (z * u))) \ (x * ((y * z) * u)) != w | L(a(y,z,u),y * (z * u),x) = w. x * K(x \ 1,x) != y | L(x,x \ 1,x) = y. L(x,y,y) != z | L(x,y,1 / y) = z. ((x * (1 / y)) * (y / z)) / (1 / z) != u | R(x,1 / y,y / z) = u. L(x,y,y) != z | R(x,y,y \ 1) = z. T(1 / T(x,y),T(x,z)) = T(x,z) \ (T(x,z) / T(x,y)). T(x,y) \ (T(x,y) / T(x,z)) = T(1 / T(x,z),T(x,y)). x * T(((1 / y) * z) * x,u) = T(x / (z \ y),u) * x. (x \ y) * (T(y / x,z) \ 1) = T(y / x,z) \ T(y / x,x). T(x / y,z) \ T(x / y,y) = (y \ x) * (T(x / y,z) \ 1). x * (y * ((x \ 1) \ 1)) = (1 / (x * y)) \ x. x != y * (((1 / z) * u) * y) | x = (y / z) * (u * y). (x / (y \ z)) * x = (x / z) * (y * x). x * y != z * (((1 / u) * w) * z) | ((z / u) * (w * z)) / y = x. ((x / y) * (z * x)) / x = x / (z \ y). x * y != (z / (u \ z)) * w | (u * w) / y = x. (x * (y * z)) / z = z / (y \ (x \ z)). (x / y) * x = (x / (z * y)) * (z * x). (x / (y * z)) * (y * x) = (x / z) * x. ((x / y) * (z * x)) \ 1 = x \ ((x / (z \ y)) \ 1). (x / (y \ z)) * x != u | u = (x / z) * (y * x). (x / (y \ z)) * x != u | (x / z) * (y * x) = u. (x / (y \ (z \ x))) \ 1 = x * ((z * (y * x)) \ 1). x / ((1 / x) * y) = (x / y) * x. (x * y) / (z * y) = y / (z * (x \ y)). (x / ((y / x) * z)) * y = (x / z) * x. ((x / y) * x) \ x = (1 / x) * y. x / (1 / y) = (x / (x / y)) * x. (x / (x / y)) * x = x / (1 / y). x / (((1 / y) * z) * (y \ 1)) = (1 / x) \ ((y / z) * y). (x \ y) / ((1 / (x \ y)) * y) = ((y * x) \ y) * (x \ y). (x * y) \ y = (1 / y) * (x \ y). (1 / x) * (y \ x) = (y * x) \ x. ((x / y) * (z * x)) \ x = (1 / x) * (z \ y). x * y != (z / (z / u)) * z | x \ (z / (1 / u)) = y. x \ (x / (1 / y)) = (1 / (x / y)) * x. x != (1 / y) * (z \ y) | x = T(z \ 1,y). (x * y) \ y = T(x \ 1,y). T(x \ 1,y) = (x * y) \ y. T(x \ 1,y) * z = ((x * y) \ y) * z. T((x / y) \ 1,y) = x \ y. x / T(y \ 1,x) = y * x. T(x,y) = ((1 / x) * y) \ y. T(x * (y \ 1),z) = ((y / x) * z) \ z. x * y != T((z / u) \ 1,u) | x \ (z \ u) = y. (1 / x) \ (y \ x) = (y / x) \ x. x * (y \ x) = ((y / x) \ 1) * x. ((x / y) \ 1) * y = y * (x \ y). T(x * (y \ 1),x) = y \ x. x / T(y,x) = (1 / y) * x. R(x \ 1,y,z) / (x \ 1) = x * R(x \ 1,y,z). x != y \ (1 / z) | x = (y \ 1) / z. T(x,1 / y) = (((1 / x) * (1 / y)) \ 1) / y. (((1 / x) * (1 / y)) \ 1) / y = T(x,1 / y). x / T(y,x) != z | z = (1 / y) * x. x / T(y,x) != z | (1 / y) * x = z. T(x,y) = (1 / (y \ x)) \ y. T(x * y,x) = (1 / y) \ x. T(x,y) = (T(y,x) / x) \ y. (T(x,y) / y) \ x = T(y,x). T(x * x,y) = ((x \ (x \ 1)) * y) \ y. ((x \ (x \ 1)) * y) \ y = T(x * x,y). T(x,x * y) = L(y,x,x) \ (x * y). L(x,y,y) \ (y * x) = T(y,y * x). x * y != T(z * (u \ 1),z) | (u \ z) / y = x. (x \ y) / y = R(x \ 1,y,y \ 1). R(x \ 1,y,y \ 1) = (x \ y) / y. T(x \ y,z) = T(T(y * (x \ 1),z),y). T(T(x * (y \ 1),z),x) = T(y \ x,z). x * (y \ x) = (x * (y \ 1)) * x. (x * (y \ 1)) * x = x * (y \ x). (x * (y \ x)) / x = x * (y \ 1). T(x * (y \ (z \ 1)),x) = (z * y) \ x. T(x * (y * (z \ 1)),x) = (z / y) \ x. (x \ y) \ (y \ 1) = y \ ((y * (x \ 1)) \ 1). x \ ((x * (y \ 1)) \ 1) = (y \ x) \ (x \ 1). x * ((y \ x) \ 1) = (x * (y \ 1)) \ x. (x * (y \ 1)) \ x = x * ((y \ x) \ 1). T(x \ y,y) = T(x,y) \ y. T(x,y) \ y = T(x \ y,y). x != (1 / y) * z | x = T(z,y) / y. x / T(y,x) = T(x,y) / y. T(x,y) / y = x / T(y,x). x / T(y,x) = T(x / y,x). x / (x \ y) = (1 / (y / x)) * x. (1 / (x / y)) * y = y / (y \ x). (x \ y) / (y / x) = (1 / (y / x)) * (x \ y). (1 / (x / y)) * (y \ x) = (y \ x) / (x / y). ((1 / x) * y) \ y != z | z = T(x,y). ((1 / x) * y) \ y != z | T(x,y) = z. T(x,y) = (x / T(y,x)) * y. (x / T(y,x)) * y = T(x,y). R(x,y,z) / x = (1 / x) * R(x,y,z). (1 / x) * R(x,y,z) = R(x,y,z) / x. x != (1 / y) \ z | x = y / (z \ 1). T(x,y) = (y \ x) / (y \ 1). T(x,y) != z | (y \ x) / (y \ 1) = z. T(x * y,x) = y / (x \ 1). x * ((1 / y) \ x) = (x * y) * x. T(x * y,x) \ y = x \ 1. T((1 / x) * y,1 / x) != z | y / x = z. T(x * y,x) != z | y / (x \ 1) = z. T(x * y,x) * y = y * (x * y). T(T(x * y,x),y) = x * y. x * (((1 / y) \ x) \ 1) = (x * y) \ x. x != T(y \ z,z) | x = y \ T(z,y). T(x,y) \ y = x \ T(y,x). x * (T(x,y) \ y) = T(y,x). (x / T(y,x)) * y != z | z = T(x,y). (x / T(y,x)) * y != z | T(x,y) = z. T(x,y) * (y \ 1) = y \ x. T(T(x,y),y \ 1) = (y \ 1) \ (y \ x). (x \ 1) \ (x \ y) = T(T(y,x),x \ 1). x * (y / (x \ 1)) = (x * y) * x. T(T(x * y,x),x \ 1) = (x \ 1) \ y. (x * (y / (x \ 1))) / x = x * y. T(x * (y \ 1),x) != z | y \ x = z. T(x * y,x) != z | (1 / y) \ x = z. x / (y \ 1) != z | z = T(y * x,y). x / (y \ 1) != z | T(y * x,y) = z. T(x,y) * (x \ T(y,x)) = y. T(x,y) / (T(y,x) \ x) = y. x * y != T(z,x) | T(z / T(x,z),x) = y. T(x / T(y,x),y) = T(y,x) \ x. T(x,1 / y) * y = (1 / y) \ x. (x \ y) * (x \ 1) = x \ (y / x). x * (y \ 1) = y \ ((y * x) / y). x \ ((x * y) / x) = y * (x \ 1). (x \ y) \ 1 = (x \ 1) \ (T(y,x) \ 1). (x \ 1) \ (T(y,x) \ 1) = (x \ y) \ 1. T(x,(1 / y) * z) * (z \ y) = ((1 / y) * z) \ x. (x * y) * (y \ 1) = y \ ((1 / y) \ x). x \ ((1 / x) \ y) = (y * x) * (x \ 1). x * (R(x,y,z) \ 1) = R(x,y,z) \ x. L(x \ y,z,u) * (x \ 1) = x \ L(y / x,z,u). T(x,y) \ y != z | z = x \ T(y,x). T(x,y) \ y != z | x \ T(y,x) = z. T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,z). (1 / ((x / y) \ y)) \ ((y \ x) \ 1) = (y / ((x / y) \ y)) \ ((x / y) \ y). x != y * ((z \ y) \ y) | x = (z \ 1) \ y. (x * ((y \ x) \ 1)) * x = (y \ 1) \ x. (x * (y * (z \ 1))) * x = x * ((z / y) \ x). (x * (y \ x)) \ (x * (y \ 1)) = (y \ 1) \ ((y \ 1) / x). (x * y) / x = x * ((x / y) \ 1). x * ((x / y) \ 1) = (x * y) / x. (x * (y \ 1)) \ x != z | x * ((y \ x) \ 1) = z. 1 / (x \ (y / x)) = x / (x \ y). (x / (x \ y)) / x != z | z = 1 / (y / x). (x / (x \ y)) / x != z | 1 / (y / x) = z. (1 / x) \ (y / (y \ z)) = x / (y \ (z / y)). x != y * (z \ y) | x = (z * (y \ 1)) \ y. (x * y) * x = ((1 / y) * (x \ 1)) \ x. ((1 / x) * (y \ 1)) \ y = (y * x) * y. x * (x * y) = (x * T(y,x \ 1)) * x. (x * T(y,x \ 1)) * x = x * (x * y). x * ((1 / (x \ 1)) \ (y / (x \ 1))) = (x * ((x \ 1) * y)) * x. (x * y) / x = x * (y * (x \ 1)). x * (y * (x \ 1)) = (x * y) / x. x * y != (z \ u) * (z \ 1) | x \ (z \ (u / z)) = y. x \ (y \ (1 / y)) = (x \ (y \ 1)) * (y \ 1). (x \ (y \ 1)) * (y \ 1) = x \ (y \ (1 / y)). ((x * y) \ z) * (y \ (x \ 1)) = (x * y) \ (z / (x * y)). ((x / y) \ z) * (y * (x \ 1)) = (x / y) \ (z / (x / y)). 1 / (x \ (y / x)) != z | x / (x \ y) = z. ((1 / x) \ (y \ 1)) * (y \ 1) = x * (y \ (1 / y)). T(x \ (y / x),x \ y) = x \ (x \ y). x != y * (z \ 1) | x = ((y * z) / y) \ y. x \ ((x * y) / x) = ((y * x) / y) \ y. ((x * y) / x) \ x = y \ ((y * x) / y). x * (y * (x \ 1)) != z | z = (x * y) / x. x * (y * (x \ 1)) != z | (x * y) / x = z. 1 / ((x * y) / x) = (x / y) / x. 1 / (x \ (1 / x)) = (1 / x) \ x. 1 / (x / (x \ y)) != z | ((x \ (y / x)) \ 1) \ 1 = z. 1 / (x \ (x / (y \ (z \ x)))) = x / (x \ (z * (y * x))). (x * y) / x != x * z | y * (x \ 1) = z. (1 / x) * (y * x) = ((1 / x) * y) / (1 / x). ((1 / x) * y) / (1 / x) = (1 / x) * (y * x). x \ ((x * y) / x) != z | z = y * (x \ 1). x \ ((x * y) / x) != z | y * (x \ 1) = z. T(x,y) / x != z | (1 / x) * T(x,y) = z. L(x,y,z) / x != u | (1 / x) * L(x,y,z) = u. x \ (1 / T(y,x \ 1)) != z | (1 / y) * (x \ 1) = z. L(x \ 1,y,y) = (x \ y) / y. x != (y \ z) / z | x = (z * y) \ z. L(x \ 1,y,y) = (y * x) \ y. L(x,y,y) = ((1 / x) \ y) / y. ((1 / x) \ y) / y = L(x,y,y). L(x \ 1,y,y) != z | (y * x) \ y = z. L((x * y) \ x,z,u) = L(L(y \ 1,z,u),x,x). L(L(x \ 1,y,z),u,u) = L((u * x) \ u,y,z). L(x,y,y) = (y * (1 / x)) \ y. (x * (1 / y)) \ x = L(y,x,x). L(x,y,y) * y = (1 / x) \ y. L(x,y,y) * y != z | z = (1 / x) \ y. L(x,y,y) * y != z | (1 / x) \ y = z. (x / y) / (1 / y) = L(x,1 / y,1 / y). L(x,1 / y,1 / y) = (x / y) / (1 / y). R(L(x,y,y),y,z) = (((1 / x) \ y) * z) / (y * z). (x / (x \ y)) / x = L(x / y,x,x). x != (y * (1 / z)) \ y | x = (z / y) / (1 / y). L(x,y,y) = (x / y) / (1 / y). (x / y) / (1 / y) = L(x,y,y). x != (y * (1 / (z * y))) \ y | x = z / (1 / y). L(x * y,y,y) = x / (1 / y). x / L(y,x,x) = x * (1 / y). x / L(y,x,x) != z | z = x * (1 / y). x / L(y,x,x) != z | x * (1 / y) = z. x * y != L(z,u,u) * u | x \ ((1 / z) \ u) = y. x \ ((1 / y) \ x) = L(T(y,x),x,x). L(T(x,y),y,y) = y \ ((1 / x) \ y). L(x,y,y) * (1 / y) = x / y. (x / (y \ z)) / ((1 / z) * y) = L(x,y \ z,y \ z). L(x * y,y,1 / y) = x / (1 / y). x != L(y,z,z) | x = T(T(y,z),z \ 1). x / (1 / y) = T(T(x * y,y),y \ 1). T(T(x * y,y),y \ 1) = x / (1 / y). (x * (1 / y)) \ x != z | z = L(y,x,x). (x * (1 / y)) \ x != z | L(y,x,x) = z. L(x,1 / y,L(z,y,y)) = (z / y) \ (L(z,y,y) * ((1 / y) * x)). (x / y) \ (L(x,y,y) * ((1 / y) * z)) = L(z,1 / y,L(x,y,y)). (x / y) / (1 / y) != z | z = L(x,y,y). (x / y) / (1 / y) != z | L(x,y,y) = z. ((1 / x) * y) * (1 / x) = (x \ y) / x. ((x / y) * z) \ z != u | T(y * (x \ 1),z) = u. (x * y) / x != z | (y \ ((x * y) / x)) / (y \ 1) = z. T(x * (y \ z),x) != u | ((1 / z) * y) \ x = u. T(x \ y,y) != z | x \ T(y,x) = z. (1 / x) \ (y / (1 / x)) != z | x * (y * x) = z. R(x,y,z) = z / (y * ((x * y) \ z)). ((x / y) * x) / z = x / ((z / x) * y). x != ((y / z) * y) \ y | x = (1 / y) * z. T(x * (y \ 1),y) = (1 / y) * x. T(x * (y \ 1),y) = x * T(1 / y,x). ((1 / x) * y) * (x \ 1) = x \ (y * (x \ 1)). ((x * x) \ y) \ y = T(x * x,y). T((1 / x) * y,y) = T(x \ y,x). T(x \ y,x) = T((1 / x) * y,y). ((x * y) \ z) * (y \ (x \ 1)) = (y \ (x \ 1)) * (z * (y \ (x \ 1))). (x \ (y \ 1)) * (z * (x \ (y \ 1))) = ((y * x) \ z) * (x \ (y \ 1)). T(1 / x,R(x,y,z)) = R(x,y,z) \ (R(x,y,z) / x). R(x,y,z) \ (R(x,y,z) / x) = T(1 / x,R(x,y,z)). (R(x,y,z) / x) / R(x,y,z) = 1 / x. R(x,y,z) * u != R(x,y,z) / x | T(1 / x,R(x,y,z)) = u. R(x,y,z) / x != R(x,y,z) * u | T(1 / x,R(x,y,z)) = u. L(R(x,y,z) \ u,R(x,y,z),1 / x) = (R(x,y,z) / x) \ ((1 / x) * u). x * ((x \ 1) * (y \ 1)) = (x * y) \ x. x != T(T(y,z),z \ 1) | x = L(y,z,z). (x \ 1) \ (x \ y) = L(y,x,x). (x \ 1) \ (x \ y) = L(y,x,1 / x). (x \ 1) \ y = L(x * y,x,x). L(x * y,x,x) = (x \ 1) \ y. (x \ 1) * L(y,x,x) = x \ y. (x \ 1) * L(y,x,x) != z | z = x \ y. (x \ 1) * L(y,x,x) != z | x \ y = z. x != L(y,z,z) | x = (z * (1 / y)) \ z. (x \ 1) \ y = (x * (1 / (x * y))) \ x. (x * (1 / (x * y))) \ x = (x \ 1) \ y. x * y != L(z * u,z,z) | x \ ((z \ 1) \ u) = y. (1 / x) \ ((x \ 1) \ y) = x * (x * y). L(((1 / x) \ y) * z,x,x) = (x \ 1) \ ((y * (z / x)) * x). (x \ 1) \ ((y * (z / x)) * x) = L(((1 / x) \ y) * z,x,x). ((x \ 1) \ y) * x = (1 / (x * y)) \ x. (1 / (x * y)) \ x = ((x \ 1) \ y) * x. ((x \ 1) \ y) * (1 / x) = (x * y) / x. x \ y != (x \ 1) * z | L(y,x,x) = z. (x \ 1) * L(L(y,x,x),z,u) = x \ L(y,z,u). (x * (y \ 1)) * L(z,y / x,y / x) = (y / x) \ z. (x \ 1) * ((1 / x) * y) = x \ (x \ y). (x \ 1) * (y * (x \ 1)) = x \ (y / x). (x \ 1) * ((y \ x) / x) = x \ (y \ 1). (x \ 1) * ((x * y) \ x) = x \ (y \ 1). x != (y * z) * (z \ 1) | x = L(y,z,z). x \ ((1 / x) \ y) = L(y,x,x). x \ ((1 / x) \ y) != z | L(y,x,x) = z. x \ ((1 / x) \ y) = L(y,x,1 / x). x != L(y \ 1,z,z) | x = (z * y) \ z. x \ ((1 / x) \ (y \ 1)) = (x * y) \ x. x * L(y,x,x) = (1 / x) \ y. x * L(y,x,x) = ((1 / x) \ y) * 1. ((1 / x) \ y) * 1 = x * L(y,x,x). x \ (x / (y \ 1)) = L(y,x,x). x \ (x / y) = L(1 / y,x,x). L(1 / x,y,y) = y \ (y / x). (x * (1 / y)) \ (((y \ 1) \ (1 / x)) \ z) = L(z,x * (1 / y),x * (1 / y)). x * ((1 / x) * y) = (1 / x) \ (x \ y). (1 / x) \ (x \ y) = x * ((1 / x) * y). x * (y / (1 / x)) = (1 / x) \ (y * x). (1 / x) \ (y * x) = x * (y / (1 / x)). x * ((x \ 1) \ y) = (1 / x) \ (x * y). (1 / x) \ (x * y) = x * ((x \ 1) \ y). L(1 / x,y,1 / y) = y \ (y / x). L(x,y,1 / y) \ y = (x \ 1) * y. x * y != ((1 / x) \ z) * u | y = (z * (u / x)) * x. L(x,y,y) = (x * (1 / y)) * y. (x * (1 / y)) * y = L(x,y,y). x * y = L(x / (1 / y),y,y). L(x / (1 / y),y,y) = x * y. L(x,y,y) / y = x * (1 / y). x * y != L(z \ u,z,z) | ((1 / z) * u) / y = x. ((1 / x) * y) / x = (x \ y) * (1 / x). ((1 / x) \ y) * L(z,x,x) = x * ((y * (z * (1 / x))) * x). x * ((y * (z * (1 / x))) * x) = ((1 / x) \ y) * L(z,x,x). (x \ 1) * (y * x) = x \ (y / (1 / x)). x \ (y / (1 / x)) = (x \ 1) * (y * x). x * (1 / y) != z / y | x = L(z,y,y). x = L(L(x,y,y),y,y). L(L(x,y,y),y,y) = x. L((x \ 1) \ y,x,x) = x * y. (x \ 1) * y = x \ L(y,x,x). x \ L(y,x,x) = (x \ 1) * y. L(x,y,y) = y * ((y \ 1) * x). x * ((x \ 1) * y) = L(y,x,x). x * ((x \ 1) * y) != z | z = L(y,x,x). x * ((x \ 1) * y) != z | L(y,x,x) = z. x \ (y * (x \ 1)) = (x \ 1) * (y / x). L(x,y \ 1,y) = L(x,y,y). x * ((x \ 1) * y) = T(T(y,x),x \ 1). T(T(x,y),y \ 1) = y * ((y \ 1) * x). x != L(y * z,z,z) | x = y / (1 / z). x * ((x \ 1) * (y * x)) = y / (1 / x). x * y != L(z,x,x) | T(z * (1 / x),x) = y. T(x * (1 / y),y) = (y \ 1) * x. (x * y) * ((y \ (x \ 1)) * z) = L(z,x * y,x * y). (x / y) * ((y * (x \ 1)) * z) = L(z,x / y,x / y). ((1 / x) * y) * ((y \ x) * z) = L(z,(1 / x) * y,(1 / x) * y). L(x,(1 / y) * z,(1 / y) * z) = ((1 / y) * z) * ((z \ y) * x). x * ((y \ x) \ 1) = L(T(y,y \ 1),x,x). L(T(x,x \ 1),y,y) = y * ((x \ y) \ 1). L(x,y,y) != z | L(x,y \ 1,y) = z. x != L(y,z,z) | x = (z \ (z / y)) \ 1. L(x,y \ 1,y) = (y \ (y / x)) \ 1. (x \ (x / y)) \ 1 = L(y,x \ 1,x). L(x,y,y) != z | y * ((y \ 1) * x) = z. x != y * ((1 / y) \ z) | x = (y * y) * z. T(((1 / (x \ 1)) \ y) * (1 / x),x) = ((x \ 1) * (x \ 1)) * y. T(x * y,y \ 1) = ((y \ 1) \ 1) * x. ((1 / x) * y) \ x = ((x \ y) \ 1) * x. ((x \ y) \ 1) \ x = ((y \ x) \ 1) * x. ((1 / x) * (y * (z \ 1))) \ (z / y) = ((z / y) * x) * (z / y). (x * T(x \ 1,y)) * x = x * (x * T(x \ 1,y)). x / ((x \ 1) \ y) != z | x * (1 / (x * y)) = z. T(T(x * y,y \ 1),y) = x / (1 / y). (x * ((1 / y) * z)) \ x != u | L(z \ y,x,x) = u. (((x / y) * x) / z) \ x = (z / x) * y. (((x / y) * x) / z) \ x != u | u = (z / x) * y. (((x / y) * x) / z) \ x != u | (z / x) * y = u. T(x * (y \ 1),y) != z | (1 / y) * x = z. (1 / x) * R(x,y,z) != u | u = R(x,y,z) / x. (1 / x) * R(x,y,z) != u | R(x,y,z) / x = u. (x \ 1) * (y * (x \ 1)) != z | x \ (y / x) = z. (1 / (x * y)) \ ((y \ (x \ 1)) \ z) = (x * y) * ((x * y) * z). (1 / (x * y)) \ x != z * x | (x \ 1) \ y = z. x * y != (z * T(u,z)) / z | u / y = x. x / (1 / y) = (y \ 1) \ T(x,y). (x \ 1) \ T(y,x) = y / (1 / x). (x \ (y / x)) \ 1 = (y * (x \ 1)) \ ((x \ 1) \ 1). (x * (y \ 1)) \ ((y \ 1) \ 1) = (y \ (x / y)) \ 1. (x \ 1) * (1 / T(x,y)) = x \ (T(x,y) \ 1). T(x * ((1 / x) * y),x) = (x \ y) * x. (x * ((x \ 1) \ y)) \ x = y \ (x \ 1). x != ((1 / y) * z) / u | x = 1 / (u * (z \ y)). (x \ y) * (1 / x) = 1 / (x * (y \ x)). 1 / (x * (y \ x)) = (x \ y) * (1 / x). ((x \ y) / x) / x = (x \ (y / x)) * (1 / x). (x \ (y / x)) * (1 / x) = ((x \ y) / x) / x. (x * y) * ((y \ (x \ 1)) * z) != u | L(z,x * y,x * y) = u. (((1 / x) * y) * z) * ((z \ (y \ x)) * u) != w | L(u,((1 / x) * y) * z,((1 / x) * y) * z) = w. x * y != T(z,x \ 1) | y = (1 / z) \ (x \ 1). (x \ 1) * y = (1 / T(y,x)) \ (x \ 1). (1 / T(x,y)) \ (y \ 1) = (y \ 1) * x. T(x * y,y \ 1) = T(y,y \ 1) * x. x != T(T(y * z,y),z) | x = y * z. (x \ 1) / (1 / x) = (x \ 1) * x. (x \ 1) / (1 / x) = K(x \ 1,x). x \ (1 / (1 / x)) = K(x \ 1,x). K(x \ 1,x) * (1 / x) = x \ 1. K(x \ 1,x) \ (x \ 1) = 1 / x. x * K(x \ 1,x) = 1 / (1 / x). (x \ 1) * L(y,1 / x,K(x \ 1,x)) = K(x \ 1,x) * ((1 / x) * y). L((1 / x) \ y,1 / x,K(x \ 1,x)) = (x \ 1) \ (K(x \ 1,x) * y). R(x,K(y \ 1,y),1 / y) * (y \ 1) = (x * K(y \ 1,y)) * (1 / y). ((x * (1 / y)) / z) \ x = (z / x) * (x * y). (1 / ((1 / x) * y)) \ x = (x \ y) * x. (x * y) \ x = ((x \ 1) * y) \ (x \ 1). ((x \ 1) * y) \ (x \ 1) = (x * y) \ x. (x \ (y \ 1)) * y = ((y \ 1) \ x) \ y. ((x \ 1) \ y) \ x = (y \ (x \ 1)) * x. 1 / ((x * y) * (y \ (y / x))) = ((x * y) \ ((x * y) * x)) * (1 / (x * y)). ((x * y) \ ((x * y) * x)) * (1 / (x * y)) = 1 / ((x * y) * (y \ (y / x))). (x \ 1) / ((x \ 1) * y) = 1 / T(y,x). (1 / (x * y)) \ (y \ 1) = (y \ 1) * ((1 / y) \ x). x * y != T(z,z \ 1) * u | x \ T(u * z,z \ 1) = y. (T(x,x \ 1) * T(x,x \ 1)) \ T(((T(x,x \ 1) * y) / T(x,x \ 1)) * x,x \ 1) = y / T(x,x \ 1). (((x \ y) \ 1) \ 1) \ y = (y \ x) * y. x != y / (y * z) | x = (y * (1 / z)) / y. 1 / T(x,y) = ((y \ 1) * (1 / x)) / (y \ 1). ((x \ 1) * (1 / y)) / (x \ 1) = 1 / T(y,x). ((x \ 1) \ 1) \ y = (y \ (y / x)) * y. (x * ((y \ 1) \ 1)) \ x = x \ (x / y). x / (x \ (x / y)) = x * ((y \ 1) \ 1). x / (x \ y) = x * (((y \ x) \ 1) \ 1). x * (((y \ x) \ 1) \ 1) = x / (x \ y). 1 / (x / (x \ y)) = ((y \ x) \ 1) / x. ((x \ y) \ 1) / y = 1 / (y / (y \ x)). (x \ y) \ (1 / y) = 1 / (y / (y \ x)). 1 / (x / (x \ y)) = (y \ x) \ (1 / x). 1 / (x / y) = L(y / x,y,y). L(x / y,x,x) = 1 / (y / x). L(x / y,x,x) != z | 1 / (y / x) = z. x != (y / z) / (1 / z) | x = L(y,z,z). L(x,1 / y,1 / y) = L(x,y,y). L(x,1 / y,1 / y) != z | L(x,y,y) = z. ((1 / x) * (1 / y)) \ (1 / x) != z | L(y,x,x) = z. x * y != z * L(u \ 1,u,w) | (z * ((w * u) \ w)) / y = x. (x * ((y * x) \ y)) / x = L(1 / x,x,y). T(x,L(T(x,y),z,u)) = x. L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u). L(T(x,y),z,u) / x = (1 / x) * L(T(x,y),z,u). (1 / x) * L(T(x,y),z,u) = L(T(x,y),z,u) / x. (x * L(y,z,u)) / x = L((x * y) / x,z,u). L((x * y) / x,z,u) = (x * L(y,z,u)) / x. (x * (y * z)) / (x * y) = L(((x * y) * z) / (x * y),y,x). L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y). R(R(x,y,K(y,x)),z,u) * (y * K(y,x)) = (y * K(y,x)) * R((y * K(y,x)) \ (y * x),z,u). (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = R(R(y,x,K(x,y)),z,u) * (x * K(x,y)). T(x,R(T(x,y),z,u)) = x. ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y). (x * R(y,z,u)) / x = R((x * y) / x,z,u). R((x * y) / x,z,u) = (x * R(y,z,u)) / x. x * y != R((z * u) / z,w,v5) * z | T(x,y) = y \ (z * R(u,w,v5)). T(((x * y) / x) * z,z \ x) = (z \ x) \ (x * R(y,z,z \ x)). (x \ y) \ (y * R(z,x,x \ y)) = T(((y * z) / y) * x,x \ y). x * y != R((z * u) / z,w,v5) * z | (z * R(u,w,v5)) / y = x. (x * R(y,z,z \ x)) / (z \ x) = ((x * y) / x) * z. L(x / y,z,u) * y != w | w = y * L(y \ x,z,u). L(x / y,z,u) * y != w | y * L(y \ x,z,u) = w. T(L(x / y,z,u),y) != w | w = L(y \ x,z,u). T(L(x / y,z,u),y) != w | L(y \ x,z,u) = w. (x * ((y * x) \ z)) / x = L((y \ z) / x,x,y). L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z. ((x / y) * R(y,z,u)) / (x / y) = R(x / (x / y),z,u). R(x / y,z,u) * y != w | w = y * R(y \ x,z,u). R(x / y,z,u) * y != w | y * R(y \ x,z,u) = w. (1 / x) \ (y \ (1 / y)) = x / ((1 / y) \ y). x * ((y * (x \ z)) / y) = ((y * (z / x)) / y) * x. ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x). (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y). (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y. ((x * (y / z)) / x) \ (z * ((x * (z \ y)) / x)) = z. x * ((y * (x \ z)) / y) != u | ((y * (z / x)) / y) * x = u. T((R(x,y,z) * (1 / x)) / R(x,y,z),x) = (x \ R(x,y,z)) / R(x,y,z). ((1 / x) * y) * (1 / ((y \ x) / z)) = 1 / ((y \ x) / ((y \ x) \ z)). (x \ (x / y)) \ y = (1 / y) \ L(y,x,x). (1 / x) \ L(x,y,y) = (y \ (y / x)) \ x. x != (1 / y) \ L(z,u,u) | x = y / ((u * z) \ u). (x \ (x / y)) \ y = y / ((x * y) \ x). x / ((y * x) \ y) = (y \ (y / x)) \ x. R(T(x \ y,z),u,w) = T(T(R(y / x,u,w),z),x). T(T(R(x / y,z,u),w),y) = R(T(y \ x,w),z,u). (x * (y * z)) / (u * z) = (1 / z) \ ((((1 / z) * x) * y) / u). (1 / x) \ ((((1 / x) * y) * z) / u) = (y * (z * x)) / (u * x). (x \ (y * (z * x))) / x = ((1 / x) * y) * z. (x / y) * (y \ 1) = x / (y * y). x != y * (z \ 1) | x = z \ ((z * y) / z). (x \ 1) \ (((1 / (x \ 1)) \ y) * z) = x \ ((x * (y * (z / (x \ 1)))) / x). x * y != (z * (u / w)) * w | (w \ (((1 / w) \ z) * u)) / y = x. (x \ (((1 / x) \ y) * z)) / x = y * (z / x). (x * (y / (1 / z))) * (1 / z) = z / (y \ (((1 / (1 / z)) \ x) \ 1)). x / (y \ (((1 / (1 / x)) \ z) \ 1)) = (z * (y / (1 / x))) * (1 / x). x \ ((x / y) * z) = ((1 / y) * (z / x)) * x. ((1 / x) * (y / z)) * z = z \ ((z / x) * y). (1 / x) \ ((L(1 * x,x,x) \ y) * z) = (y * (z / (1 / x))) * (1 / x). (x * (y * (x * y))) \ x = 1 / (y * (x * y)). (x \ (1 / x)) \ y = x * ((x \ 1) \ y). x != ((y * z) \ z) * u | x = T(y \ 1,z) * u. T(x,y) \ (1 / y) = T(x \ 1,y) * (1 / y). T(x \ 1,y) * (1 / y) = T(x,y) \ (1 / y). x != (y \ 1) / (1 / y) | x = K(y \ 1,y). K(1 / x,1 / (1 / x)) = K(x \ 1,x). L(x,x \ 1,x) = 1 / (1 / x). R(1 / (1 / x),y,z) = L(R(x,y,z),x \ 1,x). L(R(x,y,z),x \ 1,x) = R(1 / (1 / x),y,z). x != (1 / (y * z)) \ y | x = ((y \ 1) \ z) * y. x * (y * ((x \ 1) \ 1)) = ((x \ 1) \ y) * x. x * y != (1 / (x * z)) \ x | T((x \ 1) \ z,x) = y. T((x \ 1) \ y,x) = y * ((x \ 1) \ 1). T((x \ 1) \ y,x) = y * T(x,x \ 1). x != (y \ 1) * ((z \ 1) \ 1) | x = (z \ y) \ 1. T((x \ 1) \ (y \ 1),x) = (x \ y) \ 1. x * (((x \ y) \ 1) \ 1) = ((x \ 1) \ (y \ 1)) \ x. ((x \ 1) \ (y \ 1)) \ x = x * (((x \ y) \ 1) \ 1). ((x / y) * z) \ x = (1 / x) * ((z / x) \ y). (1 / x) * ((y / x) \ z) = ((x / z) * y) \ x. (x * (y * z)) \ z = (1 / z) * (y \ (x \ z)). (1 / x) * (y \ (z \ x)) = (z * (y * x)) \ x. ((x / y) * (z \ 1)) \ x = (1 / x) * ((z \ (1 / x)) \ y). (1 / x) * ((y \ (1 / x)) \ z) = ((x / z) * (y \ 1)) \ x. x \ ((y \ 1) \ (x \ 1)) = (y \ x) \ (x \ 1). T(1 / (x / y),y \ x) = (y \ x) \ ((y \ x) / (x / y)). (x \ y) \ ((x \ y) / (y / x)) = T(1 / (y / x),x \ y). (x \ y) * z != (x \ y) / (y / x) | T(1 / (y / x),x \ y) = z. T(1 / (1 / x),x \ 1) = x. x != T(1 / (1 / y),z) | x = L(T(y,z),1 / y,y). x = L(T(x,x \ 1),1 / x,x). L(T(x,x \ 1),1 / x,x) = x. T(x,y) = T(T(1 / (1 / x),y),x \ 1). T(T(1 / (1 / x),y),x \ 1) = T(x,y). x != y \ (z * (y \ 1)) | x = (y \ 1) * (z / y). ((1 / x) * y) * (x \ 1) = (x \ 1) * (y / x). (x \ 1) * y != x \ (z * (x \ 1)) | T((1 / x) * z,x \ 1) = y. T((1 / x) * y,x \ 1) = y / x. T(x,y \ 1) = ((1 / y) \ x) / y. ((1 / x) \ y) / x = T(y,x \ 1). (1 / (x / y)) \ y = y * ((1 / y) * x). T(x,y \ 1) * y = (1 / y) \ x. T(x,y \ 1) * (((1 / y) \ x) / y) = ((1 / y) \ x) * (y \ (((1 / y) \ x) / y)). ((1 / x) \ y) * (x \ (((1 / x) \ y) / x)) = T(y,x \ 1) * (((1 / x) \ y) / x). x * y != (1 / y) \ z | x = T(z,1 / y). T(x,y \ 1) = T(x,1 / y). T(x,1 / y) = T(x,y \ 1). T(x,y) * (1 / y) = (1 / (1 / y)) \ x. (1 / (1 / x)) \ y = T(y,x) * (1 / x). ((1 / x) \ (y \ 1)) * y = (1 / y) \ ((y \ 1) * x). (1 / x) \ ((x \ 1) * y) = ((1 / y) \ (x \ 1)) * x. T(x,y) = T(x,(y \ 1) \ 1). T(x,(y \ 1) \ 1) = T(x,y). T(x,1 / (1 / y)) = T(x,y). (1 / x) * T(y,x \ 1) = y * (1 / x). x != T(T(y * z,z \ 1),z) | x = y / (1 / z). T(T(x * y,y \ 1),(y \ 1) \ 1) = x / (1 / y). x * T(y,(x \ 1) \ 1) = y * x. T(x,(y \ (z \ y)) \ 1) = T(x,T(z,y)). (1 / (1 / x)) \ y = T(y / (1 / (1 / x)),x). T(x / (1 / (1 / y)),y) = (1 / (1 / y)) \ x. x != (1 / (1 / y)) \ z | x = ((y \ 1) \ 1) \ z. T(x,y) * (1 / y) = ((y \ 1) \ 1) \ x. ((x \ 1) \ 1) \ y = T(y,x) * (1 / x). x != (1 / T(y,z)) * T(y,u) | x = T(y,u) / T(y,z). x * (1 / T(x,y)) = T(x,T(x,y) \ 1) / T(x,y). T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y)). (1 / x) * (y * (x \ 1)) = (x \ y) * (1 / x). T(x,y) * (1 / y) = T(y,y \ 1) \ x. T(x,x \ 1) \ y = T(y,x) * (1 / x). x != ((y \ 1) \ 1) \ (1 / z) | x = 1 / (z * y). T(1 / x,y) * (1 / y) = 1 / (x * y). T(x \ (1 / T(y,y \ 1)),T(y,y \ 1)) = T(x \ 1,y) * (1 / y). x * y != 1 / z | x = 1 / (y * z). T(1 / x,y) = 1 / ((1 / y) * (x * y)). 1 / ((1 / x) * (y * x)) = T(1 / y,x). 1 / T(x,x * y) = T(1 / x,y). 1 / T(x,y) = T(1 / x,x \ y). T(1 / x,x \ y) = 1 / T(x,y). T(1 / x,y) \ 1 = T(x,x * y). T(x,x * y) = T(1 / x,y) \ 1. T((1 / 1) \ (x * y),(y \ (x \ 1)) \ z) = 1 / T(y \ (x \ 1),z). x != T(y,z) \ 1 | x = z \ (y \ z). T(x,x * y) = y \ ((1 / x) \ y). T(x \ 1,(x \ 1) * y) = T(x,y) \ 1. x != y \ ((1 / z) \ y) | x = L(T(z,y),y,y). T(x,x * y) = L(T(x,y),y,y). x * y != T(z \ 1,(z \ 1) * u) | x \ (T(z,u) \ 1) = y. (1 / x) \ (T(y,x) \ 1) = (y \ 1) * x. (T(x,y) \ 1) * y = T((x \ 1) * y,y). T((x \ 1) * y,y) = (T(x,y) \ 1) * y. x * y != (1 / y) \ z | x = T(z,y \ 1). x \ 1 = T(T(x,y) \ 1,y \ 1). T(T(x,y) \ 1,y \ 1) = x \ 1. (1 / (1 / x)) * ((y \ 1) * x) = ((1 / x) * (1 / x)) \ (T(y,x) \ 1). ((1 / x) * (1 / x)) \ (T(y,x) \ 1) = (1 / (1 / x)) * ((y \ 1) * x). T((x \ y) \ 1,x \ 1) = (y / x) \ 1. x * (y \ 1) = (T(y,x \ 1) \ 1) * x. (T(x,y \ 1) \ 1) * y = y * (x \ 1). (1 / x) * (y \ 1) = (T(y,x) \ 1) * (1 / x). (T(x,y) \ 1) * (1 / y) = (1 / y) * (x \ 1). ((x \ 1) \ 1) * y = y * ((T(x,y) \ 1) \ 1). x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x. (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1). x != (y \ 1) * (1 / z) | x = 1 / (z / (1 / y)). x \ (T(x,y) \ 1) = 1 / (T(x,y) / (1 / x)). 1 / (T(x,y) / (1 / x)) = x \ (T(x,y) \ 1). T(1 / T(x,y),y \ 1) = 1 / x. L((x * y) / x,z,u) * x != w | w = x * L(y,z,u). L((x * y) / x,z,u) * x != w | x * L(y,z,u) = w. L((x * (y \ z)) / x,y,u) = (x * ((u * y) \ (u * z))) / x. L((x * (y \ (z \ u))) / x,y,z) = (x * ((z * y) \ u)) / x. L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x. L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x. R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x. ((x * R(y,z,u)) / x) * (z * u) = (((x * y) / x) * z) * u. R((x * (y / (1 / z))) / x,1 / z,z) = (x * (y * z)) / x. ((x * R(y,z,u)) / x) * (z * u) != w | (((x * y) / x) * z) * u = w. (x \ (y * z)) / x = ((1 / x) * y) * (z / x). ((1 / x) * y) * (z / x) = (x \ (y * z)) / x. ((1 / x) * (1 / (y * z))) * y = y \ ((y / x) * (1 / z)). (x \ ((x / y) * z)) \ 1 = x \ ((z / x) \ y). ((x \ (x \ 1)) * (y / z)) * z = z \ ((z / (x * x)) * y). (1 / x) * ((y / x) \ 1) = (x * y) \ x. (((x / y) * z) \ x) \ 1 = ((z / x) \ y) \ x. x \ (y \ (x \ 1)) = ((1 / y) \ x) \ (x \ 1). ((1 / x) \ y) \ (y \ 1) = y \ (x \ (y \ 1)). T((1 / x) \ (y \ 1),y) = (1 / (1 / y)) \ x. (1 / x) * (y \ 1) = (x \ (y \ x)) * (1 / x). (x \ (y \ x)) * (1 / x) = (1 / x) * (y \ 1). (T(x,y) \ 1) * (1 / x) = (1 / x) * (T(x,y) \ 1). ((x \ y) \ y) * (1 / y) = (1 / y) * ((x \ 1) \ 1). T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1. (T(x,y) \ 1) \ 1 = T((x \ 1) \ 1,y). 1 / T((x \ 1) \ 1,y) = T(x,y) \ 1. (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y). ((x \ y) \ 1) \ 1 = T(((y / x) \ 1) \ 1,x). T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1. (x \ y) \ 1 = T(((x / y) \ 1) \ 1,x). T(((x / y) \ 1) \ 1,x) = (x \ y) \ 1. 1 / T(x,y) = T(1 / (1 / x),y) \ 1. T(1 / (1 / x),y) \ 1 = 1 / T(x,y). (T(x,y \ 1) \ 1) \ y = y * ((x \ 1) \ 1). x * (((x \ y) \ 1) \ 1) = (((x / y) \ 1) \ 1) \ x. (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1). 1 / (1 / T(x,y)) = T(1 / (1 / x),y). x != 1 / (1 / y) | x = y * K(y \ 1,y). T(1 / (1 / x),y) = T(x,y) * K(T(x,y) \ 1,T(x,y)). T(x,y) * K(T(x,y) \ 1,T(x,y)) = T(1 / (1 / x),y). 1 / (1 / (x \ y)) = T(1 / (1 / (y / x)),x). T(1 / (1 / (x / y)),y) = 1 / (1 / (y \ x)). ((1 / (x * y)) * x) * ((y * z) / (x * y)) = L(z,y,x) / (x * y). ((x \ (y * z)) / x) \ 1 = (z / x) \ (((1 / x) * y) \ 1). (x / y) \ (((1 / y) * z) \ 1) = ((y \ (z * x)) / y) \ 1. L(x,y,y) * (z / y) = (y \ ((y * x) * z)) / y. (x \ ((x * y) * z)) / x = L(y,x,x) * (z / x). (x \ (y * z)) \ 1 = x \ ((z / x) \ (y \ x)). x \ ((y / x) \ (z \ x)) = (x \ (z * y)) \ 1. K(x \ ((y / x) \ z),x \ ((x / z) * y)) = ((x \ ((x / z) * y)) \ 1) * (x \ ((x / z) * y)). ((x \ ((x / y) * z)) \ 1) * (x \ ((x / y) * z)) = K(x \ ((z / x) \ y),x \ ((x / y) * z)). ((x / y) \ (((x / y) / z) * 1)) \ 1 = (x / y) \ ((((y \ 1) \ 1) * (1 / x)) \ z). (x / y) \ ((((y \ 1) \ 1) * (1 / x)) \ z) = ((x / y) \ (((x / y) / z) * 1)) \ 1. L(((x \ 1) \ (((x \ 1) / y) * z)) \ 1,x,x) = x * ((z / (x \ 1)) \ y). T((1 / x) \ (y \ 1),y) = ((y \ 1) \ 1) \ x. x != (1 / y) * ((z / y) \ 1) | x = (y * z) \ y. (x \ ((y / x) \ x)) * (1 / x) = (x * y) \ x. (x \ (y / x)) * (1 / x) = (1 / x) * ((x * (x / y)) \ 1). (1 / x) * ((x * (x / y)) \ 1) = (x \ (y / x)) * (1 / x). (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1. x * (1 / (1 / (x \ y))) = (1 / (1 / (y / x))) * x. (1 / (1 / (x / y))) * y = y * (1 / (1 / (y \ x))). (x * (y * z)) \ ((z / (x * (y * z))) \ ((x * y) \ (x * (y * z)))) = a(x,y,z) \ 1. ((x \ y) \ 1) * (1 / x) = (x * y) \ x. (T(x,y) * ((x \ T(y,x)) * z)) \ (y * z) = a(T(x,y),T(x,y) \ y,z). (x * y) \ (y * (x \ T(x,y))) = L(x \ 1,T(x,y),y). (x * y) \ (y * (y \ x)) = L(y \ 1,T(x,y),y). x != (y * T(z,u)) / y | x = T((y * z) / y,u). R(x,y,T(x,y)) = T(((x * y) * x) / (x * y),y). T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y)). (x * y) * (y \ (x \ z)) = R(1 / z,x,y) \ 1. (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). x != L(y \ z,y,u) | x = (u * y) \ (u * z). L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y). (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u)). (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u)). (x * y) * L(L(z,T(x,y),y),u,w) = y * (T(x,y) * L(z,u,w)). (x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u)). T((x * y) \ (y * z),u) = L(T(T(x,y) \ z,u),T(x,y),y). L(T(T(x,y) \ z,u),T(x,y),y) = T((x * y) \ (y * z),u). (x * y) * T((x * y) \ (x * z),u) != w | x * (y * T(y \ z,u)) = w. T(x / (y * z),u) * (y * z) = (T((x / z) / y,u) * y) * z. (T((x / y) / z,u) * z) * y = T(x / (z * y),u) * (z * y). (x * y) * ((z * ((x * y) \ (u * y))) / z) = ((z * R(u / x,x,y)) / z) * (x * y). ((x * R(y / z,z,u)) / x) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x). R(T(T(x / y,z),y * u),y,u) = T((y * u) \ (x * u),z). (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = ((R(z / x,x,y) \ 1) \ 1) * (x * y). ((R(x / y,y,z) \ 1) \ 1) * (y * z) = (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1). R(x,T(y,x),T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x). x \ T(x * y,z) = (x \ 1) * T((x \ 1) \ y,z). (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z). T(x * y,z) / y = T(x / (1 / y),z) * (1 / y). T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y. (x * y) * T((x * y) \ z,u) != w | x * (y * T(y \ (x \ z),u)) = w. (x \ y) * ((z \ 1) \ 1) != u | (z \ ((1 / y) * x)) \ 1 = u. (1 / (x * y)) * ((z \ 1) \ 1) != u | (z \ ((y \ (x \ 1)) \ 1)) \ 1 = u. (x \ (y \ (z \ 1))) / u != w | ((z * y) * x) \ (1 / u) = w. ((x \ 1) / y) \ (1 / y) = y / (y * (1 / x)). (x \ (1 / y)) \ (1 / y) = y / (y * (1 / x)). T(x,x \ (1 / y)) = y / (y * (1 / x)). T(x \ y,x) \ ((1 / z) * u) != w | T(y \ x,x) / (u \ z) = w. (1 / x) \ L(y,z,z) != u | x / ((z * y) \ z) = u. x * T(x \ (x / y),z) = (x / y) * (y * T(y \ 1,z)). (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z). x \ (y \ x) = R(T(1 / y,x),y,y \ x). R(T(1 / x,y),x,x \ y) = y \ (x \ y). T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y). x != L(T(y,z \ 1),z \ 1,z) | x = z * (y * (z \ 1)). T(x * y,x \ 1) = x * (((x \ 1) \ y) * (x \ 1)). x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1). x != L(T(y,z),z,1 / z) | x = (1 / z) * (y * z). T((1 / x) * y,x) = (1 / x) * ((x \ y) * x). (1 / x) * ((x \ y) * x) = T((1 / x) * y,x). x * y != L(T(z \ u,w),z,1 / z) | x \ T((1 / z) * u,w) = y. (1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z). x * y != R(T(z / u,w),u,u \ 1) | T(z * (u \ 1),w) / y = x. T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y. L(x,y,(y * x) / y) * y = y * T(x,y * x). x != L(y \ 1,y,z) * u | x = ((z * y) \ z) * u. x * (y * T(y \ 1,x * y)) = ((x * y) \ x) * (x * y). ((x * y) \ x) * (x * y) = x * (y * T(y \ 1,x * y)). x * y != (z * (u * w)) * a(z,u,w) | x \ ((z * u) * w) = y. ((x * y) * a(z,x,y)) \ ((z * x) * y) = R(T(z,(x * y) * a(z,x,y)),x * y,a(z,x,y)). R(T(x,(y * z) * a(x,y,z)),y * z,a(x,y,z)) = ((y * z) * a(x,y,z)) \ ((x * y) * z). (x * y) * (y \ z) != z * u | R(T(x,z),y,y \ z) = u. (x \ y) \ 1 != z | (y \ 1) * T(x,x \ 1) = z. T(x,y) * (x \ z) != u | (x \ z) * T((x \ z) \ z,y) = u. (x * y) / a(z,z \ y,T(x,y)) = z * ((z \ y) * T(x,y)). (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u)). x != T(L(y,z,u),w) | x = L(T(y,w),z,u). T(T((x * y) / x,z),y * x) = L(T(y,z),x,y). R(1 / x,x,x \ y) != z | (x \ y) / y = z. (x \ (x \ 1)) * y != z | (1 / x) * (x \ y) = z. x != ((y * z) \ y) \ 1 | x = y * ((z \ y) \ 1). L(x,y * x,1 / (y * x)) = y * ((x \ y) \ 1). L(T(x,x \ 1),1 / x,x) = T(x,K(x,1 / x)). R(x,y,z) \ R(T(x,x \ 1),y,z) = a(R(x,y,z),1 / x,x). ((x \ 1) \ 1) \ y != z | 1 / ((y \ 1) * x) = z. x * (((1 / y) * z) * x) != u | (x / y) * (z * x) = u. (x \ 1) * L(y * (x \ 1),z,u) = x \ L(y / x,z,u). (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u). ((x * (1 / y)) / z) \ x != u | (z / x) * (x * y) = u. L(((x / y) \ z) / y,y,x / y) = (y * (x \ z)) / y. L((x \ (y * (x * z))) / z,z,x) = (z * T(y,x * z)) / z. (x * y) \ x = L(y \ 1,T(x,y),y). L(x \ 1,T(y,x),x) = (y * x) \ y. x * T(y,x * y) != z * x | L(y,x,(x * y) / x) = z. L(x,y * x,y * x) = y * ((x \ y) \ 1). x != L(T(y,y \ 1),1 / y,y) | x = y. T(x,K(x,1 / x)) = x. T(1 / x,K(x \ 1,x)) = 1 / x. K(x \ 1,x) * L(1 / x,y,z) = L(1 / x,y,z) * K(x \ 1,x). L(1 / x,y,z) * K(x \ 1,x) = K(x \ 1,x) * L(1 / x,y,z). x != T(y,z) * (y \ 1) | x = y \ T(y,z). (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y). (x * ((y * x) \ y)) * (x \ 1) = L(x \ 1,x,y). x * y != L(z \ 1,z,u) | ((u * z) \ u) / y = x. ((x * y) \ x) / (y \ 1) = y * ((x * y) \ x). (1 / ((x * y) \ x)) \ y = y * ((x * y) \ x). (1 / ((x * y) \ x)) * (y * ((x * y) \ x)) = y. x != (1 / y) * (z * y) | x = T(z,z * y). x = T(x,x * ((y * x) \ y)). T(x,x * ((y * x) \ y)) = x. T(x \ y,(x \ y) * (y \ x)) = x \ y. (((x * y) \ x) * y) / ((x * y) \ x) = L(y,(x * y) \ x,y). T(x / y,(x / y) * (y / x)) = x / y. x * y != T(z \ u,(z \ u) * (u \ z)) | T(x,y) = y \ (z \ u). T(1 / (x \ y),(y \ x) * (x \ y)) = ((y \ x) * (x \ y)) \ (y \ x). x * y != T(z / u,(z / u) * (u / z)) | x \ (z / u) = y. (1 / (x / y)) \ (y / x) = (y / x) * (x / y). (x / y) / ((y / x) \ 1) = (y / x) * (x / y). x / (((x \ y) / y) \ 1) = ((x \ y) / y) * (y / (x \ y)). ((x \ y) / y) * (y / (x \ y)) = x / (((x \ y) / y) \ 1). T(x * L(x \ 1,y,z),x) = x * L(x \ 1,y,z). (1 / x) * L(1 / x,y,y) = ((y * x) \ y) / x. (x \ 1) * (((y \ 1) \ 1) * (z \ 1)) = ((y * (1 / z)) \ x) \ 1. (((x \ (y / z)) \ 1) \ (z * (y \ 1))) \ 1 = (z * (y \ 1)) * ((((x \ 1) \ 1) \ (z * (y \ 1))) \ 1). (x * (y \ 1)) * ((((z \ 1) \ 1) \ (x * (y \ 1))) \ 1) = (((z \ (y / x)) \ 1) \ (x * (y \ 1))) \ 1. (1 / x) \ (((1 / y) * z) * T((1 / y) * z,u)) = x / ((z * T((1 / y) * z,u)) \ y). (x * (1 / y)) * ((y \ 1) * x) = x * ((1 / y) * T(x * (1 / y),y)). x * ((1 / y) * T(x * (1 / y),y)) = (x * (1 / y)) * ((y \ 1) * x). ((x * y) \ z) \ 1 = (z \ 1) * (1 / ((1 / y) / x)). (x \ 1) * (1 / ((1 / y) / z)) = ((z * y) \ x) \ 1. K((x \ 1) * (1 / (y / z)),(z * (y \ 1)) \ x) = (((z * (y \ 1)) \ x) \ 1) * ((z * (y \ 1)) \ x). (((x \ 1) * (1 / (y / z))) \ 1) \ ((z * (y \ 1)) \ x) = ((1 \ ((z * (y \ 1)) \ x)) \ 1) * ((z * (y \ 1)) \ x). ((x \ (y \ 1)) \ 1) * ((1 / z) * u) = 1 / ((u \ z) / (y * x)). ((x \ 1) \ 1) * (((1 / y) * z) * u) = 1 / ((u \ (z \ y)) / x). x \ (x / (y / (1 / z))) = (x * ((y \ 1) \ z)) \ x. (x * ((y \ 1) \ z)) \ x = x \ (x / (y / (1 / z))). (x * y) \ ((y / z) \ 1) = y \ ((y / (x \ z)) \ 1). (x \ (y \ z)) * (z \ 1) = z * ((y * (x * z)) \ 1). T(x * R(x \ 1,y,z),x) = x * R(x \ 1,y,z). (x \ 1) * L(x \ 1,y,z) = x \ L(1 / x,y,z). x != (y \ (z \ 1)) * (z \ 1) | x = y \ (z \ (1 / z)). x * (y \ (1 / y)) = (1 / x) \ (y \ (1 / y)). (1 / x) \ (y \ (1 / y)) = x * (y \ (1 / y)). x != (1 / y) \ (z \ (1 / z)) | x = y / ((1 / z) \ z). x * (y \ (1 / y)) = x / ((1 / y) \ y). x / ((1 / y) \ y) = x * (y \ (1 / y)). x / (y \ (1 / y)) = x * ((1 / y) \ y). x != R(L(y,z,u),w,v5) | x = L(R(y,w,v5),z,u). (((1 / x) \ y) * z) / (y * z) = L(R(x,y,z),y,y). L(R(x,y,z),y,y) = (((1 / x) \ y) * z) / (y * z). T(x,x * T(x \ 1,y)) = x. R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x). L(x,y,z) * (1 / x) = L(T(x,1 / x),y,z) / x. L(T(x,1 / x),y,z) / x = L(x,y,z) * (1 / x). (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y. ((x * (y / z)) / x) * z != u | u = z * ((x * (z \ y)) / x). ((x * (y / z)) / x) * z != u | z * ((x * (z \ y)) / x) = u. ((x * (y / (y / z))) / x) \ ((y / z) * ((x * z) / x)) = y / z. T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y). T((x * y) \ (z * y),x) = R(T(x \ z,x * y),x,y). R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x). ((x \ 1) \ 1) \ y = y * (((y \ (x \ y)) \ 1) \ 1). x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x. x != (y \ (z \ 1)) * z | x = ((z \ 1) \ y) \ z. (1 / x) \ ((x \ 1) * y) = ((x \ 1) \ (1 / y)) \ x. ((x \ 1) \ (1 / y)) \ x = (1 / x) \ ((x \ 1) * y). x * y != T(T(z * u,u \ 1),(u \ 1) \ 1) | x \ (z / (1 / u)) = y. (x \ 1) \ (y / (1 / x)) = ((x \ 1) \ 1) * (y * x). ((R(x,y,z) \ 1) \ 1) \ ((x * y) * z) = ((x * y) * z) * (((((x * y) * z) \ (y * z)) \ 1) \ 1). ((x * y) * z) * (((((x * y) * z) \ (y * z)) \ 1) \ 1) = ((R(x,y,z) \ 1) \ 1) \ ((x * y) * z). x / (x * (((x \ y) \ 1) \ 1)) = ((x / y) \ 1) \ 1. (((x / y) \ 1) \ 1) * y != z | z = y * (((y \ x) \ 1) \ 1). (((x / y) \ 1) \ 1) * y != z | y * (((y \ x) \ 1) \ 1) = z. (1 / (1 / ((x * y) / (x * z)))) * (x * z) = (x * z) * (1 / (1 / L(z \ y,z,x))). T(x,y) * (z \ 1) = z \ T(z * (x * (z \ 1)),y). x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1). (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z). (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z). (1 / x) * T(y,z) = T(((1 / x) * y) * x,z) / x. T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z). (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x. (1 / x) \ T(y,z) = x * T(x \ ((1 / x) \ y),z). x * T(x \ ((1 / x) \ y),z) = (1 / x) \ T(y,z). x != T(y / z,u) * z | x = z * T(z \ y,u). T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z). T(x,x * L(x \ 1,y,z)) = x. (x * ((y \ (z \ 1)) \ u)) \ x = x \ (x / ((z * y) / (1 / u))). (x * y) \ (z * (y \ 1)) = y \ ((y / (x \ z)) \ 1). (x \ (y \ z)) * (z \ 1) = z * ((x * z) \ (y \ 1)). T(x,x * R(x \ 1,y,z)) = x. T(1 / x,(1 / x) * R(x,y,z)) = 1 / x. (R(x,y,z) * (1 / x)) / R(x,y,z) = L(1 / x,R(x,y,z),1 / x). (((x * y) \ x) \ 1) * L(((x * y) \ x) \ 1,z,u) = ((x * y) \ x) \ L((1 / 1) \ L(y,x,x),z,u). 1 / (x \ L(1 / x,y,y)) = (y \ (y / (x \ 1))) / (x \ 1). (x \ (x / (y \ 1))) / (y \ 1) = 1 / (y \ L(1 / y,x,x)). (x \ 1) * ((y * x) \ y) = x \ L(1 / x,y,y). (x \ 1) * ((y * x) \ y) = x \ (y \ (y / x)). L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x). x * (1 / T(y,x)) = ((y \ 1) \ 1) \ x. ((x \ 1) \ 1) \ y = y * (1 / T(x,y)). ((x \ 1) \ y) \ y = 1 / T(x,y). (((x \ y) \ 1) \ 1) \ (y \ 1) = (y \ 1) * (x * (y \ 1)). ((x \ 1) \ y) \ y = T(x \ 1,x * y). T(x \ 1,x * y) = ((x \ 1) \ y) \ y. ((x \ 1) \ y) * (1 / T(x,y)) = y. x / T(y \ 1,y * x) = (y \ 1) \ x. (1 / (x * (y * z))) \ (z \ (y \ 1)) = (1 / (z \ (y \ 1))) \ (((z \ (y \ 1)) \ 1) * x). (1 / (x \ (y \ 1))) \ (((x \ (y \ 1)) \ 1) * z) = (1 / (z * (y * x))) \ (x \ (y \ 1)). x / (x * ((y \ 1) \ 1)) = ((x / (x * y)) \ 1) \ 1. x * (T(y,z) * (x \ 1)) = T(x * (y * (x \ 1)),z). T(x * (y * (x \ 1)),z) = x * (T(y,z) * (x \ 1)). R(x,y,z) \ T(R(x,y,z) * (R(x,y,z) \ x),u) = T(x,u) * (R(x,y,z) \ 1). (x \ 1) * T((x \ 1) \ y,z) != u | u = x \ T(x * y,z). (x \ 1) * T((x \ 1) \ y,z) != u | x \ T(x * y,z) = u. T(x,y) / x = (1 / x) * T((1 / x) \ 1,y). (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x. (1 / x) * T((1 / x) \ (y / x),z) = T(y,z) / x. ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((1 / x) \ y),x). x != (y \ 1) * T((y \ 1) \ z,u) | x = y \ T(y * z,u). T(x * ((y \ 1) \ 1),z) / ((y \ 1) \ 1) = y \ T(y * x,z). (x * T(x \ y,z)) * (x \ 1) = T(y * (x \ 1),z). (x * y) \ (z * (y \ 1)) = y \ ((x \ z) * (y \ 1)). x != (y \ z) * ((u \ 1) \ 1) | x = (u \ ((1 / z) * y)) \ 1. (x \ 1) * ((y * (x \ 1)) \ (z \ 1)) = (x \ ((1 / (z \ (x \ 1))) * y)) \ 1. (x \ ((1 / (y \ (x \ 1))) * z)) \ 1 = (x \ 1) * ((z * (x \ 1)) \ (y \ 1)). (x \ (y \ (1 / z))) * z = (1 / z) * ((x * (1 / z)) \ (y \ 1)). (1 / x) * ((y * (1 / x)) \ (z \ 1)) = (y \ (z \ (1 / x))) * x. T(L(x,y,z) * (1 / x),x) = x \ L((x \ 1) \ 1,y,z). x != (1 / y) * T(z,y \ 1) | x = z * (1 / y). T(x,y \ 1) / y = ((1 / y) \ (x / y)) * (1 / y). ((1 / x) \ (y / x)) * (1 / x) = T(y,x \ 1) / x. (x * y) \ (z * (y \ 1)) = (y \ 1) * ((x \ z) / y). ((1 / (x \ y)) \ x) * (1 / (x \ y)) = T(y,(x \ y) \ 1) / (x \ y). T(x,(y \ x) \ 1) / (y \ x) = ((1 / (y \ x)) \ y) * (1 / (y \ x)). (x * y) \ (z \ 1) = (y \ 1) * ((x \ (z \ y)) / y). (x \ 1) * ((y \ (z \ x)) / x) = (y * x) \ (z \ 1). a(x,y,z) * (z \ ((x * y) \ 1)) = (x * (y * z)) \ 1. K(x,1 / x) \ (x * (T(x,y) / x)) = L(T(x,y),1 / x,x). (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). (x * y) * L((x * y) \ (x * z),u,w) = x * (y * L(y \ z,u,w)). (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w)). (x * y) * L(x * y,z,u) = x * (y * L(x * y,z,u)). x != y * (z * (z \ u)) | x = y * u. K(x \ 1,x) * L(x \ y,x,x \ 1) = (x \ 1) * y. K(x \ 1,x) * T(((x \ 1) * x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z)). L(x \ (y / z),x,1 / y) != u | (x \ y) / z = u. L((x * y) / (z * y),u,w) * (z * y) = (L(x / z,u,w) * z) * y. R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y. x \ L(L(y,x \ 1,x),z,u) != (x \ 1) * w | L(y,z,u) = w. x \ R(x * y,z,u) = (x \ 1) * R((x \ 1) \ y,z,u). (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u). x \ R(x * (y * (x \ 1)),z,u) = (x \ 1) * R(T(y,x \ 1),z,u). L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y. R(R(x,1 / y,y),z,u) / y != w * (1 / y) | R(x,z,u) = w. R(x * y,z,u) / y = R(x / (1 / y),z,u) * (1 / y). R(x / (1 / y),z,u) * (1 / y) = R(x * y,z,u) / y. K(x \ 1,x) * R(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * R(x \ ((x \ 1) \ y),z,u)). K(x \ 1,x) * L(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u)). (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z). (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u). (x * L(x \ 1,y,z)) \ x = L(1 / x,y,z) \ 1. (1 / x) * (x * R(x \ y,z,u)) = R((1 / x) * y,z,u). (1 / x) * (x * L(x \ y,z,u)) = L((1 / x) * y,z,u). (R(x / y,z,u) * y) * (y \ 1) = R(x * (y \ 1),z,u). (x / (y * z)) \ (x / z) = R(y,z,x \ 1). ((x * y) / (z * y)) \ x = R(z,y,(x * y) \ 1). R(x,y,1 \ 1) * (1 / y) = (x * y) * ((1 / y) * (1 / y)). (x * y) * ((1 / y) * (1 / y)) = R(x,y,1 \ 1) * (1 / y). ((x * y) / (z * y)) \ x = R(z,y,y \ (x \ 1)). ((x * (1 / y)) / (z / y)) \ x = R(L(z,y,y),1 / y,(1 / y) \ (x \ 1)). R(L(x,y,y),1 / y,(1 / y) \ (z \ 1)) = ((z * (1 / y)) / (x / y)) \ z. (x * (x \ (y \ 1))) * ((x \ (y \ 1)) \ (x \ z)) = (((y * x) / ((1 / z) * x)) \ y) \ 1. L(x \ T(x,y),x,y) = T((y * x) \ (x * y),x \ 1). T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x). x * T(x \ (y * z),u) = y * ((y \ x) * T((y \ x) \ z,u)). x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u). T((x * y) / z,u) * z = (T(x / (z / y),u) * (z / y)) * y. (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y. x \ (T(y * x,y) * z) != u | (y * (z / x)) * x = u. ((x \ (y / x)) \ 1) \ 1 = (y \ x) \ (1 / x). R(R(x,y,z),T(1 / x,R(x,y,z)),x) \ R(x,y,z) = (R(x,y,z) \ (R(x,y,z) / x)) * x. ((1 / x) * ((y \ 1) \ 1)) * (((1 / x) \ (((y \ x) \ x) \ 1)) * z) = L(z,((y \ x) \ x) * (1 / x),((y \ x) \ x) * (1 / x)). L(x,((y \ z) \ z) * (1 / z),((y \ z) \ z) * (1 / z)) = ((1 / z) * ((y \ 1) \ 1)) * (((1 / z) \ (((y \ z) \ z) \ 1)) * x). (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y. ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y. R(T(x,y * z),y,z) = T((y * z) \ ((y * x) * z),y). T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y). a(x,y,z) * (z \ (y \ (x \ 1))) = (x * (y * z)) \ 1. (x \ 1) * y != K(x \ 1,x) * z | L(x \ y,x,x \ 1) = z. K(x \ 1,x) * y != (x \ 1) * z | L(x \ z,x,x \ 1) = y. x != L(y \ T(y,z),y,z) | x = K(y,z). T((x * y) \ (y * x),y \ 1) = K(y,x). K(x,y) = T((y * x) \ (x * y),x \ 1). K(x,y) = T(K(x,y),x \ 1). T(K(x,y),x \ 1) = K(x,y). (x * K(x,y)) * (x \ 1) = K(x,y). T(x \ 1,K(x,y)) = x \ 1. x * y != T(K(z,u),z \ 1) | K(z,u) / y = x. K(x,y) / (x \ 1) = x * K(x,y). (x \ 1) * K(x,y) != z | K(x,y) * (x \ 1) = z. K(x,y) * x = (1 / x) \ K(x,y). (1 / x) \ K(x,y) = K(x,y) * x. x * K(x \ 1,y) = K(x \ 1,y) * x. K(x \ 1,y) * x = x * K(x \ 1,y). K(x,y) * (x \ 1) != z | (x \ 1) * K(x,y) = z. T((x * y) \ x,K(y,z)) = L(y \ 1,y,x). x != y * K(y \ 1,y) | x = 1 / (1 / y). K(x \ 1,x) * x = 1 / (1 / x). T(x,K(x \ 1,y)) = x. T(1 / x,K(x,y)) = 1 / x. R(1 / (x / y),x / y,y) = T((1 * y) / x,K(x / y,z)). T((1 * x) / y,K(y / x,z)) = R(1 / (y / x),y / x,x). x != L(y \ 1,y,z) | x = (z * y) \ z. T((x * y) \ x,K(y,z)) = (x * y) \ x. T(K(x,y),(z * x) \ z) = K(x,y). (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,z)) = T(K(y,z),((x * y) \ x) \ 1). x * y != (z * u) \ 1 | x \ (u \ (z \ 1)) = y. a(x,y,z) \ ((y * z) \ (x \ 1)) = z \ (y \ (x \ 1)). x \ ((y * z) / x) = (x \ y) * (z * (x \ 1)). (x \ y) * (z * (x \ 1)) = x \ ((y * z) / x). ((x \ 1) \ 1) * ((x \ (y / z)) \ 1) = ((x \ 1) \ z) * ((y \ 1) * ((x \ 1) \ 1)). ((x \ 1) \ y) * ((z \ 1) * ((x \ 1) \ 1)) = ((x \ 1) \ 1) * ((x \ (z / y)) \ 1). x * (y * (z \ 1)) = z \ (((z * x) * y) / z). x \ (((x * y) * z) / x) = y * (z * (x \ 1)). 1 / (x \ ((y * z) / x)) = (x / z) / (x \ y). (x \ y) * ((z * x) * (x \ 1)) = x \ (x / (z \ (y \ x))). ((x \ 1) \ y) * ((x \ (z / u)) \ 1) = (x \ 1) \ ((y * (u * (z \ 1))) / (x \ 1)). (x \ 1) \ ((y * (z * (u \ 1))) / (x \ 1)) = ((x \ 1) \ y) * ((x \ (u / z)) \ 1). x * (y * (z * (x \ 1))) = ((x * y) * z) / x. x / (x \ (y * z)) = (x / z) / (x \ y). (x / y) / (x \ z) = x / (x \ (z * y)). (x / y) / z = x / (x \ ((x * z) * y)). x / (x \ ((x * y) * z)) = (x / z) / y. ((x / y) / z) \ x = x \ ((x * z) * y). (1 / x) * ((x / y) / z) = 1 / (x \ ((x * z) * y)). 1 / (x \ ((x * y) * z)) = (1 / x) * ((x / z) / y). (x * ((x / y) / z)) \ x = (x \ ((x * z) * y)) / x. (x \ ((x * y) * z)) / x = (x * ((x / z) / y)) \ x. (x / y) \ (x * z) = (x * z) \ (((x * z) * y) * z). (x * y) \ (((x * y) * z) * y) = (x / z) \ (x * y). ((x / y) / (z \ (z \ 1))) \ x = x \ ((x / (z * z)) * y). (((x / y) * x) / z) \ x = x \ ((x * z) * ((1 / x) * y)). x \ ((x * y) * ((1 / x) * z)) = (((x / z) * x) / y) \ x. (1 / x) \ (x \ ((x * y) * z)) = (((x / z) / y) / x) \ x. ((x * (1 / y)) / z) \ x = x \ ((x * z) * L(y,x,x)). x \ ((x * y) * L(z,x,x)) = ((x * (1 / z)) / y) \ x. x != (y \ ((y * z) * u)) / y | x = L(z,y,y) * (u / y). (x * ((x / y) / z)) \ x = L(z,x,x) * (y / x). x != y * (T(z,u) / u) | x = y * ((1 / u) * z). (x * ((x / T(y,x)) / z)) \ x = L(z,x,x) * ((1 / x) * y). x * y != (z * ((z / u) / w)) \ z | (L(w,z,z) * (u / z)) / y = x. (L(x,y,y) * (z / y)) / (1 / y) = (y \ ((y / z) / x)) \ 1. (T(x,y) * (((1 / y) * x) / z)) \ T(x,y) = L(z,T(x,y),T(x,y)) * (y / T(x,y)). (T(x,y) * (T(x / y,x) / z)) \ T(x,y) = L(z,T(x,y),T(x,y)) * (y / T(x,y)). (x * ((1 / y) * (x / z))) \ x = L(T(y,x / z),x,x) * (z / x). L(T(x,y / z),y,y) * (z / y) = (y * ((1 / x) * (y / z))) \ y. x != T(((y / z) \ 1) \ 1,z) | x = ((z \ y) \ 1) \ 1. T(x,((y * x) / y) \ 1) = ((y \ (y * x)) \ 1) \ 1. T(x,((y * x) / y) \ 1) = (x \ 1) \ 1. x * y != (x \ 1) \ 1 | y = K(x,x \ 1). K(x * y,y \ (x \ 1)) = K(x * y,(x * y) \ 1). K(x * y,(x * y) \ 1) = K(x * y,y \ (x \ 1)). (1 / x) * (y * ((1 / x) * y)) = (y \ x) \ ((1 / x) * y). ((x \ y) \ ((1 / y) * x)) \ 1 = ((1 / y) * x) \ (x \ y). x != L(y,z,u) * (y \ 1) | x = y \ L(y,z,u). (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z). T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1. ((x \ 1) \ y) * L(1 / T(x,y),z,u) = L(x \ 1,z,u) * ((x \ 1) \ y). T(x \ 1,x \ L(x,y,z)) = x \ 1. (x \ 1) * ((x \ L(x,y,z)) \ 1) = (x \ L(x,y,z)) \ (x \ 1). x != R(y,z,u) * (y \ 1) | x = y \ R(y,z,u). (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z). x * y != R(z,u,w) * x | y = R(T(z,x),u,w). R((x \ y) \ y,z,u) = R(T(x,x \ y),z,u). R(T(x,x \ y),z,u) = R((x \ y) \ y,z,u). x * y != R(T(z,z \ u),w,v5) | x \ R((z \ u) \ u,w,v5) = y. ((x \ y) \ y) \ R((z \ u) \ u,w,v5) = T(x,x \ y) \ R(T(z,z \ u),w,v5). T(x,x \ y) \ R(T(z,z \ u),w,v5) = ((x \ y) \ y) \ R((z \ u) \ u,w,v5). x != (1 / y) * R(y,z,u) | x = R(y,z,u) / y. R(1 / (1 / x),y,z) * (1 / x) = R(x,y,z) / x. (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x. L(x \ 1,x,x \ 1) = 1 / x. L(T(x \ 1,y),x,x \ 1) = T(1 / x,y). L(1 / x,y,z) = L(L(x \ 1,y,z),x,x \ 1). L(L(x \ 1,y,z),x,x \ 1) = L(1 / x,y,z). K(x \ 1,x) * T(1 / x,y) = (x \ 1) * (x * T(x \ 1,y)). K(x \ 1,x) * L(1 / x,y,z) = (x \ 1) * (x * L(x \ 1,y,z)). T(x,x * (y * T(y \ 1,x))) = x. T(x,y) * (x * z) = x * (z * T(T(x,z),y)). x * (y * T(T(x,y),z)) = T(x,z) * (x * y). x * (T(x,y) * z) = T(x,y) * (x * z). T(x,y) * (x * z) = x * (T(x,y) * z). x \ y = T(x,z) * (x \ (T(x,z) \ y)). T(x,y) * (x \ (T(x,y) \ z)) = x \ z. T(x,y) * z = x * (T(x,y) * (x \ z)). x * (T(x,y) * (x \ z)) = T(x,y) * z. T(x,y) * (x * (T(x,y) \ z)) = x * z. x * y != z * (u * (u \ w)) | x \ (z * w) = y. T(x,y) \ (x * z) = x * (T(x,y) \ z). T(x / y,z) * x = (x / y) * (T(x / y,z) * y). (x / y) * (T(x / y,z) * y) = T(x / y,z) * x. T(x,y) * (z * x) = x * (T(x,y) * T(z,x)). x * (T(x,y) * T(z,x)) = T(x,y) * (z * x). (x \ y) * ((y / x) * z) = (y / x) * (T(y / x,x) * z). (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z). T(x,y) \ (x * (T(x,y) * z)) != u * w | u \ (x * z) = w. T(x,y) \ (x * (T(x,y) * z)) != u * w | (x * z) / w = u. T(x,y) \ (x \ z) = x \ (T(x,y) \ z). x * y = T(x,y) * T(y,x). T(x,y) * T(y,x) = x * y. T(T(x,y),T(y,x)) = T(y,x) \ (x * y). T(x,y) \ (y * x) = T(T(y,x),T(x,y)). T(x,T(y,x)) = T(x,y). (x * y) / T(y,x) = T(x,y). T(x,y) \ (x * y) = T(y,x). x * y != z * (z \ u) | x \ u = y. T(x,x \ y) \ y = T(x \ y,x). a(T(x,y),T(y,x),z) = (T(x,y) * (T(y,x) * z)) \ ((x * y) * z). (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). T(x,T(y / x,z)) * T(x \ y,z) = x * T(y / x,z). R(x,T(y,z),T(z,y)) * (y * z) = (x * T(y,z)) * T(z,y). ((x \ y) \ y) \ y = T(x \ y,x). T(x \ y,x) = ((x \ y) \ y) \ y. x != T(y,z) | x = z * (T(z,y) \ y). T(x,T(y,x)) = y * (T(y,x) \ x). x * (T(x,y) \ y) = T(y,T(x,y)). x != T(y,z) | x = (y / T(z,y)) * z. T(x,T(y,x)) = (x / T(y,x)) * y. (x / T(y,x)) * y = T(x,T(y,x)). T(R(x,y,z),u) = R(T(x,T(u,R(x,y,z))),y,z). R(T(x,T(y,R(x,z,u))),z,u) = T(R(x,z,u),y). T(T(x,y),z) = T(T(x,z),T(y,x)). T(T(x,y),T(z,x)) = T(T(x,z),y). T(x,T(T(y,x),z)) = T(x,T(y,z)). T(x,L(T(y,x),z,u)) = T(x,L(y,z,u)). T(x,x \ y) = T(x,y / x). T(x,y / x) = T(x,x \ y). T(x,y * x) = T(x,x / (y \ 1)). T(x,x / (y \ 1)) = T(x,y * x). T(x,y) * L(T(y,x),z,u) = L(y,z,u) * T(x,y). T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y). T(x,T(y,y * x)) = T(x,L(y,x,y)). T(x,y) * T(T(y,x),z) != u | T(y,z) * T(x,y) = u. T(x,y \ x) = T(x,x * (y \ 1)). T(x,x * (y \ 1)) = T(x,y \ x). T(x,(1 / y) \ x) = T(x,x * y). T(x,T(y \ x,z)) = T(x,T(x * (y \ 1),z)). T(x,T(x * (y \ 1),z)) = T(x,T(y \ x,z)). T(x,T(y,T(z,T(y,x)))) / (T(T(y,x),z) \ x) = T(y,T(z,T(y,x))). (x \ (y * x)) \ (y * x) = T(x,y). T(x,y) = (x \ (y * x)) \ (y * x). (x / y) * T(y,y \ x) = y * (x / y). x / T(y,x / y) = y \ x. T(x,y / x) != z | (x \ y) \ y = z. (x * (y / x)) * x = y * T(x,x \ y). x / T(y \ x,y) = (y \ x) \ x. L((((x \ y) \ z) \ z) \ z,x \ y,x) = T(y \ (x * z),x \ y). (x / y) * ((y \ x) \ y) = T(y,T(x / y,y)). T(x,T(y,x)) != z | T(x,y) = z. T(T(x,y),L(T(z,x),u,w)) = T(T(x,L(z,u,w)),y). T(x,x * y) = T(x,T(x * y,y)). T(x,T(x * y,y)) = T(x,x * y). T(x,T(T(y,x),z)) = T(x,T(y,T(z,T(y,x)))). T(x,T(y,T(z,T(y,x)))) = T(x,T(T(y,x),z)). x * (T(x,y) \ ((x \ T(x,y)) * z)) = L(z,x \ T(x,y),x). x * y != z * (x / z) | y = K(z,x / z). x * (T(x,y) \ (T(x,y) / x)) = K(x,T(x,y) / x). T(x,y) \ (x * z) != u | u = x * (T(x,y) \ z). T(x,y) \ (x * z) != u | x * (T(x,y) \ z) = u. T(x,y) * (x \ (T(x,y) \ z)) != u | u = x \ z. T(x,y) * (x \ (T(x,y) \ z)) != u | x \ z = u. x != T(T(y,z),T(u,y)) | x = T(T(y,u),z). T(x,y) \ (y * x) = T(T(y,x),x). T(x,y) * T(T(y,x),x) = y * x. L(T(x,y),z,u) \ (y * L(x,z,u)) = T(T(y,L(x,z,u)),L(x,z,u)). x != y * T(z,z \ y) | x = (z \ 1) \ y. (x * (y / x)) * x = (x \ 1) \ y. (x * T(y,y \ x)) / y = y * (x / y). x * y != (z * (u / z)) * z | x \ (u * T(z,z \ u)) = y. (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x). (x * (y / x)) * x != z | (x \ 1) \ y = z. x / y = y * (((y \ 1) * x) / y). x * (((x \ 1) * y) / x) = y / x. (x * y) * x = (x \ 1) \ (y * x). (x \ 1) \ (y * x) = (x * y) * x. x \ (y / x) = ((x \ 1) * y) / x. ((x \ 1) * y) / x = x \ (y / x). (x \ (y / x)) * x = (x \ 1) * y. x * y != (z \ 1) \ (u * z) | ((z * u) * z) / y = x. ((x * ((1 / (x \ 1)) \ y)) * x) / (x \ 1) = y * (x / (x \ 1)). (x \ 1) * ((x * y) * x) = y * x. (x \ y) * x = (x \ 1) * (y * x). (x \ 1) * (y * x) = (x \ y) * x. L(x,y,y \ (z / y)) = ((y \ 1) * z) \ ((y \ (z / y)) * (y * x)). ((x \ 1) * y) \ ((x \ (y / x)) * (x * z)) = L(z,x,x \ (y / x)). (x \ 1) \ (y * x) != z | z = (x * y) * x. (x \ 1) \ (y * x) != z | (x * y) * x = z. x * (y * x) = (x * y) / (1 / x). (x * y) / (1 / x) = x * (y * x). x != (y \ 1) * (z * y) | x = y \ (z / (1 / y)). (x \ y) * x = x \ (y / (1 / x)). x \ (y / (1 / x)) = (x \ y) * x. (1 / x) * (y * ((x \ 1) \ 1)) = (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1). (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (1 / x) * (y * ((x \ 1) \ 1)). 1 / ((x \ y) * x) = (((y * x) \ 1) \ 1) \ x. (((x * y) \ 1) \ 1) \ y = 1 / ((y \ x) * y). x * ((x \ y) * x) = y / (1 / x). (x * y) / (1 / y) = y * (T(x,y) * y). (((1 / x) * y) * z) / (((y \ x) \ 1) \ 1) = ((1 / x) * y) * (z * ((1 / x) * y)). x \ y = (x \ (y * (1 / x))) * x. (x \ (y * (1 / x))) * x = x \ y. (x \ 1) \ (y / x) = ((x \ 1) \ y) * (x \ 1). ((x \ 1) \ y) * (x \ 1) = (x \ 1) \ (y / x). x != y / (1 / z) | x = (y / (y / z)) * y. x * ((x \ y) * x) = (y / (y / x)) * y. (x / (x / y)) * x = y * ((y \ x) * y). x * ((x \ y) / x) = y * (1 / x). (x \ (1 / (x / y))) * x = x \ ((y \ 1) \ 1). x * (y / x) = (x * y) * (1 / x). (x * y) * (1 / x) = x * (y / x). (x * T(y,x)) * (1 / x) = x * ((1 / x) * y). (x * (y \ x)) / (x / y) = (x / y) * (x / (x / y)). x != y * (T(z,y) * y) | x = z * (y * y). (x * y) / (1 / y) = x * (y * y). x / (y * y) = (x * (1 / y)) / y. (x * (1 / y)) / y = x / (y * y). (x / y) * (y * y) != z | x / (1 / y) = z. (x / (y * y)) * y = x * (1 / y). x * y != z * (1 / x) | T(z / (x * x),x) = y. T(x / (y * y),y) = (y \ x) / y. x != y / (z * (u \ 1)) | x = (1 / y) \ (u / z). T(x / ((y * (z \ 1)) * (y * (z \ 1))),y * (z \ 1)) = (1 / ((y * (z \ 1)) \ x)) \ (z / y). x * y != T(z / (u * u),u) | ((u \ z) / u) / y = x. ((x \ y) / x) / x = (1 / x) * (y / (x * x)). (1 / x) * (y / (x * x)) = ((x \ y) / x) / x. T(x / ((y / z) * (y / z)),y / z) = T(x * (z * (y \ 1)),x) / (y / z). x * y != z * ((z \ x) * z) | T(x / (x / z),x) = y. T(x / (x / y),x) = L(y,y \ x,y). L(T(x,y),x \ z,x) = T(T(z / (z / x),z),y). T(T(x / (x / y),x),z) = L(T(y,z),y \ x,y). x * (y * y) != z | (x * y) / (1 / y) = z. T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,T(x,y)). x * (x * y) = T(x,y) * (y * x). T(x,y) * (y * x) = x * (x * y). (x / y) * ((y \ x) \ y) = T(y,y \ x). ((x * y) / x) * (y \ x) = T(x,x \ (x * y)). x != T(y,T(T(z,y),u)) | x = T(y,T(z,u)). T(x,T(y,T(z,T(y,x)))) = T(x,T(y,z)). ((x \ (y \ 1)) \ 1) \ x = 1 / ((x \ y) * x). (x * y) * (1 / y) = y * ((1 / y) * x). (x * ((1 / x) * y)) \ 1 = (1 / x) \ ((y * x) \ 1). ((x * y) / x) * (y \ x) = T(x,y). T(x,y) = ((x * y) / x) * (y \ x). x * y != ((z * u) / z) * (u \ z) | T(z,u) / y = x. T(x,y) / (y \ x) = (x * y) / x. x * y != ((z * u) / z) * (u \ z) | x \ T(z,u) = y. ((x * y) / x) \ T(x,y) = y \ x. T(x,x / y) / y = (x * (x / y)) / x. T(x,x / y) = ((x * (x / y)) / x) * y. ((x * (x / y)) / x) * y = T(x,x / y). T(x,R(1 / y,y,x)) = ((x * R(1 / y,y,x)) / x) * (y * x). ((x * R(1 / y,y,x)) / x) * (y * x) = T(x,R(1 / y,y,x)). T(x,R(y,y \ 1,x)) = ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x). ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x)). T(x * y,x) / y = ((x * y) * x) / (x * y). ((x * y) * x) / (x * y) = T(x * y,x) / y. T(T(x,x / y) / y,x) = x / y. ((x * (x / y)) / x) * y != z | z = T(x,x / y). ((x * (x / y)) / x) * y != z | T(x,x / y) = z. T(x / y,y) = T(y \ T(x,x / y),x). T(x \ T(y,y / x),y) = T(y / x,x). x != ((y * (z / u)) / y) * u | x = u * ((y * (u \ z)) / y). T(x,x / y) = y * ((x * (y \ x)) / x). x * ((y * (x \ y)) / y) = T(y,y / x). x * y != ((z * (z / u)) / z) * u | x \ T(z,z / u) = y. x \ T(y,y / x) = (y * (x \ y)) / y. x != T(y / z,z) | x = z \ y. T(x \ T(y,y / x),y) = x \ y. T((x \ y) \ T(y,x),y) = (x \ y) \ y. (x / y) * ((x * y) / x) = T(x,x / (x / y)). (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y)). x * ((y * (x \ y)) / y) != z | z = T(y,y / x). x * ((y * (x \ y)) / y) != z | T(y,y / x) = z. x * ((y * (x \ y)) / y) != z * u | z \ T(y,y / x) = u. x != ((y \ z) \ 1) \ y | x = ((z \ y) \ 1) * y. 1 / ((x \ y) * x) = (((y \ 1) \ x) \ 1) * x. (((x \ 1) \ y) \ 1) * y = 1 / ((y \ x) * y). T(T(x * y,x) / y,y) = R(x,y,T(x,y)). x * R(y,x,T(y,x)) = T(y * x,y). R(x,y,T(x,y)) != z | y \ T(x * y,x) = z. ((x \ 1) * (1 / y)) * x = 1 / ((x \ y) * x). R(T(x,T(y,R(x,z,u))),z,u) = R(T(x,y),z,u). R(T(x,T(1 / x,R(x,y,z))),y,z) = R(T(x,x \ 1),y,z). (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x. T(x,y) * z != L(y,T(x,y),y) * T(x,y) | z = T(y,x * y). L(T(x,y),T(y,x),x) = T(x,y * x). T(x,y) * T(y,y * x) = L(y,x,y) * T(x,y). x * T(y,x * y) = L(y,T(x,y),y) * x. L(x,T(y,x),x) * y = y * T(x,y * x). x * T(y,x * y) != z * x | L(y,T(x,y),y) = z. (x * (R(x,y,z) * T(u,x))) \ ((u * x) * R(T(x,u),y,z)) = a(x,T(u,x),R(T(x,u),y,z)). x * T(1 / x,T(x,y)) = K(x,T(x,y) / x). ((1 / x) * y) \ (x \ 1) = (1 / x) \ ((y * x) \ 1). T(x / y,z) * u != (x / y) * (y * T(y \ x,z)) | u = x. ((1 / x) * y) \ (x \ 1) = (1 / x) \ (x \ (y \ 1)). x != (1 / y) \ (y \ z) | x = y * ((1 / y) * z). ((1 / x) * y) \ (x \ 1) = x * ((1 / x) * (y \ 1)). ((1 / (x * y)) * z) \ (y \ (x \ 1)) = (x * y) * ((1 / (x * y)) * (z \ 1)). x * (y * ((x \ y) / y)) = T(y,y / (x * y)). (x * (x * y)) \ ((x * y) * x) = K(y * x,T(x,y)). K(x * y,x) = K(y * x,T(x,y)). K(x * y,T(y,x)) = K(y * x,y). K(x * y,T(y,x)) != z | K(y * x,y) = z. (1 / (x * y)) * (y \ (x \ 1)) = (x * y) \ (y \ (x \ 1)). (x \ 1) * ((y \ 1) * (1 / x)) = ((1 / y) \ x) \ (x \ 1). x / ((y \ 1) * (z / y)) = (1 / x) \ ((y / z) * y). (x \ y) / (((1 / y) * x) * y) = ((y * x) \ y) * (x \ y). (x * (y \ x)) \ (x * (y \ 1)) = (y \ 1) \ (y \ (1 / x)). (x \ (y \ 1)) * (x \ (y \ 1)) = (y * x) \ (1 / (y * x)). (((1 / x) * (y \ 1)) \ z) * ((1 / x) \ ((T(y,x) \ 1) \ 1)) = ((T(y,x) \ 1) * (1 / x)) \ (z / ((T(y,x) \ 1) * (1 / x))). ((T(x,y) \ 1) * (1 / y)) \ (z / ((T(x,y) \ 1) * (1 / y))) = (((1 / y) * (x \ 1)) \ z) * ((1 / y) \ ((T(x,y) \ 1) \ 1)). ((x * x) \ (y / z)) * z = z \ ((z / (x * x)) * y). x \ ((x / (y * y)) * z) = ((y * y) \ (z / x)) * x. (x / y) \ (((1 / y) * z) \ 1) = y * ((y \ (z * x)) \ 1). x != (y \ (z / y)) * (1 / y) | x = ((y \ z) / y) / y. (1 / x) * ((x * (x / y)) \ 1) = ((x \ y) / x) / x. (1 / x) * ((x / y) \ (x \ 1)) = ((x \ y) / x) / x. (1 / x) * y != ((x \ z) / x) / x | y = z / (x * x). (x / y) \ (x \ 1) = y / (x * x). x \ (y \ 1) = (x \ y) / (y * y). (x \ y) / (y * y) = x \ (y \ 1). (x \ (y \ 1)) \ 1 = (y * y) * ((x \ y) \ 1). (x * x) * ((y \ x) \ 1) = (y \ (x \ 1)) \ 1. (x \ (y \ 1)) * y = (x \ y) * (1 / y). (x \ y) * (1 / y) = ((y \ 1) \ x) \ y. ((x \ 1) \ y) \ x = (y \ x) * (1 / x). x * y != (z \ (u \ 1)) * u | x \ ((z \ u) * (1 / u)) = y. x \ (((1 / x) \ (y * x)) * (1 / (y * x))) = (((y * x) \ 1) * y) * x. (x \ 1) * y = ((y \ x) \ y) * (1 / y). ((x \ y) \ x) * (1 / x) = (y \ 1) * x. R(x,x \ (y \ (z \ 1)),z) = ((y \ z) * (1 / z)) / ((x \ (y \ (z \ 1))) * z). x != ((y \ 1) \ (z \ 1)) \ y | x = y * (((y \ z) \ 1) \ 1). ((x \ 1) \ y) * (1 / y) = y * (((y \ x) \ 1) \ 1). (x \ y) * (1 / y) = y * (((y \ (1 / x)) \ 1) \ 1). x * (((x \ (1 / y)) \ 1) \ 1) = (y \ x) * (1 / x). ((x * (y \ 1)) \ z) * (1 / z) = z * (((z \ (y / x)) \ 1) \ 1). ((1 / x) * y) * ((((y \ x) / z) \ 1) \ 1) = (z \ ((1 / x) * y)) * (1 / ((1 / x) * y)). (x \ ((1 / y) * z)) * (1 / ((1 / y) * z)) = ((1 / y) * z) * ((((z \ y) / x) \ 1) \ 1). (x / y) \ (x * T(x \ (x / y),z)) = y * T(y \ 1,z). (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y). x * T(x \ (y \ x),z) = (T(1 / y,z) * y) * (y \ x). (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y). K((x * y) \ x,x * y) = y * T(y \ 1,x * y). x * y != z * T(z \ 1,u * z) | K((u * z) \ u,u * z) / y = x. K((x * y) \ x,x * y) / y = T(1 / y,x * y). (x \ 1) * ((y * (x \ 1)) \ z) = x \ L(x * (y \ z),x \ 1,y). x \ L(x * (y \ z),x \ 1,y) = (x \ 1) * ((y * (x \ 1)) \ z). ((x \ y) / y) * x = x / (((x \ y) / y) \ 1). x / (((x \ y) / y) \ 1) = ((x \ y) / y) * x. x != (y \ 1) * (z * (y \ 1)) | x = y \ (z / y). (((x \ y) \ 1) \ 1) \ (y \ 1) = y \ (x / y). (x * y) * L(x * y,y,y) = x * ((1 / y) \ (x * y)). (x * y) * (x / (1 / y)) = x * ((1 / y) \ (x * y)). (x * y) * (x / (1 / y)) = x * (y * (x / (1 / y))). x != L(y / z,u,w) * z | x = z * L(z \ y,u,w). L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u). R(x * y,z,u) / y != w * (1 / y) | R(x / (1 / y),z,u) = w. (1 / x) \ L(y,z,u) = x * L(x \ ((1 / x) \ y),z,u). x * L(x \ ((1 / x) \ y),z,u) = (1 / x) \ L(y,z,u). (1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z). R(1 / x,y,z) \ 1 = (x * R(x \ 1,y,z)) \ x. (x * R(x \ 1,y,z)) \ x = R(1 / x,y,z) \ 1. (R(x,y,z) / x) \ (1 / x) = R(1 / (1 / x),y,z) \ 1. R(1 / (1 / x),y,z) \ 1 = (R(x,y,z) / x) \ (1 / x). (1 / x) * (L(y,z,u) * x) = L((1 / x) * (y * x),z,u). L((1 / x) * (y * x),z,u) = (1 / x) * (L(y,z,u) * x). (x * R(x \ y,z,u)) * (x \ 1) = R(y * (x \ 1),z,u). (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x). (x \ y) * L(z,x,x) = x \ (x / (z \ (y \ x))). x \ (x / (y \ (z \ x))) = (x \ z) * L(y,x,x). x * ((x \ y) * L(z,x,x)) = x / (z \ (y \ x)). x * ((x \ y) * L(z,x,x)) != u | u = x / (z \ (y \ x)). x * ((x \ y) * L(z,x,x)) != u | x / (z \ (y \ x)) = u. T((x \ y) * L(z,x,x),x) = 1 / T(z \ (y \ x),x). 1 / ((x \ y) * L(z,x,x)) = x / (x \ (y * (z * x))). x / (y \ (z \ x)) != u * w | u \ (x * ((x \ z) * L(y,x,x))) = w. ((1 / ((x \ y) * L(z,x,x))) \ x) * ((x \ y) * L(z,x,x)) = ((x \ y) * L(z,x,x)) * (x / (z \ (y \ x))). ((x / y) * (z * z)) \ x = x \ ((x / (z * z)) * y). x != y \ ((y / (z * z)) * u) | x = ((z * z) \ (u / y)) * y. ((x / y) * (z * z)) \ x = ((z * z) \ (y / x)) * x. x != (((y / z) * y) / u) \ y | x = (u / y) * z. x \ ((x * y) * ((1 / x) * z)) = (y / x) * z. x \ ((x * y) * z) = (y / x) * ((1 / x) \ z). (x / y) * ((1 / y) \ z) = y \ ((y * x) * z). x \ ((x * y) * (1 / z)) = (y / x) * (x / z). x * y != z \ ((z * u) * w) | x \ ((u / z) * ((1 / z) \ w)) = y. x \ ((y / z) * ((1 / z) \ u)) = x \ (z \ ((z * y) * u)). (((x / y) / z) / x) \ x = x * ((1 / x) * ((x * z) * y)). x * ((1 / x) * ((x * y) * z)) = (((x / z) / y) / x) \ x. (1 / x) * ((y / x) * y) = (y \ x) \ ((1 / x) * y). (x \ y) \ ((1 / y) * x) = (1 / y) * ((x / y) * x). ((1 / x) * ((y / x) * y)) \ 1 = ((1 / x) * y) \ (y \ x). (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z). ((x * y) / x) * (y * z) = (x \ (x * y)) * (((x * y) / x) * z). (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z). (x \ y) \ ((y / x) * z) = (y / x) * ((x \ y) \ z). x != (y \ 1) * ((1 / y) * z) | x = y \ (y \ z). (1 / x) * ((x \ 1) * y) = x \ (x \ y). x != y * ((1 / z) * z) | x = y. (1 / x) * ((x \ 1) * x) = x \ 1. (1 / (1 / x)) * (x * (1 / x)) = (1 / x) \ 1. (1 / x) * K(x \ 1,x) = x \ 1. L(x,K(y \ 1,y),1 / y) = (y \ 1) \ ((1 / y) * (K(y \ 1,y) * x)). (x \ 1) \ ((1 / x) * (K(x \ 1,x) * y)) = L(y,K(x \ 1,x),1 / x). (x \ 1) * L(y,K(x \ 1,x),1 / x) = (1 / x) * (K(x \ 1,x) * y). (x * (1 / y)) * K(y \ 1,y) != z * (y \ 1) | R(x,1 / y,K(y \ 1,y)) = z. x * (((x \ 1) \ 1) * y) = (x \ 1) \ ((x \ 1) \ y). (x \ 1) \ ((x \ 1) \ y) = x * (((x \ 1) \ 1) * y). (1 / x) * ((y \ x) \ 1) = x \ (x \ ((y \ 1) \ 1)). x \ (x \ ((y \ 1) \ 1)) = (1 / x) * ((y \ x) \ 1). x != (y / z) \ y | x = z. (1 / (1 / x)) * (x * (1 / x)) = x. x * ((1 / x) * ((y \ x) \ 1)) = x \ ((y \ 1) \ 1). x != ((1 / y) \ z) \ (z \ 1) | x = z \ (y \ (z \ 1)). (x \ 1) * ((y \ 1) * (1 / x)) = x \ (y \ (x \ 1)). ((x \ 1) \ 1) * ((y \ 1) * x) = (x \ 1) \ (y \ ((x \ 1) \ 1)). (x \ 1) \ (y \ ((x \ 1) \ 1)) = ((x \ 1) \ 1) * ((y \ 1) * x). (x \ 1) * (y * (1 / x)) = x \ ((1 / y) \ (x \ 1)). x \ ((1 / y) \ (x \ 1)) = (x \ 1) * (y * (1 / x)). x \ ((x * (1 / y)) \ 1) = (x \ 1) * (y * (1 / x)). (x \ 1) * y != x \ (z \ 1) | y = (x * z) \ x. x * (1 / y) = (y * (y * (1 / x))) \ y. (x * (x * (1 / y))) \ x = y * (1 / x). (x * (1 / y)) * (1 / y) = (y * (1 / x)) \ (1 / y). (x * (1 / y)) \ (1 / x) = (y * (1 / x)) * (1 / x). (x \ y) / T(x,y) = ((y * x) \ y) * (x \ y). ((x * y) \ x) * (y \ x) = (y \ x) / T(y,x). x != (y \ 1) \ (y \ z) | x = L(z,y,1 / y). (x * (y \ x)) \ (x * (y \ 1)) = L(1 / x,y,1 / y). x != L(1 / y,z,1 / z) | x = z \ (z / y). (x * (y \ x)) \ (x * (y \ 1)) = y \ (y / x). x != y * ((y \ z) \ 1) | x = (z / y) \ y. (x / y) \ (((1 / y) * z) \ 1) = ((z * x) / y) \ y. (x / y) \ (z \ y) = ((z * x) / y) \ y. ((x * y) / z) \ z = (y / z) \ (x \ z). (1 / (x * (y \ z))) \ x = (y / x) \ ((1 / z) \ x). (x / y) \ ((1 / z) \ y) = ((y \ 1) \ (x \ z)) * y. ((((x \ 1) \ (y \ z)) \ x) \ 1) * (1 / ((x \ 1) \ (y \ z))) = ((y / x) \ ((1 / z) \ x)) \ ((x \ 1) \ (y \ z)). K(x \ (x / y),x) = y * T(y \ 1,x). x * y != z \ (u * T(u \ z,u)) | x \ K(u \ z,u) = y. x \ K(y \ (y / x),y) = T(x \ 1,y). x * T(x \ 1,y) != z | K(y \ (y / x),y) = z. x != (1 / y) * T((1 / y) \ 1,z) | x = T(y,z) / y. K(x \ (x / (1 / y)),x) = T(y,x) / y. x != (y \ 1) * T((y \ 1) \ 1,z) | x = y \ T(y,z). K(x \ (x / (y \ 1)),x) = y \ T(y,x). x * y != z * T(z \ 1,u) | K(u \ (u / z),u) / y = x. K(x \ (x / y),x) / y = T(1 / y,x). K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y)). (x \ y) \ K(y \ x,y) = T((x \ y) \ 1,y). (x \ y) \ K(T(y,x) \ ((y * x) / y),T(y,x)) = T((x \ y) \ 1,T(y,x)). K(x \ (x / (1 / y)),x) * y = T(y,x). T(x,y) = K(y \ (y / (1 / x)),y) * x. K(T(1 / (1 / x),x \ 1),x \ 1) = T(x,x \ 1) / x. K(x \ (x / ((y / x) \ 1)),x) = (y / x) \ (x \ y). K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y. K(T(1 / T(x,y),T(x,z)),T(x,z)) / T(x,y) = T(1 / T(x,y),T(x,z)). ((x * y) \ x) \ K(y,x) = T(((x * y) \ x) \ 1,x). T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x). K(R(x,y,z) \ (R(x,y,z) / (((x \ R(x,y,z)) / R(x,y,z)) \ 1)),R(x,y,z)) = ((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1). ((x * y) \ x) * T(((x * y) \ x) \ 1,x) = K(y,x). K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y). T(L(x \ 1,x,y) \ 1,y) = ((y * x) \ y) \ K(x,y). T(x,x * K(y,x)) = x. T(x * K(y,x),x) = x * K(y,x). K(x,y) / (y \ 1) = y * K(x,y). (x * K(y,x)) \ K(y,x) = x \ 1. (x * K(y,x)) * ((x \ 1) * T((x \ 1) \ 1,z)) = K(y,x) * T(K(y,x) \ (K(y,x) / (x \ 1)),z). K(x,y) * T(K(x,y) \ (K(x,y) / (y \ 1)),z) = (y * K(x,y)) * ((y \ 1) * T((y \ 1) \ 1,z)). x != (y * z) \ z | x = T(y \ 1,z). x \ 1 = T(x \ 1,K(y,x)). T(x \ 1,K(y,x)) = x \ 1. T(K(x,y),y \ 1) = K(x,y). T((x * y) \ x,K(z,y)) = L(y \ 1,y,x). (1 / x) * K(y,x) = K(y,x) * (1 / x). K(x,y) * (1 / y) = (1 / y) * K(x,y). (K(x,y) \ 1) * y = y * (K(x,y) \ 1). (K(x,y) * (1 / y)) * z != (1 / y) * K(x,y) | 1 = z. 1 = K(1 / x,K(y,x)). K(1 / x,K(y,x)) = 1. K(x,K(y,x \ 1)) = 1. T(x,K(y,x \ 1)) = x. K(x,y \ 1) * L(y,z,u) = L(y,z,u) * K(x,y \ 1). L(x,y,z) * K(u,x \ 1) = K(u,x \ 1) * L(x,y,z). K(x,y \ 1) / y = (1 / y) * K(x,y \ 1). (1 / x) * K(y,x \ 1) = K(y,x \ 1) / x. T(x \ y,K(z,y \ x)) = L((y \ x) \ 1,y \ x,y). L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y) = K(x,y). K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y). x != L((y \ z) \ 1,y \ z,y) | x = z \ y. T(x \ y,K(z,y \ x)) = x \ y. K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z). ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x). (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y). (x * (1 / x)) * ((1 / x) \ y) = y * T(y \ ((1 / x) \ y),x \ 1). K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x). L(x * y,z,u) / ((1 / y) \ 1) = (1 / y) * L((1 / y) \ x,z,u). x * L((x \ 1) \ 1,y,z) = (1 / x) \ L(x,y,z). x * L(T(x,x \ 1),y,z) = (1 / x) \ L(x,y,z). x * L(T(x,x \ 1),y,y) = x / ((y * x) \ y). x * (y * ((x \ y) \ 1)) = x / ((y * x) \ y). x != y / ((z * y) \ z) | x = (z \ (z / y)) \ y. x * (y * ((x \ y) \ 1)) = (y \ (y / x)) \ x. L(x \ 1,y,z) = (1 / x) * (L(x \ 1,y,z) * x). (1 / x) * (L(x \ 1,y,z) * x) = L(x \ 1,y,z). (1 / x) * (L(x \ 1,x,y) * x) = (y * x) \ y. (x * y) \ x = (1 / y) * (L(y \ 1,y,x) * y). (x * y) \ x = (1 / y) * (((x * y) \ x) * y). (1 / x) * (((y * x) \ y) * x) = (y * x) \ y. 1 / ((x * y) \ x) = T(1 / ((x * y) \ x),y). T(1 / ((x * y) \ x),y) = 1 / ((x * y) \ x). T(1 / ((x * y) \ x),z) = T(T(1 / ((x * y) \ x),z),y). T(T(1 / ((x * y) \ x),z),y) = T(1 / ((x * y) \ x),z). R(x * (y \ 1),z,u) / (y \ 1) = y * R(y \ x,z,u). x \ (y \ ((y * z) * u)) = w / ((x \ ((z / y) * ((1 / y) \ u))) \ w). x / ((y \ ((z / u) * ((1 / u) \ w))) \ x) = y \ (u \ ((u * z) * w)). x * y != (z / x) \ x | y = (x \ z) \ 1. (1 / x) * ((x * y) * z) = (x \ ((x / z) / y)) \ 1. (x \ ((x / y) / z)) \ 1 = (1 / x) * ((x * z) * y). x * ((1 / x) * ((x * y) * z)) != u | (((x / z) / y) / x) \ x = u. ((x / y) * x) \ y = ((1 / y) * x) \ (x \ y). ((1 / x) * y) \ (y \ x) = ((y / x) * y) \ x. K(x,x \ 1) = T(x,x \ 1) / x. T(x,x \ 1) / x = K(x,x \ 1). x != T(y,y \ 1) / y | x = K(y,1 / y). K(x,x \ 1) = K(x,1 / x). K(x,1 / x) = K(x,x \ 1). K(x,x \ 1) * x = T(x,x \ 1). ((x \ 1) \ 1) / x = K(x,x \ 1). x * (1 / x) = K(x,x \ 1). K(x,x \ 1) = x * (1 / x). x != K(y,1 / y) | x = y / (1 / (1 / y)). K(x,x \ 1) = x / (1 / (1 / x)). x / (1 / (1 / x)) = K(x,x \ 1). x != K(y,z) | x = K((u / y) \ u,z). K(x,x \ 1) = K((y / x) \ y,1 / x). K((x / y) \ x,1 / y) = K(y,y \ 1). x != K(1 / y,1 / (1 / y)) | x = K(y \ 1,y). K(1 / x,(1 / x) \ 1) = K(x \ 1,x). x * y != K(z,1 / z) | x \ K(z,z \ 1) = y. x \ K(x,x \ 1) = 1 / x. K(x \ 1,x) = K(x \ 1,(x \ 1) \ 1). K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x). K(x,x \ 1) != y | x * (1 / x) = y. (x \ 1) * K(x,x \ 1) = 1 / x. K(x,x \ 1) * (1 / (1 / x)) = x. x != y * (1 / y) | x = (y \ 1) * y. K(x,x \ 1) = (x \ 1) * x. K(x,x \ 1) \ 1 = K(1 / x,x). K(x,x \ 1) * x = (x \ 1) \ 1. (1 / (1 / x)) * K(x,x \ 1) = x. K(x * y,(x * y) \ 1) = (y \ (x \ 1)) * (x * y). R(x,K(y,y \ 1),y) = ((x * K(y,y \ 1)) * y) / T(y,y \ 1). ((x * K(y,y \ 1)) * y) / T(y,y \ 1) = R(x,K(y,y \ 1),y). T(x,x \ 1) * L(y,x,K(x,x \ 1)) = K(x,x \ 1) * (x * y). T(x,x \ 1) * y != K(x,x \ 1) * (x * z) | L(z,x,K(x,x \ 1)) = y. (x * K(y,y \ 1)) \ (x * T(y,y \ 1)) != z | L(y,K(y,y \ 1),x) = z. K(x,x \ 1) \ x = 1 / (1 / x). K(x,x \ 1) * (x \ 1) = 1 / x. 1 / x != (x \ 1) * y | K(x,x \ 1) = y. (x \ 1) * y != 1 / x | K(x,x \ 1) = y. x * L(y,1 / (1 / x),K(x,x \ 1)) = K(x,x \ 1) * ((1 / (1 / x)) * y). L((1 / (1 / x)) \ y,1 / (1 / x),K(x,x \ 1)) = x \ (K(x,x \ 1) * y). ((x \ 1) \ 1) / L(y \ x,y,K(x,x \ 1)) = K(x,x \ 1) * y. x * L(y,K(x,x \ 1),1 / (1 / x)) = (1 / (1 / x)) * (K(x,x \ 1) * y). R(x,1 / (1 / y),K(y,y \ 1)) * y = (x * (1 / (1 / y))) * K(y,y \ 1). (1 / x) / L(y,(x \ 1) / y,K(x,x \ 1)) = K(x,x \ 1) * ((x \ 1) / y). K(1 / x,x) = K(x \ 1,x). x != K((y / z) \ y,1 / z) | x = K(z,z \ 1). K(1 / (1 / x),1 / x) = K(x,x \ 1). x != K(1 / y,y) | x = K(y,y \ 1) \ 1. K(x \ 1,x) = K(x,x \ 1) \ 1. K(x,x \ 1) \ 1 = K(x \ 1,x). K(x,x \ 1) = K((x \ 1) \ 1,x \ 1). K((x \ 1) \ 1,x \ 1) = K(x,x \ 1). 1 / (x * K(y \ 1,y)) = K(y,y \ 1) / x. x != K(y * z,(y * z) \ 1) | x = K(y * z,z \ (y \ 1)). (x \ (y \ 1)) * (y * x) = K(y * x,x \ (y \ 1)). K(x * y,y \ (x \ 1)) = (y \ (x \ 1)) * (x * y). T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) = (((x * y) / x) \ y) \ y. K(x,y \ 1) * L(y,z,u) != L(y,z,u) * w | K(x,y \ 1) = w. L(x,y,z) * u != K(w,x \ 1) * L(x,y,z) | K(w,x \ 1) = u. R(x,y,z) / (u \ 1) = u * R(u \ (x / (u \ 1)),y,z). x * R(x \ (y / (x \ 1)),z,u) = R(y,z,u) / (x \ 1). ((x \ y) / y) * R(((x \ y) / y) \ (((x \ y) / y) * x),z,u) = R(x,z,u) / (((x \ y) / y) \ 1). (x * (y * z)) * ((x * y) \ 1) = T(L(z,y,x),y \ (x \ 1)). T(T(x,y / z),z * (y \ 1)) = R(x,y / z,z * (y \ 1)). x != (y * z) * R(L(u,z,y),w,v5) | x = y * (z * R(u,w,v5)). R(x,y,z) * (x * u) = x * (u * R(T(x,u),y,z)). x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y). x * (R(x,y,z) * u) = R(x,y,z) * (x * u). R(x,y,z) * (x * u) = x * (R(x,y,z) * u). x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x. R(x,y,z) * u = x * (R(x,y,z) * (x \ u)). x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. R(x,y,z) \ (x * (R(x,y,z) * u)) = x * u. R(x,y,z) * (u * x) = x * (R(x,y,z) * T(u,x)). x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x). x \ (R(x,y,z) * u) != w | w = R(x,y,z) * (x \ u). x \ (R(x,y,z) * u) != w | R(x,y,z) * (x \ u) = w. x * y != R(z,u,x) * (u * x) | T(z * u,x) = y. T(x * y,x) = R(x,y,x) * (x \ (y * x)). R(x,y,x) * (x \ (y * x)) = T(x * y,x). R(x,y,x) * T(y,x) = T(x * y,x). R(x,y,x) \ T(x * y,x) = T(y,x). L((x \ y) / y,z,u) * y = (L(1 / x,z,u) * x) * (x \ y). T(x / (x / y),y \ x) = y. T(x,y) = T(T(z / (z / x),y),x \ z). T(T(x / (x / y),z),y \ x) = T(y,z). T(x / (x / (x / y)),y) = x / y. (x \ y) * x = (y / (y / x)) * (x \ y). (x / (x / y)) * (y \ x) = (y \ x) * y. ((x \ y) * x) / (x \ y) = y / (y / x). ((x \ y) * x) / (x \ y) != z | z = y / (y / x). ((x \ y) * x) / (x \ y) != z | y / (y / x) = z. ((x \ y) * x) / (x \ y) != z * u | z \ (y / (y / x)) = u. (x * (y / x)) / x = y / (y / (y / x)). R(x / y,x / (x / y),x / y) = T((x * (x / y)) / x,y). R(1 / (1 / (1 / x)),x,y) = (x * (y / (x * y))) / x. x * L(x \ (y * z),u,w) = y * ((y \ x) * L((y \ x) \ z,u,w)). x * ((x \ y) * L((x \ y) \ z,u,w)) = y * L(y \ (x * z),u,w). x * L(x \ ((x / y) * z),u,w) = (x / y) * (y * L(y \ z,u,w)). (x / y) * (y * L(y \ z,u,w)) = x * L(x \ ((x / y) * z),u,w). x * R(x \ (y * z),u,w) = y * ((y \ x) * R((y \ x) \ z,u,w)). x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w). R((x * y) / z,u,w) * z = (R(x / (z / y),u,w) * (z / y)) * y. (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y. x != L(R(y,z,u),w,v5) * (z * u) | x = (L(y,w,v5) * z) * u. (x * y) * L(T(y,x),z,u) = (L(y,z,u) * x) * y. x != R(R(y,z,u),w,v5) * (z * u) | x = (R(y,w,v5) * z) * u. (x * y) * R(T(y,x),z,u) = (R(y,z,u) * x) * y. (x * (y * (z / x))) * x = L(((1 / x) \ y) * z,x,x). L(((1 / x) \ y) * z,x,x) = (x * (y * (z / x))) * x. (((x * (y * z)) / (x * y)) * x) * y = (x * y) * R(L(z,y,x),x,y). (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z)). (x * y) * ((z * ((x * y) \ (x * u))) / z) != w | x * (y * ((z * (y \ u)) / z)) = w. (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z)). x * ((y * (x \ (x / z))) / y) = (x / z) * (z * ((y * (z \ 1)) / y)). (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z). x * y != R((z * (u / (1 / w))) / z,1 / w,w) | ((z * (u * w)) / z) / y = x. ((x * (y * z)) / x) / z = ((x * (y / (1 / z))) / x) * (1 / z). ((x * (y / (1 / z))) / x) * (1 / z) = ((x * (y * z)) / x) / z. (x * y) * T((x * y) \ (y * z),u) = y * (T(x,y) * T(T(x,y) \ z,u)). (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y. x != y * ((y \ z) * T(u,z)) | x = L(u,y \ z,y) * z. (x * y) / a(z,z \ y,T(x,y)) = L(x,z \ y,z) * y. (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z)). L((x \ (y * (x * z))) / z,z,x) = T((z * y) / z,x * z). (x \ (x / (y \ 1))) / (y \ 1) = 1 / (y \ (x \ (x / y))). (x \ (x / (y \ 1))) / (y \ 1) = (1 / (x \ (x / y))) * y. (x \ (x / (y \ 1))) / (y \ 1) = ((1 / (x / y)) * x) * y. x != L(T(y,z),1 / y,y) | x = T(1 / (1 / y),z). K(x,1 / x) \ (x * (T(x,y) / x)) = T(1 / (1 / x),y). K(x,1 / x) * T(1 / (1 / x),y) = x * (T(x,y) / x). K(x,x \ 1) * T(1 / (1 / x),y) = x * (T(x,y) / x). K(x,x \ 1) * T(K(x,x \ 1) \ x,y) = x * (T(x,y) / x). (x * y) * ((1 / y) * (1 / y)) = R(x,y,1) * (1 / y). (x * y) * ((1 / y) * (1 / y)) = x * (1 / y). (x * y) * (1 * (y \ (1 / y))) = x * (1 / y). (x * y) * (y \ (1 / y)) = x * (1 / y). x * (y \ (1 / y)) = (x / y) * (1 / y). (x / y) * (1 / y) = x * (y \ (1 / y)). x * (1 / y) != z * (y \ (1 / y)) | x * y = z. x * (y \ (1 / y)) != z * (1 / y) | z * y = x. x != (y / z) * (1 / z) | x = (z / y) \ (1 / z). x * (y \ (1 / y)) = (y / x) \ (1 / y). (x / y) \ (1 / x) = y * (x \ (1 / x)). (x * (y \ (1 / y))) * y = x * (y \ 1). x != (y \ z) * y | x = z * K(y \ z,y). (((x \ 1) \ y) * (x \ (1 / x))) * x = y * K((x \ 1) \ y,x \ 1). x != (y \ (z / y)) * y | x = (y \ 1) * z. (((x \ 1) \ (y / (x \ 1))) * (x \ (1 / x))) * x = ((x \ 1) \ 1) * y. x * y != (z \ (u / z)) * z | ((z \ 1) * u) / y = x. (((x \ 1) \ 1) * y) / x = ((x \ 1) \ (y / (x \ 1))) * (x \ (1 / x)). ((x \ 1) \ (y / (x \ 1))) * (x \ (1 / x)) = (((x \ 1) \ 1) * y) / x. x != R(1 / (y / z),y / z,z) | x = z / y. T((1 * x) / y,K(y / x,z)) = x / y. T(x / y,K(y / x,z)) = x / y. T(x / y,y) = T(y \ x,K(y / x,z)). T(x \ y,K(x / y,z)) = T(y / x,x). T(x \ y,K(x / y,z)) = x \ y. (x * (T(x / y,x) / z)) \ x = L(z,x,x) * ((1 / x) * y). x * (y * z) != (z * T(y,z)) * T(z,y) | x = R(z,y,z). R(x,T(y,x),T(x,y)) = R(x,y,x). R(R(x,y,x),z,u) = R(R(x,z,u),T(y,x),T(x,y)). R(R(x,y,z),T(u,x),T(x,u)) = R(R(x,u,x),y,z). R(R(x,y,x),z,u) * (y * x) = (R(x,z,u) * T(y,x)) * T(x,y). (R(x,y,z) * T(u,x)) * T(x,u) = R(R(x,u,x),y,z) * (u * x). (x * (y * z)) * ((x * y) \ 1) = L(T(z,y \ (x \ 1)),y,x). x != T((y * (z / u)) / y,u) | x = (y * (u \ z)) / y. R(x / y,x / (x / y),x / y) = (x * (y \ x)) / x. R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * ((x / y) \ x)) / x. (x * (y * z)) * (y \ (x \ 1)) = L(T(z,y \ (x \ 1)),y,x). (x * y) \ ((z * y) * R(x / z,z,y)) = K(z * y,R(x / z,z,y)). R(T(x \ y,x * z),x,z) != u | T((x * z) \ (y * z),x) = u. (x * y) * R((x * y) \ (x * z),u,w) != v5 | x * (y * R(y \ z,u,w)) = v5. (x * y) * L(x * y,z,u) != w | x * (y * L(x * y,z,u)) = w. T(x / y,z) \ (y \ x) = (y \ x) * (T(x / y,z) \ 1). (x \ y) * (T(y / x,z) \ 1) = T(y / x,z) \ (x \ y). ((x \ y) \ y) * (T(x,z) \ 1) = T(y / (x \ y),z) \ ((x \ y) \ y). T(x / (y \ x),z) \ ((y \ x) \ x) = ((y \ x) \ x) * (T(y,z) \ 1). x * (x \ (y / (x \ 1))) = (x * ((x \ 1) * y)) * x. (x * ((x \ 1) * y)) * x = x * (x \ (y / (x \ 1))). (x * ((x \ 1) * y)) * x = y / (x \ 1). (x * (((1 / (x \ 1)) \ y) * z)) * x = ((y * (z / (x \ 1))) * (x \ 1)) / (x \ 1). ((x * (y / (z \ 1))) * (z \ 1)) / (z \ 1) = (z * (((1 / (z \ 1)) \ x) * y)) * z. T(((1 / (x \ 1)) \ y) * (1 / x),x) = (x \ (1 / x)) * y. T((x \ y) * (1 / x),x) = (x \ (1 / x)) * y. x != T(y * (1 / z),z) | x = (z \ 1) * y. (x \ (1 / x)) * y = (x \ 1) * (x \ y). ((x \ y) \ ((1 / y) * x)) * z = ((x \ y) \ 1) * ((x \ y) \ z). x != ((y * z) / y) * (z \ 1) | x = z \ ((y * z) / y). (x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y). (1 / x) \ (1 / (y * (z \ (u \ x)))) = (u * (z * x)) / (y * x). (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u). L(x,y,z) * (x * u) = x * (u * L(T(x,u),y,z)). x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y). x * (L(x,y,z) * u) = L(x,y,z) * (x * u). L(x,y,z) * (x * u) = x * (L(x,y,z) * u). x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u). x \ y = L(x,z,u) * (x \ (L(x,z,u) \ y)). L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u. L(x,y,z) * u = x * (L(x,y,z) * (x \ u)). x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u. L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u). x * y != z * (u * (u \ w)) | T(x,y) = y \ (z * w). T(x,L(x,y,z) * (x \ u)) = (L(x,y,z) * (x \ u)) \ (L(x,y,z) * u). (L(x,y,z) * (x \ u)) \ (L(x,y,z) * u) = T(x,L(x,y,z) * (x \ u)). L(x,y,z) * K(x,x \ 1) = x * (L(x,y,z) * (1 / x)). L(x,y,z) \ (x \ u) = x \ (L(x,y,z) \ u). x * y != z \ (u * z) | x \ T(u,z) = y. L(x,y,z) \ T(u,x) = x \ (L(x,y,z) \ (u * x)). x \ (L(x,y,z) \ (u * x)) = L(x,y,z) \ T(u,x). L((x * y) / y,y,L(x,z,u)) = T((y * x) / y,L(x,z,u) * y). T((x * y) / x,L(y,z,u) * x) = L((y * x) / x,x,L(y,z,u)). L(x,y,z) \ K(x,x \ 1) = x * (L(x,y,z) \ (1 / x)). L(x,y,z) * (x \ (L(x,y,z) \ u)) != w | w = x \ u. L(x,y,z) * (x \ (L(x,y,z) \ u)) != w | x \ u = w. x * (L(x,y,z) \ (x \ u)) != w | w = L(x,y,z) \ u. x * (L(x,y,z) \ (x \ u)) != w | L(x,y,z) \ u = w. L(x,y,z) * (x \ 1) != u | x \ L(x,y,z) = u. (x \ 1) * L((x \ 1) \ 1,y,z) != u | x \ L(x,y,z) = u. x * (L(x,y,z) \ u) != w | L(x,y,z) \ (x * u) = w. x != L(y,z,u) * K(w,y \ 1) | x = K(w,y \ 1) * L(y,z,u). x * (L(x,y,z) * (1 / x)) = K(x,x \ 1) * L(x,y,z). K(x,x \ 1) * L(x,y,z) = x * (L(x,y,z) * (1 / x)). ((x * (y / (y / T(z,x)))) / x) \ ((y / T(z,x)) * z) = y / T(z,x). (1 / x) * ((y * (1 / x)) \ ((1 / z) \ 1)) = (y \ (z / x)) * x. (1 / x) * ((y * (1 / x)) \ T(z * z,1)) = (y \ (((z * z) \ 1) \ (1 / x))) * x. x \ (y * T(y \ (x * z),u)) = (x \ y) * T((x \ y) \ z,u). x * y != z * T(u,z) | x \ (u * z) = y. x \ ((y \ (x * z)) * y) = (x \ y) * T((x \ y) \ z,y). (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y). x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z). x \ (y * T(y \ x,z)) = (x \ y) * T((x \ y) \ 1,z). (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). x * K((x \ y) \ 1,x \ y) = y * T(y \ x,x \ y). x * T(x \ y,y \ x) = y * K((y \ x) \ 1,y \ x). x * K(y \ (y / (x \ z)),y) = z * T(z \ x,y). x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z). x \ (y * T(y \ x,z)) = K(z \ (z / (x \ y)),z). K(x \ (x / (y \ z)),x) = y \ (z * T(z \ y,x)). x != (y \ 1) * T((y \ 1) \ (y \ z),u) | x = y \ T(z,u). (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z). x * T(y,z) = (x * y) * K(z \ (z / ((x * y) \ x)),z). (x * y) * K(z \ (z / ((x * y) \ x)),z) = x * T(y,z). (x * (y * z)) * T((x * (y * z)) \ (x * y),u) = (x * y) * K(u \ (u / L(z,y,x)),u). K((x * (y \ z)) \ x,x * (y \ z)) = y \ (z * T(z \ y,x * (y \ z))). K(x \ (x / T(y,z)),x) = z \ ((y * z) * T((y * z) \ z,x)). K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x)). x * T(y,(x * y) \ x) = (x * y) * K(((x * y) \ x) \ 1,(x * y) \ x). (x * y) * K(((x * y) \ x) \ 1,(x * y) \ x) = x * T(y,(x * y) \ x). x * y != T(z / u,w) * u | (u * T(u \ z,w)) / y = x. (x * T(x \ (y * z),u)) / z = T(y / (x / z),u) * (x / z). x * ((y \ 1) * (y * T(y \ 1,x * K(y \ 1,y)))) = L(1 / y,K(y \ 1,y),x) * (x * K(y \ 1,y)). ((x * (x \ y)) * x) / (x \ 1) = y * (x / (x \ 1)). (x * y) / (y \ 1) = x * (y / (y \ 1)). (1 / (x * y)) \ y = x * (y / (y \ 1)). (1 / (x * y)) \ y = x * ((1 / y) \ y). x * y != (1 / (z * u)) \ u | (z * ((1 / u) \ u)) / y = x. (x * ((1 / y) \ y)) / y = x / (1 / y). x != ((y * R(z,u,w)) / y) * (u * w) | x = (((y * z) / y) * u) * w. T(x,R(1 / y,y,x)) = (((x * (1 / y)) / x) * y) * x. (((x * (1 / y)) / x) * y) * x = T(x,R(1 / y,y,x)). (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y)). (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,R(1 / T(x,y),T(x,y),x)). x * (((y * x) / y) * z) = ((y * x) / y) * (x * z). ((x * y) / x) * (y * z) = y * (((x * y) / x) * z). x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z). ((x * y) / x) \ (y * z) = y * (((x * y) / x) \ z). L(x,((y * z) / y) \ z,(y * z) / y) = ((y * z) / y) * (z \ ((((y * z) / y) \ z) * x)). ((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x). x * L(x \ (y \ x),z,u) = (L(1 / y,z,u) * y) * (y \ x). (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z). T(x,x / (1 / y)) = ((x * (x * y)) / x) / y. ((x * (x * y)) / x) / y = T(x,x / (1 / y)). ((x * y) / x) / (x \ y) = T(x,x / (1 / (x \ y))). T(x,x / (1 / (x \ y))) = ((x * y) / x) / (x \ y). (x * y) * T(y,z) = (T((x * y) / x,z) * x) * y. (T((x * y) / x,z) * x) * y = (x * y) * T(y,z). (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y. (x * T(y,z)) * y = (x * y) * T(y,z). (x * y) / T(y,z) = (x / T(y,z)) * y. x * y != ((z / u) * u) * w | T(x,y) = y \ (z * w). T((x / y) * T(y,z),y) = y \ (x * T(y,z)). x != y * T(z,y) | x = z * y. (x * T(y,x * y)) * y = y * (x * y). ((x / y) * T(y,z)) * y = x * T(y,z). x * y != (z * x) * T(x,u) | T(z * T(x,u),x) = y. T(x * T(y,x * y),y) = x * y. (x * T(y,z)) \ ((x * y) * T(y,z)) = y. x * y != ((z / u) * u) * w | (z * w) / y = x. (x * T(y,z)) / y = (x / y) * T(y,z). x * y != (((z / u) / w) * w) * u | z / y = x. x / y = ((x / T(y,z)) / y) * T(y,z). ((x / T(y,z)) / y) * T(y,z) = x / y. ((x / y) * T(y,z)) \ (x * T(y,z)) = y. (x * (y \ z)) * (z / y) = (x * (z / y)) * T(z / y,y). (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z). x * y != y * (z * y) | x = (1 / y) \ z. x * T(y,x * y) = (1 / y) \ x. T(x,y * x) = T(1 / x,y) \ 1. x != T(1 / y,z) \ 1 | x = T(y,y * z). T(x,y * x) = T(x,x * y). x != T(y,y * z) | x = L(T(y,z),z,y). T(x,y * x) = L(T(x,y),y,x). L(T(x,y),y,x) = T(x,y * x). T(R(x,y,z),R(x,y,z) * u) = R(T(x,u * R(x,y,z)),y,z). R(T(x,y * R(x,z,u)),z,u) = T(R(x,z,u),R(x,z,u) * y). T(x,(x \ y) * x) = T(x,y). T(T(x,x * y),z) = T(T(x,z),y * x). T(T(x,y * x),z) = T(T(x,z),x * y). x * T(y,x * y) = L(y,x,y) * x. R(T(x,x * y),y,x) = T(x,y). R(T(x,y),x \ y,x) = T(x,x \ y). T(x,(x \ 1) * (y * x)) = T(x,y). T(x,y * x) != z | T(x,x * y) = z. (x * y) * T(x,y) = R(x,y,x) * (x * y). R(x,y,x) * (x * y) = (x * y) * T(x,y). T(x * y,x) * T(x,y) = R(x,y,x) * T(x * y,x). R(x,y,x) * T(x * y,x) = T(x * y,x) * T(x,y). L(x,T(y,x),x) = L(x,y,x). L(x,y,(y * x) / y) = L(x,y,x). T(L(x,y,x) * y,x) = y * x. (L(x,y,x) * y) * x = x * (y * x). (x * (y * x)) / x = L(x,y,x) * y. T(x,y * x) = T(x,L(x,y,x) * y). T(x,L(x,y,x) * y) = T(x,y * x). x != T(y,y \ z) | x = (y \ z) \ z. R(T(x,y),x \ y,x) = (x \ y) \ y. x * (y * z) != (L(u,w,v5) * y) * z | x = L(R(u,y,z),w,v5). x = L(R(x,y,x),y,x). L(R(x,y,x),y,x) = x. x * y != L(z,u,z) * u | x \ ((z * (u * z)) / z) = y. L(x,y,x) \ ((x * (y * x)) / x) = y. x != T(y,z * y) | x = T(y,y * z). T(x,L(x,y,x) * y) = T(x,x * y). T(x,(x \ y) * T(x,y)) = T(x,(x \ y) * x). x * y != z * T(x,u) | T((z / x) * T(x,u),x) = y. T((x / y) * T(y,x),y) = x. x * y != z * T(u,z) | (u * z) / y = x. (x * y) / x = (y / x) * T(x,y). (x / y) * T(y,x) = (y * x) / y. T(x * T(x \ y,y),x \ y) = y. T(x / y,T(y,x)) = T(y,x) \ ((y * x) / y). T(x,y) \ ((x * y) / x) = T(y / x,T(x,y)). x * y != (z / u) * T(u,z) | ((u * z) / u) / y = x. ((x * y) / x) / T(y / x,T(x,y)) = T(x,y). (x * (1 / y)) * T(L(y,1 / y,x),x) = (L(y,1 / y,x) * x) / L(y,1 / y,x). (L(x,1 / x,y) * y) / L(x,1 / x,y) = (y * (1 / x)) * T(L(x,1 / x,y),y). T(x,y) * T(T(y,x),x * y) = (T(y,x) * (x * y)) / T(y,x). (T(x,y) * (y * x)) / T(x,y) = T(y,x) * T(T(x,y),y * x). K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y). T(T(x,y),y \ x) = x. T(T(x,y \ x),y) = x. (x \ y) * y = T(y,x) * (x \ y). T(x,y) * (y \ x) = (y \ x) * x. (x * y) / x = T(y,x \ y). T(x,y \ x) = (y * x) / y. T(T(x,y),x / y) = x. (x * y) / x != z | z = T(y,x \ y). (x * y) / x != z | T(y,x \ y) = z. T(x,y) = T(x,T(y,y / x)). T(x,T(y,y / x)) = T(x,y). x != (y * z) / y | x = y * (z * (y \ 1)). T(x,y \ x) = y * (x * (y \ 1)). T(x,y \ x) * ((y * x) \ 1) = (y * x) / ((y * x) * y). (x * y) / ((x * y) * x) = T(y,x \ y) * ((x * y) \ 1). T((x * y) / x,x) * (y * (x \ 1)) = (x \ ((x * y) / x)) * ((x * y) / x). T(x,y \ x) = y * ((x * (y \ x)) / x). x * ((y * (x \ y)) / y) = T(y,x \ y). T(x,y \ x) != z | (y * x) / y = z. T(x,y) = R(T(x,y * T(x,z)),y,T(x,z)). R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y). ((x / T(y,z)) / y) * T(y,z) != u | x / y = u. ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x. T(T(x,y),x * z) = T(T(x,y),z * x). T(T(x,y),z * x) = T(T(x,y),x * z). T(T(x,y),x * z) != u | T(T(x,y),z * x) = u. T(x,x / y) = T(x,y \ x). x != T(y,(1 / z) \ y) | x = T(y,y * z). T(x,x / (1 / y)) = T(x,x * y). x != T(y,y / (z \ 1)) | x = T(y,z * y). T(x,(y \ 1) \ x) = T(x,y * x). T(x,y) = T(x,(y \ x) \ x). T(x,(y \ x) \ x) = T(x,y). T(x,x / (x / y)) = T(x,y). T(T(x,y \ x) / y,x) = x / y. T(x,T(y,y \ x)) = T(x,y). x * y != T(z,z / (z / u)) | x \ T(z,u) = y. (x / y) \ T(x,y) = (x * y) / x. T(x * y,T(x,y)) = T(x * y,x). x != T(y,z) | x = T(y,y / (y / z)). T(x,x / (1 / y)) = T(x,x / (x / (x * y))). T(x,x / (x / (x * y))) = T(x,x / (1 / y)). T(x,y \ x) = T(x,(1 / y) * x). T(x,(1 / y) * x) = T(x,y \ x). x \ T(x * y,y) = ((x * y) * y) / (x * y). ((x * y) * y) / (x * y) = x \ T(x * y,y). T(x,x * (1 / y)) = T(x,y \ x). T(T(x,y),z * x) != u | T(T(x,x * z),y) = u. x * (y * z) != (u * z) * T(y,z) | x = R(u,z,T(y,z)). R(x,y,x) = R(x,y,T(x,y)). R(x,y,T(x,y)) = R(x,y,x). x \ T(y * x,y) = R(y,x,y). R(x,T(y,x),T(x,y)) = R(x,T(y,x),x). x * R(y,x,y) = T(y * x,y). (x \ y) \ T(y,x) = R(x,x \ y,x). R(x,x \ y,x) = (x \ y) \ T(y,x). L(R(x,y,x),y,z) = (z * y) \ (z * T(x * y,x)). (x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x). x \ T(y * x,y) != z | z = R(y,x,y). x \ T(y * x,y) != z | R(y,x,y) = z. x != R(y,T(z,y),T(y,z)) | x = R(y,z,y). R(x,T(y,x),x) = R(x,y,x). R(x,x \ y,x) = R(x,y / x,x). R(x,y / x,x) = R(x,x \ y,x). x != R(y,y \ z,y) | x = (y \ z) \ T(z,y). R(x,y / x,x) = (x \ y) \ T(y,x). R(x,y,x) = (x \ (y * x)) \ T(y * x,x). (x \ (y * x)) \ T(y * x,x) = R(x,y,x). R(T(x,L(x,y,x) * y),y,T(x,x * y)) = T(x,y). x != T(y,(y \ z) * y) | x = T(y,z). T(x,(x \ y) * T(x,y)) = T(x,y). R(T(x,y),x \ y,T(x,y)) = T(x,x \ y). T(x,x / (x / y)) = T(x,x / (1 / (x \ y))). T(x,x / (1 / (x \ y))) = T(x,x / (x / y)). (x \ T(x * y,y)) * x = x * R(y,x,y). (x * R(y,x,y)) \ T(x * y,y) = K(x,x \ T(x * y,y)). x != T(y,y / (1 / (y \ z))) | x = ((y * z) / y) / (y \ z). T(x,x / (x / y)) = ((x * y) / x) / (x \ y). ((x * y) / x) / (x \ y) = T(x,x / (x / y)). T(x,x / (x / y)) * (x \ y) = (x * y) / x. T(x,y) * (x \ y) = (x * y) / x. T(x,y) * z != (x * y) / x | T(y / x,T(x,y)) = z. T(x / y,T(y,x)) = y \ x. T(x,y) \ ((x * y) / x) = x \ y. T(x,(y \ x) * y) * K(y \ x,y) = (x * ((y \ x) * y)) / x. ((x * y) / x) \ (T(x,y) * ((x \ y) * z)) != u | L(z,x \ y,T(x,y)) = u. x * ((x * y) / x) = T(x,y) * y. T(x,y) * y = x * ((x * y) / x). T(x \ y,x) = T(x \ y,T(x,y)). T(x \ y,T(x,y)) = T(x \ y,x). T(x,x \ y) * (x \ y) = x * (y / x). T(x,y) * T(x \ y,x) = (x \ y) * T(x,y). x \ (y * T(y \ x,T(y,x))) != z | K(y \ x,y) = z. (x / y) * T(y,z) != u | (x * T(y,z)) / y = u. R(T(x,x * y),y,T(x,x * y)) = T(x,y). (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z). (x * ((y * z) / y)) * z = (x * (y \ (y * z))) * ((y * z) / y). (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z. (x * (y / (y / z))) * z = (x * ((y / z) \ y)) * (y / (y / z)). (x * ((y / z) \ y)) * (y / (y / z)) = (x * (y / (y / z))) * z. (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z). (x * (y / z)) / (z \ y) = (x / (z \ y)) * (y / z). x != (y / (y / z)) * (z \ y) | x = (z \ y) * z. (x * (y \ x)) / (x / y) = (y \ x) * y. x != (y * (z \ y)) / (y / z) | x = (y / z) * (y / (y / z)). (x \ y) * x = (y / x) * (y / (y / x)). (x / y) * (x / (x / y)) = (y \ x) * y. ((x \ y) * x) * (y / x) = y * (x \ y). (x * y) / ((x * y) * x) = T(y,x \ y) * (y \ (x \ 1)). (x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),y). ((1 / x) * ((y / x) * y)) * z = ((y \ x) \ 1) * ((y \ x) \ z). x / (y * (z \ (u \ x))) = (u * (z * x)) / (y * x). (x * (y * z)) / (u * z) = z / (u * (y \ (x \ z))). (x * (y * z)) / (u * z) != w | z / (u * (y \ (x \ z))) = w. x != (y * z) * T((y * z) \ u,w) | x = y * (z * T(z \ (y \ u),w)). (T((x / y) / z,u) * z) * y = z * (y * T(y \ (z \ x),u)). ((x \ (y / z)) * x) * z = (x * z) * T((x * z) \ y,x). (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y. ((x \ (y / z)) * x) * z = x * (z * T(z \ (x \ y),x)). x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y. x != (y * z) * T((y * z) \ (y * u),w) | x = y * (z * T(z \ u,w)). ((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,x)). x != (y * z) * T((y * z) \ y,u) | x = y * (z * T(z \ 1,u)). ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x)). x * (y \ T(y * (x \ z),x)) = ((x \ (z / (y \ 1))) * x) * (y \ 1). ((x \ (y / (z \ 1))) * x) * (z \ 1) = x * (z \ T(z * (x \ y),x)). x * (T((x \ y) * z,x) / z) = ((x \ (y / (1 / z))) * x) * (1 / z). ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z). x * (K(x \ 1,x) * (x \ y)) = ((x \ (y / y)) * x) * y. ((x \ (y / y)) * x) * y = x * (K(x \ 1,x) * (x \ y)). ((x \ y) * x) * x = x * (x * T(x \ T(y,x),x)). x * (x * T(x \ T(y,x),x)) = ((x \ y) * x) * x. x * ((x \ T(y,x)) * x) = ((x \ y) * x) * x. T((x \ y) * x,x) = (x \ T(y,x)) * x. x * y != (z \ T(u,z)) * z | T((z \ u) * z,z) / y = x. T((x \ y) * x,x) / x = x \ T(y,x). x * y != (z \ T(u,z)) * z | x \ T((z \ u) * z,z) = y. T(x,y) \ T((y \ x) * y,y) = K(y \ T(x,y),y). x * (T((x \ y) * x,x) / x) = T(y,x). T(x * y,y) / y = y \ T(y * x,y). (x \ T(y,x)) * x != z | z = T((x \ y) * x,x). (x \ T(y,x)) * x != z | T((x \ y) * x,x) = z. T(x,y) / y = y \ T(y * (x / y),y). x \ T(x * (y / x),x) = T(y,x) / x. x * (T(y * x,x) / x) = T(x * y,x). x * (T(y,x) / x) = T(x * (y / x),x). T(x * (y / x),x) = x * (T(y,x) / x). T(x * T(y,z),x) / x = x \ T(x * T((x * y) / x,z),x). x \ T(x * T((x * y) / x,z),x) = T(x * T(y,z),x) / x. T(x * L(y,z,u),x) / x = x \ T(x * L((x * y) / x,z,u),x). x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x. T(x * y,x) = x * ((1 / x) * (y * x)). x * ((1 / x) * (y * x)) = T(x * y,x). T(x * (y / x),x) = x * (y / T(x,y)). T(x * y,x) \ T(y * x,x) = K(x \ T(x * y,x),x). ((x \ 1) * x) * y = x * (K(x \ 1,x) * (x \ y)). x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y. x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y. (x \ 1) * (K(x,x \ 1) * ((x \ 1) \ y)) = K((x \ 1) \ 1,x \ 1) * y. (1 / x) * ((y * (1 / x)) \ z) = (y \ (z / x)) * x. (1 / x) * ((y \ (1 / x)) \ z) = (((x * y) \ x) \ (z / x)) * x. (((x * y) \ x) \ (z / x)) * x = (1 / x) * ((y \ (1 / x)) \ z). (x * ((x \ (y / z)) * z)) \ y = a(x,1 / z,(x * (1 / z)) \ y). a(x,1 / y,(x * (1 / y)) \ z) = (x * ((x \ (z / y)) * y)) \ z. x \ (y * T(y \ z,u)) = (x \ y) * T((x \ y) \ (x \ z),u). (x \ y) * T((x \ y) \ (x \ z),u) = x \ (y * T(y \ z,u)). (x * T(x \ (y * z),u)) / z = (x / z) * T((x / z) \ y,u). (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z). (x * T(x \ y,z)) * u = x * (u * T(u \ (x \ (y * u)),z)). x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y. x * y != (z * x) * T((z * x) \ (u * x),w) | T(z * T(z \ u,w),x) = y. T(x * T(x \ y,z),x) = x * T(x \ (x \ (y * x)),z). x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x). (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y. x * T(x \ T(y,x),z) = T(x * T(x \ y,z),x). T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z). x * y != z * T(z \ T(u,z),w) | x \ T(z * T(z \ u,w),z) = y. x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z). x \ T(x * T(y,z),x) = T(x \ T(x * y,x),z). x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z). x * T(T(y,x) / x,z) = T(x * T(y / x,z),x). T(x * T(y / x,z),x) = x * T(T(y,x) / x,z). x \ T(x * T(y / x,z),x) != u | u = T(T(y,x) / x,z). x \ T(x * T(y / x,z),x) != u | T(T(y,x) / x,z) = u. (x * T(x \ 1,y)) * z = x * (z * T(z \ (x \ z),y)). x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y. K(x \ (x / T(y,z)),x) = z \ ((y * T(y \ 1,x)) * z). x * ((y \ (x \ y)) * y) = (x * T(x \ 1,y)) * y. (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y). (x * ((y \ (x \ y)) * y)) / y = x * T(x \ 1,y). (x * ((x \ 1) * R(x,y,z))) / R(x,y,z) = x * T(x \ 1,R(x,y,z)). x != y \ (z * y) | x = T(z,y). K(x \ (x / T(y,z)),x) = T(y * T(y \ 1,x),z). T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y). T(K(x \ 1,x),y) = K(x \ (x / T(x,y)),x). K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y). T(K(x,y),z) = K(y \ (y / T(L(x \ 1,x,y),z)),y). K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z). K(x \ (x / ((L(y \ 1,y,x) \ z) \ z)),x) = T(K(y,x),L(y \ 1,y,x) \ z). T(K(x,y),L(x \ 1,x,y) \ z) = K(y \ (y / ((L(x \ 1,x,y) \ z) \ z)),y). K(x \ (x / T(y \ x,z)),x) = T(K(x \ y,x),z). K(x \ (x / (((y \ x) \ z) \ z)),x) = T(K(x \ y,x),(y \ x) \ z). T(K(x \ y,x),(y \ x) \ z) = K(x \ (x / (((y \ x) \ z) \ z)),x). (T(x,y) * (y * x)) / T(x,y) != z | T(x,y * x) * T(y,x) = z. T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x. (x * ((y \ x) * y)) / x != z * K(y \ x,y) | T(x,(y \ x) * y) = z. (x * y) * ((z * y) / z) = (x * ((z * y) / z)) * y. (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y). (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y. (x * y) * (z / (z / y)) = (x * (z / (z / y))) * y. (x * (y / (y / z))) * z = (x * z) * (y / (y / z)). x / (y / (y / z)) = ((x / z) / (y / (y / z))) * z. ((x / y) / (z / (z / y))) * y = x / (z / (z / y)). (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u)). T(T(x * y,x) / x,z) = T(x * T(y,z),x) / x. T(x * T(y,z),x) / x = T(T(x * y,x) / x,z). x != (1 / y) * ((z \ (1 / y)) \ u) | x = ((y / u) * (z \ 1)) \ y. (((x * y) \ x) \ (z / x)) * x = ((x / z) * (y \ 1)) \ x. T(x,y) * T((y \ (x * y)) \ (y \ z),u) = y \ ((x * y) * T((x * y) \ z,u)). (x * T(x \ y,z)) / y = (x / y) * T((x / y) \ 1,z). (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y. ((x \ (y * z)) * x) / z = (x / z) * T((x / z) \ y,x). (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y. (x * (y * T(y \ z,u))) / z = ((x * y) / z) * T(((x * y) / z) \ x,u). ((x * y) / z) * T(((x * y) / z) \ x,u) = (x * (y * T(y \ z,u))) / z. K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z. K(x \ (x / (y / z)),x) * z = y * T(y \ z,x). K(x \ (x / R(y,z,u)),x) = (((y * z) * u) * T(((y * z) * u) \ (z * u),x)) / (z * u). K(x \ (x / ((y \ x) / T(x,y))),x) = ((y \ x) * ((y \ x) \ x)) / T(x,y). K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y). x != y * T(y \ (z * y),u) | x = T(z,u) * y. K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x. (x * (1 / x)) * (x \ y) = y * L(y \ (x \ y),x,x \ 1). x * L(x \ (y \ x),y,y \ 1) = (y * (1 / y)) * (y \ x). x * L(x \ (y \ x),y,y \ 1) = K(y,y \ 1) * (y \ x). x * ((y \ z) * T((y \ z) \ (x \ z),u)) = (x * T(x \ y,u)) * (y \ z). (x \ 1) * (y * T(y \ ((x \ 1) \ (K(x \ 1,x) * y)),z)) = ((x \ 1) * T(x,z)) * y. T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x. x \ (y * (x * T(x \ (y \ z),u))) != w | T(y * T(y \ (z / x),u),x) = w. (x \ T(x * (y / z),u)) * z = (x \ 1) * (z * T(z \ ((x \ 1) \ y),u)). (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y. ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y)). ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y)). ((x / y) * K(y \ 1,y)) * y = x * ((y \ 1) * y). ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y). x * y != R(z,u,y) * (u * y) | x = z * u. (R(x,y \ 1,y) / y) * K(y \ 1,y) = x * (y \ 1). (L(1 / x,x,y) * K(x \ 1,x)) * x = (x * ((y * x) \ y)) * K(x \ 1,x). x * (y \ 1) != z * K(y \ 1,y) | R(x,y \ 1,y) / y = z. x * K(y \ 1,y) != z * (y \ 1) | R(z,y \ 1,y) / y = x. R(x,y / z,z * (y \ 1)) != u | u = (x * (y / z)) * (z * (y \ 1)). R(x,y / z,z * (y \ 1)) != u | (x * (y / z)) * (z * (y \ 1)) = u. x * ((y * (x \ (z * u))) / y) = z * ((z \ x) * ((y * ((z \ x) \ u)) / y)). x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z). (1 / x) * ((x * y) / (z * x)) = L(y,x,z) / (z * x). L(x,y,z) / (z * y) = (1 / y) * ((y * x) / (z * y)). (x * y) * L((x * y) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w)). R(x,T(1 / x,y),x) = T(x,(x * T(x \ 1,y)) / x). T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x). T(x,T(1 / x,y)) = R(x,T(1 / x,y),x). R(x,T(1 / x,y),x) = T(x,T(1 / x,y)). R(T(x,T(1 / x,y)),z,u) = R(R(x,z,u),T(1 / x,y),x). R(R(x,y,z),T(1 / x,u),x) = R(T(x,T(1 / x,u)),y,z). L(T(x,y / z),y,y) * (z / y) != u | L((y / z) \ x,y,y) = u. x != (y * z) / T(z,u) | x = (y / T(z,u)) * z. R(x,K(y,y \ 1),y) = ((x * K(y,y \ 1)) / T(y,y \ 1)) * y. ((x * K(y,y \ 1)) / T(y,y \ 1)) * y = R(x,K(y,y \ 1),y). (R(x,y,z) * T(u,x)) * T(x,u) = (R(x,y,z) * u) * x. T(x * y,x) * T(x,y) = (R(x,y,x) * y) * x. T((x * y) / x,L(y,z,u) * x) = L(y,x,L(y,z,u)). L(x,y,L(x,z,u)) * y = y * T(x,L(x,z,u) * y). x * T(y,L(y,z,u) * x) = L(y,x,L(y,z,u)) * x. x * y != L(z,u,w) * x | y = L(T(z,x),u,w). T(x,L(x,y,z) * u) = L(T(x,u),u,L(x,y,z)). L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y). ((x \ (y / (x \ z))) * x) * (x \ z) = T(y / z,x) * z. ((x \ (y / (x \ z))) * x) * (x \ z) = z * T(z \ y,x). ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x). R(T(x \ y,z),x,x \ z) = T(z \ (y * (x \ z)),x). R(T(1 / x,y),x,x \ y) = T(y \ (K(x,x \ 1) * (x \ y)),x). T(x \ (K(y,y \ 1) * (y \ x)),y) = R(T(1 / y,x),y,y \ x). x != R(T(1 / y,z),y,y \ z) | x = z \ (y \ z). T(x \ (K(y,y \ 1) * (y \ x)),y) = x \ (y \ x). T(x \ (K(y \ 1,y) * ((y \ 1) \ x)),y \ 1) = x \ ((y \ 1) \ x). (x * y) * (y * (x \ 1)) = T(y,x \ 1) * T(y,x \ 1). T(x,y \ 1) * T(x,y \ 1) = (y * x) * (x * (y \ 1)). x != ((y * z) \ u) * (z \ (y \ 1)) | x = (y * z) \ (u / (y * z)). (x \ (y \ 1)) * (z * (x \ (y \ 1))) = (y * x) \ (z / (y * x)). x != 1 / (y / (y \ z)) | x = (z \ y) \ (1 / y). ((1 / x) * y) * (1 / ((y \ x) / z)) = (z \ (y \ x)) \ (1 / (y \ x)). x / (y \ ((((x \ 1) \ 1) \ z) \ 1)) = (z * (y / (1 / x))) * (1 / x). x != T(y \ 1,z) * (1 / z) | x = T(y,z) \ (1 / z). T(x \ (1 / T(y,y \ 1)),T(y,y \ 1)) = T(x,y) \ (1 / y). T(x \ (y \ 1),T(y,y \ 1)) = T(x,y) \ (1 / y). T(1 \ (x * y),(y \ (x \ 1)) \ z) = 1 / T(y \ (x \ 1),z). T(x * y,(y \ (x \ 1)) \ z) = 1 / T(y \ (x \ 1),z). ((1 / x) * (1 / x)) \ (T(y,x) \ 1) = ((x \ 1) \ 1) * ((y \ 1) * x). x * ((1 / y) * ((y \ 1) * x)) = (x * (1 / y)) * ((y \ 1) * x). (x * (1 / y)) * ((y \ 1) * x) = x * ((1 / y) * ((y \ 1) * x)). (x * (1 / y)) * ((y \ 1) * x) = x * (y \ (y \ x)). (x * y) * L(y,z,u) = (L((x * y) / x,z,u) * x) * y. (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u). (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y. (x * L(y,z,u)) * y = (x * y) * L(y,z,u). ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u). (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y. (x * L(y,z,u)) / y = (x / y) * L(y,z,u). ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y. (x \ y) * y = ((x \ 1) * y) * L(y,x,x). ((x \ 1) * y) * L(y,x,x) = (x \ y) * y. (x * y) / L(y,z,u) != w | w = (x / L(y,z,u)) * y. (x * y) / L(y,z,u) != w | (x / L(y,z,u)) * y = w. T(x,y) = R(T(x,y * L(x,z,u)),y,L(x,z,u)). R(T(x,y * L(x,z,u)),y,L(x,z,u)) = T(x,y). (x * (y * z)) / z = ((x * y) / z) * L(z,y,x). ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z. (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u). L(x,y,z) * u != (z * (y * x)) / x | T((z * y) / x,L(x,y,z)) = u. T((x * y) / x,L(x,y,x)) = y. ((x * y) / z) \ ((x * (y * z)) / z) = L(z,y,x). L(x,y,z) = ((z * y) / x) \ ((z * (y * x)) / x). T(x,y) = T(x,L(y,x,y)). T(x,L(y,x,y)) = T(x,y). x != T(y,L(z,y,z)) | x = T(y,T(z,z * y)). T(x,y) = T(x,T(y,y * x)). T(x,T(y,y * x)) = T(x,y). L(x,y,x) * T(y,x) = y * L(x,y,x). T(x,x * y) * L(T(y,x),z,u) = L(y,z,u) * T(x,x * y). T(x,x * y) * R(T(y,x),z,u) = R(y,z,u) * T(x,x * y). x != L(y,z,y) * T(z,y) | x = T(z,y) * T(y,y * z). x * L(y,x,y) = T(x,y) * T(y,y * x). T(x,y) * T(y,y * x) = x * L(y,x,y). T(x,y) * T(y,x * y) = x * L(y,x,y). (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y. x != y * R(T(z,y),u,w) | x = R(z,u,w) * y. x \ R(x * (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1). T(x,y) \ R(T(x,y) * (T(x,y) \ x),z,u) = R(x,z,u) * (T(x,y) \ 1). (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y. ((x * ((y * z) / (R(u,y,z) * (y * z)))) / x) * ((u * y) * z) = (((x * (1 / R(u,y,z))) / x) * R(u,y,z)) * (y * z). x != K(y \ 1,y) * L(1 / y,z,u) | x = L(1 / y,z,u) * K(y \ 1,y). (x \ 1) * (x * L(x \ 1,y,z)) = L(1 / x,y,z) * K(x \ 1,x). L(1 / x,y,z) * K(x \ 1,x) = (x \ 1) * (x * L(x \ 1,y,z)). T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,T(z,T(y,x))). x != T(y,T(z,u)) / (T(T(z,y),u) \ y) | x = T(z,u). T(x,T(y,T(x,z))) = T(x,y). T(x / (x / y),T(z,y)) = T(x / (x / y),z). T(T(T(x,y) / (T(x,y) / y),x),z) = L(T(y,z),y \ T(x,y),y). L(T(x,y),z,u) \ (y * L(x,z,u)) != w | T(T(y,L(x,z,u)),L(x,z,u)) = w. (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) != (1 / x) * z | y * ((x \ 1) \ 1) = z. (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x)). (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y)). (T(x,y) \ x) * y = T(y,R(T(x,y),T(x,y) \ 1,y)). T(x,R(T(y,x),T(y,x) \ 1,x)) = (T(y,x) \ y) * x. T(x,R(y,y \ 1,x)) / x != z | z = y \ ((x * y) / x). T(x,R(y,y \ 1,x)) / x != z | y \ ((x * y) / x) = z. x \ (((T(y,x) \ y) * x) \ x) = T(x,R(T(y,x),T(y,x) \ 1,x)) \ 1. T(x,R(T(y,x),T(y,x) \ 1,x)) \ 1 = x \ (((T(y,x) \ y) * x) \ x). (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = T(x,R(T(y,x),T(y,x) \ 1,x)). K(x,x \ 1) * ((1 / x) \ y) = y * T(y \ ((1 / x) \ y),x \ 1). L(x * y,z,u) / y = (1 / y) * L((1 / y) \ x,z,u). (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x. (1 / x) * L((1 / x) \ 1,y,z) = L(x,y,z) / x. T(1 / x,L(x,y,z) / x) = 1 / x. (L(x,y,z) / x) \ (1 / x) = L(1 / (1 / x),y,z) \ 1. L(1 / (1 / x),y,z) \ 1 = (L(x,y,z) / x) \ (1 / x). (x * (1 / y)) / x = T((x * (1 / y)) / x,L(y,z,u) / y). T((x * (1 / y)) / x,L(y,z,u) / y) = (x * (1 / y)) / x. 1 / L(((x / y) * ((1 / y) \ z)) \ u,u,u) = u \ (y \ ((y * x) * z)). x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w). (x / y) * (y * L(y \ ((x / y) \ z),u,w)) = x * L(x \ z,u,w). x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w). (R(1 / (x / y),z,u) * (x / y)) * y = R(y / x,z,u) * x. x != R(y / z,u,w) * z | x = z * R(z \ y,u,w). (R(1 / (x / y),z,u) * (x / y)) * y = x * R(x \ y,z,u). ((x / y) * R((x / y) \ 1,z,u)) * y = x * R(x \ y,z,u). (x * R(x \ y,z,u)) / y = (x / y) * R((x / y) \ 1,z,u). (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y. R(x,y,z) * R((((x * y) * z) / (y * z)) \ 1,u,w) = (((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z). (((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * R((((x * y) * z) / (y * z)) \ 1,u,w). (((x * (y * z)) / (x * y)) * x) * y = x * (y * R(z,x,y)). (((x * (y * z)) / (x * z)) * x) * z = x * (z * R(T(y,z),x,z)). (((x * (y * z)) / (x * z)) * x) * z = x * (R(y,x,z) * z). (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z). x != (((y \ 1) \ 1) * z) / u | x = 1 / (u * (z \ (1 / y))). ((x \ 1) \ (y / (x \ 1))) * (x \ (1 / x)) = 1 / (x * (y \ (1 / x))). T(x,y) \ ((x \ z) \ z) = ((x \ z) \ z) * (T(x,y) \ 1). ((x \ y) \ y) * (T(x,z) \ 1) = T(x,z) \ ((x \ y) \ y). ((x * (1 / (1 / T(y,x)))) / x) \ (y / T(y,x)) = 1 / T(y,x). ((x * T(1 / (1 / y),x)) / x) \ (y / T(y,x)) = 1 / T(y,x). (1 / (1 / x)) \ (x / T(x,y)) = 1 / T(x,y). ((1 / x) * y) * (1 / ((y \ x) / z)) = (z \ (y \ x)) \ ((1 / x) * y). x / (y \ ((z \ 1) * (1 / (x \ 1)))) = (z * (y / (1 / x))) * (1 / x). (1 * (x \ (1 / x))) \ (T(y,x) \ 1) = ((x \ 1) \ 1) * ((y \ 1) * x). (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y. (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y. (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y. x \ (y * L(y \ x,z,u)) = (x \ y) * L((x \ y) \ 1,z,u). (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u)). L(x,y,z) * L(((z * y) \ (z * (y * x))) \ 1,u,w) = (z * y) \ ((z * (y * x)) * L((z * (y * x)) \ (z * y),u,w)). (x * y) \ ((x * (y * z)) * L((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * L(((x * y) \ (x * (y * z))) \ 1,u,w). x \ (y * R(y \ x,z,u)) = (x \ y) * R((x \ y) \ 1,z,u). (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u)). (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x). K(x,(x / y) / x) = y * ((x * (y \ 1)) / x). x != (y \ 1) * ((z * ((y \ 1) \ 1)) / z) | x = y \ ((z * y) / z). K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x). K(x,y / x) = (y \ x) * ((x * ((y \ x) \ 1)) / x). (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y). K(L(x,y,z),1 / x) = x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)). x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = K(L(x,y,z),1 / x). K(R(x,y,z),1 / x) = x * ((R(x,y,z) * (x \ 1)) / R(x,y,z)). x * ((R(x,y,z) * (x \ 1)) / R(x,y,z)) = K(R(x,y,z),1 / x). x * ((x \ R(x,y,z)) / R(x,y,z)) = K(R(x,y,z),1 / x). ((x \ (y \ z)) \ ((1 / z) * y)) \ 1 = (1 / ((y \ z) / x)) \ (((1 / z) * y) \ 1). (1 / ((x \ y) / z)) \ (((1 / y) * x) \ 1) = ((z \ (x \ y)) \ ((1 / y) * x)) \ 1. ((1 / x) * y) * (1 / ((y \ x) / T(z,z \ (y \ x)))) = T(z \ (y \ x),z) \ ((1 / x) * y). x / (y \ ((z \ 1) * x)) = (z * (y / (1 / x))) * (1 / x). (x * (y / (1 / z))) * (1 / z) = z / (y \ ((x \ 1) * z)). (x \ (1 / x)) \ (T(y,x) \ 1) = ((x \ 1) \ 1) * ((y \ 1) * x). x != (y \ (1 / y)) \ z | x = y * ((y \ 1) \ z). ((x \ 1) \ 1) * ((y \ 1) * x) = x * ((x \ 1) \ (T(y,x) \ 1)). ((x \ 1) \ 1) * ((y \ 1) * x) = x * ((x \ y) \ 1). ((x \ 1) \ 1) * ((y \ 1) * x) = (y / x) \ x. x != ((y \ 1) \ 1) * ((z \ 1) * y) | x = (y \ 1) \ (z \ ((y \ 1) \ 1)). (x / y) \ y = (y \ 1) \ (x \ ((y \ 1) \ 1)). (x \ 1) \ (y \ ((x \ 1) \ 1)) = (y / x) \ x. x != (y * z) * L((y * z) \ u,w,v5) | x = y * (z * L(z \ (y \ u),w,v5)). (x * L(x \ y,z,u)) * w = x * (w * L(w \ (x \ (y * w)),z,u)). x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y. x != (y * z) * L((y * z) \ y,u,w) | x = y * (z * L(z \ 1,u,w)). ((x * y) * L((x * y) \ x,z,u)) * y = (x * y) * (y * L(y \ 1,z,u)). x * y != (z * x) * L((z * x) \ (u * x),w,v5) | T(z * L(z \ u,w,v5),x) = y. T(x * L(x \ y,z,u),x) = x * L(x \ (x \ (y * x)),z,u). x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x). (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y. (x * y) * L((x * y) \ (z * y),u,w) != y * v5 | T(x * L(x \ z,u,w),y) = v5. x * L(x \ T(y,x),z,u) = T(x * L(x \ y,z,u),x). T(x * L(x \ y,z,u),x) = x * L(x \ T(y,x),z,u). x * y != z * L(z \ T(u,z),w,v5) | x \ T(z * L(z \ u,w,v5),z) = y. x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u). x \ T(x * L(y,z,u),x) = L(x \ T(x * y,x),z,u). L(x \ T(x * y,x),z,u) = x \ T(x * L(y,z,u),x). L(T(x,y) / y,z,u) = y \ T(y * L(x / y,z,u),y). x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u). x != y \ T(y * L((y * z) / y,u,w),y) | x = T(y * L(z,u,w),y) / y. L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x. (x * L(x \ 1,y,z)) * u = x * (u * L(u \ (x \ u),y,z)). x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y. x * y != (z * x) * L((z * x) \ x,u,w) | T(z * L(z \ 1,u,w),x) = y. T(x * L(x \ 1,T(x,y),y),y) = T(x,y) * ((x * y) \ y). x * y != (z / u) * (u * L(u \ ((z / u) \ w),v5,v6)) | (z * L(z \ w,v5,v6)) / y = x. (x * L(x \ y,z,u)) / y = (x / y) * L((x / y) \ 1,z,u). (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y. x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y. x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y. x * y != (x * z) * L(u,z,x) | y = z * u. K(x,x \ 1) * (x \ L(y,1 / x,x)) = (1 / x) * y. x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y. x * y != K(x,x \ 1) * L(x,z,u) | y = L(x,z,u) * (1 / x). K(x,x \ 1) * (x \ L(x,y,z)) = L(x,y,z) * (1 / x). x * (K(x,x \ 1) * y) = K(x,x \ 1) * (x * y). K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y). x * (K(x,x \ 1) * T(y,x)) = K(x,x \ 1) * (y * x). (x \ 1) * (K(x \ 1,x) * ((x \ 1) \ y)) = K(x \ 1,(x \ 1) \ 1) * y. x != K(y,y \ 1) * (y * z) | x = T(y,y \ 1) * L(z,y,K(y,y \ 1)). x * (K(x,x \ 1) * y) = T(x,x \ 1) * L(y,x,K(x,x \ 1)). T(x,x \ 1) * L(y,x,K(x,x \ 1)) = x * (K(x,x \ 1) * y). (1 / x) * y != K(x,x \ 1) * z | x \ L(y,1 / x,x) = z. K(x,x \ 1) * y != (1 / x) * z | x \ L(z,1 / x,x) = y. R(x,y,z) * L((((x * y) * z) / (y * z)) \ 1,u,w) = (((x * y) * z) * L(((x * y) * z) \ (y * z),u,w)) / (y * z). (((x * y) * z) * L(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * L((((x * y) * z) / (y * z)) \ 1,u,w). T(x,x \ 1) * y != x * (K(x,x \ 1) * z) | y = L(z,K(x,x \ 1),x). L(x,y,K(y,y \ 1)) = L(x,K(y,y \ 1),y). L(x,K(y,y \ 1),y) = L(x,y,K(y,y \ 1)). L(x,K(y \ 1,y),1 / y) = L(x,1 / y,K(1 / y,(1 / y) \ 1)). L(x,1 / y,K(1 / y,(1 / y) \ 1)) = L(x,K(y \ 1,y),1 / y). x != (y * z) * R((y * z) \ u,w,v5) | x = y * (z * R(z \ (y \ u),w,v5)). (x * R(x \ y,z,u)) * w = x * (w * R(w \ (x \ (y * w)),z,u)). x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y. x * y != (z * x) * R((z * x) \ (u * x),w,v5) | T(z * R(z \ u,w,v5),x) = y. T(x * R(x \ y,z,u),y) = (y \ (x * y)) * R((y \ (x * y)) \ y,z,u). (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x). T(x * R(x \ y,z,u),x) = x * R(x \ (x \ (y * x)),z,u). x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x). x * y != (z * u) * R((z * u) \ (w * u),v5,v6) | x \ ((z * R(z \ w,v5,v6)) * u) = y. x \ ((y * R(y \ x,z,u)) * w) = (x \ (y * w)) * R((x \ (y * w)) \ w,z,u). (x \ (y * z)) * R((x \ (y * z)) \ z,u,w) = x \ ((y * R(y \ x,u,w)) * z). (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y. (x * y) * R(y,z,u) = (x * R(x \ (x * y),z,u)) * y. (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u). (R(x,y,z) * z) * R(L(T(y,z),z,R(x,y,z)),u,w) = (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z. (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = (R(x,y,z) * z) * R(L(T(y,z),z,R(x,y,z)),u,w). (x * R(y,z,u)) * y = (x * y) * R(y,z,u). ((x / R(y,z,u)) * y) \ (x * y) = R(y,z,u). (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y. (x * y) / R(y,z,u) != w | w = (x / R(y,z,u)) * y. (x * y) / R(y,z,u) != w | (x / R(y,z,u)) * y = w. T(x,y) = R(T(x,y * R(x,z,u)),y,R(x,z,u)). R(T(x,y * R(x,z,u)),y,R(x,z,u)) = T(x,y). (x * R(y,z,u)) * T(y,x) = R(y,x,R(y,z,u)) * (x * R(y,z,u)). R(x,y,R(x,z,u)) * (y * R(x,z,u)) = (y * R(x,z,u)) * T(x,y). (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u). T(x * y,x) * T(x,y) = (x * y) * R(x,y,x). x != T(y * z,y) * T(y,z) | x = R(y,z,y) * T(y * z,y). (x * y) * R(x,y,x) = R(x,y,x) * T(x * y,x). R(x,y,x) * T(x * y,x) = (x * y) * R(x,y,x). x != T(y * z,y) * T(y,z) | x = (R(y,z,y) * z) * y. (x * y) * R(x,y,x) = (R(x,y,x) * y) * x. (R(x,y,x) * y) * x = (x * y) * R(x,y,x). (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) != z | z = x. (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) = L(R(x,y,x),y,R(x,y,x)). x * R(x \ T(y,x),z,u) = T(x * R(x \ y,z,u),x). T(x * R(x \ y,z,u),x) = x * R(x \ T(y,x),z,u). x * y != z * R(z \ T(u,z),w,v5) | T(z * R(z \ u,w,v5),z) / y = x. T(x * R(x \ y,z,u),x) / x = R(T(y,x) / x,z,u). x * y != z * R(z \ T(u,z),w,v5) | x \ T(z * R(z \ u,w,v5),z) = y. x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u). T(x * R(y,z,u),x) / x = R(T(x * y,x) / x,z,u). R(T(x * y,x) / x,z,u) = T(x * R(y,z,u),x) / x. (x * R(x \ 1,y,z)) * u = x * (u * R(u \ (x \ u),y,z)). x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y. (x * y) * (y / (x * y)) = (x * (((x * y) * (x \ 1)) / (x * y))) * y. (x * (((x * y) * (x \ 1)) / (x * y))) * y = (x * y) * (y / (x * y)). x != (y * (z * u)) \ ((y * z) * u) | x = a(y,z,u). L(L(x,y,z) \ x,L(x,y,z),z * y) = a(z,y,x). a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y). ((x * y) * z) * ((x * (y * z)) \ 1) = T(a(x,y,z),(y * z) \ (x \ 1)). L(x,y,z) \ (1 / (z * y)) != u * (1 / (z * y)) | (z * (y * x)) \ (z * y) = u. L(x \ L(y,1 / x,K(x \ 1,x)),x,x \ 1) = (1 / x) * y. (1 / x) \ ((L(x,x,x) \ y) * z) = (y * (z / (1 / x))) * (1 / x). L(((x \ 1) \ ((x \ (1 / y)) * z)) \ 1,x,x) = x * ((z / (x \ 1)) \ y). x != (y \ z) \ ((z / y) * u) | x = (z / y) * ((y \ z) \ u). L(x,K(y \ 1,y),1 / y) = (1 / y) * ((y \ 1) \ (K(y \ 1,y) * x)). (1 / x) * ((x \ 1) \ (K(x \ 1,x) * y)) = L(y,K(x \ 1,x),1 / x). (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,(1 * x) / (x * T(x,y))). (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,x / (x * T(x,y))). (T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y))). T(x,x / (x * T(x,y))) = T(x,T(x,y) \ 1). L(R(x,y,z),x \ 1,x) / R(x,y,z) = x * T(x \ 1,R(x,y,z)). R(1 / (1 / x),y,z) / R(x,y,z) = x * T(x \ 1,R(x,y,z)). ((T(x,y) \ x) * y) \ 1 = y \ (((T(x,y) \ x) * y) \ y). x \ (((T(y,x) \ y) * x) \ x) = ((T(y,x) \ y) * x) \ 1. 1 / (((((x / y) * ((1 / y) \ z)) \ u) * (1 / u)) * u) = u \ (y \ ((y * x) * z)). L(R(x,y,x),y,R(x,y,x)) = x. ((x * y) * z) * ((y * z) \ (x \ 1)) = T(a(x,y,z),(y * z) \ (x \ 1)). ((1 / x) * (y / x)) \ ((x \ y) \ 1) = (x / ((y / x) \ x)) \ ((y / x) \ x). (x / ((y / x) \ x)) \ ((y / x) \ x) = ((1 / x) * (y / x)) \ ((x \ y) \ 1). x * (1 / (x * y)) = 1 / ((x * y) * (y \ (y / x))). 1 / ((x * y) * (y \ (y / x))) = x * (1 / (x * y)). T(L(1 / x,R(x,y,z),1 / x),x) = (x \ R(x,y,z)) / R(x,y,z). L(x \ 1,R(x,y,z),1 / x) = (x \ R(x,y,z)) / R(x,y,z). (x \ 1) \ ((x \ y) * z) = x \ ((x * (y * (z / (x \ 1)))) / x). x \ ((x * (y * (z / (x \ 1)))) / x) = (x \ 1) \ ((x \ y) * z). x \ ((x * (y * ((1 / z) \ x))) / x) = (x \ 1) \ ((x \ y) * z). (x * ((1 / y) \ z)) * (z \ 1) = (z \ 1) \ ((z \ x) * y). (x \ (((1 / 1) \ (x * y)) * z)) \ 1 = (x \ 1) * ((z * (x \ 1)) \ (y \ 1)). T(x / (y * (z \ (y / z))),y / z) = T(x * (z * (y \ 1)),x) / (y / z). (x \ y) \ K(T(x / y,T(y,x)),T(y,x)) = T((x \ y) \ 1,T(y,x)). (x \ y) * T((x \ y) \ 1,T(y,x)) = K(T(x / y,T(y,x)),T(y,x)). x != (y \ z) * T((y \ z) \ 1,u) | x = y \ (z * T(z \ y,u)). K(T(x / y,T(y,x)),T(y,x)) = x \ (y * T(y \ x,T(y,x))). K(x \ y,T(x,y)) = y \ (x * T(x \ y,T(x,y))). x \ (y * T(y \ x,T(y,x))) = K(y \ x,T(y,x)). K(x \ y,x) = K(x \ y,T(x,y)). K(x \ y,T(x,y)) = K(x \ y,x). x != K(y \ (y * z),u) | x = K(z,u). K(x \ (x * y),x) = K(y,T(x,x * y)). K(x,T(y,y * x)) = K(x,y). x != K(y,z) | x = K(u \ (u * y),z). K(x,T(y,y * x)) = K(z \ (z * x),y). K(x \ (x * y),z) = K(y,T(z,z * y)). K(x,T(y,x * y)) = K(x,y). K(x,T(x \ y,y)) = K(x,x \ y). x != (y * z) * ((u * ((y * z) \ z)) / u) | x = (y * ((u * (y \ 1)) / u)) * z. x * ((x * y) * ((z * ((x * y) \ y)) / z)) = (x * ((z * (x \ 1)) / z)) * (x * y). (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z)). x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x). T(x,x / (x * y)) = x * (y * ((x * (y \ 1)) / x)). x * (y * ((x * (y \ 1)) / x)) = T(x,x / (x * y)). (x * (y * z)) * ((u * (((x * y) * L(z,y,x)) \ (x * y))) / u) = (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)). x != y * ((z * (y \ 1)) / z) | x = K(z,(z / y) / z). x \ T(x,x / (x * y)) = K(x,(x / y) / x). x * y != z \ T(z,z / (z * u)) | (u * ((z * (u \ 1)) / z)) / y = x. (x * ((y * (x \ 1)) / y)) / (y \ 1) = T(y,y / (y * x)). (x \ T(x,x / (x * y))) * x = T(x,R(1 / y,y,x)). T(x,R(1 / y,y,x)) = (x \ T(x,x / (x * y))) * x. x * K(x,(x / y) / x) = T(x,x / (x * y)). x * K(x,y / x) = T(x,x / (x * (y \ x))). T(x,x / (x * (y \ x))) = x * K(x,y / x). T(x,R(y,x,(y * x) \ x)) = x * K(x,(y * x) / x). x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y))). T(x,R(y,x,(y * x) \ x)) = x * K(x,y). (x \ (x * K(x,y))) \ x = x * (T(x,R(y,x,(y * x) \ x)) \ x). x * (T(x,R(y,x,(y * x) \ x)) \ x) = (x \ (x * K(x,y))) \ x. (x * ((x \ R(x,y,z)) / R(x,y,z))) / (R(x,y,z) \ 1) = T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x)). x != T(y,y / (y * T(y,z))) | x = T(y,T(y,z) \ 1). x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1). x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1). x * (T(x,R(y,x,(y * x) \ x)) \ x) = K(x,y) \ x. (x * y) * T(K(y,x),z) = y * (T(x,y) * T(T(x,y) \ x,z)). x * (T(y,x) * T(T(y,x) \ y,z)) = (y * x) * T(K(x,y),z). x * L(y,T(y,x) \ y,T(y,x)) = (y * x) * T(K(x,y),y). x * y = (y * x) * T(K(x,y),y). (x * y) * T(K(y,x),x) = y * x. K(x,y) = T(K(x,y),y). T(K(x,y),y) = K(x,y). T(x,K(y,x)) = x. x * y != T(K(z,u),u) | K(z,u) / y = x. K(x,y) / y = (1 / y) * K(x,y). (1 / x) * K(y,x) = K(y,x) / x. x * K(y,x) = K(y,x) * x. K(x,y) * y = y * K(x,y). (x * K(y,x)) / x = K(y,x). (x * K(y,x)) / x != z | z = K(y,x). (x * K(y,x)) / x != z | K(y,x) = z. x * (K(y,x) \ 1) = K(y,x) \ x. x * L(K(y,x),z,u) = L(K(y,x),z,u) * x. L(K(x,y),z,u) * y = y * L(K(x,y),z,u). T(x,y) = T(T(x,y),K(z,x)). T(T(x,y),K(z,x)) = T(x,y). K(x,y) * T(y,z) = T(y,z) * K(x,y). T(x,y) * K(z,x) = K(z,x) * T(x,y). x \ (K(y,x) \ 1) = (x * K(y,x)) \ 1. (x * K(y,x)) \ 1 = x \ (K(y,x) \ 1). K(x,y) * L(y,z,u) = L(y,z,u) * K(x,y). L(x,y,z) * K(u,x) = K(u,x) * L(x,y,z). K(x,y) * R(y,z,u) = R(y,z,u) * K(x,y). R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z). K(x,y) * T(y,z) != u | T(y,z) * K(x,y) = u. T(x,y \ T(y,x)) = x. T(x,x \ ((y * x) / y)) = x. T(x \ T(x,y),y) = x \ T(x,y). R(x,K(y,z),z) * (z * K(y,z)) = (x * K(y,z)) * z. R(K(x,y),y,(y * K(x,y)) \ z) \ z = y * ((y * K(x,y)) \ z). T(K(x,y),T(y,z)) = K(x,y). ((x * y) / x) / y = y \ ((x * y) / x). T(x,y) * K(z,x) != u * T(x,y) | u = K(z,x). T(x,y) * K(z,x) != u * T(x,y) | K(z,x) = u. T(x,y) * K(z,x) != u | K(z,x) * T(x,y) = u. T(K(x,T(y,z)),y) = K(x,T(y,z)). x * y != (1 / z) * K(u,z) | x \ (K(u,z) / z) = y. K(x,y) \ (K(x,y) / y) = 1 / y. x * y != z * (K(u,z) \ 1) | x \ (K(u,z) \ z) = y. (K(x,y) \ 1) \ (K(x,y) \ y) = y. K(x,y) \ y != y * z | K(x,y) \ 1 = z. x * (y \ T(y,x)) != z | (y \ T(y,x)) * x = z. T(x,K(y,T(x,z))) = x. K(x,y) / (y * K(x,y)) = 1 / y. (1 / x) * (x * K(y,x)) = K(y,x). (K(x,y) \ 1) * T(y,z) = K(x,y) \ T(y,z). (1 / x) \ K(y,x) = x * K(y,x). x * y != (1 / z) * (z * K(u,z)) | x \ K(u,z) = y. x \ K(y,x \ 1) = (x \ 1) * K(y,x \ 1). (x \ 1) * K(y,x \ 1) = x \ K(y,x \ 1). x * (((y * x) / y) / x) = (y * x) / y. R(x / (x / y),z,u) / R(y,z,u) = R(y,z,u) \ (((x / y) * R(y,z,u)) / (x / y)). R(x,y,z) \ (((u / x) * R(x,y,z)) / (u / x)) = R(u / (u / x),y,z) / R(x,y,z). (x \ 1) * (x * ((y * (x \ 1)) / y)) = (y * (x \ 1)) / y. T(x,L(K(y,x),z,u)) = x. T(K(x,y),L(y,z,u)) = K(x,y). x != y * T(z,z \ u) | x = y * ((z \ u) \ u). K(x,y) \ T(y,y \ z) = (K(x,y) \ 1) * ((y \ z) \ z). x != y \ T(z,z \ u) | x = y \ ((z \ u) \ u). (K(x,y) \ 1) * ((y \ z) \ z) = K(x,y) \ ((y \ z) \ z). T((x * K(y,x)) * (R(K(y,x),x,(x * K(y,x)) \ 1) \ 1),z) = (x * K(y,x)) * (T(x,z) * ((x * K(y,x)) \ 1)). K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = y \ (x * (x \ y)). x * (x * (y \ 1)) = (y \ ((y * x) / y)) * ((y * x) / y). (x \ ((x * y) / x)) * ((x * y) / x) = y * (y * (x \ 1)). x * (y * (y * (x \ 1))) = (x * y) * (x \ ((x * y) / x)). (x * y) * (x \ ((x * y) / x)) = x * (y * (y * (x \ 1))). (x * y) * (y * (x \ 1)) = x * (y * (y * (x \ 1))). x != (y * z) * (z * (y \ 1)) | x = T(z,y \ 1) * T(z,y \ 1). x * (y * (y * (x \ 1))) = T(y,x \ 1) * T(y,x \ 1). T(x,y \ 1) * T(x,y \ 1) = y * (x * (x * (y \ 1))). (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * (K(x,x \ 1) \ 1),y). (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * K(x \ 1,x),y). (x * (T(x,y) / x)) * K(x \ 1,x) = T(1 / (1 / x),y). (x \ 1) * (K(x,x \ 1) * ((x \ 1) \ y)) = K(x,x \ 1) * y. (x \ 1) \ (K(x,x \ 1) * y) = K(x,x \ 1) * ((x \ 1) \ y). K(x \ (x / ((y \ x) / T(x,y))),x) = x / T(x,y). x != y / T(y,z) | x = T(y,z) \ y. K(x \ (x / ((y \ x) / T(x,y))),x) = T(x,y) \ x. T(x \ 1,T(x,y) \ x) = x \ 1. (T(x,y) \ x) * (x \ 1) = (x \ 1) * (T(x,y) \ x). (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x. T(x,y) \ 1 = (x \ 1) * (T(x,y) \ x). (x \ 1) * (T(x,y) \ x) = T(x,y) \ 1. x != (y \ 1) \ (T(y,z) \ 1) | x = (y \ T(y,z)) \ 1. T(x,y) \ x = (x \ T(x,y)) \ 1. (x \ T(x,y)) \ 1 = T(x,y) \ x. (T(x,y) \ 1) * T(x,x \ 1) = T(x,y) \ x. (T(x,y) \ 1) * ((x \ 1) \ 1) = T(x,y) \ x. (R(x,y,z) \ R(T(x,u),y,z)) \ 1 = T(R(x,y,z),u) \ R(x,y,z). ((x / y) \ (y \ x)) \ 1 = T(x / y,y) \ (x / y). T(x / y,y) \ (x / y) = ((x / y) \ (y \ x)) \ 1. (x \ (x * K(x,y))) \ 1 = T(x,R(y,x,(y * x) \ x)) \ x. T(x,R(y,x,(y * x) \ x)) \ x = (x \ (x * K(x,y))) \ 1. (T(x,y) \ 1) * z != T(x,y) \ x | T(x,T(x,y) \ 1) = z. T(x,T(x,y) \ 1) = (x \ 1) \ 1. x != (y \ 1) \ 1 | x = y * K(y,y \ 1). T(x,T(x,y) \ 1) = x * K(x,x \ 1). T(x / y,x \ y) = ((x / y) \ 1) \ 1. T(x / (x * y),y) = ((x / (x * y)) \ 1) \ 1. x != ((y / (y * z)) \ 1) \ 1 | x = y / (y * ((z \ 1) \ 1)). T(x / (x * y),y) = x / (x * ((y \ 1) \ 1)). T(x / (x * y),y) = x / (x * T(y,y \ 1)). x / (x * T(y,y \ 1)) = T(x / (x * y),y). T(x / (x * y),y) \ x = x * T(y,y \ 1). (x \ y) \ (y / x) = ((y / x) \ (x \ y)) \ 1. ((x / y) \ (y \ x)) \ 1 = (y \ x) \ (x / y). (((x * y) / x) \ y) \ 1 = (x \ (x * y)) \ ((x * y) / x). (x \ (x * y)) \ ((x * y) / x) = (((x * y) / x) \ y) \ 1. x \ ((y * x) / y) = (((y * x) / y) \ x) \ 1. (((x * y) / x) \ y) \ 1 = y \ ((x * y) / x). 1 / (x \ ((y * x) / y)) = ((y * x) / y) \ x. T(x,R(y,x,(y * x) \ x)) \ x = K(x,y) \ 1. x * (K(x,y) \ 1) = K(x,y) \ x. x * (y \ 1) != y \ z | x = T(z,y). x = T(x,K(x,y)). T(x,K(x,y)) = x. T(K(x,y),x) = K(x,y). K(x,y) * x = x * K(x,y). K(x,y) * x != z | x * K(x,y) = z. K(x,y) * T(x,z) = T(x,z) * K(x,y). T(x,y) * K(x,z) = K(x,z) * T(x,y). T(T(T(x,y),z),K(x,u)) = T(T(x,y),z). x \ 1 = K(x,y) \ (x \ K(x,y)). K(x,y) \ (x \ K(x,y)) = x \ 1. K(x,y) * (x \ 1) = x \ K(x,y). K(x,y) * L(x,z,u) = L(x,z,u) * K(x,y). L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z). K(x,y) * R(x,z,u) = R(x,z,u) * K(x,y). R(x,y,z) * K(x,u) = K(x,u) * R(x,y,z). (x * y) / x = T((x * y) / x,K(y,z)). T((x * y) / x,K(y,z)) = (x * y) / x. K(x,y) / x = (1 / x) * K(x,y). (1 / x) * K(x,y) = K(x,y) / x. K(x,y) * L(x,z,u) != w | L(x,z,u) * K(x,y) = w. T(x,y \ ((x * y) / x)) = x. x * R(K(x,y),z,u) = R(K(x,y),z,u) * x. R(K(x,y),z,u) * x = x * R(K(x,y),z,u). T(x,T(y,x) \ y) = x. (T(x,y) \ x) * y = y * (T(x,y) \ x). K(x,y) * (x \ 1) != z | z = x \ K(x,y). K(x,y) * (x \ 1) != z | x \ K(x,y) = z. (x \ 1) * K(x,y) = x \ K(x,y). (K(x,y) / x) * L(z,K(x,y),1 / x) = (1 / x) * (K(x,y) * z). T(K(x,y),T(T(x,z),u)) = K(x,y). T(K(x,y),(z * x) / z) = K(x,y). T(K(x \ y,z),y / x) = K(x \ y,z). x != (T(y,z) \ y) * z | x = T(z,R(T(y,z),T(y,z) \ 1,z)). x * (T(y,x) \ y) = T(x,R(T(y,x),T(y,x) \ 1,x)). T(x,R(T(y,x),T(y,x) \ 1,x)) = x * (T(y,x) \ y). x \ ((x * (T(y,x) \ y)) \ x) = ((T(y,x) \ y) * x) \ 1. T(x / y,K(y \ x,z)) = x / y. T(K(x,y),L(x,z,u)) = K(x,y). L(x,y,z) * R(K(x,u),w,v5) != v6 | R(K(x,u),w,v5) * L(x,y,z) = v6. T(K(x,y),R(x,z,u)) = K(x,y). (R(K(x,y),z,u) * x) * w != x * R(K(x,y),z,u) | 1 = w. 1 = K(x,R(K(x,y),z,u)). K(x,R(K(x,y),z,u)) = 1. x \ ((x * (T(y,x) \ y)) \ x) = (x * (T(y,x) \ y)) \ 1. (R(x,y,z) \ R(T(x,u),y,z)) \ 1 = R(T(x,u),y,z) \ R(x,y,z). (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = (x \ T(x * (z / y),y)) * y. (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z). T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x). T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y). T((x \ 1) * y,x) = (x \ 1) * ((x \ y) * x). (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x). (x \ 1) * (y * x) = T((x \ 1) * (x * y),x). T((x \ 1) * (x * y),x) = (x \ 1) * (y * x). (x \ 1) * (K(y \ x,y) * x) = T((x \ 1) * ((y \ x) * y),x). T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * (K(y \ x,y) * x). ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1). T(x,T((x \ 1) * y,x)) = T(x,x \ y). T(x,(x \ 1) * y) = T(x,x \ y). T((x \ 1) * (x * y),x) != (x \ 1) * z | y * x = z. x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z). x * ((x \ y) * ((z * ((x \ y) \ 1)) / z)) = y * ((z * (y \ x)) / z). x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ (x * 1))) / y). x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y). x * K(y,(y / T(z,x)) / y) = (z * x) * ((y * ((z * x) \ x)) / y). (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z). x * y != (z * x) * ((u * ((z * x) \ x)) / u) | T(z * ((u * (z \ 1)) / u),x) = y. T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y). x != K(y,(y / z) / y) | x = z * ((y * (z \ 1)) / y). T(x * ((y * (x \ 1)) / y),z) = T(x,z) * ((y * (T(x,z) \ 1)) / y). T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y). T(K(x,y / x),z) = K(x,(x / T(y \ x,z)) / x). K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z). T(x \ T(x,x / (x * y)),z) = K(x,(x / T(y,z)) / x). K(x,(x / (y \ x)) / x) = T(K(x,y / x),K(y / x,z)). T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x). T(K(x,y / x),K(y / x,z)) = K(x,y / x). T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x). T(K(x,y),K(y,z)) = K(x,(y * x) / x). T(K(x,y),K(y,z)) = K(x,y). T(K(x,y),K(z,x)) = K(x,y). K(x,y) * K(z,x) = K(z,x) * K(x,y). K(x,y) * K(z,x) != u | K(z,x) * K(x,y) = u. K(x,y) * T(K(z,x),u) = T(K(z,x),u) * K(x,y). T(K(x,y),z) * K(y,u) = K(y,u) * T(K(x,y),z). K(x,y) * L(K(z,x),u,w) = L(K(z,x),u,w) * K(x,y). L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u). K(x,y) * R(K(z,x),u,w) = R(K(z,x),u,w) * K(x,y). R(K(x,y),z,u) * K(y,w) = K(y,w) * R(K(x,y),z,u). K(x,y) * L(K(z,x),u,w) != v5 | L(K(z,x),u,w) * K(x,y) = v5. K(x,y) * K(y,z) != u | K(y,z) * K(x,y) = u. K(x,y) * R(K(y,z),u,w) = R(K(y,z),u,w) * K(x,y). R(K(x,y),z,u) * K(w,x) = K(w,x) * R(K(x,y),z,u). K(x,y) * R(K(y,z),u,w) != v5 | R(K(y,z),u,w) * K(x,y) = v5. T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y). T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y). T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y). x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1). x * y != T(x,T(x,z) \ 1) | y = K(x,x \ 1). T(K(x,x \ 1),y) = K(x,x \ 1). T(x,K(y,y \ 1)) = x. x * y != T(K(z,z \ 1),u) | K(z,z \ 1) / y = x. K(x,x \ 1) / y = (1 / y) * K(x,x \ 1). (1 / x) * K(y,y \ 1) = K(y,y \ 1) / x. x * K(y,y \ 1) = K(y,y \ 1) * x. K(x,x \ 1) * y = y * K(x,x \ 1). x * K(y,y \ 1) != K(y,y \ 1) * z | z = x. K(x,x \ 1) * y != z * K(x,x \ 1) | y = z. x * K(y,y \ 1) != z | K(y,y \ 1) * x = z. ((x * y) * K(z,z \ 1)) / (K(z,z \ 1) * y) = R(x,y,T(K(z,z \ 1),y)). K(x,x \ 1) * y != z | y * K(x,x \ 1) = z. K(x,x \ 1) * (y \ 1) != z | y \ K(x,x \ 1) = z. T(x,K(y \ 1,y)) = x. x * K(y \ 1,y) = K(y \ 1,y) * x. K(x \ 1,x) * y = y * K(x \ 1,x). (1 / x) * K(y \ 1,y) = K(y \ 1,y) / x. T(K(x \ 1,x),y) = K(x \ 1,x). K(x \ 1,x) * y != z * K(x \ 1,x) | z = y. K(x \ 1,x) * y != z | y * K(x \ 1,x) = z. x != T(K(y \ 1,y),z) | x = K(y \ (y / T(y,z)),y). K(x \ 1,x) = K(x \ (x / T(x,y)),x). K(x \ (x / T(x,y)),x) = K(x \ 1,x). T((x \ 1) * x,y) = K(x \ 1,x). x * K(y \ 1,y) != K(y \ 1,y) * z | z = x. K(x \ 1,x) * y != z * K(x \ 1,x) | y = z. x * K(y \ 1,y) != z | K(y \ 1,y) * x = z. x != K(y,y \ 1) * (y \ L(y,z,u)) | x = L(y,z,u) * (1 / y). (x \ L(x,y,z)) * K(x,x \ 1) = L(x,y,z) * (1 / x). x * y != K(z,z \ 1) * u | x \ (u * K(z,z \ 1)) = y. (x * K(y,y \ 1)) \ ((T(x,K(y,y \ 1)) * z) * K(y,y \ 1)) = L(z,T(x,K(y,y \ 1)),K(y,y \ 1)). K(x * y,(x * y) \ 1) * z = z * K(x * y,y \ (x \ 1)). R(x,x \ y,K(z,z \ 1)) \ (K(z,z \ 1) * y) = (x \ y) * K(z,z \ 1). x * (K(y \ 1,y) * z) = x * (z * K(y \ 1,y)). (x * K(y \ 1,y)) * L(z,x,K(y \ 1,y)) = K(y \ 1,y) * (x * z). R(x,x \ y,K(z \ 1,z)) \ (K(z \ 1,z) * y) = (x \ y) * K(z \ 1,z). (x * K(y \ 1,y)) \ 1 = x \ K(y,y \ 1). (K(x \ 1,x) * y) \ ((z * y) * K(x \ 1,x)) = R(T(z,y * K(x \ 1,x)),y,K(x \ 1,x)). (K(x \ 1,x) * y) \ ((z * y) * K(x \ 1,x)) != u | L(T(z,y),y,K(x \ 1,x)) = u. K(x \ 1,x) / T(x,y) = T(1 / T(x,y),x). x != y * K(z,z \ 1) | x = K(z,z \ 1) * y. K(x,x \ 1) / y = K(x,x \ 1) * (1 / y). K(x,x \ 1) * (1 / y) = K(x,x \ 1) / y. x / (y \ K(z,z \ 1)) = (1 / x) \ (y * K(z \ 1,z)). (1 / x) \ (y * K(z \ 1,z)) = x / (y \ K(z,z \ 1)). x != T(1 / T(y,z),y) | x = T(y,z) \ 1. K(x \ 1,x) / T(x,y) = T(x,y) \ 1. (T(x,y) \ 1) * T(x,y) = K(x \ 1,x). K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x). K(x \ 1,x) * (1 / T(x,y)) = T(x,y) \ 1. T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y). x * K(y \ 1,y) != T(1 / (1 / y),z) | x = y * (T(y,z) / y). T(x,y) = x * (T(x,y) / x). x * (T(x,y) / x) = T(x,y). x \ T(x,y) = T(x,y) / x. T(x,y) / x = x \ T(x,y). T(x,y) * z != x * (T(x,y) / x) | 1 = z. 1 = K(x,T(x,y) / x). K(x,T(x,y) / x) = 1. (x \ T(x,y)) * x = T(x,y). x * y != K(z,T(z,u) / z) | x \ 1 = y. x \ 1 = T(1 / x,T(x,y)). T(1 / x,T(x,y)) = x \ 1. x \ ((y * x) / y) = y \ T(y,R(x,x \ 1,y)). x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x). (1 / x) * T(x,y) = x \ T(x,y). x * T(x \ 1,y) = (x \ 1) \ T(x \ 1,y). (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y). x != T(y,z) / y | x = (1 / y) * T((1 / y) \ 1,z). x \ T(x,y) = (1 / x) * T((1 / x) \ 1,y). (1 / x) * T((1 / x) \ 1,y) = x \ T(x,y). (x \ T(x,y)) * x != z | z = T(x,y). (x \ T(x,y)) * x != z | T(x,y) = z. (x \ 1) \ T(x \ 1,y) != z | x * T(x \ 1,y) = z. K(x,x \ T(x,y)) = 1. T(x,x \ T(x,y)) = x. T(x,K(y \ (y / (x \ 1)),y)) = x. x != (y \ T(y,y / (y * z))) * y | x = T(y,R(1 / z,z,y)). T(x,x / (x * y)) = T(x,R(1 / y,y,x)). T(x,R(1 / y,y,x)) = T(x,x / (x * y)). L(x,y,y \ T(y,z)) = T(y,z) \ ((y \ T(y,z)) * (y * x)). T(x,y) \ ((x \ T(x,y)) * (x * z)) = L(z,x,x \ T(x,y)). (x \ ((x \ y) \ y)) * x = T(x,x \ y). T(1 / (1 / x),T(1 / x,y)) = x. T(x \ 1,x) = T(x \ 1,T(x,y)). T(x \ 1,T(x,y)) = T(x \ 1,x). K(x \ 1,T(x,y)) = x * T(x \ 1,T(x,y)). x * T(x \ 1,T(x,y)) = K(x \ 1,T(x,y)). T(x,x \ 1) = T(x,T(1 / x,y)). T(x,T(1 / x,y)) = T(x,x \ 1). T(x * T(x \ 1,x),y) = K(T(x,z) \ (T(x,z) / T(x,y)),T(x,z)). K(T(x,y) \ (T(x,y) / T(x,z)),T(x,y)) = T(x * T(x \ 1,x),z). T(x,x \ 1) * T(x \ 1,y) = x * T(1 / x,y). T(x,x / (y * x)) = T(x,x / (x * y)). x != y * T(y \ 1,z) | x = K(z \ (z / y),z). (x \ 1) \ T(x \ 1,y) = K(y \ (y / x),y). K(x \ (x / y),x) = (y \ 1) \ T(y \ 1,x). K(x \ 1,y) = L(x * T(x \ 1,y),x \ 1,y). L(x * T(x \ 1,y),x \ 1,y) = K(x \ 1,y). L(x * T(x \ 1,y),x \ 1,y) != z | K(x \ 1,y) = z. x * T(x \ 1,x) = K(x \ 1,T(x,y)). K(x \ 1,T(x,y)) = x * T(x \ 1,x). x != y * T(y \ 1,y) | x = K(y \ 1,y). K(x \ 1,T(x,y)) = K(x \ 1,x). (x \ ((y * x) / y)) \ y = y * (T(y,R(x,x \ 1,y)) \ y). x * (T(x,R(y,y \ 1,x)) \ x) = (y \ ((x * y) / x)) \ x. 1 / (x \ ((y * x) / y)) = T(y,R(x,x \ 1,y)) \ y. T(x,R(y,y \ 1,x)) \ x = 1 / (y \ ((x * y) / x)). x != 1 / (y \ ((z * y) / z)) | x = ((z * y) / z) \ y. T(x,R(y,y \ 1,x)) \ x = ((x * y) / x) \ y. T(x,R(T(y,x),T(y,x) \ 1,x)) \ x = y \ T(y,x). (x * (T(y,x) \ y)) \ x = y \ T(y,x). (x * (T(y,x) \ y)) * (y \ T(y,x)) = x. x / (y \ T(y,x)) = x * (T(y,x) \ y). x \ (y \ T(y,x)) = (x * (T(y,x) \ y)) \ 1. (x * (T(y,x) \ y)) \ 1 = x \ (y \ T(y,x)). x / ((((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x))) = x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)). x * L(y,x,x \ T(x,z)) = L(x * y,x \ T(x,z),x). L(x * y,x \ T(x,z),x) = x * L(y,x,x \ T(x,z)). L(x * y,x \ T(x,z),x) != x * u | L(y,x,x \ T(x,z)) = u. x * (((x * y) / x) \ y) = (y \ ((x * y) / x)) \ x. (x \ ((y * x) / y)) \ y = y * (((y * x) / y) \ x). (T(x,y) \ x) \ y = y * (((y * T(x,y)) / y) \ T(x,y)). x * (((x * T(y,x)) / x) \ T(y,x)) = (T(y,x) \ y) \ x. x * (y \ T(y,x)) = (T(y,x) \ y) \ x. (T(x,y) \ x) \ y = y * (x \ T(x,y)). (T(x,y) \ x) * (y * (x \ T(x,y))) = y. K(x * y,y \ (x \ 1)) * z = z * K(x * y,y \ (x \ 1)). K(T(1 / T(x,y),T(x,z)),T(x,z)) = T(x * T(x \ 1,x),y). K(T(1 / T(x,y),T(x,z)),T(x,z)) = T((x \ 1) * x,y). x != T((y \ 1) * y,z) | x = K(y \ 1,y). K(T(1 / T(x,y),T(x,z)),T(x,z)) = K(x \ 1,x). K(x \ 1,x) / T(x,y) = T(1 / T(x,y),T(x,z)). T(1 / T(x,y),T(x,z)) = K(x \ 1,x) / T(x,y). x != K(y \ 1,y) / T(y,z) | x = T(y,z) \ 1. T(1 / T(x,y),T(x,z)) = T(x,y) \ 1. K(T(x,y) \ 1,T(x,z)) = K(x \ 1,x). T(x,y) \ R(x,z,u) = R(x,z,u) * (T(x,y) \ 1). R(x,y,z) * (T(x,u) \ 1) = T(x,u) \ R(x,y,z). (x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u)). (x * (y * (1 / y))) * y = (x * y) * (y * L(y \ 1,y,1 / y)). (x * y) * (y * L(y \ 1,y,1 / y)) = (x * (y * (1 / y))) * y. (x * y) * (y * (1 / y)) = (x * (y * (1 / y))) * y. (x * (y * (1 / y))) * y = (x * y) * (y * (1 / y)). (x * K(y,y \ 1)) * y = (x * y) * (y * (1 / y)). (x * K(y,y \ 1)) * y = (x * y) * K(y,y \ 1). (x * K(y,y \ 1)) \ ((x * y) * K(y,y \ 1)) = y. T(x,y) = R(T(x,y * K(x,x \ 1)),y,K(x,x \ 1)). R(T(x,y * K(x,x \ 1)),y,K(x,x \ 1)) = T(x,y). (x \ 1) * (K(x \ 1,x) * ((x \ 1) \ y)) = K(x \ 1,x) * y. (x \ 1) \ (K(x \ 1,x) * y) = K(x \ 1,x) * ((x \ 1) \ y). x != (y \ 1) \ (K(y \ 1,y) * z) | x = L((1 / y) \ z,1 / y,K(y \ 1,y)). K(x \ 1,x) * ((x \ 1) \ y) = L((1 / x) \ y,1 / x,K(x \ 1,x)). L((1 / x) \ y,1 / x,K(x \ 1,x)) = K(x \ 1,x) * ((x \ 1) \ y). T(x,y) * R((y \ (x * y)) \ y,z,u) = T(x * R(x \ y,z,u),y). T(x,y) * R(T(x,y) \ y,z,u) = T(x * R(x \ y,z,u),y). T(x,x * y) * R(T(x,x * y) \ (x * y),z,u) = T(x * R(y,z,u),x * y). (x / ((y / x) \ x)) \ ((y / x) \ x) = ((x \ y) / x) \ ((x \ y) \ 1). x != (y / z) \ (y \ 1) | x = z / (y * y). (x / ((y / x) \ x)) \ ((y / x) \ x) = x / ((x \ y) * (x \ y)). (x / y) \ ((x / y) \ y) = y / ((y \ x) * (y \ x)). x / ((x \ y) * (x \ y)) = (y / x) \ ((y / x) \ x). (x \ ((1 \ (x * y)) * z)) \ 1 = (x \ 1) * ((z * (x \ 1)) \ (y \ 1)). (x \ 1) * ((y * (x \ 1)) \ (z \ 1)) = (x \ ((1 \ (x * z)) * y)) \ 1. (x \ 1) * ((y * (x \ 1)) \ (z \ 1)) = (x \ ((x * z) * y)) \ 1. (x \ 1) * ((y * (x \ 1)) \ z) = (x \ ((x * (1 / z)) * y)) \ 1. (x \ ((x * (1 / y)) * z)) \ 1 = (x \ 1) * ((z * (x \ 1)) \ y). x != y \ (z * (z \ y)) | x = 1. K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = 1. 1 / (x \ y) = T(1 / (x \ y),(y \ x) * (x \ y)). T(1 / (x \ y),(y \ x) * (x \ y)) = 1 / (x \ y). x != T(1 / (y \ z),(z \ y) * (y \ z)) | x = ((z \ y) * (y \ z)) \ (z \ y). 1 / (x \ y) = ((y \ x) * (x \ y)) \ (y \ x). ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x). L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y). (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y)). L(((x * y) \ x) \ 1,(x * y) \ x,y) = 1 / ((x * y) \ x). (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y. L(x \ 1,x,(y * x) \ y) = 1 / x. (((x * y) \ x) * y) * (1 / y) = (x * y) \ x. ((x * y) \ x) / (1 / y) = ((x * y) \ x) * y. L(x \ 1,x,y / (x * y)) = 1 / x. L(1 / x,x,y) = L((y * x) \ y,x,(z * x) \ z). L((x * y) \ x,y,(z * y) \ z) = L(1 / y,y,x). L(x \ 1,x,R(1 / x,x,y)) = 1 / x. R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x. (L(x \ 1,x,y) * x) * (1 / x) = (y * x) \ y. (x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y). T(x,(y * x) \ y) = K(((y * x) \ y) \ (((y * x) \ y) * x),(y * x) \ y) * x. K(((x * y) \ x) \ (((x * y) \ x) * y),(x * y) \ x) * y = T(y,(x * y) \ x). L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x. T(1 / (1 / x),R(1 / x,x,y)) = x. T(1 / (1 / x),y / (x * y)) = x. T(x,x \ 1) = T(x,y / (x * y)). T(x,y / (x * y)) = T(x,x \ 1). T(x,y / (x * y)) = (x \ 1) \ 1. x * y != T(z,z \ 1) | x \ T(z,u / (z * u)) = y. x \ T(x,y / (x * y)) = K(x,x \ 1). T(x,(x \ y) / y) = T(x,x \ 1). K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x. T(x / y,y / x) = ((x / y) \ 1) \ 1. x \ T(x,y / (x * y)) != z | K(x,x \ 1) = z. T(x \ y,y \ x) = ((x \ y) \ 1) \ 1. T(x,(y * x) \ y) = T(x,x \ 1). T(x,(y * x) \ y) = (x \ 1) \ 1. T(K(x,y),(x * y) \ (y * x)) = T(K(x,y),K(x,y) \ 1). T(x / (y * x),y) = ((x / (y * x)) \ 1) \ 1. T(x \ (x / y),y) = ((x \ (x / y)) \ 1) \ 1. T(x \ y,y \ x) \ 1 = (1 / y) * x. x * (((x \ y) \ 1) \ 1) = y * K((y \ x) \ 1,y \ x). x * K((x \ y) \ 1,x \ y) = y * (((y \ x) \ 1) \ 1). T(K(x \ y,x),(y \ x) \ 1) = K(x \ (x / T(y \ x,x \ y)),x). K(x \ (x / T(y \ x,x \ y)),x) = T(K(x \ y,x),(y \ x) \ 1). x != T(y / (z * y),z) | x = R(z \ 1,z,y). ((x / (y * x)) \ 1) \ 1 = R(y \ 1,y,x). R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1. R(R(x,y,z) \ 1,R(x,y,z),y * z) = (((y * z) / ((x * y) * z)) \ 1) \ 1. T(x,R(y \ 1,y,z)) = T(x,z / (y * z)). x != T(y,y / (z * y)) | x = T(y,y / (y * z)). T(x,R(y \ 1,y,x)) = T(x,x / (x * y)). T(x,R(y \ 1,y,z)) = T(x,R(1 / y,y,z)). T(x,R(1 / y,y,z)) = T(x,R(y \ 1,y,z)). (x * (((x \ (x / y)) \ 1) \ 1)) * y = x * (y * T(y \ (x \ x),y)). x != T(y,R(1 / z,z,y)) | x = (z * ((y * (z \ 1)) / y)) * y. T(x,R(y \ 1,y,x)) = (y * ((x * (y \ 1)) / x)) * x. (x * ((y * (x \ 1)) / y)) * y = T(y,R(x \ 1,x,y)). T(K(x,y),K(y,x)) = T(K(x,y),K(x,y) \ 1). T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x)). (K(x,y) \ 1) \ 1 = T(K(x,y),K(y,x)). T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1. x != T(K(y,z),K(u,y)) | x = K(y,z). (K(x,y) \ 1) \ 1 = K(x,y). 1 / (1 / K(x,y)) = K(x,y). K(x,y) \ 1 != z | z = 1 / K(x,y). K(x,y) \ 1 != z | 1 / K(x,y) = z. (x * ((y * x) \ y)) \ x = 1 / ((y * x) \ y). x != K(y \ (y / T(z \ y,u)),y) | x = T(K(y \ z,y),u). T(K(x \ y,x),(y \ x) \ 1) = T(K(x \ y,x),x \ y). T(K(x,y),((y * x) \ y) \ 1) = T(K(y \ (y * x),y),y \ (y * x)). T(K(x \ (x * y),x),x \ (x * y)) = T(K(y,x),((x * y) \ x) \ 1). (x * (((x \ (x / y)) \ 1) \ 1)) * y = x * (y * T(y \ 1,y)). (x * (((x \ (x / y)) \ 1) \ 1)) * y = x * K(y \ 1,y). T(K(x,y),y \ (y * x)) = T(K(x,y),((y * x) \ y) \ 1). T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),y \ (y * x)). T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),x). x \ (y * ((z * (y \ u)) / z)) = (x \ y) * ((z * ((x \ y) \ (x \ u))) / z). (x \ y) * ((z * ((x \ y) \ (x \ u))) / z) = x \ (y * ((z * (y \ u)) / z)). ((x \ (y / z)) \ 1) / ((x \ y) \ 1) = R(z,y \ 1,(x \ 1) \ 1). R(x,y \ 1,(z \ 1) \ 1) != u | (z \ (y / x)) \ (z \ y) = u. R(x,T(y,z) \ y,y \ T(y,z)) = (x * (T(y,z) \ y)) * (y \ T(y,z)). (x * (T(y,z) \ y)) * (y \ T(y,z)) = R(x,T(y,z) \ y,y \ T(y,z)). x != (y * (T(z,y) \ z)) * (z \ T(z,y)) | x = y. R(x,T(y,x) \ y,y \ T(y,x)) = x. R((x * y) / x,T(z,y) \ z,z \ T(z,y)) = (x * y) / x. x != R(y,T(z,u) \ z,z \ T(z,u)) | x = (y * (T(z,u) \ z)) * (z \ T(z,u)). (x * y) / x = (((x * y) / x) * (T(z,y) \ z)) * (z \ T(z,y)). (((x * y) / x) * (T(z,y) \ z)) * (z \ T(z,y)) = (x * y) / x. R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * y) / x. ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x). x != T(y,R(T(z,y),T(z,y) \ 1,y)) | x = (T(z,y) \ z) * y. (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = (T(y,x) \ y) * x. (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = (T(y,x) \ y) * x. x != (T(y,z) \ y) * z | x = z * (T(y,z) \ y). (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = x * (T(y,x) \ y). (x * (y \ T(y,x))) \ (x * x) = x * (T(y,x) \ y). (x * (y \ T(y,x))) \ (x * x) != x * z | T(y,x) \ y = z. ((((x * y) / ((z * x) * y)) \ 1) \ 1) * ((z * x) * y) = ((R(z,x,y) \ 1) * R(z,x,y)) * (x * y). (x * (y \ 1)) * ((z * (y / x)) * (x * (y \ 1))) = ((y / x) \ z) * 1. (x * (y \ 1)) * ((z * (y / x)) * (x * (y \ 1))) = (y / x) \ z. (((1 / x) * y) \ (y \ x)) \ z = (T(y / x,y) * ((1 / x) * y)) * z. (T(x / y,x) * ((1 / y) * x)) * z = (((1 / y) * x) \ (x \ y)) \ z. (T(x / y,x) * ((1 / y) * x)) * z = (((x / y) * x) \ y) \ z. x * ((1 / y) * z) != (z \ y) \ ((1 / y) * z) | x = (1 / y) * z. T(x / y,x) * ((1 / y) * x) = (1 / y) * ((x / y) * x). (T(x / y,x) * ((1 / y) * x)) * z = ((x \ y) \ 1) * ((x \ y) \ z). ((x \ y) \ 1) * ((x \ y) \ z) != u * z | T(x / y,x) * ((1 / y) * x) = u. x != (1 / y) \ ((y \ 1) \ z) | x = y * (y * z). T(x / y,x) \ ((((1 / y) * x) * ((1 / y) * x)) * ((((1 / y) * x) \ 1) \ z)) = ((1 / y) * x) * (((1 / y) * x) * z). T(x / y,x) \ (((x \ y) \ ((1 / y) * x)) * z) = (1 / ((1 / y) * x)) \ z. T(x / y,x) \ (((x \ y) \ ((1 / y) * x)) * z) = (((x \ y) \ 1) \ 1) \ z. T(x / y,x) \ (((x \ y) \ 1) * ((x \ y) \ z)) = (((x \ y) \ 1) \ 1) \ z. L(x,y,T(z,z \ u)) = L(x,y,(z \ u) \ u). ((1 / x) \ y) * (x \ (((1 / x) \ y) / x)) = T(y,x \ 1) * T(y,x \ 1). (x / y) \ ((((y \ 1) \ 1) * (1 / x)) \ z) = ((x / y) \ ((x / y) / z)) \ 1. (x * y) * R((x * y) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u)). x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * x) * R((y * x) \ x,z,u). x * y != (z * x) * R((z * x) \ x,u,w) | T(z * R(z \ 1,u,w),x) = y. T(x * R(x \ 1,y,z),u) = T(x,u) * R(T(x,u) \ 1,y,z). T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y). T(x \ 1,x \ L(x,y,z)) * R((x \ 1) \ 1,u,w) = T((x \ 1) * R((x \ 1) \ 1,u,w),x \ L(x,y,z)). T((x \ 1) * R((x \ 1) \ 1,y,z),x \ L(x,u,w)) = T(x \ 1,x \ L(x,u,w)) * R((x \ 1) \ 1,y,z). R(x,y,z) \ T(x,u) = T(x,u) * (R(x,y,z) \ 1). T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y). (x \ y) * (R(y / x,z,u) \ 1) = R(y / x,z,u) \ T(y / x,x). R(x / y,z,u) \ T(x / y,y) = (y \ x) * (R(x / y,z,u) \ 1). R(x / y,z,u) \ (y \ x) = (y \ x) * (R(x / y,z,u) \ 1). (x \ y) * (R(y / x,z,u) \ 1) = R(y / x,z,u) \ (x \ y). x * (R((y * x) / y,z,u) \ 1) = R((y * x) / y,z,u) \ (y \ (y * x)). R((x * y) / x,z,u) \ (x \ (x * y)) = y * (R((x * y) / x,z,u) \ 1). R((x * y) / x,z,u) \ y = y * (R((x * y) / x,z,u) \ 1). x * (R((y * x) / y,z,u) \ 1) = R((y * x) / y,z,u) \ x. ((x \ 1) \ y) * ((x \ z) \ 1) = ((x \ 1) \ 1) * ((x \ (z / y)) \ 1). ((x \ 1) \ 1) * ((x \ (y / z)) \ 1) = ((x \ 1) \ z) * ((x \ y) \ 1). (x \ 1) \ ((1 / (y * (z * (u \ 1)))) \ x) = ((x \ 1) \ y) * ((x \ (u / z)) \ 1). (1 / (((1 / x) * y) * z)) \ ((y \ x) \ 1) = ((1 / x) * y) * (z * ((1 / x) * y)). x != T(y,K(z \ (z / (y \ 1)),z)) | x = y. (((x * y) / x) \ y) \ y = (x * y) / x. (((x * y) / x) \ y) * ((x * y) / x) = y. (((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1)) \ (x \ 1) = (R(x,y,z) * (x \ 1)) / R(x,y,z). ((x * (y / (z \ 1))) * (z \ 1)) / (z \ 1) = (z * ((z \ x) * y)) * z. (x * ((x \ y) * z)) * x = y * (z / (x \ 1)). (x * (y * z)) * x = (x * y) * (z / (x \ 1)). (x * y) * (z / (x \ 1)) = (x * (y * z)) * x. (x * y) * (z \ x) = (x * (y * (z \ 1))) * x. (x * (y * (z \ 1))) * x = (x * y) * (z \ x). (x * y) * ((1 / z) \ x) = (x * (y * z)) * x. (x * y) * T(z,x) = (x * (y * (x \ z))) * x. (x * (y * (x \ z))) * x = (x * y) * T(z,x). x != (y * (z * (u \ 1))) * y | x = y * ((u / z) \ y). (x * y) * (z \ x) = x * ((z / y) \ x). (x * y) * ((1 / z) \ x) != u * x | x * (y * z) = u. (x * y) * x = (x * x) * T(y,x). (x * x) * T(y,x) = (x * y) * x. x != ((1 / y) * z) * u | x = T(z / y,z) * u. ((1 / x) * y) * (1 / x) = T((1 / x) / x,1 / x) * T(y,1 / x). T((1 / x) / x,1 / x) * T(y,1 / x) = ((1 / x) * y) * (1 / x). (x * x) * (x \ y) = (x * (y / x)) * x. (x * (y / x)) * x = (x * x) * (x \ y). (x * x) * ((x \ 1) * y) = (x * (y * (1 / x))) * x. (x * (y * (1 / x))) * x = (x * x) * ((x \ 1) * y). (x \ 1) \ y = (x * x) * (x \ y). (x * x) * (x \ y) = (x \ 1) \ y. (x * ((1 / x) * y)) * x = (x * x) * (x \ T(y,x)). (x * x) * (x \ y) != z | (x \ 1) \ y = z. x != (y \ 1) \ T(z,y) | x = z / (1 / y). (x * x) * (x \ T(y,x)) = y / (1 / x). x * y != ((z \ u) \ 1) \ z | (((u \ z) \ 1) * z) / y = x. (((x \ y) \ 1) * y) / ((y \ x) \ y) = (y \ x) * (y \ x). x * y != (z \ 1) \ ((z \ 1) / u) | x \ ((u * (z \ u)) \ (u * (z \ 1))) = y. (x * x) \ ((y * (x \ y)) \ (y * (x \ 1))) = x \ ((x \ 1) / y). x * y != (z \ 1) \ T(u,z \ 1) | x \ T(z * u,z \ 1) = y. (x * x) \ T(x * y,x \ 1) = x \ T(y,x \ 1). x * y != (z \ 1) \ ((u \ z) \ 1) | x \ ((u \ 1) \ 1) = y. (x * x) \ ((y \ 1) \ 1) = x \ ((y \ x) \ 1). (x * x) \ y = x \ ((x \ 1) * y). x \ ((x \ 1) * y) = (x * x) \ y. x * y != (z * z) * (z \ u) | x \ ((z \ 1) \ u) = y. x \ ((x \ 1) \ y) = (1 / x) \ (x \ y). (1 / x) \ (x \ y) = x \ ((x \ 1) \ y). ((x / y) * (x / y)) * y = ((x / y) \ 1) \ x. x * ((x * x) \ y) = (x \ 1) * y. (x * y) * (((x * y) * (x * y)) \ z) = (y \ (x \ 1)) * z. x * (1 / ((y \ x) * x)) = (x \ 1) * y. x * ((1 / x) * (x \ y)) = (x \ 1) * y. x * (1 / (y * x)) = (x \ 1) * (x / y). (x \ 1) * (x / y) = x * (1 / (y * x)). x * ((1 / x) * y) = (x \ 1) * (x * y). (x \ 1) * (x * y) = x * ((1 / x) * y). (x \ (y \ 1)) * (((y * x) \ (1 / (y * x))) \ z) = ((x \ (y \ 1)) \ 1) * z. x \ ((x \ 1) \ y) = x * ((1 / x) * y). (x \ (y \ 1)) * ((y * x) / z) = (y * x) * (1 / (z * (y * x))). (x * (y \ 1)) * ((y / x) / z) = (y / x) * (1 / (z * (y / x))). (x \ ((y / x) \ z)) * ((x \ ((x / z) * y)) / u) = (x \ ((x / z) * y)) * (1 / (u * (x \ ((x / z) * y)))). (x \ ((x / y) * z)) * (1 / (u * (x \ ((x / y) * z)))) = (x \ ((z / x) \ y)) * ((x \ ((x / y) * z)) / u). x * ((1 / x) * y) = (1 / x) * ((1 / (1 / x)) * y). (1 / x) * ((1 / (1 / x)) * y) = x * ((1 / x) * y). x != y * ((1 / y) * z) | x = (z * y) * (1 / y). (x \ 1) * (x * y) = (y * x) * (1 / x). (x \ (y \ 1)) * ((y * x) * z) = (y * x) * ((1 / (y * x)) * z). (x * (y \ 1)) * ((y / x) * z) = (y / x) * ((1 / (y / x)) * z). (T(x / y,x) \ 1) * (((1 / y) * x) * z) = T(x / y,x) * ((1 / T(x / y,x)) * z). T(x / y,x) * ((1 / T(x / y,x)) * z) = (T(x / y,x) \ 1) * (((1 / y) * x) * z). ((x * y) / ((x \ 1) * z)) * (x * ((1 / x) * y)) = ((x * y) / z) * (x * y). (x * ((1 / x) * y)) \ (x \ 1) = (x * (x * y)) \ x. x \ ((x \ 1) \ y) = (y * x) * (1 / x). x * (x * ((1 / x) * y)) = (x \ 1) \ y. (x * y) \ ((y \ (x \ 1)) \ z) = (x * y) * ((1 / (x * y)) * z). x != (y \ 1) * z | x = T(z * (1 / y),y). (x * y) * (1 / y) = T((y * x) * (1 / y),y). T((x * y) * (1 / x),x) = (y * x) * (1 / x). x \ ((x \ 1) \ (y / x)) = y * (1 / x). x * (x * y) = (x \ 1) \ ((1 / x) \ y). (x \ 1) \ ((1 / x) \ y) = x * (x * y). x * (x * (K(y,x) / x)) = (x \ 1) \ K(y,x). x * (y * (1 / x)) = (x \ 1) \ (y / x). (x \ 1) \ (y / x) = x * (y * (1 / x)). ((x \ 1) \ 1) \ (x \ y) = (x \ 1) * ((x \ 1) * y). x != (y \ 1) \ (z / y) | x = ((y \ 1) \ z) * (y \ 1). x * (y * (1 / x)) = ((x \ 1) \ y) * (x \ 1). ((x \ 1) \ y) * (x \ 1) = x * (y * (1 / x)). x * y != (z \ 1) \ (u / z) | (z * (u * (1 / z))) / y = x. (x * (y * (1 / x))) / x = x * ((y / x) / x). (x * (y \ 1)) \ (z / (y / x)) = (y / x) * (z * (1 / (y / x))). 1 / (x * (y * (1 / x))) != z | (1 / (y / x)) * (x \ 1) = z. (x \ 1) \ (((y / x) / (x \ 1)) \ (x \ 1)) = (x * (y * (1 / x))) \ 1. (x \ 1) \ ((y / ((1 / x) * (1 / x))) / x) = x * (y * (1 / (1 / x))). (x * (y \ (x / y))) * y = ((x / y) \ 1) \ x. T(x * (1 / y),y) = ((y \ x) * y) * (1 / y). ((x \ y) * x) * (1 / x) = T(y * (1 / x),x). T((x * y) * (1 / x),x) != z * (1 / x) | y * x = z. x * y != z * (z * (K(u,z) / z)) | x \ ((z \ 1) \ K(u,z)) = y. T(x,y) \ ((x \ 1) \ K(z,x)) = x * (T(x,y) \ (x * (K(z,x) / x))). x * (T(x,y) \ (x * (K(z,x) / x))) = T(x,y) \ ((x \ 1) \ K(z,x)). x != (y \ z) * y | x = (y \ 1) * (z * y). x * (y * (1 / x)) = ((x \ 1) \ 1) * (y * (x \ 1)). ((x \ 1) \ 1) * (y * (x \ 1)) = x * (y * (1 / x)). x * y != ((z \ 1) \ u) * (z \ 1) | (z * (u * (1 / z))) / y = x. (x * (y * (1 / x))) / x = ((x \ 1) \ y) * (x \ (1 / x)). ((x \ 1) \ y) * (x \ (1 / x)) = (x * (y * (1 / x))) / x. (x * (1 / y)) * (y \ 1) = (x / y) / y. x != y / (z \ (u \ 1)) | x = (1 / y) \ (u * z). (x * (1 / (y \ (z \ 1)))) * ((y \ (z \ 1)) \ 1) = (1 / (x / (y \ (z \ 1)))) \ (z * y). (x * (1 / (y \ (1 / z)))) * (z * ((y \ 1) \ 1)) = (x / (y \ (1 / z))) / (y \ (1 / z)). (x * (y \ (x / y))) * y = (y * (x \ 1)) \ x. T(x * (1 / y),y) != z * (1 / y) | (y \ x) * y = z. x * y != (z * (u \ 1)) \ u | (u * (z \ u)) / y = x. (x * (y \ x)) / y = x * (y \ (x / y)). T(((1 / x) \ y) * (x \ (((1 / x) \ y) / x)),x) = (y * ((x \ ((1 / x) \ y)) / x)) * x. x != (y * y) * (y \ T(z,y)) | x = z / (1 / y). (x * ((1 / x) * y)) * x = y / (1 / x). ((x \ 1) * y) * x = (x \ y) / (1 / x). (x \ y) / (1 / x) = ((x \ 1) * y) * x. ((x \ 1) * (x * y)) * x = y / (1 / x). x != ((y \ 1) * (y * L(y \ 1,y,z))) * y | x = (y * ((z * y) \ z)) * K(y \ 1,y). L(x \ 1,x,y) / (1 / x) = (x * ((y * x) \ y)) * K(x \ 1,x). (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x). (1 / x) * (1 / (y / x)) = x * ((1 / x) * (1 / y)). 1 / (((x \ y) \ 1) * x) = (x \ 1) * ((x \ 1) * y). (((x \ y) \ 1) * y) / ((x \ y) * y) = (y \ x) * (y \ x). (x * y) * ((x * (y * (x * y))) \ z) = (y \ (x \ 1)) * z. x * y != ((z * u) \ z) * z | (u \ z) / y = x. (x \ (y \ 1)) / ((y * (((y \ 1) * x) * (y * ((y \ 1) * x)))) \ (y \ 1)) = y * ((y \ 1) * x). (x * x) \ (x \ (x / y)) = x \ ((x \ 1) / y). (x * x) \ (x \ (x / y)) = x \ (x \ (1 / y)). x != (y * y) \ (y \ (y / z)) | x = 1 / ((z * y) * y). x \ (x \ (1 / y)) = 1 / ((y * x) * x). 1 / ((x * y) * y) = y \ (y \ (1 / x)). x * (1 / ((y * x) * x)) = x \ (1 / y). x * (1 / (y * x)) = x \ (1 / (y / x)). x \ (1 / (y / x)) = x * (1 / (y * x)). x * (x * (1 / (y * x))) = 1 / (y / x). (1 / x) * y != 1 / (z / (1 / x)) | y = x * (1 / (z * x)). (1 / x) * (1 / (y * (1 / x))) = x * (1 / (y * x)). x * (x * (1 / (1 / T(y,x)))) = 1 / ((1 / (y * x)) / x). (1 / (x / (1 / y))) / z = 1 / (z * (((1 / y) * (1 / (x * (1 / y)))) \ y)). 1 / (x * (((1 / y) * (1 / (z * (1 / y)))) \ y)) = (1 / (z / (1 / y))) / x. (x * (1 / (y / z))) / (z * (1 / (y * z))) = (z * (1 / (y * z))) / (z \ (x \ (z * (1 / (y * z))))). (x * (1 / (y * x))) / (x \ (z \ (x * (1 / (y * x))))) = (z * (1 / (y / x))) / (x * (1 / (y * x))). (1 / x) * ((x \ 1) \ (1 / y)) = x * (1 / (y * x)). 1 / (x * (y * (1 / (z * y)))) = (((1 / (z * (1 / y))) \ y) \ 1) \ (1 / x). (((1 / (x * (1 / y))) \ y) \ 1) \ (1 / z) = 1 / (z * (y * (1 / (x * y)))). (1 / x) * ((x \ 1) \ ((y * y) \ (1 / z))) = x * (1 / ((z * (y * y)) * x)). x * (x * ((T(y,x) \ 1) \ 1)) = 1 / ((1 / (y * x)) / x). x * (((y \ 1) \ 1) * x) = 1 / ((1 / (y * x)) / x). 1 / ((1 / (x * y)) / y) = y * (((x \ 1) \ 1) * y). x != y * (((z \ 1) \ 1) * y) | x = (y / (1 / z)) * y. 1 / ((1 / (x * y)) / y) = (y / (1 / x)) * y. (x \ 1) * ((y / (1 / z)) * y) = ((y * (z * y)) \ x) \ 1. (x \ 1) * y != ((z * u) \ x) \ 1 | y = (u \ (z \ 1)) \ 1. (x / (1 / y)) * x = ((y * x) \ (x \ 1)) \ 1. ((x * y) \ (y \ 1)) \ 1 = (y / (1 / x)) * y. (x \ 1) * y != (((1 / z) * u) \ x) \ 1 | y = (u \ z) \ 1. ((1 / x) / (1 / y)) * (1 / x) = ((y * (1 / x)) \ x) \ 1. ((x * (y \ 1)) \ ((y \ 1) \ 1)) \ y = (y \ 1) / (1 / x). ((1 / x) / (1 / ((y \ 1) \ 1))) * (1 / x) = ((1 / (x / y)) \ x) \ 1. x != (y \ 1) / z | x = y \ (1 / z). ((x * (y \ 1)) \ ((y \ 1) \ 1)) \ y = y \ (1 / (1 / x)). ((x * (y \ 1)) \ ((y \ 1) \ 1)) \ y = y \ ((x \ 1) \ 1). ((x \ (y / x)) \ 1) \ x = x \ ((y \ 1) \ 1). x \ ((y \ 1) \ 1) = (((y / x) \ x) \ 1) * x. (((x / y) \ y) \ 1) * y = y \ ((x \ 1) \ 1). x * y != y \ ((z \ 1) \ 1) | x = y \ (1 / (y / z)). ((x / y) \ y) \ 1 = y \ (1 / (y / x)). x * y != (z * u) \ ((u \ (z \ 1)) \ w) | x \ ((z * u) * ((1 / (z * u)) * w)) = y. ((x \ (y \ 1)) \ z) \ ((y * x) * ((1 / (y * x)) * z)) = T(y * x,(x \ (y \ 1)) \ z) \ 1. ((x * y) * z) \ ((z \ (y \ (x \ 1))) \ u) = ((x * y) * z) * ((1 / ((x * y) * z)) * u). ((x \ (y \ 1)) \ z) / (((x \ (y \ 1)) \ z) \ ((y * x) * ((1 / (y * x)) * z))) = (1 / (y * x)) \ ((x \ (y \ 1)) \ z). x != L(y \ 1,y,z) / (1 / y) | x = L(y \ 1,y,z) * y. (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x. (x * ((y * x) \ y)) * K(x \ 1,x) = ((y * x) \ y) * x. K((x * y) \ x,y) = K(y \ 1,y). K(x \ y,y \ x) = K((y \ x) \ 1,y \ x). K((x \ y) \ 1,x \ y) = K(y \ x,x \ y). K(x \ (x / y),y) = K(y \ 1,y). K((x * y) \ y,T(x,y)) = K(T(x,y) \ 1,T(x,y)). K(T(x,y) \ 1,T(x,y)) = K((x * y) \ y,T(x,y)). K(x / y,y / x) = K((y / x) \ 1,y / x). K((x / y) \ 1,x / y) = K(y / x,x / y). K(x / (y * x),y) = K(y \ 1,y). K(((x * y) / x) \ T(x,y),T(y / x,T(x,y))) = K(T(y / x,T(x,y)) \ 1,T(y / x,T(x,y))). K(T(x / y,T(y,x)) \ 1,T(x / y,T(y,x))) = K(((y * x) / y) \ T(y,x),T(x / y,T(y,x))). K(((x * y) \ x) \ 1,(x * y) \ x) = K(y,(x * y) \ x). x != K(y \ 1,y) | x = K(1 / y,y). K(x \ y,y \ x) = K(1 / (y \ x),y \ x). K(1 / (x \ y),x \ y) = K(y \ x,x \ y). T(x,K(y \ z,z \ y)) = x. x * K(y \ x,x \ y) = y * (((y \ x) \ 1) \ 1). x * K(y \ z,z \ y) = K(y \ z,z \ y) * x. K(x \ y,y \ x) * z = z * K(x \ y,y \ x). (1 / x) * K(y \ z,z \ y) = K(y \ z,z \ y) / x. K((x / (y * x)) \ 1,x / (y * x)) = K(y,x / (y * x)). K((1 / x) * y,y \ x) = K(x \ y,y \ x). K(x * y,y \ (x \ 1)) = K((x \ 1) \ y,y \ (x \ 1)). K((x \ 1) \ y,y \ (x \ 1)) = K(x * y,y \ (x \ 1)). x != K(T(y,z) \ 1,T(y,u)) | x = K(y \ 1,y). K((x * y) \ y,T(x,y)) = K(x \ 1,x). K((x * y) \ y,y \ (x * y)) = K(x \ 1,x). x * K(y \ 1,y) = (y * x) * ((((y * x) \ x) \ 1) \ 1). (x * y) * ((((x * y) \ y) \ 1) \ 1) = y * K(x \ 1,x). (x * y) * K(y,(x * y) \ x) = x * T(y,(x * y) \ x). x != ((1 / y) * z) * (1 / y) | x = (y \ z) / y. T((1 / x) / x,1 / x) * T(y,1 / x) = (x \ y) / x. T(x \ (x \ 1),1 / x) * T(y,1 / x) = (x \ y) / x. T(x \ (x \ 1),x \ 1) * T(y,1 / x) = (x \ y) / x. (x \ T(x \ 1,x)) * T(y,1 / x) = (x \ y) / x. (x \ (1 / x)) * T(y,1 / x) = (x \ y) / x. (x \ (1 / x)) * T(y,x \ 1) = (x \ y) / x. x != (y \ (1 / y)) * z | x = (y \ 1) * (y \ z). (x \ y) / x = (x \ 1) * (x \ T(y,x \ 1)). (x \ 1) * (x \ T(y,x \ 1)) = (x \ y) / x. (x \ 1) \ (((1 / (y / x)) \ x) \ (x \ 1)) = (x * (y * (1 / x))) \ 1. (x \ 1) \ ((y / (1 * (x \ (1 / x)))) / x) = x * (y * (1 / (1 / x))). x * (x * (T(x,y) \ (K(z,x) / x))) = T(x,y) \ ((x \ 1) \ K(z,x)). ((1 / x) / (1 / ((y \ 1) \ 1))) * (1 / x) = (x / (x \ y)) \ 1. ((1 / x) / (1 / ((y \ 1) \ 1))) * (1 / x) = (x \ y) * (x \ 1). x != (y \ z) * (y \ 1) | x = y \ (z / y). ((1 / x) / (1 / ((y \ 1) \ 1))) * (1 / x) = x \ (y / x). ((1 / x) / (y \ 1)) * (1 / x) = x \ (y / x). ((1 / (1 / x)) \ y) * (1 / x) = x \ (y / x). (1 / x) * (y * (1 / x)) = x \ (y / x). (((x \ 1) \ 1) \ y) * (1 / x) = x \ (y / x). (x \ 1) \ ((x * ((1 / x) * y)) \ (x \ 1)) = (x * (y * (1 / x))) \ 1. (x \ 1) \ ((y / (x \ (1 / x))) / x) = x * (y * (1 / (1 / x))). (x \ 1) \ ((y * ((1 / x) \ x)) / x) = x * (y * (1 / (1 / x))). (x \ 1) \ (y / (1 / x)) = x * (y * (1 / (1 / x))). x != (y \ 1) \ (z / (1 / y)) | x = ((y \ 1) \ 1) * (z * y). x * (y * (1 / (1 / x))) = ((x \ 1) \ 1) * (y * x). ((x \ 1) \ 1) * (y * x) = x * (y * (1 / (1 / x))). ((x \ 1) \ 1) * (y * x) = x * (y * ((x \ 1) \ 1)). x != y * (z * ((y \ 1) \ 1)) | x = ((y \ 1) \ z) * y. ((x \ 1) \ 1) * (y * x) = ((x \ 1) \ y) * x. (x \ 1) \ ((x * (x * y)) \ x) = (x * (y * (1 / x))) \ 1. (x \ (y \ 1)) * ((y * x) * (((y * x) \ 1) \ z)) = ((x \ (y \ 1)) \ 1) * z. ((((x \ 1) \ 1) * y) / ((1 / x) * z)) * (((x \ 1) \ 1) * ((1 / ((x \ 1) \ 1)) * y)) = ((((x \ 1) \ 1) * y) / z) * (((x \ 1) \ 1) * y). 1 / (x * (((1 / y) * (1 / (z * (1 / y)))) \ y)) = ((y \ 1) * (1 / z)) / x. (x \ (y \ 1)) * ((y * x) * ((x \ (y \ 1)) \ z)) = ((x \ (y \ 1)) \ 1) * z. x != ((y \ 1) * (1 / z)) / u | x = ((z \ 1) \ y) \ (1 / u). 1 / (x * (((1 / y) * (1 / (z * (1 / y)))) \ y)) = ((z \ 1) \ y) \ (1 / x). x * y != (z \ (u \ 1)) * ((u * z) * ((z \ (u \ 1)) \ w)) | x \ (((z \ (u \ 1)) \ 1) * w) = y. (x * y) \ (((y \ (x \ 1)) \ 1) * z) = (1 / (x * y)) * ((y \ (x \ 1)) \ z). 1 / (x * ((y * (1 / (z * y))) \ y)) = ((z \ 1) \ y) \ (1 / x). 1 / (x * (y / (1 / z))) = ((y \ 1) \ z) \ (1 / x). (1 / x) * ((y * (1 / x)) \ (z * z)) = (y \ (((z * z) \ 1) \ (1 / x))) * x. (x \ (((y * y) \ 1) \ (1 / z))) * z = (1 / z) * ((x * (1 / z)) \ (y * y)). (x \ (((y * y) \ 1) \ (1 / z))) * z = (1 / z) * (((x * (1 / z)) \ y) * y). (x \ ((y \ (y \ 1)) \ (1 / z))) * z = (1 / z) * (((x * (1 / z)) \ y) * y). (x \ ((y * y) * (1 / z))) * z = (1 / z) * (((x * (1 / z)) \ y) * y). (1 / x) * (((y * (1 / x)) \ z) * z) = (y \ ((z * z) * (1 / x))) * x. (1 / x) * (((y * (1 / x)) \ z) * z) = (y \ (z * (z / x))) * x. T(x,y) * T(T(x,y) \ (y \ z),u) = y \ ((x * y) * T((x * y) \ z,u)). x \ ((y * x) * T((y * x) \ z,u)) = T(y,x) * T(T(y,x) \ (x \ z),u). x \ (y * (x * T(x \ (y \ z),u))) = T(y,x) * T(T(y,x) \ (x \ z),u). T(x * T(x \ (y / z),u),z) = T(x,z) * T(T(x,z) \ (z \ y),u). T(x,y) * T(T(x,y) \ (y \ z),u) = T(x * T(x \ (z / y),u),y). T(x,y) * T(T(x,y) \ z,u) = T(x * T(x \ ((y * z) / y),u),y). T(x * T(x \ ((y * z) / y),u),y) = T(x,y) * T(T(x,y) \ z,u). T(x * T(x \ y,z),u) = T(x,u) * T(T(x,u) \ T(y,u),z). T(x,y) * T(T(x,y) \ T(z,y),u) = T(x * T(x \ z,u),y). T(x * L(x \ y,z,u),y) = T(x,y) * L(T(x,y) \ y,z,u). T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y). (x * y) * L((x * y) \ y,z,u) = y * (T(x,y) * L(T(x,y) \ 1,z,u)). x * (T(y,x) * L(T(y,x) \ 1,z,u)) = (y * x) * L((y * x) \ x,z,u). T(x * L(x \ 1,y,z),u) = T(x,u) * L(T(x,u) \ 1,y,z). T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y). T(x,y) \ T(x * L(x \ 1,z,u),y) = L(T(x,y) \ 1,z,u). x != y * L(z \ 1,z,u) | x = y * ((u * z) \ u). T(x * L(x \ 1,T(x,y),z),y) = T(x,y) * ((z * T(x,y)) \ z). T(x * L(x \ 1,y,z),u) != T(x,u) * w | L(T(x,u) \ 1,y,z) = w. T(x \ y,z) \ T((x \ y) * (y \ x),z) = L(T(x \ y,z) \ 1,x \ y,x). (x \ ((y \ x) * z)) * R((x \ ((y \ x) * z)) \ z,u,w) = x \ ((R(y,u,w) * (y \ x)) * z). 1 / (((((x / y) * (y * L(z,y,y))) \ u) * (1 / u)) * u) = u \ (y \ ((y * x) * z)). x * ((x * ((y * (x \ 1)) / y)) * z) = (x * ((y * (x \ 1)) / y)) * (x * z). (x * ((y * (x \ 1)) / y)) * (x * z) = x * ((x * ((y * (x \ 1)) / y)) * z). x != (y * ((z * (y \ 1)) / z)) * z | x = T(z,R(y \ 1,y,z)). x * ((x * (((x * y) * (x \ 1)) / (x * y))) * y) = T(x * y,R(x \ 1,x,x * y)). T(x,x * y) * R(x \ T(x * y,x),z,u) = T(x * R(y,z,u),x * y). K(x,(y * x) \ y) * x = T(x,(y * x) \ y). x * y != T(z,(u * z) \ u) | ((z \ 1) \ 1) / y = x. ((x \ 1) \ 1) / x = K(x,(y * x) \ y). K(x,(y * x) \ y) = ((x \ 1) \ 1) / x. x != ((y \ 1) \ 1) / y | x = K(y,y \ 1). K(x,(y * x) \ y) = K(x,x \ 1). K(x \ y,y \ x) = K(x \ y,(x \ y) \ 1). K(x \ y,(x \ y) \ 1) = K(x \ y,y \ x). K(x,y \ (y / x)) = K(x,x \ 1). K(x,y / (x * y)) = K(x,x \ 1). (x * y) * K(y,y \ 1) = x * T(y,(x * y) \ x). K(x,x \ 1) = K((y / x) \ y,z \ (z / x)). K((x / y) \ x,z \ (z / y)) = K(y,y \ 1). x != K(y,y \ 1) | x = y \ T(y,z / (y * z)). K(x,y / (x * y)) = x \ T(x,z / (x * z)). x != K(y,z / (y * z)) | x = K((z / (y * z)) \ 1,z / (y * z)). K(x,x \ 1) = K((y / (x * y)) \ 1,y / (x * y)). K((x / (y * x)) \ 1,x / (y * x)) = K(y,y \ 1). (x \ y) * (1 / (x \ y)) = K(x \ y,y \ x). K(x \ y,(x \ y) \ 1) = K(x \ y,T(x / y,T(y,x))). K(x \ y,T(x / y,T(y,x))) = K(x \ y,(x \ y) \ 1). K(x,y / (x * y)) != z | K(x,x \ 1) = z. K(x / y,y / x) != z | K(x / y,(x / y) \ 1) = z. x != y | x = 1 * y. (x \ y) * (1 / (x \ y)) = 1 * K(x \ y,y \ x). x * y != K((z \ 1) \ u,u \ (z \ 1)) | x \ K(z * u,u \ (z \ 1)) = y. ((x \ 1) \ y) \ K(x * y,y \ (x \ 1)) = 1 / ((x \ 1) \ y). (x * y) * K(y,y \ 1) = x * T(y,y \ 1). (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1). K(x,x \ 1) * (y * x) = y * T(x,x \ 1). (x * K(y,y \ 1)) / T(y,y \ 1) = x / y. x * K(y,y \ 1) = (x / y) * T(y,y \ 1). (x / y) * T(y,y \ 1) = x * K(y,y \ 1). x != (y * z) * K(z,z \ 1) | x = (y * K(z,z \ 1)) * z. x * T(y,y \ 1) = (x * K(y,y \ 1)) * y. (x * K(y,y \ 1)) * y = x * T(y,y \ 1). x * y != (z * u) * K(u,u \ 1) | x \ (z * T(u,u \ 1)) = y. (x * K(y,y \ 1)) \ (x * T(y,y \ 1)) = y. x * K(y,y \ 1) = (x / y) * ((y \ 1) \ 1). (x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1). x * ((y \ 1) \ 1) = (x * K(y,y \ 1)) * y. (x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1). (x / y) * y = R(x,K(y,y \ 1),y). R(x,K(y,y \ 1),y) = (x / y) * y. R(x,K(y,y \ 1),y) = x. R(x,K(y \ 1,y),1 / y) = x. x * (y \ 1) = (x * K(y \ 1,y)) * (1 / y). (x * K(y \ 1,y)) * (1 / y) = x * (y \ 1). (K(x,x \ 1) * y) * x = y * T(x,x \ 1). L(x,K(x,x \ 1),y) = x. L(1 / x,K(x \ 1,x),y) = 1 / x. x != (1 / y) * K(z,z \ 1) | x = K(z,z \ 1) / y. ((1 / x) / y) * ((y \ 1) \ 1) = K(y,y \ 1) / x. (K(x,x \ 1) * y) * x = y * ((x \ 1) \ 1). (x * (y \ 1)) / (1 / y) = x * K(y \ 1,y). x / (1 / y) = (x / (y \ 1)) * K(y \ 1,y). (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y). x * (y / z) != (u * (y / z)) * (z \ y) | x = u * (z \ y). (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1). x != y * T(z,z \ 1) | x = K(z,z \ 1) * (y * z). (K(x,x \ 1) * y) * x = K(x,x \ 1) * (y * x). K(x \ 1,x) * (y * (1 / x)) = y * (x \ 1). R(x,y \ 1,y) / y = x * (1 / y). R(x,1 / y,K(y \ 1,y)) = x. R(x,1 / (1 / y),K(y,y \ 1)) = x. R(x / (1 / y),y \ 1,y) = x * y. R(x,y \ 1,y) = R(x,1 / y,y). R(x,1 / y,y) = R(x,y \ 1,y). (x * (1 / y)) * y = R(x,y \ 1,y). x != R(T(y / (1 / z),u),1 / z,z) | x = T(y * z,u). R(T(x / (1 / y),z),y \ 1,y) = T(x * y,z). x * y = (x * (1 / (1 / y))) * K(y,y \ 1). (x * (1 / (1 / y))) * K(y,y \ 1) = x * y. R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y. x * K(y,y \ 1) = (x / (1 / (1 / y))) * y. (x / (1 / (1 / y))) * y = x * K(y,y \ 1). x != ((y / z) / (u / (u / z))) * z | x = y / (u / (u / z)). (x / y) * K(y,y \ 1) = x / (1 / (1 / y)). R(((x / (1 / y)) \ 1) \ 1,y \ 1,y) = T(x * y,x \ (1 / y)). T(x * y,x \ (1 / y)) = R(((x / (1 / y)) \ 1) \ 1,y \ 1,y). K(x,x \ 1) * (x * y) = T(x,x \ 1) * y. (x * y) * K(x,x \ 1) = T(x,x \ 1) * y. T(x,x \ 1) \ (K(x,x \ 1) * y) = x \ y. K(x,x \ 1) * y = T(x,x \ 1) * (x \ y). T(x,x \ 1) * (x \ y) = K(x,x \ 1) * y. x != T(y,y \ 1) * z | x = T(z * y,y \ 1). K(x,x \ 1) * (x * y) = T(y * x,x \ 1). x != T(y,y \ z) * u | x = ((y \ z) \ z) * u. K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y. L(x,y,K(y,y \ 1)) = x. x != K(y,y \ 1) * (y * z) | x = y * (K(y,y \ 1) * z). T(x,x \ 1) * y = x * (K(x,x \ 1) * y). x * (K(x,x \ 1) * y) = T(x,x \ 1) * y. K(x,x \ 1) * L(y,x \ 1,x) = T(x,x \ 1) * ((x \ 1) * y). x != L(y,1 / z,K(1 / z,(1 / z) \ 1)) | x = L(y,K(z \ 1,z),1 / z). x = L(x,K(y \ 1,y),1 / y). L(x,K(y \ 1,y),1 / y) = x. L(x,1 / y,K(1 / y,y)) = x. L(x,1 / y,K(y \ 1,y)) = x. x * y != L(z,K(u \ 1,u),1 / u) | x \ z = y. (1 / x) \ y = (x \ 1) \ (K(x \ 1,x) * y). (x \ 1) \ (K(x \ 1,x) * y) = (1 / x) \ y. L(x,K(y,y \ 1),1 / (1 / y)) = x. (x \ 1) * y = (1 / x) * (K(x \ 1,x) * y). (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y. L(x,1 / (1 / y),K(y,y \ 1)) = x. x != L((1 / y) \ z,1 / y,K(y \ 1,y)) | x = K(y \ 1,y) * ((y \ 1) \ z). (1 / x) \ y = K(x \ 1,x) * ((x \ 1) \ y). K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y. (x \ 1) * y = K(x \ 1,x) * ((1 / x) * y). K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y. L(x \ y,x,x \ 1) = (1 / x) * y. x * y = (1 / (1 / x)) * (K(x,x \ 1) * y). (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y. x != L((1 / (1 / y)) \ z,1 / (1 / y),K(y,y \ 1)) | x = y \ (K(y,y \ 1) * z). (1 / (1 / x)) \ y = x \ (K(x,x \ 1) * y). x \ (K(x,x \ 1) * y) = (1 / (1 / x)) \ y. x * y = K(x,x \ 1) * ((1 / (1 / x)) * y). K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y. L(x,y,y \ 1) = (1 / y) * (y * x). (1 / x) * (x * y) = L(y,x,x \ 1). L(T(x,y),y,y \ 1) = (1 / y) * (x * y). x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x. ((x \ 1) * y) / ((1 / x) * y) = K(x \ 1,x). L(x,y,y) = L(x,y,y \ 1). L(x,y,y \ 1) = L(x,y,y). L(x,y,1 / y) = L(x,y,y \ 1). (1 / x) \ L(y,x,x \ 1) = x * y. L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y). L(x,y \ 1,y) = L(x,y \ 1,(y \ 1) \ 1). L(x,y \ 1,(y \ 1) \ 1) = L(x,y \ 1,y). (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y. x * y != (z * u) * K(z,z \ 1) | (T(z,z \ 1) * u) / y = x. (T(x,x \ 1) * y) / T(x,x \ 1) = (x * y) / x. ((x \ 1) \ 1) * (x \ y) = K(x,x \ 1) * y. x \ y = K(x,x \ 1) * (T(x,x \ 1) \ y). K(x,x \ 1) * (T(x,x \ 1) \ y) = x \ y. T(x * y,y \ 1) = y * (K(y,y \ 1) * x). x * (K(x,x \ 1) * y) = T(y * x,x \ 1). K(x,x \ 1) \ y = x * (((x \ 1) \ 1) \ y). x * (((x \ 1) \ 1) \ y) = K(x,x \ 1) \ y. ((x \ 1) \ 1) * y = x * (K(x,x \ 1) * y). x * (K(x,x \ 1) * y) = ((x \ 1) \ 1) * y. x * y != T(x,x \ 1) * T(x \ 1,z) | y = T(1 / x,z). K(x,x \ 1) * T(x \ 1,y) = T(1 / x,y). (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y. (1 / x) \ ((x \ 1) * y) = K(x \ 1,x) * y. x != y * (K(z \ 1,z) * u) | x = y * (u * K(z \ 1,z)). (x \ 1) * y = (1 / x) * (y * K(x \ 1,x)). (1 / x) * (y * K(x \ 1,x)) = (x \ 1) * y. ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y. T(x \ ((1 / y) \ x),y \ 1) = x \ ((y \ 1) \ x). ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y. K(x \ 1,x) * (T(x,y) / x) = (x \ 1) * T(x,y). ((x \ 1) * y) \ (K(x \ 1,x) * ((1 / x) * (y * z))) = L(L(z,y,1 / x),(1 / x) * y,K(x \ 1,x)). (1 / (1 / x)) \ y = K(x,x \ 1) * (x \ y). K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y. x * ((1 / (1 / x)) \ y) = K(x,x \ 1) * y. K(x,x \ 1) * (1 / y) = x * ((1 / x) / y). K(x,x \ 1) * ((y \ (1 / (1 / x))) * y) = x * K(y \ (1 / (1 / x)),y). K(x \ 1,x) * ((1 / x) * y) != z | z = (x \ 1) * y. K(x \ 1,x) * ((1 / x) * y) != z | (x \ 1) * y = z. ((x \ 1) * (y * T(y \ ((1 / x) \ y),z))) / (((1 / x) * T((1 / x) \ 1,z)) * y) = K(x \ 1,x). K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y. K(x,x \ 1) * y = (1 / (y * x)) \ (x \ 1). (1 / (x * y)) \ (y \ 1) = K(y,y \ 1) * x. x * y != ((x \ 1) \ 1) * (z * (x \ 1)) | y = z * (1 / x). K(x,x \ 1) * (y * (x \ 1)) = y * (1 / x). x * (y * K(x,x \ 1)) = ((x \ 1) \ 1) * y. x * (((x \ 1) \ 1) * y) = ((x \ 1) \ 1) * (x * y). ((x \ 1) \ 1) * (x * y) = x * (((x \ 1) \ 1) * y). (1 / ((x / y) \ y)) \ ((y \ (1 / (y / x))) * z) = K(((x / y) \ y) \ 1,(x / y) \ y) * z. x != y | x = T(y,K(z \ 1,z)). (1 / x) * (y * K(x \ 1,x)) = T((x \ 1) * y,K(z \ 1,z)). T((x \ 1) * y,K(z \ 1,z)) = (1 / x) * (y * K(x \ 1,x)). (1 / x) * (y / (1 / x)) = (x \ 1) * (y / (x \ 1)). x != (1 / y) \ K(z,y) | x = y * K(z,y). ((x \ 1) \ K(y,x)) * K(x \ 1,x) = x * K(y,x). ((1 / x) \ y) * (1 / x) = ((x \ 1) \ y) * (x \ 1). K(x,x \ 1) * (x \ y) = ((x \ 1) \ 1) \ y. ((1 / (1 / x)) \ y) * x = (x \ y) * ((x \ 1) \ 1). x * (1 / ((y \ 1) * x)) = K(x,x \ 1) * y. x * (((x \ 1) \ 1) \ y) = K(x,x \ 1) * y. x != K(y,y \ 1) * (1 / z) | x = K(y,y \ 1) / z. x * ((1 / x) / y) = K(x,x \ 1) / y. K(x,x \ 1) / y = x * ((1 / x) / y). K(x,x \ 1) / y = x * (1 / (y * x)). x * (K(y,y \ 1) / z) = x * (y * (1 / (z * y))). x != K(y,y \ 1) / z | x = (1 / z) * K(y,y \ 1). x * (1 / (y * x)) = (1 / y) * K(x,x \ 1). (1 / x) * K(y,y \ 1) = y * (1 / (x * y)). K(x * y,y \ (x \ 1)) / z = (x * y) * (1 / (z * (x * y))). K(x \ y,y \ x) / z = (x \ y) * (1 / (z * (x \ y))). (x \ y) * (1 / (z * (x \ y))) = K(x \ y,y \ x) / z. (((x \ 1) \ 1) \ y) * K(x,x \ 1) = x \ y. x * y != (z / u) \ z | x \ u = y. K(x / y,(x / y) \ 1) \ y = (((x / y) \ 1) \ 1) \ x. (x \ y) * x = (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1). (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x. (1 / T(x,K(y,y \ 1) * z)) \ (y * (1 / (z * y))) = (y * (1 / (z * y))) * x. (x * (1 / (y * x))) * ((K(x,x \ 1) * y) * z) = L(z,x * (1 / (y * x)),x * (1 / (y * x))). (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y). K(x,x \ 1) * (y \ 1) = (y \ x) * (1 / x). x != ((y \ 1) \ 1) * z | x = (y * z) * K(y,y \ 1). x * (y * K(x,x \ 1)) = (x * y) * K(x,x \ 1). (x * y) * K(x,x \ 1) = x * (y * K(x,x \ 1)). K(x,x \ 1) * y = ((x \ 1) \ 1) \ (x * y). ((x \ 1) \ 1) \ (x * y) = K(x,x \ 1) * y. x * (1 / (((y / (1 / z)) * y) * x)) = K(x,x \ 1) * ((z * y) \ (y \ 1)). K(x,x \ 1) * ((y * z) \ (z \ 1)) = x * (1 / (((z / (1 / y)) * z) * x)). (x * (1 / ((y * z) * x))) \ (z \ (y \ 1)) = (y * z) * ((1 / (y * z)) * (K(x,x \ 1) \ 1)). (x * y) * ((1 / (x * y)) * (K(z,z \ 1) \ 1)) = (z * (1 / ((x * y) * z))) \ (y \ (x \ 1)). x * K(y,y \ 1) = (x / (y \ 1)) * (1 / y). (x / (y \ 1)) * (1 / y) = x * K(y,y \ 1). ((x * y) * (1 / z)) / ((y * (z \ 1)) * K(z,z \ 1)) = R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1)). x \ K(y,y \ 1) = (x \ y) * (1 / y). K(x,x \ 1) * y = ((1 / y) \ x) * (1 / x). ((1 / x) \ y) * (1 / y) = K(y,y \ 1) * x. K(x,x \ 1) * (y \ (z \ 1)) = ((z * y) \ x) * (1 / x). K(x,x \ 1) * (y * (z \ 1)) = ((z / y) \ x) * (1 / x). K(x,x \ 1) * (y \ z) = (((1 / z) * y) \ x) * (1 / x). (((1 / x) * y) \ z) * (1 / z) = K(z,z \ 1) * (y \ x). T(x * ((y \ z) * (1 / z)),x) = (y / K(z,z \ 1)) \ x. (x \ y) * (1 / y) != z | x \ K(y,y \ 1) = z. x \ K(y * z,z \ (y \ 1)) = (x \ (y * z)) * (1 / (y * z)). x \ (K(y * x,(y * x) \ 1) * x) = (((y * x) \ 1) * y) * x. (((L(x,y,y \ 1) * y) / y) \ ((1 / y) * (x * y))) * ((y * ((1 / y) * (x * y))) / y) = (1 / y) * (x * y). (1 / (x * y)) * ((x \ 1) \ 1) = K(x,x \ 1) / y. x * y != K(x,x \ 1) * (z * x) | T(K(x,x \ 1) * z,x) = y. T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x). x != T(y,z \ 1) | x = T(y,1 / z). x \ ((y \ 1) \ x) = T(x \ ((1 / y) \ x),1 / y). T(x \ ((1 / y) \ x),1 / y) = x \ ((y \ 1) \ x). x * T(x \ ((1 / y) \ x),y \ 1) = (y \ 1) \ x. L(x,T(y,z) / y,K(y \ 1,y)) = ((y \ 1) * T(y,z)) \ (K(y \ 1,y) * ((T(y,z) / y) * x)). ((x \ 1) * T(x,y)) \ (K(x \ 1,x) * ((T(x,y) / x) * z)) = L(z,T(x,y) / x,K(x \ 1,x)). (1 / x) * (y / (1 / x)) = T((x \ 1) * (y / (x \ 1)),K(z \ 1,z)). T((x \ 1) * (y / (x \ 1)),K(z \ 1,z)) = (1 / x) * (y / (1 / x)). x != (((y \ 1) \ 1) \ z) * ((y \ 1) \ 1) | x = (1 / y) * (z * ((y \ 1) \ 1)). (x \ y) * x = (1 / x) * (y * ((x \ 1) \ 1)). (1 / x) * (y * ((x \ 1) \ 1)) = (x \ y) * x. (1 / x) \ ((x \ y) * x) != z | z = y * ((x \ 1) \ 1). (1 / x) \ ((x \ y) * x) != z | y * ((x \ 1) \ 1) = z. (1 / ((x * (y \ 1)) \ z)) * (1 * ((((x * (y \ 1)) \ z) \ 1) \ 1)) = ((z \ 1) * (1 / (y / x))) * ((x * (y \ 1)) \ z). R(x,y,K(x,x \ 1)) = x. R(T(x,y),z,K(x,x \ 1)) = T(x,y). x != R(T(y,z * K(y,y \ 1)),z,K(y,y \ 1)) | x = T(y,z). T(x,y * K(x,x \ 1)) = T(x,y). T(x \ 1,y * K(x \ 1,x)) = T(x \ 1,y). T(x,K(x,x \ 1) * y) = T(x,y). (x \ ((y \ (x \ 1)) \ 1)) \ 1 = K(x,x \ 1) / y. x != y * T(y \ ((1 / z) \ y),z \ 1) | x = K(z,z \ 1) * ((1 / z) \ y). (x \ 1) \ y = K(x,x \ 1) * ((1 / x) \ y). K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y. K(x,x \ 1) * y != (x \ 1) \ (K(x,x \ 1) * z) | y = (x \ 1) \ z. (1 / x) \ (K(x,x \ 1) * y) = (x \ 1) \ y. x * y != z \ (z * (x * u)) | y = u. (1 / x) \ ((x \ 1) * (K(x,x \ 1) * y)) = y. x * y != K(z,z \ 1) * ((1 / z) \ u) | x \ ((z \ 1) \ u) = y. ((x \ 1) \ 1) \ ((x \ 1) \ y) = x \ ((1 / x) \ y). K(x,x \ 1) * y = (x \ 1) \ ((1 / x) * y). (x \ 1) \ ((1 / x) * y) = K(x,x \ 1) * y. (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y. x != (1 / y) \ ((y \ 1) * z) | x = K(y \ 1,y) * z. x = K(y \ 1,y) * (K(y,y \ 1) * x). K(x \ 1,x) * (K(x,x \ 1) * y) = y. x * y != (1 / z) \ ((z \ 1) * (K(z,z \ 1) * u)) | x \ u = y. K(x \ 1,x) \ y = K(x,x \ 1) * y. K(x \ 1,x) * y != (1 / x) \ ((x \ 1) * z) | y = z. x = K(y,y \ 1) * (K(y \ 1,y) * x). K(x,x \ 1) * (K(x \ 1,x) * y) = y. K(x,x \ 1) * (y * K(x \ 1,x)) = y. (K(x,x \ 1) * y) * K(x \ 1,x) = y. K(x \ 1,x) * y != (x \ 1) * z | y = (1 / x) * z. K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y. x != K(y \ 1,y) * z | K(y,y \ 1) * x = z. K(x \ 1,x) * y != z | K(x,x \ 1) * z = y. K(x \ 1,x) * (y * K(x,x \ 1)) = y. x != y * K(z \ 1,z) | y = K(z,z \ 1) * x. y * K(z \ 1,z) != x | y = K(z,z \ 1) * x. x * K(y \ 1,y) != z | K(y,y \ 1) * z = x. K(x \ 1,x) * (y * T(x,x \ 1)) = y * x. K(x \ 1,x) * (((x \ 1) \ 1) * y) = x * y. K(x \ 1,x) * ((1 / (1 / x)) \ y) = x \ y. K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y. (x * K(y \ 1,y)) \ x = K(y,y \ 1). x != K(y,y \ 1) * (y * z) | x = ((y \ 1) \ 1) * z. K(x \ 1,x) \ (x * y) = ((x \ 1) \ 1) * y. K(x,x \ 1) * (K(x \ 1,x) * y) != z | z = y. T(x,K(x \ 1,x) \ y) = T(x,y). T(x,y) = T(x,K(x \ 1,x) * y). T(x,K(x \ 1,x) * y) = T(x,y). T(x,(x \ 1) * y) = T(x,(1 / x) * y). T(x,(1 / x) * y) = T(x,(x \ 1) * y). (K(x \ 1,x) * y) * K(x,x \ 1) = y. x * y = (K(y \ 1,y) * x) * ((y \ 1) \ 1). (K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x. x * y = T(x,x \ 1) * (K(x \ 1,x) * y). T(x,x \ 1) * (K(x \ 1,x) * y) = x * y. (1 / (1 / x)) * y = x * (K(x \ 1,x) * y). x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y. x * y = ((x \ 1) \ 1) * (K(x \ 1,x) * y). ((x \ 1) \ 1) * (K(x \ 1,x) * y) = x * y. (x * K(y \ 1,y)) * K(y,y \ 1) = x. (x * K(y,y \ 1)) * K(y \ 1,y) = x. K(x,x \ 1) * y != x \ z | y = ((x \ 1) \ 1) \ z. (x \ y) * K(x \ 1,x) = ((x \ 1) \ 1) \ y. K(x,x \ 1) * y != x * z | y = (1 / (1 / x)) * z. (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y. K(x,x \ 1) * y != z * T(x,x \ 1) | y = z * x. (x * T(y,y \ 1)) * K(y \ 1,y) = x * y. x * y != K(z,z \ 1) * (u * K(z \ 1,z)) | u / y = x. x / K(y,y \ 1) = x * K(y \ 1,y). x != K(y,y \ 1) * z | x * K(y \ 1,y) = z. K(x,x \ 1) * y != z | z * K(x \ 1,x) = y. K(x,x \ 1) \ y != z | z = y * K(x \ 1,x). K(x,x \ 1) \ y != z | y * K(x \ 1,x) = z. K(x,x \ 1) * (y / (1 / x)) = y / (x \ 1). x * (1 / y) = (K(y,y \ 1) * x) * (y \ 1). (K(x,x \ 1) * y) * (x \ 1) = y * (1 / x). ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y. K(x \ 1,x) * y != T(x,z) \ 1 | y = 1 / T(x,z). (T(x,y) \ 1) * K(x,x \ 1) = 1 / T(x,y). x * y != K(z \ 1,z) * (u * K(z,z \ 1)) | u / y = x. x / K(y \ 1,y) = x * K(y,y \ 1). K(x \ 1,x) * (y * x) = y * (1 / (1 / x)). (x * K(y \ 1,y)) * K(y,y \ 1) != z | z = x. x * K(y,y \ 1) != z * ((y \ 1) \ 1) | x = z * y. (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y. (x * K(y,y \ 1)) * K(y \ 1,y) != z | z = x. R((x * K(y,y \ 1)) / z,z,K(y \ 1,y)) != u | x / (z * K(y \ 1,y)) = u. x != K(y,y \ 1) * z | x = z * K(y,y \ 1). (1 / x) * ((x \ 1) \ y) = y * K(x,x \ 1). (1 / x) * L(y,x,x) = K(x,x \ 1) * (x \ y). K(x,x \ 1) * (x \ y) = (1 / x) * L(y,x,x). x \ L(y,1 / x,x) = (x \ 1) * y. x * ((1 / x) * y) = T(x,x \ 1) * ((x \ 1) * y). T(x,x \ 1) * ((x \ 1) * y) = x * ((1 / x) * y). x * ((1 / x) * y) = ((x \ 1) \ 1) * ((x \ 1) * y). ((x \ 1) \ 1) * ((x \ 1) * y) = x * ((1 / x) * y). L(x,1 / y,y) = L(x,y \ 1,y). x != L(y,z \ 1,z) | x = L(y,z,z). L(x,1 / y,y) = L(x,y,y). L(x,y,y \ 1) = L(x,(y \ 1) \ 1,y \ 1). L(x,(y \ 1) \ 1,y \ 1) = L(x,y,y \ 1). K(x \ 1,x) * (K(1 / x,y) * (1 / x)) = x \ K(1 / x,y). x != K(y \ 1,y) * (y \ z) | x = z * T(z \ (y \ z),y). ((x \ 1) \ 1) \ y = y * T(y \ (x \ y),x). x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x. (x * y) \ ((K(x \ 1,x) * y) * ((x \ 1) \ 1)) = K(K(x \ 1,x) * y,(x \ 1) \ 1). T(x,y) * (K(x \ 1,x) * z) = (1 / (1 / T(x,y))) * z. x * y != ((z \ 1) \ 1) * (K(z \ 1,z) * u) | x \ (z * u) = y. ((x \ 1) \ 1) \ (x * y) = y * K(x \ 1,x). x != ((y \ 1) \ 1) \ z | x = z * (((z \ (y \ z)) \ 1) \ 1). (x \ y) * K(x \ 1,x) = y * (((y \ (x \ y)) \ 1) \ 1). x * y != (z * ((u * z) \ u)) * K(z \ 1,z) | (((u * z) \ u) * z) / y = x. (((x * y) \ x) * y) / ((x * y) \ x) = 1 / (1 / y). ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z. ((1 / (1 / x)) * y) * (1 / x) = (x * y) * (x \ 1). x * K(y \ 1,y) = (x / ((y \ 1) \ 1)) * y. (x / ((y \ 1) \ 1)) * y = x * K(y \ 1,y). K(1 / T(x,y),(1 / T(x,y)) \ 1) * (z / T(1 / (1 / x),y)) = z / ((1 / T(x,y)) \ 1). K(T(x,y),T(x,y) \ 1) = K(x,x \ 1). T(x,y) * (((T(x,y) \ 1) \ 1) \ z) = K(x,x \ 1) * z. (x * (T(y,z) \ 1)) * K(y,y \ 1) = x * (1 / T(y,z)). K(x \ 1,x) * (y * T(x,z)) = y * (1 / (1 / T(x,z))). x * K(y \ 1,y) != (z * (y \ 1)) * y | x = R(z,y \ 1,y). (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y). x * y != (1 / z) * ((z \ 1) \ ((u * u) \ (1 / w))) | x \ (z * (1 / ((w * (u * u)) * z))) = y. ((x * x) \ (1 / y)) \ (z * (1 / ((y * (x * x)) * z))) = K(z,z \ 1). (x \ 1) * y = L(((x \ 1) \ 1) \ y,x,x \ 1). L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y. x * y != ((z \ 1) \ 1) \ x | y = ((x \ (z \ x)) \ 1) \ 1. T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1. x * y != z * K(y \ 1,y) | x = z * (((z \ (z / y)) \ 1) \ 1). x / ((y \ 1) \ 1) = x * (((x \ (x / y)) \ 1) \ 1). x * (((x \ (x / y)) \ 1) \ 1) = x / ((y \ 1) \ 1). x * y != z * K(y \ 1,y) | x = (z / y) * K(y \ 1,y). x / ((y \ 1) \ 1) = (x / y) * K(y \ 1,y). (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1). (x \ T(x * y,z)) * x = T(y * ((x \ 1) \ 1),z) * K(x \ 1,x). T(x * ((y \ 1) \ 1),z) * K(y \ 1,y) = (y \ T(y * x,z)) * y. 1 / T(x \ (y \ x),y) = (x \ (y \ x)) \ 1. x * y != (z / u) * K(u \ 1,u) | x \ (z / ((u \ 1) \ 1)) = y. x \ (x / ((y \ 1) \ 1)) = T(x \ (x / y),y). T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1)). 1 / (x \ ((y \ 1) \ x)) = (x \ ((1 / y) \ x)) \ 1. x != T(y \ (y / z),z) | x = ((y \ (y / z)) \ 1) \ 1. x \ (x / ((y \ 1) \ 1)) = ((x \ (x / y)) \ 1) \ 1. ((x \ (x / y)) \ 1) \ 1 = x \ (x / ((y \ 1) \ 1)). x * K(y \ 1,y) = y * (((y \ 1) \ 1) \ x). x * (((x \ 1) \ 1) \ y) = y * K(x \ 1,x). x * y != ((x \ 1) \ K(z,x)) * K(x \ 1,x) | y = K(z,x). ((x \ 1) \ 1) \ ((x \ 1) \ K(y,x)) = K(y,x). x * K(y \ 1,y) != y * z | ((y \ 1) \ 1) \ x = z. x * ((((x \ 1) \ 1) \ 1) * y) = L(y,((x \ 1) \ 1) \ 1,(x \ 1) \ 1) * K(x \ 1,x). L(x,((y \ 1) \ 1) \ 1,(y \ 1) \ 1) * K(y \ 1,y) = y * ((((y \ 1) \ 1) \ 1) * x). ((x \ 1) \ 1) * K(y,x) = (x \ 1) \ K(y,x). x != ((y \ 1) \ 1) * z | x = y * (z * K(y,y \ 1)). (x \ 1) \ K(y,x) = x * (K(y,x) * K(x,x \ 1)). x * (K(y,x) * K(x,x \ 1)) = (x \ 1) \ K(y,x). K(x \ 1,x) * (y * K(x,x \ 1)) != z | z = y. x != K(y,y \ 1) * (y \ z) | x = ((y \ 1) \ 1) \ z. (1 / x) * L(y,x,x) = ((x \ 1) \ 1) \ y. (1 / x) * ((1 / x) * y) = ((x \ 1) \ 1) \ (x \ y). ((x \ 1) \ 1) \ (x \ y) = (1 / x) * ((1 / x) * y). (1 / x) * (1 / (y / x)) = ((x \ 1) \ 1) \ (x / y). ((x \ 1) \ 1) \ (x / y) = (1 / x) * (1 / (y / x)). (x \ 1) * ((y \ 1) \ 1) = R(x \ y,y \ 1,y). R(x \ y,y \ 1,y) = (x \ 1) * ((y \ 1) \ 1). (x * ((y / z) \ 1)) * T(y / z,z / y) = R(x,(y / z) \ 1,y / z). L(x * K(y \ 1,y),y,y \ 1) = (y \ 1) * (y * x). K(x \ 1,x) * (x \ y) != z | z = ((x \ 1) \ 1) \ y. K(x \ 1,x) * (x \ y) != z | ((x \ 1) \ 1) \ y = z. x != (K(y,z) \ 1) * ((z \ u) \ u) | x = K(y,z) \ ((z \ u) \ u). R(K(x,y) \ y,y \ 1,y) = K(x,y) \ ((y \ 1) \ 1). x != (((y * z) \ y) * z) / ((y * z) \ y) | x = L(z,(y * z) \ y,z). 1 / (1 / x) = L(x,(y * x) \ y,x). L(x,(y * x) \ y,x) = 1 / (1 / x). L(x \ y,y \ x,x \ y) = 1 / (1 / (x \ y)). L((x * y) \ x,y,(x * y) \ x) = 1 / (1 / ((x * y) \ x)). ((x \ (1 / (1 / y))) * x) * (1 / y) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1). (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 / (1 / x))) * y) * (1 / x). x * (((x \ y) \ 1) \ 1) = x / (((y \ x) \ 1) \ 1). x / (((y \ x) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1). 1 / (x \ (y \ x)) = (x \ ((1 / (1 / y)) \ x)) \ 1. (x \ ((1 / (1 / y)) \ x)) \ 1 = 1 / (x \ (y \ x)). 1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1. ((x \ (x / (1 / y))) \ 1) \ 1 = x \ (x / (y \ 1)). x * y != (x \ 1) \ K(z,x) | y = x * (K(z,x) / x). K(x,y) * K(y,y \ 1) = y * (K(x,y) / y). x != ((y \ 1) \ 1) \ (y \ z) | x = (y \ 1) * ((y \ 1) * z). (1 / x) * ((1 / x) * y) = (x \ 1) * ((x \ 1) * y). x != (1 / y) * (1 / (z / y)) | x = y * ((1 / y) * (1 / z)). ((x \ 1) \ 1) \ (x / y) = x * ((1 / x) * (1 / y)). (1 / x) \ ((y \ x) \ 1) = x * (((x \ y) \ 1) \ 1). (x * (((x \ y) \ 1) \ 1)) \ 1 != z | (((y \ x) \ 1) \ 1) * (x \ 1) = z. 1 / (1 / (x \ (y \ x))) = x \ ((1 / (1 / y)) \ x). 1 / (x \ (x / y)) = (x \ (x / (1 / (1 / y)))) \ 1. (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y)). 1 / (1 / (x \ (x / (y \ 1)))) = x \ (x / (1 / y)). (1 / x) \ ((((1 / x) * y) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1). 1 / (x * (y * (((y \ z) \ 1) \ 1))) = ((z \ y) * (1 / y)) / x. x / (y * (((y \ z) \ 1) \ 1)) = (1 / x) \ ((z \ y) * (1 / y)). (1 / ((1 / x) * y)) \ (((1 / z) \ ((1 / x) * y)) \ 1) = ((1 / x) * y) * ((((y \ x) / z) \ 1) \ 1). x * (x * (((x \ y) \ 1) \ 1)) = (x * x) * ((y \ x) \ 1). x * (1 / (1 / (x \ (y \ x)))) = (1 / (1 / y)) \ x. 1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y))). x * y != z * (1 / (1 / (z \ (u \ z)))) | ((1 / (1 / u)) \ z) / y = x. ((1 / (1 / x)) \ y) / y = 1 / (1 / ((x \ y) / y)). x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y)). ((1 / x) \ y) / y = 1 / (1 / (((x \ 1) \ y) / y)). 1 / (1 / (((x \ 1) \ y) / y)) = ((1 / x) \ y) / y. x != y / (1 / (1 / z)) | x = (y / z) * K(z,z \ 1). x * (1 / (1 / (x \ (x / y)))) = (x / y) * K(y,y \ 1). (x / y) * K(y,y \ 1) = x * (1 / (1 / (x \ (x / y)))). x * (1 / (1 / (x \ y))) = x / (1 / (1 / (y \ x))). x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y))). x / (1 / (1 / ((x * y) \ x))) = x * (1 / (1 / y)). (x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x)). (x * (1 / (1 / T(y,x)))) \ x = 1 / (1 / ((y * x) \ x)). K(x / (y * x),y) != z | K(x / (y * x),(x / (y * x)) \ 1) = z. R(((x \ (x / (y \ 1))) * x) * K(y \ 1,y),y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y. x * ((y \ 1) \ 1) = y * ((y \ x) / (1 / y)). x * ((x \ y) / (1 / x)) = y * ((x \ 1) \ 1). x * (y / (1 / x)) = (x * y) * ((x \ 1) \ 1). (x * y) * ((x \ 1) \ 1) = x * (y / (1 / x)). x * (((x \ 1) * y) * x) = y * ((x \ 1) \ 1). 1 / (x * (y / (1 / x))) = (x \ 1) / (x * y). (x * ((1 / x) * y)) * ((x \ 1) \ 1) = x * ((1 / x) * (y * x)). x * (y * x) = ((x \ 1) \ y) * ((x \ 1) \ 1). ((x \ 1) \ y) * ((x \ 1) \ 1) = x * (y * x). 1 / (x * (y / (1 / x))) = x \ (1 / (x * y)). (x \ ((1 / y) * (x \ 1))) \ 1 = x * (y * x). x * (y * x) = (x \ 1) \ (y / (x \ 1)). (x \ 1) \ (y / (x \ 1)) = x * (y * x). (x \ 1) \ (y \ x) = x * ((y \ 1) * x). x != (y \ 1) \ ((y * (y * z)) \ y) | x = (y * (z * (1 / y))) \ 1. x * (((x * (x * y)) \ 1) * x) = (x * (y * (1 / x))) \ 1. (x \ 1) \ (y \ x) != x * z | (y \ 1) * x = z. (x * (y \ 1)) \ (z \ (y / x)) = (y / x) * ((z \ 1) * (y / x)). x != 1 / (y * (z / (1 / u))) | x = ((z \ 1) \ u) \ (1 / y). x \ (1 / (x * y)) = ((y \ 1) \ x) \ (1 / x). ((x \ 1) \ y) \ (1 / y) = y \ (1 / (y * x)). x * y != 1 / (z * (u / (1 / z))) | (z \ (1 / (z * u))) / y = x. (x \ (1 / (x * y))) / z = 1 / (z * (x * (y / (1 / x)))). 1 / (x * (y * (z / (1 / y)))) = (y \ (1 / (y * z))) / x. (x \ (y * (x \ 1))) \ 1 = x * ((y \ 1) * x). ((x \ 1) * ((1 / y) / x)) \ 1 = x * (y * x). ((x \ 1) \ (y \ z)) \ ((1 / z) * y) = (y \ z) \ (1 / ((y \ z) * x)). ((x \ 1) \ ((y \ x) \ 1)) \ (1 / ((y \ x) \ 1)) = ((y \ x) \ 1) \ (1 / (((x \ y) \ 1) \ x)). x != y * (z * y) | x = ((1 / y) \ z) * y. (x \ (y * (x \ 1))) \ 1 = ((1 / x) \ (y \ 1)) * x. (x \ (y \ 1)) \ 1 = x * (((y \ x) \ 1) * x). x * (((y \ x) \ 1) * x) = (x \ (y \ 1)) \ 1. 1 / (x * (y * x)) = (x \ 1) * ((1 / y) / x). (x \ 1) * ((1 / y) / x) = 1 / (x * (y * x)). (x \ (y * (x \ 1))) \ 1 = (x / ((y \ 1) \ 1)) * x. (x \ (x \ y)) \ 1 = (x / ((T(y,x) \ 1) \ 1)) * x. (x / ((T(y,x) \ 1) \ 1)) * x = (x \ (x \ y)) \ 1. (x / T((y \ 1) \ 1,x)) * x = (x \ (x \ y)) \ 1. ((x \ 1) * y) * y = (y \ (y \ x)) \ 1. (x \ (x \ y)) \ 1 = ((y \ 1) * x) * x. (x \ (x \ ((y \ 1) \ 1))) \ 1 = ((1 / y) * x) * x. ((1 / x) * ((y \ x) \ 1)) \ 1 = ((1 / y) * x) * x. ((x \ y) \ 1) \ y = ((1 / x) * y) * y. ((x * y) \ 1) \ x = ((1 / (1 / T(y,x \ 1))) * x) * x. ((1 / (1 / T(x,y \ 1))) * y) * y = ((y * x) \ 1) \ y. (((1 / x) * (1 / y)) * (1 / y)) \ 1 = y * ((((x \ (1 / y)) \ 1) \ 1) \ 1). x != K(y \ z,(y \ z) \ 1) | x = K(y \ z,z \ y). K(x \ y,T(x / y,T(y,x))) = K(x \ y,y \ x). x != ((y * z) \ y) * (1 / y) | x = z \ (1 / y). K(x,x \ 1) * (y \ (x \ 1)) = y \ (1 / x). (x \ (1 / y)) * K(y \ 1,y) = x \ (y \ 1). x != ((y * (z \ 1)) \ u) * (1 / u) | x = u * (((u \ (z / y)) \ 1) \ 1). K(x,x \ 1) * ((y \ 1) \ z) = x * (((x \ (y / (1 / z))) \ 1) \ 1). x * (((x \ (y / (1 / z))) \ 1) \ 1) = K(x,x \ 1) * ((y \ 1) \ z). T(x * ((y \ z) * (1 / z)),x) = (y * K(z \ 1,z)) \ x. T(x,y) * (K(x \ 1,x) * z) = T(1 / (1 / x),y) * z. x * y != z * (((z \ x) \ 1) \ 1) | y = K((x \ z) \ 1,x \ z). K(x \ 1,x) = K(((x \ y) \ y) \ 1,(x \ y) \ y). K(((x \ y) \ y) \ 1,(x \ y) \ y) = K(x \ 1,x). T(x,y) * (T((x \ 1) \ 1,y) \ z) = K(x,x \ 1) * z. (T(x,y) \ T(x,z)) * K(x,x \ 1) = T(x,z) * (1 / T(x,y)). K(x \ 1,x) * (y * T((x \ z) \ z,u)) = y * (1 / (1 / T((x \ z) \ z,u))). x * y != (z * z) * ((u \ z) \ 1) | x \ ((u \ (z \ 1)) \ 1) = y. x \ ((y \ (x \ 1)) \ 1) = x * (((x \ y) \ 1) \ 1). (x * (((x \ y) \ 1) \ 1)) \ 1 = K(x,x \ 1) / y. (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = (x * (y * z)) * (1 / (1 / ((x * (y * z)) \ ((x * (y * z)) / L(z,y,x))))). (x * (y * z)) * (1 / (1 / ((x * (y * z)) \ ((x * (y * z)) / L(z,y,x))))) = (x * y) * K(L(z,y,x),L(z,y,x) \ 1). (x * T(1 / (1 / y),x)) \ x = 1 / (1 / ((y * x) \ x)). x * (((x * y) \ (x \ 1)) * x) = (x * (y * (1 / x))) \ 1. ((1 / (1 / T(x,y \ 1))) * y) * y = (x \ (y \ 1)) \ y. T(x,y) \ z = K(x \ 1,x) * (T(1 / (1 / x),y) \ z). K(x \ 1,x) * (T(1 / (1 / x),y) \ z) = T(x,y) \ z. x != T(y / z,y) * u | x = ((1 / z) * y) * u. K(x / y,(x / y) \ 1) * z = ((1 / y) * x) * (T(((x / y) \ 1) \ 1,x) \ z). ((1 / x) * y) * (T(((y / x) \ 1) \ 1,y) \ z) = K(y / x,(y / x) \ 1) * z. ((1 / (1 / x)) * y) \ y = 1 / (1 / ((x * y) \ y)). 1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y. (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y). (((1 / x) * y) \ y) \ 1 = 1 / (((x \ 1) * y) \ y). 1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1. ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y. ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x). x * (((x * y) \ x) * (1 / x)) = (x * (y * (1 / x))) \ 1. (((T(x,y \ 1) \ 1) \ 1) * y) * y = (x \ (y \ 1)) \ y. ((x \ 1) \ 1) * (T(x,y) \ z) = x * (T(1 / (1 / x),y) \ z). x * (y \ (1 / x)) = (x * (y * (1 / x))) \ 1. (x * (y * (1 / x))) \ 1 = x * (y \ (1 / x)). 1 / (x * (y \ (1 / x))) = x * (y * (1 / x)). x != 1 / (y * (z \ (1 / y))) | x = ((y \ 1) \ (z / (y \ 1))) * (y \ (1 / y)). x * (y * (1 / x)) = ((x \ 1) \ (y / (x \ 1))) * (x \ (1 / x)). ((x \ 1) \ (y / (x \ 1))) * (x \ (1 / x)) = x * (y * (1 / x)). (T((x \ 1) \ 1,y \ 1) * y) * y = (x \ (y \ 1)) \ y. ((1 / x) \ ((y \ 1) \ 1)) * x = (y \ (x \ 1)) \ x. (x / (1 / y)) * x = (y \ (x \ 1)) \ x. (x \ (y \ 1)) \ y = (y / (1 / x)) * y. x != L((y * z) \ y,z,(u * z) \ u) | x = L(1 / z,z,y). 1 / (1 / ((x * y) \ x)) = L(1 / y,y,x). L(1 / x,x,y) = 1 / (1 / ((y * x) \ y)). L(x,x \ 1,y) = 1 / (1 / ((y * (x \ 1)) \ y)). L(1 / x,x,y) = 1 / (1 / L(x \ 1,x,y)). 1 / (1 / L(x \ 1,x,y)) = L(1 / x,x,y). (L(1 / x,x,y) \ 1) \ 1 = L(x \ 1,x,y). (L(x \ 1,T(x,x \ 1),y) \ 1) \ 1 = L(T(x,x \ 1) \ 1,T(x,x \ 1),y). L(T(x,x \ 1) \ 1,T(x,x \ 1),y) = (L(x \ 1,T(x,x \ 1),y) \ 1) \ 1. x / L(y,y \ 1,x) = x * (1 / (1 / (y \ 1))). x / L(y,y \ 1,x) = x * (1 / y). (x * (1 / y)) \ x = L(y,y \ 1,x). L(x,x \ 1,y) = (y * (1 / x)) \ y. x != (y * (1 / z)) \ y | x = L(z,1 / z,y). L(x,x \ 1,y) = L(x,1 / x,y). L(x,1 / x,y) = L(x,x \ 1,y). L(x \ 1,x,y) = L(x \ 1,(x \ 1) \ 1,y). L(x \ 1,(x \ 1) \ 1,y) = L(x \ 1,x,y). L(x \ 1,T(x,x \ 1),y) = L(x \ 1,x,y). x \ K((1 / y) * z,z \ ((1 / y) \ 1)) = (x \ ((1 / y) * z)) * (((z \ y) \ 1) \ 1). x \ (K(y * x,x \ (y \ 1)) * x) = (((y * x) \ 1) * y) * x. ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z. x != y * (((y \ z) \ 1) \ 1) | x = z * K(y \ z,z \ y). (1 / x) \ ((((1 / x) * y) \ 1) \ 1) = y * K(x \ y,y \ x). 1 / (x * (y * (1 / (z * y)))) = (((z \ 1) \ y) * (1 / y)) / x. (((x \ 1) \ y) * (1 / y)) / z = 1 / (z * (y * (1 / (x * y)))). x / (y * (1 / (z * y))) = (1 / x) \ (((z \ 1) \ y) * (1 / y)). (1 / x) \ (((y \ 1) \ z) * (1 / z)) = x / (z * (1 / (y * z))). (((x \ 1) \ 1) \ (x / y)) * ((x \ 1) \ 1) = x * ((1 / x) * ((1 / y) * x)). x * K(y,y \ 1) != T(y,y \ 1) * z | x = y * z. T(x,y) \ T(x,x \ 1) = x * (1 / T(x,y)). x * (1 / T(x,y)) = T(x,y) \ ((x \ 1) \ 1). T(x,y) \ ((x \ 1) \ 1) = x * (1 / T(x,y)). (x * (y * (1 / x))) * x = ((x \ 1) \ 1) * y. x != (y * (z * (1 / y))) * y | x = (y * y) * ((y \ 1) * z). ((x \ 1) \ 1) * y = (x * x) * ((x \ 1) * y). (x * x) * ((x \ 1) * y) = ((x \ 1) \ 1) * y. x * y != (z * z) * ((z \ 1) * u) | (((z \ 1) \ 1) * u) / y = x. ((((1 / x) \ 1) \ 1) * y) / (((1 / x) \ 1) * y) = T((1 / x) / x,1 / x). T((1 / x) / x,1 / x) = ((((1 / x) \ 1) \ 1) * y) / (((1 / x) \ 1) * y). T(K(x * y,y \ (x \ 1)),y) = (((x * y) \ 1) * x) * y. T(K(x * y,y \ (x \ 1)),y) = ((y \ (x \ 1)) * x) * y. T(K(x * y,y \ (x \ 1)),y) = ((y \ x) * (1 / x)) * y. (x * (((x \ y) \ 1) \ 1)) / z = 1 / (z * (x * (1 / (y * x)))). ((1 / x) * y) \ (((z \ 1) \ u) * (1 / u)) = (y \ x) / (u * (1 / (z * u))). (((x \ y) \ 1) / x) \ (1 / z) = 1 / (z * (x * (1 / (y * x)))). 1 / (x * (y * (1 / (z * y)))) = (((y \ z) \ 1) / y) \ (1 / x). 1 / (x * (y * (1 / (z * y)))) = ((y \ z) \ (1 / y)) \ (1 / x). 1 / (x * (y * (1 / (z * y)))) = ((z \ y) * (1 / y)) \ (1 / x). x != 1 / (y * (z * (1 / (u * z)))) | x = (((1 / (u * (1 / z))) \ z) \ 1) \ (1 / y). ((x \ y) * (1 / y)) \ (1 / z) = (((1 / (x * (1 / y))) \ y) \ 1) \ (1 / z). (((1 / (x * (1 / y))) \ y) \ 1) \ (1 / z) = ((x \ y) * (1 / y)) \ (1 / z). x != T(y,y \ 1) * ((y \ 1) * z) | x = y * ((1 / y) * z). K(x,x \ 1) * L(y,x \ 1,x) = x * ((1 / x) * y). K(x / (y * x),(x / (y * x)) \ 1) = K(y \ 1,y). K(x \ 1,x) \ (x * y) = (((y / (x * y)) \ 1) \ 1) \ y. K(x \ 1,x) \ (x * y) = R(x \ 1,x,y) \ y. R(x \ 1,x,y) \ y = K(x \ 1,x) \ (x * y). x != K(y \ 1,y) \ (y * z) | x = ((y \ 1) \ 1) * z. R(x \ 1,x,y) \ y = ((x \ 1) \ 1) * y. x / (((y \ 1) \ 1) * x) = R(y \ 1,y,x). R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y). R(x,1 / x,y) \ y = (((1 / x) \ 1) \ 1) * y. x != y / ((z \ 1) * y) | x = R(z,z \ 1,y). R(x \ 1,x,y) = R(x \ 1,(x \ 1) \ 1,y). R(x \ 1,(x \ 1) \ 1,y) = R(x \ 1,x,y). (x * ((y * (x \ 1)) / y)) * y = T(y,R(x \ 1,(x \ 1) \ 1,y)). T(x,R(y \ 1,(y \ 1) \ 1,x)) = (y * ((x * (y \ 1)) / x)) * x. R(x,1 / x,y) \ y = (x \ 1) * y. x / ((y \ 1) * x) = R(y,1 / y,x). R(x,1 / x,y) = y / ((x \ 1) * y). R(x,1 / x,y) = R(x,x \ 1,y). L(R(x,x \ 1,y),x \ 1,x) = R(1 / (1 / x),1 / x,y). x != L(R(y,z,u),y \ 1,y) | x = R(1 / (1 / y),z,u). R(1 / (1 / x),1 / x,y) = R(1 / (1 / x),x \ 1,y). ((1 / x) \ y) / y = R(1 / (1 / x),x \ 1,(1 / x) \ y). R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y. ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((1 / x) \ y) / y). T(x,R((y \ x) \ 1,((y \ x) \ 1) \ 1,x)) = K(x,y / x) * x. T(x,R((y \ x) \ 1,((y \ x) \ 1) \ 1,x)) != z | x * K(x,y / x) = z. x * (((x \ (y / (1 / z))) \ 1) \ 1) != u | ((y \ 1) \ z) * K(x,x \ 1) = u. ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z. (((x \ y) \ 1) \ 1) * (y \ 1) = K(y,y \ 1) / x. x != K(y,y \ 1) / z | x = y * (1 / (z * y)). (((x \ y) \ 1) \ 1) * (y \ 1) = y * (1 / (x * y)). (x \ 1) * (y * (1 / (z * y))) = (((z \ y) * (1 / y)) \ x) \ 1. (((x \ y) * (1 / y)) \ z) \ 1 = (z \ 1) * (y * (1 / (x * y))). x != K(y,y \ 1) * (z \ (u \ 1)) | x = ((u * z) \ y) * (1 / y). x * (1 / (((y / (1 / z)) * y) * x)) = ((y * (z * y)) \ x) * (1 / x). x != (((1 / y) * z) * u) \ 1 | x = u \ (z \ y). x * ((((y \ (1 / x)) \ 1) \ 1) \ 1) = (1 / x) \ ((1 / x) \ y). x * (((x * ((y \ 1) \ 1)) \ 1) \ 1) = (1 / x) \ ((1 / x) \ y). x * ((((y \ 1) \ 1) \ (x \ 1)) \ 1) = (1 / x) \ ((1 / x) \ y). x * (((x \ 1) \ 1) * (1 / (y \ 1))) = (1 / x) \ ((1 / x) \ y). x * (((x \ 1) \ 1) * y) = (1 / x) \ ((1 / x) \ y). (1 / x) \ ((1 / x) \ y) = x * (((x \ 1) \ 1) * y). x * ((x \ (1 / y)) * L(1 / y,x,x)) = x / (y * (((y \ 1) \ 1) * x)). (((x \ 1) \ 1) \ (x / y)) * ((x \ 1) \ 1) = x * ((1 / x) * (1 / (x \ y))). T((1 / x) / x,1 / x) = ((x \ 1) * y) / (((1 / x) \ 1) * y). T((1 / x) / x,1 / x) = ((x \ 1) * y) / (x * y). T(x \ (x \ 1),1 / x) = ((x \ 1) * y) / (x * y). x != T(y,1 / z) | x = T(y,z \ 1). ((x \ 1) * y) / (x * y) = T(x \ (x \ 1),x \ 1). T(x \ (x \ 1),x \ 1) = ((x \ 1) * y) / (x * y). x \ T(x \ 1,x) = ((x \ 1) * y) / (x * y). x \ (1 / x) = ((x \ 1) * y) / (x * y). ((x \ 1) * y) / (x * y) = x \ (1 / x). x != (((y \ z) \ 1) * z) / ((y \ z) * z) | x = (z \ y) * (z \ y). (x \ y) \ (1 / (x \ y)) = (y \ x) * (y \ x). ((x \ y) * (x \ y)) * z = ((y \ x) \ 1) * ((y \ x) \ z). ((x \ y) \ 1) * ((x \ y) \ z) = ((y \ x) * (y \ x)) * z. T(x / y,x) * ((1 / y) * x) = (y \ x) * (y \ x). (L(x,y,z) \ 1) * (((z * y) \ (z * (y * x))) \ u) = (((z * (y * x)) \ (z * y)) * ((z * (y * x)) \ (z * y))) * u. (((x * (y * z)) \ (x * y)) * ((x * (y * z)) \ (x * y))) * u = (L(z,y,x) \ 1) * (((x * y) \ (x * (y * z))) \ u). ((x \ y) * (x \ y)) * z = (((y / x) * y) \ x) \ z. (((x / y) * x) \ y) \ z = ((y \ x) * (y \ x)) * z. x \ ((y / x) * y) = (x \ y) * (x \ y). x * ((x \ y) * (x \ y)) = (y / x) * y. ((x / y) * x) \ y = (y \ x) \ ((y \ x) \ 1). (x \ y) \ ((x \ y) \ 1) = ((y / x) * y) \ x. x * (((y / z) * y) \ z) = x / ((z \ y) * (z \ y)). x / ((y \ z) * (y \ z)) = x * (((z / y) * z) \ y). x != y / ((y \ z) * (y \ z)) | x = (z / y) \ ((z / y) \ y). x * (((y / x) * y) \ x) = (y / x) \ ((y / x) \ x). (x / y) \ ((x / y) \ y) = y * (((x / y) * x) \ y). ((1 / x) * y) \ (z * (((z \ u) \ 1) \ 1)) = (y \ x) / (z * (1 / (u * z))). x != y * ((1 / y) * (1 / z)) | x = (1 / y) * (1 / (z / y)). (((x \ 1) \ 1) \ (x / y)) * ((x \ 1) \ 1) = (1 / x) * (1 / ((x \ y) / x)). (x / y) * ((x \ 1) \ 1) = 1 / ((x \ y) / x). (x \ 1) \ (((y / z) / u) \ x) = ((x \ 1) \ u) * ((x \ (y / z)) \ 1). ((x \ 1) \ y) * ((x \ (z / u)) \ 1) = (x \ 1) \ (((z / u) / y) \ x). x != ((y \ 1) \ 1) * ((y \ (z / u)) \ 1) | x = ((y \ 1) \ u) * ((y \ z) \ 1). (x \ 1) \ (((y / z) / 1) \ x) = ((x \ 1) \ z) * ((x \ y) \ 1). (x \ 1) \ ((y / z) \ x) = ((x \ 1) \ z) * ((x \ y) \ 1). ((x \ 1) \ y) * ((x \ z) \ 1) = (x \ 1) \ ((z / y) \ x). x != (y \ 1) \ (z \ y) | x = y * ((z \ 1) * y). ((x \ 1) \ y) * ((x \ z) \ 1) = x * (((z / y) \ 1) * x). ((x \ 1) \ y) * ((x \ z) \ 1) = x * ((y * (z \ 1)) * x). (((x \ (y \ z)) \ 1) \ 1) \ ((y \ z) \ 1) = ((1 / z) * y) * (x * ((1 / z) * y)). x != y * z | x = R(y,z,z \ 1) / (z \ 1). (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = R((y \ (1 / (1 / x))) * y,1 / x,(1 / x) \ 1) / ((1 / x) \ 1). R((x \ (1 / (1 / y))) * x,1 / y,(1 / y) \ 1) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1). K(x \ 1,x) * (y * T((x \ 1) \ 1,z)) = y * (1 / (T(x,z) \ 1)). K(x \ 1,x) * (y * T((x \ 1) \ 1,z)) = y * T(x,z). L(T(x \ 1,x),T(x,x \ 1),y) = (L(x \ 1,T(x,x \ 1),y) \ 1) \ 1. L(T(x \ 1,x),T(x,x \ 1),y) = (L(x \ 1,x,y) \ 1) \ 1. x / ((L(y \ 1,y,x) \ 1) \ 1) = x * T(y,y \ 1). T(K(x,y),L(x \ 1,x,y) \ 1) = K(y \ (y * T(x,x \ 1)),y). T(K(x,y),L(x \ 1,x,y) \ 1) = K(T(x,x \ 1),y). T(K(x,y),L(x \ 1,x,y) \ 1) = K((x \ 1) \ 1,y). T(K(x,y),((y * x) \ y) \ 1) = K((x \ 1) \ 1,y). x != T(K(y,z),((u * y) \ u) \ 1) | x = (((u * y) \ u) \ 1) \ (((u * y) \ u) \ K(y,z)). K((x \ 1) \ 1,y) = (((y * x) \ y) \ 1) \ (((y * x) \ y) \ K(x,y)). (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K((y \ 1) \ 1,x). x != T(K(y,z),((z * y) \ z) \ 1) | x = T(K(y,z),y). K((x \ 1) \ 1,y) = T(K(x,y),x). T(K(x,y),x) = K((x \ 1) \ 1,y). x != T(K(y,z),y) | x = K(y,z). K((x \ 1) \ 1,y) = K(x,y). K(x \ 1,y) = K(1 / x,y). K(1 / x,y) = K(x \ 1,y). K((x \ (y \ 1)) \ 1,z) = K(y * x,z). x != K(y \ 1,z) | x = L(y * T(y \ 1,z),y \ 1,z). K(1 / x,y) = L(x * T(x \ 1,y),x \ 1,y). L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y). K(1 / x,y) * (1 / x) = (1 / x) * K(x \ 1,y). x != L(y,z,u / z) | x = u \ ((u / z) * (z * y)). K(1 / x,y / (x \ 1)) = y \ ((y / (x \ 1)) * ((x \ 1) * (x * T(x \ 1,y / (x \ 1))))). x \ ((x / (y \ 1)) * ((y \ 1) * (y * T(y \ 1,x / (y \ 1))))) = K(1 / y,x / (y \ 1)). K(1 / x,y) != z | K(x \ 1,y) = z. K(x \ 1,x) * ((1 / x) * K(x \ 1,y)) = x \ K(1 / x,y). (x \ 1) * K(x \ 1,y) = x \ K(1 / x,y). (x \ K(1 / x,y)) * ((x \ 1) \ 1) = K(x \ 1,y). (x \ (y \ ((1 / x) * (y / (1 / x))))) * ((x \ 1) \ 1) = K(x \ 1,y / (1 / x)). x != K((y \ 1) \ 1,z) | x = K(y,z). (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K(y,x). ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z. x != (((y \ z) \ 1) \ 1) \ (z \ 1) | x = z \ (y / z). ((1 / x) * y) * (z * ((1 / x) * y)) = (y \ x) \ (z / (y \ x)). (x * (y * z)) \ ((z / (x * (y * z))) \ L(z,y,x)) = a(x,y,z) \ 1. (((x * (y / z)) / x) * z) * u = (z * u) * ((x * ((z * u) \ (y * u))) / x). (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y. (x * y) * ((z * ((x * y) \ u)) / z) = (((z * ((u / y) / x)) / z) * x) * y. (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x). (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y. (x * ((y / z) / x)) * z = (x * z) * ((x * ((x * z) \ y)) / x). (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y. (x * y) * ((x * ((x * y) \ z)) / x) != u | (x * ((z / y) / x)) * y = u. T(x,x / (x * y)) = (x * ((x / y) / x)) * y. (x * ((x / y) / x)) * y = T(x,x / (x * y)). x != (y * z) * ((u * ((y * z) \ w)) / u) | x = y * (z * ((u * (z \ (y \ w))) / u)). (x * ((y / z) / x)) * z = x * (z * ((x * (z \ (x \ y))) / x)). x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y. x * ((y * (z \ u)) * ((x * ((y * (z \ u)) \ (x \ u))) / x)) = (x * (R(z / y,y,z \ u) / x)) * (y * (z \ u)). (x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = x * ((z * (y \ u)) * ((x * ((z * (y \ u)) \ (x \ u))) / x)). x * ((y * ((x * (y \ 1)) / x)) * (x \ z)) = (x * ((z / (y * (x \ z))) / x)) * (y * (x \ z)). (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y)). T(x,x / (x * y)) != z | (x * ((x / y) / x)) * y = z. x * ((y * (((x / z) * z) \ (u * z))) / y) = ((x / z) * ((y * ((x / z) \ u)) / y)) * z. ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z). x != (1 / (1 / (y / z))) * z | x = z * (1 / (1 / (z \ y))). (x * y) * (1 / (1 / L(y \ z,y,x))) = (x * y) * (1 / (1 / ((x * y) \ (x * z)))). (T(x,y) * (1 / (z * (x \ y)))) \ T(x,y) = L(z,T(x,y),T(x,y)) * (y / T(x,y)). x != (y * z) * T(L(u,z,y),w) | x = y * (z * T(u,w)). (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * ((1 / x) * T(x,y)). (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (T(x,y) / x). (x \ ((L(y,1 / y,x) * x) / L(y,1 / y,x))) / (x \ 1) = x * (T(y,x) / y). (x * (T(y,x) / y)) \ (x * z) = x * (((L(y,1 / y,x) * x) / L(y,1 / y,x)) \ z). x * (((L(y,1 / y,x) * x) / L(y,1 / y,x)) \ z) = (x * (T(y,x) / y)) \ (x * z). (x \ (x * (T(y,x) / y))) / (x \ 1) = x * (T(y,x) / y). (T(x,y) / x) / (y \ 1) = y * (T(x,y) / x). (x \ T(x,y)) / (y \ 1) = y * (T(x,y) / x). (x \ T(x,y)) / (y \ 1) = y * (x \ T(x,y)). (x * (y \ T(y,x))) * (x \ 1) = y \ T(y,x). (x * y) * L((x * y) \ z,u,w) != y * v5 | T(x * L(x \ (z / y),u,w),y) = v5. x * ((x * y) * (y / (x * y))) = T(x * y,R(x \ 1,x,x * y)). T(x * y,R(x \ 1,x,x * y)) = x * ((x * y) * (y / (x * y))). L(x * (y \ z),T(y,z),T(y,z)) = L(x,T(y,z),T(y,z)) * (z / T(y,z)). L(x,T(y,z),T(y,z)) * (z / T(y,z)) = L(x * (y \ z),T(y,z),T(y,z)). T(x * L(x \ ((y * z) / y),u,w),y) = T(x,y) * L(T(x,y) \ z,u,w). T(T(x,y) * L(x \ y,z,u),x) = T(T(x,y),x) * L(T(T(x,y),x) \ y,z,u). T(T(x,y),x) * L(T(T(x,y),x) \ y,z,u) = T(T(x,y) * L(x \ y,z,u),x). T(x,y) * L(T(T(x,y),x) \ y,z,u) = T(T(x,y) * L(x \ y,z,u),x). T(x,y) * L(T(x,y) \ y,z,u) = T(T(x,y) * L(x \ y,z,u),x). T(T(x,y) * L(x \ y,z,u),x) = T(x,y) * L(T(x,y) \ y,z,u). x != T(y,z) * L(T(y,z) \ z,u,w) | x = T(y * L(y \ z,u,w),z). T(T(x,y) * L(x \ y,z,u),x) = T(x * L(x \ y,z,u),y). T(T(x,x * y) * L(y,z,u),x) = T(x * L(x \ (x * y),z,u),x * y). T(x * L(x \ (x * y),z,u),x * y) = T(T(x,x * y) * L(y,z,u),x). T(x * L(y,z,u),x * y) = T(T(x,x * y) * L(y,z,u),x). T(T(x,x * y) * L(y,z,u),x) = T(x * L(y,z,u),x * y). (x * ((y \ 1) \ 1)) \ ((1 / (1 / x)) * y) = (1 \ (y \ (1 / x))) * (1 / (y \ (1 / x))). ((1 / 1) \ (x * y)) \ (((y \ (x \ 1)) \ 1) * z) = (1 / (z * (x * y))) \ (y \ (x \ 1)). K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z)). (x \ 1) * ((y \ (x \ 1)) \ (y \ z)) = (((x * y) / ((1 / z) * y)) \ x) \ 1. (((x * y) / ((1 / z) * y)) \ x) \ 1 = (x \ 1) * ((y \ (x \ 1)) \ (y \ z)). (x \ ((1 / y) * z)) * (((z \ y) \ 1) \ 1) = ((1 / y) * z) * ((((z \ y) / x) \ 1) \ 1). (x \ 1) * (y * T(y \ ((1 / x) \ y),z)) = ((x \ 1) * T(x,z)) * y. R(x,y,z) \ R(u / (u / x),y,z) = R(u / (u / x),y,z) / R(x,y,z). R(x / (x / y),z,u) / R(y,z,u) = R(y,z,u) \ R(x / (x / y),z,u). x != R(1 / (1 / y),z,u) / R(y,z,u) | x = y * T(y \ 1,R(y,z,u)). R(x,y,z) \ R(1 / (1 / x),y,z) = x * T(x \ 1,R(x,y,z)). T(x / y,x) * ((1 / T(x / y,x)) * z) = (x \ y) * (((1 / y) * x) * z). (x * ((1 / 1) \ (y * z))) * ((z \ (y \ 1)) \ 1) = (1 / (x / (z \ (y \ 1)))) \ (y * z). (x * ((1 / (1 / y)) * z)) * (y * ((z \ 1) \ 1)) = (x / (z \ (1 / y))) / (z \ (1 / y)). T(((1 / x) \ y) * (x \ T(y,x \ 1)),x) = (y * ((x \ ((1 / x) \ y)) / x)) * x. T(((1 / x) \ y) * (x \ T(y,x \ 1)),x) = (y * (L(y,x,x) / x)) * x. T(((1 / x) \ y) * (x \ T(y,x \ 1)),x) = (y * (y * (1 / x))) * x. (x * y) \ (y * x) = K(K(x \ 1,x) * y,(x \ 1) \ 1). K(K(x \ 1,x) * y,(x \ 1) \ 1) = (x * y) \ (y * x). K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x). K(x,(y \ 1) \ 1) = K(K(y,y \ 1) * x,y). K(K(x,x \ 1) * y,x) = K(y,(x \ 1) \ 1). ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z). (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y). (x * ((y * (x \ z)) / y)) / z = (x / z) * ((y * ((x / z) \ 1)) / y). (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y. x * ((x * (T(y,x) / y)) \ z) = (x * (T(y,x) / y)) \ (x * z). (x * (T(y,x) / y)) \ (x * z) = x * ((x * (T(y,x) / y)) \ z). (x * (y \ T(y,x))) \ (x * z) = x * ((x * (T(y,x) / y)) \ z). (x * (y \ T(y,x))) \ (x * z) = x * ((x * (y \ T(y,x))) \ z). T(x,y) \ x = (y * (x \ T(x,y))) \ y. (x * (y \ T(y,x))) \ x = T(y,x) \ y. (x * ((y \ 1) \ 1)) \ (((x \ 1) \ 1) * y) = (1 \ (y \ (1 / x))) * (1 / (y \ (1 / x))). (1 \ (x * y)) \ (((y \ (x \ 1)) \ 1) * z) = (1 / (z * (x * y))) \ (y \ (x \ 1)). (x * y) \ (((y \ (x \ 1)) \ 1) * z) = (1 / (z * (x * y))) \ (y \ (x \ 1)). (1 / (x * (y * z))) \ (z \ (y \ 1)) = (y * z) \ (((z \ (y \ 1)) \ 1) * x). x != (y \ 1) * (z * T(z \ ((y \ 1) \ u),w)) | x = (y \ T(y * (u / z),w)) * z. K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x. K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x. (x * (1 \ (y * z))) * ((z \ (y \ 1)) \ 1) = (1 / (x / (z \ (y \ 1)))) \ (y * z). (x * (y * z)) * ((z \ (y \ 1)) \ 1) = (1 / (x / (z \ (y \ 1)))) \ (y * z). (1 / (x / (y \ (z \ 1)))) \ (z * y) = (x * (z * y)) * ((y \ (z \ 1)) \ 1). (1 / ((1 / x) \ (y * z))) \ (y * z) = (x * (y * z)) * ((z \ (y \ 1)) \ 1). ((1 / (x * y)) * (1 / z)) \ (x * y) = (z * (x * y)) * ((y \ (x \ 1)) \ 1). x != ((1 / y) * z) \ y | x = ((y \ z) \ 1) * y. (x * (y * z)) * ((z \ (y \ 1)) \ 1) = (((y * z) \ (1 / x)) \ 1) * (y * z). (((x * y) \ (1 / z)) \ 1) * (x * y) = (z * (x * y)) * ((y \ (x \ 1)) \ 1). (x * (((y * z) \ 1) \ 1)) * (y * z) = (x * (y * z)) * ((z \ (y \ 1)) \ 1). (x * (((y \ 1) \ 1) * z)) * (y * ((z \ 1) \ 1)) = (x / (z \ (1 / y))) / (z \ (1 / y)). (x * ((y \ 1) \ 1)) \ (((x \ 1) \ 1) * y) = (y \ (1 / x)) * (1 / (y \ (1 / x))). x != T((y * (1 / z)) / y,L(z,u,w) / z) | x = (y * (1 / z)) / y. L(1 / x,L(x,y,z),1 / x) = (L(x,y,z) * (1 / x)) / L(x,y,z). (L(x,y,z) * (1 / x)) / L(x,y,z) = L(1 / x,L(x,y,z),1 / x). L(1 / x,L(x,y,z),1 / x) * x = x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)). x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = L(1 / x,L(x,y,z),1 / x) * x. x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = x * L(x \ 1,L(x,y,z),1 / x). x != y * ((L(y,z,u) * (y \ 1)) / L(y,z,u)) | x = K(L(y,z,u),1 / y). x * L(x \ 1,L(x,y,z),1 / x) = K(L(x,y,z),1 / x). x != T(R(y,z,u),w) * (z * u) | x = (T(y,w) * z) * u. (x * K(x,y)) * T((x * K(x,y)) \ (x * y),z) = (T(y,z) * x) * K(x,y). x * (K(x,y) * T(K(x,y) \ y,z)) = (T(y,z) * x) * K(x,y). x * ((K(x,y) \ y) * K(x,y)) = (T(y,K(x,y)) * x) * K(x,y). (T(x,K(y,x)) * y) * K(y,x) = y * ((K(y,x) \ x) * K(y,x)). (x * y) * K(y,x) = y * ((K(y,x) \ x) * K(y,x)). x * ((K(x,y) \ y) * K(x,y)) = (y * x) * K(x,y). x * y != (z * x) * K(x,z) | y = z. (K(x,y) \ y) * K(x,y) = y. x / K(y,x) = K(y,x) \ x. x * y != (K(z,u) \ u) * K(z,u) | x \ u = y. (K(x,y) \ 1) \ y = y * K(x,y). x * ((y * z) * T((y * z) \ y,u)) = (x * y) * K(u \ (u / L(z,y,x)),u). (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z)). (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z))). L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y). K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u). K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u). K(x \ (x / R(y,z,u)),x) = R(y * T(y \ 1,x),z,u). R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y). K(x \ (x / R(y,z,u)),x) != w | R(y * T(y \ 1,x),z,u) = w. x != K(y \ (y / z),z) | x = K(z \ 1,z). R(x * T(x \ 1,R(x,y,z)),y,z) = K(R(x,y,z) \ 1,R(x,y,z)). L(x,y \ 1,(y \ 1) \ 1) * K(y \ 1,y) = y * ((((y \ 1) \ 1) \ 1) * x). L(x,y \ 1,y) * K(y \ 1,y) = y * ((((y \ 1) \ 1) \ 1) * x). ((x \ 1) \ 1) \ L(y,x \ 1,x) = (((x \ 1) \ 1) \ 1) * y. (((x \ ((x / y) * z)) * 1) \ 1) * (x \ ((x / y) * z)) = K(x \ ((z / x) \ y),x \ ((x / y) * z)). (x \ ((y / x) \ z)) * (x \ ((x / z) * y)) = K(x \ ((y / x) \ z),x \ ((x / z) * y)). K(x \ ((y / x) \ z),x \ ((x / z) * y)) = (x \ ((y / x) \ z)) * (x \ ((x / z) * y)). K(x \ 1,x) * R(K(x \ 1,x) \ y,z,u) = (x \ 1) * (x * R(x \ ((x \ 1) \ y),z,u)). K(x \ 1,x) * L(K(x \ 1,x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u)). R(T(x,T(1 / x,R(x,y,z))),y,z) \ R(x,y,z) = (R(x,y,z) \ (R(x,y,z) / x)) * x. R(T(x,x \ 1),y,z) \ R(x,y,z) = (R(x,y,z) \ (R(x,y,z) / x)) * x. R(T(x,x \ 1),y,z) \ R(x,y,z) = T(1 / x,R(x,y,z)) * x. R(T(x,x \ 1),y,z) \ R(x,y,z) != u | x * T(x \ 1,R(x,y,z)) = u. T(x / (y * ((z \ 1) * (y * (z \ 1)))),y * (z \ 1)) = (1 / ((y * (z \ 1)) \ x)) \ (z / y). (R(x,y,z) * (u * x)) \ ((u * x) * R(T(x,u),y,z)) = a(x,T(u,x),R(T(x,u),y,z)). (R(x,y,z) * (u * x)) \ ((R(x,y,z) * u) * x) = a(x,T(u,x),R(T(x,u),y,z)). a(R(x,y,z),u,x) = a(x,T(u,x),R(T(x,u),y,z)). a(x,T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x). ((1 / x) * y) * (1 / (z \ (y \ x))) = T(z \ (y \ x),z) \ ((1 / x) * y). T(x \ (y \ z),x) \ ((1 / z) * y) = ((1 / z) * y) * (1 / (x \ (y \ z))). T(x \ (y \ z),x) \ ((1 / z) * y) = ((1 / z) * y) * ((1 / (y \ z)) * x). T(x \ (y \ z),x) \ ((1 / z) * y) = ((1 / z) * y) * (((1 / z) * y) * x). T((x \ y) \ z,z) / (x \ y) = ((1 / y) * x) * (((1 / y) * x) * z). (((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1)) \ (x \ 1) = (x \ R(x,y,z)) / R(x,y,z). (x \ (y \ 1)) / ((y * (((y \ 1) * x) * L(x,y,y))) \ (y \ 1)) = y * ((y \ 1) * x). (x \ (y \ 1)) / ((y * ((y \ x) * x)) \ (y \ 1)) = y * ((y \ 1) * x). (x \ (y \ 1)) / ((x * x) \ (y \ 1)) = y * ((y \ 1) * x). (1 / (x \ (y \ 1))) \ (y * (x * x)) = y * ((y \ 1) * x). ((1 / 1) \ (x * y)) \ (x * (y * y)) = x * ((x \ 1) * y). (1 \ (x * y)) \ (x * (y * y)) = x * ((x \ 1) * y). (x * y) \ (x * (y * y)) = x * ((x \ 1) * y). x \ L(y,y,x) = (x \ 1) * y. L(L(x,x,y),y,y) = x. x * y != L(L(z,z,u),u,u) | x \ z = y. (1 / x) \ y = x * L(y,y,x). x * L(y,y,x) = (1 / x) \ y. L(x,y,y) = L(x,x,y). (x * y) * y = x * (y * L(y,x,x)). x * (y * L(y,x,x)) = (x * y) * y. x != L(y,z * y,z * y) | x = z * ((y \ z) \ 1). L(x,x,y * x) = y * ((x \ y) \ 1). x != L(1 / y,z,z) | x = z \ (z / y). L(1 / x,1 / x,y) = y \ (y / x). (x * y) * L(L(y,x,x),z,u) = x * (y * L(y,z,u)). x \ ((x * y) * y) = y * L(y,x,x). x * y != z * (u * x) | y = (((1 / x) * z) * u) * x. (x * y) * L(x * y,y,y) = (((1 / y) * (y * (x * y))) * x) * y. (((1 / x) * (x * (y * x))) * y) * x = (y * x) * L(y * x,x,x). ((x \ y) \ z) * L(x,x,y * x) = (x \ y) \ ((z * y) / (x \ y)). (x \ y) \ ((z * y) / (x \ y)) = ((x \ y) \ z) * L(x,x,y * x). x != y \ (y / z) | x = 1 / L(z,y,y). L(1 / x,1 / x,y) = 1 / L(x,y,y). L(1 / x,1 / x,y) = 1 / L(x,x,y). ((x \ y) \ 1) * L(L((x \ 1) \ 1,y \ 1,y \ 1),z,u) = (y \ 1) * (((x \ 1) \ 1) * L((x \ 1) \ 1,z,u)). (x \ y) * L(L(L(y,x,x),x \ 1,x \ 1),z,u) = (x \ 1) * (L(y,x,x) * L(L(y,x,x),z,u)). (((1 / x) * (x * (y * x))) * y) * x = (y * x) * (y / (1 / x)). x != (y * z) * (y / (1 / z)) | x = y * (z * (y / (1 / z))). (((1 / x) * (x * (y * x))) * y) * x = y * (x * (y / (1 / x))). (L(x * y,y,y) * x) * y = x * (y * (x / (1 / y))). ((x / (1 / y)) * x) * y = x * (y * (x / (1 / y))). x != (1 / y) * ((y * z) * u) | x = (y \ ((y / u) / z)) \ 1. (((1 / x) / (1 / (x * y))) * (1 / x)) * (x * y) = (x \ ((x / ((1 / x) / (1 / (x * y)))) / y)) \ 1. (x \ ((x / ((1 / x) / (1 / (x * y)))) / y)) \ 1 = (((1 / x) / (1 / (x * y))) * (1 / x)) * (x * y). x != y * ((y \ z) * u) | x = z * L(u,y \ z,y). ((x / (1 / (x \ y))) * x) * (x \ y) = y * L(x / (1 / (x \ y)),x \ y,x). x * L(y / (1 / (y \ x)),y \ x,y) = ((y / (1 / (y \ x))) * y) * (y \ x). 1 / (((x / (1 / y)) * x) * y) = (y \ (1 / (y * x))) / x. x * L(y / (1 / (y \ x)),y \ x,y) = ((y / ((1 / x) * y)) * y) * (y \ x). x * L(y / (1 / (y \ x)),y \ x,y) = ((y \ (y / (1 / x))) * y) * (y \ x). ((x \ (y \ 1)) \ z) \ ((y * x) * ((1 / (y * x)) * z)) = (1 / T(x \ (y \ 1),z)) \ 1. ((x \ (y \ 1)) \ z) \ ((y * x) * ((1 / (y * x)) * z)) = T(x \ (y \ 1),z). K(x \ y,x) * R((y \ ((x \ y) * x)) \ x,z,u) = y \ ((R(x,z,u) * (x \ y)) * x). K(x \ y,x) * R(K(x \ y,x) \ x,z,u) = y \ ((R(x,z,u) * (x \ y)) * x). ((1 / x) * (y / x)) \ ((x \ (1 / (x / y))) * z) = K(((y / x) \ x) \ 1,(y / x) \ x) * z. K(T(x,y) \ 1,T(x,y)) * (z / T(1 / (1 / x),y)) = z / ((1 / T(x,y)) \ 1). K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / ((1 / T(x,z)) \ 1). K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / T(x,z). ((x \ 1) \ 1) * (y / T(x,z)) = x * (y / T(1 / (1 / x),z)). ((x \ 1) \ 1) \ (1 / ((x \ y) \ 1)) = ((x \ y) \ 1) \ (1 / (((y \ x) \ 1) \ y)). ((x \ y) \ 1) \ (1 / (((y \ x) \ 1) \ y)) = ((x \ 1) \ 1) \ (1 / ((x \ y) \ 1)). ((x \ y) \ 1) \ (1 / (((y \ x) \ 1) \ y)) = ((x \ 1) \ 1) \ (x \ y). ((x \ y) \ 1) \ (1 / (((y \ x) \ 1) \ y)) = (x \ 1) * ((x \ 1) * y). ((x \ y) \ 1) \ (1 / (((x \ y) \ 1) * y)) = (x \ 1) * ((x \ 1) * y). x != y * (z * R(z \ (y \ (u * z)),w,v5)) | x = (y * R(y \ u,w,v5)) * z. K(x \ 1,x) * R(K(x \ 1,x) \ (y * x),z,u) = ((x \ 1) * R((x \ 1) \ y,z,u)) * x. x != y * (z * L(z \ (y \ (u * z)),w,v5)) | x = (y * L(y \ u,w,v5)) * z. K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = ((x \ 1) * L((x \ 1) \ y,z,u)) * x. T(x / (y * (z \ (y / z))),y * (z \ 1)) = (1 / ((y * (z \ 1)) \ x)) \ (z / y). ((x \ y) / x) \ ((x \ (1 / (x / y))) * z) = K(((y / x) \ x) \ 1,(y / x) \ x) * z. ((x \ y) / x) \ ((x \ (1 / (x / y))) * z) = K(x \ (1 / (x / y)),(y / x) \ x) * z. K(x \ 1,x) * R(K(x \ 1,x) \ (y * x),z,u) = (x \ R(x * y,z,u)) * x. K(x \ 1,x) * R(K(x,x \ 1) * (y * x),z,u) = (x \ R(x * y,z,u)) * x. K(x \ 1,x) * R(y * T(x,x \ 1),z,u) = (x \ R(x * y,z,u)) * x. K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = (x \ L(x * y,z,u)) * x. K(x \ 1,x) * L(K(x,x \ 1) * (y * x),z,u) = (x \ L(x * y,z,u)) * x. K(x \ 1,x) * L(y * T(x,x \ 1),z,u) = (x \ L(x * y,z,u)) * x. K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = (x \ L(x * (y / x),z,u)) * x. (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = (R(y,z,u) * x) * K(x,y). x * (K(x,y) * R(K(x,y) \ y,z,u)) = (R(y,z,u) * x) * K(x,y). x * (K(x,y) * R(K(x,y) \ y,y \ 1,y)) = (T(y,y \ 1) * x) * K(x,y). x * (K(x,y) * (K(x,y) \ ((y \ 1) \ 1))) = (T(y,y \ 1) * x) * K(x,y). (T(x,x \ 1) * y) \ (y * ((x \ 1) \ 1)) = K(y,x). K(x,y) = (T(y,y \ 1) * x) \ (x * ((y \ 1) \ 1)). x != (T(y,y \ z) * u) \ (u * ((y \ z) \ z)) | x = K(u,(y \ z) \ z). K(x,y) = K(x,(y \ 1) \ 1). K(x,(y \ 1) \ 1) = K(x,y). x != K(y,(z \ 1) \ 1) | x = K(K(z,z \ 1) * y,z). K(x,y) = K(K(y,y \ 1) * x,y). K(K(x,x \ 1) * y,x) = K(y,x). K(x,y \ 1) = K(x,1 / y). K(x,1 / y) = K(x,y \ 1). K(x,(y * (z \ 1)) \ 1) = K(x,z / y). K(x,y) = K(x,1 / (1 / y)). K(x,1 / (1 / y)) = K(x,y). K(x,1 / y) = 1 * K(x,y \ 1). 1 * K(x,y \ 1) = K(x,1 / y). x != K(R(y,z,u),1 / y) | x = y * ((y \ R(y,z,u)) / R(y,z,u)). K(R(x,y,z),x \ 1) = x * ((x \ R(x,y,z)) / R(x,y,z)). x * ((x \ R(x,y,z)) / R(x,y,z)) = K(R(x,y,z),x \ 1). x * y != K(z,1 / u) | x \ K(z,u \ 1) = y. x \ K(R(x,y,z),x \ 1) = (x \ R(x,y,z)) / R(x,y,z). (x \ R(x,y,z)) / R(x,y,z) = x \ K(R(x,y,z),x \ 1). (1 / x) * K(y,1 / x) = K(y,x \ 1) / x. K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z). K(x \ y,x) = K(((x \ 1) \ 1) \ y,x). K(((x \ 1) \ 1) \ y,x) = K(x \ y,x). K(x * (1 / y),y) = K(x * (y \ 1),y). K(T(K(x,x \ 1) * y,x),x) = K(T(y,x),x). K(x,1 / y) != z | z = K(x,y \ 1). K(x,1 / y) != z | K(x,y \ 1) = z. K(x,(y \ 1) \ (z \ 1)) = K(x,y / z). K(x \ ((1 / x) \ y),x) = K(x \ ((x \ 1) \ y),x). K(T((1 / x) * y,x),x) = K(T((x \ 1) * y,x),x). x != K(y,((1 / z) \ y) / y) | x = ((1 / z) \ y) \ (y * R(1 / (1 / z),z \ 1,(1 / z) \ y)). K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ (x * R(1 / (1 / y),y \ 1,(1 / y) \ x)). ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((x \ 1) \ y) / y). x != K(y \ ((1 / y) \ z),y) | x = ((1 / y) \ z) \ ((1 / y) \ T(z,y)). K(x \ ((x \ 1) \ y),x) = ((1 / x) \ y) \ ((1 / x) \ T(y,x)). ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x). x != y \ K(z,y \ 1) | x = (y \ 1) * K(z,y \ 1). (x \ R(x,y,z)) / R(x,y,z) = (x \ 1) * K(R(x,y,z),x \ 1). (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z)) != u | u = K(R(x,y,z),x \ 1). (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z)) != u | K(R(x,y,z),x \ 1) = u. L(T(x,y),y,K(z \ 1,z)) = R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)). R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) = L(T(x,y),y,K(z \ 1,z)). (x \ 1) * (((y \ 1) \ 1) * ((x \ 1) * ((y \ 1) \ 1))) = ((y \ x) \ 1) * ((y \ x) \ 1). (x \ 1) * (((y \ 1) \ 1) * ((x \ 1) * ((y \ 1) \ 1))) = (y \ x) \ (1 / (y \ x)). x != (y \ z) \ (1 / (y \ z)) | x = (z \ y) * (z \ y). (x \ 1) * (((y \ 1) \ 1) * ((x \ 1) * ((y \ 1) \ 1))) = (x \ y) * (x \ y). (x \ 1) * (((y \ 1) \ 1) * ((y \ x) \ 1)) = (x \ y) * (x \ y). (x \ 1) * (y * ((1 * (x \ 1)) * y)) = (x \ y) * (x \ y). (x \ 1) * (y * ((x \ 1) * y)) = (x \ y) * (x \ y). x \ (x / ((y \ z) * (y \ z))) = ((y \ 1) * z) \ (((y \ 1) * z) \ 1). ((x \ 1) * y) \ (((x \ 1) * y) \ 1) = z \ (z / ((x \ y) * (x \ y))). ((x \ 1) * y) \ (((x \ 1) * y) \ 1) = z \ (z * (((y / x) * y) \ x)). x != y \ (y * z) | x = z. ((x \ 1) * y) \ (((x \ 1) * y) \ 1) = ((y / x) * y) \ x. ((x \ 1) * y) \ (y \ ((x \ 1) \ 1)) = ((y / x) * y) \ x. K(x,y) * T(K(x,y) \ (K(x,y) / (y \ 1)),z) = (y * K(x,y)) * (y \ T(y,z)). K(x,y) * T(K(x,y) \ (y * K(x,y)),z) = (y * K(x,y)) * (y \ T(y,z)). K(x,y) * T(T(y,K(x,y)),z) = (y * K(x,y)) * (y \ T(y,z)). K(x,y) * T(y,z) = (y * K(x,y)) * (y \ T(y,z)). (x * K(y,x)) * (x \ T(x,z)) = K(y,x) * T(x,z). ((x \ y) / y) * R(x,z,u) = R(x,z,u) / (((x \ y) / y) \ 1). R(x,y,z) / (((x \ u) / u) \ 1) = ((x \ u) / u) * R(x,y,z). ((x * y) * z) * (((((x * y) * z) \ (y * z)) \ 1) \ 1) = ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z). K(T(x / y,T(y,x)) \ 1,T(x / y,T(y,x))) = K(x \ y,T(x / y,T(y,x))). x != K(y \ z,T(y / z,T(z,y))) | x = K(y \ z,z \ y). K(T(x / y,T(y,x)) \ 1,T(x / y,T(y,x))) = K(x \ y,y \ x). K(x \ y,y \ x) = K((x / y) \ 1,x / y). K((x / y) \ 1,x / y) = K(x \ y,y \ x). x != K((y / z) \ 1,y / z) | x = K(z / y,y / z). K(x \ y,y \ x) = K(y / x,x / y). K(x / y,y / x) = K(y \ x,x \ y). K(x / y,(x / y) \ 1) = K(y \ x,x \ y). K(x \ y,y \ x) / z = (y / x) * (1 / (z * (y / x))). (x / y) * (1 / (z * (x / y))) = K(y \ x,x \ y) / z. x \ K(y \ z,z \ y) = (x \ (z / y)) * (1 / (z / y)). (x \ (y / z)) * (1 / (y / z)) = x \ K(z \ y,y \ z). ((1 / x) * y) * (T(((y / x) \ 1) \ 1,y) \ z) = K(x \ y,y \ x) * z. x != (y / z) * (1 / (u * (y / z))) | x = (z * (y \ 1)) * ((y / z) / u). K(x \ y,y \ x) / z = (x * (y \ 1)) * ((y / x) / z). (x * (y \ 1)) * ((y / x) / z) = K(x \ y,y \ x) / z. (x * (y \ 1)) * (1 / ((y * x) / y)) = y \ K(y \ (y * x),(y * x) \ y). x \ K(x \ (x * y),(x * y) \ x) = (y * (x \ 1)) * (1 / ((x * y) / x)). ((1 / x) * y) * (((y \ x) \ 1) \ z) = K(x \ y,y \ x) * z. x \ K(y,(x * y) \ x) = (y * (x \ 1)) * (1 / ((x * y) / x)). (x * (y \ 1)) * (1 / ((y * x) / y)) = y \ K(x,(y * x) \ y). (x * (y \ 1)) * (1 / ((y * x) / y)) = y \ K(x,x \ 1). x != y \ K(z,z \ 1) | x = (y \ z) * (1 / z). (x * (y \ 1)) * (1 / ((y * x) / y)) = (y \ x) * (1 / x). (x * (y \ 1)) * ((y / x) / y) = (y \ x) * (1 / x). x != (y * (z \ 1)) * ((z / y) / u) | x = K(y \ z,z \ y) / u. (x \ y) * (1 / y) = K(y \ x,x \ y) / x. K(x \ y,y \ x) / y = (y \ x) * (1 / x). ((x \ y) * (1 / y)) * x = K(y \ x,x \ y). ((x \ y) * (1 / y)) * x != z | z = K(y \ x,x \ y). ((x \ y) * (1 / y)) * x != z | K(y \ x,x \ y) = z. ((x \ 1) * (y * T(y \ ((1 / x) \ y),z))) / ((T(x,z) / x) * y) = K(x \ 1,x). (((x \ 1) * T(x,y)) * z) / ((T(x,y) / x) * z) = K(x \ 1,x). K(x \ 1,x) * ((T(x,y) / x) * z) = ((x \ 1) * T(x,y)) * z. ((x \ 1) * T(x,y)) \ (((x \ 1) * T(x,y)) * z) = L(z,T(x,y) / x,K(x \ 1,x)). L(x,T(y,z) / y,K(y \ 1,y)) = x. x != K(y,1 / z) | x = K(y,z \ 1). L(K(x,1 / y),T(z,u) / z,K(z \ 1,z)) = K(x,y \ 1). (((x \ y) \ 1) \ 1) \ (((1 / z) \ ((1 / y) * x)) \ 1) = ((1 / y) * x) * ((((x \ y) / z) \ 1) \ 1). x * y != (((z \ ((z / u) * w)) * 1) \ 1) * (z \ ((z / u) * w)) | K(z \ ((w / z) \ u),z \ ((z / u) * w)) / y = x. K(x \ ((y / x) \ z),x \ ((x / z) * y)) / (x \ ((x / z) * y)) = T((x \ ((x / z) * y)) \ 1,1). (x \ ((x / ((1 / x) / (1 / (x * y)))) / y)) \ 1 = ((1 / ((1 / (x * y)) * x)) * (1 / x)) * (x * y). (((x \ y) \ 1) \ 1) \ ((z / (x \ y)) \ 1) = ((1 / y) * x) * ((((x \ y) / z) \ 1) \ 1). (((x \ y) \ 1) \ 1) \ ((x \ y) * (z \ 1)) = ((1 / y) * x) * ((((x \ y) / z) \ 1) \ 1). x != ((y \ 1) \ 1) \ (y * z) | x = K(y,y \ 1) * z. ((1 / x) * y) * ((((y \ x) / z) \ 1) \ 1) = K(y \ x,(y \ x) \ 1) * (z \ 1). ((1 / x) * y) * ((((y \ x) / z) \ 1) \ 1) = K(y \ x,x \ y) * (z \ 1). (x \ ((x / ((1 / x) / (1 / (x * y)))) / y)) \ 1 = ((1 / (1 / y)) * (1 / x)) * (x * y). (x \ ((x / ((1 / x) / (1 / (x * y)))) / y)) \ 1 = (1 / (x / y)) * (x * y). (x * ((y \ x) \ 1)) * L(((x * y) \ x) \ 1,z,u) = ((x * y) \ x) \ L((1 / 1) \ L(y,x,x),z,u). R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y. R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y. (x * ((y \ x) \ 1)) * L(x * ((y \ x) \ 1),z,u) = ((x * y) \ x) \ L((1 / 1) \ L(y,x,x),z,u). x * (((y \ x) \ 1) * L(x * ((y \ x) \ 1),z,u)) = ((x * y) \ x) \ L((1 / 1) \ L(y,x,x),z,u). x * ((y \ x) \ L(x / (y \ x),z,u)) = ((x * y) \ x) \ L((1 / 1) \ L(y,x,x),z,u). ((x * y) \ x) \ L((1 / 1) \ L(y,x,x),z,u) = x * ((y \ x) \ L(x / (y \ x),z,u)). ((x * y) \ x) \ L((1 / 1) \ L(y,x,x),z,u) = x * ((y \ x) \ L(y,z,u)). K(R(x,y,z),x \ 1) / (R(x,y,z) \ 1) = T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x)). T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x)) = K(R(x,y,z),x \ 1) / (R(x,y,z) \ 1). x != K(y,z) / (y \ 1) | x = y * K(y,z). T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x)) = R(x,y,z) * K(R(x,y,z),x \ 1). x != T(y,y / (y * z)) | x = T(y,y / (z * y)). R(x,y,z) * K(R(x,y,z),x \ 1) = T(R(x,y,z),R(x,y,z) / (x * R(x,y,z))). T(R(x,y,z),R(x,y,z) / (x * R(x,y,z))) = R(x,y,z) * K(R(x,y,z),x \ 1). R(x,y,z) * K(R(x,y,z),x \ 1) = R(T(x,R(x,y,z) / (x * R(x,y,z))),y,z). R(T(x,R(x,y,z) / (x * R(x,y,z))),y,z) = R(x,y,z) * K(R(x,y,z),x \ 1). R((x \ 1) \ 1,y,z) = R(x,y,z) * K(R(x,y,z),x \ 1). R(x,y,z) * K(R(x,y,z),x \ 1) = R((x \ 1) \ 1,y,z). x * y != R((z \ u) \ u,w,v5) | x \ R(T(z,z \ u),w,v5) = y. R(x,y,z) \ R(T(x,x \ 1),y,z) = K(R(x,y,z),x \ 1). x != R(y,z,u) \ R(T(y,y \ 1),z,u) | x = a(R(y,z,u),1 / y,y). K(R(x,y,z),x \ 1) = a(R(x,y,z),1 / x,x). a(R(x,y,z),1 / x,x) = K(R(x,y,z),x \ 1). K(R(x,y,z),x \ 1) \ 1 = R(T(x,x \ 1),y,z) \ R(x,y,z). R(T(x,x \ 1),y,z) \ R(x,y,z) = K(R(x,y,z),x \ 1) \ 1. x != K(R(y,z,u),y \ 1) | x = y * ((y \ R(y,z,u)) / R(y,z,u)). a(R(x,y,z),1 / x,x) = x * ((x \ R(x,y,z)) / R(x,y,z)). x * ((x \ R(x,y,z)) / R(x,y,z)) = a(R(x,y,z),1 / x,x). x * L(x \ 1,R(x,y,z),1 / x) = a(R(x,y,z),1 / x,x). K(R(x,y,z),x \ 1) \ 1 != u | x * T(x \ 1,R(x,y,z)) = u. x != (y \ z) * (1 / (u * (y \ z))) | x = K(y \ z,z \ y) / u. (x \ ((y / x) \ z)) * ((x \ ((x / z) * y)) / u) = K(x \ ((x / z) * y),((x / z) * y) \ x) / u. K(x \ ((x / y) * z),((x / y) * z) \ x) / u = (x \ ((z / x) \ y)) * ((x \ ((x / y) * z)) / u). ((x \ 1) * y) \ ((x \ 1) * (y * z)) = L(L(z,y,1 / x),(1 / x) * y,K(x \ 1,x)). L(L(x,y,1 / z),(1 / z) * y,K(z \ 1,z)) = ((z \ 1) * y) \ ((z \ 1) * (y * x)). L(L(x,y,1 / z),(1 / z) * y,K(z \ 1,z)) != u | L(x,y,z \ 1) = u. ((x * y) * (1 / z)) / (y * (1 / z)) = R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1)). R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1)) = ((x * y) * (1 / z)) / (y * (1 / z)). R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1)) != u | R(x,y,1 / z) = u. ((x / (x \ (y * (z * x)))) \ x) * ((x \ y) * L(z,x,x)) = ((x \ y) * L(z,x,x)) * (x / (z \ (y \ x))). (x \ (y * (z * x))) * ((x \ y) * L(z,x,x)) = ((x \ y) * L(z,x,x)) * (x / (z \ (y \ x))). ((x \ y) * L(z,x,x)) * (x / (z \ (y \ x))) = (x \ (y * (z * x))) * ((x \ y) * L(z,x,x)). x * ((y \ 1) * (y * T(y \ 1,x))) = L(1 / y,K(y \ 1,y),x) * (x * K(y \ 1,y)). L(1 / x,K(x \ 1,x),y) * (y * K(x \ 1,x)) = y * ((x \ 1) * (x * T(x \ 1,y))). (1 / x) * (y * K(x \ 1,x)) = y * ((x \ 1) * (x * T(x \ 1,y))). x * ((y \ 1) * (y * T(y \ 1,x))) = (1 / y) * (x * K(y \ 1,y)). x != (1 / y) * (z * K(y \ 1,y)) | x = T((y \ 1) * z,K(u \ 1,u)). x * ((y \ 1) * (y * T(y \ 1,x))) = T((y \ 1) * x,K(z \ 1,z)). T((x \ 1) * y,K(z \ 1,z)) = y * ((x \ 1) * (x * T(x \ 1,y))). x \ T((y \ 1) * (x / (y \ 1)),K(z \ 1,z)) = K(1 / y,x / (y \ 1)). x \ ((1 / y) * (x / (1 / y))) = K(1 / y,x / (y \ 1)). (x \ K(1 / x,y / (x \ 1))) * ((x \ 1) \ 1) = K(x \ 1,y / (1 / x)). x != (y \ K(1 / y,z)) * ((y \ 1) \ 1) | x = K(y \ 1,z). K(x \ 1,y / (1 / x)) = K(x \ 1,y / (x \ 1)). K(x \ 1,y) = K(x \ 1,(y * (1 / x)) / (x \ 1)). K(x \ 1,(y * (1 / x)) / (x \ 1)) = K(x \ 1,y). K(x \ 1,(y / (x \ 1)) * (1 / x)) = K(x \ 1,y). K(x \ 1,y * K(x,x \ 1)) = K(x \ 1,y). K(x \ 1,((x \ 1) \ 1) * y) = K(x \ 1,x * y). (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = R(x,y,z) * (z * R(T(y,z),u,w)). (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = R(x,y,z) * (R(y,u,w) * z). (x * K(y,y \ 1)) \ ((x * z) * K(y,y \ 1)) = L(z,T(x,K(y,y \ 1)),K(y,y \ 1)). (L(x,y,y \ 1) \ ((1 / y) * (x * y))) * ((y * ((1 / y) * (x * y))) / y) = (1 / y) * (x * y). (1 / x) * (y * x) != z * ((x * ((1 / x) * (y * x))) / x) | L(y,x,x \ 1) \ ((1 / x) * (y * x)) = z. x * ((y * ((1 / y) * (z * y))) / y) != (1 / y) * (z * y) | L(z,y,y \ 1) \ ((1 / y) * (z * y)) = x. T((x \ 1) \ T(x,x \ 1),x) \ T(((T(x,x \ 1) * y) / T(x,x \ 1)) * x,x \ 1) = y / T(x,x \ 1). ((1 / (x / y)) \ ((z \ 1) \ 1)) \ ((y * (x \ 1)) \ z) = ((1 \ ((y * (x \ 1)) \ z)) \ 1) * ((y * (x \ 1)) \ z). ((((x \ y) \ z) * (1 / z)) \ 1) * (1 / ((z \ 1) \ (x \ y))) = ((x / z) \ ((1 / y) \ z)) \ ((z \ 1) \ (x \ y)). x / K(y,x) = x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)). x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = x / K(y,x). x != y / K(z,y) | x = K(z,y) \ y. x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = K(y,x) \ x. (K(x,y) \ y) \ 1 = y \ ((((y * x) \ y) \ 1) \ T(((y * x) \ y) \ 1,y)). x \ ((((x * y) \ x) \ 1) \ T(((x * y) \ x) \ 1,x)) = (K(y,x) \ x) \ 1. x \ (((x * y) \ x) * T(((x * y) \ x) \ 1,x)) = (K(y,x) \ x) \ 1. x \ K(y,x) = (K(y,x) \ x) \ 1. (K(x,y) \ y) \ 1 = y \ K(x,y). 1 / (x \ K(y,x)) = K(y,x) \ x. T((x \ 1) * R((x \ 1) \ 1,y,z),x \ L(x,u,w)) = (x \ 1) * R((x \ 1) \ 1,y,z). x != (y \ 1) * R((y \ 1) \ 1,z,u) | x = y \ R(y,z,u). T((x \ 1) * R((x \ 1) \ 1,y,z),x \ L(x,u,w)) = x \ R(x,y,z). T(x \ R(x,y,z),x \ L(x,u,w)) = x \ R(x,y,z). T(x \ L(x,y,z),x \ R(x,u,w)) = x \ L(x,y,z). T(T((x \ 1) \ x,x),x) \ T(((T(x,x \ 1) * y) / T(x,x \ 1)) * x,x \ 1) = y / T(x,x \ 1). T(T(x * x,x),x) \ T(((T(x,x \ 1) * y) / T(x,x \ 1)) * x,x \ 1) = y / T(x,x \ 1). (x * x) \ T(((T(x,x \ 1) * y) / T(x,x \ 1)) * x,x \ 1) = y / T(x,x \ 1). (x * x) \ T(((x * y) / x) * x,x \ 1) = y / T(x,x \ 1). (x * x) \ T(x * y,x \ 1) = y / T(x,x \ 1). x != (y * y) \ T(y * z,y \ 1) | x = y \ T(z,y \ 1). x / T(y,y \ 1) = y \ T(x,y \ 1). ((x / y) / (1 / z)) \ ((y * (x \ 1)) \ z) = ((1 \ ((y * (x \ 1)) \ z)) \ 1) * ((y * (x \ 1)) \ z). ((1 \ ((x * (y \ 1)) \ z)) \ 1) * ((x * (y \ 1)) \ z) = ((y / x) / (1 / z)) \ ((x * (y \ 1)) \ z). (((x * (y \ 1)) \ z) \ 1) * ((x * (y \ 1)) \ z) = ((y / x) / (1 / z)) \ ((x * (y \ 1)) \ z). x != (((y * (z \ 1)) \ u) \ 1) * ((y * (z \ 1)) \ u) | x = K((u \ 1) * (1 / (z / y)),(y * (z \ 1)) \ u). ((x / y) / (1 / z)) \ ((y * (x \ 1)) \ z) = K((z \ 1) * (1 / (x / y)),(y * (x \ 1)) \ z). K((x \ 1) * (1 / (y / z)),(z * (y \ 1)) \ x) = ((y / z) / (1 / x)) \ ((z * (y \ 1)) \ x). ((x \ 1) * (1 / (y / z))) * ((z * (y \ 1)) \ x) = ((y / z) / (1 / x)) \ ((z * (y \ 1)) \ x). ((1 / x) \ (((y \ z) \ x) \ 1)) * (1 / ((x \ 1) \ (y \ z))) = ((y / x) \ ((1 / z) \ x)) \ ((x \ 1) \ (y \ z)). (x * (((x \ (y \ z)) \ 1) \ 1)) * (1 / ((x \ 1) \ (y \ z))) = ((y / x) \ ((1 / z) \ x)) \ ((x \ 1) \ (y \ z)). (x * (((x \ (y \ z)) \ 1) \ 1)) * ((1 / (y \ z)) * (x \ 1)) = ((y / x) \ ((1 / z) \ x)) \ ((x \ 1) \ (y \ z)). (x * (((x \ (y \ z)) \ 1) \ 1)) * (((1 / z) * y) * (x \ 1)) = ((y / x) \ ((1 / z) \ x)) \ ((x \ 1) \ (y \ z)). (((x * (y * z)) \ (x * y)) * ((x * (y * z)) \ (x * y))) * u != w * (((x * y) \ (x * (y * z))) \ u) | L(z,y,x) \ 1 = w. R((x \ (1 / (1 / y))) * x,1 / y,y) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1). R((x \ (1 / (1 / y))) * x,y \ 1,y) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1). x != y * (z * ((y * (z \ (y \ u))) / y)) | x = (y * ((u / z) / y)) * z. (x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u)). T(x / y,x) \ (((1 / y) * (x * ((1 / y) * x))) * ((((1 / y) * x) \ 1) \ z)) = ((1 / y) * x) * (((1 / y) * x) * z). ((x \ (y \ 1)) \ z) / T(x \ (y \ 1),z) = (1 / (y * x)) \ ((x \ (y \ 1)) \ z). x != (1 / (y * z)) \ ((z \ (y \ 1)) \ u) | x = (y * z) * ((y * z) * u). ((x \ (y \ 1)) \ z) / T(x \ (y \ 1),z) = (y * x) * ((y * x) * z). ((1 / x) * (y * (z \ 1))) * (1 * ((((y * (z \ 1)) \ x) \ 1) \ 1)) = ((x \ 1) * (1 / (z / y))) * ((y * (z \ 1)) \ x). T(x / y,x) \ (((1 / y) * ((x / y) * x)) * ((((1 / y) * x) \ 1) \ z)) = ((1 / y) * x) * (((1 / y) * x) * z). T(x / y,x) \ (((1 / y) * ((x / y) * x)) * ((x \ y) \ z)) = ((1 / y) * x) * (((1 / y) * x) * z). T(x / y,x) \ (((x \ y) \ 1) * ((x \ y) \ ((x \ y) \ z))) = ((1 / y) * x) * (((1 / y) * x) * z). x != T(y / z,y) \ (((y \ z) \ 1) * ((y \ z) \ u)) | x = (((y \ z) \ 1) \ 1) \ u. ((1 / x) * y) * (((1 / x) * y) * z) = (((y \ x) \ 1) \ 1) \ ((y \ x) \ z). (((x \ y) \ 1) \ 1) \ ((x \ y) \ z) = ((1 / y) * x) * (((1 / y) * x) * z). ((1 / x) * y) * (((1 / x) * y) * z) = ((y \ x) \ 1) * (((y \ x) \ 1) * z). ((x \ y) \ 1) * (((x \ y) \ 1) * z) = ((1 / y) * x) * (((1 / y) * x) * z). ((1 / x) * (y * (z \ 1))) * (1 * (((x \ 1) * (1 / (z / y))) \ 1)) = ((x \ 1) * (1 / (z / y))) * ((y * (z \ 1)) \ x). ((1 / x) * (y * (z \ 1))) * (1 * ((1 / (z / y)) \ ((x \ 1) \ 1))) = ((x \ 1) * (1 / (z / y))) * ((y * (z \ 1)) \ x). ((1 / x) * (y * (z \ 1))) * (1 * ((z / y) / (1 / x))) = ((x \ 1) * (1 / (z / y))) * ((y * (z \ 1)) \ x). ((1 / x) * (y * (z \ 1))) * ((z / y) / (1 / x)) = ((x \ 1) * (1 / (z / y))) * ((y * (z \ 1)) \ x). ((x * ((y * z) / ((u * y) * z))) / x) * ((u * y) * z) = (((x * (1 / R(u,y,z))) / x) * R(u,y,z)) * (y * z). (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((x * ((z * u) / ((y * z) * u))) / x) * ((y * z) * u). (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((y * z) * u) * ((x * (((y * z) * u) \ (z * u))) / x). x != (y * z) * ((u * ((y * z) \ (w * z))) / u) | x = (y * ((u * (y \ w)) / u)) * z. (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u. (R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u)) * (y * z) = ((x * y) * ((u * ((x * y) \ y)) / u)) * z. (R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u)) * (y * z) = ((x * ((u * (x \ 1)) / u)) * y) * z. x * (y * z) != (u * y) * z | x = R(u,y,z). R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u) = R(x * ((u * (x \ 1)) / u),y,z). R(x,y,z) * (1 / R(x,y,z)) = R(x * ((R(x,y,z) * (x \ 1)) / R(x,y,z)),y,z). R(x * ((R(x,y,z) * (x \ 1)) / R(x,y,z)),y,z) = R(x,y,z) * (1 / R(x,y,z)). x != y * (1 / y) | x = K(y,y \ 1). R(x * ((R(x,y,z) * (x \ 1)) / R(x,y,z)),y,z) = K(R(x,y,z),R(x,y,z) \ 1). R(x * ((x \ R(x,y,z)) / R(x,y,z)),y,z) = K(R(x,y,z),R(x,y,z) \ 1). R(K(R(x,y,z),x \ 1),y,z) = K(R(x,y,z),R(x,y,z) \ 1). (((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * R(R(x,y,z) \ 1,u,w). (((x * y) * R((x * y) \ y,z,u)) * w) / (y * w) = R(x,y,w) * R(R(x,y,w) \ 1,z,u). (((x * R(x \ 1,y,z)) * u) * w) / (u * w) = R(x,u,w) * R(R(x,u,w) \ 1,y,z). R(x * R(x \ 1,y,z),u,w) = R(x,u,w) * R(R(x,u,w) \ 1,y,z). R(x,y,z) * R(R(x,y,z) \ 1,u,w) = R(x * R(x \ 1,u,w),y,z). (x * y) \ ((x * (y * z)) * L((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * L(L(z,y,x) \ 1,u,w). (x * y) \ (x * ((y * z) * L((y * z) \ y,u,w))) = L(z,y,x) * L(L(z,y,x) \ 1,u,w). (x * y) \ (x * (y * (z * L(z \ 1,u,w)))) = L(z,y,x) * L(L(z,y,x) \ 1,u,w). L(x * L(x \ 1,y,z),u,w) = L(x,u,w) * L(L(x,u,w) \ 1,y,z). L(x,y,z) * L(L(x,y,z) \ 1,u,w) = L(x * L(x \ 1,u,w),y,z). L(x,y,z) * ((L(x,y,z) / x) \ ((1 / x) * 1)) = L(x * L(x \ 1,L(x,y,z),1 / x),y,z). L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)) = L(x * L(x \ 1,L(x,y,z),1 / x),y,z). L(x * L(x \ 1,L(x,y,z),1 / x),y,z) = L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)). L(K(L(x,y,z),1 / x),y,z) = L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)). L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)) = L(K(L(x,y,z),1 / x),y,z). (((x * y) * z) * L(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * L(R(x,y,z) \ 1,u,w). (((x * y) * L((x * y) \ y,z,u)) * w) / (y * w) = R(x,y,w) * L(R(x,y,w) \ 1,z,u). (((x * L(x \ 1,y,z)) * u) * w) / (u * w) = R(x,u,w) * L(R(x,u,w) \ 1,y,z). R(x * L(x \ 1,y,z),u,w) = R(x,u,w) * L(R(x,u,w) \ 1,y,z). R(x,y,z) * L(R(x,y,z) \ 1,u,w) = R(x * L(x \ 1,u,w),y,z). R(x,y,z) * ((R(x,y,z) / x) \ ((1 / x) * 1)) = R(x * L(x \ 1,R(x,y,z),1 / x),y,z). R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = R(x * L(x \ 1,R(x,y,z),1 / x),y,z). R(x * L(x \ 1,R(x,y,z),1 / x),y,z) = R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)). R(a(R(x,y,z),1 / x,x),y,z) = R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)). R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = R(a(R(x,y,z),1 / x,x),y,z). R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = R(K(R(x,y,z),x \ 1),y,z). x != R(K(R(y,z,u),y \ 1),z,u) | x = K(R(y,z,u),R(y,z,u) \ 1). R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = K(R(x,y,z),R(x,y,z) \ 1). x * y != K(x,x \ 1) | y = 1 / x. (R(x,y,z) / x) \ (1 / x) = 1 / R(x,y,z). x != (R(y,z,u) / y) \ (1 / y) | x = R(1 / (1 / y),z,u) \ 1. 1 / R(x,y,z) = R(1 / (1 / x),y,z) \ 1. R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z). 1 / (1 / R(x,y,z)) = R(1 / (1 / x),y,z). R(1 / (1 / x),y,z) = 1 / (1 / R(x,y,z)). R(1 / x,y,z) \ 1 = 1 / R(x \ 1,y,z). 1 / R(x \ 1,y,z) = R(1 / x,y,z) \ 1. R(x,y,z) \ 1 = 1 / R((x \ 1) \ 1,y,z). 1 / R((x \ 1) \ 1,y,z) = R(x,y,z) \ 1. R(T(1 / (1 / x),y),z,u) \ 1 = 1 / R(T(x,y),z,u). R(1 / x,y,z) = 1 / (1 / R(x \ 1,y,z)). 1 / (1 / R(x \ 1,y,z)) = R(1 / x,y,z). (R(1 / x,y,z) \ 1) \ 1 = R(x \ 1,y,z). (R(x,y,z) \ 1) \ 1 = R((x \ 1) \ 1,y,z). R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1. T(x,R(1 / y,z,u)) = T(x,R(y \ 1,z,u)). R(((x / y) \ 1) \ 1,y,y \ 1) = ((x * (y \ 1)) \ 1) \ 1. T(x,R((y \ 1) \ 1,z,u)) = T(x,R(y,z,u)). R(((x / (1 / y)) \ 1) \ 1,y \ 1,y) = ((x * y) \ 1) \ 1. R(((x / y) \ 1) \ 1,y,z) * (y * z) = (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1). T(x,R(K(y,y \ 1) / z,u,w)) = T(x,R((z * K(y \ 1,y)) \ 1,u,w)). T(x,R((y * K(z \ 1,z)) \ 1,u,w)) = T(x,R(K(z,z \ 1) / y,u,w)). (((1 / x) * y) \ y) \ 1 = 1 / R(T(x,(1 / x) * y),1 / x,y). 1 / R(T(x,(1 / x) * y),1 / x,y) = (((1 / x) * y) \ y) \ 1. x != R(((y / (1 / z)) \ 1) \ 1,z \ 1,z) | x = T(y * z,y \ (1 / z)). ((x * y) \ 1) \ 1 = T(x * y,x \ (1 / y)). T(x * y,x \ (1 / y)) = ((x * y) \ 1) \ 1. T(x,R(y \ K(z,z \ 1),u,w)) = T(x,R(K(z,z \ 1) / y,u,w)). T(x,R(K(y,y \ 1) / z,u,w)) = T(x,R(z \ K(y,y \ 1),u,w)). ((((x / y) \ 1) \ 1) * y) * z = (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1). (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = ((((z / x) \ 1) \ 1) * x) * y. (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = (x * (((x \ z) \ 1) \ 1)) * y. x != ((y * z) * u) * (((((y * z) * u) \ (z * u)) \ 1) \ 1) | x = ((R(y,z,u) \ 1) * R(y,z,u)) * (z * u). ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z = ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z). ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z. x != ((y * z) * u) * (((((y * z) * u) \ (z * u)) \ 1) \ 1) | x = ((R(y,z,u) \ 1) \ 1) \ ((y * z) * u). ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z = ((R(x,y,z) \ 1) \ 1) \ ((x * y) * z). ((R(x,y,z) \ 1) \ 1) \ ((x * y) * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z. R((x \ 1) \ 1,y,z) \ ((x * y) * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z. R((x \ 1) \ 1,y,z) \ ((x * y) * z) = (y * K(x \ 1,x)) * z. (((x * (y \ 1)) \ 1) \ 1) \ (((x / y) * y) * (y \ 1)) = (y * K((x / y) \ 1,x / y)) * (y \ 1). ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = (y * K(x \ 1,x)) * z. (((x * (y \ 1)) \ 1) \ 1) \ (x * (y \ 1)) = (y * K((x / y) \ 1,x / y)) * (y \ 1). K((x * (y \ 1)) \ 1,x * (y \ 1)) = (y * K((x / y) \ 1,x / y)) * (y \ 1). (x * K((y / x) \ 1,y / x)) * (x \ 1) = K((y * (x \ 1)) \ 1,y * (x \ 1)). (x * (y * z)) * ((u * ((x * (y * z)) \ (x * y))) / u) = (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)). x * ((y * z) * ((u * ((y * z) \ y)) / u)) = (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)). (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)) = x * ((y * z) * ((u * ((y * z) \ y)) / u)). (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)) = x * (y * (z * ((u * (z \ 1)) / u))). L(x * ((y * (x \ 1)) / y),z,u) = L(x,z,u) * ((y * (L(x,z,u) \ 1)) / y). L(x,y,z) * ((u * (L(x,y,z) \ 1)) / u) = L(x * ((u * (x \ 1)) / u),y,z). (x * y) \ (x * (y * (z * ((u * (z \ 1)) / u)))) = L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u). L(x,y,z) * (1 / L(x,y,z)) = L(x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)),y,z). L(x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)),y,z) = L(x,y,z) * (1 / L(x,y,z)). L(x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)),y,z) = K(L(x,y,z),L(x,y,z) \ 1). L(K(L(x,y,z),1 / x),y,z) = K(L(x,y,z),L(x,y,z) \ 1). x != L(K(L(y,z,u),1 / y),z,u) | x = L(y,z,u) * ((L(y,z,u) / y) \ (1 / y)). K(L(x,y,z),L(x,y,z) \ 1) = L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)). L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)) = K(L(x,y,z),L(x,y,z) \ 1). (L(x,y,z) / x) \ (1 / x) = 1 / L(x,y,z). x != (L(y,z,u) / y) \ (1 / y) | x = L(1 / (1 / y),z,u) \ 1. 1 / L(x,y,z) = L(1 / (1 / x),y,z) \ 1. L(1 / (1 / x),y,z) \ 1 = 1 / L(x,y,z). 1 / (1 / L(x,y,z)) = L(1 / (1 / x),y,z). L(1 / (1 / x),y,z) = 1 / (1 / L(x,y,z)). L(1 / x,y,z) \ 1 = 1 / L(x \ 1,y,z). 1 / L(x \ 1,y,z) = L(1 / x,y,z) \ 1. L(K(x,y),z,u) \ 1 = 1 / L(K(x,y),z,u). 1 / L(K(x,y),z,u) = L(K(x,y),z,u) \ 1. L(1 / (1 / (x \ (y \ z))),x,y) = 1 / (1 / ((y * x) \ z)). (x * y) * L(1 / (1 / (y \ z)),y,x) = (x * y) * (1 / (1 / ((x * y) \ (x * z)))). (L(1 / x,y,z) \ 1) \ 1 = L(x \ 1,y,z). (L(x,y,z) \ 1) \ 1 = L((x \ 1) \ 1,y,z). L((x \ 1) \ 1,y,z) = (L(x,y,z) \ 1) \ 1. (L(x \ 1,y,z) \ u) \ (1 / u) = u \ (1 / (u * (L(1 / x,y,z) \ 1))). x \ (1 / (x * (L(1 / y,z,u) \ 1))) = (L(y \ 1,z,u) \ x) \ (1 / x). (x \ 1) * L((y \ 1) \ 1,z,u) = (L(y,z,u) \ x) \ 1. L((((x \ y) \ z) \ 1) \ 1,x \ y,x) = ((y \ (x * z)) \ 1) \ 1. x \ L(x,y,z) = (L(x,y,z) \ x) \ 1. (L(x,y,z) \ x) \ 1 = x \ L(x,y,z). x * ((L(y,z,u) \ x) \ 1) = L(L((y \ 1) \ 1,z,u),x,x). L(L((x \ 1) \ 1,y,z),u,u) = u * ((L(x,y,z) \ u) \ 1). ((x \ y) \ 1) * L((x \ 1) \ 1,z,u) = (x \ (L(x,z,u) \ y)) \ 1. 1 / (x \ L(x,y,z)) = L(x,y,z) \ x. (1 / L(x,y,z)) * x = L(x,y,z) \ x. x / L(x,y,z) = L(x,y,z) \ x. (L(x,y,z) \ x) * L(x,y,z) = x. (x \ ((L(x,y,z) \ x) * u)) \ 1 = x \ ((u / x) \ L(x,y,z)). (x \ 1) * (L(x,y,z) \ x) = x * (1 / (L(x,y,z) * x)). (x \ 1) * (L(x,y,z) \ x) = x * (1 / (x * L(x,y,z))). (x * y) * (1 / (1 / ((x * y) \ z))) = x * (y * (1 / (1 / (y \ (x \ z))))). x != L(L(y \ 1,z,u),w,w) | x = L((w * y) \ w,z,u). x * ((L(y,z,u) \ x) \ 1) = L((x * (y \ 1)) \ x,z,u). L((x * (y \ 1)) \ x,z,u) = x * ((L(y,z,u) \ x) \ 1). L(x * ((y \ x) \ 1),z,u) = x * ((L(y,z,u) \ x) \ 1). L(x * ((y \ x) \ 1),z \ y,z) = x * ((y \ x) \ 1). L(T((x \ y) \ z,z \ (x \ y)),x \ y,x) = ((y \ (x * z)) \ 1) \ 1. x != (y \ 1) * L(y \ 1,z,u) | x = y \ L(1 / y,z,u). (x \ (L(x,y,z) \ 1)) \ 1 = (x \ 1) \ L(1 / (x \ 1),y,z). (x \ 1) \ L(1 / (x \ 1),y,z) = (x \ (L(x,y,z) \ 1)) \ 1. (x \ 1) \ L(x,y,z) = (x \ (L(x,y,z) \ 1)) \ 1. (x \ (L(x,y,z) \ 1)) \ 1 = (x \ 1) \ L(x,y,z). x != L(T((y \ z) \ u,w),y \ z,y) | x = T(z \ (y * u),w). ((x \ (y * z)) \ 1) \ 1 = T(x \ (y * z),z \ (y \ x)). T(x \ (y * z),z \ (y \ x)) = ((x \ (y * z)) \ 1) \ 1. x \ (L(1 / y,z,u) / x) = (L(y \ 1,z,u) \ x) \ (1 / x). (L(x \ 1,y,z) \ u) \ (1 / u) = u \ (L(1 / x,y,z) / u). (x * y) * (1 / (1 / ((x * y) \ (x * z)))) != u | x * (y * (1 / (1 / (y \ z)))) = u. L(x,y,z) * ((u * (L(x,y,z) \ 1)) / u) != w | L(x * ((u * (x \ 1)) / u),y,z) = w. (x * (y * z)) * (1 / (1 / ((x * (y * z)) \ (x * y)))) = (x * y) * K(L(z,y,x),L(z,y,x) \ 1). x * ((y * z) * (1 / (1 / ((y * z) \ y)))) = (x * y) * K(L(z,y,x),L(z,y,x) \ 1). (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * ((y * z) * (1 / (1 / ((y * z) \ y)))). (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * (z * (1 / (1 / (z \ (y \ y)))))). (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * (z * (1 / (1 / (z \ 1))))). (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * (z * (1 / z))). (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * K(z,z \ 1)). x * (y * K(z,z \ 1)) != (x * y) * u | K(L(z,y,x),L(z,y,x) \ 1) = u. (x * y) * z != x * (y * K(u,u \ 1)) | K(L(u,y,x),L(u,y,x) \ 1) = z. ((T(x,y) \ 1) * (1 / y)) \ (z / ((T(x,y) \ 1) * (1 / y))) = (((1 / y) * (x \ 1)) \ z) * ((1 / y) \ T((x \ 1) \ 1,y)). ((T(x,y) \ 1) * (1 / y)) \ (z / ((T(x,y) \ 1) * (1 / y))) = (((1 / y) * (x \ 1)) \ z) * ((1 / ((x \ 1) \ 1)) \ y). ((T(x,y) \ 1) * (1 / y)) \ (z / ((T(x,y) \ 1) * (1 / y))) = (((1 / y) * (x \ 1)) \ z) * ((x \ 1) \ y). x != (((1 / y) * z) \ u) * (z \ y) | x = (z \ y) * (u * (z \ y)). ((T(x,y) \ 1) * (1 / y)) \ (z / ((T(x,y) \ 1) * (1 / y))) = ((x \ 1) \ y) * (z * ((x \ 1) \ y)). ((1 / x) * (y \ 1)) \ (z / ((T(y,x) \ 1) * (1 / x))) = ((y \ 1) \ x) * (z * ((y \ 1) \ x)). ((1 / x) * (y \ 1)) \ (z / ((1 / x) * (y \ 1))) = ((y \ 1) \ x) * (z * ((y \ 1) \ x)). ((1 / x) * (y \ 1)) \ ((1 / z) \ (y / (1 / x))) = ((y \ 1) \ x) * (z * ((y \ 1) \ x)). x != (y * (z \ 1)) \ (u \ (z / y)) | x = (z / y) * ((u \ 1) * (z / y)). ((x \ 1) \ y) * (z * ((x \ 1) \ y)) = (x / (1 / y)) * (((1 / z) \ 1) * (x / (1 / y))). (x / (1 / y)) * (((1 / z) \ 1) * (x / (1 / y))) = ((x \ 1) \ y) * (z * ((x \ 1) \ y)). (x / (1 / y)) * (z * (x / (1 / y))) = ((x \ 1) \ y) * (z * ((x \ 1) \ y)). K(R(x,y,z) \ (((x \ R(x,y,z)) / R(x,y,z)) * R(x,y,z)),R(x,y,z)) = ((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1). K(R(x,y,z) \ (x \ R(x,y,z)),R(x,y,z)) = ((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1). K(x \ 1,R(x,y,z)) = ((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1). ((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1) = K(x \ 1,R(x,y,z)). K(x \ 1,R(x,y,z)) \ (x \ 1) = (x \ R(x,y,z)) / R(x,y,z). x * y != K(z \ 1,R(z,u,w)) \ (z \ 1) | x \ ((z \ R(z,u,w)) / R(z,u,w)) = y. (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z)) = K(x \ 1,R(x,y,z)) \ 1. K(R(x,y,z),x \ 1) = K(x \ 1,R(x,y,z)) \ 1. K(x \ 1,R(x,y,z)) \ 1 = K(R(x,y,z),x \ 1). K(R(x,y,z),x \ 1) \ 1 = K(x \ 1,R(x,y,z)). x * T(x \ 1,R(x,y,z)) = K(x \ 1,R(x,y,z)). x != y * T(y \ 1,R(y,z,u)) | x = R(y,z,u) \ R(1 / (1 / y),z,u). K(x \ 1,R(x,y,z)) = R(x,y,z) \ R(1 / (1 / x),y,z). R(x,y,z) \ R(1 / (1 / x),y,z) = K(x \ 1,R(x,y,z)). R(K(x \ 1,R(x,y,z)),y,z) = K(R(x,y,z) \ 1,R(x,y,z)). R(x,y,z) * K(x \ 1,R(x,y,z)) = R(1 / (1 / x),y,z). x != R(1 / (1 / y),z,u) | x = 1 / (1 / R(y,z,u)). R(x,y,z) * K(x \ 1,R(x,y,z)) = 1 / (1 / R(x,y,z)). x * y != z / (1 / x) | y = (x \ z) * x. K(x \ 1,R(x,y,z)) = (R(x,y,z) \ 1) * R(x,y,z). (R(x,y,z) \ 1) * R(x,y,z) = K(x \ 1,R(x,y,z)). x * y != 1 / (1 / x) | y = K(x \ 1,x). K(x \ 1,R(x,y,z)) = K(R(x,y,z) \ 1,R(x,y,z)). K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,R(x,y,z)). K(x \ 1,R(x,y,z)) != u | K(R(x,y,z) \ 1,R(x,y,z)) = u. K(x \ 1,R(x,y,z)) * (y * z) = (y * K(x \ 1,x)) * z. K((x / (y * z)) \ 1,R((x / z) / y,y,z)) = K(((x / z) / y) \ 1,R((x / z) / y,y,z)). K(((x / y) / z) \ 1,R((x / y) / z,z,y)) = K((x / (z * y)) \ 1,R((x / y) / z,z,y)). (x * K(y \ 1,y)) * z != u * (x * z) | K(y \ 1,R(y,x,z)) = u. K(x,R(x \ 1,y,z)) * (y * z) = (y * K((x \ 1) \ 1,x \ 1)) * z. R(K(x,R(x \ 1,y,z)),y,z) = K(R(x \ 1,y,z) \ 1,R(x \ 1,y,z)). K(R(x \ 1,y,z) \ 1,R(x \ 1,y,z)) = R(K(x,R(x \ 1,y,z)),y,z). K(x,R(x \ 1,y,z)) * (y * z) = (y * K(x,x \ 1)) * z. x != K(R(y,z,u) \ 1,R(y,z,u)) | x = K(y \ 1,R(y,z,u)). R(K(x,R(x \ 1,y,z)),y,z) = K((x \ 1) \ 1,R(x \ 1,y,z)). R(K(x,R(x \ 1,y,z)),y,z) = K(x,R(x \ 1,y,z)). K(x,R(x \ 1,y,z)) * (y * z) = (K(x,R(x \ 1,y,z)) * y) * z. (K(x,R(x \ 1,y,z)) * y) * z = K(x,R(x \ 1,y,z)) * (y * z). L(x,y,K(z,R(z \ 1,y,x))) = x. x * y != K(z,R(z \ 1,u,y)) * (u * y) | x = u * K(z,z \ 1). K(x,R(x \ 1,y,z)) * y = y * K(x,x \ 1). x * y != y * K(z,z \ 1) | x = K(z,z \ 1). K(x,R(x \ 1,y,z)) = K(x,x \ 1). K(x,x \ 1) * (y * z) = (y * K(x,x \ 1)) * z. (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z). L(x,y,K(z,z \ 1)) = x. x != L(y,T(z,K(u,u \ 1)),K(u,u \ 1)) | x = (z * K(u,u \ 1)) \ ((z * y) * K(u,u \ 1)). x = (y * K(z,z \ 1)) \ ((y * x) * K(z,z \ 1)). (x * K(y,y \ 1)) \ ((x * z) * K(y,y \ 1)) = z. x \ y = (K(z,z \ 1) * x) \ (K(z,z \ 1) * y). (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) = y \ z. (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z). (K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z). (K(x,x \ 1) * y) * z != u | K(x,x \ 1) * (y * z) = u. (K(x,x \ 1) * y) * z != K(x,x \ 1) * u | y * z = u. K(x,x \ 1) * y != (K(x,x \ 1) * z) * u | z * u = y. L(x,y,K(z \ 1,z)) = x. ((x \ 1) \ 1) / (y \ x) = K(x,x \ 1) * y. (1 / x) / y = K(x,x \ 1) * ((x \ 1) / y). K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y. L(x,y,K(z \ u,u \ z)) = x. L(x,y,z \ 1) = L(x,y,1 / z). L(x,y,1 / z) = L(x,y,z \ 1). x != y | x = z \ (z * y). L(x,y,K(z \ 1,z)) = u \ (u * x). (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z). (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z). (K(x \ 1,x) * y) * z != K(x \ 1,x) * u | y * z = u. K(x \ 1,x) * y != (K(x \ 1,x) * z) * u | z * u = y. (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z). (K(x \ y,y \ x) * z) * u = K(x \ y,y \ x) * (z * u). (K(x \ y,y \ x) * z) * u != K(x \ y,y \ x) * w | z * u = w. K(x \ y,y \ x) * z != (K(x \ y,y \ x) * u) * w | u * w = z. (x \ y) / z = L(x \ (y / z),x,y \ 1). L(x \ (y / z),x,y \ 1) = (x \ y) / z. x != L(K(y,z),z * y,1 / z) | x = L(y,z,z \ 1) \ ((1 / z) * (y * z)). L(K(x,y),y * x,y \ 1) = L(x,y,y \ 1) \ ((1 / y) * (x * y)). L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,y \ 1). L(x,y,z) = L(x,y,(z \ 1) \ 1). L(x,y,(z \ 1) \ 1) = L(x,y,z). L(x,y,z / u) = L(x,y,(u * (z \ 1)) \ 1). L(x,y,(z * (u \ 1)) \ 1) = L(x,y,u / z). L(x,y,(1 / z) * u) = L(x,y,(u \ z) \ 1). L(x,y,(z \ u) \ 1) = L(x,y,(1 / u) * z). L(x,y,(z \ u) * (1 / z)) = L(x,y,(z * (u \ z)) \ 1). L(x,y,(z * (u \ z)) \ 1) = L(x,y,(z \ u) * (1 / z)). L(x,y,K(z \ 1,z)) != u | u = x. (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) != u | u = y \ z. (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) != u | y \ z = u. R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) != u | u = T(x,y). R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) != u | T(x,y) = u. K(x,y \ 1) != z | z = K(x,1 / y). K(x,y \ 1) != z | K(x,1 / y) = z. L(x \ y,x,z \ 1) = (x \ z) / (y \ z). (x \ y) / (z \ y) = ((y \ 1) * x) \ ((y \ 1) * z). ((x \ 1) * y) \ ((x \ 1) * z) = (y \ x) / (z \ x). L(x,y,z \ 1) = (y \ z) / ((y * x) \ z). (x \ y) / ((x * z) \ y) = L(z,x,y \ 1). x / ((y * z) \ (y * x)) = L(z,y,(y * x) \ 1). ((x \ 1) \ 1) / (y \ x) = y * K(x,x \ 1). ((x \ 1) / y) * K(x,x \ 1) = (1 / x) / y. L(x,y,(z \ 1) \ u) = L(x,y,z / (1 / u)). L(x,y,z / (1 / u)) = L(x,y,(z \ 1) \ u). L(x,y,z \ (1 / (z / u))) = L(x,y,(1 / z) * (u / z)). ((x \ 1) \ 1) / y = (x / y) * K(x,x \ 1). (x / y) * K(x,x \ 1) = ((x \ 1) \ 1) / y. (x \ ((y \ 1) \ 1)) * K(y \ 1,(y \ 1) \ 1) = (1 / (y \ 1)) / T(x,x \ T(y,y \ 1)). (1 / (x \ 1)) / T(y,y \ T(x,x \ 1)) = (y \ ((x \ 1) \ 1)) * K(x \ 1,(x \ 1) \ 1). x / ((y * z) \ (y * x)) = L(z,y,x \ (y \ 1)). x / (((y * z) * u) \ ((y * (z * u)) * x)) = L(a(y,z,u),y * (z * u),x \ ((y * (z * u)) \ 1)). L(a(x,y,z),x * (y * z),u \ ((x * (y * z)) \ 1)) = u / (((x * y) * z) \ ((x * (y * z)) * u)). x * y != (z * K(u,u \ 1)) * w | (K(u,u \ 1) * (z * w)) / y = x. (K(x,x \ 1) * (y * z)) / (K(x,x \ 1) * z) = R(y,K(x,x \ 1),z). x * y = K(z,z \ 1) * ((K(z \ 1,z) * x) * y). K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * z. T(x,y) = R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)). R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y). x \ (K(y,y \ 1) * z) = (x * K(y \ 1,y)) \ z. (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z). ((x \ y) * (1 / y)) * z = K(y,y \ 1) * ((x \ 1) * z). K(x,x \ 1) * ((y \ 1) * z) = ((y \ x) * (1 / x)) * z. (x * (1 / (y * x))) * (K(x,x \ 1) * (y * z)) = L(z,x * (1 / (y * x)),x * (1 / (y * x))). (x * K(y,y \ 1)) / z = K(y,y \ 1) * (x / z). R(K(x \ 1,x) * y,z,u) = ((K(x \ 1,x) * (y * z)) * u) / (z * u). ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u). (((x \ 1) \ 1) \ y) * z = K(x \ 1,x) * ((x \ y) * z). K(x \ 1,x) * ((x \ y) * z) = (((x \ 1) \ 1) \ y) * z. (1 / (1 / x)) / y = K(x \ 1,x) * (x / y). K(x \ 1,x) * (x / y) = (1 / (1 / x)) / y. K(x \ 1,x) * (y \ x) = (1 / (1 / x)) / T(y,y \ x). (1 / (1 / x)) / T(y,y \ x) = K(x \ 1,x) * (y \ x). K(x \ 1,R(x,y,z)) = K(x \ 1,x). L(x,y,z * K(u \ 1,u)) = (K(u \ 1,u) * (z * y)) \ ((z * K(u \ 1,u)) * (y * x)). (K(x \ 1,x) * (y * z)) \ ((y * K(x \ 1,x)) * (z * u)) = L(u,z,y * K(x \ 1,x)). (x * (y * K(z \ 1,z))) \ (x * (K(z \ 1,z) * (y * u))) != w | L(u,y * K(z \ 1,z),x) = w. K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x). K(((x / y) / z) \ 1,x / (z * y)) = K(((x / y) / z) \ 1,(x / y) / z). K(((x / y) / z) \ 1,(x / y) / z) = K(((x / y) / z) \ 1,x / (z * y)). (x \ R(x,y,z)) * K(x \ 1,x) = (x \ 1) * R(x,y,z). (x \ (1 / R(y,z,u))) * K(y \ 1,y) = x \ (R(y,z,u) \ 1). (((1 / x) \ 1) * (1 / y)) \ (((1 / x) \ 1) * z) = (y / x) / (z \ (1 / x)). ((((x \ y) \ 1) \ 1) * (y \ 1)) \ ((((x \ y) \ 1) \ 1) * z) = ((x \ 1) \ 1) / (z \ ((x \ y) \ 1)). (((x / y) \ 1) * (x * x)) \ (((x / y) \ 1) * z) = (1 / (y * x)) / (z \ (x / y)). (((x / y) \ 1) * (y \ 1)) \ (((x / y) \ 1) * z) = (y * (x * (1 / y))) / (z \ (x / y)). x != ((y * z) * K(u,u \ 1)) / (K(u,u \ 1) * z) | x = R(y,z,T(K(u,u \ 1),z)). K(x,x \ 1) * ((y * z) / (K(x,x \ 1) * z)) = R(y,z,T(K(x,x \ 1),z)). R(K(x,x \ 1) * (y / z),z,K(x \ 1,x)) != u | y / (z * K(x \ 1,x)) = u. L(x,y,z \ (1 / (z / u))) = L(x,y,(z \ u) / z). ((x \ y) * (1 / y)) * z != K(y,y \ 1) * u | (x \ 1) * z = u. K(x,x \ 1) * y != ((z \ x) * (1 / x)) * u | (z \ 1) * u = y. x * K(y \ 1,y) != (y \ 1) * z | x = (1 / y) * z. x \ R(x,y,z) = (1 / x) * R(x,y,z). (1 / x) * R(x,y,z) = x \ R(x,y,z). R(x,y,z) / x = x \ R(x,y,z). (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x. x \ R(x,y,z) != u | R(x,y,z) / x = u. (x \ R(x,y,z)) * x = R(x,y,z). R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z)). T(x,x \ R(x,y,z)) = x. (x \ 1) \ (R(x,y,z) \ 1) = R(x,y,z) \ x. T(R(x,y,z) \ x,x \ 1) = R(x,y,z) \ x. K(R(x,y,z) \ x,x \ 1) = 1. x \ (K(y \ 1,y) * z) != u | (K(y,y \ 1) * x) \ z = u. (x * K(y \ z,z \ y)) * u = K(y \ z,z \ y) * (x * u). x * K(y \ 1,y) != (1 / y) \ z | x = (y \ 1) \ z. (1 / x) \ (1 / R(x,y,z)) = (x \ 1) \ (R(x,y,z) \ 1). x != (y \ 1) \ (R(y,z,u) \ 1) | x = R(y,z,u) \ y. (1 / x) \ (1 / R(x,y,z)) = R(x,y,z) \ x. x / R(x,y,z) = R(x,y,z) \ x. (R(x,y,z) \ x) * R(x,y,z) = x. T((R(x \ R(x,y,z),x,y * z) \ 1) \ 1,x * (y * z)) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1. (x * K(y \ z,z \ y)) * (x \ 1) != u | u = K(y \ z,z \ y). (x * K(y \ z,z \ y)) * (x \ 1) != u | K(y \ z,z \ y) = u. x != (K(y,y \ 1) * z) / u | x = K(y,y \ 1) * (z / u). R(x,K(y,y \ 1),z) = K(y,y \ 1) * ((x * z) / (K(y,y \ 1) * z)). K(x,x \ 1) * ((y * z) / (K(x,x \ 1) * z)) = R(y,K(x,x \ 1),z). (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u). x != (K(y \ 1,y) * z) / u | x = K(y \ 1,y) * (z / u). R(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * (((y * z) * u) / (z * u)). K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u). K(x \ 1,x) * R(y,z,u) = R(K(x \ 1,x) * y,z,u). R(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * R(y,z,u). x != K(y \ 1,y) * R(z * T(y,y \ 1),u,w) | x = (y \ R(y * z,u,w)) * y. R(K(x \ 1,x) * (y * T(x,x \ 1)),z,u) = (x \ R(x * y,z,u)) * x. K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z,u). K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) != w | w = R(y,z,u). K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) != w | R(y,z,u) = w. K(x,x \ 1) * R(y,z,u) = R(K(x,x \ 1) * y,z,u). R(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * R(y,z,u). R(K(x,x \ 1) * y,z,u) = R(y,z,u) * K(x,x \ 1). (x * (1 / y)) \ (((1 / x) \ 1) * z) = (y / x) / (z \ (1 / x)). (x * (1 / y)) \ (x * z) = (y / x) / (z \ (1 / x)). (x / y) / (z \ (1 / y)) = (y * (1 / x)) \ (y * z). R(x * y,z,u) = (y \ R(y * x,z,u)) * y. (x \ R(x * y,z,u)) * x = R(y * x,z,u). R(x * y,z,u) / y = y \ R(y * x,z,u). (x \ R(y,z,u)) * x = R((x \ y) * x,z,u). R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x. R(x,y,z) / u = u \ R(u * (x / u),y,z). x \ R(x * (y / x),z,u) = R(y,z,u) / x. R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x. R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x. x * (R(y,z,u) / x) = R(x * (y / x),z,u). R(x * (y / x),z,u) = x * (R(y,z,u) / x). R(x * ((y / z) / x),z,y \ u) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u)). x * y != R((z \ (u / w)) * z,w,w \ 1) | ((z \ (u * (w \ 1))) * z) / y = x. ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z. x != R((y \ (y / (1 / z))) * y,z \ 1,z) | x = (y * (z \ T(z,y))) * z. (x \ (x * y)) * x = (x * (y \ T(y,x))) * y. x * y != R((z \ (u / (1 / w))) * z,w \ 1,w) | ((z \ (u * w)) * z) / y = x. ((x \ (y * z)) * x) / z = ((x \ (y / (1 / z))) * x) * (1 / z). ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z. ((x \ (1 * y)) * x) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1). (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1). x * y = (y * (x \ T(x,y))) * x. (x * (y \ T(y,x))) * y = y * x. (x * y) / x = y * (x \ T(x,y)). x * (y \ T(y,x)) = (y * x) / y. x * y != z * (z \ u) | u / y = x. x / y = (y \ x) * (y \ T(y,y \ x)). (x \ y) * (x \ T(x,x \ y)) = y / x. T(x,y) * (y \ T(y,T(x,y))) = x. (x \ T(x,y)) * y = (x * y) / x. x \ ((y * x) / y) = y \ T(y,x). x * (y \ T(y,z)) != (u * z) / u | x = ((u * z) / u) * (T(y,z) \ y). x = ((y * x) / y) * (T(y,x) \ y). ((x * y) / x) * (T(x,y) \ x) = y. (x \ 1) * y != (z * (x \ 1)) / z | y = x * ((z * (x \ 1)) / z). x \ T(x,y \ 1) = y * ((x * (y \ 1)) / x). x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1). x * y != (z * x) / z | y = ((z * x) / z) / x. x \ T(x,y) = ((x * y) / x) / y. ((x * y) / x) / y = x \ T(x,y). (x * y) \ ((x * y) / x) = L(x \ 1,T(x,y),y). x * (y * T(y \ 1,x)) = ((y \ 1) * x) / (y \ 1). ((x \ 1) * y) / (x \ 1) = y * (x * T(x \ 1,y)). (T(x,y) \ x) * ((x * y) / x) = y. ((x * y) / x) * (y \ 1) = x \ T(x,y). ((x * y) / x) \ y = T(x,y) \ x. T(x,y) * (y \ T(y,x)) = x. x \ T(x,y) = T(y,T(x,y)) \ y. T(x,T(y,x)) \ x = y \ T(y,x). T(x,y) \ x = y \ T(y,x). x != (y \ 1) \ T(y \ 1,z) | x = K(z \ (z / y),z). T(x,y \ 1) \ x = K(x \ (x / y),x). K(x \ (x / y),x) = T(x,y \ 1) \ x. x != (y \ 1) \ T(y \ 1,z) | x = y * T(y \ 1,z). T(x,y \ 1) \ x = y * T(y \ 1,x). T(x,y \ 1) \ x != z | y * T(y \ 1,x) = z. x * (T(x,y) \ x) = (y * x) / y. (x * y) / x = y * (T(y,x) \ y). (x \ T(x,y)) * x = T(x,R(y,y \ 1,x)). T(x,R(y,y \ 1,x)) = (x \ T(x,y)) * x. L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y. ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x). x * (T(x,T(y,x)) \ x) = (y * x) / y. (x * y) / x = y * (T(y,T(x,y)) \ y). x \ (y / (y / x)) = T(x,x \ y) \ x. T(x,x \ y) \ x = x \ (y / (y / x)). x / (x / y) = y * (T(y,y \ x) \ y). x * y != ((z / u) * u) / w | x \ (z / w) = y. x \ (y / (y / x)) = T(x,y / x) \ x. T(x,y / x) \ x = x \ (y / (y / x)). T(x * (T(x,y) \ x),y) = x. (x * (T(x,y) \ x)) \ y = x \ ((x * y) / x). ((x * y) / x) \ x = y \ (x * (T(x,y) \ x)). x \ (y * (T(y,x) \ y)) = ((y * x) / y) \ y. x != y | x = L(R(y,z,y),z,y). T(x * (T(x,y) \ x),y) = L(R(x,z,x),z,x). (x \ y) * (x \ ((x \ y) \ y)) = y / x. K(x \ (x / y),x) \ x = T(x,y \ 1). T(T(x,y \ 1) \ x,z) = K(x \ (x / T(y,z)),x). (x \ y) \ (y / x) = x \ ((x \ y) \ y). K(x \ y,x) \ x = T(x,(y \ x) \ 1). T(x,(y \ x) \ 1) = K(x \ y,x) \ x. x != (y \ T(y,z)) * y | x = T(y,z). T(x,R(y,y \ 1,x)) = T(x,y). x * K(x,y / x) = T(x,(y \ x) \ 1). T(x,(y \ x) \ 1) = x * K(x,y / x). x * y != T(z,R(u,u \ 1,z)) | T(z,u) / y = x. T(x,y \ 1) / x = y * ((x * (y \ 1)) / x). x * ((y * (x \ 1)) / y) = T(y,x \ 1) / y. T(x,R(y \ 1,y,x)) = T(x,y \ 1). x != T(y * z,R(y \ 1,y,y * z)) | x = y * ((y * z) * (z / (y * z))). T(x * y,x \ 1) = x * ((x * y) * (y / (x * y))). x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1). x != T(y,R(z \ 1,z,y)) | x = T(y,y / (y * z)). T(x,y \ 1) = T(x,x / (x * y)). T(x,x / (x * y)) = T(x,y \ 1). x != T(y,R(z \ 1,z,u)) | x = T(y,u / (z * u)). T(x,y \ 1) = T(x,x / (y * x)). T(x,x / (y * x)) = T(x,y \ 1). (x * ((x / y) / x)) * y = T(x,y \ 1). x * y != T(z,z / (z * u)) | T(x,y) = y \ T(z,u \ 1). T(x * ((x / y) / x),y) = y \ T(x,y \ 1). x != T(y,y / z) | x = T(y,z \ y). T(x,y \ 1) = T(x,(x * y) \ x). T(x,(x * y) \ x) = T(x,y \ 1). x * y != T(z,z / (z * u)) | x \ T(z,u \ 1) = y. x \ T(x,y \ 1) = K(x,(x / y) / x). K(x,(x / y) / x) = x \ T(x,y \ 1). T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x). x * y != T(z,z / (u * z)) | x \ T(z,u \ 1) = y. x \ T(y,x \ 1) = y * ((x \ y) / y). T(x,x \ y) = T(x,(y \ x) \ 1). T(x,(y \ x) \ 1) = T(x,x \ y). T(T(x,y \ 1),x * y) = x. T(x,x \ y) / (y \ x) = ((1 / (y \ x)) \ y) * (1 / (y \ x)). x != T(y,(z \ y) \ 1) | x = K(y \ z,y) \ y. x * K(x,y / x) = K(x \ y,x) \ x. K(x \ y,x) \ x = x * K(x,y / x). T(x,T(y,y \ x) \ 1) = x * K(x,(y \ x) / x). x * y != z * ((u \ z) / z) | x \ (u \ T(z,u \ 1)) = y. T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x). x \ (y \ T(x,y \ 1)) = (y \ x) / x. (x / y) \ T(x,(x / y) \ 1) = x * (y / x). x \ T(y,x \ 1) = y * R(1 / x,x,x \ y). x * R(1 / y,y,y \ x) = y \ T(x,y \ 1). ((x \ T(y,x \ 1)) * y) / (x \ y) = R(y,(x \ y) / y,y). R(x,(y \ x) / x,x) = ((y \ T(x,y \ 1)) * x) / (y \ x). (x \ T(y,x \ 1)) * y = (x \ y) * T(y,y \ (x \ y)). (x \ y) * T(y,y \ (x \ y)) = (x \ T(y,x \ 1)) * y. K(x \ y,x) \ 1 = K(x,y / x). K(x,y) \ 1 = K(y,(y * x) / y). K(x,(x * y) / x) = K(y,x) \ 1. K(x,y) = K(T(y,x),x) \ 1. K(T(x,y),y) \ 1 = K(y,x). K(T(x,y),y) * K(y,x) = 1. K(x,y) \ 1 = K(T(y,x),x). K(T(x,y),y) = K(y,x) \ 1. K(x,y) \ x = x * K(T(y,x),x). x * K(T(y,x),x) = K(x,y) \ x. K(T(x,y),y) \ 1 != z | z = K(y,x). K(T(x,y),y) \ 1 != z | K(y,x) = z. x != K(y,z) \ 1 | x = K(z,(z * y) / z). K(T(x,y),y) = K(x,(x * y) / x). x != K(T(y,z),z) \ 1 | x = K(z,y). K(T(x,T(y,x)),T(y,x)) = K(x,y). K(T(x,y),y) * z = K(x,(x * y) / x) * z. K(T(x,y),T(y,x)) = K(x,y). K(x \ y,x) \ 1 != z | K(x,y / x) = z. K(T(x,T(y,x)),T(y,x)) != z | K(x,y) = z. K(T(x,x \ y),x \ y) != z | K(x,y / x) = z. L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1). x != y * ((z * (y \ 1)) / z) | x = (z * ((y \ z) / z)) / (y \ z). x \ T(x,y \ 1) = (x * ((y \ x) / x)) / (y \ x). (x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1). (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y)). x / (y \ ((y * x) / y)) = y * (T(y,x) \ y). T((x * y) / x,T(x,y)) = L(R(y,z,y),z,y). ((x * (1 / y)) / x) * y = T(x,y \ 1) / x. T(((x / y) / x) * ((x \ 1) \ 1),y) * K(x \ 1,x) = (x \ (y \ T(x,y \ 1))) * x. K(x,(x * y) / x) * (K(T(x,y),y) \ z) = z. ((x * y) / x) * T(((x * y) / x) \ x,y) = x * K(y \ (x * (T(x,y) \ x)),y). T(x \ T(x * y,y),T(x * y,y)) = L(R(y,z,y),z,y). (K(x,y) \ 1) * (K(T(y,x),x) \ z) = z. K(T(x,y),y) != z | K(y,x) \ 1 = z. x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y). (((x * y) \ 1) * x) / ((x * y) \ 1) = x * (((x \ (1 / y)) * x) * y). x * y != T(x * z,x \ 1) | y = ((x \ 1) \ z) * (x \ 1). (x * y) * (y / (x * y)) = ((x \ 1) \ y) * (x \ 1). ((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y)). x != K(y,(y / z) / y) | x = y \ T(y,z \ 1). T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1). x \ T(x,T(y,z) \ 1) = T(x \ T(x,y \ 1),z). T(x,T(y,y \ x) \ 1) != x * z | K(x,(y \ x) / x) = z. x != (((y \ 1) \ 1) \ z) * ((y \ 1) \ 1) | x = (y \ z) * y. ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x. ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x. x * y != ((z \ 1) * u) * R(z,z \ 1,u) | ((z \ u) * z) / y = x. ((x \ y) * x) / y = ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1). ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y. x != L(R(y,z,y),z,y) | x = y. T(x \ T(x * y,y),T(x * y,y)) = y. K(x,y) = K(x,x \ T(x * y,y)). K(x,x \ T(x * y,y)) = K(x,y). x != K(y,y \ T(y * z,z)) | x = (y * R(z,y,z)) \ T(y * z,z). K(x,y) = (x * R(y,x,y)) \ T(x * y,y). K(x,y) = T(y * x,y) \ T(x * y,y). x != T(y * z,y) \ T(z * y,y) | x = K(y \ T(y * z,y),y). K(x,y) = K(y \ T(y * x,y),y). K(x \ T(x * y,x),x) = K(y,x). K(x \ T(y,x),x) = K(x \ y,x). K(x \ (y \ x),x) = K(y \ 1,x). K(x \ (y / (x \ 1)),x) = K(y,x). K(x \ y,x) = K((x / y) \ 1,x). K((x / y) \ 1,x) = K(x \ y,x). K(x \ y,x) = K(y * (x \ 1),x). K(x * (y \ 1),y) = K(y \ x,y). x != K(y * (z \ 1),z) | x = K(y * (1 / z),z). K(x \ y,x) = K(y * (1 / x),x). K(x * (1 / y),y) = K(y \ x,y). x * K(x * (y \ 1),y) = (y \ x) * y. K(((x * y) / x) \ x,y) = K(y \ x,y). K(x * y,y \ 1) = K((y \ 1) \ x,y \ 1). K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1). x * K(y \ 1,y * x) = ((y * x) \ x) * (y * x). ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y). x * K(x * y,1 / y) = ((1 / y) \ x) * (1 / y). ((1 / x) \ y) * (1 / x) = y * K(y * x,1 / x). x * K(x * y,y \ 1) = ((y \ 1) \ x) * (y \ 1). ((x \ 1) \ y) * (x \ 1) = y * K(y * x,x \ 1). (((x \ y) \ 1) \ x) * ((x \ y) \ 1) = x * K(y,(x \ y) \ 1). x != R(y,z / y,y) | x = R(y,y \ z,y). ((x \ T(y,x \ 1)) * y) / (x \ y) = R(y,y \ (x \ y),y). R(x,x \ (y \ x),x) = ((y \ T(x,y \ 1)) * x) / (y \ x). x != ((y \ (z / (1 / u))) * y) * (1 / u) | x = y * (T((y \ z) * u,y) / u). ((x \ (y * z)) * x) / z = x * (T((x \ y) * z,x) / z). x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z. x != ((1 / y) \ z) * (1 / y) | x = ((y \ 1) \ z) * (y \ 1). T(x,x \ y) / (y \ x) = (((y \ x) \ 1) \ y) * ((y \ x) \ 1). L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1). x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y). ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(y,((x \ 1) \ y) / y). K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y)). x != ((1 / y) \ z) \ ((1 / y) \ T(z,y)) | x = K(y \ ((y \ 1) \ z),y). K(x,((y \ 1) \ x) / x) = K(y \ ((y \ 1) \ x),y). K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y). (((x * y) \ 1) * x) / ((x * y) \ 1) != x * z | ((x \ (1 / y)) * x) * y = z. x != ((y * z) / y) * (z \ 1) | x = y \ T(y,z). ((x \ y) * x) / y = ((x \ 1) * y) \ T((x \ 1) * y,x). ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y. x != ((y \ 1) * z) \ T((y \ 1) * z,y) | x = L(K(y \ z,y),z,y \ 1). ((x \ y) * x) / y = L(K(x \ y,x),y,x \ 1). L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y. L(K(x,y),y * x,y \ 1) = ((y \ (y * x)) * y) / (y * x). ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1). (x * y) / (y * x) = L(K(x,y),y * x,y \ 1). L(K(x,y),y * x,y \ 1) = (x * y) / (y * x). x != L(y,z,z \ 1) \ ((1 / z) * (y * z)) | x = L(K(y,z),z * y,z \ 1). T(x,(1 / x) * (y * x)) \ x = L(K(y,x),x * y,x \ 1). L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y. L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y. x != L(K(y,z),z * y,z \ 1) | x = (y * z) / (z * y). T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y). T(x,y) \ x = (y * x) / (x * y). (x * y) / (y * x) = T(y,x) \ y. x / (y * (x / y)) = T(y,x / y) \ y. T(x,y / x) \ x = y / (x * (y / x)). (T(x,y) \ x) * (x * y) = y * x. (x * (y / x)) / y = T(y / x,x) \ (y / x). T(x / y,y) \ (x / y) = (y * (x / y)) / x. (x * y) * z != y * x | T(T(x,y) \ x,x * y) = z. T(T(x,y) \ x,x * y) = K(y,x). K(x,y) = T(T(y,x) \ y,y * x). K(x,y) = T(x \ T(x,y),y * x). x != T(y \ T(y,z \ 1),u) | x = y \ T(y,T(z,u) \ 1). K(x,y \ 1) = x \ T(x,T(y,(y \ 1) * x) \ 1). x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1). x != T(y,z / y) \ y | x = y \ (z / (z / y)). x / (y * (x / y)) = y \ (x / (x / y)). (x \ y) \ (y / x) = (x * (y / x)) / y. (x * (y / x)) / y = (x \ y) \ (y / x). x != (y \ z) \ (z / y) | x = y \ ((y \ z) \ z). (x * (y / x)) / y = x \ ((x \ y) \ y). x != (y * ((z \ y) / y)) / (z \ y) | x = y \ T(y,z \ 1). x \ ((x \ (y \ x)) \ (y \ x)) = x \ T(x,y \ 1). x \ T(x,T(y,y \ x) \ 1) = K(x,y \ 1). x * K(x,y \ 1) = T(x,T(y,y \ x) \ 1). T(x,T(y,y \ x) \ 1) = x * K(x,y \ 1). K(x,(y \ x) / x) = K(x,y \ 1). x != K(y,((z \ 1) \ y) / y) | x = K(z \ ((z \ 1) \ y),z). K(x,(y \ 1) \ 1) = K(y \ ((y \ 1) \ x),y). K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1). x != K(y,(z \ 1) \ 1) | x = K(y,z). K(x \ ((x \ 1) \ y),x) = K(y,x). x != K(y \ ((y \ 1) \ z),y) | x = K(y \ ((1 / y) \ z),y). K(x,y) = K(y \ ((1 / y) \ x),y). K(x \ ((1 / x) \ y),x) = K(y,x). x != K(y \ z,y) | x = K((y / z) \ 1,y). K(x,y) = K((y / ((1 / y) \ x)) \ 1,y). K((x / ((1 / x) \ y)) \ 1,x) = K(y,x). K(x \ y,x) = K((1 / x) * y,x). K((1 / x) * y,x) = K(x \ y,x). K((1 / x) * (y * x),x) = K(T(y,x),x). K(x * y,x \ 1) = K((x \ 1) \ y,x \ 1). K((x \ 1) \ y,x \ 1) = K(x * y,x \ 1). K(T((1 / x) * y,x),x) = K(T(x \ y,x),x). x != K((y \ 1) \ z,y \ 1) | x = K(z * y,y \ 1). K(x * y,x \ 1) = K(y * x,x \ 1). K(x * y,y \ 1) = K(y * x,y \ 1). (((x \ 1) \ y) * (x \ (1 / x))) * x = y * K(x * y,x \ 1). x != K(T((1 / y) * z,y),y) | x = K(T((y \ 1) * z,y),y). K(T(x \ y,x),x) = K(T((x \ 1) * y,x),x). K(T((x \ 1) * y,x),x) = K(T(x \ y,x),x). K(T(x \ y,x),x) \ 1 = K(x,(x \ 1) * y). K(x,x \ y) = K(x,(x \ 1) * y). K(x,(x \ 1) * y) = K(x,x \ y). x != K(y \ 1,((y \ 1) \ 1) * z) | x = K(y \ 1,y * z). K(x \ 1,(x \ 1) \ y) = K(x \ 1,x * y). (x \ T(x,y \ 1)) * x = T(x,x \ (y \ x)). T(x,y \ 1) = T(x,x \ (y \ x)). T(x,x \ (y \ x)) = T(x,y \ 1). T(x,x \ y) = T(x,(x / y) \ 1). T(x,(x / y) \ 1) = T(x,x \ y). x \ T(y,z \ 1) = x \ ((y \ (z \ y)) \ (z \ y)). x \ ((y \ (z \ y)) \ (z \ y)) = x \ T(y,z \ 1). T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x). (x \ y) * T(y,x \ 1) = (x \ T(y,x \ 1)) * y. (x \ T(y,x \ 1)) * y = (x \ y) * T(y,x \ 1). (x / y) \ T(x,x \ y) = x * (y / x). (x / (y * x)) \ T(x,x \ (y * x)) = x * y. (x / (y * x)) \ T(x,T(y,x)) = x * y. (x / (y * x)) \ T(x,y) = x * y. (x / (y * x)) * (x * y) = T(x,y). T(x,y) = (x / (y * x)) * (x * y). x * y != (z / (u * z)) * (z * u) | T(z,u) / y = x. T(x,y) / (x * y) = R(1 / y,y,x). R(1 / x,x,T(y,x)) = R(1 / x,x,y). R(1 / x,x,x \ y) = R(1 / x,x,y / x). R(1 / x,x,y / x) = R(1 / x,x,x \ y). R(1 / x,x,x \ y) \ (y / x) = x * (y / x). ((x \ y) / y) * (x * (y / x)) = y / x. T(L(x,y,y \ 1),(1 / y) \ 1) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x). R(x,x \ (y \ x),x) = ((y \ x) * T(x,y \ 1)) / (y \ x). ((x * (y * (1 / x))) / x) * x = y * K(x * y,x \ 1). x * K(y * x,y \ 1) = y * (x * (1 / y)). x != K(y,y \ 1) * ((z * u) / (K(y,y \ 1) * u)) | x = R(z,K(y,y \ 1),u). R(x,y,T(K(z,z \ 1),y)) = R(x,K(z,z \ 1),y). R(x,y,K(z,z \ 1)) = R(x,K(z,z \ 1),y). R(x,K(y,y \ 1),z) = R(x,z,K(y,y \ 1)). R(x,K(y \ 1,y),z) = R(x,z,K(y \ 1,(y \ 1) \ 1)). R(x,y,K(z \ 1,(z \ 1) \ 1)) = R(x,K(z \ 1,z),y). R(x,y,K(z \ 1,z)) = R(x,K(z \ 1,z),y). R(x,K(y \ 1,y),z) = R(x,z,K(y \ 1,y)). (((x / y) \ x) * x) \ (((x / y) \ 1) * z) = (1 / (y * x)) / (z \ (x / y)). (x * y) \ (((y / x) \ 1) * z) = (1 / (x * y)) / (z \ (y / x)). (1 / (x * y)) / (z \ (y / x)) = (x * y) \ (((y / x) \ 1) * z). (1 / (x * y)) / (z \ (y / x)) = (x * y) \ ((x * (y \ 1)) * z). (x * y) \ ((x * (y \ 1)) * z) != u | 1 / ((z \ (y / x)) * (x * y)) = u. (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1). (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x. x != ((y * z) / u) * T(((y * z) / u) \ y,w) | x = (y * (z * T(z \ u,w))) / u. x * K(y \ (x * (T(x,y) \ x)),y) = (x * (y * T(y \ x,y))) / x. x * K(y \ (x * (T(x,y) \ x)),y) = (x * ((y \ x) * y)) / x. x * K(((x * y) / x) \ x,y) = (x * ((y \ x) * y)) / x. x * K(y \ x,y) = (x * ((y \ x) * y)) / x. (x * ((y \ x) * y)) / x = x * K(y \ x,y). T(x,(y \ x) * y) = x. ((x \ y) * x) * (y \ 1) = K(x \ y,x). ((x \ y) * x) / y != z | (1 / y) * ((x \ y) * x) = z. (x * y) * ((y * x) \ 1) = K(y \ (y * x),y). K(x \ (x * y),x) = (y * x) * ((x * y) \ 1). (x * y) * ((y * x) \ 1) = K(x,y). K(x,y) = (x * y) * ((y * x) \ 1). ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x). ((x * (y \ 1)) * (x \ 1)) \ (((y / x) \ 1) * z) = (x * (y * (1 / x))) / (z \ (y / x)). T((x / y) * K(x,x \ 1),y) * K(x \ 1,x) = (x \ (y \ T(x,y \ 1))) * x. T(((x \ 1) \ 1) / y,y) * K(x \ 1,x) = (x \ (y \ T(x,y \ 1))) * x. (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = (y \ (x \ T(y,x \ 1))) * y. (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = ((x \ y) / y) * y. (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = x \ y. (x \ y) * (1 / y) = (x \ ((y \ 1) \ 1)) * (y \ 1). (x \ ((y \ 1) \ 1)) * (y \ 1) = (x \ y) * (1 / y). x != (y \ (z \ 1)) * z | x = (y \ z) * (1 / z). (x \ y) * (1 / y) = (x \ (y \ 1)) * (1 / (y \ 1)). (x \ (y \ 1)) * (1 / (y \ 1)) = (x \ y) * (1 / y). x * y != (z \ (u \ 1)) * (1 / (u \ 1)) | x \ ((z \ u) * (1 / u)) = y. (x * y) \ ((y \ x) * (1 / x)) = (x * (y * (x * y))) \ (1 / (x \ 1)). (x * (y * (x * y))) \ (1 / (x \ 1)) = (x * y) \ ((y \ x) * (1 / x)). T(x \ 1,y \ 1) \ (((x / y) \ 1) * z) = (y * (x * (1 / y))) / (z \ (x / y)). T(x \ 1,y \ 1) \ ((y * (x \ 1)) * z) = (y * (x * (1 / y))) / (z \ (x / y)). (K(x \ 1,x) * (y * z)) \ (K(x \ 1,x) * (y * (z * u))) = L(u,z,y * K(x \ 1,x)). L(L(x,y,z),z * y,K(u \ 1,u)) = L(x,y,z * K(u \ 1,u)). L(x,y,z * K(u \ 1,u)) = L(x,y,z). L(x,y,K(z \ 1,z) * u) = L(x,y,u). L(x,y,z * (u \ 1)) = L(x,y,z * (1 / u)). L(x,y,z * (1 / u)) = L(x,y,z * (u \ 1)). L(x,y,z * u) = L(x,y,z * ((u \ 1) \ 1)). L(x,y,z * ((u \ 1) \ 1)) = L(x,y,z * u). L(x,y,z * u) = L(x,y,((z \ 1) \ 1) * u). L(x,y,((z \ 1) \ 1) * u) = L(x,y,z * u). L(x,y,(z \ u) * (1 / u)) = L(x,y,z \ 1). L(x,y,z / (z \ u)) = L(x,y,z * (u \ z)). L(x,y,T(z * u,u \ 1)) = L(x,y,u * z). K(((x / y) / z) \ 1,R((x / y) / z,z,y)) = K((x / (z * y)) \ 1,x / (z * y)). x != K((y / z) \ 1,y / z) | x = K(y \ z,z \ y). K(((x / y) / z) \ 1,R((x / y) / z,z,y)) = K(x \ (z * y),(z * y) \ x). K(((x / y) / z) \ 1,x / (z * y)) = K(x \ (z * y),(z * y) \ x). (1 / (x \ 1)) / T(y,y \ T(x,x \ 1)) = (y \ ((x \ 1) \ 1)) * K(x \ 1,x). x / T(y,y \ T(x,x \ 1)) = (y \ ((x \ 1) \ 1)) * K(x \ 1,x). x != (y \ ((z \ 1) \ 1)) * K(z \ 1,z) | x = y \ z. x / T(y,y \ T(x,x \ 1)) = y \ x. (1 / x) / T(y,y \ (x \ 1)) = y \ (1 / x). (1 / (1 / x)) / T(y,y \ x) = y \ (1 / (1 / x)). x != (1 / (1 / y)) / T(z,z \ y) | x = K(y \ 1,y) * (z \ y). x \ (1 / (1 / y)) = K(y \ 1,y) * (x \ y). K(x \ 1,x) * (y \ x) = y \ (1 / (1 / x)). K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z. x != K(y,y \ 1) * ((z \ (1 / (1 / y))) * z) | x = y * K(z \ (1 / (1 / y)),z). (x \ y) * x = y * K(x \ (1 / (1 / y)),x). x * K(y \ (1 / (1 / x)),y) = (y \ x) * y. ((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y. x != ((y \ z) * y) * (z \ 1) | x = K(y \ z,y). ((x \ y) * x) / y = K(x \ y,x). (1 / x) * ((y \ x) * y) = K(y \ x,y). K(x \ y,x) * y = (x \ y) * x. T(x,K(y \ x,y)) = x. T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * ((y \ x) * y). T(x * y,K(y,x)) = x * y. K(x,y) \ (x * y) = y * x. (x * y) / (y * x) = K(x,y). K(x,y) = (x * y) / (y * x). K(x,y) * (y * x) = x * y. x != (y * z) / (z * y) | x = T(z,y) \ z. K(x,y) = T(y,x) \ y. x != T(y,z \ 1) \ y | x = K(y \ (y / z),y). K(x \ 1,y) = K(y \ (y / x),y). K(x \ (x / y),x) = K(y \ 1,x). x != T(y,z) \ y | x = ((y * z) / y) \ z. K(x,y) = ((y * x) / y) \ x. x != T(y,z) \ y | x = (1 / T(y,z)) * y. K(x,y) = (1 / T(y,x)) * y. x != T(y,z) \ y | x = y / T(y,z). K(x,y) = y / T(y,x). K(x,y) = y * (T(y,x) \ 1). x != y \ (z \ 1) | x = (z * y) \ 1. K(x,y \ 1) = (y * T(y \ 1,x)) \ 1. (x * T(x \ 1,y)) \ 1 = K(y,x \ 1). x != T(y,y \ z) \ y | x = y \ (z / (z / y)). K(x \ y,x) = x \ (y / (y / x)). x \ (y / (y / x)) = K(x \ y,x). x != T(y,z \ 1) \ y | x = z * T(z \ 1,y). K(x \ 1,y) = x * T(x \ 1,y). x * T(x \ 1,y) = K(x \ 1,y). x != T(y,z) \ y | x = z \ T(z,y). K(x,y) = x \ T(x,y). x != T(y,T(z,y)) \ y | x = z \ T(z,y). K(T(x,y),y) = x \ T(x,y). x * y != T(z,u) \ z | K(u,z) / y = x. K(x,y) / y = 1 / T(y,x). x * y != T(z,u) \ z | x \ K(u,z) = y. (T(x,y) \ 1) \ K(y,x) = T(x,x \ 1). x \ K(y,x) = T(x,y) \ 1. T(x,y) \ 1 = x \ K(y,x). T(x,y) * K(y,x) = x. K(x,L(y,z,u)) = L(T(y,x),z,u) \ L(y,z,u). L(T(x,y),z,u) \ L(x,z,u) = K(y,L(x,z,u)). K(x,R(y,z,u)) = R(T(y,x),z,u) \ R(y,z,u). R(T(x,y),z,u) \ R(x,z,u) = K(y,R(x,z,u)). x / K(y,x) = T(x,y). T(x,y) = x / K(y,x). K(x,y) * T(y,x) = y. K(x,y) \ y = T(y,x). T(x,y) = K(y,x) \ x. (K(x,y) / y) \ 1 = T(y,x). T(x,y) = (K(y,x) / x) \ 1. K(x * (1 / y),x) = T(x,y \ x) \ x. (x \ 1) * K(y,x) = T(x,y) \ 1. ((x * y) / x) * K(y,x) = y. K(x,y) * ((y * x) / y) = x. (x * y) / x = y * K(x,y). T(x * K(y,x),y) = x. x / (x / y) = y * K(y \ x,y). x \ (y * K(x,y)) = ((y * x) / y) \ y. ((x * y) / x) \ x = y \ (x * K(y,x)). K(x \ 1,y) != z | x * T(x \ 1,y) = z. T(K(x \ 1,y),z) = K(y \ (y / T(x,z)),y). K(x \ (x / T(y,z)),x) = T(K(y \ 1,x),z). (1 / (1 / x)) \ K(y,x) = 1 / T(x,y). x * y != z \ T(z,u) | T(x,y) = y \ K(z,u). T(T(x,y),x \ 1) = (x \ 1) \ K(x,y). (x \ 1) \ K(x,y) = T(T(x,y),x \ 1). x != y \ T(y,L(z,u,w) \ 1) | x = L(y \ T(y,z \ 1),u,w). K(x,L(y,z,u) \ 1) = L(x \ T(x,y \ 1),z,u). L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1). x != y \ T(y,z) | x = ((y * z) / y) / z. K(x,y) = ((x * y) / x) / y. x != y \ T(y,z \ 1) | x = z * ((y * (z \ 1)) / y). K(x,y \ 1) = y * ((x * (y \ 1)) / x). x * ((y * (x \ 1)) / y) = K(y,x \ 1). x != y \ T(y,z) | x = z \ ((y * z) / y). K(x,y) = y \ ((x * y) / x). x != y \ T(y,z) | x = (1 / y) * T((1 / y) \ 1,z). K(x,y) = (1 / x) * T((1 / x) \ 1,y). x != y \ T(y,z) | x = (1 / y) * T(y,z). K(x,y) = (1 / x) * T(x,y). x != y \ T(y,z) | x = T(y,z) / y. K(x,y) = T(x,y) / x. x != y \ T(y,z) | x = T(y,z) * (y \ 1). K(x,y) = T(x,y) * (x \ 1). x * y != z \ T(z,u) | x \ K(z,u) = y. T(x,y) \ K(x,y) = x \ 1. x * K(x,y) = T(x,y). T(x,y) = x * K(x,y). K(L(x,y,z),u) = L(x,y,z) \ L(T(x,u),y,z). L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u). T(x,y) / K(x,y) = x. x * K(y,z) != T(y,z) | x = y. x * K(x,y) != z | z = T(x,y). x * K(x,y) != z | T(x,y) = z. L(K(x,y),x,z) = (z * x) \ (z * T(x,y)). (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). K(x,y) * x = T(x,y). T(x,y) = K(x,y) * x. K(x,y) * x != z | T(x,y) = z. (x * K(y,x)) * K(x,z) = K(y,x) * T(x,z). K(x \ (y * z),z \ (y \ x)) = (x \ (y * z)) \ (((x \ (y * z)) \ 1) \ 1). (x \ (y * z)) \ (((x \ (y * z)) \ 1) \ 1) = K(x \ (y * z),z \ (y \ x)). (x * K(y,x)) * y = y * x. T(x,y) * K(y,T(x,y)) = x. K(x,y) * y = (x * y) / x. (x * y) / x = K(x,y) * y. (x \ y) * K(x,x \ y) = y / x. T(x,y) \ x != z | z = K(y,x). T(x,y) \ x != z | K(y,x) = z. L(x,y,(y * x) / y) * K(y * x,(y * x) / y) = (y * x) / y. x != y * T(x,z) | K(z,x) = y. x * T(y,z) != y | K(z,y) = x. T(1 / (1 / x),y) = (1 / (1 / x)) / K(y,x). (1 / (1 / x)) / K(y,x) = T(1 / (1 / x),y). K(x,y / x) * (x \ y) = y / x. x / T(x,y) != z | z = K(y,x). x / T(x,y) != z | K(y,x) = z. x != K(y,z) \ z | x = 1 / (z \ K(y,z)). T(x,y) = 1 / (x \ K(y,x)). K(x \ y,x) * R(T(x,x \ y),z,u) = y \ ((R(x,z,u) * (x \ y)) * x). T(x,y) = T(T(x * K(z,x),y),z). T(T(x * K(y,x),z),y) = T(x,z). (x * K(y,x)) \ (y * x) = y. (x * y) / x != z | z = y * K(x,y). (x * y) / x != z | y * K(x,y) = z. x * T(y,z) = T(y * K(x,y),z) * x. T(x * K(y,x),z) * y = y * T(x,z). (x * T(y,z)) / x = T(y * K(x,y),z). T(x * K(y,x),z) = (y * T(x,z)) / y. x * L(y,z,u) = L(y * K(x,y),z,u) * x. L(x * K(y,x),z,u) * y = y * L(x,z,u). x * R(y,z,u) = R(y * K(x,y),z,u) * x. R(x * K(y,x),z,u) * y = y * R(x,z,u). x * T(T(y,z),u) = T(T(y * K(x,y),z),u) * x. T(T(x * K(y,x),z),u) * y = y * T(T(x,z),u). (x * y) * R(z,x,y) = ((z * K(x * y,z)) * x) * y. ((x * K(y * z,x)) * y) * z = (y * z) * R(x,y,z). (1 / (x * K(y,x))) * L(x,z,u) = L(T(x * K(y,x),y),z,u) / (x * K(y,x)). L(T(x * K(y,x),y),z,u) / (x * K(y,x)) = (1 / (x * K(y,x))) * L(x,z,u). T(x,L(y,z,u)) = T(x,L(y * K(x,y),z,u)). T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u)). T(K(x,y) * y,x) = y. T(x \ K(y,x \ 1),y) = x \ 1. T(K(x,y \ 1) / y,x) = 1 / y. x != T(y,z \ 1) / y | x = ((y * (1 / z)) / y) * z. K(x,y \ 1) = ((x * (1 / y)) / x) * y. ((x * (1 / y)) / x) * y = K(x,y \ 1). x != T(y,z) | x = T(y,T(z,T(y,u))). x * K(x,y) = T(x,T(y,T(x,z))). T(x,T(y,T(x,z))) = x * K(x,y). T(x,y) != x * z | K(x,y) = z. R(x,y,K(y,z)) = ((x * y) * K(y,z)) / T(y,z). ((x * y) * K(y,z)) / T(y,z) = R(x,y,K(y,z)). x \ T(x,y) != z | z = K(x,y). x \ T(x,y) != z | K(x,y) = z. (x * y) * K(y,z) != u * T(y,z) | R(x,y,K(y,z)) = u. T(1 / x,y) = (1 / x) * K(x \ 1,y). (1 / x) * K(x \ 1,y) = T(1 / x,y). (x \ y) \ y = K(x,y / x) * x. K(x / y,x) \ ((1 / y) * x) = x / y. T(T(x,y),z) = K(T(x,z),y) * T(x,z). K(T(x,y),z) * T(x,y) = T(T(x,z),y). K(L(x,y,z),u) * L(x,y,z) = L(T(x,u),y,z). x * (K(y,x) * y) = y * x. T(x,y) / L(z,x / z,K(x,y)) = K(x,y) * (x / z). (x * K(y,z)) \ (x * T(y,z)) != u | L(y,K(y,z),x) = u. (x * K(y,z)) * y != u * T(y,z) | R(x,K(y,z),y) = u. (K(x,y) * z) \ T(x,y) != u | L(z \ x,z,K(x,y)) = u. T(x,y) / R(x,z,u) != w | (K(x,y) / R(x,z,u)) * x = w. T(x,y) != z | x * K(x,y) = z. (x * y) \ (K(x,y) * ((y * x) * z)) != u | L(z,y * x,K(x,y)) = u. (x * y) \ (K(x,y) * (y * (x * z))) = L(L(z,x,y),y * x,K(x,y)). x != ((y * z) / y) \ z | x = z * (((y * z) / y) \ 1). K(x,y) = x * (((y * x) / y) \ 1). x * y != ((z * u) / z) \ u | x \ K(u,z) = y. x \ K(x,y) = ((y * x) / y) \ 1. ((x * y) / x) \ 1 = y \ K(y,x). K(x \ y,x) = T(x \ 1,y) * x. T(x \ 1,y) * x = K(x \ y,x). L(T(x,y) \ 1,x,z) = (z * x) \ (z * K(y,x)). (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x). x \ (y * K(z,y \ x)) = L(T(y \ x,z) \ 1,y \ x,y). L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y)). K(x \ y,y \ x) = (y \ x) * ((1 / x) * y). (x \ y) * ((1 / y) * x) = K(y \ x,x \ y). x != y \ T(y,z) | x = K(y,z). K(T(x,y),y) = K(x,y). x * K(T(x,y),y) = T(x,y). K(x,y) \ 1 = K(y,x). K(x,y / x) = K(x,x \ y). K(x,y) = K(x,T(y,x)). K(x,T(y,x)) = K(x,y). K(x \ (y * x),x) = K(y,x). K(x \ y,x) = K(y / x,x). K(x / y,y) = K(y \ x,y). K(T(x,y),y * x) = K(R(x,y,x),y * x). K(R(x,y,x),y * x) = K(T(x,y),y * x). K(x \ y,y) = K(y * (x \ 1),y). K(x * (y \ 1),x) = K(y \ x,x). K(x,x \ y) = K(y / (y / x),x \ y). K(x / (x / y),y \ x) = K(y,y \ x). K(x \ (y * T(x,z)),x) = K((y / x) * T(x,z),x). K(x,y) * K(y,x) = 1. x * K(y,x) = K(x,y) \ x. K(x,y) \ x = x * K(y,x). K(x,y) \ 1 != z | K(y,x) = z. K(x,T(y,x)) != z | K(x,y) = z. K(x,y) != z | K(y,x) \ 1 = z. K(x,y) = K(x * K(y,x),y). K(x * K(y,x),y) = K(x,y). 1 / K(x,y) = K(y,x). (x \ K(y,z)) \ (x \ 1) = K(z,y). x * y != K(z,u) \ 1 | x \ K(u,z) = y. x \ K(y,z) = (K(z,y) * x) \ 1. (K(x,y) * z) \ 1 = z \ K(y,x). (x \ K(y,z)) * K(z,y) = x \ 1. (K(x,y) / z) \ 1 = z * K(y,x). 1 / K(x,y) != z | z = K(y,x). 1 / K(x,y) != z | K(y,x) = z. 1 / (x * K(y,z)) = K(z,y) / x. x \ K(y,z) != u | (K(z,y) * x) \ 1 = u. 1 / (x * (y * K(z,u))) = (K(u,z) / y) / x. x / (y \ K(z,u)) = (1 / x) \ (K(u,z) * y). (1 / x) \ (K(y,z) * u) = x / (u \ K(z,y)). x / (y * K(z,u)) = (1 / x) \ (K(u,z) / y). (1 / x) \ (K(y,z) / u) = x / (u * K(z,y)). (x * K(y,z)) \ K(z,y) = K(z,y) * (x \ K(z,y)). T(K(x,y),z) = (K(y,x) * z) \ z. (K(x,y) * z) \ z = T(K(y,x),z). (x * K(y,x)) \ 1 = x \ K(x,y). K(x,L(T(y,x),z,u)) = K(x,L(y,z,u)). K(x,R(x \ y,z,u)) = K(x,R(y / x,z,u)). K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u)). K(x,y) = K(x,T(y,x \ y)). K(x,T(y,x \ y)) = K(x,y). K(x,y) = K(x,y * K(x,y)). K(x,y * K(x,y)) = K(x,y). 1 != K(x,y) * z | K(y,x) = z. K(x,y) * z != 1 | K(y,x) = z. (K(x,y) * z) \ 1 != u | z \ K(y,x) = u. K(x,y) \ (1 / z) != u | K(y,x) / z = u. K(x,y) \ z != u | K(y,x) / (z \ 1) = u. T(K(x,y) \ z,K(y,x)) = z * K(y,x). T(x,K(y,z)) = (K(z,y) * x) * K(y,z). (K(x,y) * z) * K(y,x) = T(z,K(y,x)). T(K(x,y) \ z,K(y,x)) != u | z * K(y,x) = u. ((x \ 1) \ 1) * K(y,z) = 1 / (K(z,y) / x). (K(x,y) * z) \ z != u | T(K(y,x),z) = u. K(x,y) * ((z / K(y,x)) \ u) = ((K(y,x) / u) * z) \ K(y,x). ((K(x,y) / z) * u) \ K(x,y) = K(y,x) * ((u / K(x,y)) \ z). T(x * K(y,z),x \ K(z,y)) = ((x * K(y,z)) \ 1) \ 1. 1 / (x \ K(y,x)) != z | z = T(x,y). 1 / (x \ K(y,x)) != z | T(x,y) = z. T(x,y) * L(x \ K(y,x),z,u) = T(x * L(x \ 1,z,u),y). (x / y) * K(y \ x,y) = y \ x. x / ((y * x) / y) = K(x,y). K(x,y) = x / ((y * x) / y). K(a(x,y,z),x * (y * z)) * (((x * y) * z) / (x * (y * z))) = a(x,y,z). ((x \ (1 / y)) * x) * y = K((x * y) \ 1,x). T(x,y * x) * T(y,x) = (y * x) * K(T(x,y),y * x). (x * y) * K(T(y,x),x * y) = T(y,x * y) * T(x,y). T(x,y \ x) = x * K(y,x). (1 / x) \ (y / (y * x)) = K(y,1 / x). x * y != z * K(u,z) | x \ ((u * z) / u) = y. T(x,y) \ ((z * x) / z) = x * (T(x,y) \ K(z,x)). x * ((y * z) / y) = x * (z * K(y,z)). T(x * K(y,x),y) != z | z = x. ((x * y) * z) / R(x,y,z) = (y * z) * K(R(x,y,z),y * z). R(x * K(y,x),y,z) = ((y * x) * z) / (y * z). R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x). R(x,y,x) = T(x * K(y * x,x),y). T(x * K(y * x,x),y) = R(x,y,x). L(x * K(y,x),z,u) = (y * L(x,z,u)) / y. R(x * K(y,x),z,u) = (y * R(x,z,u)) / y. T(x * K(x \ y,x),y) = L(x,x \ y,x). T(T(x * K(y,x),z),x * y) = L(T(x,z),y,x). L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z). ((x * y) * T(y,z)) / (x * T(y,z)) = y * K(x * T(y,z),y). T(x,y) * y = x * (y * K(x,y)). x * (y * K(x,y)) = T(x,y) * y. (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y. ((x * y) * L(y,z,u)) / (x * L(y,z,u)) = y * K(x * L(y,z,u),y). L(x,y,x) = (y * K(x,y)) \ ((x * (y * x)) / x). (x * K(y,x)) \ ((y * (x * y)) / y) = L(y,x,y). ((x * y) * R(y,z,u)) / (x * R(y,z,u)) = y * K(x * R(y,z,u),y). ((x * y) / x) / y != z | K(x,y) = z. K(x,x \ y) = (y / x) / (x \ y). (x / y) / (y \ x) = K(y,y \ x). K(1 / (x * y),x) = ((1 / y) / (1 / (x * y))) / x. ((1 / x) / (1 / (y * x))) / y = K(1 / (y * x),y). K(x,(y * z) / y) = ((y * ((x * z) / x)) / y) / ((y * z) / y). ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x). K((x * y) * z,(y * z) \ (x \ 1)) = (T(a(x,y,z),(y * z) \ (x \ 1)) / ((x * y) * z)) / ((y * z) \ (x \ 1)). (T(a(x,y,z),(y * z) \ (x \ 1)) / ((x * y) * z)) / ((y * z) \ (x \ 1)) = K((x * y) * z,(y * z) \ (x \ 1)). x * (y * K(z,y)) != u | x * ((z * y) / z) = u. K(x \ L(x,y,z),u) = (L(x,y,z) \ x) * T(x \ L(x,y,z),u). (L(x,y,z) \ x) * T(x \ L(x,y,z),u) = K(x \ L(x,y,z),u). (x * T(y,z)) \ (x * K(y,z)) != u | L(y \ 1,T(y,z),x) = u. K(x,x * y) = T(x,y * x) * (x \ 1). T(x,y * x) * (x \ 1) = K(x,x * y). K(K(x,y),z) = T(K(x,y),z) * K(y,x). T(K(x,y),z) * K(y,x) = K(K(x,y),z). T(x,y) * (x \ 1) != z | z = K(x,y). T(x,y) * (x \ 1) != z | K(x,y) = z. x * (y * R(z,u,w)) != (y * R(z,u,w)) * T(z,y) | x = R(z,y,R(z,u,w)). T(x,y) * K(y * R(x,z,u),T(x,y)) = R(x,y,R(x,z,u)). x * (y * z) != (y * z) * T(z,y) | x = R(z,y,z). T(x,y) * K(y * x,T(x,y)) = R(x,y,x). ((x * y) * z) * a(z * K(x * y,z),x,y) = ((z * K(x * y,z)) * x) * y. (x * K(y,x)) * ((y \ 1) \ 1) = ((y \ 1) \ 1) * x. x != K(y,z / u) | x = K(y,(z \ 1) \ (u \ 1)). K(x,x \ y) = K(x,(y \ 1) \ (x \ 1)). K(x,(y \ 1) \ (x \ 1)) = K(x,x \ y). x * K(y,y \ x) = y * (x / y). x != K(y / z,z) | x = (z * (y / z)) \ y. K(x \ y,x) = (x * (y / x)) \ y. (x * (y / x)) \ y = K(x \ y,x). L(x * K(y,x),K(x,y),z) = (z * K(x,y)) \ (z * x). x * y != T(x,z) | y = K(x,z). K(x,y) = K(y,x \ y). K(x,y \ x) = K(y,x). T(x,y \ x) != x * z | K(y,x) = z. K(x * y,y) = K(x,x * y). K(x,y) = K(x / y,x). K(x / y,x) = K(x,y). K((x * y) \ (z \ 1),y \ (x \ (z \ 1))) = K(a(z,x,y),(x * y) \ (z \ 1)). T(K(x,y),K(z,y)) = K(x,y). 1 / K(x,y) = K(x \ y,y). K(x \ y,y) = 1 / K(x,y). T(x / y,K(x,y)) = x / y. T(K(x,y),K(x,z)) = K(x,y). T(x,K(y,y * T(x,z))) = x. K(x,y) * K(z,y) = K(z,y) * K(x,y). x != 1 / K(y,z) | x = K(z,y). K(x \ y,y) = K(y,x). x != K(y,z) | x = K(y / z,y). K(x \ y,y) = K(y / x,y). K(x / y,x) = K(y \ x,x). x != K(y,z \ y) | x = K(z,y). K((x \ y) \ y,y) = K(x,y). x != K(y,z) | x = K(z,y \ z). K(x,y) = K(x,(y \ x) \ x). K(x,(y \ x) \ x) = K(x,y). x != K((y / z) \ y,u) | x = K(z,u). K(x,x / y) = K(y,x). K(x * y,x) = K(y,x * y). K(x,x / y) = K(x,y \ x). K(x,y) * (x / y) != z | (x / y) * K(x,y) = z. K(x,y) * K(x,z) = K(x,z) * K(x,y). T(K(x,x * T(y,z)),y) = K(x,x * T(y,z)). K(x * y,T(y,x)) = K(x * y,y). L(T(x,y),z,u) \ L(x,z,u) != w | K(y,L(x,z,u)) = w. R(T(x,y),z,u) \ R(x,z,u) != w | K(y,R(x,z,u)) = w. K(x \ (x / y),x) != z | K(y \ 1,x) = z. L(x,y,z) \ L(T(x,u),y,z) != w | K(L(x,y,z),u) = w. x \ L(T(x,y),y,x) != z | K(x,x * y) = z. (x \ K(y,z)) \ (x \ 1) != u | K(z,y) = u. K(x,x \ (y * x)) != z | K(x,y) = z. K(x,R(T(y,x * z),x,z)) != u | K(x,(x * z) \ ((x * y) * z)) = u. K(x \ y,y) != z | K(y,x) = z. K(a(x,y,z),(x * y) * z) != u | K((x * y) * z,x * (y * z)) = u. R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y). x != K(y \ (y / (z / u)),y) | x = (z * T(z \ u,y)) / u. K((x / y) \ 1,z) = (x * T(x \ y,z)) / y. (x * T(x \ y,z)) / y = K((x / y) \ 1,z). x != K(y \ (y / (z \ u)),y) | x = z \ (u * T(u \ z,y)). K((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z). x * T(x \ y,z) = y * K((y \ x) \ 1,z). (x * y) * K(((x * y) \ x) \ 1,z) = x * T(y,z). (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z). K((x / y) \ 1,z) * y = x * T(x \ y,z). x != y \ (z / (z / y)) | x = z / (y * (z / y)). K(x \ y,x) = y / (x * (y / x)). x / (y * (x / y)) = K(y \ x,y). x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z). (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z). ((x * y) \ x) * (x * y) = x * K(y \ 1,x * y). K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y). (x * y) * T((x * y) \ y,z) = K(x \ 1,z) * y. x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y. x * y != (z \ 1) * K(u,z) | (T(z,u) \ 1) / y = x. (T(1 / x,y) \ 1) / K(y,1 / x) = x. x != (y \ 1) * K(z,y \ 1) | x = y \ K(z,y \ 1). x / (x / (y \ 1)) = y \ K((y \ 1) \ x,y \ 1). x \ K((x \ 1) \ y,x \ 1) = y / (y / (x \ 1)). (x * K(x \ y,x)) * (y / x) = y. (x / y) * (y * K(y \ x,y)) = (y \ x) * y. T(x,y) / (T(x,y) / y) = y * K(y \ x,y). (x / y) \ K(y,y \ x) = (y \ x) \ 1. T(1 / x,R(x,y,z) \ x) = 1 / x. T(x,y * K(y,z)) = T(x,T(y,z)). T(x,T(y,T(x,z))) != u | T(x,y) = u. R(x,y,z) * (x * (((u * R(x,y,z)) / u) \ 1)) = x * K(R(x,y,z),u). (x / y) \ 1 = (y \ x) \ K(y \ x,y). (x \ y) \ K(x \ y,x) = (y / x) \ 1. T(x,x \ K(x,y)) = (x \ 1) \ 1. (L(x,y,x) * y) \ 1 = (y * x) \ K(y * x,x). (x * y) \ K(x * y,y) = (L(y,x,y) * x) \ 1. x != T(y \ 1,z) * y | x = y * T(1 / y,z). K(x \ y,x) = x * T(1 / x,y). x * T(1 / x,y) = K(x \ y,x). K(x * (y \ K(y,z)),x) = K(((z * y) / z) \ x,x). K(((x * y) / x) \ z,z) = K(z * (y \ K(y,x)),z). (x \ K(y,z)) * (u * u) = ((K(z,y) * x) \ u) * u. ((K(x,y) * z) \ u) * u = (z \ K(y,x)) * (u * u). (x \ K(y,z)) * L(u,K(z,y) * x,K(z,y) * x) = (K(z,y) * x) \ u. T(x,(y \ K(z,u)) \ 1) = T(x,K(u,z) * y). (x \ K(x,y)) \ 1 = (x \ 1) \ K(y,x). 1 / (K(x,y) * T(x,z)) = K(y,x) / T(x,z). 1 / ((x * y) / x) = K(y,x) / y. K(x,y) / x = 1 / ((y * x) / y). (K(x,y) * z) * T(K(y,x),z) = z. x * ((K(y,z) * x) \ x) = K(z,y) * x. K(x,y) * (y \ K(y,x)) = y \ 1. T((x * K(y,x)) * (R(K(y,x),x,(x * K(y,x)) \ 1) \ 1),z) = (x * K(y,x)) * (T(x,z) * (x \ K(x,y))). R(x,y,z * K(y,z)) = ((x * y) * (z * K(y,z))) / (T(y,z) * z). ((x * y) * (z * K(y,z))) / (T(y,z) * z) = R(x,y,z * K(y,z)). L(K(x,x \ y) \ z,K(x,x \ y),y) = (x * (y / x)) \ (y * z). (x * (y / x)) * K(x \ y,x) = y. K(x * y,x) = K(y * x,x). K(x * y,y) = K(y * x,y). K(x * y,y) != z | K(y * x,y) = z. x != K(y * (z \ 1),y) | x = K(z \ y,y). K((x \ 1) * y,y) = K(x \ y,y). T(x * K(x * y,x),y * x) = x. K(x \ y,x) * (x * (y / x)) = y. K(x,y) / ((x \ 1) \ 1) = x \ K(x,y). (x \ K(x,y)) * T((x \ 1) \ 1,z) = T(x,z) * (x \ K(x,y)). x * y != K(z,x) | y = T(x,z) \ 1. T(1 / x,y) = T(x,x \ y) \ 1. T(x,x \ y) \ 1 = T(1 / x,y). x != 1 / ((y * z) / y) | x = (y / z) / y. K(x,y) / x = (y / x) / y. (K(x,y) / x) * y = y / x. x * y != ((z * u) * w) / a(z,u,w) | x \ (z * (u * w)) = y. (K(a(x,y,z),(x * y) * z) / a(x,y,z)) \ (x * (y * z)) = (x * y) * z. (K(x,y) * K(y,z)) * K(y,x) = K(y,z). (x \ 1) / (x \ K(x,y)) = K(y,x). (x \ 1) / (x \ K(x,y)) != z | z = K(y,x). (x \ 1) / (x \ K(x,y)) != z | K(y,x) = z. T(1 / x,y) = ((x \ y) \ y) \ 1. ((x \ y) \ y) \ 1 = T(1 / x,y). (x \ y) \ 1 = T(1 / (y / x),y). T(1 / (x / y),x) = (y \ x) \ 1. T(((x \ y) \ y) * z,(x \ y) \ y) = z / T(1 / x,y). L(x,((y \ z) \ z) * (1 / z),((y \ z) \ z) * (1 / z)) = ((1 / z) * ((y \ 1) \ 1)) * (((1 / z) \ T(1 / y,z)) * x). x * ((y \ x) \ 1) = (1 / (x / y)) * x. (1 / (x / y)) * x = x * ((y \ x) \ 1). T(x * K(x * y,x),y) = R(x,y,x). T(x * K(y \ x,x),y \ 1) = R(x,y \ 1,x). (1 / x) * R(T(1 / x,R(x,y,z) \ x) \ 1,u,w) = T((1 / x) * R((1 / x) \ 1,u,w),R(x,y,z) \ x). T((1 / x) * R((1 / x) \ 1,y,z),R(x,u,w) \ x) = (1 / x) * R(T(1 / x,R(x,u,w) \ x) \ 1,y,z). T(x,R(T(x,y) \ z,u,w)) != v5 | T(x,R(z / T(x,y),u,w)) = v5. T(R(x,y,x),z) = T(T(x * K(x * y,x),z),y). T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z). R(x * T(x \ 1,y),z,u) * R(R(x * T(x \ 1,y),z,u) \ 1,w,v5) = R((x * T(x \ 1,y)) * R(K(y,x \ 1),w,v5),z,u). (x \ 1) \ K(y,x * K(y,x)) = T(x * K(y,x),(x * K(y,x)) \ 1). T(x * K(y,x),(x * K(y,x)) \ 1) = (x \ 1) \ K(y,x * K(y,x)). x != T(y,z) \ y | x = K(z,y). K(x * (1 / y),x) = K(y \ x,x). K(x * (1 / y),x) != z | K(y \ x,x) = z. x != K(y \ z,z) | x = K(z / y,z). K(x * (1 / y),x) = K(x / y,x). x != K(y * z,y) | x = K(z * y,y). K(x \ y,y) = K((1 / x) * y,y). K((1 / x) * y,y) = K(x \ y,y). K(x * y,x) = K((y \ 1) \ x,x). K((x \ 1) \ y,y) = K(y * x,y). K(x,y \ 1) = K(x * y,x). K(x * y,x) = K(x,y \ 1). K(x,y \ 1) = K(y * x,x). K(x * y,y) = K(y,x \ 1). x != K(y * z,y) | x = K(z,y * z). K(x,y \ 1) = K(y,x * y). K(x,y) = K(y,(y \ x) \ 1). K(x,(x \ y) \ 1) = K(y,x). K(x * K(y,z),x) = K(x,K(z,y)). x != K(y * z,z) | x = K(y,y * z). K(x,y \ 1) = K(y,y * x). K(x,y \ 1) != z | K(x * y,x) = z. K(x \ 1,y * (x \ 1)) = K(y,x). T(x,y * x) = K(y,x \ 1) * x. K(x,y \ 1) * y = T(y,x * y). x != K(y,z \ 1) | x = K(z,y * z). K(x,x * y) = K(x,y * x). K(x,y * x) = K(x,x * y). K(x \ y,x \ 1) = K(x,y). K(x,y) = K(x,x * (y / x)). K(x,x * (y / x)) = K(x,y). K(x * (y * z),a(x,y,z) * (x * (y * z))) = K(x * (y * z),(x * y) * z). K(x,y * (1 / x)) = K(x,x \ y). K(x \ 1,y * x) = K(x \ 1,(x \ 1) \ y). K(x \ 1,(x \ 1) \ y) = K(x \ 1,y * x). (x * K(y,x)) \ y = x \ (y * K(x,y)). K(x,y) / (1 / T(y,x)) = 1 / (1 / y). x != R(y,z,u) * ((w * (R(y,z,u) \ 1)) / w) | x = R(y * ((w * (y \ 1)) / w),z,u). K(x,R(y,z,u) \ 1) = R(y * ((x * (y \ 1)) / x),z,u). R(x * ((y * (x \ 1)) / y),z,u) = K(y,R(x,z,u) \ 1). x != (y / z) * ((u * ((y / z) \ 1)) / u) | x = (y * ((u * (y \ z)) / u)) / z. K(x,(y / z) \ 1) = (y * ((x * (y \ z)) / x)) / z. (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1). (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1). x * K(y,(x \ z) \ 1) = z * ((y * (z \ x)) / y). ((1 / x) * y) * T(((1 / x) * y) \ y,z) = K(x,z) * y. x * y != y * z | x = z * K(y,z). T(x * K(y,x),z) = T(x,z) * K(y,T(x,z)). T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y). T(x * K(y * R(x,z,u),x),y) = R(x,y,R(x,z,u)). T(x * K(y,x),z) = T((y * x) / y,z). T((x * y) / x,z) = T(y * K(x,y),z). x != ((y \ z) * T(z,y \ 1)) / (y \ z) | x = R(z,z \ (y \ z),z). T(x * K(y \ x,x),y \ 1) = R(x,x \ (y \ x),x). x != (y * z) / y | x = K(y,z) * z. T(x * K(y,x),z) = K(y,T(x,z)) * T(x,z). K(x,T(y,z)) * T(y,z) = T(y * K(x,y),z). x * y != (z * T(u,w)) / z | x \ T(u * K(z,u),w) = y. T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y)). T(T(x * K(y,x),z),y) != u | u = T(x,z). T(T(x * K(y,x),z),y) != u | T(x,z) = u. K(T(x,y),z) = T(x * K(z,x),y) \ T(x,y). T(x * K(y,x),z) \ T(x,z) = K(T(x,z),y). T(x * K(y,x),z) != u | T(x,z) * K(y,T(x,z)) = u. (x / (x * y)) * y = K(x,y \ 1). K(x \ y,y) \ ((1 / x) * y) = y / x. x / T(x,y \ 1) = K(y,1 / x). K(x \ 1,y) = K(x,1 / y). K(x,1 / y) != z | K(x \ 1,y) = z. K(x \ 1,y) = K(x,y \ 1). K(x \ 1,y \ 1) = K(x,y). K(x \ 1,y) != z | K(x,y \ 1) = z. K(x \ 1,K(y,z)) = K(x,K(z,y)). x != K(y \ 1,z) | x = K(1 / y,z). K(x,y \ 1) = K(1 / x,y). K(1 / x,y) = K(x,y \ 1). K(1 / x,y \ 1) = K(x,y). x * y != K(z \ 1,u) | x \ K(z,u \ 1) = y. x \ K(x,y \ 1) = T(x \ 1,y). x \ K(y,x \ 1) = T(x,y \ 1) \ 1. T(x,y \ 1) \ 1 = x \ K(y,x \ 1). (1 / x) \ (y * K(z,z \ 1)) = x / (y \ K(z,z \ 1)). K(x,x \ 1) * (y * (1 / x)) = y * (x \ 1). K(x,x \ 1) * (y * K(x,x \ 1)) = y. K(x,x \ 1) * (x \ y) != z | ((x \ 1) \ 1) \ y = z. T(x * ((y \ z) * (1 / z)),x) = (y * K(z,z \ 1)) \ x. x != K(y,z \ 1) | x = K(z,z * y). K(x,y) = K(y,y * (x \ 1)). K(x,x * (y \ 1)) = K(y,x). K(x * K(y,z),u \ 1) = K(K(z,y) / x,u). K(x,y \ 1) != z | K(x \ 1,y) = z. K(x,y) = K(y,(1 / x) * y). K(x,(1 / y) * x) = K(y,x). K(x,(1 / y) * x) = K(x,y \ x). x \ K(x,y \ (z \ 1)) = T(x \ 1,z * y). K(x,y * x) = K(x,(y \ 1) \ x). K(x,(y \ 1) \ x) = K(x,y * x). x != K(y,z * y) | x = K(y,y * z). K(x,(y \ 1) \ x) = K(x,x * y). K(x,(R(y,z,u) \ y) \ x) = K(x,x * (y \ R(y,z,u))). K(x,K(y,z)) != u | K(x \ 1,K(z,y)) = u. K(x \ (y \ 1),z) != u | K(y * x,z \ 1) = u. K(x,x * y) != z | K(x,y * x) = z. K(x,y \ 1) != z | K(y,x * y) = z. (T(1 / x,y) \ 1) / K(y,x \ 1) = x. (x \ y) \ K(x \ y,x) = x * (y \ 1). (x \ K(x,y)) * T(x,x \ 1) = K(x,y). x != (1 / (y / z)) * y | x = y \ (y / (1 / z)). x * ((y \ x) \ 1) = x \ (x / (1 / y)). x \ (x / (1 / y)) = x * ((y \ x) \ 1). (x * ((y \ x) \ 1)) \ 1 = x \ (x / y). (x \ (x / (y \ 1))) / (y \ 1) = (x * ((y \ x) \ 1)) * y. K(x,y) / (K(x,y) / y) = 1 / (1 / y). ((K(x,y \ 1) \ 1) \ y) * (1 / y) = y * (((T(y,x \ 1) \ 1) \ 1) \ 1). (K(x,x \ 1) / y) * (z * K(x,x \ 1)) = (1 / y) * z. x * K(y,x \ 1) = T(1 / x,y) \ 1. T(1 / x,y) \ 1 = x * K(y,x \ 1). (x * y) \ ((x * y) / (1 / x)) = (x * y) * (y \ 1). x * L(y / (1 / (y \ x)),y \ x,y) = ((y * ((x \ y) \ 1)) * y) * (y \ x). ((x \ y) \ 1) \ (y \ 1) = y \ (y / x). ((x \ (y / z)) \ 1) \ (z * (y \ 1)) = (y / z) \ ((y / z) / x). T(x,y) * K(x * y,x) = R(x,y,x). K(x * y,x) * T(x,y) = R(x,y,x). L(K(x * y,x),T(x,y),z) = (z * T(x,y)) \ (z * R(x,y,x)). (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x). L(x * T(x \ 1,y),z,u) != w | K(L(x,z,u) \ 1,y) = w. K(x / y,x) != z | K(y \ x,x) = z. K(T(x,y) \ 1,z) = T(K(x \ 1,z),y). K(T(1 / x,y) \ 1,z) = T(K(x,z),y). K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). K(T(K(x,y) * z,u) \ 1,w) = T(K(z \ K(y,x),w),u). K(x * K(y,x \ 1),z) = T(K(x,z),y). K((x \ y) \ y,z) = T(K(x,z),y). K(x \ y,z) = T(K(y / x,z),y). T(K(x / y,z),x) = K(y \ x,z). K((x \ 1) \ 1,y) != z | z = K(x,y). K((x \ 1) \ 1,y) != z | K(x,y) = z. K(T(x,x \ y),z) = T(K(x,z),y). x != T(K(y,z),L(z,u,w)) | x = K(y,z). K(x \ L(y,z,u),y) = K(L(y,z,u) / x,y). K(L(x,y,z) / u,x) = K(u \ L(x,y,z),x). K(x \ 1,y) != z | z = K(1 / x,y). K(x \ 1,y) != z | K(1 / x,y) = z. K((x \ (y \ 1)) \ 1,z) != u | K(y * x,z) = u. K(x \ 1,K(y,z)) != u | K(x,K(z,y)) = u. T(K(x,y),z) \ 1 != u | K(y,x * K(z,x \ 1)) = u. L(x * K(y,x),z,u) = L(x,z,u) * K(y,L(x,z,u)). L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z). R(x * K(y,x),z,u) = R(x,z,u) * K(y,R(x,z,u)). R(x,y,z) * K(u,R(x,y,z)) = R(x * K(u,x),y,z). (K(x,y) / z) \ (K(u,w) / v5) = (z * K(y,x)) / (v5 * K(w,u)). (x * K(y,z)) / (u * K(w,v5)) = (K(z,y) / x) \ (K(v5,w) / u). x != K((y * z) \ 1,u) | x = K(z \ (y \ 1),u). ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x). x * y != (z * L(u,w,v5)) / z | L(u * K(z,u),w,v5) / y = x. L(x * K(y,x),z,u) / L(x,z,u) = K(y,L(x,z,u)). K(L(x,y,z),u) = L(x * K(u,x),y,z) \ L(x,y,z). L(x * K(y,x),z,u) \ L(x,z,u) = K(L(x,z,u),y). K(L(x,y,z),u) = L(x,y,z) / L(x * K(u,x),y,z). L(x,y,z) / L(x * K(u,x),y,z) = K(L(x,y,z),u). L(x * K(y,x),z,u) / L(x,z,u) != w | K(y,L(x,z,u)) = w. x * y != (z * R(u,w,v5)) / z | x \ R(u * K(z,u),w,v5) = y. R(x,y,z) \ R(x * K(u,x),y,z) = K(u,R(x,y,z)). R(x * K(y,x),z,u) \ y = R(x,z,u) \ ((R(x,z,u) * y) / R(x,z,u)). K(R(x,y,z),u) = R(x * K(u,x),y,z) \ R(x,y,z). R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y). (x \ T(x * y,z)) / y = K(((x \ 1) / y) \ 1,z). K(((x \ 1) / y) \ 1,z) = (x \ T(x * y,z)) / y. (x * (y * T(y \ z,u))) / (x * z) = K(((x * y) / (x * z)) \ 1,u). x \ T(x * y,z) = y * K((y \ (x \ 1)) \ 1,z). T(x,y) * z = (x * z) * K(((x * z) \ z) \ 1,y). (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y. x * y != z * T(z \ u,w) | (u * K((u \ z) \ 1,w)) / y = x. (x * K((x \ y) \ 1,z)) / y = T(x / y,z). x != (1 / y) * T((1 / y) \ (z / y),u) | x = T(z,u) / y. K(((1 / x) / (y / x)) \ 1,z) * (y / x) = T(y,z) / x. K((x / (x * y)) \ 1,z) * (x * y) = x * T(y,z). ((x / y) * (y * K(y \ x,y))) * (x / y) = x * (y \ x). T(T(x * K(x \ y,x),y),z) = L(T(x,z),x \ T(y,x),x). T((x \ K(y,z)) \ 1,K(z,y) * x) = (x \ K(y,z)) \ 1. x != K(y \ 1,(y \ 1) \ z) | x = K(y \ 1,y * z). K(x \ 1,y * x) = K(x \ 1,x * y). x * T(x \ 1,y * x) = K(x \ 1,x * y). ((x * y) \ y) * (x * y) = y * K(x \ 1,y * x). T(x,y) \ T(x * K(z,x),y) != u | u = K(z,T(x,y)). T(x,y) \ T(x * K(z,x),y) != u | K(z,T(x,y)) = u. T(x,y) \ T(z / (z / x),y) = K(x \ z,T(x,y)). T(x,y) \ T(x * K(x * z,x),y) = K(z * x,T(x,y)). T(T(x * K(y,x),z),u) \ T(T(x,z),u) = K(T(T(x,z),u),y). (x * (y \ 1)) * (y \ 1) = (x * (1 / y)) * (1 / y). (x * (1 / y)) * (1 / y) = (x * (y \ 1)) * (y \ 1). x != T(y \ 1,y * z) | x = ((T(y,z) \ 1) \ 1) \ 1. x \ K(x,y \ (x \ 1)) = ((T(x,y) \ 1) \ 1) \ 1. ((T(x,y) \ 1) \ 1) \ 1 = x \ K(x,y \ (x \ 1)). x * y != K(x \ 1,z) | y = T(x \ 1,z). T(x \ 1,y * x) = T(x \ 1,x * y). x != T(y \ 1,y * z) | x = ((y \ 1) \ z) \ z. T(x \ 1,y * x) = ((x \ 1) \ y) \ y. T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) = T((x \ 1) * L((x \ 1) \ 1,z,u),y * x). T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) = T((x \ 1) * L((x \ 1) \ 1,z,u),x * y). T((x \ y) \ 1,y) = (((x \ y) \ 1) \ x) \ x. R(x,y,z) \ R(x,y,z) = K(x \ R(x,u,w),R(x,y,z)). K(x \ R(x,y,z),R(x,u,w)) = R(x,u,w) \ R(x,u,w). L(K(L(x,y,z),u),L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * L(T(x,u),y,z)). (x * (y * z)) \ ((x * y) * L(T(z,u),y,x)) = L(K(L(z,y,x),u),L(z,y,x),x * y). (x * y) \ T(x,y) = L(T(y,x) \ 1,y,x). L(T(x,y) \ 1,x,y) = (y * x) \ T(y,x). T(x,K(y,z)) != u | (K(z,y) * x) * K(y,z) = u. ((x * K(y,x)) \ ((y * (x * y)) / y)) \ ((y * (x * y)) / y) = x. T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x). K(x \ (y * (z \ 1)),u) != w | K((z / y) * x,u \ 1) = w. T(T(x * K(y * x,x),z),y) = R(T(x,z),y,x). L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1). L(K(x,y),z,u) = K(x,L(1 / y,z,u) \ 1). K(x,L(1 / y,z,u) \ 1) = L(K(x,y),z,u). L(K(x,y),z,u) = K(x,L(y \ 1,z,u) \ 1). K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u). K(x,(y \ z) \ 1) = L(K(x,z \ y),z \ y,z). L(K(x,y \ z),y \ z,y) = K(x,(z \ y) \ 1). R(T(x,y),z,x) * (z * x) = (z * x) * T(T(x,y),z). x != y * ((z / u) \ y) | x = (y * u) * (z \ y). ((x / y) * K(z,u)) \ K(u,z) = (K(u,z) * y) * (x \ K(u,z)). T((x / (y * K(z,y))) * y,(z * y) / z) != u | ((z * y) / z) \ (x * y) = u. (1 / ((1 / (x * y)) * y)) / x = K(1 / (x * y),x). R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y). R(K(x,y),z,u) = K(R(1 / x,z,u) \ 1,y). K(R(1 / x,y,z) \ 1,u) = R(K(x,u),y,z). R(K((x / y) \ 1,z),y,u) = K(((x * u) / (y * u)) \ 1,z). R(K(x,y),z,u) = K(R(x \ 1,z,u) \ 1,y). K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z). R(R(K(x,y),z,u),w,v5) = K(R(R(1 / x,z,u),w,v5) \ 1,y). K(R(R(1 / x,y,z),u,w) \ 1,v5) = R(R(K(x,v5),y,z),u,w). R(K(x,y),z,u) \ 1 = K(y,R(x \ 1,z,u) \ 1). K(x,R(y \ 1,z,u) \ 1) = R(K(y,x),z,u) \ 1. x != y * ((z \ u) * T((z \ u) \ (y \ u),w)) | x = (y * T(y \ z,w)) * (z \ u). K((x * (y \ 1)) \ 1,z) = (x * T(x \ y,z)) * (y \ 1). (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z). x * ((y \ (x \ 1)) * y) = K((x * y) \ 1,y). K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),T(x,z)). x * (K(x \ 1,y) * (x \ z)) = K(x \ 1,y) * z. x \ K(x * y,x \ 1) = y / (y / (x \ 1)). (x \ K(x * y,x \ 1)) \ y = y / (x \ 1). K(x,(y / z) \ 1) * z = y * ((x * (y \ z)) / x). (x * (y * ((z * (y \ (x \ u))) / z))) / u = K(z,((x * y) / u) \ 1). (x * y) \ (x * (y * x)) = (x * y) * (y \ 1). L(x,y,x) = (x * y) * (y \ 1). L(x,y,x) = L(x,y,y). L(x,y,y) = L(x,y,x). x * ((x \ 1) * y) = L(y,x,y). L(x,y,x) = y * ((y \ 1) * x). x != L(y,z,z) | x = L(y,y,z). L(x,y,x) = L(x,x,y). (x * y) * L(x,y,y) = x * (y * x). 1 / (x * (y * x)) = (y \ (y / x)) / (x * y). (x \ (x / y)) / (y * x) = 1 / (y * (x * y)). ((x \ (y / x)) \ ((x \ (y / x)) / x)) / (x * (x \ (y / x))) = 1 / (x * ((x \ 1) * y)). x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z). x \ T(x * y,z) = y * K(x * y,z). x * (y * K(x * y,z)) = T(x * y,z). x * (y * K(x * y,z)) != u | u = T(x * y,z). x * (y * K(x * y,z)) != u | T(x * y,z) = u. x \ (((x * y) \ 1) \ 1) = y * K(x * y,y \ (x \ 1)). x * K(y * x,x \ (y \ 1)) = y \ (((y * x) \ 1) \ 1). x * y != T(x * z,x \ 1) | y = (x * z) * (z / (x * z)). x * K(y * x,y \ 1) = (y * x) * (x / (y * x)). (x * y) * (y / (x * y)) = y * K(x * y,x \ 1). x != (y * (1 / z)) * (1 / z) | x = (z * (1 / y)) \ (1 / z). (x * (y \ 1)) * (y \ 1) = (y * (1 / x)) \ (1 / y). (x * (1 / y)) \ (1 / x) = (y * (x \ 1)) * (x \ 1). x * (((T(x,y) \ 1) \ 1) \ 1) = K(x,y \ (x \ 1)). (1 / (1 / T(x,y))) / x = K(1 / (x * y),x). K(1 / (x * y),x) != z | 1 / (x * (1 / T(x,y))) = z. (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z. (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K((x \ 1) \ 1,y) * z. x != y * ((z * (y \ u)) / z) | x = u * K(z,(u \ y) \ 1). K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1). K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u). (x * y) * (y \ (y / x)) = y * K(x * y,x \ 1). x * (1 / T(x,y)) = K(x,y \ (x \ 1)). K(x,y \ (x \ 1)) = x * (1 / T(x,y)). K(x,y \ K(y,z)) * z = z * K(x,(z \ (z * y)) \ 1). x != y * K(z * y,z \ 1) | x = z * (y * (1 / z)). (x * y) * (y \ (y / x)) = x * (y * (1 / x)). L(1 / x,y,x) = y \ (y / x). 1 / (x * (y * (1 / x))) = x * (1 / (x * y)). x != y \ (y / z) | x = L(1 / z,1 / z,y). L(1 / x,y,x) = L(1 / x,1 / x,y). L(1 / x,1 / x,y) = L(1 / x,y,x). x * L(1 / y,x,y) = x / y. L(1 / x,y,x) \ (1 / y) = ((y / x) \ y) * (1 / y). (x / y) / (L(1 / z,y,z) \ (1 / y)) = (y * (1 / x)) \ (y / z). x != L(1 / y,1 / y,z) | x = 1 / L(y,y,z). L(1 / x,y,x) = 1 / L(x,x,y). x * y != 1 / L(z,z,u) | L(1 / z,u,z) / y = x. L(1 / x,y,x) / z = 1 / (z * L(x,x,y)). (1 / (x / y)) * (y \ 1) = y * (1 / (y * x)). L(x * K(y,x),K(x * K(y,x),y),z) = (z * K(x,y)) \ (z * x). x != T(y * K(z \ y,y),z \ 1) | x = R(y,z \ 1,y). R(x,x \ (y \ x),x) = R(x,y \ 1,x). (1 / (1 / x)) \ y != z | ((x \ 1) \ 1) \ y = z. R(x * K(y \ x,x),z,u) \ R(x,z,u) = K(R(x,z,u),x * (y \ 1)). R(T(T(x,y),z * x),z,x) = T(T(x,y),z). 1 / (x * (1 / T(x,y))) = K(x * y,x \ 1). (T(x,y) \ 1) \ (1 / x) = K(x * y,x \ 1). x != y \ (1 / z) | x = ((z * y) \ z) * (1 / z). K(x * y,x \ 1) = ((x * (T(x,y) \ 1)) \ x) * (1 / x). ((x * (T(x,y) \ 1)) \ x) * (1 / x) = K(x * y,x \ 1). ((T(x,y) \ 1) * (T(x,y) \ 1)) * K(x * y,x \ 1) = ((T(x,y) \ 1) \ 1) \ (1 / x). x != ((y / z) \ y) * u | x = z * u. L(1 / x,y,x) \ (1 / y) = x * (1 / y). T(K(x,y) * K(x,z),K(x,y) \ K(z,x)) = ((K(x,z) * K(x,y)) \ 1) \ 1. (x \ R(y,z,u)) * K(((x \ R(y,z,u)) \ (x \ 1)) \ 1,w) = x \ R(T(y,w),z,u). ((1 / x) * y) \ ((z \ u) \ u) = (y \ x) / T(1 / z,u). R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1). R(K(x,y),z,u) = K(x,R(1 / y,z,u) \ 1). K(x,R(1 / y,z,u) \ 1) = R(K(x,y),z,u). K(x,R(y,z,u) \ 1) * (z * u) = (K(x,y \ 1) * z) * u. R(K(x,y),z,u) = K(x,R(y \ 1,z,u) \ 1). K(x,R(y \ 1,z,u) \ 1) = R(K(x,y),z,u). x != K(y,R(z \ 1,u,w) \ 1) | x = R(K(z,y),u,w) \ 1. R(K(x,y),z,u) = R(K(y,x),z,u) \ 1. R(K(x,y),z,u) \ 1 = R(K(y,x),z,u). T(x,R(y \ 1,z,u) \ 1) = x * R(K(x,y),z,u). (R(K(x,y),z,u) \ K(R(K(x,y),z,u) * w,R(K(y,x),z,u))) \ w = w / (R(K(x,y),z,u) \ 1). (x * y) * (x / (x * y)) = x * K(x * y,y \ 1). (1 / x) \ (y * K(z,z \ 1)) = x / ((y \ z) * (1 / z)). ((x * K(y,y \ 1)) \ z) * ((x \ y) * (1 / y)) = ((x \ y) * (1 / y)) * (z * ((x \ y) * (1 / y))). (x * K(y,y \ 1)) \ (1 / z) != u | ((x \ y) * (1 / y)) / z = u. K(x,(y / R(y,z,u)) \ x) = K(x,x * (y \ R(y,z,u))). L(x,y,y) / (x \ 1) = (y * ((x \ y) \ 1)) * x. (x * ((y \ x) \ 1)) * y = L(y,x,x) / (y \ 1). (x * ((y \ x) \ 1)) * y = (1 / L(y,x,x)) \ y. (x * ((y \ x) \ 1)) * y = (x \ (x / y)) \ y. (K(x,x \ 1) / y) * (K(x,x \ 1) * z) = (1 / y) * z. K(x \ 1,y) = T(K(x \ K(x,z),y),z). T(K(x \ K(x,y),z),y) = K(x \ 1,z). x * K(y \ 1,z) = K(y \ K(y,x),z) * x. K(x \ K(x,y),z) * y = y * K(x \ 1,z). K(x * y,T(x,z)) = K(y * x,T(x,z)). K(x * y,T(y,z)) = K(y * x,T(y,z)). x != y \ y | x = 1. K(x \ R(x,y,z),R(x,u,w)) = 1. K(x \ R(x,y,z),R(x,u,w)) != v5 | 1 = v5. K(x \ R(x,y,z),R(x,u,w)) * v5 != 1 | 1 = v5. 1 = K(R(x,y,z),x \ R(x,u,w)). K(R(x,y,z),x \ R(x,u,w)) = 1. (x * K((x \ y) \ 1,z)) * (x \ 1) = K((y * (x \ 1)) \ 1,z). ((x \ 1) \ 1) \ y = y * T(y \ (x \ y),T(x,z)). x * T(x \ (y \ x),T(y,z)) = ((y \ 1) \ 1) \ x. x * y != (1 / z) \ ((((1 / z) * x) \ 1) \ 1) | y = K(z \ x,x \ z). K((1 / x) * y,y \ ((1 / x) \ 1)) = K(x \ y,y \ x). K(x,y \ K(y,z)) * z = z * K(x,y \ 1). (K(x,y) \ y) * (1 / y) = K(y * x,y \ 1). T(x,y) * (1 / x) = K(x * y,x \ 1). K(x * y,x \ 1) = T(x,y) * (1 / x). x * y != T(z,u) * (1 / z) | x \ K(z * u,z \ 1) = y. T(x,y) \ K(x * y,x \ 1) = 1 / x. (1 / x) * ((1 / x) * (1 / K(x * y,x \ 1))) = 1 / (T(x,y) / (1 / x)). T(x,y) * (1 / x) != z | z = K(x * y,x \ 1). T(x,y) * (1 / x) != z | K(x * y,x \ 1) = z. (1 / x) * K(x \ 1,x * y) = T(x,y) \ 1. (1 / x) * K(x,(x * y) \ 1) = T(x,y) \ 1. (1 / x) * K(x,y \ (x \ 1)) = T(x,y) \ 1. ((x \ y) / T(1 / z,(1 / y) * x)) * (1 / ((1 / y) * x)) = (1 / ((1 / y) * x)) * ((z \ ((1 / y) * x)) \ 1). (x * (1 / (y * x))) * (K(x,x \ 1) * z) = (1 / y) * z. x \ K(y \ z,z \ y) = (x \ ((1 / y) * z)) * (((z \ y) \ 1) \ 1). (x \ ((1 / y) * z)) * (((z \ y) \ 1) \ 1) = x \ K(y \ z,z \ y). (x * (1 / (y * x))) \ z = K(x,x \ 1) * ((1 / y) \ z). K(x,x \ 1) * ((1 / y) \ z) = (x * (1 / (y * x))) \ z. ((1 / x) \ y) * K(z,z \ 1) = (z * (1 / (x * z))) \ y. x != L(T(y \ z,u) \ 1,y \ z,y) | x = T(y \ z,u) \ T((y \ z) * (z \ y),u). x \ (y * K(z,y \ x)) = T(y \ x,z) \ T((y \ x) * (x \ y),z). T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y)). L(K(x \ 1,y),z,u) != w | K(L(x,z,u) \ 1,y) = w. K(L(x,y,z) \ 1,u) = L(K(x \ 1,u),y,z). L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). L(K(x,y),z,u) = K(L(x \ 1,z,u) \ 1,y). K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). L(K(K(x,y),z),u,w) = K(L(K(y,x),u,w) \ 1,z). K(L(K(x,y),z,u) \ 1,w) = L(K(K(y,x),w),z,u). L(T(K(x,y),z),u,w) = K(L(T(1 / x,z),u,w) \ 1,y). K(L(T(1 / x,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u). K(((x * y) \ x) \ 1,z) = L(K(y,z),y,x). L(K(x,y),x,z) = K(((z * x) \ z) \ 1,y). L(K(x,y),z,u) \ 1 = K(y,L(x \ 1,z,u) \ 1). K(x,L(y \ 1,z,u) \ 1) = L(K(y,x),z,u) \ 1. x != K(y,L(z \ 1,u,w) \ 1) | x = L(K(y,z),u,w). L(K(x,y),z,u) \ 1 = L(K(y,x),z,u). x != L(K(y,z),u,w) \ 1 | x = 1 / L(K(y,z),u,w). L(K(x,y),z,u) = 1 / L(K(y,x),z,u). 1 / L(K(x,y),z,u) = L(K(y,x),z,u). L(K(x,y),z,u) \ 1 != w | w = L(K(y,x),z,u). L(K(x,y),z,u) \ 1 != w | L(K(y,x),z,u) = w. T(L(x,x \ y,x),z) = L(T(x,z),x \ T(y,x),x). L(T(x,y),x \ T(z,x),x) = T(L(x,x \ z,x),y). L(T(x,y),x \ T(z,x),x) = L(T(x,y),x \ z,x). R(L(T(x,y),x \ z,x),u,w) = L(R(T(x,y),u,w),x \ T(z,x),x). L(R(T(x,y),z,u),x \ T(w,x),x) = R(L(T(x,y),x \ w,x),z,u). R(K(x \ y,x),y,z) = K(((x * z) / (y * z)) \ 1,x). R(K(x \ (y / z),x),y / z,z) = K(((x * z) / y) \ 1,x). (K(x,y \ 1) * z) * u != w * (z * u) | K(x,R(y,z,u) \ 1) = w. ((x * y) / R(x,y,x)) * x = (y * x) * K(R(x,y,x),y * x). (x * y) * K(R(y,x,y),x * y) = ((y * x) / R(y,x,y)) * y. T(T(x * K(y * T(x,z),x),u),y) = R(T(y \ (y * x),u),y,T(x,z)). K((((x \ y) * z) / (y * z)) \ 1,u) = R(R(K(x,u),x,x \ y),y,z). R(R(K(x,y),x,x \ z),z,u) = K((((x \ z) * u) / (z * u)) \ 1,y). (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z. (1 / x) * (K(x,y) * z) = K(x,y) * ((1 / x) * z). K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z). x * y != (1 / z) * (K(z,u) * w) | T(x,y) = y \ (K(z,u) * ((1 / z) * w)). T(1 / x,K(x,y) * z) = (K(x,y) * z) \ (K(x,y) * ((1 / x) * z)). (K(x,y) * z) \ (K(x,y) * ((1 / x) * z)) = T(1 / x,K(x,y) * z). x * y != (1 / z) * (K(z,u) * w) | (K(z,u) * ((1 / z) * w)) / y = x. (K(x,y) * ((1 / x) * z)) / (K(x,y) * z) = 1 / x. (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K(x,y) * z. (x \ 1) * (K(x,y) * T(z,x \ 1)) = K(x,y) * (z * (x \ 1)). K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u). K(x,y) * (T(z,u) * K(y,x)) = T(K(x,y) * (z * K(y,x)),u). T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x)). K((x * ((1 / y) \ 1)) \ 1,z) / y = (1 / y) * K(((1 / y) \ x) \ 1,z). (x * y) * K(T(y,x),x * y) = ((y * x) / R(y,x,y)) * y. ((x * y) / R(x,y,x)) * x = (y * x) * K(T(x,y),y * x). x != (y * z) * K(T(z,y),y * z) | x = T(z,y * z) * T(y,z). ((x * y) / R(x,y,x)) * x = T(x,y * x) * T(y,x). (x / R(y,y \ x,y)) * y = T(y,(y \ x) * y) * T(y \ x,y). T(x,(x \ y) * x) * T(x \ y,x) = (y / R(x,x \ y,x)) * x. K(x,y) \ T(K(x,y) * z,u) = K(y,x) * T(K(y,x) \ z,u). T(K(x,y) * (z * K(y,x)),u) != K(x,y) * w | T(z,u) * K(y,x) = w. (x / y) / (z * (1 / y)) = (y * (1 / x)) \ (y / z). T(x,y) * T(x \ y,x) = (y / R(x,x \ y,x)) * x. (x / R(y,y \ x,y)) * y = T(y,x) * T(y \ x,y). x != T(y,z) * T(y \ z,y) | x = (y \ z) * T(y,z). (x / R(y,y \ x,y)) * y = (y \ x) * T(y,x). T(x * K(y,x),(x * K(y,x)) \ 1) = (x \ 1) \ K(y,x). T(x * K(y,x),x \ K(x,y)) = (x \ 1) \ K(y,x). (K(x,y) * (((1 / x) * z) * T(((1 / x) * z) \ z,u))) / (K(x,y) * z) = K((1 / x) \ 1,u). (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1). x != (y \ ((1 / z) * u)) * (((u \ z) \ 1) \ 1) | x = ((1 / z) * u) * ((((u \ z) / y) \ 1) \ 1). x \ K(y \ z,z \ y) = ((1 / y) * z) * ((((z \ y) / x) \ 1) \ 1). ((1 / x) * y) * ((((y \ x) / z) \ 1) \ 1) = z \ K(x \ y,y \ x). T(x \ y,z) * (y \ (x * K(z,x \ y))) = T((x \ y) * (y \ x),z). L(R(T(x,y),z,u),x \ T(w,x),x) = L(R(T(x,y),z,u),x \ w,x). L(T(1 / x,y),y,K(x,z)) = T(1 / x,K(x,z) * y). K(T(1 / x,K(x,y) * z) \ 1,u) = L(T(K(x,u),z),z,K(x,y)). L(T(K(x,y),z),z,K(x,u)) = K(T(1 / x,K(x,u) * z) \ 1,y). x != K(T(1 / y,z) \ 1,u) | x = T(K(y,u),z). L(T(K(x,y),z),z,K(x,u)) = T(K(x,y),K(x,u) * z). x != ((1 / y) * z) * ((((z \ y) / u) \ 1) \ 1) | x = K(z \ y,y \ z) * (u \ 1). x \ K(y \ z,z \ y) = K(z \ y,y \ z) * (x \ 1). K(x \ y,y \ x) * (z \ 1) = z \ K(y \ x,x \ y). R(x,y,L(x,z,u)) = T(x * K(y * L(x,z,u),x),y). T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u)). T(x,y) * K(y * L(x,z,u),T(x,y)) = R(x,y,L(x,z,u)). T(T(x * K(y * R(x,z,u),x),w),y) = R(T(y \ (y * x),w),y,R(x,z,u)). R(x,y,z) * (x * (R((u * x) / u,y,z) \ 1)) = x * K(R(x,y,z),u). x != R(y * K(z,y),u,w) \ R(y,u,w) | x = K(R(y,u,w),z). K(R(x,y,z),x * (u \ 1)) = K(R(x,y,z),u \ x). K(L(R(x,y,z),u,w),L(x,u,w) * (v5 \ 1)) = K(R(L(x,u,w),y,z),v5 \ L(x,u,w)). T(T(x * K(y * T(x,z),x),u),y) = R(T(x,u),y,T(x,z)). R(x,y,z) * (R((u * x) / u,y,z) \ x) = x * K(R(x,y,z),u). K(x \ (y * z),(x \ (y * z)) \ 1) = K(x \ (y * z),z \ (y \ x)). K(x \ (y * z),z \ (y \ x)) = K(x \ (y * z),(y * z) \ x). K(x \ (y * z),(y * z) \ x) = K(x \ (y * z),z \ (y \ x)). x != K(y \ (z * u),(z * u) \ y) | x = K(((y / u) / z) \ 1,y / (z * u)). K(x \ (y * z),z \ (y \ x)) = K(((x / z) / y) \ 1,x / (y * z)). K(((x / y) / z) \ 1,x / (z * y)) = K(x \ (z * y),y \ (z \ x)). x != K(((y / z) / u) \ 1,y / (u * z)) | x = K(((y / z) / u) \ 1,(y / z) / u). K(x \ (y * z),z \ (y \ x)) = K(((x / z) / y) \ 1,(x / z) / y). K(((x / y) / z) \ 1,(x / y) / z) = K(x \ (z * y),y \ (z \ x)). K(x \ (y * z),z \ (y \ x)) = K((x / z) \ y,y \ (x / z)). K((x / y) \ z,z \ (x / y)) = K(x \ (z * y),y \ (z \ x)). x != K(y \ (z * u),u \ (z \ y)) | x = K(y \ (z * u),(z * u) \ y). K((x / y) \ z,z \ (x / y)) = K(x \ (z * y),(z * y) \ x). K((x * y) \ 1,z) / y = (1 / y) * K(((1 / y) \ x) \ 1,z). (1 / x) * K(((1 / x) \ y) \ 1,z) = K((y * x) \ 1,z) / x. x != ((y * K(z * u,y)) * z) * u | x = (z * u) * R(y,z,u). ((x * y) * z) * a(z * K(x * y,z),x,y) = (x * y) * R(z,x,y). ((x * y) * z) \ ((x * y) * R(z,x,y)) != u | u = a(z * K(x * y,z),x,y). ((x * y) * z) \ ((x * y) * R(z,x,y)) != u | a(z * K(x * y,z),x,y) = u. K(x * (y * z),(z \ (y \ (x \ 1))) \ 1) = K(a(x,y,z),(y * z) \ (x \ 1)). x * L(y / (1 / (y \ x)),y \ x,y) = ((x \ 1) \ y) * (y \ x). x * L(y / ((1 / x) * y),y \ x,y) = ((x \ 1) \ y) * (y \ x). x * L(y \ (y / (1 / x)),y \ x,y) = ((x \ 1) \ y) * (y \ x). x * L(y * ((x \ y) \ 1),y \ x,y) = ((x \ 1) \ y) * (y \ x). x * (y * ((x \ y) \ 1)) = ((x \ 1) \ y) * (y \ x). ((x \ 1) \ y) * (y \ x) = x * (y * ((x \ y) \ 1)). x != y * (z * ((y \ z) \ 1)) | x = (z \ (z / y)) \ y. ((x \ 1) \ y) * (y \ x) = (y \ (y / x)) \ x. T(T(x * K(y * R(x,z,u),x),w),y) = R(T(x,w),y,R(x,z,u)). L(T(x * K(y,x),y),z,u) / (x * K(y,x)) = (K(x,y) / x) * L(x,z,u). L(x,y,z) / (x * K(u,x)) = (K(x,u) / x) * L(x,y,z). ((K(x,y) / x) * L(x,z,u)) \ L(x,z,u) = x * K(y,x). ((K(R(x,y,x),z) / R(x,y,x)) * x) \ L(R(x,y,x),y,x) = R(x,y,x) * K(z,R(x,y,x)). (x \ R(y,z,u)) * K((R(y,z,u) \ 1) \ 1,w) = x \ R(T(y,w),z,u). (x \ R(y,z,u)) * K(R(y,z,u),w) = x \ R(T(y,w),z,u). (x * (y * z)) \ (x * (y * T(z,u))) = L(K(L(z,y,x),u),L(z,y,x),x * y). L(K(L(x,y,z),u),L(x,y,z),z * y) = (z * (y * x)) \ (z * (y * T(x,u))). (((x / y) * y) \ (x / y)) / (y * (y \ (x / y))) = 1 / (y * ((y \ 1) * x)). (x \ (x / y)) / (y * (y \ (x / y))) = 1 / (y * ((y \ 1) * x)). (x \ (x / y)) / (x / y) = 1 / (y * ((y \ 1) * x)). ((x / y) * x) \ (x / y) = 1 / (y * ((y \ 1) * x)). ((x / y) * x) \ (x / y) = 1 / L(x,y,y). ((x / y) * x) \ (x / y) != z | y \ (y / x) = z. (T(x,y) \ (1 / T(x,y))) * K(x * y,x \ 1) = ((T(x,y) \ 1) \ 1) \ (1 / x). ((T(x,y) \ 1) \ 1) \ (1 / x) = (T(x,y) \ 1) * (T(x,y) \ K(x * y,x \ 1)). (T(x,y) \ 1) * (T(x,y) \ K(x * y,x \ 1)) = ((T(x,y) \ 1) \ 1) \ (1 / x). (T(x,y) \ 1) * (1 / x) = ((T(x,y) \ 1) \ 1) \ (1 / x). ((T(x,y) \ 1) \ 1) \ (1 / x) = (T(x,y) \ 1) * (1 / x). (K(x,y) * (K(x,z) * u)) / (K(x,y) * u) = K((1 / x) \ 1,z). (K(x,y) * (K(x,z) * u)) / (K(x,y) * u) = K(x,z). K(x,y) * (K(x,z) * u) = K(x,z) * (K(x,y) * u). K(x,y) * (z * K(x,u)) = K(x,u) * (K(x,y) * T(z,K(x,u))). K(x,y) * (K(x,z) * T(u,K(x,y))) = K(x,z) * (u * K(x,y)). K(x,y) * z = K(x,z) * (K(x,y) * T(z,x)). K(x,y) * (K(x,z) * T(y,x)) = K(x,z) * y. ((K(R(x,y,x),z) / R(x,y,x)) * x) \ x = R(x,y,x) * K(z,R(x,y,x)). x != R(y,z,u) * K(w,R(y,z,u)) | x = R(y * K(w,y),z,u). ((K(R(x,y,x),z) / R(x,y,x)) * x) \ x = R(x * K(z,x),y,x). x != (y * (1 / (z * y))) * (K(y,y \ 1) * u) | x = (1 / z) * u. L(x,y * (1 / (z * y)),y * (1 / (z * y))) = (1 / z) * (z * x). x != (1 / y) * (y * z) | x = L(z,y,y). L(x,y * (1 / (z * y)),y * (1 / (z * y))) = L(x,z,z). L(a(x,y,z),x * (y * z),u \ ((y * z) \ (x \ 1))) = u / (((x * y) * z) \ ((x * (y * z)) * u)). (x * (1 / (y * x))) \ ((((y \ x) \ 1) \ 1) * z) = ((y \ 1) \ 1) / (z \ ((y \ x) \ 1)). ((x * ((y / z) / x)) * z) * (y \ u) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u)). (x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) = ((x * ((u / z) / x)) * z) * (u \ y). x != (y * ((z / (u * (y \ z))) / y)) * (u * (y \ z)) | x = y * ((y \ T(y,u \ 1)) * (y \ z)). ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z)). T(x,y \ 1) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z)). x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z). x * ((x \ T(x,y)) * (x \ z)) = T(x,(y \ 1) \ 1) * (x \ z). T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z)). T(x,y) * (x \ z) = x * ((x \ T(x,y)) * (x \ z)). x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z). x * ((x \ T(x,y)) * z) = T(x,y) * (x \ (x * z)). T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z). T(x,y) * z = x * ((x \ T(x,y)) * z). x * ((x \ T(x,y)) * z) = T(x,y) * z. L(x,y \ T(y,z),y) = x. (T(x,y) * z) / ((x \ T(x,y)) * z) = x. x * (K(x,y) * z) = T(x,y) * z. L(x,y,y \ T(y,z)) = x. L(x,T(y,T(z,y)) \ y,z) = x. L(x,K(y,z),y) = x. x != y | x = L(y,z,K(u,u \ 1)). L(x,K(y,z),y) = L(x,u,K(w,w \ 1)). L(x,K(y,z),z) = x. L(x,K(y,z),1 / y) = x. K(x,y) * (1 / x) = K(x,y) / x. (x * K(y,x)) * z = x * (K(y,x) * z). L(x,y,K(y,z)) = x. L(x,y,K(y,z)) = 1 * x. (K(x,y) * x) * z = K(x,y) * (x * z). L(x,y,K(z,y)) = x. L(x,y / z,K(y,z)) = x. (K(x,y) * y) * z = K(x,y) * (y * z). (K(x,y) / x) * z = (1 / x) * (K(x,y) * z). (1 / x) * (K(x,y) * z) = (K(x,y) / x) * z. L(x,y,K(y,z)) != u | u = x. T(x,y) / y = K(x,y) * (x / y). K(x,y) * (x / y) = T(x,y) / y. L(x,y,K(z,y)) != u | u = x. L(x,T(y,z) \ y,(y * z) / y) = x. T(x,y) \ z = K(x,y) \ (x \ z). K(x,y) \ (x \ z) = T(x,y) \ z. x * y = T(x,z) * (K(x,z) \ y). T(x,y) * (K(x,y) \ z) = x * z. x != T(y,z) * L(y \ K(z,y),u,w) | x = T(y * L(y \ 1,u,w),z). x * (K(x,y) * L(x \ K(y,x),z,u)) = T(x * L(x \ 1,z,u),y). x * y != T(z,u) * K(z * u,z) | x \ R(z,u,z) = y. x \ R(x,y,x) = K(x,y) * K(x * y,x). K(x,y) * K(x * y,x) = x \ R(x,y,x). x \ y = K(x,z) * (T(x,z) \ y). K(x,y) * (T(x,y) \ z) = x \ z. (x / y) * z != T(x / y,u) * x | z = y * T(y \ x,u). K(x / y,z) * x = y * T(y \ x,z). x * y != T(x,z) * (u * x) | y = T(x,z) * T(u,x). K(x,y) * (z * x) = T(x,y) * T(z,x). x * y != T(x,z) * u | y = T(x,z) * (x \ u). K(x,y) * z = T(x,y) * (x \ z). T(x,y) * (x \ z) = K(x,y) * z. x * y != T(x,z) * (x * u) | y = u * T(T(x,u),z). K(x,y) * (x * z) = z * T(T(x,z),y). x * y != T(x,z) * T(z,x * z) | y = L(z,x,z). K(x,y) * T(y,x * y) = L(y,x,y). x * y != T(x,z) * T(z,z * x) | y = L(z,x,z). K(x,y) * T(y,y * x) = L(y,x,y). x * y != T(x,z) * (x * u) | y = T(x,z) * u. K(x,y) * (x * z) = T(x,y) * z. T(x,y) * z != x * u | K(x,y) * z = u. a(x,K(x,y) * z,u) = (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u). (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u). x * (y * K(x,z)) = T(x,z) * T(y,K(x,z)). T(x,y) * T(z,K(x,y)) = x * (z * K(x,y)). x \ (T(x,y) * z) != u | u = K(x,y) * z. x \ (T(x,y) * z) != u | K(x,y) * z = u. ((x * y) * (K(y,z) * u)) / (T(y,z) * u) != w | R(x,y,K(y,z) * u) = w. x * (K(y,x) * K(x,z)) = T(x,z) * K(y,x). (x / y) * K(x,y) = T(x,y) / y. (x \ y) / (T(x,z) \ y) = K(x,z). K(x,y) * (T(x,y) \ z) != u | u = x \ z. K(x,y) * (T(x,y) \ z) != u | x \ z = u. x * y != T(x,z) * u | K(x,z) \ y = u. T(x,y) * z != x * u | K(x,y) \ u = z. x \ y != K(x,z) * u | T(x,z) \ y = u. K(x / y,y) * ((y \ x) \ z) = (x / y) \ z. K(x,y) \ (x \ z) != u | u = T(x,y) \ z. K(x,y) \ (x \ z) != u | T(x,y) \ z = u. (x \ y) * T((x \ y) \ y,z) = K(x,z) * y. x != K(y,z) * K(y,u) | x = K(y,u) * K(y,z). T(x,y) * (x \ K(x,z)) = K(x,z) * K(x,y). T(x,y) \ z = x \ (K(x,y) \ z). x \ (K(x,y) \ z) = T(x,y) \ z. x != T(y,z) * u | x = y * (K(y,z) * u). K(x,y) * z = x * (K(x,y) * (x \ z)). x * (K(x,y) * (x \ z)) = K(x,y) * z. x != T(y,z \ y) * (y \ (z \ 1)) | x = (z * y) / ((z * y) * z). K(x,y \ x) * (y \ 1) = (y * x) / ((y * x) * y). (x * y) / ((x * y) * x) = K(y,x \ y) * (x \ 1). x * y != T(z,u) * (z \ w) | x \ (K(z,u) * w) = y. x \ (K(x,y) * z) = K(x,y) * (x \ z). T(x * y,z) * L(u,y,x) = K(x * y,z) * (x * (y * u)). K(x * y,z) * (x * (y * u)) = T(x * y,z) * L(u,y,x). (x \ y) * ((y / x) \ z) = K(y / x,x) * z. ((K(x,y) * z) \ T(x,y)) * T(x,y) = (x \ z) \ T(x,y). T(x,y) * K(x,z) = K(x,y) * T(x,z). K(x,y) * T(x,z) = T(x,y) * K(x,z). K(x,y) * (x * z) = x * (K(x,y) * z). K(x,x \ y) * (x * z) = ((x \ y) \ y) * z. K(R(x,y,z),u) * (R(x,y,z) * w) = R(T(x,u),y,z) * w. T(x,y) * (x \ z) != u | K(x,y) * z = u. K(x,y) * (L(z,u,w) * x) = T(x,y) * L(T(z,x),u,w). K(x,y) * (R(z,u,w) * x) = T(x,y) * R(T(z,x),u,w). (T(x,y) * z) \ (K(x,y) * (x * (z * u))) = L(L(u,z,x),x * z,K(x,y)). (K(x * y,z) * (x * (y * u))) \ (T(x * y,z) * u) = L(a(x,y,u),x * (y * u),K(x * y,z)). K(x \ 1,y) * ((1 / x) * z) = T(1 / x,y) * z. (L(x,y,z) \ u) / (L(T(x,w),y,z) \ u) = K(L(x,y,z),w). x * y != L(z,T(u,w) \ u,(u * w) / u) | x \ z = y. ((x * y) / x) \ z = y \ ((T(x,y) \ x) * z). x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z. T(x,x * y) * K(y,x) = L(x,y,x). x * y != K(z,u) * T(u,u * z) | x \ L(u,z,u) = y. (x * K(y,x)) \ L(x,y,x) = K(x,x * y). x * y != T(z,z * u) * K(u,z) | x \ L(z,u,z) = y. x \ L(x,y,x) = K(x,x * y) * K(y,x). K(x,x * y) * K(y,x) = x \ L(x,y,x). R(x,x \ T(x,y),z) = x. R(x,K(x,y),z) = x. L(x,y,z) * (K(x,u) * w) = (L(x,y,z) * K(x,u)) * w. (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w). R(x,K(y,x),z) = x. T(x,y) * (K(z,x) * u) = (T(x,y) * K(z,x)) * u. (T(x,y) * K(z,x)) * u = T(x,y) * (K(z,x) * u). L(x,K(y,z),y) != u | u = x. L(x,K(y,z),z) != u | u = x. ((x * y) / x) * z = y * (K(x,y) * z). (x / (x / y)) * z = y * (K(y \ x,y) * z). (x / y) * z = (y \ x) * (K(y,y \ x) * z). (x \ y) * (K(x,x \ y) * z) = (y / x) * z. K(x,R(y,x,z) \ 1) = K(x,y \ 1). R(K(x,y),x,z) = K(x,y). R(K(x,y),z,u) = K((((x \ z) * u) / (z * u)) \ 1,y). K((((x \ y) * z) / (y * z)) \ 1,u) = R(K(x,u),y,z). K(x,R(R(y,x,z),u,w) \ 1) = K(x,R(y,u,w) \ 1). R(K(x,y),y,z) = K(x,y). (x * K(y,x)) * z = K(y,x) * (x * z). ((x * y) / x) * z = K(x,y) * (y * z). K(x,y) * (y * z) = ((x * y) / x) * z. x * y != z * T(z \ x,u) | T(K(x / z,u),x) = y. T(K(x / y,z),x) = K((x \ y) \ 1,z). x * y != (z \ 1) * T((z \ 1) \ u,w) | (z \ T(z * u,w)) / y = x. (x \ T(x * y,z)) / y = K(y / (x \ 1),z). x * y != (z * u) * T((z * u) \ (z * w),v5) | (z * (u * T(u \ w,v5))) / y = x. (x * (y * T(y \ z,u))) / (x * z) = K((x * z) / (x * y),u). x * (y \ z) != z * T(z \ (y \ z),u) | x = K(y \ 1,u). K((x \ y) / y,z) = K(x \ 1,z). x * y != z * T(z \ y,u) | x = K((z / y) \ 1,u). K(x / y,z) = K((y / x) \ 1,z). K((x / y) \ 1,z) = K(y / x,z). x * y != (z * y) * T((z * y) \ y,u) | x = K(z \ 1,u). K(x / (y * x),z) = K(y \ 1,z). K((x * y) \ x,z) = K(y \ 1,z). K(1 / (x / y),z) = K(y / x,z). K(x * (y \ 1),z) = K(x / y,z). K(x / y,z) \ 1 = K(z,(y / x) \ 1). K(x,(y / z) \ 1) = K(z / y,x) \ 1. x != K(y \ 1,z) | x = K(y,z \ 1). K(x / (y * x),z) = K(y,z \ 1). K(x \ y,z) = K((y \ x) \ 1,z). K((x \ y) \ 1,z) = K(y \ x,z). K((x * y) \ y,z) = K(T(x,y) \ 1,z). K(T(x,y) \ 1,z) = K((x * y) \ y,z). K(x * (y * (z \ 1)),u) = K(x / (z / y),u). K(x * (y \ z),u) = K(x / ((1 / z) * y),u). K(x / ((1 / y) * z),u) = K(x * (z \ y),u). K(x \ y,z) = K(y / T(x,y),z). K(x / T(y,x),z) = K(y \ x,z). K(x \ y,z) = K(T(y,x) / x,z). K(T(x,y) / y,z) = K(y \ x,z). K(x \ y,z) = K(y \ x,z \ 1). K(x \ y,z \ 1) = K(y \ x,z). K(x / (y * x),z) != u | K(y \ 1,z) = u. K(x * y,z) = K((x \ 1) \ y,z). K((x \ 1) \ y,z) = K(x * y,z). K((x \ y) \ 1,(y \ x) \ 1) = K(y \ x,x \ y). K(((x * y) \ x) \ 1,z) = K(y,z). x != K((y \ z) \ 1,u) | x = y \ (z * T(z \ y,u)). K(x \ y,z) = y \ (x * T(x \ y,z)). x \ (y * T(y \ x,z)) = K(y \ x,z). x * y != K((z \ u) \ 1,w) | x \ K(u \ z,w) = y. (x \ y) \ K(y \ x,z) = T((x \ y) \ 1,z). K(L(x \ y,x,z) \ 1,u) = K((z * y) \ (z * x),u). K(x \ y,z) \ 1 = K(z,(y \ x) \ 1). K(x,(y \ z) \ 1) = K(z \ y,x) \ 1. x * T(x \ y,z) = y * K(x \ y,z). K((x \ 1) \ y,z) != u | K(x * y,z) = u. x \ T(x * y,z) = y * K((x \ 1) \ y,z). L(K(x \ y,z),u,w) = K(L(y \ x,u,w) \ 1,z). K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u). (1 / x) * K(y \ (1 / x),z) = K((y * x) \ 1,z) / x. K((1 / x) * y,z) = K(x \ y,z). K(T(x / y,x),z) = K(y \ x,z). x != K(y \ z,u) | x = K(z / T(y,z),u). K(T(x,y) / y,z) = K(x / T(y,x),z). K(x,(y \ z) * x) = K(z \ y,x). K(x \ y,z) = K(z,z * (y \ x)). K(x,x * (y \ z)) = K(z \ y,x). K(x \ y,x \ 1) != z | K(x,y) = z. T((x \ 1) \ y,z) = ((x \ 1) \ y) * K(x * y,z). ((x \ 1) \ y) * K(x * y,z) = T((x \ 1) \ y,z). x != K(((y * z) \ y) \ 1,u) | x = L(K(z,u),z,y). K(x,y) = L(K(x,y),x,z). L(K(x,y),x,z) = K(x,y). (1 / ((x * y) \ x)) * K(y,z) = T(1 / ((x * y) \ x),z). (x * y) * K(y,z) = x * T(y,z). a(x,y,K(y,z)) = 1. x != L(K(y,z),y,u) | x = (u * y) \ (u * T(y,z)). K(x,y) = (z * x) \ (z * T(x,y)). (x * y) \ (x * T(y,z)) = K(y,z). x != L(K(L(y,z,u),w),L(y,z,u),u * z) | x = (u * (z * y)) \ (u * (z * T(y,w))). K(L(x,y,z),u) = (z * (y * x)) \ (z * (y * T(x,u))). (x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u). (1 / x) \ L(K(x,y),z,u) = x * L(K(x,y),z,u). L(x \ T(x,y),x,z) = K(x,y). a(x,y,K(z,y)) = 1. a(x,y,K(y * z,z)) = 1. a(x,y,K(z,y * z)) = 1. a(x,y \ 1,K(y,z)) = 1. L(K(x,y),y,z) = K(x,y). L(K(x * y,y),x,z) = K(x * y,y). L(K(x,y * x),y,z) = K(x,y * x). L(K(x,y),x \ 1,z) = K(x,y). x != L(K(y,z \ u),z \ u,z) | x = K(y,(u \ z) \ 1). K(x,y \ z) = K(x,(z \ y) \ 1). K(x,(y \ z) \ 1) = K(x,z \ y). L(K(x,y),z,u) = L(L(K(x,y),z,u),y,w). L(L(K(x,y),z,u),y,w) = L(K(x,y),z,u). (x * y) * K(z,y) = x * (y * K(z,y)). x != L(y \ z,y,u / z) | x = ((u / z) * y) \ u. K(x,y) = ((z / T(x,y)) * x) \ z. ((x / T(y,z)) * y) \ x = K(y,z). x != L(K(y,z \ 1),u,w) | x = K(y,L(z,u,w) \ 1). K(x,y \ 1) = K(x,L(y,x \ 1,z) \ 1). K(x,L(y,x \ 1,z) \ 1) = K(x,y \ 1). (x * (y \ 1)) * K(y,z) = x * ((y \ 1) * K(y,z)). x != K(y \ z,y \ 1) | x = K(y,z). K((1 / x) * y,x \ 1) = K(x,y). K(x,y) = K(z \ ((1 / z) \ x),y). K(x \ ((1 / x) \ y),z) = K(y,z). (1 / x) * K(x \ (y \ 1),y) = (y \ (1 / x)) * y. K(T(x,y),z) = K((x \ y) \ y,z). K((x \ y) \ y,z) = K(T(x,y),z). K(x,x * (y \ z)) = K(x,(z \ y) \ x). K(x,(y \ z) \ x) = K(x,x * (z \ y)). R(x,y,K(y,z)) = x. x * K(y,z) = (x / y) * T(y,z). (x / y) * T(y,z) = x * K(y,z). (x * (y \ z)) * K(y \ z,y \ 1) = x * (z * (y \ 1)). R(x * y,K(y,x),K(x,z)) \ (y * T(x,z)) = K(y,x) * K(x,z). ((x * y) * T(z,u)) / ((y * z) * K(z,u)) = R(R(x,y,z),y * z,K(z,u)). x * K(T(x,y),z) = K(y,x) * T(T(x,y),z). K(x,y) * T(T(y,x),z) = y * K(T(y,x),z). (x * R(R(x,y,K(y,z)) \ (x * y),u,w)) * K(y,z) = R(x,y,K(y,z)) * (R(y,u,w) * K(y,z)). R(x,y,K(z,y \ 1)) = x. (x * y) * K(y,z) != u | u = x * T(y,z). (x * y) * K(y,z) != u | x * T(y,z) = u. K(x * (y \ z),x) = K(x,z \ y). K(x,1 / (y \ z)) = K(x,z \ y). x != K(y \ z,u \ 1) | x = K(z \ y,u). K(x \ y,z \ u) = K(y \ x,u \ z). x != K(y * (z * u),(u \ (z \ (y \ 1))) \ 1) | x = K(a(y,z,u),(z * u) \ (y \ 1)). K(x * (y * z),(y \ (x \ 1)) \ z) = K(a(x,y,z),(y * z) \ (x \ 1)). K(x,y \ 1) = K(x,(z * y) \ z). K(x,(y * z) \ y) = K(x,z \ 1). K(x,((y * z) \ y) \ 1) = K(x,z). K(x,a(y,z,u) \ 1) = K(x,((y * z) * u) \ (y * (z * u))). K(x,((y * z) * u) \ (y * (z * u))) = K(x,a(y,z,u) \ 1). K(x,(y \ (y / z)) \ 1) = K(x,z). K(x,y \ ((z / y) \ u)) = K(x,((y / u) * z) \ y). K(x,((y / z) * u) \ y) = K(x,y \ ((u / y) \ z)). (((x \ y) \ 1) \ x) * ((x \ y) \ 1) = x * K(y,y \ x). x * K(y,z \ x) = z * ((y * (z \ x)) / y). K(x,(y / z) \ 1) * z = z * K(x,y \ z). R(K(x,y \ z),u,w) = K(x,R(z \ y,u,w) \ 1). K(x,R(y \ z,u,w) \ 1) = R(K(x,z \ y),u,w). R(x,y \ z,K(u,z \ y)) = x. x \ (y * K(z,y \ x)) = (x \ y) * K(z,y \ x). x != ((y / z) * u) \ y | x = (1 / y) * ((u / y) \ z). K(x,y) = (1 / z) * ((x / z) \ T(x,y)). (1 / x) * ((y / x) \ T(y,z)) = K(y,z). x * y != ((z / T(u,w)) * u) \ z | x \ K(u,w) = y. (1 / x) \ K(y,z) = (y / x) \ T(y,z). K((x \ y) \ T(y,x),z) = K(x,z). x != K((y \ z) \ z,u) | x = T(K(y,u),z). K(T(x,y),z) = T(K(x,z),y). K(T(x,y),z) = K(T(x,y * x),z). K(T(x,y * x),z) = K(T(x,y),z). x != T(K(y,z),K(z,u)) | x = K(y,z). K(T(x,K(y,z)),y) = K(x,y). x != K(T(y,y \ z),u) | x = T(K(y,u),z). T(K(x,y),x \ z) = T(K(x,y),z). x * K(T(y,x),z) = K(y,z) * x. T(T(x,y),z) = T(K(x,z),y) * T(x,y). T(K(x,y),z) * T(x,z) = T(T(x,z),y). T(K(x,y),z) \ 1 = K(y,T(x,z)). T(K(x,y),z) \ 1 != u | K(y,T(x,z)) = u. (K(x,y) * z) * K(T(y,z),x) = z. T(T(x,K(y,z)),y) = K(x,y) * T(x,K(y,z)). K(x,y) * T(x,K(y,z)) = T(T(x,K(y,z)),y). T(x,x * T(y,K(x,z))) * K(y,x) = L(x,T(y,K(x,z)),x). (x * T(y,z)) / y = x * K(y,z). x / y = (x / T(y,z)) * K(y,z). (x / T(y,z)) * K(y,z) = x / y. x * y != ((z / T(u,w)) / u) * T(u,w) | x \ (z / u) = y. (x / T(y,z)) \ (x / y) = K(y,z). (x * K(y,z)) * y = x * T(y,z). (x * K(y,z)) \ (x * T(y,z)) = y. T(x * K(y,z),y) = y \ (x * T(y,z)). x \ (y * T(x,z)) = T(y * K(x,z),x). x != K(y,z) | x = K(z \ y,y). K(x * (y \ z),x) = K((z \ y) \ x,x). K((x \ y) \ z,z) = K(z * (y \ x),z). K(x,(1 / y) * z) = K(x,y \ z). K(x,T(y / z,y)) = K(x,z \ y). K(x,T(y \ 1,z)) = K(x,z \ (y \ z)). ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (x \ y),y \ x). K(x,y / z) = K(x,(z / y) \ 1). K(x,(y / z) \ 1) = K(x,z / y). K(x,y / (z * y)) = K(x,z \ 1). x != K(y,z) | x = L(K(y,z),z,u). K(x,((y * z) \ y) \ 1) = L(K(x,z),z,u). L(K(x,y),y,z) = K(x,((u * y) \ u) \ 1). x != K(y * z,z \ 1) | x = K((z \ 1) \ y,z \ 1). K(x * ((y * z) \ y),z) = K((((y * z) \ y) \ 1) \ x,((y * z) \ y) \ 1). K((((x * y) \ x) \ 1) \ z,((x * y) \ x) \ 1) = K(z * ((x * y) \ x),y). K(x,L(y,z,z)) = K(x,y). K(x,L(y,z \ 1,z)) = K(x,y). K(x,T(T(y,z),z \ 1)) = K(x,y). K(x,y * (z \ 1)) = K(x,y / z). K(x,y / (1 / z)) = K(x,y * z). K(x,(y \ 1) \ z) = K(x,y * z). K(x,T(y,y * z)) = K(x,T(y,z)). K(x,L(y,z,z \ 1)) = K(x,y). T(x,L(y,z,z)) = K(x,y) * x. K(x,L(y,z,y)) = K(x,y). K(x,y) = K(x,R(y,z,y)). K(x,R(y,z,y)) = K(x,y). x != K(y,z) | x = 1 / K(z,y). K(x,R(y,z,y)) = 1 / K(y,x). K(x,T(y,y \ z)) = K(x,T(y,z)). R(x,y,x) * K(z,x) = R(x * K(z,x),y,x). R(x * K(y,x),z,x) = R(x,z,x) * K(y,x). K(x,T(y * z,u)) = K(x,T((y \ 1) \ z,u)). K(x,T((y \ 1) \ z,u)) = K(x,T(y * z,u)). x != K(y,z) * y | x = T(y,z). T(x,L(y,z,z)) = T(x,y). T(x,L(y,z,z)) != u | T(x,y) = u. T(x,(1 / y) * z) = T(x,y \ z). T(x,y * (z \ 1)) = T(x,y / z). T(x,(y \ z) \ 1) = T(x,z \ y). T(x,(y \ z) / z) = T(x,y \ 1). T(x,(y * z) \ y) = T(x,z \ 1). T(x,y / (1 / z)) = T(x,y * z). T(x,(y \ 1) \ z) = T(x,y * z). T(x,T(y,y * z)) = T(x,T(y,z)). T(x,L(y,z,y)) = T(x,y). L(x,y,x) \ z = T(z / L(x,y,x),x). T(x / L(y,z,y),y) = L(y,z,y) \ x. L(x,y,x) * T(z,x) = z * L(x,y,x). T(x,y) = T(x,R(y,z,y)). T(x,R(y,z,y)) = T(x,y). R(x,y,x) \ z = T(z / R(x,y,x),x). T(x / R(y,z,y),y) = R(y,z,y) \ x. R(x,y,x) * T(z,x) = z * R(x,y,x). T(x,T(y,y \ z)) = T(x,T(y,z)). T(x,(y * z) / y) = T(x,y / (y / z)). K(x,R(y,z,y)) != u | K(x,y) = u. K(R(x,y,x),z) = K(x,z). K(T(x,y),z) = K(T(x,x * y),z). K(T(x,x * y),z) = K(T(x,y),z). T(x,y) = x * K(R(x,z,x),y). x * K(R(x,y,x),z) = T(x,z). T(R(x,y,x),z) = K(x,z) * R(x,y,x). K(x,y) * R(x,z,x) = T(R(x,z,x),y). ((K(x,y) / R(x,z,x)) * x) \ x = R(x * K(y,x),z,x). x * y != z * K(R(z,u,z),w) | x \ T(z,w) = y. R(x,y,x) \ T(x,z) = R((z * x) / z,y,x) \ x. R((x * y) / x,z,y) \ y = R(y,z,y) \ T(y,x). K(x,y \ 1) = K(T(x,L(y,z,u)),y \ 1). K(T(x,L(y,z,u)),y \ 1) = K(x,y \ 1). x * K(T(y,z),u) != K(y,u) * z | x = z. x * K(y,z) = K((x * y) / x,z) * x. K((x * y) / x,z) * x = x * K(y,z). K(x,K(y,z)) = K(y,z) * K(z,T(y,x)). K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). x != y * K(T(z,x),u) | K(u,z) * x = y. x * K(T(y,z),u) != z | K(u,y) * z = x. x * T(y * K(x,z),x) = y * T(x,z). (x * K(y,z)) * y != u | u = x * T(y,z). (x * K(y,z)) * y != u | x * T(y,z) = u. T(x * K(y,z),y) != u | y \ (x * T(y,z)) = u. (x \ (1 / y)) * K(x,x \ (y \ 1)) = (1 / y) / x. T(x \ 1,y) \ (1 / x) = K(x,x \ y). R(x,K(y,z),y) = x. x != K(y,z) * T(z,u) | x = T(z,u) * K(y,z). (K(x,y) * K(y,z)) * y = T(y,z) * K(x,y). x * y != (y \ z) * T(y,z) | x = z / R(y,y \ z,y). (x \ y) * K(x,y) = y / R(x,x \ y,x). x / R(y,y \ x,y) = (y \ x) * K(y,x). a(x,y * K(z,u),z) = (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z). (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z). L(x \ 1,x,y * K(x,z)) = (y * T(x,z)) \ (y * K(x,z)). T(x,y) * T(x,y) = x * T(T(x,y),y). R(x,K(y,z),z) = x. x * (y * K(z,y)) = (x * K(z,y)) * y. (x * K(y,z)) * z = x * (z * K(y,z)). L(x,K(x,y),z) = x. x != L(y * K(z,y),K(y * K(z,y),z),u) | x = (u * K(y,z)) \ (u * y). x * K(y,x) = (z * K(x,y)) \ (z * x). (x * K(y,z)) \ (x * y) = y * K(z,y). L(T(x,y),K(x,z),u) = T(x,y). (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w)). L(x,K(y,x),z) = x. (x * K(y,z)) * R(z,u,w) = x * (K(y,z) * R(z,u,w)). (x * K(y,z)) * L(z,u,w) = x * (K(y,z) * L(z,u,w)). L(T(x,y),z,u) = L(L(T(x,y),z,u),K(x,w),v5). L(L(T(x,y),z,u),K(x,w),v5) = L(T(x,y),z,u). (x * K(y,z)) * L(T(y,u),w,v5) != v6 | x * (K(y,z) * L(T(y,u),w,v5)) = v6. x != K(y,y \ z) | x = K(y,z / y). K(x,(1 / x) * y) = K(x,y / x). K(x,(y / z) * u) = K(x,(z * (y \ 1)) \ u). K(x,(y * (z \ 1)) \ u) = K(x,(z / y) * u). K(x,T(y,z)) = K(x,(y \ z) \ z). K(x,(y \ z) \ z) = K(x,T(y,z)). K(x * (y / z),x) = K(x,z / y). x != K(y,((z * y) / u) \ 1) | x = (z * (y * ((z \ u) / y))) / u. K(x,y / (z * x)) = (z * (x * ((z \ y) / x))) / y. (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y)). K(x,R(y / z,z,u) \ 1) = K(x,(z * u) / (y * u)). R(K(x,y / z),u,w) = K(x,R(z / y,u,w) \ 1). K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w). x != K(y,z \ 1) | x = K(y,1 / z). K(x,y / (z * y)) = K(x,1 / z). K(x,T(y,L(y,z,u) \ 1)) = K(x,y). K(x,T(y,z \ 1)) = K(x,T(y,z \ y)). K(x,T(y,z) \ 1) = K(x,T(y \ 1,z)). K(x,T(y,z * y)) = K(x,T(y,z)). K(x,T(y,y * x)) != z | K(x,y) = z. T(x,(1 / y) * z) != u | T(x,y \ z) = u. T(x,T(y,y \ 1)) != z | T(x,y) = z. T(x,y * (z \ 1)) != u | T(x,y / z) = u. T(x,(y \ z) \ 1) != u | T(x,z \ y) = u. T(x,(y * z) \ y) != u | T(x,z \ 1) = u. T(x,(y \ 1) \ z) != u | T(x,y * z) = u. T(x,y * z) != u | T(x,(y \ 1) \ z) = u. T(x,T(y,z) / z) = T(x,z \ y). T(x,T(y \ 1,z)) = T(x,z \ (y \ z)). T(x,(y * z) \ z) = T(x,z \ (y \ z)). T(x,y \ z) * (z \ y) = ((1 / y) * z) \ x. T(x,K(y,z \ 1) / z) = T(x,z \ K(y,z \ 1)). x != T(y / (z * (u \ (z / u))),z * (u \ 1)) | x = (1 / ((z * (u \ 1)) \ y)) \ (u / z). T(x / (y * (z \ (y / z))),y / z) = (1 / ((y * (z \ 1)) \ x)) \ (z / y). x != T(T(y,z / u),u * (z \ 1)) | x = R(y,z / u,u * (z \ 1)). T(T(x,y / z),z / y) = R(x,y / z,z * (y \ 1)). R(x,y / z,z * (y \ 1)) = T(T(x,y / z),z / y). T(x,(y / z) \ 1) = T(x,z / y). L(x,y \ z,y \ z) = T(T(x,y \ z),z \ y). T(T(x,y \ z),z \ y) = L(x,y \ z,y \ z). x != T(y,(z \ (u \ z)) \ 1) | x = T(y,T(u,z)). T(x,(y \ z) \ z) = T(x,T(y,z)). T(x \ y,y \ x) != z | ((x \ y) \ 1) \ 1 = z. ((x \ y) * T(z,y \ x)) * (x \ y) = (x \ y) * ((x \ y) * z). ((x \ y) \ 1) * ((x \ y) \ T(z,y \ x)) = ((x \ y) \ z) / (x \ y). T(x,y * (z * y)) = T(x,(y * z) * y). T(x,(y * z) * y) = T(x,y * (z * y)). T(x,T(y,z \ y)) = T(x,T(y,z \ 1)). T(x,T(y,z \ 1)) = T(x,T(y,z \ y)). K(x,(y \ 1) \ 1) != z | K(x,y) = z. K(x,T(y,y \ z)) != u | K(x,T(y,z)) = u. x != K(y,z / (1 / u)) | x = K(y,z * u). K(1 / x,(1 / (1 / x)) * y) = K(1 / x,y * x). K(x * (y / z),x) = K((z / y) \ x,x). K((x / y) \ z,z) = K(z * (y / x),z). K(x,y / (z * y)) != u | K(x,z \ 1) = u. 1 / T(x,y / z) = (z / y) / ((z / y) * x). (x / y) / ((x / y) * z) = 1 / T(z,y / x). T(x,y / z) * (z / y) = (1 / (z / y)) \ x. ((x \ y) \ y) \ z = T(z / ((x \ y) \ y),T(x,y)). T(x / ((y \ z) \ z),T(y,z)) = ((y \ z) \ z) \ x. K(x,y \ 1) != z | K(y,y * x) = z. x != K(y * z,z) | x = K(z * y,z). L(K(x * y,y),x,z) = K(y * x,y). K(x \ (x * y),z) != u | K(y,z) = u. T(x \ (y \ 1),y) = T(x,y) \ (1 / y). T(x,y) \ (1 / y) = T(x \ (y \ 1),y). K(x,(y \ K(z,u)) \ 1) != w | K(x,K(u,z) * y) = w. K(x \ y,z \ 1) != u | K(y \ x,z) = u. K(x * y,y) != z | K(x,x * y) = z. K(x * y,x) != z | z = K(y * x,x). K(x * y,x) != z | K(y * x,x) = z. L(K(x * y,x),y,z) = K(x * y,x). K((x / y) \ x,z) != u | K(y,z) = u. K((x \ y) \ (x \ 1),z) != u | K(y \ 1,z) = u. K(((x * y) \ x) \ 1,z) != u | K(y,z) = u. K(x,x / y) != z | K(y,x) = z. K(x,y \ x) != z | K(y,x) = z. K((x * y) * z,a(x,y,z)) != u | K(x * (y * z),(x * y) * z) = u. K(x,y) * (x * z) != u | T(x,y) * z = u. x != y * K(z,u) | x = (K(u,z) / y) \ 1. K(x,y) * T(x,z) = (K(z,x) / T(x,y)) \ 1. (K(x,y) / T(y,z)) \ 1 = K(y,z) * T(y,x). x != T(y,z) * K(y,u) | x = K(y,u) * T(y,z). K(x,y) * T(x,z) = K(x,z) * T(x,y). x != (y / z) * K(y,z) | x = T(y,z) / z. x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y. ((x * y) / x) * (x * z) = y * (T(x,y) * z). (x * K(y,x)) * (x \ z) = K(y,x) * z. x != (y * K(z,y)) * u | x = y * (K(z,y) * u). K(x,y) * (y * z) = y * (K(x,y) * z). (x / y) * z = K(y,y \ x) * ((y \ x) * z). K(x,x \ y) * ((x \ y) * z) = (y / x) * z. K(x,y) * z = ((x * y) / x) * (y \ z). ((x * y) / x) * (y \ z) = K(x,y) * z. K(x,(y / z) \ 1) != u | K(x,z / y) = u. x != K(T(y \ 1,z) \ 1,u) | x = T(K(y,u),z). K(((x \ 1) * y) \ y,z) = T(K(x,z),y). L(K(x \ (y \ z),u),y \ z,y) = z \ (y * (x * T(x \ (y \ z),u))). x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y). K(x,(y \ z) \ 1) != u | K(x,z \ y) = u. x \ (y * T(y \ x,z)) != u | u = K(y \ x,z). x \ (y * T(y \ x,z)) != u | K(y \ x,z) = u. K(T(x * K(y,x),z) / z,u) = K(((y * x) / y) / T(z,(y * x) / y),u). x != y * (z * K(u,z)) | x = y * ((u * z) / u). (x * y) * K(z,y) = x * ((z * y) / z). x != y * (z * K(y,z)) | x = T(y,z) * z. (x * y) * K(x,y) = T(x,y) * y. (x * (y \ z)) * K(y,y \ z) = x * (z / y). (x * (y * K(z,y))) * z = (x * y) * T(z,y). K(x,y \ x) = K(x,x * ((z * y) \ z)). K(x,x * ((y * z) \ y)) = K(x,z \ x). (1 / x) * (y * (x / y)) = K(y,y \ x). (1 / (x \ y)) \ K(y,z) = x \ T(y,z). K(x,T((y / z) \ 1,y)) = K(x,y \ z). x * (L(x,y,x) \ z) = (z / L(x,y,x)) * x. (x / L(y,z,y)) * y = y * (L(y,z,y) \ x). L(x,y,x) * (x \ z) = (z / x) * L(x,y,x). x * (R(x,y,x) \ z) = (z / R(x,y,x)) * x. (x / R(y,z,y)) * y = y * (R(y,z,y) \ x). (x * (R(x,y,x) \ z)) / x = z / R(x,y,x). R(x,y,x) * (x \ z) = (z / x) * R(x,y,x). ((x * y) / x) \ (z * y) = T((z / (y * K(x,y))) * y,x / (x / y)). T((x / (y * K(z,y))) * y,z / (z / y)) = ((z * y) / z) \ (x * y). K(x,y) * R(x,z,x) = R(T(x,y),z,x). K(x,K(y,z)) * K(z,y) = K(z,T(y,x)). K(x,y) * K(y,T(x,z)) = K(x * z,K(x,y)). x != T(y,z \ 1) * T(y,z \ 1) | x = ((1 / z) \ y) * (z \ (((1 / z) \ y) / z)). x * T(T(x,y \ 1),y \ 1) = ((1 / y) \ x) * (y \ (((1 / y) \ x) / y)). ((1 / x) \ y) * (x \ (((1 / x) \ y) / x)) = y * T(T(y,x \ 1),x \ 1). x != T(y,z \ 1) * T(y,z \ 1) | x = z * (y * (y * (z \ 1))). x * T(T(x,y \ 1),y \ 1) = y * (x * (x * (y \ 1))). x != y * (z * K(u,z)) | x = (y * z) * K(u,z). (x * K(y,z)) * z = (x * z) * K(y,z). (x * T(y,z)) * z = (x * y) * (z * K(y,z)). (x * y) * (z * K(y,z)) = (x * T(y,z)) * z. (x * y) / (y * K(z,y)) = x * K(y,z). x / (y * K(z,y)) = (x / y) * K(y,z). K(x,T(y,z \ u)) = K(x,T(y,(u \ z) \ y)). K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z)). T(x,T((y / z) \ 1,y)) = T(x,y \ z). T(x,y * (z \ y)) = T(x,(y / z) * ((z * K(z \ y,z)) * (y / z))). T(x,(y / z) * ((z * K(z \ y,z)) * (y / z))) = T(x,y * (z \ y)). K(x,y) * T(x,z) != K(x,z) * u | T(x,y) = u. (K(x,y) * T(x,z)) \ 1 = T(x,y) \ K(z,x). (x / y) * ((y \ x) \ z) = K(y,y \ x) * z. R(K(x,y),y * z,u) * ((y * z) * u) = (y * (K(x,y) * z)) * u. x * (K(y,x) * (x \ z)) != u | K(y,x) * z = u. (x * y) \ (y * (K(x,y) * (x * z))) = L(L(z,x,y),y * x,K(x,y)). x * y != K(z,u) * (z * w) | x \ (T(z,u) * w) = y. ((x * y) / x) \ (T(x,y) * z) = y \ (x * z). (1 / (x * y)) * ((y \ (x \ 1)) \ z) = K(x * y,y \ (x \ 1)) * z. K(x,x * (y / z)) = K(x,(z / y) \ x). K(x,(y / z) \ x) = K(x,x * (z / y)). x * (y * ((x \ 1) / y)) = K(y,y \ (x \ 1)). x * y != K(z,u) * R(z,w,z) | x \ R(T(z,u),w,z) = y. T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x). (x * y) / ((z * y) / z) = x * K(y,z). x / (y / z) = (x / (z \ y)) * K(z \ y,z). (x / (y \ z)) * K(y \ z,y) = x / (z / y). K(x,R(y,z,u) \ x) = K(x,x * ((z * u) / ((y * z) * u))). K(x,x * ((y * z) / ((u * y) * z))) = K(x,R(u,y,z) \ x). x != (y * z) / ((u * z) / u) | x = (y / (z * K(u,z))) * z. x * K(y,z) = (x / (y * K(z,y))) * y. (x / (y * K(z,y))) * y = x * K(y,z). (x / (y / (y / z))) * z = x * K(z,z \ y). (x / (y / z)) * (z \ y) = x * K(z \ y,z). K(x * y,x) * K(x,y) = x \ R(x,y,x). x \ R(x,y,x) != z | K(x * y,x) * K(x,y) = z. K(x,y) * K(y * x,x) = x \ R(x,y,x). K(x,y \ z) * K(x * ((z \ y) \ 1),x) = x \ R(x,(z \ y) \ 1,x). x \ R(x,y,x) != z | K(x,y) * K(x * y,x) = z. T(x,y) * z != u | K(x,y) * (x * z) = u. K(x,y) * K(y,y * x) = y \ L(y,x,y). K((x \ y) / y,z) != u | K(x \ 1,z) = u. T(x,L(y,x \ 1,z) \ 1) = x * K(x,y \ 1). ((x * y) * z) * K(y * z,u) != w | R(x,y,z) * T(y * z,u) = w. (x * (y * y)) * K(y,z) != u | ((1 / x) \ y) * T(y,z) = u. K(x,((y * z) \ y) \ 1) != u | u = K(x,z). K(x,((y * z) \ y) \ 1) != u | K(x,z) = u. (x * ((y * z) / y)) * y != u | (x * z) * T(y,z) = u. T(x,y * (z \ (u \ 1))) != w | T(x,y / (u * z)) = w. T(x,(y * z) / y) != u | T(x,y / (y / z)) = u. (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) != u | K(z,T(x,y)) = u. K(x,T(y,L(y,z,u) * (y \ w))) != v5 | K(x,T(y,L(y,z,u) * w)) = v5. K(x,y \ (y / z)) != u | K(x,z \ 1) = u. K((x \ y) \ 1,z) != u | K(y \ x,z) = u. K((x / y) \ 1,z) != u | K(y / x,z) = u. L(K(x,y),x,z) != u | K(x,y) = u. K(x,y) * (z * x) != u | T(x,y) * T(z,x) = u. K(x,y * (z \ 1)) != u | K(x,y / z) = u. (x * (y * ((x \ z) / y))) / z != u | K(y,z / (x * y)) = u. K(x,L(y \ z,y,u) \ 1) != w | K(x,(u * z) \ (u * y)) = w. K(x,1 / (y \ z)) != u | K(x,z \ y) = u. K(x,y) * K(y,y \ x) = y \ R(y,y \ x,y). x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y). K(x * y,y) * K(y,x) = y \ R(y,x,y). K(x,y * K(x,z)) * K(y * T(x,z),x) = x \ R(x,y * K(x,z),x). L(K(x,y),y,z) != u | K(x,y) = u. K(x,((y * z) * u) \ (y * (z * u))) != w | K(x,a(y,z,u) \ 1) = w. T(K(x / y,z),x) != u | K(y \ x,z) = u. K(x / y,z \ 1) != u | K(y / x,z) = u. R(K(x \ (y / z),x),y / z,z) != u | K(y / (x * z),x) = u. K(x,(1 / y) * z) != u | K(x,y \ z) = u. K(x,T(y / z,y)) != u | K(x,z \ y) = u. K(T(x / y,x),z) != u | K(y \ x,z) = u. K(x,y * z) != u | K(x,(y \ 1) \ z) = u. K(x,(y * z) \ z) != u | K(x,z \ (y \ z)) = u. K(x,((y / z) * u) \ y) != w | K(x,y \ ((u / y) \ z)) = w. K((1 / x) * y,z) != u | K(x \ y,z) = u. K(T(x,y) / y,z) != u | K(y \ x,z) = u. K(x / T(y,x),z) != u | K(y \ x,z) = u. K(x / (x \ y),z) != u | K((y / x) \ x,z) = u. K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z. x != T(y,z) * (y \ K(y,u)) | x = (y \ K(y,u)) * T((y \ 1) \ 1,z). K(x,y) * K(x,z) = (x \ K(x,y)) * T((x \ 1) \ 1,z). (x \ K(x,y)) * T((x \ 1) \ 1,z) = K(x,y) * K(x,z). (x \ y) * ((y / x) \ z) = K(x \ y,x) * z. x * (((y * x) / y) \ z) = (T(y,x) \ y) * z. (x \ y) \ z = K(x,x \ y) * ((y / x) \ z). K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z. (x \ y) * (T(x,x \ y) * z) = (y / x) * (x * z). (x * (y * (z \ 1))) * (1 / (x * (y * (z \ 1)))) = K(x / (z / y),(x * (y * (z \ 1))) \ 1). K((x / y) * x,z) = K(x * (y \ x),z). x != (y * z) * ((y * ((y * z) \ u)) / y) | x = (y * ((u / z) / y)) * z. x * K(y,(y * z) \ x) = (y * ((x / z) / y)) * z. (x * ((y / z) / x)) * z = y * K(x,(x * z) \ y). K(x,y / z) * y = y * K(x,z \ y). x * y != x * K(z,u \ x) | T(K(z,x / u),x) = y. T(K(x,y / z),y) = K(x,z \ y). x * y != y * K(T(z,y),u) | x = K(z,u). K(T(x,y),y / z) = K(x,z \ y). K(x,y \ z) * T(x,z) = T(T(x,z),z / y). K(x,R(T(x,y),z,u) / w) = K(x,w \ R(T(x,y),z,u)). x != R(y,z,u) * K(w,y) | x = K(w,y) * R(y,z,u). R(x * K(y,x),z,x) = K(y,x) * R(x,z,x). R(x * K(R(y \ 1,z,u) \ 1,x),w,x) = R(x,w,x) * R(K(y,x),z,u). x != K((y \ 1) * (1 / (z / u)),(u * (z \ 1)) \ y) | x = ((z / u) / (1 / y)) \ ((u * (z \ 1)) \ y). K((x \ 1) * (1 / (y / z)),(y / z) * x) = ((y / z) / (1 / x)) \ ((z * (y \ 1)) \ x). (x / y) * T(T(z,x / y),y / x) = (1 / (x / y)) \ z. (x / y) * z != (1 / (x / y)) \ u | T(T(u,y / x),x / y) = z. T(T(x,y / z),z / y) = L(x,z / y,z / y). L(T(x,y / z),u,w) * (z / y) = (1 / (z / y)) \ L(x,u,w). (x * y) / (1 / x) = y * (T(x,y) * x). (x * y) / (1 / x) = y * (x * T(x,y)). x != (y * z) / (1 / y) | x = y * (z * y). x * (y * T(y,x)) = y * (x * y). x * (y * (z * T(y * z,x))) = (y * z) * (x * (y * z)). x * y != (z * (u \ w)) * K(u,u \ w) | (z * (w / u)) / y = x. (x * (y / z)) / (z \ y) = x * K(z,z \ y). x * y != (z * (u * K(w,u))) * w | ((z * u) * T(w,u)) / y = x. ((x * y) * T(z,y)) / ((y * K(z,y)) * z) = R(x,y * K(z,y),z). (x / R(y,z,y)) * y != u | u = y * (R(y,z,y) \ x). (x / R(y,z,y)) * y != u | y * (R(y,z,y) \ x) = u. x != K(y,z) * K(z,T(y,u)) | x = K(u,K(y,z)). K(x * y,K(x,z)) = K(y,K(x,z)). K(x,K(y,z)) = K(y \ x,K(y,z)). K(x \ y,K(x,z)) = K(y,K(x,z)). K(x * y,K(x,z)) != u | K(y,K(x,z)) = u. K(x,K(y,z)) != u | K(y \ x,K(y,z)) = u. ((x * T(y,z)) * z) / (T(y,z) * z) = R(x,y,z * K(y,z)). (x / y) * ((y \ x) \ ((1 / K(y,y \ x)) \ z)) = (K(y,y \ x) * K(y,y \ x)) * z. ((x / y) * ((y \ x) \ K(y,y \ x))) * T(z,K(y,y \ x)) = (K(y,y \ x) * z) * K(y,y \ x). L(x,y \ z,T(y,z)) = z \ (y * ((y \ z) * x)). x \ (y * ((y \ x) * z)) = L(z,y \ x,T(y,x)). x * (y \ z) = (x * (z / y)) * K(y \ z,y). (x * (y / z)) * K(z \ y,z) = x * (z \ y). K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y)). (x \ y) * z = K(x \ y,x) * ((y / x) * z). K(x \ y,x) * ((y / x) * z) = (x \ y) * z. x * (((y * x) / y) \ z) = K(x,y) * z. x * y != K(x,z) * u | y = K(x,z) * (x \ u). ((x * y) / x) \ z = K(y,x) * (y \ z). x * y != K(x,z) * (x * u) | y = K(x,z) * u. ((x * y) / x) \ (y * z) = K(y,x) * z. x * y = K(x,z) * (((z * x) / z) * y). K(x,y) * (((y * x) / y) * z) = x * z. x * (y \ 1) = K(y,x) * (y \ x). K(x,y) * (x \ y) = y * (x \ 1). (x * K(y,x)) \ z = K(x,y) * (x \ z). x != K(y,z) * u | x = T(y,z) * (y \ u). ((x * y) / x) \ (y * z) = T(y,x) * (y \ z). x * y != K(z,u) * (((u * z) / u) * w) | x \ (z * w) = y. T(x,y) \ (x * z) = x \ (((y * x) / y) * z). x \ (((y * x) / y) * z) = T(x,y) \ (x * z). x / (K(y,z) * (y \ x)) = y * K(z,y). (x * K(y,x)) \ z != u | u = K(x,y) * (x \ z). (x * K(y,x)) \ z != u | K(x,y) * (x \ z) = u. K(T(x,y \ x) / y,z \ x) * (x / y) = T(T(T(x,y \ x) / y,x),x / z). x / (y \ z) = (x / (z / y)) * K(y,y \ z). (x / (y / z)) * K(z,z \ y) = x / (z \ y). x != (y \ z) * (z / y) | x = (z / y) * (y \ z). K(x \ y,x) * ((y / x) * (y / x)) = (y / x) * (x \ y). x != T(y,z) \ (y * u) | x = y * (T(y,z) \ u). x \ (((y * x) / y) * z) = x * (T(x,y) \ z). x != y \ (((z * y) / z) * u) | x = ((z * y) / z) * (y \ u). x * (T(x,y) \ z) = ((y * x) / y) * (x \ z). ((x * y) / x) * (y \ z) = y * (T(y,x) \ z). x != ((y * z) / y) * (z \ u) | x = K(y,z) * u. x * (T(x,y) \ z) = K(y,x) * z. x * y != ((z * u) / z) * (u \ w) | x \ (K(z,u) * w) = y. x \ (K(y,x) * z) = T(x,y) \ z. x * y != ((z * x) / z) * u | y = K(z,x) * u. T(x,y) \ z = K(y,x) * (x \ z). K(x,y) * (y \ z) = T(y,x) \ z. x != K(y,z) * K(u,z) | x = K(u,z) * K(y,z). x * (T(x,y) \ K(z,x)) = K(z,x) * K(y,x). x * y != K(z \ u,z) * R(T(z,z \ u),w,v5) | x \ (u \ ((R(z,w,v5) * (z \ u)) * z)) = y. x \ (y \ ((R(x,z,u) * (x \ y)) * x)) = T(x,x \ y) \ R(T(x,x \ y),z,u). T(x,x \ y) \ R(T(x,x \ y),z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x)). x * y != K(z,x) * (x * u) | y = K(z,x) * u. T(x,y) \ (x * z) = K(y,x) * z. x * y = K(z,x) * (T(x,z) * y). K(x,y) * (T(y,x) * z) = y * z. (x * x) \ (K(y,x) * z) = (1 / x) * (T(x,y) \ z). T(x,y) * (K(y,x) * z) = x * z. K(x,y) * (K(z,y) * u) = y * (K(x,y) * (T(y,z) \ u)). x * (K(y,x) * (T(x,z) \ u)) = K(y,x) * (K(z,x) * u). T(x,y) * (T(x,z) \ u) != w | K(x,y) * (K(z,x) * u) = w. K(x \ y,x) * (x \ z) = ((x \ y) \ y) \ z. ((x \ y) \ y) \ z = K(x \ y,x) * (x \ z). K(x \ y,1 / x) * ((1 / x) \ z) = (1 / T(x,y)) \ z. K(x,y) * K(y,z) = T(y,x) \ T(y,z). T(x,y) \ T(x,z) = K(y,x) * K(x,z). K(x,y) * (T(y,x) \ z) = T(T(y,x),x) \ z. (x * y) / (T(x,z) * y) = K(z,x). K(x,y) \ (y * z) = T(y,x) * z. L(T(x,y),z,u) \ (L(x,z,u) * w) = K(y,L(x,z,u)) * w. K(x,y) * z != u | y * (T(y,x) \ z) = u. K(x,y) \ (y * z) != u | u = T(y,x) * z. K(x,y) \ (y * z) != u | T(y,x) * z = u. (x * y) \ (K(z,x) * (T(x,z) * (y * u))) = L(L(u,y,T(x,z)),T(x,z) * y,K(z,x)). L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) = (z * y) \ (K(u,z) * (T(z,u) * (y * x))). x * (y * z) = T(x,y) * (T(y,x) * z). T(x,y) * (T(y,x) * z) = x * (y * z). K(x,y) \ z = K(y,x) * z. K(x,y) * (K(y,x) * z) = z. K(x,y / z) * (z * T(z \ y,x)) = y. T(x,y) * z != x * (K(u,x) * K(x,y)) | z = K(u,x). K(x,y) * (K(z,y) * K(y,x)) = K(z,y). (x \ y) * (K(y,y * (x \ 1)) * z) = (y * (x \ 1)) * z. T(x \ y,x) * (K(y,(1 / x) * y) * z) = ((1 / x) * y) * z. T(x \ y,z) * ((y \ x) * K(z,x \ y)) = (x \ y) * (y \ x). K(x,y) / (z \ 1) = K(x,y) * z. K(x,y) / z = K(x,y) * (1 / z). K(x,y) * (1 / z) = K(x,y) / z. (K(x,y) * K(z,u)) \ 1 = K(u,z) * K(y,x). (x * K(y,z)) \ x = K(z,y). x / (K(y,z) * x) = K(z,y). x * y != K(z,u) * w | T(x,y) = y \ (K(u,z) \ w). T(K(x,y),z) = z \ (K(y,x) \ z). x \ (K(y,z) \ x) = T(K(z,y),x). x != K(y,z) * u | x = u * K(T(y,u),z). K(x,y) \ z = z * K(T(y,z),x). x * K(T(y,x),z) = K(z,y) \ x. K(x,y) \ K(z,x) = K(z,x) * K(y,x). x != y * ((z * u) * y) | x = ((1 / y) \ z) * (u * y). K(x,y) \ ((z * u) * K(y,x)) = ((1 / K(y,x)) \ z) * (u * K(y,x)). ((1 / K(x,y)) \ z) * (u * K(x,y)) = K(y,x) \ ((z * u) * K(x,y)). x != K(y \ z,z) \ ((1 / y) * z) | x = z / y. K(x,y \ x) * ((1 / y) * x) = x / y. x * y != K(z,u) \ x | T(K(u,z),x) = y. T(K(x,y),z) = T(K(y,x),z) \ 1. T(K(x,y),z) \ 1 = T(K(y,x),z). K(x,y) * (K(y,x) * z) != u | u = z. x / (K(y,z) * x) != u | u = K(z,y). x / (K(y,z) * x) != u | K(z,y) = u. 1 / (K(x,y) * z) = (1 / z) * K(y,x). (K(x,y) \ z) * L(u,z,K(y,x)) = K(y,x) * (z * u). L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u. L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u. R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(y,z) \ u). (1 / x) * ((K(y,z) * (1 / x)) \ u) = (K(z,y) * (u / x)) * x. R(K(x,y) * R(K(y,x),z,u),K(y,x),z * u) = ((K(y,x) * z) * u) / (K(y,x) * (z * u)). (K(x,y) \ 1) \ z = K(x,y) * z. T(K(x,y) * z,K(x,y)) = z * K(x,y). (K(x,y) \ z) * K(x,y) = T(z,K(x,y)). K(x,y \ 1) \ z = K(y,x \ 1) * z. K(x,y) * (1 / z) != u | K(x,y) / z = u. T(K(x,y) * z,K(x,y)) != u | z * K(x,y) = u. L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z). K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y)). K(x,y) * (y \ z) != u | T(y,x) \ z = u. K(x,(K(y,z) * u) \ 1) != w | K(x,u \ K(z,y)) = w. K(x,y) * z != K(x,u) * T(x,y) | z = T(x,u). K(x,y) * (K(y,z) * T(y,x)) = T(y,z). K(x,y) * z != K(u,K(x,y)) | z = K(y,T(x,u)). K(x,y) * K(z,K(y,x)) = K(x,T(y,z)). K(x,y) * z != K(x,u) * (K(x,y) * w) | z = K(x,u) * w. K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u. K(x,y) * z != K(y,u) * K(x,y) | z = K(y,u). K(x,y) * (K(x,z) * K(y,x)) = K(x,z). x != K(y,z) * u | K(z,y) * x = u. K(x,y) * z != u | K(y,x) * u = z. K(x,y) \ z != u | u = K(y,x) * z. K(x,y) \ z != u | K(y,x) * z = u. R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(z,y) * u). x \ 1 = (K(y,z) * x) \ K(y,z). (K(x,y) * z) \ K(x,y) = z \ 1. x * y != (z * K(u,w)) \ z | K(w,u) / y = x. K(x,y) / (1 / z) = (z \ K(y,x)) \ 1. (x * K(y,z)) * K(z,y) = x. x / K(y,z) = x * K(z,y). x * K(y,z) != u | x = u * K(z,y). x * K(y,z) != u | u * K(z,y) = x. (x * K(y,z)) * K(z,y) != u | u = x. x / K(y,z) != u | u = x * K(z,y). x / K(y,z) != u | x * K(z,y) = u. (K(x,y) * z) \ z = K(y,T(x,z)). (x / y) \ (x / T(y,z)) = K(z,y). (x * T(x \ y,z)) \ y = K(z,x \ y). T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z). x / (y * T(y \ x,z)) = K(z,x / y). K(x,y) * z = z * K(x,T(y,z)). x * K(y,T(z,x)) = K(y,z) * x. (K(x,y) * z) * K(y,T(x,z)) = z. K(x,y) * z != u | T(u * K(y,x),K(x,y)) = z. T(x * K(y,z),K(z,y)) = K(y,z) * x. x * K(y,z) != u / y | x = u / T(y,z). (x / y) * K(z,y) = x / T(y,z). x * K(y,z) != u * T(y,z) | x = u * y. (x * T(y,z)) * K(z,y) = x * y. x * K(y,z) != T(u,K(y,z)) | x = K(z,y) * u. T(x,K(y,z)) * K(z,y) = K(z,y) * x. x * K(y,z) != u \ 1 | x = u \ K(z,y). (x \ 1) * K(y,z) = x \ K(y,z). x * y != (z * K(u,w)) * K(w,u) | z / y = x. x / T(y,z) = (x * K(z,y)) / y. (x * K(y,z)) / z = x / T(z,y). a(x,y * K(z,u),K(u,z)) = (x * y) \ ((x * (y * K(z,u))) * K(u,z)). (x * y) \ ((x * (y * K(z,u))) * K(u,z)) = a(x,y * K(z,u),K(u,z)). (x * K(y,z)) \ x != u | u = K(z,y). (x * K(y,z)) \ x != u | K(z,y) = u. x * L(y,K(z,u),x * K(u,z)) = (x * K(u,z)) * (K(z,u) * y). x \ ((x * K(y,z)) * (K(z,y) * u)) != w | L(u,K(z,y),x * K(y,z)) = w. x * y = (x * K(z,y)) * T(y,z). (x * K(y,z)) * T(z,y) = x * z. x != y * K(z,u) | x = T(K(u,z) \ y,K(z,u)). x / K(y,z) = T(K(y,z) \ x,K(z,y)). T(K(x,y) \ z,K(y,x)) = z / K(x,y). x / K(y,z) != x * u | K(z,y) = u. R((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y). ((K(x,y) / z) * u) \ K(x,y) = K(y,x) * ((u * K(y,x)) \ z). (1 / x) * ((1 / x) * (1 * K(x \ 1,x * y))) = 1 / (T(x,y) / (1 / x)). (R(x,y,z) * u) / (R(T(x,w),y,z) * u) = K(w,R(x,y,z)). K(x,y) / (z \ u) = K(x,y) * ((1 / u) * z). K(x,y) * ((1 / z) * u) = K(x,y) / (u \ z). K(x,y) = L(K(x,y),z,z). L(K(x,y),z,z) = K(x,y). R(x,K(y,z),1 / u) = ((x * K(y,z)) * (1 / u)) / (K(y,z) / u). ((x * K(y,z)) * (1 / u)) / (K(y,z) / u) = R(x,K(y,z),1 / u). L(K(x,y),z \ 1,z) = K(x,y). L(K(x,y),z,1 / z) = K(x,y). (1 / x) * (x * K(y,z)) = K(y,z). x * y != L(K(z,u),w,w) | x \ K(z,u) = y. (x * y) \ K(z,u) = (y \ (x \ 1)) * K(z,u). (x \ (y \ 1)) * K(z,u) = (y * x) \ K(z,u). (1 / x) \ K(y,z) = x * K(y,z). ((1 / x) * y) \ K(z,u) = (y \ x) * K(z,u). (x * x) * K(y,z) = x * (x * K(y,z)). x * ((x \ y) * K(z,u)) = x / (K(z,u) \ (y \ x)). x / (K(y,z) \ (u \ x)) = x * ((x \ u) * K(y,z)). L(K(x,y),z \ 1,z) = u \ (u * K(x,y)). K(x,x \ 1) * K(y,z) = x * ((1 / x) * K(y,z)). (1 / x) \ K(y,z) != u | x * K(y,z) = u. (1 / x) \ L(K(y,z),u,w) = x * L(K(y,z),u,w). K(x,y) * (z * L(T(K(y,x),z),u,w)) = (K(x,y) * L(K(x,y) \ 1,u,w)) * z. K(x,y) * (z * R(T(K(y,x),z),u,w)) = (K(x,y) * R(K(x,y) \ 1,u,w)) * z. x != y * K(z,u) | x = y / K(u,z). K(x,y) \ z = z / K(x,T(y,z)). x / K(y,T(z,x)) = K(y,z) \ x. K(x,T(y,z)) = T(K(x,y),z). K(x,y * K(z,y \ 1)) = T(K(x,y),z). (x * T(K(y,z),u)) * T(K(z,y),u) = R(x,T(K(y,z),u),T(K(y,z),u) \ 1). R(x,T(K(y,z),u),T(K(y,z),u) \ 1) = (x * T(K(y,z),u)) * T(K(z,y),u). T(K(x,y),z) != u | K(x,T(y,z)) = u. x != T(K(y,z),u) | x = K(T(y,u),z). K(x,T(y,z)) = K(T(x,z),y). K(T(x,y),z) = K(x,T(z,y)). x != T(K(y,z),u) | x = K((y \ u) \ u,z). K(x,T(y,z)) = K((x \ z) \ z,y). K((x \ y) \ y,z) = K(x,T(z,y)). x != T(K(y \ 1,z),u) | x = K(T(y,u) \ 1,z). K(x \ 1,T(y,z)) = K(T(x,z) \ 1,y). K(T(x,y) \ 1,z) = K(x \ 1,T(z,y)). x != T(K(y,z),y \ u) | x = T(K(y,z),u). K(x,T(y,x \ z)) = T(K(x,y),z). x != T(K(y / z,u),y) | x = K(z \ y,u). K(x / y,T(z,x)) = K(y \ x,z). x != T(K(y,z),K(y,u)) | x = K(y,z). K(x,T(y,K(x,z))) = K(x,y). x != T(K(y,z),R(y,u,w)) | x = K(y,z). K(x,T(y,R(x,z,u))) = K(x,y). x != T(K(y,z),T(T(y,u),w)) | x = K(y,z). K(x,T(y,T(T(x,z),u))) = K(x,y). x * K(y,T(z,u)) = x * T(K(y,z),u). x != K(y,T(z,u)) | x = K(u,K(z,y)) * K(y,z). T(K(x,y),z) = K(z,K(y,x)) * K(x,y). K(x,K(y,z)) * K(z,y) = T(K(z,y),x). x != K(y,T(z \ 1,u)) | x = K(y,T(z,u) \ 1). T(K(x,y \ 1),z) = K(x,T(y,z) \ 1). K(x,T(y,z) \ 1) = T(K(x,y \ 1),z). x != K(y,T(z,u)) | x = K(y,T(z,z \ u)). T(K(x,y),z) = K(x,T(y,y \ z)). K(x,T(y,y \ z)) = T(K(x,y),z). K(x,T(T(y,z),u)) = T(K(x,T(y,u)),z). x * (y * K(z,T(u,x * y))) = L(K(z,u),y,x) * (x * y). T(x,K(y,T(z,x))) = T(x,K(y,z)). K(x,R(T(K(x,y),z),u,w)) = 1. T(x,T(y,z)) = x * T(K(x,y),z). x * T(K(x,y),z) = T(x,T(y,z)). x * T(K(x,y),z) != u | T(x,T(y,z)) = u. K(x,T(y,z)) \ T(u / (u / K(x,y)),z) = K(K(x,y) \ u,T(K(x,y),z)). K(x,T(y,z)) \ 1 = K(y,T(x,z)). K(x,T(y,z)) * T(x,z) = T(T(x,z),y). K(x,K(y,T(z,u))) = T(K(x,K(y,z)),u). x * K(T(y,z),u) = x * K(y,T(u,z)). x != K(y,z) | x = (u * K(z,y)) \ u. K(x,T(y,z)) = (u * K(y,T(x,z))) \ u. (x * K(y,T(z,u))) \ x = K(z,T(y,u)). x != K(T(T(y,z),u),w) | x = T(T(y * K(w,y),z),u) \ T(T(y,z),u). K(T(x,y),T(z,u)) = T(T(x * K(z,x),y),u) \ T(T(x,y),u). T(T(x * K(y,x),z),u) \ T(T(x,z),u) = K(T(x,z),T(y,u)). x != K(T(y,y * z),u) | x = K(T(y,z),u). K(x,T(y,x * z)) = K(T(x,z),y). x * y != K(T(z,u),w) | x \ K(z,T(w,u)) = y. x \ K(y,T(x,z)) = T(x,T(y,z)) \ 1. T(x,T(y,z)) \ 1 = x \ K(y,T(x,z)). K(T(x,y),T(z,u)) = K(x,T(T(z,y),u)). K(R(T(x,y),z,u),w) = K(R(x,z,u),T(w,y)). K(x \ y,z) = K(y / x,T(z,x)). K(x / y,T(z,y)) = K(y \ x,z). K(T(x,y),z / y) = K(x,y \ z). K(x,y) = K((z * x) / z,T(y,z)). K((x * y) / x,T(z,x)) = K(y,z). K(T(x,y),L(y,z,u)) = K(x,L(y,z,u)). K(L((x \ y) \ y,z,u),w) = K(L(x,z,u),T(w,x \ y)). K(x,y) = K(x,T(y,R(T(x,z),u,w))). K(x,T(y,R(T(x,z),u,w))) = K(x,y). x * K(T(x,y),z) != u | T(x,T(z,y)) = u. 1 / (x \ K(y,T(x,z))) != u | T(x,T(y,z)) = u. K(x,T(y,z)) * T(x,z) = T(T(x,y),z). a(x,y,K(z,T(y,u))) = 1. K(x,T(y,z)) * (y \ u) = T(y,T(x,z)) \ u. K(x,T(y,z)) \ u = K(y,T(x,z)) * u. x / K(y,T(z,u)) = x * K(z,T(y,u)). L(K(x,T(y,z)),y,u) = K(x,T(y,z)). a(x,T(y,z),K(u,y)) = 1. L(K(x,y),T(y,z),u) = K(x,y). K(x,R(T(y,K(x,z)),u,w)) = K(x,R(y,u,w)). K(x,R(x,y,z) \ u) = K(x,u / R(x,y,z)). K(x,y / R(x,z,u)) = K(x,R(x,z,u) \ y). K(x,y \ R(x,z,u)) = K(x,R(x,z,u) * (y \ 1)). K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z)). K(x,R(x,y,z) / u) != w | K(x,u \ R(x,y,z)) = w. x != L(K(y * z,y),T(y,z),u) | x = (u * T(y,z)) \ (u * R(y,z,y)). K(x * y,x) = (z * T(x,y)) \ (z * R(x,y,x)). (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y). (x * T(y,z)) * L(K(u,y),w,v5) != v6 | x * (T(y,z) * L(K(u,y),w,v5)) = v6. (K(x,y \ 1) * y) * (1 / y) = y * (((T(y,x \ 1) \ 1) \ 1) \ 1). (x \ 1) \ K(y,z) = ((x * K(y,z)) \ 1) \ 1. ((x * K(y,z)) \ 1) \ 1 = (x \ 1) \ K(y,z). K(x,T(y,z)) != u | T(K(x,y),z) = u. (x / y) * K(z,y) != u | u = x / T(y,z). (x / y) * K(z,y) != u | x / T(y,z) = u. x * y != K(z,u) * w | x \ (w * K(z,T(u,w))) = y. x \ (y * K(z,T(x,y))) = T(x,z) \ y. x * (y * K(z,T(u,y))) = x * (K(z,u) * y). K(x,y) * z != u | z = K(y,x) * u. x = K(y,z) * (x * K(z,T(y,x))). K(x,y) * (z * K(y,T(x,z))) = z. K(x,y) * z != z * u | K(x,T(y,z)) = u. T(x,y) * K(z,T(x * y,x)) = K(z,x * y) * T(x,y). K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z). (x \ y) * K(x,y) = K(x,y) * (x \ y). K(x,y) * (x \ y) = (x \ y) * K(x,y). x * K(y,K(z,T(u,x))) = K(y,K(z,u)) * x. x != ((y * z) / y) * u | x = z * (K(y,z) * u). (x * y) / T(x,z) = y * (K(x,y) * K(z,x)). x * (K(y,x) * K(z,y)) = (y * x) / T(y,z). x * y != (z / u) * K(w,u) | (z / T(u,w)) / y = x. (x / T(y,z)) / T(z,y) = (x / y) / z. x * y != (z / u) * K(w,u) | x \ (z / T(u,w)) = y. x \ (y / T(y / x,z)) = K(x \ y,x) * K(z,y / x). K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z)). x * K(y,z) = (x / T(z,y)) * z. (x / T(y,z)) * y = x * K(z,y). x * K(y,z) != (K(y,z) * K(z,u)) * z | x = T(z,u). (K(x,y) * K(y,z)) * T(y,x) = T(y,z). T(x / T(y,z),y) = y \ (x * K(z,y)). x \ (y * K(z,x)) = T(y / T(x,z),x). (((x * y) * T(z,u)) * K(u,z)) / (y * z) = R(R(x,y,T(z,u)),y * T(z,u),K(u,z)). R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = (((x * y) * T(z,u)) * K(u,z)) / (y * z). (x * y) * z = (x * T(y,z)) * T(z,y). (x * T(y,z)) * T(z,y) = (x * y) * z. K(x,y) * z != u \ K(x,y) | T(u \ 1,K(x,y)) = z. T(x \ 1,K(y,z)) = T(x,K(y,z)) \ 1. T(x,K(y,z)) \ 1 = T(x \ 1,K(y,z)). x != ((y \ 1) \ 1) * K(z,u) | x = 1 / (K(u,z) / y). (x \ 1) \ K(y,z) = 1 / (K(z,y) / x). 1 / (K(x,y) / z) = (z \ 1) \ K(y,x). (x \ (y \ z)) * K(u,w) = (((1 / z) * y) * x) \ K(u,w). (((1 / x) * y) * z) \ K(u,w) = (z \ (y \ x)) * K(u,w). T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,z \ (x * K(y,z)),z). T(T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)),u) = L(T(z,u),z \ (x * K(y,z)),z). (x / T(y,z)) * T(y,u) = (x * K(z,y)) * K(y,u). (x / T(y / (y / z),u)) * z = (x * K(u,y / (y / z))) * K(z,z \ y). (x * K(y,z / (z / u))) * K(u,u \ z) = (x / T(z / (z / u),y)) * u. (x * K(y,z)) \ (x * z) = T(z,y). (1 / x) * y != K(z,u) | y = (z / x) \ T(z,u). x * K(y,z) = (y / x) \ T(y,z). (x / y) \ T(x,z) = y * K(x,z). x != (1 / (y \ z)) \ K(z,u) | x = y \ T(z,u). (x \ y) * K(y,z) = x \ T(y,z). x \ ((x * K(y,z)) * u) = (K(y,z) * (u / x)) * x. L((x * K(y,z)) * u,x,x) = (x * (K(y,z) * (u / x))) * x. (x * (K(y,z) * (u / x))) * x = L((x * K(y,z)) * u,x,x). (x * (1 / (x * y))) \ K(z,u) = (x * (y * (1 / x))) * K(z,u). x != T(K(y,z),u) | x = K(y,T(z,u)). K(x,T(y,x \ z)) = K(x,T(y,z)). T(x,T(y,T(T(x,z),u))) = K(x,y) * x. K(x,T(y,z / y)) = T(K(x,y),z). T(x,K(y,x \ z)) = T(x,K(y,z / x)). T(x,K(y,z / x)) = T(x,K(y,x \ z)). K(x,T(y,z)) != u | K(T(x,z),y) = u. x != K(T(y,z),u) | x = K(y,T(u,z)). K(x,T(y,x * z)) = K(x,T(y,z)). K(x \ 1,T(y,z)) = K(z \ (x \ z),y). K(x \ (y \ x),z) = K(y \ 1,T(z,x)). K(x / T(y,z),y) = K(T(y,z) \ x,y). K(x / y,L(y,z,u)) = K(y \ x,L(y,z,u)). T(x / y,T(z,y)) = K(y \ x,z) * (x / y). K(x \ y,z) * (y / x) = T(y / x,T(z,x)). K(x \ y,z) * (y / x) != u | T(y / x,T(z,x)) = u. K((x * y) / x,T(z,x)) != u | K(y,z) = u. K(x,y / R(T(x,z),u,w)) = K(x,R(T(x,z),u,w) \ y). R(x,K(y,z),T(z,u)) = x. x * K(y,z) != u * z | x / T(z,y) = u. x \ (y * K(z,x)) != u | T(y / T(x,z),x) = u. (x \ (1 / y)) * x = (1 / y) * K(x \ (y \ 1),x). (1 / x) * K(y \ (x \ 1),y) = (y \ (1 / x)) * y. (x * K(y,T(z,u))) \ (x * z) = T(z,T(y,u)). x != (y * z) * K(y,z) | x = T(y,z) * z. (x / (x * y)) \ T(x,y) = T(x,y) * y. (x * y) \ T(y * x,z) = K(y,x) * K(y * x,z). x \ y = (x \ T(y,z)) * K(z,y). (x \ T(y,z)) * K(z,y) = x \ y. (x \ T(y,z)) * y = (x \ y) * T(y,z). (x \ T(y,z)) \ (x \ y) = K(z,y). K(x,R(T(y,x \ z),u,w)) = K(x,T(R(y,u,w),z)). T(x,T(y,x \ z)) = x * K(x,T(y,z)). K(x * y,T(z,y \ 1)) = K(x * y,T(z,x)). x * K(y,z) = (T(z,y) / x) \ z. (T(x,y) / z) \ x = z * K(y,x). K(x,y) * z != u | u = K(y,x) \ z. K(x,y) * z != u | K(y,x) \ z = u. K(x \ y,x) * ((y / x) * z) != u | u = (x \ y) * z. K(x \ y,x) * ((y / x) * z) != u | (x \ y) * z = u. (x * y) / ((K(z,u \ 1) * x) * y) != w | K(R(u,x,y) \ 1,z) = w. T(x,K(y,z)) != u | K(z,y) * (x * K(y,z)) = u. K(x,T(y,z)) \ u != w | K(y,T(x,z)) * u = w. x * K(y,T(z,u)) != w | w * K(z,T(y,u)) = x. x / K(y,T(z,u)) != w | x * K(z,T(y,u)) = w. (x / (x / y)) \ y != z | K(y,y \ x) = z. L(x * K(y,x),z,u) \ L(x,z,u) != w | K(L(x,z,u),y) = w. R(x * K(y,x),z,u) \ R(x,z,u) != w | K(R(x,z,u),y) = w. (x * T(x \ y,z)) \ y != u | K(z,x \ y) = u. K(T(x,y),z) != u | K(x,T(z,y)) = u. K(x,T(y,x \ z)) != u | K(x,T(y,z)) = u. K(x,y \ R(T(x,z),u,w)) = K(x,R(T(x,z),u,w) * (y \ 1)). K(x,R(T(x,y),z,u) * (w \ 1)) = K(x,w \ R(T(x,y),z,u)). T(K(x,y),z) != u | K(T(x,z),y) = u. K(x,T(y,x * z)) != u | K(x,T(y,z)) = u. x != K(y,z) * K(z,u) | x = K(z,u) * K(y,z). T(x,y) \ T(x,z) = K(x,z) * K(y,x). (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z. (K(x,y) * K(x,z)) \ 1 = K(y,x) * K(z,x). T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = ((K(x,z) * K(x,y)) \ 1) \ 1. K(x,y) * ((1 / x) * y) = y / x. (x * y) * ((1 / (x * y)) * (K(z,z \ 1) * 1)) = (z * (1 / ((x * y) * z))) \ (y \ (x \ 1)). K(x,y) * T(x,z) != u | u = K(x,z) * T(x,y). K(x,y) * T(x,z) != u | K(x,z) * T(x,y) = u. x != K(y,T(z,u)) | x = T(K(y,z),u). K(x,y) * K(z,K(y,x)) = T(K(x,y),z). (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z). (((x \ (y / z)) * x) * z) \ y = K(x,(x * z) \ y). ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u)). T(x * T(x \ y,z),u) \ T(y,u) = K(z,T(x,u) \ T(y,u)). x / (((y \ (x / z)) * y) * z) = K(y,x / (y * z)). x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z)). T(x,K(y,z)) = x * K(K(z,y),x). x * K(K(y,z),x) = T(x,K(z,y)). K(K(x,y),z) = K(z,K(y,x)). T(T(x,K(y,z)),K(z,y)) != u | u = x. K(x,K(y,z)) \ 1 = K(x,K(z,y)). K(x,K(y,z)) \ 1 != u | K(x,K(z,y)) = u. K(x,K(y,z)) * (K(z,y) * u) = T(K(z,y),x) * u. K(x,K(y,z)) != u | K(K(z,y),x) = u. K(x,y * K(y * z,y \ 1)) = T(K(x,y),z * y). K(x \ 1,y) = K(x \ 1,T(y,L(x,z,u))). K(x \ 1,T(y,L(x,z,u))) = K(x \ 1,y). T(K(x,y),z) * K(y,x) != u | u = K(z,K(y,x)). T(K(x,y),z) * K(y,x) != u | K(z,K(y,x)) = u. K(x,T(y,z) \ 1) != u | K(x,T(y \ 1,z)) = u. K(x,T(T(y,z),u)) = T(T(K(x,y),u),z). x != K(y,z) * T(y,u) | x = K(y,u) * T(y,z). T(T(x,y),z) = K(x,y) * T(x,T(z,y)). K(x,y) * T(x,T(z,y)) = T(T(x,y),z). x * y != z * K(T(u,w),v5) | T(x,y) = y \ (z * K(u,T(v5,w))). T(x / T(y,T(z,u)),y) = y \ (x * K(z,T(y,u))). x \ (y * K(z,T(x,u))) = T(y / T(x,T(z,u)),x). R(x,y,z) * (x \ K(u,T(x,w))) = T(x,T(u,w)) \ R(x,y,z). K(T(T(x,y),z),u) = K(x,T(T(u,y),z)). K(R(T(x,y),z,u),L(y,w,v5)) = K(R(x,z,u),L(y,w,v5)). x != (y \ z) * K(y,z) | x = z / R(y,y \ z,y). K(x,y) * (x \ y) = y / R(x,x \ y,x). x / R(y,y \ x,y) = K(y,x) * (y \ x). K(x,K(y,z)) * T(z,y) = T(z,T(y,x)). x * y != (z * u) * L(w,u,z) | x \ (z * (u * w)) = y. (x * T(y,L(z,y,x))) \ (x * (y * z)) = T(L(z,y,x),y). T(x \ 1,K(y,z)) \ (1 / x) = K(x * K(y,z),x \ 1). ((x \ 1) \ K(y,z)) \ (K(u,w) * v5) = (K(z,y) / x) / (v5 \ K(w,u)). T(x,T(y,T(T(x,z),u))) = T(x,y). T(x * K(y,x),T(z,T(x,u))) = T(x * K(y,x),z). T(x,K(y,z * (x \ 1))) = T(x,K(y,x \ z)). (x \ T(y,z)) * y = (x \ y) * (u / (T(y,z) \ u)). (x \ y) * (z / (T(y,u) \ z)) = (x \ T(y,u)) * y. x != y * K(y,z) | x = T(y,z). T(x,T(y,x \ z)) = T(x,T(y,z)). T(x,T(y,x \ z)) != u | T(x,T(y,z)) = u. L(x,y,z) \ L(T(x,T(u,w)),y,z) = K(L(x,y,z),T(u,x \ w)). T(x / (x / y),z) \ y = K(x / (x / y),y \ x) * K(z,x / (x / y)). K(x / (x / y),y \ x) * K(z,x / (x / y)) = T(x / (x / y),z) \ y. K(x,T(T(x * T(y,z),u),y)) = T(K(x,x * T(y,z)),u). K(x,y) * K(y,z) != u | T(y,x) \ T(y,z) = u. L(K(x,y),z \ 1,z) != u | u = K(x,y). L(K(x,y),z \ 1,z) != u | K(x,y) = u. ((1 / x) / y) \ K(z,u) != w | (y * x) * K(z,u) = w. T(x / y,x) \ K(z,u) != w | (x \ y) * K(z,u) = w. x * K(y,T(z,x)) != u | (z * x) / T(T(z,x),y) = u. (x / (y / z)) * K(u,z \ y) != w | x / T(y / z,T(u,z)) = w. K(x / y,T(z,y)) != u | K(y \ x,z) = u. K(K(x,y),z) != u | K(z,K(y,x)) = u. x != K(y,z) * (y \ u) | x = (y * K(z,y)) \ u. x / R(y,y \ x,y) = (y * K(x,y)) \ x. T(x,(x \ y) \ z) != u | T(x,T(z / (x \ y),y)) = u. K(x / y,L(y,z,u)) != w | K(y \ x,L(y,z,u)) = w. x / ((y \ x) \ T(x,y)) = (y * K(x,y)) \ x. x != y * (T(y,z) \ K(u,y)) | x = T(y,z) \ ((u * y) / u). K(x,y) * K(z,y) = T(y,z) \ ((x * y) / x). T(x,y) \ ((z * x) / z) = K(z,x) * K(y,x). L(x,y,((z \ 1) \ 1) * (T(z,u) \ K(w,z))) = L(x,y,K(w,z) * K(u,z)). (x \ y) * (T(T(x \ y,x),x) \ z) = (y / x) * (T(x \ y,x) \ z). x != y * ((1 / z) * u) | x = y * (T(u,z) / z). K(x,y) / (z \ u) = K(x,y) * (T(z,u) / u). K(x,y) * (T(z,u) / u) = K(x,y) / (z \ u). (x \ (y \ (z \ 1))) * K(u,w) = ((z * y) * x) \ K(u,w). (x \ (y * K(z,u))) * K(w,v5) = ((K(u,z) / y) * x) \ K(w,v5). ((K(x,y) / z) * u) \ K(w,v5) = (u \ (z * K(y,x))) * K(w,v5). K(T(x,y),z) = K(R(x,y,R(x,u,w)),T(z,y * R(x,u,w))). K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) = K(T(x,y),w). K(x,R(K(y,x) * z,u,w)) = K(x,R(z * K(y,x),u,w)). x != K(y,T(z,L(z,u,w) \ 1)) | x = K(y,z). K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y). ((x * K(y,x)) \ y) \ y = (x \ y) \ T(y,x). ((x * y) / x) \ (T(y,z) * ((K(x,y) * K(z,y)) * u)) = L(u,T(y,z) \ ((x * y) / x),T(y,z)). (x \ (y * K(x,y))) \ y = (x \ y) \ T(y,x). (x \ ((x * y) / x)) \ y = (x \ y) \ T(y,x). x != L(y,z \ u,z \ u) | x = (y / (z \ u)) / ((1 / u) * z). T(T(x,y \ z),z \ y) = (x / (y \ z)) / ((1 / z) * y). (x / (y \ z)) / ((1 / z) * y) = T(T(x,y \ z),z \ y). x \ (y * (z * T(z \ (y \ x),u))) != w | K((y * z) \ x,u) = w. x \ (y \ ((z \ (y * x)) * z)) != u | K((y \ z) \ x,z) = u. T(x,L(y,x \ 1,z) \ 1) = T(x,y \ 1). L(x,y \ z,y) = L(x,y \ z,T(y,z)). L(x,y \ z,T(y,z)) = L(x,y \ z,y). K(T(x,y),z) * u != w | K(x,T(z,y)) * u = w. x * K(T(y,z),u) != w | x * K(y,T(u,z)) = w. (x * (y * T(y \ (x \ z),u))) \ z != w | K(u,(x * y) \ z) = w. K(x,y \ (z \ y)) != u | K(x,T(z \ 1,y)) = u. K(x,y) * K(z,x) != u | T(x,z) \ T(x,y) = u. T(K(x,y),z) * u != w | K(x,T(y,z)) * u = w. x * T(K(y,z),u) != w | x * K(y,T(z,u)) = w. (x * y) / ((x * y) * x) = K(x,y) * (x \ 1). (x * y) / ((x * y) * x) != z | x \ K(x,y) = z. K(T(x,y) \ 1,y \ 1) * ((1 / T(x,y)) * z) = (1 / x) * z. (x * (y \ 1)) * K(y,z) = x * (y \ K(y,z)). x * y != (y * z) * (u \ y) | x = y * (z * (u \ 1)). (K(x,y) * z) * (x \ 1) = K(x,y) * (z * (x \ 1)). (1 / x) / T(y,x \ (y \ 1)) = y \ (1 / x). (x \ (1 / y)) * K(x,y \ (x \ 1)) = (1 / y) / x. K(x \ ((x / y) * z),x \ ((z / x) \ y)) / u = (x \ ((z / x) \ y)) * ((x \ ((x / y) * z)) / u). T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z). R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y. x * (y \ R(y,x,y)) = T(y * x,y) / y. K(x,y) * (K(y,z) * u) = K(y,z) * (K(x,y) * u). K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u). x / (K(y,z) * (u \ x)) = x * ((x \ u) * K(z,y)). (L(K(x,y),z,u) \ 1) \ w = L(K(x,y),z,u) * w. K(x,y \ R(x,z,u)) != w | K(x,R(x,z,u) / y) = w. (1 / x) * y != (z \ (1 / x)) * z | y = K(x \ (z \ 1),z). K(x \ (y \ 1),x) = K(y \ (x \ 1),x). K(x \ (y \ 1),y) = K(y \ (x \ 1),y). K(x \ 1,y) = K(y \ ((y \ x) \ 1),y). K(x \ ((x \ y) \ 1),x) = K(y \ 1,x). T(x,x \ ((x \ y) \ 1)) = 1 / (x \ K(y \ 1,x)). (x * y) * (K(y,x) * K(y * x,z)) = T(y * x,z). K(x,R(T(y,x \ z),u,w)) = K(x,R(T(y,z),u,w)). K(x,T(y,z)) * u = K(z,K(y,x)) * (K(x,y) * u). K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u. K(x,K(y,z)) * (K(z,y) * u) != w | K(z,T(y,x)) * u = w. x != K(y,z * K(u,z \ 1)) | x = T(K(y,z),u). T(K(x,y),z * y) = T(K(x,y),y * z). T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z). x != y \ (z * K(u,T(y,z))) | x = T(y,u) \ z. T(x / T(y,T(z,x)),y) = T(y,z) \ x. T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u)). R(K(x,y),z,x \ 1) = K(x,y). L(x \ 1,y,K(x,z)) = x \ 1. (x \ 1) * T(K(x,y) * z,x \ 1) = K(x,y) * (z * (x \ 1)). (x \ 1) * y != K(x,z) * (u * (x \ 1)) | T(K(x,z) * u,x \ 1) = y. T(K(x,y) * z,x \ 1) = K(x,y) * T(z,x \ 1). L(x \ 1,x,y) = (K(x,z) * (y * x)) \ (K(x,z) * y). (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,z). (x \ (1 / y)) * z != (1 / y) / x | z = K(x,x \ (y \ 1)). K(x,y \ (x \ 1)) = K(x,x \ (y \ 1)). x != K(y,y \ (z \ 1)) | x = z * (y * ((z \ 1) / y)). K(x,y \ (x \ 1)) = y * (x * ((y \ 1) / x)). x * (y * ((x \ 1) / y)) = K(y,x \ (y \ 1)). x != K(y,z) * u | x = T(z,y) \ (z * u). K(x,y) * (K(z,x) * u) = T(x,z) \ (x * (K(x,y) * u)). T(x,y) \ (x * (K(x,z) * u)) = K(x,z) * (K(y,x) * u). x != y * (z * K(y * z,u)) | x = T(y * z,u). K(x,y) * (K(z,x) * K(K(z,x) * K(x,y),u)) = T(K(z,x) * K(x,y),u). K(x,y) * (K(z,x) * (K(y,x) * u)) = K(z,x) * u. x != y / (z * (u \ y)) | x = (u * y) / (z * y). x * ((x \ y) * K(z,u)) = (y * x) / (K(u,z) * x). (x * y) / (K(z,u) * y) = y * ((y \ x) * K(u,z)). (x * ((x \ y) * K(z,u))) \ 1 = (K(u,z) * (y \ x)) * (x \ 1). L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w. (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x). (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w). L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w. x / L(K(y,z),u,w) = x * L(K(z,y),u,w). (x * ((x \ y) * K(z,u))) \ y = L(K(u,z),x \ y,x). L(K(x,y),z,u) \ w != v5 | v5 = L(K(y,x),z,u) * w. L(K(x,y),z,u) \ w != v5 | L(K(y,x),z,u) * w = v5. x * y = (x * (y * K(z,u))) * L(K(u,z),y,x). (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y. (x * (K(y,z) * u)) \ (x * u) = L(K(z,T(y,u)),u,x). x * y != (x * (y * K(z,u))) * w | L(K(u,z),y,x) = w. (x * (y * K(z,u))) * w != x * y | L(K(u,z),y,x) = w. x != 1 / (y \ K(z,y)) | x = T(y,z). T(x,x \ ((x \ y) \ 1)) = T(x,y \ 1). T(x,x \ (y \ 1)) = T(x,(x * y) \ 1). T(x,(x * y) \ 1) = T(x,x \ (y \ 1)). T(x,x \ (((x \ 1) * ((y * (x \ 1)) \ z)) \ 1)) = T(x,L(x * (y \ z),x \ 1,y) \ 1). T(x,L(x * (y \ z),x \ 1,y) \ 1) = T(x,x \ (((x \ 1) * ((y * (x \ 1)) \ z)) \ 1)). T(x,y \ (x \ 1)) = T(x,x \ (y \ 1)). T(x,y \ 1) = T(x,x \ (((x \ 1) * y) \ 1)). T(x,x \ (((x \ 1) * y) \ 1)) = T(x,y \ 1). K(x,R(T(y,z),u,w)) = K(x,R(T(y,x * z),u,w)). K(x,R(T(y,x * z),u,w)) = K(x,R(T(y,z),u,w)). K(x * y,K(y,z)) = K(K(z,y),y * x). K(K(x,y),y * z) = K(z * y,K(y,x)). K(x * y,K(x,z)) = K(y * x,K(x,z)). K(x * y,K(y,z)) = K(y * x,K(y,z)). x != K(y * z,K(y,u)) | x = K(z,K(y,u)). K(x * y,K(y,z)) = K(x,K(y,z)). T(K(x,y) * L(z,u,w),x \ 1) = K(x,y) * L(T(z,x \ 1),u,w). K(x,y) * (K(z,y) * u) = K(z,y) * (K(x,y) * u). (x * ((x \ y) * K(z,u))) \ 1 = (K(u,z) * x) * ((y * x) \ 1). K(x,(x * y) \ ((x * z) * y)) = K(x,R(T(z,y),x,y)). (((K(x,y) * (K(z,y) * u)) / (K(z,y) * u)) * K(z,y)) * u = K(z,y) * (R(K(x,y),K(z,y),u) * u). K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y). K((x * y) / (z * y),u) = R(K(x / z,u),x,y). R(K(x / y,z),x,u) = K((x * u) / (y * u),z). K(R(x,x \ y,z),u) = R(K(x,u),y,z). x != R(y,1,z) | x = y. K(R(x,x \ 1,y),z) = K(x,z). x != K(R(y,z,y),u) | x = K(y,u). R(K(x,y),z,x) = K(x,y). K(R(x,y,z),u) = R(K(x,u),x * y,z). R(K(x,y),x * z,u) = K(R(x,z,u),y). K(R(x,K(x,y) * (x \ z),u),w) = R(K(x,w),K(x,y) * z,u). K(R(x,T(x,y) \ z,u),w) = R(K(x,w),K(y,x) * z,u). R(K(x,y),K(z,x) * u,w) = K(R(x,T(x,z) \ u,w),y). (x * R(K(y,z),u,w)) \ x = K(z,R(y,y \ u,w)). K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w. K(x,y) * (z * x) = (K(x,y) * z) * x. (K(x,y) * z) * x = K(x,y) * (z * x). x != K(y,L(z,u,u \ 1)) | x = K(y,z). K(R(x,x \ 1,y),L(z,u,u \ 1)) = K(x,z). R(K(R(x,y,z),u),w,v5) = R(R(K(x,u),w,v5),x * y,z). R(R(K(x,y),z,u),x * w,v5) = R(K(R(x,w,v5),y),z,u). R(K(x,x * (y / z)),x * u,w) = K(R(x,u,w),(z / y) \ x). R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z)). L(x,y,K(x,z)) = x. x != K(y,z) * (u * y) | x = T(y,z) * T(u,y). (K(x,y) * z) * x = T(x,y) * T(z,x). x * y != K(x,z) * (u * x) | T(K(x,z) * u,x) = y. T(K(x \ y,x) * z,x \ y) = (y / x) \ (z * (x \ y)). (K(x,y) * (z * x)) \ 1 = x \ ((K(x,y) * z) \ 1). L(x \ 1,x,K(x,y) * z) = (K(x,y) * (z * x)) \ (K(x,y) * z). (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,K(x,y) * z). (x * (K(y,x) * z)) * y = K(y,x) * ((x * z) * y). L(x,y,z) = L(L(x,y,z),u,K(x,w)). L(L(x,y,z),u,K(x,w)) = L(x,y,z). (K(x,y) * z) * x != u | K(x,y) * (z * x) = u. (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w)). (K(x,y) * z) * L(x,u,w) = K(x,y) * (z * L(x,u,w)). L(x,y,K(z,x)) = x. L(x,y,z) = L(L(x,y,z),u,K(w,x)). L(L(x,y,z),u,K(w,x)) = L(x,y,z). (K(x,y) * z) * y = K(x,y) * (z * y). x * y != T(x,z) * T(u,x) | T(K(x,z) * u,x) = y. T(K(x,y) * z,x) = K(x,y) * T(z,x). (x \ y) * x = T(x,z) * T(T(x,z) \ y,x). T(x,y) * T(T(x,y) \ z,x) = (x \ z) * x. (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x). K(K(x,y) * z,y) * T(y,K(x,y) * (z * y)) = L(y,K(x,y) * z,y). T(x,y) * K(z,y) = T(x * K(z,y),y). T(x * K(y,z),z) = T(x,z) * K(y,z). T(x,y) = K(y,z) * T(K(y,z) \ x,y). K(x,y) * T(K(x,y) \ z,x) = T(z,x). T(K(x,y) * T(z,u),x) = K(x,y) * T(T(z,x),u). T(K(x,y) * L(z,u,w),x) = K(x,y) * L(T(z,x),u,w). K(x,y) * T(K(x,z) * y,x) = K(x,z) * y. T(x,y) * K(y,z) = T(x * K(y,z),y). T(x * K(y,z),y) = T(x,y) * K(y,z). T(x / y,z) * y = K(z,u) * (y * T(y \ (K(z,u) \ x),z)). K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = T(u / z,x) * z. x \ (y * T(x,z)) = T(y,x) * K(x,z). x != y * K(z,u) | x = (y / z) * T(z,u). T(x * K(y,z),y) = (T(x,y) / y) * T(y,z). (T(x,y) / y) * T(y,z) = T(x * K(y,z),y). x \ T(x * K(y,z),y) != u | K(x,y) * K(y,z) = u. x != T(y,z) * T(T(y,z) \ T(u,z),w) | x = T(y * T(y \ u,w),z). (x \ T(y,z)) * x = T(x * T(x \ y,x),z). T(x * T(x \ y,x),z) = (x \ T(y,z)) * x. x * y != T(z,u) * T(T(z,u) \ w,z) | x \ ((z \ w) * z) = y. x \ ((y \ x) * y) = K(T(y,z) \ x,y). K(T(x,y) \ z,x) = z \ ((x \ z) * x). K(T(x,y) \ z,x) = K(x \ z,x). x != K(T(y,z) \ u,y) | x = K(u / T(y,z),y). K(x \ y,x) = K(y / T(x,z),x). K(x / T(y,z),y) = K(y \ x,y). K(x,y) = K(y \ (x * T(y,z)),y). K(x \ (y * T(x,z)),x) = K(y,x). x != K(y \ (z * T(y,u)),y) | x = K((z / y) * T(y,u),y). K(x,y) = K((x / y) * T(y,z),y). K((x / y) * T(y,z),y) = K(x,y). K(x * T(y,z),y) = K(x * y,y). K(x * K(y,z),y) = K(x,y). K(x * K(y,z),z) = K(x,z). R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y * K(x,w)). K(R(x,y,z),u * K(x,w)) = R(x * K(u,x),y,z) \ R(x,y,z). K(x * K(y \ z,u),z \ y) = K(x,z \ y). K(K(x,y) * z,x) = K(z,x). K(x,y) = K(K(z,y) * x,y). K(K(x,y) * z,y) = K(z,y). K(x * y,z) = K(x * T(y,z),z). K(x * T(y,z),z) = K(x * y,z). K(x \ K(y,z),y) = K(x \ 1,y). K(x \ T(y,z),y) = K(x \ y,y). K(x * K(y,z),z) = 1 / K(z,x). K(x * L(K(y,z),u,w),z) = K(x,z). K(K(x,y) \ z,x) = K(z,x). K(x * K(y,T(z,u)),z) = K(x,z). K(x * K(y,z),T(z,u)) = K(x,T(z,u)). K(R(K(x,y),z,u) * w,x) = K(w,x). L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y). K(T(x,T(y,z)),z) = K(T(x,y),z). K(K(x,y) * z,T(y,u)) = K(z,T(y,u)). K(K(x,y) * z,x) != u | K(z,x) = u. K(x * T(y,z),y) = K(y * x,y). T(T(x * K(y * T(x,z),x),u),y) = R(T(x,u),y,x). K(x * (R(y,z,y) \ u),y) = K(x * (u / R(y,z,y)),y). K(x * (y / R(z,u,z)),z) = K(x * (R(z,u,z) \ y),z). K(x \ L(K(y,z),u,w),y) = K(x \ 1,y). x * T(x \ K(y,z),y) = K(y,z) * K(x \ 1,y). K(x,y) * K(z \ 1,x) = z * T(z \ K(x,y),x). x != K(y \ z,z) | x = K(z,y). K(x \ T(y,z),y) = K(y,x). K(x \ (y \ z),z / y) = K(x \ (z / y),z / y). K(x \ (y / z),y / z) = K(x \ (z \ y),y / z). K(x \ (y * K(z,y)),y) = K(x \ y,y). K(x \ y,T(y,z)) = K(T(y,z),x). K(x * K(y,z),z) != u | K(x,z) = u. K(x * T(y,z),y) = K(T(y,z) * x,y). K(T(x,y) * z,x) = K(z * T(x,y),x). K(T(x,T(y,z)) * u,y) = K(x * u,y). K(T(x,y \ z),y) = K(T(x,(y / z) \ 1),y). K(T(x,(y / z) \ 1),y) = K(T(x,y \ z),y). K(x,y) = K(y * (x / T(y,z)),y). K(x * (y / T(x,z)),x) = K(y,x). K(x * ((y * z) / y),z) = K(z * x,z). K(x \ y,T(y,z)) = K(y,T(x,z)). x != K(y,z) | x = K(z \ T(y,u),y). K(x \ y,T(y,z)) = K(T(x,z) \ T(y,u),y). K(T(x,y) \ T(z,u),z) = K(x \ z,T(z,y)). K(x * (y * K(z,u)),u) = K(x * y,u). K(x * y,z) = K(x * (y * K(z,u)),z). K(x * (y * K(z,u)),z) = K(x * y,z). K((K(x,y) * z) * u,x) = K(z * u,x). K(K(R(x,y,z),u) * w,x) = K(w,x). K((x \ y) \ z,x) != u | K((y / x) \ z,x) = u. K(x \ T(y,z),z) != u | K(x \ y,z) = u. K(R(x,y,z) * u,x) = K(u * R(x,y,z),x). K(x * y,z) = K(T(x,R(z,u,w)) * y,z). K(T(x,R(y,z,u)) * w,y) = K(x * w,y). K(x * y,T(y,z)) = K(x * T(y,u),T(y,z)). K(x * T(y,z),T(y,u)) = K(x * y,T(y,u)). K(x * y,T(x,z)) = K(T(x,u) * y,T(x,z)). K(T(x,y) * z,T(x,u)) = K(x * z,T(x,u)). K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y). T(x * K(y * R(x,z,u),x),T(y,T(x,w))) = R(x,T(y,T(x,w)),R(x,z,u)). K(x * y,z) = K(x * (K(z,u) * y),z). K(x * (K(y,z) * u),y) = K(x * u,y). L(x,y,z) / L(x * K(u * w,x),y,z) = K(L(x,y,z),u * (K(x,v5) * w)). K(L(x,y,z),u * (K(x,w) * v5)) = L(x,y,z) / L(x * K(u * v5,x),y,z). R(x,y,z) \ R(x * K(u * w,x),y,z) = K(u * (K(x,v5) * w),R(x,y,z)). K(x * (K(y,z) * u),R(y,w,v5)) = R(y,w,v5) \ R(y * K(x * u,y),w,v5). L(x * K(y \ 1,x),z,u) \ L(x,z,u) = K(L(x,z,u),y \ L(K(x,w),v5,v6)). K(L(x,y,z),u \ L(K(x,w),v5,v6)) = L(x * K(u \ 1,x),y,z) \ L(x,y,z). K(x \ (y \ (z * y)),y) != u | K(x \ z,y) = u. x * y != T(x,z) * T(u,x) | T(T(x,z) * (x \ u),x) = y. T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x)). K(x,K(x,y) * z) = K(x,z). K(x,y) = K(x,K(x,z) \ y). K(x,K(x,y) \ z) = K(x,z). K(x,K(y,x) * z) = K(x,z). K(x,K(x \ 1,y) * z) = K(x,z). K(x,R(K(x,y),z,u) * w) = K(x,w). K(x,T(y,x) \ z) = K(x,y \ z). K(x,K(y,x) \ z) = K(x,z). K(x,T(y,T(z,x))) = K(x,T(y,z)). K(x,T(y,x) / z) = K(x,y / z). K(x,y * K(z,x)) = K(x,y). K(x,y * K(x,z)) = K(x,y). R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x)). K(x,y / (z / x)) = K(x,y / (x \ z)). K(x,y \ x) = K(x,y \ T(x,z)). K(x,y \ T(x,z)) = K(x,y \ x). x != K(y,z) | x = y \ T(y,z). K(x,y * K(x,z)) = x \ T(x,y). T(x,K(x \ 1,y) * z) = x * K(x,z). K(x,T(y,x \ 1) \ z) = K(x,y \ z). T(x,T(y,x) \ z) = x * K(x,y \ z). K(x,T(y,x \ z)) = K(x,T(y,z / x)). K(x,T(y,z / x)) = K(x,T(y,x \ z)). K(x,T(y,R(x \ z,x,x \ u))) = K(x,T(y,(z * (x \ u)) / u)). K(x * y,T(z,T(x,y))) = K(x * y,T(z,x)). K(x,(x \ y) / z) = K(x,(y / x) / z). K(x,(y / x) / z) = K(x,(x \ y) / z). K(x,y * K(x,z)) != u | K(x,y) = u. K(x,(K(x,y) * z) * u) = K(x,z * u). K(x,K(R(x,y,z),u) * w) = K(x,w). K(x,y * K(z,x)) != u | K(x,y) = u. K(x,K(y,R(x,z,u)) * w) = K(x,w). K(x,R(x,y,z) \ u) = K(x,T(R(x,y,z),w) \ u). K(x,T(R(x,y,z),u) \ w) = K(x,R(x,y,z) \ w). K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z)). K(x,y \ T(z,x)) != u | K(x,y \ z) = u. K(x,y / (z / x)) != u | K(x,y / (x \ z)) = u. K(x,y * K(z,R(x,u,w))) = K(x,y). T(x,K(x \ 1,y) * z) = T(x,z). T(x,K(y,x) * z) = T(x,z). T(x,K(x,y) * z) = T(x,z). T(x,((x \ 1) \ y) \ z) = T(x,(y / (x \ 1)) \ z). T(x,(y / (x \ 1)) \ z) = T(x,((x \ 1) \ y) \ z). T(x,T(y,x \ 1) \ z) = T(x,y \ z). T(x,y * K(z,x)) = T(x,y). T(x,T(x,y) \ z) = T(x,x \ z). L(x,y \ (K(z,y) * u),T(y,u)) = L(x,y \ (K(z,y) * u),y). T(x,y) * K(z,T(x,K(x,u) * y)) = T(x * K(z,x),K(x,u) * y). K(T(x,y),z) = K(x,T(z,K(x,u) * y)). K(x,T(y,K(x,z) * u)) = K(T(x,u),y). T(x,T(y,T(z,x))) = T(x,T(y,z)). T(x,y \ z) = T(x,y \ T(z,x)). T(x,y \ T(z,x)) = T(x,y \ z). T(x,y * K(x,z)) = T(x,y). T(x,y \ 1) = T(x,y \ K(x,z)). T(x,y \ K(x,z)) = T(x,y \ 1). L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u * K(w,x)). K(L(x,y,z),u * K(w,x)) = L(x,y,z) \ L(T(x,u),y,z). T(x,y / (z / x)) = T(x,y / (x \ z)). T(x,y * x) = T(x,y * T(x,z)). T(x,y * T(x,z)) = T(x,y * x). (x * K(y,z)) * L(T(y,x),u,w) = L(y,u,w) * (x * K(y,z)). T(x * K(y,z),L(T(y,x),u,w)) = T(x * K(y,z),L(y,u,w)). T(x,y * L(K(x,z),u,w)) = T(x,y). T(x,T(x,y) \ z) = (x \ z) \ z. T(x,T(y,x \ z)) = T(x,T(y,z / x)). T(x,T(y,z / x)) = T(x,T(y,x \ z)). T(x,y \ (x \ z)) = T(x,y \ (z / x)). T(x,y \ (z / x)) = T(x,y \ (x \ z)). (x \ K(x,y)) * (T(x,x \ 1) * z) = (K(x,y) / x) * (x * z). T(x,(x \ y) * T(x,z)) = T(x,y). T(T(x,y),x \ z) = (T(x,y) \ z) \ z. R(T(x,y),x \ y,T(x,z)) = T(x,x \ y). T(x,y * (z * K(x,u))) = T(x,y * z). T(x,T(y,x) \ z) != u | T(x,y \ z) = u. x != K(y,T(z,y \ u)) | x = K(y,T(z,u)). K(x,T(y,z / x)) = K(x,T(y,z)). K(x,T(y,z)) = K(x,T(y,z * x)). K(x,T(y,z * x)) = K(x,T(y,z)). K(a(x,y,z),T(u,x * (y * z))) = K(a(x,y,z),T(u,(x * y) * z)). K(a(x,y,z),T(u,(x * y) * z)) = K(a(x,y,z),T(u,x * (y * z))). K(x,T(y,z \ 1)) = K(x,T(y,z \ x)). K(x,T(y,(x \ z) * x)) = K(x,T(y,z)). (x * y) * K(y,T(z,x)) = K(y,z) * (x * y). K(x,(x * y) * z) = K(x,(y * x) * z). K(x,(y * x) * z) = K(x,(x * y) * z). K(x,T(y,K(x,z) * u)) = K(x,T(y,u)). x != T(y,T(z,y \ u)) | x = T(y,T(z,u)). T(x,T(y,z / x)) = T(x,T(y,z)). T(x,T(y,z)) = T(x,T(y,z * x)). T(x,T(y,z * x)) = T(x,T(y,z)). T(x \ y,T(z,x)) = T(x \ y,T(z,y)). T(x \ y,T(z,y)) = T(x \ y,T(z,x)). T(x,(y * x) \ z) = T(x,T(z / (y * x),y)). T(x,T(y / (z * x),z)) = T(x,(z * x) \ y). T(T(x,x \ y),z) = (T(x,z) \ y) \ y. T(x,y * (x * z)) = T(x,y * (z * x)). T(x,y * (z * x)) = T(x,y * (x * z)). K(x,T(y,K(z,x) * u)) = K(x,T(y,u)). K(x,T(y,R(K(x,z),u,w) * v5)) = K(x,T(y,v5)). K(x,T(y \ x,T(z,y))) = K(x,T(y \ x,z)). x / T(T(y,y \ x),z) = T(y,z) \ x. T(x \ y,z) = (T(y / x,z) \ y) \ y. (T(x / y,z) \ x) \ x = T(y \ x,z). K(x,T(y,z * K(u,x))) = K(x,T(y,z)). x / T(y,z) = T(x / (x / y),z) \ x. T(x / (x / y),z) \ x = x / T(y,z). K(x,T(y \ z,u)) = K(x,T(T(z / y,u),z)). K(x,T(T(y / z,u),y)) = K(x,T(z \ y,u)). K(x,T(y,z * K(x,u))) = K(x,T(y,z)). K(x,T(y,z * L(K(u,x),w,v5))) = K(x,T(y,z)). x / (x / T(y,z)) = T(x / (x / y),z). T(1 / (1 / x),y) \ K(z,x) = K(z,x) / T(x,y). K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w / R(x,z,u))). K(x,T(y,z / R(x,u,w))) = K(x,T(y,R(x,u,w) \ z)). R(T(x,y),x \ y,T(x,z)) = (x \ y) \ y. T(x,(x \ y) \ z) != u | T(x,(y / x) \ z) = u. ((1 / ((x * y) \ x)) / y) * T(y,z) = T((1 / ((x * y) \ x)) * K(y,z),y). T((1 / ((x * y) \ x)) * K(y,z),y) = ((1 / ((x * y) \ x)) / y) * T(y,z). T((x \ y) * x,z) = (x \ T(y,z)) * x. x * y != (z \ T(u,w)) * z | T(x,y) = y \ T((z \ u) * z,w). T(x \ T(y,z),x) = x \ T((x \ y) * x,z). x \ T((x \ y) * x,z) = T(x \ T(y,z),x). x * y != (z \ T(u,w)) * z | T((z \ u) * z,w) / y = x. T((x \ y) * x,z) / x = x \ T(y,z). T(x * y,z) = (y \ T(y * x,z)) * y. (x \ T(x * y,z)) * x = T(y * x,z). T((x \ y) * x,z) != u * x | x \ T(y,z) = u. x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x. T(x,y) = (z \ T(z * (x / z),y)) * z. (x \ T(x * (y / x),z)) * x = T(y,z). T((x \ y) * x,z) / x != u | u = x \ T(y,z). T((x \ y) * x,z) / x != u | x \ T(y,z) = u. T(x * y,z) / y = y \ T(y * x,z). T(x,y) / z = z \ T(z * (x / z),y). x \ T(x * (y / x),z) = T(y,z) / x. T(x,y) / R(x,z,u) = R(x,z,u) \ T(x,y). T(x \ T(x * y,z),x) = x \ T(y * x,z). x * (T(y * x,z) / x) = T(x * y,z). T(x,T(y * x,z)) = T(x,T(x * y,z)). (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u). K(x,T(y,T(z * x,u))) = K(x,T(y,T(x * z,u))). x != (y \ T(y * (z / y),u)) * y | x = K(y \ 1,y) * T(K(y,y \ 1) * z,u). T(x,y) = K(z \ 1,z) * T(K(z,z \ 1) * x,y). K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z). x != y \ T(y * z,u) | x = (y \ 1) * T((y \ 1) \ z,u). T(x * y,z) / y = (y \ 1) * T((y \ 1) \ x,z). (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x. x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y. T(x * y,z) / (y * x) = (y * x) \ T((y * x) * K(x,y),z). (x * y) \ T((x * y) * K(y,x),z) = T(y * x,z) / (x * y). K(x \ T(x * y,z),T(u,x)) != w | K(x \ T(y * x,z),u) = w. x * (y * (T(z,x) / y)) = (y * (z / y)) * x. (T(x,y) / z) / (x / z) = K((x / z) / (z \ 1),y). K((x / y) / (y \ 1),z) = (T(x,z) / y) / (x / y). T(x * y,z) != x * u | T(y * x,z) / x = u. K(x * (y \ z),z \ y) = K(x * (z / y),z \ y). K(x * (y / z),y \ z) = K(x * (z \ y),y \ z). x / K(y \ z,T(z,u)) != x * w | K(z,T(y,u) \ T(z,v5)) = w. T(T(x,y),z) \ T(T(x,y) * K(x * u,T(x,y)),z) = K(T(x,w) * u,T(T(x,y),z)). K(T(x,y) * z,T(T(x,u),w)) = T(T(x,u),w) \ T(T(x,u) * K(x * z,T(x,u)),w). T(x,y) * K(x * y,T(z,x)) = K(x * y,z) * T(x,y). x * T(y,T(z,x)) = K(y,z) * (x * y). K(x,y) * (z * x) = z * T(x,T(y,z)). (x * y) * z != (x * y) * K(y,T(u,x)) | T(K(y,u),x * y) = z. T(K(x,y),z * x) = T(K(x,y),z). T(K(x,y),z * x) != u | K(x,T(y,z)) = u. K(x,T(y,z * x)) != u | K(x,T(y,z)) = u. K((x \ y) * y,T(z,y * y)) != u | K((x \ y) * y,T(z,x)) = u. K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z / y)). K(x,T(y \ x,z / y)) = K(x,T(y \ x,y \ z)). x * ((y \ (x \ z)) * y) = ((y \ (z / x)) * y) * x. ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x). (K(x,y) / R(x,z,u)) * x = R(x,z,u) \ T(x,y). T(x * K(y * x,z),y) = y \ T(x * y,z). T(x * K((y \ 1) \ x,z),y) = y \ T(x * y,z). x * (y * ((x \ z) / y)) = (y * ((z / x) / y)) * x. (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x)). x != K(y / z,T(u,y)) | x = K(z \ y,u). R(K(x / y,T(z,x * u)),x,u) = K((y * u) \ (x * u),z). R(K((x / y) / z,u),x / y,y) = K(x / (z * y),u). R(K(x / (y / z),u),x,z) = K((x * z) / y,u). R(K(x \ y,z),y,u) = K((y * u) / (x * u),T(z,y)). K((x * y) / (z * y),T(u,x)) = R(K(z \ x,u),x,y). K(x,T(y,(K(x,z) * u) * w)) = K(x,T(y,u * w)). K(x,T(y,z * (u * K(w,x)))) = K(x,T(y,z * u)). T(x \ 1,y) / x != z | x \ T(1 / x,y) = z. x != R(K(y,z),z,u) | x = K(y,z). K((x * y) / z,x) = K(x / (z / y),x). x != K(y / z,y) | x = K(z \ y,y). K((x * y) / z,x) = K((z / y) \ x,x). (x * y) \ K(z,y) = y \ ((K(y,z) * x) \ 1). x \ ((K(x,y) * z) \ 1) = (z * x) \ K(y,x). x \ (y \ K(z,x)) = (y * x) \ K(z,x). (x * y) \ K(z,y) = y \ (x \ K(z,y)). x != K(y,z) * T(T(z,y),u) | x = z * K(T(z,y),u). T(K(x,y) * T(y,z),x) = y * K(T(y,x),z). R((x \ y) * K(z \ (x \ y),x \ y),u,w) \ R(x \ y,u,w) = K(R(x \ y,u,w),z \ (y / x)). T(T(x,y) * z,x) = T(x,y) * (x \ T(x * z,x)). T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x). K(x,R(T(x,y),z,u) \ w) = K(x,R(x,z,u) \ w). K(x,x \ 1) * T(y,z) = T(K(x,x \ 1) * y,z). T(K(x,x \ 1) * y,z) = K(x,x \ 1) * T(y,z). ((x * ((y * x) \ y)) \ 1) * T(((x * ((y * x) \ y)) \ 1) \ (1 / ((y * x) \ y)),z) = T(x,z) / (x * ((y * x) \ y)). x != ((y \ (z / u)) * y) * u | x = ((y \ (z * (u \ 1))) * y) / (u \ 1). x * ((y \ (x \ z)) * y) = ((y \ (z * (x \ 1))) * y) / (x \ 1). ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x). ((x \ (y / z)) * x) * z = z * (x * T(x \ (z \ y),x)). x * (y * T(y \ (x \ z),y)) = ((y \ (z / x)) * y) * x. ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x). x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z * y)). x != (y * ((z / (u * (w \ z))) / y)) * (u * (w \ z)) | x = ((y * ((w / u) / y)) * u) * (w \ z). (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z). (x * ((y / (y * z)) / x)) * (y * z) = (y * z) * (x * (L(z \ 1,z,y) / x)). K(x,T(y,z * (u * x))) = K(x,T(y,z * (x * u))). (x * K(y,T(z,u * w))) \ x = K(T(z,u * (w * K(v5,y))),y). K(T(x,y * (z * K(u,w))),w) = (v5 * K(w,T(x,y * z))) \ v5. T(x,y) * R(x \ T(z,x),u,w) = T(T(x,y) * R(x \ z,u,w),x). T(T(x,y) * R(x \ z,u,w),x) = T(x,y) * R(x \ T(z,x),u,w). x != y * T(z,u) | x = (y * z) * K(z,u). T(K(x,x \ 1) * y,z) = (K(x,x \ 1) * y) * K(y,z). (K(x,x \ 1) * y) * K(y,z) = T(K(x,x \ 1) * y,z). T(x * K(y,y \ 1),z) = K(y,y \ 1) * T(x,z). x != K(y,z / u) | x = K(y,(u / z) \ 1). x / (y * ((z \ (y \ x)) * z)) = K(z,((z * y) / x) \ 1). K(x,(((y * z) * u) / ((x * z) * u)) \ 1) = K(x,R(y / x,x * z,u) \ 1). K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1). x != K(L(y \ z,u,w) \ 1,v5) | x = L(K(z \ y,v5),u,w). K((x * y) \ (x * z),u) = L(K(y \ z,u),z,x). L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z). x != L(K(y,T(z,u)),z,w) | x = K(y,T(z,u)). K((x * y) \ (x * z),T(z,u)) = K(y \ z,T(z,u)). L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u). L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u). L(K(x,y),z,u) = K((u * (z / x)) \ (u * z),y). K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x). L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z). K(x \ y,y) = K(L(x \ y,x,z),y). K(L(x \ y,x,z),y) = K(x \ y,y). L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u). K(x \ (y * z),z) = K((y \ x) \ z,z). K((x \ y) \ z,z) = K(y \ (x * z),z). x != K((y \ z) \ u,u) | x = K(u * (z \ y),u). K(x \ (y * z),z) = K(z * (x \ y),z). x != K(y * z,y) | x = L(K(y * z,y),z,u). K(x \ (y * z),z) = L(K(z * (x \ y),z),x \ y,u). L(K(x * (y \ z),x),y \ z,u) = K(y \ (z * x),x). L(x * K(x * (y \ z),x),u,w) / L(x,u,w) = K(y \ (z * x),L(x,u,w)). K(L(x,y / x,z),u) = L(K(x,u),y,z). x != L(y,z,u) | x = (u * z) \ (u * (z * y)). K(L(x,y / x,z),u) = (z * y) \ (z * (y * K(x,u))). K(L(x,y,z),u) = L(K(x,u),y * x,z). L(K(x,y),z * x,u) = K(L(x,z,u),y). L(K(x,y),z,u) \ 1 = K(y,L(x,z / x,u)). K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1. K(x,y) * (L(K(z,x),u,w) * v5) = K(L(z,u / z,w),x) * (K(x,y) * v5). K(L(x,y / x,z),u) * (K(u,w) * v5) = K(u,w) * (L(K(x,u),y,z) * v5). K(x,y) = L(K(x,y),z,K(x,u)). L(K(x,y),z,K(x,u)) = K(x,y). K(x,y) = L(K(x,y),z,K(u,x)). L(K(x,y),z,K(u,x)) = K(x,y). L(T(K(x,y),z),u,K(x,w)) = T(K(x,y),z). (K(x,y) * z) * K(x,u) = K(x,y) * (z * K(x,u)). (K(x,y) * z) * K(y,u) = K(x,y) * (z * K(y,u)). x != L(K(y,z),K(z,u) * y,w) | x = K(K(z,u) * y,z). K(L(x,K(y,z),u),y) = K(K(y,z) * x,y). (x * (y * z)) / K(L(y,z,x),z) = x * (z * y). T(x,y * K(L(x,z,u),w)) = T(x,y). T(x,L(x,y,z) * (z * y)) = T(x,z * (y * x)). L(T(x,y),z,u) \ L(x,z,u) = K(y * K(L(x,w,v5),v6),L(x,z,u)). K(x * K(L(y,z,u),w),L(y,v5,v6)) = L(T(y,x),v5,v6) \ L(y,v5,v6). x != L(T(K(y,z),u),u,K(y,w)) | x = T(K(y,z),K(y,w) * u). T(K(x,y),z) = T(K(x,y),K(x,u) * z). T(K(x,y),K(x,z) * u) = T(K(x,y),u). T(K(x,y),K(z,x) * u) = T(K(x,y),u). T(K(x,y),R(K(z,x),u,w) * v5) = T(K(x,y),v5). T(K(x,y),z * K(u,x)) = T(K(x,y),z). T(K(x,y),z * L(K(u,x),w,v5)) = T(K(x,y),z). x != K(K(y,z) * u,y) | x = K(u,y). K(L(x,K(y,z),u),y) = K(x,y). K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y). x != L(K(y,z),u,w) \ 1 | x = L(K(z,y),u,w). K(x,L(y,z / y,u)) = L(K(x,y),z,u). K(x,L(y,z / y,u)) != w | L(K(x,y),z,u) = w. x != K(y,L(z,u,z)) | x = K(y,z). L(K(x,y),z,y) = K(x,y). K(x,L(y,z,u)) = L(K(x,y),z * y,u). L(K(x,y),z * y,u) = K(x,L(y,z,u)). K(x,L(y \ z,y,u)) = L(K(x,y \ z),z,u). L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u)). K(x,(y * ((y \ z) / u)) \ z) = L(K(x,u),y \ z,y). K(x,L(y,z * K(y,u),w)) = L(K(x,y),z * T(y,u),w). L(K(x,y),z * T(y,u),w) = K(x,L(y,z * K(y,u),w)). K(x,y) = L(K(x,y),z,K(u,y)). L(K(x,y),z,K(u,y)) = K(x,y). a(x,y,K(z,x)) = 1. x != L(K(y,z),u * y,w) | x = K(L(y,u,w),z). K(x,y) = K(L(x,z,y),y). K(L(x,y,z),z) = K(x,z). x != L(K((y \ z) \ u,w),u,y) | x = K(z \ (y * u),w). K((x \ y) \ z,x) = K(y \ (x * z),x). (x * y) * K(z,x) = x * (y * K(z,x)). a(x,y,K(x,z)) = 1. a(x,y,K(z,x \ 1)) = 1. L(K(x,y),z,x) = K(x,y). a(x,y,K(x * z,z)) = 1. K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z). T(x * K(y,x),L(y,z,x)) = x. R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),L(y,w,x)). K(R(x,y,z),L(u,w,x)) = R(x * K(u,x),y,z) \ R(x,y,z). L(K(x,y),z,x) = u \ (u * K(x,y)). K(x,y) = K(L(x,z,x),y). K(L(x,y,x),z) = K(x,z). (x * y) * K(x,z) = x * (y * K(x,z)). L(K(x * y,y),z,x) = K(x * y,y). x != K(y,T(z,u)) | x = K(y,T(z,u * y)). K(L(x,y,x),T(z,u)) = K(x,T(z,u * x)). K(x,y) * L(x,z,x) = L(T(x,y),z,x). K(L(x,x,y),z) = K(x,z). K(x,y) = K(L(x,z,K(u,y)),y). K(L(x,y,K(z,u)),u) = K(x,u). (K(x,y) * z) * K(u,y) = K(x,y) * (z * K(u,y)). T(x,y) = T(x,L(y,z,x)). T(x,L(y,z,x)) = T(x,y). T(x,(x * y) \ z) = T(x,y \ (x \ z)). T(x,y \ (x * z)) = T(x,(x \ y) \ z). T(x,(x \ y) \ z) = T(x,y \ (x * z)). T(x,L(y,z,K(u,x))) = (K(y,x) / x) \ 1. L(K(x,y),z,x) != u | u = K(x,y). L(K(x,y),z,x) != u | K(x,y) = u. K(L(x,y,x),z) != u | K(x,z) = u. K(x,y) != z | K(R(x,u,x),y) = z. K(x,y) = K(x,L(y,z,x)). K(x,L(y,z,x)) = K(x,y). x != L(K(y,z),u,w) | x = L(L(K(y,z),u,w),z,v5). K(x,L(y,z,u)) = L(L(K(x,y),z * y,u),y,w). L(L(K(x,y),z * y,u),y,w) = K(x,L(y,z,u)). x != L(K(y,z),u,K(w,y)) | x = K(y,z). K(x,L(y,z,K(u,x))) = K(x,y). x != L(K(y,z),u,K(y,w)) | x = K(y,z). K(x,L(y,z,K(x,u))) = K(x,y). T(x,K(y,L(x,z,u))) = x. K(x * K(y,L(z,u,w)),z) = K(x,z). K(x,L(y,z,x)) != u | K(x,y) = u. K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w)). K(x,(x * y) \ z) = K(x,y \ (x \ z)). K(x,y \ (x * z)) = K(x,(x \ y) \ z). K(x,(x \ y) \ z) = K(x,y \ (x * z)). L(K(x,y),z * x,u) = K(L(x,z,u),L(y,w,x)). K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z). K(x,y) = K(x,T(y,K(z,L(x,u,w)))). K(x,T(y,K(z,L(x,u,w)))) = K(x,y). K(x,L(L(y,z,K(u,x)),w,v5)) = K(x,L(y,w,v5)). K(x,(x * y) \ z) != u | K(x,y \ (x \ z)) = u. K((L(x,y,z) \ u) * L(x,y,z),x) = K(u,x). K((x \ y) \ (x \ z),x) = K(y \ z,x). L(x * K(y \ (x * z),x),u,w) / L(x,u,w) = K((x \ y) \ z,L(x,u,w)). x \ (y * K(z,x)) = (x \ y) * K(z,x). R(x,y,K(z,x)) = x. T(x,y) * (z * K(u,x)) = (T(x,y) * z) * K(u,x). (T(x,y) * z) * K(u,x) = T(x,y) * (z * K(u,x)). L(x,y,z) * (u * K(w,x)) = (L(x,y,z) * u) * K(w,x). (L(x,y,z) * u) * K(w,x) = L(x,y,z) * (u * K(w,x)). R(x,y,T(K(z,x),u)) = x. R(x,y,K(x,z)) = x. R(x \ 1,y,K(x,z)) = x \ 1. R(x,y,K(z,T(x,u))) = x. R(x,y,z) = R(R(x,y,z),u,K(x,w)). R(R(x,y,z),u,K(x,w)) = R(x,y,z). T(x,y) * (z * K(x,u)) = (T(x,y) * z) * K(x,u). (T(x,y) * z) * K(x,u) = T(x,y) * (z * K(x,u)). L(x,y,z) * (u * K(x,w)) = (L(x,y,z) * u) * K(x,w). (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w)). x \ (y * T(K(z,x),u)) = (x \ y) * T(K(z,x),u). L(x,y,z) * (u * K(w,T(x,v5))) = (L(x,y,z) * u) * K(w,T(x,v5)). (L(x,y,z) * u) * K(w,T(x,v5)) = L(x,y,z) * (u * K(w,T(x,v5))). (x \ 1) * (y * K(x,z)) = ((x \ 1) * y) * K(x,z). ((x \ 1) * y) * K(x,z) = (x \ 1) * (y * K(x,z)). x != y * (z * K(y,u)) | x = T(y,u) * T(z,K(y,u)). (x * y) * K(x,z) = T(x,z) * T(y,K(x,z)). T(x,y) * T(z,K(x,y)) = (x * z) * K(x,y). (x * (y * K(x,z))) * x = (x * y) * T(x,z). L(x,y,x) * K(x,z) = L(T(x,z),y,x). x * y != K(z,u) * L(z,w,z) | x \ L(T(z,u),w,z) = y. T(x,y) \ L(T(x,y),z,x) = x \ L(x,z,x). T(x,(y / x) \ z) = T(x,y \ (x * z)). x != K(y,(y * z) \ u) | x = (((y \ (u / z)) * y) * z) \ u. K(x,y \ (x \ z)) = (((x \ (z / y)) * x) * y) \ z. (((x \ (y / z)) * x) * z) \ y = K(x,z \ (x \ y)). K(x,L(y,x \ 1,x) \ z) = K(x,((x \ 1) * y) \ (x \ z)). K(x,((x \ 1) * y) \ (x \ z)) = K(x,L(y,x \ 1,x) \ z). (x * ((y / z) / x)) * z = y * K(x,z \ (x \ y)). K((x \ y) \ z,x) = K(y \ (z * x),x). T(x / T(y,z),y) = (y \ x) * K(z,y). L(x,y,x) * K(x,R(z \ 1,u,w) \ 1) = L(x * R(K(x,z),u,w),y,x). T(x,(y * (1 / x)) \ z) = T(x,R(y,x \ 1,x) \ (x * z)). T(x,R(y,x \ 1,x) \ (x * z)) = T(x,(y * (1 / x)) \ z). K((x / y) \ z,y) = K(x \ (z * y),y). x != K((y \ z) \ (y \ u),y) | x = K(z \ u,y). K(x \ ((y \ z) * y),y) = K(x \ z,y). x != y * K(z,u) | x = (y / T(u,z)) * u. T(x / T(y,z),y) = ((y \ x) / T(y,z)) * y. ((x \ y) / T(x,z)) * x = T(y / T(x,z),x). x != K(y \ (z * u),u) | x = K(u * (y \ z),u). K((x / y) \ z,y) = K(y * (x \ z),y). K(x \ y,z) = K((x * z) \ (y * z),z). K((x * y) \ (z * y),y) = K(x \ z,y). K(x \ y,z) = K(z * (x \ (z \ y)),z). K(x * (y \ (x \ z)),x) = K(y \ z,x). K(x \ y,z) = K(z * ((x * z) \ y),z). K(x * ((y * x) \ z),x) = K(y \ z,x). x != K(y \ ((z \ u) * z),z) | x = K(y \ u,z). K(x \ (y \ z),y) = K((x * y) \ z,y). K((x * y) \ z,y) = K(x \ (y \ z),y). L(x * K(y \ (x \ z),x),u,w) / L(x,u,w) = K((y * x) \ z,L(x,u,w)). (x * y) * T((x * y) \ z,y) = z * K(x \ (y \ z),y). K((x * y) \ (z * y),y) != u | K(x \ z,y) = u. x != (K(y,z) / z) \ 1 | x = T(z,y). T(x,L(y,z,K(u,x))) = T(x,y). T(x,(K(y,x) * z) \ (K(y,x) * u)) = T(x,z \ u). K(x,y \ x) = K(x,L(y \ x,y,z)). K(x,L(y \ x,y,z)) = K(x,y \ x). L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z)). L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u). L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u)). K(x,(y * z) \ (y * x)) = K(x,z \ x). K(x \ y,(x * z) \ y) = K(x \ y,z \ (x \ y)). K(x,y \ (z * x)) = K(x,(z \ y) \ x). K(x,(y \ z) \ x) = K(x,z \ (y * x)). T(x,(y * z) \ (y * x)) = x * K(x,z \ x). x != K(y,(z \ u) \ y) | x = K(y,y * (u \ z)). K(x,y \ (z * x)) = K(x,x * (y \ z)). K(x,T((y \ z) \ 1,z) \ x) = K(x,y \ ((((y \ z) \ 1) \ y) * x)). K(x,y \ ((y * z) * x)) = K(x,x * z). L(K(x,x * (y \ z)),u * x,w) = K(L(x,u,w),y \ (z * x)). x != K(y,y * z) | x = K(y,z * y). K(x,y \ ((y * z) * x)) = K(x,z * x). x != K(y,z * y) | x = L(K(y,z * y),z,u). K(x,y \ ((y * z) * x)) = L(K(x,z * x),z,u). L(K(x,y * x),y,z) = K(x,u \ ((u * y) * x)). T(x,y) * z != u * K(x,y) | T(u / x,T(x,y)) = z. T((x * y) / x,T(x,z)) = T(y,K(x,z)). K(x,y) * z != T(x,y) * T(u,K(x,y)) | T(x * u,K(x,y)) = z. T(x * y,K(x,z)) = x * T(y,K(x,z)). T(x,T(y,z)) = T(T(x,y),K(y,z)). T(T(x,y),K(y,z)) = T(x,T(y,z)). T(T(x,K(y,z)),y) = T(x,T(y,z)). x != T(y,T(z,u)) | x = y * T(K(y,z),u). T(T(x,y),K(y,z)) = x * T(K(x,y),z). K(x,T(y,T(z,L(x,u,w)))) = K(x,T(y,z)). x != T(T(y,K(z,u)),z) | x = K(y,z) * T(y,K(z,u)). T(x,T(y,z)) = K(x,y) * T(x,K(y,z)). K(x,y) * T(x,K(y,z)) = T(x,T(y,z)). L(x,T(y,T(x,z)),x) = L(x,T(y,K(x,z)),x). L(x,T(y,K(x,z)),x) = L(x,T(y,T(x,z)),x). T(K(x,y),z) = T(K(x,y),T(z,y)). T(K(x,y),T(z,y)) = T(K(x,y),z). x != T(y,T(z,z \ u)) | x = T(y,T(z,u)). T(K(x,y \ z),y) = T(K(x,y \ z),T(y,z)). T(K(x,y \ z),T(y,z)) = T(K(x,y \ z),y). T(x * y,K(y,z)) / y = T(x,K(y,z)). T(T(x,y),K(y,z)) != u | T(x,T(y,z)) = u. K(x,K(y,z)) * T(x,y) = T(x,T(y,z)). x \ T(y,K(x,z)) = T(x \ y,K(x,z)). T(x,K(y,z)) * y = T(x * y,K(y,z)). T(x * y,K(y,z)) = T(x,K(y,z)) * y. x * T(y,z) != T(y,T(z,u)) | x = K(u,K(z,y)). K(x,K(y,z)) = K(z,K(y,x)). K(K(x,y),z) = K(x,K(y,z)). K(x,K(y,z)) = K(y,K(z,x \ 1)). K(x,K(y,z \ 1)) = K(z,K(x,y)). K(x \ 1,K(y,z)) = K(y,K(z,x)). x != K(y,K(z,u)) | x = K(y * z,K(z,u)). K(x,K(y,z)) = K(z * y,K(y,x)). K(x * y,K(y,z)) = K(z,K(y,x)). T(K(x,y),z) = K(y,K(x,z)) \ K(x,y). K(x,K(y,z)) \ K(y,x) = T(K(y,x),z). T(x,K(y,z)) = x * K(z,K(y,x)). x * K(y,K(z,x)) = T(x,K(z,y)). K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). K(x,K(y,z)) \ 1 = K(z,K(x,y)). K(x,K(y,z)) * K(x,y) = T(K(x,y),z). K(x,y) * K(x,K(y,z)) = T(K(x,y),z). K(x,K(y,z)) * (K(x,y) * u) = T(K(x,y),z) * u. K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u. x != K(R(y \ 1,z,u) \ 1,w) | x = R(K(y,w),z,u). K(K(R(x \ 1,y,z) \ 1,u),w) = R(K(x,K(u,w)),y,z). T(x,K(y,z)) * K(y,K(z,x)) = x. K(x,y) * K(x,K(y,z)) != u | T(K(x,y),z) = u. K(L(K(x,y),z,u) \ 1,w) = L(K(y,K(x,w)),z,u). (x * K(y,z)) * K(y,K(z,u)) = x * T(K(y,z),u). K(x,K(y,z)) != u | K(z,K(y,x)) = u. K(K(x,y),z) = K(K(y,u) * x,K(y,z)). K(K(x,y) * z,K(x,u)) = K(K(z,x),u). K(K(x,y),z) = K(x,K(K(x,u) \ y,z)). K(x,K(K(x,y) \ z,u)) = K(K(x,z),u). K(x,K(y,z * y)) = K(y,K(x,z)). K(x,K(y,y * z)) = K(y,K(x,z)). x != K(L(y,z,u) \ 1,w) | x = L(K(y \ 1,w),z,u). K(x,K(y,L(z,u,w))) = L(K(z \ 1,K(x,y)),u,w). L(K(x \ 1,K(y,z)),u,w) = K(y,K(z,L(x,u,w))). x != K(y,K(z,u)) | x = K(u,K(z,y)). K(x,K(y,z)) = K(x,K(y,z * y)). K(x,K(y,z * y)) = K(x,K(y,z)). K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z)). K(x,K(y,z)) = K(y,K(x,z)). K(K(x,y),z) = K(y,K(z,x)). K(x,K(y,z)) != u | K(y,K(x,z)) = u. K(x \ y,K(x,z)) = K(x,K(y,z)). x != K(y,K(z,u)) | x = K(z,K(u,y \ 1)). K(x,K(y,z)) = K(x,K(z,y \ 1)). K(x,K(y,z \ 1)) = K(x,K(z,y)). x != K(y,K(z,u)) | x = K(K(y,z),u). K(x,K(y,z)) = K(K(y,x),z). K(K(x,y),z) = K(y,K(x,z)). K(x,K(y,z)) = K(z,K(x,y)). T(x,K(y,z)) = K(y,K(x,z)) * x. K(x,K(y,z)) * y = T(y,K(x,z)). (x * K(y,z)) \ K(y,K(x * K(y,z),z)) = (L(K(y,z),x,K(y,z)) * x) \ 1. K(x,y) * K(y,K(z,x)) = T(K(x,y),z). K(x,K(y,z)) = K(y,K(x,K(y,u) * z)). K(x,K(y,K(x,z) * u)) = K(y,K(x,u)). K(x,K(y,z)) = K(y,K(x,L(z,u,K(y,w)))). K(x,K(y,L(z,u,K(x,w)))) = K(y,K(x,z)). x * K(y,K(z,x)) = T(x,K(y,z)). K(K(x,y),z) = K(x,K(z,y)). K(K(x,y),z) = K(z,K(x,y)). x != K(K(y,z),u) | x = K(z,K(u,y)). K(x,K(y,z)) = K(x,K(z,y)). K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z. K(R(K(x,y),z,u),w) = K(y,K(R(x \ 1,z,u) \ 1,w)). K(x,K(R(y \ 1,z,u) \ 1,w)) = K(R(K(y,x),z,u),w). K(x,K(y,z)) != u | K(z,K(x,y)) = u. x * K(K(y,z),x) = T(x,K(y,z)). K(x,K(y,z)) = K(y,K(x \ 1,z)). K(x,K(y \ 1,z)) = K(y,K(x,z)). K(x \ 1,K(y,z)) = K(y,K(x,z)). K(x,K(y,z)) = K(x,K(y,z \ 1)). K(x,K(y,z \ 1)) = K(x,K(y,z)). x != K(y,K(z,u)) | x = K(z,u) * K(u,T(z,y)). K(x,K(y,z)) = K(x,y) * K(y,T(x,z)). K(x,y) * K(y,T(x,z)) = K(x,K(y,z)). x != K(y \ z,K(y,u)) | x = K(z,K(y,u)). K(x,K(y,x \ z)) = K(z,K(x,y)). x != K(y,K(z,u)) | x = K(u \ 1,K(y,z)). K(x,K(y,z)) = K(x \ 1,K(y,z)). K(x \ 1,K(y,z)) = K(x,K(y,z)). T(x,K(y,z)) = K(z,K(x,y)) * x. K(x,K(y,z)) * y = T(y,K(z,x)). K(x,K(y,y / z)) = K(y,K(x,z)). K(x,(y \ T(y * z,u)) / z) = K(u,K(x,((y \ 1) / z) \ 1)). K(x,K(y,((z \ 1) / u) \ 1)) = K(y,(z \ T(z * u,x)) / u). K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(z,K(x,y)) * w). K(x,K(y,z)) * K(y,x) = K(y,T(x,z)). K(x,K(y,z)) * (z * u) != w | T(z,K(x,y)) * u = w. K(x,K(y,T(z,u))) = K(z,K(x,T(y,u))). (x * K(y,K(z,u))) / K(y,z) = x / T(K(y,z),u). (x \ y) * K(z,K(u,y)) = x \ T(y,K(z,u)). K(x,y) * K(x,K(z,y)) = K(x,T(y,z)). x * K(x,K(y,z)) = T(x,K(z,y)). K(x,K(y,z)) != u | K(y,K(z,x)) = u. K(K(x,y),z) * u != K(z,K(x,y)) | 1 = u. 1 = K(x,K(y,z)) * K(x,K(y,z)). K(x,K(y,z)) * K(x,K(y,z)) = 1. T(K(x,y),z) = K(x,y) * K(z,K(x,y)). K(x,y) * K(z,K(x,y)) = T(K(x,y),z). K(x,K(y,z)) * (x \ u) = T(x,K(y,z)) \ u. x / K(y,K(z,u)) = x * K(y,K(z,u)). K(x,K(y,z)) * u != w | K(x,K(y,z)) \ u = w. K(x,K(y,z)) != u | K(x,K(z,y)) = u. x != K(y \ L(y,z,u),w) | x = (L(y,z,u) \ y) * T(y \ L(y,z,u),w). K(x \ L(x,y,z),K(u,w)) = (L(x,y,z) \ x) * T(x \ L(x,y,z),K(w,u)). (L(x,y,z) \ x) * T(x \ L(x,y,z),K(u,w)) = K(x \ L(x,y,z),K(w,u)). T(x,K(y,z)) = K(x,K(z,y)) * x. K(x,K(y,z)) * x = T(x,K(z,y)). K(x,K(y,z)) = K(x,K(y \ z,z)). K(x,K(y \ z,z)) = K(x,K(y,z)). K(x,y) * K(z,K(x,y)) = K(x,T(y,z)). T(x,y * z) = T(x,y * T(z,K(x,u))). T(x,y * T(z,K(x,u))) = T(x,y * z). x != K(y,K(z,u)) | x = K(y,K(u,z)). K(x,K(y,y * z)) = K(y,K(z,x)). x != K(y,K(z,u)) | x = K(z,K(y,u)). K(x,K(y,y * z)) = K(x,K(y,z)). K(x,K(y,z \ (u * y))) = K(y,K(x,z \ u)). K(x,K(a(y,z,u),(y * z) * u)) = K(x,K(a(y,z,u),y * (z * u))). K(x,K(y \ z,u)) = K(x,K(u,z \ y)). K(x,K(y,z)) = K(x,K(y \ 1,z)). K(x,K(y \ 1,z)) = K(x,K(y,z)). x != y * K(z,K(u,y)) | x = T(y,K(u,z)). T(x,K(y,z)) = T(x,K(z,y)). T(T(x,K(y,z)),K(y,z)) = x. K(x,y) * (z * K(y,x)) = T(z,K(x,y)). x * K(y,z) = T(K(y,z) * x,K(z,y)). T(K(x,y) * z,K(y,x)) = z * K(x,y). (K(x,y) * z) * K(y,x) = T(z,K(x,y)). x * K(y,z) = T(K(z,y) \ x,K(z,y)). T(K(x,y) \ z,K(x,y)) = z * K(y,x). x != T(T(y,z),K(z,u)) | x = T(y,T(z,u)). T(T(x,y),K(z,y)) = T(x,T(y,z)). T(T(x,K(y,z)),u) != w | T(T(x,u),K(z,y)) = w. T(T(x,y),K(z,u)) != w | T(T(x,K(u,z)),y) = w. T(x,K(y,z)) * K(y,z) = K(y,z) * x. T(T(x,K(y,z)),K(y,z)) != u | u = x. T(T(x,K(y,z)),z) = T(x,T(z,y)). K(x,y) * z != u * K(x,y) | u = T(z,K(x,y)). K(x,y) * z != u * K(x,y) | T(z,K(x,y)) = u. T(K(x,y),z) * z = z * K(x,y). T(x,K(y,z)) != u | u = T(x,K(z,y)). T(x,K(y,z)) != u | T(x,K(z,y)) = u. T(x,K(y,z \ 1)) = x * K(x,K(y,z)). K(x,K(y,z / u)) = K(x,K(y,u / z)). T(x,K(y,x \ z)) = K(z,K(x,y)) * x. K(x,K(y,z)) = K(1 / x,K(y,z)). K(1 / x,K(y,z)) = K(x,K(y,z)). x != K(y,K(z,u)) | x = K(z,K(u,y)). K(x,K(y,z)) = K(x,K(x / z,y)). K(x,K(x / y,z)) = K(x,K(z,y)). K(x,K(y,z)) * K(x * y,x) = K(x * y,T(x,z)). K(x * y,x) * K(x,K(y,z)) = K(x * y,T(x,z)). K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u)). x * y != K(z,K(u \ 1,w)) | x \ K(z,K(u,w)) = y. (x * K(y \ 1,z)) \ K(x,K(y,z)) = (K(y \ 1,z) * x) \ 1. K(x,y * ((z \ (y \ 1)) * z)) = K(x,K(y * z,z)). T(x,T(y,z)) * K(y,z) = K(y,z) * T(x,y). K(x,T(y,z)) * z = z * K(x,y). x * y != x * K(z,u) | T(T(K(z,u),x),x) = y. T(T(K(x,y),z),z) = K(x,y). x * y != y * K(z,u \ y) | x = K(z,y / u). T(K(x,y \ z),z) = K(x,z / y). x * y != y * K(z,T(u,y)) | x = K(z,u). T(K(x,T(y,z)),z) = K(x,y). x * (x * K(y,z)) = K(y,z) * (x * x). K(x,y) * (z * z) = z * (z * K(x,y)). K(x,y \ z) * z = z * K(x,z / y). x != T(T(K(y,z),u),w) | x = K(y,T(T(z,w),u)). K(x,y) = K(x,T(T(y,z),z)). K(x,T(T(y,z),z)) = K(x,y). x * L(K(y,z),u,w) = L(T(K(y,z),x),u,w) * x. L(T(K(x,y),z),u,w) * z = z * L(K(x,y),u,w). x * R(K(y,z),u,w) = R(T(K(y,z),x),u,w) * x. R(T(K(x,y),z),u,w) * z = z * R(K(x,y),u,w). L(T(K(x,y),z),u,w) \ (z * L(K(x,y),u,w)) = z. K(T(x,y),T(z,y)) = K(x,z). K(x \ y,T(z,y)) = K(y / x,z). T(K(x,y \ z),y) = K(x,z / y). x * R(K(y,z),u,w) = R(K(y,T(z,x)),u,w) * x. R(K(x,T(y,z)),u,w) * z = z * R(K(x,y),u,w). T(K(x,y),z \ 1) = K(x,T(y,z)). K(x \ y,T(z,x)) = K(y / x,z). K(x,T(y,z)) = K((z * x) / z,y). K((x * y) / x,z) = K(y,T(z,x)). x != K(R(y,z,u),T(w,v5)) | x = K(R(T(y,v5),z,u),w). K(R(x,y,z),u) = K(R(T(x,w),y,z),T(u,w)). K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w). x != K(y,T(T(z / u,w),z)) | x = K(y,T(u \ z,w)). K(x,y / z) = K(x,T(z \ y,y)). K(x,T(y \ z,z)) = K(x,z / y). K(x,T(y \ z,y)) = K(x,z / y). K(x,T(y * z,z)) = K(x,T(y * z,y)). K(x,T(y,z \ y)) = K(x,T(y,z)). x != K(y,T(T(z,u),u \ 1)) | x = K(y,z). K(x,T(y,z)) = K(T(x,z \ 1),y). K(T(x,y \ 1),z) = K(x,T(z,y)). K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w). K(T(x,y),L(T(z,y),u,w)) = K(x,L(z,u,w)). K(T(x,y),R(T(z,y),u,w)) = K(x,R(z,u,w)). K(T(x,y),y \ z) = K(x,z / y). K(T(x,y),z) = K(x,(y * z) / y). K(x,(y * z) / y) = K(T(x,y),z). K(T(x,y),R(T(z,y * u),y,u)) = K(x,(y * u) \ ((y * z) * u)). K(T(x,y \ z),y) = K(x,z / (z / y)). K(T(x,y),T(z,x \ u)) = K(T(u / (u / x),y),z). K(T(x / (x / y),z),u) = K(T(y,z),T(u,y \ x)). K(x,T(y,z)) = K(x * K(z,x),y). K(x * K(y,x),z) = K(x,T(z,y)). K(T(x,y),z) = K(x,z * K(y,z)). K(x,y * K(z,y)) = K(T(x,z),y). T(x,y) = x * K(T(x,z),T(y,z)). x * K(T(x,y),T(z,y)) = T(x,z). K(T(x,y),T(z,u)) = K(T(x * K(u,x),y),z). K(T(x * K(y,x),z),u) = K(T(x,z),T(u,y)). K(x,y) * T(y,z) = T(y * K(T(x,z),y),z). T(x * K(T(y,z),x),z) = K(y,x) * T(x,z). K(x,T(y,z)) * (z * K(y,x)) = z. K(x * K(T(x,y),z),T(u,y)) = K(K(y,x) * T(x,z),u). L(K(x,y),z * T(x,u),w) = K(L(T(x,u),z,w),T(y,u)). K(x,T(y,L(z,u,x))) = K(x * K(z,x),y). L(K(x,y),z * T(y,u),w) = K(T(x,u),L(T(y,u),z,w)). K(x,K(y,z)) = K(x,K(z,y \ x)). K(x,K(y,z \ x)) = K(x,K(z,y)). x * y != K(z,T(u,w)) * w | (w * K(z,u)) / y = x. (x * K(y,z)) / (y \ x) = T(y,T(z,x)). (x * y) \ ((x * K(z,u)) * y) = R(T(K(z,T(u,x)),x * y),x,y). R(T(K(x,T(y,z)),z * u),z,u) = (z * u) \ ((z * K(x,y)) * u). x * (y * K(x,z)) = T(x,T(z,y)) * y. T(x,T(y,z)) * z = x * (z * K(x,y)). T(K(x,y),z) * (z / y) = (z / y) * K(x,y). K(x,T(y \ (z * x),z)) = K(x,(z * x) / y). K(x / y,x / z) != u | K(y \ x,z \ x) = u. K(x,T(y,z)) = K(z / (z / x),y). K(x / (x / y),z) = K(y,T(z,x)). x != K(y,T(z,z * u)) | x = K(y,T(z,u)). K((x * y) / z,x) = K(z \ (x * y),T(x,y)). K(x \ (y * z),T(y,z)) = K((y * z) / x,y). x / K(x / y,z) = K(y \ x,z) \ x. K(x \ (K(y,z) * u),T(y,u)) = K((K(y,z) * u) / x,y). x != T(K(y * z,z \ (y \ 1)),z) | x = ((z \ y) * (1 / y)) * z. K(x * y,(x \ 1) / y) = ((y \ x) * (1 / x)) * y. K(x,T(y,z \ 1)) = K(x,T(y,z)). T(K(x,y),z \ 1) != u | T(K(x,y),z) = u. K(a(x,y,z),T(u,x * (y * z))) = K(((x * y) * z) / (x * (y * z)),u). K(((x * y) * z) / (x * (y * z)),u) = K(a(x,y,z),T(u,x * (y * z))). K((x \ y) * y,T(z,y \ x)) = K(y / (y \ x),z). K(x \ y,(1 / z) \ x) = K(y / x,x * z). K(x \ T(x * y,y),z) = K(y,T(z,x * y)). K(x,T(T(y,z),z)) != u | K(x,y) = u. K(x,T(y,z)) = K(x,z / (z / y)). K(x,y / (y / z)) = K(x,T(z,y)). K(x,T(a(y,z,u),y * (z * u))) = K(x,((y * z) * u) / (y * (z * u))). K(x,((y * z) * u) / (y * (z * u))) = K(x,T(a(y,z,u),y * (z * u))). K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x))). x != K(y,(z * u) / z) | x = ((z * ((y * u) / y)) / z) / ((z * u) / z). K(T(x,y),z) = ((y * ((x * z) / x)) / y) / ((y * z) / y). ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z). K(x,R((y * z) / y,u,w)) = K(T(x,y),R(z,u,w)). L(x,y,(y * x) / y) * K(T(y * x,y),x) = (y * x) / y. K(x * K(y,T(x,z)),u) = K(x,T(u,T(y,z))). T(x,y * K(T(y,z),u)) = T(x,T(y,u * K(z,u))). T(x,T(y,z * K(u,z))) = T(x,y * K(T(y,u),z)). T(x,T(T(y,z),z)) = T(x,y). x * K(T(x,y),z \ 1) = T(x,z \ K(y,z \ 1)). T(x,y \ K(z,y \ 1)) = x * K(T(x,z),y \ 1). T(x,T(y \ z,y)) = T(x,z / y). T(x,T(y,z)) = T(x,(z * y) / z). T(x,(y * z) / y) = T(x,T(z,y)). T(x,T(T(y \ z,u),y)) = T(x,T(z / y,u)). T(x,T(y * z,z)) = T(x,(1 / z) \ y). T(x,T(y,z \ y)) = T(x,T(y,z)). T(x,T(y,z)) = T(x,y * K(z,y)). T(x,y * K(z,y)) = T(x,T(y,z)). T(x / T(y,z),y) = T(y,T(z,x)) \ x. K(x,T(y,z)) * (z * x) = z * T(x,y). K(x,T(y,z * u)) = K(x,T(y,(z * K(w,x)) * u)). K(x,T(y,(z * K(u,x)) * w)) = K(x,T(y,z * w)). T(x,K(y,z \ x)) = x * K(x,K(z,y)). K(x / (x / y),T(z,u)) = K(y,T(T(z,x),u)). K(T(x / (x / y),z),u) = K(T(y,z),T(u,x)). x != K(y,T(z,u \ 1)) | x = K(y,T(z,u \ y)). K(x,T(y,z)) = K(x,T(y,z \ x)). K(x,T(y,z \ x)) = K(x,T(y,z)). K(x,y / (y / z)) != u | K(T(x,y),z) = u. T(x,y / (y / z)) = T(x,T(z,y)). T(x,R((y * z) / y,u,w)) = T(x,T(R(z,u,w),y)). T(x,(((y \ 1) \ 1) \ z) / z) = T(x,T(T(z \ (y \ z),T(y,u)),z)). T(x,T(T(y \ (z \ y),T(z,u)),y)) = T(x,(((z \ 1) \ 1) \ y) / y). x != T(y,T(z,u \ z)) | x = T(y,T(z,u \ 1)). T(x,T(y,z)) = T(x,T(y,z \ 1)). T(x,T(y,z \ 1)) = T(x,T(y,z)). T(x,(y \ 1) \ K(z,y)) = T(x,T(y,z)). T(x,y / z) = T(x,T(z \ y,y)). T(x,T(y \ z,z)) = T(x,z / y). T(x,(y / z) \ 1) = T(x,T((z \ y) \ 1,z)). T(x,T((y \ z) \ 1,y)) = T(x,(z / y) \ 1). T(x,T(y,z \ u)) = T(x,T(y,u \ z)). T(x,y \ (z \ y)) = T(x,y / (y * z)). T(x,y / (y * z)) = T(x,y \ (z \ y)). K(K(x,y),z) != u | K(z,K(x,y)) = u. K(x,K(y,T(z,u))) != w | K(z,K(x,T(y,u))) = w. K(x,K(y,z \ 1)) != u | K(x,K(y,z)) = u. K(x,K(y,z * y)) != u | K(x,K(z,y)) = u. K(x,K(y \ z,z)) != u | K(x,K(y,z)) = u. (L(x,y,z) \ x) * T(x \ L(x,y,z),K(u,w)) != v5 | K(x \ L(x,y,z),K(w,u)) = v5. K(x,K(y,T(z,u))) != w | K(x,K(z,T(y,u))) = w. K(x,K(y / z,T(u,z))) != w | K(x,K(u,z \ y)) = w. K(x,K(x / y,z)) != u | K(x,K(y,z)) = u. T(x * K(y,z),K(y,z)) != u | u = K(y,z) * x. T(x * K(y,z),K(y,z)) != u | K(y,z) * x = u. K(x,T(y \ z,y)) != u | K(x,z / y) = u. T(K(x,T(y,z)),z) != u | K(x,y) = u. K(T(x,y),T(z,y)) != u | K(x,z) = u. K(x \ y,T(z,y)) != u | K(y / x,z) = u. K(x \ y,T(z,x)) != u | K(y / x,z) = u. K(x,T(y,R(T(x,z),u,w))) != v5 | K(x,y) = v5. K(x,T(y \ z,z)) != u | K(x,z / y) = u. K(x,T(T(y,z),z * x)) != u | K(L(x,w,x),y) = u. K(x,T(T(y,z),z \ 1)) != u | K(x,y) = u. K(T(x,y),T(T(z,y),u)) != w | K(x,T(z,u)) = w. K(L(T(x,y),z,u),T(w,y)) != v5 | K(L(x,z,u),w) = v5. K(T(x,y),R(T(z,y),u,w)) != v5 | K(x,R(z,u,w)) = v5. K(T(x,y),y \ z) != u | K(x,z / y) = u. K((x \ y) * y,T(z,x)) != u | K(y * (y / x),z) = u. K(T(x,y \ 1),z) != u | K(x,T(z,y)) = u. x != T(y,K(z,u)) | x = T(y,K(u,z)). x \ T(y,K(x,z)) = T(x \ y,K(z,x)). K(x,K(y,T(z,u))) \ K(y,x) = T(K(y,x),T(z,y \ u)). x != K(y,T(z,u)) | x = T(K(y,z),u \ 1). K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ 1). K(x,y) * z != K(x,T(y,R(T(x,u),w,v5))) | 1 = z. 1 = K(x,K(y,R(T(x,z),u,w))). K(x,K(y,R(T(x,z),u,w))) = 1. K(x,y) * z != K(x,T(y,R(x,u,w))) | 1 = z. 1 = K(x,K(y,R(x,z,u))). K(x,K(y,R(x,z,u))) = 1. K(x,T(y,z)) != K(x,y) * u | K(x,K(y,z)) = u. T(x,K(y,R(x,z,u))) = x. T(x,y) = T(T(x,y),K(z,R(x,u,w))). T(T(x,y),K(z,R(x,u,w))) = T(x,y). K(x,K(y,z)) * K(x,y) = T(K(x,y),T(z,K(y,u))). T(K(x,y),T(z,K(y,u))) = K(x,K(y,z)) * K(x,y). K(x,y) * K(x,K(y,z)) != u | K(x,T(y,z)) = u. K(x,y) * K(x,K(y,z)) = T(K(x,y),K(u,y) \ z). T(K(x,y),K(z,y) \ u) = K(x,y) * K(x,K(y,u)). x != K(K(y,z),u) | x = K(y,K(z,u)). K(K(x,y) * z,K(x,u)) = K(z,K(x,u)). K(x,K(K(x,y) \ z,u)) = K(x,K(z,u)). T(K(x,y),T(z,K(u,x))) = K(x,T(y,z)). K(x,y) * K(y,K(z,T(x,u))) = T(K(x,y),T(z,u)). K(x,K(y,K(x,z) * u)) = K(x,K(y,u)). K(x,T(y,z)) * K(y,x) = K(y,K(x,z)). x * K(y,T(x,z)) = T(x,K(y,z)) * K(y,x). T(x,K(y,z)) * K(y,x) = x * K(y,T(x,z)). x != K(y \ z,K(y,u)) | x = K(y,K(z,u)). K(x,K(y \ z,T(y,u))) = K(y,K(z,T(x,u))). K(x,K(y,T(z,u / x))) = K(z,K(x,T(y,u))). x != K(y,T(z / u,z)) | x = K(y,u \ z). K(x,y / z) * K(x,K(y,y / z)) = K(x,z \ y). K(x,y / z) * K(x,K(u,z \ y)) = K(x,T(y / z,T(u,z))). R(K(x,y),z,u) \ R(T(K(x,y),w),z,u) = K(w,R(K(x,y),z,u)). L(K(x,T(y,z * u)),u,z) = (z * (u * K(x,y))) / (z * u). (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x). K(x,K(y,z \ u)) != w | K(x,K(y,u \ z)) = w. K(x,y) * T(z * K(y,x),u) = T(K(y,x) * z,u) * K(x,y). T(K(x,y) * z,u) * K(y,x) = K(y,x) * T(z * K(x,y),u). x != K(y,z) * (K(u,y) * w) | x = K(u,y) * (K(y,z) * w). T(K(x,y) * z,K(y,u)) * K(y,u) = K(x,y) * (K(y,u) * z). T(x,K(y,z \ 1)) = T(x,K(y,z)). T(x,K(y,z)) = T(x,K(z,z \ y)). T(x,K(y,y \ z)) = T(x,K(z,y)). T(x,K(y,y * z)) = T(x,K(z,y)). T(x,K(y \ 1,z)) = T(x,K(y,z)). T(T(x,K(y,z)),z \ 1) = T(x,T(z \ 1,y)). T(x,K(y,y \ z)) = T(x,K(y,z)). T(x,K(y,y \ z)) != u | T(x,K(y,z)) = u. T(x,K(y,y * z)) = T(x,K(y,z)). T(T(x,K(y,z)),z * y) = T(x,T(z * y,z)). T(x,K(y \ 1,z)) != u | T(x,K(z,y)) = u. x != T(K(y,z) * u,K(z,y)) | x = u * K(y,z). T(K(x * y,x) * z,K(x,y)) = z * K(x * y,x). x != K(y,K(z,u)) * z | x = T(z,K(u,y)). T(x,K(y,x \ z)) = T(x,K(y,z)). x != T(y,K(z,y \ u)) | x = T(y,K(z,u * (y \ 1))). T(x,K(y,z)) = T(x,K(y,z * (x \ 1))). T(x,K(y,z * (x \ 1))) = T(x,K(y,z)). T(x,K(y,z)) = T(x,K(y,x * z)). T(x,K(y,x * z)) = T(x,K(y,z)). T(x,K(y,x * z)) = T(x,K(z,y)). T(T(x,K(y,z)),x * y) = T(x,T(x * y,z)). (x * x) * y != x * (x * K(z,u)) | T(K(z,u),x * x) = y. T(K(x,y),z * z) = K(x,y). K(x,y) = K(x,T(y,z * z)). K(x,T(y,z * z)) = K(x,y). T(x,T(y,z)) * T(z,x) = z * T(x,y). x * y != K(z,T(u,w)) * (w * z) | (w * T(z,u)) / y = x. (x * T(y,z)) / T(x,y) = T(y,T(z,x)). T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y). x != y * K(y,K(z,u)) | x = T(y,K(u,z)). T(x,K(y,z \ x)) = T(x,K(y,z)). T(x,K(y,z)) * K(y,z \ x) = K(y,z \ x) * x. x \ K(x,y) = T(x \ K(x,y),K(z,x)). T(x \ K(x,y),K(z,x)) = x \ K(x,y). K(K(x,y) * z,K(y,u)) = K(z,K(y,u)). R(x,K(y,z) * u,K(u,K(y,w))) = x. K(x * K(y,z),K(y,u)) = K(x,K(y,u)). K(K(x,y) \ z,K(x,u)) = K(x,K(z,u)). K(x,K(y,(x \ z) \ u)) = K(x,K(y,(z / x) \ u)). K(x,K(y,(z / x) \ u)) = K(x,K(y,(x \ z) \ u)). K(x,K(y,z)) * K(y,x) != u | u = K(y,T(x,z)). K(x,K(y,z)) * K(y,x) != u | K(y,T(x,z)) = u. x * y != z * T(u,u \ w) | (z * ((u \ w) \ w)) / y = x. (x * ((y \ z) \ z)) / T(x,y) = T(y,T(y \ z,x)). (x * T(y,z)) / T(x,y) = T(y,T(z * K(y,u),x)). T(x,T(y * K(x,z),u)) = (u * T(x,y)) / T(u,x). T(x \ K(x,y),x) = T(x \ K(x,y),T(x,z)). T(x \ K(x,y),T(x,z)) = T(x \ K(x,y),x). K(x,x * K(y,z)) = K(x,K(y,z)). x != K(y,K(z,u)) | x = K(y * K(u,z),y). K(x,x * K(y,z)) = K(x * K(z,y),x). K(x * K(y,z),x) = K(x,x * K(z,y)). K(K(x,y) \ z,T(K(x,u),w)) = K(x,K(z,T(u,w))). T(T(x * K(x,x * K(y,z)),u),K(z,y)) = R(T(x,u),K(z,y),x). K(x,T(y,L(x,z,u) \ w)) = K(x,T(y,w / L(x,z,u))). K(x,T(y,z / L(x,u,w))) = K(x,T(y,L(x,u,w) \ z)). T(T(x,y),K(z,y)) != u | T(x,T(y,z)) = u. x != K(y * K(z,y),u) | x = K(y,T(u,z)). K(x,T(y,L(z,u,x))) = K(x,T(y,z)). K(x,T(y,z \ (x * u))) = K(x,T(y,(x \ z) \ u)). K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ (x * u))). K(T(x,y \ z),y) != u | K(T(x,z),y) = u. K(x,K(y,z \ (u \ 1))) != w | K(x,K(y,u * z)) = w. K(x,K(y,z / (u * z))) != w | K(x,K(y,u)) = w. K(x / y,K(x,z)) != u | K(x,K(y,z)) = u. K(((x \ y) \ y) \ y,z) != u | K(y / x,z) = u. K(L(x,y,z) \ u,x) != w | K(u / L(x,y,z),x) = w. K(T(x \ y,x),z) != u | K(y / x,z) = u. K(x,y \ T(z,y)) != u | K(x,z / y) = u. K(x,(y \ 1) \ z) != u | K(x,y * z) = u. K(x,T(y,z \ 1)) != u | K(x,T(y,z)) = u. K(x,y \ z) != u | K(x,(1 / y) * z) = u. K(x,(y \ (z \ 1)) \ u) != w | K(x,(z * y) * u) = w. K(x,(y * (z \ 1)) \ u) != w | K(x,(z / y) * u) = w. K(x,y / z) != u | K(x,y * (z \ 1)) = u. K(x,T(y,z \ (u \ 1))) != w | K(x,T(y,u * z)) = w. K(x,T(y,z \ (u \ z))) != w | K(x,T(y,T(u,z))) = w. K(x,y) * (x \ L(x,z,x)) != u | x \ L(T(x,y),z,x) = u. x * y != T(z / T(u,z),u) | (T(u,z) \ z) / y = x. (T(x,y) \ y) / x = (x \ y) / T(x,y). T(x \ y,y) / x = (x \ y) / T(x,y). T(x,(y * z) \ (y * x)) = T(x,z \ x). T(x,y \ (z * x)) = T(x,(z \ y) \ x). T(x,(y \ z) \ x) = T(x,z \ (y * x)). K(x,T(y,z \ (u * y))) = K(x,T(y,z \ u)). K(x,K(y,z)) * (z / K(x,y)) = K(y,x) * z. (x / y) \ T(x,K(z,u)) != w | y * K(z,K(u,x)) = w. K(x,K(y,z \ (u * x))) = K(x,K(y,z \ u)). K(x,K(y,R(z,u,w) * (z \ y))) = K(x,K(y,z \ R(z,u,w))). T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y). K(R(x,y,z),T(u,x \ w)) = K(R(w / (w / x),y,z),u). K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,y \ x)). K(K(R(x,y,z),u) * w,T(x,v5)) = K(w,T(x,v5)). K(T(x,L(x,y,z) * u),T(w,u)) = K(L(x,u,L(x,y,z)),w). K(T(x,y),T(z,L(z,u,w) * y)) = K(x,L(z,y,L(z,u,w))). K(K(x,y) * T(y,z),T(u,z)) = K(y * K(T(x,z),y),u). x != (y / z) * K(u,z) | x = y / T(z,u). T(K(x,y),z) * (z / y) = z / T(y,x). K(x,y) * (K(z,y) / y) = K(z,y) / T(y,x). x != K((y * z) / u,y) | x = K((u / z) \ y,y). K(x \ (y * z),T(y,z)) = K((x / z) \ y,y). (x \ (1 / y)) * (1 / (x \ (1 / y))) = 1 * K((1 / y) / x,x * y). K(T(x * y,y) / x,z) = K(y,T(T(z,x),x * y)). K(x * K(y,T(x,z)),u) = K(x,T(u,T(y,z \ x))). K(x,K(y,T(z,u / x))) != w | K(x,K(z,T(y,u))) = w. T(T(x,K(y,z)),(y \ z) \ 1) = T(x,T((y \ z) \ 1,y)). T(T(x,K(y,z)),y * x) = T(x,T(x * y,z)). T(x,y) * T(x \ K(x,z),x) != u | (x \ K(x,z)) * T(x,y) = u. K(x,1) * ((y \ R(y,z,u)) / K(x,R(y,w,v5))) = K(R(y,w,v5),x) * (y \ R(y,z,u)). K(x,y) * K(x,K(y,z \ u)) = T(K(x,y),(z \ (u * x)) \ 1). T(K(x,y),(z \ (u * x)) \ 1) = K(x,y) * K(x,K(y,z \ u)). x * (T(x,y) \ (K(z,x) / x)) = K(z,x) / T(x,y). K(x,y) * T(z,T(z * x,y)) = T(z,x * z) * K(x,y). (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y). x * y != (z * (u * w)) / K(L(u,w,z),w) | x \ (z * (w * u)) = y. (x * (y * z)) \ (x * (z * y)) = K(z,L(y,z,x)). T(K(x,y),z * (u * K(w,x))) = T(K(x,y),z * u). K(x,L(y \ z,y,u)) != w | L(K(x,y \ z),z,u) = w. L(K(x,L(y,z,u)),y,w) = K(x,L(y,z,u)). K((x \ y) \ z,L(z,u,w)) = K(y \ (x * z),L(z,u,w)). K(L(x,y,z),L(u,w,x)) = K(L(x,y,z),u). K(L(x,y,z),u \ (x * w)) = K(L(x,y,z),(x \ u) \ w). K(L(x,y,z),(x \ u) \ w) = K(L(x,y,z),u \ (x * w)). K((x * y) \ z,y) != u | K(x \ (y \ z),y) = u. L(K(x,T(y,z)),z,u) = K(x,(u * (y \ z)) \ (u * z)). K(x,(y * (z \ u)) \ (y * u)) = L(K(x,T(z,u)),u,y). K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z). L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w). (x * y) * K(z,u \ (x * y)) = x * (y * K(z,(x \ u) \ y)). K(x,y \ (z * K(u,z))) != w | w = K(x,(z \ y) \ K(u,z)). K(x,y \ (z * K(u,z))) != w | K(x,(z \ y) \ K(u,z)) = w. L(K(x,x * y),y,z) = K(x,u \ ((u * y) * x)). K(x,y) * K(y,K(z,T(x,u))) != w | T(K(x,y),T(z,u)) = w. K(x,K(y \ z,T(y,u))) != w | K(y,K(x,T(z,u))) = w. K(x * y,y) * K(x,K(y,z)) != u | K(x * y,T(y,z)) = u. (x * (y * z)) * K(z,L(y,z,x)) != u | u = x * (z * y). (x * (y * z)) * K(z,L(y,z,x)) != u | x * (z * y) = u. K(L(x \ y,x,z / y),x) != u | K((z / y) \ (x \ z),x) = u. L(K(x,x * (y \ z)),y \ z,u) = K(x,y \ (z * x)). K(x,y) * z != K(x,u) * (w * K(x,y)) | T(K(x,u) * w,K(x,y)) = z. T(K(x,y) * z,K(x,u)) = K(x,y) * T(z,K(x,u)). T((K(x,y) * K(y,z)) \ (K(x,y) * (u * K(y,z))),K(x,y)) = R(T(u,K(x,y) * K(y,z)),K(x,y),K(y,z)). x != K(K(y,z) \ u,y) | x = K(u,y). K((x * K(y,z)) \ u,y) = K(x \ u,y). K((x * K(y,z)) \ u,z) = K(x \ u,z). K(x \ y,z) = K((K(u,z) * x) \ y,z). K((K(x,y) * z) \ u,y) = K(z \ u,y). K((x * (y * z)) \ u,y) = K((x * (z * y)) \ u,y). K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z). K(T(x * K(y * K(z,u),w),y * K(z,u)),u) = K(y \ (x * T(y * K(z,u),w)),u). (x * K(y \ z,u)) \ x = K(u,(y * K(w,u)) \ z). K(x,(y * K(z,x)) \ u) = (w * K(y \ u,x)) \ w. K(x,y) * (K(z,x) * (u * K(y,x))) = T(K(z,x) * u,K(x,y)). L(K(x,y),z,T(y,u)) = K(x,y). L(K(x,y),z,T(x,u)) = K(x,y). x \ (y * K(z,T(x,u))) = (x \ y) * T(K(z,x),u). L(K(x,y),z,x \ 1) = K(x,y). x != L(K(y,(z \ u) \ w),w,z) | x = K(y,u \ (z * w)). K(x,((x \ 1) \ y) \ z) = K(x,y \ ((x \ 1) * z)). x != L(K(y,z),u * z,w) | x = K(y,L(z,u,w)). K(x,y) = K(x,L(y,z,x \ 1)). K(x,L(y,z,x \ 1)) = K(x,y). (((x \ y) * x) * z) \ (y * z) = K(x,z \ (x \ (y * z))). x != (y * ((z / u) / y)) * u | x = u * (y * ((u \ z) / y)). x * K(y,z \ (y \ x)) = z * (y * ((z \ x) / y)). K(x \ y,z \ (x \ y)) * (y / x) = T(y / x,T((x * z) \ y,x)). K(x,K(y,z)) * (K(x,y) * u) != w | K(x,T(y,z)) * u = w. K(x,y) * (K(x,K(y,z)) * u) = K(x,T(y,z)) * u. K(L(K(x,y),z,u),w) = L(K(x,K(y,w)),z,u). L(K(x,K(y,z)),u,w) = K(L(K(x,y),u,w),z). x * K(y,K(z,u)) = (x * K(z,y)) * T(K(y,z),u). (x * K(y,z)) * T(K(z,y),u) = x * K(z,K(y,u)). L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,u,w))). L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w))). x != L(K(y,K(z,u)),w,v5) | x = K(y,K(u,L(z,w,v5))). K(x,K(y,L(z,u,w))) = K(z,K(y,L(x,u,w))). x != L(K(y,K(z,u)),w,v5) | x = K(L(K(y,z),w,v5),u). K(x,K(y,L(z,u,w))) = K(L(K(z,x),u,w),y). K(L(K(x,y),z,u),w) = K(y,K(w,L(x,z,u))). K(x,K(y,L(z,u,w))) = K(z,K(x,L(y,u,w))). K(L(K(x,y),z,u),w) = K(w,K(y,L(x,z,u))). K(x,K(y,L(z,u,w))) = K(x,K(z,L(y,u,w))). K(x,K(y \ (z \ u),L(w,y,z))) = K(w,K(x,(z * y) \ u)). K(L(K(x,y),z,u),w) != v5 | K(y,K(w,L(x,z,u))) = v5. K(x,K(y,z * u)) = K(x,K(z * u,L(y,u,z))). K(x,K(y * z,L(u,z,y))) = K(x,K(u,y * z)). K(x,K(y,T(z,u))) * K(x * T(y,u),x) = K(x * T(y,u),T(x,z)). K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y \ z,z)). x * y != (z * (u * K(w,v5))) * L(K(v5,w),u,z) | (z * u) / y = x. (x * y) / (x * (y * K(z,u))) = L(T(K(u,z),x * (y * K(z,u))),y,x). L(T(K(x,y),z * (u * K(y,x))),u,z) = (z * u) / (z * (u * K(y,x))). T(R(K(x,y),z,u),w) * w = w * R(K(x,y),z,u). T(T(x,L(K(y,z),u,w)),L(K(y,z),u,w)) = x. T(x,L(K(y,z),u,w)) = x * K(L(K(y,z),u,w),x). x * K(L(K(y,z),u,w),x) = T(x,L(K(y,z),u,w)). T(L(K(x,y),z,u) \ w,L(K(x,y),z,u)) = w / L(K(x,y),z,u). R(K(x,T(y,z)),u,w) * (z * K(y,v5)) = (z * K(y,v5)) * R(K(x,y),u,w). x != K(T(y / (y / z),u),w) | x = K(T(z,u),T(w,y)). K(T(x,y),T(z,x \ u)) = K(T(x,y),T(z,u)). K(T(x,y),T(z,u)) = K(T(x,y),T(z,x * u)). K(T(x,y),T(z,x * u)) = K(T(x,y),T(z,u)). K(x * y,x \ (1 / y)) = ((y \ x) * (1 / x)) * y. K((x \ y) * y,T(z,y \ x)) != u | K((x / y) \ y,z) = u. T(x,R((y * z) / y,u,w)) = x * K(T(x,y),R(z,u,w)). K(T(x,y * K(z,y)),u) = u / T(u,x * K(T(x,z),y)). x != T(y,z \ K(u,z \ 1)) | x = T(y,K(u,z \ 1) / z). x * K(T(x,y),z \ 1) = T(x,K(y,z \ 1) / z). T(x,K(y,z \ 1) / z) = x * K(T(x,y),z \ 1). K(x,T(((y * K(z,x)) * u) / w,y * u)) != v5 | K(x,w \ ((y * K(z,x)) * u)) = v5. T(x,R((y * z) / y,u,w)) = T(x,R(T(z,y),u,w)). x != K(y,K(z,u)) * K(y,z) | x = T(K(y,z),u). T(K(x,y),T(z,K(y,u))) = T(K(x,y),z). T(K(x,y),z / K(u,y)) = T(K(x,y),K(u,y) \ z). x != K(y,z) * K(y,K(z,u)) | x = T(K(y,z),u). T(K(x,y),K(z,y) \ u) = T(K(x,y),u). K(x,y) * K(y,K(z,T(x,x * u))) = T(K(x,y),T(z,u * x)). x != K(y,z \ u) * u | x = u * K(y,u / z). T(x,K(y,z)) * K(y,z \ x) = x * K(y,x / z). (T(x,T(x \ y,z)) * z) \ (z * ((x \ y) \ y)) = K(z,x). x != (y * T(z,u)) / T(y,z) | x = T(z,T(u,y)). T(x,T(y * K(x,z),u)) = T(x,T(y,u)). T(x,T(y / (x \ z),u)) = T(x,T(y / (z / x),u)). T(x,T(y / (z / x),u)) = T(x,T(y / (x \ z),u)). K(x,T(y,T(((z * u) / z) * x,x \ z))) = K(x,T(y,z \ (x * (z * R(u,x,x \ z))))). K(x,T(y,z \ (x * (z * R(u,x,x \ z))))) = K(x,T(y,T(((z * u) / z) * x,x \ z))). K(L(x,y,x),z) = K(T(u * x,x) / u,z). K(x,y) = K(T(z * x,x) / z,y). K(T(x * y,y) / x,z) = K(y,z). K(T(x,y \ x) / y,z) = K(y \ x,z). x != K(y * K(z,T(y,u)),w) | x = K(y,T(w,T(z,u))). K(x,T(y,T(z,u \ x))) = K(x,T(y,T(z,u))). K(x,T(y,T(z,x \ u))) = K(x,T(y,T(z,u))). x * (K(y,x) / T(x,z)) = T(x,z) \ ((x \ 1) \ K(y,x)). T(x,y) \ ((x \ 1) \ K(z,x)) = x * (K(z,x) / T(x,y)). T(x,K(y,z)) * K(u,y) = T(x * K(u,y),K(y,z)). T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z). T(T(x,K(y,z)),K(y,u)) = K(y,K(x,z)) * T(x,K(y,u)). K(x,K(y,z)) * T(y,K(x,u)) = T(T(y,K(x,z)),K(x,u)). x != (y * K(z,u)) \ y | x = K(u,z). K(x,(y * K(z,x)) \ u) = K(x,y \ u). K(x,(y * K(z,x)) \ u) != w | K(x,y \ u) = w. K(x,(y * x) \ z) = K(x,(x * y) \ z). K(x,(y * K(x,z)) \ u) = K(x,y \ u). K(x,(y * L(K(z,x),u,w)) \ v5) = K(x,y \ v5). K(x,y \ z) = K(x,(K(x,u) * y) \ z). K(x,(K(x,y) * z) \ u) = K(x,z \ u). K(x,(y * (x \ z)) \ u) = K(x,(y * (z / x)) \ u). K(x,(y * (z / x)) \ u) = K(x,(y * (x \ z)) \ u). K(T(x,y),(z * K(u,x)) \ w) = K(T(x,y),z \ w). x != K(y,(y * z) \ u) | x = K(y,z \ (y \ u)). K(x,(y * x) \ z) = K(x,y \ (x \ z)). K(x,(y * x) \ z) != u | K(x,y \ (x \ z)) = u. T(x,(y * K(x,z)) \ u) = x * K(x,y \ u). K(x,a(K(x,y),z,u)) = K(x,(z * u) \ ((K(x,y) * z) * u)). K(x,(y * z) \ ((K(x,u) * y) * z)) = K(x,a(K(x,u),y,z)). K(x,L(T(y,x),x,z)) = K(x,z \ (x \ (z * (y * x)))). K(x,y \ (x \ (y * (z * x)))) = K(x,L(T(z,x),x,y)). T(x,(y * K(x,z)) \ u) = T(x,y \ u). T(x,y \ z) = T(x,(K(u,x) * y) \ z). T(x,(K(y,x) * z) \ u) = T(x,z \ u). T(x,(y * (x * z)) \ u) = T(x,(y * (z * x)) \ u). T(x,(y * (z * x)) \ u) = T(x,(y * (x * z)) \ u). x != T(y,(K(z,y) * u) \ (K(z,y) * w)) | x = T(y,u \ w). T(x,y \ (K(z,x) * u)) = T(x,y \ u). T(x,y \ ((x \ z) * x)) = T(x,y \ z). T(x,y \ (z * x)) = T(x,y \ (x * z)). T(x,y \ ((z / x) \ u)) = T(x,y \ ((x \ z) \ u)). L(T(x,y \ z),u,w) \ L(x,u,w) = K(y \ ((x \ z) * x),L(x,u,w)). K(x \ ((y \ z) * y),L(y,u,w)) = L(T(y,x \ z),u,w) \ L(y,u,w). K(x,T(y,z \ u)) = K(x,T(y,z \ (y \ u))). K(x,T(y,z \ (y \ u))) = K(x,T(y,z \ u)). x != T(y,z \ (y * u)) | x = T(y,(z / y) \ u). T(x,y \ (z * x)) = T(x,(y / x) \ z). T(x,(y / x) \ z) = T(x,y \ (z * x)). L(x,y,z) \ L(T(x,u \ (x * w)),y,z) = K(L(x,y,z),u \ (w * x)). L(T(x,y \ (z * x)),u,w) \ L(x,u,w) = K((y / x) \ z,L(x,u,w)). K(x,T(y,(y * z) \ u)) = K(x,T(y,z \ u)). K(x * y,T(x,z)) = K(x * y,T(x,y \ z)). K(x * y,T(x,y \ z)) = K(x * y,T(x,z)). x != K(y * z,T(y,u)) | x = K(z * y,T(y,u)). K(x * y,T(x,y \ z)) = K(y * x,T(x,z)). K(x * y,T(y,z)) = K(x * y,T(y,x \ z)). K(x * y,T(y,x \ z)) = K(x * y,T(y,z)). K(x * y,T(y,z)) = K(x * y,T(y,x * z)). K(x * y,T(y,x * z)) = K(x * y,T(y,z)). K(x,(x \ y) \ z) != u | K(x,(y / x) \ z) = u. K(x,(K(y,x) * z) \ u) != w | K(x,z \ u) = w. K(x,(y * (x \ z)) \ u) != w | K(x,(y * (z / x)) \ u) = w. K(x,(y * (z * K(u,x))) \ w) = K(x,(y * z) \ w). K(x,L(x \ y,x,z)) != u | K(x,z \ (x \ (z * y))) = u. K(x,(y / x) \ z) = K(x,y \ (x * z)). K(x,y \ (x * z)) != u | K(x,(y / x) \ z) = u. R(x,y,z) * (x \ K(u,T(x,w))) = (x \ R(x,y,z)) * T(K(u,x),w). (x \ R(x,y,z)) * T(K(u,x),w) = R(x,y,z) * (x \ K(u,T(x,w))). x * (y * ((x \ z) / y)) != z * u | K(y,x \ (y \ z)) = u. T(K(x,y) \ T(K(x,T(y,z)) * u,w),K(x,y)) = K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w). K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = T(K(x,y) \ T(K(x,T(y,z)) * u,w),K(x,y)). (x \ R(x,y,x)) * T(K(y,x),z) = K(y * x,x) * K(y,K(x,z)). R(K(x,y),z,u) * w != T(R(K(x,y),z,u),v5) * v5 | T(v5,R(K(x,y),z,u)) = w. T(R(K(x,y),z,u) \ w,R(K(x,y),z,u)) = w / R(K(x,y),z,u). K(L(K(x,y),z,u),w) = K(w,L(K(x,y),z,u)). x != K(L(K(y,z),u,w),v5) | x = K(v5,K(z,L(y,u,w))). K(x,L(K(y,z),u,w)) = K(x,K(z,L(y,u,w))). x != K(y,K(z,L(u,w,v5))) | x = K(y,K(u,L(z,w,v5))). K(x,L(K(y,z),u,w)) = K(x,K(y,L(z,u,w))). K(x,K(y,L(z,u,w))) = K(x,K(y,L(z,u * z,w))). K(x,K(y,L(z,u * z,w))) = K(x,K(y,L(z,u,w))). K(x * y,x \ (1 / y)) != z | K(x \ y,y \ x) = z. K(x,K(y,z \ 1) / z) = K(T(x,y),z \ 1). K(x,K(y,z \ 1) / z) = K(T(x,((z \ 1) / ((1 / (z \ 1)) \ y)) \ 1),z \ 1). K(T(x,((y \ 1) / ((1 / (y \ 1)) \ z)) \ 1),y \ 1) = K(x,K(z,y \ 1) / y). T(x,R(y / (y / z),u,w)) = T(x,R(T(z,z \ y),u,w)). T(x,R(T(y,y \ z),u,w)) = T(x,R(z / (z / y),u,w)). x != T(K(y,z),K(u,z) \ w) | x = T(K(y,z),w). T(K(x,y),z / K(u,y)) = T(K(x,y),z). T(K(x,y),z * K(y,u)) = T(K(x,y),z). K(x,K(y,z)) * K(y,z \ x) = K(y,x / z). K(x,K(y,z)) * K(y,x \ z) = K(y,z / x). K(x,K(y,z)) * K(x,y \ z) = K(x,z / y). K(x,K(y,z)) * K(y,x \ (y * z)) = K(y,(y * z) / x). (K(x,y / z) * K(K(x,z \ y),u)) / T(K(x,z \ y),u) = R(K(x,K(z,y)),K(x,z \ y),K(K(x,z \ y),u)). T(x * K(L(y \ 1,z,u) \ 1,w),K(w,v5)) = T(x,K(w,v5)) * L(K(y,w),z,u). T(x * K(y,z),K(z,u)) \ T(x,K(z,u)) = K(z,y). (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x). L(T(x,y \ ((x \ z) \ u)),w,v5) \ L(x,w,v5) = K(y \ ((z / x) \ u),L(x,w,v5)). K(x,(y * (K(z,x) * u)) \ w) = K(x,(y * u) \ w). x != K(y,K(z,L(u,w,v5))) | x = K(u,K(z,L(y,w,v5))). K(x,K(y,L(z,u,w))) = K(z,K(y,L(x,u * z,w))). K(x,K(y,L(z,u * x,w))) = K(z,K(y,L(x,u,w))). T(x,K(y,z)) \ T(x * K(y,u),K(y,z)) = K(y,u). T(x,K(y,z)) * K(y,u) = T(x * K(y,u),K(y,z)). T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z). x != T(y,K(z,u)) * K(z,y) | x = y * K(z,T(y,u)). T(x * K(y,x),K(y,z)) = x * K(y,T(x,z)). T(x * K(y,x),K(y,z)) != x * u | K(y,T(x,z)) = u. (x * (y * z)) * K(L(z,y,x),u) = x * (y * T(z,u)). x != K(y,R(z / u,w,v5) \ 1) | x = R(K(y,u / z),w,v5). K(x,(y * z) / (u * z)) = R(K(x,y / u),y,z). R(K(x,y / z),y,u) = K(x,(y * u) / (z * u)). R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z)). R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z). R(K(x,y),z,u) = K(x,(z * u) / ((y \ z) * u)). K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z). R(K(x,R(y,z,u) \ y),y,w) = K(x,(y * w) / (R(y,z,u) * w)). x != R(K(y,z),u,y) | x = K(y,z). K(x,(y * x) / z) = K(x,y / (z / x)). R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y). x != K(y,z / (u / y)) | x = K(y,z / (y \ u)). K(x,(y * x) / z) = K(x,y / (x \ z)). K(x,R(y,y \ z,u)) = R(K(x,y),z,u). x != K(y,R(z,z \ u,w)) | x = (v5 * R(K(z,y),u,w)) \ v5. R(K(x,y),z,u) = (w * R(K(y,x),z,u)) \ w. (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w). K(x,R(y,z,u)) = R(K(x,y),y * z,u). R(K(x,y),y * z,u) = K(x,R(y,z,u)). K(x,R(y,T(z,y),u)) = R(K(x,y),z * y,u). R(K(x,y),z * y,u) = K(x,R(y,T(z,y),u)). K(x,R(R(y,z,u),z * u,w)) = R(K(x,R(y,z,u)),(y * z) * u,w). R(K(x,R(y,z,u)),(y * z) * u,w) = K(x,R(R(y,z,u),z * u,w)). K(x,R(y,T(y,z) \ u,w)) = R(K(x,y),K(z,y) * u,w). R(K(x,y),K(z,y) * u,w) = K(x,R(y,T(y,z) \ u,w)). x != R(K(y,z),z * K(u,y),w) | x = K(y,z * K(u,y)). K(x,R(y,K(z,x),u)) = K(x,y * K(z,x)). K(x,R(y,z,x)) = K(x,y). x != R(K(y,z),u,y \ 1) | x = K(y,z). K(x,R(y,z,x \ 1)) = K(x,y). x != R(K(y,z),y,u) | x = K(y,z). K(x * y,R(x,y,z)) = K(x * y,x). x != R(K(y \ 1,z),u,w) | x = K(R(y,u,w) \ 1,z). K(x \ 1,R(y,z,u)) = K(R(x,y * z,u) \ 1,y). K(R(x,y * z,u) \ 1,y) = K(x \ 1,R(y,z,u)). R(T(K(x,y),z),y * u,w) = T(K(x,R(y,u,w)),z). R(K(x,y),(y * K(z,x)) * u,w) = K(x,R(y * K(z,x),u,w)). R(K(x,y),T(y,z) * u,w) = K(T(x,z),R(T(y,z),u,w)). R(K(x,y),T(y,T(z,u)) * u,w) = K(x,R(y,u * K(y,z),w)). K(x,y / (z * x)) = K(x,(y / x) / z). K(x,(y / x) / z) = K(x,y / (z * x)). T(x,R(y,z,x)) = x * K(x,y). K(x,K(y,R(z,u,x))) = K(x,K(y,z)). T(x,R(y,z,x \ 1)) = x * K(x,y). T(x,R(y,z,x)) = T(x,y). T(x,(y * x) / z) = T(x,y / (z / x)). T(x,T(y / (z * x),z)) = T(x,z \ (y / x)). T(x,T((y * x) / z,u)) = T(x,T(y / (z / x),u)). K(x,K(y,T((z * x) / u,u / x))) = K(x,K(y,(u / x) \ z)). T(x,R(y,z,x \ 1)) = T(x,y). T(x,T((y * (x \ 1)) / z,z / (x \ 1))) = T(x,(z / (x \ 1)) \ y). x != K(y,(z / y) / u) | x = K(y,(y \ z) / u). K(x,y / (z * x)) = K(x,(x \ y) / z). K(x,(x \ y) / z) = K(x,y / (z * x)). x != T(y,z / (u / y)) | x = T(y,z / (y \ u)). T(x,(y * x) / z) = T(x,y / (x \ z)). K(x,y / z) = K(x,(x * y) / (z * x)). K(x,(x * y) / (z * x)) = K(x,y / z). K(x,(x \ y) / (z / x)) = K(x,y / z). K(x,(x \ y) / (x \ z)) = K(x,y / z). x != K(y,(y \ z) / u) | x = K(y,z / (u * y)). K(x,y / z) = K(x,y / ((x \ z) * x)). K(x,y / ((x \ z) * x)) = K(x,y / z). K(x,y / (x \ z)) = K(x,(x * y) / z). K(x,(x * y) / z) = K(x,y / (x \ z)). K(x,y / (z * x)) = K(x,y / (x * z)). x != K(y,z / (y \ u)) | x = K(y,(z * y) / u). K(x,(x * y) / z) = K(x,(y * x) / z). K(x,(y * x) / z) = K(x,(x * y) / z). K(x,(y * z) / (z * x)) = K(x,R(y / x,x,z)). K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x)). T(x,(y * x) / z) = x * K(x,(x * y) / z). x * K(x,(x * y) / z) = T(x,(y * x) / z). x != K(y,z * K(u,y)) | x = K(y,z). K(x,R(y,K(z,x),u)) = K(x,y). K(x,R(R(y,K(z,x),u),w,v5)) = K(x,R(y,w,v5)). x / (R(K(y,z),u,w) * x) = R(K(z,y),u,w). (x * R(K(y,z),u,w)) * R(K(z,y),u,w) = x. R(K(x,y),z,u) * w = R(K(y,x),z,u) \ w. R(K(x,y),z,u) \ w = R(K(y,x),z,u) * w. x != T(y,T(z / (u * y),u)) | x = T(y,(u * y) \ z). T(x,y \ (z / x)) = T(x,(y * x) \ z). T(x,(y * x) \ z) = T(x,y \ (z / x)). x != T(y,z \ (u / y)) | x = T(y,z \ (y \ u)). T(x,(y * x) \ z) = T(x,y \ (x \ z)). T(x,L(x \ y,x,z)) = T(x,z \ (x \ (z * y))). (x * y) / ((K(z,u) * x) * y) = R(K(u,z),x,y). R(K(x,y),z,u) \ (z * u) = (K(y,x) * z) * u. R(K(x,(y / z) \ x),x,z) = K(x,(y / (x * z)) \ 1). K(x,(x * y) / z) = K(x,(z / y) \ x). x != K(y,z) | x = R(K(y,z),y,u). K(x,(x * y) / z) = R(K(x,(z / y) \ x),x,u). R(K(x,(y / z) \ x),x,u) = K(x,(x * z) / y). x != K(y,(z / u) \ y) | x = K(y,y * (u / z)). K(x,(x * y) / z) = K(x,x * (y / z)). x != K(y,(y * z) / u) | x = K(y,(z * y) / u). K(x,(y / z) \ x) = K(x,(z * x) / y). K(x,(y * x) / z) = K(x,(z / y) \ x). x != K(y,(y * z) / u) | x = K(y,z / (y \ u)). K(x,(y / z) \ x) = K(x,z / (x \ y)). K(x,y / (x \ z)) = K(x,(z / y) \ x). K(x,x * (y / z)) = K(x,(y * x) / z). K(x,(y * x) / z) = K(x,x * (y / z)). x * K(x,x * (y / z)) = T(x,(y * x) / z). x != K(y,(z * y) / u) | x = K(y,T(u \ (z * y),z)). K(x,(y / z) \ x) = K(x,T(y \ (z * x),z)). K(x,T(y \ (z * x),z)) = K(x,(y / z) \ x). x != K(y,z / u) | x = T(K(y,u \ z),u). K(x,(y / z) \ x) = T(K(x,y \ (z * x)),y). T(K(x,y \ (z * x)),y) = K(x,(y / z) \ x). K(x,y / (x \ z)) * u = K(x,(z / y) \ x) * u. K(x,y / z) = K(x,((x * z) / y) \ x). K(x,((x * y) / z) \ x) = K(x,z / y). (x * K(y,y * (z / u))) / (y \ x) = T(y,T((z * y) / u,x)). T(x,(y * x) / z) != u | T(x,x * (y / z)) = u. x != K(y,R(z / y,u,w)) | x = K(y,R(y \ z,u,w)). K(x,(y * z) / (z * x)) = K(x,R(x \ y,x,z)). K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x)). K(x,(x * y) / z) != u | u = K(x,(z / y) \ x). K(x,(x * y) / z) != u | K(x,(z / y) \ x) = u. K(x,(y * x) / z) != u | K(x,(z / y) \ x) = u. K(x,T(y \ (z * x),z)) != u | K(x,(y / z) \ x) = u. R(T(K(x,y),z),y * u,w) = K(x,T(R(y,u,w),z)). x != T(y,T(z / (u / y),w)) | x = T(y,T(z / (y \ u),w)). T(x,T((y * x) / z,u)) = T(x,T(y / (x \ z),u)). T(x,y / (x \ z)) = T(x,(z / y) \ x). x != T(y,z / (y \ u)) | x = T(y,(z * y) / u). T(x,(y / z) \ x) = T(x,(z * x) / y). T(x,(y * x) / z) = T(x,(z / y) \ x). T(x,x * (y / z)) = T(x,(z / y) \ x). T(x,(y / z) \ x) = T(x,x * (z / y)). T(x,(y / (z * y)) \ x) = T(x,x * z). R(T(K(x,y),z),y * u,w) = K(x,R(T(y,z),u,w)). R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w)). R(K(x,T(y,z)),u,w) = K(x,R(T(y,z),y \ u,w)). K(x,R(T(y,z),y \ u,w)) = R(K(x,T(y,z)),u,w). R(K(x,T(y / (z / u),w)),(y / (z / u)) * (z / u),u) = K(x,T((y * u) / z,w)). K(x,R(T(y,z),y \ 1,u)) = K(x,T(y,z)). K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z). x != T(T(y,z / u),u / z) | x = L(y,u / z,u / z). R(x,y / z,z * (y \ 1)) = L(x,z / y,z / y). x * y != K(z,u) * w | x \ (K(u,z) \ w) = y. (K(x,y) \ z) \ (K(x,y) \ (z * u)) = L(u,z,K(y,x)). L(K(x,y) * (K(z,u) * w),K(y,x),K(u,z)) = (K(u,z) * K(y,x)) \ w. K((K(x,y) * z) \ u,y) = K(z \ (K(y,x) * u),y). K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u)). x != K((K(y,z) * u) \ w,z) | x = K(u \ w,z). K(x \ (K(y,z) * u),y) = K(x \ u,y). K(x \ (K(y,z) * u),z) = K(x \ u,z). K(x \ (y \ z),y) = K(x \ (T(y,u) \ z),y). K(x \ (T(y,z) \ u),y) = K(x \ (y \ u),y). K(x \ (K(y,z) * u),T(y,w)) = K(x \ u,T(y,w)). K(x \ (y * K(z,u)),z) = K(x \ y,z). K(x \ (y * T(z,u)),u) = K(x \ (y * z),u). K(x \ (y * K(z,u)),T(z,w)) = K(x \ y,T(z,w)). K(x \ (y * (z * u)),z) = K(x \ (y * (u * z)),z). K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u). K(a(x,y,T(z,y)),y) = K((x * (z * y)) \ ((x * y) * z),y). K((x * (y * z)) \ ((x * z) * y),z) = K(a(x,z,T(y,z)),z). K(x,y \ z) = K(x,y \ (K(x,u) * z)). K(x,y \ (K(x,z) * u)) = K(x,y \ u). K(x,y \ (x * z)) = K(x,y \ (z * x)). K(x,y \ (z * x)) = K(x,y \ (x * z)). K(x,y \ (x \ z)) = K(x,y \ (T(x,u) \ z)). K(x,y \ (T(x,z) \ u)) = K(x,y \ (x \ u)). K(x,T(y \ (K(x,z) * u),w)) = T(K(x,y \ u),w). K(x,y \ z) = K(x,y \ (z * K(u,x))). K(x,y \ (z * K(u,x))) = K(x,y \ z). x != K(y,z \ (y * u)) | x = K(y,(z / y) \ u). K(x,y \ (z * x)) = K(x,(y / x) \ z). K(x,(y / x) \ z) = K(x,y \ (z * x)). x != K(y,z \ (y * u)) | x = K(y,(y \ z) \ u). K(x,y \ (z * x)) = K(x,(x \ y) \ z). K(x,(x \ y) \ z) = K(x,y \ (z * x)). x != K(y,z \ (u * y)) | x = K(y,y * (z \ u)). K(x,y \ (x * z)) = K(x,x * (y \ z)). K(x,y \ ((x \ z) * x)) = K(x,y \ z). K(x,y \ (z * L(K(u,x),w,v5))) = K(x,y \ z). K(x,y \ (z * (x \ u))) = K(x,y \ (z * (u / x))). K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u))). K(x,y \ (z \ K(u,x))) = K(x,y \ (z \ 1)). K(x,y \ z) = K(x,(x * y) \ (z * x)). K(x,(x * y) \ (z * x)) = K(x,y \ z). K(x,y \ ((x \ 1) * (z * x))) = K(x,y \ z). K(x,K(y,z \ u)) = K(x,K(y,z \ (y \ u))). K(x,K(y,z \ (y \ u))) = K(x,K(y,z \ u)). x != K(y,z \ ((y \ 1) * u)) | x = K(y,((y \ 1) \ z) \ u). K(x,y \ z) = K(x,((x \ 1) \ y) \ (z * x)). K(x,((x \ 1) \ y) \ (z * x)) = K(x,y \ z). K(x,y \ (z * x)) = K(x,((x \ 1) * y) \ z). K(x,((x \ 1) * y) \ z) = K(x,y \ (z * x)). x != K(y,z \ ((y \ u) * y)) | x = K(y,z \ u). K(x,((x \ 1) * y) \ (x \ z)) = K(x,y \ z). K(x,y \ (z * (u * K(w,x)))) = K(x,y \ (z * u)). K(x \ (y * z),T(y,u)) = K(x \ (z * y),T(y,u)). K(x \ (y * z),T(z,u)) = K(x \ (z * y),T(z,u)). K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(L(u,z,y),y * z,x),y). K(x,T(y \ (K(x,z) * u),w)) = K(x,T(y \ u,w)). K(x,(y * (z / x)) \ (u \ (y * (z / x)))) = K(x,(u * (y * (z / x))) \ (y * (x \ z))). K(x,(y * (z * (u / x))) \ (z * (x \ u))) = K(x,(z * (u / x)) \ (y \ (z * (u / x)))). K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w)). x != K(y \ (z * u),T(z,u)) | x = K((y / u) \ z,z). K(x \ (y * z),T(z,y)) = K((x / y) \ z,z). K(x \ (y * T(z,u)),T(z,w)) = K(x \ (z * (y * K(z,u))),T(z,w)). K(x \ (y * (z * K(y,u))),T(y,w)) = K(x \ (z * T(y,u)),T(y,w)). x != K((y * z) \ (y * u),T(u,w)) | x = K(z \ u,T(u,w)). K(((x * y) / x) \ z,z) = K(y \ z,T(z,x)). x != K(((y * z) / y) \ u,u) | x = K(u * (z \ K(z,y)),u). K(x \ y,T(y,z)) = K(y * (x \ K(x,z)),y). K(x * (y \ K(y,z)),x) = K(y \ x,T(x,z)). K((x \ K(x,y)) * z,z) = K(x \ z,T(z,y)). K(x,T(y \ T(x,z),u)) = K(x,T(y \ x,u)). K(x,T(y \ (x * z),u)) = K(x,T(y \ (z * x),u)). K(x,T(y \ (z * x),u)) = K(x,T(y \ (x * z),u)). K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ T(x,u),w)). K(x,L(L(y,z,K(u,x)),K(u,x) * z,w)) = K(x,(w * (K(u,x) * z)) \ (w * (z * y))). x != K(y,T(z \ (u * y),u)) | x = K(y,(z / u) \ y). K(x,T(y \ (x * z),z)) = K(x,(y / z) \ x). x != K(y,(z / u) \ y) | x = K(y,u / (y \ z)). K(x,T(y \ (x * z),z)) = K(x,z / (x \ y)). x * K(y,T((z / u) \ y,x)) = K(y,T(z \ (y * u),u)) * x. K(x,T(y \ (x * z),z)) * u = u * K(x,T((y / z) \ x,u)). K(x,T(y \ (x * z),z)) * u != u * w | K(x,T(z / (x \ y),u)) = w. x != R(y,K(z,u),T(u,w)) | x = y. x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y). x / T(1 / y,z) = (x / T(y \ 1,z)) * K(y \ 1,y). (x / T(y \ 1,z)) * K(y \ 1,y) = x / T(1 / y,z). x / R(y,z,y) = (x / T(y,z)) * K(y,y * z). (x / T(y,z)) * K(y,y * z) = x / R(y,z,y). x / L(y,z,y) = (x / T(y,y * z)) * K(y,z). (x / T(y,y * z)) * K(y,z) = x / L(y,z,y). (x / R(y,z,y)) * y = (x / T(y,z)) * T(y,y * z). (x / T(y,z)) * T(y,y * z) = (x / R(y,z,y)) * y. K(x * (y / R(z,u,z)),z) = K(x * (y / T(z,u)),z). a(x,y,z) = a(T(x,y),T(y,x),z). a(T(x,y),T(y,x),z) = a(x,y,z). a(T(x,y),T(y,x),z) != u | a(x,y,z) = u. x != a(y,T(z,y),R(T(y,z),u,w)) | x = a(R(y,u,w),z,y). a(T(x,T(y,x)),T(T(y,x),x),R(T(x,y),z,u)) = a(R(x,z,u),y,x). (x * y) / T(T(x,y),z) = K(z,x) * y. (x * L(y,z,y)) / T(T(x,y),u) = K(u,x) * L(y,z,y). T(x,T(y / (x \ z),z)) = T(x,z \ (x * y)). x * y != T(z,u) * K(u * L(z,w,v5),z) | x \ R(z,u,L(z,w,v5)) = y. x \ R(x,y,L(x,z,u)) = K(y * L(x,z,u),x) * K(x,y). K(x * L(y,z,u),y) * K(y,x) = y \ R(y,x,L(y,z,u)). L(K(x * L(y,z,u),y),T(y,x),w) = (w * T(y,x)) \ (w * R(y,x,L(y,z,u))). (x * T(y,z)) \ (x * R(y,z,L(y,u,w))) = L(K(z * L(y,u,w),y),T(y,z),x). K(x,y \ (x \ ((x * z) * y))) = K(x,R(T(z,y),x,y)). x != T(T(y * K(z * T(y,u),y),w),z) | x = R(T(y,w),z,T(y,u)). R(T(x,y),z,x) = R(T(x,y),z,T(x,u)). R(T(x,y),z,T(x,u)) = R(T(x,y),z,x). R(T(x,y),z,x) \ T(T(x,y) * z,T(x,y)) = T(z,T(x,y)). K(x,R(T(y,z),u,y)) = K(x,T(y,z)). K(x,T(R(y,z,y),u)) = K(x,T(y,u)). K(x,T(T(y,z),u)) = K(x,T(T(y,y * z),u)). K(x,T(T(y,y * z),u)) = K(x,T(T(y,z),u)). K(x,T((y \ z) \ z,u)) = K(x,T(T(y,z),u)). K(x,T(T(y,z) \ 1,u)) = K(x,T(T(y \ 1,z),u)). K(x,T((y \ z) \ 1,u)) = K(x,T(T((z / y) \ 1,y),u)). K(x,T(T((y / z) \ 1,z),u)) = K(x,T((z \ y) \ 1,u)). R(K(x \ (y / z),y / z),y / z,z) = K(y / (x * z),y / z). x != L(K(y,z),u,T(z,w)) | x = K(y,z). K((T(x,y) * z) \ u,x) = K(z \ (T(x,y) \ u),x). x * K((y * z) \ x,u) = y * ((y \ x) * K(z \ (y \ x),u)). x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u). x != K(y \ (T(z,u) \ w),z) | x = K(y \ (z \ w),z). K((T(x,y) * z) \ u,x) = K(z \ (x \ u),x). K((x \ y) \ z,y) = K((x \ 1) \ (y \ z),y). K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y). K((T(x,y) * z) \ u,K(x,w)) = K(w,K(z \ (x \ u),x)). K(x \ (y * z),z) != u | u = K(z * (x \ y),z). K(x \ (y * z),z) != u | K(z * (x \ y),z) = u. K((x \ y) \ z,z) != u | K(z * (y \ x),z) = u. K((x \ y) \ z,x) != u | K(x * (y \ z),x) = u. K((x / y) \ z,y) != u | K(y * (x \ z),y) = u. K(L(x,y / x,z),u) != w | L(K(x,u),y,z) = w. K(x,(y * K(z,u)) \ w) = L(K(x,K(u,z) * (y \ w)),y \ w,y). L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(z,y)) \ w). K(x,y \ (z \ 1)) = K(x,(z * y) \ 1). K(x,(y * z) \ 1) = K(x,z \ (y \ 1)). x != L(K(y,z),u,T(y,w)) | x = K(y,z). K(x,(T(x,y) * z) \ u) = K(x,z \ (T(x,y) \ u)). K(x,(y * z) \ 1) != u | K(x,z \ (y \ 1)) = u. L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * T(y,x \ 1)) \ u). L(K(x,y \ (x \ (z \ u))),z \ u,z) = K(x,(z * (x * y)) \ u). L(K(x,x \ (y \ z)),y \ z,y) != u | K(x,y \ (x \ z)) = u. L(K(x,(y * (x \ z)) \ (u \ w)),u \ w,u) = K(x,(u * (y * (z / x))) \ w). L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (y / x)) \ u). L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u). x != K(y,z \ (T(y,u) \ w)) | x = K(y,z \ (y \ w)). K(x,(T(x,y) * z) \ u) = K(x,z \ (x \ u)). K(x,(y * z) \ (y * u)) != w | L(K(x,z \ u),u,y) = w. K(x,T(y,L(y,z,u) * (y \ w))) = L(K(x,T(y,w)),w,L(y,z,u)). L(K(x,T(y,z)),z,L(y,u,w)) = K(x,T(y,L(y,u,w) * (y \ z))). K(x,y \ (z * x)) != u | u = K(x,x * (y \ z)). K(x,y \ (z * x)) != u | K(x,x * (y \ z)) = u. K(x,y * (L(y,z,u) \ x)) != w | K(x,x * (L(y,z,u) \ y)) = w. K(x,y \ (x * z)) != u | K(x,x * (y \ z)) = u. x != K(y,L(T(z,y),u,w)) | x = K(y,L(z,u,w)). K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y)). (x * (y * y)) * K(y,z) = x * (y * T(y,z)). (x * ((y / z) * (y / z))) * K(y / z,z) = x * ((y / z) * (z \ y)). (x * (y * T(y,z))) \ 1 = K(y,z) \ ((x * (y * y)) \ 1). K(x,y) \ ((z * (x * x)) \ 1) = (z * (x * T(x,y))) \ 1. (x * ((y * (1 / z)) * (y * (1 / z)))) * K(y * (1 / z),z) = x * ((y * (1 / z)) * ((z \ 1) * y)). ((x * (y * T(y,z))) \ (K(y,z) \ 1)) \ 1 = (K(y,z) / (1 / (x * (y * y)))) * K(y,z). R(K(x,(y / (z / u)) \ x),z / u,u) = K(x,z / ((x \ y) * u)). R(T(K(x,(y / z) \ x),u),x,z) = T(K(x,(y / (x * z)) \ 1),u). (K(x,y) \ (z * u)) \ (K(x,y) \ (z * (u * w))) = L(L(w,u,z),z * u,K(y,x)). x != (y / T(z,u)) * T(z,w) | x = (y * K(u,z)) * K(z,w). (x / R(y,z,y)) * y = (x * K(z,y)) * K(y,y * z). (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z. x != ((K(y,z) * u) \ w) * w | x = (u \ K(z,y)) * (w * w). (x \ y) \ T(x,z) = (y \ K(z,x)) * (T(x,z) * T(x,z)). (x \ K(y,z)) * (T(z,y) * T(z,y)) = (z \ x) \ T(z,y). x != T(y,y * z) * L(T(z,y),u,w) | x = L(z,u,w) * T(y,y * z). K(x,x * y) * (L(y,z,u) * x) = L(y,z,u) * T(x,x * y). x != T(y,y * z) * R(T(z,y),u,w) | x = R(z,u,w) * T(y,y * z). K(x,x * y) * (R(y,z,u) * x) = R(y,z,u) * T(x,x * y). L(x,K(y,z),L(y,u,w)) = x. (K(x,y) * L(x,z,u)) * w = L(x,z,u) * (K(x,y) * w). x != L(K(y,z) * (u \ w),K(z,y),u) | x = (u * K(z,y)) \ w. K(x,y) * (L(y,z,u) \ w) = (L(y,z,u) * K(y,x)) \ w. (L(x,y,z) * K(x,u)) \ w = K(u,x) * (L(x,y,z) \ w). (1 / x) * y != K(z \ 1,z) / x | y = K(z \ 1,z). K(x \ (1 / y),x * y) = K((x * y) \ 1,x * y). K((x * y) \ 1,x * y) = K(x \ (1 / y),x * y). K((x * (y \ 1)) \ 1,x * (y \ 1)) = K(x \ y,x * (y \ 1)). (x * (y \ z)) * K(y,z) = x * (z * (y \ 1)). x != y * K(z,z \ y) | x = z * (y / z). (((x \ y) \ 1) \ x) * ((x \ y) \ 1) = y * (x / y). x != (((y \ z) \ 1) \ y) * ((y \ z) \ 1) | x = T(z,z \ y) / (y \ z). x * (y / x) = T(x,x \ y) / (y \ x). T(x,x \ y) / (y \ x) = x * (y / x). (x \ y) / (y \ (y / x)) = (y / x) * (y / (y / x)). x != (y / z) * (y / (y / z)) | x = (z \ y) * z. (x \ y) / (y \ (y / x)) = (x \ y) * x. ((x \ y) * x) \ (x \ y) = y \ (y / x). L(x \ 1,x,x \ y) = y \ (y / x). L(x \ 1,x,y) = (x * y) \ ((x * y) / x). (x * y) \ ((x * y) / x) = L(x \ 1,x,y). x != (y * z) \ ((y * z) / y) | x = L(y \ 1,T(y,z),z). L(x \ 1,x,y) = L(x \ 1,T(x,y),y). L(x \ 1,T(x,y),y) = L(x \ 1,x,y). T(x * L(x \ 1,x,y),y) = T(x,y) * ((x * y) \ y). L(T(x,y) \ 1,x,y) = (x * y) \ y. x != L(T(y,z) \ 1,y,z) | x = (z * y) \ T(z,y). (x * y) \ y = (y * x) \ T(y,x). (x * y) \ T(x,y) = (y * x) \ x. (x * y) * ((y * x) \ x) = T(x,y). T(x,y) = (x * y) * ((y * x) \ x). (R(x,y,x) \ T(x,z)) \ x = R(x * K(z,x),y,x). R(x,K(y,z),R(z,u,w)) = x. x != R((y / z) * K(u,w),K(w,u),z) | x = y / (K(w,u) * z). (x / R(y,z,u)) * K(y,w) = x / (K(w,y) * R(y,z,u)). x / (K(y,z) * R(z,u,w)) = (x / R(z,u,w)) * K(z,y). R(x,K(y,z),L(z,u,w)) = x. R(x,K(y,z),L(T(z,u),w,v5)) = x. x \ (((y \ x) * y) * L(T(y,z),u,w)) = K(y \ x,y) * L(T(y,z),u,w). x != y * (z * (u * (y \ 1))) | x = ((y * z) * u) / y. x * T(T(x,y \ 1),y \ 1) = ((y * x) * x) / y. K(x \ 1,x) * (K(x,y) * K(x,z)) = (x \ K(x,y)) * T(x,z). (x / y) * L(z,y / x,y / x) = (1 / (x / y)) \ z. x * ((x \ y) * (L(z,x,x) * T((x \ y) * L(z,x,x),x))) = ((x \ y) * L(z,x,x)) * (x / (z \ (y \ x))). K(x \ y,x) * (y * (x \ (y / x))) = (y / x) * (x \ y). (x / y) * (y \ x) != z | (y \ x) * (x / y) = z. x * (T(T(x,y),y) \ z) = K(y,x) * (K(y,x) * z). K(x,y) * (K(x,y) * z) = y * (T(T(y,x),x) \ z). K(x,y \ x) * (K(x,y \ x) * z) = (y \ x) * (T(y \ T(x,y),x) \ z). T(x * (T(T(x,y),y) \ z),K(y,x)) != u | (1 / (K(y,x) * z)) \ K(y,x) = u. K(x \ y,x \ 1) * ((1 / x) \ z) = (1 / T(x,y)) \ z. (x \ y) * (K(x,y) * z) = (y * (x \ 1)) * z. (x \ y) * (y / x) = (y * (x \ 1)) * ((1 / x) * y). (x * (y \ 1)) * ((1 / y) * x) = (y \ x) * (x / y). ((1 / (x / ((1 / y) * z))) * (((1 / y) * z) \ 1)) \ K(u,w) = ((1 / (((1 / y) * z) * x)) \ (z \ y)) * K(u,w). x != K(y,R(T(y,z),u,w) \ v5) | x = K(y,R(y,u,w) \ v5). K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y). (x * ((y \ (x \ z)) * y)) \ z = K(y,(x * y) \ z). (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u). (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z). (x * ((y \ (x \ z)) * y)) \ z != u | K(y,x \ (y \ z)) = u. (x * T(y,L(z,y,x))) \ (x * (y * z)) = L(T(z,y),y,x). T(x \ 1,K(y,z)) \ (1 / x) = K(x * K(z,y),x \ 1). K(x,T(T(x * T(y,z),u),y)) != w | K(x,T(x * T(y,z),u)) = w. (((1 / x) * y) * (1 / z)) \ ((1 / x) * y) = T(T(z,y \ x),x \ y). T(x,y) \ (T(x,z) * u) = K(x,z) * (K(y,x) * u). x != R(K(y,z),y * u,w) | x = K(R(y,u,w),z). K(R(x,y,z),T(u,x \ w)) = K(R(x,y,z),T(u,w)). K(R(x,y,z),T(u,x \ w)) * v5 != K(R(x,y,z),T(u,w)) | 1 = v5. 1 = K(R(x,y,z),T(u,w)) * K(T(u,x \ w),R(x,y,z)). K(R(x,y,z),T(u,w)) * K(T(u,x \ w),R(x,y,z)) = 1. R(K(x,y),z,R(x,u,w)) = K(x,y). (x * y) * R(x,z,u) = K(x,y) * ((y * x) * R(x,z,u)). K(x,y) * ((y * x) * R(x,z,u)) = (x * y) * R(x,z,u). K(x,y) = K(R(x,z,R(x,u,w)),y). K(R(x,y,R(x,z,u)),w) = K(x,w). T(R(x,y,R(x,z,u)),w) = K(x,w) * R(x,y,R(x,z,u)). K(x,y) * R(x,z,R(x,u,w)) = T(R(x,z,R(x,u,w)),y). (K(x,y) / z) \ 1 = z * K(y,R(x,u,R(x,w,v5))). x * K(y,R(z,u,R(z,w,v5))) = (K(z,y) / x) \ 1. x * y != (K(z,u) / x) \ 1 | y = K(u,z). K(x,R(y,z,R(y,u,w))) = K(x,y). K(x,R(y,z,R(T(y,u),w,v5))) = K(T(x,u),T(y,u)). K(T(x,y),T(z,y)) = K(x,R(z,u,R(T(z,y),w,v5))). K(x,y) = K(x,R(y,z,R(T(y,u),w,v5))). K(x,R(y,z,R(T(y,u),w,v5))) = K(x,y). R(K(x,y),z,L(x,u,w)) = K(x,y). K(x,y) = K(R(x,z,L(x,u,w)),y). K(R(x,y,L(x,z,u)),w) = K(x,w). x != K(R(T(y,z),u,w),T(v5,z)) | x = K(R(y,u,w),v5). K(T(x,y),T(z,y)) = K(R(x,u,L(T(x,y),w,v5)),z). K(x,y) = K(R(x,z,L(T(x,u),w,v5)),y). K(R(x,y,L(T(x,z),u,w)),v5) = K(x,v5). T(x,R(y,z,L(T(y,u),w,v5))) = (K(y,x) / x) \ 1. T(x,R(y,z,L(T(y,u),w,v5))) = T(x,y). x != K(y * (z / R(u,w,u)),u) | x = K(y * (z / T(u,w)),u). K(x * (R(y,z,y) \ u),y) = K(x * (u / T(y,z)),y). x != K(y * (z / T(y,u)),y) | x = K(z,y). K(x * (R(x,y,x) \ z),x) = K(z,x). K(x * y,x) = K(R(x,z,x) * y,x). K(R(x,y,x) * z,x) = K(x * z,x). x != K(R(y,z,u) * w,y) | x = K(w * R(y,z,u),y). K(x * y,x) = K(y * R(x,z,x),x). K(x * R(y,z,y),y) = K(y * x,y). T(x,y * R(x,z,x)) = 1 / (x \ K(x * y,x)). T(x,y * R(x,z,x)) = T(x,x * y). x != T(y,z) | x = y * K(y,z). T(x,y * R(x,z,x)) = x * K(x,x * y). K(x,y * R(x,z,x)) = K(x,x * y). x != y * (z \ T(z * (y \ u),y)) | x = ((y \ (u / (z \ 1))) * y) * (z \ 1). ((x \ (y * z)) * x) / z = ((x \ (y / (z \ 1))) * x) * (z \ 1). ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z. x != y * (z * T(z \ (y \ u),w)) | x = (y * z) * T((y * z) \ u,w). ((x \ (y / z)) * x) * z = (z * x) * T((z * x) \ y,x). (x * y) * T((x * y) \ z,y) = ((y \ (z / x)) * y) * x. K(x,y) = K(K(z,z \ 1) * x,y). K(K(x,x \ 1) * y,z) = K(y,z). K(((x \ 1) \ 1) * y,z) = K(x * y,z). K(x \ y,z) = K(((x \ 1) \ 1) \ y,z). K(((x \ 1) \ 1) \ y,z) = K(x \ y,z). K((x \ 1) \ y,z) = K((1 / x) \ y,z). K((1 / x) \ y,z) = K((x \ 1) \ y,z). K((1 / x) * y,z) = K((x \ 1) * y,z). K(x \ (1 / y),z) = K(x \ (y \ 1),z). K(((x * K(y,z)) \ 1) * u,w) = K((K(z,y) / x) * u,w). K((x \ 1) * y,z) = K(x \ y,z). K(x * y,z) = K((1 / x) \ y,z). K((1 / x) \ y,z) = K(x * y,z). K(x \ (1 / y),z) = K(y * x,z \ 1). K(x / y,z) = K(x * (1 / y),z). K(x * (1 / y),z) = K(x / y,z). K(T(x * y,x),z) = K(y * x,z). x != K(y / (z * y),u) | x = K(z,u \ 1). K(x * (1 / (y * x)),z) = K(y,z \ 1). K((x \ 1) * y,T(z,x)) = K(y * (x \ 1),z). K(x * y,z) = K(y * x,T(z,x)). K(x * y,T(z,y)) = K(y * x,z). K(x * y,T(z,x)) = K(y * x,z). x * K(y * x,z) = K(x * y,z) * x. K(x * y,z) * x = x * K(y * x,z). K(x * y,T(z,y)) != u | K(y * x,z) = u. K(x,T(y,z)) = K(z * (x / z),y). K(x * (y / x),z) = K(y,T(z,x)). K(x * T(x \ y,z),T(u,x)) = K(x * T(y / x,z),u). K(x * T(y,z),T(u,K(y,z))) = K(K(y,z) * (x * y),u). K(x * y,T(z,x)) != u | K(y * x,z) = u. K(x * R(y,z,u),T(y,x)) = K(x * R(y,z,u),y). x * (y * K(y * x,z)) != u | T(x * y,T(z,x)) = u. T(x,y) * K(y * x,z) = K(x * y,z) * T(x,y). K(x * y,z) * T(x,y) = T(x,y) * K(y * x,z). K(x * T(y / x,z),u) = K(y * K((y \ x) \ 1,z),T(u,x)). K(x * K((x \ y) \ 1,z),T(u,y)) = K(y * T(x / y,z),u). K((1 / x) \ y,z) != u | K(x * y,z) = u. K((x \ 1) * y,z) != u | K(x \ y,z) = u. K(x \ (1 / y),z) != u | K(y * x,z \ 1) = u. K(x \ ((1 / y) * z),u) = K((z \ y) * x,u \ 1). x * y != y * K(z * u,u \ (z \ 1)) | x = K(z * u,u \ (z \ 1)). K(x * y,x \ (y \ 1)) = K(y * x,x \ (y \ 1)). K(x * y,y \ (x \ 1)) = K(y * x,y \ (x \ 1)). K(x * y,T(x,z)) != u | K(y * x,T(x,z)) = u. K(x * K(y,(x \ z) \ 1),T(u,z)) != w | K(((y * (z \ x)) / y) * z,u) = w. K((x / y) \ y,z) != u | K(y * (x \ y),z) = u. K(x \ (1 * ((y * (1 \ z)) / y)),T(u,x)) = K(((y * ((x \ 1) \ (x \ z))) / y) * (x \ 1),u). K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) = K(y \ (1 * ((x * (1 \ z)) / x)),T(u,y)). K((x \ 1) * (1 / y),z) != u | K(y * x,z \ 1) = u. T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u)). K(x * R(y,z,u),y) * K(y,K(w,x * R(y,z,u))) = T(K(x * R(y,z,u),T(y,x)),w). (K(x * y,z) * T(x,y)) \ T(x,y) = K(z,y * x). T(x,y) * K(z,y * x) = K(z,x * y) * T(x,y). K(x,y * z) * T(y,z) = T(y,z) * K(x,z * y). T(x,y) * z != K(u,x * y) * T(x,y) | z = K(u,T(x * y,x)). K(x,y * z) = K(x,T(z * y,z)). K(x,T(y * z,y)) = K(x,z * y). x != K(y,z * u) | x = K(y,(z \ 1) \ u). K(x,T(y * z,y)) = K(x,(z \ 1) \ y). x != K(y,T(z * u,z)) | x = K(y,T(z * u,u)). K(x,y * z) = K(x,T(z * y,y)). K(x,T(y * z,z)) = K(x,z * y). K(x,T(y,z)) = K(x,(z \ y) * z). K(x,(y \ z) * y) = K(x,T(z,y)). K(x,y \ z) = K(x,(y \ 1) * z). K(x,(y \ 1) * z) = K(x,y \ z). K(x,(1 / y) \ z) = K(x,y * z). K(x,y / (z \ 1)) = K(x,y * z). T(x * y,T(z,x)) \ 1 = (x * y) \ K(z,y * x). K(x,y * z) * T(x,y) = T(T(x,y),z * y). K(x,T(y * z,u)) = K(x,T(T(z * y,u),z)). K(x,T(T(y * z,u),y)) = K(x,T(z * y,u)). K(x,((y \ 1) \ 1) \ z) = K(x,y \ z). K(x,(y \ 1) / z) = K(x,y \ (z \ 1)). x != K(y,z \ u) | x = K(y,(1 / z) * u). K(x,(y \ 1) * z) = K(x,(1 / y) * z). K(x,(1 / y) * z) = K(x,(y \ 1) * z). K(x,(y \ z) * u) = K(x,((1 / z) * y) \ u). K(x,((1 / y) * z) \ u) = K(x,(z \ y) * u). K(x,y * (z \ y)) = K(x,(z / y) \ y). K(x,(y / z) \ z) = K(x,z * (y \ z)). K(x,(1 / (1 / y)) * z) = K(x,y * z). K(x,y * ((z \ 1) \ 1)) = K(x,y * z). K(x,K(y,z * u)) = K(x,K(z / (u \ 1),y)). K(x,K(y / (z \ 1),u)) = K(x,K(u,y * z)). K(x,K(y,z * u)) = K(x,K(y,(u \ 1) / z)). K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z)). K(x,T(y * z,y)) != u | K(x,z * y) = u. K(x,y \ (z / y)) = K(x,(z \ y) \ (y \ 1)). K(x,(y \ z) \ (z \ 1)) = K(x,z \ (y / z)). K(x,R(y \ 1,z,u) \ w) = K(x,R(1 / y,z,u) \ w). K(x,R(1 / y,z,u) \ w) = K(x,R(y \ 1,z,u) \ w). K(x,y \ z) = K(x,y \ ((z \ 1) \ 1)). K(x,y \ ((z \ 1) \ 1)) = K(x,y \ z). K(x,y \ (1 / z)) = K(x,y \ (z \ 1)). K(x,y) = K(x,(z \ 1) * ((1 / z) \ y)). K(x,(y \ 1) * ((1 / y) \ z)) = K(x,z). K(x,L(y,z,z \ 1)) = K(x,(z \ 1) * (z * y)). K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1)). ((x \ y) / x) \ ((x \ (1 / (x / y))) * z) = K(x \ (1 / (x / y)),x * (y \ x)) * z. x != K(1 / y,(1 / (1 / y)) * z) | x = K(1 / y,z * y). K(1 / x,x * y) = K(1 / x,y * x). K(1 / x,y * x) = K(1 / x,x * y). K(x,y * T(z,z \ 1)) = K(x,y * z). T(x \ 1,K(y,z * x)) = T(x \ 1,K(y,z)). K(x,y \ z) = K(x,y \ (1 / (1 / z))). K(x,y \ (1 / (1 / z))) = K(x,y \ z). K(x \ y,y \ x) = K(x * y,x \ (y \ 1)). K(x * y,x \ (y \ 1)) = K(x \ y,y \ x). K(x * y,x \ (y \ 1)) != z | K(x \ y,y \ x) = z. K(x,(1 / (y * z)) \ (z \ 1)) = K(x,y). K(x,K(y \ 1,y) * z) = K(x,z). K(x,K(y,y \ 1) * z) = K(x,z). K(x,y) = K(x,y * K(z,z \ 1)). K(x,y * K(z,z \ 1)) = K(x,y). K(x,T(y * K(z,z \ 1),u)) = K(x,T(y,u)). x * K(1 / y,z * y) = x * K(1 / y,y * z). x != K(y \ (z \ 1),u) | x = K(y \ (1 / z),u). K(x \ (y \ 1),z * T(u,u \ 1)) = K(x \ (1 / y),z * u). K(x,T(y * z,z)) != u | K(x,z * y) = u. K(x,y * R(x,z,u)) != w | K(x,R(x,z,u) * y) = w. K(x,T(y * (z \ x),z)) != u | K(x,(z \ x) * y) = u. K(x,y) * T(x,y * z) = T(T(x,y),z * y). K(x,T(y * x,z)) != u | K(x,T(x * y,z)) = u. K(x,K(y / (z \ 1),u)) = K(x,K(y * z,u)). K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u)). T(x \ 1,K(y,z)) * L((x \ 1) \ K(K(y,z * x),x \ 1),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x)). x != K(y * z,y \ (z \ 1)) | x = K(z * y,y \ (z \ 1)). K(x \ y,y \ x) = K(y * x,x \ (y \ 1)). K(x * y,y \ (x \ 1)) = K(y \ x,x \ y). K(x,T((1 / y) * z,u)) = K(x,T((y \ 1) * z,u)). K(x,y) * z != T(T(x,y),u) | z = T(x,T(u,y)). T(x,y * z) = T(x,T(z * y,y)). T(x,T(y * z,z)) = T(x,z * y). x != T(y,T(z * u,u)) | x = T(y,(1 / u) \ z). T(x,y * z) = T(x,(1 / y) \ z). T(x,(1 / y) \ z) = T(x,y * z). x != T(y,z * u) | x = T(y,(z \ 1) \ u). T(x,(1 / y) \ z) = T(x,(y \ 1) \ z). T(x,y \ z) = T(x,(y \ 1) * z). T(x,(y \ 1) * z) = T(x,y \ z). T(x,T(y * z,y)) = T(x,z * y). T(x,((y \ 1) \ 1) \ z) = T(x,y \ z). T((x \ 1) * y,K(z,T(u,x \ y))) = T((x \ 1) * y,K(z,u)). K(x \ 1,T(y,x \ z)) = K(x \ 1,T(y,z)). x != T(y,T(z * u,z)) | x = T(T(y,K(u,z)),z * u). T(x,y * z) = T(T(x,K(y,z)),z * y). T(T(x,K(y,z)),z * y) = T(x,y * z). T(x,(1 / y) \ z) != u | T(x,y * z) = u. T(x,R(y \ 1,y,z) \ u) = T(x,(z / (y * z)) \ u). T(T(x,y * z),K(y,z)) = T(x,z * y). T(T(x,y * z),K(y,z)) != u | u = T(x,z * y). T(T(x,y * z),K(y,z)) != u | T(x,z * y) = u. T(x,T(y * z,y)) != u | T(x,z * y) = u. T(T(x,K(y,z)),z * y) != u | T(x,y * z) = u. K(x,K(y / (z \ 1),u)) != w | K(x,K(u,y * z)) = w. K(x,K(y,(z \ 1) / (u / z))) != w | K(y,K(x,u)) = w. x != K(y * z,z \ (y \ 1)) | x = (z \ (y \ 1)) * (y * z). K(x \ y,y \ x) = (x \ (y \ 1)) * (y * x). (x \ (y \ 1)) * (y * x) = K(x \ y,y \ x). K(x \ y,y \ x) / z = (y * x) * (1 / (z * (y * x))). (x * y) * (1 / (z * (x * y))) = K(y \ x,x \ y) / z. x \ K(y \ z,z \ y) = (x \ (z * y)) * (1 / (z * y)). (x \ (y * z)) * (1 / (y * z)) = x \ K(z \ y,y \ z). T(T(x,K(y,K(z,u))),K(u,z) * y) != w | T(x,y * K(u,z)) = w. T(T(x,K(y,K(z,u))),K(z,z * u) * y) != w | T(x,y * K(z,z * u)) = w. T(T(x,K(y,z)),T(T(z,u),u) * y) != w | T(x,y * T(T(z,u),u)) = w. x * K(y / z,u * (z / y)) = x * K(1 / (z / y),(z / y) * u). x * K(1 / (y / z),(y / z) * u) = x * K(z / y,u * (y / z)). K(x,T(K(y \ z,y),u)) = K(x,T((z \ 1) * ((y \ z) * y),u)). K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,T(K(z \ y,z),u)). x * y != T(z,u) * K(u * R(z,w,v5),z) | x \ R(z,u,R(z,w,v5)) = y. x \ R(x,y,R(x,z,u)) = K(y * R(x,z,u),x) * K(x,y). K(x * R(y,z,u),y) * K(y,x) = y \ R(y,x,R(y,z,u)). R(x,y,R(x,z,u)) * w = T(x,y) * (K(y * R(x,z,u),x) * w). T(x,y) * (K(y * R(x,z,u),x) * w) = R(x,y,R(x,z,u)) * w. K(x * y,y \ (x \ 1)) != z | K(y \ x,x \ y) = z. K(x,R(x,y,x) * z) = K(x,x * z). K(R(x,y,x),R(x,z,x) * u) = K(x,x * u). x != T(y,(z / (u * z)) \ y) | x = T(y,y * u). T(x,R(y \ 1,y,z) \ x) = T(x,x * y). T(x,R(y \ 1,y,z) \ x) = x * K(x,x * y). K(x,R(y \ 1,y,z) \ x) = K(x,x * y). x / (y * ((z \ (y \ x)) * z)) != u | K(z,x / (z * y)) = u. L(K(x,y),z,L(y,u,w)) = K(x,y). K(x,y) = K(x,L(y,z,L(y,u,w))). K(x,L(y,z,L(y,u,w))) = K(x,y). K(x,y) = K(L(x,z,L(y,u,w)),y). K(L(x,y,L(z,u,w)),z) = K(x,z). K(T(x \ (L(y,z,u) * w),L(y,z,u) \ x),y) = K((((L(y,z,u) \ x) \ w) \ w) \ w,y). L(K(x,y),z,L(x,u,w)) = K(x,y). (L(x,y,z) * (u * K(x,w))) \ (L(x,y,z) * u) != v5 | K(w,x) = v5. K(x,y) = K(L(x,z,L(x,u,w)),y). K(L(x,y,L(x,z,u)),w) = K(x,w). K(R(K(x,y),z,u),w) = R(K(x,K(y,w)),z,u). R(K(x,K(y,z)),u,w) = K(R(K(x,y),u,w),z). K(x,R(K(y,z),u,w)) = K(R(K(y,x),u,w),z). K(R(K(x,y),z,u),w) = K(y,R(K(x,w),z,u)). x != K(R(K(y,z),u,w),v5) | x = R(K(y,K(z,v5)),u,w). K(x,R(K(y,z),u,w)) = R(K(y,K(x,z)),u,w). R(K(x,K(y,z)),u,w) = K(y,R(K(x,z),u,w)). R(K(x,K(y,z)),u,w) = K(x,R(K(y,z),u,w)). x * R(K(x,K(y,z)),u,w) != v5 | T(x,R(K(y,z),u,w)) = v5. R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w) \ 1)). R(K(x,K(y,z)),y,u) = K(x,K(y,z)). x != K(L(T(y,z),u,w),T(v5,z)) | x = K(L(y,u,w),v5). L(K(x,y),z * T(x,u),w) = K(L(x,z,w),y). L(K(x,y),x * z,u) = K(L(x,z,u),y). L(K(x,y),z,u) = K(L(x,x \ z,u),y). K(L(x,x \ y,z),u) = L(K(x,u),y,z). K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y))). L(K(x,y),T(x,z) * u,w) = K(L(T(x,z),u,w),T(y,z)). x != L(y,1,z) | x = y. K(L(x,x \ 1,y),z) = K(x,z). K(L(x,T(x,y) \ 1,z),u) = K(T(x,y),T(u,y)). K(T(x,y),T(z,y)) = K(L(x,T(x,y) \ 1,u),z). K(L(x,T(x,y) \ 1,z),u) != w | K(x,u) = w. K(L(x,x \ K(y,x),z),u) != w | K(x,u) = w. K(x,y) = L(K(x,y),K(z,x),u). L(K(x,y),K(z,x),u) = K(x,y). R(K(x,y),z,u) = L(R(K(x,y),z,u),K(w,x),v5). L(R(K(x,y),z,u),K(w,x),v5) = R(K(x,y),z,u). (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u)). (x * K(y,z)) * R(K(z,u),w,v5) = x * (K(y,z) * R(K(z,u),w,v5)). (x * K(y,z)) * L(K(z,u),w,v5) = x * (K(y,z) * L(K(z,u),w,v5)). (x * (K(y,z) * K(z,u))) * K(u,z) = x * K(y,z). R(x,K(y,z),K(z,u)) = x. x != (y * K(z,u)) * K(u,u * z) | x = (y / R(u,z,u)) * u. x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z. (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z)). R(x,T(K(y,z),u),K(z,w)) = x. (x * R(R(x,K(y,z),K(z,u)) \ (x * K(y,z)),w,v5)) * K(z,u) = R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u)). R(x,L(K(y,z),u,w),K(z,v5)) = x. R(x,T(K(y,z),u),T(K(z,w),v5)) = x. (x / L(K(y,z),u,w)) \ (x * K(z,v5)) = L(K(y,z),u,w) * K(z,v5). x \ (K(y,z) * (K(u,y) * x)) = T(K(u,y),x) * T(K(y,z),K(u,y) * x). T(K(x,y),z) * T(K(y,u),K(x,y) * z) = z \ (K(y,u) * (K(x,y) * z)). L(K(x,y),K(z,y),u) = K(x,y). (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y). L(K(x,y),K(y,z),u) = K(x,y). (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y)). L(K(x,T(y,z)),K(y,u),w) = K(x,T(y,z)). (x * K(y,z)) * K(u,T(y,w)) != v5 | x * (K(y,z) * K(u,T(y,w))) = v5. K(x,y) * z != u * (K(x,y) * K(w,x)) | T(u * K(w,x),K(x,y)) = z. T(L(x,K(y,z),K(z,u)) * K(y,z),K(z,u)) = K(y,z) * T(x,K(z,u) * K(y,z)). (x / T(y,z)) * K(y,u) = (x / y) * (K(y,u) * K(z,y)). (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z). x * K(y,z) != u * K(w,z) | x = u * (K(w,z) * K(z,y)). x = (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)). (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)) = x. (x * K(y,z)) * K(z,u) != w | w = x * (K(z,u) * K(y,z)). (x * K(y,z)) * K(z,u) != w | x * (K(z,u) * K(y,z)) = w. R(x,K(y,z),K(u,y)) = x. x != y * (K(z,u) * K(w,z)) | x = (y * K(w,z)) * K(z,u). (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z). ((K(x,y) \ z) * ((K(x,y) \ 1) \ 1)) * K(u,x) = ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)). x * K(y,z) = (x * K(u,z)) * (K(z,u) * K(y,z)). (x * K(y,z)) * (K(z,y) * K(u,z)) = x * K(u,z). (x * K(y,z)) \ ((K(z,u) * K(y,z)) * (x / K(z,u))) = K(K(z,u) * K(y,z),R(x / K(z,u),K(z,u),K(y,z))). K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = (u * K(z,x)) \ ((K(x,y) * K(z,x)) * (u / K(x,y))). x != (x * (K(y,z) * K(u,y))) * w | K(z,y) * K(y,u) = w. (x * (K(y,z) * K(u,y))) * w != x | K(z,y) * K(y,u) = w. x / (K(y,z) * K(z,u)) != w | w = x * (K(z,y) * K(u,z)). x / (K(y,z) * K(z,u)) != w | x * (K(z,y) * K(u,z)) = w. (x * K(y,z)) * K(u,T(y,w)) = (x * K(T(u,w),y)) * K(y,z). (x * K(T(y,z),u)) * K(u,w) = (x * K(u,w)) * K(y,T(u,z)). ((x * K(y,z)) / (x * K(u,z))) \ 1 = (K(z,u) * K(y,z)) \ K(K(z,u) * K(y,z),x * K(u,z)). x * (y \ L(y,z,y)) = (x / R(y,z,y)) * y. (x / R(y,z,y)) * y = x * (y \ L(y,z,y)). x * (R(x,y,x) \ z) = z * (x \ L(x,y,x)). 1 * x != (1 / R(y,z,u)) * y | x = y / R(y,z,u). x \ L(x,y,x) = x / R(x,y,x). x / R(x,y,x) = x \ L(x,y,x). (x * ((y \ L(y,z,y)) \ 1)) * T(y / R(y,z,y),R(y,z,y) / y) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y)). x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y). x \ L(T(x,y),z,x) = R(x,z,x) \ T(x,y). R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x). x != R(y,z,y) \ T(y,u) | x = R((u * y) / u,z,y) \ y. x \ L(T(x,y),z,x) = R((y * x) / y,z,x) \ x. R((x * y) / x,z,y) \ y = y \ L(T(y,x),z,y). (x \ L(T(x,y),z,x)) \ x = R(x * K(y,x),z,x). T(x / ((y \ L(T(y,z),u,y)) \ y),T(R((z * y) / z,u,y),y)) = ((R((z * y) / z,u,y) \ y) \ y) \ x. x != K(T(y,z),L(T(u,z),w,v5)) | x = K(y,L(u,w,v5)). L(K(x,y),z * T(y,u),w) = K(x,L(y,z,w)). x != L(K(y,z),u * T(z,w),v5) | x = K(y,L(z,u * K(z,w),v5)). K(x,L(y,z,u)) = K(x,L(y,z * K(y,w),u)). K(x,L(y,z * K(y,u),w)) = K(x,L(y,z,w)). L(K(x,y),y * z,u) = K(x,L(y,z,u)). L(K(x,y),z,u) = K(x,L(y,y \ z,u)). K(x,L(y,y \ z,u)) = L(K(x,y),z,u). L(K(x,y),z * K(y,u),w) = K(x,L(y,z / y,w)). K((x \ y) \ (z * u),L(z,u,x)) = K(y \ (x * (z * u)),z). (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y)). L(K(x,y),T(y,z) * u,w) = K(x,L(y,K(y,z) * u,w)). K(x,L(y,K(y,z) * u,w)) = K(x,L(y,u,w)). x != K(y,L(z,u / z,w)) | x = L(K(y,z),u,w). L(K(x,y),z * K(y,u),w) = L(K(x,y),z,w). x != K(y \ (K(z,u) * w),T(z,v5)) | x = K(y \ w,T(z,v5)). K((K(x,y) * z) / u,x) = K(u \ z,T(x,z)). K(x \ y,T(z,y)) = K((K(z,u) * y) / x,z). K(x / y,z) = K((K(z,u) * x) / y,z). K((K(x,y) * z) / u,x) = K(z / u,x). (x * K(y / z,u)) \ x = K(u,(K(u,w) * y) / z). K(x,(K(x,y) * z) / u) = (w * K(z / u,x)) \ w. K(x,(K(x,y) * z) / u) = K(x,z / u). K(x,((y / x) * z) / u) = K(x,((x \ y) * z) / u). x != K(T(y,z),(u * K(w,y)) \ v5) | x = K(T(y,z),u \ v5). K(x,y / (z * K(u,x))) = K(T(x,z),z \ y). K(T(x,y),y \ z) = K(x,z / (y * K(u,x))). K(x,y / z) = K(x,y / (z * K(u,x))). K(x,y / (z * K(u,x))) = K(x,y / z). ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y). x != K(y,K(z,u)) \ K(z,y) | x = T(K(z,y),u). T(K(x,y),T(z,x \ u)) = T(K(x,y),T(z,u)). T(K(x,y),T(z,u)) = T(K(x,y),T(z,x * u)). T(K(x,y),T(z,x * u)) = T(K(x,y),T(z,u)). x != K(R(y,z,u),T(w,y \ v5)) | x = K(R(y,z,u),T(w,v5)). K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,x)). K((x * y) / ((x / z) * y),u) = K(R(z,x / z,y),T(u,x)). K(R(x,y / x,z),T(u,y)) = K((y * z) / ((y / x) * z),u). K(K(x,y) * T(y,z),T(u,z)) = K(y,T(u,T(x,z))). x != T(y,T((z \ u) \ 1,z)) | x = T(y,(u / z) \ 1). T(T(x,K(y,z)),(y \ z) \ 1) = T(x,(z / y) \ 1). x != T(y,(z / u) \ 1) | x = T(y,u / z). T(T(x,K(y,z)),(y \ z) \ 1) = T(x,y / z). T(T(x,K(y,z)),z \ y) = T(x,y / z). T(T(x,K(y,z \ u)),(((z \ 1) \ 1) \ u) \ y) = T(x,y / (((z \ 1) \ 1) \ u)). K(x,y) * T(z,T(x * z,y)) = T(z,x * z) * K(x,y). K(L(x,y,z),(x \ u) \ L(K(x,w),v5,v6)) = K(L(x,y,z),u \ ((1 / x) \ L(K(x,w),v5,v6))). K(L(x,y,z),u \ ((1 / x) \ L(K(x,w),v5,v6))) = K(L(x,y,z),(x \ u) \ L(K(x,w),v5,v6)). ((x * y) * z) \ ((y * x) * z) = K(y,z \ (y \ ((y * x) * z))). K(x,y \ (x \ ((x * z) * y))) = ((z * x) * y) \ ((x * z) * y). T(x,R(y / (y / z),u,w)) = x * K(T(x,z \ y),R(z,u,w)). x != y / T(y,z) | x = K(z,y). K(T(x,y * K(z,y)),u) = K(x * K(T(x,z),y),u). K(T(x * K(x * y,x),z * K(y * x,z)),u) = K((x * K(x * y,x)) * K(x,z),u). K(T(x,y * K(z * x,y)),u) = K(x * K(T(x,z),y),u). L((x * (K(y,x) / T(x,z))) \ u,T(x,z) \ ((x \ 1) \ K(y,x)),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u). x != K(y,(y * z) / u) | x = K(y,y * (z / u)). K(x,K(y,z)) * K(y,x \ (y * z)) = K(y,y * (z / x)). x != K(T(y,z),R(T(u,z),w,v5)) | x = K(y,R(u,w,v5)). R(K(x,y),T(y,z) * u,w) = K(x,R(y,u,w)). R(K(x,y),T(y,z) * u,w) != v5 | K(x,R(y,u,w)) = v5. R(K(x,y),z,u) = K(x,R(y,T(y,w) \ z,u)). K(x,R(y,T(y,z) \ u,w)) = R(K(x,y),u,w). x != K(y,R(z,T(z,u) \ w,v5)) | x = R(K(y,z),K(u,z) * w,v5). R(K(x,y),z,u) = R(K(x,y),K(w,y) * z,u). R(K(x,y),K(z,y) * u,w) = R(K(x,y),u,w). R(K(x,y),K(y,z) * u,w) = R(K(x,y),u,w). R(K(x,y \ z),(y \ z) * y,u) = R(K(x,y \ z),z,u). R(K(x,y),y * z,u) != w | K(x,R(y,z,u)) = w. x != K(y,T(z,u)) | x = K(T(y,u),z). K(x,T(y \ T(T(x,z),u),w)) = K(T(x,w),y \ T(x,u)). x != K(y,T(z \ T(y,u),w)) | x = K(y,T(z \ y,w)). K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ x,w)). (x / T(1 / y,z)) \ 1 = (x / T(y \ 1,z)) \ K(y,y \ 1). (x / T(y \ 1,z)) \ K(y,y \ 1) = (x / T(1 / y,z)) \ 1. K(x,T(y \ z,u)) = K(x,T((z \ y) \ 1,u)). K(x,T((y \ z) \ 1,u)) = K(x,T(z \ y,u)). K(x,T(y \ 1,z)) = K(x,T((u * y) \ u,z)). K(x,T((y * z) \ y,u)) = K(x,T(z \ 1,u)). K(x,T(y / z,u)) = K(x,T((z / y) \ 1,u)). K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u)). x != K(y,K(z,u)) | x = K(u,K(y,z)). K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,z \ (x \ u))). x != ((1 / y) * z) \ 1 | x = z \ y. K(x,y) \ (((1 / z) * (x * x)) \ 1) = (x * T(x,y)) \ z. (x \ K(y,z)) * (z * T(T(z,y),y)) = (z \ x) \ T(z,y). L(T(x,y),z,x) \ u = K(y,x) * (L(x,z,x) \ u). K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u. T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u). x / R(y * K(z,y),u,y) = (x / R(y,u,y)) * K(y,z). K(x,y) * ((1 / x) \ z) = (1 / T(x,y)) \ z. K(x,y) * ((1 / T(y,x)) \ z) = (1 / y) \ z. x * y != K(z,u) * ((1 / z) \ w) | x \ ((1 / T(z,u)) \ w) = y. T(x,y) \ ((1 / T(x,y)) \ z) = x \ ((1 / x) \ z). K(x,y) * (x / z) = (1 / T(x,y)) \ (1 / z). (1 / T(x,y)) \ (1 / z) = K(x,y) * (x / z). T(x,y) / z = K(x,y) * (x / z). K(x,y) * (x / z) = T(x,y) / z. K(x,y) * (T(y,x) / z) = y / z. x * y != K(z,u) * (z / w) | x \ (T(z,u) / w) = y. (x \ y) \ (T(y / x,x) / z) = (y / x) \ ((y / x) / z). K(x,y) * z = T(x,y) / (z \ x). T(x,y) / (z \ x) = K(x,y) * z. K((1 / x) * y,x \ 1) * (((1 / x) * y) / z) = (y / x) / z. K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u. K(x,y) * z = y / (z \ T(y,x)). x / (y \ T(x,z)) = K(z,x) * y. K(x,K(y,z)) * (T(x,K(z,y)) / u) = x / u. (K(x,y) * z) \ T(x,y) = z \ x. (K(x,y) * z) \ x = (z \ x) * K(y,x). (x * x) \ (K(y,x) * z) = 1 / ((z \ T(x,y)) * x). L(x \ y,x,K(y,z)) = x \ y. (T(x,y) * z) \ T(x,y) = (x * z) \ x. (x \ y) * T(y,z) = (y \ x) \ T(y,z). (x \ y) \ T(x,z) = (y \ x) * T(x,z). a(K(x,y),z,z \ x) = 1. a(K(x * y,z),x,y) = 1. a(K(x,y),z,z \ y) = 1. a(K(x,K(y,z * u)),z,u) = 1. x != 1 | x = K(y,K(z,u)) * K(y,K(z,u)). a(K(x,y),z,z \ y) = K(u,K(w,v5)) * K(u,K(w,v5)). (K(x,y) * T(x,z)) \ x = K(z,x) * K(y,x). x != (T(y,z) * (T(y / z,y) / u)) \ T(y,z) | x = L(u,T(y,z),T(y,z)) * (z / T(y,z)). (x * (T(x / y,x) / z)) \ x = L(z,T(x,y),T(x,y)) * (y / T(x,y)). x != (y \ z) * T(z,u) | x = (y \ T(z,u)) * z. (x \ y) \ T(x,z) = (y \ T(x,z)) * x. (x \ 1) \ T(x,y) = x * T(x,y). (x \ y) \ T((1 / y) * x,z) = ((1 / y) * x) * T((1 / y) * x,z). ((1 / x) * y) * T((1 / x) * y,z) = (y \ x) \ T((1 / x) * y,z). x / y != z * (T(x,K(u,w)) / y) | K(x,K(w,u)) = z. x * (T(y,K(z,u)) / w) != y / w | K(y,K(u,z)) = x. (K(x,y) * T(x,K(z,u))) \ x = K(z,K(u,x)) * K(y,x). L(x,T(y,z),T(y,z)) = y \ ((1 / y) \ x). x != y \ ((1 / y) \ z) | x = L(z,y,y). L(x,T(y,z),T(y,z)) = L(x,y,y). x != L(y * (z \ u),T(z,u),T(z,u)) | x = L(y,T(z,u),T(z,u)) * (u / T(z,u)). L(x * (y \ z),y,y) = L(x,T(y,z),T(y,z)) * (z / T(y,z)). L(x,T(y,z),T(y,z)) * (z / T(y,z)) = L(x * (y \ z),y,y). (x * x) \ (K(y,x) * z) = 1 / ((z \ x) * T(x,y)). (x * T(y,L(z * K(y,z),y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x). x != K(y * K(z,u),w \ 1) | x = K(K(u,z) / y,w). T(x \ 1,K(y,z)) \ (1 / x) = K(K(y,z) / x,x). x != K(y / z,z) | x = K(z \ y,z). T(x \ 1,K(y,z)) \ (1 / x) = K(x \ K(y,z),x). x != T(y \ 1,z) \ (1 / y) | x = K(y,y \ z). K(x \ K(y,z),x) = K(x,x \ K(y,z)). ((x / y) * K(z,z \ K(u,w))) \ K(z,z \ K(u,w)) = (K(z,z \ K(u,w)) * y) * (x \ K(z,z \ K(u,w))). K(T(x,y),R(z,u,w)) = K(T(x,z \ y),R(z,u,w)). K(T(x,y \ z),R(y,u,w)) = K(T(x,z),R(y,u,w)). K(x,y) * ((y * R(x,z,u)) * x) = (x * y) * R(x,z,u). K(x,y) * R(x,z,R(x,u,w)) = R(T(x,y),z,R(x,u,w)). x != (y * z) * T((y * z) \ u,z) | x = u * K(y \ (z \ u),z). ((x \ (y / z)) * x) * z = y * K(z \ (x \ y),x). x != ((y \ (z / u)) * y) * u | x = u * ((y \ (u \ z)) * y). x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z). ((x \ y) * x) * z = (y * z) * K(z \ (x \ (y * z)),x). (x * y) * K(y \ (z \ (x * y)),z) = ((z \ x) * z) * y. (x * K(y \ (z \ x),z)) * u = (y * ((z \ (y \ x)) * z)) * u. K((x \ K(x,y)) * z,u) = K((K(x,y) / x) * z,u). K((K(x,y) / x) * z,u) = K((x \ K(x,y)) * z,u). K((x \ 1) * T((x \ 1) \ y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u). x != K(K(R(y,z,u),w) * v5,T(y,v6)) | x = K(v5,T(y,v6)). K(x * T(R(y,z,u),w),T(T(y,v5),K(R(y,z,u),w))) = K(x * R(y,z,u),T(y,v5)). (x \ ((x / y) * z)) * (1 / (u * (((1 / y) * (z / x)) * x))) = K(x \ ((1 / y) * (z / x)),((1 / y) * (z / x)) \ x) / u. K(x \ ((1 / y) * (z / x)),((1 / y) * (z / x)) \ x) / u = (x \ ((x / y) * z)) * (1 / (u * (((1 / y) * (z / x)) * x))). x != ((y * (z * u)) \ (y * z)) * (1 / (y * z)) | x = L(u,z,y) \ (1 / (y * z)). (x * (y * z)) \ K(y \ x,x \ y) = L(z,y,x) \ (1 / (x * y)). x * (1 / (y * x)) = y \ K(x \ y,y \ x). x \ K(y \ x,x \ y) = y * (1 / (x * y)). x * (y * (1 / (x * y))) != z | z = K(y \ x,x \ y). x * (y * (1 / (x * y))) != z | K(y \ x,x \ y) = z. x != K(y,K(z,u \ 1)) | x = K(y,K(z,u)). R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w))). R(K(x,K(y,z \ 1)),u,w) * x = T(x,K(R(z,u,w) \ 1,y)). R(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w))). R(K(x,K(y,z)),u,w) = K(x,K(y,R(z,u,w))). x != R(K(y,K(z,u)),w,v5) | x = K(z,R(K(y,u),w,v5)). K(x,K(y,R(z,u,w))) = K(x,R(K(z,y),u,w)). K(x,R(K(y,z),u,w)) = K(x,K(z,R(y,u,w))). x != R(K(y,K(z,u)),z,w) | x = K(y,K(z,u)). K(x,K(y,R(z,y,u))) = K(x,K(y,z)). x != R(K(y,K(z,u)),w,v5) | x = K(y,R(K(z,u),w,v5)). K(x,K(y,R(z,u,w))) = K(x,R(K(y,z),u,w)). K(x,R(K(y,z),u,w)) = K(x,K(y,R(z,u,w))). T(x,K(y,R(z,u,w))) = x * R(K(x,K(y,z)),u,w). x * R(K(x,K(y,z)),u,w) = T(x,K(y,R(z,u,w))). L(K(x,y),T(x,z) * u,w) != v5 | K(L(x,u,w),y) = v5. L(K(x,y),x * z,u) != w | K(L(x,z,u),y) = w. K(x,L(y,x,z)) != u | K(L(x,y,z),y) = u. x != (y / T(z,z * u)) * K(z,u) | x = y / L(z,u,z). (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y). x != K(y,L(z,K(z,u) * w,v5)) | x = K(y,L(z,w,v5)). L(K(x,y),T(y,z) * u,w) = K(x,L(y,u,w)). K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y. K(x,K(y,z)) * K(y,y * (x \ z)) = K(y,y * (z / x)). K(x,R(y \ z,y,u)) = R(K(x,y \ z),z,u). R(K(x,y \ z),z,u) = K(x,R(y \ z,y,u)). R(K(x,y \ R(y,z,u)),R(y,z,u),z * u) = K(x,((y * z) * u) / (y * (z * u))). K(x,y) \ ((x * x) \ z) = (x * T(x,y)) \ z. K(x,y) * ((y * y) \ z) = (y * T(y,x)) \ z. K(x,y / x) * (((y / x) * (y / x)) \ z) = ((y / x) * (x \ y)) \ z. K(x,y * (1 / x)) * (((y * (1 / x)) * (y * (1 / x))) \ z) = ((y * (1 / x)) * ((x \ 1) * y)) \ z. x != (y \ z) \ T(y,u) | x = (z \ T(y,u)) * y. (x \ K(y,z)) * (z * T(T(z,y),y)) = (x \ T(z,y)) * z. (x \ y) \ ((x \ y) / z) = (y / x) \ ((y / x) / z). (x / y) \ ((x / y) / z) = (y \ x) \ ((y \ x) / z). x != (y / z) \ ((y / z) / u) | x = ((u \ (y / z)) \ 1) \ (z * (y \ 1)). (x \ y) \ ((x \ y) / z) = ((z \ (y / x)) \ 1) \ (x * (y \ 1)). ((x \ (y / z)) \ 1) \ (z * (y \ 1)) = (z \ y) \ ((z \ y) / x). (x / y) \ ((((y \ 1) \ 1) * (1 / x)) \ z) = ((y \ x) \ ((y \ x) / z)) \ 1. (K(x,K(y,z)) * T(x,K(u,w))) \ x = K(u,K(w,x)) * K(z,K(x,y)). x * y != K(z,u) * R(z,w,R(z,v5,v6)) | x \ R(T(z,u),w,R(z,v5,v6)) = y. x \ R(T(x,y),z,R(x,u,w)) = K(x,y) * (x \ R(x,z,R(x,u,w))). K(x,y) * (x \ R(x,z,R(x,u,w))) = x \ R(T(x,y),z,R(x,u,w)). (x * R(T(y,x),z,R(y,u,w))) * y = K(y,x) * ((x * R(y,z,R(y,u,w))) * y). K(x,y) * ((y * R(x,z,R(x,u,w))) * x) = (y * R(T(x,y),z,R(x,u,w))) * x. K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u)). K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u)). ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x)). x != (y \ T(z,u)) * z | x = (y \ z) * (w / (T(z,u) \ w)). (x \ K(y,z)) * (z * T(T(z,y),y)) = (x \ z) * (u / (T(z,y) \ u)). ((x * y) / x) / ((x * (y * K(z / u,y))) / x) = K(y,T((K(y,w) * z) / u,x)). K(x,T((K(x,y) * z) / u,w)) = ((w * x) / w) / ((w * (x * K(z / u,x))) / w). K(x,y) * (R(x,z,x) * u) = R(T(x,y),z,x) * u. (R(x,y,z) * u) / (R(T(x,w),y,z) * u) != v5 | K(w,R(x,y,z)) = v5. K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w). K(x * (y * z),a(x,y,z) \ 1) != u | K((x * y) * z,x * (y * z)) = u. T(x,x * y) * K(y,x) = L(x,T(y,K(x,z)),x). L(x,T(y,K(x,z)),x) = T(x,x * y) * K(y,x). x != T(y,y * z) * K(z,y) | x = L(y,z,y). L(x,T(y,K(x,z)),x) = L(x,y,x). x != L(y,T(z,K(y,u)),y) | x = L(y,T(z,T(y,u)),y). L(x,y,x) = L(x,T(y,T(x,z)),x). L(x,T(y,T(x,z)),x) = L(x,y,x). L(x,T(x,y) \ z,x) = L(x,z / T(x,y),x). L(x,y / T(x,z),x) = L(x,T(x,z) \ y,x). L(x \ 1,x,y * K(x,z)) != u | L(x \ 1,T(x,z),y) = u. ((1 / x) \ y) * T(y,z) = x * (y * T(y,z)). R(x,T(y,z),z) = R(x,y,z * K(y,z)). R(x,y,z * K(y,z)) = R(x,T(y,z),z). R(x,K(y,z),T(u,K(y,z))) = R(x,T(K(y,z),u),u). R(x,T(K(y,z),u),u) = R(x,K(y,z),T(u,K(y,z))). x * (y * K(x * z,T(z,x * y))) = K(x * z,z) * (x * y). K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) = K(x,T(w,y)). x != L(y,z,u) \ L(T(y,w),z,u) | x = K(L(y,z,u),w). K(L(x,y,z),u * K(w,x)) = K(L(x,y,z),u). K(L(x,y,z),K(u,x) * w) = K(L(x,y,z),w). K(L(x,y,z),L(K(u,x),w,v5) * v6) = K(L(x,y,z),v6). R(K(x,T(T(y,z),z * u)),z,u) = K(((z / x) * u) \ (z * u),y). x != K(y,((y \ 1) * z) \ (y \ u)) | x = K(y,z \ u). K(x,L(y,x \ 1,x) \ z) = K(x,y \ z). L(x,y,x) * K(T(y * x,y),x) = (y * x) / y. K(x * ((y * z) / y),z) = K(x * L(z,y,z),z). K(x * L(y,z,y),y) = K(x * ((z * y) / z),y). x != K(y * ((z * u) / z),u) | x = K(u * y,u). K(x * L(y,z,y),y) = K(y * x,y). x != K((L(y,z,u) \ w) * L(y,z,u),y) | x = K(w,y). K(x * (L(x,y,x) \ z),x) = K(z,x). T(x * K(y,x),x * (L(x,z,x) \ y)) = x. T(x,y) = T(x,x * (L(x,z,x) \ y)). T(x,x * (L(x,y,x) \ z)) = T(x,z). T(x,x * y) = T(x,L(x,z,x) * y). T(x,L(x,y,x) * z) = T(x,x * z). T(x,L(x,y,x) * z) = x * K(x,x * z). K(x,L(x,y,x) * z) = K(x,x * z). (x * (K(y,z) * u)) / (x * u) = L(K(y,T(T(z,u),x * u)),u,x). L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z). K(x,T(y,z)) = K(L(x,z,L(x,u,w)),T(y,L(x,u,w) * z)). K(L(x,y,L(x,z,u)),T(w,L(x,z,u) * y)) = K(x,T(w,y)). L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w)). x != K(y,K(z,L(u,w * y,v5))) | x = K(u,K(z,L(y,w,v5))). K(x,K(y,(z * (u * y)) \ w)) = K(x,K((u * y) \ (z \ w),L(y,u,z))). K(x,K((y * z) \ (u \ w),L(z,y,u))) = K(x,K(z,(u * (y * z)) \ w)). K(x,R(T(K(x,y),z * u),z,u)) = K(x,a(K(x,y),z,u)). x != K(y,R(T(K(y,z),u),w,v5)) | x = 1. K(x,a(K(x,y),z,u)) = 1. K(x,a(K(x,y),z,u)) * w != 1 | 1 = w. 1 = K(a(K(x,y),z,u),x). K(a(K(x,y),z,u),x) = 1. T(x,a(K(x,y),z,u)) = x. T(a(K(x,y),z,u),x) = a(K(x,y),z,u). a(K(x,y),z,u) * x = x * a(K(x,y),z,u). a(K(x,y),z,u) * K(x,w) = K(x,w) * a(K(x,y),z,u). K(x,y) * a(K(x,z),u,w) = a(K(x,z),u,w) * K(x,y). x * K(a(K(x,y),z,u),w) = K(a(K(x,y),z,u),w) * x. K(a(K(x,y),z,u),w) * x = x * K(a(K(x,y),z,u),w). K(K(a(x,y,T(z,y)),y),u) = K((x * (z * y)) \ ((x * y) * z),K(y,u)). K((x * (y * z)) \ ((x * z) * y),K(z,u)) = K(K(a(x,z,T(y,z)),z),u). K(x,y) * (y \ R(y,x,L(y,z,u))) = K(x * L(y,z,u),y). R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,T(x,K(y,z))) = T(K(z,y),T(x,K(y,z))). T(x,R(K(y,z),u,w)) = T(x,K(y,R(z,u,w))). K(L(x,y * z,u),(u \ (u * (x * y))) \ (x * (y * z))) = K(x,L(L(z,y,x),x * y,u)). (x * (y * z)) * K(u,L(y,z,x)) = x * (y * (z * K(u,y))). K(R(x,y / x,z),u) = K((y * z) / ((y / x) * z),T(u,y)). x != K(R(y,z,R(y,u,w)),v5) | x = K(y,v5). K(x,T(y,z)) = K(x,T(y,z * R(x,u,w))). K(x,T(y,z * R(x,u,w))) = K(x,T(y,z)). K(x,T(y,z)) = K(x,T(y,z / R(x,u,w))). K(x,T(y,z / R(x,u,w))) = K(x,T(y,z)). x != K(y,T(z,u / R(y,w,v5))) | x = K(y,T(z,R(y,w,v5) \ u)). K(x,T(y,z)) = K(x,T(y,R(x,u,w) \ z)). K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w)). K(x,T(y,z)) = K(x,T(y,R(x,u,w) * z)). K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w)). x != K(y,T(z,u)) | x = K(y,z) * K(y,K(z,u)). K(x,T(y,R(x,z,u) * w)) = K(x,y) * K(x,K(y,w)). K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w)). K(x,K(y,z)) = K(x,K(y,R(x,u,w) \ z)). K(x,K(y,R(x,z,u) \ w)) = K(x,K(y,w)). K(x,K(y,(x * z) * u)) = K(x,K(y,z * u)). K(x,K(y,z \ R(x,u,w))) = K(x,K(y,z)). K(x,K(y,z)) = K(x,K(y,R(x,u,w) / z)). K(x,K(y,R(x,z,u) / w)) = K(x,K(y,w)). K(x,K(y,z)) = K(x,K(y,z * R(x,u,w))). K(x,K(y,z * R(x,u,w))) = K(x,K(y,z)). K(x,K(y,(y * z) * u)) = K(y,K(x,z * u)). K(x,K(y,z * u)) * K(y,x) = K(y,T(x,(x * z) * u)). K(x,K(y,(y * z) * u)) = K(x,K(y,z * u)). K(x,K(y,(z * y) * u)) = K(x,K(y,z * u)). K(x,T(y,z * u)) = K(x,T(y,(y * z) * u)). K(x,T(y,(y * z) * u)) = K(x,T(y,z * u)). K(x,T(y,z * u)) = K(x,T(y,(y \ z) * u)). K(x,T(y,(y \ z) * u)) = K(x,T(y,z * u)). K(x \ y,T(x,z)) = K(x \ y,T(x,y * z)). K(x \ y,T(x,y * z)) = K(x \ y,T(x,z)). x != K(L(y,z,L(y,u,w)),v5) | x = K(y,v5). K(x,T(y,z)) = K(x,T(y,L(x,u,w) * z)). K(x,T(y,L(x,z,u) * w)) = K(x,T(y,w)). K(x,T(y,z)) = K(x,T(y,L(x,u,w) \ z)). K(x,T(y,L(x,z,u) \ w)) = K(x,T(y,w)). x != K(y,T(z,L(y,u,w) \ v5)) | x = K(y,T(z,v5 / L(y,u,w))). K(x,T(y,z)) = K(x,T(y,z / L(x,u,w))). K(x,T(y,z / L(x,u,w))) = K(x,T(y,z)). K(x,T(y,z * u)) = K(x,T(y,z * (u * x))). K(x,T(y,z * (u * x))) = K(x,T(y,z * u)). K(x,T(y,z * (u / x))) = K(x,T(y,z * u)). x != K(y,T(z,u * (w * y))) | x = K(y,T(z,u * (y * w))). K(x,T(y,z * u)) = K(x,T(y,z * (x * u))). K(x,T(y,z * (x * u))) = K(x,T(y,z * u)). K(x,T(y,z * u)) = K(x,T(y,z * (x \ u))). K(x,T(y,z * (x \ u))) = K(x,T(y,z * u)). K(x,T((y * (x \ z)) \ u,y * z)) != w | K(x,u / (y * (x \ z))) = w. L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w)). (x * (y * (K(z,y) \ (y \ u)))) * K(z,L(y,K(z,y) \ (y \ u),x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y). x != K((y * z) / (u * z),T(w,y)) | x = R(K(u \ y,w),y,z). K(R(x,y / x,z),u) = R(K((y / x) \ y,u),y,z). R(K((x / y) \ x,z),x,u) = K(R(y,x / y,u),z). R(K(x,y),z,u) = K(R(x,z / x,u),y). K(R(x,y / x,z),u) = R(K(x,u),y,z). K(R(x,y,z),u) = R(K(x,u),y * x,z). R(K(x,y),z * x,u) = K(R(x,z,u),y). K(R(x,y,z),y) != u | K(x,R(y,x,z)) = u. K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u)). K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x). K(x,T((y \ z) \ x,y)) != u | K(x,(z / y) \ x) = u. K(x,T(y \ x,z)) = K(x,((z * y) / z) \ x). K(x,((y * z) / y) \ x) = K(x,T(z \ x,y)). K(x,(y / (y / z)) \ x) = K(x,T(z \ x,z \ y)). K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x). K(x,R(1 / (1 / (1 / y)),y,z) \ x) = K(x,T((z / (y * z)) \ x,y)). K(x,T((y / (z * y)) \ x,z)) = K(x,R(1 / (1 / (1 / z)),z,y) \ x). (x * (K(y,z) * u)) / (x * u) = K((x * u) / (x * (y \ u)),z). K((x * y) / (x * (z \ y)),u) = (x * (K(z,u) * y)) / (x * y). L((x / y) \ z,x,x) = (1 / (y / x)) \ L(z,x,x). (1 / (x / y)) \ L(z,y,y) = L((y / x) \ z,y,y). (x / y) / ((y * z) \ y) = L((y / x) \ z,y,y). (x / y) / (z * (1 / y)) = L((y / x) \ (y * (1 / z)),y,y). L((x / y) \ (x * (1 / z)),x,x) = (y / x) / (z * (1 / x)). T(x \ y,x) * (K(x,y) * z) = ((1 / x) * y) * z. K(x \ y,x) * ((x \ y) * (K(x,y) * z)) = ((1 / x) * y) * z. T(T(x * K(y,x),z),u) \ T(T(x,z),u) = K(x,T(T(y,u),z)). T(T(x * K(y,x),z),u) \ T(T(x,z),u) != w | K(x,T(T(y,u),z)) = w. x != K(y \ z,y) * K(u,z / y) | x = y \ (z / T(z / y,u)). K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x)). K(R(x,y,z),x * (u \ 1)) != w | K(R(x,y,z),u \ x) = w. x != K(y,R(T(y,z),u,w) * v5) | x = K(y,R(y,u,w) * v5). K(x,y \ R(T(x,z),u,w)) = K(x,R(x,u,w) * (y \ 1)). x != K(y,R(y,z,u) * (w \ 1)) | x = K(y,w \ R(y,z,u)). K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w)). x != K(y,z \ R(T(y,u),w,v5)) | x = K(y,R(T(y,u),w,v5) / z). K(x,y \ R(x,z,u)) = K(x,R(T(x,w),z,u) / y). K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u)). K(x,R(x,y,z) / u) = K(x,R(T(x,w),y,z) / u). K(x,R(T(x,y),z,u) / w) = K(x,R(x,z,u) / w). K(x,R(T(x,y),z,u) / w) != v5 | K(x,w \ R(x,z,u)) = v5. (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u)). T(K(x,y) * z,u) \ T(z,u) = K(y,T(x \ z,u) \ T(z,u)). K(x,T(y \ z,u) \ T(z,u)) = T(K(y,x) * z,u) \ T(z,u). x != ((K(y,z) / u) * w) \ K(y,z) | x = K(z,y) * ((w * K(z,y)) \ u). (x \ (y * K(z,u))) * K(u,z) = K(z,u) * ((x * K(z,u)) \ y). K(T(x,y),y) * ((1 / T(x,y)) * z) = (1 / x) * z. K(x,y) * ((1 / T(x,y)) * z) = (1 / x) * z. x * ((1 / x) * y) = T(x,z) * ((1 / T(x,z)) * y). T(x,y) * ((1 / T(x,y)) * z) = x * ((1 / x) * z). x != T(y / z,y) * ((1 / T(y / z,y)) * u) | x = (y \ z) * (((1 / z) * y) * u). (x / y) * ((1 / (x / y)) * z) = (x \ y) * (((1 / y) * x) * z). ((x \ y) * K(z,u)) \ (x \ 1) = (K(u,z) * (y \ x)) * (x \ 1). x != (y * ((y \ z) * K(u,w))) \ 1 | x = (K(w,u) * (z \ y)) * (y \ 1). (K(x,y) * z) * ((u * z) \ 1) = (K(x,y) * (u \ z)) * (z \ 1). (K(x,y) * (z \ u)) * (u \ 1) = (K(x,y) * u) * ((z * u) \ 1). K(R(x,y,z),(u / w) \ x) = K(R(x,y,z),x * (w / u)). K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = z * T(z \ u,x). L(x,T(y,z) \ u,T(y,u)) = L(x,y \ (K(z,y) * u),y). L(x,T(y,z) \ u,T(y,u)) = L(x,T(y,z) \ u,y). x * L(y,T(z,x) \ x,z) = T(z,x) * ((T(z,x) \ x) * y). T(x,y) * ((T(x,y) \ y) * z) = y * L(z,T(x,y) \ y,x). T(x,y) * ((x \ T(y,x)) * z) = y * L(z,T(x,y) \ y,x). T(x,y) * ((x \ T(y,x)) * z) = y * L(z,x \ T(y,x),x). (x * L(y,z \ T(x,z),z)) \ (x * y) = a(T(z,x),T(z,x) \ x,y). (((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z)) * K((K(x,y) / x) * (x * z),u) = T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),u). (K(x,y) * T(z,u)) * K(y,x) = T((K(x,y) * z) * K(y,x),u). T((K(x,y) * z) * K(y,x),u) = (K(x,y) * T(z,u)) * K(y,x). (x * y) \ T(y * x,z) = T(y * x,z) / (x * y). T(x * y,z) / (y * x) = (y * x) \ T(x * y,z). ((x * y) \ T(y * x,z)) * (x * y) = T(y * x,z). (K(x,y) * K(x * y,z)) * (y * x) = T(x * y,z). x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1))). K(x,y / (x / (z \ 1))) != u | K(x,y / (x * z)) = u. x != (y * K(z,T(u,w))) \ y | x = K(u,T(z,w)). K(T(x,y * (z * K(u,w))),w) = K(x,T(w,y * z)). K(R(x,y,z),L(u,w,x)) != v5 | K(R(x,y,z),u) = v5. K(x,K(y,(z \ 1) / u)) = K(y,(z \ T(z * u,x)) / u). K(x,(y \ T(y * z,u)) / z) = K(u,K(x,(y \ 1) / z)). K(x,(T(y,z) / u) / (y / u)) = K(z,K(x,(u \ 1) / (y / u))). K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z)). K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(x,K(y,z)) * w). K(K(x,y),z) * (K(x,y) * T(u * K(y,x),w)) = T(K(y,x) * u,w) * T(K(x,y),T(z,T(K(y,x) * u,w))). T(K(x,y) * z,u) * T(K(y,x),T(w,T(K(x,y) * z,u))) = K(K(y,x),w) * (K(y,x) * T(z * K(x,y),u)). (x * K(y * z,y)) * K(y,z) = K(y * z,y) * (K(y,z) * x). K(x,K(y,R(z,u,w) * (z \ y))) != v5 | K(x,K(y,R(z,u,w) \ z)) = v5. x != K(y \ z,y) * T(u,y \ z) | x = (z / y) \ (u * (y \ z)). T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y)). x * y != T(z,u / w) * K(w \ u,w) | x \ ((u / w) \ (z * (w \ u))) = y. x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z). T(K(x,y),(z \ (u * x)) \ 1) = T(K(x,y),z \ u). T(K(x,y),z \ (u * x)) = T(K(x,y),z \ u). T(K(x,y),z \ u) = T(K(x,y),z \ (u / x)). T(K(x,y),z \ (u / x)) = T(K(x,y),z \ u). L(K(x,y),z,u) \ L(T(K(x,y),w \ v5),z,u) = K(L(K(x,y),z,u),w \ (v5 / x)). K((x \ 1) \ y,z \ (x * y)) = K(x * y,(x \ z) \ y). K(x,K(y * z,(y \ u) \ z)) = K(x,K(u \ (y * z),z \ (y \ 1))). K(x,K(y \ (z * u),u \ (z \ 1))) = K(x,K(z * u,(z \ y) \ u)). x * (y * K(z,(x \ u) \ y)) != (x * y) * w | K(z,u \ (x * y)) = w. (x * y) * z != x * (y * K(u,(x \ w) \ y)) | K(u,w \ (x * y)) = z. x != K(y,K(z \ u,u)) | x = K(y,K(z,u)). K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y,z)). K(x,(1 / y) * ((z \ y) * z)) = K(x,K(y,z)). x != K(y,(1 / z) * u) | x = K(y,(z \ 1) * u). K(x,K(y,z)) = K(x,(y \ 1) * ((z \ y) * z)). K(x,(y \ 1) * ((z \ y) * z)) = K(x,K(y,z)). T(K(x,y),T(z,x * u)) = T(K(x,y),T(z,u * x)). T(K(x,y),T(z,u * x)) = T(K(x,y),T(z,x * u)). x != T(K(y,z \ u),T(z,u)) | x = T(K(y,z \ u),z). T(K(x,y \ (z * x)),T(y,x * z)) = T(K(x,y \ (z * x)),y). K(x,R(y,z,u)) = K(x,R(y,z * K(y,w),u)). K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w)). K(x,R(y,z,u)) = K(x,R(y,T(z,y),u)). K(x,R(y,T(z,y),u)) = K(x,R(y,z,u)). K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w)). x != K(y,R(z,T(u,z),w)) | x = R(K(y,z),u * z,w). K(x,R(y,z,u)) = R(K(x,y),z * y,u). R(K(x,y),z * y,u) = K(x,R(y,z,u)). R(K(x,y),z * (y * K(u,x)),w) = K(x,R(y * K(u,x),z,w)). (x * K(y,R(z,u,w))) \ x = K(R(z,K(z,v5) * u,w),y). K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5. K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w). x != K(R(y,K(y,z) * (y \ u),w),v5) | x = R(K(y,v5),K(y,z) * u,w). K(R(x,x \ y,z),u) = R(K(x,u),K(x,w) * y,z). R(K(x,y),K(x,z) * u,w) = K(R(x,x \ u,w),y). x != K(R(y,y \ z,u),w) | x = R(K(y,w),z,u). R(K(x,y),K(x,z) * u,w) = R(K(x,y),u,w). R(K(x,y),K(z,x) * u,w) = R(K(x,y),u,w). R(K(x,y),z,u) = R(K(x,y),z * K(w,x),u). R(K(x,y),z * K(u,x),w) = R(K(x,y),z,w). x != R(K(y,z),K(u,y) * w,v5) | x = K(R(y,T(y,u) \ w,v5),z). R(K(x,y),z,u) = K(R(x,T(x,w) \ z,u),y). K(R(x,T(x,y) \ z,u),w) = R(K(x,w),z,u). K(R(x,y,z),u) = R(K(x,u),T(x,w) * y,z). R(K(x,y),T(x,z) * u,w) = K(R(x,u,w),y). R(K(x,x * y),T(x,z) * u,w) = K(R(x,u,w),L(x,v5,x) * y). K(x,K((y * x) / z,T(u,z))) = K(x,K(u,(z / x) \ y)). K(x,K(y,z \ (u * x))) = K(x,K(y,(z / x) \ u)). K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ (u * x))). x != K(y,K(z,u \ (w * y))) | x = K(y,K(z,u \ w)). K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ u)). x != K(y,K(z,(u / y) \ w)) | x = K(y,K(z,(y \ u) \ w)). K(x,K(y,z \ u)) = K(x,K(y,(x \ z) \ u)). K(x,K(y,(x \ z) \ u)) = K(x,K(y,z \ u)). K(x,K(y,z \ (x \ u))) = K(x,K(y,u \ z)). K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(x \ z) \ u)). x != K(y,K(z,u \ (y \ w))) | x = K((T(y,v5) * u) \ w,K(y,z)). K(x,K(y,z \ u)) = K((T(x,w) * u) \ z,K(x,y)). K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,u \ z)). K(x,K(y,(T(x,z) * u) \ w)) = K(x,K(y,w \ u)). K(x,T(y,z \ u)) = K(x,T(y,(x \ z) \ u)). K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ u)). x != K(y,T(z,(y \ u) \ w)) | x = K(y,T(z,u \ (y * w))). K(x,T(y,z \ u)) = K(x,T(y,z \ (x * u))). K(x,T(y,z \ (x * u))) = K(x,T(y,z \ u)). K(x,T(y,z \ u)) = K(x,T(y,(x * z) \ u)). K(x,T(y,(x * z) \ u)) = K(x,T(y,z \ u)). K(x,T(y,a(x,z,u))) = K(x,T(y,(z * u) \ ((x * z) * u))). K(x,T(y,(z * u) \ ((x * z) * u))) = K(x,T(y,a(x,z,u))). K(x,T(y,R(T(x,z * u),z,u))) = K(x,T(y,a(x,z,u))). K(x,y) = K(x,T(y,a(x,z,u))). K(x,T(y,a(x,z,u))) = K(x,y). T(x,T(y,a(x,z,u))) = x * K(x,y). T(x,T(y,a(x,z,u))) = T(x,y). (T(x,x \ y) * a(x,z,u)) \ (a(x,z,u) * ((x \ y) \ y)) = K(a(x,z,u),x). x != (y * K(z,u)) / (z \ y) | x = T(z,T(u,y)). T(x,T((y * x) / z,u)) = T(x,T(x * (y / z),u)). x != T(y,T((z * y) / u,w)) | x = T(y,T(z / (y \ u),w)). T(x,T(x * (y / z),u)) = T(x,T(y / (x \ z),u)). T(x,T(y / (x \ z),u)) = T(x,T(x * (y / z),u)). (x * ((x \ y) * K(z \ (x \ y),u))) \ y != w | K(u,(x * z) \ y) = w. K(R(x,L(y,z,u),x),R(x,L(y,z,u),x) * y) * T(x * L(y,z,u),x) = L(y,z,u) * T(R(x,L(y,z,u),x),R(x,L(y,z,u),x) * y). K(R(x,R(y,z,u),x),R(x,R(y,z,u),x) * y) * T(x * R(y,z,u),x) = R(y,z,u) * T(R(x,R(y,z,u),x),R(x,R(y,z,u),x) * y). x != K((y * (z \ 1)) \ 1,y * (z \ 1)) | x = (z * K((y / z) \ 1,y / z)) * (z \ 1). K(x \ y,x * (y \ 1)) = (y * K((x / y) \ 1,x / y)) * (y \ 1). (x * K((y / x) \ 1,y / x)) * (x \ 1) = K(y \ x,y * (x \ 1)). ((x \ K(x,y)) * T(x,z)) \ 1 = (K(x,y) * K(x,z)) \ K(x,x \ 1). (K(x,y) * K(x,z)) \ K(x,x \ 1) = ((x \ K(x,y)) * T(x,z)) \ 1. ((x \ (y * z)) * x) / z = (z \ 1) * ((x \ ((z \ 1) \ y)) * x). (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x. K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,K(z \ y,T(z,u))). (x * K(y,T(z,u))) * K(z,w) = (x * K(z,w)) * K(y,T(z,u)). x != K(y,z \ (y \ ((y * u) * z))) | x = K(y,R(T(u,z),y,z)). ((x * y) * z) \ ((y * x) * z) = K(y,R(T(x,z),y,z)). T(x,R(y / (y / z),u,w)) = x * K(T(x,y),R(z,u,w)). x != y * K(T(y,z),R(u,w,v5)) | x = T(y,R((z * u) / z,w,v5)). T(x,R(y / (y / z),u,w)) = T(x,R((y * z) / y,u,w)). T(x,R((y * z) / y,u,w)) = T(x,R(y / (y / z),u,w)). x != T(y,R((z * u) / z,w,v5)) | x = T(y,R(T(u,z),w,v5)). T(x,R(y / (y / z),u,w)) = T(x,R(T(z,y),u,w)). x != T(y,R(z / (z / u),w,v5)) | x = T(y,R(T(u,u \ z),w,v5)). T(x,R(T(y,z),u,w)) = T(x,R(T(y,y \ z),u,w)). T(x,R(T(y,y \ z),u,w)) = T(x,R(T(y,z),u,w)). T(x,R((y \ z) \ z,u,w)) = T(x,R(T(y,z),u,w)). T(x,R(((y / T(1 / z,u)) \ 1) \ K(z,z \ 1),w,v5)) = T(x,R(T(y / T(z \ 1,u),K(z,z \ 1)),w,v5)). K(x,y) * (((1 / x) * y) / z) = (y / x) / z. K(x,y) * (1 / (z * (y \ x))) = (y / x) / z. K(x,y) / (z * (y \ x)) = (y / x) / z. R(K(x,K(y,z)),u,w) * x = T(x,K(R(y,u,w) \ 1,z)). T(x,K(R(y,z,u) \ 1,w)) = R(K(x,K(y,w)),z,u) * x. T(x,K(R(y,z,u) \ 1,w)) = K(x,R(K(y,w),z,u)) * x. T(x,K(R(y,z,u) \ 1,w)) = T(x,R(K(y,w),z,u)). T(x,K(y,R(z,u,w))) = T(x,R(K(z,y),u,w)). T(x,R(K(y,z),u,w)) = T(x,K(z,R(y,u,w))). x != T(y,R(K(z,u),w,v5)) | x = T(y,K(z,R(u,w,v5))). T(x,K(y,R(z,u,w))) = T(x,K(z,R(y,u,w))). T(x,K(R(y,z,u),w)) = T(x,K(y,R(w,z,u))). T(K(x,y) * z,K(x,R(u,w,v5))) = K(x,y) * T(z,K(u,R(x,w,v5))). T(x,K(y,R(z,u,w))) != v5 | T(x,K(z,R(y,u,w))) = v5. (x * (y \ 1)) * ((((z \ 1) \ 1) \ (x * (y \ 1))) \ 1) = ((x \ y) \ ((x \ y) / z)) \ 1. x * (y * K(x * z,T(z,y))) = K(x * z,z) * (x * y). x != y * (z * K(u,T(w,z))) | x = y * (K(u,w) * z). K(x * y,y) * (x * z) = x * (K(x * y,y) * z). K(x \ y,x) * ((y * (x \ 1)) * z) = ((1 / x) * y) * z. (K(x \ y,x) * (y * (x \ 1))) / (1 / (y * (x \ 1))) = ((1 / x) * y) * (y * (x \ 1)). K(x \ y,x) * (y * ((x \ 1) * (y * (x \ 1)))) = ((1 / x) * y) * (y * (x \ 1)). T(T(x * K(y * T(x,z),x),u),w) \ T(T(x,u),w) = K(x,T(T(T(x,z) * y,w),u)). T(K(x,y) * z,u) * K(y,T(x \ z,u) \ T(z,u)) = T(z,u). ((1 / x) \ ((1 / y) * K(z,u))) * K(u,z) = K(z,u) * ((K(z,u) \ x) / y). x != (y / z) * ((1 / (y / z)) * u) | x = (z * (y \ 1)) * ((y / z) * u). (x \ y) * (((1 / y) * x) * z) = (y * (x \ 1)) * ((x / y) * z). (x * (y \ 1)) * ((y / x) * z) = (y \ x) * (((1 / x) * y) * z). (K(x,y) * (z \ u)) * (u \ 1) = (K(x,y) * u) * (u \ (z \ 1)). K(x,y) * (z * T(z \ u,x)) = z * T(z \ (K(x,y) * u),x). T((K(x,y) * z) * K(y,x),u) != w * K(y,x) | K(x,y) * T(z,u) = w. K(x,K(y,z)) = K(x,(T(z,y) / u) / (z / u)). K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y)). K(x,(T(y,z) / u) / (y / u)) * (y / w) = T(y,K(x,z)) / w. K(x,K(y,z)) * u = K(z,w) * (K(x,K(y,z)) * (K(z,w) \ u)). K(x,y) * (K(z,K(u,x)) * (K(x,y) \ w)) = K(z,K(u,x)) * w. x * (K(y,z) * K(y * z,y)) = K(y * z,y) * (K(y,z) * x). K(x * y,x) * (K(x,y) * z) = z * (K(x,y) * K(x * y,x)). x != K(y,z / u) * K(u \ z,u) | x = u \ (z / T(z / u,y)). x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x)). x != T(K(y,z),T(u,y * w)) | x = T(K(y,z),T(u,w)). T(K(x,y \ (z * x)),y) = T(K(x,y \ (z * x)),T(y,z)). T(K(x,y \ (z * x)),T(y,z)) = T(K(x,y \ (z * x)),y). K(x,T(y \ (z * x),T(y,z))) = T(K(x,y \ (z * x)),y). x != T(K(y,z \ (u * y)),z) | x = K(y,(z / u) \ y). K(x,T(y \ (z * x),T(y,z))) = K(x,(y / z) \ x). x != K(y,(z / R(z,u,w)) \ y) | x = K(y,y * (z \ R(z,u,w))). K(x,T(y \ (R(y,z,u) * x),T(y,R(y,z,u)))) = K(x,x * (y \ R(y,z,u))). K(x,T((y \ 1) * ((z \ y) * z),u)) != w | K(z,K(x,T(y,u))) = w. K(x,T(y,z)) = K(x,T(K(u,x) * y,z)). K(x,T(K(y,x) * z,u)) = K(x,T(z,u)). K(x,T(K(x,y) * z,u)) = K(x,T(z,u)). K(x,T(y * K(x,z),u)) = K(x,T(y,u)). K(x,T(T(y,z),u)) = K(x,T(T(K(w,x) * y,z),u)). K(x,T(T(K(y,x) * z,u),w)) = K(x,T(T(z,u),w)). K(x,T(T(x * y,z),u)) = K(x,T(T(T(x,w) * y,z),u)). K(x,T(T(T(x,y) * z,u),w)) = K(x,T(T(x * z,u),w)). x != (K(y,z) * (u \ w)) * (w \ 1) | x = ((w \ u) * K(z,y)) \ (w \ 1). (K(x,y) * z) * (z \ (u \ 1)) = ((z \ u) * K(y,x)) \ (z \ 1). ((x \ y) * K(z,u)) \ (x \ 1) = (K(u,z) * x) * (x \ (y \ 1)). K(x,y) * (K(z,x) * u) = ((1 / z) * u) * T(((1 / z) * u) \ (K(x,y) * u),x). ((1 / x) * y) * T(((1 / x) * y) \ (K(z,u) * y),z) = K(z,u) * (K(x,z) * y). K((T(x,y) / z) / (x / z),u) * (T(x,K(u,y)) / w) = x / w. ((T(x,K(y,z)) / u) * u) / x = R(K(y,(T(x,z) / w) / (x / w)),x / u,u). R(K(x,(T(y,z) / u) / (y / u)),y / w,w) = ((T(y,K(x,z)) / w) * w) / y. K(x,y) * (K(z,K(x,u)) * (K(x,y) \ w)) = K(u,K(z,x)) * w. K(x,K(y,z)) = K((T(x,y) / u) / (x / u),z). K((T(x,y) / z) / (x / z),u) = K(x,K(y,u)). (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z). x != K(y * R(z,u,w),z) * K(z,y) | x = z \ R(z,y,R(z,u,w)). (x * (y * R(x,z,u))) \ ((y * R(x,z,u)) * T(x,y)) = x \ R(x,y,R(x,z,u)). x != K(y * L(z,u,w),z) * K(z,y) | x = z \ R(z,y,L(z,u,w)). (x * (y * L(x,z,u))) \ ((y * L(x,z,u)) * T(x,y)) = x \ R(x,y,L(x,z,u)). x != (y * z) \ (z * T(y,y \ z)) | x = a(y,z / y,y). K(x,y) * K(y,y \ x) = a(y,x / y,y). (x * y) \ (y * T(x,z)) != u | K(x,z) * K(y,x) = u. x != K(y,z) * K(z,z \ y) | x = z \ R(z,z \ y,z). a(x,y / x,x) = x \ R(x,x \ y,x). x \ R(x,x \ y,x) = a(x,y / x,x). x \ R(x,y,x) = a(x,(x * y) / x,x). a(x,(x * y) / x,x) = x \ R(x,y,x). a(x,y,x) = x \ R(x,T(y,x),x). x \ R(x,T(y,x),x) = a(x,y,x). x \ R(x,y,x) = a(x,y,x). K(x,y) * K(x * y,x) = a(x,y,x). K(x * y,x) * K(x,y) = a(x,y,x). R(x,y,x) / x = a(x,y,x). x != y \ R(y,z,y) | x = T(y,u) \ R(T(y,u),z,y). a(x,y,x) = T(x,z) \ R(T(x,z),y,x). T(x,y) \ R(T(x,y),z,x) = a(x,z,x). x * a(x,y,x) = R(x,y,x). a(x,y,x) * x = R(x,y,x). x \ R(x,y \ 1,x) = a(x,x \ (y \ x),x). a(x,x \ (y \ x),x) = x \ R(x,y \ 1,x). K(x,T(y,z)) * a(y,u,y) = T(y,T(x,z)) \ R(y,u,y). T(x,T(y,z)) \ R(x,u,x) = K(y,T(x,z)) * a(x,u,x). x * a(y,x,y) = T(y * x,y) / y. T(x * y,x) / x = y * a(x,y,x). x \ R(x,y,x) != z | z = a(x,y,x). x \ R(x,y,x) != z | a(x,y,x) = z. a(x,y,x) * K(x,x * y) = K(x,y). K(x,y) * a(y,x,y) = K(y * x,y). K(x,x * y) * a(x,y,x) = K(x,y). (x * y) * a(y,x,y) = T(y * x,y). (x / y) * a(y,z,y) = x / L(y,z,y). a(x,y,x) * (y * x) = T(x * y,x). K(x * y,x) * (K(x,y) * z) = z * a(x,y,x). a(x,y,x) * K(y,x) = K(x * y,x). x != T(y * R(z,u,w),y) / y | x = R(T(y * z,y) / y,u,w). R(x,y,z) * a(u,R(x,y,z),u) = R(T(u * x,u) / u,y,z). R(T(x * y,x) / x,z,u) = R(y,z,u) * a(x,R(y,z,u),x). T(x * a(y,x,y),y) = y \ T(y * x,y). (x * y) \ (y * (T(z * T(x,y),z) / z)) = L(a(z,T(x,y),z),T(x,y),y). (x * (y * z)) \ ((x * y) * (T(u * L(z,y,x),u) / u)) = L(a(u,L(z,y,x),u),L(z,y,x),x * y). (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) != w | L(L(a(u,z,u),z,y),y * z,x) = w. K(x,y) * K(x * y,x) != z | a(x,y,x) = z. K(x * y,x) * K(x,y) != z | a(x,y,x) = z. a(x,x \ y,x) * K(x,y) = K(x,x \ y). K(x,y) * a(y,x,y) = K(x * y,y). K(x,y) * a(x,x \ y,x) = K(x,x \ y). R(T(x,T(x * y,x)),y * x,a(x,y,x)) = ((y * x) * a(x,y,x)) \ ((x * y) * x). a(T(x,y * z),z,T(x,y * z)) * K(z,T(x,y)) = K(T(x,y * z) * z,T(x,y * z)). T(x,y) \ ((x \ y) \ y) = a(x,x \ y,x). a(x,x \ y,x) = T(x,y) \ ((x \ y) \ y). a(x,y,x) * T(x,z) = R(T(x,z),y,x). x * a(y,z,y) = (x * y) / L(y,z,y). (x * y) / L(y,z,y) = x * a(y,z,y). (x / L(y,z,y)) * y = x * a(y,z,y). (x * a(y,z,y)) \ (x * y) = L(y,z,y). x != (y / L(z,u,z)) * z | x = z * (L(z,u,z) \ y). x * a(y,z,y) = y * (L(y,z,y) \ x). x * (L(x,y,x) \ z) = z * a(x,y,x). x * y = (x * L(y,z,y)) * a(y,z,y). (x * L(y,z,y)) * a(y,z,y) = x * y. a(x,y,x) \ x = L(x,y,x). ((x * y) * a(T(y,x),z,T(y,x))) \ ((y * x) * y) = L(T(y,x),z,T(y,x)). L(x,y,x) \ (x * z) = z * a(x,y,x). x * y != z * a(z,u,z) | x \ R(z,u,z) = y. x \ R(x,y,x) = L(x,y,x) \ x. L(x,y,x) \ x = x \ R(x,y,x). x != y * (L(y,z,y) \ u) | x = T(y,w) * (L(T(y,w),z,y) \ u). x * a(y,z,y) = T(y,u) * (L(T(y,u),z,y) \ x). T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x). L(x,y,x) * (z * a(x,y,x)) = x * z. L(x,y,x) * z = x * (z / a(x,y,x)). x * (y / a(x,z,x)) = L(x,z,x) * y. x * y != L(x,z,u) * w | y = L(x,z,u) * (x \ w). x / a(y,z,y) = L(y,z,y) * (y \ x). L(x,y,x) * (x \ z) = z / a(x,y,x). x * y != L(z,u,z) * (z \ w) | x \ (w / a(z,u,z)) = y. (x / y) \ (x / a(y,z,y)) = L(y,z,y). a(x,x \ (y \ x),x) != z | a(x,y \ 1,x) = z. K(x,x * y) * (z * a(x,y,x)) = K(x,y) * z. a(x,y,x) * z != K(x * y,x) * (K(x,y) * u) | T(u,a(x,y,x)) = z. K(x * y,x) * (K(x,y) * z) != a(x,y,x) * u | T(z,a(x,y,x)) = u. T(x,y \ x) \ ((x \ (y \ x)) \ (y \ x)) != z | a(x,y \ 1,x) = z. K(x * y,x) * (K(x,y) * z) != u | u = z * a(x,y,x). K(x * y,x) * (K(x,y) * z) != u | z * a(x,y,x) = u. K(x,x * y) * (z * x) = K(x,y) * (z * L(x,y,x)). K(x,y) * (z * L(x,y,x)) = K(x,x * y) * (z * x). T(x,y) * (L(T(x,y),z,x) \ u) != u * w | a(x,z,x) = w. K(x,y) * (z * a(y,u,y)) = y * (L(T(y,x),u,y) \ z). R(x * a(y,x,y),z,u) = R(x,z,u) * a(y,R(x,z,u),y). R(x,y,z) * a(u,R(x,y,z),u) = R(x * a(u,x,u),y,z). K(x,R(y,z,u)) * ((y * z) * u) = (y * (K(x,y) * z)) * u. ((x * y) * T(z,y)) / (y * T(z,y)) = R(x,y * K(z,y),z). R(x,y,T(z,y)) = R(x,y * K(z,y),z). R(x,y * K(z,y),z) = R(x,y,T(z,y)). R(x,y / z,z) = R(x,z \ y,T(z,z \ y)). R(x,y \ z,T(y,y \ z)) = R(x,z / y,y). K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y). K(x,(y * (x / y)) \ (x * z)) != u | K(x,K(y \ x,y) * z) = u. R(x,K(T(y,z),u),z * K(u,y)) * z = (x * K(T(y,z),u)) * (K(u,T(y,z)) * z). (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = R(x,K(T(y,z),u),z * K(u,y)) * z. x * R(K(y,z),u,w) = (x * K(y,v5)) * (K(v5,y) * R(K(y,z),u,w)). (x * K(y,z)) * (K(z,y) * R(K(y,u),w,v5)) = x * R(K(y,u),w,v5). K(L(x,y,z),T(u,w)) = K(L(x,y,z),T(u,x \ w)). K(L(x,y,z),T(u,x \ w)) = K(L(x,y,z),T(u,w)). x != K(L(y,z,u),T(w,y \ v5)) | x = K(L((y \ v5) \ v5,z,u),w). K(L(x,y,z),T(u,w)) = K(L((x \ w) \ w,y,z),u). K(L((x \ y) \ y,z,u),w) = K(L(x,z,u),T(w,y)). (x * K(L(y,z,u),T(w,v5))) \ (x * w) = T(w,L((y \ v5) \ v5,z,u)). T(x,L((y \ z) \ z,u,w)) = (v5 * K(L(y,u,w),T(x,z))) \ (v5 * x). (x * (y \ ((z \ (y * (x \ u))) * z))) \ u != w | K(z,(x * (y \ z)) \ u) = w. x != (K(y,z) * (u * y)) \ (K(y,z) * u) | x = L(y \ 1,y,u). L(x \ 1,x,K(x,y) * z) = L(x \ 1,x,z). L(x \ 1,x,y * K(x,z)) = L(x \ 1,x,y). L(x \ 1,T(x,y),z) = L(x \ 1,x,z). T(x * L(x \ 1,x,y),z) = T(x,z) * ((y * T(x,z)) \ y). L(x \ 1,x,y) * L(L(x \ 1,T(x,z),y) \ 1,u,w) = L((x \ 1) * L((x \ 1) \ 1,u,w),T(x,z),y). K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u). K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u). K(x,T(y,z) \ T(x,u)) = K(T(x,z),y \ x). K(x,T(y,z) \ T(x,u)) != w | K(x,T(y \ x,z)) = w. K(x,T(y \ x,z)) = K(x,T(y,z) \ x). K(x,T(y,z) \ x) = K(x,T(y \ x,z)). x != K(y,T((z \ 1) \ u,w)) | x = K(y,T(z * u,w)). K(x,T(y \ 1,z) \ x) = K(x,T(y * x,z)). K((x \ y) * y,T(z,x)) = K((x \ y) * y,z). K(x * (x / y),z) = K((y \ x) * x,z). K((x \ y) * y,z) = K(y * (y / x),z). K((x / y) \ y,z) = K(y * (y / x),T(z,y \ x)). K(x * (x / y),T(z,x \ y)) = K((y / x) \ x,z). K(x * (x / y),x \ (x \ y)) = K((y / x) \ x,x \ (y / x)). K((x / y) \ y,y \ (x / y)) = K(y * (y / x),y \ (y \ x)). x != K((y / z) \ u,u \ (y / z)) | x = K(y \ (u * z),(u * z) \ y). K(x * (x / y),x \ (x \ y)) = K(y \ (x * x),(x * x) \ y). K(x \ (y * y),(y * y) \ x) = K(y * (y / x),y \ (y \ x)). K(x * (x / y),x \ (x \ y)) != z | K(x * (y \ x),x \ (y / x)) = z. K(x,K(y,(z * u) \ ((z * x) * u))) = 1. R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * u). x * y != R(K(z,u),w,v5) \ R(T(K(z,u),v6),w,v5) | x \ K(v6,R(K(z,u),w,v5)) = y. R(K(x,y),z,u) \ K(w,R(K(y,x),z,u)) = R(T(K(y,x),w),z,u). T(T(T(x,x * K(y,z)),u),K(z,y)) = R(T(x,u),K(z,y),x). R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z)). x / (x / R(K(y,z),u,w)) = (R(K(y,z),u,w) \ x) \ x. K(x,K(y,(z * u) / (R(z,w,v5) * u))) = K(x,K(R(z,w,v5) \ z,R(y,z,u))). K(x,K(R(y,z,u) \ y,R(w,y,v5))) = K(x,K(w,(y * v5) / (R(y,z,u) * v5))). R(K(x \ (y \ z),z / y),z / y,y) = K(z / (x * y),z / y). L(K(x,K(y,z \ 1) * (u \ w)),u \ w,u) = K(x,(K(z \ K(z,u),y) * u) \ w). L(K(x,K(y \ 1,z) * (u \ w)),u \ w,u) = K(x,(K(z,y \ K(y,u)) * u) \ w). x != L(K(y,z \ (u \ w)),u \ w,u) | x = K(y,(u * z) \ w). K(x,(y * T(z,x \ 1)) \ u) = K(x,(y * z) \ u). K(x,(y * (x \ 1)) \ z) = K(x,((x \ 1) * y) \ z). K(x,((x \ 1) * y) \ z) = K(x,(y * (x \ 1)) \ z). K(x,(y * z) \ u) = K(x,(y * (((x \ 1) * z) / (x \ 1))) \ u). K(x,(y * (((x \ 1) * z) / (x \ 1))) \ u) = K(x,(y * z) \ u). K(x,(y * (x \ 1)) \ (x \ z)) = K(x,y \ z). x != K(y,((y \ 1) * z) \ u) | x = K(y,z \ (u * y)). K(x,(y * (x \ 1)) \ z) = K(x,y \ (z * x)). K(x,y \ (x \ z)) = K(x,(y / (x \ 1)) \ z). K(x,(y / (x \ 1)) \ z) = K(x,y \ (x \ z)). K(x,(x / y) * z) = K(x,y \ (z * x)). K(x,y \ (z * x)) = K(x,(x / y) * z). K(x,(y * (x \ 1)) \ z) = K(x,x * (y \ z)). K(x,y * (L(y,z,u) \ x)) = K(x,(x / L(y,z,u)) * y). K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x)). L(K(x,y \ (x \ (z \ u))),z \ u,z) = K(x,(z * (y / (x \ 1))) \ u). T(x,(y * (x \ 1)) \ z) = x * K(x,x * (y \ z)). T(x,(y * (x \ 1)) \ z) != u | T(x,x * (y \ z)) = u. x != K(y,z) | x = K((y \ 1) \ 1,z). L(K(x,y \ ((z \ u) * x)),z \ u,z) = K((x \ 1) \ 1,(z * (y / x)) \ u). R(T(K(x,(y / z) \ x),u),x,z) = K(x,T((y / (x * z)) \ 1,u)). x != (y * (K(z,u) * w)) / (y * w) | x = K((y * w) / (y * (z \ w)),u). L(K(x,T(T(y,z),u * z)),z,u) = K((u * z) / (u * (x \ z)),y). L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u). x != R(K(y,z),T(y,u) * w,v5) | x = K(R(y,w,v5),z). K(R(x,y,z),L(x,u,x) * w) = K(R(x,y,z),x * w). x != R(K(y,T(T(z,u),u * w)),u,w) | x = K(((u / y) * w) \ (u * w),z). (x * y) \ ((x * K(z,u)) * y) = K(((x / z) * y) \ (x * y),u). K(((x / y) * z) \ (x * z),u) = (x * z) \ ((x * K(y,u)) * z). ((x * y) \ ((x * K(z,u)) * y)) \ 1 = R(K(T(T(u,x),x * y),z),x,y). R(K(T(T(x,y),y * z),u),y,z) = ((y * z) \ ((y * K(u,x)) * z)) \ 1. R(T(K(x,y),R(K(y,x),z,u) * w),z,u) \ w = w / (R(K(y,x),z,u) \ 1). K(x / (y * z),x / z) = K(y \ (z \ x),x / z). K((x * y) \ z,y \ z) = K(x \ (y \ z),z / y). (x * K(y \ (z \ u),u / z)) \ x = K(z \ u,(y * z) \ u). K(x / y,z \ (y \ x)) = K(y \ x,(z * y) \ x). R(K(x,T((y / z) \ x,u)),x,z) = K(x,T((y / (x * z)) \ 1,u)). L(K(x,T(T(y,z * u),u)),u,z) = K((z * u) / (z * (x \ u)),y). K((x * y) / (x * (z \ y)),u) \ w = L(K(T(T(u,y),x * y),z),y,x) * w. L(K(T(T(x,y),z * y),u),y,z) * w = K((z * y) / (z * (u \ y)),x) \ w. L(T(K(x \ y,T(x,z)),z),z,y) = (y * (K(x \ y,x) * z)) / (y * z). K(x,T((y / (x * z)) \ 1,u)) = K(x,T((y / z) \ x,u)). x != K(y,T((z / u) \ 1,z)) | x = K(y,z \ u). K(x,T((y / z) \ x,y)) = K(x,y \ (x * z)). x != K(y,z \ (y * u)) | x = K(y,z \ (u * y)). K(x,T((y / z) \ x,y)) = K(x,y \ (z * x)). K(x,T(y \ x,z)) = K(x,z \ (x * (y \ z))). K(x,y \ (x * (z \ y))) = K(x,T(z \ x,y)). K(x,T(y \ x,z)) = K(x,z \ ((y \ z) * x)). K(x,y \ ((z \ y) * x)) = K(x,T(z \ x,y)). K(x,(y / x) \ (z \ y)) = K(x,T(z \ x,y)). x != K(y,(y * z) \ (u * y)) | x = K(y,z \ u). K(x,T(y \ x,x * z)) = K(x,z \ (y \ (x * z))). K(x \ y,x \ (z \ y)) = K(x \ y,T(z \ (x \ y),y)). K(x \ y,T(z \ (x \ y),y)) = K(x \ y,x \ (z \ y)). K(x,T(y \ x,z)) = K(x,z \ (y \ (x * z))). K(x,y \ (z \ (x * y))) = K(x,T(z \ x,y)). K(x,L(K(y,z),u,w) * (v5 \ (x * L(K(z,y),u,w)))) = K(x,T(v5 \ x,L(K(z,y),u,w))). K(x / y,z \ (y \ x)) = K(y \ x,y \ (z \ x)). x != K(y / z,u \ (z \ y)) | x = K(z \ y,(u * z) \ y). K(x \ y,x \ (z \ y)) = K(x \ y,(z * x) \ y). K(x \ y,(z * x) \ y) = K(x \ y,x \ (z \ y)). K(((x \ y) / z) \ y,(x * ((x \ y) / z)) \ y) = K(((x \ y) / z) \ y,z). x != T((y \ 1) * z,K(u,T(w,y \ z))) | x = T((y \ 1) * z,K(u,w)). (x \ 1) * (K(x \ 1,K(y,T(z,x \ L((x \ 1) \ 1,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (y / x),y \ x). x != ((y \ z) \ 1) * ((y \ z) \ u) | x = ((z \ y) * (z \ y)) * u. ((x \ y) \ z) / (x \ y) = ((y \ x) * (y \ x)) * T(z,y \ x). ((x \ y) * (x \ y)) * T(z,x \ y) = ((y \ x) \ z) / (y \ x). x != (y * y) * T(z,y) | x = (y * z) * y. ((x \ y) \ z) / (x \ y) = ((y \ x) * z) * (y \ x). ((x \ y) \ z) / (x \ y) != u * (y \ x) | (y \ x) * z = u. T((x \ y) \ z,z) / (x \ y) = ((y \ x) * T(z,x \ y)) * (y \ x). ((x \ y) \ K(y \ x,z)) / (x \ y) = T(y \ x,z) * (y \ x). T((x \ y) \ 1,z) / (x \ y) = T(y \ x,z) * (y \ x). (x \ y) \ T(1 / (x \ y),z) = T(y \ x,z) * (y \ x). (x \ y) \ T((1 / y) * x,z) = T(y \ x,z) * (y \ x). x != T(y,z) * y | x = y * T(y,z). (x \ y) \ T((1 / y) * x,z) = (y \ x) * T(y \ x,z). T(x * K(y,z),z / (z / y)) = ((z * y) / z) \ (x * y). T(x,(y / z) * y) = T(x,y * (z \ y)). (x * y) \ (y * (T(x,y) * z)) = L(L(z,x,y),y * x,K(x,y)). L(L(x,y,z),z * y,K(y,z)) = (y * z) \ (z * (T(y,z) * x)). L(L(x,y,z),z * y,K(y,z)) != u | L(x,T(y,z),z) = u. (1 / (x * y)) * ((y \ (x \ 1)) \ z) = K(y \ x,x \ y) * z. K(x,L(y \ L(y,z,u),y,u * z)) != w | K(x,a(u,z,y) \ 1) = w. (K(x,y) \ z) * (u * K(y,x)) = K(x,y) \ ((z * u) * K(y,x)). K(x,y) \ ((z * u) * K(y,x)) = (K(x,y) \ z) * (u * K(y,x)). K(x,y) \ ((z * u) * K(y,x)) = (K(y,x) * z) * (u * K(y,x)). K(x,y) * ((z * u) * K(x,y)) = (K(x,y) * z) * (u * K(x,y)). (K(x,y) * z) * (u * K(x,y)) = K(x,y) * ((z * u) * K(x,y)). x * (y * K(z \ u,u \ z)) = (x * y) * K(z \ u,u \ z). (x * y) * K(z \ u,u \ z) = x * (y * K(z \ u,u \ z)). x * (y * K(z \ 1,z)) = (x * y) * K(z \ 1,z). (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z)). x * (y * K(z,z \ 1)) = (x * y) * K(z,z \ 1). (x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1)). K(x,x \ 1) * (y * (z * K(x \ 1,x))) = y * z. K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x)). x \ (y * K(z \ 1,z)) = (x \ y) * K(z \ 1,z). R(x,y,K(z \ 1,z)) = x. x != y * (z * K(u \ 1,u)) | x = y * (K(u \ 1,u) * z). (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y). (x * (y * K(z \ 1,z))) * u = K(z \ 1,z) * ((x * y) * u). (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u). x / (y * K(z \ 1,z)) = K(z,z \ 1) * (x / y). T(x,y) = T(x,y * K(z \ 1,z)). T(x,y * K(z \ 1,z)) = T(x,y). x / (y * K(z \ 1,z)) = (x * K(z,z \ 1)) / y. (x * K(y,y \ 1)) / z = x / (z * K(y \ 1,y)). x != R(y,z,K(u \ 1,u)) | x = R(y,K(u \ 1,u),z). x = R(x,K(y \ 1,y),z). R(x,K(y \ 1,y),z) = x. R(x,y,K(z,z \ 1)) = x. x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y). x * (K(y \ 1,y) * z) = (x * K(y \ 1,y)) * z. (x * K(y \ 1,y)) * z = x * (K(y \ 1,y) * z). R(x,y,1 / z) = R(x,y,z \ 1). x != R(T(y,z * K(u,u \ 1)),z,K(u,u \ 1)) | x = T(y,z). T(x,y * K(z,z \ 1)) = T(x,y). x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1). x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1). T(x,K(y \ 1,y) * z) = T(x,z). T(x,y) = T(x,K(z,z \ 1) * y). T(x,K(y,y \ 1) * z) = T(x,z). T(x,y \ (z \ 1)) = T(x,y \ (1 / z)). T(x,y \ (1 / z)) = T(x,y \ (z \ 1)). R(x,y,z) = R(x,y,(z \ 1) \ 1). R(x,y,(z \ 1) \ 1) = R(x,y,z). R(x,y,(z \ 1) \ (1 / u)) = R(x,y,(u * (1 / z)) \ 1). R(x,y,(z * (1 / u)) \ 1) = R(x,y,(u \ 1) \ (1 / z)). x != T(y,R(1 / z,u,w)) | x = T(y,R(z \ 1,u,w)). T(x,R(1 / y,z,u) * K(w,w \ 1)) = T(x,R(y \ 1,z,u)). T(x,L(y,z,u) * (1 / y)) = T(x,y \ L(y,z,u)). T(x,T(y,y \ 1) * z) = T(x,y * z). T(x,y * (z * K(u,u \ 1))) = T(x,y * z). T(x,K(y \ z,z \ y) * u) = T(x,u). T(x,(((y \ 1) \ 1) \ z) * u) = T(x,(y \ z) * u). (x \ (y / z)) \ (x \ y) = R(z,y \ 1,x). R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1). K((x \ (1 / y)) / z,T(u,x \ (y \ 1))) = K(z \ (x \ (1 / y)),u). T(x,K(y \ z,z \ y) / (u * w)) = T(x,w \ (u \ 1)). T(x,y * (z * (1 / u))) = T(x,y * (z * (u \ 1))). K(L(x,y,z),L(x,y,z) \ 1) = K(x,x \ 1). K(x,x \ 1) * (y * z) = y * (z * K(x,x \ 1)). L(K(x,x \ 1),y,z) = K(x,x \ 1). (x * y) * K(z,z \ 1) = x * (K(z,z \ 1) * y). K(L(x,y,z),x \ 1) = K(x,x \ 1). K(x,x \ 1) * L(x,y,z) = L(T(x,x \ 1),y,z). x * y != K(L(z,u,w),L(z,u,w) \ 1) | x \ K(z,z \ 1) = y. L(x,y,z) \ K(x,x \ 1) = 1 / L(x,y,z). x * y != L(z,u,w) \ K(z,z \ 1) | x \ (1 / L(z,u,w)) = y. x \ (1 / L(x,y,z)) = L(x,y,z) \ (1 / x). L(x,y,z) \ (1 / x) = x \ (1 / L(x,y,z)). (x \ (1 / L(x,y,z))) * x = L(x,y,z) \ 1. x * y != L(z,u,u) \ 1 | ((u * z) \ u) / y = x. ((x * y) \ x) / y = y \ (1 / L(y,x,x)). x \ (1 / L(x,y,y)) = ((y * x) \ y) / x. x \ (y \ (y / x)) = ((y * x) \ y) / x. ((x * y) \ x) / y = y \ (x \ (x / y)). x != ((y * z) \ y) / z | x = (1 / z) * L(1 / z,y,y). x \ (y \ (y / x)) = (1 / x) * L(1 / x,y,y). (1 / x) * L(1 / x,y,y) = x \ (y \ (y / x)). (1 / x) * (y \ (y / x)) = x \ (y \ (y / x)). (x \ (y \ (y / x))) \ 1 != z | (y \ (y / x)) \ x = z. K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z. K(x,x \ 1) * (y * (z * (x \ 1))) = y * (z * (1 / x)). K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z). x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z). x / (K(y \ 1,y) * z) = K(y,y \ 1) * (x / z). x / (y * K(z,z \ 1)) = K(z,z \ 1) * (x / y). (x * K(y,y \ 1)) / (z * ((y \ 1) \ 1)) = x / (z * y). (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x). L(x,K(y \ 1,y),z) = x. L(x,K(y,y \ 1),z) = x. L(x,K(y \ z,z \ y),u) = x. a(x,K(y,y \ 1),z) = 1. K(x \ 1,x) * (y \ z) = (y * K(x,x \ 1)) \ z. (x * K(y,y \ 1)) \ z = K(y \ 1,y) * (x \ z). (x * K(y,y \ 1)) * z = x * (K(y,y \ 1) * z). x \ (y * K(z,z \ 1)) = K(z,z \ 1) * (x \ y). x \ (y * (1 / (z * y))) = (x \ (1 / z)) * K(y,y \ 1). (x \ (1 / y)) * K(z,z \ 1) = x \ (z * (1 / (y * z))). x \ (K(y,y \ 1) * z) = K(y,y \ 1) * (x \ z). x \ (K(y,y \ 1) * z) != u | K(y,y \ 1) * (x \ z) = u. K(x,y \ (K(z,z \ 1) * u)) = K(x,y \ u). K(x,y \ (z * T(u,u \ 1))) = K(x,y \ (z * u)). K(x,y \ (z \ (1 / u))) = K(x,y \ (z \ (u \ 1))). K(x,y \ z) = K(x,(K(u,u \ 1) * y) \ z). K(x,(K(y,y \ 1) * z) \ u) = K(x,z \ u). K(x,(y * (1 / z)) \ u) = K(x,(y * (z \ 1)) \ u). T(x,(((y \ 1) \ K(z,u)) \ w) * v5) = T(x,((y * K(z,u)) \ w) * v5). (x \ 1) * (y * K(z,z \ 1)) = ((x \ z) * (1 / z)) * y. K(x,x \ 1) * (y * (1 / z)) = y * (x * (1 / (z * x))). (x * (K(y,y \ 1) * z)) / u = K(y,y \ 1) * ((x * z) / u). K(x,x \ 1) * (y * (K(x,x \ 1) * z)) = y * z. K(x,y * (K(z,z \ 1) * u)) = K(x,y * u). x \ (y * (K(z,z \ 1) * u)) = (x \ (y * u)) * K(z,z \ 1). K(x,x \ 1) * (y * (z * u)) = y * (z * (K(x,x \ 1) * u)). K(x,y * ((z \ 1) \ u)) = K(x,y * ((1 / z) \ u)). K(x,y * ((1 / z) \ u)) = K(x,y * ((z \ 1) \ u)). x != K(y,y \ 1) * L(y,z,u) | x = y * (L(y,z,u) * (1 / y)). L(T(x,x \ 1),y,z) = x * (L(x,y,z) * (1 / x)). x * (L(x,y,z) * (1 / x)) = L(T(x,x \ 1),y,z). a(x,K(y,y \ 1) * z,u) = (x * ((K(y,y \ 1) * z) * u)) \ ((K(y,y \ 1) * (x * z)) * u). (x * ((K(y,y \ 1) * z) * u)) \ ((K(y,y \ 1) * (x * z)) * u) = a(x,K(y,y \ 1) * z,u). K(x,x \ 1) * (y * (z \ 1)) = y * ((z \ x) * (1 / x)). x / (K(y,y \ 1) * z) = K(y,y \ 1) * (x / z). x != y * K(z \ 1,z) | x = K(z \ 1,z) * y. (K(x,x \ 1) * y) \ z = K(x \ 1,x) * (y \ z). T(x,(K(y,y \ 1) * z) \ u) = T(x,z \ u). (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y). T(x,(y \ z) \ u) = T(x,(((y \ 1) \ 1) \ z) \ u). T(x,(((y \ 1) \ 1) \ z) \ u) = T(x,(y \ z) \ u). T(x,(y * (1 / z)) \ u) = T(x,(y * (z \ 1)) \ u). (x * K(y,y \ 1)) \ z = K(y,y \ 1) * (x \ z). x != (1 / y) \ (z * K(u,u \ 1)) | x = y / ((z \ u) * (1 / u)). K(x,x \ 1) * ((1 / y) \ z) = y / ((z \ x) * (1 / x)). x \ (y * (1 / (z * y))) = K(y,y \ 1) * (x \ (1 / z)). K(x,x \ 1) * (y \ (1 / z)) = y \ (x * (1 / (z * x))). x \ (K(y,y \ 1) * z) != u | (x \ z) * K(y,y \ 1) = u. x \ (((y \ z) * (1 / z)) * u) = K(z,z \ 1) * (x \ ((y \ 1) * u)). K(x,x \ 1) * (y \ ((z \ 1) * u)) = y \ (((z \ x) * (1 / x)) * u). K(x,y \ ((z \ u) \ 1)) = K(x,y \ ((u \ 1) * z)). K(x,x \ 1) * (y * ((z \ x) * (1 / x))) = y * (z \ 1). K(x,y * ((1 / z) \ K(z \ 1,u))) = K(x,y * (((u * (z \ 1)) / u) \ 1)). K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * ((1 / u) \ K(u \ 1,z))). x * (L(x,y,z) * (1 / x)) = L((x \ 1) \ 1,y,z). x / T(y * z,z \ 1) = K(z,z \ 1) * (x / (z * y)). K(x,x \ 1) * (y / (x * z)) = y / T(z * x,x \ 1). (K(x,x \ 1) * y) \ z = K(x,x \ 1) * (y \ z). x != T(y,(z * (1 / y)) \ u) | x = T(y,R(z,y \ 1,y) \ (y * u)). T(x,(y * (x \ 1)) \ z) = T(x,R(y,x \ 1,x) \ (x * z)). T(x,R(y,x \ 1,x) \ (x * z)) = T(x,(y * (x \ 1)) \ z). ((x \ y) * (1 / y)) / z = K(y,y \ 1) * (x \ (1 / z)). K(x,x \ 1) * (y \ (1 / z)) = ((y \ x) * (1 / x)) / z. (K(x,x \ 1) * (y \ z)) * ((y \ x) * (1 / x)) = ((y \ x) * (1 / x)) * (z * ((y \ x) * (1 / x))). K(x \ (y \ z),(y \ z) \ x) = K((y \ z) * x,x \ ((z \ 1) * y)). K((x \ y) * z,z \ ((y \ 1) * x)) = K(z \ (x \ y),(x \ y) \ z). x != K(y,z \ (u \ 1)) | x = K(y,(u * z) \ 1). K(x,y \ ((z \ 1) * u)) = K(x,((u \ z) * y) \ 1). K(x,((y \ z) * u) \ 1) = K(x,u \ ((z \ 1) * y)). x \ L((x \ 1) \ 1,y,z) = L(x,y,z) * (1 / x). (K(x,x \ 1) * y) \ (z \ 1) = ((z * y) \ x) * (1 / x). x != y \ L((y \ 1) \ 1,z,u) | x = T(L(y,z,u) * (1 / y),y). L(x,y,z) * (1 / x) = T(L(x,y,z) * (1 / x),x). T(L(x,y,z) * (1 / x),x) = L(x,y,z) * (1 / x). (x \ L(x,y,z)) * x = L(x,y,z). T(x,x \ L(x,y,z)) = x. L(x,y,z) / x = x \ L(x,y,z). x * (y \ 1) != L(y \ 1,z,u) | x = y * L(y \ 1,z,u). (x \ 1) \ L(x \ 1,y,z) = x * L(x \ 1,y,z). T(x,x \ (((y * x) \ y) \ 1)) = x. (1 / x) * L(x,y,z) = x \ L(x,y,z). (x \ L(x,y,z)) * x != u | u = L(x,y,z). (x \ L(x,y,z)) * x != u | L(x,y,z) = u. T(x / y,(x / y) \ ((y / x) \ 1)) = x / y. (1 / ((x * y) \ x)) / y = y \ (1 / ((x * y) \ x)). 1 / (L(x,y,z) \ x) = x \ L(x,y,z). (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x. T(x,L(y,z,u) \ y) / (L(y,z,u) \ y) = (y \ L(y,z,u)) * x. x != L(y,z,y) \ y | x = y \ R(y,z,y). (x \ L(x,y,x)) \ 1 = x \ R(x,y,x). (x \ 1) * (L(x,y,z) \ x) = (x \ L(x,y,z)) \ (x \ 1). (x \ L(x,y,z)) \ (x \ 1) = (x \ 1) * (L(x,y,z) \ x). ((x / y) \ ((y / x) \ 1)) * (x / y) = (y / x) \ 1. R(x,y,(1 / z) \ (u \ 1)) = R(x,y,(z \ 1) \ (1 / u)). K(x * (y * (1 / z)),u) = K(x * (y * (z \ 1)),u). x != K(y * (z * (u \ 1)),w) | x = K(y / (u / z),w). K(x * (y * (1 / z)),u) = K(x / (z / y),u). K(x * ((y \ z) * (1 / z)),u) = K(x / y,u). K(x * ((y \ 1) * z),u) = K(x / (z \ y),u). K(x * (y * z),u) = K(x / (z \ (1 / y)),u). K(x / (y \ (1 / z)),u) = K(x * (z * y),u). K((x \ (1 / y)) / z,u) = K(z * (y * x),u \ 1). x / (y * ((x \ 1) \ 1)) = (1 / (1 / x)) / (y * x). (1 / (1 / x)) / (y * x) = x / (y * ((x \ 1) \ 1)). (1 / (1 / x)) / (x * y) = x / ((y * K(x,y)) * ((x \ 1) \ 1)). x / ((y * K(x,y)) * ((x \ 1) \ 1)) = (1 / (1 / x)) / (x * y). x != (1 / y) \ ((z * u) * w) | x = y / (w \ (u \ (z \ 1))). ((1 / x) \ (1 / y)) * K(z * u,(z * u) \ 1) = x / ((1 / (y * (z * u))) \ (u \ (z \ 1))). (L(x,y * (1 / (z * y)),y * (1 / (z * y))) * (u / (y * (1 / (z * y))))) / K(y,y \ 1) = ((y * (1 / (z * y))) * (((y * (1 / (z * y))) / u) / x)) \ (1 / z). (x \ (1 / y)) * K(z * u,u \ (z \ 1)) = x \ ((z * u) * (1 / (y * (z * u)))). (1 / (K(x,x \ 1) / (y \ (1 / z)))) * ((y \ (1 / z)) \ 1) = (y \ (1 / z)) * (1 / (y \ (x * (1 / (z * x))))). (x \ 1) * (y * K(z,z \ 1)) != u * y | (x \ z) * (1 / z) = u. K(x,x \ 1) * (y * ((1 / z) * u)) = y * (x * (1 / ((u \ z) * x))). x != K(y,y \ 1) * (z * (u \ 1)) | x = ((u / z) \ y) * (1 / y). x * ((y \ z) * (1 / z)) = ((y / x) \ z) * (1 / z). ((x / y) \ z) * (1 / z) = y * ((x \ z) * (1 / z)). (((x / y) / z) \ x) * (1 / x) = z * (y * (1 / x)). (x * ((y \ z) * (1 / z))) \ 1 = (1 / z) \ (((y / x) \ z) \ 1). ((x \ y) \ z) * (1 / z) = (y \ 1) * (((x \ 1) \ z) * (1 / z)). (x \ 1) * (((y \ 1) \ z) * (1 / z)) = ((y \ x) \ z) * (1 / z). (x \ ((x * y) * z)) * (1 / x) = y * (z * (1 / x)). (x * (y * (1 / z))) / (1 / z) = z \ ((z * x) * y). x * y != (z \ ((z * u) * w)) * (1 / z) | x \ (u * (w * (1 / z))) = y. (1 / x) \ (y * (z * (1 / x))) = ((x * y) * z) * (x \ 1). x != (y * (z * u)) / u | x = u / (z \ (y \ u)). x \ ((x * y) * z) = (1 / x) / (z \ (y \ (1 / x))). (1 / x) / (y \ (z \ (1 / x))) = x \ ((x * z) * y). (x * (y / z)) / (1 / z) = z \ ((z * x) * L(y,z,z)). x \ ((x * y) * L(z,x,x)) = (y * (z / x)) / (1 / x). 1 / ((x \ (y \ (1 / z))) * z) = z \ ((z * y) * x). x != (y \ 1) \ z | x = (y * y) * (y \ z). 1 / ((x \ (y \ (1 / (z \ 1)))) * (z \ 1)) = (z * z) * (z \ (((z \ 1) * y) * x)). (x \ ((x * y) * z)) \ 1 = (z \ (y \ (1 / x))) * x. (x \ ((x * (1 / y)) * z)) \ 1 = (z \ (y / x)) * x. (x \ ((x * ((y \ 1) \ 1)) * (1 / z))) \ 1 = (z / (((1 / x) \ 1) * y)) * x. x != (y \ ((y * (1 / z)) * u)) \ 1 | x = (y \ 1) * ((u * (y \ 1)) \ z). (x \ (y / z)) * z = (z \ 1) * ((x * (z \ 1)) \ y). (x \ 1) * ((y * (x \ 1)) \ z) = (y \ (z / x)) * x. ((x \ ((x * (1 / y)) * z)) / u) \ 1 = u * ((z \ (y / x)) * x). (x \ 1) * y != z * x | y = (x * z) * x. (x * (y \ 1)) \ z = (y * (x \ (z / y))) * y. (x * (y \ (z / x))) * x = (y * (x \ 1)) \ z. ((x \ 1) \ 1) * (((x \ y) \ 1) \ z) = ((y \ 1) \ (z / (x \ 1))) * (x \ 1). ((x \ 1) \ (y / (z \ 1))) * (z \ 1) = ((z \ 1) \ 1) * (((z \ x) \ 1) \ y). (x \ 1) * ((y \ (x \ 1)) \ z) = ((((x \ 1) * y) \ (x \ 1)) \ (z / x)) * x. ((((x \ 1) * y) \ (x \ 1)) \ (z / x)) * x = (x \ 1) * ((y \ (x \ 1)) \ z). R(x,y \ 1,z) = z / ((x \ (z / y)) * y). x / ((y \ (x / z)) * z) = R(y,z \ 1,x). x * y != (z * (u \ 1)) \ w | x \ ((u * (z \ (w / u))) * u) = y. ((x \ 1) \ K(y,z)) \ ((x * (K(z,y) \ (u / x))) * x) = L(u,K(z,y) * (x \ 1),K(z,y) * (x \ 1)). (x * (y \ z)) * x = (y * (x \ 1)) \ (z * x). (x * (y \ 1)) \ (z * y) = (y * (x \ z)) * y. x != y \ ((y * z) * L(u,y,y)) | x = ((y * (1 / u)) / z) \ y. (x * (y / z)) / (1 / z) = ((z * (1 / y)) / x) \ z. R(x,1 / y,y / z) = ((z * (1 / y)) / (x * (1 / y))) \ z. ((x * (1 / y)) / (z * (1 / y))) \ x = R(z,1 / y,y / x). x != (L(y,z,z) * (u / z)) / (1 / z) | x = (z \ ((z / u) / y)) \ 1. ((x * (1 / y)) / L(z,x,x)) \ x = (x \ ((x / y) / z)) \ 1. ((((x * (1 / y)) / z) \ x) \ u) * (1 / u) = (1 / x) * (((z * (y / x)) \ u) * (1 / u)). x != K(y,y \ 1) * ((1 / z) \ u) | x = (y * (1 / (z * y))) \ u. x / ((y \ z) * (1 / z)) = (z * (1 / (x * z))) \ y. (1 / x) * ((y / x) \ ((z \ u) * (1 / u))) = (((u * (1 / (x * u))) \ z) * y) \ x. L(x,(y * (1 / (1 * y))) \ z,(z \ y) * (1 / y)) = L(x,(z \ y) * (1 / y),(z \ y) * (1 / y)). K(x,x \ 1) * (y / z) = (1 / y) \ (x * (1 / (z * x))). (1 / x) \ (y * (1 / (z * y))) = K(y,y \ 1) * (x / z). x != K(y,y \ 1) * (z \ (1 / u)) | x = z \ (y * (1 / (u * y))). ((x \ y) * (1 / y)) / z = x \ (y * (1 / (z * y))). x != ((y \ z) * (1 / z)) / ((u \ (y \ (z \ 1))) * z) | x = R(u,u \ (y \ (z \ 1)),z). x \ (y * (1 / (((z \ (x \ (y \ 1))) * y) * y))) = R(z,z \ (x \ (y \ 1)),y). R(x,x \ (y \ (z \ 1)),z) = y \ (z * (1 / (((x \ (y \ (z \ 1))) * z) * z))). (x \ (1 / y)) / z = (y * x) \ (y * (1 / (z * y))). (x * y) \ (x * (1 / (z * x))) = (y \ (1 / x)) / z. ((x \ 1) * y) / z = (y \ x) \ (y * (1 / (z * y))). (x \ y) \ (x * (1 / (z * x))) = ((y \ 1) * x) / z. K(x * y,x \ 1) / z = K(y,x) \ (x * (1 / (z * x))). K(x,y) \ (y * (1 / (z * y))) = K(y * x,y \ 1) / z. (x \ y) \ ((x \ 1) * z) = ((y \ 1) * x) / (z \ x). ((x \ 1) * y) / (z \ y) = (y \ x) \ ((y \ 1) * z). (x * y) / (z \ y) = (y \ (1 / x)) \ ((y \ 1) * z). (x \ (1 / y)) \ ((x \ 1) * z) = (y * x) / (z \ x). ((1 / x) \ (1 / y)) \ (((1 / x) \ 1) * (1 / z)) = (y * (1 / x)) / (z / x). L(x,y,z) \ 1 = (x \ 1) * (L(x,y,z) \ x). (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1. x * y != (z \ 1) * (L(z,u,w) \ z) | x \ (L(z,u,w) \ 1) = y. x \ (L(x,y,z) \ 1) = 1 / (x * L(x,y,z)). 1 / (x * L(x,y,z)) = x \ (L(x,y,z) \ 1). (x \ (L(x,y,z) \ 1)) \ 1 = x * L(x,y,z). x != (y \ (L(y,z,u) \ 1)) \ 1 | x = (y \ 1) \ L(y,z,u). x * L(x,y,z) = (x \ 1) \ L(x,y,z). (x \ 1) \ L(x,y,z) = x * L(x,y,z). ((x * y) \ x) \ L(L(y,x,x),z,u) = L(y,x,x) * L(L(y,x,x),z,u). T(((x * y) * z) * (x \ 1),x) = (y * (z * (1 / x))) * x. (x \ 1) \ (((x * y) * z) * (x \ 1)) = x * (x * (y * (z * (1 / x)))). x != (1 / T(y,K(z,z \ 1) * u)) \ (z * (1 / (u * z))) | x = (z * (1 / (u * z))) * y. K(x,x \ 1) * (T(y,K(x,x \ 1) * z) / z) = (x * (1 / (z * x))) * y. T(x,y) * (1 / (z * x)) = K(x * y,x \ 1) / z. K(x * y,x \ 1) / z = T(x,y) * (1 / (z * x)). K(x,y \ 1) / z = T(y,y \ x) * (1 / (z * y)). T(x,x \ y) * (1 / (z * x)) = K(y,x \ 1) / z. (T(x,y) * (1 / ((z * u) * x))) \ (K(x * y,x \ 1) / u) = R(z,u,K(x * y,x \ 1) \ 1). (1 / x) * ((x * y) * z) = (y * (z * (1 / x))) * x. (x * (y * (1 / z))) * z = (1 / z) * ((z * x) * y). x != (y * (y * (1 / z))) * z | x = T(((1 / z) \ y) * (z \ T(y,z \ 1)),z). (1 / x) * ((x * y) * y) = T(((1 / x) \ y) * (x \ T(y,x \ 1)),x). T(((1 / x) \ y) * (x \ T(y,x \ 1)),x) = (1 / x) * ((x * y) * y). x * ((1 / x) * ((x * y) * z)) = ((1 / x) \ y) * L(z,x,x). (1 / (x / y)) * (x * y) = (1 / (x * y)) * (((x * y) * y) * y). (1 / (x * y)) * (((x * y) * y) * y) = (1 / (x / y)) * (x * y). (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1)) | R(x,y,z) = u. T(x,R(y,x \ 1,x) \ z) = T(x,(y * (x \ 1)) \ (x \ z)). T(x,(y * (x \ 1)) \ (x \ z)) = T(x,R(y,x \ 1,x) \ z). x != ((y * z) / (u * z)) \ y | x = R(u,z,z \ (y \ 1)). R(x,1 / y,y / z) = R(x,1 / y,(1 / y) \ (z \ 1)). R(x,1 / y,(1 / y) \ (z \ 1)) = R(x,1 / y,y / z). x != R(y,z,(1 / u) \ (w \ 1)) | x = R(y,z,(u \ 1) \ (1 / w)). R(x,1 / y,y / z) = R(x,1 / y,(y \ 1) \ (1 / z)). R(x,1 / y,(y \ 1) \ (1 / z)) = R(x,1 / y,y / z). x != (y \ ((y / z) / u)) \ 1 | x = (1 / y) * ((y * u) * z). ((x * (1 / y)) / L(z,x,x)) \ x = (1 / x) * ((x * z) * y). (((x / y) / z) / x) \ x = ((1 / x) \ z) * L(y,x,x). ((1 / x) \ y) * L(z,x,x) = (((x / z) / y) / x) \ x. ((x \ 1) \ y) * L(z,T(x,x \ 1),T(x,x \ 1)) = (((T(x,x \ 1) / z) / y) / T(x,x \ 1)) \ T(x,x \ 1). (((T(x,x \ 1) / y) / z) / T(x,x \ 1)) \ T(x,x \ 1) = ((x \ 1) \ z) * L(y,T(x,x \ 1),T(x,x \ 1)). (L(x,y,y) / y) * (y * z) = (1 / y) * ((y * x) * z). (x * (1 / y)) * (y * z) = (1 / y) * ((y * x) * z). x * y != z * u | x \ L((z \ 1) \ u,z,z) = y. (1 / x) \ L(((y * (1 / x)) \ 1) \ (x * z),y * (1 / x),y * (1 / x)) = (x * y) * z. (x * (1 / (y \ 1))) * (y \ z) = (1 / (y \ 1)) * (((y \ 1) * x) * L(z,y,y)). (1 / (x \ 1)) * (((x \ 1) * y) * L(z,x,x)) = (y * (1 / (x \ 1))) * (x \ z). (x \ (y / x)) * (x * z) = (1 / x) * ((x * (((x \ 1) \ 1) \ y)) * z). (1 / x) * ((x * (((x \ 1) \ 1) \ y)) * z) = (x \ (y / x)) * (x * z). x * y != (y / z) * (u * y) | x = y / (u \ z). (K(x \ y,y \ x) / z) * u = K(x \ y,y \ x) / (u \ z). K(x \ y,y \ x) / (z \ u) = (K(x \ y,y \ x) / u) * z. x * y != (y / (z * u)) * (z * y) | x = y / u. (K(x \ y,y \ x) / (z * u)) * z = K(x \ y,y \ x) / u. x * (y * K(z \ u,u \ z)) != w * K(z \ u,u \ z) | x * y = w. x * K(y \ z,z \ y) != u * (w * K(y \ z,z \ y)) | u * w = x. x * y != (z * (u * K(w \ 1,w))) * v5 | (K(w \ 1,w) * ((z * u) * v5)) / y = x. (K(x \ 1,x) * ((y * z) * u)) / ((z * K(x \ 1,x)) * u) = R(y,z * K(x \ 1,x),u). L(x,y * K(z \ 1,z),u) = (u * y) \ (K(z,z \ 1) * (u * (K(z \ 1,z) * (y * x)))). (x * y) \ (K(z,z \ 1) * (x * (K(z \ 1,z) * (y * u)))) = L(u,y * K(z \ 1,z),x). T(x,R(K(y,y \ 1) * (1 / z),u,w)) = T(x,R(z \ 1,u,w)). (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y,x) * K(z \ 1,z). a(x,y,K(z,z \ 1) * u) = ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1). ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1) = a(x,y,K(z,z \ 1) * u). (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y,y \ 1). x / (((x \ 1) \ 1) * y) = (1 / (1 / x)) / (x * y). (1 / (1 / x)) / (x * y) = x / (((x \ 1) \ 1) * y). (1 / (1 / x)) / (x * (T(x,y) \ 1)) = x / (T(x,y) \ ((x \ 1) \ 1)). ((x \ y) * (1 / y)) \ (z \ 1) = (1 / y) \ (((x / z) \ y) \ 1). (x \ 1) * (y * (((y \ z) \ 1) \ 1)) = ((z \ x) \ y) * (1 / y). (L(1 / x,y,y) * (z / y)) \ 1 = y * ((z \ (x / y)) * y). ((x \ (x / y)) * (z / x)) \ 1 = x * ((z \ (y / x)) * x). (x / y) \ ((y \ (y / z)) \ 1) = y * ((x \ (z / y)) * y). (x / y) \ L(z,y,y) = y * ((x \ (z / y)) * y). x * ((y \ (z / x)) * x) = (y / x) \ L(z,x,x). (K(x \ y,y \ x) / z) / u = K(x \ y,y \ x) / (u * z). T(x,R(K(y,y \ 1) / z,u,w)) = T(x,R(z \ 1,u,w)). x != T(y,R(K(z,z \ 1) / u,w,v5)) | x = T(y,R(u \ K(z,z \ 1),w,v5)). T(x,R(y \ 1,z,u)) = T(x,R(y \ K(w,w \ 1),z,u)). T(x,R(y \ K(z,z \ 1),u,w)) = T(x,R(y \ 1,u,w)). T(x * y,y \ 1) \ z = ((y * x) \ z) * K(y,y \ 1). ((x * y) \ z) * K(x,x \ 1) = T(y * x,x \ 1) \ z. x / (T(y * z,z \ 1) \ u) = K(z,z \ 1) * (x / ((z * y) \ u)). K(x,x \ 1) * (y / ((x * z) \ u)) = y / (T(z * x,x \ 1) \ u). x != (1 / y) \ ((z \ y) \ 1) | x = y * (((y \ z) \ 1) \ 1). ((x \ y) * (1 / y)) \ (z \ 1) = y * (((y \ (x / z)) \ 1) \ 1). x * (y * (((y \ z) \ 1) \ 1)) = ((z \ (1 / x)) \ y) * (1 / y). ((x \ (1 / y)) \ z) * (1 / z) = y * (z * (((z \ x) \ 1) \ 1)). (x \ 1) * (y * (1 / (z * y))) = (((z \ 1) \ x) \ y) * (1 / y). (((x \ 1) \ y) \ z) * (1 / z) = (y \ 1) * (z * (1 / (x * z))). x != K(y \ z,z \ y) / u | x = (z * y) * (1 / (u * (z * y))). (K(x \ y,y \ x) / z) / u = (y * x) * (1 / ((u * z) * (y * x))). (x * y) * (1 / ((z * u) * (x * y))) = (K(y \ x,x \ y) / u) / z. (K(x \ y,y \ x) / (z * u)) * z != w * v5 | w \ (K(x \ y,y \ x) / u) = v5. ((x \ y) * (1 / y)) \ z = y * (((y \ (x / (1 / z))) \ 1) \ 1). x * (((x \ (y / (1 / z))) \ 1) \ 1) = ((y \ x) * (1 / x)) \ z. (((1 / ((x \ (1 / y)) * (1 / z))) \ z) \ 1) \ (1 / u) = (y * (z * (((z \ x) \ 1) \ 1))) \ (1 / u). ((x \ 1) \ y) \ K(z,z \ 1) = (y \ 1) * (z * (1 / (x * z))). ((x \ 1) \ y) * K(z,z \ 1) = ((x \ z) * (1 / z)) \ y. (x \ y) * K(z,z \ 1) = (((1 / x) \ z) * (1 / z)) \ y. (((1 / x) \ y) * (1 / y)) \ z = (x \ z) * K(y,y \ 1). ((x \ (y \ 1)) \ z) * K(u,u \ 1) = (((y * x) \ u) * (1 / u)) \ z. (((x \ y) * (1 / y)) \ z) * u = ((x \ 1) \ z) * (K(y,y \ 1) * u). ((x \ 1) \ y) * (K(z,z \ 1) * u) = (((x \ z) * (1 / z)) \ y) * u. (((1 / x) \ (y / z)) * (1 / (y / z))) \ u = (x \ u) * K(z \ y,y \ z). T(x,y * x) * (1 / x) = x * (((T(x,y \ 1) \ 1) \ 1) \ 1). T(x,y * x) * (1 / x) = x * (1 / T(x,y \ 1)). T(x,x * y) * (1 / x) = x * (1 / T(x,y \ 1)). K(x * (x * y),x \ 1) = x * (1 / T(x,y \ 1)). x != y * (1 / T(y,z)) | x = K(y,z \ (y \ 1)). K(x * (x * y),x \ 1) = K(x,(y \ 1) \ (x \ 1)). x != K(y,(z \ 1) \ (y \ 1)) | x = K(y,y \ z). K(x * (x * y),x \ 1) = K(x,x \ y). x * y != K(z * (z * u),z \ 1) | K(z,z \ u) / y = x. K(x,x \ y) / x = (x * (x * y)) / ((x * (x * y)) * x). (x * (x * y)) / ((x * (x * y)) * x) = K(x,x \ y) / x. x \ K(x,x * y) = K(x,x \ y) / x. K(x,x \ y) / x = x \ K(x,x * y). R(K(x \ 1,y),z,u) != w | K(R(x,z,u) \ 1,y) = w. (x \ y) * (T(T((1 / x) * y,y),x) \ z) = (y / x) * (T(x \ y,x) \ z). x != T(y \ z,u) * ((z \ y) * K(u,y \ z)) | x = (y \ z) * (z \ y). T((x \ y) * (y \ x),z) = (x \ y) * (y \ x). T(x,(y \ z) * (z \ y)) = x. T(x,y * ((z * y) \ z)) = x. (x * ((y * x) \ y)) \ z = z / (x * ((y * x) \ y)). x / (y * ((z * y) \ z)) = (y * ((z * y) \ z)) \ x. T(x * ((y * x) \ y),z) = x * ((y * x) \ y). T(x * L(x \ 1,x,y),z) = x * ((y * x) \ y). x != T(y * L(y \ 1,y,z),u) | x = T(y,u) * ((z * T(y,u)) \ z). x * ((y * x) \ y) = T(x,z) * ((y * T(x,z)) \ y). T(x,y) * ((z * T(x,y)) \ z) = x * ((z * x) \ z). (1 / ((x * y) \ x)) / y = (y * ((x * y) \ x)) \ 1. (x * ((y * x) \ y)) \ T(x,z) = 1 / ((y * T(x,z)) \ y). x != (1 / ((y * z) \ y)) / z | x = z \ (1 / ((y * z) \ y)). (x * ((y * x) \ y)) \ 1 = x \ (1 / ((y * x) \ y)). ((x * ((y * x) \ y)) \ 1) \ (1 / ((y * x) \ y)) = x. T(x,y) * K(z,T(x,y)) = T(x * K(z,x),K(x,u) * y). T(x * K(y,x),K(x,z) * u) = T(x,u) * K(y,T(x,u)). x != T(y,z) * K(u,T(y,z)) | x = T(y * K(u,y),z). T(x * K(y,x),K(x,z) * u) = T(x * K(y,x),u). x != T(y * K(z * R(y,u,w),y),z) | x = R(y,z,R(y,u,w)). T(x * K((K(x,y) * z) * R(x,u,w),x),z) = R(x,K(x,y) * z,R(x,u,w)). K(a(x,y,z),(((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u)) = K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))). K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(a(x,y,z),(((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u)). x != T(y,y * z) * R(y \ T(y * z,y),u,w) | x = T(y * R(z,u,w),y * z). T(T(x,x * y) * R(x \ (x * y),z,u),x) = T(x * R(y,z,u),x * y). x != L(T(y,z),u,w) \ L(y,u,w) | x = K(z,L(y,u,w)). K(x * K(L(y,z,u),w),L(y,v5,v6)) = K(x,L(y,v5,v6)). K(K(L(x,y,z),u) * w,L(x,v5,v6)) = K(w,L(x,v5,v6)). K(K(x,y) * z,L(x,u,w)) = K(z,L(x,u,w)). K(x \ y,L(z,u,w)) = K(x \ T(y,z),L(z,u,w)). K(x \ T(y,z),L(z,u,w)) = K(x \ y,L(z,u,w)). K(x \ (y \ z),L(y,u,w)) = K(x \ (z / y),L(y,u,w)). K(x \ (y / z),L(z,u,w)) = K(x \ (z \ y),L(z,u,w)). L(K(x,T(y,z)),u,L(y,w,v5)) = K(x,T(y,z)). x != K(y,T(z \ 1,u) \ y) | x = K(y,T(z * y,u)). K(x,y \ ((((y \ z) \ 1) \ y) * x)) = K(x,T((y \ z) * x,z)). K(x,T((y \ z) * x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x)). x != K(y,z \ ((u \ z) * y)) | x = K(y,T(u \ y,z)). K(x,T((y \ z) * x,z)) = K(x,T(((y \ z) \ 1) \ x,y)). K(x,T(((y \ z) \ 1) \ x,y)) = K(x,T((y \ z) * x,z)). K(x,T((y \ z) * x,z)) = K(x,T((y \ z) * x,y)). x != T(y,T(T(z \ u,w),z)) | x = T(y,T(u / z,w)). T(x,(((y \ 1) \ 1) \ z) / z) = T(x,T((y \ z) / z,T(y,u))). T(x,T((y \ z) / z,T(y,u))) = T(x,(((y \ 1) \ 1) \ z) / z). x != T(y,(z \ u) / u) | x = T(y,z \ 1). T(x,T((y \ z) / z,T(y,u))) = T(x,((y \ 1) \ 1) \ 1). x != T(y,((z \ 1) \ 1) \ u) | x = T(y,z \ u). T(x,T((y \ z) / z,T(y,u))) = T(x,y \ 1). (x \ (1 / y)) * (1 / (x \ (1 / y))) = 1 * K(1 / (x * y),x * y). T(x / y,T((y * z) \ x,y)) != u | T(x / y,T(z \ (y \ x),y)) = u. x != R(y,z,u) * (y \ K(w,T(y,v5))) | x = T(y,T(w,v5)) \ R(y,z,u). (x \ R(x,y,z)) * T(K(u,x),w) = T(x,T(u,w)) \ R(x,y,z). x != (y \ R(y,z,y)) * T(K(z,y),u) | x = K(z * y,y) * K(z,K(y,u)). T(x,T(y,z)) \ R(x,y,x) = K(y * x,x) * K(y,K(x,z)). K(x * y,y) * K(x,K(y,z)) = T(y,T(x,z)) \ R(y,x,y). K(x * y,T(y,z)) = T(y,T(x,z)) \ R(y,x,y). T(x,T(y,z)) \ R(x,y,x) = K(y * x,T(x,z)). x != T(y,T(z,u)) \ R(y,w,y) | x = K(z,T(y,u)) * a(y,w,y). K(x * y,T(y,z)) = K(x,T(y,z)) * a(y,x,y). K(x,T(y,z)) * a(y,x,y) = K(x * y,T(y,z)). K(x / y,z) * a(z,y \ x,z) = K((y \ x) * z,T(z,y)). K((x * (y / z)) \ u,z) != w | K((x * (z \ y)) \ u,z) = w. R(K(x * y,x),(x * y) * z,u) = K(x * y,R(R(x,y,z),y * z,u)). R(K(x,y),(y * K(z,x)) * u,w) = K(x,R(R(y,K(z,x),u),K(z,x) * u,w)). K(x \ ((y * z) * K(y,u)),T(y,w)) = K(x \ (z * T(y,u)),T(y,w)). a(T(x,y),T(T(y,x),x),R(T(x,y),z,u)) = a(R(x,z,u),y,x). (x * (y * (z \ (y / z)))) * K(y / z,z) = x * ((y / z) * (z \ y)). L(x,(1 / y) * z,(1 / y) * z) = T(T(x,z \ y),y \ z). x != T(T(y,z),u) | x = T(T(y,u),z). L(x,(1 / y) * z,(1 / y) * z) = T(T(x,y \ z),z \ y). x != L(y,(1 / z) * u,(1 / z) * u) | x = ((1 / z) * u) * ((u \ z) * y). T(T(x,y \ z),z \ y) = ((1 / z) * y) * ((y \ z) * x). ((1 / x) * y) * ((y \ x) * z) = T(T(z,y \ x),x \ y). x != T(T(y,z \ u),u \ z) | x = L(y,z \ u,z \ u). L(x,(1 / y) * z,(1 / y) * z) = L(x,y \ z,y \ z). L(x,y \ z,y \ z) = ((1 / y) * z) * ((z \ y) * x). ((1 / x) * y) * ((y \ x) * z) = L(z,x \ y,x \ y). (((1 / x) * y) * z) * ((z \ (y \ x)) * u) = L(u,(y \ x) \ z,(y \ x) \ z). x * K(y / z,(z / y) * u) = x * K(y / z,u * (z / y)). x * K(y / z,(z / y) * u) != w * K(y / z,u * (z / y)) | x = w. (x * K(y,z)) * R(K(z,u),w,v5) = x * (R(K(z,u),w,v5) * K(y,z)). x * L(K(y,z),u,w) = (x * K(y,v5)) * (K(v5,y) * L(K(y,z),u,w)). (x * K(y,z)) * (K(z,y) * L(K(y,u),w,v5)) = x * L(K(y,u),w,v5). (x * L(K(y,z),u,w)) \ (x * K(y,v5)) = L(K(z,y),u,w) * K(y,v5). x != (y \ z) \ T((1 / z) * y,u) | x = (z \ y) * T(z \ y,u). ((1 / x) * y) * T((1 / x) * y,z) = (x \ y) * T(x \ y,z). (1 / x) \ ((y \ z) * T(y \ z,u)) = x / ((z * T((1 / y) * z,u)) \ y). x / ((y * T((1 / z) * y,u)) \ z) = (1 / x) \ ((z \ y) * T(z \ y,u)). K(x,x \ y) * (((y / x) * (y / x)) \ z) = ((y / x) * (x \ y)) \ z. (K(x,K(y,z)) * T(y,K(u,w))) \ y = K(u,K(w,y)) * K(x,K(y,z)). (x \ K(y,z)) * (T(z,y) * T(z,y)) = (x \ z) * (u / (T(z,y) \ u)). ((x * K(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u)). K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u). K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = (y * (K(z,x) * L(z,u,w))) \ (y * L(z,u,w)). K(x,K(y \ (z * u),z * u)) = K(x,K(z * u,(z \ y) \ u)). K(x,K(y,z * u)) = K(x,K(z * u,(z \ y) \ u)). K(x,K(y * z,(y \ u) \ z)) = K(x,K(u,y * z)). K(x,K(y * z,z \ (y \ u))) = K(x,K(u,y * z)). K(x,K((y * z) * u,u \ ((y * z) \ (y * (z * u))))) = K(x,K(y * (z * u),a(y,z,u) * (y * (z * u)))). (x * K(y \ x,x \ y)) * (x \ 1) = K(y \ x,y * (x \ 1)). K(x \ y,y \ x) = K(x \ y,x * (y \ 1)). K(x \ y,x * (y \ 1)) = K(x \ y,y \ x). K(x \ (y \ 1),x * T(y,y \ 1)) = K(x \ (y \ 1),(y \ 1) \ x). x * y != (z * R(K(u,w),v5,v6)) * R(K(w,u),v5,v6) | z / y = x. x / (K(y,z) * R(K(z,u),w,v5)) = (x * R(K(u,z),w,v5)) * K(z,y). x != (y * K(z,T(u,w))) \ (y * u) | x = T(u,T(z,w)). T(x,L((y \ z) \ z,u,w)) = T(x,T(L(y,u,w),z)). T(x,L((y \ z) \ z,u,w)) = T(x,L(T(y,z),u,w)). T(x,L(T(y,z),u,w)) = T(x,L(T(y,z * y),u,w)). T(x,L(T(y,z * y),u,w)) = T(x,L(T(y,z),u,w)). x != ((y \ z) * T(u,z \ y)) * (y \ z) | x = (y \ z) * ((y \ z) * u). T((x \ y) \ z,z) / (x \ y) = (y \ x) * ((y \ x) * z). x != T(y \ z,z) / y | x = (y \ z) / T(y,z). (x \ y) * ((x \ y) * z) = ((y \ x) \ z) / T(y \ x,z). ((x \ y) \ z) / T(x \ y,z) = (y \ x) * ((y \ x) * z). x != T((y \ z) \ u,u) / (y \ z) | x = ((1 / z) * y) * (((1 / z) * y) * u). (x \ y) * ((x \ y) * z) = ((1 / x) * y) * (((1 / x) * y) * z). ((1 / x) * y) * (((1 / x) * y) * z) = (x \ y) * ((x \ y) * z). x != ((y \ (z \ 1)) \ u) / T(y \ (z \ 1),u) | x = (z * y) * ((z * y) * u). ((x \ 1) \ y) * (((x \ 1) \ y) * z) = (x * y) * ((x * y) * z). x != ((1 / y) * z) * (((1 / y) * z) * u) | x = ((z \ y) \ 1) * (((z \ y) \ 1) * u). (x \ y) * ((x \ y) * z) = ((y \ x) \ 1) * (((y \ x) \ 1) * z). ((x \ y) \ 1) * (((x \ y) \ 1) * z) = (y \ x) * ((y \ x) * z). (((x \ y) \ y) * (1 / y)) * (((1 / y) * ((x \ 1) \ 1)) * z) = (y \ ((x \ 1) \ 1)) * ((y \ ((x \ 1) \ 1)) * z). (1 / (x * y)) * ((((y \ 1) \ 1) \ (1 / x)) * z) = ((y \ 1) * (1 / x)) * (((y \ 1) * (1 / x)) * z). ((x \ 1) * (1 / y)) * (((x \ 1) * (1 / y)) * z) = (1 / (y * x)) * ((((x \ 1) \ 1) \ (1 / y)) * z). ((((x \ y) \ y) \ 1) \ (1 / y)) * (((((x \ y) \ y) \ 1) \ (1 / y)) * z) = (((x \ y) \ y) * (1 / y)) * (((1 / y) * ((x \ 1) \ 1)) * z). ((x \ 1) \ ((1 / x) * ((y \ x) \ 1))) * (((x \ 1) \ ((1 / x) * ((y \ x) \ 1))) * z) = (x \ ((y \ 1) \ 1)) * ((x * ((1 / x) * ((y \ x) \ 1))) * z). K((x \ (1 / y)) / z,T(u,y * x)) = K(z \ (x \ (1 / y)),u). x != K((y \ (1 / z)) / u,w) | x = K(u * (z * y),w \ 1). K(x \ (y \ (1 / z)),u) = K(x * (z * y),T(u,z * y) \ 1). K(x * (y * z),T(u,y * z) \ 1) = K(x \ (z \ (1 / y)),u). K(x * (y * z),T(u \ 1,y * z)) = K(x \ (z \ (1 / y)),u). K(x \ (y \ (1 / z)),u) != w | K((z * y) * x,u \ 1) = w. T(x,(((y \ 1) \ K(z,u)) \ (K(z,u) * y)) * w) = T(x,K(K(z,u),y) * w). K(x,x \ 1) * y != (x * (1 / (z * x))) \ u | y = (1 / z) \ u. (x * (1 / (y * x))) \ ((z \ 1) * u) = (1 / y) \ (((z \ x) * (1 / x)) * u). x * y != K(z,z \ 1) * (x * (u * w)) | y = u * (K(z,z \ 1) * w). x * (1 / ((y \ z) * x)) = (1 / z) * (K(x,x \ 1) * y). (1 / x) * (K(y,y \ 1) * z) = y * (1 / ((z \ x) * y)). (1 / x) * (y * (z * (1 / (u * z)))) = z * (1 / (((y * (1 / u)) \ x) * z)). T((x * y) * z,x \ 1) = x * (x * (y * (z * (1 / x)))). x * (x * (y * (z * (1 / x)))) = T((x * y) * z,x \ 1). (1 / x) * ((K(x,x \ 1) * y) * z) = (x \ (y / x)) * (x * z). (1 / x) * (K(x,x \ 1) * (y * z)) = (x \ (y / x)) * (x * z). x != (1 / y) * (K(y,z) * u) | x = (K(y,z) / y) * u. (x \ (y / x)) * (x * z) = (K(x,x \ 1) / x) * (y * z). (K(x,x \ 1) / x) * (y * z) = (x \ (y / x)) * (x * z). (x \ K(x,x * 1)) * (y * z) = (x \ (y / x)) * (x * z). (x \ K(x,x)) * (y * z) = (x \ (y / x)) * (x * z). (x \ 1) * (y * z) = (x \ (y / x)) * (x * z). (x \ (y / x)) * (x * z) = (x \ 1) * (y * z). ((x \ 1) * y) \ ((x \ 1) * (y * z)) = L(z,x,x \ (y / x)). L(x,y,y \ (z / y)) = ((y \ 1) * z) \ ((y \ 1) * (z * x)). L(x,y,y \ (z / y)) != u | L(x,z,y \ 1) = u. L(x,y,z * (y \ 1)) != u | L(x,y * z,y \ 1) = u. (1 / (1 / x)) / K(y,x) = x / (T(x,y) \ ((x \ 1) \ 1)). x / (T(x,y) \ ((x \ 1) \ 1)) = (1 / (1 / x)) / K(y,x). x != (1 / (1 / y)) / K(z,y) | x = T(1 / (1 / y),z). x / (T(x,y) \ ((x \ 1) \ 1)) = T(1 / (1 / x),y). x / (x * (1 / T(x,y))) = T(1 / (1 / x),y). T(1 / (1 / x),y) \ x = x * (1 / T(x,y)). (((x * y) * ((1 / (x * y)) * 1)) \ z) * K(u,u \ 1) = ((((y \ (x \ 1)) * (x * y)) \ u) * (1 / u)) \ z. ((x \ 1) \ y) * (1 / y) = ((x \ y) * (1 / y)) \ 1. ((x \ y) * (1 / y)) \ 1 = ((x \ 1) \ y) * (1 / y). ((x \ 1) \ y) * (z * K(u,u \ 1)) = (((x \ u) * (1 / u)) \ y) * z. ((x \ 1) \ y) * (K(z,z \ 1) / (u \ w)) = (((x \ z) * (1 / z)) \ y) * ((1 / w) * u). (((x \ y) * (1 / y)) \ z) * ((1 / u) * w) = ((x \ 1) \ z) * (K(y,y \ 1) / (w \ u)). (((x \ 1) \ y) * (1 / y)) \ ((1 / ((x \ y) * (1 / y))) \ z) = ((x \ y) * (1 / y)) * (((x \ y) * (1 / y)) * z). (x \ (1 / y)) * (1 / (x \ (1 / y))) = 1 * K(x * y,(x * y) \ 1). x != K(y \ (z * K(u,w)),T(u,v5)) | x = K(y \ z,T(u,v5)). K(x \ (y * T(z,u)),T(z,w)) = K(x \ (z * y),T(z,w)). (x * (y * (z \ (y / z)))) * K(z \ y,z) = x * ((y / z) * (z \ y)). x != L(K(y,z),u,w) * K(z,v5) | x = K(z,v5) * L(K(y,z),u,w). (x * L(K(y,z),u,w)) \ (x * K(y,v5)) = K(y,v5) * L(K(z,y),u,w). K(x,x \ y) * ((y * (x \ (y / x))) \ z) = ((y / x) * (x \ y)) \ z. T(T(x,K(y,z)),K(y,u)) \ x = K(y,K(u,x)) * K(y,K(x,z)). T(T(x,K(y,z)),K(y,u)) \ x = K(x,K(y,u)) * K(y,K(x,z)). T(T(x,K(y,z)),K(y,u)) \ x = K(x,K(y,u)) * K(x,K(y,z)). (x \ K(y,z)) * ((T(z,y) \ 1) \ T(z,y)) = (x \ z) * (u / (T(z,y) \ u)). x != K(y \ (z \ 1),u * T(w,w \ 1)) | x = K(y \ (1 / z),u * w). K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (1 / y),x * y). K(x \ (y \ 1),y * x) = K(x \ (1 / y),x * y). K(x \ (1 / y),x * y) = K(x \ (y \ 1),y * x). x != K(y \ (1 / z),y * z) | x = K((y * z) \ 1,y * z). K(x \ (y \ 1),y * x) = K((x * y) \ 1,x * y). K((x * y) \ 1,x * y) = K(x \ (y \ 1),y * x). x != y * ((1 / y) * K(z,u)) | x = K(y,y \ 1) * K(z,u). (((x \ y) * (1 / y)) \ z) * (1 / ((x \ 1) \ z)) = K((x \ 1) \ z,((x \ 1) \ z) \ 1) * K(y,y \ 1). K((x \ 1) \ y,((x \ 1) \ y) \ 1) * K(z,z \ 1) = (((x \ z) * (1 / z)) \ y) * (1 / ((x \ 1) \ y)). x != (y \ (z \ 1)) * ((z * y) * u) | x = (z * y) * ((1 / (z * y)) * u). (((x \ y) * (1 / y)) \ (z \ 1)) * (z * (x \ 1)) = (z * (x \ 1)) * ((1 / (z * (x \ 1))) * K(y,y \ 1)). (x * (y \ 1)) * ((1 / (x * (y \ 1))) * K(z,z \ 1)) = (((y \ z) * (1 / z)) \ (x \ 1)) * (x * (y \ 1)). (x \ (1 / y)) * (1 / (x \ (1 / y))) = 1 * K(x * y,y \ (x \ 1)). K(x,y) * L(K(z,x),u,w) != v5 | L(K(x,z),u,w) \ K(x,y) = v5. (x * y) \ ((x * (y * K(z,u))) * K(u,w)) = K(u,w) * L(K(z,u),y,x). 1 * x != (y \ (1 / z)) * (1 / (y \ (1 / z))) | x = (z * ((y \ 1) \ 1)) \ (((z \ 1) \ 1) * y). K(x * y,y \ (x \ 1)) = (y * ((x \ 1) \ 1)) \ (((y \ 1) \ 1) * x). (x * ((y \ 1) \ 1)) \ (((x \ 1) \ 1) * y) = K(y * x,x \ (y \ 1)). x != K(y * z,z \ (y \ 1)) | x = K(z \ y,y \ z). (x * ((y \ 1) \ 1)) \ (((x \ 1) \ 1) * y) = K(x \ y,y \ x). (x * (K(x,y) * (z * R(x,u,w)))) \ ((T(x,y) * z) * R(x,u,w)) = a(x,K(x,y) * z,R(x,u,w)). K(x * (y * z),(x * y) * z) = K(a(x,y,z),(y * z) \ (x \ 1)). K(a(x,y,z),(y * z) \ (x \ 1)) = K(x * (y * z),(x * y) * z). (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x). a(x,y * K(x,z),x) != u | a(x,y,T(x,z)) = u. L(K(x \ (y \ z),u),y \ z,y) != w | K((y * x) \ z,u) = w. K(x \ (y \ z),y) != u | K((y * x) \ z,y) = u. K((x * y) \ z,y) != u | K((y * x) \ z,y) = u. K(x,y \ z) * K((z \ y) \ x,x) = x \ R(x,(z \ y) \ 1,x). K(x,y \ z) * K(y \ (z * x),x) = x \ R(x,(z \ y) \ 1,x). x != y \ R(y,z,y) | x = a(y,z,y). K(x,y \ z) * K(y \ (z * x),x) = a(x,(z \ y) \ 1,x). K(x,y \ z) * K(x * (y \ z),x) = a(x,(z \ y) \ 1,x). a(x,(y \ z) \ 1,x) != u | a(x,z \ y,x) = u. K(x,T(y,L(y,z,u) * w)) = L(K(x,T(y,w)),w,L(y,z,u)). L(K(x,T(y,z)),z,L(y,u,w)) = K(x,T(y,L(y,u,w) * z)). x != L(K(y,T(z,u)),w,L(z,v5,v6)) | x = K(y,T(z,u)). K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w)). K(x,T(y,z)) = K(x,T(y,L(y,u,w) \ z)). K(x,T(y,L(y,z,u) \ w)) = K(x,T(y,w)). K(x,T(y,z * (u * y))) = K(x,T(y,z * u)). K(x,T(y \ z,u * z)) = K(x,T(y \ z,u * y)). K(x,T(y,z * (y * u))) = K(x,T(y,z * u)). K(x * y,T(x,z)) = K(x * y,T(x,z * y)). K(x * y,T(x,z * y)) = K(x * y,T(x,z)). K(x * y,T(x,z * y)) != u | K(x * y,T(x,z)) = u. K(x * y,T(y,z * x)) = K(y * x,T(y,z)). K(x * (y \ z),T(x,z)) = K(x * (y \ z),T(x,y)). K(x,T(y \ x,z)) = K(x,T(y \ x,z * y)). K(x,T(y \ x,z * y)) = K(x,T(y \ x,z)). K(x,T(y \ x,z)) = K(x,T(y \ x,z / y)). K(x,T(y \ x,z / y)) = K(x,T(y \ x,z)). x != K(y,T(z \ y,u / z)) | x = K(y,T(z \ y,z \ u)). K(x,T(y \ x,z)) = K(x,T(y \ x,y \ z)). K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z)). x != K(y,T(z \ y,z \ u)) | x = K(y,(u / (u / z)) \ y). K(x,T(y \ x,z)) = K(x,(z / (z / y)) \ x). K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y)). x != K(y,((y * z) / u) \ y) | x = K(y,u / z). K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z). K(x,T(y \ x,z)) = K(x,((x * z) / y) / z). K(x,((x * y) / z) / y) = K(x,T(z \ x,y)). x != K(y,z / R(T(y,u),w,v5)) | x = K(y,R(y,w,v5) \ z). K(x,T(y \ x,R(T(x,z),u,w))) = K(x,R(x,u,w) \ ((x * R(T(x,z),u,w)) / y)). K(x,R(x,y,z) \ ((x * R(T(x,u),y,z)) / w)) = K(x,T(w \ x,R(T(x,u),y,z))). K(T(x,y) * z,T(x,u * z)) != w | K(x * z,T(x,u)) = w. K(x,y) * K(y * T(x,z),x) = x \ R(x,y * K(x,z),x). x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x). x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x). x != K(y,z) * K(z * y,y) | x = y \ R(y,z,y). x \ R(x,y * K(x,z),x) = x \ R(x,y,x). a(x,y * K(x,z),x) = x \ R(x,y,x). a(x,y,T(x,z)) = x \ R(x,y,x). a(x,y,T(x,z)) != u | a(x,y,x) = u. K(x,y) * T(y,K(z,y) * (x * y)) = L(y,K(z,y) * x,y). K(x,y) * T(y,x * y) = L(y,K(z,y) * x,y). L(x,K(y,x) * z,x) = K(z,x) * T(x,z * x). x != K(y,z) * T(z,y * z) | x = L(z,y,z). L(x,K(y,x) * z,x) = L(x,z,x). L(x,T(x,y) \ z,x) = L(x,x \ z,x). x != L(y,T(y,z) \ u,y) | x = L(y,u / T(y,z),y). L(x,x \ y,x) = L(x,y / T(x,z),x). L(x,y / T(x,z),x) = L(x,x \ y,x). K(R(x \ R(x,y,z),x,y * z),u) = K(a(x,y,z),T(u,x * (y * z))). K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u)) * K(x,K(a(y,z,u),y * (z * u))). K(x,a(y,z,u)) * K(x,K(a(y,z,u),y * (z * u))) = K(x,((y * z) * u) / (y * (z * u))). L(T(K(x,y),z * u),u,z) = (z * u) / (z * (u * K(y,x))). (x * y) / (x * (y * K(z,u))) = L(T(K(u,z),x * y),y,x). (x * y) / (x * (y * K(z,u))) = L(K(u,T(z,x * y)),y,x). (x * y) / (x * (K(z,u) * y)) = L(K(u,T(T(z,y),x * y)),y,x). L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z)). x != L(K(y,T(T(z,u),w * u)),u,w) | x = K((w * u) / (w * (y \ u)),z). (x * y) / (x * (K(z,u) * y)) = K((x * y) / (x * (u \ y)),z). K((x * y) / (x * (z \ y)),u) = (x * y) / (x * (K(u,z) * y)). K(x \ ((y \ z) * y),L(y,u,w)) = K(x \ z,L(y,u,w)). K(x \ (y * z),L(z,u,w)) = K(x \ (z * y),L(z,u,w)). K(L(x,y,z),u \ (x * w)) = K(L(x,y,z),u \ (w * x)). K(L(x,y,z),u \ (w * x)) = K(L(x,y,z),u \ (x * w)). K(x \ (y * z),L(z,u,w)) = K((x / z) \ y,L(z,u,w)). K((x / y) \ z,L(y,u,w)) = K(x \ (z * y),L(y,u,w)). K(x,T(y / (x \ z),u)) = K(x,T((z / y) \ x,u)). T(x,T(y / (x \ z),u)) = x * K(x,T((z / y) \ x,u)). x * K(x,T((y / z) \ x,u)) = T(x,T(z / (x \ y),u)). T(x,T((y / z) \ x,u)) = T(x,T(z / (x \ y),u)). T(x,T(y / (x \ z),u)) = T(x,T((z / y) \ x,u)). x != T(y,T(z / (y \ u),w)) | x = T(y,T(y * (z / u),w)). T(x,T((y / z) \ x,u)) = T(x,T(x * (z / y),u)). x != T(y,T(z / (y \ u),u)) | x = T(y,u \ (y * z)). T(x,T((y / z) \ x,y)) = T(x,y \ (x * z)). T(x,T(y \ x,z)) = T(x,z \ (x * (y \ z))). T(x,y \ (x * (z \ y))) = T(x,T(z \ x,y)). (x * K(y,T(z,u))) * K(z,w) != v5 | x * (K(z,w) * K(y,T(z,u))) = v5. x != (y * (T(y / z,y) / u)) \ y | x = L(u,y,y) * ((1 / y) * z). L(x,T(y,z),T(y,z)) * (z / T(y,z)) = L(x,y,y) * ((1 / y) * z). x != L(y,T(z,u),T(z,u)) * (u / T(z,u)) | x = L(y * (z \ u),z,z). L(x,y,y) * ((1 / y) * z) = L(x * (y \ z),y,y). (x / y) \ L(x * (y \ z),y,y) = L(z,1 / y,L(x,y,y)). K((x * (y * z)) \ ((x * z) * y),K(z,u)) = K(z,K(u,a(x,z,T(y,z)))). L(K(x,y \ (z \ u)),z \ u,z) != w | K(x,(z * y) \ u) = w. L(K(x,K(y,z) * (u \ w)),u \ w,u) != v5 | K(x,(u * K(z,y)) \ w) = v5. L(K(x,y \ ((z \ u) * x)),z \ u,z) != w | K(x,(z * (x \ y)) \ u) = w. R(K(x,T(T(y,z),z * u)),z,u) = ((z * u) \ ((z * K(y,x)) * u)) \ 1. L(K(x \ y,x),z,y) = (y * (K(x \ y,x) * z)) / (y * z). (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x). L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z). L(K(x,y),z,y * x) * ((y * x) * z) = (y * x) * (K(y \ (y * x),y) * z). (x * y) \ (x * (y * (z * K(u \ 1,u)))) = L(z,y,x) * K(u \ 1,u). K(x * y,R(R(x,y,z),y * z,u)) = K(R(x * y,z,u),x). x / (K(R(y * z,u,w),y) * x) = K(R(R(y,z,u),z * u,w),y * z). K(R(R(x,y,z),y * z,u),x * y) = w / (K(R(x * y,z,u),x) * w). x != (y * z) \ ((y * (z * K(u,w))) * K(w,u)) | x = a(y,z * K(u,w),K(w,u)). K(x,y) * L(K(y,x),z,u) = a(u,z * K(y,x),K(x,y)). a(x,y * K(z,u),K(u,z)) = K(u,z) * L(K(z,u),y,x). a(x,y,K(z,u)) = K(z,u) * L(K(u,z),y * K(z,u),x). K(x,y) * L(K(y,x),z * K(x,y),u) = a(u,z,K(x,y)). K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y)). L(K(x,y),z,u) \ K(x,y) = a(u,z,K(x,y)). L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x)). a(x,y,K(z,u)) != K(z,u) * w | L(K(u,z),y,x) = w. x * a(y,z,K(x,u)) = T(x,u) * L(K(u,x),z,y). T(x,y) * L(K(y,x),z,u) = x * a(u,z,K(x,y)). K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y)). (x * K(y,z)) * a(u,w,K(z,y)) = x * L(K(y,z),w,u). L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y). x * a(y,z,K(u,w)) != K(u,w) | x = L(K(u,w),z,y). x * a(y,z,K(u,w)) != K(u,w) | L(K(u,w),z,y) = x. a(x,y,K(z,u)) * L(K(z,u),y,x) = K(z,u). K(x,y \ ((y * z) * x)) * a(u,z,K(x,x * z)) = K(x,x * z). K(a(x,y,z),u) * a(x * y,z,K(L(z,y,x) \ z,u)) = K(L(z,y,x) \ z,u). (x / (x / y)) * K(L(y,z,u),y \ x) = y * a(u,z * y,K(y \ x,y)). (x * y) * a(z,u,K(y,w)) = (x * T(y,w)) * L(K(w,y),u,z). (x * T(y,z)) * L(K(z,y),u,w) = (x * y) * a(w,u,K(y,z)). K(x,y) * z != K(x,u) | z = K(x,u) * K(y,x). a(x,y,K(z,z * y)) = K(z,z * y) * K(u \ ((u * y) * z),z). L(K(x * y,x),y,z) = K(u \ ((u * y) * x),x). L(K(x * y,y),x,z) = K(u \ ((u * x) * y),y). x != K(y \ (z * T(u,w)),T(u,v5)) | x = K(y \ (u * z),T(u,v5)). L(K(x * T(y,z),T(y,z)),x,u) = K(w \ (y * (w * x)),T(y,z)). L(K(x * y,T(y,z)),x,u) = K(w \ (y * (w * x)),T(y,z)). L(K(x * y,T(x,z)),y,u) = K(w \ (x * (w * y)),T(x,z * y)). L(K(x * y,T(x,z)),y,u) = K((z / (z * y)) \ x,x). K(x * y,T(x,z)) = K((z / (z * y)) \ x,x). K((x / (x * y)) \ z,z) = K(z * y,T(z,x)). x != K((y / z) \ u,u) | x = K(u * (z / y),u). K(x * y,T(x,z)) = K(x * ((z * y) / z),x). K(x * ((y * z) / y),x) = K(x * z,T(x,y)). K((x / y) \ z,z) = K(z * (x \ y),T(z,x)). K(x * (y \ z),T(x,y)) = K((y / z) \ x,x). K(x * (y / z),x) = K(x * (z \ y),T(x,z)). K(x * (y \ z),T(x,y)) = K(x * (z / y),x). K((x \ y) * z,T(z,x)) = K((x / y) \ z,z). x != K(y * (z \ u),T(y,z)) | x = K(y * (z \ u),T(y,u)). K(x * (y / z),x) = K(x * (z \ y),T(x,y)). K(x * (y \ z),T(x,z)) = K(x * (z / y),x). x != K((y \ z) * u,T(u,y)) | x = K(z / y,u) * a(u,y \ z,u). K((x / y) \ z,z) = K(y / x,z) * a(z,x \ y,z). K(x / y,z) * a(z,y \ x,z) = K((y / x) \ z,z). K(x,y / z) * K((z / y) \ x,x) = a(x,z \ y,x). T(x,(y / z) \ x) \ T(x,z / y) = a(x,y \ z,x). T(x,(y / z) \ x) \ T(x,(y / z) \ 1) = a(x,y \ z,x). x != y \ T(z,u \ 1) | x = y \ ((z \ (u \ z)) \ (u \ z)). a(x,y \ z,x) = T(x,(y / z) \ x) \ ((x \ ((y / z) \ x)) \ ((y / z) \ x)). T(x,(y / z) \ x) \ ((x \ ((y / z) \ x)) \ ((y / z) \ x)) = a(x,y \ z,x). K(x \ R(x,y,z),R(x,x \ R(x,y,z),y * z)) = K(a(x,y,z),T(x,x * (y * z))). K(R(K(x,y) \ R(K(x,y),z,u),K(x,y),z * u),((z * u) \ K(y,x)) \ 1) = K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1). K(x,K(y,R(z \ R(z,u,w),z,u * w) \ 1)) = K(x,K(a(z,u,w),T(y,z * (u * w)))). K(x,K(y,(z * (u * x)) \ ((z * x) * u))) = K(x,K(y,a(z,x,T(u,x)))). x != R(K(y,T(T(z,u),u * w)),u,w) | x = (u * w) \ ((u * K(y,z)) * w). ((x * y) \ ((x * K(z,u)) * y)) \ 1 = (x * y) \ ((x * K(u,z)) * y). K(((x / y) * z) \ (x * z),u) \ 1 = (x * z) \ ((x * K(u,y)) * z). (x * y) \ ((x * K(z,u)) * y) != w | K(z,((x / u) * y) \ (x * y)) = w. L(x * K(y \ 1,y),z,u) = L(x,z,u) * K(y \ 1,y). L(x * K(y \ 1,y),z,u) = K(y \ 1,y) * L(x,z,u). L(x,y,z) = K(u \ 1,u) * L(x * K(u,u \ 1),y,z). K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u). K(x,x \ 1) * L(y,z,u) = L(y * K(x,x \ 1),z,u). L(x * K(y,y \ 1),z,u) = K(y,y \ 1) * L(x,z,u). x != K(y \ 1,y) * L(z * K(y,y \ 1),u,w) | x = (y \ L(y * (z / y),u,w)) * y. L(x,y,z) = (u \ L(u * (x / u),y,z)) * u. (x \ L(x * (y / x),z,u)) * x = L(y,z,u). x * (L(y,z,u) / x) = L(x * (y / x),z,u). L(x * (y / x),z,u) = x * (L(y,z,u) / x). (x \ L(y,z,u)) * x = L((x \ y) * x,z,u). L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x. (x * y) * ((z \ L(u,y,x)) * z) = x * (y * ((z \ u) * z)). L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x. x \ L(y * K(z,z \ 1),u,w) = (x \ L(y,u,w)) * K(z,z \ 1). (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z)). x * y != L((z \ ((u \ 1) \ w)) * z,u \ 1,u) | x \ ((z \ (u * w)) * z) = y. x \ ((y \ (x * z)) * y) = (x \ 1) * ((y \ ((x \ 1) \ z)) * y). (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y). x != (y \ 1) * ((z \ ((y \ 1) \ u)) * z) | x = ((z \ (u * y)) * z) / y. x \ ((y \ (x * z)) * y) = ((y \ (z * x)) * y) / x. ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x). (x * K((y \ 1) \ (z \ x),z)) * u = (y \ ((z \ (y * x)) * z)) * u. (x \ ((y \ (x * z)) * y)) * u = (z * K((x \ 1) \ (y \ z),y)) * u. (x \ ((y \ (x * z)) * y)) * x = (y \ (z * x)) * y. (x \ ((y \ (x * z)) * y)) * x != u | u = (y \ (z * x)) * y. (x \ ((y \ (x * z)) * y)) * x != u | (y \ (z * x)) * y = u. x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z). (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u). K((x \ y) \ z,y) = K((y / x) \ z,y). K((x / y) \ z,x) = K((y \ x) \ z,x). L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y). K((x * (y \ z)) \ u,z) = K((x * (z / y)) \ u,z). K((x * (y / z)) \ u,y) = K((x * (z \ y)) \ u,y). K((x * (y / x)) \ z,y) = K(y \ z,y). x != K((y * (z / y)) \ (z * u),z) | x = K(K(y \ z,y) * u,z). K(x \ (x * y),x) = K(K(z \ x,z) * y,x). K(x,y) = K(K(z \ y,z) * x,y). K(K(x \ y,x) * z,y) = K(z,y). T(K(x \ y,x) * z,y) = (K(x \ y,x) * z) * K(z,y). (K(x \ y,x) * z) * K(z,y) = T(K(x \ y,x) * z,y). K(x \ y,x) * T(z,y) = T(K(x \ y,x) * z,y). T(K(x \ y,x) * z,y) = K(x \ y,x) * T(z,y). T(K(x \ (y * x),x) * z,y * x) = K(y,x) * T(z,y * x). T(K(x,y) * z,x * y) = K(x,y) * T(z,x * y). T(x,y * z) * K(z,y) = T(x * K(z,y),y * z). T(x * K(y,z),z * y) = T(x,z * y) * K(y,z). (x * (y * z)) \ ((y * z) * T(x * K(z,y),y * z)) = L(K(z,y),T(x,y * z),y * z). (x * (y * z)) * L(K(z,y),T(x,y * z),y * z) = (y * z) * T(x * K(z,y),y * z). (x \ (y * z)) * x = (y * K((z \ 1) \ (x \ y),x)) * z. (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z. (x * K(y * (z \ x),z)) * y = (z \ (x * y)) * z. (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z. x * y != (z \ ((y \ (z * u)) * y)) * z | x = y \ (u * z). (x \ (y * z)) * K(x * (y \ (x \ (y * z))),y) = x \ (z * y). K(x,y \ (z * R(x,u,w))) = K(x,y \ (R(x,u,w) * z)). K(x,y \ (R(x,z,u) * w)) = K(x,y \ (w * R(x,z,u))). K(x,y \ ((x * z) * u)) = K(x,y \ ((z * u) * R(x,z,u))). K(x,y \ ((z * u) * R(x,z,u))) = K(x,y \ ((x * z) * u)). K(R(R(x,y,z),y * z,u),x * y) != w | K(x,R(x * y,z,u)) = w. R(x,y,K(y,z) * u) = u / (T(y,z) * (K(y,z) \ ((x * y) \ u))). x / (T(y,z) * (K(y,z) \ ((u * y) \ x))) = R(u,y,K(y,z) * x). x / (y * ((z * y) \ x)) = R(z,y,K(y,u) * x). R(x,y,K(y,z) * u) = u / (y * ((x * y) \ u)). x != y / (z * ((u * z) \ y)) | x = R(u,z,y). R(x,y,K(y,z) * u) = R(x,y,u). R(x,y,z) = R(x,y,T(z,y)). R(x,y,T(z,y)) = R(x,y,z). R(x,y,K(z,T(u,y))) = R(x,y,K(z,u)). x != R(y,K(z,u),T(w,K(z,u))) | x = R(y,T(K(z,u),w),w). R(x,K(y,z),u) = R(x,T(K(y,z),u),u). R(x,T(K(y,z),u),u) = R(x,K(y,z),u). x != R(y,z \ u,T(z,z \ u)) | x = R(y,u / z,z). R(x,y \ z,y) = R(x,z / y,y). R(x,y / z,z) = R(x,z \ y,z). R(x,y,z) * (z * y) = (x * y) * T(z,y). x != R(K(y,(z / (u / w)) \ y),u / w,w) | x = K(y,u / ((y \ z) * w)). R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u)). x != R(K(y,(z / u) / w),z / u,u) | x = K(y,z / (w * u)). R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z)). R(x,T(K(y,z),u),u * K(z,w)) = R(x,K(y,z),u * K(z,w)). (x * T(y,z)) / (y * z) = R(x / z,z,y). (x * R(y,z,y)) / (x * y) = R(R(y,z,y) / y,y,x). R(R(x,y,x) / x,x,z) = (z * R(x,y,x)) / (z * x). R(a(x,y,x),x,z) = (z * R(x,y,x)) / (z * x). (x * R(y,z,y)) / (x * y) = R(a(y,z,y),y,x). R(x,K(y,T(z,u)),u * K(z,w)) = R(x,K(y,z),u * K(z,w)). (T(x,y) * z) \ (T(x,y) * (z * u)) = L(L(u,z,x),x * z,K(x,y)). L(L(x,y,z),z * y,K(z,u)) = (T(z,u) * y) \ (T(z,u) * (y * x)). L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u)). L(L(x,y,z),z * y,K(z,u)) != w | L(x,y,T(z,u)) = w. L(x,y,T(z,z * y)) = L(x,y,z). x != L(L(y,z,u),w,K(v5,y)) | x = L(y,z,u). L(x,y,T(z,x)) = L(x,y,z). x != L(L(y,z,u),w,K(y,v5)) | x = L(y,z,u). L(x,y,T(x,z)) = L(x,y,x). L(L(x,1 / y,L(z,y,y)),z / y,K(L(z,y,y),u)) = L(x,1 / y,T(L(z,y,y),u)). L(T(x,y),z,T(x,u)) = T(L(x,z,x),y). L(x,y,T(z,y) \ 1) = L(x,y,z \ 1). L(T(x,y),z,T(x,u)) = L(T(x,y),z,x). L(x,y,y \ z) = L(x,y,(y / z) \ 1). L(x,y,(y / z) \ 1) = L(x,y,y \ z). T(x,y) * (L(T(x,y),z,x) \ u) = u * a(T(x,y),z,T(x,y)). L(x,y,z * (y \ 1)) = L(x,y,y \ z). L(x,y * z,y \ 1) = L(x,y,y \ z). L(x,y,z / (y * y)) = L(x,y,y \ (z / y)). K(x,L(y,x,x \ z)) = K(x,y). K(x,L(y,x,z)) = K(x,y). K(L(x,y,z),y) = K(x,y). K(x,y \ (x \ (y * z))) = K(x,x \ z). L(K(x,x \ y),y,z) = K(x,x \ y). T(x,L(y,x,z)) = x * K(x,y). K((x / y) \ (z \ x),z) = K(z \ y,z). K((x * y) \ z,y) = K(y \ (x \ z),y). K((x * (y * z)) \ ((x * y) * u),L(z,y,x)) = K(L(z,y,x) \ u,L(z,y,x)). L(K(x,y),T(y,z) * u,w) = K(L(x,y,v5),L(y,u,w)). T(x,L(y,x,z)) = T(x,y). x != T(y,L(y \ z,y,u)) | x = T(y,u \ (y \ (u * z))). T(x,x \ y) = T(x,z \ (x \ (z * y))). T(x,y \ (x \ (y * z))) = T(x,x \ z). T(L(x,y,z),(z * (y * x)) \ ((z * y) * u)) = T(L(x,y,z),L(x,y,z) \ u). K(x,y \ (x \ z)) = K(x,x \ (y \ z)). K(x,y \ z) = K(x,x \ (y \ (x * z))). K(x,x \ (y \ (x * z))) = K(x,y \ z). K(x \ (y \ z),y) = K(y \ (x \ z),y). K((x * y) \ z,x) = K(x \ (y \ z),x). K(x \ ((x \ y) \ z),x) = K(y \ z,x). K((x \ y) \ z,L(x,u,w)) = K(L(x,u,w) \ ((x \ (L(x,u,w) \ y)) \ z),L(x,u,w)). K(L(x,y,z) \ ((x \ (L(x,y,z) \ u)) \ w),L(x,y,z)) = K((x \ u) \ w,L(x,y,z)). K(L(x,y,z) \ ((x \ (1 / L(x,y,z))) \ u),L(x,y,z)) = K((1 / x) \ u,L(x,y,z)). L(x,y,z / (y * y)) != u | L(x,z,y \ 1) = u. x != L(K(y,z),T(z,u) * w,v5) | x = K(y,L(z,w,v5)). K(L(x,y,z),L(y,u,w)) = K(x,L(y,u,w)). L(K(x,y),T(y,z) * u,w) != v5 | K(x,L(y,u,w)) = v5. K((x * (y \ z)) / x,L(x,u,w)) = K(((y / x) \ z) / x,L(x,u,w)). K(((x / y) \ z) / y,L(y,u,w)) = K((y * (x \ z)) / y,L(y,u,w)). K(L(x,y,z),L(y,u,w)) != v5 | K(x,L(y,u,w)) = v5. a(x,y,x) = a(T(x,z),y,T(x,z)). a(T(x,y),z,T(x,y)) = a(x,z,x). x != K(y / z,L(z,u,w)) | x = K(z \ y,L(z,u,w)). K(((x / y) \ z) / y,L(y,u,w)) = K(y \ (y * (x \ z)),L(y,u,w)). K(((x / y) \ z) / y,L(y,u,w)) = K(x \ z,L(y,u,w)). K(x \ ((y / x) \ z),L(x,u,w)) = K(y \ z,L(x,u,w)). ((x * y) * T(z,u)) / (y * T(z,u)) = R(R(x,y,z),y * z,K(z,u)). R(R(x,y,z),y * z,K(z,u)) = ((x * y) * T(z,u)) / (y * T(z,u)). R(R(x,y,z),y * z,K(z,u)) = R(x,y,T(z,u)). x != R(y,K(z,u) * w,K(w,K(z,v5))) | x = y. R(x,K(y,z),T(u,K(y,w))) = R(x,K(y,z),u). x != R(R(y,z,u),w,K(y,v5)) | x = R(y,z,u). R(x,y,T(x,z)) = R(x,y,x). R(x,y,(x \ z) \ z) = R(x,y,x). R(x,K(y,z),T(K(z,y) * u,K(y,w))) * u = (x * K(y,z)) * (K(y,z) \ u). K((((x * y) \ x) \ 1) \ z,y) = K(z * ((x * y) \ x),y). T(x / (y * (z \ (y / z))),y / z) = ((1 / x) * (y * (z \ 1))) \ (z / y). K(T(x * K(y,x),z) / z,u) = K(((y * x) / y) / T(z,T(x,y)),u). x != y * T(T(y,z \ 1),z \ 1) | x = ((z * y) * y) / z. ((1 / x) \ y) * (x \ (((1 / x) \ y) / x)) = ((x * y) * y) / x. ((1 / x) \ y) * (x \ T(y,x \ 1)) = ((x * y) * y) / x. T(((x * y) * y) / x,x) = (1 / x) * ((x * y) * y). x \ ((x * y) * y) = (1 / x) * ((x * y) * y). (1 / x) * ((x * y) * y) = x \ ((x * y) * y). x != (1 / (y * z)) * (((y * z) * z) * z) | x = (1 / (y / z)) * (y * z). (x * y) \ (((x * y) * y) * y) = (1 / (x / y)) * (x * y). x != (y * z) \ (((y * z) * u) * z) | x = (y / u) \ (y * z). (1 / (x / y)) * (x * y) = (x / y) \ (x * y). x != (1 / (y / z)) * (y * z) | x = (y \ ((y / ((1 / y) / (1 / (y * z)))) / z)) \ 1. (x / y) \ (x * y) = (x \ ((x / ((1 / x) / (1 / (x * y)))) / y)) \ 1. (x \ ((x / ((1 / x) / (1 / (x * y)))) / y)) \ 1 = (x / y) \ (x * y). (x \ ((x / (1 / ((1 / (x * y)) * x))) / y)) \ 1 = (x / y) \ (x * y). (x \ ((x / (1 / (1 / y))) / y)) \ 1 = (x / y) \ (x * y). (x \ (((1 / x) \ (y \ 1)) / y)) \ 1 = (x / y) \ (x * y). (x \ ((y * (1 / x)) \ (1 / y))) \ 1 = (x / y) \ (x * y). (x \ ((x * (y \ 1)) * (y \ 1))) \ 1 = (x / y) \ (x * y). ((x \ 1) * L(x \ 1,y,y)) \ 1 = (y / x) \ (y * x). ((x \ 1) * ((y * x) \ y)) \ 1 = (y / x) \ (y * x). (x \ (y \ (y / x))) \ 1 = (y / x) \ (y * x). (x \ (x / y)) \ y = (x / y) \ (x * y). x != (y \ (y / z)) \ z | x = ((z \ 1) \ y) * (y \ z). (x / y) \ (x * y) = ((y \ 1) \ x) * (x \ y). ((x \ 1) \ y) * (y \ x) = (y / x) \ (y * x). x != (y \ (y / z)) \ z | x = (y * ((z \ y) \ 1)) * z. (x / y) \ (x * y) = (x * ((y \ x) \ 1)) * y. (x * ((y \ x) \ 1)) * y = (x / y) \ (x * y). R(x * R(K(y,x),z,u),w,x) = R(x,w,x) * R(K(y,x),z,u). R(x * R(K(y,x),z,u),w,x) \ R(x,w,x) = R(K(x,y),z,u). (K(x,y) * ((K(y,x) * z) / u)) * u != w | L(z,K(y,x),u * K(x,y)) = w. (1 / x) * ((1 / x) * (1 * K(x,(x * y) \ 1))) = 1 / (T(x,y) / (1 / x)). K(x / y,T(z,u)) \ T(x / (K(y \ x,z) \ x),u) = K(K(x / y,z) \ x,T(K(x / y,z),u)). (x * K(y,T(z,u))) * K(z,z \ u) = (x / T(u / (u / z),y)) * z. x * (K(y,y \ z) * K(u,T(y,z))) = (x / T(z / (z / y),u)) * y. T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = (K(z,x) * K(y,x)) \ 1. x != (K(y,z) * K(u,w)) \ 1 | x = K(w,u) * K(z,y). T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = K(x,y) * K(x,z). K(K(x,y) * K(x,z),K(z,x) * K(y,x)) = 1. K(K(x,y) * K(x,z),(K(x,y) * K(x,z)) \ 1) = 1. K((K(x,y) * K(x,z)) \ 1,K(x,y) * K(x,z)) = 1. L(x * 1,K(y,z) * K(y,u),(K(y,z) * K(y,u)) \ 1) = ((K(y,z) * K(y,u)) \ 1) * ((K(y,z) * K(y,u)) * x). K(x,x \ y) * K(z,y / (y / x)) = T(y / (y / x),z) \ x. K(x,x \ y) * K(z,T(x,y)) = T(y / (y / x),z) \ x. x * (T(y / (y / z),u) \ z) = (x / T(y / (y / z),u)) * z. (x / T(y / (y / z),u)) * z = x * (T(y / (y / z),u) \ z). (x / T(1 / (1 / y),z)) * y = x * (y * (1 / T(y,z))). L(x,y,z * (T(1 / (1 / z),u) \ K(w,z))) = L(x,y,K(w,z) * K(u,z)). T(K(x,y) * K(z,x),T(u,K(x,y))) = T(K(z,x) * K(x,y),u). T((1 / ((x * y) \ x)) * K(y,z),y) = (y \ (1 / ((x * y) \ x))) * T(y,z). L(K(x,y),z,u) * (K(y,w) * v5) = K(y,w) * (L(K(x,y),z,u) * v5). L(x,y,x) * R(K(x,z),u,w) = L(x * R(K(x,z),u,w),y,x). L(x * R(K(x,y),z,u),w,x) = L(x,w,x) * R(K(x,y),z,u). R(K(x,y),z,u) * L(x,w,x) = L(x * R(K(x,y),z,u),w,x). L(x * R(K(x,y),z,u),w,x) = R(K(x,y),z,u) * L(x,w,x). x != (y * K(z,u)) * R(K(u,w),v5,v6) | x = y * (R(K(u,w),v5,v6) * K(z,u)). R(K(x,T(y,z)),u,w) * (z * K(y,x)) = z * (R(K(x,y),u,w) * K(y,x)). x != K(L(L(y,z,u),w,v5),u) | x = K(L(y,w,v5),u). K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y). x \ ((L(y,z,u) * (y \ x)) * y) = K(y \ x,y) * L(T(y,y \ x),z,u). K(x \ y,x) * L(T(x,x \ y),z,u) = y \ ((L(x,z,u) * (x \ y)) * x). K(x,y) * (K(y,x \ y) * z) = (x \ y) * (T(x \ T(y,x),y) \ z). (x \ y) * (T(x \ T(y,x),y) \ z) = K(x,y) * (K(y,x \ y) * z). (x \ y) * (T(x \ T(y,x),y) \ z) = K(x,y) * (K(x,y) * z). x != K(y,z) * (K(y,z) * u) | x = z * (T(T(z,y),y) \ u). (x \ y) * (T(x \ T(y,x),y) \ z) = y * (T(T(y,x),x) \ z). (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u). T(K(x,y),z) * T(K(y,u),z) = z \ (K(y,u) * (K(x,y) * z)). x \ (K(y,z) * (K(u,y) * x)) = T(K(u,y),x) * T(K(y,z),x). (x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x). (x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x). (x * T(y,z)) \ (x * (T(y,z) * z)) = L(z,y,x). L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x)). L(x,y,z) = L(x,T(y,x),z). L(x,T(y,x),z) = L(x,y,z). L(x,x \ y,z) = L(x,y / x,z). L(x,y / x,z) = L(x,x \ y,z). x != L(y,(z \ u) / y,z) | x = (z * ((z \ u) / y)) \ u. L(x,x \ (y \ z),y) = (y * ((y \ z) / x)) \ z. K(L(x,x \ y,z),u) != w | L(K(x,u),y,z) = w. x != (y \ (y / z)) \ 1 | x = L(z,y,y). (x / y) \ ((((y \ 1) \ 1) * (1 / x)) \ z) = L(z,y \ x,y \ x). (x / y) \ ((1 / (x / y)) \ z) = L(z,y \ x,y \ x). L(x,y / z,y / z) = L(x,z \ y,z \ y). L(x,y,y) = L(x,y \ 1,y \ 1). L(x,y \ 1,y \ 1) = L(x,y,y). x != L(y,z / u,z / u) | x = R(y,u / z,z * (u \ 1)). L(x,y \ z,y \ z) = R(x,y / z,z * (y \ 1)). R(x,y / z,z * (y \ 1)) = L(x,y \ z,y \ z). x != L(y,z / u,z / u) | x = (z / u) * ((u * (z \ 1)) * y). L(x,y \ z,y \ z) = (z / y) * ((y * (z \ 1)) * x). (x / y) * ((y * (x \ 1)) * z) = L(z,y \ x,y \ x). L(x,y \ 1,y \ 1) != z | L(x,y,y) = z. (x * (y \ 1)) * L(z,x \ y,x \ y) = (y / x) \ z. (x / y) * L(z,x \ y,x \ y) = (1 / (x / y)) \ z. (x \ y) * L(L(L(y,x,x),x,x),z,u) = (x \ 1) * (L(y,x,x) * L(L(y,x,x),z,u)). (x \ 1) * (L(y,x,x) * L(L(y,x,x),z,u)) = (x \ y) * L(L(L(y,x,x),x,x),z,u). ((x \ y) \ 1) * L(L((x \ 1) \ 1,y,y),z,u) = (y \ 1) * (((x \ 1) \ 1) * L((x \ 1) \ 1,z,u)). L(x,y \ (z \ 1),(z * y) \ 1) != u | L(x,z * y,z * y) = u. (x * (y / z)) * (z * (y \ 1)) = L(x,y \ z,y \ z). (x * (y \ 1)) \ ((y / x) \ z) = L(z,x \ y,x \ y). L(x,y / (1 / (z / u)),y / (1 / (z / u))) = L(x,(z / u) * L(y,z \ u,z \ u),(1 / (z / u)) \ y). L(x,(y / z) * L(u,y \ z,y \ z),(1 / (y / z)) \ u) = L(x,u / (1 / (y / z)),u / (1 / (y / z))). (x * ((y / z) / u)) * (u * (z * (y \ 1))) = L(x,(y / z) \ u,(y / z) \ u). (x * ((y / z) / u)) * ((y \ ((y * u) * z)) * (y \ 1)) = L(x,y \ (y \ ((y * u) * z)),y \ (y \ ((y * u) * z))). L(x,y \ (y \ ((y * z) * u)),y \ (y \ ((y * z) * u))) = (x * ((y / u) / z)) * ((y \ ((y * z) * u)) * (y \ 1)). (x * (y \ 1)) * L(z,y \ x,y \ x) = (y / x) \ z. (x * (y * (z \ 1))) \ (((z / y) / x) \ u) = L(u,x \ (z / y),x \ (z / y)). (x * ((1 / y) \ 1)) \ ((1 / (x * y)) \ z) = L(z,x \ (1 / y),x \ (1 / y)). (x * (((y \ 1) \ 1) \ 1)) \ ((((y \ 1) \ 1) / x) \ z) = L(z,x * ((1 / x) * ((y \ x) \ 1)),x \ ((y \ 1) \ 1)). L(x,y * ((1 / y) * ((z \ y) \ 1)),y \ ((z \ 1) \ 1)) = (y * (((z \ 1) \ 1) \ 1)) \ ((((z \ 1) \ 1) / y) \ x). ((x * (y \ z)) * (K(z,y) \ 1)) \ (((y / z) / x) \ u) = L(u,(x * (y \ z)) \ K(z,y),(x * (y \ z)) \ K(z,y)). L(x,(y * (z \ u)) \ K(u,z),(y * (z \ u)) \ K(u,z)) = ((y * (z \ u)) * (K(u,z) \ 1)) \ (((z / u) / y) \ x). (x * (y \ 1)) * z != (y / x) \ u | z = L(u,x \ y,x \ y). L(x,y \ z,y \ z) = L(x,z \ y,z \ y). L(x,y \ (z \ 1),y \ (z \ 1)) != u | L(x,z * y,z * y) = u. L(x,(y \ z) \ (z \ 1),(z \ y) * (1 / z)) != u | L(x,z * (y \ z),z * (y \ z)) = u. L(x,y * z,y * z) = L(x,(y \ 1) \ z,(y \ 1) \ z). L(x,(y \ 1) \ z,(y \ 1) \ z) = L(x,y * z,y * z). L(x,y * z,y * z) = L(x,z \ (y \ 1),z \ (y \ 1)). L(x,y \ (z \ 1),y \ (z \ 1)) = L(x,z * y,z * y). L(x,(y \ 1) \ z,(y \ 1) \ z) != u | L(x,y * z,y * z) = u. (((x \ 1) \ y) * z) \ ((x \ 1) \ y) = L(z \ 1,x * y,x * y). x != L(y,z * u,z * u) | x = (y * (z * u)) * (u \ (z \ 1)). L(x,y \ (z \ 1),y \ (z \ 1)) = (x * (z * y)) * (y \ (z \ 1)). L(x,y \ (z \ (u \ 1)),y \ ((u * z) \ 1)) = L(x,(u * z) * y,(u * z) * y). L(x,y \ K(z,u),y \ (K(u,z) \ 1)) = L(x,K(u,z) * y,K(u,z) * y). (((x \ 1) \ y) * z) \ ((x \ 1) \ y) != u | ((x * y) * z) \ (x * y) = u. (x \ (y \ 1)) * z != L(u,x \ (y \ 1),x \ (y \ 1)) | T(u * (y * x),x \ (y \ 1)) = z. T(x * (y * z),z \ (y \ 1)) = ((z \ (y \ 1)) \ 1) * x. T(x * (y * (z \ 1)),z * (y \ 1)) = (((z \ 1) \ (y \ 1)) \ 1) * x. T(x * (y * (z \ 1)),z / y) = (((z \ 1) \ (y \ 1)) \ 1) * x. T(x * (y * ((z \ 1) \ 1)),z \ (1 / y)) = ((((z \ 1) \ 1) \ (y \ 1)) \ 1) * x. (x / (K(y,z) \ u)) * K(z,y) = K(y,z) * ((K(y,z) \ x) / u). (x / (K(y,z) * u)) * K(y,z) = K(z,y) * ((K(z,y) \ x) / u). (x / (K(y,z) * u)) * K(y,z) = K(z,y) * ((K(y,z) * x) / u). (x * y) \ (y * T(T(z * x,z) / z,y)) = L(a(z,T(x,y),z),T(x,y),y). ((x * y) * a(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x)). K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u \ 1,z))). ((((x \ 1) \ 1) / y) * (y / z)) \ 1 = (z / (((1 / y) \ 1) * x)) * y. (((x \ 1) \ (1 / y)) * (y / z)) \ 1 = (z / (((1 / y) \ 1) * x)) * y. (x / y) \ (((z \ 1) \ (1 / x)) \ 1) = (y / (((1 / x) \ 1) * z)) * x. (x / y) \ (x * (((z \ 1) \ 1) \ 1)) = (y / (((1 / x) \ 1) * z)) * x. (x / y) \ (x * (1 / z)) = (y / (((1 / x) \ 1) * z)) * x. (x / (((1 / y) \ 1) * z)) * y = (y / x) \ (y * (1 / z)). (x / (y * z)) * y = (y / x) \ (y * (1 / z)). (x / y) \ (x * (1 / z)) = (y / (x * z)) * x. (x / y) \ (x * z) = (y / (x * (z \ 1))) * x. (x / (y * (z \ 1))) * y = (y / x) \ (y * z). (K(x,y) / z) \ (K(x,y) / u) = (z / (K(x,y) * u)) * K(x,y). L((x / (y * z)) * y,y,y) = (x / y) / (z * (1 / y)). ((1 / x) \ (y / z)) * z = (z / x) \ (z * y). (x / y) / (z * (1 / y)) = (x / (y * z)) / (1 / y). (x / (y * z)) / (1 / y) = (x / y) / (z * (1 / y)). x != (y / z) / (u * (1 / z)) | x = (z * (1 / y)) \ (z / u). (x / (y * z)) / (1 / y) = (y * (1 / x)) \ (y / z). ((x \ 1) \ ((1 / y) \ z)) * (z \ 1) = ((z \ 1) \ 1) * (((z \ x) \ 1) \ y). (((x * y) \ x) \ (z / x)) * x = (x \ 1) * ((y \ (x \ 1)) \ z). x != (((y * z) \ y) \ (u / y)) * y | x = ((y / u) * (z \ 1)) \ y. (x \ 1) * ((y \ (x \ 1)) \ z) = ((x / z) * (y \ 1)) \ x. x != (y \ 1) * ((z \ (y \ 1)) \ (z \ u)) | x = (((y * z) / ((1 / u) * z)) \ y) \ 1. ((x / (y \ z)) * (y \ 1)) \ x = (((x * y) / ((1 / z) * y)) \ x) \ 1. (((x * y) / ((1 / z) * y)) \ x) \ 1 = ((x / (y \ z)) * (y \ 1)) \ x. R(1 / x,y,y \ (z \ 1)) \ 1 = ((z / (y \ x)) * (y \ 1)) \ z. (x / y) \ (((1 / x) \ 1) * (1 / z)) = (y * (1 / x)) / (z / x). (x / y) \ (x * (1 / z)) = (y * (1 / x)) / (z / x). (x * (1 / y)) / (z / y) = (y / x) \ (y * (1 / z)). x != (y / z) \ (y * (1 / u)) | x = (z / (y * u)) * y. (x * (1 / y)) / (z / y) = (x / (y * z)) * y. R(L(x,y,y),1 / y,(1 / y) \ (z \ 1)) = ((y / z) \ (y * (1 / x))) \ z. (x * (1 / y)) / (1 / (y * z)) = (x / (y * (1 / z))) * y. (x * (1 / (1 / y))) / ((z \ 1) / (1 / y)) = (x / ((T(z,y) \ 1) * (1 / y))) * (1 / y). (x * (1 / (y \ 1))) / (L(y \ 1,z,u) / (y \ 1)) = (x / (y \ L(1 / y,z,u))) * (y \ 1). (x * (1 / (y \ 1))) / ((z * (1 / (u * z))) / (y \ 1)) = (x / ((((u \ z) * (1 / z)) \ y) \ 1)) * (y \ 1). (x * (1 / ((y \ z) * (1 / z)))) / (u / ((y \ z) * (1 / z))) = (x / ((y \ 1) * (u * K(z,z \ 1)))) * ((y \ z) * (1 / z)). K(x,x \ 1) * (T(y,z) / z) = (x * (1 / (z * x))) * y. x != K(y,z) * (T(u,w) / w) | x = K(y,z) / (u \ w). (x * (1 / (y * x))) * z = K(x,x \ 1) / (z \ y). K(x,x \ 1) / (y \ z) = (x * (1 / (z * x))) * y. (x * (1 / (y * x))) * z = x * (1 / ((z \ y) * x)). x * y != (z * (1 / (u * z))) * w | (z * (1 / ((w \ u) * z))) / y = x. (x * (1 / (((y * y) \ z) * x))) / y = (1 / (x * (1 / (z * x)))) \ y. x * y != (z * u) * (1 / (w * (z * u))) | x \ (K(z * u,u \ (z \ 1)) / w) = y. x \ (K(x * (1 / (y * x)),(1 / (y * x)) \ (x \ 1)) / z) = 1 / (((1 / (z * (x * (1 / (y * x))))) \ y) * x). x * y != (z * (1 / (u * z))) * w | x \ (z * (1 / ((w \ u) * z))) = y. ((1 / (x * y)) \ (y \ 1)) \ (y * (1 / (((1 / (z * (y * (1 / (x * y))))) \ x) * y))) = (y * (1 / (x * y))) / z. (x * (((x \ y) \ 1) \ 1)) * z = x * (1 / ((z \ (1 / y)) * x)). (x * (1 / (K(y \ z,z \ y) * (u * x)))) * w = x * (1 / ((w \ (K(y \ z,z \ y) * u)) * x)). x != (y * (((y \ (z \ u)) \ 1) \ 1)) * (((1 / u) * z) * (y \ 1)) | x = ((z / y) \ ((1 / u) \ y)) \ ((y \ 1) \ (z \ u)). x * (1 / (((((1 / y) * z) * (x \ 1)) \ (1 / (z \ y))) * x)) = ((z / x) \ ((1 / y) \ x)) \ ((x \ 1) \ (z \ y)). (x * (((x \ y) \ 1) \ 1)) * z != u * w | u \ (x * (1 / ((z \ (1 / y)) * x))) = w. (x * (1 / (((y * y) \ z) * x))) / y = (((z * x) \ 1) \ (1 / x)) \ y. (x * (1 / (((y * y) \ z) * x))) / y = ((x \ (z \ 1)) \ (1 / x)) \ y. (x * (1 / (((y * y) \ z) * x))) / y = (((z \ 1) \ x) * (1 / x)) \ y. (x * (1 / (((y * y) \ z) * x))) / y = (x * (((x \ z) \ 1) \ 1)) \ y. ((1 / x) \ K(y \ z,z \ y)) \ u = (x \ u) * K(y \ z,z \ y). (x * K(y \ z,z \ y)) \ u = (x \ u) * K(y \ z,z \ y). x / ((y \ (z \ 1)) * K(u \ w,w \ u)) = (1 / x) \ (z * (y * K(u \ w,w \ u))). (1 / T(x,(y \ (z \ 1)) * K(u \ w,w \ u))) \ (z * (y * K(u \ w,w \ u))) = (z * (y * K(u \ w,w \ u))) * x. ((1 / T(x,y \ (z \ 1))) * K(u \ w,w \ u)) \ (z * y) = ((z * y) * x) * K(u \ w,w \ u). (x \ y) * (T(x \ T(y,x),y) \ z) = (y / x) * (T(x \ y,x) \ z). x != (y \ z) * (T(y \ T(z,y),z) \ u) | x = z * (T(T(z,y),y) \ u). (x / y) * (T(y \ x,y) \ z) = x * (T(T(x,y),y) \ z). T(T(x,x * y) * R(y,z,u),x) = T(x * R(y,z,u),x * y). x != y \ (z * T(z,u)) | x = (y \ z) * T(z,u). x / ((y * T((1 / z) * y,u)) \ z) = ((1 / x) \ (z \ y)) * T(z \ y,u). T(x,((K(y,z) / u) / (u \ K(y,z))) * w) = T(x,K(K(z,y),u) * w). T(x,K(y,y \ K(z,u)) * w) = T(x,K(K(u,z),y) * w). x != (y * (1 / (z * y))) \ ((((z \ y) \ 1) \ 1) * u) | x = ((z \ 1) \ 1) / (u \ ((z \ y) \ 1)). (1 / x) \ (((((x \ y) \ 1) \ y) * (1 / y)) * z) = ((x \ 1) \ 1) / (z \ ((x \ y) \ 1)). (x \ K(y,z)) * ((T(z,y) \ 1) \ (u / (T(z,y) \ u))) = (x \ z) * (w / (T(z,y) \ w)). K(x,(y * (z / x)) \ u) != w | K(x,(y * (x \ z)) \ u) = w. x / T(x / y,T(L(y,z,u),y)) = y * a(u,z * y,K(y \ x,y)). x / T(x / y,L(y,z,u)) = y * a(u,z * y,K(y \ x,y)). ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u). K(x,(y * z) \ (x \ u)) = K(x,(y * (z * x)) \ u). K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u)). K(x,(y * (z * x)) \ u) != w | K(x,(y * z) \ (x \ u)) = w. K(x,(y * z) \ u) = K(x,(y * (z / x)) \ (x \ u)). K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u). (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y). K(x,(y * (x \ z)) \ (x \ u)) = K(x,(y * z) \ u). x != K(y,z \ (y \ u)) | x = K(y,y \ (z \ u)). K(x,(y * z) \ u) = K(x,x \ ((y * (x \ z)) \ u)). K(x,x \ ((y * (x \ z)) \ u)) = K(x,(y * z) \ u). K(x,(y * z) \ (x \ u)) = K(x,(y * (x * z)) \ u). K(x,(y * (x * z)) \ u) = K(x,(y * z) \ (x \ u)). L(K(x,(y * z) \ u),w * x,v5) = K(L(x,w,v5),x \ ((y * (x \ z)) \ u)). K(L(x,y,z),x \ ((u * (x \ w)) \ v5)) = L(K(x,(u * w) \ v5),y * x,z). K(L(x,y,z),L(x,y,z) \ ((u * (x \ (1 / L(x,y,z)))) \ w)) = K(L(x,y,z),(u * (1 / x)) \ w). x != K(y,(z * (y * u)) \ w) | x = L(K(y,u \ (y \ (z \ w))),z \ w,z). K(x,(y * z) \ (x \ u)) = L(K(x,z \ (x \ (y \ u))),y \ u,y). L(K(x,y \ (x \ (z \ u))),z \ u,z) = K(x,(z * y) \ (x \ u)). K((x * (y * z)) \ u,z) != w | K((x * y) \ (z \ u),z) = w. K((x * y) \ (z \ u),z) = K((x * (z * y)) \ u,z). K((x * (y * z)) \ u,y) = K((x * z) \ (y \ u),y). x != K((y * (z * u)) \ (y * ((u * w) * z)),z) | x = K(L(w,z * u,y),z). K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z). T(x,(y * (x * z)) \ u) = 1 / (x \ K((y * z) \ (x \ u),x)). 1 / (x \ K((y * z) \ (x \ u),x)) = T(x,(y * (x * z)) \ u). T(x,(y * z) \ (x \ u)) = T(x,(y * (x * z)) \ u). T(x,(y * (x * z)) \ u) = T(x,(y * z) \ (x \ u)). x != T(y,(z * (y * u)) \ w) | x = T(y,(z * (u * y)) \ w). T(x,(y * z) \ (x \ u)) = T(x,(y * (z * x)) \ u). T(x,(y * (z * x)) \ u) = T(x,(y * z) \ (x \ u)). L(T(x,(y * z) \ (x \ u)),w,v5) \ L(x,w,v5) = K((y * (z * x)) \ u,L(x,w,v5)). x != L(K(y,z \ (y \ (u \ w))),u \ w,u) | x = K(y,(u * (z / (y \ 1))) \ w). K(x,(y * z) \ (x \ u)) = K(x,(y * (z / (x \ 1))) \ u). K(x,(y * (z / (x \ 1))) \ u) = K(x,(y * z) \ (x \ u)). x != K(y,(z * (((y \ 1) * u) / (y \ 1))) \ w) | x = K(y,(z * u) \ w). K(x,(y * ((x \ 1) * z)) \ (x \ u)) = K(x,(y * z) \ u). K(x,(y * ((x \ 1) * z)) \ T(u,x)) = K(x,(y * z) \ (u * x)). K(x,(y * ((x \ 1) * z)) \ u) = K(x,(y * z) \ (u * x)). x != ((1 / y) * (z * (u \ 1))) \ (u / z) | x = ((u / z) * y) * (u / z). T(x / (y * (z \ (y / z))),y / z) = ((z / y) * x) * (z / y). x != T(y / (z * (u \ (z / u))),z / u) | x = T(y * (u * (z \ 1)),y) / (z / u). ((x / y) * z) * (x / y) = T(z * (x * (y \ 1)),z) / (y / x). T(x * (y * (z \ 1)),x) / (z / y) = ((y / z) * x) * (y / z). ((x / y) \ z) / (x / y) = ((y / x) * z) * (y / x). (((x / y) \ 1) * z) / (x / y) = ((y / x) * L(z,x / y,x / y)) * (y / x). ((x / y) * L(z,y / x,y / x)) * (x / y) = (((y / x) \ 1) * z) / (y / x). (1 / x) * ((1 / x) * (1 * K(x,y \ (x \ 1)))) = 1 / (T(x,y) / (1 / x)). L(x,y,z * (K(u,z) / T(z,w))) = L(x,y,K(u,z) * K(w,z)). x != K(y,z) * L(T(u,y),w,v5) | x = T(K(y,z) * L(u,w,v5),y). x \ ((L(y,z,u) * (y \ x)) * y) = T(K(y \ x,y) * L(y,z,u),y \ x). T(K(x \ y,x) * L(x,z,u),x \ y) = y \ ((L(x,z,u) * (x \ y)) * x). L(x,y \ K(z,u),y \ K(z,u)) = L(x,K(u,z) * y,K(u,z) * y). (x * y) \ ((T(z * x,z) / z) * y) = L(a(z,T(x,y),z),T(x,y),y). L(a(x,T(y,z),x),T(y,z),z) = (y * z) \ ((T(x * y,x) / x) * z). x != (y \ (z \ u)) * (u \ 1) | x = u * ((y * u) \ (z \ 1)). ((x \ 1) \ 1) * (((x \ y) \ 1) \ z) = x * (((y \ 1) * x) \ ((1 / z) \ 1)). ((x / y) \ (x * (1 / z))) \ y = R(L(z,x,x),1 / x,(x \ 1) \ (1 / y)). R(L(x,y,y),1 / y,(y \ 1) \ (1 / z)) = ((y / z) \ (y * (1 / x))) \ z. x != ((1 / y) \ z) * T(z,u) | x = y * (z * T(z,u)). x / ((y * T((1 / z) * y,u)) \ z) = x * ((z \ y) * T(z \ y,u)). x / ((T(y / z,u) * y) \ z) = x * ((z \ y) * T(z \ y,u)). (1 / x) * ((1 / x) * K(x,y \ (x \ 1))) = 1 / (T(x,y) / (1 / x)). (1 / x) * (T(x,y) \ 1) = 1 / (T(x,y) / (1 / x)). 1 / (T(x,y) / (1 / x)) = (1 / x) * (T(x,y) \ 1). x != 1 / (T(y,z) / (1 / y)) | x = y \ (T(y,z) \ 1). (1 / x) * (T(x,y) \ 1) = x \ (T(x,y) \ 1). x != (1 / y) * (T(y,z) \ 1) | x = (T(y,z) \ 1) * (1 / y). x \ (T(x,y) \ 1) = (T(x,y) \ 1) * (1 / x). (T(x,y) \ 1) * (1 / x) = x \ (T(x,y) \ 1). x != (T(y,z) \ 1) * (1 / y) | x = ((T(y,z) \ 1) \ 1) \ (1 / y). x \ (T(x,y) \ 1) = ((T(x,y) \ 1) \ 1) \ (1 / x). ((T(x,y) \ 1) \ 1) \ (1 / x) = x \ (T(x,y) \ 1). 1 / (x * T(x,y)) = x \ (T(x,y) \ 1). (x * (y * T(y,z))) * (y \ (T(y,z) \ 1)) = (y * T(y,z)) * ((1 / (y * T(y,z))) * x). x != T(K(y \ z,y) * u,y \ z) | x = (z / y) \ (u * (y \ z)). x \ ((L(y,z,u) * (y \ x)) * y) = (x / y) \ (L(y,z,u) * (y \ x)). (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y). ((x \ 1) \ 1) * (((x \ y) \ 1) \ z) = x * (((y \ 1) * x) \ z). x * (K(y,z) * L(T(y,x),u,w)) = L(y,u,w) * (x * K(y,z)). x * y != z * (K(u,w) * L(T(u,z),v5,v6)) | T(x,y) = y \ (L(u,v5,v6) * (z * K(u,w))). T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = L(L(T(y,x),u,w),K(y,z),x) \ (L(y,u,w) * (x * K(y,z))). L(L(T(x,y),z,u),K(x,w),y) \ (L(x,z,u) * (y * K(x,w))) = T(y * K(x,w),L(L(T(x,y),z,u),K(x,w),y)). R(x,T(K(y,z),u),T(K(z,y),u)) = (x * T(K(y,z),u)) * T(K(z,y),u). (x * T(K(y,z),u)) * T(K(z,y),u) = R(x,T(K(y,z),u),T(K(z,y),u)). R(x,T(K(y,z),u),T(K(z,y),u)) != w * T(K(z,y),u) | x * T(K(y,z),u) = w. x * (T(y,z) * L(K(z,y),u,w)) = (x * y) * a(w,u,K(y,z)). x * (y * a(z,u,K(y,w))) = (x * y) * a(z,u,K(y,w)). (x * y) * a(z,u,K(y,w)) = x * (y * a(z,u,K(y,w))). (x * (y * a(z,u,K(y,w)))) * v5 != (x * y) * a(z,u,K(y,w)) | 1 = v5. 1 = a(x,y,a(z,u,K(y,w))). a(x,y,a(z,u,K(y,w))) = 1. a(x,T(y,z),a(u,w,K(y,v5))) = 1. T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,T(x / T(z,y),z),z). x != T(y * K(z,y),T(u,T(y,w))) | x = T(y * K(z,y),u). R(x,T(y,T(x,z)),R(x,u,w)) = T(x * K(y * R(x,u,w),x),y). T(x * K(y * R(x,z,u),x),y) = R(x,T(y,T(x,w)),R(x,z,u)). R(x,T(y,T(x,z)),R(x,u,w)) = R(x,y,R(x,u,w)). R(T(x,y),T(z,x),R(T(x,y),u,w)) = R(T(x,y),z,R(T(x,y),u,w)). x != L(y,z,u) / L(y * K(w,y),z,u) | x = K(L(y,z,u),w). K(L(x,y,z),u * (K(x,w) * v5)) = K(L(x,y,z),u * v5). x != R(y,z,u) \ R(y * K(w,y),z,u) | x = K(w,R(y,z,u)). K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5)). K(x * y,R(x,z,u)) = K(y * x,R(x,z,u)). K(x * y,R(y,z,u)) = K(y * x,R(y,z,u)). R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x). (x * y) * (z * (L(y \ 1,y,x) / z)) = (x * y) * (z * (((x * y) \ x) / z)). x != K(y,(z / u) \ 1) | x = K(y,u / z). K(x,R(y / x,x * z,u) \ 1) = K(x,((x * z) * u) / ((y * z) * u)). K(x,((x * y) * z) / ((u * y) * z)) = R(K(x,x / u),x * y,z). R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u)). R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u)). K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x). K(x,(y * z) / ((u * (x \ y)) * z)) = K(R(x,x \ y,z),u \ x). K(R(x,x \ y,z),u \ x) = K(x,(y * z) / ((u * (x \ y)) * z)). K(L(x,y,x),(((x * (y * x)) / x) * z) / ((u * y) * z)) = K(R(L(x,y,x),y,z),u \ L(x,y,x)). K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z). K(x * (y \ z),L(x,u,w)) = K(y \ (z * x),L(x,u,w)). K(x \ (y * z),L(z,u,w)) = K(z * (x \ y),L(z,u,w)). x != K(y \ (z * u),L(u,w,v5)) | x = K((z \ y) \ u,L(u,w,v5)). K(x * (y \ z),L(x,u,w)) = K((z \ y) \ x,L(x,u,w)). K((x \ y) \ z,L(z,u,w)) = K(z * (y \ x),L(z,u,w)). K(x \ (y * z),L(y,u,w)) = K((y \ x) \ z,L(y,u,w)). K((x \ y) \ z,L(x,u,w)) = K(y \ (x * z),L(x,u,w)). K(x \ (y \ z),L(y,u,w)) = K((x * y) \ z,L(y,u,w)). K((x * y) \ z,L(y,u,w)) = K(x \ (y \ z),L(y,u,w)). K(L(x \ y,x,z),L(x,u,w)) = K(z \ (x \ (z * y)),L(x,u,w)). K(x,K(y \ (z \ (u \ w)),L(z,y,u))) = K(x,K(z,(u * (y * z)) \ w)). K(x \ (y \ (x * z)),L(y,u,w)) != v5 | K(y \ z,L(y,u,w)) = v5. (1 / (K(x,y) * z)) \ K(x,y) = T(y * (T(T(y,x),x) \ z),K(y,x)). T(x * (T(T(x,y),y) \ z),K(x,y)) = (1 / (K(y,x) * z)) \ K(y,x). T(x * (T(T(x,y),y) \ z),K(x,y)) = ((1 / z) * K(x,y)) \ K(y,x). x != (y * K(z,u)) \ K(u,z) | x = K(u,z) * (y \ K(u,z)). T(x * (T(T(x,y),y) \ z),K(x,y)) = K(y,x) * ((1 / z) \ K(y,x)). T(x * (T(T(x,y),y) \ z),K(x,y)) = K(y,x) * (z * K(y,x)). K(a(x,y,z),T(x,u)) = K(a(x,y,z),x). K(x,T(R(y,z,u) * (y \ x),T(y,R(y,z,u)))) = K(x,x * (y \ R(y,z,u))). x != ((y / z) * z) / u | x = y / u. R(K(x,(T(y,z) / u) / (y / u)),y / w,w) = T(y,K(x,z)) / y. x != T(y,z) / y | x = K(y,z). R(K(x,(T(y,z) / u) / (y / u)),y / w,w) = K(y,K(x,z)). R(K(x,(T(y,z) / u) / (y / u)),y / w,w) = K(x,K(y,z)). R(K(x,K(y,z)),z / u,u) = K(x,K(z,y)). R(K(x,K(y,z)),y / u,u) = K(x,K(y,z)). x != R(K(y,K(z,u)),w,v5) | x = K(z,K(u,R(y,w,v5))). K(x,K(y,z)) = K(y,K(z,R(x,y / u,u))). K(x,K(y,R(z,x / u,u))) = K(z,K(x,y)). K(x,K(y,R(z,u,u \ x))) = K(z,K(x,y)). a(K(x,y),z,z \ y) = K(u,K(w,R(v5,v6,v6 \ u))) * K(v5,K(u,w)). a(K(x,y),z,z \ y) = K(u,K(w,R(v5,v6,v6 \ u))) * K(u,K(w,v5)). a(K(x,y),z,z \ x) = K(u,K(w,R(v5,v6,v6 \ u))) * K(u,K(w,v5)). K(x,(y * (z \ x)) \ u) = K(x,(y * (x / z)) \ u). K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u). K(x,(y * (x / y)) \ z) = K(x,x \ z). K(x,K(y \ x,y) * z) = K(x,x \ (x * z)). K(x,x \ (x * y)) = K(x,K(z \ x,z) * y). K(x,y) = K(x,K(z \ x,z) * y). K(x,K(y \ x,y) * z) = K(x,z). K(x * y,K(y,x) * z) = K(x * y,z). K(x,(y \ x) * z) = K(x,(x / y) * z). K(x,(x / y) * z) = K(x,(y \ x) * z). K(x,((y \ x) \ x) \ z) = K(x,y \ z). T((K(x,y) * z) * K(y * x,z),y * x) = K(x,y) * z. (x * y) * (K(y,x) * z) = (K(y,x) * z) * T(x * y,z). (K(x,y) * z) * T(y * x,z) = (y * x) * (K(x,y) * z). K(x,K(R(y,z,u),R(z,w,v5) \ z)) = K(x,K(y,(z * u) / (R(z,w,v5) * u))). L(K(x,y \ ((z \ u) * x)),z \ u,z) = K((x \ 1) \ 1,(z * (L(y,x \ 1,x) / x)) \ u). R(T(K(x,y),R(K(y,x),z,u) * w),z,u) \ w = w / R(K(x,y),z,u). R(T(K(x,y),z),u,w) \ z = z / R(K(x,y),u,w). x / (x / R(K(y,z),u,w)) = R(T(K(y,z),x),u,w). x != y / (y / R(K(z,u),w,v5)) | x = (R(K(z,u),w,v5) \ y) \ y. R(T(K(x,y),z),u,w) = (R(K(x,y),u,w) \ z) \ z. (R(K(x,y),z,u) \ w) \ w = R(T(K(x,y),w),z,u). ((K(x,y) * z) * u) \ (z * u) = R(T(K(y,x),z * u),z,u). ((K(x,y) * z) * u) \ (z * u) = R(K(y,T(x,z * u)),z,u). ((K(x,T(y,z)) * L(x,u,w)) * z) \ (L(x,u,w) * z) = R(K(y,L(x,z,L(x,u,w))),L(x,u,w),z). x != K(y,z) \ u | x = K(z,y) * u. L(K(T(T(x,y),z * y),u),y,z) * w = K(x,(z * y) / (z * (u \ y))) * w. R(x,x \ (y \ (z \ 1)),z) = y \ (z * (z \ (z \ (1 / (x \ (y \ (z \ 1))))))). (1 / (x \ 1)) * (((x \ 1) * y) * L(z,x,x)) = (y * x) * (x \ z). x * (((x \ 1) * y) * L(z,x,x)) = (y * x) * (x \ z). T(x * K(y * R(x,z,u),x),y) = R(x,K(x,w) * y,R(x,z,u)). R(x,K(x,y) * z,R(x,u,w)) = R(x,z,R(x,u,w)). L(x,((1 / y) * z) * u,((1 / y) * z) * u) = L(x,(z \ y) \ u,(z \ y) \ u). L(K(x,y),z,y * x) * ((y * x) * z) = (y * x) * (K(x,y) * z). ((x * y) * (K(y,x) * z)) / ((x * y) * z) = L(K(y,x),z,x * y). ((x * y) * (K(y,x) * z)) / ((x * y) * z) != u | u = L(K(y,x),z,x * y). ((x * y) * (K(y,x) * z)) / ((x * y) * z) != u | L(K(y,x),z,x * y) = u. ((x * y) * (K(y,x) * z)) / (z * T(x * y,z)) = L(K(y,x),z,x * y). ((K(x,y) * z) * T(y * x,z)) / (z * T(y * x,z)) = L(K(x,y),z,y * x). a(x,(y / z) \ 1,x) = a(x,y \ z,x). a(x,y \ 1,x) = a(x,(y * z) \ z,x). a(x,(y * z) \ z,x) = a(x,y \ 1,x). T(L(x,y,z),L(x,y,z) \ u) = L(T(x,(z * (y * x)) \ ((z * y) * u)),y,z). L(T(x,(y * (z * x)) \ ((y * z) * u)),z,y) = T(L(x,z,y),L(x,z,y) \ u). R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(y,z) \ u). R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u). (x * y) \ ((1 / (x * y)) \ z) = L(z,x \ (1 / y),x \ (1 / y)). L(x,y \ (1 / z),y \ (1 / z)) = (y * z) \ ((1 / (y * z)) \ x). L(x,y \ (1 / z),y \ (1 / z)) != u | L(x,y * z,y * z) = u. L(x,(1 / y) \ z,(1 / y) \ z) != u | L(x,z * y,z * y) = u. x != ((y \ 1) * z) / y | x = y \ (z / y). ((x / y) * L(z,y / x,y / x)) * (x / y) = (y / x) \ (z / (y / x)). ((1 / (x / y)) \ z) * (x / y) = (y / x) \ (z / (y / x)). (x / y) * (z * (x / y)) = (y / x) \ (z / (y / x)). (x / y) \ (z / (x / y)) = (y / x) * (z * (y / x)). x != (y / z) \ (u / (y / z)) | x = ((y / z) \ u) * (z * (y \ 1)). (x / y) * (z * (x / y)) = ((y / x) \ z) * (x * (y \ 1)). ((x / y) \ z) * (y * (x \ 1)) = (y / x) * (z * (y / x)). (1 / (x * y)) \ (z / ((1 / y) / x)) = (x / (1 / y)) * (z * (x / (1 / y))). (1 / (x * y)) \ (z / (1 / (x * y))) = (x / (1 / y)) * (z * (x / (1 / y))). (x * y) * (z * (x * y)) = (x / (1 / y)) * (z * (x / (1 / y))). (x / (1 / y)) * (z * (x / (1 / y))) = (x * y) * (z * (x * y)). x != (y / (1 / z)) * (u * (y / (1 / z))) | x = ((y \ 1) \ z) * (u * ((y \ 1) \ z)). (x * y) * (z * (x * y)) = ((x \ 1) \ y) * (z * ((x \ 1) \ y)). ((x \ 1) \ y) * (z * ((x \ 1) \ y)) = (x * y) * (z * (x * y)). x * (y * ((z \ 1) \ ((z \ 1) * x))) = (z * ((z \ 1) * x)) * (y * (z * ((z \ 1) * x))). (x * ((x \ 1) * y)) * (z * (x * ((x \ 1) * y))) = y * (z * ((x \ 1) \ ((x \ 1) * y))). ((((x \ y) \ y) \ 1) \ (1 / y)) * (z * ((((x \ y) \ y) \ 1) \ (1 / y))) = (((x \ y) \ y) * (1 / y)) * (z * ((1 / y) * ((x \ 1) \ 1))). ((x \ 1) \ ((1 / x) * ((y \ x) \ 1))) * (z * ((x \ 1) \ ((1 / x) * ((y \ x) \ 1)))) = (x \ ((y \ 1) \ 1)) * (z * (x * ((1 / x) * ((y \ x) \ 1)))). x != L(y,T(z,y),u) | x = L(y,z,u). T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,x / T(z,y),z). x != L(y,z / T(y,u),y) | x = L(y,y \ z,y). T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,z \ x,z). (((x \ (1 / y)) * x) * y) * z = (y * z) * ((x \ ((y * z) \ z)) * x). (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y. (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y. x / (K(y \ (z \ 1),z) * x) = K(z,x / (z / ((y * x) \ 1))). K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y). x != y / (K(z,u) * y) | x = K(u,z). K(x,y / (x / ((z * y) \ 1))) = K(x,z \ (x \ 1)). K(x,y / (x * (z * y))) = K(x,z \ (x \ 1)). x != K(y,z / (y * u)) | x = K(y,z / (u * y)). K(x,y \ (x \ 1)) = K(x,z / ((y * z) * x)). K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1)). K(x,y / (z * x)) = K(x,(z / y) \ (x \ 1)). K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x)). K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1)). x != K(y,(z / u) \ (y \ 1)) | x = K(y,u / (z * y)). K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x)). x != K(y,(z * u) / (u * y)) | x = K(y,R(y \ z,y,u)). K(x,y / ((z \ y) * x)) = K(x,R(x \ z,x,y / z)). K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x)). K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x)). (x * y) * L(z * ((y \ 1) / z),y,x) = (x * y) * (z * (((x * y) \ x) / z)). K(x,T(R(y,z,u) * (y \ x),y)) = K(x,x * (y \ R(y,z,u))). K(x,(y \ x) * R(y,z,u)) = K(x,x * (y \ R(y,z,u))). K(x,K(y,(z * u) / (R(z,w,v5) * u))) != v6 | K(x,K(R(z,w,v5) \ z,R(y,z,u))) = v6. L(K(T(x,y),T(z,u * y)),y,u) * w = K(x,(u * y) / (u * (z \ y))) * w. R(x,x \ (y \ (z \ 1)),z) = y \ (z * (z \ (z \ ((1 / 1) \ ((z * y) * x))))). L(K(x,y),z,y * x) != u | R(K(x,y),z,T(y * x,z)) = u. L(T(x,(y * z) \ (x \ ((y * z) * u))),z,y) = T(L(x,z,y),L(x,z,y) \ u). x * (y * (z * ((y \ 1) / z))) = (x * y) * (z * (((x * y) \ x) / z)). (x * y) * (z * (((x * y) \ x) / z)) = x * (y * (z * ((y \ 1) / z))). (x * y) * (z * (((x * y) \ x) / z)) = x * K(z,y \ (z \ 1)). K(x,(y * z) \ (x \ y)) = K(x,z \ (x \ 1)). (x * K(y,z \ (y \ 1))) \ x = K((u * z) \ (y \ u),y). K((x * y) \ (z \ x),z) = (u * K(z,y \ (z \ 1))) \ u. K((x * y) \ (z \ x),z) = K(y \ (z \ 1),z). K(x \ (y \ z),y) = K((z \ x) \ (y \ 1),y). K((x \ y) \ (z \ 1),z) = K(y \ (z \ x),z). T(x,(y \ z) \ (x \ 1)) = 1 / (x \ K(z \ (x \ y),x)). 1 / (x \ K(y \ (x \ z),x)) = T(x,(z \ y) \ (x \ 1)). T(x,y \ (x \ z)) = T(x,(z \ y) \ (x \ 1)). T(x,(y \ z) \ (x \ 1)) = T(x,z \ (x \ y)). x != T(y,z \ (y \ u)) | x = T(y,(y * z) \ u). T(x,y \ (x \ z)) = T(x,(x * (z \ y)) \ 1). T(x,(x * (y \ z)) \ 1) = T(x,z \ (x \ y)). x != T(y,z \ 1) | x = T(y,L(z,y \ 1,u) \ 1). T(x,y \ (x \ z)) = T(x,L(x * (z \ y),x \ 1,u) \ 1). T(x,L(x * (y \ z),x \ 1,u) \ 1) = T(x,z \ (x \ y)). L(K(x,T(T(y,z * u),u)),u,z) * w = K(x,(z * u) / (z * (y \ u))) * w. R(x,x \ (y \ (z \ 1)),z) = y \ (z * (z \ (z \ (1 \ ((z * y) * x))))). R(x,x \ (y \ (z \ 1)),z) = y \ (z * (z \ (z \ ((z * y) * x)))). R(x,x \ (y \ (z \ 1)),z) = y \ (z \ ((z * y) * x)). L(R(x,x \ (y \ (z \ 1)),z),y,z) = x. L(T(x,x \ y),z,u) = T(L(x,z,u),L(x,z,u) \ y). T(L(x,y,z),L(x,y,z) \ u) = L(T(x,x \ u),y,z). (L(x,y,z) \ u) / (L(T(x,x \ w),y,z) \ u) = K(L(x,y,z),L(x,y,z) \ w). K((x * y) / (x * (z \ y)),u) * w = K(z,(x * y) / (x * (u \ y))) * w. K((x * y) / (x * (z \ y)),u) = K(z,(x * y) / (x * (u \ y))). x != K((y * z) / (y * (u \ z)),w) | x = (y * z) / (y * (K(w,u) * z)). K(x,(y * z) / (y * (u \ z))) = (y * z) / (y * (K(u,x) * z)). x != K((y * z) / (y * (u \ z)),w) | x = (y * (K(u,w) * z)) / (y * z). K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z). K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z. K(x,((y * x) * z) / ((y * x) * (y \ z))) != u | L(K(x,y),z,y * x) = u. K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w. R(K(x,y),z * u,w) = R(K(x,y),z * (K(v5,x) * u),w). R(K(x,y),z * (K(u,x) * w),v5) = R(K(x,y),z * w,v5). K(x,y) * (R(y,z,u) * w) = R(y,z,u) * (K(x,y) * w). R(x,y,z) * (K(u,x) * w) = K(u,x) * (R(x,y,z) * w). R(K(x,y),z * (u * K(w,x)),v5) = R(K(x,y),z * u,v5). R(x,y,x) * (K(z,x) * (x \ u)) = K(z,x) * ((u / x) * R(x,y,x)). x != R(K(y,z),u * (z * K(w,y)),v5) | x = K(y,R(z * K(w,y),u,v5)). R(K(x,y),z * y,u) = K(x,R(y * K(w,x),z,u)). x != R(K(y,z),u * z,w) | x = K(y,R(z,u,w)). K(x,R(y * K(z,x),u,w)) = K(x,R(y,u,w)). x != K(y,R(z * K(u,y),w,v5)) | x = R(K(y,z),(z * K(u,y)) * w,v5). K(x,R(y,z,u)) = R(K(x,y),(y * K(w,x)) * z,u). R(K(x,y),(y * K(z,x)) * u,w) = K(x,R(y,u,w)). x != R(K(y,z),(z * K(u,y)) * w,v5) | x = K(y,R(R(z,K(u,y),w),K(u,y) * w,v5)). K(x,R(y,z,u)) = K(x,R(R(y,K(w,x),z),K(w,x) * z,u)). K(x,R(R(y,K(z,x),u),K(z,x) * u,w)) = K(x,R(y,u,w)). x != K(y,R(R(z,K(u,y),w),v5,v6)) | x = K(y,R(z,v5,v6)). K(x,R(y,z,u)) = K(x,R(y,K(w,x) * z,u)). K(x,R(y,K(z,x) * u,w)) = K(x,R(y,u,w)). x != K(y,R(z,u,w)) | x = K(y,R(z * K(v5,y),u,w)). K(x,R(y,K(z,x) * u,w)) = K(x,R(y * K(v5,x),u,w)). K(x,R(y * K(z,x),u,w)) = K(x,R(y,K(v5,x) * u,w)). (x * K(y,R(z,u,w))) \ x = K(R(z,K(v5,y) * u,w),y). K(R(x,K(y,z) * u,w),z) = (v5 * K(z,R(x,u,w))) \ v5. x != K(y,R(z * K(u,y),w,v5)) | x = K(y,R(K(u,y) * z,w,v5)). K(x,R(y,K(z,x) * u,w)) = K(x,R(K(v5,x) * y,u,w)). K(x,R(K(y,x) * z,u,w)) = K(x,R(z,K(v5,x) * u,w)). K(R(x,K(y,z) * u,w),z) = K(R(x,u,w),z). T(x,R(y,K(z,x) * u,w)) = 1 / (x \ K(R(y,u,w),x)). T(x,R(K(y,x) * z,u,w)) = x * K(x,R(z,K(v5,x) * u,w)). T(x,R(y,K(z,x) * u,w)) != v5 | T(x,R(y,u,w)) = v5. T(x,R(K(y,x) * z,u,w)) = T(x,R(z,K(v5,x) * u,w)). T(x,R(T(x,y) \ z,u,w)) = T(x,R(x \ z,K(v5,x) * u,w)). T(x,R(x \ y,z,u)) = T(x,R(T(x,w) \ y,z,u)). T(x,R(T(x,y) \ z,u,w)) = T(x,R(x \ z,u,w)). T(x,R(y / T(x,z),u,w)) = T(x,R(x \ y,u,w)). R(x,y,x) * (T(x,z) \ u) = K(z,x) * ((u / x) * R(x,y,x)). K(x,y) * ((z / y) * R(y,u,y)) = R(y,u,y) * (T(y,x) \ z). K(x \ y,z \ y) * (y / x) = T(T(T(y,x \ y) / x,y),y / z). T(T(T(x,y \ x) / y,x),x / z) = K(y \ x,z \ x) * (x / y). x != K(y \ z,u) * (z / y) | x = T(z / y,T(u,y)). T(T(T(x,y \ x) / y,x),x / z) = T(x / y,T(z \ x,y)). T(x / y,x / z) = T(x / y,T(z \ x,y)). T(x / y,T(z \ x,y)) = T(x / y,x / z). T(x / y,T(z \ (y \ x),y)) = T(x / y,x / (y * z)). x != T(y,y \ z) \ R(T(u,u \ w),v5,v6) | x = ((y \ z) \ z) \ R((u \ w) \ w,v5,v6). x \ (y \ ((R(x,z,u) * (x \ y)) * x)) = ((x \ y) \ y) \ R((x \ y) \ y,z,u). ((x \ y) \ y) \ R((x \ y) \ y,z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x)). K(x,y) * (L(K(y,x),z,u) * w) = (K(x,y) * L(K(x,y) \ 1,z,u)) * w. (K(x,y) * L(K(x,y) \ 1,z,u)) * w = K(x,y) * (L(K(y,x),z,u) * w). (K(x,y) * L(K(y,x),z,u)) * w = K(x,y) * (L(K(y,x),z,u) * w). a(x,y,K(z,u)) * w = K(z,u) * (L(K(u,z),y,x) * w). K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w. x != K(y,z) * (L(K(u,y),w,v5) * v6) | x = L(K(u,y),w,v5) * (K(y,z) * v6). a(x,y,K(z,u)) * w = L(K(u,z),y,x) * (K(z,u) * w). L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(y,x)) * w. K(x,y) * z = a(u,w,K(x,y)) * (L(K(x,y),w,u) * z). a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w. x * y != K(z,u) * (K(u,z) * w) | x \ w = y. a(x,y,K(z,u)) \ w = L(K(z,u),y,x) * (K(u,z) * w). L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(x,y)) \ w. x != L(K(y,z),u,w) * (K(z,y) * v5) | x = a(w,u,K(z,y)) * v5. a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w. (x * a(y,z,K(u,w))) \ x = a(y,z,K(w,u)). x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u)). a(x,y,K(z,u)) \ w != v5 * w | a(x,y,K(u,z)) = v5. x / (a(y,z,K(u,w)) * x) != v5 | v5 = a(y,z,K(w,u)). x / (a(y,z,K(u,w)) * x) != v5 | a(y,z,K(w,u)) = v5. a(x,y,K(z,u)) = (T(w,w \ v5) * a(x,y,K(u,z))) \ ((w \ v5) \ v5). (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) = a(z,u,K(v5,w)). x / a(y,z,K(u,w)) = x * a(y,z,K(w,u)). x / a(y,z,K(u,w)) != v5 | v5 = x * a(y,z,K(w,u)). x / a(y,z,K(u,w)) != v5 | x * a(y,z,K(w,u)) = v5. K(x,y) * (R(K(y,x),z,u) * w) = (K(x,y) * R(K(x,y) \ 1,z,u)) * w. (K(x,y) * R(K(x,y) \ 1,z,u)) * w = K(x,y) * (R(K(y,x),z,u) * w). (K(x,y) * R(K(y,x),z,u)) * w = K(x,y) * (R(K(y,x),z,u) * w). x != L(y * K(z,y),u,w) \ L(y,u,w) | x = K(L(y,u,w),z). K(L(x,y,z),u \ L(K(x,w),v5,v6)) = K(L(x,y,z),u \ 1). x != K(y,K(z,u \ 1) / u) | x = K(T(y,z),u \ 1). K(T(x,((y \ 1) / ((1 / (y \ 1)) \ z)) \ 1),y \ 1) = K(T(x,z),y \ 1). K(T(x,((y \ 1) / (y \ z)) \ 1),y \ 1) = K(T(x,z),y \ 1). x != K(T(y,(z / u) \ 1),z) | x = K(T(y,z \ u),z). K(T(x,y),z \ 1) = K(T(x,(z \ 1) \ (z \ y)),z \ 1). K(T(x,(y \ 1) \ (y \ z)),y \ 1) = K(T(x,z),y \ 1). K(T(x,y \ z),y \ 1) = K(T(x,z),y \ 1). T(x * L(K(y,z),u,w),K(z,v5)) = T(x,K(z,v5)) * L(K(y,z),u,w). L(K(x,y),z,u) \ T(w,K(y,v5)) = T(L(K(x,y),z,u) \ w,K(y,v5)). L(K(x,y),z,u) \ T(w,K(y,v5)) = T(L(K(y,x),z,u) * w,K(y,v5)). L(K(x,y),z,u) * T(w,K(x,v5)) = T(L(K(x,y),z,u) * w,K(x,v5)). T(L(K(x,y),z,u) * w,K(x,v5)) = L(K(x,y),z,u) * T(w,K(x,v5)). x != y * T(T(z,y),u) | x = T(z,u) * y. T(L(K(x,y),z,u) * T(w,L(K(x,y),z,u)),K(x,v5)) = T(w,K(x,v5)) * L(K(x,y),z,u). x != L(K(y,z),T(z,u),w) | x = K(y,z). (x * T(y,z)) \ (x * R(y,z,L(y,u,w))) = K(z * L(y,u,w),y). x != T(y,(((z \ 1) \ 1) \ u) \ w) | x = T(y,(z \ u) \ w). T(x,y / (((z \ 1) \ 1) \ u)) = T(T(x,K(y,z \ u)),(z \ u) \ y). T(T(x,K(y,z \ u)),(z \ u) \ y) = T(x,y / (((z \ 1) \ 1) \ u)). x != T(T(y,K(z,u)),u \ z) | x = T(y,z / u). T(x,y / (((z \ 1) \ 1) \ u)) = T(x,y / (z \ u)). K(x \ T(x * y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u). K(x \ T(y * x,z),u) = K((x \ 1) * T(y / (x \ 1),z),u). K((x \ 1) * T(y / (x \ 1),z),u) = K(x \ T(y * x,z),u). K(x,y) * ((y * R(x,z,R(x,u,w))) * x) = (R(x,z,R(x,u,w)) * y) * x. x != K(y,z) * ((z * R(y,u,w)) * y) | x = (y * z) * R(y,u,w). (R(x,y,R(x,z,u)) * w) * x = (x * w) * R(x,y,R(x,z,u)). x != ((y * z) / y) / ((y * (z * K(u,z))) / y) | x = K(z,T(u,y)). K(x,T((K(x,y) * z) / u,w)) = K(x,T(z / u,w)). K(x,T(y / z,u)) = K(x,T((y * K(w,x)) / z,u)). K(x,T((y * K(z,x)) / u,w)) = K(x,T(y / u,w)). K(x \ y,x) * (y * (x \ (y / x))) = ((1 / x) * y) * (y * (x \ 1)). x != K(y \ z,y) * (z * (y \ (z / y))) | x = (z / y) * (y \ z). ((1 / x) * y) * (y * (x \ 1)) = (y / x) * (x \ y). x != (y / z) * (z \ y) | x = (z \ y) * (y / z). ((1 / x) * y) * (y * (x \ 1)) = (x \ y) * (y / x). x != (y * z) * T((y * z) \ (u * z),w) | x = (y * T(y \ u,w)) * z. K(x,y) * (K(z,x) * u) = ((1 / z) * T((1 / z) \ K(x,y),x)) * u. ((1 / x) * T((1 / x) \ K(y,z),y)) * u = K(y,z) * (K(x,y) * u). (K(x,y) * K((1 / z) \ 1,x)) * u = K(x,y) * (K(z,x) * u). (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u). L(x,K(y,z),K(z,u)) = x. (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u). x \ (K(y,z) * (K(u,y) * x)) != w | T(K(y,z) * K(u,y),x) = w. (K(x,y) * K(y,z)) * u = K(y,z) * (K(x,y) * u). a(x,y,x) * z = K(x,y) * (K(x * y,x) * z). K(x,y) * (K(x * y,x) * z) = a(x,y,x) * z. x != T(y / (y / z),z \ y) | x = z. L(T(x / (x / y),y \ x),K(z,u),K(u,w)) = y. x != L(K(y,z) * (K(u,w) * v5),K(z,y),K(w,u)) | x = (K(w,u) * K(z,y)) \ v5. K(x,y) * (K(z,x) * u) = (K(x,z) * K(y,x)) \ u. (K(x,y) * K(z,x)) \ u = K(x,z) * (K(y,x) * u). L(x,K(y,z),K(y,u)) = x. L(x,K(y,T(z,u)),K(z,w)) = x. L(x,K(y,z),K(u,K(z,w))) = x. K(x,y) * (K(z,y) * u) = (K(y,z) * K(y,x)) \ u. (K(x,y) * K(x,z)) \ u = K(z,x) * (K(y,x) * u). (K(x,y) * K(x,z)) * u = K(x,y) * (K(x,z) * u). L(x,K(y,z),K(u,y)) = x. K(x,y) * (K(y,z) * u) = (K(z,y) * K(y,x)) \ u. (K(x,y) * K(y,z)) \ u = K(z,y) * (K(y,x) * u). x != L(y * K(z * u,y),u,z) | x = (z * (u * y)) / (z * u). x * K(K(y,z) * K(z,u),x) = (K(y,z) * (K(z,u) * x)) / (K(y,z) * K(z,u)). (K(x,y) * (K(y,z) * u)) / (K(x,y) * K(y,z)) = u * K(K(x,y) * K(y,z),u). (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u). (K(x,y) * K(z,T(x,u))) * w = K(x,y) * (K(z,T(x,u)) * w). (K(x,K(y,z)) * K(u,y)) * w = K(x,K(y,z)) * (K(u,y) * w). a(x,y,x) * z = K(x * y,x) * (K(x,y) * z). K(x * y,x) * (K(x,y) * z) = a(x,y,x) * z. K(x,y) * z = a(x,y,x) * (K(x,x * y) * z). a(x,y,x) * (K(x,x * y) * z) = K(x,y) * z. T(x,R(y / (y / z),u,z)) = T(x,y / (y / z)). x * a(y,z,y) = a(y,z,y) * x. a(x,y,x) * z = z * a(x,y,x). T(x,a(y,z,y)) = x. K(x,x * y) * (a(x,y,x) * z) = K(x,y) * z. x * y != K(z * u,z) * (K(z,u) * x) | T(a(z,u,z),x) = y. T(a(x,y,x),z) = a(x,y,x). K(x * y,y) * (K(y,x) * z) = a(y,x,y) * z. (a(x,y,x) \ z) * a(x,y,x) = z. a(x,y,x) \ z = z / a(x,y,x). x / a(y,z,y) = a(y,z,y) \ x. K(x,a(y,z,y)) = 1. x / a(y,z,y) != u | a(y,z,y) \ x = u. x * K(y,a(z,u,z)) = x. x != T(y,a(z,u,z)) | x = y. T(x,a(y,z,y)) != u | u = x. R(a(x,y,x),z,u) * w = w * R(a(x,y,x),z,u). x * a(y,z,y) != u * x | u = a(y,z,y). x * a(y,z,y) != u * x | a(y,z,y) = u. x * a(y,z,y) = (a(y,z,y) \ 1) \ x. (a(x,y,x) \ 1) \ z = z * a(x,y,x). x != R(y,z,u) * a(w,R(y,z,u),w) | x = R(y * a(w,y,w),z,u). a(x,R(y,z,u),x) * R(y,z,u) = R(y * a(x,y,x),z,u). x * y != z * a(u,w,u) | x \ (a(u,w,u) * z) = y. (x * a(y,z,y)) \ (a(y,z,y) * (u * x)) = R(T(u,x * a(y,z,y)),x,a(y,z,y)). L(x \ (a(y,z,y) \ u),x,a(y,z,y)) = (x * a(y,z,y)) \ u. (x * y) \ ((x * a(z,u,z)) * y) = R(T(a(z,u,z),x * y),x,y). (x * a(y,z,y)) \ (a(y,z,y) * (u * x)) != w | L(T(u,x),x,a(y,z,y)) = w. K(x,x * y) * z = K(x,y) * (a(x,y,x) \ z). K(x,y) * (a(x,y,x) \ z) = K(x,x * y) * z. (x / y) \ (a(y,z,y) \ x) = L(y,z,y). x != y * a(z,u,z) | x = a(z,u,z) * y. (a(x,y,x) \ 1) \ z = a(x,y,x) * z. (x \ 1) * a(y,z,y) = x \ a(y,z,y). a(x,y,x) \ z = (a(x,y,x) \ 1) * z. (a(x,y,x) \ 1) * z = a(x,y,x) \ z. T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y). (x \ 1) * y != x \ (z / x) | y = z * (x \ 1). x / a(y,z,y) = x * (a(y,z,y) \ 1). x * (a(y,z,y) \ 1) = x / a(y,z,y). L(x,y,x) * z != u / a(x,y,x) | z = x \ u. a(x,y,x) \ 1 = x \ L(x,y,x). x * (y \ L(y,z,y)) = x / a(y,z,y). x != y / a(z,u,z) | x = a(z,u,z) \ y. x * (y \ L(y,z,y)) = a(y,z,y) \ x. x != y * (z \ L(z,u,z)) | x = (y / R(z,u,z)) * z. a(x,y,x) \ z = (z / R(x,y,x)) * x. (x / R(y,z,y)) * y = a(y,z,y) \ x. (a(x,y,x) * (z * x)) / R(x,y,x) = z. x * R(y,z,y) = a(y,z,y) * (x * y). a(x,y,x) * (z * x) = z * R(x,y,x). (x * R(y,z,y)) / (x * y) = a(y,z,y). x != a(y,z,y) * u | x = u * a(y,z,y). x * R(y,z,y) = (x * y) * a(y,z,y). (x * y) * a(y,z,y) = x * R(y,z,y). x * y != a(z,u,z) * (w * z) | x \ (w * R(z,u,z)) = y. (x * y) \ (x * R(y,z,y)) = a(y,z,y). x != (y * R(z,u,z)) / (y * z) | x = R(a(z,u,z),z,y). a(x,y,x) = R(a(x,y,x),x,z). R(a(x,y,x),x,z) = a(x,y,x). a(x,y,x) * (z * x) != u | u = z * R(x,y,x). a(x,y,x) * (z * x) != u | z * R(x,y,x) = u. x != R(y,R(z,u,w),u * w) | x = ((y * R(z,u,w)) * (u * w)) / ((z * u) * w). a(R(x,y,z),u,R(x,y,z)) = ((a(R(x,y,z),u,R(x,y,z)) * R(x,y,z)) * (y * z)) / ((x * y) * z). ((a(R(x,y,z),u,R(x,y,z)) * R(x,y,z)) * (y * z)) / ((x * y) * z) = a(R(x,y,z),u,R(x,y,z)). x * a(y,z,y) = (x / y) * R(y,z,y). (x / y) * R(y,z,y) = x * a(y,z,y). (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x)). x != (y / z) * R(z,u,z) | x = R(z,u,z) * (z \ y). x * a(y,z,y) = R(y,z,y) * (y \ x). R(x,y,x) * (x \ z) = z * a(x,y,x). (x / y) * ((y \ z) \ T(z,y)) = x * a(y,y \ z,y). K(x,y) * ((z / y) * R(y,u,y)) = y * (L(T(y,x),u,y) \ z). R(x,y,x) * z = (x * z) * a(x,y,x). (x * y) * a(x,z,x) = R(x,z,x) * y. x * (y * a(x,z,x)) = R(x,z,x) * y. R(x,y,x) * z = a(x,y,x) * (x * z). a(x,y,x) * (x * z) = R(x,y,x) * z. (x * y) \ (R(x,z,x) * y) != u | u = a(x,z,x). (x * y) \ (R(x,z,x) * y) != u | a(x,z,x) = u. x * y != z * (u * a(z,w,z)) | x \ (R(z,w,z) * u) = y. (x * y) \ (R(x,z,x) * y) = L(a(x,z,x),y,x). ((R(x,y,x) * z) * u) / ((x * z) * u) != w | R(a(x,y,x),x * z,u) = w. x * (y \ L(y,z,y)) != u | a(y,z,y) \ x = u. K(x,y) * z != K(x,x * y) * u | a(x,y,x) * z = u. K(x,x * y) * z != K(x,y) * u | a(x,y,x) * u = z. K(x * y,y) * (x * (K(y,x) * z)) = a(y,x,y) * (x * z). a(x,y,x) = L(a(x,y,x),z,x). L(a(x,y,x),z,x) = a(x,y,x). x != a(y,z,y) | x = (u * y) \ (u * R(y,z,y)). L(a(x,y,x),z,x) = (u * x) \ (u * R(x,y,x)). L(a(x \ y,z,x \ y),u,x \ y) = y \ (x * R(x \ y,z,x \ y)). x * y != K(z,u) * (K(w,z) * (K(u,z) * v5)) | (K(w,z) * v5) / y = x. (K(x,y) * z) / (K(u,y) * z) = K(x,y) * K(y,u). (K(x,y) * K(y,z)) \ u = K(y,x) * (K(z,y) * u). x != (K(y,z) * K(y,u)) \ K(y,y \ 1) | x = ((y \ K(y,z)) * T(y,u)) \ 1. K(x,y) * (K(z,y) * K(y,y \ 1)) = ((y \ K(y,z)) * T(y,x)) \ 1. x != K(y,z) * (K(z,u) * w) | x = (K(z,u) * K(y,z)) * w. (K(x,y) * K(y,z)) \ u = (K(y,x) * K(z,y)) * u. R(K(x,y),K(y,z),u) = K(x,y). x * y != K(z,u) * (K(u,w) * (K(u,z) * v5)) | (K(u,w) * v5) / y = x. (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y). x \ (K(y,z) * (K(z,u) * x)) != w | T(K(y,z) * K(z,u),x) = w. K(x,y) * R(R(K(x,y),K(y,z),u) \ 1,w,v5) = R(K(x,y) * R(K(x,y) \ 1,w,v5),K(y,z),u). R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(R(K(x,y),K(y,w),v5) \ 1,z,u). R(K(x,y),K(z,y),u) = K(x,y). T(x,R(a(y,z,y),u,w)) = x. (x * K(y,z)) / (K(u,T(z,x)) * x) = K(y,T(z,x)) * K(T(z,x),u). (K(x,T(y,z)) * K(y,u)) \ w = K(y,T(x,z)) * (K(u,y) * w). x * y != (K(z,u) * K(u,w)) \ x | T(K(u,z) * K(w,u),x) = y. T(K(x,y) * K(z,x),u) = T(K(y,x) * K(x,z),u) \ 1. T(K(x,y) * K(y,z),u) \ 1 = T(K(y,x) * K(z,y),u). x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y). (x \ T(x * (y \ 1),x)) * R(T(y \ a(x,y \ 1,x),x) \ 1,z,u) = T((y \ a(x,y \ 1,x)) * R((y \ a(x,y \ 1,x)) \ 1,z,u),x). T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = (y \ T(y * (x \ 1),y)) * R(T(x \ a(y,x \ 1,y),y) \ 1,z,u). x != L(T(y,z),u,T(y,w)) | x = L(T(y,z),u,y). (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,y). x != L(T(y,z),u,y) | x = L(T(y,z),u,T(y,w)). (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,u)). L(T(x,y),z,T(x,u)) = (y * R(x,z,x)) \ ((x * y) * x). x != K(y * z,z) * (y * u) | x = y * (K(y * z,z) * u). a(x,y,x) * (y * z) = y * (K(y * x,x) * (K(x,y) * z)). x * (K(x * y,y) * (K(y,x) * z)) = a(y,x,y) * (x * z). x * (a(y,x,y) * z) = a(y,x,y) * (x * z). a(x,y,x) * (y * z) = y * (a(x,y,x) * z). a(x,y,x) * z = y * (a(x,y,x) * (y \ z)). x * (a(y,x,y) * (x \ z)) = a(y,x,y) * z. R(x,T(K(y,z),x),T(K(u,K(z,w)),K(y,z) * x)) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x). x != L(y \ (z \ u),y,z) | x = (z * y) \ u. (x * a(y,z,y)) \ u = (a(y,z,y) * x) \ u. (a(x,y,x) * z) \ u = (z * a(x,y,x)) \ u. x != K(y,z) * ((u / z) * R(z,w,z)) | x = R(z,w,z) * (T(z,y) \ u). x * (L(T(x,y),z,x) \ u) = R(x,z,x) * (T(x,y) \ u). R(x,y,x) * (T(x,z) \ u) = x * (L(T(x,z),y,x) \ u). K(x,y) * (x * (L(T(x,z),u,x) \ w)) = R(T(x,y),u,x) * (T(x,z) \ w). T(K(x,y),z) * T(K(y,u),z) != w | T(K(y,u) * K(x,y),z) = w. (x * y) \ ((x * a(z,u,z)) * y) = R(a(z,u,z),x,y). (x * y) \ ((T(z * x,z) / z) * y) = R(a(z,x,z),x,y). x != (y * z) \ ((T(u * y,u) / u) * z) | x = L(a(u,T(y,z),u),T(y,z),z). R(a(x,y,x),y,z) = L(a(x,T(y,z),x),T(y,z),z). L(a(x,T(y,z),x),T(y,z),z) = R(a(x,y,x),y,z). L(a(x,y,x),T(y * K(z,y),z),z) = R(a(x,y * K(z,y),x),y * K(z,y),z). R(a(x,y * K(z,y),x),y * K(z,y),z) = L(a(x,y,x),T(y * K(z,y),z),z). K(x,y) * (y * (K(z,y) / y)) = ((y \ K(y,z)) * T(y,x)) \ 1. ((x \ K(x,y)) * T(x,z)) \ 1 = K(z,x) * (x * (K(y,x) / x)). x != K(y,z) * (z * u) | x = z * (K(y,z) * u). ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(z,x) * (K(y,x) / x)). ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(y,x) / T(x,z)). (x * K(y,z)) / (x * K(u,z)) = K(y,T(z,x)) * K(T(z,x),u). x != y * K(T(z,u),w) | x = y * K(z,T(w,u)). (x * K(y,z)) / (x * K(u,z)) = K(y,T(z,x)) * K(z,T(u,x)). x / (K(((y \ 1) * x) \ x,z) * (((y \ 1) * x) * R(y,y \ 1,x))) = K(z,((y \ 1) * x) \ x) * K(((y \ 1) * x) \ x,(y \ 1) * x). L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = y \ (R(x,z,(x \ y) \ y) * (x \ y)). T(x,y) * (L(T(x,z),u,x) \ w) = R(T(x,y),u,x) * (T(x,z) \ w). R(T(x,y),z,x) * (T(x,u) \ w) = T(x,y) * (L(T(x,u),z,x) \ w). (x * (y * R(x,z,u))) \ ((x * y) * R(x,z,u)) = x \ R(x,y,R(x,z,u)). a(x,y,R(x,z,u)) = x \ R(x,y,R(x,z,u)). x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u)). x \ R(x,y,R(x,z,u)) != w | a(x,y,R(x,z,u)) = w. x != y \ R(y,z,R(y,u,w)) | x = K(z * R(y,u,w),y) * K(y,z). a(x,y,R(x,z,u)) = K(y * R(x,z,u),x) * K(x,y). K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u)). x * a(x,y,R(x,z,u)) = R(x,y,R(x,z,u)). a(x,y,R(x,z,u)) \ 1 = R(x,y,R(x,z,u)) \ x. R(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u)) \ 1. K(x,y) * a(x,z,R(x,u,w)) = x \ R(T(x,y),z,R(x,u,w)). x \ R(T(x,y),z,R(x,u,w)) = K(x,y) * a(x,z,R(x,u,w)). T(x,y) \ R(T(x,y),T(z,x),R(T(x,y),u,w)) = a(T(x,y),z,R(T(x,y),u,w)). R(T(x,y),T(y,x),R(T(x,y),z,u)) \ T(x,y) = a(x,y,R(T(x,y),z,u)) \ 1. a(x,y,R(x,z,u)) * K(x,y * R(x,z,u)) = K(x,y). K(x * R(y,z,u),y) * K(y,T(x,R(y,w,v5))) = a(y,T(x,R(y,w,v5)),R(y,z,u)). a(x,y,R(x,z,u)) * T(K(y,x),w) = K(y * R(x,z,u),x) * K(y,K(x,w)). K(x * R(y,z,u),y) * K(x,K(y,w)) = a(y,x,R(y,z,u)) * T(K(x,y),w). a(x,y / R(x,z,u),R(x,z,u)) * K(x,y) = K(x,y / R(x,z,u)). T(x,y) \ R(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w)). a(x,y,R(x,z,u)) = ((x \ w) \ w) \ R((x \ w) \ w,y,R(x,z,u)). ((x \ y) \ y) \ R((x \ y) \ y,z,R(x,u,w)) = a(x,z,R(x,u,w)). T(x,y) * a(x,z,R(x,u,w)) = R(T(x,y),z,R(x,u,w)). (x * (y * L(x,z,u))) \ ((x * y) * L(x,z,u)) = x \ R(x,y,L(x,z,u)). a(x,y,L(x,z,u)) = x \ R(x,y,L(x,z,u)). x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u)). K(x,y) * a(y,x,L(y,z,u)) = K(x * L(y,z,u),y). K(x * L(y,z,u),y) != K(x,y) * w | a(y,x,L(y,z,u)) = w. (x \ (1 / y)) * K(z \ u,u \ z) = x \ ((u * z) * (1 / (y * (u * z)))). x \ ((y * z) * (1 / (u * (y * z)))) = (x \ (1 / u)) * K(z \ y,y \ z). x \ (K(y \ z,z \ y) / u) = (x \ (1 / u)) * K(y \ z,z \ y). (x \ (1 / y)) * K(z \ u,u \ z) = x \ (K(z \ u,u \ z) / y). 1 / ((x \ (y \ z)) * (z \ 1)) = (z * z) * (z \ (((z \ 1) * y) * x)). (x * x) * (x \ (((x \ 1) * y) * z)) = 1 / ((z \ (y \ x)) * (x \ 1)). x != 1 / (y * (z \ 1)) | x = z / y. (x * x) * (x \ (((x \ 1) * y) * z)) = x / (z \ (y \ x)). (x \ 1) \ (((x \ 1) * y) * z) = x / (z \ (y \ x)). L(x / (y \ (z \ x)),x,x) = x * (((x \ 1) * z) * y). (x \ 1) \ ((x \ (y / x)) * z) = x / (z \ ((y * (x \ 1)) \ x)). x / (y \ ((z * (x \ 1)) \ x)) = (x \ 1) \ ((x \ (z / x)) * y). (x * (x / (y \ (z \ x)))) \ x = (((x \ 1) * z) * y) \ (x \ 1). (((x \ 1) * y) * z) \ (x \ 1) = (x * (x / (z \ (y \ x)))) \ x. 1 / (x / (y \ (z \ x))) = (1 / (x \ 1)) * (((x \ 1) / y) / z). (1 / (x \ 1)) * (((x \ 1) / y) / z) = 1 / (x / (y \ (z \ x))). L(x,y,(z \ 1) / (z / (u \ (w \ z)))) = L(x,y,(z \ 1) * ((((z \ 1) * w) * u) \ (z \ 1))). L(x,y,(z \ 1) * ((((z \ 1) * u) * w) \ (z \ 1))) = L(x,y,(z \ 1) / (z / (w \ (u \ z)))). 1 / ((x \ (y \ z)) / z) = z * (((z \ 1) * y) * x). x / (y \ (x * (z \ x))) = (x \ 1) \ ((x \ (z / x)) * y). (x \ 1) \ ((x \ (y / x)) * z) = x / (z \ (x * (y \ x))). x != (y * (y / z)) \ y | x = z / y. (((x \ 1) * y) * z) \ (x \ 1) = (z \ (y \ x)) / x. x * (((x \ 1) / y) / z) = 1 / (x / (y \ (z \ x))). 1 / (x / (y \ (z \ x))) = x * (((x \ 1) / y) / z). 1 / (x / (y \ (z \ x))) = x * ((x \ (1 / y)) / z). L(x,y \ (z \ (u \ 1)),y \ (z \ (u \ 1))) = L(x,(u * z) * y,(u * z) * y). T(x * (y * ((z \ 1) \ 1)),z \ (1 / y)) = (((y \ 1) \ 1) * (1 / (z \ 1))) * x. x != y * T(K(z,u),w) | x * T(K(u,z),w) = y. x * T(K(y,z),u) != w | w * T(K(z,y),u) = x. x != (L(y,z,u) \ w) / (L(T(y,v5),z,u) \ w) | x = K(L(y,z,u),v5). K(L(x,y,z),L(x,y,z) \ u) = K(L(x,y,z),x \ u). ((x \ y) \ y) \ R((x \ y) \ y,K(x,z) * u,R(x,w,v5)) = x \ (y \ ((R(x,u,R(x,w,v5)) * (x \ y)) * x)). (K(x,y) * (K(y,z) * u)) * (K(y,x) * K(z,y)) = u * K(K(x,y) * K(y,z),u). R(a(x,y * K(z,y),x),y * K(z,y),z) = L(a(x,y,x),y,z). a(T(x,y),T(z,x),R(T(x,y),u,w)) = a(T(x,y),z,R(T(x,y),u,w)). x != a(T(y,z),T(T(z,y),y),R(T(y,z),u,w)) | x = a(R(y,u,w),z,y). a(T(x,y),T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x). a(x,y,R(T(x,y),z,u)) = a(R(x,z,u),y,x). R(T(x,y),y,R(T(x,y),z,u)) \ T(x,y) = a(x,y,R(T(x,y),z,u)) \ 1. R(T(x,y),y,R(T(x,y),z,u)) \ T(x,y) = a(R(x,z,u),y,x) \ 1. x != R(y,z,R(y,u,w)) \ y | x = a(y,z,R(y,u,w)) \ 1. a(R(x,y,z),u,x) \ 1 = a(T(x,u),u,R(T(x,u),y,z)) \ 1. a(T(x,y),y,R(T(x,y),z,u)) \ 1 = a(R(x,z,u),y,x) \ 1. T(x * (y * ((z \ 1) \ 1)),z \ (1 / y)) = (((y \ 1) \ 1) * z) * x. x != T(y,z \ (1 / u)) | x = T(y,z \ (u \ 1)). (((x \ 1) \ 1) * y) * z = T(z * (x * ((y \ 1) \ 1)),y \ (x \ 1)). T(x * (y * ((z \ 1) \ 1)),z \ (y \ 1)) = (((y \ 1) \ 1) * z) * x. x != y * ((1 / z) * y) | x = (y / z) * y. T(((1 / x) * (((y \ 1) \ 1) * z)) * (y * ((z \ 1) \ 1)),z \ (y \ 1)) = ((((y \ 1) \ 1) * z) / x) * (((y \ 1) \ 1) * z). ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u)). K(x \ ((y / z) \ u),L(z,w,v5)) != v6 | K(x \ ((z \ y) \ u),L(z,w,v5)) = v6. K(x \ ((x \ y) \ z),L(x,u,w)) = K(y \ z,L(x,u,w)). R(K(x,T(y / (z / u),w)),y,u) = K(x,T((y * u) / z,w)). x != R(K(y,z),u * K(w,y),v5) | x = R(K(y,z),u,v5). K(x,T(((y * K(z,x)) * u) / w,v5)) = R(K(x,T((y * K(z,x)) / (w / u),v5)),y,u). R(K(x,T((y * K(z,x)) / (u / w),v5)),y,w) = K(x,T(((y * K(z,x)) * w) / u,v5)). T(x * K(y,z),K(z,u)) = K(y,z) * T(x,K(z,u) * K(y,z)). K(x,y) * T(z,K(y,u) * K(x,y)) = T(z * K(x,y),K(y,u)). K(x,y) * T(z,K(x,y) * K(y,u)) = T(z * K(x,y),K(y,u)). T((K(x,y) \ z) * K(x,y),K(y,u)) \ z = K(K(x,y) * K(y,u),K(x,y) \ z). T(T(x,K(y,z)),K(z,u)) \ x = K(K(y,z) * K(z,u),K(y,z) \ x). K(K(x,y) * K(y,z),K(x,y) \ u) = T(T(u,K(x,y)),K(y,z)) \ u. K(x * R(T(y,z),u,w),T(T(y,v5),K(R(y,u,w),z))) = K(x * R(y,u,w),T(y,v5)). K(L(K(x,y),z,u),w \ v5) = K(L(K(x,y),z,u),w \ (v5 / x)). K(L(K(x,y),z,u),w \ (v5 / x)) = K(L(K(x,y),z,u),w \ v5). x != K(L(K(y,z),u,w),v5) | x = K(z,K(v5,L(y,u,w))). K(L(K(x,y),z,u),w \ (v5 / x)) = K(y,K(w \ v5,L(x,z,u))). K(x,K(y \ (z / u),L(u,w,v5))) = K(x,K(y \ z,L(u,w,v5))). K(x,K(y \ (z \ u),L(z,w,v5))) = K(x,K(y \ u,L(z,w,v5))). x != K(y,K(z \ (u \ (w \ v5)),L(u,z,w))) | x = K(y,K(u,(w * (z * u)) \ v5)). K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,(z * (y * w)) \ u)). x != K(y,K(z \ (u \ w),L(v5,z,u))) | x = K(v5,K(y,(u * z) \ w)). K(x,K(y,(z * (u * y)) \ w)) = K(y,K(x,(z * u) \ w)). K(x,K(y,(z * (u * x)) \ w)) = K(x,K(y,(z * u) \ w)). x != K(y,K(z,(u * (w * y)) \ ((u * y) * w))) | x = K(y,K(z,a(u,y,T(w,y)))). K(x,K(y,(z * u) \ ((z * x) * u))) = K(x,K(y,a(z,x,T(u,x)))). K(x,K(y,a(z,x,T(u,x)))) = K(x,K(y,(z * u) \ ((z * x) * u))). x != K(y,K(z,(u * w) \ ((u * y) * w))) | x = 1. K(x,K(y,a(z,x,T(u,x)))) = 1. K(x,K(y,a(z,x,u))) = 1. a(x,y,z) * 1 = T(a(x,y,z),K(u,y)). T(a(x,y,z),K(u,y)) = a(x,y,z) * 1. T(a(x,y,z),K(u,y)) = a(x,y,z). T(a(x,y \ z,u),K(y,z)) = a(x,y \ z,u). K(x,y) * a(z,x \ y,u) = a(z,x \ y,u) * K(x,y). a(x,y \ z,u) * K(y,z) = K(y,z) * a(x,y \ z,u). R(T(x,x * y),y * x,a(x,y,x)) = ((y * x) * a(x,y,x)) \ ((x * y) * x). ((x * y) * a(y,x,y)) \ ((y * x) * y) = R(T(y,y * x),x * y,a(y,x,y)). (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = R(x,K(y,T(u,z)),z * K(u,y)) * z. K(x,R(x,y,z) \ ((x * R(T(x,u),y,z)) / w)) != v5 | K(x,w \ x) = v5. K((x * (y * z)) \ u,L(z,w,v5)) != v6 | K((x * y) \ (z \ u),L(z,w,v5)) = v6. K((x * y) \ (z \ ((x * y) * u)),L(z,y,x)) = K(L(z,y,x) \ u,L(z,y,x)). K(L(x,y,z) \ u,L(x,y,z)) != w | K(x \ u,L(x,y,z)) = w. R(T(x,y * a(z,u,z)),y,a(z,u,z)) != w | L(T(x,y),y,a(z,u,z)) = w. K(x * R(y,z,u),y) * K(y,x) = a(y,T(x,R(y,w,v5)),R(y,z,u)). a(x,T(y,R(x,z,u)),R(x,w,v5)) = K(y * R(x,w,v5),x) * K(x,y). x != K(y * R(z,u,w),z) * K(z,y) | x = a(z,y,R(z,u,w)). a(x,T(y,R(x,z,u)),R(x,w,v5)) = a(x,y,R(x,w,v5)). a(x,R(x,y,z) \ u,R(x,w,v5)) = a(x,u / R(x,y,z),R(x,w,v5)). a(x,y / R(x,z,u),R(x,w,v5)) = a(x,R(x,z,u) \ y,R(x,w,v5)). a(x,T(y,x),R(x,z,u)) = a(x,y,R(x,z,u)). a(x,R(x,y,z) \ u,R(x,y,z)) * K(x,u) = K(x,u / R(x,y,z)). x != K(y,z / R(y,u,w)) | x = K(y,R(y,u,w) \ z). a(x,R(x,y,z) \ u,R(x,y,z)) * K(x,u) = K(x,R(x,y,z) \ u). R(K(x,T(y / (z / u),w)),y,u) = K(x,T(((y * K(v5,x)) * u) / z,w)). x != R(K(y,T(z / (u / w),v5)),z,w) | x = K(y,T((z * w) / u,v5)). K(x,T(((y * K(z,x)) * u) / w,v5)) = K(x,T((y * u) / w,v5)). K(x,y \ ((z * K(u,x)) * w)) = K(x,T((z * w) / y,z * w)). K(x,T((y * z) / u,y * z)) = K(x,u \ ((y * K(w,x)) * z)). K(x,y \ (z * u)) = K(x,y \ ((z * K(w,x)) * u)). K(x,y \ ((z * K(u,x)) * w)) = K(x,y \ (z * w)). K(x,y \ (z * u)) = K(x,y \ ((x * (z / x)) * u)). K(x,y \ ((x * (z / x)) * u)) = K(x,y \ (z * u)). K(x * R(T(y,z),u,w),T(T(y,v5),K(z,R(y,u,w)))) = K(x * R(y,u,w),T(y,v5)). (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = R(x,K(y,u),z * K(u,y)) * z. x != R(y,K(z,u),w * K(u,z)) * w | x = (y * K(z,u)) * (K(u,z) * w). (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = (x * K(y,u)) * (K(u,y) * z). (x * K(y,T(z,u))) * (K(z,T(y,u)) * u) = (x * K(y,z)) * (K(z,y) * u). (x * K(y,T(z,u))) * (u * K(z,y)) = (x * K(y,z)) * (K(z,y) * u). (K(x,T(y,z)) * a(K(x,u),w,v5)) * (z * K(y,x)) = (a(K(x,u),w,v5) * K(x,y)) * (K(y,x) * z). K(x * R(T(y,z),u,w),T(y,v5)) = K(x * R(y,u,w),T(y,v5)). T(T(x,y) * K(z * R(x,u,w),T(x,y)),z) = R(T(x,y),z,R(T(x,y),u,w)). T(T(x * K(y * R(x,z,u),x),w),y) = R(T(x,w),y,R(T(x,w),z,u)). x != T(T(y * K(z * R(y,u,w),y),v5),z) | x = R(T(y,v5),z,R(y,u,w)). R(T(x,y),z,R(T(x,y),u,w)) = R(T(x,y),z,R(x,u,w)). T(T(x,y),z) * (K(z * R(T(x,y),u,w),T(x,y)) * v5) = R(T(x,y),z,R(x,u,w)) * v5. K((x / y) * z,((x / y) * z) \ 1) = ((x / y) / (1 / z)) \ ((y * (x \ 1)) \ z). ((x / y) / (1 / z)) \ ((y * (x \ 1)) \ z) = K((x / y) * z,((x / y) * z) \ 1). x != K(y,(z * u) \ 1) | x = K(y,u \ (z \ 1)). ((x / y) / (1 / z)) \ ((y * (x \ 1)) \ z) = K((x / y) * z,z \ ((x / y) \ 1)). ((x / y) / (1 / z)) \ ((y * (x \ 1)) \ z) = K((x / y) * z,z \ (y * (x \ 1))). (x / y) * ((y \ x) \ (K(y \ x,y) \ z)) = (K(y,y \ x) * K(y,y \ x)) * z. (x / y) * (T(y \ x,y) \ z) = (K(y,y \ x) * K(y,y \ x)) * z. (K(x,x \ y) * K(x,x \ y)) * z = (y / x) * (T(x \ y,x) \ z). ((x / y) * ((y \ x) \ K(y,y \ x))) * z = (x / y) * (T(y \ x,y) \ z). ((x / y) * (T(y \ x,y) \ 1)) * z = (x / y) * (T(y \ x,y) \ z). ((x / y) * T(x \ y,y)) * z = (x / y) * (T(y \ x,y) \ z). L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) = (z * y) \ (z * (y * x)). L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) != w | L(x,y,z) = w. R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = ((x * y) * z) / (y * z). R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) != w | R(x,y,z) = w. R(R(x,y,(z \ u) \ u),y * T(z,z \ u),K(z \ u,z)) != w | R(x,y,z) = w. R(x,y,(z \ 1) \ 1) != u | R(x,y,z) = u. K(x,y) != z | R(K(x,y),y,u) = z. x != T(y,z) \ T(y * K(u,y),z) | x = K(u,T(y,z)). K(T(x,y) * z,T(T(x,u),w)) = K(x * z,T(T(x,u),w)). K(((x \ y) \ y) * z,T(T(x,u),w)) = K(x * z,T(T(x,u),w)). (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z). 1 * ((x \ R(x,y,z)) / K(u,R(x,w,v5))) = K(R(x,w,v5),u) * (x \ R(x,y,z)). 1 * ((x \ R(x,y,z)) * K(R(x,u,w),v5)) = K(R(x,u,w),v5) * (x \ R(x,y,z)). 1 * (x \ R(T(x,y),z,u)) = K(R(x,z,u),y) * (x \ R(x,z,u)). K(R(x,y,z),u) * (x \ R(x,y,z)) = 1 * (x \ R(T(x,u),y,z)). K(R(x,y,z),u) * (x \ R(x,y,z)) = x \ R(T(x,u),y,z). K(x,R(y,z,u)) * (y \ R(T(y,x),z,u)) = y \ R(y,z,u). K(x * y,R(T(y,z),x,y)) * (T(y,z) \ T(T(y,z),x)) = T(y,z) \ R(T(y,z),x,y). K(x,y) * (y \ R(T(y,x),z,R(T(y,u),w,v5))) = y \ R(y,z,R(T(y,u),w,v5)). T(x,y) \ R(T(x,y),z,R(T(x,u),w,v5)) = x \ R(x,z,R(T(x,u),w,v5)). K(x,y) * (y \ R(T(y,x),z,R(y,u,w))) = y \ R(y,z,R(T(y,x),u,w)). a(T(x,y),z,R(T(x,y),u,w)) = x \ R(x,z,R(T(x,y),u,w)). x \ R(x,y,R(T(x,z),u,w)) != v5 | a(T(x,z),y,R(T(x,z),u,w)) = v5. K(x,y) * (K(y,x) * a(y,z,R(y,u,w))) = y \ R(y,z,R(T(y,x),u,w)). x \ R(x,y,R(T(x,z),u,w)) = a(x,y,R(x,u,w)). x \ R(x,y,R(T(x,z),u,w)) != v5 | v5 = a(x,y,R(x,u,w)). x \ R(x,y,R(T(x,z),u,w)) != v5 | a(x,y,R(x,u,w)) = v5. a(T(x,y),z,R(T(x,y),u,w)) = a(x,z,R(x,u,w)). a(x,y,R(x,z,u)) \ 1 = a(R(x,z,u),y,x) \ 1. a(R(x,y,z),u,x) \ 1 = a(x,u,R(x,y,z)) \ 1. a(T(x,y),z,R(T(x,y),u,w)) != v5 | a(x,z,R(x,u,w)) = v5. K(x * K(y * K(z,u),w),T(u,y * K(z,u))) = K(y \ (x * T(y * K(z,u),w)),u). x != K(y,L(L(z,u,K(w,y)),v5,v6)) | x = K(y,L(z,v5,v6)). K(x,(y * (K(z,x) * u)) \ (y * (u * w))) = K(x,L(w,K(z,x) * u,y)). x != K(y,(z * (K(u,y) * w)) \ v5) | x = K(y,(z * w) \ v5). K(x,L(y,K(z,x) * u,w)) = K(x,(w * u) \ (w * (u * y))). K(x,L(y,K(z,x) * u,w)) = K(x,L(y,u,w)). K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w)). K(x,L(y,K(x,z) \ u,w)) = K(x,L(y,u,w)). (x \ 1) / (x \ K(x,L(y,z,u))) = K(L(y,K(x,w) * z,u),x). K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w))). x != (y \ 1) / (y \ K(y,z)) | x = K(z,y). K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y). K(L(x,y,z),u) = K(L(x,T(y,u),z),u). K(L(x,T(y,z),u),z) = K(L(x,y,u),z). ((x * (y * T(y,z))) \ K(z,y)) \ 1 = (K(y,z) / (1 / (x * (y * y)))) * K(y,z). (K(x,y) / (1 / (z * (x * x)))) * K(x,y) = ((z * (x * T(x,y))) \ K(y,x)) \ 1. (K(x,y) / (1 / ((1 / z) * (x * x)))) * K(x,y) = (((x * T(x,y)) \ z) * K(y,x)) \ 1. ((x \ y) / x) \ ((x \ (1 / (x / y))) * z) = K((x / y) * x,(x * (y \ x)) \ 1) * z. x != K(T(y * K(z,y),u),w) | x = K(T(y,u),T(w,z)). K((x * K(x * y,x)) * K(x,z),u) = K(T(x,z * K(y * x,z)),T(u,x * y)). K(T(x,y * K(z * x,y)),T(u,x * z)) = K((x * K(x * z,x)) * K(x,y),u). x != K(T(y,z),T(u,y * w)) | x = K(T(y,z),T(u,w)). K((x * K(x * y,x)) * K(x,z),u) = K(T(x,z * K(y * x,z)),T(u,y)). K(T(x,y * K(z * x,y)),T(u,z)) = K((x * K(x * z,x)) * K(x,y),u). x != K(T(y,z * K(u * y,z)),w) | x = K(y * K(T(y,u),z),w). K((x * K(x * y,x)) * K(x,z),u) = K(x * K(T(x,y),z),T(u,y)). x != K(y * K(T(y,z),u),T(w,z)) | x = K(K(z,y) * T(y,u),w). K((x * K(x * y,x)) * K(x,z),u) = K(K(y,x) * T(x,z),u). K(K(x * y,x) * T(x,z),u) = K(K(y,x) * T(x,z),u). x != K(K(y,z) * T(z,u),T(w,u)) | x = K(z,T(w,T(y,u))). K(K(x * y,x) * T(x,z),T(u,z)) = K(x,T(u,T(y,z))). K(x,T(y,T(z,u))) = K(x,T(y,T(x * z,u))). K(x,T(y,T(x * z,u))) = K(x,T(y,T(z,u))). x != K(y,T(z,T(y * u,w))) | x = K(y,T(z,T(u * y,w))). K(x,T(y,T(z,u))) = K(x,T(y,T(z * x,u))). K(x,T(y,T(z * x,u))) = K(x,T(y,T(z,u))). (x * (y \ 1)) * ((((z \ 1) \ 1) \ (x * (y \ 1))) \ 1) = L(z,x \ y,x \ y). (x * (y \ 1)) * (((x * (y \ 1)) \ 1) * (1 / (z \ 1))) = L(z,x \ y,x \ y). (x * (y \ 1)) * (((y \ 1) \ (x \ 1)) * (1 / (z \ 1))) = L(z,x \ y,x \ y). (x * (y \ 1)) * (((y \ 1) \ (x \ 1)) * z) = L(z,x \ y,x \ y). L(x,y * (z \ 1),y * (z \ 1)) = L(x,y \ z,y \ z). x != ((1 / y) * z) * (z * (y \ 1)) | x = (y \ z) * (z / y). (K(x \ y,x) * (y * (x \ 1))) / (1 / (y * (x \ 1))) = (x \ y) * (y / x). K(x,T(T(T(x,y) * z,u),w)) != v5 | K(x,T(T(z * T(x,y),u),w)) = v5. K(x,T(T(y * T(x,z),u),w)) = K(x,T(T(x * y,u),w)). x != y * (K(z,z \ 1) / u) | x = y * (z * (1 / (u * z))). (((x \ y) * (1 / y)) \ z) * ((1 / u) * w) = ((x \ 1) \ z) * (y * (1 / ((w \ u) * y))). x != K(a(y,z,u),T(y,w)) | x = K(a(y,z,u),y). K(x \ R(x,y,z),R(x,x \ R(x,y,z),y * z)) = K(a(x,y,z),x). 1 = K(a(x,y,z),x). K(a(x,y,z),x) = 1. T(a(x,y,z),x) = a(x,y,z). x * a(x,y,z) = a(x,y,z) * x. a(x,y,z) * x = x * a(x,y,z). K(x \ ((x \ (L(x,y,z) \ u)) \ w),L(x,y,z)) = K((x \ u) \ w,L(x,y,z)). x != K(y \ ((y \ z) \ u),L(y,w,v5)) | x = K(z \ u,L(y,w,v5)). K((x \ y) \ z,L(x,u,w)) = K((L(x,u,w) \ y) \ z,L(x,u,w)). K((L(x,y,z) \ u) \ w,L(x,y,z)) = K((x \ u) \ w,L(x,y,z)). K(L(x,y,z) * (u \ w),L(x,y,z)) = K((x \ u) \ w,L(x,y,z)). x != K((y \ z) \ u,L(y,w,v5)) | x = K(z \ (y * u),L(y,w,v5)). K(L(x,y,z) * (u \ w),L(x,y,z)) = K(u \ (x * w),L(x,y,z)). K((x \ y) * L(z,u,w),L(z,u,w)) = K(x \ (z * y),L(z,u,w)). K(x \ ((x \ (1 / L(x,y,z))) \ u),L(x,y,z)) = K((1 / x) \ u,L(x,y,z)). K((1 / x) \ y,L(x,z,u)) = K((1 / L(x,z,u)) \ y,L(x,z,u)). K((1 / L(x,y,z)) \ u,L(x,y,z)) = K((1 / x) \ u,L(x,y,z)). K(L(x,y,z) * u,L(x,y,z)) = K((1 / x) \ u,L(x,y,z)). K(x * L(y,z,u),L(y,z,u)) = K((1 / y) \ x,L(y,z,u)). x != K((y / z) \ u,L(z,w,v5)) | x = K(y \ (u * z),L(z,w,v5)). K(x * L(y,z,u),L(y,z,u)) = K(1 \ (x * y),L(y,z,u)). K(x * L(y,z,u),L(y,z,u)) = K(x * y,L(y,z,u)). x != K((y \ z) * L(u,w,v5),L(u,w,v5)) | x = K(y \ (u * z),L(u,w,v5)). K((x \ y) * z,L(z,u,w)) = K(x \ (z * y),L(z,u,w)). K(x \ (y * z),L(y,u,w)) = K((x \ z) * y,L(y,u,w)). x != K(y \ (z * u),L(z,w,v5)) | x = K((z \ y) \ u,L(z,w,v5)). K((x \ y) * z,L(z,u,w)) = K((z \ x) \ y,L(z,u,w)). K((x \ y) \ z,L(x,u,w)) = K((y \ z) * x,L(x,u,w)). x != K(y \ (z * u),L(z,w,v5)) | x = K(y \ (u * z),L(z,w,v5)). K((x \ y) * z,L(z,u,w)) = K(x \ (y * z),L(z,u,w)). K(x \ (y * z),L(z,u,w)) = K((x \ y) * z,L(z,u,w)). x != K((y \ z) \ (u * w),L(u,w,y)) | x = K(z \ (y * (u * w)),u). K(((x \ y) \ z) * u,L(u,z,x)) = K(y \ (x * (u * z)),u). x != K(y \ (z * u),L(u,w,v5)) | x = K((y / u) \ z,L(u,w,v5)). K((x \ y) * z,L(z,u,w)) = K((x / z) \ y,L(z,u,w)). K((x / y) \ z,L(y,u,w)) = K((x \ z) * y,L(y,u,w)). (x \ 1) * (L(y,x,x) * L(L(y,x,x),z,u)) = (x \ y) * L(y,z,u). (x * ((y \ 1) \ 1)) / ((z \ 1) / (1 / y)) = (x / ((T(z,y) \ 1) * (1 / y))) * (1 / y). x / ((y * z) \ K(u \ w,w \ u)) = (1 / x) \ (y * (z * K(u \ w,w \ u))). (1 / x) \ (y * (z * K(u \ w,w \ u))) = x / ((y * z) \ K(u \ w,w \ u)). (1 / x) \ (((((1 / x) * y) * y) * (1 / y)) * z) = ((x \ 1) \ 1) / (z \ ((x \ y) \ 1)). (x \ y) * (T(y,z) \ 1) = x \ K(z,y). (x \ y) * T(1 / y,z) = x \ K(y \ z,y). (x \ y) * (K(z,K(1 / y,u)) * (1 / y)) = x \ K(y \ K(z,u),y). (x \ y) * (K(z,K(y,u \ 1)) * (1 / y)) = x \ K(y \ K(z,u),y). (x \ y) * (K(y,K(z,u \ 1)) * (1 / y)) = x \ K(y \ K(z,u),y). (x \ y) * (K(y,K(z,u)) * (1 / y)) = x \ K(y \ K(z,u),y). (x \ y) * (K(y,K(z,u)) / y) = x \ K(y \ K(z,u),y). (x \ y) * (K(y,K(z,u)) / y) = x \ K(y,y \ K(z,u)). (x * ((x \ 1) * y)) * (z * (x * ((x \ 1) * y))) = y * (z * y). L(x,y,y) * (z * (y * ((y \ 1) * x))) = x * (z * x). L(x,y,y) * (z * L(x,y,y)) = x * (z * x). (x * y) * (z * (((x * ((u / y) \ u)) \ u) / z)) = (x * (z * ((x \ (u / y)) / z))) * ((u / y) \ u). (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * ((z / u) \ z)) \ z) / y)). K(x * y,T(y,z)) * (T(y,z) \ T(T(y,z),x)) = T(y,z) \ R(T(y,z),x,y). K(x * y,T(y,z)) * K(T(y,z),x) = T(y,z) \ R(T(y,z),x,y). K(x * y,T(x,z)) * K(T(x,z),y) = T(x,z) \ R(T(x,z),y,x). x != T(y,z) \ R(T(y,z),u,y) | x = y \ R(y,u,y). K(x * y,T(x,z)) * K(T(x,z),y) = x \ R(x,y,x). K(T(x,y),z) * K(x * z,T(x,y)) = x \ R(x,z,x). K(x * K(y * K(z,u),w),T(u,y)) = K(y \ (x * T(y * K(z,u),w)),u). K(x \ (y * T(x * K(z,u),w)),u) = K(y * K(x * K(z,u),w),T(u,x)). (K(x,y) / (1 / ((1 / z) * (x * x)))) * K(x,y) = K(y,x) \ (((x * T(x,y)) \ z) \ 1). ((x \ y) / x) \ ((x \ (1 / (x / y))) * z) = K((x / y) * x,(y \ x) \ (x \ 1)) * z. (x * ((y \ 1) \ 1)) / (z \ (1 / (1 / y))) = (x / ((T(z,y) \ 1) * (1 / y))) * (1 / y). (1 / x) \ ((y * ((1 / y) * ((1 / x) * y))) * z) = ((x \ 1) \ 1) / (z \ ((x \ y) \ 1)). (K(x,y) / (1 / ((1 / z) * (x * x)))) * K(x,y) = K(x,y) * (((x * T(x,y)) \ z) \ 1). ((x \ y) / x) \ ((x \ (1 / (x / y))) * z) = K((x / y) * x,x \ (y / x)) * z. ((x \ y) / x) \ ((x \ (1 / (x / y))) * z) = K(x * (y \ x),x \ (y / x)) * z. (x * ((y \ 1) \ 1)) / (z \ ((y \ 1) \ 1)) = (x / ((T(z,y) \ 1) * (1 / y))) * (1 / y). (1 / x) \ (T(y * (1 / x),y) * z) = ((x \ 1) \ 1) / (z \ ((x \ y) \ 1)). (x * (y / (1 / z))) * (1 / z) = ((z \ 1) \ 1) / (y \ ((z \ x) \ 1)). ((x \ 1) \ 1) / (y \ ((x \ z) \ 1)) = (z * (y / (1 / x))) * (1 / x). x != (y * (z / (1 / u))) * (1 / u) | x = u / (z \ ((y \ 1) * u)). ((x \ 1) \ 1) / (y \ ((x \ z) \ 1)) = x / (y \ ((z \ 1) * x)). (1 / ((x \ 1) \ 1)) \ ((x \ y) * z) = x / (z \ ((y \ 1) * x)). (x \ 1) \ ((x \ y) * z) = x / (z \ ((y \ 1) * x)). x / (y \ ((z \ 1) * x)) = (x \ 1) \ ((x \ z) * y). x != y / (z \ ((u \ 1) * y)) | x = (u * (z / (1 / y))) * (1 / y). (x \ 1) \ ((x \ y) * z) = (y * (z / (1 / x))) * (1 / x). (x * (y / (1 / z))) * (1 / z) = (z \ 1) \ ((z \ x) * y). x / (y \ (z * x)) = (x \ 1) \ ((x \ (1 / z)) * y). (x \ 1) \ ((x \ (1 / y)) * z) = x / (z \ (y * x)). L((x / (y \ (z * x))) \ 1,x,x) = x * ((y / (x \ 1)) \ z). x != (y * (z / (1 / u))) * (1 / u) | x = (1 / u) \ ((L(u,u,u) \ y) * z). (x \ 1) \ ((x \ y) * z) = (1 / x) \ ((L(x,x,x) \ y) * z). (1 / x) \ ((L(x,x,x) \ y) * z) = (x \ 1) \ ((x \ y) * z). (x * (x / (y \ (z * x)))) \ x = x * ((y / (x \ 1)) \ z). (x \ (y * z)) / z = z * ((x / (z \ 1)) \ y). x * ((y / (x \ 1)) \ z) = (y \ (z * x)) / x. (1 / x) * ((y / x) \ z) = (y \ (z * (1 / x))) / (1 / x). (x \ (y * (1 / z))) / (1 / z) = (1 / z) * ((x / z) \ y). (x / (((1 / y) \ 1) * (z / (1 / y)))) / (1 / y) = (1 / y) * (((1 / x) / y) \ ((1 / y) / z)). (K(x,y) \ (z * (1 / (1 / u)))) / (1 / (1 / u)) = (1 / (1 / u)) * (((u \ K(y,x)) \ 1) \ z). (1 / (1 / T(x,y \ 1))) \ ((L(1 / T(x,y \ 1),1 / T(x,y \ 1),1 / T(x,y \ 1)) \ y) * z) = ((1 / T(x,y \ 1)) \ 1) \ ((y * x) * z). (K(x,y) / ((x * x) \ (1 / (1 / z)))) * K(x,y) = K(x,y) * (((x * T(x,y)) \ z) \ 1). (1 / (x * ((y \ 1) \ 1))) \ ((y \ 1) * z) = (x / ((T(z,y) \ 1) * (1 / y))) * (1 / y). (K(x,y) / ((x * x) \ ((z \ 1) \ 1))) * K(x,y) = K(x,y) * (((x * T(x,y)) \ z) \ 1). ((1 / 1) \ ((x \ 1) / y)) \ ((x \ 1) * z) = (y / ((T(z,x) \ 1) * (1 / x))) * (1 / x). (K(x,y) / (x \ ((z \ x) \ 1))) * K(x,y) = K(x,y) * (((x * T(x,y)) \ z) \ 1). ((1 / K(x,y)) \ ((z \ x) * x)) * K(x,y) = K(x,y) * (((x * T(x,y)) \ z) \ 1). K(x,y) * (((z \ x) * x) * K(x,y)) = K(x,y) * (((x * T(x,y)) \ z) \ 1). K(x,y) * (((x * T(x,y)) \ z) \ 1) = K(x,y) * (((z \ x) * x) * K(x,y)). K(x,y) * (((x * T(x,y)) \ z) \ 1) = K(x,y) * ((z \ x) * T(x,y)). (x \ y) * T(y,z) = ((y * T(y,z)) \ x) \ 1. ((x * T(x,y)) \ z) \ 1 = (z \ x) * T(x,y). 1 / ((x \ y) * T(y,z)) = (y * T(y,z)) \ x. x != 1 / ((y \ z) * T(z,u)) | x = (z * z) \ (K(u,z) * y). (x * T(x,y)) \ z = (x * x) \ (K(y,x) * z). (x * x) \ (K(y,x) * z) = (x * T(x,y)) \ z. x != (y * y) \ (K(z,y) * u) | x = (1 / y) * (T(y,z) \ u). (x * T(x,y)) \ z = (1 / x) * (T(x,y) \ z). (1 / x) * (T(x,y) \ z) = (x * T(x,y)) \ z. x != (y * z) \ ((z \ (y \ 1)) \ u) | x = (y * z) * ((1 / (y * z)) * u). (1 / x) * (T(x,y) \ ((T(x,y) \ (x \ 1)) \ z)) = (x * T(x,y)) * ((1 / (x * T(x,y))) * z). (1 / (x \ 1)) * ((1 / T(x,y)) \ z) = ((x \ 1) * T(x \ 1,x * y)) \ z. ((x \ 1) * T(x \ 1,x * y)) \ z = (1 / (x \ 1)) * ((1 / T(x,y)) \ z). (1 / (x * (y \ 1))) * (((1 / y) * x) \ z) = ((x * (y \ 1)) * T(x * (y \ 1),y)) \ z. ((x * (y \ 1)) * T(x * (y \ 1),y)) \ z = (1 / (x * (y \ 1))) * (((1 / y) * x) \ z). ((x \ 1) * T(x \ 1,x * y)) \ z = x * ((1 / T(x,y)) \ z). ((x \ 1) * (1 / T(x,y))) \ z = x * ((1 / T(x,y)) \ z). (x \ (T(x,y) \ 1)) \ z = x * ((1 / T(x,y)) \ z). (1 \ ((x \ 1) / y)) \ ((x \ 1) * z) = (y / ((T(z,x) \ 1) * (1 / x))) * (1 / x). (x / ((T(y,z) \ 1) * (1 / z))) * (1 / z) = (1 \ ((z \ 1) / x)) \ ((z \ 1) * y). (x / ((T(y,z) \ 1) * (1 / z))) * (1 / z) = (1 \ (z \ (1 / x))) \ ((z \ 1) * y). (x / ((T(y,z) \ 1) * (1 / z))) * (1 / z) = (z \ (1 / x)) \ ((z \ 1) * y). x != (y \ (1 / z)) \ ((y \ 1) * u) | x = (z * y) / (u \ y). (x / ((T(y,z) \ 1) * (1 / z))) * (1 / z) = (x * z) / (y \ z). (x / ((1 / y) * (z \ 1))) * (1 / y) = (x * y) / (z \ y). (x / ((1 / y) * z)) * (1 / y) = (x * y) / ((1 / z) \ y). ((x * (y \ 1)) * T(x * (y \ 1),y)) \ z = (y / x) * (((1 / y) * x) \ z). ((x * (y \ 1)) * ((1 / y) * x)) \ z = (y / x) * (((1 / y) * x) \ z). T(L(x,x \ y,x),z) = L(T(x,z),x \ (y * K(u,x)),x). L(T(x,y),x \ (z * K(u,x)),x) = T(L(x,x \ z,x),y). L(T(x,y),x \ (K(z,x) * u),x) = T(L(x,x \ u,x),y). L(T(x,y),x \ (K(z,x) * u),x) = L(T(x,y),x \ u,x). L(T(x,y),T(x,z) \ u,x) = L(T(x,y),x \ u,x). L(T(x,y),T(z / T(x,u),x),x) = L(T(x,y),x \ z,x). x != T(y,y \ (((y \ 1) * z) \ 1)) | x = T(y,z \ 1). T(x,L(x * (y \ z),x \ 1,y) \ 1) = T(x,((y * (x \ 1)) \ z) \ 1). x != T(y,(z \ u) \ 1) | x = T(y,u \ z). T(x,L(x * (y \ z),x \ 1,y) \ 1) = T(x,z \ (y * (x \ 1))). x != T(y,L(y * (z \ u),y \ 1,w) \ 1) | x = T(y,u \ (y \ z)). T(x,y \ (z * (x \ 1))) = T(x,y \ (x \ z)). x != K(y,T(z,T(u,y \ w))) | x = K(y,T(z,T(u,w))). K(x,T(y,z \ (x * (z * R(u,x,x \ z))))) = K(x,T(y,T(((z * u) / z) * x,z))). x != K(y,T(z,T(u * y,w))) | x = K(y,T(z,T(u,w))). K(x,T(y,z \ (x * (z * R(u,x,x \ z))))) = K(x,T(y,T((z * u) / z,z))). K(x,T(y,z \ (x * (z * R(u,x,x \ z))))) = K(x,T(y,u)). x != K(y,T(z,u \ (y * w))) | x = K(y,T(z,u \ w)). K(x,T(y,z)) = K(x,T(y,u \ (u * R(z,x,x \ u)))). K(x,T(y,z \ (z * R(u,x,x \ z)))) = K(x,T(y,u)). K(x,T(y,R(z,x,x \ u))) = K(x,T(y,z)). x != K(y,T(z,R(y \ u,y,y \ w))) | x = K(y,T(z,(u * (y \ w)) / w)). K(x,T(y,x \ z)) = K(x,T(y,(z * (x \ u)) / u)). K(x,T(y,(z * (x \ u)) / u)) = K(x,T(y,x \ z)). K(x,T(y,(z * (x \ u)) / u)) = K(x,T(y,z)). K(x,T(y,z / u)) = K(x,T(y,z / (x \ u))). K(x,T(y,z / (x \ u))) = K(x,T(y,z / u)). T(x,T(y,z / (x \ u))) = x * K(x,T(y,z / u)). T(x,T(y,z / (x \ u))) = T(x,T(y,z / u)). x != T(y,T((z * (y \ 1)) / u,u / (y \ 1))) | x = T(y,(u / (y \ 1)) \ z). T(x,T((y * (x \ 1)) / z,z / 1)) = T(x,(z / (x \ 1)) \ y). T(x,T((y * (x \ 1)) / z,z)) = T(x,(z / (x \ 1)) \ y). T(x,y \ (z * (x \ 1))) = T(x,(y / (x \ 1)) \ z). T(x,(y / (x \ 1)) \ z) = T(x,y \ (z * (x \ 1))). x != T(y,z \ (u * (y \ 1))) | x = T(y,z \ (y \ u)). T(x,(y / (x \ 1)) \ z) = T(x,y \ (x \ z)). x != T(y,(z / (y \ 1)) \ u) | x = T(y,((y \ 1) \ z) \ u). T(x,y \ (x \ z)) = T(x,((x \ 1) \ y) \ z). T(x,((x \ 1) \ y) \ z) = T(x,y \ (x \ z)). T(x,T(y,x \ 1) \ z) = T(x,(y * (x \ 1)) \ (x \ z)). T(x,(y * (x \ 1)) \ (x \ z)) = T(x,T(y,x \ 1) \ z). x != T(y,(z * (y \ 1)) \ (y \ u)) | x = T(y,R(z,y \ 1,y) \ u). T(x,T(y,x \ 1) \ z) = T(x,R(y,x \ 1,x) \ z). T(x,R(y,x \ 1,x) \ z) = T(x,T(y,x \ 1) \ z). x != T(y,T(z,y \ 1) \ u) | x = T(y,z \ u). T(x,R(y,x \ 1,x) \ z) = T(x,y \ z). x != T(y,R(z,y \ 1,y) \ (y * u)) | x = T(y,(z * (y \ 1)) \ u). T(x,y \ (x * z)) = T(x,(y * (x \ 1)) \ z). T(x,(y * (x \ 1)) \ z) = T(x,y \ (x * z)). T(x,x * (y \ z)) = T(x,y \ (x * z)). T(x,y \ (x * z)) = T(x,x * (y \ z)). x != T(y,z \ (y * (u \ z))) | x = T(y,T(u \ y,z)). T(x,x * (y \ (z \ y))) = T(x,T(z \ x,y)). K(x \ (y \ x),z) * T(z,T(y \ z,x)) = L(z,x \ (y \ x),z). K(x * R(y,z,u),y) * K(y,K(w,x)) = T(K(x * R(y,z,u),T(y,x)),w). K(x * R(y,z,u),y) * K(x,K(y,w)) = T(K(x * R(y,z,u),T(y,x)),w). K(x * R(y,z,u),y) * K(x,K(y,w)) = T(K(x * R(y,z,u),y),w). x != K(y * R(z,u,w),z) * K(y,K(z,v5)) | x = a(z,y,R(z,u,w)) * T(K(y,z),v5). T(K(x * R(y,z,u),y),w) = a(y,x,R(y,z,u)) * T(K(x,y),w). a(x,y,R(x,z,u)) * T(K(y,x),w) = T(K(y * R(x,z,u),x),w). T(K(x * R(y,z,u),y),w) * T(K(y,x),w) = a(y,x,R(y,z,u)). T(K(x,y) * K(y * R(x,z,u),x),w) = a(x,y,R(x,z,u)). K(x \ (L(y,z,u) * w),T(y,L(y,z,u) \ x)) = K((((L(y,z,u) \ x) \ w) \ w) \ w,y). K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K(u \ (L(x,y,z) * w),T(x,L(x,y,z) \ u)). R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,x) = T(K(z,y),T(x,K(y,z))). x != T(K(y,z),T(u,K(w,y))) | x = K(y,T(z,u)). R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,x) = K(z,T(y,x)). T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x)). K(L(x,y * z,u),(x * y) \ (x * (y * z))) = K(x,L(L(z,y,x),x * y,u)). K(L(x,y * z,u),L(z,y,x)) = K(x,L(L(z,y,x),x * y,u)). x != K(L(y,z,u),L(w,v5,y)) | x = K(L(y,z,u),w). K(x,L(L(y,z,x),x * z,u)) = K(L(x,z * y,u),y). K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u)). x != K(y,L(L(z,u,y),w,v5)) | x = K(y,L(z,w,v5)). K(L(x,y * z,u),z) = K(x,L(z,x * y,u)). K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u)). K(L(x,y,z),u) = K(x,L(u,x * (y / u),z)). K(x,L(y,x * (z / y),u)) = K(L(x,z,u),y). K(L(x,T(y * (x \ z),y),u),R(y,x \ z,y)) = K(x,L(R(y,x \ z,y),z,u)). K(R(x,y,z),u) = K(L(R(x,y,z),w,x),u). K(L(R(x,y,z),u,x),w) = K(R(x,y,z),w). x != K(L(R(y,z,u),w,v5),L(y,w,v5) * (v6 \ 1)) | x = K(R(L(y,w,v5),z,u),v6 \ L(y,w,v5)). K(R(x,y,z),L(x,u,x) * (w \ 1)) = K(R(L(x,u,x),y,z),w \ L(x,u,x)). K(R(L(x,y,x),z,u),w \ L(x,y,x)) = K(R(x,z,u),L(x,y,x) * (w \ 1)). x != K(R(y,z,u),L(y,w,y) * v5) | x = K(R(y,z,u),y * v5). K(R(L(x,y,x),z,u),w \ L(x,y,x)) = K(R(x,z,u),x * (w \ 1)). K(R(L(x,y,x),z,u),w \ L(x,y,x)) != v5 | K(R(x,z,u),w \ x) = v5. K(L(x,T(y * (x \ z),y),u),y) = K(x,L(R(y,x \ z,y),z,u)). x != K(L(y,T(z,u),w),u) | x = K(L(y,z,w),u). K(x,L(R(y,x \ z,y),z,u)) = K(L(x,y * (x \ z),u),y). a(x,y,x) * K(y,T(x,z)) = K(T(x,z * y) * y,T(x,z * y)). K(T(x,y * z) * z,T(x,y * z)) = a(x,z,x) * K(z,T(x,y)). K(x * y,T(x,z)) = a(x,y,x) * K(y,T(x,z)). a(x,y,x) * K(y,T(x,z)) = K(x * y,T(x,z)). K(x * y,T(x,z)) * K(x,T(y,z)) = a(x,y,x). K(x * T(y,z),T(x,u)) * K(x,T(T(y,u),z)) = a(x,T(y,z),x). K(((x \ y) \ y) * z,T(T(x,y),u)) * K((x \ y) \ y,T(z,u)) = a((x \ y) \ y,z,(x \ y) \ y). K(x * (y / z),x) * K(x,T(z \ y,y)) = a(x,z \ y,x). K(x * (y / z),x) * K(x,y / z) = a(x,z \ y,x). a(x,y / z,x) = a(x,z \ y,x). x != a(y,(z * u) \ u,y) | x = a(y,z \ 1,y). a(x,y / (z * y),x) = a(x,z \ 1,x). a(x,y,x) = a(x,(y \ z) \ z,x). a(x,(y \ z) \ z,x) = a(x,y,x). a(x,R(y / z,z,u),x) = a(x,(z * u) \ (y * u),x). a(x,T(y,z),x) = a(x,y,x). a(x,R(y \ z,u,w),x) = a(x,R(z / y,u,w),x). a(x,R(y / z,u,w),x) = a(x,R(z \ y,u,w),x). x != a(y,R(z / u,w,v5),y) | x = a(y,R(u \ z,w,v5),y). a(x,(y * z) \ (u * z),x) = a(x,R(y \ u,y,z),x). a(x,R(y \ z,y,u),x) = a(x,(y * u) \ (z * u),x). (x / y) \ (a(y,R(z \ u,z,w),y) \ x) = L(y,(z * w) \ (u * w),y). L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,R(y \ u,y,z),x) \ w). a(x,T(y,z),x) != u * K(x,T(T(y,w),z)) | K(x * T(y,z),T(x,w)) = u. x != K(L(y,z,u),L(K(w,y),v5,v6) * v7) | x = K(L(y,z,u),v7). K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))) = K(L(x,y,z),u \ (L(x,y,z) * L(K(x,w),v5,v6))). K(L(x,y,z),u \ (L(x,y,z) * L(K(x,w),v5,v6))) = K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))). (1 / x) \ L(((1 / x) \ (y \ 1)) \ (x * z),y * (1 / x),y * (1 / x)) = (x * y) * z. (K(x \ 1,x) * ((y * z) * u)) / (K(x \ 1,x) * (z * u)) = R(y,z * K(x \ 1,x),u). (x * y) \ (x * (y * z)) = L(z,y * K(u \ 1,u),x). L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x)). L(x,y * K(z \ 1,z),u) = L(x,y,u). L(x,y,z) = L(x,(y \ 1) \ 1,z). L(x,(y \ 1) \ 1,z) = L(x,y,z). L(x,y,z) = L(x,T(y,y \ 1),z). L(x,T(y,y \ 1),z) = L(x,y,z). L(x,y \ 1,z) = L(x,1 / y,z). L(x,1 / y,z) = L(x,y \ 1,z). L(x,K(y \ 1,y) * z,u) = L(x,z,u). L(x,y * (z \ 1),u) = L(x,y * (1 / z),u). L(x,y * (1 / z),u) = L(x,y * (z \ 1),u). L(x,y / T(1 / z,u),w) = L(x,y / T(z \ 1,u),w). (x * T(y,y \ 1)) * L(z,y,x) = x * (T(y,y \ 1) * z). L(x,((y \ 1) \ 1) \ z,u) = L(x,((z \ 1) * y) \ 1,u). L(x,(y \ z) * (1 / y),u) = L(x,(y * (z \ y)) \ 1,u). L(x,(y * (z \ y)) \ 1,u) = L(x,(y \ z) * (1 / y),u). L(x,1 / ((y / z) \ z),u) = L(x,z \ (1 / (z / y)),u). L(L(x,y \ 1,L(z,y,y)),z / y,K(L(z,y,y),u)) = L(x,1 / y,T(L(z,y,y),u)). L(x,K(y \ z,z \ y) * u,w) = L(x,u,w). L(x,(y \ K(y,z)) * T(y,u),w) = L(x,K(y,z) * K(y,u),w). L(x,y * (K(z,u) / T(u,w)),v5) = L(x,y * ((K(u,z) * T(u,w)) \ 1),v5). L(x,y * ((K(z,u) * T(z,w)) \ 1),v5) = L(x,y * (K(u,z) / T(z,w)),v5). L(x,K(y \ z,z \ y) * u,w) = v5 * (v5 \ L(x,u,w)). L(x,((y \ 1) \ 1) \ z,u) = L(x,y \ ((z \ 1) \ 1),u). L(x,(y \ z) \ (z \ 1),u) = L(x,(z \ y) * (1 / z),u). L(x,(1 / y) * (z / y),u) = L(x,y \ (1 / (y / z)),u). L(x,y \ (1 / (y / z)),u) = L(x,(1 / y) * (z / y),u). L(x,K(y \ z,z \ y) * u,w) != v5 | L(x,u,w) = v5. L(x,K(y,y \ 1) * z,u) != w | L(x,z,u) = w. L(x,(y \ 1) \ 1,z) != u | L(x,y,z) = u. L(x,1 / y,z) != u | L(x,y \ 1,z) = u. (x / y) \ L(x * (y \ z),y,y) != u | L(z,y \ 1,L(x,y,y)) = u. L(x,(y \ 1) \ z,u) = L(x,(1 / y) \ ((z \ 1) \ 1),u). L(x,(1 / y) \ ((z \ 1) \ 1),u) = L(x,(y \ 1) \ z,u). L(x,y \ (1 / (y / z)),u) = L(x,(y \ z) / y,u). L(x,y / (1 / z),u) = L(x,(y \ 1) \ z,u). L(x,T(y,(1 / z) \ y),u) = L(x,(((1 / z) * y) \ 1) \ z,u). x * (T(y,y \ 1) * z) != (x * T(y,y \ 1)) * u | L(z,y,x) = u. (x * T(y,y \ 1)) * z != x * (T(y,y \ 1) * u) | L(u,y,x) = z. L(x,T(y,y * z),u) = L(x,(((1 / z) * y) \ 1) \ z,u). L(x,T(y,y * z),u) = L(x,(y \ z) \ z,u). L(x,y * (T(z,u) \ K(w,z)),v5) = L(x,y * (K(u,z) / T(z,w)),v5). L(x,y * (K(z,u) / T(u,w)),v5) = L(x,y * (T(u,z) \ K(w,u)),v5). K(x,R(K(y,R(z,u,w) \ z),z,u * w)) = K(x,K(a(z,u,w),T(y,z * (u * w)))). x != K(y,R(K(z,u),w,v5)) | x = K(y,K(u,R(z,w,v5))). K(x,K(a(y,z,u),T(w,y * (z * u)))) = K(x,K(R(y,z,u) \ y,R(w,y,z * u))). K(x,K(R(y,z,u) \ y,R(w,y,z * u))) = K(x,K(a(y,z,u),T(w,y * (z * u)))). (x * (y * z)) \ ((x * K(z,y)) * (y * z)) = L(K(z,y),T(x,y * z),y * z). K(x,((y / z) * (z * x)) \ (y * (z * x))) = L(K(x,z),T(y,z * x),z * x). K(x,((y / z) * z) \ (x \ (y * (z * x)))) = L(K(x,z),T(y,z * x),z * x). K(x,y \ (x \ (y * (z * x)))) = L(K(x,z),T(y,z * x),z * x). L(K(x,y),T(z,y * x),y * x) = K(x,z \ (x \ (z * (y * x)))). x != K(y,z \ (y \ (z * (u * y)))) | x = K(y,L(u,y,z)). L(K(x,y),T(z,y * x),y * x) = K(x,L(y,x,z)). L(K(x,y),z,y * x) = K(x,L(y,x,((y * x) * z) / (y * x))). K(x,L(y,x,((y * x) * z) / (y * x))) = L(K(x,y),z,y * x). x != K(y,L(z,y,u)) | x = K(y,z). L(K(x,y),z,y * x) = K(x,y). x != K(y,z) | x = K(y,L(z,y,u)). L(K(x,y),z,y * x) = K(x,L(y,x,u)). K(x,y) * ((y * x) * z) = (y * x) * (K(x,y) * z). K(x,L(y,x,z)) != u | u = K(x,y). K(x,L(y,x,z)) != u | K(x,y) = u. L(K(x,y),z,y * x) != u | K(x,y) = u. L(K(x,y),z * x,u) != w | K(L(x,z,u),y) = w. K(L(x,y,z),u \ (w * x)) != v5 | K(L(x,y,z),x * (u \ w)) = v5. K(L(x,y,z),x \ ((u * (x \ w)) \ v5)) != v6 | K(L(x,y,z),(u * w) \ v5) = v6. (x * y) \ (K(x,y) * ((y * x) * z)) = L(z,K(x,y),y * x). L(x,y * z,K(z,y)) = L(x,K(z,y),y * z). L(x,K(y,z),z * y) = L(x,z * y,K(y,z)). L(x,K(y,z),z * y) != u | L(x,z * y,K(y,z)) = u. L(L(x,y,z),K(y,z),z * y) != u | L(x,T(y,z),z) = u. K(L(x,y,z),u \ (x * w)) != v5 | K(L(x,y,z),x * (u \ w)) = v5. (x * (y * z)) * K(z,L(y,z,x)) = (y * z) * T(x * K(z,y),y * z). x * (y * z) = (z * y) * T(x * K(y,z),z * y). (x * y) * T(z * K(y,x),x * y) = z * (y * x). x * y != (z * u) * T(w * K(u,z),z * u) | (w * (u * z)) / y = x. (x * (y * z)) / (z * y) = x * K(y,z). x / (y * z) = (x / (z * y)) * K(z,y). (x / (y * z)) * K(y,z) = x / (z * y). (x / (y * z)) * y = (x / (z * y)) * (y * K(z,y)). (x / (y * z)) * (z * K(y,z)) = (x / (z * y)) * z. K(x / (y * z),y) != u | K(x / (z * y),y) = u. K(x,y / (z * x)) != u | K(x,y / (x * z)) = u. (x / (y * z)) * ((y * z) / y) = (x / (z * y)) * z. ((x / (y * z)) * y) * z != u | ((x / (z * y)) * y) * T(z,y) = u. L(x,(y \ z) * (1 / y),(y \ z) * (1 / y)) != u | L(x,y * (z \ y),y * (z \ y)) = u. T(x * L(K(y,z),u,w),K(y,v5)) = T(x,K(y,v5)) * L(K(y,z),u,w). T(T(x,y),z) * (K(z * R(x,u,w),T(x,y)) * v5) = R(T(x,y),z,R(x,u,w)) * v5. T(T(x,y),z) * (T(T(x,y),z * R(x,u,w)) \ v5) = R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5). x != K(y,T(z,L(z,u,w) \ v5)) | x = K(y,T(z,v5)). K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K(u \ (L(x,y,z) * w),T(x,u)). x != K(y \ z,T(u,y)) | x = K(z / y,u). K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((L(x,y,z) * w) / u,x). (1 / x) \ L(((1 / x) \ (y \ 1)) \ (x * z),y * (1 / x),y * (x \ 1)) = (x * y) * z. x != y / (K(z \ 1,z) * u) | x = K(z,z \ 1) * (y / u). R(x,y * K(z \ 1,z),u) = K(z,z \ 1) * ((K(z \ 1,z) * ((x * y) * u)) / (y * u)). K(x,x \ 1) * ((K(x \ 1,x) * ((y * z) * u)) / (z * u)) = R(y,z * K(x \ 1,x),u). K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z * K(x \ 1,x),u). R(x,y,z) = R(x,y * K(u \ 1,u),z). R(x,y * K(z \ 1,z),u) = R(x,y,u). R(x,y,z) = R(x,(y \ 1) \ 1,z). R(x,(y \ 1) \ 1,z) = R(x,y,z). R(x,y \ 1,z) = R(x,1 / y,z). R(x,1 / y,z) = R(x,y \ 1,z). R(x,y,z) * (((y \ 1) \ 1) * z) = (x * ((y \ 1) \ 1)) * z. x != R(y,1 / z,z / u) | x = R(y,1 / z,(z \ 1) \ (1 / u)). R(x,y \ 1,y / z) = R(x,1 / y,(y \ 1) \ (1 / z)). R(x,1 / y,(y \ 1) \ (1 / z)) = R(x,y \ 1,y / z). 1 / R(T(x,(1 / x) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1. x != R(L(y,z,z),1 / z,(z \ 1) \ (1 / u)) | x = ((z / u) \ (z * (1 / y))) \ u. R(L(x,y,y),y \ 1,y / z) = ((y / z) \ (y * (1 / x))) \ z. (x * ((y \ 1) \ 1)) * z != u * (((y \ 1) \ 1) * z) | R(x,y,z) = u. ((x / y) \ (x * (1 / z))) \ y = L(R(z,x \ 1,x / y),x,x). L(R(x,y \ 1,y / z),y,y) = ((y / z) \ (y * (1 / x))) \ z. 1 / R(T(x,(x \ 1) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1. 1 / R(T(x,y),x \ 1,y * x) = (((1 / x) * (y * x)) \ (y * x)) \ 1. (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x). (x * (y * (z \ 1))) * (1 / (x * (y * (z \ 1)))) = K(x / (z / y),(y * (z \ 1)) \ (x \ 1)). (x * y) * ((1 / (x * y)) * K(z,z \ 1)) = (z * (1 / ((x * y) * z))) \ (y \ (x \ 1)). (x * (1 / ((y * z) * x))) \ (z \ (y \ 1)) = (y * z) * ((1 / (y * z)) * K(x,x \ 1)). (x * (1 / ((y * z) * x))) \ (z \ (y \ 1)) = (y * z) * (x * (1 / ((y * z) * x))). (x * (1 / ((y * z) * x))) \ (z \ (y \ 1)) != u | K(x \ (y * z),(y * z) \ x) = u. K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) = K(y \ (1 * ((x * z) / x)),T(u,y)). K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) = K(y \ ((x * z) / x),T(u,y)). K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) != w | K(((x * z) / x) / y,u) = w. x != K(L(y,z,u),w \ L(K(y,v5),v6,v7)) | x = K(L(y,z,u),w \ 1). K(L(x,y,z),u \ ((1 / x) \ L(K(x,w),v5,v6))) = K(L(x,y,z),(x \ u) \ 1). x != K(y,(z \ u) \ 1) | x = K(y,u \ z). K(L(x,y,z),u \ ((1 / x) \ L(K(x,w),v5,v6))) = K(L(x,y,z),u \ x). K(L(x,y,z),u \ (x * L(K(x,w),v5,v6))) = K(L(x,y,z),u \ x). K(L(x,y,z),x * (u \ L(K(x,w),v5,v6))) = K(L(x,y,z),u \ x). (x / y) * K(z * u,(z * u) \ 1) = x / ((1 / (y * (z * u))) \ (u \ (z \ 1))). x / ((1 / (y * (z * u))) \ (u \ (z \ 1))) = (x / y) * K(z * u,(z * u) \ 1). x / ((1 / (y * (z * u))) \ (u \ (z \ 1))) = (x / y) * K(z * u,u \ (z \ 1)). x / ((1 / (y * (z * u))) \ (u \ (z \ 1))) = (x / y) * K(u \ z,z \ u). x / ((y * z) \ (((z \ (y \ 1)) \ 1) * u)) = (x / u) * K(z \ y,y \ z). x / ((1 / (y * z)) * ((z \ (y \ 1)) \ u)) = (x / u) * K(z \ y,y \ z). x / (K(y \ z,z \ y) * u) = (x / u) * K(y \ z,z \ y). (x * y) / (L(y \ 1,z,u) / (y \ 1)) = (x / (y \ L(1 / y,z,u))) * (y \ 1). (x * y) / (y * L(y \ 1,z,u)) = (x / (y \ L(1 / y,z,u))) * (y \ 1). (x / (y \ L(1 / y,z,u))) * (y \ 1) = (x * y) / (y * L(y \ 1,z,u)). K(x,(y * (x \ z)) \ u) = K((x \ 1) \ 1,(y * (L(z,x \ 1,x) / x)) \ u). K((x \ 1) \ 1,(y * (L(z,x \ 1,x) / x)) \ u) = K(x,(y * (x \ z)) \ u). K(x,(y * (L(z,x \ 1,x) / x)) \ u) = K(x,(y * (x \ z)) \ u). K(x,(y * (x \ L(z,x \ 1,x))) \ u) = K(x,(y * (x \ z)) \ u). K(x,(y * ((x \ 1) * z)) \ u) = K(x,(y * (x \ z)) \ u). x != K(y,(z * ((y \ 1) * u)) \ w) | x = K(y,(z * u) \ (w * y)). K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x)). K(x,(y * (x \ z)) \ u) = K(x,x * ((y * z) \ u)). x != K(y,(z * (y \ u)) \ w) | x = L(K(y,u \ ((z \ w) * y)),z \ w,z). K(x,(y * z) \ (u * x)) = L(K(x,z \ ((y \ u) * x)),y \ u,y). L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x)). (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x). L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w). K(x,(y * (z / x)) \ u) = K(x,x * ((y * z) \ u)). K((x * y) \ (z * u),u) = K((x * (y / u)) \ z,u). K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z). K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y). K((x * (y \ z)) \ u,y) = K(y * ((x * z) \ u),y). T(x,x * K((y * z) \ (u * w),w)) \ T(K(w,(y * (w \ z)) \ u) * x,x) = K(w,T((y * (w \ z)) \ u,x)). L(x * K(x * ((y * z) \ u),x),w,v5) \ L(x,w,v5) = K(L(x,w,v5),(y * (x \ z)) \ u). x != L(K(y,z \ ((u \ w) * y)),u \ w,u) | x = K(y,(u * z) \ (w * y)). K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x)). x != K(y,(z * (u * (w / y))) \ (u * (y \ w))) | x = K(y,(u * (w / y)) \ (z \ (u * (w / y)))). K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,(z * (u / x)) \ (y \ (z * (u / x)))). K(x,(y * (z / x)) \ (u \ (y * (z / x)))) = K(x,(u * (y * z)) \ ((y * (x \ z)) * x)). K(x,T(y \ 1,z * (u / x))) = K(x,(y * (z * u)) \ ((z * (x \ u)) * x)). K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x))). x != K(y,T(z,u * (w / y))) | x = K(y,T(z,u * w)). K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u)). K(x,y \ ((z * (x \ u)) * x)) = K(x,T((y / (z * u)) \ 1,z * u)). K(x,T((y / (z * u)) \ 1,z * u)) = K(x,y \ ((z * (x \ u)) * x)). K(x,y \ (z * u)) = K(x,y \ ((z * (x \ u)) * x)). K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u)). K(x,y * (x \ z)) = K(x,x \ (y * z)). K(x,x \ (y * z)) = K(x,y * (x \ z)). (x * K(y,z * (y \ u))) \ x = K(y \ (z * u),y). K(x * (y \ z),y) = K(y \ (x * z),y). K(x \ (y * z),x) = K(y * (x \ z),x). K(x \ y,x) = K(z * (x \ (z \ y)),x). K(x * (y \ (x \ z)),y) = K(y \ z,y). (x \ (y * z)) * K(y \ (y * z),y) = x \ (z * y). (x \ (y * z)) * K(z,y) = x \ (z * y). (x * y) * K(y,z * x) = R(z,x,y) \ (y * (z * x)). R(x,y,z) \ (z * (x * y)) = (y * z) * K(z,x * y). x != (y * z) * K(z,u) | x = y * T(z,u). R(x,y,z) \ (z * (x * y)) = y * T(z,x * y). (x * (y * z)) / (z * T(x,y * z)) = R(y,z,x). R(x,y,z) = (z * (x * y)) / (y * T(z,x * y)). K(L(x,y,z),x * ((u * w) \ v5)) = K(L(x,y,z),(u * (x \ w)) \ v5). K(L(x,y,z),(u * (x \ w)) \ v5) = K(L(x,y,z),x * ((u * w) \ v5)). L(x,y,(z \ 1) * ((((z \ 1) * u) * w) \ (z \ 1))) = L(x,y,z \ (1 / (z / (w \ (u \ z))))). (x / (y * (z / (1 / y)))) / (1 / y) = (1 / y) * (((1 / x) / y) \ ((1 / y) / z)). (1 / x) * (((1 / y) / x) \ ((1 / x) / z)) = (y / (x * (z / (1 / x)))) / (1 / x). x != (y / (z * u)) / (1 / z) | x = (z * (1 / y)) \ (z / u). (1 / x) * (((1 / y) / x) \ ((1 / x) / z)) = (x * (1 / y)) \ (x / (z / (1 / x))). (1 / x) * (((1 / y) / x) \ ((1 / x) / z)) = (x * (1 / y)) \ (x * (1 / (z * x))). x != (y * z) \ (y * (1 / (u * y))) | x = (z \ (1 / y)) / u. (1 / x) * (((1 / y) / x) \ ((1 / x) / z)) = ((1 / y) \ (1 / x)) / z. (1 / x) * (((1 / y) / x) \ ((1 / x) / z)) = (y / x) / z. (1 / x) * ((1 / (x * y)) \ ((1 / x) / z)) = (y / x) / z. (1 / x) * ((1 / (x * y)) \ (1 / (z * x))) = (y / x) / z. (1 / x) * ((x * y) / (z * x)) = (y / x) / z. x != (1 / y) * ((y * z) / (u * y)) | x = L(z,y,u) / (u * y). (x / y) / z = L(x,y,z) / (z * y). L(x,y,z) / (z * y) = (x / y) / z. ((x / y) / z) * (z * y) = L(x,y,z). L(x,y,z) = ((x / y) / z) * (z * y). ((x / y) / z) * (z * y) != u | u = L(x,y,z). ((x / y) / z) * (z * y) != u | L(x,y,z) = u. L(x,y,z) / (z * y) != u | u = (x / y) / z. L(x,y,z) / (z * y) != u | (x / y) / z = u. (K(x,y) \ (z * ((u \ 1) \ 1))) / (1 / (1 / u)) = (1 / (1 / u)) * (((u \ K(y,x)) \ 1) \ z). (1 / x) * (T(x,y) \ ((x \ (T(x,y) \ 1)) \ z)) = (x * T(x,y)) * ((1 / (x * T(x,y))) * z). x != K(y,(z * (u \ 1)) \ w) | x = K(y,(u / z) * w). (x * (y * (z \ 1))) * (1 / (x * (y * (z \ 1)))) = K(x / (z / y),(z / y) * (x \ 1)). x != K(y,z * (u \ 1)) | x = K(y,z / u). (x * (y * (z \ 1))) * (1 / (x * (y * (z \ 1)))) = K(x / (z / y),(z / y) / x). x != K(y / z,z / y) | x = K(z \ y,y \ z). (x * (y * (z \ 1))) * (1 / (x * (y * (z \ 1)))) = K((z / y) \ x,x \ (z / y)). (x * (y * (z \ 1))) * ((z / y) / x) = K((z / y) \ x,x \ (z / y)). x != ((1 / y) * (z * (u \ 1))) * ((u / z) / (1 / y)) | x = ((y \ 1) * (1 / (u / z))) * ((z * (u \ 1)) \ y). K((x / y) \ (1 / z),(1 / z) \ (x / y)) = ((z \ 1) * (1 / (x / y))) * ((y * (x \ 1)) \ z). ((x \ 1) * (1 / (y / z))) * ((z * (y \ 1)) \ x) = K((y / z) \ (1 / x),(1 / x) \ (y / z)). L(x,y,(z \ 1) * ((((z \ 1) * u) * w) \ (z \ 1))) = L(x,y,z \ (z * ((z \ (1 / w)) / u))). (K(x,y) * (z * ((u \ 1) \ 1))) / (1 / (1 / u)) = (1 / (1 / u)) * (((u \ K(x,y)) \ 1) \ z). (1 / x) * (T(x,y) \ (x * ((1 / T(x,y)) \ z))) = (x * T(x,y)) * ((1 / (x * T(x,y))) * z). x != K(y,(1 / z) \ u) | x = K(y,z * u). ((x \ 1) * (1 / (y / z))) * ((z * (y \ 1)) \ x) = K((y / z) \ (1 / x),x * (y / z)). x != K(y \ (1 / z),u) | x = K(z * y,u \ 1). ((x \ 1) * (1 / (y / z))) * ((z * (y \ 1)) \ x) = K(x * (y / z),(x * (y / z)) \ 1). ((x \ 1) * (1 / (y / z))) * ((z * (y \ 1)) \ x) = K(x * (y / z),(y / z) \ (x \ 1)). ((x \ 1) * (1 / (y / z))) * ((z * (y \ 1)) \ x) = K((y / z) \ x,x \ (y / z)). x != ((y \ 1) * (1 / (z / u))) * ((u * (z \ 1)) \ y) | x = ((z / u) / (1 / y)) \ ((u * (z \ 1)) \ y). K((x / y) \ z,z \ (x / y)) = ((x / y) / (1 / z)) \ ((y * (x \ 1)) \ z). ((x / y) / (1 / z)) \ ((y * (x \ 1)) \ z) = K((x / y) \ z,z \ (x / y)). x != ((y / z) / (1 / u)) \ ((z * (y \ 1)) \ u) | x = K((y / z) * u,u \ (z * (y \ 1))). K((x / y) \ z,z \ (x / y)) = K((x / y) * z,z \ (y * (x \ 1))). K((x / y) * z,z \ (y * (x \ 1))) = K((x / y) \ z,z \ (x / y)). L(x,y,(z \ 1) * ((((z \ 1) * u) * w) \ (z \ 1))) = L(x,y,(z \ (1 / w)) / u). L(x,y,(z \ 1) * ((u \ (w \ z)) / z)) = L(x,y,(z \ (1 / u)) / w). L(x,y,(z * u) \ (w \ 1)) = L(x,y,(u \ (1 / z)) / w). L(x,y,(z \ (1 / u)) / w) = L(x,y,(u * z) \ (w \ 1)). (1 / (K(x,y) * (z * ((u \ 1) \ 1)))) \ (u \ 1) = (1 / (1 / u)) * (((u \ K(x,y)) \ 1) \ z). (1 / x) * (K(y,x) * ((1 / T(x,y)) \ z)) = (x * T(x,y)) * ((1 / (x * T(x,y))) * z). (1 / x) * ((1 / x) \ y) = (x * T(x,z)) * ((1 / (x * T(x,z))) * y). (x * T(x,y)) * ((1 / (x * T(x,y))) * z) = (1 / x) * ((1 / x) \ z). (x * T(x,y)) * ((1 / (x * T(x,y))) * z) = z. x * y != (z * T(z,u)) * ((1 / (z * T(z,u))) * w) | x \ w = y. (x * (y * T(y,z))) \ x = y \ (T(y,z) \ 1). x \ (x / (y * T(y,z))) = y \ (T(y,z) \ 1). (x \ (T(x,y) \ 1)) * z = (x * T(x,y)) \ z. x * (y \ (T(y,z) \ 1)) = x / (y * T(y,z)). ((x / y) \ ((y \ x) \ 1)) * z = ((x / y) * T(x / y,y)) \ z. ((x / y) * T(x / y,y)) \ z = ((x / y) \ ((y \ x) \ 1)) * z. x * (y \ (y \ K(z,y))) = x / (y * T(y,z)). x * ((y / z) \ ((y / z) \ K(z,y / z))) = x / ((y / z) * (z \ y)). ((x / y) * (y \ x)) \ z = ((x / y) \ ((y \ x) \ 1)) * z. ((x / y) \ ((y \ x) \ 1)) * z = ((x / y) * (y \ x)) \ z. x * ((y / z) \ ((y / z) \ K(z,z \ y))) = x / ((y / z) * (z \ y)). x * ((y / z) \ ((z \ y) \ 1)) = x / ((y / z) * (z \ y)). ((1 / 1) \ (((x \ 1) / y) / K(z,u))) \ (x \ 1) = (1 / (1 / x)) * (((x \ K(z,u)) \ 1) \ y). (1 \ (((x \ 1) / y) / K(z,u))) \ (x \ 1) = (1 / (1 / x)) * (((x \ K(z,u)) \ 1) \ y). (1 \ ((x \ (1 / y)) / K(z,u))) \ (x \ 1) = (1 / (1 / x)) * (((x \ K(z,u)) \ 1) \ y). (1 \ ((x \ (1 / y)) * K(z,u))) \ (x \ 1) = (1 / (1 / x)) * (((x \ K(u,z)) \ 1) \ y). ((x \ (1 / y)) * K(z,u)) \ (x \ 1) = (1 / (1 / x)) * (((x \ K(u,z)) \ 1) \ y). (1 / (1 / x)) * (((x \ K(y,z)) \ 1) \ u) = ((x \ (1 / u)) * K(z,y)) \ (x \ 1). x != ((y \ z) * K(u,w)) \ (y \ 1) | x = (K(w,u) * y) * (y \ (z \ 1)). (1 / (1 / x)) * (((x \ K(y,z)) \ 1) \ u) = (K(y,z) * x) * (x \ ((1 / u) \ 1)). (1 / (1 / x)) * (((x \ K(y,z)) \ 1) \ u) = (K(y,z) * x) * (x \ u). ((x \ 1) \ 1) * (((x \ K(y,z)) \ 1) \ u) = (K(y,z) * x) * (x \ u). x != ((y \ 1) \ 1) * (((y \ z) \ 1) \ u) | x = y * (((z \ 1) * y) \ u). (K(x,y) * z) * (z \ u) = z * (((K(x,y) \ 1) * z) \ u). x * (((K(y,z) \ 1) * x) \ u) = (K(y,z) * x) * (x \ u). x * ((K(y,z) * x) \ u) = (K(z,y) * x) * (x \ u). (K(x,y) * z) * (z \ u) = z * ((K(y,x) * z) \ u). (K(x,y) * (1 / z)) * (z / (u \ K(w,v5))) = (1 / z) * ((K(y,x) * (1 / z)) \ (K(v5,w) * u)). (1 / x) * ((K(y,z) * (1 / x)) \ (K(u,w) * v5)) = (K(z,y) * (1 / x)) * (x / (v5 \ K(w,u))). (1 / x) * ((K(y,z) * (1 / x)) \ (K(u,w) * v5)) = (K(z,y) / x) * (x / (v5 \ K(w,u))). x != (1 / y) * ((K(z,u) * (1 / y)) \ w) | x = (K(u,z) * (w / y)) * y. (K(x,y) / z) * (z / (u \ K(w,v5))) = (K(x,y) * ((K(v5,w) * u) / z)) * z. (K(x,y) * ((K(z,u) * w) / v5)) * v5 = (K(x,y) / v5) * (v5 / (w \ K(u,z))). (x * (K(y,y \ 1) * (z * u))) \ ((K(y,y \ 1) * (x * z)) * u) = a(x,K(y,y \ 1) * z,u). (T(x,y) * (1 / ((z * u) * x))) \ (T(x,y) * (1 / (u * x))) = R(z,u,K(x * y,x \ 1) \ 1). ((x * (K(y,y \ 1) * (z * u))) \ ((x * z) * u)) * K(y,y \ 1) = a(x,z,K(y,y \ 1) * u). L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = y \ (R(x,z,x) * (x \ y)). L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = y \ (y * a(x,z,x)). L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = a(x,z,x). a(x,y,x) = a((x \ z) \ z,y,(x \ z) \ z). a((x \ y) \ y,z,(x \ y) \ y) = a(x,z,x). K(T(x,y),z) * (K(z * R(x,u,w),T(x,y)) * v5) = R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5). (x * (K(y,y \ 1) * (z * u))) \ (K(y,y \ 1) * ((x * z) * u)) = a(x,K(y,y \ 1) * z,u). (T(x,y) * (1 / ((z * u) * x))) \ (T(x,y) * (1 / (u * x))) = R(z,u,K(x,(x * y) \ 1) * 1). (((x * (y * z)) \ ((x * y) * z)) * K(u \ 1,u)) * K(u,u \ 1) = a(x,y,K(u,u \ 1) * z). K(x,T(y,z)) * (K(y * R(x,u,w),T(x,z)) * v5) = R(T(x,z),y,R(x,u,w)) * (T(x,z) \ v5). ((x * (K(y,y \ 1) * (z * u))) \ ((x * z) * u)) * K(y,y \ 1) = a(x,K(y,y \ 1) * z,u). (T(x,y) * (1 / ((z * u) * x))) \ (T(x,y) * (1 / (u * x))) = R(z,u,K(x,y \ (x \ 1)) * 1). (a(x,y,z) * K(u \ 1,u)) * K(u,u \ 1) = a(x,y,K(u,u \ 1) * z). a(x,y,K(z,z \ 1) * u) = a(x,y,u). a(x,y,K(z,z \ 1) * u) != w | w = a(x,y,u). a(x,y,K(z,z \ 1) * u) != w | a(x,y,u) = w. x != a(y,z,K(u,u \ 1) * w) | x = ((y * (z * (K(u,u \ 1) * w))) \ ((y * z) * w)) * K(u,u \ 1). a(x,y,z) = ((x * (y * (K(u,u \ 1) * z))) \ ((x * y) * z)) * K(u,u \ 1). ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1) = a(x,y,u). a(x,y,1 / z) = a(x,y,z \ 1). a(x,y,z * (u * (1 / w))) = a(x,y,z * (u * (w \ 1))). a(x,y,(1 / z) * u) = a(x,y,(u \ z) \ 1). a(x,y,(z \ u) \ 1) = a(x,y,(1 / u) * z). a(x,y,(1 / z) * u) != w | a(x,y,(z \ 1) * u) = w. a(x,y,(z \ u) \ 1) != w | a(x,y,(u \ 1) * z) = w. ((x * (y * (z * K(u,u \ 1)))) \ ((x * y) * z)) * K(u,u \ 1) = a(x,y,z). a(x,K(y,y \ 1) / a(z,u,w),x) = a(x,((z * (u * (w * K(y,y \ 1)))) \ ((z * u) * w)) \ 1,x). a(x,((y * (z * (u * K(w,w \ 1)))) \ ((y * z) * u)) \ 1,x) = a(x,K(w,w \ 1) / a(y,z,u),x). (((x * (y * z)) \ ((x * y) * z)) * K(u \ 1,u)) * K(u,u \ 1) = a(x,K(u,u \ 1) * y,z). (T(x,y) * (1 / ((z * u) * x))) \ (T(x,y) * (1 / (u * x))) = R(z,u,K(x,y \ (x \ 1))). (a(x,y,z) * K(u \ 1,u)) * K(u,u \ 1) = a(x,K(u,u \ 1) * y,z). a(x,K(y,y \ 1) * z,u) = a(x,z,u). a(x,y * K(z,z \ 1),u) = a(x,y,u). (T(x * y,z) * L(u,y,x)) \ (T(x * y,z) * u) = L(a(x,y,u),x * (y * u),K(x * y,z)). K(x * y,K(z,L(a(x,y,u),x * (y * u),K(x * y,w)))) = K(x * y,K(z,(T(x * y,w) * u) \ L(u,y,x))). (x * R(x \ (x * y),z,u)) * K(y,w) = R(x,y,K(y,w)) * (R(y,z,u) * K(y,w)). R(x,y,K(y,z)) * (R(y,u,w) * K(y,z)) = (x * R(x \ (x * y),u,w)) * K(y,z). R(x,y,K(y,z)) * (R(y,u,w) * K(y,z)) = (x * R(y,u,w)) * K(y,z). x * (R(y,z,u) * K(y,w)) = (x * R(y,z,u)) * K(y,w). (x * R(y,z,u)) * K(y,w) = x * (R(y,z,u) * K(y,w)). K(x,y \ (z * R(x,u,w))) = K(x,(z \ y) \ R(x,u,w)). K(x,(y \ z) \ R(x,u,w)) = K(x,z \ (y * R(x,u,w))). ((x / y) * (T(y \ x,y) \ 1)) * T(z,K(y,y \ x)) = (K(y,y \ x) * z) * K(y,y \ x). ((x / y) * T(x \ y,y)) * T(z,K(y,y \ x)) = (K(y,y \ x) * z) * K(y,y \ x). ((x / y) * T(x \ y,y)) * T(z,K(x,y)) = (K(y,y \ x) * z) * K(y,y \ x). x != ((y / z) * T(y \ z,z)) * u | x = (y / z) * (T(z \ y,z) \ u). (K(x,x \ y) * z) * K(x,x \ y) = (y / x) * (T(x \ y,x) \ T(z,K(y,x))). (x / y) * (T(y \ x,y) \ T(z,K(x,y))) = (K(y,y \ x) * z) * K(y,y \ x). x != (K(y,z) * u) * K(w,z) | x = K(y,z) * (u * K(w,z)). (x / y) * (T(y \ x,y) \ T(z,K(x,y))) = K(y,y \ x) * (z * K(y,y \ x)). x != (y / z) * (T(z \ y,z) \ u) | x = y * (T(T(y,z),z) \ u). K(x,x \ y) * (z * K(x,x \ y)) = y * (T(T(y,x),x) \ T(z,K(y,x))). x != T(K(y,z) \ u,K(y,z)) | x = u * K(z,y). K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = T(K(x,T(y,z)) * u,w) * K(y,x). (x * (y * ((1 / z) * (y * (1 / z))))) * K(y * (1 / z),z) = x * ((y * (1 / z)) * ((z \ 1) * y)). ((K(x,y) * z) * ((K(y,x) \ 1) \ 1)) * K(u,y) = ((1 / (1 / K(y,x))) \ z) * (K(y,x) * K(u,y)). (K(x,T(y,z)) * K(y,T(u,z))) \ 1 = (K(y,u) * K(x,y)) \ K(K(y,u) * K(x,y),z * K(u,y)). K(x,x \ y) * (((y * (1 / x)) * (y * (1 / x))) \ z) = ((y * (1 / x)) * ((x \ 1) * y)) \ z. K(x,x \ y) * ((y * ((1 / x) * (y * (1 / x)))) \ z) = ((y * (1 / x)) * ((x \ 1) * y)) \ z. K(x,x \ y) * ((y * (x \ (y / x))) \ z) = ((y * (1 / x)) * ((x \ 1) * y)) \ z. x != K(y,y \ z) * ((z * (y \ (z / y))) \ u) | x = ((z / y) * (y \ z)) \ u. ((x * (1 / y)) * ((y \ 1) * x)) \ z = ((x / y) * (y \ x)) \ z. (x * (y \ (y \ x))) \ z = ((x / y) * (y \ x)) \ z. ((x / y) * (y \ x)) \ z = (x * (y \ (y \ x))) \ z. x != ((y / z) * (z \ y)) \ u | x = ((y / z) \ ((z \ y) \ 1)) * u. (x * (y \ (y \ x))) \ z = ((x / y) \ ((y \ x) \ 1)) * z. ((x / y) \ ((y \ x) \ 1)) * z = (x * (y \ (y \ x))) \ z. K(x,x \ 1) * ((y \ z) * ((y \ x) * (1 / x))) = ((y \ x) * (1 / x)) * (z * ((y \ x) * (1 / x))). ((x \ y) * (1 / y)) * (z * ((x \ y) * (1 / y))) = K(y,y \ 1) * ((x \ z) * ((x \ y) * (1 / y))). L(x,(y * (1 / y)) \ z,(z \ y) * (1 / y)) = L(x,(z \ y) * (1 / y),(z \ y) * (1 / y)). L(x,K(y,y \ 1) \ z,(z \ y) * (1 / y)) = L(x,(z \ y) * (1 / y),(z \ y) * (1 / y)). L(x,K(y,y \ 1) * z,(z \ y) * (1 / y)) = L(x,(z \ y) * (1 / y),(z \ y) * (1 / y)). L(x,y,(y \ z) * (1 / z)) = L(x,(y \ z) * (1 / z),(y \ z) * (1 / z)). L(x,(y \ z) * (1 / z),(y \ z) * (1 / z)) = L(x,y,(y \ z) * (1 / z)). ((((x \ 1) \ (1 / (y \ (1 / z)))) \ x) \ 1) \ (1 / u) = (z * (x * (((x \ y) \ 1) \ 1))) \ (1 / u). x != (y * (K(z,u) * w)) \ (y * w) | x = L(K(u,T(z,w)),w,y). K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = L(K(x,T(z,L(z,u,w))),L(z,u,w),y). K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = L(K(x,z),L(z,u,w),y). K(x,y) = L(K(x,y),L(y,z,u),w). L(K(x,y),L(y,z,u),w) = K(x,y). K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z). ((x \ 1) * (1 / y)) * (((x \ 1) * (1 / y)) * z) = (1 / (y * x)) * ((1 / (y * x)) * z). x != (1 / y) * ((1 / y) * z) | x = (y \ 1) * ((y \ 1) * z). ((x \ 1) * (1 / y)) * (((x \ 1) * (1 / y)) * z) = ((y * x) \ 1) * (((y * x) \ 1) * z). ((x \ 1) * (1 / y)) * (((x \ 1) * (1 / y)) * z) = (x \ (y \ 1)) * (((y * x) \ 1) * z). ((x \ 1) * (1 / y)) * (((x \ 1) * (1 / y)) * z) = (x \ (y \ 1)) * ((x \ (y \ 1)) * z). (T(x,y) * (z * R(x,u,w))) \ ((T(x,y) * z) * R(x,u,w)) = a(x,K(x,y) * z,R(x,u,w)). a(T(x,y),z,R(x,u,w)) = a(x,K(x,y) * z,R(x,u,w)). a(x,K(x,y) * z,R(x,u,w)) = a(T(x,y),z,R(x,u,w)). a(x,K(x,y) * z,R(x,u,w)) != v5 | a(T(x,y),z,R(x,u,w)) = v5. a(x,x \ y,R(x,z,u)) = a(T(x,w),T(x,w) \ y,R(x,z,u)). a(T(x,y),T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w)). K(x / y,T(z,u)) \ T(K(y \ x,z),u) = K(K(x / y,z) \ x,T(K(x / y,z),u)). K(K(x / y,z) \ x,T(K(x / y,z),u)) = K(x / y,T(z,u)) \ T(K(y \ x,z),u). K(K(x / y,z) \ x,T(K(x / y,z),u)) = K(x / y,T(z,u)) \ K(y \ x,T(z,u)). x != K(y,T(z,u)) \ w | x = K(z,T(y,u)) * w. K(K(x / y,z) \ x,T(K(x / y,z),u)) = K(z,T(x / y,u)) * K(y \ x,T(z,u)). x != K(K(y,z) \ u,T(K(y,w),v5)) | x = K(y,K(u,T(w,v5))). K(x,T(y / z,u)) * K(z \ y,T(x,u)) = K(y / z,K(y,T(x,u))). K(x,T(y / z,u)) * K(z \ y,T(x,u)) != w | K(y,K(z,T(x,u))) = w. (x * ((1 / (y * x)) * K(z \ u,u \ z))) * w = x * (1 / ((w \ (K(z \ u,u \ z) * y)) * x)). (K(x \ y,y \ x) / T(z,u \ (w \ 1))) \ (w * u) = ((w * u) * z) * K(x \ y,y \ x). x != K(L(y,z,u),L(y,z,u) \ w) | x = K(L(y,z,u),y \ w). K(L(x,y,z),(u * (1 / x)) \ w) = K(L(x,y,z),x \ ((u * (x \ (1 / L(x,y,z)))) \ w)). K(L(x,y,z),x \ ((u * (x \ (1 / L(x,y,z)))) \ w)) = K(L(x,y,z),(u * (1 / x)) \ w). K(L(x,y,z),(u * (1 / L(x,y,z))) \ w) = K(L(x,y,z),(u * (1 / x)) \ w). x != K(y,(z * (u / y)) \ w) | x = K(y,y * ((z * u) \ w)). K(L(x,y,z),(u * (1 / x)) \ w) = K(L(x,y,z),L(x,y,z) * ((u * 1) \ w)). K(L(x,y,z),L(x,y,z) * ((u * 1) \ w)) = K(L(x,y,z),(u * (1 / x)) \ w). K(L(x,y,z),L(x,y,z) * (u \ w)) = K(L(x,y,z),(u * (1 / x)) \ w). x != K(y,(z * (1 / u)) \ w) | x = K(y,(z * (u \ 1)) \ w). K(L(x,y,z),L(x,y,z) * (u \ w)) = K(L(x,y,z),(u * (x \ 1)) \ w). x != K(L(y,z,u),(w * (y \ v5)) \ v6) | x = K(L(y,z,u),y * ((w * v5) \ v6)). K(L(x,y,z),L(x,y,z) * (u \ w)) = K(L(x,y,z),x * ((u * 1) \ w)). K(L(x,y,z),L(x,y,z) * (u \ w)) = K(L(x,y,z),x * (u \ w)). K(x,(((x * (y * x)) / x) * z) / ((u * y) * z)) = K(R(L(x,y,x),y,z),u \ L(x,y,x)). K(R(L(x,y,x),y,z),u \ L(x,y,x)) = K(x,(((x * (y * x)) / x) * z) / ((u * y) * z)). x != K(y,((z / y) * u) / w) | x = K(y,((y \ z) * u) / w). K(R(L(x,y,x),y,z),u \ L(x,y,x)) = K(x,((x \ (x * (y * x))) * z) / ((u * y) * z)). K(R(L(x,y,x),y,z),u \ L(x,y,x)) = K(x,((y * x) * z) / ((u * y) * z)). K(x,((y * x) * z) / ((u * y) * z)) != w | K(R(x,y,z),u \ x) = w. (L(x,y,z) * (K(x,T(u,w)) * w)) \ (L(x,y,z) * w) = R(K(u,L(x,w,L(x,y,z))),L(x,y,z),w). R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(K(x,y) \ 1,z,u). R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(K(y,x),z,u). R(K(x,y) * R(K(y,x),z,u),K(y,w),v5) = K(x,y) * R(K(y,x),z,u). x != R(K(y,z) * R(K(z,y),u,w),K(z,y),u * w) | x = ((K(z,y) * u) * w) / (K(z,y) * (u * w)). K(x,y) * R(K(y,x),z,u) = ((K(y,x) * z) * u) / (K(y,x) * (z * u)). ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = K(y,x) * R(K(x,y),z,u). ((K(x,y) * R(K(y,x),z,u)) * K(y,w)) \ (((K(x,y) * R(K(y,x),z,u)) * K(y,w)) * v5) = L(v5,K(y,w),R(K(x,y) * R(K(y,x),z,u),K(y,w),v5)). L(x,K(y,z),R(K(u,y) * R(K(y,u),w,v5),K(y,z),x)) = ((K(u,y) * R(K(y,u),w,v5)) * K(y,z)) \ (((K(u,y) * R(K(y,u),w,v5)) * K(y,z)) * x). R(K(x,y) * R(K(y,x),z,u),K(y,w),v5) * v6 = K(x,y) * (R(K(y,x),z,u) * v6). R(K(x,K(y,z)) * R(K(y,K(z,x)),u,w),K(K(y,z),v5),v6) * v7 = K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * v7). (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * u) \ z) / y)). (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y)). ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y)). K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u)). K(x,y / (x * (z * u))) = K(x,y / ((z * x) * u)). K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u))). L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * (y * (y \ z)))). K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x). x != K(y,z / ((u * y) * w)) | x = K(y,z / ((y * u) * w)). K(x,y / (x * (z * u))) = K(x,y / ((x * z) * u)). K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u))). T(x,y / ((x * z) * u)) = x * K(x,y / (x * (z * u))). x * K(x,y / (x * (z * u))) = T(x,y / ((x * z) * u)). K(x,((y * x) * z) / (x * z)) = L(K(x,y),z,y * x). L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z)). L(K(x,y),z,y * x) = K(x,R(y,x,z)). K(x,y) = K(x,R(y,x,z)). K(x,R(y,x,z)) = K(x,y). R(K(x,y),z,T(y * x,z)) = K(x,R(y,x,z)). K(x,R(y,x,z)) != u | K(x,y) = u. x != K(y,R(y \ (z / u),y,z / (z / u))) | x = K(y,z / (u * y)). K(x,x \ (y / z)) = K(x,y / (z * x)). K(x,y / (z * x)) = K(x,x \ (y / z)). x != K(y,R(z,z \ u,w)) | x = R(K(y,z),u,w). K(x \ y,x) = R(K(x \ y,x),y,z). R(K(x \ y,x),y,z) = K(x \ y,x). K(x,R(R(y,x,z),u,w)) = K(x,R(y,u,w)). T(x,R(y,x,z)) = x * K(x,y). T(x,R(y,x,z)) = T(x,y). T(R(x,y,z),(u * (y * z)) / ((x * y) * z)) = T(R(x,y,z),u / R(x,y,z)). ((x * y) * z) \ ((y * x) * z) != u | K(y,T(x,z)) = u. K(x / (y * z),y) = K(y \ (x / z),y). K(x,y / (x * z)) = K(x,x \ (y / z)). x != K(y,z / ((u * w) * y)) | x = K(y,z / ((u * y) * w)). K(x,x \ (y / (z * u))) = K(x,y / ((z * x) * u)). K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u))). x != K(y,(y * z) / (u * y)) | x = K(y,z / u). K(x,x \ ((x * y) / z)) = K(x,y / z). K(x / (y * z),z) = K(z \ (x / y),z). x * K(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u)). K(x,x \ ((y \ 1) \ (x * z))) = K(x,z / T(y \ 1,y * (x * z))). x != K(y,R(R(z,u,w),u * w,v5)) | x = R(K(y,R(z,u,w)),(z * u) * w,v5). K(x,R(y,x * z,u)) = R(K(x,R(y,x,z)),(y * x) * z,u). R(K(x,R(y,x,z)),(y * x) * z,u) = K(x,R(y,x * z,u)). K(x,R(y,x,z)) * ((y * x) * z) = (K(x,y) * z) * T(y * x,z). x != K(y,z / (((y \ u) * y) * w)) | x = K(y,z / (u * w)). K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u)). x != K(y,y \ ((y * z) / u)) | x = K(y,z / u). K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u)). K(x,y / ((x \ z) * u)) != w | K(x,((z * u) / y) \ x) = w. T(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u)). T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u))). R(K(x,y),(y * x) * z,u) = K(x,R(y,x * z,u)). x != K(y,R(z,u,w)) * ((z * u) * w) | x = (z * (K(y,z) * u)) * w. (K(x,y) * z) * T(y * x,z) = (y * (K(x,y) * x)) * z. (K(x,y) * z) * T(y * x,z) = (x * y) * z. x != (K(y,z) * u) * T(z * y,u) | x = (z * y) * (K(y,z) * u). (x * y) * z = (y * x) * (K(x,y) * z). (x * y) * (K(y,x) * z) = (y * x) * z. L(x,K(y,z),z * y) = x. (x * y) \ z = K(y,x) * ((y * x) \ z). K(x,y) * ((x * y) \ z) = (y * x) \ z. x != (y * z) * (K(z,y) * u) | x = K(z,y) * ((y * z) * u). (x * y) * z = K(x,y) * ((y * x) * z). K(x,y) * ((y * x) * z) = (x * y) * z. L(x,T(y,z),z) = L(x,y,z). L(x,y * z,K(z,y)) = x. x != L(L(y,z,u),u * z,K(z,u)) | x = (z * u) \ (u * (T(z,u) * y)). L(x,y,z) = (y * z) \ (z * (T(y,z) * x)). L(x,T(y,z) * z,K(z,y)) = x. x != y | x = L(y,z * u,K(u,z)). L(x,T(y,z),z) = L(L(x,y,z),u * w,K(w,u)). L(L(x,y,z),u * w,K(w,u)) = L(x,T(y,z),z). x != L(T(y,z),T(u / T(y,w),y),y) | x = L(T(y,z),y \ u,y). L(T(x,y),z / T(x,u),x) = L(T(x,y),x \ z,x). x != L(y \ 1,T(z,y),y) | x = (z * y) \ z. L(x \ 1,y,x) = (y * x) \ y. (x * y) * L(z,x,y) = y * (T(x,y) * z). L(x,y,z) = L(x,y,T(z,y)). L(x,y,T(z,y)) = L(x,y,z). L(x,y,T(z,y)) != u | L(x,y,z) = u. L(x,y,y \ z) = L(x,y,z / y). L(x,y,z / y) = L(x,y,y \ z). L(x,y,z \ y) = L(x,y,y * (z \ 1)). L(x,y,y * (z \ 1)) = L(x,y,z \ y). L(x \ 1,x,y) * z = L(x \ 1,y,x) * z. L(x \ 1,y,x) * z = L(x \ 1,x,y) * z. x != L(y \ z,y,u / y) | x = u \ ((u / y) * z). L(x \ y,x,x \ z) = z \ ((z / x) * y). x * L(y,z,z \ x) = (x / z) * (z * y). L(x,y * z,(y * (1 / (u * y))) / (y * z)) = L(x,y * z,(z \ (1 / y)) / u). L(x,y,y \ z) != u | L(x,y,z / y) = u. (x * R(y,z,y)) \ ((y * x) * y) != u | L(T(y,x),z,y) = u. (x * y) \ (K(x,y) * z) = (y * x) \ z. K(x \ y,x) * (y * z) = ((x \ y) * x) * z. (x * y) \ (T(x,y) * z) = (y * x) \ (x * z). (x * y) \ (T(x,y) * R(T(z,x),u,w)) = (y * x) \ (R(z,u,w) * x). (x * (T(y,x) * z)) / L(z,y,x) = y * x. x * y != (x / z) * (z * x) | y = x. L(x,y,y \ x) = x. x \ ((x / y) * (y * z)) != u | u = L(z,y,y \ x). x \ ((x / y) * (y * z)) != u | L(z,y,y \ x) = u. L(x * y,x,y) = x * y. x * (L(y \ 1,z,y) * u) = x * (L(y \ 1,y,z) * u). (((x \ y) * x) * (x \ 1)) / (1 / (y * (x \ 1))) = (x \ y) * (y / x). L(x,T(y,z),z) != u | u = L(x,y,z). L(x,T(y,z),z) != u | L(x,y,z) = u. L(T(x,y),z,T(x,u)) != w | L(T(x,y),z,x) = w. x != K(y,y \ (z \ (y * u))) | x = K(y,z \ u). K(x,y / T(z \ 1,z * (x * y))) = K(x,(z \ 1) \ y). K(x,y / T(z \ 1,z * (x * y))) != u | K(x,z * y) = u. (x * y) \ (R(y,z,u) * T(x,y)) = (y * x) \ (R(y,z,u) * x). ((x * y) * z) \ (R(z,x,y) * T(x * y,z)) = (z * (x * y)) \ ((z * x) * y). L(x \ y,x,x) / (1 / (y * (x \ 1))) = (x \ y) * (y / x). ((1 / x) * y) / (1 / (y * (x \ 1))) = (x \ y) * (y / x). ((1 / x) * y) / (x / y) = (x \ y) * (y / x). 1 / ((x / y) * (y \ x)) = (x \ y) * (y / x). 1 * x != 1 / ((y / z) * (z \ y)) | x = (y \ z) * (z / y). (x / y) \ ((y \ x) \ 1) = (x \ y) * (y / x). ((x \ y) * (y / x)) * z = (x * (y \ (y \ x))) \ z. (x * (y \ (y \ x))) \ z = ((x \ y) * (y / x)) * z. T(R(x,y,z),u / R(x,y,z)) = R(T(x,(u * (y * z)) / ((x * y) * z)),y,z). R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = T(R(x,z,u),y / R(x,z,u)). x != T(y,z / y) | x = T(y,y \ z). R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = T(R(x,z,u),R(x,z,u) \ y). R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = R(T(x,R(x,z,u) \ y),z,u). R(T(x,x \ ((y * (z * u)) / (z * u))),z,u) = R(T(x,R(x,z,u) \ y),z,u). R(T(x,x \ y),z,u) = R(T(x,R(x,z,u) \ y),z,u). R(T(x,R(x,y,z) \ u),y,z) = R(T(x,x \ u),y,z). (R(x,y,z) \ u) \ u = R(T(x,x \ u),y,z). R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y. (R(x,y,z) * u) / (R(T(x,x \ w),y,z) * u) = K(R(x,y,z) \ w,R(x,y,z)). x != R(T(y,y \ z),u,w) | x = R((y \ z) \ z,u,w). (R(x,y,z) \ u) \ u = R((x \ u) \ u,y,z). R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y. R(T(x,y),z,u) = (R(x,z,u) \ (x * y)) \ (x * y). (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z). R(x \ y,z,u) = (R(y / x,z,u) \ y) \ y. (R(x / y,z,u) \ x) \ x = R(y \ x,z,u). R(((x * K(y,x)) \ y) \ y,z,u) = (R(x,z,u) \ ((R(x,z,u) * y) / R(x,z,u))) \ y. K(x,R(y \ x,z,u) \ w) = K(x,R(x / y,z,u) \ w). K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w). (x * y) \ (x * (R(x,z,u) * y)) = R(T(x,R(x,z,u) * y),z,u). R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u)). x != (y * z) \ (y * (u * z)) | x = L(T(u,z),z,y). R(T(x,R(x,y,z) * u),y,z) = L(T(R(x,y,z),u),u,x). R(T(x,R(x,y,z) * u),y,z) = L(R(T(x,u),y,z),u,x). x != L(R(T(y,z),u,w),z,y) | x = R(T(y,y * z),u,w). R(T(x,R(x,y,z) * u),y,z) = R(T(x,x * u),y,z). R(T(x,x * y),z,u) \ R(x,z,u) = K(R(x,z,u) * y,R(x,z,u)). K(x * y,R(x,z,u)) = K(R(x,z,u) * y,R(x,z,u)). K(R(x,y,z) * u,R(x,y,z)) = K(x * u,R(x,y,z)). K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u)). x != K(y * z,R(y,u,w)) | x = K(z * y,R(y,u,w)). K(x * R(y,z,u),R(y,z,u)) = K(x * y,R(y,z,u)). K(x \ y,R(x,z,u)) = K(R(x,z,u) \ y,R(x,z,u)). K(R(x,y,z) \ u,R(x,y,z)) = K(x \ u,R(x,y,z)). T(R(x,y,z) * K(x \ u,R(x,y,z)),u) = L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)). x != (y \ ((y * z) / y)) \ z | x = (y \ z) \ T(z,y). R(((x * K(y,x)) \ y) \ y,z,u) = (R(x,z,u) \ y) \ T(y,R(x,z,u)). R((x \ y) \ T(y,x),z,u) = (R(x,z,u) \ y) \ T(y,R(x,z,u)). (R(x,y,z) \ u) \ T(u,R(x,y,z)) = R((x \ u) \ T(u,x),y,z). (x / R(y,z,u)) * R((y \ w) \ T(w,y),z,u) = x * a(R(y,z,u),R(y,z,u) \ w,R(y,z,u)). T(R(x * K(x \ y,x),z,u),y) = L(R(x,z,u),R(x,z,u) \ y,R(x,z,u)). L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = R(T(x * K(x \ u,x),u),y,z). R(T(x * K(x \ y,x),y),z,u) = L(R(x,z,u),R(x,z,u) \ y,R(x,z,u)). R(L(x,x \ y,x),z,u) = L(R(x,z,u),R(x,z,u) \ y,R(x,z,u)). L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = R(L(x,x \ u,x),y,z). L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = L(R(x,y,z),x \ u,x). (L(R(x,y,z),x \ u,x) * u) \ (R(x,y,z) * u) = a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)). a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = (L(R(x,y,z),x \ u,x) * u) \ (R(x,y,z) * u). (x * (y * (z \ (y / z)))) * K(y * (1 / z),z) = x * ((y * (1 / z)) * ((z \ 1) * y)). (x * (y * (z \ (y / z)))) * K(z \ y,z) = x * ((y * (1 / z)) * ((z \ 1) * y)). x != (y * (z * (u \ (z / u)))) * K(u \ z,u) | x = y * ((z / u) * (u \ z)). x * ((y * (1 / z)) * ((z \ 1) * y)) = x * ((y / z) * (z \ y)). x * (y * (z \ (z \ y))) = x * ((y / z) * (z \ y)). x * ((y / z) * (z \ y)) = x * (y * (z \ (z \ y))). x * (y \ (y \ x)) = (x / y) * (y \ x). (x / y) * (y \ x) = x * (y \ (y \ x)). (x \ y) * (y / x) = y * (x \ (x \ y)). x != (y \ z) * (z / y) | x = (z * (y \ 1)) * ((1 / y) * z). x * (y \ (y \ x)) = (x * (y \ 1)) * ((1 / y) * x). (x * (y \ 1)) * ((1 / y) * x) = x * (y \ (y \ x)). (x * (y \ (y \ x))) \ ((y \ x) * ((x / y) * z)) != u | L(z,x / y,y \ x) = u. (x * (y \ (y \ x))) \ z = (y * (x \ (x \ y))) * z. (x * (y \ (y \ x))) \ z = (y / x) * (((1 / y) * x) \ z). (x / y) * (((1 / x) * y) \ z) = (y * (x \ (x \ y))) \ z. x != (y * (z \ (z \ y))) \ u | x = (z * (y \ (y \ z))) * u. (x / y) * (((1 / x) * y) \ z) = (x * (y \ (y \ x))) * z. (x / (y / x)) * (((x \ y) / x) \ z) = (x * ((y / x) \ ((y / x) \ x))) * z. (x * ((y / x) \ ((y / x) \ x))) * z = (x / (y / x)) * (((x \ y) / x) \ z). (x * ((y / x) \ ((y / x) \ x))) * z = (x * (x / y)) * (((x \ y) / x) \ z). L(x,y / z,z \ y) = (z * (y \ (y \ z))) * ((z \ y) * ((y / z) * x)). (x * (y \ (y \ x))) * ((x \ y) * ((y / x) * z)) = L(z,y / x,x \ y). ((K(x,y) * z) * K(y,x)) * K(u,y) = ((1 / (1 / K(y,x))) \ z) * (K(y,x) * K(u,y)). ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = ((K(y,x) * z) * K(x,y)) * K(u,x). ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = T(z,K(x,y)) * K(u,x). x != T(y,K(z,u)) * K(w,z) | x = T(y * K(w,z),K(z,u)). ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y)). (K(x,y) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y)). (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(y,x)). x != (K(y,z) * (K(z,u) * w)) * (K(z,y) * K(u,z)) | x = w * K(K(y,z) * K(z,u),w). T((K(x,y) * z) * K(y,x),K(x,u)) = z * K(K(u,x) * K(x,y),z). T(T(x,K(y,z)),K(y,u)) = x * K(K(u,y) * K(y,z),x). x * K(K(y,z) * K(z,u),x) = T(T(x,K(z,u)),K(z,y)). x != (K(y,T(z,u)) * K(z,w)) \ v5 | x = K(z,T(y,u)) * (K(w,z) * v5). (K(x,y) * K(z,x)) \ K(K(x,y) * K(z,x),u * K(y,x)) = K(x,T(z,u)) * (K(T(y,u),x) * 1). x != K(y,y \ 1) * (z * ((u \ y) * (1 / y))) | x = z * (u \ 1). ((x \ y) * (1 / y)) * (z * ((x \ y) * (1 / y))) = (x \ z) * (x \ 1). ((x \ y) * (1 / y)) * (z * ((x \ y) * (1 / y))) = x \ (z / x). ((((x \ 1) \ ((1 / (1 / y)) * z)) \ x) \ 1) \ (1 / u) = (y * (x * (((x \ z) \ 1) \ 1))) \ (1 / u). (x * (K(y \ z,z \ y) / (u * x))) * w = x * (1 / ((w \ (K(y \ z,z \ y) * u)) * x)). x * (1 / ((y \ (K(z \ u,u \ z) * w)) * x)) = (x * (K(z \ u,u \ z) / (w * x))) * y. (L(x,y,z) * (u * K(x,w))) \ (L(x,y,z) * u) = R(K(w,L(x,u,L(x,y,z))),L(x,y,z),u). K(x,y) = R(K(x,L(y,z,L(y,u,w))),L(y,u,w),z). R(K(x,L(y,z,L(y,u,w))),L(y,u,w),z) = K(x,y). R(K(x,y),L(y,z,u),w) = K(x,y). x != R(K(y / (z / u),w),y,u) | x = K((y * u) / z,w). K(L(x,y,z) / (u / w),x) = K((L(x,y,z) * w) / u,x). K((L(x,y,z) * u) / w,x) = K(L(x,y,z) / (w / u),x). x != K(L(y,z,u) / w,y) | x = K(w \ L(y,z,u),y). K((L(x,y,z) * u) / w,x) = K((w / u) \ L(x,y,z),x). x != K((L(y,z,u) * w) / v5,y) | x = K((((L(y,z,u) \ v5) \ w) \ w) \ w,y). K((x / y) \ L(z,u,w),z) = K((((L(z,u,w) \ x) \ y) \ y) \ y,z). K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((u / w) \ L(x,y,z),x). K((x / y) \ L(z,u,w),z) != v5 | K(y / (L(z,u,w) \ x),z) = v5. (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(R(y,z,u),R(y,z,u) \ (w * y),R(y,z,u)). x * a(R(y,z,u),R(y,z,u) \ (w * y),R(y,z,u)) = (x / R(y,z,u)) * R(R(y,w,y),z,u). (K(x,y) * K(z,x)) \ K(K(x,y) * K(z,x),u * K(y,x)) = K(x,T(z,u)) * (K(y,T(x,u)) * 1). ((((x \ 1) \ (((y \ 1) \ 1) * z)) \ x) \ 1) \ (1 / u) = (y * (x * (((x \ z) \ 1) \ 1))) \ (1 / u). (K(x,y) * K(z,x)) \ K(K(x,y) * K(z,x),u * K(y,x)) = K(x,T(z,u)) * K(y,T(x,u)). ((((((x \ 1) \ 1) * y) \ z) * (1 / z)) \ 1) \ (1 / u) = (x * (z * (((z \ y) \ 1) \ 1))) \ (1 / u). ((1 / x) \ (((((y \ 1) \ 1) * z) \ x) \ 1)) \ (1 / u) = (y * (x * (((x \ z) \ 1) \ 1))) \ (1 / u). (x * (((x \ (((y \ 1) \ 1) * z)) \ 1) \ 1)) \ (1 / u) = (y * (x * (((x \ z) \ 1) \ 1))) \ (1 / u). (K(x,y) * K(z,y)) * u = K(z,y) * (R(K(x,y),K(z,y),u) * u). K(x,y) * (R(K(z,y),K(x,y),u) * u) = (K(z,y) * K(x,y)) * u. K(x,y) * (K(z,y) * u) = (K(z,y) * K(x,y)) * u. (K(x,y) * K(z,y)) * u = K(z,y) * (K(x,y) * u). ((x * y) / x) \ (T(y,z) * (K(z,y) * (K(x,y) * u))) = L(u,T(y,z) \ ((x * y) / x),T(y,z)). ((x * y) / x) \ (y * (K(x,y) * z)) = L(z,T(y,u) \ ((x * y) / x),T(y,u)). L(x,T(y,z) \ ((u * y) / u),T(y,z)) = ((u * y) / u) \ (y * (K(u,y) * x)). x != ((y * z) / y) \ (z * u) | x = K(z,y) * u. L(x,T(y,z) \ ((u * y) / u),T(y,z)) = K(y,u) * (K(u,y) * x). x != K(y,z) * (K(z,y) * u) | x = u. L(x,T(y,z) \ ((u * y) / u),T(y,z)) = x. L(x,K(y,z) * K(u,z),T(z,u)) = x. K(R(x \ y,z,u),w \ (x \ y)) = K(R(x \ y,z,u),w \ (y / x)). K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y)). K(R(x \ (x * y),z,u),w * K(x,y)) = K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))). K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(x \ (x * y),z,u),w * K(x,y)). (x * (y * z)) \ ((x * y) * L(T(u * z,u) / u,y,x)) = L(a(u,L(z,y,x),u),L(z,y,x),x * y). ((x \ 1) \ K(y,z)) \ ((x * (K(y,z) * (u / x))) * x) = L(u,K(z,y) * (x \ 1),K(z,y) * (x \ 1)). ((x \ y) \ 1) * L((y * (x \ 1)) \ y,z,u) = (y \ 1) * (((x \ 1) \ 1) * L((x \ 1) \ 1,z,u)). ((x \ y) \ 1) * L(y * ((x \ y) \ 1),z,u) = (y \ 1) * (((x \ 1) \ 1) * L((x \ 1) \ 1,z,u)). x != (y \ 1) * L(z * (y \ 1),u,w) | x = y \ L(z / y,u,w). (x \ 1) * (((y \ 1) \ 1) * L((y \ 1) \ 1,z,u)) = (y \ x) \ L(x / (y \ x),z,u). (x \ y) \ L(y / (x \ y),z,u) = (y \ 1) * (((x \ 1) \ 1) * L((x \ 1) \ 1,z,u)). (x \ y) \ L(x,z,u) = (y \ 1) * (((x \ 1) \ 1) * L((x \ 1) \ 1,z,u)). (x \ 1) * (((y \ 1) \ 1) * L((y \ 1) \ 1,z,u)) = (y \ x) \ L(y,z,u). (x \ 1) * ((y \ 1) \ L(1 / (y \ 1),z,u)) = (y \ x) \ L(y,z,u). (x \ 1) * ((y \ 1) \ L(y,z,u)) = (y \ x) \ L(y,z,u). (x \ 1) * (y * L(y,z,u)) = (y \ x) \ L(y,z,u). (1 / (x * L(x,y,z))) / (u \ 1) = 1 / ((x \ u) \ L(x,y,z)). x * ((y \ x) \ L(y,z,u)) = L(y * L(y,z,u),x,x). x != y * ((z \ y) \ L(z,u,w)) | x = ((y * z) \ y) \ L((1 / 1) \ L(z,y,y),u,w). L(x * L(x,y,z),u,u) = ((u * x) \ u) \ L((1 / 1) \ L(x,u,u),y,z). ((x * y) \ x) \ L((1 / 1) \ L(y,x,x),z,u) = L(y * L(y,z,u),x,x). ((x \ y) * (y \ 1)) \ (L(x,z,u) * y) = L(x * L(x,z,u),y,y) * y. (x \ (L(x,y,z) \ 1)) / (u \ 1) = 1 / ((x \ u) \ L(x,y,z)). (1 / (x \ (L(x,y,z) \ 1))) \ u = 1 / ((x \ u) \ L(x,y,z)). ((1 / 1) \ (L(x,y,z) * x)) \ u = 1 / ((x \ u) \ L(x,y,z)). (1 \ (L(x,y,z) * x)) \ u = 1 / ((x \ u) \ L(x,y,z)). 1 / ((x \ y) \ L(x,z,u)) = (1 \ (L(x,z,u) * x)) \ y. 1 / ((x \ y) \ L(x,z,u)) = (1 \ (x * L(x,z,u))) \ y. 1 / ((x \ y) \ L(x,z,u)) = (x * L(x,z,u)) \ y. (1 / L(x,y,z)) * (x \ u) = (x * L(x,y,z)) \ u. (x \ 1) * (((x * L(x,y,z)) \ 1) \ u) = ((1 / L(x,y,z)) \ (u / x)) * x. (x \ 1) \ (L(x,y,z) * u) = L(x * L(x,y,z),u,u) * u. L(x * L(x,y,z),u,u) * u = (x \ 1) \ (L(x,y,z) * u). (1 / (x * L(x,y,z))) \ u = (x \ 1) \ (L(x,y,z) * u). (x \ (L(x,y,z) \ 1)) \ u = (x \ 1) \ (L(x,y,z) * u). ((x * y) \ x) \ L(1 \ L(y,x,x),z,u) = L(y * L(y,z,u),x,x). ((x * y) \ x) \ L(L(y,x,x),z,u) = L(y * L(y,z,u),x,x). x != ((y * z) \ y) \ L(L(z,y,y),u,w) | x = L(z,y,y) * L(L(z,y,y),u,w). L(x * L(x,y,z),u,u) = L(x,u,u) * L(L(x,u,u),y,z). L(x,y,y) * L(L(x,y,y),z,u) = L(x * L(x,z,u),y,y). (x \ 1) * L(y * L(y,z,u),x,x) = (x \ y) * L(y,z,u). x \ (y * L(y,z,u)) = (x \ y) * L(y,z,u). (x \ ((1 / x) \ (y * L(y,z,u)))) / x = y * (L(y,z,u) / x). x \ (y \ (z \ (z / y))) = (x \ (1 / y)) * L(1 / y,z,z). (x \ (1 / y)) * L(1 / y,z,z) = x \ (y \ (z \ (z / y))). x * (x \ (y \ (x \ (x / y)))) = x / (y * (((y \ 1) \ 1) * x)). x / (y * (((y \ 1) \ 1) * x)) = x * (x \ (y \ (x \ (x / y)))). L(x * L(x,y,z),u,u) / u = x * (L(x,y,z) / u). (x * (L(x,y,z) / u)) * u = L(x * L(x,y,z),u,u). x / (y * (((y \ 1) \ 1) * x)) = y \ (x \ (x / y)). (x \ 1) * ((x \ (L(x,y,z) \ 1)) \ u) = ((1 / L(x,y,z)) \ (u / x)) * x. (x \ 1) * ((x \ 1) \ (L(x,y,z) * u)) = ((1 / L(x,y,z)) \ (u / x)) * x. ((1 / L(x,y,z)) \ (u / x)) * x = L(x,y,z) * u. x != ((1 / y) \ (z / u)) * u | x = (u / y) \ (u * z). L(x,y,z) * u = (x / L(x,y,z)) \ (x * u). (x / L(x,y,z)) \ (x * u) = L(x,y,z) * u. (L(x,y,z) \ x) \ (x * u) = L(x,y,z) * u. L(x,y,z) \ u = x \ ((L(x,y,z) \ x) * u). x \ ((L(x,y,z) \ x) * u) = L(x,y,z) \ u. (L(x,y,z) \ x) \ u = L(x,y,z) * (x \ u). (L(x,y,z) \ u) \ 1 = x \ ((u / x) \ L(x,y,z)). x \ ((y / x) \ L(x,z,u)) = (L(x,z,u) \ y) \ 1. x != L(y,z,u) * (y \ (L(y,z,u) \ w)) | x = y \ w. (L(x,y,z) \ x) \ (L(x,y,z) \ u) = x \ u. (L(x,y,z) \ x) * (x \ u) = L(x,y,z) \ u. (L(x,y,z) \ x) * u = L(x,y,z) \ (x * u). L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. x * ((L(x,y,z) \ u) \ 1) != w | w = (u / x) \ L(x,y,z). x * ((L(x,y,z) \ u) \ 1) != w | (u / x) \ L(x,y,z) = w. (R(R(x,y,z),u,R(x,y,z)) * (y * z)) / ((x * y) * z) = a(R(x,y,z),u,R(x,y,z)). ((R(x,y,R(x,z,u)) * z) * u) / ((x * z) * u) = a(R(x,z,u),y,R(x,z,u)). K(x * y,T(T(x,z),u)) * K((x \ z) \ z,T(y,u)) = a((x \ z) \ z,y,(x \ z) \ z). a((x \ y) \ y,z,(x \ y) \ y) = K(x * z,T(T(x,y),u)) * K((x \ y) \ y,T(z,u)). a((x \ y) \ y,z,(x \ y) \ y) = K(x * z,T(T(x,y),u)) * K(x,T(T(z,u),y)). x != a((y \ z) \ z,u,(y \ z) \ z) | x = a(y,u,y). K(x * y,T(T(x,z),u)) * K(x,T(T(y,u),z)) = a(x,y,x). K(x * y,T(T(x,z),u)) * K(x,T(T(y,z),u)) = a(x,y,x). x != a(y,z,y) | x = a(y,T(z,u),y). K(x * y,T(T(x,z),u)) * K(x,T(T(y,z),u)) = a(x,T(y,w),x). a(x,T(y,z),x) = K(x * y,T(T(x,u),w)) * K(x,T(T(y,u),w)). K(x * T(y,z),T(x,u)) = K(x * y,T(T(x,u),z)). K(x * T(y,z),T(x,u)) = T(K(x * y,T(x,u)),z). K(x * T(y,z),T(x,u)) = T(K(x * y,x) * K(x,K(y,u)),z). T(K(x * y,x) * K(x,K(y,z)),u) = K(x * T(y,u),T(x,z)). T(K(x * y,y) * K(y,K(x,z)),u) = K(y * T(x,u),T(y,z)). a(x,((y * z) * u) \ (y * (z * (u * K(w,w \ 1)))),x) = a(x,K(w,w \ 1) / a(y,z,u),x). x != (L(y,z \ u,z) * u) \ (y * u) | x = a(z,z \ u,T(y,u)). a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,T(R(x,y,z),u)). a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,R(T(x,u),y,z)). (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = L(a(u,L(z,y,x),u),L(z,y,x),x * y). L(a(x,L(y,z,u),x),L(y,z,u),u * z) = (u * (z * y)) \ (u * (z * (T(x * y,x) / x))). ((x \ 1) \ K(y,z)) \ L((x * K(y,z)) * u,x,x) = L(u,K(z,y) * (x \ 1),K(z,y) * (x \ 1)). T(R(((x \ R(x,y,z)) \ 1) \ 1,x,y * z),x * (y * z)) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1. T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) = T(x \ L(x,z,u),y * x). x != T(y \ 1,z * y) * L(T(y \ 1,y * z) \ 1,u,w) | x = T(y \ L(y,u,w),z * y). T((x \ 1) * L((x \ 1) \ 1,y,z),x * u) = T(x \ L(x,y,z),u * x). T(x \ L(x,y,z),x * u) = T(x \ L(x,y,z),u * x). T(x \ L(x,y,z),u * x) = T(x \ L(x,y,z),x * u). K((T(x \ L(x,y,z),x * u) / w) / ((x \ L(x,y,z)) / w),v5) = K(x \ L(x,y,z),K(u * x,v5)). K(K(((x \ L(x,y,z)) / u) / (u \ 1),x * w),v5) = K(x \ L(x,y,z),K(w * x,v5)). K(x,K(((y \ L(y,z,u)) / w) / (w \ 1),y * v5)) = K(y \ L(y,z,u),K(v5 * y,x)). K(x,K(y * z,((y \ L(y,u,w)) / v5) * v5)) = K(y \ L(y,u,w),K(z * y,x)). K(x,K(y * z,y \ L(y,u,w))) = K(y \ L(y,u,w),K(z * y,x)). K(x \ L(x,y,z),K(u * x,w)) = K(w,K(x * u,x \ L(x,y,z))). K(x,K(y * z,y \ L(y,u,w))) != v5 | K(x,K(z * y,y \ L(y,u,w))) = v5. (((x * y) * (1 / (x * y))) \ z) * K(u,u \ 1) = ((((y \ (x \ 1)) * (x * y)) \ u) * (1 / u)) \ z. ((((x \ (y \ 1)) * (y * x)) \ z) * (1 / z)) \ u = (((y * x) * (1 / (y * x))) \ u) * K(z,z \ 1). ((((x \ (y \ 1)) * (y * x)) \ z) * (1 / z)) \ u = (K(y * x,(y * x) \ 1) \ u) * K(z,z \ 1). ((((x \ (y \ 1)) * (y * x)) \ z) * (1 / z)) \ u = (K(y * x,x \ (y \ 1)) \ u) * K(z,z \ 1). ((((x \ (y \ 1)) * (y * x)) \ z) * (1 / z)) \ u = (K(x \ y,y \ x) \ u) * K(z,z \ 1). ((((x \ (y \ 1)) * (y * x)) \ z) * (1 / z)) \ u = (K(y \ x,x \ y) * u) * K(z,z \ 1). x != (y * z) * K(u,u \ 1) | x = y * (K(u,u \ 1) * z). ((((x \ (y \ 1)) * (y * x)) \ z) * (1 / z)) \ u = K(y \ x,x \ y) * (K(z,z \ 1) * u). ((K(x \ y,y \ x) \ z) * (1 / z)) \ u = K(y \ x,x \ y) * (K(z,z \ 1) * u). K((x \ 1) \ y,y \ (x \ 1)) * K(z,z \ 1) = (((x \ z) * (1 / z)) \ y) * (1 / ((x \ 1) \ y)). K(x * y,y \ (x \ 1)) * K(z,z \ 1) = (((x \ z) * (1 / z)) \ y) * (1 / ((x \ 1) \ y)). (((x \ y) * (1 / y)) \ z) * (1 / ((x \ 1) \ z)) = K(x * z,z \ (x \ 1)) * K(y,y \ 1). (((x \ y) * (1 / y)) \ z) * (1 / ((x \ 1) \ z)) = K(z \ x,x \ z) * K(y,y \ 1). (((x \ y) * (1 / y)) \ z) * ((1 / z) * (x \ 1)) = K(z \ x,x \ z) * K(y,y \ 1). x != (((y \ z) * (1 / z)) \ u) * ((1 / w) * v5) | x = ((y \ 1) \ u) * (z * (1 / ((v5 \ w) * z))). K(x \ y,y \ x) * K(z,z \ 1) = ((y \ 1) \ x) * (z * (1 / (((y \ 1) \ x) * z))). ((x \ 1) \ y) * (z * (1 / (((x \ 1) \ y) * z))) = K(y \ x,x \ y) * K(z,z \ 1). (x * (y \ 1)) * ((1 / (x * (y \ 1))) * K(z,z \ 1)) = (z * (((z \ (y / x)) \ 1) \ 1)) * (x * (y \ 1)). (x * y) / ((z * (1 / (u * z))) / (y \ 1)) = (x / ((((u \ z) * (1 / z)) \ y) \ 1)) * (y \ 1). (x / ((((y \ z) * (1 / z)) \ u) \ 1)) * (u \ 1) = (x * u) / ((z * (1 / (y * z))) / (u \ 1)). K(L(x,y,z),L(x,y,z) * (u \ L(K(x,w),v5,v6))) = K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))). K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))) = K(L(x,y,z),L(x,y,z) * (u \ L(K(x,w),v5,v6))). x != (y * (((y \ z) \ 1) \ 1)) * u | x = y * (1 / ((u \ (1 / z)) * y)). (x * (y \ 1)) * ((1 / (x * (y \ 1))) * K(z,z \ 1)) = z * (1 / (((x * (y \ 1)) \ (1 / (y / x))) * z)). x != K(L(y,z,u),L(y,z,u) * (w \ v5)) | x = K(L(y,z,u),y * (w \ v5)). K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))) = K(L(x,y,z),x * (u \ L(K(x,w),v5,v6))). x != K(L(y,z,u),y * (w \ L(K(y,v5),v6,v7))) | x = K(L(y,z,u),w \ y). K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))) = K(L(x,y,z),u \ x). K(L(x,y,z),u \ L(x,y,z)) = K(L(x,y,z),u \ x). (x * K(L(y,z,u),w \ y)) \ x = K(w \ L(y,z,u),L(y,z,u)). K(x \ L(y,z,u),L(y,z,u)) = (w * K(L(y,z,u),x \ y)) \ w. K(x \ L(y,z,u),L(y,z,u)) = K(x \ y,L(y,z,u)). T(L(x,y,z) * K((u \ 1) \ x,L(x,y,z)),u) = u \ T(L(x,y,z) * u,L(x,y,z)). T(L(x,y,z) * K(x * (1 \ u),L(x,y,z)),u) = u \ T(L(x,y,z) * u,L(x,y,z)). T(L(x,y,z) * K(x * u,L(x,y,z)),u) = u \ T(L(x,y,z) * u,L(x,y,z)). T(L(x * K(x * y,x),z,u),y) = y \ T(L(x,z,u) * y,L(x,z,u)). x \ T(L(y,z,u) * x,L(y,z,u)) = L(T(y * K(y * x,y),x),z,u). L(T(x * K(x * y,x),y),z,u) = y \ T(L(x,z,u) * y,L(x,z,u)). L(R(x,y,x),z,u) = y \ T(L(x,z,u) * y,L(x,z,u)). x \ T(L(y,z,u) * x,L(y,z,u)) = L(R(y,x,y),z,u). R(L(x,y,z),u,L(x,y,z)) = L(R(x,u,x),y,z). (x * y) * L(R(z,u,z),y,x) = x * (y * R(z,u,L(z,y,x))). K(x,L(R(y,z,y),u,w)) != v5 | K(x,L(y,u,w)) = v5. K(L(x,y * (x \ z),u),y) != w | K(x,L(y,z,u)) = w. x * R(y,z,y) = x * R(y,z,L(y,x,u)). x * R(y,z,L(y,x,u)) = x * R(y,z,y). R(x,y,x) = R(x,y,L(x,z,u)). R(x,y,L(x,z,u)) = R(x,y,x). x != R(y,z,y) | x = T(y * K(z * y,y),z). R(x,y,L(x,z,u)) = T(x * K(y * x,x),y). T(x * K(y * x,x),y) = R(x,y,L(x,z,u)). (x * T(y,z)) \ (x * R(y,z,y)) = K(z * L(y,u,w),y). K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y)). T(R(x,y,z) * K(u * x,R(x,y,z)),u) = R(R(x,y,z),u,L(R(x,y,z),w,v5)). x != (y * T(z,u)) \ (y * R(z,u,z)) | x = K(z * u,z). K(x * L(y,z,u),y) = K(y * x,y). K(x \ L(y,z,u),y) = K(y * (x \ 1),y). x != K(y * z,y) | x = K(z,y) * a(y,z,y). K(x * L(y,z,u),y) = K(x,y) * a(y,x,y). K(x * (L(x,y,z) \ u),x) = K(u,x). x != K(y * (z \ (y \ u)),y) | x = K(z \ u,y). K(x \ y,x) = K(L(x,z,u) \ y,x). K(L(x,y,z) \ u,x) = K(x \ u,x). K(x / L(y,z,u),y) = K(y \ x,y). K((((x * y) \ x) \ 1) \ z,y) = K(y \ z,y). K(x \ L(y,z,u),y) = K(x \ y,y). K(x / (L(y,z,u) \ w),y) = K((w / x) \ y,y). x != K((y \ z) \ L(u,w,v5),u) | x = K(z \ (y * L(u,w,v5)),u). K((x \ y) \ z,z) = K(y \ (x * L(z,u,w)),z). K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z). (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x. a(x,y,L(x,z,u)) = a(x,y,x). (x / y) * R(y,z,y) = x * a(y,z,L(y,u,w)). x != K((((y * z) \ y) \ 1) \ u,z) | x = K(u * ((y * z) \ y),z). K(x \ y,x) = K(y * ((z * x) \ z),x). K(x * ((y * z) \ y),z) = K(z \ x,z). K(x * (y \ z),z \ y) = K((z \ y) \ x,z \ y). K((x \ y) \ z,x \ y) = K(z * (y \ x),x \ y). K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z). (x / y) * R(y,z,L(y,u,w)) = x * a(y,z,L(y,v5,v6)). K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u). x != K(y * (z \ u),u \ z) | x = K(y * (u / z),u \ z). K((x \ y) \ z,x \ y) = K(z * (x / y),x \ y). K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y). x != K(y \ (z * (u * w)),w) | x = K(y \ (z * (w * u)),w). K(x * (y \ (z * u)),x) = K(y \ (z * (x * u)),x). K(x \ (y * (z * u)),z) = K(z * (x \ (y * u)),z). x * K(x * (y / z),y \ z) = ((y \ z) \ x) * (y \ z). x != K(y \ (z * (u * w)),u) | x = K(((z \ y) \ w) * u,L(u,w,z)). K(x * (y \ (z * u)),x) = K(((z \ y) \ u) * x,L(x,u,z)). K(((x \ y) \ z) * u,L(u,z,x)) = K(u * (y \ (x * z)),u). x != y * K(y * (z / u),z \ u) | x = ((1 / (u \ z)) \ y) * (1 / (u \ z)). ((x \ y) \ z) * (x \ y) = ((1 / (y \ x)) \ z) * (1 / (y \ x)). ((1 / (x \ y)) \ z) * (1 / (x \ y)) = ((y \ x) \ z) * (y \ x). x != K(y * ((z * y) \ u),y) | x = K(z \ u,y). K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y). x != K((y * z) \ (u \ (y * ((z * w) * u))),u) | x = K(L(w,u * z,y),u). K((x * y) \ (x * (y * z)),u) = K(L(z,u * y,x),u). K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y). K(L(x,y * z,u),y) = K(L(x,z,u),y). K(x,L(y,z,u)) = K(L(x,x \ z,u),y). K(L(x,x \ y,z),u) = K(x,L(u,y,z)). L(K(x,y),z,u) = K(x,L(y,z,u)). K(L(x,y,z),u) = K(x,L(u,y * x,z)). K(x,L(y,z * x,u)) = K(L(x,z,u),y). x != K(y,z) | x = K(z,y) \ 1. L(K(x,y),z,u) = K(L(y,z,u),x) \ 1. K(L(x,y,z),u) \ 1 = L(K(u,x),y,z). (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u)). K(x,y) \ (K(x,L(y,z,u)) \ (w * K(x,y))) = L(K(x,y),z,u) \ T(w,K(x,y)). T(L(K(x,y),z,u) \ w,K(x,L(y,z,u))) = w / L(K(x,y),z,u). K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x)). a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u). L(K(x,y),z,u) != w | K(x,L(y,z,u)) = w. K(x,(y * ((y \ z) / u)) \ z) != w | K(x,L(u,y \ z,y)) = w. K(L(x,y,z),u) * a(z,y,K(x,u)) = K(x,u). x * a(y,z,K(u,x)) = T(x,L(u,z,y)) * K(u,x). T(x,L(y,z,u)) * K(y,x) = x * a(u,z,K(y,x)). K(x,y) * K(L(y,z,u),x) = a(u,z,K(x,y)). L(K(x,y),z,u) = K(L(x,z,u),y). K(x,L(y,z,u)) = K(L(x,z,u),y). K(L(x,y,z),u) = K(x,L(u,y,z)). x != K(L(y,z,u),w) | x = K(y,L(w,z * y,u)). K(x,L(y,z,u)) = K(x,L(y,z * x,u)). K(x,L(y,z * x,u)) = K(x,L(y,z,u)). L(L(x,y \ 1,L(z,y,y)),z / y,K(z,L(u,y,y))) = L(x,1 / y,T(L(z,y,y),u)). K(x * y,z) = K(x * y,L(z,x,y)). K(x * y,L(z,x,y)) = K(x * y,z). K(x \ y,L(z,y,u)) = K(x \ y,L(z,x,u)). x != K(y,z) * K(L(z,u,w),y) | x = a(w,u * z,K(y,z)). a(x,y,K(z,u)) = a(x,y * u,K(z,u)). a(x,y * z,K(u,z)) = a(x,y,K(u,z)). x * a(y,z,K(u,x)) = (u * x) / T(u,L(x,z,y)). (x * y) / T(x,L(y,z,u)) = y * a(u,z,K(x,y)). x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y)). K((x \ (y \ z)) \ u,L(x,u,y)) = K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z). x * (y * K(x * y,z)) != u | T(x * y,L(z,y,x)) = u. (x * L(y,x,y)) / T(T(x,y),L(T(y,x * y),z,u)) = T(y,x * y) * a(u,z,K(T(x,y),T(y,x * y))). L(x,y,z) \ ((u / x) \ (L(x,y,z) * (x \ u))) = x \ (x * a(z,y,K(x \ u,x))). T(x * y,L(z,y,x)) = T(x * y,z). (x * (y * z)) / T(x * y,z) = L(z,y,x). L(x,y,z) = (z * (y * x)) / T(z * y,x). L(x,K(y,T(z,x)),u) = (u * (x * K(y,z))) / T(u * K(y,T(z,x)),x). (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) = L(y,K(z,T(u,y)),x). ((x \ y) \ z) * (x \ y) = (((y \ x) \ 1) \ z) * ((y \ x) \ 1). (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = ((y \ x) \ z) * (y \ x). K(((x \ y) / z) \ y,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z). 1 / (((x \ y) \ z) * (x \ y)) = (y \ x) / (((y \ x) \ 1) \ z). (x \ y) / (((x \ y) \ 1) \ z) = 1 / (((y \ x) \ z) * (y \ x)). (x \ y) * (1 / ((x \ y) * z)) = 1 / (((y \ x) \ z) * (y \ x)). 1 / (((x \ y) \ z) * (x \ y)) = (y \ x) * (1 / ((y \ x) * z)). T(L(K(x,y),z,u) * w,K(y,L(x,z,u))) = w / L(K(y,x),z,u). x != K((y / z) \ u,L(z,w,v5)) | x = K((y \ u) * z,L(z,w,v5)). K(((x \ y) / z) \ y,z) = K(((x \ y) \ y) * z,L(z,x \ y,x)). K(((x \ y) \ y) * z,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z). x != y / L(K(z,u),w,v5) | x = y * L(K(u,z),w,v5). T(L(K(x,y),z,u) * w,K(y,L(x,z,u))) = w * L(K(x,y),z,u). T(x * L(K(y,z),u,w),K(z,L(y,u,w))) = L(K(y,z),u,w) * x. (L(x,y,z) * K(u,x)) * u = (x \ (L(x,y,z) * u)) * x. (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u. x != (y * K(z,u)) * z | x = y * T(z,u). (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x). (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x). (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y)). x != y \ (z * T(y,u)) | x = T(z * K(y,u),y). (x / y) \ (L(y,z,u) * (y \ x)) = T(L(y,z,u) * K(x,y),x). T(R(x * K(y * x,x),z,u),y) = R(R(x,z,u),y,L(R(x,z,u),w,v5)). T(R(x * K(x * y,x),z,u),y) = R(R(x,z,u),y,L(R(x,z,u),w,v5)). R(R(x,y,z),u,L(R(x,y,z),w,v5)) = R(T(x * K(x * u,x),u),y,z). R(T(x * K(x * y,x),y),z,u) = R(R(x,z,u),y,L(R(x,z,u),w,v5)). R(R(x,y,x),z,u) = R(R(x,z,u),y,L(R(x,z,u),w,v5)). R(R(x,y,z),u,L(R(x,y,z),w,v5)) = R(R(x,u,x),y,z). x != R(y,z,L(y,u,w)) | x = R(y,z,y). R(R(x,y,x),z,u) = R(R(x,z,u),y,R(x,z,u)). R(R(x,y,z),u,R(x,y,z)) = R(R(x,u,x),y,z). (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(R(y,z,u),w,L(R(y,z,u),v5,v6)). R(R(x,y,x),z,u) * (z * u) = (R(x,y,R(x,z,u)) * z) * u. (R(x,y,R(x,z,u)) * z) * u = R(R(x,y,x),z,u) * (z * u). (R(x,y,R(x,z,u)) * z) * u = (R(x,y,x) * z) * u. (R(T(x,y),z,R(x,u,w)) * u) * w = (R(T(x,y),z,T(x,y)) * u) * w. (R(T(x,y),z,T(x,y)) * u) * w = (R(T(x,y),z,R(x,u,w)) * u) * w. ((R(x,y,x) * z) * u) / ((x * z) * u) = a(R(x,z,u),y,R(x,z,u)). a(R(x,y,z),u,R(x,y,z)) != w | R(a(x,u,x),x * y,z) = w. K(x,y) \ (K(L(y,z,u),x) * (w * K(x,y))) = L(K(x,y),z,u) \ T(w,K(x,y)). K(x,y) \ (K(y,L(x,z,u)) * (w * K(x,y))) = L(K(x,y),z,u) \ T(w,K(x,y)). K(x,y) \ (T(y,L(x,z,u)) * K(x,y)) = L(K(x,y),z,u) \ T(y,K(x,y)). K(x,y) \ (y * a(z,u,K(x,y))) = L(K(x,y),u,z) \ T(y,K(x,y)). L(K(x,y),z,u) \ T(y,K(x,y)) = K(x,y) \ (y * a(u,z,K(x,y))). x != K((y \ z) \ u,L(y,w,v5)) | x = K((z \ u) * y,L(y,w,v5)). K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z) = K(((y \ z) \ u) * x,L(x,u,y)). L(x,y,z) \ T(L(x,y,z) * K(u,x),u) = x \ (x * a(z,y,K(x \ u,x))). K(L(x,y,z),u) * K(u,x) = x \ (x * a(z,y,K(x \ u,x))). x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x). x \ (x * a(y,z,K(x \ u,x))) = K(x,L(u,z,y)) * K(u,x). x != K(y,L(z,u,w)) * K(z,y) | x = a(w,u,K(z,y)). x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x)). a(x,y,K(z,u)) = a(x,y,K(u \ z,u)). a(x,y,K(z \ u,z)) = a(x,y,K(u,z)). a(x,y,K(z,u)) != w | w = a(x,y,K(u \ z,u)). a(x,y,K(z,u)) != w | a(x,y,K(u \ z,u)) = w. a(x,y,K(z,u)) = a(x,y,K(u * z,u)). a(x,y,K(z * u,z)) = a(x,y,K(u,z)). a(x,y,K(z \ 1,u)) = a(x,y,K(z \ u,u)). a(x,y,K(z,u)) = a(x,y,K(z * u,u)). a(x,y,K(z * u,u)) = a(x,y,K(z,u)). a(x,y,K(z,u \ w)) = a(x,y,K(w \ u,z)). a(x,y,K(z \ u,w)) = a(x,y,K(w,u \ z)). a(x,y,K(z,z * u)) = a(x,y,K(z,u)). L(K(x * y,y),z,u) \ T(y,K(x * y,y)) = K(x * y,y) \ (y * a(u,z,K(x,y))). a(x,y,K(z,u)) = a(x,y,K(z,z \ u)). a(x,y,K(z,z \ u)) = a(x,y,K(z,u)). a(x,y,K(z \ 1,u)) = a(x,y,K(u,z)). x != K(((y \ z) \ u) * w,L(w,u,y)) | x = K(w * (z \ (y * u)),w). K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z) = K(x * (z \ (y * u)),x). K((x \ (y \ z)) \ u,L(x,y \ z,y)) = K(x * (z \ (y * u)),x). K(x * (y \ (z * u)),x) = K(((z \ y) \ u) * x,L(x,z \ y,z)). K(((x \ y) \ z) * u,L(u,x \ y,x)) = K(u * (y \ (x * z)),u). x != K(((y \ z) \ z) * u,L(u,y \ z,y)) | x = K(((y \ z) / u) \ z,u). K(x * (y \ (z * y)),x) = K(((z \ y) / x) \ y,x). K(((x \ y) / z) \ y,z) = K(z * (y \ (x * y)),z). K(((x \ y) / z) \ y,z) = K(z * T(x,y),z). K(x * ((y \ z) \ z),x) = K(x * T(y,z),x). T(x,x * K(y * T(z,u),y)) \ T(K(y,y * ((z \ u) \ u)) * x,x) = K(y,T(y * ((z \ u) \ u),x)). L(L(x,y \ 1,L(z,y,y)),z / y,K(z,u)) = L(x,1 / y,T(L(z,y,y),u)). L(L(x,y \ 1,L(z,y,y)),z / y,K(z,u)) = L(x,1 / y,L(T(z,u),y,y)). x != L(y,1 / z,u) | x = L(y,z \ 1,u). L(L(x,y \ 1,L(z,y,y)),z / y,K(z,u)) = L(x,y \ 1,L(T(z,u),y,y)). x != K(y,z) \ (z * u) | x = T(z,y) * u. L(K(x * y,y),z,u) \ T(y,K(x * y,y)) = T(y,x * y) * a(u,z,K(x,y)). (x * (y \ 1)) * ((1 / (x * (y \ 1))) * K(z,z \ 1)) = z * (1 / (((y / x) * (1 * (1 / (y / x)))) * z)). (x * (y \ 1)) * ((1 / (x * (y \ 1))) * K(z,z \ 1)) = z * (1 / (((y / x) * (1 / (y / x))) * z)). (x * (y \ 1)) * ((1 / (x * (y \ 1))) * K(z,z \ 1)) = z * (1 / (K(y / x,(y / x) \ 1) * z)). (x * (y \ 1)) * ((1 / (x * (y \ 1))) * K(z,z \ 1)) = z * (1 / (K(x \ y,y \ x) * z)). (x * (y \ 1)) * ((1 / (x * (y \ 1))) * K(z,z \ 1)) = z * ((1 / z) * K(x \ y,y \ x)). T((x * K(y,x)) * (K(y,x) \ 1),z) = (x * K(y,x)) * (T(x,z) * (x \ K(x,y))). (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T((x * K(y,x)) * (K(y,x) \ 1),z). (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T((x * K(y,x)) * K(x,y),z). (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T(x,z). T(x,y) / (T(x,y) * (x \ K(x,z))) = x * K(z,x). T(x * K(y,x),x \ K(x,y)) \ T(x,z) = T(x,z) * T(x \ K(x,y),(x \ K(x,y)) \ 1). T(x,y) * T(x \ K(x,z),(x \ K(x,z)) \ 1) = T(x * K(z,x),x \ K(x,z)) \ T(x,y). T(x,y) * T(x \ K(x,z),(x \ K(x,z)) \ 1) = ((x \ 1) \ K(z,x)) \ T(x,y). T(x,y) * T(x \ K(x,z),(x \ 1) \ K(z,x)) = ((x \ 1) \ K(z,x)) \ T(x,y). T(x,y) * T(x \ K(x,z),T(x,z)) = ((x \ 1) \ K(z,x)) \ T(x,y). T(x,y) * T(x \ K(x,z),x) = ((x \ 1) \ K(z,x)) \ T(x,y). ((x \ 1) \ K(y,x)) \ T(x,z) = T(x,z) * T(x \ K(x,y),x). (x \ K(x,y)) * T(x,z) = ((x \ 1) \ K(y,x)) \ T(x,z). ((x \ 1) \ K(y,x)) \ T(x,z) = (x \ K(x,y)) * T(x,z). (((x \ K(x,y)) \ 1) \ T(x,z)) \ K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ K(x,y)) \ 1)) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z)). K((T(x,y) \ ((x \ 1) \ K(z,x))) \ 1,((x \ K(x,z)) * T(x,y)) \ 1) = K(((x \ 1) \ K(z,x)) \ T(x,y),T(x,y) \ ((x \ 1) \ K(z,x))). T(L(T(x,K(y,z)),K(y,z),K(u,y)),K(u,y)) = R(T(x,K(u,y) * K(y,z)),K(u,y),K(y,z)). R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(L(T(x,K(z,u)),K(z,u),K(y,z)),K(y,z)). R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(T(x,K(z,u)),K(y,z)). R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(T(x,K(z,u)),K(z,y)). x != R(y,K(z,u),K(u,w)) | x = y. T(T(x,K(y,z)),K(y,u)) = T(x,K(u,y) * K(y,z)). T(T(x,K(y,z)),K(z,u)) = T(x,K(y,z) * K(z,u)). T(T(x,K(y,z)),K(y,u)) = T(x,K(y,z) * K(u,y)). T(x,K(y,z) * K(z,u)) \ x = K(x,K(z,y)) * K(x,K(z,u)). T(T(x,K(y,z)),K(z,u)) = T(x,K(z,u) * K(y,z)). T(T(x,K(y,z)),K(u,R(y,w,v5))) = T(x,K(y,z) * K(R(u,w,v5),y)). T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(z,y)). T(T(x,K(y,z)),K(y,u)) = x * K(x,K(y,z) * K(u,y)). x * K(x,K(y,z) * K(u,y)) = T(T(x,K(y,z)),K(y,u)). x != T(T(y,K(z,u)),K(z,w)) | x = y * K(K(w,z) * K(z,u),y). T(x,K(y,z) * K(u,y)) = x * K(K(u,y) * K(y,z),x). x * K(K(y,z) * K(z,u),x) = T(x,K(z,u) * K(y,z)). T(T(x,R(K(y,z),u,w)),K(z,v5)) = T(x,K(z,v5) * K(R(y,u / y,w),z)). T(x,K(y,z) * K(R(u,w / u,v5),y)) = T(T(x,R(K(u,y),w,v5)),K(y,z)). K(K(x,y) * K(y,z),K(x,y) \ u) = T(u,K(y,z) * K(x,y)) \ u. x != T(T(y,K(z,u)),K(z,w)) | x = T(y,K(z,u) * K(w,z)). T(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y)). T(x * K(K(y,z) * K(u,y),x),K(y,u) * K(z,y)) = x. x * K(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y)). T(T(x,K(y,z)),K(y,u)) != w | T(x,K(y,z) * K(u,y)) = w. x * K(K(y,z) * K(u,y),x) = T(x,K(y,z) * K(u,y)). T(x,K(y,z) * K(u,y)) != w | T(x,K(y,u) * K(z,y)) = w. x * y != T(x,K(z,u) * K(w,z)) | y = K(K(w,z) * K(z,u),x). K(x,K(y,z) * K(u,y)) = K(K(z,y) * K(y,u),x). K(K(x,y) * K(y,z),u) = K(u,K(y,x) * K(z,y)). K(K(x,y) * K(z,x),u) = K(u,K(x,z) * K(y,x)). K(K(x,y) * K(z,x),u) = K(u,K(y,x) * K(x,z)). K(K(x,y) * K(z,x),u) = K(u,K(x,y) * K(z,x)). x != K(K(y,z) * K(u,y),w) | x = K(w,K(z,y) * K(y,u)). K(x,K(y,z) * K(u,y)) = K(x,K(z,y) * K(y,u)). T(T(x,K(y,z)),K(y,u)) != w | T(x,K(y,u) * K(z,y)) = w. K(K(x,y) * K(y,z),u) = K(u,K(y,x)) * K(u,K(y,z)). K(x,K(y,z)) * K(x,K(y,u)) = K(K(z,y) * K(y,u),x). x != K(K(y,z) * K(z,u),w) | x = K(w,K(z,y) * K(u,z)). K(x,K(y,z)) * K(x,K(y,u)) = K(x,K(y,z) * K(u,y)). K(x,K(y,z)) * K(x,R(K(y,u),w,v5)) = K(K(z,y) * K(y,(w * v5) / ((u \ w) * v5)),x). K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(v5,K(y,x)) * K(v5,R(K(y,w),z,u)). x != K(y,K(z,u) * K(w,z)) | x = K(K(z,u) * K(w,z),y). K(x,K(y,z)) * K(x,K(y,u)) = K(K(y,z) * K(u,y),x). x != K(y,K(z,R(u,w,w \ y))) * K(y,K(z,u)) | x = a(K(v5,v6),v7,v7 \ v5). K(x,K(y,R(z,u,u \ x)) * K(z,y)) = a(K(w,v5),v6,v6 \ w). x != K(y,K(z,u)) * w | x = K(u,v5) * (K(z,K(u,y)) * (K(u,v5) \ w)). K(x,K(y,z) * K(u,y)) = K(z,w) * (K(y,K(z,x)) * (K(z,w) \ K(x,K(y,u)))). K(x,y) * (K(z,K(x,u)) * (K(x,y) \ K(u,K(z,w)))) = K(u,K(z,x) * K(w,z)). K(x,K(y,z)) * K(x,K(z,u)) = K(x,K(z,y) * K(u,z)). K(x,K(y,z)) * K(x * K(y,u),K(y,w)) = K(x * K(y,u),K(y,z) * K(w,y)). x != K(y,K(z,u) * K(w,z)) | x = K(y,K(u,z) * K(z,w)). K(x,K(y,z)) * K(x,K(z,u)) = K(x,K(y,z) * K(z,u)). x != a(y,K(z,z \ 1),u) | x = 1. K(x,K(y,R(z,u,u \ x)) * K(z,y)) = 1. K(x,K(y,z) * K(z,R(y,u,u \ x))) = 1. K(x * y,K(z,u) * K(u,R(z,x,y))) = 1. x != T(T(y,K(z,u)),K(u,w)) | x = T(y,K(z,u) * K(u,w)). T(x,K(y,z) * K(R(z,u,w),y)) = T(x,K(y,z) * K(z,R(y,u,w))). K(K(x,y) * K(y,z),K(x,y) \ u) = K(K(y,z) * K(x,y),u). K(K(x,y) * K(y,z),K(y,x) * u) = K(K(y,z) * K(x,y),u). T(x,K(y,R(z,u,w)) * K(z,y)) = T(x,K(y,z) * K(z,R(y,u,w))). T(x,K(y,R(z,u,w)) * K(z,y)) = x * K(x,K(y,z) * K(z,R(y,u,w))). x * K(x,K(y,z) * K(z,R(y,u,w))) = T(x,K(y,R(z,u,w)) * K(z,y)). T(x,K(y,z) * K(R(u,w / u,v5),y)) = T(T(x,K(y,R(u,w,v5))),K(y,z)). K(x,K(y,z) * K(z,R(y,u,w))) = K(x,K(y,R(z,u,w)) * K(z,y)). K(x,K(y,R(z,u,w)) * K(z,y)) = K(x,K(y,z) * K(z,R(y,u,w))). x != T(T(y,K(z,u)),K(z,w)) | x = T(y,K(z,w) * K(u,z)). T(x,K(y,z) * K(R(u,w / u,v5),y)) = T(x,K(y,z) * K(R(u,w,v5),y)). T(x,K(y,z) * R(K(u,y),w,v5)) = T(x,K(y,z) * K(R(u,w,v5),y)). x != T(y,K(z,u) * K(w,z)) | x = T(y,K(z,w) * K(u,z)). T(x,K(y,z) * R(K(u,y),w,v5)) = T(x,K(y,R(u,w,v5)) * K(z,y)). T(x,K(y,R(z,u,w)) * K(v5,y)) = T(x,K(y,v5) * R(K(z,y),u,w)). K(x,y) * (K(z,K(x,u)) * (K(x,y) \ K(z,K(u,w)))) = K(u,K(z,x) * K(w,z)). K(x,K(y,z)) * K(x,K(y,u)) = K(x * K(y,w),K(y,z) * K(u,y)). K(x * K(y,z),K(y,u) * K(w,y)) = K(x,K(y,u)) * K(x,K(y,w)). K(x,K(y,z)) * K(x,K(y,u)) != w | K(x,K(y,z) * K(u,y)) = w. K(K(x,y) * K(y,z),u) != w | K(u,K(y,x) * K(z,y)) = w. K(K(x,y) * K(z,x),u) != w | K(u,K(x,y) * K(z,x)) = w. K(K(x,y) * K(y,z),K(y,x) * u) != w | K(u,K(y,z) * K(x,y)) = w. K(x,K(y,z)) * K(x,K(z,u)) = K(z,K(x,y) * K(u,x)). K(x,K(y,z)) * K(y,K(z,u)) = K(z,K(y,x) * K(u,y)). K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(v5,K(y,x)) * K(v5,K(y,R(w,z,u))). x != K(y,K(z,u)) * K(y,K(z,w)) | x = K(K(u,z) * K(z,w),y). K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(K(x,y) * K(y,R(w,z,u)),v5). K(K(x,y) * R(K(y,z),u,w),v5) = K(K(x,y) * K(y,R(z,u,w)),v5). x * ((x \ y) * (L(z,x,x) * (1 / T(z \ (y \ x),x)))) = ((x \ y) * L(z,x,x)) * (x / (z \ (y \ x))). T(x / R(y * K(z,y),u,y),T(R((z * y) / z,u,y),y)) = ((R((z * y) / z,u,y) \ y) \ y) \ x. T((x / R(y,z,y)) * K(y,u),T(R((u * y) / u,z,y),y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x. T((x / R(y,z,y)) * K(y,u),R(T((u * y) / u,y),z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x. T((x / R(y,z,y)) * K(y,u),R((u * y) / u,z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x. x != T(y,R((z * u) / z,w,v5)) | x = T(y,R(z / (z / u),w,v5)). ((R((x * y) / x,z,y) \ y) \ y) \ u = T((u / R(y,z,y)) * K(y,x),R(x / (x / y),z,y)). T((x / R(y,z,y)) * K(y,u),R(u / (u / y),z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x. x != T(y,R(z / (z / u),w,u)) | x = T(y,z / (z / u)). ((R((x * y) / x,z,y) \ y) \ y) \ u = T((u / R(y,z,y)) * K(y,x),x / (x / y)). T((x / R(y,z,y)) * K(y,u),u / (u / y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x. x != T(y * K(z,u),u / (u / z)) | x = ((u * z) / u) \ (y * z). ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ ((u / R(y,z,y)) * y). ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ (y * (R(y,z,y) \ u)). x != ((y * z) / y) \ (z * u) | x = T(z,y) * (z \ u). ((R((x * y) / x,z,y) \ y) \ y) \ u = T(y,x) * (y \ (R(y,z,y) \ u)). ((x \ L(T(x,y),z,x)) \ x) \ u = T(x,y) * (x \ (R(x,z,x) \ u)). R(x * K(y,x),z,x) \ u = T(x,y) * (x \ (R(x,z,x) \ u)). T(x,y) * (x \ (R(x,z,x) \ u)) = R(x * K(y,x),z,x) \ u. R(x * K(y,x),z,x) \ u != w | K(x,y) * (R(x,z,x) \ u) = w. L(x \ 1,x,y) * L(L(x \ 1,x,y) \ 1,z,u) = L((x \ 1) * L((x \ 1) \ 1,z,u),T(x,w),y). L((x \ 1) * L((x \ 1) \ 1,y,z),T(x,u),w) = L(x \ 1,x,w) * L(L(x \ 1,x,w) \ 1,y,z). x != L(y,z,u) * L(L(y,z,u) \ 1,w,v5) | x = L(y * L(y \ 1,w,v5),z,u). L((x \ 1) * L((x \ 1) \ 1,y,z),T(x,u),w) = L((x \ 1) * L((x \ 1) \ 1,y,z),x,w). L((x \ 1) * L((x \ 1) \ 1,y,z),T(x,u),w) = L(x \ L(x,y,z),x,w). L(x \ L(x,y,z),T(x,u),w) = L(x \ L(x,y,z),x,w). a(x,T(y,z),K(u,y \ L(y,w,v5))) * K(u,L(y \ L(y,w,v5),y,x)) = K(u,y \ L(y,w,v5)). K(x,K((y * z) * u,u \ L(u,z,y))) = K(x,K(y * (z * u),a(y,z,u) * (y * (z * u)))). K(x,K(y * (z * u),a(y,z,u) * (y * (z * u)))) = K(x,K((y * z) * u,u \ L(u,z,y))). x != L(y,z,u / (1 / w)) | x = L(y,z,(u \ 1) \ w). L(x,(y / z) * L(u,y \ z,y \ z),(1 / (y / z)) \ u) = L(x,u / (1 / (y / z)),(u \ 1) \ (y / z)). K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(y,z,u),w * K(x,y)). x != K(R(y,z,u),w * K(v5,y)) | x = K(R(y,z,u),w). K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(y,z,u),w). K(R(x,y,z),R(x / u,u,K(w,x)) \ (w \ (w * x))) = K(R(x,y,z),u). K(R(x,y,z),R(x / u,u,K(w,x)) \ x) = K(R(x,y,z),u). K(R(x,y,z),R(x / u,u,L(K(w,x),v5,v6)) \ x) = K(R(x,y,z),u). (x * L(y,x,y)) / T(T(x,y),L(T(y,x),z,u)) = T(y,x * y) * a(u,z,K(T(x,y),T(y,x * y))). (x * L(y,x,y)) / T(T(x,L(y,z,u)),y) = T(y,x * y) * a(u,z,K(T(x,y),T(y,x * y))). T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = (y * L(x,y,x)) / T(T(y,L(x,u,z)),x). T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = (y * L(x,y,x)) / T(T(y,x),L(x,u,z)). x != (y * L(z,u,z)) / T(T(y,z),w) | x = K(w,y) * L(z,u,z). T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = K(L(x,u,z),y) * L(x,y,x). T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = K(x,L(y,u,z)) * L(x,y,x). x != K(y,z) * L(y,u,y) | x = L(T(y,z),u,y). T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = L(T(x,L(y,u,z)),y,x). T(x,y * x) * a(z,u,K(T(y,x),T(x,y))) = L(T(x,L(y,u,z)),y,x). T(x,y * x) * a(z,u,K(y,x)) = L(T(x,L(y,u,z)),y,x). x != T(y,z * y) * a(u,w,K(z,y)) | x = L(K(z * y,y),w,u) \ T(y,K(z * y,y)). L(T(x,L(y,z,u)),y,x) = L(K(y * x,x),z,u) \ T(x,K(y * x,x)). L(K(x * y,y),z,u) \ T(y,K(x * y,y)) = L(T(y,L(x,z,u)),x,y). K(x * y,L(y,z,u)) \ T(y,K(x * y,y)) = L(T(y,L(x,z,u)),x,y). K(x * y,L(y,z,u)) \ y = L(T(y,L(x,z,u)),x,y). L(T(x,L(y,z,u)),y,x) = K(y * x,L(x,z,u)) \ x. L(T(x,L(y,z,u)),y,x) = K(L(x,z,u),y * x) * x. L(T(x,L(y,z,u)),y,x) = K(x,L(y * x,z,u)) * x. L(T(x,L(y,z,u)),y,x) = T(x,L(y * x,z,u)). x != L(y,z / (1 / u),w) | x = L(y,(z \ 1) \ u,w). L(x,(y / z) * L(u,y \ z,y \ z),(1 / (y / z)) \ u) = L(x,(u \ 1) \ (y / z),(u \ 1) \ (y / z)). T((1 / x) * R((1 / x) \ 1,y,z),R(x,u,w) \ x) = (1 / x) * R((1 / x) \ 1,y,z). T((1 / x) * R((1 / x) \ 1,y,z),R(x,u,w) \ x) = (1 / x) * R(x,y,z). x != (1 / y) * R(y,z,u) | x = y \ R(y,z,u). T((1 / x) * R((1 / x) \ 1,y,z),R(x,u,w) \ x) = x \ R(x,y,z). T((1 / x) * R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z). T(x \ R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z). ((x \ R(x,y,z)) \ 1) \ 1 = x \ R(x,y,z). T(R(x \ R(x,y,z),x,y * z),x * (y * z)) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1. T((x * (y * z)) \ (R(x,y,z) * (y * z)),x) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1. T((x * (y * z)) \ ((x * y) * z),x) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1. T(a(x,y,z),x) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1. (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 = T(a(x,y,z),x). x != T(a(y,z,u),y) | x = a(y,z,u). (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 = a(x,y,z). a(x,y,z) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1. a(x,y,z) = (a(x,y,z) \ 1) \ 1. (a(x,y,z) \ 1) \ 1 = a(x,y,z). 1 / a(x,y,z) = a(x,y,z) \ 1. T(a(x,y,z),u) = ((a(x,y,z) \ 1) * u) \ u. ((a(x,y,z) \ 1) * u) \ u = T(a(x,y,z),u). (a(x,y,R(x,z,u)) \ 1) \ 1 = a(R(x,z,u),y,x). (a(x,y,z) \ 1) \ 1 != u | u = a(x,y,z). (a(x,y,z) \ 1) \ 1 != u | a(x,y,z) = u. a(x,y,R(x,z,u)) = a(R(x,z,u),y,x). a(R(x,y,z),u,x) = a(x,u,R(x,y,z)). a(R(x,y,z),u,x) != w | a(x,u,R(x,y,z)) = w. x != a(T(y,z),T(y,z) \ z,u) | x = (z * L(u,y \ T(z,y),y)) \ (z * u). a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = (y * L(R(T(x,y),z,u),x \ T(y,x),x)) \ (y * R(T(x,y),z,u)). (x * L(R(T(y,x),z,u),y \ T(x,y),y)) \ (x * R(T(y,x),z,u)) = a(R(T(y,x),z,u),T(y,x) \ x,T(y,x)). ((x \ y) / T(1 / z,y \ x)) * (1 / ((1 / y) * x)) = (1 / ((1 / y) * x)) * ((z \ ((1 / y) * x)) \ 1). ((x \ y) / T(1 / z,y \ x)) * (((x \ y) \ 1) \ 1) = (1 / ((1 / y) * x)) * ((z \ ((1 / y) * x)) \ 1). x != (y / z) * ((y \ 1) \ 1) | x = 1 / ((y \ z) / y). (1 / ((1 / x) * y)) * ((z \ ((1 / x) * y)) \ 1) = 1 / (((y \ x) \ T(1 / z,x \ y)) / (y \ x)). 1 / (((x \ y) \ T(1 / z,y \ x)) / (x \ y)) = (1 / ((1 / y) * x)) * ((z \ ((1 / y) * x)) \ 1). 1 / (((x \ y) * T(1 / z,x \ y)) * (x \ y)) = (1 / ((1 / x) * y)) * ((z \ ((1 / x) * y)) \ 1). 1 / (((1 / x) * (y \ z)) * (y \ z)) = (1 / ((1 / y) * z)) * ((x \ ((1 / y) * z)) \ 1). (1 / ((1 / x) * y)) * ((z \ ((1 / x) * y)) \ 1) = 1 / (((1 / z) * (x \ y)) * (x \ y)). x != 1 / ((y * z) * z) | x = z \ (z \ (1 / y)). (1 / ((1 / x) * y)) * ((z \ ((1 / x) * y)) \ 1) = (x \ y) \ ((x \ y) \ (1 / (1 / z))). (1 / ((1 / x) * y)) * ((z \ ((1 / x) * y)) \ 1) = (x \ y) \ ((x \ y) \ ((z \ 1) \ 1)). x != y \ (y \ ((z \ 1) \ 1)) | x = (1 / y) * ((z \ y) \ 1). (1 / ((1 / x) * y)) * ((z \ ((1 / x) * y)) \ 1) = (1 / (x \ y)) * ((z \ (x \ y)) \ 1). (1 / ((1 / x) * y)) * ((z \ ((1 / x) * y)) \ 1) = ((1 / y) * x) * ((z \ (x \ y)) \ 1). (((x \ y) \ 1) \ 1) * ((z \ ((1 / y) * x)) \ 1) = ((1 / x) * y) * ((z \ (y \ x)) \ 1). (((x \ y) \ 1) \ 1) * ((x \ y) * ((z \ 1) \ 1)) = ((1 / x) * y) * ((z \ (y \ x)) \ 1). x != ((y \ 1) \ 1) * (y * z) | x = y * (((y \ 1) \ 1) * z). ((1 / x) * y) * ((z \ (y \ x)) \ 1) = (x \ y) * ((((x \ y) \ 1) \ 1) * ((z \ 1) \ 1)). (x \ y) * ((((x \ y) \ 1) \ 1) * ((z \ 1) \ 1)) = ((1 / x) * y) * ((z \ (y \ x)) \ 1). (x \ y) * ((z \ ((x \ y) \ 1)) \ 1) = ((1 / x) * y) * ((z \ (y \ x)) \ 1). ((1 / x) * y) * ((z \ (y \ x)) \ 1) = (x \ y) * ((z \ ((x \ y) \ 1)) \ 1). T((x \ y) * ((z \ ((x \ y) \ 1)) \ 1),(1 / x) * y) = (z \ (y \ x)) \ ((1 / x) * y). T((x \ y) * ((z \ ((x \ y) \ 1)) \ 1),x \ y) = (z \ (y \ x)) \ ((1 / x) * y). (x \ ((y \ z) \ 1)) \ (y \ z) = (x \ (z \ y)) \ ((1 / y) * z). x != (y \ (z \ 1)) \ z | x = (z / (1 / y)) * z. (x \ (y \ z)) \ ((1 / z) * y) = ((z \ y) / (1 / x)) * (z \ y). x != ((y \ 1) \ (z \ u)) \ ((1 / u) * z) | x = (z \ u) \ (1 / ((z \ u) * y)). ((x \ y) / (1 / (z \ 1))) * (x \ y) = (y \ x) \ (1 / ((y \ x) * z)). (1 / ((x \ y) / z)) \ (((1 / y) * x) \ 1) = (((y \ x) / (1 / z)) * (y \ x)) \ 1. ((x \ y) / z) * (x \ y) = (y \ x) \ (1 / ((y \ x) * z)). (x \ y) \ (1 / ((x \ y) * z)) = ((y \ x) / z) * (y \ x). (1 / ((x \ y) / z)) \ (((1 / y) * x) \ 1) = (y \ x) \ (((y \ x) / (1 / z)) \ 1). (1 / ((x \ y) / z)) \ (((1 / y) * x) \ 1) = (y \ x) \ ((1 / z) * ((y \ x) \ 1)). (1 / ((x \ y) / z)) \ (((1 / y) * x) \ 1) = ((y \ x) \ 1) * ((1 / z) / (y \ x)). x != (y \ 1) * ((1 / z) / y) | x = 1 / (y * (z * y)). (1 / ((x \ y) / z)) \ (((1 / y) * x) \ 1) = 1 / ((y \ x) * (z * (y \ x))). (1 / ((x \ y) / z)) \ (x \ y) = 1 / ((y \ x) * (z * (y \ x))). 1 / ((x \ y) * (z * (x \ y))) = (1 / ((y \ x) / z)) \ (y \ x). x != (1 / (y / z)) \ y | x = y / (y \ z). 1 / ((x \ y) * (z * (x \ y))) = (y \ x) / ((y \ x) \ z). ((x \ y) / ((x \ y) \ z)) \ 1 = (y \ x) * (z * (y \ x)). ((x \ y) \ z) * ((x \ y) \ 1) = (y \ x) * (z * (y \ x)). (x \ y) * (z * (x \ y)) = (y \ x) \ (z / (y \ x)). (x \ y) \ (z / (x \ y)) = (y \ x) * (z * (y \ x)). x != (y \ z) \ (u / (y \ z)) | x = ((1 / z) * y) * (u * ((1 / z) * y)). (x \ y) * (z * (x \ y)) = ((1 / x) * y) * (z * ((1 / x) * y)). ((1 / x) * y) * (z * ((1 / x) * y)) = (x \ y) * (z * (x \ y)). x != (y \ z) \ ((u * z) / (y \ z)) | x = ((y \ z) \ u) * L(y,y,z * y). (x \ y) * ((z * x) * (x \ y)) = ((y \ x) \ z) * L(y,y,x * y). ((x \ y) \ z) * L(x,x,y * x) = (y \ x) * ((z * y) * (y \ x)). (((x \ y) \ y) * (1 / y)) * (z * ((1 / y) * ((x \ 1) \ 1))) = (y \ ((x \ 1) \ 1)) * (z * (y \ ((x \ 1) \ 1))). ((((x \ y) \ 1) * (1 / z)) * (((1 / y) * x) \ 1)) \ K(u,w) = ((1 / (((1 / y) * x) * z)) \ (x \ y)) * K(u,w). T(x * (y \ 1),K(z,z \ K(u,w))) = (K(z,z \ K(u,w)) * x) * (y \ K(z,z \ K(u,w))). (K(x,x \ K(y,z)) * u) * (w \ K(x,x \ K(y,z))) = T(u * (w \ 1),K(x,x \ K(y,z))). x != T(y,K(z,z \ u)) | x = T(y,K(z,u)). (K(x,x \ K(y,z)) * u) * (w \ K(x,x \ K(y,z))) = T(u * (w \ 1),K(x,K(y,z))). T(K(x,y) * z,u) * T(K(y,x),T(w,T(K(x,y) * z,u))) = K(y,K(x,w)) * (K(y,x) * T(z * K(x,y),u)). x != T(y,R(z \ K(u,u \ 1),w,v5)) | x = T(y,R(z \ 1,w,v5)). T(x,R(T(y / T(z \ 1,u),K(z,z \ 1)),w,v5)) = T(x,R(((y / T(1 / z,u)) \ 1) \ 1,w,v5)). x != T(y,R((z \ 1) \ 1,u,w)) | x = T(y,R(z,u,w)). T(x,R(T(y / T(z \ 1,u),K(z,z \ 1)),w,v5)) = T(x,R(y / T(1 / z,u),w,v5)). T(x,R(y / T(z \ 1,u),w,v5)) = T(x,R(y / T(1 / z,u),w,v5)). T(x,R(y / T(1 / z,u),w,v5)) = T(x,R(y / T(z \ 1,u),w,v5)). (1 / (x * (1 / ((y \ (1 / z)) * x)))) * ((y \ (1 / z)) \ 1) = (y \ (1 / z)) * (1 / (y \ (x * (1 / (z * x))))). (x * (((x \ y) \ 1) \ 1)) \ ((1 / ((y \ x) * (1 / x))) \ z) = ((y \ x) * (1 / x)) * (((y \ x) * (1 / x)) * z). x \ (K(x * (1 / (y * x)),y) / z) = 1 / (((1 / (z * (x * (1 / (y * x))))) \ y) * x). 1 / (((1 / (x * (y * (1 / (z * y))))) \ z) * y) = y \ (K(y * (1 / (z * y)),z) / x). 1 / (((1 / (x * (y * (1 / (z * y))))) \ z) * y) = y \ (K(z,z \ 1) / x). 1 / (((1 / (x * (y * (1 / (z * y))))) \ z) * y) = y \ (z * (1 / (x * z))). (K(x,x \ 1) * y) \ (x * (1 / (((1 / (z * (x * (1 / (y * x))))) \ y) * x))) = (x * (1 / (y * x))) / z. (K(x,x \ 1) * y) \ (x * (x \ (y * (1 / (z * y))))) = (x * (1 / (y * x))) / z. (K(x,x \ 1) * y) \ (y * (1 / (z * y))) = (x * (1 / (y * x))) / z. x != (K(y,y \ 1) * z) \ u | x = K(y,y \ 1) * (z \ u). (x * (1 / (y * x))) / z = K(x,x \ 1) * (y \ (y * (1 / (z * y)))). K(x,x \ 1) * (y \ (y * (1 / (z * y)))) = (x * (1 / (y * x))) / z. K(x,x \ 1) * (1 / (y * z)) = (x * (1 / (z * x))) / y. K(x,x \ 1) / (y * z) = (x * (1 / (z * x))) / y. (x * (1 / (y * x))) / z = K(x,x \ 1) / (z * y). (x * (1 / (y * x))) / z = x * (1 / ((z * y) * x)). x \ ((x * (1 / (y * x))) * (((x * (1 / (y * x))) \ z) * L(u,x * (1 / (y * x)),x * (1 / (y * x))))) = 1 / (((u \ (z \ (x * (1 / (y * x))))) * y) * x). x != (y * (1 / (((z * z) \ u) * y))) / z | x = (y * (((y \ u) \ 1) \ 1)) \ z. x * (1 / ((y * ((y * y) \ z)) * x)) = (x * (((x \ z) \ 1) \ 1)) \ y. x != (y * (1 / (z * y))) / (y \ (u \ (y * (1 / (z * y))))) | x = (u * (1 / (z / y))) / (y * (1 / (z * y))). x * (1 / (((x \ (y \ (x * (1 / (z * x))))) * z) * x)) = (y * (1 / (z / x))) / (x * (1 / (z * x))). ((x * (y \ 1)) * ((y / x) / z)) / u = (x * (y \ 1)) * (1 / ((u * z) * (x * (y \ 1)))). (x * (y \ 1)) * (1 / ((z * u) * (x * (y \ 1)))) = ((x * (y \ 1)) * ((y / x) / u)) / z. (((1 / x) * y) * (1 / (1 / ((y \ x) / z)))) / u = ((1 / x) * y) * (1 / ((u * ((z \ 1) \ 1)) * ((1 / x) * y))). ((1 / x) * y) * (1 / ((z * ((u \ 1) \ 1)) * ((1 / x) * y))) = (((1 / x) * y) * (1 / (1 / ((y \ x) / u)))) / z. (x * (1 / (K(y \ z,z \ y) * x))) / (u * w) = x * (1 / ((u * (w * K(y \ z,z \ y))) * x)). L(x,y * z,y * (1 / (((y * z) * u) * y))) = L(x,y * z,(z \ (1 / y)) / u). (x / ((((y \ z) * (1 / z)) \ u) \ 1)) * (u \ 1) = (x * u) / (z * (1 / (((u \ 1) * y) * z))). x * (1 / (((y \ 1) * z) * x)) = (x * (((x \ z) \ 1) \ 1)) \ y. (x * (((x \ y) \ 1) \ 1)) \ z = x * (1 / (((z \ 1) * y) * x)). x != (y * (((y \ (((z \ 1) \ 1) * u)) \ 1) \ 1)) \ (1 / w) | x = (z * (y * (((y \ u) \ 1) \ 1))) \ (1 / w). x * (1 / ((((1 / y) \ 1) * (((z \ 1) \ 1) * u)) * x)) = (z * (x * (((x \ u) \ 1) \ 1))) \ (1 / y). (x \ (1 / y)) \ ((x \ 1) * (z * (((z \ u) \ 1) \ 1))) = (y * x) / (z * (1 / (((x \ 1) * u) * z))). (x * (((x \ (L(y \ 1,z,u) / x)) \ 1) \ 1)) \ y = x * (1 / L((y \ 1) * L(y \ 1,z,u),x,x)). x != L(y,z,u * (1 / w)) | x = L(y,z,u * (w \ 1)). L(x,y * z,(z \ (1 / y)) / u) = L(x,y * z,y * ((((y * z) * u) * y) \ 1)). L(x,y * z,y * ((((y * z) * u) * y) \ 1)) = L(x,y * z,(z \ (1 / y)) / u). L(x,y * z,y * (y \ (((y * z) * u) \ 1))) = L(x,y * z,(z \ (1 / y)) / u). L(x,y * z,y * (y \ (u \ ((y * z) \ 1)))) = L(x,y * z,(z \ (1 / y)) / u). L(x,y * z,y * (y \ (u \ (z \ (y \ 1))))) = L(x,y * z,(z \ (1 / y)) / u). L(x,y * z,u \ (z \ (y \ 1))) = L(x,y * z,(z \ (1 / y)) / u). L(x,y * z,(z \ (1 / y)) / u) = L(x,y * z,u \ (z \ (y \ 1))). x != L(y,z,(u \ (1 / w)) / v5) | x = L(y,z,(w * u) \ (v5 \ 1)). L(x,y * z,u \ (z \ (y \ 1))) = L(x,y * z,(y * z) \ (u \ 1)). L(x,y * z,(y * z) \ (u \ 1)) = L(x,y * z,u \ (z \ (y \ 1))). (x * (y \ 1)) * (1 / ((z * y) * (x * (y \ 1)))) = ((y \ x) * (1 / x)) / z. x != ((y \ z) * (1 / z)) / u | x = y \ (z * (1 / (u * z))). (x * (y \ 1)) * (1 / ((z * y) * (x * (y \ 1)))) = y \ (x * (1 / (z * x))). (x * (y \ 1)) * ((y / x) / (z * y)) = y \ (x * (1 / (z * x))). x \ (y * (1 / (z * y))) = K(y \ x,x \ y) / (z * x). K(x \ y,y \ x) / (z * y) = y \ (x * (1 / (z * x))). K(x \ y,y \ x) / (z * x) = x \ (y * (1 / (z * y))). (x * ((1 / x) * K(y \ z,z \ y))) / (u * w) = x * (1 / ((u * (w * K(y \ z,z \ y))) * x)). x * (1 / ((y * (((z \ 1) \ 1) * u)) * x)) = (z * (x * (((x \ u) \ 1) \ 1))) \ (1 / y). (x * (y * (((y \ z) \ 1) \ 1))) \ (1 / u) = y * (1 / ((u * (((x \ 1) \ 1) * z)) * y)). (x \ (1 / y)) \ (((z \ x) \ u) * (1 / u)) = (y * x) / (u * (1 / (((x \ 1) * z) * u))). (x * y) / (z * (1 / (((y \ 1) * u) * z))) = (y \ (1 / x)) \ (((u \ y) \ z) * (1 / z)). (x * ((L(y \ 1,z,u) \ x) \ (1 / x))) \ y = x * (1 / L((y \ 1) * L(y \ 1,z,u),x,x)). x * (1 / L((y \ 1) * L(y \ 1,z,u),x,x)) = (x * ((L(y \ 1,z,u) \ x) \ (1 / x))) \ y. x * (1 / L((y \ 1) * L(y \ 1,z,u),x,x)) = (x * (x \ (L(1 / y,z,u) / x))) \ y. x * (1 / L((y \ 1) * L(y \ 1,z,u),x,x)) = (L(1 / y,z,u) / x) \ y. x * (1 / L(y \ L(1 / y,z,u),x,x)) = (L(1 / y,z,u) / x) \ y. x * (x \ (x / (y \ L(1 / y,z,u)))) = (L(1 / y,z,u) / x) \ y. (L(1 / x,y,z) / u) \ x = u / (x \ L(1 / x,y,z)). x / (y \ L(1 / y,z,u)) = (L(1 / y,z,u) / x) \ y. ((L(1 / x,y,z) / u) \ x) * (x \ 1) = (u * x) / (x * L(x \ 1,y,z)). (L(1 / x,y,z) / u) \ 1 = (u * x) / (x * L(x \ 1,y,z)). (x * y) / (y * L(y \ 1,z,u)) = (L(1 / y,z,u) / x) \ 1. (x * y) / (y * L(y \ 1,z,u)) = x * (L(1 / y,z,u) \ 1). x * (1 / (((((1 / y) * z) * (x \ 1)) \ ((1 / y) * z)) * x)) = ((z / x) \ ((1 / y) \ x)) \ ((x \ 1) \ (z \ y)). x != ((y \ z) \ z) \ R((y \ z) \ z,u,R(y,w,v5)) | x = a(y,u,R(y,w,v5)). x \ (y \ ((R(x,z,R(x,u,w)) * (x \ y)) * x)) = a(x,K(x,v5) * z,R(x,u,w)). a(x,K(x,y) * z,R(x,u,w)) = x \ (v5 \ ((R(x,z,R(x,u,w)) * (x \ v5)) * x)). a(T(x,y),z,R(x,u,w)) = x \ (v5 \ ((R(x,z,R(x,u,w)) * (x \ v5)) * x)). a(T(x,y),z,R(x,u,w)) = x \ (v5 \ ((x * (x \ v5)) * R(x,z,R(x,u,w)))). a(T(x,y),z,R(x,u,w)) = x \ (v5 \ (v5 * R(x,z,R(x,u,w)))). a(T(x,y),z,R(x,u,w)) = x \ R(x,z,R(x,u,w)). x != y \ R(y,z,R(y,u,w)) | x = a(y,z,R(y,u,w)). a(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w)). x != a(T(y,z),T(y,z) \ u,R(y,w,v5)) | x = a(y,y \ u,R(y,w,v5)). a(x,T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w)). T(x,x * K((y * z) \ (u * w),w)) \ T(K(w,(y * z) \ (u * w)) * x,x) = K(w,T((y * (w \ z)) \ u,x)). x != (y \ (z \ 1)) * (u * (y \ (z \ 1))) | x = (z * y) \ (u / (z * y)). (((x \ y) \ y) * (1 / y)) * (z * ((1 / y) * ((x \ 1) \ 1))) = ((x \ 1) * y) \ (z / ((x \ 1) * y)). ((((x \ y) \ 1) * (1 / z)) * (x \ y)) \ K(u,w) = ((1 / (((1 / y) * x) * z)) \ (x \ y)) * K(u,w). (1 / (((x \ y) \ z) * (x \ y))) \ K(u,w) = ((1 / (((1 / y) * x) * z)) \ (x \ y)) * K(u,w). ((1 / (((1 / x) * y) * z)) \ (y \ x)) * K(u,w) = (1 / (((y \ x) \ z) * (y \ x))) \ K(u,w). ((1 / (((1 / x) * y) * z)) \ (y \ x)) * K(u,w) = ((x \ y) * (1 / ((x \ y) * z))) \ K(u,w). x != (y * (1 / (y * z))) \ K(u,w) | x = (y * (z * (1 / y))) * K(u,w). ((1 / (((1 / x) * y) * z)) \ (y \ x)) * K(u,w) = ((x \ y) * (z * (1 / (x \ y)))) * K(u,w). ((1 / (((1 / x) * y) * z)) \ (y \ x)) * K(u,w) = ((x \ y) * (z * ((1 / y) * x))) * K(u,w). ((((x \ (y \ z)) \ 1) \ 1) \ (y \ z)) * K(u,w) = ((z \ y) * (x * ((1 / y) * z))) * K(u,w). (((x \ y) \ z) * (x \ y)) * K(u,w) = ((y \ x) * (z * ((1 / x) * y))) * K(u,w). ((x \ y) * (z * ((1 / y) * x))) * K(u,w) = (((y \ x) \ z) * (y \ x)) * K(u,w). (x \ y) * (z * ((1 / y) * x)) = ((y \ x) \ z) * (y \ x). (((x / y) * z) \ x) * (1 * ((1 / x) * ((x / y) * z))) = (x \ ((z / x) \ y)) * (x \ ((x / y) * z)). (((x / y) * z) \ x) * ((1 / x) * ((x / y) * z)) = (x \ ((z / x) \ y)) * (x \ ((x / y) * z)). x != (y \ z) * ((1 / z) * y) | x = K(z \ y,y \ z). (x \ ((y / x) \ z)) * (x \ ((x / z) * y)) = K(x \ ((x / z) * y),((x / z) * y) \ x). K(x \ ((x / y) * z),((x / y) * z) \ x) = (x \ ((z / x) \ y)) * (x \ ((x / y) * z)). K(x \ ((x / y) * z),x \ ((z / x) \ y)) = (x \ ((z / x) \ y)) * (x \ ((x / y) * z)). x != (y \ ((z / y) \ u)) * (y \ ((y / u) * z)) | x = K(y \ ((z / y) \ u),y \ ((y / u) * z)). K(x \ ((x / y) * z),x \ ((z / x) \ y)) = K(x \ ((z / x) \ y),x \ ((x / y) * z)). K(x \ ((y / x) \ z),x \ ((x / z) * y)) = K(x \ ((x / z) * y),x \ ((y / x) \ z)). K(x \ ((x / y) * z),x \ ((z / x) \ y)) / (x \ ((x / y) * z)) = T((x \ ((x / y) * z)) \ 1,1). x != K(y,K(z,u)) * (K(y,z) * w) | x = K(y,T(z,u)) * w. T(K(x,y) * z,u) * T(K(y,x),T(w,T(K(x,y) * z,u))) = K(y,T(x,w)) * T(z * K(x,y),u). ((((x \ (1 / y)) * z) \ 1) \ (1 / z)) * ((x \ (1 / y)) \ 1) = (x \ (1 / y)) * (1 / (x \ (z * (1 / (y * z))))). (x * (((x \ y) \ 1) \ 1)) \ (((x * (1 / (1 * x))) \ y) \ z) = ((y \ x) * (1 / x)) * (((y \ x) * (1 / x)) * z). ((1 / x) * y) * (1 / ((z * ((u \ 1) \ 1)) * ((1 / x) * y))) = (((1 / x) * y) * ((((y \ x) / u) \ 1) \ 1)) / z. x * (1 / ((((1 / y) * z) * ((x \ ((1 / y) * z)) \ 1)) * x)) = ((z / x) \ ((1 / y) \ x)) \ ((x \ 1) \ (z \ y)). x != T(y,y * K(z,u)) \ T(K(u,z) * y,y) | x = K(u,T(z,y)). K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w)). K(x,y / (z * (x \ u))) = K(x,T((z * u) \ (y * x),z * u)). K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z))). K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u))). K(x,((y * z) / u) \ x) = K(x,u / (y * (x \ z))). K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x). R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w)). x != R(K(y,(z / (u / w)) \ y),w \ u,w) | x = K(y,u / ((y \ z) * w)). K(x,y / ((z * (x \ u)) * w)) = K(x,y / ((x \ (z * u)) * w)). K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w)). K(x,(((y * z) * u) / w) \ x) = K(x,w / ((y * (x \ z)) * u)). K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x). x != K(y,(z * u) / ((w * (y \ z)) * u)) | x = R(K(y,w \ y),z,u). K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u). K(x,R(y,z,u) \ x) = R(K(x,y \ x),z,u). R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x). R(K(x,R(1 / y,y,z) \ x),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x). R(K(x,y),z,u) = K(x,R(y \ x,z,u) \ x). K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u). R(K(x,x * y),z,u) = K(x,R(y \ 1,z,u) \ x). K(x,R(y \ 1,z,u) \ x) = R(K(x,x * y),z,u). R(K(x,R(y \ x,z,u) \ x),w,v5) = K(x,R(R(x / y,z,u),w,v5) \ x). x != K(y,R(z \ 1,u,w) \ v5) | x = K(y,R(1 / z,u,w) \ v5). R(K(x,x * y),z,u) = K(x,R(1 / y,z,u) \ x). K(x,R(1 / y,z,u) \ x) = R(K(x,x * y),z,u). R(R(K(x,y),z,u),w,v5) = K(x,R(R(x / y,z,u),w,v5) \ x). K(x,R(R(x / y,z,u),w,v5) \ x) = R(R(K(x,y),z,u),w,v5). R(K(x,R(y \ 1,y,z) \ x),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x). R(K(x,x * y),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x). R(K(x,x * y),y * z,u) = K(x,x * (((y * z) * u) / (z * u))). R(K(x,x * y),y * z,u) = K(x,x * R(y,z,u)). ((x \ ((y \ (1 / z)) \ 1)) \ (1 / x)) * ((y \ (1 / z)) \ 1) = (y \ (1 / z)) * (1 / (y \ (x * (1 / (z * x))))). (x * (((x \ y) \ 1) \ 1)) \ (((x * (1 / x)) \ y) \ z) = ((y \ x) * (1 / x)) * (((y \ x) * (1 / x)) * z). (x * (((x \ y) \ 1) \ 1)) \ ((K(x,x \ 1) \ y) \ z) = ((y \ x) * (1 / x)) * (((y \ x) * (1 / x)) * z). (x * (((x \ y) \ 1) \ 1)) \ ((K(x,x \ 1) * y) \ z) = ((y \ x) * (1 / x)) * (((y \ x) * (1 / x)) * z). (x * (((x \ y) \ 1) \ 1)) \ (K(x,x \ 1) * (y \ z)) = ((y \ x) * (1 / x)) * (((y \ x) * (1 / x)) * z). K(x,x \ 1) * ((x * (((x \ y) \ 1) \ 1)) \ (y \ z)) = ((y \ x) * (1 / x)) * (((y \ x) * (1 / x)) * z). K(x,x \ 1) * (x * (1 / ((((y \ z) \ 1) * y) * x))) = ((y \ x) * (1 / x)) * (((y \ x) * (1 / x)) * z). T(x,x \ 1) * (1 / ((((y \ z) \ 1) * y) * x)) = ((y \ x) * (1 / x)) * (((y \ x) * (1 / x)) * z). x != T(y,y \ z) * (1 / (u * y)) | x = K(z,y \ 1) / u. ((x \ y) * (1 / y)) * (((x \ y) * (1 / y)) * z) = K(1,y \ 1) / (((x \ z) \ 1) * x). ((x \ y) * (1 / y)) * (((x \ y) * (1 / y)) * z) = 1 / (((x \ z) \ 1) * x). x != 1 / (((y \ z) \ 1) * y) | x = (y \ 1) * ((y \ 1) * z). ((x \ y) * (1 / y)) * (((x \ y) * (1 / y)) * z) = (x \ 1) * ((x \ 1) * z). ((1 / x) * y) * (1 / ((z * ((u \ 1) \ 1)) * ((1 / x) * y))) = (((1 / x) * y) * ((u * ((y \ x) \ 1)) \ 1)) / z. x * (1 / ((((1 / y) * z) * ((z \ y) * ((x \ 1) \ 1))) * x)) = ((z / x) \ ((1 / y) \ x)) \ ((x \ 1) \ (z \ y)). ((x \ (y * ((z \ 1) \ 1))) \ (1 / x)) * ((z \ (1 / y)) \ 1) = (z \ (1 / y)) * (1 / (z \ (x * (1 / (y * x))))). ((1 / x) * y) * (1 / ((z * ((u \ 1) \ 1)) * ((1 / x) * y))) = (((1 / x) * y) * (((y \ x) \ 1) \ (u \ 1))) / z. (((x * ((y \ 1) \ 1)) \ z) * (1 / z)) * ((y \ (1 / x)) \ 1) = (y \ (1 / x)) * (1 / (y \ (z * (1 / (x * z))))). ((1 / x) * y) * (1 / ((z * ((u \ 1) \ 1)) * ((1 / x) * y))) = (K(x \ y,y \ x) * (u \ 1)) / z. ((1 / x) * y) * (1 / ((z * ((u \ 1) \ 1)) * ((1 / x) * y))) = (u \ K(y \ x,x \ y)) / z. (x * (((x \ ((y \ 1) / z)) \ 1) \ 1)) * ((y \ (1 / z)) \ 1) = (y \ (1 / z)) * (1 / (y \ (x * (1 / (z * x))))). (x * (((x \ (y \ (1 / z))) \ 1) \ 1)) * ((y \ (1 / z)) \ 1) = (y \ (1 / z)) * (1 / (y \ (x * (1 / (z * x))))). (x * (((x \ (y \ (1 / z))) \ 1) \ 1)) * (z * ((y \ 1) \ 1)) = (y \ (1 / z)) * (1 / (y \ (x * (1 / (z * x))))). (x \ (1 / y)) * (1 / (x \ (z * (1 / (y * z))))) = z * (1 / (((y * ((x \ 1) \ 1)) \ (1 / (x \ (1 / y)))) * z)). x * (1 / (((y * ((z \ 1) \ 1)) \ (1 / (z \ (1 / y)))) * x)) = (z \ (1 / y)) * (1 / (z \ (x * (1 / (y * x))))). x * (1 / (((y * ((z \ 1) \ 1)) \ ((1 / (1 / y)) * z)) * x)) = (z \ (1 / y)) * (1 / (z \ (x * (1 / (y * x))))). x * (1 / (((y * ((z \ 1) \ 1)) \ (((y \ 1) \ 1) * z)) * x)) = (z \ (1 / y)) * (1 / (z \ (x * (1 / (y * x))))). x * (1 / (K(y \ z,z \ y) * x)) = (z \ (1 / y)) * (1 / (z \ (x * (1 / (y * x))))). (x \ (1 / y)) * (1 / (x \ (z * (1 / (y * z))))) = z * (1 / (K(y \ x,x \ y) * z)). (x \ (1 / y)) * (1 / (x \ (z * (1 / (y * z))))) = z * ((1 / z) * K(x \ y,y \ x)). (x \ (1 / y)) * (1 / (x \ (z * (1 / (y * z))))) = z * (K(x \ y,y \ x) / z). (x \ (1 / y)) * ((1 / (z * (1 / (y * z)))) * x) = z * (K(x \ y,y \ x) / z). (x \ (1 / y)) * ((((y * z) \ 1) \ (1 / z)) * x) = z * (K(x \ y,y \ x) / z). (x \ (1 / y)) * (((z \ (y \ 1)) \ (1 / z)) * x) = z * (K(x \ y,y \ x) / z). (x \ (1 / y)) * ((((y \ 1) \ z) * (1 / z)) * x) = z * (K(x \ y,y \ x) / z). (x \ (1 / y)) * ((z * (((z \ y) \ 1) \ 1)) * x) = z * (K(x \ y,y \ x) / z). (x \ (1 / y)) * (z * (1 / ((x \ (1 / y)) * z))) = z * (K(x \ y,y \ x) / z). K(x \ (y \ (1 / z)),(y \ (1 / z)) \ x) = x * (K(y \ z,z \ y) / x). K((x * y) * z,((y \ (1 / x)) \ z) \ 1) = z * (K(y \ x,x \ y) / z). K((x * y) * z,z \ (y \ (1 / x))) = z * (K(y \ x,x \ y) / z). x != K(y,z \ (u \ (1 / w))) | x = K(y,z \ (u \ (w \ 1))). x * (K(y \ z,z \ y) / x) = K((z * y) * x,x \ (y \ (z \ 1))). K((x * y) * z,z \ (y \ (x \ 1))) = z * (K(y \ x,x \ y) / z). T(L(x,y,y \ 1),y) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x). L(T(x,y),y,y \ 1) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x). ((1 / x) * (y * x)) \ ((1 / x) \ T(L(y,x,x \ 1),(1 / x) \ 1)) = L(y,x,x \ 1) \ (x * y). ((1 / x) * (y * x)) \ ((1 / x) \ T(L(y,x,x \ 1),x)) = L(y,x,x \ 1) \ (x * y). ((1 / x) * (y * x)) \ ((1 / x) \ L(T(y,x),x,x \ 1)) = L(y,x,x \ 1) \ (x * y). ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y). ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y). (L(x,y,y \ 1) \ (y * x)) \ 1 = 1 / R(T(y,x),y \ 1,x * y). 1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1. ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = R(T(y,x),y \ 1,x * y). x != ((L(y,z,z \ 1) \ (z * y)) \ 1) \ 1 | x = ((z \ 1) * (z * y)) \ (z * y). R(T(x,y),x \ 1,y * x) = ((x \ 1) * (x * y)) \ (x * y). ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x). (K(x,y / z) * K(x,K(u,z \ y))) / T(K(x,z \ y),u) = R(K(x,K(z,y)),K(x,z \ y),K(K(x,z \ y),u)). K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = (u * K(z,x)) \ ((K(x,y) * K(z,x)) * (u * K(y,x))). (x * (y * (K(y,z) * (y \ u)))) * K(z,L(y,K(z,y) \ (y \ u),x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y). (((T(x,x \ 1) / y) / z) / T(x,x \ 1)) \ T(x,x \ 1) = ((x \ 1) \ z) * L(y,x,x). (x \ T((T(x,x \ 1) / y) / z,x \ 1)) \ T(x,x \ 1) = ((x \ 1) \ z) * L(y,x,x). x != (y \ z) \ T(y,u) | x = (z \ y) * T(y,u). ((x \ 1) \ y) * L(z,x,x) = (T((T(x,x \ 1) / z) / y,x \ 1) \ x) * T(x,x \ 1). (T((T(x,x \ 1) / y) / z,x \ 1) \ x) * T(x,x \ 1) = ((x \ 1) \ z) * L(y,x,x). x != y * T(z,z \ 1) | x = T((z \ 1) \ y,z). ((x \ 1) \ y) * L(z,x,x) = T((x \ 1) \ (T((T(x,x \ 1) / z) / y,x \ 1) \ x),x). T((x \ 1) \ (T((T(x,x \ 1) / y) / z,x \ 1) \ x),x) = ((x \ 1) \ z) * L(y,x,x). T(x * ((T((T(x,x \ 1) / y) / z,x \ 1) \ 1) * x),x) = ((x \ 1) \ z) * L(y,x,x). T(x * (x * (((T(x,x \ 1) / y) / z) \ 1)),x) = ((x \ 1) \ z) * L(y,x,x). T(x * (x * (y * ((T(x,x \ 1) / z) \ 1))),x) = ((x \ 1) \ y) * L(z,x,x). T(x * (x * (y * (z * (T(x,x \ 1) \ 1)))),x) = ((x \ 1) \ y) * L(z,x,x). T(x * (x * (y * (z * (1 / x)))),x) = ((x \ 1) \ y) * L(z,x,x). T(T((x * y) * z,x \ 1),x) = ((x \ 1) \ y) * L(z,x,x). T(T((x * y) * z,x),x \ 1) = ((x \ 1) \ y) * L(z,x,x). x * y != T(T(z,u),u \ 1) | x \ L(z,u,u) = y. ((x \ 1) \ y) \ L((x * y) * z,x,x) = L(z,x,x). x != ((y \ 1) \ K(z,u)) \ L((y * K(z,u)) * w,y,y) | x = L(w,K(u,z) * (y \ 1),K(u,z) * (y \ 1)). L(x,y,y) = L(x,K(z,u) * (y \ 1),K(z,u) * (y \ 1)). L(x,K(y,z) * (u \ 1),K(y,z) * (u \ 1)) = L(x,u,u). x != L(y,z * (u \ 1),z * (u \ 1)) | x = L(y,z \ u,z \ u). L(x,y,y) = L(x,K(z,u) \ y,K(z,u) \ y). L(x,K(y,z) \ u,K(y,z) \ u) = L(x,u,u). L(x,K(y,z) * u,K(z,y) \ u) = L(x,u,u). L(x,K(y,z) * u,K(y,z) * u) = L(x,u,u). L(x,K(y,z) * K(y,u),(K(y,z) * K(y,u)) \ 1) = ((K(y,z) * K(y,u)) \ 1) * ((K(y,z) * K(y,u)) * x). ((K(x,y) * K(x,z)) \ 1) * ((K(x,y) * K(x,z)) * u) = L(u,K(x,y) * K(x,z),(K(x,y) * K(x,z)) \ 1). ((K(x,y) * K(x,z)) \ 1) * ((K(x,y) * K(x,z)) * u) = L(u,K(x,y) * K(x,z),K(y,x) * K(z,x)). (K(x,y) * K(z,y)) * ((K(y,x) * K(y,z)) * u) = L(u,K(y,x) * K(y,z),K(x,y) * K(z,y)). (K(x,y) * K(z,y)) * (K(y,x) * (K(y,z) * u)) = L(u,K(y,x) * K(y,z),K(x,y) * K(z,y)). x != (K(y,z) * K(u,z)) * w | x = K(u,z) * (K(y,z) * w). L(x,K(y,z) * K(y,u),K(z,y) * K(u,y)) = K(u,y) * (K(z,y) * (K(y,z) * (K(y,u) * x))). K(x,y) * (K(z,y) * (K(y,z) * (K(y,x) * u))) = L(u,K(y,z) * K(y,x),K(z,y) * K(x,y)). K(x,y) * (K(y,x) * z) = L(z,K(y,u) * K(y,x),K(u,y) * K(x,y)). L(x,K(y,z) * K(y,u),K(z,y) * K(u,y)) = K(u,y) * (K(y,u) * x). L(x,K(y,z) * K(y,u),K(z,y) * K(u,y)) = x. L(x,y \ (y \ ((y * z) * u)),y \ (y \ ((y * z) * u))) = (x * ((y / u) / z)) * (y \ (((y * z) * u) / y)). L(x,y \ (y \ ((y * z) * u)),y \ (y \ ((y * z) * u))) = (x * ((y / u) / z)) * (z * (u * (y \ 1))). x != (y * ((z / u) / w)) * (w * (u * (z \ 1))) | x = L(y,(z / u) \ w,(z / u) \ w). L(x,y \ (y \ ((y * z) * u)),y \ (y \ ((y * z) * u))) = L(x,(y / u) \ z,(y / u) \ z). L(x,y * ((1 / y) * ((z \ y) \ 1)),y \ ((z \ 1) \ 1)) = (y * (1 / z)) \ ((((z \ 1) \ 1) / y) \ x). L(x,y * ((1 / y) * ((z \ y) \ 1)),y \ ((z \ 1) \ 1)) = (y * (1 / z)) \ (((z \ 1) \ (1 / y)) \ x). x != (y * (1 / z)) \ (((z \ 1) \ (1 / y)) \ u) | x = L(u,y * (1 / z),y * (1 / z)). L(x,y * ((1 / y) * ((z \ y) \ 1)),y \ ((z \ 1) \ 1)) = L(x,y * (1 / z),y * (1 / z)). L(x,y \ ((z \ 1) \ 1),y \ ((z \ 1) \ 1)) = L(x,y * (1 / z),y * (1 / z)). L(x,(y \ 1) * z,(y \ 1) * z) = L(x,z * (1 / y),z * (1 / y)). L(x,(y * (z \ u)) \ K(u,z),(y * (z \ u)) \ K(u,z)) = ((y * (z \ u)) * K(z,u)) \ (((z / u) / y) \ x). L(x,(y * (z \ u)) \ K(u,z),(y * (z \ u)) \ K(u,z)) = (y * (u * (z \ 1))) \ (((z / u) / y) \ x). x != (y * (z * (u \ 1))) \ (((u / z) / y) \ w) | x = L(w,y \ (u / z),y \ (u / z)). L(x,(y * (z \ u)) \ K(u,z),(y * (z \ u)) \ K(u,z)) = L(x,y \ (z / u),y \ (z / u)). x != L(y,z \ K(u,w),z \ K(u,w)) | x = L(y,K(w,u) * z,K(w,u) * z). L(x,y \ (z / u),y \ (z / u)) = L(x,K(z,u) * (y * (z \ u)),K(z,u) * (y * (z \ u))). L(x,K(y,z) * (u * (y \ z)),K(y,z) * (u * (y \ z))) = L(x,u \ (y / z),u \ (y / z)). x != L(y,K(z,u) * w,K(z,u) * w) | x = L(y,w,w). L(x,y \ (z / u),y \ (z / u)) = L(x,y * (z \ u),y * (z \ u)). x != L(y,(z \ 1) \ (u / w),(z \ 1) \ (u / w)) | x = L(y,(u / w) * L(z,u \ w,u \ w),(1 / (u / w)) \ z). L(x,(y \ 1) * (z \ u),(y \ 1) * (z \ u)) = L(x,(z / u) * L(y,z \ u,z \ u),(1 / (z / u)) \ y). L(x,(y / z) * L(u,y \ z,y \ z),(1 / (y / z)) \ u) = L(x,(u \ 1) * (y \ z),(u \ 1) * (y \ z)). x != L(y,z \ u,z \ u) | x = L(y,u \ z,u \ z). L(x,y * (z \ u),y * (z \ u)) = L(x,(z / u) \ y,(z / u) \ y). L(x,(y / z) \ u,(y / z) \ u) = L(x,u * (y \ z),u * (y \ z)). L(T(x,y),z,u) \ (L(x,z,u) * (y * K(x,w))) = T(y * K(x,w),L(L(T(x,y),z,u),K(x,w),y)). T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = L(T(y,x),u,w) \ (L(y,u,w) * (x * K(y,z))). x != L(T(y,z),u,w) \ (L(y,u,w) * v5) | x = K(z,L(y,u,w)) * v5. T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = K(x,L(y,u,w)) * (x * K(y,z)). x != K(y,z) * (y * u) | x = T(y,z) * u. T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = T(x,L(y,u,w)) * K(y,z). x != T(y * z,L(u,z,y)) | x = T(y * z,u). T(x,L(y,z,u)) * K(y,w) = T(x * K(y,w),L(T(y,x),z,u)). T(x * K(y,z),L(T(y,x),u,w)) = T(x,L(y,u,w)) * K(y,z). x != T(y * K(z,u),L(T(z,y),w,v5)) | x = T(y * K(z,u),L(z,w,v5)). T(x,L(y,z,u)) * K(y,w) = T(x * K(y,w),L(y,z,u)). T(x * K(y,z),L(y,u,w)) = T(x,L(y,u,w)) * K(y,z). x != T(y,L(z,u,w)) * K(z,y) | x = y * a(w,u,K(z,y)). T(x * K(y,x),L(y,z,u)) = x * a(u,z,K(y,x)). T(x * a(y,z,K(u,x)),u) = T(x,L(u,z,y)). T(x * a(y,z,K(u,x)),x * u) = L(T(x,L(u,z,y)),u,x). x != L(T(y,L(z,u,w)),z,y) | x = T(y,L(z * y,u,w)). T(x * a(y,z,K(u,x)),x * u) = T(x,L(u * x,z,y)). x != K(y,K(z,L(u,w,K(y,v5)))) | x = K(z,K(y,u)). K(x * y,K(z,(T(x * y,u) * w) \ L(w,y,x))) = K(z,K(x * y,a(x,y,w))). K(x,K(y * z,(T(y * z,u) * w) \ L(w,z,y))) = K(x,K(y * z,a(y,z,w))). K(x,K(y * z,u \ ((y * z) \ L(u,z,y)))) = K(x,K(y * z,a(y,z,u))). x != K(y,K(z,u \ (z \ w))) | x = K(y,K(z,u \ w)). K(x,K(y * z,a(y,z,u))) = K(x,K(y * z,u \ L(u,z,y))). K(x,K(y * z,u \ L(u,z,y))) = K(x,K(y * z,a(y,z,u))). R(K(x,K(y,z)) * K(y,K(z,R(x,u,w))),K(K(y,z),v5),v6) * v7 = K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * v7). (x * L(R(T(y,x),z,u),y \ x,y)) \ (x * R(T(y,x),z,u)) = a(R(T(y,x),z,u),T(y,x) \ x,T(y,x)). (L(R(x,y,z),x \ u,x) * u) \ (u * R(T(x,u),y,z)) = a(R(T(x,u),y,z),T(x,u) \ u,T(x,u)). (L(R(x,y,z),x \ u,x) * u) \ (R(x,y,z) * u) = a(R(T(x,u),y,z),T(x,u) \ u,T(x,u)). a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = (L(R(x,z,u),x \ y,x) * y) \ (R(x,z,u) * y). a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = a(x,x \ y,T(R(x,z,u),y)). a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = a(x,x \ y,R(T(x,y),z,u)). a(T(x,y),T(x,y) \ y,R(T(x,y),z,u)) = a(x,x \ y,R(T(x,y),z,u)). a(x,T(x,y) \ y,R(x,z,u)) = a(x,x \ y,R(T(x,y),z,u)). x != a(y,T(y,z) \ u,R(y,w,v5)) | x = a(y,y \ u,R(y,w,v5)). a(x,x \ y,R(T(x,y),z,u)) = a(x,x \ y,R(x,z,u)). x != a(y,y \ z,R(T(y,z),u,w)) | x = a(R(y,u,w),R(y,u,w) \ z,T(R(y,u,w),z)). a(x,x \ y,R(x,z,u)) = a(R(x,z,u),R(x,z,u) \ y,T(R(x,z,u),y)). a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,R(x,y,z)). a(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = a(x,x \ u,R(x,y,z)). x * a(y,y \ (z * y),R(y,u,w)) = (x / R(y,u,w)) * R(R(y,z,y),u,w). (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,y \ (w * y),R(y,z,u)). (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,T(w,y),R(y,z,u)). (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,w,R(y,z,u)). x != (y / R(z,u,w)) * R(R(z,v5,z),u,w) | x = y * a(R(z,u,w),v5,L(R(z,u,w),v6,v7)). x * a(y,z,R(y,u,w)) = x * a(R(y,u,w),z,L(R(y,u,w),v5,v6)). x * a(R(y,z,u),w,L(R(y,z,u),v5,v6)) = x * a(y,w,R(y,z,u)). x * a(R(y,z,u),w,R(y,z,u)) = x * a(y,w,R(y,z,u)). a(R(x,y,z),u,R(x,y,z)) = a(x,u,R(x,y,z)). R(a(x,y,x),x * z,u) = a(x,y,R(x,z,u)). x != a(R(y,z,u),R(y,z,u) \ w,R(y,z,u)) | x = a(y,y \ w,R(y,z,u)). a(x,R(x,y,z) \ u,R(x,y,z)) = a(x,x \ u,R(x,y,z)). R(a(x,y,x),z,u) = a(x,y,R(x,x \ z,u)). a(x,y,R(x,x \ z,u)) = R(a(x,y,x),z,u). x * R(a(x,y,x),z,u) = R(x,y,R(x,x \ z,u)). R(x,y,R(x,x \ z,u)) = x * R(a(x,y,x),z,u). T(x,y) * R(a(x,z,x),u,w) = R(T(x,y),z,R(x,x \ u,w)). R(T(x,y),z,R(x,x \ u,w)) = T(x,y) * R(a(x,z,x),u,w). x != R(T(y,z),u,R(T(y,z),w,v5)) | x = R(T(y,z),u,R(y,w,v5)). T(x,y) * R(a(T(x,y),z,T(x,y)),u,w) = R(T(x,y),z,R(x,T(x,y) \ u,w)). a(x,x \ y,R(x,z,u)) * K(x,y) = K(x,R(x,z,u) \ y). x != a(y,z \ u,w) * K(z,u) | x = K(z,u) * a(y,z \ u,w). K(x,R(x,y,z) \ u) = K(x,u) * a(x,x \ u,R(x,y,z)). K(x,y) * a(x,x \ y,R(x,z,u)) = K(x,R(x,z,u) \ y). T(x,y) * R(a(x,z,x),u,w) = R(T(x,y),z,R(x,T(x,y) \ u,w)). R(T(x,y),z,R(x,T(x,y) \ u,w)) = T(x,y) * R(a(x,z,x),u,w). x != T(y,z) * R(a(y,u,y),w,v5) | x = R(T(y,z),u,R(y,y \ w,v5)). R(T(x,y),z,R(x,T(x,y) \ u,w)) = R(T(x,y),z,R(x,x \ u,w)). (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (R(T(x,y),z,R(x,x \ u,w)) * (T(x,y) \ u)) * w. K(x,T(y / z,T(u,z))) / T(K(x,z \ y),u) = R(K(x,K(z,y)),K(x,z \ y),K(K(x,z \ y),u)). R(K(x,K(y,z)),K(x,y \ z),K(K(x,y \ z),u)) = K(x,T(z / y,T(u,y))) / T(K(x,y \ z),u). R(K(x,K(y,z)),K(x,y \ z),K(K(x,y \ z),u)) = K(x,T(z / y,T(u,y))) / K(x,T(y \ z,u)). x != y / K(z,T(u,w)) | x = y * K(u,T(z,w)). R(K(x,K(y,z)),K(x,y \ z),K(K(x,y \ z),u)) = K(x,T(z / y,T(u,y))) * K(y \ z,T(x,u)). R(K(x,K(y,z)),K(x,z \ y),K(K(x,z \ y),u)) = K(x,T(y / z,T(u,z))) * K(z \ y,T(x,u)). x != R(y,z,K(z,u)) | x = y. K(x,T(y / z,T(u,z))) * K(z \ y,T(x,u)) = K(x,K(y,z)). K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = (u * K(z,x)) \ (K(x,y) * (K(z,x) * (u * K(y,x)))). (x * (K(y,z) * u)) * K(z,L(y,K(z,y) \ (y \ u),x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y). (x * (K(y,z) * u)) * K(z,L(y,y \ u,x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y). (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y). (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * (((K(y,z) * (u / y)) * K(z,y)) * y). (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * (T(u / y,K(y,z)) * y). (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * T((u / y) * y,K(y,z)). (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * T(u,K(y,z)). ((x * (K(y,z) * u)) / (x * T(u,K(y,z)))) \ T(x * (K(y,z) * u),L(K(z,y),u,x)) = T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x). R(K(x,K(y,z) * K(R(z,u,w),y)),K(K(y,x),v5),v6) * v7 = K(z,K(y,x)) * (R(K(K(y,x),z),u,w) * v7). K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = (u * K(z,x)) \ T(K(z,x) * u,K(x,y)). x != (y * z) \ T(z * y,u) | x = K(z,y) * K(z * y,u). K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = K(K(z,x),u) * K(K(z,x) * u,K(x,y)). K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = K(u,K(z,x)) * K(K(z,x) * u,K(x,y)). K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = K(u,K(z,x)) * K(u,K(x,y)). x != K(y,K(z,u)) * K(y,K(u,w)) | x = K(y,K(z,u) * K(u,w)). K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = K(u,K(z,x) * K(x,y)). K(K(x,y) * K(z,x),R(u * K(y,x),K(x,y),K(z,x))) = K(u,K(z,x) * K(x,y)). K(K(x,y) * K(z,x),u * K(y,x)) = K(u,K(z,x) * K(x,y)). (K(x,y) * K(z,x)) \ K(u,K(z,x) * K(x,y)) = K(x,T(z,u)) * K(y,T(x,u)). x != (y * z) \ K(u,z * y) | x = T(y * z,T(u,y)) \ 1. K(x,T(y,z)) * K(u,T(x,z)) = T(K(x,u) * K(y,x),T(z,K(x,u))) \ 1. T(K(x,y) * K(z,x),T(u,K(x,y))) \ 1 = K(x,T(z,u)) * K(y,T(x,u)). T(K(x,y) * K(y,z),u) \ 1 = K(y,T(x,u)) * K(z,T(y,u)). x != T(K(y,z) * K(z,u),w) \ 1 | x = T(K(z,y) * K(u,z),w). K(x,T(y,z)) * K(u,T(x,z)) = T(K(x,y) * K(u,x),z). T(K(x,y) * K(z,x),u) * w = K(x,T(y,u)) * (K(z,T(x,u)) * w). K(x,T(y,z)) * (K(u,T(x,z)) * w) = T(K(x,y) * K(u,x),z) * w. x != K(y,T(z,u)) * (K(z * R(y,w,v5),T(y,u)) * v6) | x = R(T(y,u),z,R(y,w,v5)) * (T(y,u) \ v6). T(K(x,y) * K(y * R(x,z,u),x),w) * v5 = R(T(x,w),y,R(x,z,u)) * (T(x,w) \ v5). a(x,y,R(x,z,u)) * w = R(T(x,v5),y,R(x,z,u)) * (T(x,v5) \ w). R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5) = a(x,z,R(x,u,w)) * v5. (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (a(x,z,R(x,x \ u,w)) * u) * w. (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (R(a(x,z,x),u,w) * u) * w. (R(T(x,y),z,x) * (T(x,y) \ u)) * w = (R(a(x,z,x),u,w) * u) * w. (T(x,y) * (L(T(x,y),z,x) \ u)) * w = (R(a(x,z,x),u,w) * u) * w. (x * a(y,z,y)) * u = (R(a(y,z,y),x,u) * x) * u. (R(a(x,y,x),z,u) * z) * u = (z * a(x,y,x)) * u. x * y != (R(a(z,u,z),w,v5) * w) * v5 | x \ ((w * a(z,u,z)) * v5) = y. ((a(x,y,x) * z) * u) \ ((z * a(x,y,x)) * u) = a(R(a(x,y,x),z,u),z,u). K(x,T(a(y,z,y),u)) = a(R(a(y,z,y),x,u),x,u). a(R(a(x,y,x),z,u),z,u) = K(z,T(a(x,y,x),u)). a(R(a(x,y,x),z,u),z,u) = K(z,a(x,y,x)). x != K(y,a(z,u,z)) | x = 1. a(R(a(x,y,x),z,u),z,u) = 1. L(x,y,R(a(z,u,z),y,x)) = x. (R(a(x,y,x),z,u) * (T(z,R(a(x,y,x),z,u)) * u)) / u = z * R(a(x,y,x),z,u). (R(a(x,y,x),z,u) * (z * u)) / u = z * R(a(x,y,x),z,u). a(x,y,x) * z = z * R(a(x,y,x),z,u). x * R(a(y,z,y),x,u) = a(y,z,y) * x. x * y != a(z,u,z) * x | y = a(z,u,z). R(a(x,y,x),z,u) = a(x,y,x). a(x,y,x) = ((a(x,y,x) * R(z,u,w)) * (u * w)) / ((z * u) * w). ((a(x,y,x) * R(z,u,w)) * (u * w)) / ((z * u) * w) = a(x,y,x). x != R(a(y,z,y),y * u,w) | x = a(y,z,R(y,u,w)). a(x,y,x) = a(x,y,R(x,z,u)). a(x,y,R(x,z,u)) = a(x,y,x). x != R(a(y,z * K(u,z),y),z * K(u,z),u) | x = L(a(y,z,y),z,u). a(x,y * K(z,y),x) = L(a(x,y,x),y,z). a(x,y,x) * (z * u) = (a(x,y,x) * z) * u. (a(x,y,x) * z) * u = a(x,y,x) * (z * u). L(a(x,y,x),z,u) = a(x,y,x). L(x,y,a(z,u,z)) = x. R(x,a(y,z,y),a(y,z,y) \ 1) = x. x != y | x = T(y,a(z,u,z)). L(x,y,a(z,u,z)) = T(x,a(w,v5,w)). T(x,a(y,z,y)) = L(x,u,a(w,v5,w)). (a(x,y,x) * z) / u = a(x,y,x) * (z / u). ((a(x,y,x) * (z * u)) * w) / (u * w) = R(a(x,y,x) * z,L(u,z,a(x,y,x)),w). R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = ((a(x,y,x) * (z * u)) * w) / (u * w). K(x,y) * a(x,x \ y,x) = K(x,R(x,z,u) \ y). K(x,R(x,y,z) \ u) = K(x,u) * a(x,x \ u,x). (x * y) * a(z,u,z) = x * (y * a(z,u,z)). R(x,a(y,z,y),y \ L(y,z,y)) = x. L(x,y,a(z,u,z)) != w | w = x. R(x,y \ R(y,z,y),y \ L(y,z,y)) = x. a(x,L(y * K(z,y),u,w),x) = L(a(x,L(y,u,w),x),L(y,u,w),z). L(a(x,L(y,z,u),x),L(y,z,u),w) = a(x,L(y * K(w,y),z,u),x). a(a(x,y,x) * z,u,w) = (a(x,y,x) * (z * (u * w))) \ (((a(x,y,x) * z) * u) * w). (a(x,y,x) * (z * (u * w))) \ (((a(x,y,x) * z) * u) * w) = a(a(x,y,x) * z,u,w). L(x,y,a(z,u,z) * w) = (a(z,u,z) * (w * y)) \ ((a(z,u,z) * w) * (y * x)). (a(x,y,x) * (z * u)) \ ((a(x,y,x) * z) * (u * w)) = L(w,u,a(x,y,x) * z). (x * (a(y,z,y) * (u * w))) \ ((x * (a(y,z,y) * u)) * w) != v5 | a(x,a(y,z,y) * u,w) = v5. (x * a(y,z,y)) * u = a(y,z,y) * (x * u). R(x,y,a(z,u,z)) = x. L(T(x,y),y,a(z,u,z)) = T(x,y * a(z,u,z)). x != a(y,z,y) * (z * u) | x = z * (a(y,z,y) * u). (x * a(y,x,y)) * z = x * (a(y,x,y) * z). T(x,y * a(z,u,z)) = T(x,y). T(x,y * a(z,u,z)) != w | w = T(x,y). T(x,y * a(z,u,z)) != w | T(x,y) = w. T(x,y) = T(x,a(z,u,z) \ y). T(x,a(y,z,y) \ u) = T(x,u). T(x,a(y,z,y) \ u) = x * K(x,u). K(x,a(y,z,y) \ u) = K(x,u). K(x,y) = K(x,a(z,u,z) * y). K(x,a(y,z,y) * u) = K(x,u). K(x,y * a(z,u,z)) = K(x,y). K(x,y * R(z,u,z)) = K(x,y * z). K(x,K(y,z) * u) = K(x,K(y,y * z) * u). K(x,K(y,y * z) * u) = K(x,K(y,z) * u). K(x,y * (K(z * u,z) * K(z,u))) = K(x,y). K(x,y * T(z,u)) = K(x,y * T(z,z * u)). K(x,y * T(z,z * u)) = K(x,y * T(z,u)). K(x,y * ((z \ u) \ u)) = K(x,y * T(z,u)). K(x,K(y,z \ 1) * u) = K(x,K(z,y) * u). K(x,K(y \ z,u) * w) = K(x,K(u,z \ y) * w). K(x,(y * K(z * u,z)) * K(z,u)) = K(x,y). K(x,y * T(z,z * u)) = x \ T(x,y * T(z,u)). T(x,x * K(y * T(z,u),y)) \ T(K(y,y * T(z,u)) * x,x) = K(y,T(y * ((z \ u) \ u),x)). K(x,K(y,z) * u) = K(x,K(z \ y,z) * u). K(x,K(y \ z,y) * u) = K(x,K(z,y) * u). L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(K(y \ K(y,u),z) * u) \ w). K(x,y * K(z,u)) = K(x,y * K(z,z * u)). K(x,y * K(z,z * u)) = K(x,y * K(z,u)). K(x,y * K(z,u \ 1)) = K(x,y * K(u,z)). 1 / K(x,y * K(z,u)) = K(y * K(u,z \ 1),x). K(x * K(y,z \ 1),u) = 1 / K(u,x * K(z,y)). x != K(y,z) * a(y,y \ z,y) | x = K(y,y \ z). K(x,R(x,y,z) \ u) = K(x,x \ u). K(x,y \ x) = K(x,x \ ((x * R(T(x,z),u,w)) / y)). K(x,x \ ((x * R(T(x,y),z,u)) / w)) = K(x,w \ x). x != K(y,K(z \ u,z) * w) | x = K(y,K(u,z) * w). K(x,K(y,z \ y) * u) = K(x,K(z,y) * u). K(x,T(y / z,T(u \ (z \ y),z))) = K(x,K(u,z \ y) * (y / z)). K(x,y * T(z,z * u)) != w | K(x,y * T(z,u)) = w. K(x * K(y,z \ 1),u) = K(x * K(z,y),u). K(x * K(x \ y,z),T(u,y)) != w | K(((z * (y \ x)) / z) * y,u) = w. K(x,y \ x) = K(x,R(T(x,z),u,w) / y). K(x,R(T(x,y),z,u) / w) = K(x,w \ x). K(x,y \ R(x,z,u)) = K(x,y \ x). x != K(y,(z \ u) \ R(y,w,v5)) | x = K(y,u \ (z * R(y,w,v5))). K(x,(y \ z) \ x) = K(x,z \ (y * R(x,u,w))). K(x,y \ (z * R(x,u,w))) = K(x,(z \ y) \ x). K(x,y \ (z * R(x,u,w))) = K(x,x * (y \ z)). x != K(y,z \ ((u * w) * R(y,u,w))) | x = K(y,z \ ((y * u) * w)). K(x,x * (y \ (z * u))) = K(x,y \ ((x * z) * u)). K(x,y \ ((x * z) * u)) = K(x,x * (y \ (z * u))). x != K(y,z \ ((y * (u / y)) * w)) | x = K(y,z \ (u * w)). K(x,x * (y \ ((z / x) * u))) = K(x,y \ (z * u)). K(x,x * (y \ (z * u))) = K(x,y \ ((z * x) * u)). K(x,y \ ((z * x) * u)) = K(x,x * (y \ (z * u))). K(x,K(y,(z * y) * u)) * K(y,y * (x \ (z * u))) = K(y,((z * y) * u) / x). (R(x * a(y,x,y),z,u) * (z * u)) / ((x * z) * u) = a(y,R(x,z,u),y). x != L(a(y,L(z,u,w),y),L(z,u,w),w * u) | x = (w * (u * z)) \ (w * (u * (T(y * z,y) / y))). a(x,L(y * K(z * u,y),u,z),x) = (z * (u * y)) \ (z * (u * (T(x * y,x) / x))). (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,L(z * K(x * y,z),y,x),u). (((x * a(y,x,y)) * z) * u) / ((x * z) * u) = a(y,R(x,z,u),y). ((x * (a(y,x,y) * z)) * u) / ((x * z) * u) = a(y,R(x,z,u),y). ((x * (a(y,x,y) * (x \ z))) * u) / (z * u) = a(y,R(x,x \ z,u),y). ((a(x,y,x) * z) * u) / (z * u) = a(x,R(y,y \ z,u),x). a(x,R(y,y \ z,u),x) = ((a(x,y,x) * z) * u) / (z * u). a(x,R(y,y \ z,u),x) = R(a(x,y,x),z,u). a(x,R(y,z,u),x) = R(a(x,y,x),y * z,u). R(a(x,y,x),y * z,u) = a(x,R(y,z,u),x). x != R(a(y,z,y),u,w) | x = a(y,z,y). a(x,R(y,z,u),x) = a(x,y,x). a(x,y,x) * (R(y,z,u) * x) = T(x * R(y,z,u),x). a(x,y,x) * T(x,z) = R(T(x,z),R(y,u,w),x). R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y). L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,y \ u,x) \ w). x != a(y,z,y) * T(y,u) | x = R(T(y,u),z,y). R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x). R(x,y,z) * R(u,x,u) = T(u * R(x,y,z),u). (R(x,y,z) * R(u,x,u)) \ ((u * R(x,y,z)) * u) = T(u,u * R(x,y,z)). x != (y / z) \ (a(z,u,z) \ y) | x = L(z,u,z). L(x,(y * z) \ (u * z),x) = L(x,y \ u,x). x != (y * R(z,u,z)) \ ((z * y) * z) | x = L(T(z,y),u,T(z,w)). T(x,x * R(y,z,u)) = L(T(x,R(y,z,u)),y,T(x,w)). L(T(x,R(y,z,u)),y,T(x,w)) = T(x,x * R(y,z,u)). K(x,(y * K(z,u)) \ w) = K(x,(K(u \ K(u,y),z) * y) \ w). K(x,(K(y \ K(y,z),u) * z) \ w) = K(x,(z * K(u,y)) \ w). K(x,(y * K(z \ 1,u)) \ w) = K(x,(y * K(u,z)) \ w). K(x,(y * K(z \ 1,u)) \ K(u,K(y * K(u,z),z))) = K(x,(L(K(u,z),y,K(u,z)) * y) \ 1). (a(x,y,x) * (z * u)) \ (a(x,y,x) * (z * (u * w))) = L(w,u,a(x,y,x) * z). K(x,K(y,z * u)) * K(y,y * (x \ (z * u))) = K(y,((z * y) * u) / x). x != K(y,K(z,u)) * K(z,z * (y \ u)) | x = K(z,z * (u / y)). K(x,((y * x) * z) / u) = K(x,x * ((y * z) / u)). K(R(x,y,z),u \ x) = K(x,x * ((y * z) / ((u * y) * z))). K(x,x * ((y * z) / ((u * y) * z))) = K(R(x,y,z),u \ x). x != K(y,y * ((z * u) / ((w * z) * u))) | x = K(y,R(w,z,u) \ y). K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x). x != K(R(y,z,u),R(y / w,w,L(K(v5,y),v6,v7)) \ y) | x = K(R(y,z,u),w). K(x,R(R(x / y,y,L(K(z,x),u,w)),v5,v6) \ x) = K(R(x,v5,v6),y). x != K(y,R(R(y / z,u,w),v5,v6) \ y) | x = R(R(K(y,z),u,w),v5,v6). K(R(x,y,z),u) = R(R(K(x,u),u,L(K(w,x),v5,v6)),y,z). R(R(K(x,y),y,L(K(z,x),u,w)),v5,v6) = K(R(x,v5,v6),y). R(K(x,y),z,u) = K(R(x,z,u),y). R(x * K(R(y,z,u),x),w,x) \ R(x,w,x) = R(K(x,y),z,u). K(x,R(y,z,u)) * (R(x,w,x) \ R(x,w,x)) = R(K(x,y),z,u). K(x,R(y,z,u)) = R(K(x,y),z,u). R(K(x,y),z,u) = K(x,R(y,z,u)). R(K(x,y),z,u) != w | K(x,R(y,z,u)) = w. x != R(K(y,z),u,w) | x = K(R(y,u,w),z). K(x,R(y,z,u)) = K(R(x,z,u),y). K(R(x,y,z),u) = K(x,R(u,y,z)). x != R(K(y,y * z),z * u,w) | x = K(y,y * R(z,u,w)). K(x,R(x * y,y * z,u)) = K(x,x * R(y,z,u)). K(x,R(x * y,z,u)) = K(R(x,y,z),R(x * y,y * z,u)). K(R(x,y,z),R(x * y,y * z,u)) = K(x,R(x * y,z,u)). K(R(x,y,z),u) != w | K(x,R(u,y,z)) = w. K(x,R(R(x * y,y * z,u),y,z)) = K(x,R(x * y,z,u)). L(L(x,y,z),z * y,a(u,w,u)) = L(x,y,a(u,w,u) * z). L(x,y,a(z,u,z) * w) = L(x,y,w). L(x,y,z) = L(x,y,a(u,w,u) \ z). L(x,y,a(z,u,z) \ w) = L(x,y,w). L(x,y,T(z * u,z)) = L(x,y,u * z). L(x,y,K(z * u,z)) = L(x,y,K(u,z)). L(x,y,K(z,z \ u)) = L(x,y,K(z,u)). L(x,y,L(z,u,z)) = L(x,y,z). L(x,y,L(z,u,u)) = L(x,y,z). L(x,y,(z \ 1) \ u) = L(x,y,z * u). L(x,y,T(z,z * u)) = L(x,y,T(z,u)). L(x,y,z \ u) = L(x,y,(z \ 1) * u). L(x,y,(z \ 1) * u) = L(x,y,z \ u). L(x,y,(1 / z) \ u) = L(x,y,z * u). L(x,y,T(z,u)) = L(x,y,T(z,z \ u)). L(x,y,T(z,z \ u)) = L(x,y,T(z,u)). L(x,y,(z \ (u \ w)) * v5) = L(x,y,(((1 / w) * u) * z) \ v5). L(x,y,(((1 / z) * u) * w) \ v5) = L(x,y,(w \ (u \ z)) * v5). x != L(y,z,T(u,u \ w)) | x = L(y,z,(u \ w) \ w). L(x,y,T(z,u)) = L(x,y,(z \ u) \ u). L(x,y,(z \ u) \ u) = L(x,y,T(z,u)). R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = (a(x,y,x) * ((z * u) * w)) / (u * w). x != (a(y,z,y) * u) / w | x = a(y,z,y) * (u / w). R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = a(x,y,x) * (((z * u) * w) / (u * w)). R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = a(x,y,x) * R(z,u,w). R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w). (a(x,y,x) * (z * (u * w))) \ ((a(x,y,x) * (z * u)) * w) = a(a(x,y,x) * z,u,w). (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u). L(L(a(x,y,x),y,z),z * y,u) = a(x,(u * (z * y)) / (u * z),x). L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x). x != a(y,z / u,y) | x = a(y,u \ z,y). L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x). L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x). x != L(a(y,z,y),u,w) | x = a(y,z,y). a(x,L(y,z,u),x) = a(x,y,x). a(x,(y * z) \ u,x) = a(x,z \ (y \ u),x). a(x,a(y,z,u),x) = a(x,L(u,z,y) \ u,x). a(x,L(y,z,u) \ y,x) = a(x,a(u,z,y),x). x * a(x,y,x) = R(x,L(y,z,u),x). R(x,L(y,z,u),x) = x * a(x,y,x). x != y * a(y,z,y) | x = R(y,z,y). R(x,L(y,z,u),x) = R(x,y,x). x != a(y,((z * u) * w) \ (z * (u * (w * K(v5,v5 \ 1)))),y) | x = a(y,K(v5,v5 \ 1) / a(z,u,w),y). a(x,y \ ((z * u) \ (z * (u * (y * K(w,w \ 1))))),x) = a(x,K(w,w \ 1) / a(z,u,y),x). a(x,a(y,z,u),x) \ x = L(x,L(u,z,y) \ u,x). L(x,L(y,z,u) \ y,x) = a(x,a(u,z,y),x) \ x. x != a(y,z,y) \ y | x = L(y,z,y). L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x). (a(x,y,x) * (z * (u * w))) \ (a(x,y,x) * ((z * u) * w)) = a(a(x,y,x) * z,u,w). L(a(x,y,z),x * (y * z),a(u,w,u)) = a(a(u,w,u) * x,y,z). a(a(x,y,x) * z,u,w) = a(z,u,w). a(x,y,z) = a(a(u,w,u) \ x,y,z). a(a(x,y,x) \ z,u,w) = a(z,u,w). a(K(x * y,x),z,u) = a(K(y,x),z,u). a(x / a(y,z,y),u,w) = a(x,u,w). a(K(x,y),z,u) = a(K(y \ x,y),z,u). a(K(x \ y,x),z,u) = a(K(y,x),z,u). a(K(x,y \ 1),z,u) = a(K(y,x),z,u). a(K(x,y),z,u) = a(K(y \ 1,x),z,u). a(K(x \ 1,y),z,u) = a(K(y,x),z,u). a(K(x,R(y,z,u) \ 1),w,v5) = a(K(y,R(x,z,u)),w,v5). a(K(R(x,y * z,u) \ 1,y),w,v5) = a(R(K(y,x),(x * y) * z,u),w,v5). a(R(K(x,y),(y * x) * z,u),w,v5) = a(K(R(y,x * z,u) \ 1,x),w,v5). x != a(K(y,z \ 1),u,w) | x = a(K(z,y),u,w). a(K(x,R(y,z,u)),w,v5) = a(K(R(x,z,u),y),w,v5). a(K(R(x,y,z),u),w,v5) = a(K(x,R(u,y,z)),w,v5). a(R(K(x,y),(y * x) * z,u),w,v5) = a(K(y \ 1,R(x,z,u)),w,v5). x != a(K(y \ 1,z),u,w) | x = a(K(z,y),u,w). a(R(K(x,y),(y * x) * z,u),w,v5) = a(K(R(x,z,u),y),w,v5). a(K(x,R(y,x * z,u)),w,v5) = a(K(R(x,z,u),y),w,v5). x != a(K(R(y,z,u),w),v5,v6) | x = a(K(y,R(w,z,u)),v5,v6). a(K(x,R(y,x * z,u)),w,v5) = a(K(x,R(y,z,u)),w,v5). K(x,(y * K(z \ 1,u)) \ K(u,K(y,z))) = K(x,(L(K(u,z),y,K(u,z)) * y) \ 1). K(x,(y * K(z \ 1,u)) \ K(y,K(z,u))) = K(x,(L(K(u,z),y,K(u,z)) * y) \ 1). K(x,(K(y \ 1,z) * u) \ 1) = K(x,(L(K(z,y),u,K(z,y)) * u) \ 1). K(x,(L(K(y,z),u,K(y,z)) * u) \ 1) = K(x,(K(z \ 1,y) * u) \ 1). x != K(y,(K(z,u) * w) \ 1) | x = K(y,w \ K(u,z)). K(x,(L(K(y,z),u,K(y,z)) * u) \ 1) = K(x,u \ K(y,z \ 1)). K(x,(K(y,z) * u) \ 1) = K(x,u \ K(y,z \ 1)). K(x,y \ K(z,u \ 1)) != w | K(x,y \ K(u,z)) = w. a(x,y \ L(y * K(z,z \ 1),u,w),x) = a(x,K(z,z \ 1) / a(w,u,y),x). a(x,(y \ L(y,z,u)) * K(w,w \ 1),x) = a(x,K(w,w \ 1) / a(u,z,y),x). x != a(y,z * K(u,u \ 1),w) | x = a(y,z,w). a(x,K(y,y \ 1) / a(z,u,w),x) = a(x,w \ L(w,u,z),x). a(x,y \ L(y,z,u),x) = a(x,K(w,w \ 1) / a(u,z,y),x). a(x,y \ L(y,z,u),x) = a(x,a(u,z,y) \ K(w,w \ 1),x). a(x,a(y,z,u) \ K(w,w \ 1),x) = a(x,u \ L(u,z,y),x). a(x,a(y,z,u) \ 1,x) = a(x,u \ L(u,z,y),x). (((a(x,y,z) \ 1) * u) * a(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = R(T(u,u * (a(x,y,z) \ 1)),(a(x,y,z) \ 1) * u,a(u,a(x,y,z) \ 1,u)). K(x,T(x * ((y \ z) \ z),u)) = K(x,T(x * T(y,z),u)). ((x * ((y * x) \ y)) \ 1) * T(x,z) = T(x,z) / (x * ((y * x) \ y)). x != y / (z * ((u * z) \ u)) | x = (z * ((u * z) \ u)) \ y. ((x * ((y * x) \ y)) \ 1) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z). (x \ (1 / ((y * x) \ y))) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z). x != (y \ (1 / ((z * y) \ z))) * T(y,u) | x = T((1 / ((z * y) \ z)) * K(y,u),y). (x * ((y * x) \ y)) \ T(x,z) = T((1 / ((y * x) \ y)) * K(x,z),x). T((1 / ((x * y) \ x)) * K(y,z),y) = (y * ((x * y) \ x)) \ T(y,z). T(T(1 / ((x * y) \ x),z),y) = (y * ((x * y) \ x)) \ T(y,z). x != T(T(1 / ((y * z) \ y),u),z) | x = T(1 / ((y * z) \ y),u). (x * ((y * x) \ y)) \ T(x,z) = T(1 / ((y * x) \ y),z). x != (y * ((z * y) \ z)) \ T(y,u) | x = 1 / ((z * T(y,u)) \ z). T(1 / ((x * y) \ x),z) = 1 / ((x * T(y,z)) \ x). 1 / ((x * T(y,z)) \ x) = T(1 / ((x * y) \ x),z). T(1 / ((x * y) \ x),z) \ 1 = (x * T(y,z)) \ x. ((x * T(y,z)) \ x) \ 1 = T(((x * y) \ x) \ 1,z). K(x,T(((y * z) \ y) \ 1,u) \ x) = K(x,1 \ (((y * T(z,u)) \ y) * x)). K(x,1 \ (((y * T(z,u)) \ y) * x)) = K(x,T(((y * z) \ y) * x,u)). K(x,((y * T(z,u)) \ y) * x) = K(x,T(((y * z) \ y) * x,u)). K(x,T(((y * z) \ y) * x,u)) = K(x,((y * T(z,u)) \ y) * x). K(x,T(((y * z) \ y) * x,u)) = K(x,x * ((y * T(z,u)) \ y)). x != K(y,y * ((z * u) \ z)) | x = K(y,u \ y). K(x,T(((y * z) \ y) * x,u)) = K(x,T(z,u) \ x). x != K(y,T(z,u) \ y) | x = K(y,T(z \ y,u)). K(x,T(((y * z) \ y) * x,u)) = K(x,T(z \ x,u)). K(x,T((y \ z) * x,u)) = K(x,T((z \ y) \ x,u)). K(x,T((y \ z) \ x,u)) = K(x,T((z \ y) * x,u)). K(x,(y / z) \ x) = K(x,T((y \ z) * x,z)). K(x,T((y \ z) * x,z)) = K(x,(y / z) \ x). K(x,T(x * (y \ z),z)) = K(x,(y / z) \ x). x != K(y,T((z \ u) * y,u)) | x = K(y,T((z \ u) * y,z)). K(x,(y / z) \ x) = K(x,T((y \ z) * x,y)). K(x,T((y \ z) * x,y)) = K(x,(y / z) \ x). x != K(y,T(y * ((z \ u) \ u),w)) | x = K(y,T(y * T(z,u),w)). K(x,((y \ z) / z) \ x) = K(x,T(x * T(y,z),z)). K(x,T(y * x,z)) = K(x,(z / (z * y)) \ x). K(x,(y / (y * z)) \ x) = K(x,T(z * x,y)). x != K(T(y,z),u \ T(y,w)) | x = K(y,T(u \ T(T(y,v5),w),z)). K(T(x,y),T(z * T(x,y),u)) = K(x,T((u / (u * z)) \ T(T(x,w),y),y)). K(x,T((y / (y * z)) \ T(T(x,u),w),w)) = K(T(x,w),T(z * T(x,w),y)). R(K(x,T(x * T(y,z),z)),x * u,w) = K(R(x,u,w),((y \ z) / z) \ x). x != K(y,T(z \ T(T(y,u),w),v5)) | x = K(y,T(z \ y,v5)). K(T(x,y),T(z * T(x,y),u)) = K(x,T((u / (u * z)) \ x,y)). K(x,T(T(y * T(x,z),u),z)) = K(x,T((u / (u * y)) \ x,z)). x != K(y,T(T(z * T(y,u),w),v5)) | x = K(y,T(T(y * z,w),v5)). K(x,T((y / (y * z)) \ x,u)) = K(x,T(T(x * z,y),u)). K(x,T((y / (z * y)) \ x,u)) = K(x,T(T(x * T(z,y),y),u)). x != K(y,T((z / (u * z)) \ y,u)) | x = K(y,R(1 / (1 / (1 / u)),u,z) \ y). K(x,T(T(x * T(y,z),z),y)) = K(x,R(1 / (1 / (1 / y)),y,z) \ x). K(x,T(x * T(y,z),z)) = K(x,R(1 / (1 / (1 / y)),y,z) \ x). x != K(y,R(1 / z,u,w) \ v5) | x = K(y,R(z \ 1,u,w) \ v5). K(x,T(x * T(y,z),z)) = K(x,R((1 / (1 / y)) \ 1,y,z) \ x). K(x,T(x * T(y,z),z)) = K(x,R(1 / y,y,z) \ x). x != K(y,R(1 / z,u,w) \ y) | x = R(K(y,y * z),u,w). K(x,T(x * T(y,z),z)) = R(K(x,x * y),y,z). R(K(x,x * y),y,z) = K(x,T(x * T(y,z),z)). R(R(K(x,x * y),y,z),x * u,w) = K(R(x,u,w),T(x * T(y,z),z)). x != R(R(K(y,z),u,w),y * v5,v6) | x = R(K(R(y,v5,v6),z),u,w). K(R(x,y,z),T(x * T(u,w),w)) = R(K(R(x,y,z),x * u),u,w). R(K(R(x,y,z),x * u),u,w) = K(R(x,y,z),T(x * T(u,w),w)). K(R(x,y,z),((u \ w) / w) \ x) = K(R(x,y,z),T(x * T(u,w),w)). x != K(R(y,z,u),(w / v5) \ y) | x = K(R(y,z,u),y * (v5 / w)). K(R(x,y,z),T(x * T(u,w),w)) = K(R(x,y,z),x * (w / (u \ w))). K(R(x,y,z),T(x * T(u,w),w)) = K(R(x,y,z),x * u). x != K(R(y,z,u),T(y * T(w,v5),v5)) | x = R(K(R(y,z,u),y * w),w,v5). K(R(x,y,z),x * u) = R(K(R(x,y,z),x * u),u,w). R(K(R(x,y,z),x * u),u,w) = K(R(x,y,z),x * u). R(K(x,R(x * y,z,u)),y,w) = K(R(x,z,u),x * y). K(x,R(R(x * y,z,u),y,w)) = K(R(x,z,u),x * y). x != K(R(y,z,u),w) | x = K(y,R(w,z,u)). K(x,R(R(x * y,z,u),y,w)) = K(x,R(x * y,z,u)). x != K(y,R(R(y * z,z * u,w),z,u)) | x = K(y,R(y * z,u,w)). K(x,R(x * y,y * z,u)) = K(x,R(x * y,z,u)). x != K(y,R(y * z,z * u,w)) | x = K(y,y * R(z,u,w)). K(x,R(x * y,z,u)) = K(x,x * R(y,z,u)). T(x,x * R(y,z,u)) = K(x,R(x * y,z,u)) * x. K(x,R(x * y,z,u)) * x = T(x,x * R(y,z,u)). T(x,R(x * y,z,u)) = T(x,x * R(y,z,u)). x != T(y,y * R(z,u,w)) | x = L(T(y,R(z,u,w)),z,T(y,v5)). T(x,R(x * y,z,u)) = L(T(x,R(y,z,u)),y,T(x,w)). L(T(x,R(y,z,u)),y,T(x,w)) = T(x,R(x * y,z,u)). L(T(x,R(y,z,u)),y,x) = T(x,R(x * y,z,u)). L(T(x,R(y / T(1 / (1 / x),z),u,w)),y / T(1 / (1 / x),z),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)). (x * (y \ R(y,z,y))) * T(y / R(y,z,y),R(y,z,y) / y) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y)). (x * (y \ R(y,z,y))) * T(y \ L(y,z,y),R(y,z,y) / y) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y)). (x * (y \ R(y,z,y))) * T(y \ L(y,z,y),y \ R(y,z,y)) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y)). (x * (y \ R(y,z,y))) * (y \ L(y,z,y)) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y)). R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y)) = (x * (y \ R(y,z,y))) * (y \ L(y,z,y)). R(x,(y \ L(y,z,y)) \ 1,y / R(y,z,y)) = (x * (y \ R(y,z,y))) * (y \ L(y,z,y)). R(x,y \ R(y,z,y),y / R(y,z,y)) = (x * (y \ R(y,z,y))) * (y \ L(y,z,y)). (x * (y \ R(y,z,y))) * (y \ L(y,z,y)) = R(x,y \ R(y,z,y),y / R(y,z,y)). (x * (y \ R(y,z,y))) * (y \ L(y,z,y)) = R(x,y \ R(y,z,y),y \ L(y,z,y)). x != R(y,z \ R(z,u,z),z \ L(z,u,z)) | x = y. (x * (y \ R(y,z,y))) * (y \ L(y,z,y)) = x. (x * (K(T(y,z),u) * K(y * u,T(y,z)))) * (y \ L(y,u,y)) = x. K(x,T(y,z)) * K(T(y,z),y * x) = y \ L(y,x,y). K(x,T(y,z)) * K(y,T(y * x,z)) = y \ L(y,x,y). (x \ L(x,y,x)) * x = K(y,T(x,z)) * T(x,T(x * y,z)). K(x,T(y,z)) * T(y,T(y * x,z)) = (y \ L(y,x,y)) * y. x != (y \ L(y,z,u)) * y | x = L(y,z,u). K(x,T(y,z)) * T(y,T(y * x,z)) = L(y,x,y). K(x \ 1,T(y,z)) * T(y,T(x \ y,z)) = L(y,x \ 1,y). K(x * y,z) * T(z,T(z * (y * x),y)) = L(z,y * x,z). K(x \ (y \ x),z) * T(z,T(y \ z,x)) = L(z,y \ 1,z). K((x / y) \ 1,z) * T(z,T(z * ((y / x) * ((y / x) \ ((x / y) \ 1))),y / x)) = L(z,(y / x) * ((y / x) \ ((x / y) \ 1)),z). x != K(y \ (z \ y),u) * T(u,T(z \ u,y)) | x = L(u,y \ (z \ y),u). L(x,y \ 1,x) = L(x,z \ (y \ z),x). L(x,y \ (z \ y),x) = L(x,z \ 1,x). L(x,y \ z,x) = L(x,(y / z) \ 1,x). L(x,(y / z) \ 1,x) = L(x,y \ z,x). L(x,y * (y \ ((z / u) \ 1)),x) = L(x,z \ u,x). L(x,((y \ z) \ z) * (1 / z),((y \ z) \ z) * (1 / z)) = ((1 / z) * ((y \ 1) \ 1)) * (((1 / (1 / y)) \ z) * x). L(x,((y \ z) \ z) * (1 / z),((y \ z) \ z) * (1 / z)) = ((1 / z) * ((y \ 1) \ 1)) * ((((y \ 1) \ 1) \ z) * x). x != ((1 / y) * z) * ((z \ y) * u) | x = T(T(u,z \ y),y \ z). L(x,((y \ z) \ z) * (1 / z),((y \ z) \ z) * (1 / z)) = T(T(x,((y \ 1) \ 1) \ z),z \ ((y \ 1) \ 1)). L(x,((y \ z) \ z) * (1 / z),((y \ z) \ z) * (1 / z)) = T(T(x,(y \ 1) * z),z \ ((y \ 1) \ 1)). L(x,((y \ z) \ z) * (1 / z),((y \ z) \ z) * (1 / z)) != u | L(x,(y \ 1) * z,(y \ 1) * z) = u. L(x,(y \ 1) * z,(y \ 1) * z) = L(x,y \ z,((y \ z) \ z) * (1 / z)). L(x,y \ z,((y \ z) \ z) * (1 / z)) = L(x,(y \ 1) * z,(y \ 1) * z). x != L(y,z,(u \ w) * (1 / w)) | x = L(y,z,u \ 1). L(x,(y \ 1) * z,(y \ 1) * z) = L(x,y \ z,(y \ z) \ 1). x != L(y,z,z \ 1) | x = L(y,z,z). L(x,(y \ 1) * z,(y \ 1) * z) = L(x,y \ z,y \ z). x != L(y,(z \ 1) * (u \ w),(z \ 1) * (u \ w)) | x = L(y,(u / w) * L(z,u \ w,u \ w),(1 / (u / w)) \ z). L(x,y \ (z \ u),y \ (z \ u)) = L(x,(z / u) * L(y,z \ u,z \ u),(1 / (z / u)) \ y). L(x,(y / z) * L(u,y \ z,y \ z),(1 / (y / z)) \ u) = L(x,u \ (y \ z),u \ (y \ z)). x != L(y,(z \ 1) * u,(z \ 1) * u) | x = L(y,u * (1 / z),u * (1 / z)). L(x,y \ z,y \ z) = L(x,z * (1 / y),z * (1 / y)). L(x,y * (1 / z),y * (1 / z)) = L(x,z \ y,z \ y). L(x,y * (z \ y),y * (z \ y)) = L(x,y \ (y \ z),y \ (y \ z)). L(x,y \ (y \ z),y \ (y \ z)) = L(x,y * (z \ y),y * (z \ y)). L(x,y \ z,y \ z) = L(x,z * (1 / y),z * (y \ 1)). L(x,y * (1 / z),y * (z \ 1)) = L(x,z \ y,z \ y). L(x,y \ (y \ z),y \ (y \ z)) != u | L(x,y * (z \ y),y * (z \ y)) = u. L(x,(y / z) \ u,(y / z) \ u) != w | L(x,y * (((y * u) * z) \ y),y * (((y * u) * z) \ y)) = w. L(x,(1 / (y / z)) \ u,(1 / (y / z)) \ u) = L(x,u \ (y \ z),u \ (y \ z)). L(x,y \ (z \ u),y \ (z \ u)) != w | L(x,y * (z / u),y * (z / u)) = w. L(x,y * (((y * z) * u) \ y),y * (((y * z) * u) \ y)) = L(x,z * (y \ u),z * (y \ u)). L(T(x,R(y / T((1 / x) \ 1,z),u,w)),y / T(1 / (1 / x),z),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)). L(T(x,R(y / T(x,z),u,w)),y / T(1 / (1 / x),z),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)). L(T(x,R(x \ y,z,u)),y / T(1 / (1 / x),w),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,w)),z,u)). x != L(y,z / T(1 / u,w),v5) | x = L(y,z / T(u \ 1,w),v5). T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = L(T(x,R(x \ y,u,w)),y / T((1 / x) \ 1,z),x). L(T(x,R(x \ y,z,u)),y / T((1 / x) \ 1,w),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,w)),z,u)). L(T(x,R(x \ y,z,u)),y / T(x,w),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,w)),z,u)). T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = L(T(x,R(x \ y,u,w)),y / T(x,z),x). x != L(T(y,z),u / T(y,w),y) | x = L(T(y,z),y \ u,y). T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = L(T(x,R(x \ y,u,w)),x \ y,x). x != L(T(y,R(z,u,w)),z,y) | x = T(y,R(y * z,u,w)). T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = T(x,R(x * (x \ y),u,w)). T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = T(x,R(y,u,w)). T(x,R(x * (y / T(1 / (1 / x),z)),u,w)) = T(x,R(y,u,w)). T(x \ 1,K(y,z)) * L((x \ 1) \ K(y,K(z * x,x \ 1)),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x)). (x * R(x \ (x * K(y,z)),u,w)) * K(z,v5) = R(x,K(y,z),K(z,v5)) * (R(K(y,z),u,w) * K(z,v5)). R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u)) = (x * R(x \ (x * K(y,z)),w,v5)) * K(z,u). R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u)) = (x * R(K(y,z),w,v5)) * K(z,u). x * (R(K(y,z),u,w) * K(z,v5)) = (x * R(K(y,z),u,w)) * K(z,v5). (x * R(K(y,z),u,w)) * K(z,v5) = x * (R(K(y,z),u,w) * K(z,v5)). (x * R(K(y,z),u,w)) * K(z,v5) = x * (K(z,v5) * R(K(y,z),u,w)). x != (y * R(K(z,u),w,v5)) * K(u,v6) | x = y / (K(v6,u) * R(K(u,z),w,v5)). x * (K(y,z) * R(K(u,y),w,v5)) = x / (K(z,y) * R(K(y,u),w,v5)). x / (K(y,z) * R(K(z,u),w,v5)) = x * (K(z,y) * R(K(u,z),w,v5)). (x * (K(y,z) * R(K(z,u),w,v5))) * (K(z,y) * R(K(u,z),w,v5)) = x. K(x \ ((1 / y) * (z / x)),((1 / y) * (z / x)) \ x) / u = (x \ ((x / y) * z)) * (1 / (u * (x \ ((x / y) * z)))). x != (y \ ((y / z) * u)) * (1 / (w * (y \ ((y / z) * u)))) | x = (y \ ((u / y) \ z)) * ((y \ ((y / z) * u)) / w). K(x \ ((1 / y) * (z / x)),((1 / y) * (z / x)) \ x) / u = (x \ ((z / x) \ y)) * ((x \ ((x / y) * z)) / u). K(x \ ((1 / y) * (z / x)),((z / x) \ y) * x) / u = (x \ ((z / x) \ y)) * ((x \ ((x / y) * z)) / u). K(((x / y) \ z) * y,(((x / y) \ z) * y) \ 1) / u = (y \ ((x / y) \ z)) * ((y \ ((y / z) * x)) / u). K(((x / y) \ z) * y,y \ ((z \ 1) * (x / y))) / u = (y \ ((x / y) \ z)) * ((y \ ((y / z) * x)) / u). (x * ((y * (1 / (1 * y))) \ z)) / (u / ((z \ y) * (1 / y))) = (x / ((z \ 1) * (u * K(y,y \ 1)))) * ((z \ y) * (1 / y)). (1 / T(x,(y * z) \ K(u \ w,w \ u))) \ (y * (z * K(u \ w,w \ u))) = (y * (z * K(u \ w,w \ u))) * x. T(((1 / x) * (((y \ 1) \ 1) * z)) * (y * ((z \ 1) \ 1)),z \ (y \ 1)) = (1 / (x * (z \ (1 / y)))) * (((y \ 1) \ 1) * z). T(x \ 1,K(y,z)) * L((x \ 1) \ K(y,K(x,z * x)),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x)). T(x \ 1,K(y,z)) * L((x \ 1) \ K(x,K(y,z)),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x)). T(x \ 1,K(y,z)) * L(T(T(x,K(y,z)),x \ 1),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x)). x != T(y,z) * L(T(u,y),w,v5) | x = K(y,z) * (L(u,w,v5) * y). T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = K(x \ 1,K(u,w)) * (L(T(x,K(u,w)),y,z) * (x \ 1)). K(x \ 1,K(y,z)) * (L(T(x,K(y,z)),u,w) * (x \ 1)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x)). K(x,K(y,z)) * (L(T(x,K(y,z)),u,w) * (x \ 1)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x)). T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = K(x,K(u,w)) * (L(T(x,K(u,w)),y,z) * (x \ 1)). T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = K(x,K(u,w)) * (x \ L(T(x,K(u,w)),y,z)). x != K(y,K(z,u)) * (y \ w) | x = T(y,K(z,u)) \ w. T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = T(x,K(u,w)) \ L(T(x,K(u,w)),y,z). (x * ((y * (1 / y)) \ z)) / (u / ((z \ y) * (1 / y))) = (x / ((z \ 1) * (u * K(y,y \ 1)))) * ((z \ y) * (1 / y)). (x / ((y \ 1) * (z * K(u,u \ 1)))) * ((y \ u) * (1 / u)) = (x * ((u * (1 / u)) \ y)) / (z / ((y \ u) * (1 / u))). (x / ((y \ 1) * (z * K(u,u \ 1)))) * ((y \ u) * (1 / u)) = (x * (K(u,u \ 1) \ y)) / (z / ((y \ u) * (1 / u))). (x / ((y \ 1) * (z * K(u,u \ 1)))) * ((y \ u) * (1 / u)) = (x * (K(u,u \ 1) * y)) / (z / ((y \ u) * (1 / u))). (x / ((y \ 1) * (z * K(u,u \ 1)))) * ((y \ u) * (1 / u)) = (x * (K(u,u \ 1) * y)) / ((u * (1 / (z * u))) \ y). x != (y * (K(z,z \ 1) * u)) / w | x = K(z,z \ 1) * ((y * u) / w). (x / ((y \ 1) * (z * K(u,u \ 1)))) * ((y \ u) * (1 / u)) = K(u,u \ 1) * ((x * y) / ((u * (1 / (z * u))) \ y)). (x / (((y \ z) * (1 / z)) * u)) * ((y \ z) * (1 / z)) = K(z,z \ 1) * ((x * y) / ((z * (1 / (u * z))) \ y)). x != K(y,y \ 1) * (z / ((y * u) \ w)) | x = z / (T(u * y,y \ 1) \ w). (x / (((y \ z) * (1 / z)) * u)) * ((y \ z) * (1 / z)) = (x * y) / (T((1 / (u * z)) * z,z \ 1) \ y). (x / (((y \ z) * (1 / z)) * u)) * ((y \ z) * (1 / z)) = (x * y) / (T(1 / T(u,z),z \ 1) \ y). (x / (((y \ z) * (1 / z)) * u)) * ((y \ z) * (1 / z)) = (x * y) / ((1 / u) \ y). T(((1 / x) / (y \ (1 / z))) / (y \ (1 / z)),y \ (z \ 1)) = (1 / (x * (y \ (1 / z)))) * (((z \ 1) \ 1) * y). T((1 / ((x \ (1 / y)) * z)) / (x \ (1 / y)),x \ (y \ 1)) = (1 / (z * (x \ (1 / y)))) * (((y \ 1) \ 1) * x). T(1 / ((x \ (1 / y)) * ((x \ (1 / y)) * z)),x \ (y \ 1)) = (1 / (z * (x \ (1 / y)))) * (((y \ 1) \ 1) * x). K(R(K(x,y) * R(K(y,x),z,u),K(y,x),z * u),((z * u) \ K(x,y)) \ 1) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1). K(K(x,y) * R(K(y,x),z,u),((z * u) \ K(x,y)) \ 1) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1). K(K(x,y) * R(K(y,x),z,u),K(y,x) * (z * u)) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1). x != K(K(y,z) * R(K(z,u),w,v5),v6) | x = K(K(y,z) * K(z,R(u,w,v5)),v6). K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = K(K(y,x) * K(x,R(y,z,u)),K(x,y) * (z * u)). K(K(x,y) * K(y,R(x,z,u)),K(y,x) * (z * u)) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1). K(x * y,K(z,R(u,x,y)) * K(u,z)) = K(a(K(z,u),x,y),((x * y) \ K(u,z)) \ 1). K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = K(z * u,K(x,R(y,z,u)) * K(y,x)). x != K(y,K(z,R(u,w,v5)) * K(u,z)) | x = K(y,K(z,u) * K(u,R(z,w,v5))). K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = K(z * u,K(x,y) * K(y,R(x,z,u))). x != K(y * z,K(u,w) * K(w,R(u,y,z))) | x = 1. K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = 1. K(a(K(x,y),z,u),K(x,y) * (z * u)) = 1. 1 * (((K(x,y) * z) * u) / (K(x,y) * (z * u))) = a(K(x,y),z,u). 1 * (K(x,y) * R(K(y,x),z,u)) = a(K(y,x),z,u). K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u). 1 * (K(x,K(y,z)) * R(K(x,K(y,z)),u,w)) = a(K(x,K(y,z)),u,w). K(x,y) * a(K(x,y),z,u) = R(K(x,y),z,u). R(K(x,y),z,u) * K(y,x) = a(K(x,y),z,u). K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(y,x \ 1),z,u). K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u). a(K(x,y),z,u) * w = K(y,x) * (R(K(x,y),z,u) * w). K(x,y) * (R(K(y,x),z,u) * w) = a(K(y,x),z,u) * w. T(x,K(y,R(z,u,w)) * K(z,y)) = T(x,a(K(z,y),u,w)). K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u). (x * a(K(y,z),u,w)) * (K(y,z) * R(K(z,y),u,w)) = x. R(K(x,T(y,z)),u,w) * (z * K(y,x)) = (a(K(x,T(y,z)),u,w) * K(x,y)) * (K(y,x) * z). (a(K(x,T(y,z)),u,w) * K(x,y)) * (K(y,x) * z) = R(K(x,T(y,z)),u,w) * (z * K(y,x)). R(K(x,T(y,z)),u,w) * (z * K(y,x)) = z * a(K(x,y),u,w). K(a(K(x,y),z,u),w) = K(w,K(x,y) * K(R(y,z,u),x)). K(x,K(y,z) * K(R(z,u,w),y)) = K(a(K(y,z),u,w),x). K(a(K(x,y),z,u),w) != v5 | K(w,K(x,y) * K(R(y,z,u),x)) = v5. x != K(y,z) * K(z,R(y,u,w)) | x = a(K(z,y),u,w). a(K(x,y),z * y,u) = a(K(x,y),z,u). K(x,y) * (a(K(x,y),z,u) * w) = R(K(x,y),z,u) * w. (x * a(K(y,z),u,w)) * a(K(z,y),u,w) = x. x * y != T(z,z \ u) | x \ ((z \ u) \ u) = y. (T(x,x \ y) * a(K(z,u),w,v5)) \ ((x \ y) \ y) = a(K(u,z),w,v5). R(K(a(K(x,y),z,u),w),K(K(x,w),v5),v6) * v7 = K(y,K(x,w)) * (R(K(K(x,w),y),z,u) * v7). x != K(y,z) * (u * L(y,z,y)) | x = K(y,y * z) * (u * y). R(K(x,y),z,u) * L(x,y,x) = K(x,x * y) * (a(K(x,y),z,u) * x). K(x,x * y) * (a(K(x,y),z,u) * x) = R(K(x,y),z,u) * L(x,y,x). K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(x,y),z,u). 1 * (K(x,K(y,z)) * K(y,K(z,R(x,u,w)))) = a(K(x,K(y,z)),u,w). 1 * K(x,K(y,z) * K(R(z,u,w),y)) = a(K(z,K(y,x)),u,w). K(x,x * y) * (x * a(K(x,y),z,u)) = R(K(x,y),z,u) * L(x,y,x). T(x,x * y) * a(K(x,y),z,u) = R(K(x,y),z,u) * L(x,y,x). x != R(K(y,z),u,w) * L(y,v5,y) | x = L(y * R(K(y,z),u,w),v5,y). T(x,x * y) * a(K(x,y),z,u) = L(x * R(K(x,y),z,u),y,x). T(x,x * y) * a(K(x,y),z,u) = L(x * K(x,R(y,z,u)),y,x). T(x,x * y) * a(K(x,y),z,u) = L(T(x,R(y,z,u)),y,x). T(x,x * y) * a(K(x,y),z,u) = T(x,R(x * y,z,u)). x != R(K(y,T(z,u)),w,v5) * (u * K(z,y)) | x = u * a(K(y,z),w,v5). (a(K(x,T(y,z)),u,w) * K(x,y)) * (K(y,x) * z) = z * a(K(x,y),u,w). K(a(K(x,y),z,u),w) * v5 = K(y,K(x,w)) * (R(K(K(x,w),y),z,u) * v5). K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * v5) = K(a(K(y,x),u,w),z) * v5. x != K(a(K(y,z),u,w),v5) * y | x = y * K(a(K(y,z),u,w),v5). K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * y) = y * K(a(K(y,x),u,w),z). K(x,K(y,z)) * (R(K(y,K(z,x)),u,w) * y) = y * K(a(K(y,x),u,w),z). K(x,K(y,z)) * (K(y,K(z,R(x,u,w))) * y) = y * K(a(K(y,x),u,w),z). K(x,K(y,z)) * T(y,K(z,R(x,u,w))) = y * K(a(K(y,x),u,w),z). x != K(y,z) * T(u,K(w,R(y,v5,v6))) | x = T(K(y,z) * u,K(y,R(w,v5,v6))). x * K(a(K(x,y),z,u),w) = T(K(y,K(x,w)) * x,K(y,R(w,z,u))). T(K(x,K(y,z)) * y,K(x,R(z,u,w))) = y * K(a(K(y,x),u,w),z). T(T(x,K(y,z)),K(y,R(z,u,w))) = x * K(a(K(x,y),u,w),z). T(x,K(y,R(z,u,w)) * K(z,y)) = x * K(a(K(x,y),u,w),z). x != T(y,K(z,R(u,w,v5)) * K(u,z)) | x = T(y,a(K(u,z),w,v5)). x * K(a(K(x,y),z,u),w) = T(x,a(K(w,y),z,u)). K(a(K(x,y),z,u),w) = K(x,a(K(w,y),z,u)). K(x,K(y,z) * K(R(z,u,w),y)) = K(y,a(K(x,z),u,w)). 1 * K(x,a(K(y,z),u,w)) = a(K(z,K(x,y)),u,w). K(x,a(K(y,z),u,w)) = a(K(z,K(x,y)),u,w). a(K(x,K(y,z)),u,w) = K(y,a(K(z,x),u,w)). x != K(y,a(K(z,u),w,v5)) | x = K(a(K(y,u),w,v5),z). a(K(x,K(y,z)),u,w) = K(a(K(y,x),u,w),z). a(K(x,K(y,z)),u,w) = K(x,a(K(z,y),u,w)). a(K(x,K(y,z)),u,w) = K(a(K(x,y),u,w),z). a(K(x,K(y,z)),u,w) = K(a(K(y,x),u * x,w),z). K(a(K(x,y),z * y,u),w) = a(K(y,K(x,w)),z,u). x != K(a(K(y,z),u,w),v5) | x = a(K(y,K(z,v5)),u,w). a(K(x,K(y,z)),u,w) = a(K(y,K(x,z)),u * x,w). a(K(x,K(y,z)),u * y,w) = a(K(y,K(x,z)),u,w). (((x \ 1) \ K(y,x)) \ (T(x,x \ 1) * z)) * K((K(x,y) / x) * (x * z),u) = T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),u). K(R(x,y,z) \ 1,u) * R(R(x * T(x \ 1,u),y,z) \ 1,w,v5) = R((x * T(x \ 1,u)) * R(K(u,x \ 1),w,v5),y,z). K(R(x,y,z) \ 1,u) * R(K(R(x,y,z) \ 1,u) \ 1,w,v5) = R((x * T(x \ 1,u)) * R(K(u,x \ 1),w,v5),y,z). R((x * T(x \ 1,y)) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * R(K(R(x,w,v5) \ 1,y) \ 1,z,u). R((x * T(x \ 1,y)) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * R(K(y,R(x,w,v5) \ 1),z,u). R((x * T(x \ 1,y)) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * K(y,R(R(x,w,v5),z,u) \ 1). R(K(x \ 1,y) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * K(y,R(R(x,w,v5),z,u) \ 1). K(R(x,y,z) \ 1,u) * K(u,R(R(x,y,z),w,v5) \ 1) = R(K(x \ 1,u) * R(K(u,x \ 1),w,v5),y,z). K(R(x,y,z) \ 1,u) * K(u,R(R(x,y,z),w,v5) \ 1) = R(K(x \ 1,u) * K(u,R(x,w,v5) \ 1),y,z). x != K(y \ 1,z) * K(z,R(y,u,w) \ 1) | x = a(K(z,y \ 1),u,w). R(K(x \ 1,y) * K(y,R(x,z,u) \ 1),w,v5) = a(K(y,R(x,w,v5) \ 1),z,u). x != a(K(y,R(z,u,w) \ 1),v5,v6) | x = a(K(z,R(y,u,w)),v5,v6). R(K(x \ 1,y) * K(y,R(x,z,u) \ 1),w,v5) = a(K(x,R(y,w,v5)),z,u). R(a(K(x,y),z,u),w,v5) = a(K(x,R(y,w,v5)),z,u). a(K(x,R(y,z,u)),w,v5) = R(a(K(x,y),w,v5),z,u). K(x / y,z) * T(z,T(z * ((x / y) * ((x / y) \ ((y / x) \ 1))),x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z). K(x / y,z) * T(z,T(z * ((y / x) \ 1),x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z). K(x / y,z) * T(z,T((y / x) \ z,x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z). K(x / y,z) * T(z,T(z * (x / y),x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z). K(x / y,z) * T(z,z * (x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z). L(x,(y / z) * ((y / z) \ ((z / y) \ 1)),x) = K(y / z,x) * T(x,x * (y / z)). x != K(y,z) * T(z,z * y) | x = L(z,y,z). L(x,(y / z) * ((y / z) \ ((z / y) \ 1)),x) = L(x,y / z,x). x != L(y,z * (z \ ((u / w) \ 1)),y) | x = L(y,u \ w,y). L(x,y / z,x) = L(x,z \ y,x). L(x,y,x) = L(x,(y \ z) \ z,x). L(x,(y \ z) \ z,x) = L(x,y,x). L(x,R(y \ R(y,z,u),y,z * u),x) = L(x,(y * (z * u)) \ ((y * z) * u),x). L(x,R(y * K(z,y),z,u),x) = L(x,(z * u) \ ((z * y) * u),x). L(x,y,x) = L(x,y * K(z,y),x). L(x,y * K(z,y),x) = L(x,y,x). L(x,R(y * K(z,y),u,w),x) = L(x,R(y,u,w),x). x != L(y,R(z * K(u,z),w,v5),y) | x = L(y,R(z,w,v5),y). L(x,(y * z) \ ((y * u) * z),x) = L(x,R(u,y,z),x). x != L(y,(z * u) \ (w * u),y) | x = L(y,z \ w,y). L(x,R(y,z,u),x) = L(x,z \ (z * y),x). L(x,R(y,z,u),x) = L(x,y,x). L(x,R(y \ R(y,z,u),y,z * u),x) = L(x,a(y,z,u),x). x != L(y,R(z,u,w),y) | x = L(y,z,y). L(x,a(y,z,u),x) = L(x,y \ R(y,z,u),x). L(x,y \ R(y,z,u),x) = L(x,a(y,z,u),x). (1 / (((1 / x) * y) * (z \ (1 / x)))) * (((x \ 1) \ 1) * ((1 / ((x \ 1) \ 1)) * z)) = ((((x \ 1) \ 1) * z) / y) * (((x \ 1) \ 1) * z). (T(1 / x,y) \ (1 / y)) * (((((x \ y) \ y) \ 1) \ (1 / y)) * z) = (((x \ y) \ y) * (1 / y)) * (((1 / y) * ((x \ 1) \ 1)) * z). T((1 / x) \ (y \ 1),y) * (((((x \ y) \ y) \ 1) \ (1 / y)) * z) = (((x \ y) \ y) * (1 / y)) * (((1 / y) * ((x \ 1) \ 1)) * z). (((x \ 1) \ 1) \ y) * (((((y \ x) \ x) \ 1) \ (1 / x)) * z) = (((y \ x) \ x) * (1 / x)) * (((1 / x) * ((y \ 1) \ 1)) * z). (((x \ y) \ y) * (1 / y)) * (((1 / y) * ((x \ 1) \ 1)) * z) = (((y \ 1) \ 1) \ x) * (((((x \ y) \ y) \ 1) \ (1 / y)) * z). (((x \ y) \ y) * (1 / y)) * (((1 / y) * ((x \ 1) \ 1)) * z) = (((y \ 1) \ 1) \ x) * ((T(1 / x,y) \ (1 / y)) * z). (((x \ y) \ y) * (1 / y)) * (((1 / y) * ((x \ 1) \ 1)) * z) = (((y \ 1) \ 1) \ x) * (T((1 / x) \ (y \ 1),y) * z). (((x \ y) \ y) * (1 / y)) * (((1 / y) * ((x \ 1) \ 1)) * z) = (((y \ 1) \ 1) \ x) * ((((y \ 1) \ 1) \ x) * z). x != ((y \ 1) \ z) * (((y \ 1) \ z) * u) | x = (y * z) * ((y * z) * u). (((x \ y) \ y) * (1 / y)) * (((1 / y) * ((x \ 1) \ 1)) * z) = ((y \ 1) * x) * (((y \ 1) * x) * z). x != (((y \ z) \ z) * (1 / z)) * (((1 / z) * ((y \ 1) \ 1)) * u) | x = (z \ ((y \ 1) \ 1)) * ((z \ ((y \ 1) \ 1)) * u). ((x \ 1) * y) * (((x \ 1) * y) * z) = (x \ ((y \ 1) \ 1)) * ((x \ ((y \ 1) \ 1)) * z). (x \ ((y \ 1) \ 1)) * ((x \ ((y \ 1) \ 1)) * z) = ((x \ 1) * y) * (((x \ 1) * y) * z). (T(1 / x,y) \ (1 / y)) * (z * ((((x \ y) \ y) \ 1) \ (1 / y))) = (((x \ y) \ y) * (1 / y)) * (z * ((1 / y) * ((x \ 1) \ 1))). T((1 / x) \ (y \ 1),y) * (z * ((((x \ y) \ y) \ 1) \ (1 / y))) = (((x \ y) \ y) * (1 / y)) * (z * ((1 / y) * ((x \ 1) \ 1))). (((x \ 1) \ 1) \ y) * (z * ((((y \ x) \ x) \ 1) \ (1 / x))) = (((y \ x) \ x) * (1 / x)) * (z * ((1 / x) * ((y \ 1) \ 1))). (((x \ y) \ y) * (1 / y)) * (z * ((1 / y) * ((x \ 1) \ 1))) = (((y \ 1) \ 1) \ x) * (z * ((((x \ y) \ y) \ 1) \ (1 / y))). (((x \ y) \ y) * (1 / y)) * (z * ((1 / y) * ((x \ 1) \ 1))) = (((y \ 1) \ 1) \ x) * (z * (T(1 / x,y) \ (1 / y))). (((x \ y) \ y) * (1 / y)) * (z * ((1 / y) * ((x \ 1) \ 1))) = (((y \ 1) \ 1) \ x) * (z * T((1 / x) \ (y \ 1),y)). (((x \ y) \ y) * (1 / y)) * (z * ((1 / y) * ((x \ 1) \ 1))) = (((y \ 1) \ 1) \ x) * (z * (((y \ 1) \ 1) \ x)). x != ((y \ 1) \ z) * (u * ((y \ 1) \ z)) | x = (y * z) * (u * (y * z)). (((x \ y) \ y) * (1 / y)) * (z * ((1 / y) * ((x \ 1) \ 1))) = ((y \ 1) * x) * (z * ((y \ 1) * x)). x != (((y \ z) \ z) * (1 / z)) * (u * ((1 / z) * ((y \ 1) \ 1))) | x = ((y \ 1) * z) \ (u / ((y \ 1) * z)). ((x \ 1) * y) * (z * ((x \ 1) * y)) = ((y \ 1) * x) \ (z / ((y \ 1) * x)). ((x \ 1) * y) \ (z / ((x \ 1) * y)) = ((y \ 1) * x) * (z * ((y \ 1) * x)). (1 / ((1 / x) * ((y / z) \ (1 / x)))) * (((x \ 1) \ 1) * ((1 / ((x \ 1) \ 1)) * y)) = ((((x \ 1) \ 1) * y) / z) * (((x \ 1) \ 1) * y). (1 / (((x / y) * z) \ (1 / z))) * (((z \ 1) \ 1) * ((1 / ((z \ 1) \ 1)) * x)) = ((((z \ 1) \ 1) * x) / y) * (((z \ 1) \ 1) * x). ((1 / (1 / x)) * ((y / z) * x)) * (((x \ 1) \ 1) * ((1 / ((x \ 1) \ 1)) * y)) = ((((x \ 1) \ 1) * y) / z) * (((x \ 1) \ 1) * y). (((x \ 1) \ 1) * ((y / z) * x)) * (((x \ 1) \ 1) * ((1 / ((x \ 1) \ 1)) * y)) = ((((x \ 1) \ 1) * y) / z) * (((x \ 1) \ 1) * y). (((x \ 1) \ (y / z)) * x) * (((x \ 1) \ 1) * ((1 / ((x \ 1) \ 1)) * y)) = ((((x \ 1) \ 1) * y) / z) * (((x \ 1) \ 1) * y). (((x \ 1) \ (y / z)) * x) * (((x \ 1) \ 1) * ((x \ 1) * y)) = ((((x \ 1) \ 1) * y) / z) * (((x \ 1) \ 1) * y). (((x \ 1) \ (y / z)) * x) * (x * ((1 / x) * y)) = ((((x \ 1) \ 1) * y) / z) * (((x \ 1) \ 1) * y). ((((x \ 1) \ 1) * y) / z) * (((x \ 1) \ 1) * y) = (((x \ 1) \ (y / z)) * x) * (x * ((1 / x) * y)). (1 / (x * (y \ (1 / z)))) * (((z \ 1) \ 1) * y) = (((z \ 1) \ (y / x)) * z) * (z * ((1 / z) * y)). R(x,T(K(y,z),x),T(K(z,K(u,w)),K(y,z) * x)) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x). x / (T(K(y,z),x) * (((y \ 1) * x) * R(y,y \ 1,x))) = K(z,((y \ 1) * x) \ x) * K(((y \ 1) * x) \ x,(y \ 1) * x). x / (T(K(y,z),x) * ((y \ x) * y)) = K(z,((y \ 1) * x) \ x) * K(((y \ 1) * x) \ x,(y \ 1) * x). K(x,((y \ 1) * z) \ z) * K(((y \ 1) * z) \ z,(y \ 1) * z) = z / (T(K(y,x),z) * ((y \ z) * y)). K(x,((y \ 1) * z) \ z) * K(((y \ 1) * z) \ z,(y \ 1) * z) = z / ((y \ z) * T(y,x)). K(x,((y \ 1) * (y * z)) \ (y * z)) * K(((y \ 1) * (y * z)) \ (y * z),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x)). K(x,R(T(y,z),y \ 1,z * y)) * K(((y \ 1) * (y * z)) \ (y * z),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x)). T(K(x,y),z) * K(((y \ 1) * (y * z)) \ (y * z),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x)). T(K(x,y),z) * K(R(T(y,z),y \ 1,z * y),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x)). T(K(x,y),z) * K(R(T(y,z),y \ 1,z * y),L(z,y,y \ 1)) = (y * z) / (z * T(y,x)). T(K(x,y),z) * K(R(y,y \ 1,z * y),L(z,y,y \ 1)) = (y * z) / (z * T(y,x)). T(K(x,y),z) * K(y,z) = (y * z) / (z * T(y,x)). (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y). x != T(y,z) * K(u,z) | x = T(y * K(u,z),z). (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y). R(x,T(K(y,z),x),T(K(z,K(u,w)),x)) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x). R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x). R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ ((K(z,K(u,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x). R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x). R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * T(K(z,K(u,w)),K(y,z) * x). R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * T(K(z,K(u,w)),x). R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * K(z,K(u,T(w,x))). x \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * K(z,K(u,T(w,x))). T(K(x,y) * K(y,K(z,u)),w) = T(K(x,y),w) * K(y,K(z,T(u,w))). T(K(x,y),z) * K(y,K(u,T(w,z))) = T(K(x,y) * K(y,K(u,w)),z). x != T(K(y,z),u) * K(z,w) | x = K(z,w) * T(K(y,z),u). T(K(x,y) * K(y,K(z,u)),w) = K(y,K(z,T(u,w))) * T(K(x,y),w). K(x,K(y,T(z,u))) * T(K(w,x),u) = T(K(w,x) * K(x,K(y,z)),u). K(x,K(y,T(z,u))) * K(w,T(x,u)) = T(K(w,x) * K(x,K(y,z)),u). x != T(K(y * z,z) * K(z,K(y,u)),w) | x = K(z * T(y,w),T(z,u)). K(x,K(y,T(z,u))) * K(y * x,T(x,u)) = K(x * T(y,u),T(x,z)). K(x,K(y,T(z,u))) * w != K(x * T(y,u),T(x,z)) | w = K(x * T(y,u),x). K(x * y,T(y,z)) = K(y * T(x,z),y). K(x * T(y,z),x) = K(y * x,T(x,z)). T(x,x * T(y,z)) = 1 / (x \ K(y * x,T(x,z))). 1 / (x \ K(y * x,T(x,z))) = T(x,x * T(y,z)). T(x,T(y * x,z)) = T(x,x * T(y,z)). T(x,x * T(y,z)) != u | T(x,T(y * x,z)) = u. K(x,x * y) * T(x * L(y,z,u),x) = L(y,z,u) * T(R(x,L(y,z,u),x),R(x,L(y,z,u),x) * y). L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = K(u,u * x) * T(u * L(x,y,z),u). x != K(y,z) * T(u,y) | x = T(K(y,z) * u,y). L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = T(K(u,u * x) * (u * L(x,y,z)),u). L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = T(T(u,u * x) * L(x,y,z),u). L(x,y,z) * T(R(u,x,u),R(u,L(x,y,z),u) * x) = T(T(u,u * x) * L(x,y,z),u). L(x,y,z) * T(R(u,x,u),R(u,x,u) * x) = T(T(u,u * x) * L(x,y,z),u). L(x,y,z) * T(R(u,x,u),x * R(u,x,u)) = T(T(u,u * x) * L(x,y,z),u). L(x,y,z) * T(R(u,x,u),T(u * x,u)) = T(T(u,u * x) * L(x,y,z),u). L(x,y,z) * T(R(u,x,u),x * u) = T(T(u,u * x) * L(x,y,z),u). L(x,y,z) * T(u,x) = T(T(u,u * x) * L(x,y,z),u). T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y). x != T(T(y,y * z) * L(z,u,w),y) | x = T(y * L(z,u,w),y * z). L(x,y,z) * T(u,x) = T(u * L(x,y,z),u * x). T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y). x * y != T(z * L(u,w,v5),z * u) | x \ (L(u,w,v5) * T(z,u)) = y. (x * L(y,z,u)) \ (L(y,z,u) * T(x,y)) = K(x * L(y,z,u),x * y). K(x,y) * K(L(y,z,u),x) = K(x * L(y,z,u),x * y). K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x). x != K(y,z) * K(L(z,u,w),y) | x = a(w,u,K(y,z)). K(x * L(y,z,u),x * y) = a(u,z,K(x,y)). K(x,(x / L(y,z,u)) * y) = a(u,z,K(x / L(y,z,u),y)). x != K(y,(y / L(z,u,w)) * z) | x = K(y,z * (L(z,u,w) \ y)). a(x,y,K(z / L(u,y,x),u)) = K(z,u * (L(u,y,x) \ z)). K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x / L(y,z,u),y)). K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y)). x != a(y,z,K(u \ w,u)) | x = a(y,z,K(w,u)). K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y)). K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y)). x != K(y,y * z) | x = (y * K(z,y)) \ L(y,z,y). a(x,y,K(z,u)) = (z * K(L(u,y,x) \ u,z)) \ L(z,L(u,y,x) \ u,z). (x * K(L(y,z,u) \ y,x)) \ L(x,L(y,z,u) \ y,x) = a(u,z,K(x,y)). K(x / (L(y,z,u) \ y),x) = a(u,z,K(x / (L(y,z,u) \ y),y)). x / (a(y,z,K(u,w)) * x) = K(u * (L(w,z,y) \ w),u). K(x * (L(y,z,u) \ y),x) = w / (a(u,z,K(x,y)) * w). x != y / (a(z,u,K(w,v5)) * y) | x = a(z,u,K(v5,w)). K(x * (L(y,z,u) \ y),x) = a(u,z,K(y,x)). a(x,y,a(z,u,K(w,v5))) = a(x,y,K(L(w,u,z) \ w,v5)). a(x,y,K(L(z,u,w) \ z,v5)) = a(x,y,a(w,u,K(z,v5))). x != a(y,z,K(u \ w,v5)) | x = a(y,z,K(v5,w \ u)). a(x,y,a(z,u,K(w,v5))) = a(x,y,K(v5,w \ L(w,u,z))). a(x,y,K(z,u \ L(u,w,v5))) = a(x,y,a(v5,w,K(u,z))). K(a(x,y,z),u) * a(x * y,z,a(x,y,K(z,u))) = K(L(z,y,x) \ z,u). a(x,T(y,z),a(u,w,K(y,v5))) * K(v5,L(y \ L(y,w,u),y,x)) = K(v5,y \ L(y,w,u)). K((L(x,y,z) \ x) \ u,u) = a(z,y,K(u / (L(x,y,z) \ x),x)). K(x * (y \ L(y,z,u)),x) = a(u,z,K(x / (L(y,z,u) \ y),y)). K(x * (y \ L(y,z,u)),x) = a(u,z,K((y / x) \ y,y)). K(x * (y \ L(y,z,u)),x) = a(u,z,K(x,y)). x / (a(y,z,K(u,w)) * x) = K(u,u * (w \ L(w,z,y))). K(x,x * (y \ L(y,z,u))) = w / (a(u,z,K(x,y)) * w). K(x,x * (y \ L(y,z,u))) = a(u,z,K(y,x)). T(x,x * (y \ L(y,z,u))) = x * a(u,z,K(y,x)). (x * K(L(y,z,u) \ y,x)) \ L(x,a(u,z,y),x) = a(u,z,K(x,y)). K(x,L(y,z,u) \ y) * (x \ L(x,a(u,z,y),x)) = a(u,z,K(x,y)). x \ L(T(x,L(y,z,u) \ y),a(u,z,y),x) = a(u,z,K(x,y)). K(a(x,y,z),u) * 1 = K(L(z,y,x) \ z,u). K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1. K(L(x,y,z) \ x,u) = K(a(z,y,x),u). x / (K(a(y,z,u),w) * x) = K(w,L(u,z,y) \ u). K(x,L(y,z,u) \ y) = w / (K(a(u,z,y),x) * w). K(x,L(y,z,u) \ y) = K(x,a(u,z,y)). T(x,L(y,z,u) \ y) = x * K(x,a(u,z,y)). T(x,L(y,z,u) \ y) = T(x,a(u,z,y)). x \ L(T(x,a(y,z,u)),a(y,z,u),x) = a(y,z,K(x,u)). K(x,x * a(y,z,u)) = a(y,z,K(x,u)). a(x,y,K(z,u)) != w | K(z,z * a(x,y,u)) = w. 1 * K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u)). K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u)). K(x,a(y,z,u) \ 1) = K(x,u \ L(u,z,y)). T(x,a(y,z,u) \ 1) = x * K(x,u \ L(u,z,y)). x * K(x,y \ L(y,z,u)) = T(x,a(u,z,y) \ 1). T(x,y \ L(y,z,u)) = T(x,a(u,z,y) \ 1). T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y)). L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),x) = T(x,x * (u \ L(u,z,y))). x != T(y,y * (z \ L(z,u,w))) | x = y * a(w,u,K(z,y)). L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),x) = x * a(y,z,K(u,x)). K(x,x * y) * T(x * R(y,z,u),x) = R(y,z,u) * T(R(x,R(y,z,u),x),R(x,R(y,z,u),x) * y). R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = K(u,u * x) * T(u * R(x,y,z),u). R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(K(u,u * x) * (u * R(x,y,z)),u). R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(T(u,u * x) * R(x,y,z),u). x != T(T(y,y * z) * R(z,u,w),y) | x = T(y * R(z,u,w),y * z). R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(u * R(x,y,z),u * x). R(x,y,z) * R(T(u,x * R(u,R(x,y,z),u)),R(x,y,z),u) = T(u * R(x,y,z),u * x). R(x,y,z) * R(T(u,u * x),R(x,y,z),u) = T(u * R(x,y,z),u * x). R(x,y,z) * R(T(u,x * u),R(x,y,z),u) = T(u * R(x,y,z),u * x). R(x,y,z) * R(T(u,x * u),x,u) = T(u * R(x,y,z),u * x). R(x,y,z) * T(u,x) = T(u * R(x,y,z),u * x). T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y). K(x * y,x * R(y,z,u)) = (x * R(y,z,u)) / (R(y,z,u) * T(x,y)). (x * R(y,z,u)) / (R(y,z,u) * T(x,y)) = K(x * y,x * R(y,z,u)). x != (y * z) / (z * T(y,u)) | x = T(K(u,y) * K(y,z),z). K(x * y,x * R(y,z,u)) = T(K(y,x) * K(x,R(y,z,u)),R(y,z,u)). T(K(x,y) * K(y,R(x,z,u)),R(x,z,u)) = K(y * x,y * R(x,z,u)). T(a(K(x,y),z * y,u),R(y,z,u)) = K(x * y,x * R(y,z,u)). (((x \ 1) \ K(y,x)) \ T(x,z)) \ K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ K(x,y)) \ 1)) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z)). K((x * (K(y,x) / T(x,z))) \ 1,((x \ K(x,y)) * T(x,z)) \ 1) = K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))). K((x * (K(y,x) / T(x,z))) \ 1,x * (K(y,x) / T(x,z))) = K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))). K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K((x * (K(y,x) / T(x,z))) \ 1,x * (K(y,x) / T(x,z))). x != K((y * z) \ 1,y * z) | x = K(y \ (z \ 1),z * y). K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(x \ ((K(y,x) / T(x,z)) \ 1),(K(y,x) / T(x,z)) * x). K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(x \ (K(x,z) * T(x,y)),(K(y,x) / T(x,z)) * x). K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(T(K(x,z),x) * K(x,y),(K(y,x) / T(x,z)) * x). K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(K(x,z) * K(x,y),(K(y,x) / T(x,z)) * x). K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(K(x,z) * K(x,y),K(y,x) * K(z,x)). x != K(K(y,z) * K(y,u),K(u,y) * K(z,y)) | x = 1. K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1. K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1. ((x \ K(x,y)) * T(x,z)) \ K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ K(x,y)) \ 1)) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z)). ((x \ K(x,y)) * T(x,z)) \ K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ K(x,y)) \ 1)) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z)). ((x \ K(x,y)) * T(x,z)) \ K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z)). ((x \ K(x,y)) * T(x,z)) \ 1 = 1 / (((x \ K(x,y)) \ 1) \ T(x,z)). 1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = ((x \ K(x,y)) * T(x,z)) \ 1. x != ((y \ K(y,z)) * T(y,u)) \ 1 | x = y * (K(z,y) / T(y,u)). 1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = x * (K(y,x) / T(x,z)). 1 / (((x \ 1) \ K(y,x)) \ T(x,z)) = x * (K(y,x) / T(x,z)). 1 / ((x \ K(x,y)) * T(x,z)) = x * (K(y,x) / T(x,z)). (x * (K(y,x) / T(x,z))) \ 1 = (x \ K(x,y)) * T(x,z). (((x \ K(x,y)) * T(x,z)) \ 1) \ L(u,(x * (K(y,x) / T(x,z))) \ 1,x * (K(y,x) / T(x,z))) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u. T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = (y \ T(y * (x \ 1),y)) * R((y \ T(y * (x \ 1),y)) \ 1,z,u). x != (y \ z) * R((y \ z) \ 1,u,w) | x = y \ (z * R(z \ y,u,w)). T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ (T(y * (x \ 1),y) * R(T(y * (x \ 1),y) \ y,z,u)). T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T((y * (x \ 1)) * R((y * (x \ 1)) \ y,z,u),y). T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T(y * ((x \ 1) * R((x \ 1) \ 1,z,u)),y). T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T(y * (x \ R(x,z,u)),y). T(x \ (a(y,x \ 1,y) * R(a(y,x \ 1,y) \ x,z,u)),y) = y \ T(y * (x \ R(x,z,u)),y). T(x \ R(a(y,x \ 1,y) * (a(y,x \ 1,y) \ x),z,u),y) = y \ T(y * (x \ R(x,z,u)),y). T(x \ R(x,y,z),u) = u \ T(u * (x \ R(x,y,z)),u). x \ T(x * (y \ R(y,z,u)),x) = T(y \ R(y,z,u),x). x != K(y,(z \ 1) * ((u \ z) * u)) | x = K(y,K(z,u)). K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(a(x,y,z),K((x * y) * z,u)). K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(u,K(a(x,y,z),(x * y) * z)). (K(x,x \ 1) * ((y \ x) \ 1)) * (((x \ 1) \ ((1 / x) * ((y \ x) \ 1))) * z) = (x \ ((y \ 1) \ 1)) * ((x * ((1 / x) * ((y \ x) \ 1))) * z). (((x \ y) \ y) * (1 / y)) * (((y \ 1) \ ((1 / y) * ((x \ y) \ 1))) * z) = (y \ ((x \ 1) \ 1)) * ((y * ((1 / y) * ((x \ y) \ 1))) * z). (((x \ y) \ y) * (1 / y)) * ((K(y,y \ 1) * ((x \ y) \ 1)) * z) = (y \ ((x \ 1) \ 1)) * ((y * ((1 / y) * ((x \ y) \ 1))) * z). (((x \ y) \ y) * (1 / y)) * ((((x \ y) \ y) * (1 / y)) * z) = (y \ ((x \ 1) \ 1)) * ((y * ((1 / y) * ((x \ y) \ 1))) * z). (x \ ((y \ 1) \ 1)) * ((x * ((1 / x) * ((y \ x) \ 1))) * z) = (((y \ x) \ x) * (1 / x)) * ((((y \ x) \ x) * (1 / x)) * z). x != ((y \ z) * (1 / z)) * (((y \ z) * (1 / z)) * u) | x = (y \ 1) * ((y \ 1) * u). (x \ ((y \ 1) \ 1)) * ((x * ((1 / x) * ((y \ x) \ 1))) * z) = ((y \ x) \ 1) * (((y \ x) \ 1) * z). x != ((y \ z) \ 1) * (((y \ z) \ 1) * u) | x = (z \ y) * ((z \ y) * u). (x \ ((y \ 1) \ 1)) * ((x * ((1 / x) * ((y \ x) \ 1))) * z) = (x \ y) * ((x \ y) * z). (x \ ((y \ 1) \ 1)) * ((x \ ((y \ 1) \ 1)) * z) = (x \ y) * ((x \ y) * z). x != (y \ ((z \ 1) \ 1)) * ((y \ ((z \ 1) \ 1)) * u) | x = ((y \ 1) * z) * (((y \ 1) * z) * u). (x \ y) * ((x \ y) * z) = ((x \ 1) * y) * (((x \ 1) * y) * z). ((x \ 1) * y) * (((x \ 1) * y) * z) = (x \ y) * ((x \ y) * z). x != ((y \ 1) * (1 / z)) * (((y \ 1) * (1 / z)) * u) | x = (y \ (z \ 1)) * ((y \ (z \ 1)) * u). (x \ (1 / y)) * ((x \ (1 / y)) * z) = (x \ (y \ 1)) * ((x \ (y \ 1)) * z). T(1 / ((x \ (y \ 1)) * ((x \ (y \ 1)) * z)),x \ (y \ 1)) = (1 / (z * (x \ (1 / y)))) * (((y \ 1) \ 1) * x). T(((((x \ (y \ 1)) * z) \ 1) \ 1) \ (y * x),x \ (y \ 1)) = (1 / (z * (x \ (1 / y)))) * (((y \ 1) \ 1) * x). T(((x \ ((y \ (z \ 1)) \ 1)) \ 1) \ (z * y),y \ (z \ 1)) = (1 / (x * (y \ (1 / z)))) * (((z \ 1) \ 1) * y). T(((1 / (x * y)) * ((z \ 1) \ 1)) \ (x * y),y \ (x \ 1)) = (1 / (z * (y \ (1 / x)))) * (((x \ 1) \ 1) * y). T((((x * y) \ ((z \ 1) \ 1)) \ 1) * (x * y),y \ (x \ 1)) = (1 / (z * (y \ (1 / x)))) * (((x \ 1) \ 1) * y). T(((1 / x) * (((y * z) \ 1) \ 1)) * (y * z),z \ (y \ 1)) = (1 / (x * (z \ (1 / y)))) * (((y \ 1) \ 1) * z). T(((1 / x) * (y * z)) * ((z \ (y \ 1)) \ 1),z \ (y \ 1)) = (1 / (x * (z \ (1 / y)))) * (((y \ 1) \ 1) * z). (1 / (x \ (y \ 1))) * ((1 / z) * (y * x)) = (1 / (z * (x \ (1 / y)))) * (((y \ 1) \ 1) * x). (1 / (x * (y \ (1 / z)))) * (((z \ 1) \ 1) * y) = (1 / (y \ (z \ 1))) * ((1 / x) * (z * y)). (1 / (x * (y \ (1 / z)))) * (((z \ 1) \ 1) * y) = ((1 / 1) \ (z * y)) * ((1 / x) * (z * y)). (1 / (x * (y \ (1 / z)))) * (((z \ 1) \ 1) * y) = (1 \ (z * y)) * ((1 / x) * (z * y)). (1 / (x * (y \ (1 / z)))) * (((z \ 1) \ 1) * y) = (z * y) * ((1 / x) * (z * y)). (1 / (x * (y \ (1 / z)))) * (((z \ 1) \ 1) * y) = ((z * y) / x) * (z * y). x != (1 / (y * (z \ (1 / u)))) * (((u \ 1) \ 1) * z) | x = (((u \ 1) \ (z / y)) * u) * (u * ((1 / u) * z)). ((x * y) / z) * (x * y) = (((x \ 1) \ (y / z)) * x) * (x * ((1 / x) * y)). (((x \ 1) \ (y / z)) * x) * (x * ((1 / x) * y)) = ((x * y) / z) * (x * y). (((x \ 1) \ y) * x) * (x * ((1 / x) * z)) = ((x * z) / (y \ z)) * (x * z). ((x * y) / (z \ y)) * (x * y) = (((x \ 1) \ z) * x) * (x * ((1 / x) * y)). (((x \ 1) \ ((1 / y) \ z)) * x) * (x * ((1 / x) * y)) = ((x * y) / (z \ 1)) * (x * y). ((x * y) / y) * (z * (x * y)) = (((x \ 1) \ z) * x) * (x * ((1 / x) * y)). x * (y * (x * z)) = (((x \ 1) \ y) * x) * (x * ((1 / x) * z)). (((x \ 1) \ y) * x) * (x * ((1 / x) * z)) = x * (y * (x * z)). x != (((y \ 1) \ z) * y) * (y * ((1 / y) * u)) | x = y * (z * (y * u)). ((x * y) / (z \ 1)) * (x * y) = x * (((1 / y) \ z) * (x * y)). ((x * y) / (z \ 1)) * (x * y) = x * (y * ((z * x) * y)). ((1 / (x * y)) \ z) * (x * y) = x * (y * ((z * x) * y)). (x * y) * (z * (x * y)) = x * (y * ((z * x) * y)). x != ((1 / ((y \ z) * L(u,y,y))) \ y) * ((y \ z) * L(u,y,y)) | x = ((y \ z) * L(u,y,y)) * (y / (u \ (z \ y))). (x \ y) * (L(z,x,x) * ((x * (x \ y)) * L(z,x,x))) = ((x \ y) * L(z,x,x)) * (x / (z \ (y \ x))). x \ (x * (1 / (((y * (x * (((x \ z) \ 1) \ 1))) \ (1 / z)) * x))) = (((x \ z) \ 1) \ 1) * ((y * x) * (((x \ z) \ 1) \ 1)). (a(x,y,x) * z) * u != a(x,y,x) * (z * w) | u = w. x * (a(y,z,y) * u) = (x * a(y,z,y)) * u. (x * a(y,z,y)) * u = x * (a(y,z,y) * u). x != ((1 / y) * z) * (u * ((1 / y) * z)) | x = (y \ z) * (u * (y \ z)). (1 / x) * (y * ((z * (1 / x)) * y)) = (x \ y) * (z * (x \ y)). x * (y * ((z * x) * y)) != (x * y) * u | z * (x * y) = u. (x * y) * z != x * (y * ((u * x) * y)) | u * (x * y) = z. R(x,a(y,z,y),u) = x. x * y != z * (u * (u \ (z \ w))) | x \ w = y. (x * a(y,z,y)) \ u = a(y,z,y) \ (x \ u). a(x * a(y,z,y),u,w) = (x * (a(y,z,y) * (u * w))) \ (((x * a(y,z,y)) * u) * w). (x * (a(y,z,y) * (u * w))) \ (((x * a(y,z,y)) * u) * w) = a(x * a(y,z,y),u,w). T((a(x,y,x) * z) \ (u * z),a(x,y,x)) = T(a(x,y,x) \ u,a(x,y,x) * z). x != (y * a(z,u,z)) \ w | x = (a(z,u,z) * y) \ w. a(x,y,x) \ (z \ u) = (a(x,y,x) * z) \ u. (a(x,y,x) * z) \ u = a(x,y,x) \ (z \ u). K(x,(a(y,z,y) * u) \ w) = K(x,u \ w). L(K(x,y \ z),z,a(u,w,u)) = K(x,y \ (a(u,w,u) * z)). K(x,R(y,z,y) \ u) = K(x,y \ u). K(x,T(y * z,y) \ u) = K(x,(z * y) \ u). K(x,T(y,y \ z) \ u) = K(x,T(y,z) \ u). K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u). K(x,T(y,z) \ u) = K(x,((z \ y) * z) \ u). K(x,((y \ z) * y) \ u) = K(x,T(z,y) \ u). x != K(y,T(z,u) \ w) | x = K(y,T(z,z \ u) \ w). K(x,((y \ z) \ z) \ u) = K(x,T(y,y \ z) \ u). K(x,T(y,y \ z) \ u) = K(x,((y \ z) \ z) \ u). K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w. K(x,((y \ z) \ z) \ u) != w | K(x,T(y,z) \ u) = w. K(x,y \ (a(z,u,z) * w)) = K(x,y \ w). K(x,y \ T(z * u,z)) = K(x,y \ (u * z)). (1 / x) * (((y \ (z * (1 / x))) \ 1) * L(y,y,(z * (1 / x)) * y)) = (x \ ((y \ (z * (1 / x))) \ 1)) * (z * (x \ ((y \ (z * (1 / x))) \ 1))). (x \ ((y \ (z * (1 / x))) \ 1)) * (z * (x \ ((y \ (z * (1 / x))) \ 1))) = (1 / x) * (((y \ (z * (1 / x))) \ 1) * L(y,y,(z * (1 / x)) * y)). T(a(x,y,x) \ z,a(x,y,x) * u) = (a(x,y,x) * u) \ (z * u). T(a(x,y,x) \ z,u * a(x,y,x)) = (a(x,y,x) * u) \ (z * u). x != (a(y,z,y) * u) \ w | x = a(y,z,y) \ (u \ w). T(a(x,y,x) \ z,u * a(x,y,x)) = a(x,y,x) \ (u \ (z * u)). T(a(x,y,x) \ z,u * a(x,y,x)) = a(x,y,x) \ T(z,u). T(a(x,y,x) \ z,u) = a(x,y,x) \ T(z,u). a(x,y,x) \ T(z,u) = T(a(x,y,x) \ z,u). K(x,y) * T(a(x,y,x) \ z,u) = K(x,x * y) * T(z,u). K(x,y) * T(z,u) = K(x,x * y) * T(a(x,y,x) * z,u). K(x,x * y) * T(a(x,y,x) * z,u) = K(x,y) * T(z,u). a(x,y,x) * T(z,u) = T(a(x,y,x) * z,u). T(a(x,y,x) * z,u) = a(x,y,x) * T(z,u). (x * (y * T(a(z,u,z) * (a(z,u,z) \ (y \ (x \ w))),v5))) \ w = K(v5,(x * (y * a(z,u,z))) \ w). (x * (a(y,z,y) * (u * w))) \ ((x * (a(y,z,y) * u)) * w) = a(x * a(y,z,y),u,w). a(x,a(y,z,y) * u,w) = a(x * a(y,z,y),u,w). a(x * a(y,z,y),u,w) = a(x,a(y,z,y) * u,w). a(x,y,z) = a(x / a(u,w,u),a(u,w,u) * y,z). a(x / a(y,z,y),a(y,z,y) * u,w) = a(x,u,w). x != a(y / a(z,u,z),w,v5) | x = a(y,w,v5). a(x,y,z) = a(x,a(u,w,u) * y,z). a(x,a(y,z,y) * u,w) = a(x,u,w). a(x,T(y * z,y),u) = a(x,z * y,u). a(x,y \ z,u) = a(x,(y \ 1) * z,u). a(x,(y \ 1) * z,u) = a(x,y \ z,u). a(x,(1 / y) \ z,u) = a(x,y * z,u). (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * (y * a(w,v5,w))) \ z). K(x,(y * (z * a(u,w,u))) \ v5) = (y * (z * T(z \ (y \ v5),x))) \ v5. x != (y * (z * T(z \ (y \ u),w))) \ u | x = K(w,(y * z) \ u). K(x,(y * (z * a(u,w,u))) \ v5) = K(x,(y * z) \ v5). K(x,(y * K(z * u,u)) \ w) = K(x,(y * K(z,u)) \ w). K(x,(y * z) \ u) = K(x,(L(y,w,y) * z) \ u). K(x,(L(y,z,y) * u) \ w) = K(x,(y * u) \ w). x \ (x * (1 / ((x * (1 / ((y * (((z \ 1) \ 1) * y)) * x))) * x))) = (((x \ y) \ 1) \ 1) * ((z * x) * (((x \ y) \ 1) \ 1)). x \ (x * (1 / ((x * (1 / (((y / (1 / z)) * y) * x))) * x))) = (((x \ y) \ 1) \ 1) * ((z * x) * (((x \ y) \ 1) \ 1)). x \ (x * (1 / ((((y * (z * y)) \ x) * (1 / x)) * x))) = (((x \ y) \ 1) \ 1) * ((z * x) * (((x \ y) \ 1) \ 1)). x \ (x * (1 / L((y * (z * y)) \ x,x,x))) = (((x \ y) \ 1) \ 1) * ((z * x) * (((x \ y) \ 1) \ 1)). x \ (x * (1 / ((x \ (y * (z * y))) \ 1))) = (((x \ y) \ 1) \ 1) * ((z * x) * (((x \ y) \ 1) \ 1)). (((x \ y) \ 1) \ 1) * ((z * x) * (((x \ y) \ 1) \ 1)) = x \ (x * (1 / ((x \ (y * (z * y))) \ 1))). (((x \ y) \ 1) \ 1) * ((z * x) * (((x \ y) \ 1) \ 1)) = x \ (x * (x \ (y * (z * y)))). (((x \ y) \ 1) \ 1) * ((z * x) * (((x \ y) \ 1) \ 1)) = x \ (y * (z * y)). ((x \ y) \ 1) \ ((z * x) / ((x \ y) \ 1)) = x \ (y * (z * y)). x != (y \ 1) \ (z / (y \ 1)) | x = y * (z * y). x \ (y * (z * y)) = (x \ y) * ((z * x) * (x \ y)). (x \ y) * ((z * x) * (x \ y)) = x \ (y * (z * y)). x != (y \ z) * ((u * y) * (y \ z)) | x = ((z \ y) \ u) * L(z,z,y * z). x \ (y * (z * y)) = ((y \ x) \ z) * L(y,y,x * y). ((x \ y) \ z) * L(x,x,y * x) = y \ (x * (z * x)). (x \ ((y \ (z * (1 / x))) \ 1)) * (z * (x \ ((y \ (z * (1 / x))) \ 1))) = (1 / x) * ((z * (1 / x)) \ (y * (1 * y))). (x \ ((y \ (z * (1 / x))) \ 1)) * (z * (x \ ((y \ (z * (1 / x))) \ 1))) = (1 / x) * ((z * (1 / x)) \ (y * y)). (x \ ((y \ (z * (1 / x))) \ 1)) * (z * (x \ ((y \ (z * (1 / x))) \ 1))) = (1 / x) * (((z * (1 / x)) \ y) * y). x != (1 / y) * (((z * (1 / y)) \ u) * u) | x = (z \ (u * (u / y))) * y. (x \ ((y \ (z * (1 / x))) \ 1)) * (z * (x \ ((y \ (z * (1 / x))) \ 1))) = (z \ (y * (y / x))) * x. (K(x,x \ 1) * ((y \ x) \ 1)) * (z * ((x \ 1) \ ((1 / x) * ((y \ x) \ 1)))) = (x \ ((y \ 1) \ 1)) * (z * (x * ((1 / x) * ((y \ x) \ 1)))). (((x \ y) \ y) * (1 / y)) * (z * ((y \ 1) \ ((1 / y) * ((x \ y) \ 1)))) = (y \ ((x \ 1) \ 1)) * (z * (y * ((1 / y) * ((x \ y) \ 1)))). (((x \ y) \ y) * (1 / y)) * (z * (K(y,y \ 1) * ((x \ y) \ 1))) = (y \ ((x \ 1) \ 1)) * (z * (y * ((1 / y) * ((x \ y) \ 1)))). (((x \ y) \ y) * (1 / y)) * (z * (((x \ y) \ y) * (1 / y))) = (y \ ((x \ 1) \ 1)) * (z * (y * ((1 / y) * ((x \ y) \ 1)))). (x \ ((y \ 1) \ 1)) * (z * (x * ((1 / x) * ((y \ x) \ 1)))) = (((y \ x) \ x) * (1 / x)) * (z * (((y \ x) \ x) * (1 / x))). x != ((y \ z) * (1 / z)) * (u * ((y \ z) * (1 / z))) | x = y \ (u / y). (x \ ((y \ 1) \ 1)) * (z * (x * ((1 / x) * ((y \ x) \ 1)))) = (y \ x) \ (z / (y \ x)). x != (y \ z) \ (u / (y \ z)) | x = (z \ y) * (u * (z \ y)). (x \ ((y \ 1) \ 1)) * (z * (x * ((1 / x) * ((y \ x) \ 1)))) = (x \ y) * (z * (x \ y)). (x \ ((y \ 1) \ 1)) * (z * (x \ ((y \ 1) \ 1))) = (x \ y) * (z * (x \ y)). (x \ y) * (z * (x \ y)) = ((y \ 1) * x) \ (z / ((y \ 1) * x)). ((x \ 1) * y) \ (z / ((x \ 1) * y)) = (y \ x) * (z * (y \ x)). x != ((y \ 1) * z) \ (u / ((y \ 1) * z)) | x = ((z \ 1) * y) * (u * ((z \ 1) * y)). (x \ y) * (z * (x \ y)) = ((x \ 1) * y) * (z * ((x \ 1) * y)). ((x \ 1) * y) * (z * ((x \ 1) * y)) = (x \ y) * (z * (x \ y)). ((1 / ((x \ 1) * y)) \ z) * ((x \ 1) * y) = (x \ y) * (z * (x \ y)). ((((x \ 1) \ 1) \ y) \ z) * ((y \ 1) * x) = (y \ x) * (z * (y \ x)). ((T(x,y \ 1) \ 1) \ 1) \ ((L(1 / T(x,y \ 1),1 / T(x,y \ 1),1 / T(x,y \ 1)) \ y) * z) = ((1 / T(x,y \ 1)) \ 1) \ ((y * x) * z). L(x,K(y,z),R(K(u,y) * R(K(y,u),w,v5),K(y,z),x)) = x. L(x,K(y,z),K(u,y) * R(K(y,u),w,v5)) = x. L(x,K(y,z),a(K(y,u),w,v5)) = x. (a(K(x,y),z,u) * K(x,w)) * v5 = a(K(x,y),z,u) * (K(x,w) * v5). x != (a(K(y,T(z,u)),w,v5) * K(y,z)) * (K(z,y) * u) | x = u * a(K(y,z),w,v5). a(K(x,T(y,z)),u,w) * (K(x,y) * (K(y,x) * z)) = z * a(K(x,y),u,w). a(K(x,T(y,z)),u,w) * z = z * a(K(x,y),u,w). a(K(x,y),z,u) * w = w * a(K(x,T(y,w)),z,u). x * a(K(y,T(z,x)),u,w) = a(K(y,z),u,w) * x. T(a(K(x,y),z,u),w) = a(K(x,T(y,w)),z,u). a(K(x,T(y,z)),u,w) = T(a(K(x,y),u,w),z). x != T(a(K(y,z),u * z,w),R(z,u,w)) | x = K(y * z,y * R(z,u,w)). a(K(x,T(y,R(y,z,u))),z * y,u) = K(x * y,x * R(y,z,u)). K(x * y,x * R(y,z,u)) = a(K(x,T(y,R(y,z,u))),z * y,u). K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u). R(K(x * y,x * R(y,z,u)),x * R(y,z,u),w) = a(K(x,y),z * y,u). K(x,(x / y) * R(y,z,u)) = a(K(x / y,y),z * y,u). x != K(y,(y / z) * u) | x = K(y,(z \ y) * u). a(K(x / y,y),z * y,u) = K(x,(y \ x) * R(y,z,u)). K(x,(y \ x) * R(y,z,u)) = a(K(x / y,y),z * y,u). x != K(y,(z \ y) * R(z,u,w)) | x = K(y,y * (z \ R(z,u,w))). a(K(x / y,y),z * y,u) = K(x,x * (y \ R(y,z,u))). K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u). K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u). x != a(K(y \ z,y),u,w) | x = a(K(z,y),u,w). K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u). x != K(y,z) | x = (u \ T(z,y)) \ (u \ z). a(K(x,y),z * y,u) = (w \ T(x * (y \ R(y,z,u)),x)) \ (w \ (x * (y \ R(y,z,u)))). (x \ T(y * (z \ R(z,u,w)),y)) \ (x \ (y * (z \ R(z,u,w)))) = a(K(y,z),u * z,w). a(K(x,y),z * y,u) = (x * K(y \ R(y,z,u),x)) \ L(x,y \ R(y,z,u),x). (x * K(y \ R(y,z,u),x)) \ L(x,y \ R(y,z,u),x) = a(K(x,y),z * y,u). R(a(K(x,y),z * y,u),x * R(y,z,u),w) = a(K(x,y),z * y,u). x != R(a(K(y,z),u,w),v5,v6) | x = a(K(y,R(z,v5,v6)),u,w). a(K(x,y),z * y,u) = a(K(x,R(y,x * R(y,z,u),w)),z * y,u). a(K(x,R(y,x * R(y,z,u),w)),z * y,u) = a(K(x,y),z * y,u). x != a(K(y,R(z,y * u,w)),v5,v6) | x = a(K(y,R(z,u,w)),v5,v6). a(K(x,y),z * y,u) = a(K(x,R(y,R(y,z,u),w)),z * y,u). a(K(x,R(y,R(y,z,u),w)),z * y,u) = a(K(x,y),z * y,u). (x * K(y \ R(y,z,u),x)) \ L(x,a(y,z,u),x) = a(K(x,y),z * y,u). K(x,y \ R(y,z,u)) * (x \ L(x,a(y,z,u),x)) = a(K(x,y),z * y,u). T(x \ R(x,y,z),u) \ (u \ (u * (x \ R(x,y,z)))) = a(K(u,x),y * x,z). T(x \ R(x,y,z),u) \ (x \ R(x,y,z)) = a(K(u,x),y * x,z). K(x,y \ R(y,z,u)) = a(K(x,y),z * y,u). a(K(x,y),z * y,u) = K(x,y \ R(y,z,u)). a(K(x,K(y,z)),u * y,w) = K(x,K(z,y \ R(y,u,w))). a(K(x,y),z * y,u) * (x \ L(x,a(y,z,u),x)) = a(K(x,y),z * y,u). x != a(K(y,K(z,u)),w * z,v5) | x = a(K(z,K(y,u)),w,v5). K(x,K(y,z \ R(z,u,w))) = a(K(z,K(x,y)),u,w). x != K(y,K(z,u \ R(u,w,v5))) | x = K(y,K(z,R(u,w,v5) * (u \ z))). a(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w) * (x \ z))). K(x,K(y,R(z,u,w) * (z \ y))) = a(K(z,K(x,y)),u,w). K(x,K(y,R(z,u,w) * (z \ y))) = a(K(x,K(y,z)),u,w). K(x,K(y,R(z,u,w) \ z)) = a(K(x,K(y,z)),u,w). x != K(y,K(R(z,u,w),R(u,v5,v6) \ u)) | x = K(y,K(z,(u * w) / (R(u,v5,v6) * w))). a(K(x,K(R(y,z,u),z)),w,v5) = K(x,K(y,(z * u) / (R(z,w,v5) * u))). K(x,K(y,(z * u) / (R(z,w,v5) * u))) = a(K(x,K(R(y,z,u),z)),w,v5). K(x,K(y,(z * u) / (R(z,w,v5) * u))) = a(K(x,K(z,R(y,z,u))),w,v5). K(x,K(y,(z * u) / (R(z,w,v5) * u))) = a(K(x,K(z,y)),w,v5). K(x,K(R(y,z,u) \ y,R(w,y,v5))) = a(K(x,K(y,w)),z,u). x != K(y,K(R(z,u,w) \ z,R(v5,z,u * w))) | x = K(y,K(a(z,u,w),T(v5,z * (u * w)))). a(K(x,K(y,z)),u,w) = K(x,K(a(y,u,w),T(z,y * (u * w)))). K(x,K(a(y,z,u),T(w,y * (z * u)))) = a(K(x,K(y,w)),z,u). a(x,a(y,z,u),x) \ a(K(x,y),z * y,u) = a(K(x,y),z * y,u). (a(x,a(y,z,u),x) \ a(K(x,y),z * y,u)) * w != a(K(x,y),z * y,u) | 1 = w. 1 = a(x,a(y,z,u),x). a(x,a(y,z,u),x) = 1. L(x,a(y,z,u),x) = x. x * y != L(z,a(u,w,v5),z) | z / y = x. x / (a(y,z,u) \ 1) = x * a(y,z,u). x * y != L(z,a(u,w,v5),z) | x \ z = y. a(x,y,z) \ u = (a(x,y,z) \ 1) * u. (a(x,y,z) \ 1) * u = a(x,y,z) \ u. (1 / x) \ a(y,z,u) = x * a(y,z,u). x / a(y,z,u) = x * (a(y,z,u) \ 1). x * (a(y,z,u) \ 1) = x / a(y,z,u). x \ a(y,z,u) = (x \ 1) * a(y,z,u). (x \ 1) * a(y,z,u) = x \ a(y,z,u). (a(x,y,z) \ 1) \ u = a(x,y,z) * u. x * y != (a(z,u,w) \ 1) * v5 | (a(z,u,w) \ v5) / y = x. (a(x,y,z) \ (K(a(x,y,z) \ 1,u) * w)) / w = T(a(x,y,z) \ 1,u). (a(x,y,z) \ u) \ u = T(a(x,y,z),u). x * y != (1 / x) \ z | y = L(z,x,x). a(x,y,z) = L(a(x,y,z),u,u). L(a(x,y,z),u,u) = a(x,y,z). x * y != L(a(z,u,w),v5,v5) | a(z,u,w) / y = x. a(x,y,z) / ((x * y) * z) = 1 / (x * (y * z)). L(T(a(x,y,z),u),w,w) = T(a(x,y,z),u). K(a(x,y,z) \ 1,u) * (w * (a(x,y,z) \ 1)) = (K(a(x,y,z) \ 1,u) * w) / a(x,y,z). (a(x,y,z) * u) / a(x,y,z) != w | T(u,a(x,y,z) \ 1) = w. (1 / x) \ a(y,z,u) != w | x * a(y,z,u) = w. (x * (y \ 1)) \ (x * (y \ a(z,u,w))) != v5 | L(a(z,u,w),y \ 1,x) = v5. T(x * a(y,z,u),a(y,z,u) \ 1) = T(a(y,z,u),1) * x. T(a(x,y,z),u) \ (w * T(a(x,y,z),u)) = T(w,w * T(a(x,y,z),u)). T(x,x * T(a(y,z,u),w)) = T(a(y,z,u),w) \ (x * T(a(y,z,u),w)). (a(x,y,z) \ (K(a(x,y,z),u \ 1) * w)) / w = T(a(x,y,z) \ 1,u). T(x,x * T(a(y,z,u),w)) = T(x,T(a(y,z,u),w)). K(a(x,y,z) \ 1,u) * (w * (a(x,y,z) \ 1)) = (K(a(x,y,z),u \ 1) * w) / a(x,y,z). ((x * (K(y,z) * u)) / (x * T(u,K(y,z)))) \ T(x * (K(y,z) * u),K(z,L(y,u,x))) = T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x). (x * (K(y,x) / T(x,z))) \ L(u,(x * (K(y,x) / T(x,z))) \ 1,x * (K(y,x) / T(x,z))) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u. (x * (K(y,x) / T(x,z))) \ L(u,(x \ K(x,y)) * T(x,z),x * (K(y,x) / T(x,z))) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u. (x * (K(y,x) / T(x,z))) \ L(u,(x \ K(x,y)) * T(x,z),K(y,x) * K(z,x)) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u. (x * (K(y,x) / T(x,z))) \ L(u,K(x,y) * K(x,z),K(y,x) * K(z,x)) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u. (x * (K(y,x) / T(x,z))) \ u = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u. ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u. ((((x \ K(x,y)) * T(x,z)) \ 1) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u. ((x * (K(y,x) / T(x,z))) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u. ((x \ K(x,y)) * T(x,z)) * u = (x * (K(y,x) / T(x,z))) \ u. (x * (K(y,x) / T(x,z))) \ u = ((x \ K(x,y)) * T(x,z)) * u. L(((x \ K(x,y)) * T(x,z)) * u,T(x,z) \ ((x \ 1) \ K(y,x)),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u). L(((x \ K(x,y)) * T(x,z)) * u,x * (K(y,x) / T(x,z)),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u). x != L(y,z * (K(u,w) / T(w,v5)),v6) | x = L(y,z * (T(w,u) \ K(v5,w)),v6). ((x \ 1) \ K(y,x)) \ (T(x,z) * u) = L(((x \ K(x,y)) * T(x,z)) * u,x * (T(x,y) \ K(z,x)),T(x,z)). L(((x \ K(x,y)) * T(x,z)) * u,x * (T(x,y) \ K(z,x)),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u). L(((x \ K(x,y)) * T(x,z)) * u,K(y,x) * K(z,x),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u). x != L(y,K(z,u) * K(w,u),T(u,w)) | x = y. ((x \ 1) \ K(y,x)) \ (T(x,z) * u) = ((x \ K(x,y)) * T(x,z)) * u. (((x \ K(x,y)) * T(x,x \ 1)) * z) * K((K(x,y) / x) * (x * z),u) = T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),u). (K(x,y) * z) * K((K(x,y) / x) * (x * z),u) = T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),u). T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),u) = (K(x,y) * z) * K((K(x,y) / x) * (x * z),u). x != T(y,z * u) | x = T(y,T(z,z \ 1) * u). (K(x,y) * z) * K((K(x,y) / x) * (x * z),u * w) = T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(u,u \ 1) * w). T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(u,u \ 1) * w) = (K(x,y) * z) * K((K(x,y) / x) * (x * z),u * w). T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(u,u \ 1) * w) = (K(x,y) * z) * K((x \ K(x,y)) * (x * z),u * w). T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = (K(x,y) * z) * K(x \ (x * z),T(x * z,y)). T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = (K(x,y) * z) * K(z,T(x * z,y)). T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = K(x,y) * T(z,T(x * z,y)). x != K(y,z) * T(u,T(y * u,z)) | x = T(u,y * u) * K(y,z). T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = T(z,x * z) * K(x,y). T(((x \ 1) \ K(y,x)) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = T(z,x * z) * K(x,y). T(((x \ K(x,y)) * T(x,x \ 1)) * z,T(x,x \ 1) * z) = T(z,x * z) * K(x,y). T(K(x,y) * z,T(x,x \ 1) * z) = T(z,x * z) * K(x,y). x != T(y,T(z,z \ 1) * u) | x = T(y,z * u). T(x,y * x) * K(y,z) = T(K(y,z) * x,y * x). T(K(x,y) * z,x * z) = T(z,x * z) * K(x,y). T(K(x,y) * z,x * z) = T(z,z * x) * K(x,y). T(K(x,x * (y \ L(y,z,u))) * w,x * w) = T(w,w * x) * a(u,z,K(y,x)). T(a(x,y,K(z,u)) * w,u * w) = T(w,w * u) * a(x,y,K(z,u)). T((x \ 1) \ 1,y \ 1) \ ((L(1 / T(x,y \ 1),1 / T(x,y \ 1),1 / T(x,y \ 1)) \ y) * z) = ((1 / T(x,y \ 1)) \ 1) \ ((y * x) * z). (x * T(y,K(z,u))) * K(u,K(L(z,y,x),x * (K(z,u) * y))) = T(x * (K(z,u) * y),L(K(u,z),y,x)) * L(K(u,z),y,x). (x * T(y,K(z,u))) * K(u,K(L(z,y,x),x * y)) = T(x * (K(z,u) * y),L(K(u,z),y,x)) * L(K(u,z),y,x). T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(z,K(L(y,u,x),x * u)). T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(z,K(x * u,L(y,u,x))). T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(z,K(y,x * u)). T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(y,K(z,x * u)). T(x * (K(y,z) * u),K(z,L(y,u,x))) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(y,K(z,x * u)). x != T(y,K(z,u)) * L(K(z,w),v5,v6) | x = T(y * L(K(z,w),v5,v6),K(z,u)). (x * T(y,K(z,u))) * K(z,K(u,x * y)) = T((x * (K(z,u) * y)) * L(K(u,z),y,x),K(u,L(z,y,x))). T((x * (K(y,z) * u)) * L(K(z,y),u,x),K(z,L(y,u,x))) = (x * T(u,K(y,z))) * K(y,K(z,x * u)). T(x * T(y,K(z,u)),K(u,L(z,y,x))) = (x * T(y,K(z,u))) * K(z,K(u,x * y)). (x * T(y,K(z,u))) * K(z,K(u,x * y)) = T(x * T(y,K(z,u)),K(u,L(z,y,x))). T(x * T(y,K(z,u)),K(u,L(z,y,x))) != w * v5 | w \ ((x * T(y,K(z,u))) * K(z,K(u,x * y))) = v5. T((x \ 1) \ 1,y \ 1) \ ((L(1 / T(x,y \ 1),T(x,y \ 1),T(x,y \ 1)) \ y) * z) = ((1 / T(x,y \ 1)) \ 1) \ ((y * x) * z). T((x \ 1) \ 1,y \ 1) \ (((1 * (T(x,y \ 1) \ 1)) \ y) * z) = ((1 / T(x,y \ 1)) \ 1) \ ((y * x) * z). T((x \ 1) \ 1,y \ 1) \ (((T(x,y \ 1) \ 1) \ y) * z) = ((1 / T(x,y \ 1)) \ 1) \ ((y * x) * z). T((x \ 1) \ 1,y \ 1) \ ((y * ((x \ 1) \ 1)) * z) = ((1 / T(x,y \ 1)) \ 1) \ ((y * x) * z). T((x \ 1) \ 1,y \ 1) \ ((y * ((x \ 1) \ 1)) * z) = T(x,y \ 1) \ ((y * x) * z). x \ ((x * (1 / (y * x))) * (((x * (1 / (y * x))) \ z) * L(u,y,y))) = 1 / (((u \ (z \ (x * (1 / (y * x))))) * y) * x). x \ (x * (1 / (((((x * (1 / (y * x))) \ z) * L(u,y,y)) \ y) * x))) = 1 / (((u \ (z \ (x * (1 / (y * x))))) * y) * x). 1 / (((x \ (y \ (z * (1 / (u * z))))) * u) * z) = 1 / (((((z * (1 / (u * z))) \ y) * L(x,u,u)) \ u) * z). 1 / (((((x * (1 / (y * x))) \ z) * L(u,y,y)) \ y) * x) = 1 / (((u \ (z \ (x * (1 / (y * x))))) * y) * x). (L(x,y,y) * (z / (u * (1 / (y * u))))) / K(u,u \ 1) = ((u * (1 / (y * u))) * (((u * (1 / (y * u))) / z) / x)) \ (1 / y). ((x * (1 / (y * x))) * (((x * (1 / (y * x))) / z) / u)) \ (1 / y) = (L(u,y,y) * (z / (x * (1 / (y * x))))) / K(x,x \ 1). x != y / K(z,u) | x = y * K(u,z). ((x * (1 / (y * x))) * (((x * (1 / (y * x))) / z) / u)) \ (1 / y) = (L(u,y,y) * (z / (x * (1 / (y * x))))) * K(x \ 1,x). ((x * (1 / (y * x))) * (((x * (1 / (y * x))) / z) / u)) \ (1 / y) = (L(u,y,y) * (z / (x * (1 / (y * x))))) * K(x,x \ 1). ((x * (1 / (y * x))) * (((x * (1 / (y * x))) / z) / u)) \ (1 / y) = L(u,y,y) * (K(x,x \ 1) * (z / (x * (1 / (y * x))))). ((x * (1 / (y * x))) * (((x * (1 / (y * x))) / z) / u)) \ (1 / y) = L(u,y,y) * (z / T((1 / (y * x)) * x,x \ 1)). ((x * (1 / (y * x))) * (((x * (1 / (y * x))) / z) / u)) \ (1 / y) = L(u,y,y) * (z / T(1 / T(y,x),x \ 1)). ((x * (1 / (y * x))) * (((x * (1 / (y * x))) / z) / u)) \ (1 / y) = L(u,y,y) * (z / (1 / y)). ((x * (1 / (y * x))) * ((x * (1 / ((z * y) * x))) / u)) \ (1 / y) = L(u,y,y) * (z / (1 / y)). ((x * (1 / (y * x))) * (x * (1 / ((z * (u * y)) * x)))) \ (1 / y) = L(z,y,y) * (u / (1 / y)). (x * (1 / (((x * (1 / ((y * (z * u)) * x))) \ u) * x))) \ (1 / u) = L(y,u,u) * (z / (1 / u)). (((a(x,y,z) \ 1) * u) * a(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = R(T(u,a(x,y,z) \ u),(a(x,y,z) \ 1) * u,a(u,a(x,y,z) \ 1,u)). x != R(y,z,a(u,w,u)) | x = y. (((a(x,y,z) \ 1) * u) * a(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = T(u,a(x,y,z) \ u). ((a(x,y,z) \ 1) * R(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = T(u,a(x,y,z) \ u). L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),x) = T(x,a(y,z,u) \ x). x != L(T(y,a(z,u,w) \ 1),w \ L(w,u,z),y) | x = y * a(z,u,K(w,y)). T(x,a(y,z,u) \ x) = x * a(y,z,K(u,x)). K(a(x,y,z),u) = a(x,y,K(z,u)). a(x,y,K(z,u)) = K(a(x,y,z),u). T(T(x,a(y,z,u) \ x),u) = T(x,L(u,z,y)). T(T(x,a(y,z,u) \ x),x * u) = T(x,L(u * x,z,y)). a(x,y,K(z,T(u,w))) = T(K(a(x,y,z),u),w). K((x * y) * z,x * (y * z)) = a(x,y,K(z,(x * y) * z)). x != a(y,z,K(u,u)) | x = 1. K(a(x,y,z),z) = 1. a(x,y,K(z,(x * y) * z)) != u | K((x * y) * z,x * (y * z)) = u. (a(x,y,K(z,(x * y) * z)) / a(x,y,z)) \ (x * (y * z)) = (x * y) * z. a(x,y,K(z,u)) \ w = K(u,a(x,y,z)) * w. (a(x,y,z) \ (a(x,y,K(z,u \ 1)) * w)) / w = T(a(x,y,z) \ 1,u). K(a(x,y,z) \ 1,u) * (w * (a(x,y,z) \ 1)) = (a(x,y,K(z,u \ 1)) * w) / a(x,y,z). T(a(x,y,z),z) = a(x,y,z). x * a(y,z,x) = a(y,z,x) * x. a(x,y,z) * z = z * a(x,y,z). T(T(x,y),a(z,u,y) \ x) = T(x,L(y,u,z)). a(x,y,K(z,T(u,w))) = T(a(x,y,K(z,u)),w). a(x,y,K(z,u)) = K(z,a(x,y,u)). K(x,x * a(y,z,u)) = K(x,a(y,z,u)). T(T(x,y * (z * (u \ 1))),a(w,v5,y * (z * (1 / u))) \ x) = T(x,L(y * (z * (1 / u)),v5,w)). T(T(x,x * y),a(z,u,y) \ x) = T(x,L(y * x,u,z)). (a(x,y,K(z,z * (x * y))) / a(x,y,z)) \ (x * (y * z)) = (x * y) * z. T(T(x,y * (z * (u \ 1))),a(w,v5,y * (z * (u \ 1))) \ x) = T(x,L(y * (z * (1 / u)),v5,w)). x != T(T(y,z),a(u,w,z) \ y) | x = T(y,L(z,w,u)). T(x,L(y * (z * (1 / u)),w,v5)) = T(x,L(y * (z * (u \ 1)),w,v5)). (x \ 1) * (K(x \ 1,K(y,T(z,L(x,u,w) * (1 / x)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * (K(x \ 1,K(y,T(z,x \ L(x,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * (K(y,K(x \ 1,T(z,x \ L(x,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * (K(y,K(x \ 1,T(z,L(x,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * (K(y,K(x \ 1,z)) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(K(y,T(z,L(x,u,w) * (1 / x))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(K(y,T(z,x \ L(x,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(y,K(T(z,x \ L(x,u,w)),x \ 1)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(y,K(T(z,L(x,u,w)),x \ 1)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(y,K(z,x \ 1)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(x,K(y,z)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * (K(x,K(y,z)) * L(T(T(x,K(y,z)),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). (x \ 1) * T(K(x,K(y,z)) * L(T(x,K(y,z)),u,w),x \ 1) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). x != (y \ 1) * T(K(y,z) * u,y \ 1) | x = K(y,z) * (u * (y \ 1)). T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w)) = K(x,K(u,w)) * (L(T(x,K(u,w)),y,z) * (x \ 1)). K(x,K(y,z)) * (L(T(x,K(y,z)),u,w) * (x \ 1)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). K(x,K(y,z)) * (x \ L(T(x,K(y,z)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z)). T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w)) = K(x,K(u,w)) * (x \ L(T(x,K(u,w)),y,z)). T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w)) = T(x,K(u,w)) \ L(T(x,K(u,w)),y,z). T(x \ L(x,y,z),K(u,w)) = T(x,K(u,w)) \ L(T(x,K(u,w)),y,z). T(x,K(y,z)) \ L(T(x,K(y,z)),u,w) = T(x \ L(x,u,w),K(y,z)). x != T(y,K(z,u)) \ L(T(y,K(z,u)),w,v5) | x = T((y \ 1) * L((y \ 1) \ 1,w,v5),K(z,u * y)). T(x \ L(x,y,z),K(u,w)) = T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)). T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = T(x \ L(x,y,z),K(u,w)). T(x \ L(x,y,z),K(u,w * x)) = T(x \ L(x,y,z),K(u,w)). (L(x,y,z) \ x) * T(x \ L(x,y,z),K(u,w)) = K(x \ L(x,y,z),K(w * x,u)). K(x \ L(x,y,z),K(u,w)) = K(x \ L(x,y,z),K(u * x,w)). K(x \ L(x,y,z),K(u * x,w)) = K(x \ L(x,y,z),K(u,w)). K(x \ L(x,y,z),K(u * x,w)) = K(u,K(w,x \ L(x,y,z))). x != K(y \ L(y,z,u),K(w * y,v5)) | x = K(v5,K(y * w,y \ L(y,z,u))). K(x,K(y,z \ L(z,u,w))) = K(y,K(z * x,z \ L(z,u,w))). K(x,K(y * z,y \ L(y,u,w))) = K(z,K(x,y \ L(y,u,w))). K(x,K(y * z,y \ L(y,u,w))) = K(x,K(z,y \ L(y,u,w))). K(x,K(y * z,z \ L(z,u,w))) = K(x,K(y,z \ L(z,u,w))). x != K(y,K((z * u) * w,w \ L(w,u,z))) | x = K(y,K(z * (u * w),a(z,u,w) * (z * (u * w)))). K(x,K(y * z,u \ L(u,z,y))) = K(x,K(y * (z * u),a(y,z,u) * (y * (z * u)))). K(x,K(y * (z * u),a(y,z,u) * (y * (z * u)))) = K(x,K(y * z,u \ L(u,z,y))). x != K(y,K(z * u,w \ L(w,u,z))) | x = K(y,K(z * u,a(z,u,w))). K(x,K(y * (z * u),a(y,z,u) * (y * (z * u)))) = K(x,K(y * z,a(y,z,u))). K(x,K(a(y,z,u),y * (z * u))) = K(x,K(y * z,a(y,z,u))). K(x,K(y * z,a(y,z,u))) != w | K(x,K(a(y,z,u),y * (z * u))) = w. x != K(y,K(a(z,u,w),z * (u * w))) | x = K(y,K(a(z,u,w),(z * u) * w)). K(x,K(y * z,a(y,z,u))) = K(x,K(a(y,z,u),(y * z) * u)). K(x,K(a(y,z,u),(y * z) * u)) = K(x,K(y * z,a(y,z,u))). x != K(y,K(a(z,u,w),(z * u) * w)) | x = K(a(z,u,w),T((((z * u) * w) \ 1) * ((y \ ((z * u) * w)) * y),z * (u * w))). K(x,K(y * z,a(y,z,u))) = K(a(y,z,u),T((((y * z) * u) \ 1) * ((x \ ((y * z) * u)) * x),y * (z * u))). K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(u,K(x * y,a(x,y,z))). K(x,K(a(y,z,u),T((y * z) * u,y * (z * u)))) = K(x,K(y * z,a(y,z,u))). x != K(y,K(a(z,u,w),T(v5,z * (u * w)))) | x = a(K(y,K(z,v5)),u,w). K(x,K(y * z,a(y,z,u))) = a(K(x,K(y,(y * z) * u)),z,u). a(K(x,K(y,(y * z) * u)),z,u) = K(x,K(y * z,a(y,z,u))). a(K(x,K(y,z * u)),z,u) = K(y,K(x * z,a(x,z,u))). K(x,K(y * z,a(y,z,u))) = a(K(y,K(x,z * u)),z,u). x != a(K(y,K(z,u * w)),u,w) | x = 1. K(x,K(y * z,a(y,z,u))) = 1. K(x,K(a(y,z,u),y * (z * u))) = 1. K(x,a(y,z,u)) * 1 = K(x,((y * z) * u) / (y * (z * u))). K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u)) * 1. K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u)). x != K(y,((z * u) * w) / (z * (u * w))) | x = R(K(y,z \ R(z,u,w)),R(z,u,w),u * w). K(x,a(y,z,u)) = R(K(x,y \ R(y,z,u)),R(y,z,u),z * u). R(K(x,y \ R(y,z,u)),R(y,z,u),z * u) = K(x,a(y,z,u)). R(a(K(x,y),z * y,u),R(y,z,u),z * u) = K(x,a(y,z,u)). K(x,a(y,z,u)) = a(K(x,R(y,R(y,z,u),z * u)),z * y,u). a(K(x,R(y,R(y,z,u),z * u)),z * y,u) = K(x,a(y,z,u)). x != a(K(y,R(z,R(z,u,w),v5)),u * z,w) | x = a(K(y,z),u * z,w). K(x,a(y,z,u)) = a(K(x,y),z * y,u). a(K(x,y),z * y,u) = K(x,a(y,z,u)). x != K(y,a(z,u,w)) | x = K(y,y * a(z,u,w)). a(K(x,y),z * y,u) = K(x,x * a(y,z,u)). K(x,x * a(y,z,u)) = a(K(x,y),z * y,u). x != a(K(y,z),u * z,w) | x = a(K(y,z),u,w). K(x,x * a(y,z,u)) = a(K(x,y),z,u). x != K(y,y * a(z,u,w)) | x = a(z,u,K(y,w)). a(K(x,y),z,u) = a(y,z,K(x,u)). (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) = a(K(z,w),u,v5). x != (T(y,y \ z) * a(u,w,K(v5,v6))) \ ((y \ z) \ z) | x = a(u,w,K(v6,v5)). a(K(x,y),z,u) = a(x,z,K(u,y)). x != a(K(y,z),u,w) | x = a(z,u,K(y,w)). a(x,y,K(z,u)) = a(u,y,K(x,z)). ((K(x,y) * z) * u) / a(x,z,K(u,y)) = K(x,y) * (z * u). a(K(x,y \ 1),z,u) = a(x \ 1,z,K(u,y)). T(x,x * y) * a(x,z,K(u,y)) = T(x,R(x * y,z,u)). a(x,y,K(z \ u,z)) = a(z,y,K(x,u)). x != a(y,z,K(u,w)) | x = v5 / (a(y,z,K(w,u)) * v5). a(x,y,K(z,u)) = w / (a(u,y,K(z,x)) * w). x / (a(y,z,K(u,w)) * x) = a(w,z,K(u,y)). x != a(y,z,K(u,w)) | x = K(u,a(y,z,w)). a(x,y,K(z,u)) = K(x,a(u,y,z)). x != a(y,z,K(u \ 1,w)) | x = a(y,z,K(w,u)). a(x \ 1,y,K(z,u)) = a(u,y,K(z,x)). x / a(y,z,K(u,w)) != v5 | x * a(w,z,K(u,y)) = v5. T(x,a(y,z,u) \ x) = x * a(x,z,K(y,u)). a(x \ 1,y,K(z,u)) = K(x,a(u,y,z) \ 1). K(x * (y * z),(x * y) * z) = a((x * y) * z,y,K(z,x)). T(x,a(y,z,u)) = x * a(x,z,K(u,y)). x * a(x,y,K(z,u)) = T(x,a(u,y,z)). x * a(x,y,K(z,u)) != w | T(x,a(u,y,z)) = w. a(x,y,z) \ (a(u,y,K(z,x)) * w) = T(a(x,y,z),u) \ w. x != a(y,z,K(u,w)) | x = a(w,z,K(y,u)). a(x,y,K(z,u)) = a(x,y,K(z,x \ u)). a(x,y,K(z,x \ u)) = a(x,y,K(z,u)). x * a(y,z,K(u,x)) = T(x,a(u,z,y)). a(x,y,K(z,u)) = a(x,y,K(z,x * u)). a(x,y,K(z,x * u)) = a(x,y,K(z,u)). x != y * a(z,u,K(w,y)) | x = T(y,a(z,u,w) \ y). T(x,a(y,z,u)) = T(x,a(u,z,y) \ x). T(x,a(y,z,u) \ x) = T(x,a(u,z,y)). (a(x,y,z) * u) / a(x,y,z) = T(u,a(z,y,x)). x != a(K(y,z),u,w) | x = a(y,u,K(w,z)). a(x \ 1,y,K(z,u)) = a(x,y,K(z,u \ 1)). a(x,y,K(z,u)) != w | a(u,y,K(x,z)) = w. a(x,y,K(z \ u,z)) != w | a(z,y,K(x,u)) = w. x != a(y \ 1,z,K(u,w)) | x = K(y,a(w,z,u) \ 1). a(x,y,K(z,u \ 1)) = K(x,a(u,y,z) \ 1). x != a(y \ 1,z,K(u,w)) | x = a(w,z,K(u,y)). a(x,y,K(z,u \ 1)) = a(u,y,K(z,x)). x != a(y,z,K(u,y * w)) | x = a(y,z,K(u,w)). a(x * y,z,K(u,x \ 1)) = a(x,z,K(u,y)). (a(x,y,z) \ (a(u,y,K(z,x)) * w)) / w = T(a(x,y,z) \ 1,u). K(a(x,y,z) \ 1,u) * (w * (a(x,y,z) \ 1)) = (a(u,y,K(z,x)) * w) / a(x,y,z). K((x * y) * z,x * (y * z)) = a(x * (y * z),y,K(z,x \ 1)). a(x * (y * z),y,K(z,x \ 1)) = K((x * y) * z,x * (y * z)). x * a(y,z,K(u,x)) != w | T(x,a(u,z,y)) = w. T(x,a(y,z,u) \ 1) = T(x,a(u,z,y)). x != T(y * a(z,u,w),a(z,u,w) \ 1) | x = T(a(z,u,w),1) * y. T(x * a(y,z,u),a(u,z,y)) = T(a(y,z,u),1) * x. T(T(x,a(y,z,u)),K(a(u,z,y) \ 1,w)) = T(x,T(a(u,z,y) \ 1,w)). x * a(y,z,K(u,w)) != v5 | x * a(u,z,K(w,y)) = v5. T(x * a(y,z,u),a(u,z,y)) = a(y,z,u) * x. x * y != T(x * a(z,u,w),a(w,u,z)) | T(a(z,u,w),x) = y. T(x * a(y,z,u),a(u,z,y)) != x * w | T(a(y,z,u),x) = w. x != T(y,y * z) * a(u,w,K(v5,z)) | x = T(a(u,w,K(v5,z)) * y,z * y). T(x,R(x * y,z,u)) = T(a(x,z,K(u,y)) * x,y * x). T(a(x,y,K(z,u)) * x,u * x) = T(x,R(x * u,y,z)). T(x * a(x,y,K(z,u)),u * x) = T(x,R(x * u,y,z)). T(T(x,a(y,z,u) \ x),u * x) = T(x,R(x * u,z,y)). T(T(x,x * y),a(z,u,y) \ x) = T(x,R(x * y,u,z)). x != T(T(y,y * z),a(u,w,z) \ y) | x = T(y,L(z * y,w,u)). T(x,R(x * y,z,u)) = T(x,L(y * x,z,u)). x != T(y,R(y * (z / T(1 / (1 / y),u)),w,v5)) | x = T(y,R(z,w,v5)). T(x,L((y / T(1 / (1 / x),z)) * x,u,w)) = T(x,R(y,u,w)). ((K(x,y) * z) * u) * a(x,z,K(y,u)) = K(x,y) * (z * u). x != K(y * (z * u),(y * z) * u) | x = K(a(y,z,u),(z * u) \ (y \ 1)). a((x * y) * z,y,K(z,x)) = K(a(x,y,z),(y * z) \ (x \ 1)). K(a(x,y,z),(y * z) \ (x \ 1)) = a((x * y) * z,y,K(z,x)). T(x,L(y * (x * (1 / T(x,z))),u,w)) = T(x,R(y,u,w)). x != T(y,L(z * (u * (1 / w)),v5,v6)) | x = T(y,L(z * (u * (w \ 1)),v5,v6)). T(x,R(y,z,u)) = T(x,L(y * (x * (T(x,w) \ 1)),z,u)). T(x,L(y * (x * (T(x,z) \ 1)),u,w)) = T(x,R(y,u,w)). T(x,L(y * K(z,x),u,w)) = T(x,R(y,u,w)). T(x,L(y,z,u)) = T(x,R(y,z,u)). T(x,R(y,z,u)) = T(x,L(y,z,u)). x * y != T(z,R(u,w,v5)) | x \ T(z,L(u,w,v5)) = y. x \ T(x,L(y,z,u)) = K(x,R(y,z,u)). K(x,L(y,z,u)) = K(x,R(y,z,u)). K(x,R(y,z,u)) = K(x,L(y,z,u)). x != K(y,L(z,u,w)) | x = L(K(y,z),u,w). K(x,R(y,z,u)) = L(K(x,y),z,u). L(K(x,y),z,u) = K(x,R(y,z,u)). ((x * y) * z) * K(y * z,L(x,y,z)) = (y * z) * R(x,y,z). x != K(y,R(z,u,w)) | x = R(K(y,z),u,w). L(K(x,y),z,u) = R(K(x,y),z,u). R(K(x,y),z,u) = L(K(x,y),z,u). K(R(x,y,z) \ 1,u) = L(K(x \ 1,u),y,z). L(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y). L(K(x,y),z,u) * (z * u) = (K(x,y) * z) * u. L(K(x,y),z,u) \ (u * (K(x,y) * z)) = z * T(u,K(x,y) * z). K(L(x,y,z) \ 1,u) = K(R(x,y,z) \ 1,u). K(R(x,y,z) \ 1,u) = K(L(x,y,z) \ 1,u). (x \ K(L(y,z,u) \ 1,w)) \ (x \ 1) = K(w,R(y,z,u) \ 1). T(a(x,y,z),(y * z) \ (x \ 1)) / a((x * y) * z,y,K(z,x)) = a(x,y,z). ((x * y) * z) * K(y * z,x) = (y * z) * R(x,y,z). R(x,y,z) * T(y * z,x) = (y * z) * R(x,y,z). ((x * y) * z) \ ((x * y) * R(z,x,y)) = (z * (x * y)) \ ((z * x) * y). K(x,L(y,z,u) \ 1) = K(x,R(y,z,u) \ 1). K(x,R(y,z,u) \ 1) = K(x,L(y,z,u) \ 1). K(x,T((y * z) / u,u / z) \ 1) = K(x,L((u / z) \ y,u / z,z) \ 1). K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T((u * z) / y,y / z) \ 1). (T(a(x,y,z),u) \ w) / w = T(a(x,y,z) \ 1,u). (x * T(a(y,z,u),w)) \ x = T(a(y,z,u) \ 1,w). T(T(x,T(a(y,z,u) \ 1,w)),x * (1 * T(a(y,z,u),w))) = x. x != K((y * z) * u,y * (z * u)) | x = a(y,z,K(u,(y * z) * u)). a(x * (y * z),y,K(z,x \ 1)) = a(x,y,K(z,(x * y) * z)). a(x * (y * z),y,K(z,x \ 1)) = a(x,y,K(z,z * (x * y))). x != a(y * z,u,K(w,y \ 1)) | x = a(y,u,K(w,z)). a(x,y,K(z,z * (x * y))) = a(x,y,K(z,y * z)). x != a(y,z,K(u,z * u)) | x = 1. a(x,y,K(z,z * (x * y))) = 1. a(x,y,K(z,(x * y) * z)) = 1. (1 / a(x,y,z)) \ (x * (y * z)) = (x * y) * z. K((x * y) * z,x * (y * z)) = 1. T((x * y) * z,x * (y * z)) = (x * y) * z. (x * (y * z)) * ((x * y) * z) = ((x * y) * z) * (x * (y * z)). ((x * y) * z) * (x * (y * z)) = (x * (y * z)) * ((x * y) * z). (a(x,y,z) \ 1) \ (x * (y * z)) = (x * y) * z. x != (a(y,z,u) \ 1) \ w | x = a(y,z,u) * w. (x * y) * z = a(x,y,z) * (x * (y * z)). a(x,y,z) * (x * (y * z)) = (x * y) * z. x * y != (a(z,u,w) \ 1) \ (z * (u * w)) | ((z * u) * w) / y = x. ((x * y) * z) / (x * (y * z)) = a(x,y,z). a(x,y,z) = ((x * y) * z) / (x * (y * z)). (x * (y * z)) / ((x * y) * z) = a(x,y,z) \ 1. a(x,y,(x * y) \ z) \ z = x * (y * ((x * y) \ z)). a(x,y \ 1,(z \ 1) \ 1) = ((x * (y \ 1)) * ((z \ 1) \ 1)) / (x * ((z \ y) \ 1)). ((x * (y \ 1)) * ((z \ 1) \ 1)) / (x * ((z \ y) \ 1)) = a(x,y \ 1,(z \ 1) \ 1). (1 / (x * (y * (z \ 1)))) \ (z / (x * y)) = a(x,y,z \ 1) \ 1. x * y != z * (u * ((z * u) \ w)) | x \ (a(z,u,(z * u) \ w) \ w) = y. x \ (a(x,L(y \ 1,y,z),(x * L(y \ 1,y,z)) \ u) \ u) = L(y \ 1,z,y) * ((x * L(y \ 1,y,z)) \ u). L(K(x,y),z,u) * (u * (K(y,x) * z)) = z * T(u,K(y,x) * z). ((x / y) / z) \ (x / (z * y)) = a(z,y,x \ 1) \ 1. x != L(K(y,z),u,w) * v5 | x = T(v5 * L(K(y,z),u,w),K(z,L(y,u,w))). x * T(y,K(z,u) * x) = T((y * (K(z,u) * x)) * L(K(u,z),x,y),K(z,L(u,x,y))). T((x * (K(y,z) * u)) * L(K(z,y),u,x),K(y,L(z,u,x))) = u * T(x,K(y,z) * u). a(x * K(y * z,x),y,z) = (x * (y * z)) \ ((x * y) * z). (x * (y * z)) \ ((x * y) * z) = a(x * K(y * z,x),y,z). a(x,y,z) = a(x * K(y * z,x),y,z). a(x * K(y * z,x),y,z) = a(x,y,z). ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y). ((K(x,y) * z) * u) * a(u,z,K(x,T(y,z))) = (z * K(x,T(y,z))) * R(u,z,K(x,T(y,z))). T(a(x,y,z),(y * z) \ (x \ 1)) * a(x,y,K(z,(x * y) * z)) = a(x,y,z). x != K(y,T(z,u) \ 1) | x = K(y,T(z \ 1,u)). K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(((u * z) / y) \ 1,y / z)). T(a(x,y,z),(y * z) \ (x \ 1)) * 1 = a(x,y,z). T(a(x,y,z),(y * z) \ (x \ 1)) = a(x,y,z). ((x * y) \ (z \ 1)) * (a(z,x,y) \ 1) = a(z,x,y) \ ((x * y) \ (z \ 1)). (a(x,y,z) / ((x * y) * z)) / ((y * z) \ (x \ 1)) = K((x * y) * z,(y * z) \ (x \ 1)). x != a(y,z,u) \ ((z * u) \ (y \ 1)) | x = u \ (z \ (y \ 1)). ((x * y) \ (z \ 1)) * (a(z,x,y) \ 1) = y \ (x \ (z \ 1)). (1 / (x * y)) * ((x * y) \ (a(x * y,x,y) \ 1)) = y \ (x \ ((x * y) \ 1)). x != y * (a(z,u,w) \ 1) | x = y / a(z,u,w). x \ (y \ (z \ 1)) = ((y * x) \ (z \ 1)) / a(z,y,x). ((x * y) \ (z \ 1)) / a(z,x,y) = y \ (x \ (z \ 1)). (x * (y * z)) \ (1 / a(x,y,z)) = z \ (y \ (x \ 1)). (x * (y * z)) \ (a(x,y,z) \ 1) = z \ (y \ (x \ 1)). x != (y * (1 / (z * y))) \ u | x = ((1 / z) \ u) * K(y,y \ 1). (x * (y * (z * (1 / (u * z))))) \ (a(x,y,z * (1 / (u * z))) \ 1) = ((1 / u) \ (y \ (x \ 1))) * K(z,z \ 1). 1 / ((x * (y * z)) * ((a(x,y,z) \ 1) \ (x * (y * z)))) = (z \ (y \ (x \ 1))) * (1 / (x * (y * z))). (x * (K(y,y \ 1) * z)) \ (a(K(y,y \ 1),x,z) \ 1) = z \ (x \ (K(y,y \ 1) \ 1)). x != K(y,T((z / u) \ 1,w)) | x = K(y,T(u / z,w)). K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(y / (u * z),y / z)). K(x,(y * z) \ (y * (u / y))) = K(x,T(u / (z * y),u / y)). K(x,T(y / (z * u),y / u)) = K(x,(u * z) \ (u * (y / u))). x != K(y,((z \ u) * z) \ w) | x = K(y,T(u,z) \ w). K(x,T(y / (z * (z \ u)),y / (z \ u))) = K(x,T(u,z) \ ((z \ u) * (y / (z \ u)))). K(x,T(y / ((z / (z * u)) * (z * u)),y / (z * u))) = K(x,(z * K(z * u,u \ 1)) \ ((z * u) * (y / (z * u)))). (1 / (x * y)) * ((x * y) \ (a(x * y,x,y) \ 1)) = y \ (x \ (y \ (x \ 1))). (1 / (x * y)) * ((x * y) \ (1 \ 1)) = y \ (x \ (y \ (x \ 1))). (1 / (x * y)) * ((x * y) \ 1) = y \ (x \ (y \ (x \ 1))). (1 / (x * y)) * (y \ (x \ 1)) = y \ (x \ (y \ (x \ 1))). x != (1 / (y * z)) * (z \ (y \ 1)) | x = (y * z) \ (z \ (y \ 1)). x \ (y \ (x \ (y \ 1))) = (y * x) \ (x \ (y \ 1)). (x * y) \ (y \ (x \ 1)) = y \ (x \ (y \ (x \ 1))). x != ((y \ 1) * z) \ (z \ ((y \ 1) \ 1)) | x = ((z / y) * z) \ y. x \ ((y \ 1) \ (x \ ((y \ 1) \ 1))) = ((x / y) * x) \ y. x \ ((x / y) \ y) = ((x / y) * x) \ y. ((x / y) * x) \ y = x \ ((x / y) \ y). x / ((y \ z) * (y \ z)) = x * (z \ ((z / y) \ y)). (x / y) \ ((x / y) \ y) = y * (x \ ((x / y) \ y)). (x * (x * (y \ ((y / x) \ x)))) * z = (x * (x / y)) * (((x \ y) / x) \ z). ((x \ (y / z)) \ 1) / (z * ((x \ y) \ 1)) = a(z,y \ 1,(x \ 1) \ 1). (1 / ((x \ (y / z)) \ 1)) \ ((x \ y) / z) = a(z,y \ 1,(x \ 1) \ 1). (x \ (y / z)) \ ((x \ y) / z) = a(z,y \ 1,(x \ 1) \ 1). K(a(x,y,z),u \ 1) * (w * (a(x,y,z) \ 1)) = (a(u,y,K(z,x)) * w) / a(x,y,z). T(x * T(y,K(z,u)),K(z,L(u,y,x))) = y * T(x,K(z,u) * y). T(x * T(y,K(z,u)),K(u,L(z,y,x))) = y * T(x,K(u,z) * y). x \ ((y * T(x,K(z,u))) * K(z,K(u,y * x))) = T(y,K(u,z) * x). x \ ((y * T(x,K(z,u))) * (K(u,T(z,y * x)) * K(z,u))) = T(y,K(u,z) * x). x \ (((y * T(x,K(z,u))) * K(z,u)) * K(u,T(z,y * x))) = T(y,K(u,z) * x). x \ (((y * T(x,K(z,u))) * K(z,u)) * K(u,T(z,y * T(x,K(z,w))))) = T(y,K(u,z) * x). K(x,T(y / z,y / (u \ z))) = K(x,T(z,u) \ ((u \ z) * (y / (u \ z)))). a(x,y,K(z,u \ 1)) * (w * (a(x,y,z) \ 1)) = (a(u,y,K(z,x)) * w) / a(x,y,z). a(x,y,K(z,u)) * (w * (a(u,y,z) \ 1)) = (a(x,y,K(z,u)) * w) / a(u,y,z). x * (y * (a(z,u,w) \ 1)) != (a(v5,u,K(w,z)) * y) / a(z,u,w) | x = K(a(z,u,w) \ 1,v5). a(x,y,K(z,u)) = K(a(u,y,z) \ 1,x). K(a(x,y,z) \ 1,u) = a(u,y,K(z,x)). T(T(x,a(y,z,u)),a(w,z,K(y,u))) = T(x,T(a(u,z,y) \ 1,w)). (1 / (a(x,y,z) / ((x * y) * z))) \ (x * (y * z)) = K((x * y) * z,(y * z) \ (x \ 1)). (x * (K(y,y \ 1) * z)) \ (a(y,x,K(z,y \ 1)) \ 1) = z \ (x \ (K(y,y \ 1) \ 1)). (1 / (1 / (x * (y * z)))) \ (x * (y * z)) = K((x * y) * z,(y * z) \ (x \ 1)). K(x * (y * z),(x * (y * z)) \ 1) = K((x * y) * z,(y * z) \ (x \ 1)). K((x * y) * z,(y * z) \ (x \ 1)) = K(x * (y * z),(x * (y * z)) \ 1). K((x * y) * z,(y * z) \ (x \ 1)) = K(x * (y * z),(y * z) \ (x \ 1)). (x * (K(y,y \ 1) * z)) \ (1 \ 1) = z \ (x \ (K(y,y \ 1) \ 1)). (x * (K(y,y \ 1) * z)) \ 1 = z \ (x \ (K(y,y \ 1) \ 1)). (K(x,x \ 1) * y) \ (z \ 1) = y \ (z \ (K(x,x \ 1) \ 1)). x != (K(y,y \ 1) * z) \ (u \ 1) | x = ((u * z) \ y) * (1 / y). x \ (y \ (K(z,z \ 1) \ 1)) = ((y * x) \ z) * (1 / z). x \ (y \ (K(z,z \ 1) * 1)) = ((y * x) \ z) * (1 / z). x \ (y \ K(z,z \ 1)) = ((y * x) \ z) * (1 / z). x \ ((y \ z) * (1 / z)) = ((y * x) \ z) * (1 / z). x \ ((y \ 1) * (z * (1 / (u * z)))) = ((((u \ 1) \ y) * x) \ z) * (1 / z). x != (y \ (z * u)) * (1 / (z * u)) | x = y \ K(u \ z,z \ u). x \ ((y \ (z * u)) * (1 / (z * u))) = (y * x) \ K(u \ z,z \ u). x != (y \ (1 / z)) \ (((u \ y) \ w) * (1 / w)) | x = (z * y) / (w * (1 / (((y \ 1) * u) * w))). (((x \ y) * (y \ (1 / z))) \ u) * (1 / u) = (z * y) / (u * (1 / (((y \ 1) * x) * u))). (x * y) / (z * (1 / (((y \ 1) * u) * z))) = (((u \ y) * (y \ (1 / x))) \ z) * (1 / z). x != (y * z) \ ((z \ y) * (1 / y)) | x = (y * (z * (y * z))) \ (1 / (y \ 1)). ((x * (y * x)) \ y) * (1 / y) = (y * (x * (y * x))) \ (1 / (y \ 1)). (x * (y * (x * y))) \ (1 / (x \ 1)) = ((y * (x * y)) \ x) * (1 / x). (1 / x) * (((y * (z / x)) \ u) * (1 / u)) = (((u * (1 / (x * u))) \ y) * z) \ x. x \ (y * (1 / (z * y))) = (z * x) \ K(y \ z,z \ y). (x * y) \ K(z \ x,x \ z) = y \ (z * (1 / (x * z))). (x * (y * z)) \ K(y \ x,x \ y) = (z \ (1 / y)) / x. x != (y * (z * u)) \ K(z \ y,y \ z) | x = L(u,z,y) \ (1 / (y * z)). (x \ (1 / y)) / z = L(x,y,z) \ (1 / (z * y)). L(x,y,z) \ (1 / (z * y)) = (x \ (1 / y)) / z. (x * y) \ K((y / z) \ x,x \ (y / z)) = (z \ (1 / (y / z))) / x. ((x \ (1 / y)) / z) * (z * y) = L(x,y,z) \ 1. ((x / y) / z) * (z * y) = L(1 / x,y,z) \ 1. L(x,y,z) = L(1 / x,y,z) \ 1. L(1 / x,y,z) \ 1 = L(x,y,z). L(1 / x,y,z) \ 1 != u | L(x,y,z) = u. L(x,y,z) \ 1 = L(x \ 1,y,z). L(x \ 1,y,z) = L(x,y,z) \ 1. x / L(y,z,u) = (1 / x) \ L(1 / y,z,u). (1 / x) \ L(1 / y,z,u) = x / L(y,z,u). (x * y) / (y * L(y \ 1,z,u)) = x * L(y,z,u). x * L(x \ 1,y,z) = L(x,y,z) \ x. (x * y) / (L(y,z,u) \ y) = x * L(y,z,u). (x * L(y,z,u)) \ (x * y) = L(y,z,u) \ y. (x * y) / (L(y,z,u) \ y) != w | w = x * L(y,z,u). (x * y) / (L(y,z,u) \ y) != w | x * L(y,z,u) = w. (x * (y * (x * y))) \ x = ((y * (x * y)) \ x) * (1 / x). ((x * (y * x)) \ y) * (1 / y) = (y * (x * (y * x))) \ y. x != (y * (z * (y * z))) \ y | x = 1 / (z * (y * z)). ((x * (y * x)) \ y) * (1 / y) = 1 / (x * (y * x)). x * y != ((z * (u * z)) \ u) * (1 / u) | x \ (1 / (z * (u * z))) = y. x \ (1 / (y * (x * y))) = 1 / (((y / (1 / x)) * y) * x). 1 / (((x / (1 / y)) * x) * y) = y \ (1 / (x * (y * x))). x != 1 / (((y / (1 / z)) * y) * z) | x = (z \ (1 / (z * y))) / y. x \ (1 / (y * (x * y))) = (x \ (1 / (x * y))) / y. (x \ (1 / (x * y))) / y = x \ (1 / (y * (x * y))). 1 / (((x / (1 / ((1 / x) * y))) * x) * ((1 / x) * y)) = ((1 / x) * y) \ (1 / (x * T(y,x))). 1 / (((x / (1 / (x \ y))) * x) * (x \ y)) = (x \ y) \ (1 / (x * ((x \ 1) * (y * x)))). (((1 / x) * y) \ (1 / T(y,x))) / x = ((1 / x) * y) \ (1 / (x * (((1 / x) * y) * x))). ((1 / x) * y) \ (1 / (x * (((1 / x) * y) * x))) = (((1 / x) * y) \ (1 / T(y,x))) / x. ((x \ 1) * ((x \ 1) * y)) / y = ((x \ y) \ 1) \ (1 / (y * (((x \ y) \ 1) * y))). ((x \ y) \ 1) \ (1 / (y * (((x \ y) \ 1) * y))) = ((x \ 1) * ((x \ 1) * y)) / y. (((x \ y) / z) * (x \ y)) / z = (y \ x) \ (1 / (z * ((y \ x) * z))). (x \ y) \ (1 / (z * ((x \ y) * z))) = (((y \ x) / z) * (y \ x)) / z. (x * y) \ K((y / z) \ x,x \ (y / z)) = (z * (1 / (y * z))) / x. (x \ y) \ (1 / (x * ((x \ y) * x))) = (((x * y) \ x) * (y \ x)) / x. x != (y * (1 / (z * y))) / u | x = y * (1 / ((u * z) * y)). (x * y) \ K((y / z) \ x,x \ (y / z)) = z * (1 / ((x * y) * z)). (x \ y) \ (1 / (x * ((x \ y) * x))) = ((y \ x) / T(y,x)) / x. x != (y * z) \ K(u \ y,y \ u) | x = z \ (u * (1 / (y * u))). x * (1 / ((y * z) * x)) = z \ ((z / x) * (1 / (y * (z / x)))). x \ ((x / y) * (1 / (z * (x / y)))) = y * (1 / ((z * x) * y)). x \ (K(y \ x,x \ y) / z) = y * (1 / ((z * x) * y)). x * y != z \ (K(u \ z,z \ u) / w) | x \ (u * (1 / ((w * z) * u))) = y. (x \ (1 / y)) \ (z * (1 / ((y * x) * z))) = K(z \ x,x \ z). x * (y * (1 / ((z * x) * y))) = K(y \ x,x \ y) / z. (1 / x) * (K(y \ z,z \ y) / u) = y * (1 / (((z * (1 / (u * z))) \ x) * y)). x * (1 / (((y * (1 / (z * y))) \ u) * x)) = (1 / u) * (K(x \ y,y \ x) / z). x != ((y * y) \ (1 / z)) \ (u * (1 / ((z * (y * y)) * u))) | x = K(u,u \ 1). K(x \ (y * y),(y * y) \ x) = K(x,x \ 1). x != K(y \ (z * z),(z * z) \ y) | x = K(z * (z / y),z \ (z \ y)). K(x,x \ 1) = K(y * (y / x),y \ (y \ x)). K(x * (x / y),x \ (x \ y)) = K(y,y \ 1). K(x * (y \ x),x \ (y / x)) = K(y,y \ 1). ((x \ y) / x) \ ((x \ (1 / (x / y))) * z) = K(y,y \ 1) * z. ((((x \ 1) \ y) * (y \ (1 / z))) \ u) * (1 / u) = (z * y) / ((u * (1 / (x * u))) \ y). x != (1 / y) * (((z * (u / y)) \ w) * (1 / w)) | x = ((((y * (1 / u)) / z) \ y) \ w) * (1 / w). (((x * (1 / (y * x))) \ z) * u) \ y = ((((y * (1 / u)) / z) \ y) \ x) * (1 / x). ((((x * (1 / y)) / z) \ x) \ u) * (1 / u) = (((u * (1 / (x * u))) \ z) * y) \ x. ((x \ y) \ 1) \ (1 / (y * (((x \ y) \ 1) * y))) = y / ((x \ 1) \ ((x \ 1) \ y)). ((1 / x) * (K(y \ y,y \ y) / (z * (u * x)))) \ (1 / x) = L(z,x,x) * (u / (1 / x)). (((x / y) * (y * z)) \ u) * (1 / u) = (((u * (1 / (y * u))) \ x) * z) \ y. (((x * (1 / (y * x))) \ z) * u) \ y = (((z / y) * (y * u)) \ x) * (1 / x). 1 / (((((x * (1 / (y * x))) \ z) * L(u,y,y)) \ y) * x) = x \ (y \ ((y * z) * u)). ((x \ y) \ 1) \ (1 / (y * (((x \ y) \ 1) * y))) = y / (x * (((x \ 1) \ 1) * y)). x != y / (z * (((z \ 1) \ 1) * y)) | x = z \ (y \ (y / z)). ((x \ y) \ 1) \ (1 / (y * (((x \ y) \ 1) * y))) = x \ (y \ (y / x)). ((x \ y) \ 1) \ (1 / ((y \ (x \ 1)) \ 1)) = x \ (y \ (y / x)). ((x \ y) \ 1) \ (y \ (x \ 1)) = x \ (y \ (y / x)). x != 1 / (((((y * (1 / (z * y))) \ u) * L(w,z,z)) \ z) * y) | x = 1 / (((w \ (u \ (y * (1 / (z * y))))) * z) * y). x \ (y \ ((y * z) * u)) = 1 / (((u \ (z \ (x * (1 / (y * x))))) * y) * x). 1 / (((x \ (y \ (z * (1 / (u * z))))) * u) * z) = z \ (u \ ((u * y) * x)). x * y != z \ (u \ ((u * w) * v5)) | x \ (1 / (((v5 \ (w \ (z * (1 / (u * z))))) * u) * z)) = y. x \ (1 / (((y \ (z \ ((1 / x) * (1 / ((1 / x) * (1 / x)))))) * (1 / x)) * (1 / x))) = ((x \ 1) \ 1) * (((1 / x) * z) * y). x * (x \ (y \ ((y * z) * x))) = (z * (1 / (y / x))) / (x * (1 / (y * x))). (x * (1 / (y / z))) / (z * (1 / (y * z))) = z * (z \ (y \ ((y * x) * z))). (x * (1 / (y / z))) / (z * (1 / (y * z))) = y \ ((y * x) * z). (x * (1 / (y / z))) / (z * (1 / (y * z))) = u * (u \ (y \ ((y * x) * z))). (x * (1 / (y / z))) / (z * (1 / (y * z))) = u * (1 / (((z \ (x \ (u * (1 / (y * u))))) * y) * u)). x != (y * z) / (u * (1 / (((z \ 1) * w) * u))) | x = (y / ((((w \ u) * (1 / u)) \ z) \ 1)) * (z \ 1). (((x \ y) * (y \ (1 / z))) \ u) * (1 / u) = (z / ((((x \ u) * (1 / u)) \ y) \ 1)) * (y \ 1). (x / ((((y \ z) * (1 / z)) \ u) \ 1)) * (u \ 1) = (((y \ u) * (u \ (1 / x))) \ z) * (1 / z). 1 / (((x / ((1 / y) * x)) * x) * (x \ y)) = (x \ y) \ (1 / (x * ((x \ 1) * (y * x)))). ((1 / x) * y) \ (1 / (x * (((1 / x) * y) * x))) = ((y \ x) / T(y,x)) / x. ((1 / x) * y) \ (1 / (x * T(y,x))) = ((y \ x) / T(y,x)) / x. ((1 / x) * y) \ (1 / (y * x)) = ((y \ x) / T(y,x)) / x. (x \ y) / (x * y) = ((x \ y) / T(x,y)) / y. ((x \ y) / T(x,y)) / y = (x \ y) / (x * y). x != ((y \ z) / T(y,z)) / z | x = (z \ y) \ (1 / (z * ((z \ y) * z))). (x \ y) / (x * y) = (y \ x) \ (1 / (y * ((y \ x) * y))). (x \ y) \ (1 / (x * ((x \ y) * x))) = (y \ x) / (y * x). 1 / (((x \ (x / (1 / y))) * x) * (x \ y)) = (x \ y) \ (1 / (x * ((x \ 1) * (y * x)))). 1 / (((x * ((y \ x) \ 1)) * x) * (x \ y)) = (x \ y) \ (1 / (x * ((x \ 1) * (y * x)))). 1 / (((x \ 1) \ y) * (y \ x)) = (y \ x) \ (1 / (y * ((y \ 1) * (x * y)))). (x \ y) \ (1 / (x * ((x \ 1) * (y * x)))) = 1 / (((y \ 1) \ x) * (x \ y)). (x \ y) \ (1 / (y / (1 / x))) = 1 / (((y \ 1) \ x) * (x \ y)). 1 / (((x \ 1) \ y) * (y \ x)) = (y \ x) \ (1 / (x / (1 / y))). 1 / (((x \ 1) \ y) * (y \ x)) = (y \ x) \ ((y \ 1) * (1 / x)). 1 / ((x / y) \ (x * y)) = (x \ y) \ ((x \ 1) * (1 / y)). (x \ y) \ ((x \ 1) * (1 / y)) = 1 / ((x / y) \ (x * y)). (x \ y) \ ((x \ 1) * (1 / y)) != z | (1 / (x * y)) * (x / y) = z. ((1 / x) * (1 / (y * (z * x)))) \ (1 / x) = L(y,x,x) * (z / (1 / x)). L(x * (y * z),z,z) = L(x,z,z) * (y / (1 / z)). L(x,y,y) * (z / (1 / y)) = L(x * (z * y),y,y). L(x,y,y) * ((1 / y) / ((1 / y) * (z \ u))) = L(x * (((1 / y) * ((1 / u) * z)) * y),y,y). L(x * (((1 / y) * ((1 / z) * u)) * y),y,y) = L(x,y,y) * ((1 / y) / ((1 / y) * (u \ z))). x \ (((y * T(x,K(z,u))) * K(z,u)) * ((K(z,u) * (y * T(x,K(z,w)))) \ (y * T(x,K(z,w))))) = T(y,K(u,z) * x). 1 / (((x / (((y \ x) \ 1) \ 1)) * x) * ((1 / x) * y)) = ((1 / x) * y) \ (1 / (x * T(y,x))). ((1 / x) \ (((y \ z) * (1 / z)) \ u)) * (u \ 1) = (((y \ u) * (u \ (1 / x))) \ z) * (1 / z). L(x * (((1 / y) * ((1 / z) * u)) * y),y,y) = L(x,y,y) * (1 / T(u \ z,y / 1)). L(x * (((1 / y) * ((1 / z) * u)) * y),y,y) = L(x,y,y) * (1 / T(u \ z,y)). L(x * T((1 / y) * z,u),u,u) = L(x,u,u) * (1 / T(z \ y,u)). x * ((x \ y) * L(z * T((1 / (y \ x)) * z,x),x,x)) = ((x \ y) * L(z,x,x)) * (x / (z \ (y \ x))). 1 / ((((1 / x) \ ((y \ x) \ 1)) * x) * ((1 / x) * y)) = ((1 / x) * y) \ (1 / (x * T(y,x))). (((x \ y) * (y \ (1 / z))) \ u) * (1 / u) = y * (((1 / z) * y) \ (((x \ u) * (1 / u)) \ 1)). x * (((1 / y) * x) \ (((z \ u) * (1 / u)) \ 1)) = (((z \ x) * (x \ (1 / y))) \ u) * (1 / u). 1 / ((x * (((y \ x) \ 1) * x)) * ((1 / x) * y)) = ((1 / x) * y) \ (1 / (x * T(y,x))). 1 / (((x \ (y \ 1)) \ 1) * ((1 / x) * y)) = ((1 / x) * y) \ (1 / (x * T(y,x))). ((1 / x) * y) \ (1 / (x * T(y,x))) = 1 / (((x \ (y \ 1)) \ 1) * ((1 / x) * y)). ((1 / x) * y) \ (1 / (x * T(y,x))) = 1 / (1 / ((y \ x) / (y * x))). x != 1 / (1 / y) | x = (y \ 1) \ 1. ((1 / x) * y) \ (1 / (x * T(y,x))) = (((y \ x) / (y * x)) \ 1) \ 1. ((1 / x) * y) \ (1 / (x * T(y,x))) = ((y * x) * ((y \ x) \ 1)) \ 1. ((1 / x) * y) \ (1 / (x * T(y,x))) = ((y \ x) \ 1) \ ((y * x) \ 1). ((1 / x) * y) \ (1 / (x * T(y,x))) = ((y \ x) \ 1) \ (x \ (y \ 1)). ((1 / x) * y) \ (1 / (y * x)) = ((y \ x) \ 1) \ (x \ (y \ 1)). ((x \ y) \ 1) \ (y \ (x \ 1)) = ((1 / y) * x) \ (1 / (x * y)). x != ((1 / y) * z) \ (1 / u) | x = (z \ y) / u. ((x \ y) \ 1) \ (y \ (x \ 1)) = (x \ y) / (x * y). x != ((y \ z) \ 1) \ (z \ (y \ 1)) | x = y \ (z \ (z / y)). (x \ y) / (x * y) = x \ (y \ (y / x)). x != (y \ z) / (y * z) | x = (z \ y) \ (1 / (z * ((z \ y) * z))). x \ (y \ (y / x)) = (y \ x) \ (1 / (y * ((y \ x) * y))). (x \ y) \ (1 / (x * ((x \ y) * x))) = y \ (x \ (x / y)). (x \ y) \ (1 / (y / (1 / x))) = y \ (x \ (x / y)). (x \ y) \ ((x \ 1) * (1 / y)) = y \ (x \ (x / y)). (1 / (x * y)) * (x / y) = y \ (x \ (x / y)). x * (((1 / y) * x) \ ((1 / z) \ ((u \ z) \ 1))) = (((u \ x) * (x \ (1 / y))) \ z) * (1 / z). x * (((1 / y) * x) \ (z * (((z \ u) \ 1) \ 1))) = (((u \ x) * (x \ (1 / y))) \ z) * (1 / z). x * ((x \ y) / (z * (1 / (u * z)))) = (((u \ x) * (x \ (1 / y))) \ z) * (1 / z). (((x \ y) * (y \ (1 / z))) \ u) * (1 / u) = y * ((y \ z) / (u * (1 / (x * u)))). x != ((((y \ 1) \ z) * (z \ (1 / u))) \ w) * (1 / w) | x = (u * z) / ((w * (1 / (y * w))) \ z). x * ((x \ y) / (z * (1 / ((u \ 1) * z)))) = (y * x) / ((z * (1 / (u * z))) \ x). x * ((x \ y) / (K(z,z \ 1) * u)) = (y * x) / ((z * (1 / (u * z))) \ x). (x * y) / ((z * (1 / (u * z))) \ y) = y * ((y \ x) / (K(z,z \ 1) * u)). (x * y) / ((z * (1 / (u * z))) \ y) = y * (K(z,z \ 1) * ((y \ x) / u)). (x / ((y \ 1) * (z * K(u,u \ 1)))) * ((y \ u) * (1 / u)) = K(u,u \ 1) * (y * (K(u,u \ 1) * ((y \ x) / z))). x != y * (1 / ((z * u) * y)) | x = (y * (1 / (u * y))) / z. (x * (1 / (y / z))) / (z * (1 / (y * z))) = (u * (1 / (y * u))) / (z \ (x \ (u * (1 / (y * u))))). 1 / ((x * (y * z)) * ((x * y) * z)) = (z \ (y \ (x \ 1))) * (1 / (x * (y * z))). (x \ (y \ (z \ 1))) * (1 / (z * (y * x))) = 1 / ((z * (y * x)) * ((z * y) * x)). (x \ (y \ (z \ 1))) * (1 / (z * (y * x))) = 1 / (((z * y) * x) * (z * (y * x))). x * (1 / y) != 1 / (z * y) | x = T(1 / z,y). x \ (y \ (z \ 1)) = T(1 / ((z * y) * x),z * (y * x)). T(1 / ((x * y) * z),x * (y * z)) = z \ (y \ (x \ 1)). x * y != T(1 / ((z * u) * w),z * (u * w)) | (w \ (u \ (z \ 1))) / y = x. (x \ (y \ (z \ 1))) / (1 / ((z * y) * x)) = K(1 / ((z * y) * x),z * (y * x)). ((x * y) * z) \ (1 / (1 / ((x * y) * z))) = K(1 / ((x * y) * z),x * (y * z)). ((x * y) * z) \ ((z \ ((x * y) \ 1)) \ 1) = K(1 / ((x * y) * z),x * (y * z)). ((x * y) * z) \ ((z \ (y \ (x \ 1))) \ 1) = K(1 / ((x * y) * z),x * (y * z)). x != K(1 / y,z) | x = K(y,z \ 1). ((x * y) * z) \ ((z \ (y \ (x \ 1))) \ 1) = K((x * y) * z,(x * (y * z)) \ 1). ((x * y) * z) \ ((z \ (y \ (x \ 1))) \ 1) = K((x * y) * z,(y * z) \ (x \ 1)). x != K((y * z) * u,(z * u) \ (y \ 1)) | x = K(y * (z * u),(z * u) \ (y \ 1)). ((x * y) * z) \ ((z \ (y \ (x \ 1))) \ 1) = K(x * (y * z),(y * z) \ (x \ 1)). x != ((y * z) * u) \ ((u \ (z \ (y \ 1))) \ w) | x = ((y * z) * u) * ((1 / ((y * z) * u)) * w). K(x * (y * z),(y * z) \ (x \ 1)) = ((x * y) * z) * ((1 / ((x * y) * z)) * 1). ((x * y) * z) * ((1 / ((x * y) * z)) * 1) = K(x * (y * z),(y * z) \ (x \ 1)). ((x * y) * z) * (1 / ((x * y) * z)) = K(x * (y * z),(y * z) \ (x \ 1)). K(x * (y * z),(y * z) \ (x \ 1)) = ((x * y) * z) * (1 / ((x * y) * z)). K(x * (y * z),(y * z) \ (x \ 1)) = K((x * y) * z,((x * y) * z) \ 1). K((x * y) * z,((x * y) * z) \ 1) = K(x * (y * z),(y * z) \ (x \ 1)). K((x * y) * z,z \ ((x * y) \ 1)) = K(x * (y * z),(y * z) \ (x \ 1)). K((x * y) * z,z \ (y \ (x \ 1))) = K(x * (y * z),(y * z) \ (x \ 1)). K((x * y) * z,z \ (y \ (x \ 1))) != u | K((y * z) \ x,x \ (y * z)) = u. x * ((x \ y) * L(z * T(((1 / x) * y) * z,x),x,x)) = ((x \ y) * L(z,x,x)) * (x / (z \ (y \ x))). x / ((y * T(((1 / x) * z) * y,x)) \ (z \ x)) = ((x \ z) * L(y,x,x)) * (x / (y \ (z \ x))). x != ((y \ z) * L(u,y,y)) * (y / (u \ (z \ y))) | x = (y \ (z * (u * y))) * ((y \ z) * L(u,y,y)). x / ((y * T(((1 / x) * z) * y,x)) \ (z \ x)) = (x \ (z * (y * x))) * ((x \ z) * L(y,x,x)). x / ((T(y / (z \ x),x) * y) \ (z \ x)) = (x \ (z * (y * x))) * ((x \ z) * L(y,x,x)). (x \ (y * (z * x))) * ((x \ y) * L(z,x,x)) = x / ((T(z / (y \ x),x) * z) \ (y \ x)). x != y / ((T(z / u,w) * z) \ u) | x = y * ((u \ z) * T(u \ z,w)). (x \ (y * (z * x))) * ((x \ y) * L(z,x,x)) = x * (((y \ x) \ z) * T((y \ x) \ z,x)). x != y * (z * T(z,y)) | x = z * (y * z). (x \ (y * (z * x))) * ((x \ y) * L(z,x,x)) = ((y \ x) \ z) * (x * ((y \ x) \ z)). x != (y \ (z * (u * y))) * ((y \ z) * L(u,y,y)) | x = ((y \ z) * L(u,y,y)) * (y / (u \ (z \ y))). ((x \ y) \ z) * (y * ((x \ y) \ z)) = ((y \ x) * L(z,y,y)) * (y / (z \ (x \ y))). ((x \ y) * L(z,x,x)) * (x / (z \ (y \ x))) = ((y \ x) \ z) * (x * ((y \ x) \ z)). x != ((y \ z) * L(u,y,y)) * (y / (u \ (z \ y))) | x = (y \ z) * (L(u,y,y) * ((y * (y \ z)) * L(u,y,y))). ((x \ y) \ z) * (y * ((x \ y) \ z)) = (y \ x) * (L(z,y,y) * ((y * (y \ x)) * L(z,y,y))). (x \ y) * (L(z,x,x) * ((x * (x \ y)) * L(z,x,x))) = ((y \ x) \ z) * (x * ((y \ x) \ z)). (x \ y) * (L(z,x,x) * (y * L(z,x,x))) = ((y \ x) \ z) * (x * ((y \ x) \ z)). (x \ y) * (z * (y * z)) = ((y \ x) \ z) * (x * ((y \ x) \ z)). ((x \ y) \ z) * (y * ((x \ y) \ z)) = (y \ x) * (z * (x * z)). x != (y \ (z \ (u \ 1))) * K(w,v5) | x = ((u * z) * y) \ K(w,v5). (x * (y * (z * (1 / (u * z))))) \ (a(x,y,z * (1 / (u * z))) \ 1) = ((x * y) * (1 / u)) \ K(z,z \ 1). (x * (y * (z * (1 / (u * z))))) \ (a(x,y,z * (1 / (u * z))) \ 1) = (((x * y) * (1 / u)) \ z) * (1 / z). x != (y * (z * u)) \ (a(y,z,u) \ 1) | x = u \ (z \ (y \ 1)). (((x * y) * (1 / z)) \ u) * (1 / u) = (u * (1 / (z * u))) \ (y \ (x \ 1)). (x * (1 / (y * x))) \ (z \ (u \ 1)) = (((u * z) * (1 / y)) \ x) * (1 / x). K(x \ (y * z),(y * z) \ x) = (((y * z) * (1 / (y * z))) \ x) * (1 / x). (((x * y) * (1 / (x * y))) \ z) * (1 / z) = K(z \ (x * y),(x * y) \ z). (K(x * y,(x * y) \ 1) \ z) * (1 / z) = K(z \ (x * y),(x * y) \ z). (K(x * y,y \ (x \ 1)) \ z) * (1 / z) = K(z \ (x * y),(x * y) \ z). (K(x \ y,y \ x) \ z) * (1 / z) = K(z \ (y * x),(y * x) \ z). (K(x \ y,y \ x) * z) * (1 / z) = K(z \ (x * y),(x * y) \ z). K(x \ (y * z),(y * z) \ x) \ u = K(y \ z,z \ y) * (K(x,x \ 1) * u). K(x \ y,y \ x) * (K(z,z \ 1) * u) = K(z \ (x * y),(x * y) \ z) \ u. x != (y * z) * (1 / z) | x = z * ((1 / z) * y). K(x \ (y * z),(y * z) \ x) = x * ((1 / x) * K(y \ z,z \ y)). x * ((1 / x) * K(y \ z,z \ y)) = K(x \ (y * z),(y * z) \ x). x != y * ((1 / y) * K(z \ u,u \ z)) | x = (z * (u \ 1)) * ((1 / (z * (u \ 1))) * K(y,y \ 1)). K(x \ (y * z),(y * z) \ x) = (y * (z \ 1)) * ((1 / (y * (z \ 1))) * K(x,x \ 1)). (x * (y \ 1)) * ((1 / (x * (y \ 1))) * K(z,z \ 1)) = K(z \ (x * y),(x * y) \ z). x * (K(y \ z,z \ y) / x) = K(x \ (y * z),(y * z) \ x). K(x \ (y * z),(y * z) \ x) = x * (K(y \ z,z \ y) / x). K(x \ (y * z),(y * z) \ x) / (u * w) = x * (1 / ((u * (w * K(y \ z,z \ y))) * x)). x * (1 / ((y * (z * K(u \ w,w \ u))) * x)) = K(x \ (u * w),(u * w) \ x) / (y * z). x != y * (K(z \ u,u \ z) / y) | x = K((u * z) * y,y \ (z \ (u \ 1))). K(x \ (y * z),(y * z) \ x) = K((z * y) * x,x \ (y \ (z \ 1))). K((x * y) * z,z \ (y \ (x \ 1))) = K(z \ (y * x),(y * x) \ z). K((x * y) \ z,z \ (x * y)) = K(y \ (x * z),(x * z) \ y). x * y != K((z * u) \ w,w \ (z * u)) | K(u \ (z * w),(z * w) \ u) / y = x. K(x \ (y * z),(y * z) \ x) / z = (z \ (y * x)) * (1 / (y * x)). K(x \ ((1 / y) * z),(z \ y) * x) / z = (z \ ((1 / y) * x)) * (1 / ((1 / y) * x)). K(x \ y,y \ x) * (K(z,z \ 1) * u) = K((x * y) \ z,z \ (x * y)) * u. K(x \ y,y \ x) * (K(z,z \ 1) * u) = K(y \ (x * z),(x * z) \ y) * u. (x * (y \ 1)) * ((y / x) * K(z,z \ 1)) = K(z \ (x * y),(x * y) \ z). x != (y * (z \ 1)) * ((z / y) * u) | x = (z \ y) * (((1 / y) * z) * u). K(x \ (y * z),(y * z) \ x) = (z \ y) * (((1 / y) * z) * K(x,x \ 1)). (x \ y) * (((1 / y) * x) * K(z,z \ 1)) = K(z \ (y * x),(y * x) \ z). x != (y * (z \ 1)) * ((z / y) * u) | x = (z / y) * ((1 / (z / y)) * u). K(x \ (y * z),(y * z) \ x) = (z / y) * ((1 / (z / y)) * K(x,x \ 1)). (x / y) * ((1 / (x / y)) * K(z,z \ 1)) = K(z \ (y * x),(y * x) \ z). (x \ y) * ((1 / y) * (K(z,z \ 1) * x)) = K(z \ (y * x),(y * x) \ z). (x / y) * (z * (1 / ((x / y) * z))) = K(z \ (y * x),(y * x) \ z). K(x \ (y / z),(y / z) \ x) = K(x \ (z * y),(z * y) \ x). (x \ y) * (z * (1 / ((x \ y) * z))) = K(z \ (y * x),(y * x) \ z). K(x \ (y \ z),(y \ z) \ x) = K(x \ (z * y),(z * y) \ x). x != ((y \ 1) \ z) * (u * (1 / (((y \ 1) \ z) * u))) | x = K(z \ y,y \ z) * K(u,u \ 1). K(x \ (y * (z \ 1)),(y * (z \ 1)) \ x) = K(y \ z,z \ y) * K(x,x \ 1). x != K(y \ (z \ u),(z \ u) \ y) | x = K((z \ u) * y,y \ ((u \ 1) * z)). K(x \ (y * z),(y * z) \ x) = K((z \ y) * x,x \ ((y \ 1) * z)). K((x \ y) * z,z \ ((y \ 1) * x)) = K(z \ (y * x),(y * x) \ z). K(x \ (y * (z / x)),(y * (z / x)) \ x) / u = (x \ ((z / x) \ y)) * ((x \ ((x / y) * z)) / u). K(x \ (y * (z \ 1)),(z / y) * x) = K(y \ z,z \ y) * K(x,x \ 1). K((x / y) * z,((x / y) * z) \ 1) = K(y \ x,x \ y) * K(z,z \ 1). K((x / y) * z,z \ ((x / y) \ 1)) = K(y \ x,x \ y) * K(z,z \ 1). K((x / y) * z,z \ (y * (x \ 1))) = K(y \ x,x \ y) * K(z,z \ 1). x != K((y / z) * u,u \ (z * (y \ 1))) | x = K((y / z) \ u,u \ (y / z)). K(x \ y,y \ x) * K(z,z \ 1) = K((y / x) \ z,z \ (y / x)). K((x / y) \ z,z \ (x / y)) * u = K(y \ x,x \ y) * (K(z,z \ 1) * u). K(x \ y,y \ x) * (K(z,z \ 1) * u) = K((y / x) \ z,z \ (y / x)) * u. x * y != K(z \ u,u \ z) * (K(w,w \ 1) * y) | x = K(u \ (z * w),(z * w) \ u). K((x / y) \ z,z \ (x / y)) = K(x \ (y * z),(y * z) \ x). (K(x \ (y * z),(y * z) \ x) / (u * w)) * u = K((x / y) \ z,z \ (x / y)) / w. K(x \ ((1 / y) * z),(z \ y) * x) / z = (z \ ((1 / y) * x)) * (((x \ y) \ 1) \ 1). x != (y \ ((1 / z) * u)) * (((u \ z) \ 1) \ 1) | x = y \ K(z \ u,u \ z). K(x \ ((1 / y) * z),(z \ y) * x) / z = z \ K(y \ x,x \ y). K((x \ y) * z,((x \ y) * z) \ 1) / x = x \ K(y \ z,z \ y). K((x \ y) * z,z \ ((x \ y) \ 1)) / x = x \ K(y \ z,z \ y). K(x \ (y \ z),(y \ z) \ x) / y = y \ K(z \ x,x \ z). T(x,(y * z) \ K(u \ w,w \ u)) = T(x,z \ (y \ 1)). ((x \ y) * z) * (1 / ((u * x) * ((x \ y) * z))) = (x \ K(y \ z,z \ y)) / u. (1 / T(x,y \ (z \ 1))) \ (z * (y * K(u \ w,w \ u))) = (z * (y * K(u \ w,w \ u))) * x. K(x,T(y / z,y / (z * u))) = K(x,(z * K(z * u,u \ 1)) \ ((z * u) * (y / (z * u)))). x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u,z) * x). x \ T(y * T(x,K(z,u)),K(u,z)) = T(y,K(z,u) * x). x \ T(y * T(x,K(z,u)),K(z,z * u)) = T(y,K(z * u,z) * x). K(T(x,K(y,z) * (u * K(w,v5))),v5) = K(u \ T(x * T(u * K(w,v5),K(z,y)),K(z,y)),v5). K(x \ T(y * T(x * K(z,u),K(w,v5)),K(w,v5)),u) = K(T(y,K(v5,w) * (x * K(z,u))),u). x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z,u) * x). x != y \ T(z * T(y,K(u,w)),K(u,w)) | x = T(z,K(w,u) * y). T(x,K(y,z) * u) = T(x,K(z,y) * u). x * T(y,K(z,u) * x) = T(y * T(x,K(z,u)),K(z,u)). T(x * T(y,K(z,u)),K(z,u)) = y * T(x,K(z,u) * y). x * y != T(z,K(u,w) * v5) | x \ T(z,K(w,u) * v5) = y. x \ T(x,K(y,z) * u) = K(x,K(z,y) * u). T(x,T(y,z) * u) = T(x,K(z,y) * (y * u)). T(x,K(y,z) * (z * u)) = T(x,T(z,y) * u). K(x,K(y,z) * u) = K(x,K(z,y) * u). x != K(y,K(z,u \ 1) * w) | x = K(y,K(u,z) * w). K(x,K(y \ 1,z) * u) = K(x,K(y,z) * u). K(x,T(y,z) \ u) = K(x,K(y,z) * (y \ u)). K(x,K(y,z) * (y \ u)) = K(x,T(y,z) \ u). K(x,T(y / z,T(u,z))) = K(x,K(u,z \ y) * (y / z)). K(x,K(y,z \ u) * (u / z)) = K(x,T(u / z,T(y,z))). T(x,((y * z) / y) * u) = T(x,T(z,y) * u). K(x,K(y \ 1,z) * u) = x \ T(x,K(y,z) * u). K(x,y * T(y \ (z \ y),u)) = K(x,K(z,u) * (z \ y)). K(x,K(y,z) * (y \ u)) = K(x,u * T(u \ (y \ u),z)). L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(K(z,y \ K(y,u)) * u) \ w). K(x,((y * z) / y) \ u) = K(x,T(z,y) \ u). T(x,y * z) = T(x,T(T(y,u),u) * z). T(x,T(T(y,z),z) * u) = T(x,y * u). T(x,y * T(T(z,u),u)) = T(T(x,K(y,z)),z * y). T(T(x,K(y,z)),z * y) = T(x,y * T(T(z,u),u)). K(x,y / ((z * u) / z)) = K(x,T(u,z) \ T(y,(z * u) / z)). K(x,T(y,z) \ T(u,(z * y) / z)) = K(x,u / ((z * y) / z)). K(x,(L(y,z,y) * z) \ u) = K(x,T(z * y,y) \ u). K(x,T(y,z \ y) \ u) = K(x,T(y,z) \ u). K(x,K(y \ 1,z) * u) != w | K(x,K(y,z) * u) = w. T(x,y * z) = T(x,y * T(T(z,u),u)). T(x,y * T(T(z,u),u)) = T(x,y * z). T(x,y * T(z,u)) = T(x,y * ((u * z) / u)). T(x,y * ((z * u) / z)) = T(x,y * T(u,z)). K(x * ((y * z) / y),u) = u / T(u,x * T(z,y)). K(x * ((y * z) / y),u) = K(x * T(z,y),u). K((x \ y) * ((z * ((x \ y) \ (x \ u))) / z),w) = K(x \ (y * T(y \ u,z)),w). x != K(y,(L(z,u,z) * w) \ v5) | x = K(y,(z * w) \ v5). K(x,T(y * z,z) \ u) = K(x,(z * y) \ u). x != K(y,K(z,u \ w) * (w / u)) | x = K(y,T(w / u,T(z \ (u \ w),u))). K(x,T(y / z,T(u,z))) = K(x,T(y / z,T(u \ (z \ y),z))). K(x,T(y / z,T(u \ (z \ y),z))) = K(x,T(y / z,T(u,z))). K(x,K(y * K(z,y),u) * z) = K(x,(z * y) * T((z * y) \ ((y * K(z,y)) \ (z * y)),u)). K(x,(y * z) * T((y * z) \ ((z * K(y,z)) \ (y * z)),u)) = K(x,K(z * K(y,z),u) * y). K(x,T(y,z) \ T(u,T(y,z))) = K(x,u / ((z * y) / z)). K(x,y / ((z * u) / z)) != w | K(x,y / T(u,z)) = w. K(x,T(y / z,y / (z * u))) = K(x,T(y / z,T(u,z))). x != K(y,T(z / u,z / (u * w))) | x = K(y,(u * K(u * w,w \ 1)) \ ((u * w) * (z / (u * w)))). K(x,T(y / z,T(u,z))) = K(x,(z * K(z * u,u \ 1)) \ ((z * u) * (y / (z * u)))). K(x,(y * K(y * z,z \ 1)) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y))). K(x,T(y / z,y / (((u \ 1) \ 1) \ z))) = K(x,T(y / z,T(T(z \ (u \ z),T(u,w)),z))). K(x,T(y / z,T(T(z \ (u \ z),T(u,w)),z))) = K(x,T(y / z,y / (((u \ 1) \ 1) \ z))). x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z * u,z) * x). T(x,K(y * z,y) * u) = T(x,K(z,y) * u). x != T(y,K(z,u) * w) | x = T(y,K(u,z) * w). T(x,K(y,z) * u) = T(x,K(z,z * y) * u). T(x,K(y,y * z) * u) = T(x,K(z,y) * u). T(x,y * K(z,z * u)) = T(T(x,K(y,K(z,u))),K(u,z) * y). T(T(x,K(y,K(z,u))),K(u,z) * y) = T(x,y * K(z,z * u)). T(x,y * K(z,u)) = T(x,y * K(u,u * z)). T(x,y * K(z,z * u)) = T(x,y * K(u,z)). T(x,y * K(z,u)) = T(x,y * K(z \ 1,u)). T(x,y * K(z \ 1,u)) = T(x,y * K(z,u)). K(x,(y * K(z,u)) \ w) = K(x,(K(z,u \ K(u,y)) * y) \ w). K(x,(K(y,z \ K(z,u)) * u) \ w) = K(x,(u * K(y,z)) \ w). K(x,(y * K(z,u \ 1)) \ w) = K(x,(y * K(z,u)) \ w). K(x \ (y * ((z * (y \ u)) / z)),w) = K(x \ (y * T(y \ u,z)),w). K(x \ K(y,z \ 1),u) = K(x \ (z * T(z \ 1,y)),u). K(x \ (y * T(y \ 1,z)),u) = K(x \ K(z,y \ 1),u). K(x \ K(y \ 1,z),u) = K(x \ K(z,y \ 1),u). (x \ K(y \ K(z,u \ 1),w)) \ (x \ 1) = K(w,y \ K(u \ 1,z)). K(x,y \ K(z,u \ 1)) = K(x,y \ K(u \ 1,z)). K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z \ 1)). K(x,y \ K(z \ 1,u)) != w | K(x,y \ K(z,u)) = w. x != K(y,(z * K(u,w \ 1)) \ v5) | x = K(y,(z * K(u,w)) \ v5). K(x,T(y / z,T(u,z))) = K(x,(z * K(z * u,u)) \ ((z * u) * (y / (z * u)))). K(x,(y * K(y * z,z)) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y))). x != K(y,(z * K(u * w,w)) \ v5) | x = K(y,(z * K(u,w)) \ v5). K(x,T(y / z,T(u,z))) = K(x,(z * K(z,u)) \ ((z * u) * (y / (z * u)))). K(x,(y * K(y,z)) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y))). K(x,T(y,z) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y))). K(x,T(y,z) \ ((y * T(z,y)) * (u / (y * T(z,y))))) = K(x,T(u / y,T(T(z,y),y))). K(x,T(y,z) \ ((z * y) * (u / (y * T(z,y))))) = K(x,T(u / y,T(T(z,y),y))). K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,T(T(z,y),y))). K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,z)). x != K(T(y,z * (u * K(w,v5))),v5) | x = K(y,T(v5,z * u)). K(x \ T(y * T(x * K(z,u),K(w,v5)),K(w,v5)),u) = K(y,T(u,K(v5,w) * x)). K(x \ T(y * T(x * K(z,u),K(w,v5)),K(w,v5)),u) = K(y,T(u,K(w,v5) * x)). K(x,(y * z) * T((y * z) \ ((z * K(y,z)) \ (y * z)),u)) = K(x,K(z,T(u,y)) * y). K(x,(y * z) * T((y * z) \ ((z * K(y,z)) \ (y * z)),u)) = K(x,y * K(z,u)). K(x,(y * z) * T((y * z) \ y,u)) = K(x,y * K(z,u)). K(x,y * K(z \ 1,u)) = K(x,y * K(z,u)). 1 / K(x,y * K(z,u)) = K(y * K(z \ 1,u),x). K(x * K(y \ 1,z),u) = 1 / K(u,x * K(y,z)). K(x * K(y \ 1,z),u) = K(x * K(y,z),u). x != K(y * K((y \ z) \ 1,u),T(w,z)) | x = K(z * T(y / z,u),w). K(x * K(x \ y,z),T(u,y)) = K(y * T(x / y,z),u). K(((x * (y \ z)) / x) * y,u) = K(y * T(z / y,x),u). K(((x * y) / x) / z,u) = K((z \ 1) * T((z \ y) / (z \ 1),x),u). x != K((y \ 1) * T(z / (y \ 1),u),w) | x = K(y \ T(z * y,u),w). K(((x * y) / x) / z,u) = K(z \ T((z \ y) * z,x),u). K(x \ T((x \ y) * x,z),u) = K(((z * y) / z) / x,u). K(T(x \ T(y,z),x),u) = K(((z * y) / z) / x,u). K(T(x,y) / z,u) = K(((y * x) / y) / z,u). K(((x * y) / x) / z,u) = K(T(y,x) / z,u). x != K(((y * z) / y) / T(u,T(z,y)),w) | x = K(T(z * K(y,z),u) / u,w). K(T(x,y) / T(z,T(x,y)),u) = K(T(x * K(y,x),z) / z,u). K(T(x * K(y,x),z) / z,u) = K(T(x,y) / T(z,T(x,y)),u). K(x \ (y * K(z,y)),u) = K(T(y,z) / T(x,T(y,z)),u). K(T(x,y) / T(z,T(x,y)),u) = K(z \ (x * K(y,x)),u). K(x \ T(y,z),u) = K(x \ (y * K(z,y)),u). K(x \ (y * K(z,y)),u) = K(x \ T(y,z),u). K(x \ y,z) = K(x \ T(T(y,u),u),z). K(x \ T(T(y,z),z),u) = K(x \ y,u). 1 / K(x \ y,z) = K(z,x \ T(T(y,u),u)). K(x,y \ T(T(z,u),u)) = 1 / K(y \ z,x). K(x,y \ T(T(z,u),u)) = K(x,y \ z). K(x,y \ T(z * (u / T(z,u)),z)) = K(x,y \ (z * (u / z))). K(x,y \ T(z,u)) = K(x,y \ (z * K(u,z))). K(x,y \ (z * K(u,z))) = K(x,y \ T(z,u)). K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,u)). K(x,(y \ z) \ K(u \ 1,y)) = K(x,z \ T(y,1 / u)). K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,1 / u)). x != K(y,(z \ u) \ K(w,z)) | x = K(y,u \ T(z,w)). K(x,y \ T(z,1 / u)) = K(x,y \ T(z,u)). K(x,y \ T(z,u)) = K(x,y \ T(z,u \ 1)). K(x,y \ T(z,u \ 1)) = K(x,y \ T(z,u)). K(x,y \ T(z,u \ (w \ u))) = K(x,y \ T(z,T(w,u))). x != K(y,z \ T(u * w,u)) | x = K(y,z \ (w * u)). K(x,y \ (z * (u / z))) = K(x,y \ ((u / T(z,u)) * z)). K(x,y \ ((z / T(u,z)) * u)) = K(x,y \ (u * (z / u))). K(x,y \ T(z,u)) = K(x,y \ (u * (z / u))). K(x,y \ (z * (u / z))) = K(x,y \ T(u,z)). x != K(y,T(z,u) \ ((u * z) * (w / (u * z)))) | x = K(y,T(w / z,u)). K(x,T(y,z) \ T(u,z * y)) = K(x,T(u / y,z)). K(x,T(y * z,(y * z) \ z) \ T(u,z * K(y \ 1,z * y))) = K(x,T(u / (y * z),(y * z) \ z)). K(x,T(y / z,T(T(z \ (u \ z),T(u,w)),z))) = K(x,T(y / z,y / (u \ z))). K(x,T(y / z,T((u \ z) / z,T(u,w)))) = K(x,T(y / z,y / (u \ z))). K(x,T(y / z,u \ 1)) = K(x,T(y / z,y / (u \ z))). K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u \ 1)). x != K(y,T(z,u \ 1)) | x = K(y,T(z,u)). K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u)). x != K(y,T(z / u,z / (w \ u))) | x = K(y,T(u,w) \ ((w \ u) * (z / (w \ u)))). K(x,T(y / z,u)) = K(x,T(z,u) \ ((u \ z) * (y / (u \ z)))). K(x,T(y,z) \ ((z \ y) * (u / (z \ y)))) = K(x,T(u / y,z)). K(x,T(y,T(y,z) / z) \ (T(z,y) * (u / ((T(y,z) / z) \ y)))) = K(x,T(u / y,T(y,z) / z)). K(x,T(y,z \ y) \ (T(z,y) * (u / ((T(y,z) / z) \ y)))) = K(x,T(u / y,T(y,z) / z)). K(x,T(y,z \ y) \ (T(z,y) * (u / T(z,y)))) = K(x,T(u / y,T(y,z) / z)). x != K(y,T(z,u \ z) \ w) | x = K(y,T(z,u) \ w). K(x,T(y / z,T(z,u) / u)) = K(x,T(z,u) \ (T(u,z) * (y / T(u,z)))). K(x,T(y,z) \ (T(z,y) * (u / T(z,y)))) = K(x,T(u / y,T(y,z) / z)). K(x,T(y,z) \ (T(z,y) * (u / T(z,y)))) = K(x,T(u / y,z \ y)). x != K(y,z \ (u * (w / u))) | x = K(y,z \ T(w,u)). K(x,T(y / z,u \ z)) = K(x,T(z,u) \ T(y,T(u,z))). K(x,T(y,z) \ T(u,T(z,y))) = K(x,T(u / y,z \ y)). x != K(y,T(z,z \ u) \ w) | x = K(y,((z \ u) \ u) \ w). K(x,T(y / (z * u),(z * u) \ u)) = K(x,(((z * u) \ u) \ u) \ T(y,u * K(z \ 1,u * z))). K(x,(((y * z) \ z) \ z) \ T(u,z * K(y \ 1,z * y))) = K(x,T(u / (y * z),(y * z) \ z)). K(x,(((y * z) \ z) \ z) \ T(u,z * K(y,z * y))) = K(x,T(u / (y * z),(y * z) \ z)). K(x,(((y * z) \ z) \ z) \ T(u,z * K(y,y * z))) = K(x,T(u / (y * z),(y * z) \ z)). K(x,(((y * z) \ z) \ z) \ T(u,z * K(z,y))) = K(x,T(u / (y * z),(y * z) \ z)). K(x,(((y * z) \ z) \ z) \ T(u,T(z,y))) = K(x,T(u / (y * z),(y * z) \ z)). K(x,T(y * z,z) \ T(u,T(z,y))) = K(x,T(u / (y * z),(y * z) \ z)). x != K(y,T(z * u,u) \ w) | x = K(y,(u * z) \ w). K(x,T(y / (z * u),(z * u) \ u)) = K(x,(u * z) \ T(y,T(u,z))). K(x,T(y / (z * u),u \ (z \ u))) = K(x,(u * z) \ T(y,T(u,z))). K(x,T(y / (z * u),T(z,u))) = K(x,(u * z) \ T(y,T(u,z))). K(x,(y * z) \ T(u,T(y,z))) = K(x,T(u / (z * y),T(z,y))). K(x,(y * K(z \ 1,y * z)) \ T(u,T((y * z) \ y,y * z))) = K(x,T(u / ((y * z) * ((y * z) \ y)),T(y * z,(y * z) \ y))). K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,T((z * u) \ z,z * u))). x != K(y,y \ 1) * (z * (K(y,y \ 1) * u)) | x = z * u. (x / ((y \ 1) * (z * K(u,u \ 1)))) * ((y \ u) * (1 / u)) = y * ((y \ x) / z). (x / (((y \ z) * (1 / z)) * u)) * ((y \ z) * (1 / z)) = y * ((y \ x) / u). x \ (K(y \ z,z \ y) / u) = (x \ K(y \ z,z \ y)) / u. (x \ K(y \ z,z \ y)) / u = x \ (K(y \ z,z \ y) / u). x != (y / (((z \ u) * (1 / u)) * w)) * ((z \ u) * (1 / u)) | x = (y * z) / ((1 / w) \ z). x * ((x \ y) / z) = (y * x) / ((1 / z) \ x). (x * y) / ((1 / z) \ y) = y * ((y \ x) / z). x != (y * z) / ((1 / u) \ z) | x = (y / ((1 / z) * u)) * (1 / z). x * ((x \ y) / z) = (y / ((1 / x) * z)) * (1 / x). (x / ((1 / y) * z)) * (1 / y) = y * ((y \ x) / z). ((x * (1 / y)) / ((1 / z) \ (1 / y))) * z = z \ ((z / y) * ((1 / y) \ x)). x != (y \ K(z \ u,u \ z)) / w | x = ((y \ z) * u) * (1 / ((w * y) * ((y \ z) * u))). x \ (K(y \ z,z \ y) / u) = ((x \ y) * z) * (1 / ((u * x) * ((x \ y) * z))). ((x \ y) * z) * (1 / ((u * x) * ((x \ y) * z))) = x \ (K(y \ z,z \ y) / u). x != (y \ K(z \ u,u \ z)) / w | x = ((1 / u) * z) * (1 / ((w * ((y \ 1) \ 1)) * ((1 / u) * z))). x \ (K(y \ z,z \ y) / u) = ((1 / z) * y) * (1 / ((u * ((x \ 1) \ 1)) * ((1 / z) * y))). ((1 / x) * y) * (1 / ((z * ((u \ 1) \ 1)) * ((1 / x) * y))) = u \ (K(y \ x,x \ y) / z). ((x * (1 / y)) / (z / y)) * z = z \ ((z / y) * ((1 / y) \ x)). x \ ((x / y) * ((1 / y) \ z)) = ((z * (1 / y)) / (x / y)) * x. x \ ((x / y) * ((1 / y) \ z)) = ((z / (y * x)) * y) * x. x != y \ ((z / u) * ((1 / u) \ w)) | x = y \ (u \ ((u * z) * w)). ((x / (y * z)) * y) * z = z \ (y \ ((y * z) * x)). x \ (y \ ((y * x) * z)) = ((z / (y * x)) * y) * x. x \ ((x / y) * (y * ((y \ 1) \ z))) = (((y * z) / (y * x)) * y) * x. x * (((y / (z * x)) * z) * x) = z \ ((z * x) * y). x \ (y / (z \ (x \ y))) = ((z / ((1 / y) * x)) * (1 / y)) * x. ((x / ((1 / y) * z)) * (1 / y)) * z = z \ (y / (x \ (z \ y))). x \ (y \ ((y * x) * z)) != u | u = ((z / (y * x)) * y) * x. x \ (y \ ((y * x) * z)) != u | ((z / (y * x)) * y) * x = u. L(x,y,y) * (((z / ((1 / y) \ x)) * y) * L(x,y,y)) = y \ ((y * L(x,y,y)) * z). x * (((L(1 / y,z * x,y) / (z * x)) * z) * x) = z \ ((z * x) / y). (x * ((x \ y) / z)) * z = z \ (x / (y \ (z \ x))). x \ (y / (z \ (x \ y))) = (y * ((y \ z) / x)) * x. L((x \ 1) \ y,x,x \ z) = (((x * y) / (x * z)) * x) * z. (((x * y) / (x * z)) * x) * z = L((x \ 1) \ y,x,x \ z). x * (((1 / ((y * x) * L(z,z,y * x))) * y) * x) = y \ ((y * x) / z). x * (((1 / ((1 / (y * x)) \ z)) * y) * x) = y \ ((y * x) / z). x * ((((1 / y) * (1 / (z * x))) * z) * x) = z \ ((z * x) / y). x * ((y \ ((y / z) * (1 / x))) * x) = y \ ((y * x) / z). x != (y * z) * (1 / (u * (y * z))) | x = K(z \ y,y \ z) / u. x \ (K(y \ z,z \ y) / u) = K(z \ (x \ y),(x \ y) \ z) / (u * x). K(x \ (y \ z),(y \ z) \ x) / (u * y) = y \ (K(z \ x,x \ z) / u). K(x \ (y * z),(y * z) \ x) / (u * z) = z \ (K(y \ x,x \ y) / u). ((1 / x) * y) * (((y \ x) \ 1) \ (1 / (z * ((u \ 1) \ 1)))) = u \ (K(y \ x,x \ y) / z). ((1 / x) * y) * (((y \ x) \ 1) \ ((1 / 1) \ ((z \ 1) / u))) = z \ (K(y \ x,x \ y) / u). ((1 / x) * y) * (((y \ x) \ 1) \ (1 \ ((z \ 1) / u))) = z \ (K(y \ x,x \ y) / u). ((1 / x) * y) * (((y \ x) \ 1) \ (1 \ (z \ (1 / u)))) = z \ (K(y \ x,x \ y) / u). ((1 / x) * y) * (((y \ x) \ 1) \ (z \ (1 / u))) = z \ (K(y \ x,x \ y) / u). x != ((1 / y) * z) * (((z \ y) \ 1) \ u) | x = K(y \ z,z \ y) * u. x \ (K(y \ z,z \ y) / u) = K(z \ y,y \ z) * (x \ (1 / u)). K(x \ y,y \ x) * (z \ (1 / u)) = z \ (K(y \ x,x \ y) / u). K(x \ y,y \ x) * (z \ u) = z \ (K(y \ x,x \ y) / (u \ 1)). x \ (K(y \ z,z \ y) / (u \ 1)) = K(z \ y,y \ z) * (x \ u). x \ (K(y \ z,z \ y) * u) = K(z \ y,y \ z) * (x \ u). x * (1 / ((K(y \ z,z \ y) * (u \ w)) * x)) = (x * (K(z \ y,y \ z) / (w * x))) * u. x * (1 / (K(y \ z,z \ y) * ((u \ w) * x))) = (x * (K(z \ y,y \ z) / (w * x))) * u. x * ((1 / ((y \ z) * x)) * K(u \ w,w \ u)) = (x * (K(w \ u,u \ w) / (z * x))) * y. x * (K(y \ z,z \ y) / ((u \ w) * x)) = (x * (K(z \ y,y \ z) / (w * x))) * u. (x * (K(y \ z,z \ y) / (u * x))) * w = x * (K(z \ y,y \ z) / ((w \ u) * x)). x \ (1 / (((y \ (z \ ((1 / x) * (1 / (1 * (x \ (1 / x))))))) * (1 / x)) * (1 / x))) = ((x \ 1) \ 1) * (((1 / x) * z) * y). x \ (1 / (((y \ (z \ ((1 / x) * (1 / (x \ (1 / x)))))) * (1 / x)) * (1 / x))) = ((x \ 1) \ 1) * (((1 / x) * z) * y). x \ (1 / (((y \ (z \ ((1 / x) * ((1 / x) \ x)))) * (1 / x)) * (1 / x))) = ((x \ 1) \ 1) * (((1 / x) * z) * y). x \ (1 / (((y \ (z \ x)) * (1 / x)) * (1 / x))) = ((x \ 1) \ 1) * (((1 / x) * z) * y). x \ (1 / (((y \ (z \ x)) * (x \ 1)) * (x \ 1))) = ((x \ 1) \ 1) * (((1 / x) * z) * y). x \ (1 / ((x * ((y * x) \ (z \ 1))) * (x \ 1))) = ((x \ 1) \ 1) * (((1 / x) * z) * y). x \ (1 / T((y * x) \ (z \ 1),x \ 1)) = ((x \ 1) \ 1) * (((1 / x) * z) * y). (1 / ((x * y) \ (z \ 1))) * (y \ 1) = ((y \ 1) \ 1) * (((1 / y) * z) * x). ((1 / 1) \ (x * (y * z))) * (z \ 1) = ((z \ 1) \ 1) * (((1 / z) * x) * y). (1 \ (x * (y * z))) * (z \ 1) = ((z \ 1) \ 1) * (((1 / z) * x) * y). ((x \ 1) \ 1) * (((1 / x) * y) * z) = (1 \ (y * (z * x))) * (x \ 1). ((x \ 1) \ 1) * (((1 / x) * y) * z) = (y * (z * x)) * (x \ 1). x != ((y \ 1) \ 1) * (((1 / z) * u) * w) | x = 1 / ((w \ (u \ z)) / y). (x * (y * z)) * (z \ 1) = 1 / ((y \ (x \ z)) / z). 1 / ((x \ (y \ z)) / z) = (y * (x * z)) * (z \ 1). x != 1 / ((y \ (z \ u)) / u) | x = u * (((u \ 1) * z) * y). (x * (y * z)) * (z \ 1) = z * (((z \ 1) * x) * y). (x * ((1 / y) \ z)) * (z \ 1) = z * (((z \ 1) * x) * L(y,z,z)). x * (((x \ 1) * y) * L(z,x,x)) = (y * ((1 / z) \ x)) * (x \ 1). x != (y * ((1 / z) \ u)) * (u \ 1) | x = (u \ 1) \ ((u \ y) * z). x * (((x \ 1) * y) * L(z,x,x)) = (x \ 1) \ ((x \ y) * z). x != y * (((y \ 1) * z) * L(u,y,y)) | x = (z * y) * (y \ u). (x \ 1) \ ((x \ y) * z) = (y * x) * (x \ z). x != (y \ 1) \ ((y \ (z / y)) * u) | x = y / (u \ (y * (z \ y))). ((x / y) * y) * (y \ z) = y / (z \ (y * (x \ y))). x / (y \ (x * (z \ x))) = ((z / x) * x) * (x \ y). x / (y \ (x * (z \ x))) = z * (x \ y). (x * (y \ z)) \ y = z \ (y * (x \ y)). x / (y \ ((z \ 1) \ x)) = (z \ x) * (x \ y). (x * y) \ z = (z * y) \ (z * (x \ z)). (x * y) \ (x * (z \ x)) = (z * y) \ x. (x * y) \ (x * z) = ((x / z) * y) \ x. ((x / y) * z) \ x = (x * z) \ (x * y). (x * y) \ (x * (x \ ((x * z) * u))) = (((x / u) / z) * y) \ x. x != ((y / (z \ u)) * (z \ 1)) \ y | x = R(1 / u,z,z \ (y \ 1)) \ 1. (x * (y \ 1)) \ (x * (y \ z)) = R(1 / z,y,y \ (x \ 1)) \ 1. R(1 / x,y,y \ (z \ 1)) \ 1 = (z * (y \ 1)) \ (z * (y \ x)). (x * y) \ (x * z) = (1 / x) * ((y / x) \ z). (1 / x) * ((y / x) \ z) = (x * y) \ (x * z). (((1 / x) * y) \ ((1 / x) * z)) \ 1 = x * (((((1 / x) / z) * y) \ 1) \ 1). ((((x / y) * z) \ x) \ 1) * (((x * z) \ (x * y)) \ u) = (((x * y) \ (x * z)) * ((x * y) \ (x * z))) * u. ((x \ ((1 / y) * z)) \ 1) \ ((1 * z) \ (1 * y)) = ((1 / y) * z) \ (((1 / y) * z) / x). (x * y) \ ((x * z) * u) = (((x / u) / z) * y) \ x. (((x / y) / z) * u) \ x = (x * u) \ ((x * z) * y). (((x / y) / z) * (z * y)) \ x = a(x,z,y). a(x,y,z) = (((x / z) / y) * (y * z)) \ x. (((1 / (x / y)) \ z) * u) \ x = (x * u) \ ((x * (z \ 1)) * y). a(x,y,z) = L(x,z,y) \ x. x != L(y,z,u) \ y | x = y * L(y \ 1,z,u). a(x,y,z) = x * L(x \ 1,z,y). x != a(y,z \ u,w) | x = a(y,(z \ 1) * u,w). L(x,y,z \ u) \ x = a(x,(z \ 1) * u,y). a(x,(y \ 1) * z,u) = L(x,u,y \ z) \ x. x / a(x,y,z) = L(x,z,y). L(x,y,z) = x / a(x,z,y). a(x,y,z) \ 1 = x \ L(x,z,y). a(x,T(y,x),z) = L(x,z,y) \ x. L(x,y,z) \ (x * u) = a(x,z,y) * u. x * a(y,z,K(u,x)) = L(x,K(u,y),z). L(x,y,z) \ x != u | u = a(x,z,y). L(x,y,z) \ x != u | a(x,z,y) = u. x != y * L(y \ 1,z,u) | x = (y \ 1) \ L(y \ 1,z,u). a(x,y,z) = (x \ 1) \ L(x \ 1,z,y). (a(x,y,z) \ 1) * x = L(x,z,y). L(x,y,z) = (a(x,z,y) \ 1) * x. x * (y \ L(y,z,u)) = x / a(y,u,z). x != L(y,z,u) \ y | x = a(y,u,z). a(x,T(y,x),z) = a(x,y,z). T(x,a(y,z,u)) = L(x,K(y,u),z). L(x,K(y,z),u) = T(x,a(y,u,z)). x * (y \ L(y,z,u)) = x / (L(y,z,u) \ y). x / (L(y,z,u) \ y) = x * (y \ L(y,z,u)). x * a(y,z,u) = x / a(y \ 1,z,u). x / a(y \ 1,z,u) = x * a(y,z,u). x / a(y,z,u) = x * a(y \ 1,z,u). x * a(y \ 1,z,u) = x / a(y,z,u). x != y / a(y,z,u) | x = L(y,u,z). x * a(x \ 1,y,z) = L(x,z,y). L(x,y,z) = x * a(x \ 1,z,y). x * y != z / z | x \ 1 = y. a(x,y,z) \ 1 = a(x \ 1,y,z). a(x \ 1,y,z) = a(x,y,z) \ 1. x \ (x / a(y,z,u)) != w | w = a(y \ 1,z,u). x \ (x / a(y,z,u)) != w | a(y \ 1,z,u) = w. x != a(y,z,u) \ 1 | x = (y * (z * u)) \ ((u / (y * (z * u))) \ L(u,z,y)). a(x \ 1,y,z) = (x * (y * z)) \ ((z / (x * (y * z))) \ L(z,y,x)). (x * (y * z)) \ ((z / (x * (y * z))) \ L(z,y,x)) = a(x \ 1,y,z). a(x \ 1,y,z) \ u = a(x,y,z) * u. L(x,y,z) = a(x \ 1,z,y) * x. a(x,(y \ 1) * z,u) != w | a(x,y \ z,u) = w. x * L(y,z,u) = (x * y) * (y \ L(y,z,u)). (x * y) * (y \ L(y,z,u)) = x * L(y,z,u). (x \ L(x,y,z)) * u = (L(x,y,z) \ x) \ u. (L(x,y,z) \ x) \ u = (x \ L(x,y,z)) * u. x != ((y \ 1) \ z) * L(1 / T(y,z),u,w) | x = L(y \ 1,u,w) * ((y \ 1) \ z). (((x \ 1) \ y) * (1 / T(x,y))) * ((1 / T(x,y)) \ L(1 / T(x,y),z,u)) = L(x \ 1,z,u) * ((x \ 1) \ y). x != (L(y,z,u) \ y) \ w | x = L(y,z,u) * (y \ w). (x \ L(x,y,z)) * u = L(x,y,z) * (x \ u). (x * L(x \ 1,y,z)) * u = L(x \ 1,y,z) * ((x \ 1) \ u). L(x \ 1,y,z) * ((x \ 1) \ u) = (x * L(x \ 1,y,z)) * u. a(x,y,z) \ 1 != u | a(x \ 1,y,z) = u. ((x / y) * (z * z)) \ x = (x * z) \ ((x * (z \ 1)) * y). (x * y) \ ((x * (y \ 1)) * z) = ((x / z) * (y * y)) \ x. x != ((y / z) * (u * u)) \ y | x = ((u * u) \ (z / y)) * y. (x * y) \ ((x * (y \ 1)) * z) = ((y * y) \ (z / x)) * x. 1 / ((x \ (y / z)) * (z * y)) = ((y * y) \ (x / z)) * z. L(x \ 1,y,z) * ((x \ 1) \ u) = (L(x,y,z) \ x) * u. x * y != L(z \ 1,u,w) * ((z \ 1) \ x) | T(L(z,u,w) \ z,x) = y. L(x \ 1,y,z) * ((x \ 1) \ u) != u * w | T(L(x,y,z) \ x,u) = w. ((x \ y) / (z \ y)) \ 1 = y * (((((1 / y) / z) * x) \ 1) \ 1). x * (((((1 / x) / y) * z) \ 1) \ 1) = ((z \ x) / (y \ x)) \ 1. x * (((((1 / x) / y) * z) \ 1) \ 1) = (y \ x) * ((z \ x) \ 1). x * ((((1 / (y * x)) * z) \ 1) \ 1) = (y \ x) * ((z \ x) \ 1). x * ((y \ (z * x)) \ 1) = (z \ x) * ((y \ x) \ 1). (x \ y) * ((z \ y) \ 1) = y * ((z \ (x * y)) \ 1). (x \ y) * (y \ L(y,z,u)) = y * ((L(y,z,u) \ (x * y)) \ 1). x * ((L(x,y,z) \ (u * x)) \ 1) = (u \ x) * (x \ L(x,y,z)). ((x * y) / y) \ L(y,z,u) = (x \ y) * (y \ L(y,z,u)). x \ L(y,z,u) = (x \ y) * (y \ L(y,z,u)). (x \ y) * (y \ L(y,z,u)) = x \ L(y,z,u). x * (y \ L(y,z,u)) = (y / x) \ L(y,z,u). (x / y) \ L(x,z,u) = y * (x \ L(x,z,u)). x != y * (z \ L(z,u,w)) | x = y / a(z,w,u). (x / y) \ L(x,z,u) = y / a(x,u,z). (x * (y * z)) \ ((x * (y * z)) / a(z,x,y)) = a(x \ 1,y,z). a(x \ 1,y,z) != u | a(z \ 1,x,y) = u. a(x \ 1,y,z) = a(y,z,x) \ 1. L(x,y,z) = x * (a(z,y,x) \ 1). x * y != z * (a(u,w,z) \ 1) | x \ L(z,w,u) = y. x \ L(x,y,z) = a(z,y,x) \ 1. a(x,y,z) \ 1 = z \ L(z,y,x). ((x \ y) * ((z \ 1) \ 1)) \ ((1 * x) \ (1 * y)) = ((1 / y) * x) \ (((1 / y) * x) / z). ((x \ y) * ((z \ 1) \ 1)) \ (x \ (1 * y)) = ((1 / y) * x) \ (((1 / y) * x) / z). ((x \ y) * ((z \ 1) \ 1)) \ (x \ y) = ((1 / y) * x) \ (((1 / y) * x) / z). (x \ y) * (((z \ 1) \ (x \ y)) \ 1) = ((1 / y) * x) \ (((1 / y) * x) / z). ((1 / x) * y) \ (((1 / x) * y) / z) = (y \ x) * (((z \ 1) \ (y \ x)) \ 1). ((1 / x) * y) \ (((1 / x) * y) / z) = (y \ x) * (((y \ x) \ 1) * (1 / z)). x != y * ((y \ 1) * z) | x = L(z,y,y). ((1 / x) * y) \ (((1 / x) * y) / z) = L(1 / z,y \ x,y \ x). (((x / y) \ z) \ y) * (((y * x) \ (y * z)) \ u) = (((y * z) \ (y * x)) * ((y * z) \ (y * x))) * u. (((x * y) \ (x * z)) * ((x * y) \ (x * z))) * u = (((z / x) \ y) \ x) * (((x * z) \ (x * y)) \ u). L(x,y,z) \ 1 = ((y / z) \ (y * x)) \ z. ((x / y) \ (x * z)) \ y = L(z,x,y) \ 1. x != ((y / z) \ (y * (1 / u))) \ z | x = L(R(u,y \ 1,y / z),y,y). L(1 / x,y,z) \ 1 = L(R(x,y \ 1,y / z),y,y). L(R(x,y \ 1,y / z),y,y) = L(1 / x,y,z) \ 1. L(R(x,y \ 1,y / z),y,y) != u | L(x,y,z) = u. x * ((1 / T(y,x)) \ L(1 / T(y,x),z,u)) = L(y \ 1,z,u) * ((y \ 1) \ x). x * (T(y,x) / L(T(y,x),z,u)) = L(y \ 1,z,u) * ((y \ 1) \ x). L(x \ 1,y,z) * ((x \ 1) \ u) = u * (T(x,u) / L(T(x,u),y,z)). L(x \ 1,y,z) * ((x \ 1) \ u) = u * (L(T(x,u),y,z) \ T(x,u)). T(L(x,y,z) \ x,u) = L(T(x,u),y,z) \ T(x,u). L(T(x,y),z,u) \ T(x,y) = T(L(x,z,u) \ x,y). a(T(x,y),z,u) = T(L(x,u,z) \ x,y). T(L(x,y,z) \ x,u) = a(T(x,u),z,y). T(a(x,y,z),u) = a(T(x,u),y,z). a(T(x,y),z,u) = T(a(x,z,u),y). K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,z / (z * u))). K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,z \ (u \ z))). x != K(y,z \ T(u,w \ (v5 \ w))) | x = K(y,z \ T(u,T(v5,w))). K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,T(u,z))). x != K(y,(z * K(u \ 1,w)) \ v5) | x = K(y,(z * K(w,u)) \ v5). K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(z * u,u)) \ T(y,T(u,z))). K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(z,u)) \ T(y,T(u,z))). K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,T(z,u) \ T(y,T(u,z))). x != K(y,T(z,u) \ T(w,T(u,z))) | x = K(y,T(w / z,u \ z)). K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,T(y / z,u \ z)). K(x,T(y / z,T(z * u,(z * u) \ z))) = K(x,T(y / z,u \ z)). K(x,T(y / z,T(z * u,z))) = K(x,T(y / z,u \ z)). K(x,T(y / z,u * z)) = K(x,T(y / z,u \ z)). K(x,T(y / z,u \ z)) = K(x,T(y / z,u * z)). K(x,T(y,z \ u)) = K(x,T((y * u) / u,z * u)). K(x,T((y * z) / z,u * z)) = K(x,T(y,u \ z)). K(x,T(y / z,u)) = K(x,T(y / z,(z / u) * z)). K(x,T(y / z,(z / u) * z)) = K(x,T(y / z,u)). K(x,T(y,z * u)) = K(x,T(y,z \ u)). K(x,T(y,z \ u)) = K(x,T(y,z * u)). K(x,T(y,z * (u \ z))) != w | K(x,T(y,T(u,z))) = w. K(x,T(y / z,z * (u \ z))) = K(x,T(y / z,u)). K(x,T(y / z,T(u,z))) = K(x,T(y / z,u)). K(x,T(y / z,u)) * K(z \ y,T(x,u)) = K(x,K(y,z)). K(x,K(y,T(z,u))) = K(z,K(x,y)). K(x,K(y,T(z,u))) = K(x,K(y,z)). x * K(y,K(z,u)) = K(y,K(z,u)) * x. K(x,K(y,z)) * u = u * K(x,K(y,z)). K(x,T(y,z)) * u = (K(x,y) * u) * K(x,K(y,z)). (K(x,y) * z) * K(x,K(y,u)) = K(x,T(y,u)) * z. T(x,K(y,K(z,u))) = x. K(x,K(y,z)) \ u = u * K(x,K(y,z)). K(x,K(y,z)) * (u * x) = u * T(x,K(y,z)). (K(x,K(y,z)) * (u * w)) \ ((K(x,K(y,z)) * u) * (L(w,u,K(x,K(y,z))) * v5)) = L(v5,L(w,u,K(x,K(y,z))),u * K(x,K(y,z))). T(x,K(y,z) * u) = T(x,u * K(y,z)). K(x,T(y,K(z,u))) = K(x,y). x != T(y * (z \ 1),K(u,K(w,v5))) | x = (K(u,u \ K(w,v5)) * y) * (z \ K(u,u \ K(w,v5))). x * (y \ 1) = (K(z,z \ K(u,w)) * x) * (y \ K(z,z \ K(u,w))). (K(x,x \ K(y,z)) * u) * (w \ K(x,x \ K(y,z))) = u * (w \ 1). x * K(y,K(z,u)) != w | K(y,K(z,u)) * x = w. x \ T(y * x,K(z,K(u,w))) = T(y,K(K(u,w),z) * x). K(x,K(y,z) * u) = K(x,u * K(y,z)). K(x,T(y,T(z,u))) = K(x,T(y,z)). K(x,T(y,z * u)) = K(x,T(y,u * z)). T(K(x,y),T(z,u)) = K(x,T(y,z)). T(K(x,y) * z,u) * K(y,T(x,w)) = K(y,T(x,w)) * T(z * K(x,y),u). ((1 / K(x,K(y,z))) * u) * w = u * (w * K(x,K(y,z))). x != (y \ 1) * K(z,u) | x = y \ K(z,u). K(x,K(y,z)) \ (u \ 1) = u \ K(x,K(y,z)). T(x * T(y,K(z,u)),K(z,u)) = y * T(x,y * K(z,u)). K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y,z))). (x * y) * K(z,T(u,y * x)) = K(z,u) * (x * y). K(1 / x,K(y,z)) * (u * ((w \ x) * (1 / x))) = ((w / u) \ x) * T(1 / x,K(y,z)). x * (K(y,K(z,u)) * (w \ K(y,K(z,u)))) = x * (w \ 1). x \ (y * x) = T(y,K(K(z,u),w) * x). T(x,K(K(y,z),u) * w) = w \ (x * w). T(x,K(K(y,z),u) * w) = T(x,w). x != T(y,K(K(z,u),w) * v5) | x = T(y,K(w,w \ K(u,z)) * v5). T(x,y) = T(x,K(z,z \ K(u,w)) * y). T(x,K(y,y \ K(z,u)) * w) = T(x,w). T(x,y) = T(x,y * K(z,K(u,w))). T(x,y * K(z,K(u,w))) = T(x,y). K(x * K(y,K(z,u)),w) = w / T(w,x). K(x * K(y,K(z,u)),w) = K(x,w). K(x * K(y,K(z,u)),w) != v5 | K(x,w) = v5. K(x \ T(y,K(z,u)),w) = K(x \ y,w). T(x * K(y,K(z,u)),w) = K(x,w) * (x * K(y,K(z,u))). K(x,y) * (x * K(z,K(u,w))) = T(x * K(z,K(u,w)),y). x != K(y \ T(z * T(y * K(u,w),K(v5,v6)),K(v5,v6)),w) | x = K(z,T(w,K(v5,v6) * y)). K(x \ (y * T(x * K(z,u),K(w,v5))),u) = K(y,T(u,K(w,v5) * x)). ((1 * K(x,K(y,z))) * u) * w = u * (w * K(x,K(y,z))). T(x * T(y,x * K(z,u)),K(z,u)) = y * T(x,K(z,u)). T(x,y) * K(z,K(u,w)) = T(x * K(z,K(u,w)),y). T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u)). T(x * K(y,K(z,u)),w) / K(y,z) = T(x,w) / T(K(y,z),u). (K(x,K(y,z)) * u) * w = u * (w * K(x,K(y,z))). (x * K(y,K(z,u))) * w = x * (w * K(y,K(z,u))). (x * K(y,K(z,u))) * w = x * (K(y,K(z,u)) * w). x * (y * K(z,K(u,w))) = (x * y) * K(z,K(u,w)). (x * y) * K(z,K(u,w)) = x * (y * K(z,K(u,w))). K(x,K(y,z)) * (u * w) = u * (w * K(x,K(y,z))). L(K(x,K(y,z)),u,w) = K(x,K(y,z)). (x * (y * K(z,K(u,w)))) * v5 != (x * y) * K(z,K(u,w)) | 1 = v5. 1 = a(x,y,K(z,K(u,w))). a(x,y,K(z,K(u,w))) = 1. x != a(y,z,K(u,w)) | x = K(y,a(w,z,u)). 1 = K(x,a(K(y,z),u,w)). K(x,a(K(y,z),u,w)) = 1. T(x,a(K(y,z),u,w)) = x. T(a(x,y,K(z,u)),w) = a(x,y,K(z,u)). T(x,K(y,a(z,u,w))) = x. T(x,T(a(y,z,u),w)) = T(x,a(y,z,u)). T(x,K(a(y,z,u),w)) != v5 | v5 = x. T(x,a(y,z,K(u,w))) != v5 | v5 = x. T(x,T(a(y,z,u) \ 1,w)) = T(x,a(u,z,y)). K(x,K(y,z)) * (u * w) = (K(x,K(y,z)) * u) * w. (K(x,K(y,z)) * u) * w = K(x,K(y,z)) * (u * w). x != T(a(y,z,K(u,w)),v5) | x = a(y,z,K(u,T(w,v5))). a(x,y,K(z,u)) = a(x,y,K(z,T(u,w))). a(x,y,K(z,T(u,w))) = a(x,y,K(z,u)). x != T(y,T(a(z,u,w),v5)) | x = T(y,y * T(a(z,u,w),v5)). T(x,a(y,z,u)) = T(x,x * T(a(y,z,u),w)). T(x,x * T(a(y,z,u),w)) = T(x,a(y,z,u)). x != a(y,z,K(u,w)) | x = a(u,z,K(w,y)). a(x,y,K(z,T(u,w))) = a(z,y,K(u,x)). a(x,y,K(z,u \ w)) = a(x,y,K(z,w / u)). a(x,y,K(z,u / w)) = a(x,y,K(z,w \ u)). a(x,y,K(z \ u,w)) = a(x,y,K(u / z,w)). a(x,y,K(z / u,w)) = a(x,y,K(u \ z,w)). ((K(x,y) * z) * u) * a(x,z,K(y,u)) = (z * K(x,T(y,z))) * R(u,z,K(x,T(y,z))). T(T(x,a(y,z,u)),x * (1 * T(a(u,z,y),w))) = x. T(x,T(a(y,z,u) * x,w)) = T(x,a(y,z,u)). x != T(y,a(z,u,w)) | x = L(y,K(z,w),u). T(x,T(a(y,z,u) * x,w)) = L(x,K(y,u),z). K(x,K(y,z)) * (u * K(x,y)) = u * K(x,T(y,z)). K(x,K(y,z)) * (u * w) = u * (K(x,K(y,z)) * w). K(x,K(y,z)) * (u * (w * v5)) = u * (w * (v5 * K(x,K(y,z)))). L(x,y,K(z,K(u,w))) = x. L(x,K(y,K(z,u)) * w,v5) = (v5 * (K(y,K(z,u)) * w)) \ (v5 * (K(y,K(z,u)) * (w * x))). (x * (K(y,K(z,u)) * w)) \ (x * (K(y,K(z,u)) * (w * v5))) = L(v5,K(y,K(z,u)) * w,x). T(T(x,a(y,z,u)),x * T(a(u,z,y),w)) = x. T(L(x,K(y,z),u),x * T(a(z,u,y),w)) = x. x = L(T(x,x * T(a(y,z,u),w)),K(u,y),z). L(T(x,x * T(a(y,z,u),w)),K(u,y),z) = x. L(T(x,T(a(y,z,u) * x,w)),K(u,y),z) = x. L(L(x,K(y,z),u),K(z,y),u) = x. K(x,K(y,z)) \ (u * w) = u * (K(x,K(y,z)) * w). K(x,K(y,z)) * (u * (1 / w)) = u * (K(x,K(y,z)) / w). K(x,K(y,z)) * (u * (w * (1 / v5))) = u * (w * (K(x,K(y,z)) / v5)). K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y \ 1,z))). T(K(x,T(y,z)) * u,w) / K(x,y) = T(K(x,y) * u,w) / T(K(x,y),z). (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) != v6 | L(L(v5,w,u),u * w,K(x,K(y,z))) = v6. x != K(y,K(z,L(u,w,v5)) * (v5 * w)) | x = K(y,v5 * (w * K(z,u))). K(x,y * (z * K(u \ 1,w))) = K(x,y * (z * K(u,w))). x != K(y,z * (u * K(u \ 1,w))) | x = K(y,z * (((w * (u \ 1)) / w) \ 1)). K(x,y * (z * K(z,u))) = K(x,y * (((u * (z \ 1)) / u) \ 1)). K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u,z))). K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * T(u,z)). K(x,y / ((z * (u \ 1)) / z)) = K(x,y * T(u,z)). K(x,y / T(z \ 1,u)) = K(x,y * T(z,u)). K(x,y * z) = K(x,z * T(y,y * (x * z))). K(x,y * T(z,z * (x * y))) = K(x,z * y). K(x,y * T(z,x * y)) = K(x,z * y). T(x,y * T(z,x * y)) = K(x,z * y) * x. T(x,y * T(z,x * y)) = T(x,z * y). x != T(y,K(z,u) * w) | x = w \ T(y * T(w,K(z,u)),K(u,z)). T(x,y * K(z,u)) = T(y,x * K(z,u)) \ T(x * T(T(y,x * K(z,u)),K(z,u)),K(u,z)). T(x,y * K(z,u)) \ T(y * T(T(x,y * K(z,u)),K(z,u)),K(u,z)) = T(y,x * K(z,u)). x != (y * z) * (u \ y) | x = y * ((u / z) \ y). x * (y \ 1) = K(z,z \ K(u,w)) * ((y / x) \ K(z,z \ K(u,w))). K(x,x \ K(y,z)) * ((u / w) \ K(x,x \ K(y,z))) = w * (u \ 1). x != K(y \ (z * T(y * K(u,w),v5)),w) | x = K(z * K(y * K(u,w),v5),T(w,y)). K(x,T(y,K(z,u) * w)) = K(x * K(w * K(v5,y),K(z,u)),T(y,w)). K(x * K(y * K(z,u),K(w,v5)),T(u,y)) = K(x,T(u,K(w,v5) * y)). K(x,T(y,z)) = K(x,T(y,K(u,w) * z)). K(x,T(y,K(z,u) * w)) = K(x,T(y,w)). (x * K(y,z)) * K(u,T(w,x)) = K(u,w) * (x * K(y,z)). (x * K(y,z)) * K(u,w) = K(u,T(w,x)) * (x * K(y,z)). K(x,T(y,z)) * (z * K(u,w)) = (z * K(u,w)) * K(x,y). K(x,y) * z != K(x,T(y,u)) * (u * K(w,v5)) | T(u * K(w,v5),K(x,y)) = z. T(x * K(y,z),K(u,w)) = K(u,K(w,x)) * (x * K(y,z)). K(x,K(y,z)) * (z * K(u,w)) = T(z * K(u,w),K(x,y)). T(x,K(y,z)) * K(u,w) = T(x * K(u,w),K(y,z)). T(x * K(y,z),K(u,w)) = T(x,K(u,w)) * K(y,z). K(x,y) * T(z,K(u,w)) = T(K(x,y) * z,K(u,w)). T(K(x,y) * z,K(u,w)) = K(x,y) * T(z,K(u,w)). K(x,y) * T(K(x,y) * z,K(u,w)) = y * (T(T(y,x),x) \ T(z,K(u,w))). T(K(x,T(y,z)) * u,w) * K(y,x) = T(K(x,y) * u,w) / T(K(x,y),z). T(K(x,y) * z,u) / T(K(x,y),w) = T(K(x,T(y,w)) * z,u) * K(y,x). x != K(y,z) * T(u,K(w,v5)) | x = T(K(y,z) * u,K(w,v5)). x * (T(T(x,y),y) \ T(z,K(u,w))) = T(K(y,x) * (K(y,x) * z),K(u,w)). T(K(x,y) * (K(x,y) * z),K(u,w)) = y * (T(T(y,x),x) \ T(z,K(u,w))). T(K(x,y) * z,u) / K(x,T(y,w)) = T(K(x,T(y,w)) * z,u) * K(y,x). T(x * (T(T(x,y),y) \ z),K(u,w)) = x * (T(T(x,y),y) \ T(z,K(u,w))). T(K(x,y) * z,u) * K(y,T(x,w)) = T(K(x,T(y,w)) * z,u) * K(y,x). T(K(x,T(y,z)) * u,w) * K(y,x) = T(K(x,y) * u,w) * K(y,T(x,z)). x != y * (T(T(y,z),z) \ T(u,K(y,z))) | x = K(z,z \ y) * (u * K(z,z \ y)). T(x * (T(T(x,y),y) \ z),K(x,y)) = K(y,y \ x) * (z * K(y,y \ x)). x != T(K(y,T(z,u)) * w,v5) * K(z,y) | x = K(y,z) \ T((K(y,K(z,u)) * w) * K(y,z),v5). T(K(x,y) * z,u) * K(y,T(x,w)) = K(x,y) \ T((K(x,K(y,w)) * z) * K(x,y),u). K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = T(K(x,y) * u,w) * K(y,T(x,z)). x != T(y * (T(T(y,z),z) \ u),K(y,z)) | x = K(z,y) * (u * K(z,y)). K(x,x \ y) * (z * K(x,x \ y)) = K(x,y) * (z * K(x,y)). x != y * ((z \ 1) * y) | x = (y \ 1) \ (z \ y). K(x,x \ y) * ((z \ 1) * K(x,x \ y)) = (K(x,y) \ 1) \ (z \ K(x,y)). K(x,x \ y) * (z \ K(x,x \ y)) = (K(x,y) \ 1) \ (z \ K(x,y)). x != (K(y,z) \ 1) \ u | x = K(y,z) * u. K(x,x \ y) * (z \ K(x,x \ y)) = K(x,y) * (z \ K(x,y)). K(x,K(y,z)) * (u * ((w \ x) * (1 / x))) = ((w / u) \ x) * T(1 / x,K(y,z)). x != (y \ z) * T(1 / z,u) | x = y \ K(z \ u,z). K(x,K(y,z)) * (u * ((w \ x) * (1 / x))) = (w / u) \ K(x \ K(y,z),x). K(x,K(y,z)) * (u * ((w \ x) * (1 / x))) = (w / u) \ K(x,x \ K(y,z)). x != K(y,K(z,u)) * (w * (v5 * (1 / v6))) | x = w * (v5 * (K(y,K(z,u)) / v6)). (x / y) \ K(z,z \ K(u,w)) = y * ((x \ z) * (K(z,K(u,w)) / z)). x * ((y \ z) * (K(z,K(u,w)) / z)) = (y / x) \ K(z,z \ K(u,w)). x * (y \ K(z,z \ K(u,w))) = (y / x) \ K(z,z \ K(u,w)). (x / y) \ K(z,z \ K(u,w)) = y * (x \ K(z,z \ K(u,w))). (x * y) * K(z,z \ K(u,w)) = x * ((1 / y) \ K(z,z \ K(u,w))). x * ((1 / y) \ K(z,z \ K(u,w))) = (x * y) * K(z,z \ K(u,w)). x != T(y,z \ u) * (u \ z) | x = ((1 / z) * u) \ y. (x / T(y,K(z,z \ K(u,w)) \ x)) \ K(z,z \ K(u,w)) = ((1 / K(z,z \ K(u,w))) * x) \ y. T(x / y,x) \ K(z,z \ K(u,w)) = T(y,x) * (x \ K(z,z \ K(u,w))). ((((K(x,x \ K(y,z)) \ 1) \ 1) \ (u / w)) \ v5) * (((u / w) \ 1) * K(x,x \ K(y,z))) = (w * (u \ K(x,x \ K(y,z)))) * (v5 * ((u / w) \ K(x,x \ K(y,z)))). ((((K(x,x \ K(y,z)) \ 1) \ 1) \ u) \ w) * ((u \ 1) * K(x,x \ K(y,z))) = (u \ K(x,x \ K(y,z))) * ((u / w) \ K(x,x \ K(y,z))). K(x,x \ K(y,z)) * (u * (w \ K(x,x \ K(y,z)))) = u * (w \ 1). K(x,x \ K(y,z)) * (u * w) = (K(x,x \ K(y,z)) * u) * w. (K(x,x \ K(y,z)) * u) * w = K(x,x \ K(y,z)) * (u * w). x * (y * K(z,z \ K(u,w))) = (x * y) * K(z,z \ K(u,w)). (x * y) * K(z,z \ K(u,w)) = x * (y * K(z,z \ K(u,w))). x * (K(y,y \ K(z,u)) * w) = (x * K(y,y \ K(z,u))) * w. (x * K(y,y \ K(z,u))) * w = x * (K(y,y \ K(z,u)) * w). T(x,y) * (y \ K(z,z \ K(u,w))) != v5 | (y \ x) * K(z,z \ K(u,w)) = v5. x != ((K(y,z) * u) * w) * a(y,u,K(z,w)) | x = K(y,z) * (u * w). (x * K(y,T(z,x))) * R(u,x,K(y,T(z,x))) = K(y,z) * (x * u). (K(x,y) * z) * R(u,z,K(x,T(y,z))) = K(x,y) * (z * u). (K(x,y) * z) * R(u,z,K(x,y)) = K(x,y) * (z * u). L(x,y,K(z,u)) = R(x,y,K(z,u)). R(x,y,K(z,u)) = L(x,y,K(z,u)). x != R(y,z,K(u,w \ (u \ 1))) | x = (T(u,w) * (1 / ((y * z) * u))) \ (T(u,w) * (1 / (z * u))). L(x,y,K(z,u \ (z \ 1))) = (T(z,u) * (1 / ((x * y) * z))) \ (T(z,u) * (1 / (y * z))). (T(x,y) * (1 / ((z * u) * x))) \ (T(x,y) * (1 / (u * x))) = L(z,u,K(x,y \ (x \ 1))). L(x,y,K(z,u)) * (y * K(z,u)) = (x * y) * K(z,u). K(x,y) \ T(K(x,K(y,z)) * (u * K(x,y)),w) = T(K(x,y) * u,w) * K(y,T(x,z)). K(x,y) \ T(z * K(x,T(y,u)),w) = T(K(x,y) * z,w) * K(y,T(x,u)). K(x,y) * T(z * K(y,T(x,u)),w) = T(K(y,x) * z,w) * K(x,T(y,u)). T(K(x,y) * z,u) * K(y,T(x,w)) = K(y,x) * T(z * K(x,T(y,w)),u). x != T(K(y,z) * u,w) * K(z,T(y,v5)) | x = K(z,T(y,v5)) * T(u * K(y,z),w). K(x,y) * T(z * K(y,T(x,u)),w) = K(x,T(y,u)) * T(z * K(y,x),w). K(x,T(y,z)) * T(u * K(y,x),w) = K(x,y) * T(u * K(y,T(x,z)),w). (K(x,K(y,z)) \ (u * w)) \ (u * (K(x,K(y,z)) * (w * v5))) = L(v5,K(x,K(y,z)) * w,u). ((x \ 1) * (1 / ((y * z) * (T(x,u) \ 1)))) \ (T(T(x,u) \ 1,u \ 1) * (1 / (z * (T(x,u) \ 1)))) = L(y,z,K(T(x,u) \ 1,(u \ 1) \ ((T(x,u) \ 1) \ 1))). (K(x,K(y,z)) \ (u * w)) \ (K(x,K(y,z)) \ (u * (w * v5))) = L(v5,K(x,K(y,z)) * w,u). x != (K(y,z) \ (u * w)) \ (K(y,z) \ (u * (w * v5))) | x = L(L(v5,w,u),u * w,K(z,y)). L(x,K(y,K(z,u)) * w,v5) = L(L(x,w,v5),v5 * w,K(K(z,u),y)). L(L(x,y,z),z * y,K(K(u,w),v5)) = L(x,K(v5,K(u,w)) * y,z). L(L(x,y,z),z * y,K(u,K(w,v5))) = L(x,K(v5,K(u,w)) * y,z). x != L(y,z,K(u,K(w,v5))) | x = y. L(x,K(y,K(z,u)) * w,v5) = L(x,w,v5). x != y | x = L(y,z,K(u,K(w,v5))). L(x,K(y,K(z,u)) * w,v5) = L(L(x,w,v5),v6,K(v7,K(v8,v9))). L(L(x,y,z),u,K(w,K(v5,v6))) = L(x,K(v7,K(v8,v9)) * y,z). L(x,y * K(z,u),w) = L(x,K(z,u) * y,w). L(x,K(y,z) * u,w) = L(x,u * K(y,z),w). L(x,K(y,K(z,u)) * w,v5) != v6 | v6 = L(x,w,v5). L(x,K(y,K(z,u)) * w,v5) != v6 | L(x,w,v5) = v6. L(x,K(y,T(z,u)),w) != v5 | L(x,K(y,z),w) = v5. L(x,K(y,z / u),w) != v5 | L(x,K(y,u \ z),w) = v5. T(x,y * K(z,u)) \ T(y * T(T(x,K(z,u)),y * K(z,u)),K(u,z)) = T(y,x * K(z,u)). T(x,y * K(z,u)) \ T(y * T(T(x,K(z,u)),y * K(z,u)),K(z,u)) = T(y,x * K(z,u)). T(x,y * K(z,u)) \ (T(x,K(z,u)) * T(y,K(z,u))) = T(y,x * K(z,u)). x != T(y,z) \ (T(y,u) * w) | x = K(y,u) * (K(z,y) * w). T(x,y * K(z,u)) = K(y,K(z,u)) * (K(x * K(z,u),y) * T(x,K(z,u))). K(x,K(y,z)) * (K(u * K(y,z),x) * T(u,K(y,z))) = T(u,x * K(y,z)). K(x,K(y,z)) * T(K(u * K(y,z),x) * u,K(y,z)) = T(u,x * K(y,z)). K(x,K(y,z)) * T(u * K(K(y,z) * u,x),K(y,z)) = T(u,x * K(y,z)). K(x,K(y,z)) * (K(y,z) \ T(u * K(y,z),x)) = T(u,x * K(y,z)). K(x,K(y,z)) * (K(z,y) * T(u * K(y,z),x)) = T(u,x * K(y,z)). K(x,T(y,z)) * T(u * K(y,x),z) = T(u,z * K(y,x)). x != K(y,T(z,u)) * T(w * K(z,y),v5) | x = K(y,z) * T(w * K(z,T(y,u)),v5). T(x,y * K(z,u)) = K(u,z) * T(x * K(z,T(u,y)),y). K(x,y) * T(z * K(y,T(x,u)),u) = T(z,u * K(y,x)). K(x,y) * T(z,u * K(x,y)) = T(z * K(x,T(y,u)),u). T(x * K(y,T(z,u)),u) = K(y,z) * T(x,u * K(y,z)). R(x,K(y,z),u) = (u * (x * K(y,z))) / T(u * K(y,T(z,x)),x). (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) = R(y,K(z,u),x). x != (y * (z * K(u,w))) / T(y * K(u,T(w,z)),z) | x = L(z,K(u,T(w,z)),y). R(x,K(y,z),u) = L(x,K(y,T(z,x)),u). L(x,K(y,T(z,x)),u) = R(x,K(y,z),u). L(x,K(y,z),u) = R(x,K(y,z),u). R(x,K(y,z),u) = L(x,K(y,z),u). x != R(y,K(z,u),1 / w) | x = ((y * K(z,u)) * (1 / w)) / (K(z,u) / w). L(x,K(y,z),1 / u) = ((x * K(y,z)) * (1 / u)) / (K(y,z) / u). ((x * K(y,z)) * (1 / u)) / (K(y,z) / u) = L(x,K(y,z),1 / u). x != L(y,z,1 / u) | x = L(y,z,u \ 1). ((x * K(y,z)) * (1 / u)) / (K(y,z) / u) = L(x,K(y,z),u \ 1). x != (y * (1 / z)) / (u / z) | x = (y / (z * u)) * z. L(x,K(y,z),u \ 1) = ((x * K(y,z)) / (u * K(y,z))) * u. ((x * K(y,z)) / (u * K(y,z))) * u = L(x,K(y,z),u \ 1). ((K(x,y) / z) \ (K(x,y) / u)) * u = L(z,K(y,x),u \ 1). ((x / (K(y,z) * u)) * K(y,z)) * u = L(x,K(z,y),u \ 1). (K(x,y) * ((K(y,x) * z) / u)) * u = L(z,K(x,y),u \ 1). L(x,K(y,z),u * K(z,y)) = L(x,K(z,y),u \ 1). x != (K(y,z) * ((K(u,w) * v5) / v6)) * v6 | x = (K(y,z) / v6) * (v6 / (v5 \ K(w,u))). L(x,K(y,z),u \ 1) = (K(y,z) / u) * (u / (x \ K(y,z))). (K(x,y) / z) * (z / (u \ K(x,y))) = L(u,K(x,y),z \ 1). x != L(y,z,(u \ 1) \ 1) | x = L(y,z,u). L(x,K(y,z),(u \ 1) * K(z,y)) = L(x,K(z,y),u). x != L(y,z,(u \ 1) * w) | x = L(y,z,u \ w). L(x,K(y,z),u) = L(x,K(z,y),u \ K(y,z)). L(x,K(y,z),u \ K(z,y)) = L(x,K(z,y),u). L(x,K(y,z),y \ (u \ K(z,y))) = L(x,K(z,y),u * y). x * y != L(z,K(u \ w,w \ u),v5) | x \ z = y. (K(x \ y,y \ x) / z) \ u = z / (u \ K(x \ y,y \ x)). x / (y \ K(z \ u,u \ z)) = (K(z \ u,u \ z) / x) \ y. x != y / ((z * u) \ K(w \ v5,v5 \ w)) | x = (1 / y) \ (z * (u * K(w \ v5,v5 \ w))). (K(x \ y,y \ x) / z) \ (u * w) = (1 / z) \ (u * (w * K(x \ y,y \ x))). (1 / x) \ (y * (z * K(u \ w,w \ u))) = (K(u \ w,w \ u) / x) \ (y * z). x != (1 / T(y,z \ (u \ 1))) \ (u * (z * K(w \ v5,v5 \ w))) | x = (u * (z * K(w \ v5,v5 \ w))) * y. (K(x \ y,y \ x) / T(z,u \ (w \ 1))) \ (w * u) = (w * (u * K(x \ y,y \ x))) * z. x != (K(y \ z,z \ y) / T(u,w \ (v5 \ 1))) \ (v5 * w) | x = ((v5 * w) * u) * K(y \ z,z \ y). (x * (y * K(z \ u,u \ z))) * w = ((x * y) * w) * K(z \ u,u \ z). ((x * y) * z) * K(u \ w,w \ u) = (x * (y * K(u \ w,w \ u))) * z. (x * (y * K(z \ u,u \ z))) * w = (x * y) * (w * K(z \ u,u \ z)). x * (1 / ((y * z) * (x * K(u \ w,w \ u)))) = K(x \ (u * w),(u * w) \ x) / (y * z). x * ((K(y \ z,z \ y) / x) / (u * w)) = K(x \ (z * y),(z * y) \ x) / (u * w). K(x \ (y * z),(y * z) \ x) / (u * w) = x * ((K(z \ y,y \ z) / x) / (u * w)). K(x \ (y * z),(y * z) \ x) / (u * w) = x * (K(z \ y,y \ z) / ((u * w) * x)). x != K(y \ (z * u),(z * u) \ y) / (w * u) | x = u \ (K(z \ y,y \ z) / w). x * (K(y \ z,z \ y) / ((u * y) * x)) = y \ (K(z \ x,x \ z) / u). (x * (K(y \ z,z \ y) / ((u * w) * x))) * u = K((x / z) \ y,y \ (x / z)) / w. x != (y * (K(z \ u,u \ z) / (w * y))) * v5 | x = y * (K(u \ z,z \ u) / ((v5 \ w) * y)). K((x / y) \ z,z \ (x / y)) / u = x * (K(y \ z,z \ y) / ((w \ (w * u)) * x)). x * (K(y \ z,z \ y) / ((u \ (u * w)) * x)) = K((x / y) \ z,z \ (x / y)) / w. x * (K(y \ z,z \ y) / (u * x)) = K((x / y) \ z,z \ (x / y)) / u. K((x / y) \ z,z \ (x / y)) / u = x * (K(y \ z,z \ y) / (u * x)). K(x \ (y * z),(y * z) \ x) / u = x * (K(y \ z,z \ y) / (u * x)). x != K(y \ (z * (u / y)),(z * (u / y)) \ y) / w | x = (y \ ((u / y) \ z)) * ((y \ ((y / z) * u)) / w). x * (K(y \ (z / x),(z / x) \ y) / (u * x)) = (x \ ((z / x) \ y)) * ((x \ ((x / y) * z)) / u). (x \ ((y / x) \ z)) * ((x \ ((x / z) * y)) / u) = x * (K(z \ (y / x),(y / x) \ z) / (u * x)). (x / T(y,K(z \ K(u,w),z) * x)) \ K(z,z \ K(u,w)) = ((1 / K(z,z \ K(u,w))) * x) \ y. (x \ ((y / x) \ z)) * ((x \ ((x / z) * y)) / u) = x * (K(z \ (x * y),(x * y) \ z) / (u * x)). (x / T(y,K(z,z \ K(u,w)) * x)) \ K(z,z \ K(u,w)) = ((1 / K(z,z \ K(u,w))) * x) \ y. (x \ ((y / x) \ z)) * ((x \ ((x / z) * y)) / u) = x * (z * (K(x \ y,y \ x) / ((u * x) * z))). x != (y / z) \ K(u,u \ K(w,v5)) | x = z * (y \ K(u,u \ K(w,v5))). ((1 / K(x,x \ K(y,z))) * u) \ w = T(w,K(x,x \ K(y,z)) * u) * (u \ K(x,x \ K(y,z))). T(x,K(y,y \ K(z,u)) * w) * (w \ K(y,y \ K(z,u))) = ((1 / K(y,y \ K(z,u))) * w) \ x. (x \ ((y / x) \ z)) * ((x \ ((x / z) * y)) / u) = x * (x \ (K(y \ z,z \ y) / u)). (x \ ((y / x) \ z)) * ((x \ ((x / z) * y)) / u) = K(y \ z,z \ y) / u. x != (y \ ((z / y) \ u)) * ((y \ ((y / u) * z)) / w) | x = K(y \ ((y / u) * z),y \ ((z / y) \ u)) / w. K(x \ y,y \ x) / z = K(u \ ((u / y) * x),u \ ((x / u) \ y)) / z. K(x \ ((x / y) * z),x \ ((z / x) \ y)) / u = K(z \ y,y \ z) / u. x != K(y \ ((y / z) * u),y \ ((u / y) \ z)) / (y \ ((y / z) * u)) | x = T((y \ ((y / z) * u)) \ 1,1). K(x \ y,y \ x) / (z \ ((z / y) * x)) = T((z \ ((z / y) * x)) \ 1,1). x != K(y \ z,z \ y) / (u \ w) | x = (K(y \ z,z \ y) / w) * u. T((x \ ((x / y) * z)) \ 1,1) = (K(z \ y,y \ z) / ((x / y) * z)) * x. (K(x \ y,y \ x) / ((z / y) * x)) * z = T((z \ ((z / y) * x)) \ 1,1). (x \ (y * (1 / ((z / y) * y)))) * z = T((z \ ((z / y) * x)) \ 1,1). (x \ (y * (1 / z))) * z = T((z \ ((z / y) * x)) \ 1,1). T((x \ ((x / y) * z)) \ 1,1) = (z \ (y * (1 / x))) * x. T(x \ ((y / x) \ z),1) = (y \ (z * (1 / x))) * x. (x \ (y * (1 / z))) * z = z \ ((x / z) \ y). (x \ ((y / x) \ z)) \ 1 = x \ ((y \ (z * (1 / x))) \ 1). x \ ((y \ (z * (1 / x))) \ 1) = (x \ ((y / x) \ z)) \ 1. (x / ((1 / y) \ z)) * y = y \ (((1 / x) / y) \ (1 / z)). x \ (((1 / y) / x) \ (1 / z)) = (y / ((1 / x) \ z)) * x. x * (x \ ((y / x) \ (y / z))) = y \ ((y * x) / z). x \ ((x * y) / z) = (x / y) \ (x / z). (x / y) \ (x / z) = x \ ((x * y) / z). x != (y / (z * u)) \ (y / u) | x = R(z,u,y \ 1). x \ ((x * (y * z)) / z) = R(y,z,x \ 1). L(R(x,1 / y,z),1 / y,1 / y) = ((1 \ ((1 * x) / y)) * z) / ((1 / y) * z). ((x / y) / z) \ (x / u) = x \ ((x * (x \ ((x * z) * y))) / u). x \ ((x * (x \ ((x * y) * z))) / u) = ((x / z) / y) \ (x / u). x \ (y / (z \ (x \ y))) = R(z,y,x \ 1). x != y \ (z / (u \ (y \ z))) | x = (z * ((z \ u) / y)) * y. R(x,y,z \ 1) = (y * ((y \ x) / z)) * z. (x * ((x \ y) / z)) * z = R(y,x,z \ 1). x \ ((x * (1 / (y / z))) / (z * (1 / (y * z)))) = R(z,u * (1 / (y * u)),x \ 1). R(x,y * (1 / (z * y)),u \ 1) = u \ ((u * (1 / (z / x))) / (x * (1 / (z * x)))). (x \ 1) \ ((x \ y) * (y \ z)) = R(z,y,(x \ 1) \ 1). x != (y \ 1) \ ((y \ z) * u) | x = (z * y) * (y \ u). R(x,y,(z \ 1) \ 1) = (y * z) * (z \ (y \ x)). (x * y) * (y \ (x \ z)) = R(z,x,(y \ 1) \ 1). x != (y * z) * (z \ (y \ u)) | x = R(1 / u,y,z) \ 1. R(x,y,(z \ 1) \ 1) = R(1 / x,y,z) \ 1. R(x,y,z) = R(1 / x,y,z) \ 1. R(1 / x,y,z) \ 1 = R(x,y,z). R(1 / x,y,z) \ 1 != u | R(x,y,z) = u. x != R(1 / y,z,z \ (u \ 1)) \ 1 | x = (u * (z \ 1)) \ (u * (z \ y)). R(x,y,y \ (z \ 1)) = (z * (y \ 1)) \ (z * (y \ x)). (x * (y \ 1)) \ (x * (y \ z)) = R(z,y,y \ (x \ 1)). L(a(x,y,z),u \ 1,w) = R(a(x,y,z),u,u \ (w \ 1)). R(a(x,y,z),u,u \ (w \ 1)) = L(a(x,y,z),u \ 1,w). ((x \ ((y / x) \ z)) \ 1) * (z * (x \ ((y \ (z * (1 / x))) \ 1))) = (z \ (y * (y / x))) * x. x \ ((1 / (x * y)) \ (1 / z)) = (y / ((1 / x) \ z)) * x. x \ ((x * y) / z) = (y / ((1 / x) \ z)) * x. (x / ((1 / y) \ z)) * y = y \ ((y * x) / z). L(x,y,y) * ((y \ ((y * z) / x)) * L(x,y,y)) = y \ ((y * L(x,y,y)) * z). x \ (((x * y) * z) / u) = ((x / z) / y) \ (x / u). ((x / y) / z) \ (x / u) = x \ (((x * z) * y) / u). x != ((y / z) / u) \ (y / (u * z)) | x = a(u,z,y \ 1) \ 1. x \ (((x * y) * z) / (y * z)) = a(y,z,x \ 1) \ 1. x \ R(x,y,z) = a(y,z,x \ 1) \ 1. a(x,y,z \ 1) \ 1 = z \ R(z,x,y). a(x \ 1,y,z \ 1) = z \ R(z,x,y). a(x \ 1,y,(1 / z) \ 1) \ z = R(1 / z,x,y) \ 1. a(x \ 1,y,z) \ z = R(1 / z,x,y) \ 1. R(1 / x,y,z) \ 1 = a(y \ 1,z,x) \ x. x != a(y \ 1,z,u) \ w | x = a(y,z,u) * w. R(1 / x,y,z) \ 1 = a(y,z,x) * x. x != a(y,z,u) * u | x = u * a(y,z,u). R(1 / x,y,z) \ 1 = x * a(y,z,x). R(x,y,z) = x * a(y,z,x). x != L(y,z,z) * (u * L(y,z,z)) | x = y * (u * y). x \ ((x * L(y,x,x)) * z) = y * ((x \ ((x * z) / y)) * y). x != y * ((z \ (u / y)) * y) | x = (z / y) \ L(u,y,y). x \ ((x * L(y,x,x)) * z) = (x / y) \ L(x * z,y,y). (x / y) \ L(x * z,y,y) = x \ ((x * L(y,x,x)) * z). (x / y) \ L(x * z,y,y) = x \ (((1 / x) \ y) * z). x != y \ (((1 / y) \ z) * u) | x = (z * (u / y)) * y. (x / y) \ L(x * z,y,y) = (y * (z / x)) * x. L(x,y \ 1,L(z,y,y)) = (y * ((y \ x) / z)) * z. x != (y * ((y \ z) / u)) * u | x = R(z,y,u \ 1). L(x,y \ 1,L(z,y,y)) = R(x,y,z \ 1). x != L(y,z,L(u,w,w)) | x = L(y,z,u). R(x,y,z \ 1) = L(x,y \ 1,z). L(R(x,y,z \ 1),z / y,K(z,u)) = L(x,y \ 1,L(T(z,u),y,y)). R(x,y,z) = L(x,y \ 1,z \ 1). x != L(y,z \ 1,L(u,z,z)) | x = R(y,z,u \ 1). L(R(x,y,z \ 1),z / y,K(z,u)) = R(x,y,T(z,u) \ 1). L(L(x,y \ 1,z),z / y,K(z,u)) = R(x,y,T(z,u) \ 1). x != R(y,z,u \ 1) | x = L(y,z \ 1,u). L(L(x,y \ 1,z),z / y,K(z,u)) = L(x,y \ 1,T(z,u)). L(R(x,y \ 1,z),1 / y,1 / y) = ((1 \ ((1 * x) / y)) * z) / ((1 / y) * z). L(R(x,y \ 1,z),y,y) = ((1 \ ((1 * x) / y)) * z) / ((1 / y) * z). L(R(x,y \ 1,z),y,y) = ((1 \ (x / y)) * z) / ((1 / y) * z). L(R(x,y \ 1,z),y,y) = ((x / y) * z) / ((1 / y) * z). x != (y * z) / (u * z) | x = z / (u * (y \ z)). L(R(x,y \ 1,z),y,y) = z / ((1 / y) * ((x / y) \ z)). L(R(x,y \ 1,z),y,y) = z / ((y * x) \ (y * z)). x != y / ((z * u) \ (z * y)) | x = L(u,z,y \ (z \ 1)). L(R(x,y \ 1,z),y,y) = L(x,y,z \ (y \ 1)). L(x,y,z) = L(x,y,(y / z) \ (y \ 1)). L(x,y,(y / z) \ (y \ 1)) = L(x,y,z). L(x,y,z / (y * y)) = L(x,y,z). L(x,y,z \ 1) = L(x,z,y). x != L(y,z \ 1,u \ 1) | x = R(y,z,u). L(x,y,z \ 1) = R(x,z,y). R(x,y,z) = L(x,z,y \ 1). x != L(y,z * u,z \ 1) | x = L(y,z,z \ u). L(x,y,y * z) = L(x,y,y \ z). L(x,y,y \ z) = L(x,y,y * z). x != L(y \ z,y,u \ 1) | x = (y \ u) / (z \ u). L(x \ y,z,x) = (x \ z) / (y \ z). L(x,y \ 1,z) = L(x,z,y). L(x,y,z) = L(x,1 / z,y). L(x,1 / y,z) = L(x,z,y). R(x,y,z \ 1) = R(x,z,y). x != L(y,z,u \ 1) | x = L(y,u,z). R(x,y,z) = L(x,y,z). x != L(y,z,u \ 1) | x = R(y,u,z). L(x,y,z) = R(x,y,z). x / (y * z) = L((x / z) / y,y,z). L((x / y) / z,z,y) = x / (z * y). x != R(y,z,u) | x = y * a(z,u,y). L(x,y,z) = x * a(y,z,x). x != R(y,z,K(z,u) * w) | x = R(y,z,w). L(x,y,K(y,z) * u) = R(x,y,u). x != R(y,z,u) | x = u / (z * ((y * z) \ u)). L(x,y,z) = z / (y * ((x * y) \ z)). x * y != R(z,u,w) | x \ L(z,u,w) = y. x \ L(x,y,z) = a(y,z,x). a(x,y,z) = z \ L(z,x,y). L(x,y,z) * (y * z) = (x * y) * z. L(x,y,z) * (z * y) = (x * y) * T(z,y). x != L(y,z,u) | x = R(y,z,u). L(x,y \ 1,z) = R(x,z,y). R(x,y,z) = L(x,z \ 1,y). x != L(a(y,z,u),w \ 1,v5) | x = R(a(y,z,u),w,w \ (v5 \ 1)). L(a(x,y,z),u,w) = R(a(x,y,z),w,w \ (u \ 1)). R(a(x,y,z),u,u \ (w \ 1)) = L(a(x,y,z),w,u). x != L(y,z,(u \ w) \ w) | x = L(y,z,T(u,w)). L(x,(y \ z) \ z,u) = L(x,u \ 1,T(y,z)). L(x,y,z \ 1) != u | L(x,z,y) = u. L(x,L(y \ 1,z,u),w) = L(x,w,L(y,z,u)). R(x,y,z) = R(x,z \ 1,y). R(x,y \ 1,z) = R(x,z,y). x != y * a(z,u,y) | x = a(z,u,y) * y. L(x,y,z) = a(y,z,x) * x. x * y != L(x,z,u) | y = a(x \ 1,u,z). a(x,y,z) = a(z \ 1,y,x). a(x \ 1,y,z) = a(z,y,x). x != (y \ 1) \ L(y \ 1,z,u) | x = a(y,u,z). a(x,y,z \ 1) = a(z,y,x). x != y \ L(y,z,u) | x = a(y,u,z) \ 1. a(x,y,z) = a(z,y,x) \ 1. a(x,y,z) \ 1 = a(z,y,x). x != R(y,z \ 1,u) | x = u / ((y \ (u / z)) * z). R(x,y,z) = y / ((x \ (y / z)) * z). a(x \ 1,y,z) = a(x,z,y). x != a(y,z,u) \ 1 | x = u \ L(u,z,y). a(x,y,z) = x \ L(x,y,z). L(x,y,z) = x * a(x,y,z). x != a(y \ 1,z,u) | x = a(u,z,y). a(x,y,z) = a(y,z,x). a(x,y,z) = a(z,x,y). x != a(y \ 1,z,u) | x = a(y,z,u) \ 1. a(x,y,z) = a(x,z,y) \ 1. a(x,y,z) \ 1 = a(x,z,y). x / a(y,z,u) = x * a(y,u,z). L(x,y,z) = a(x,y,z) * x. x != a(T(y,z),u,w) | x = T(a(y,u,w),z). a(x,y,T(z,u)) = T(a(z,x,y),u). x != a(y,z,u) | x = L(y,u,z) \ y. a(x,y,z) = L(z,y,x) \ z. a(x,y,K(z,u)) = a(z,x,K(y,u)). a(x,y,K(z,u)) = a(u,x,K(z,y)). x != a(y,z,u) | x = a(u,z,y \ 1). a(x,y,z) = a(x,z,y \ 1). a(x,y,z \ 1) = a(x,z,y). x != y | x = y * 1. a(x,y,z) = a(y,z,x) * 1. a(x,y,z) * 1 = a(z,x,y). a(x,y,z) * x != u | L(x,y,z) = u. (x * y) * a(y,z,u) = x * L(y,z,u). a(x,y,z) * u = L(x,y,z) * (x \ u). L(x,y,z) * (x \ u) = a(x,y,z) * u. a(x,y,z) = x \ R(x,y,z). x != y * a(y,z,K(u,w)) | x = T(y,a(w,z,u)). L(x,y,K(z,u)) = T(x,a(u,y,z)). x * a(y,z,K(u,x)) = L(x,z,K(y,u)). (x * L(y,z,u)) * (y \ (x \ 1)) = L(T(a(y,z,u),y \ (x \ 1)),y,x). L(T(a(x,y,z),x \ (u \ 1)),x,u) = (u * L(x,y,z)) * (x \ (u \ 1)). a(x,y,z) \ 1 != u | a(x,z,y) = u. L(x,y,z) != u * x | a(x,y,z) = u. a(x,y,(z \ 1) * u) = a(x,u \ z,y). a(x,y,z) != u | u = a(y,z,x). a(x,y,z) != u | a(y,z,x) = u. a(x \ 1,y,z) != u | a(z,y,x) = u. L(x,y,z / y) = L(x,y,y * z). x != L((y \ 1) \ z,y,y \ u) | x = (((y * z) / (y * u)) * y) * u. L((x \ 1) \ y,x,x * z) = (((x * y) / (x * z)) * x) * z. (((x * y) / (x * z)) * x) * z = L((x \ 1) \ y,x,x * z). x != L(y,z * u,(z * u) \ (w \ 1)) | x = L(y,z * u,w \ (u \ (z \ 1))). L(x,y * z,(y * z) * (u \ 1)) = L(x,y * z,u \ (z \ (y \ 1))). L(x,y * z,u \ (z \ (y \ 1))) = L(x,y * z,(y * z) * (u \ 1)). x != R(y,z,u) | x = L(y,z,u). L(x,y,K(y,z) * u) = L(x,y,u). ((x * y) * z) * a(x,z,y) != u | x * (y * z) = u. a(x,y,T(z,u)) = T(a(x,y,z),u). x != a(y,z,u) | x = a(z,u,y). a(x,y,K(z,u)) = a(x,K(y,u),z). a(x,K(y,z),u) = a(x,y,K(u,z)). a(x,y,K(z,u)) = a(x,z,K(x \ u,y)). a(x,y,K(x \ z,u)) = a(x,u,K(y,z)). L(x,y,K(z,u)) = x * a(y,u,K(z,x)). x * a(y,z,K(u,x)) = L(x,y,K(u,z)). L(x,y,T(y,z)) = L(x,y,y). L(x,y,T(z,y) \ u) = L(x,y,z \ u). L(x,y / z,z \ y) = L(x,y / z,y / z). L(x,y / z,y / z) = L(x,y / z,z \ y). x != T(a(y,z,u),w) | x = a(z,u,T(y,w)). a(x,y,T(z,u)) = a(y,z,T(x,u)). a(x,y,T(z,u)) = a(z,x,T(y,u)). a(x,y,T(z,u)) = a(x,T(y,u),z). a(x,T(y,z),u) = a(x,y,T(u,z)). L((x \ 1) \ y,z / x,x \ 1) = (x * (z * (1 / x))) / (y \ (z / x)). (x * (y * (1 / x))) / (z \ (y / x)) = L((x \ 1) \ z,y / x,x \ 1). L(((x / y) / z) / u,u,T(z,y)) = (x / T(y,z)) / (u * T(z,y)). L(x,y,z) \ z = y * ((x * y) \ z). (x * y) * z != u * (y * z) | L(x,y,z) = u. L(x,L(y,z,u),z * u) * ((y * z) * u) = (x * L(y,z,u)) * (z * u). L(x,y,z \ (u \ 1)) != w | L(x,u * z,y) = w. L(x,y,y \ z) != u | L(x,y,y * z) = u. R(x,y,z) != u | L(x,y,z) = u. L(x,y \ 1,z) != u | L(x,z,y) = u. x / ((y \ (x / z)) * z) != u | L(y,x,z) = u. ((x * y) / a(y,z,u)) * ((x * y) \ 1) = (x * y) / (x * L(y,z,u)). L(x,y,z) * u = a(x,y,z) * (x * u). a(x,y,z) * (x * u) = L(x,y,z) * u. a(x,y,(z \ 1) * (u \ z)) = a(x,T(u,u \ z),y). a(x,T(y,y \ z),u) = a(x,u,(z \ 1) * (y \ z)). a(x,y,(z \ 1) * u) \ 1 = a(x,y,u \ z). x != y * a(z,u,K(w,y)) | x = L(y,u,K(z,w)). L(x,y,K(z,u)) = L(x,u,K(y,z)). x != y * a(z,u,K(w,y)) | x = L(y,K(w,z),u). L(x,y,K(z,u)) = L(x,K(z,y),u). L(x,K(y,z),u) = L(x,z,K(y,u)). x != L(y,z,K(u,w)) | x = L(y,z,K(u,u \ w)). L(x,y,K(z,u)) = L(x,u,K(y,y \ z)). L(x,y,K(z,z \ u)) = L(x,z,K(u,y)). x != L(y,z,K(u,w)) | x = L(y,z,K(w * u,w)). L(x,y,K(z,u)) = L(x,u,K(z * y,z)). L(x,y,K(z * u,z)) = L(x,u,K(z,y)). L(x,K(y,z \ u),w) = L(x,u / z,K(y,w)). x != L(y,K(z,u),z \ (w \ K(u,z))) | x = L(y,K(u,z),w * z). L(x,y,K(z,z \ (u \ K(y,z)))) = L(x,K(y,z),u * z). L(L(x,y,K(z,u)),K(y,z),u) = x. L(x,y,K(z,u \ 1)) != w | L(x,u,K(z,y)) = w. L(x,y,T(T(z,u),y) \ (u \ 1)) = L(x,y,u \ (z \ 1)). a(x,y,z) * (x * u) = (a(x,y,z) * x) * u. (a(x,y,z) * x) * u = a(x,y,z) * (x * u). x != L(y,z,K(u,w)) | x = L(y,w,K(z,u)). L(x,y,K(z,u)) = L(x,y \ z,K(u,y)). L(x,y \ z,K(u,y)) = L(x,y,K(z,u)). x != L(y,z,K(u,w)) | x = L(y,u,K(w,z)). L(x,y,K(z,u)) = L(x,z * y,K(z,u)). L(x,y * z,K(y,u)) = L(x,z,K(y,u)). L(x,y,K(z,u / w)) = L(x,w / u,K(z,y)). L(x,y / z,K(u,w)) = L(x,w,K(u,z / y)). L(x,y,T(z,u)) = L(L(x,y,z),y,K(z,u)). L(L(x,y,z),y,K(z,u)) = L(x,y,T(z,u)). L(L(x,y,z),y,K(z,u)) != w | L(x,y,T(z,u)) = w. L(x,y,T(z,u)) = L(L(x,y,z),u,K(y,z)). L(L(x,y,z),u,K(y,z)) = L(x,y,T(z,u)). L(L(x,y,T(z,u)),K(y,z),u) = L(x,y,z). L(x / (y * z),u,K(y,z)) = L((x / z) / y,y,T(z,u)). L((x / y) / z,z,T(y,u)) = L(x / (z * y),u,K(z,y)). x != L(y,K(z,u),w) | x = L(y,u,K(z,w)). L(x,y,z) = L(L(x,y,T(z,u)),z,K(y,u)). L(L(x,y,T(z,u)),z,K(y,u)) = L(x,y,z). L(L(x,y,z * u),u * z,K(y,z \ 1)) = L(x,y,u * z). x != L(y,z \ 1,u) | x = L(y,u,z). L(x,(y \ z) \ z,u) = L(x,T(y,z),u). x != L(y,(z \ u) \ u,w) | x = L(y,T(z,z * u),w). L(x,T(y,z),u) = L(x,T(y,y * z),u). L(x,T(y,y * z),u) = L(x,T(y,z),u). a(x,y,T(z,u)) = L(x,T(z,z * u),y) \ x. L(x,T(y,y * z),u) \ x = a(x,u,T(y,z)). x != L(y,z / u,z / u) | x = L(y,u \ z,u \ z). L(x,y / z,z \ y) = L(x,z \ y,z \ y). a(x,(y \ 1) * z,u) = a(x,u,z \ y). a(x,y * z,u) = a(x,u,z \ (1 / y)). a(x,y,z \ (1 / u)) = a(x,u * z,y). a(x,((y \ z) \ 1) * z,u) = a(x,u,T(y,z) \ 1). L(x,y / z,K(u,w)) = L(x,z \ y,K(u,w)). L(a(x,y,z),x,u) = a(x,y,z). a(x,y,T(z,z * u)) = a(x,y,T(z,u)). a(x,y,T(z,u)) = a(x,y,T(z,z \ u)). a(x,y,T(z,z \ u)) = a(x,y,T(z,u)). x != a(y,z,T(u,w)) | x = a(u,y,T(z,w)). a(x,y,T(z,u)) = a(z,x,T(y,z \ u)). a(x,y,T(z,x \ u)) = a(y,z,T(x,u)). a(x,y,T(z,x \ u)) = a(x,y,T(z,u)). x != L(y,z / u,u \ z) | x = (u * (z \ (z \ u))) * ((u \ z) * ((z / u) * y)). L(x,y \ z,y \ z) = (y * (z \ (z \ y))) * ((y \ z) * ((z / y) * x)). (x * (y \ (y \ x))) * ((x \ y) * ((y / x) * z)) = L(z,x \ y,x \ y). x != L(y,z \ u,K(w,z)) | x = L(y,z,K(u,w)). L(x,y / z,K(u,z)) = L(x,z,K(y,u)). x != L(L(y,z \ 1,u),u / z,K(u,w)) | x = L(y,z \ 1,T(u,w)). L(L(x,y \ 1,z),y \ z,K(z,u)) = L(x,y \ 1,T(z,u)). L(x,y,K(z * u,z)) != w | L(x,u,K(z,y)) = w. L(x,y,K(z,u)) != w | L(x,z,K(u,y)) = w. T(x,a(y,z,u)) != w | L(x,u,K(y,z)) = w. L(x,y,K(z,u)) != w | L(x,u,K(y,z)) = w. L(x * a(y,z,u),y,K(u,z)) = a(y,z,u) * x. L(x,K(y,z),u) != w | L(x,z,K(y,u)) = w. L(a(x,y,z),u,u \ (w \ 1)) = L(a(x,y,z),w,u). x != a(y,z,(u \ 1) * w) | x = a(y,w \ u,z). a(x,T(y,y \ z),u) = a(x,(y \ z) \ z,u). x != a(y,z,u \ 1) | x = a(y,u,z). a(x,((y \ z) \ 1) * z,u) = a(x,T(y,z),u). a(x,(y \ z) \ z,u) = a(x,T(y,z),u). x != a(y,(z \ u) \ u,w) | x = a(y,T(z,z \ u),w). a(x,T(y,z),u) = a(x,T(y,y \ z),u). a(x,T(y,y \ z),u) = a(x,T(y,z),u). x != a(y,T(z,u),w) | x = a(y,z,T(w,u)). a(x,T(y,z),u) = a(x,y,T(u,y \ z)). a(x,y,T(z,y \ u)) = a(x,T(y,u),z). a(x,y,T(z,y \ u)) = a(x,y,T(z,u)). L(a(x,y,z),u,u * (w \ 1)) = L(a(x,y,z),w,u). x != L(y,z,z * (u \ 1)) | x = L(y,z,u \ z). L(a(x,y,z),u,w) = L(a(x,y,z),w,u \ w). L(a(x,y,z),u,w \ u) = L(a(x,y,z),w,u). L(x,y,K(z,z \ (u \ 1))) = L(x,K(y,z),u * z). L(x,y,z \ (T(u,y) \ 1)) = L(x,y,z \ (u \ 1)). L(x,T(y,z) * u,z) = L(x,z,u \ (y \ 1)). L(x,T(y,z) * u,z) != w | L(x,y * u,z) = w. L(L(x,y,z * u),z,K(y,u * z)) = L(x,y,u * z). x != L((y / z) / u,u,T(z,w)) | x = L(y / (u * z),w,K(u,z)). (x / T(y,z)) / (u * T(z,y)) = L((x / y) / (u * z),y,K(u,z)). L((x / y) / (z * u),y,K(z,u)) = (x / T(y,u)) / (z * T(u,y)). L(x,y * z,u \ (z \ (y \ 1))) = L(x,y * z,u \ (y * z)). x != L(a(y,z,u),y * (z * u),w \ ((z * u) \ (y \ 1))) | x = w / (((y * z) * u) \ ((y * (z * u)) * w)). L(a(x,y,z),x * (y * z),u \ (x * (y * z))) = u / (((x * y) * z) \ ((x * (y * z)) * u)). ((x * y) * a(y,z,u)) * ((x * y) \ 1) = (x * y) / (x * L(y,u,z)). (x * L(y,z,u)) * ((x * y) \ 1) = (x * y) / (x * L(y,u,z)). (x * L(y,z,u)) * (y \ (x \ 1)) = (x * y) / (x * L(y,u,z)). L(a(x,y,T(z,x \ (u \ 1))),x,u) = (u * L(x,y,z)) * (x \ (u \ 1)). (x * (y * (1 / x))) / (z \ (y / x)) = L((x \ 1) \ z,x,y / x). x != L(y,z,u / z) | x = L(y,z,z * u). (x * (y * (1 / x))) / (z \ (y / x)) = L((x \ 1) \ z,x,x * y). (x * ((1 / (x / y)) \ ((1 / (x / y)) \ x))) * ((((y / x) \ x) \ 1) * (((1 / (x / y)) / x) * z)) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). x != L(a(y,z,u),y,w) | x = a(y,z,u). (x * L(y,z,u)) * (y \ (x \ 1)) = a(y,z,T(u,y \ (x \ 1))). x != a(y,z,T(u,y \ w)) | x = a(y,z,T(u,w)). (x * L(y,z,u)) * (y \ (x \ 1)) = a(y,z,T(u,x \ 1)). x != (y * L(z,u,w)) * (z \ (y \ 1)) | x = (y * z) / (y * L(z,w,u)). a(x,y,T(z,u \ 1)) = (u * x) / (u * L(x,z,y)). (x * y) / (x * L(y,z,u)) = a(y,u,T(z,x \ 1)). (x * ((y / z) / (u * w))) / (x * ((y / T(z,w)) / (u * T(w,z)))) = a((y / z) / (u * w),K(u,w),T(z,x \ 1)). R(x,y * (1 / (z * y)),u \ 1) = u \ (z \ ((z * u) * x)). R(x,y * (1 / (z * y)),u \ 1) != w | ((x / (z * u)) * z) * u = w. ((x / (y * z)) * y) * z = L(x,(u * (1 / (y * u))) \ 1,z). L(x,(y * (1 / (z * y))) \ 1,u) = ((x / (z * u)) * z) * u. L(x,(1 / (y * z)) \ (z \ 1),u) = ((x / (y * u)) * y) * u. L(x,K(y,y \ 1) * z,u) = ((x / (z * u)) * z) * u. L(x,y,z) = ((x / (y * z)) * y) * z. x != (((y * z) / (y * u)) * y) * u | x = L((y \ 1) \ z,y,y * u). L(x * y,x,z) = L((x \ 1) \ y,x,x * z). L((x \ 1) \ y,x,x * z) = L(x * y,x,z). ((x / (y * z)) * z) * T(y,z) = L(x,z,y). L(x,y,z) = ((x / (z * y)) * y) * T(z,y). L(x \ 1,y,z) = ((x \ (1 / (y * z))) * y) * z. ((x \ (1 / (y * z))) * y) * z = L(x \ 1,y,z). L(((1 / x) * (1 / (y * z))) \ 1,y,z) = (T(x,1 / (y * z)) * y) * z. x * y != ((z / (u * w)) * w) * T(u,w) | L(z,w,u) / y = x. L(x,y,z) / (z * y) = L(x / (z * y),y,z). L(x / (y * z),z,y) = L(x,z,y) / (y * z). x != L((y \ 1) \ z,y,y * u) | x = (y * (u * (1 / y))) / (z \ (u / y)). L(x * y,x,z) = (x * (z * (1 / x))) / (y \ (z / x)). (x * (y * (1 / x))) / (z \ (y / x)) = L(x * z,x,y). x != L(y,z,u) / (u * z) | x = (y / z) / u. L(x / (y * z),z,y) = (x / z) / y. L(x / (y * z),z,y) != u | (x / z) / y = u. L(x / (y * z),T(y,z),z) = (x / T(y,z)) / z. x * y != ((z \ (1 / (u * w))) * u) * w | x \ L(z \ 1,u,w) = y. ((x \ (1 / (y * z))) * (y * z)) \ L(x \ 1,y,z) = a(x \ (1 / (y * z)),y,z). L(x / (y * z),y,z) = (x / T(y,z)) / z. L(x * ((y / (z * u)) / x),z,u) = x * (((y / T(z,u)) / u) / x). x != (y * (z * (1 / y))) / (u \ (z / y)) | x = T(z \ 1,y \ 1) \ ((y * (z \ 1)) * u). L(x * y,x,z) = T(z \ 1,x \ 1) \ ((x * (z \ 1)) * y). T(x \ 1,y \ 1) \ ((y * (x \ 1)) * z) = L(y * z,y,x). x != T((y \ 1) \ 1,z \ 1) \ ((z * ((y \ 1) \ 1)) * u) | x = T(y,z \ 1) \ ((z * y) * u). L(x * y,x,z \ 1) = T(z,x \ 1) \ ((x * z) * y). T(x,y \ 1) \ ((y * x) * z) = L(y * z,y,x \ 1). T(x,y \ 1) \ ((y * x) * z) = L(y * z,x,y). L(((1 / x) * (1 / (y * z))) \ 1,y,z) = (T(x,(y * z) \ 1) * y) * z. L(((1 / x) * (1 / (y * z))) \ 1,y,z) = (T(x,z \ (y \ 1)) * y) * z. L((1 / (x * y)) \ z,x,y) = (T(z,y \ (x \ 1)) * x) * y. (T(x,y \ (z \ 1)) * z) * y = L((1 / (z * y)) \ x,z,y). (x \ 1) \ L(x \ 1,y,z) = a(x \ (1 / (y * z)),y,z). a(x \ (1 / (y * z)),y,z) = (x \ 1) \ L(x \ 1,y,z). a(x \ (1 / (y * z)),y,z) = a(x,z,y). a(x,y,z \ (1 / (x * y))) = a(z,y,x). x != a(y,z,u \ (1 / w)) | x = a(y,w * u,z). a(x,y,z) = a(z,(z * y) * x,y). a(x,(x * y) * z,y) = a(z,y,x). ((x \ ((y / x) \ z)) \ 1) * (z * ((x \ ((y / x) \ z)) \ 1)) = (z \ (y * (y / x))) * x. (x \ ((y / x) \ z)) \ (z / (x \ ((y / x) \ z))) = (z \ (y * (y / x))) * x. (x \ (y * (y / z))) * z = (((y / z) \ x) \ z) * (x * (((y / z) \ x) \ z)). (((x / y) \ z) \ y) * (z * (((x / y) \ z) \ y)) = (z \ (x * (x / y))) * y. x != ((y \ z) \ u) * (z * ((y \ z) \ u)) | x = (z \ y) * (u * (y * u)). (x \ (y * (y / z))) * z = (x \ (y / z)) * (z * ((y / z) * z)). (x \ (y / z)) * (z * ((y / z) * z)) = (x \ (y * (y / z))) * z. (x \ (y / z)) * (z * y) = (x \ (y * (y / z))) * z. (x \ (y * (y / z))) * z = (x \ (y / z)) * (z * y). x != L(a(y,z,u),w,v5 \ w) | x = L(a(y,z,u),v5,w). x / (((y * z) * u) \ ((y * (z * u)) * x)) = L(a(y,z,u),x,y * (z * u)). x / (((T(y,(z * u) \ 1) * z) * u) \ (((1 / (z * u)) \ y) * x)) = L(a(T(y,(z * u) \ 1),z,u),x,T(y,(z * u) \ 1) * (z * u)). L(a(T(x,(y * z) \ 1),y,z),u,T(x,(y * z) \ 1) * (y * z)) = u / (((T(x,(y * z) \ 1) * y) * z) \ (((1 / (y * z)) \ x) * u)). T(x,K(y,y \ K(z,u)) * w) * (w \ K(y,y \ K(z,u))) = ((1 * K(y \ K(z,u),y)) * w) \ x. T(x,K(y,y \ K(z,u)) * w) * (w \ K(y,y \ K(z,u))) = ((1 * K(y,y \ K(z,u))) * w) \ x. T(x,K(y,y \ K(z,u)) * w) * (w \ K(y,y \ K(z,u))) = (K(y,y \ K(z,u)) * w) \ x. T(x,y) * (y \ K(z,z \ K(u,w))) = (K(z,z \ K(u,w)) * y) \ x. (x \ y) * K(z,z \ K(u,w)) = (K(z,z \ K(u,w)) * x) \ y. (K(x,x \ K(y,z)) * u) \ w = (u \ w) * K(x,x \ K(y,z)). x != a(y,K(z,u),w) | x = a(y,z,K(w,u)). (x * ((y / z) / (u * w))) / (x * ((y / T(z,w)) / (u * T(w,z)))) = a((y / z) / (u * w),u,K(T(z,x \ 1),w)). (x * ((y / z) / (u * w))) / (x * ((y / T(z,w)) / (u * T(w,z)))) = a((y / z) / (u * w),u,K(z,T(w,x))). x != a(y,z,K(u,T(w,v5))) | x = a(y,z,K(u,w)). (x * ((y / z) / (u * w))) / (x * ((y / T(z,w)) / (u * T(w,z)))) = a((y / z) / (u * w),u,K(z,w)). x != a(y,z,K(u,w)) | x = a(z,u,K(y,w)). (x * ((y / z) / (u * w))) / (x * ((y / T(z,w)) / (u * T(w,z)))) = a(u,z,K((y / z) / (u * w),w)). (x * ((y / z) / (u * w))) / (x * ((y / T(z,w)) / (u * T(w,z)))) = a(u,z,K(w \ ((y / z) / u),w)). (x * ((y / z) / (u * w))) / (x * ((y / T(z,w)) / (u * T(w,z)))) = a(u,z,K((y / z) / u,w)). x != a(y,z,K(u / w,v5)) | x = a(y,z,K(w \ u,v5)). (x * ((y / z) / (u * w))) / (x * ((y / T(z,w)) / (u * T(w,z)))) = a(u,z,K(u \ (y / z),w)). x != a(y,z,K(y \ u,w)) | x = a(y,w,K(z,u)). (x * ((y / z) / (u * w))) / (x * ((y / T(z,w)) / (u * T(w,z)))) = a(u,w,K(z,y / z)). x != a(y,z,K(u,w / v5)) | x = a(y,z,K(u,v5 \ w)). (x * ((y / z) / (u * w))) / (x * ((y / T(z,w)) / (u * T(w,z)))) = a(u,w,K(z,z \ y)). x != a(y,z,K(u,u \ w)) | x = a(y,z,K(u,w)). (x * ((y / z) / (u * w))) / (x * ((y / T(z,w)) / (u * T(w,z)))) = a(u,w,K(z,y)). (K(x,K(y,z)) * (u * w)) \ ((K(x,K(y,z)) * u) * (w * v5)) = L(v5,L(w,u,K(x,K(y,z))),u * K(x,K(y,z))). (K(x,K(y,z)) * (u * w)) \ (u * ((w * v5) * K(x,K(y,z)))) = L(v5,L(w,u,K(x,K(y,z))),u * K(x,K(y,z))). (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) = L(v5,L(w,u,K(x,K(y,z))),u * K(x,K(y,z))). (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) = L(v5,w,u * K(x,K(y,z))). L(L(x,y,z),z * y,K(u,K(w,v5))) = L(x,y,z * K(u,K(w,v5))). L(x,y,z * K(u,K(w,v5))) = L(x,y,z). L(x,y,K(z,u \ w)) = L(x,y,K(z,w / u)). L(x,y,K(z,u / w)) = L(x,y,K(z,w \ u)). x != L(y,z,K(u,w / v5)) | x = L(y,v5 / w,K(u,z)). L(x,y,K(z,u \ w)) = L(x,u / w,K(z,y)). L(x,y / z,K(u,w)) = L(x,w,K(u,y \ z)). x != L(y,z / u,K(w,u)) | x = L(y,u,K(z,w)). L(x,y,K(z,u \ y)) = L(x,y,K(u,z)). L(x,y \ z,K(z,u)) = L(x,z,K(y,u)). x != L(L(y,z \ 1,u),z \ u,K(u,w)) | x = L(y,z \ 1,T(u,w)). L(L(x,y \ 1,z),z,K(y,u)) = L(x,y \ 1,T(z,u)). L(L(x,y,z),y,K(z,u)) = L(x,z \ 1,T(y,u)). L(x,y,T(z,u)) = L(x,z \ 1,T(y,u)). L(x,y \ 1,T(z,u)) = L(x,z,T(y,u)). L(x,T(y,z),u) = L(x,y,T(u,z)). x != L(y,z,T(u * w,u)) | x = L(y,z,w * u). L(x,T(y,z),z * u) = L(x,y,u * z). L(a(T(x,(y * z) \ 1),y,z),u,T(x,(y * z) \ 1) * (y * z)) = u / (((T(x,z \ (y \ 1)) * y) * z) \ (((1 / (y * z)) \ x) * u)). L(a(T(x,(y * z) \ 1),y,z),u,T(x,(y * z) \ 1) * (y * z)) = u / (L((1 / (y * z)) \ x,y,z) \ (((1 / (y * z)) \ x) * u)). L(a(T(x,(y * z) \ 1),y,z),u,T(x,(y * z) \ 1) * (y * z)) = u / (a((1 / (y * z)) \ x,z,y) * u). L(a(T(x,(y * z) \ 1),y,z),u,T(x,(y * z) \ 1) * (y * z)) = u / (a(y,(1 / (y * z)) \ x,z) * u). L(a(T(x,(y * z) \ 1),y,z),u,T(x,(y * z) \ 1) * (y * z)) = u / (a(y,(y * z) * x,z) * u). L(a(T(x,(y * z) \ 1),y,z),u,T(x,(y * z) \ 1) * (y * z)) = u / (a(x,z,y) * u). L(a(T(x,(y * z) \ 1),y,z),u,T(x,(y * z) \ 1) * (y * z)) = u \ (u / a(x,z,y)). L(a(T(x,(y * z) \ 1),y,z),u,T(x,(y * z) \ 1) * (y * z)) = u \ (u * a(x,y,z)). L(a(T(x,(y * z) \ 1),y,z),u,T(x,(y * z) \ 1) * (y * z)) = a(x,y,z). L(a(T(x,y \ (z \ 1)),z,y),u,T(x,(z * y) \ 1) * (z * y)) = a(x,z,y). L(a(x,y,T(z,y \ (x \ 1))),u,T(z,(x * y) \ 1) * (x * y)) = a(z,x,y). L(a(x,y,T(z,x \ 1)),u,T(z,(x * y) \ 1) * (x * y)) = a(z,x,y). L(a(x,y,T(z,1)),u,T(y,(z * x) \ 1) * (z * x)) = a(y,z,x). L(a(x,y,z),u,T(y,(z * x) \ 1) * (z * x)) = a(y,z,x). L(a(x,y,z),u,T(x,(y * z) \ 1) * (y * z)) = a(x,y,z). L(a(x,y,z),u,(1 / (y * z)) \ x) = a(x,y,z). x != L(y,z,(1 / u) \ w) | x = L(y,z,u * w). a(x,y,z) = L(a(x,y,z),u,(y * z) * x). L(a(x,y,z),u,(y * z) * x) = a(x,y,z). x != L(y,T(z,u),u * w) | x = L(y,z,w * u). a(x,y,z) = L(a(x,y,z),u,x * (y * z)). L(a(x,y,z),u,x * (y * z)) = a(x,y,z). ((K(x,x \ K(y,z)) \ u) \ w) * ((u \ 1) * K(x,x \ K(y,z))) = (u \ K(x,x \ K(y,z))) * ((u / w) \ K(x,x \ K(y,z))). ((K(x \ K(y,z),x) * u) \ w) * ((u \ 1) * K(x,x \ K(y,z))) = (u \ K(x,x \ K(y,z))) * ((u / w) \ K(x,x \ K(y,z))). ((K(x,x \ K(y,z)) * u) \ w) * ((u \ 1) * K(x,x \ K(y,z))) = (u \ K(x,x \ K(y,z))) * ((u / w) \ K(x,x \ K(y,z))). ((x \ y) * K(z,z \ K(u,w))) * ((x \ 1) * K(z,z \ K(u,w))) = (x \ K(z,z \ K(u,w))) * ((x / y) \ K(z,z \ K(u,w))). ((x \ y) * K(z,z \ K(u,w))) * (x \ K(z,z \ K(u,w))) = (x \ K(z,z \ K(u,w))) * ((x / y) \ K(z,z \ K(u,w))). x != (y * K(z,z \ K(u,w))) * v5 | x = y * (K(z,z \ K(u,w)) * v5). (x \ K(y,y \ K(z,u))) * ((x / w) \ K(y,y \ K(z,u))) = (x \ w) * (K(y,y \ K(z,u)) * (x \ K(y,y \ K(z,u)))). (x \ K(y,y \ K(z,u))) * ((x / w) \ K(y,y \ K(z,u))) = (x \ w) * (K(y,K(z,u)) * (x \ K(y,K(z,u)))). x != y * (K(z,K(u,w)) * (v5 \ K(z,K(u,w)))) | x = y * (v5 \ 1). (x \ K(y,y \ K(z,u))) * ((x / w) \ K(y,y \ K(z,u))) = (x \ w) * (x \ 1). (x \ K(y,y \ K(z,u))) * ((x / w) \ K(y,y \ K(z,u))) = x \ (w / x). (x \ K(y,y \ K(z,u))) * (w * (x \ K(y,y \ K(z,u)))) = x \ (w / x). (x * ((1 / (x / y)) \ (x / (x \ y)))) * ((((y / x) \ x) \ 1) * (((1 / (x / y)) / x) * z)) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). (x * ((x / y) / (x \ (y / x)))) * ((((y / x) \ x) \ 1) * (((1 / (x / y)) / x) * z)) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). (x * (x / (x \ ((y / x) * y)))) * ((((y / x) \ x) \ 1) * (((1 / (x / y)) / x) * z)) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). (x * (x / ((x \ y) * (x \ y)))) * ((((y / x) \ x) \ 1) * (((1 / (x / y)) / x) * z)) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). (x * (x * (y \ ((y / x) \ x)))) * ((((y / x) \ x) \ 1) * (((1 / (x / y)) / x) * z)) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). (x * (x * (y \ ((y / x) \ x)))) * ((x \ (1 / (x / y))) * (((1 / (x / y)) / x) * z)) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). (x * (x * (y \ ((y / x) \ x)))) * ((x \ (1 / (x / y))) * ((1 / (x * (x / y))) * z)) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). x != (y * (y * (z \ ((z / y) \ y)))) * u | x = (y * (y / z)) * (((y \ z) / y) \ u). L(x,y \ (1 / (y / z)),y \ (1 / (y / z))) = (y * (y / z)) * (((y \ z) / y) \ ((y \ (1 / (y / z))) * ((1 / (y * (y / z))) * x))). (x * (x / y)) * (((x \ y) / x) \ ((x \ (1 / (x / y))) * ((1 / (x * (x / y))) * z))) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). (x * (x / y)) * (K(y,y \ 1) * ((1 / (x * (x / y))) * z)) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). (x * (x / y)) * (K(y,y \ 1) / (z \ (x * (x / y)))) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). L(x,y \ (1 / (y / z)),y \ (1 / (y / z))) = (y * (y / z)) * (z * (1 / ((x \ (y * (y / z))) * z))). (x * (x / y)) * (y * (1 / ((z \ (x * (x / y))) * y))) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). (x * (x / y)) * (y * (1 / ((z \ (x / y)) * (y * x)))) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). (x * (x / y)) * (y * (((x * x) \ (z / y)) * y)) = L(z,x \ (1 / (x / y)),x \ (1 / (x / y))). x != L(y,z,u \ (1 / (u / w))) | x = L(y,z,(u \ w) / u). (x * (x / y)) * (y * (((x * x) \ (z / y)) * y)) = L(z,x \ (1 / (x / y)),(x \ y) / x). x != L(y,z \ (1 / (z / u)),w) | x = L(y,(z \ u) / z,w). (x * (x / y)) * (y * (((x * x) \ (z / y)) * y)) = L(z,(x \ y) / x,(x \ y) / x). (x * (x / y)) * (y * (((x * x) \ (z / y)) * y)) = L(z,x \ (x \ y),x \ (x \ y)). x != L(y,z \ (z \ u),z \ (z \ u)) | x = L(y,z * (u \ z),z * (u \ z)). (x * (x / y)) * (y * (((x * x) \ (z / y)) * y)) = L(z,x * (y \ x),x * (y \ x)). (x * (x / y)) * (((x * x) / y) \ L(z,y,y)) = L(z,x * (y \ x),x * (y \ x)). (x * (x / y)) * ((x * (x / y)) \ L(z,y,y)) = L(z,x * (y \ x),x * (y \ x)). L(x,y * (z \ y),y * (z \ y)) = L(x,z,z). x != L(y,z * (((z * u) * w) \ z),z * (((z * u) * w) \ z)) | x = L(y,u * (z \ w),u * (z \ w)). L(x,(y * z) * u,(y * z) * u) = L(x,z * (y \ u),z * (y \ u)). x != L(y,(z * u) * w,(z * u) * w) | x = L(y,w \ (u \ (z \ 1)),w \ (u \ (z \ 1))). L(x,y * (z \ u),y * (z \ u)) = L(x,u \ (y \ (z \ 1)),u \ (y \ (z \ 1))). L(x,y \ (z \ (u \ 1)),y \ (z \ (u \ 1))) = L(x,z * (u \ y),z * (u \ y)). x != L(y,((1 / z) * u) * w,((1 / z) * u) * w) | x = L(y,(u \ z) \ w,(u \ z) \ w). L(x,y * ((1 / z) \ u),y * ((1 / z) \ u)) = L(x,(y \ z) \ u,(y \ z) \ u). L(x,y * (z / (u \ 1)),y * (z / (u \ 1))) = L(x,z * (u \ y),z * (u \ y)). L(x,y * ((1 / z) \ u),y * (z / (u \ 1))) = L(x,z * (u \ y),z * (u \ y)). L(x,y * ((1 / z) \ u),y * ((1 / z) \ u)) = L(x,z * (u \ y),z * (u \ y)). x != L(y,z * ((1 / u) \ w),z * ((1 / u) \ w)) | x = L(y,(z \ u) \ w,(z \ u) \ w). L(x,y * (z \ u),y * (z \ u)) = L(x,(u \ y) \ z,(u \ y) \ z). L(x,(y \ z) \ u,(y \ z) \ u) = L(x,z * (u \ y),z * (u \ y)). L(x,y * z,y * z) = L(x,1 * (z \ y),1 * (z \ y)). L(x,1 * (y \ z),1 * (y \ z)) = L(x,z * y,z * y). L(x,y \ z,1 * (y \ z)) = L(x,z * y,z * y). L(x,y \ z,y \ z) = L(x,z * y,z * y). x != L(y,z \ u,z \ u) | x = L(y,u * (1 / z),u * (z \ 1)). L(x,y * z,y * z) = L(x,y * (1 / z),y * (z \ 1)). L(x,y * (1 / z),y * (z \ 1)) = L(x,y * z,y * z). x != L(y,z \ u,z \ u) | x = ((1 / z) * u) * ((u \ z) * y). L(x,y * z,y * z) = ((1 / z) * y) * ((y \ z) * x). ((1 / x) * y) * ((y \ x) * z) = L(z,y * x,y * x). x * (1 / (L((x \ 1) \ 1,y * z,y * z) * x)) = ((y / x) \ ((1 / z) \ x)) \ ((x \ 1) \ (y \ z)). (1 / x) \ L(((1 / x) \ (y \ 1)) \ (x * z),y * x,y * x) = (x * y) * z. x / (((y * x) * (((1 / x) \ (y \ 1)) \ (x * z))) \ (y * x)) = (x * y) * z. x / ((y * x) \ ((y * x) / ((y * (1 / x)) / (1 / (x * z))))) = (x * y) * z. x / ((y * x) \ ((y * x) / ((y / (x * (1 / z))) * x))) = (x * y) * z. x * (1 / ((((y * z) * (x \ 1)) \ (y * z)) * x)) = ((y / x) \ ((1 / z) \ x)) \ ((x \ 1) \ (y \ z)). ((x / y) \ ((1 / z) \ y)) \ ((y \ 1) \ (x \ z)) = y * (1 / ((((x * z) * (y \ 1)) \ (x * z)) * y)). ((x / y) \ ((1 / z) \ y)) \ ((y \ 1) \ (x \ z)) = y * (1 / (((x * z) * ((y \ (x * z)) \ 1)) * y)). ((x / y) \ ((1 / z) \ y)) \ ((y \ 1) \ (x \ z)) = y * (1 / (((x * z) / y) \ ((x * z) * y))). ((x / y) \ ((1 / z) \ y)) \ ((y \ 1) \ (x \ z)) = y * ((1 / ((x * z) * y)) * ((x * z) / y)). ((x / y) \ ((1 / z) \ y)) \ ((y \ 1) \ (x \ z)) = y * (y \ ((x * z) \ ((x * z) / y))). ((x / y) \ ((1 / z) \ y)) \ ((y \ 1) \ (x \ z)) = (x * z) \ ((x * z) / y). (((x \ 1) \ (y \ z)) * x) \ ((x \ 1) \ (y \ z)) = (y * z) \ ((y * z) / x). ((x * (y \ z)) * x) \ (x * (y \ z)) = (y * z) \ ((y * z) / x). (x \ y) \ ((x \ y) / z) = (x * y) \ ((x * y) / z). ((x \ 1) * (T(x,y) / (z * u))) \ (T(T(x,y) \ 1,y \ 1) * (1 / (u * (T(x,y) \ 1)))) = L(z,u,K(T(x,y) \ 1,(y \ 1) \ ((T(x,y) \ 1) \ 1))). ((x \ 1) * (T(x,y) / (z * u))) \ ((x \ 1) * (1 / (u * (T(x,y) \ 1)))) = L(z,u,K(T(x,y) \ 1,(y \ 1) \ ((T(x,y) \ 1) \ 1))). L(x,y,K(T(z,u) \ 1,(u \ 1) \ ((T(z,u) \ 1) \ 1))) = ((z \ 1) * (T(z,u) / (x * y))) \ ((z \ 1) * (1 / (y * (T(z,u) \ 1)))). L(x,y,K(T(z,u) \ 1,(u \ 1) \ ((T(z,u) \ 1) \ 1))) = ((z \ 1) * (T(z,u) / (x * y))) \ ((z \ 1) * (T(z,u) / y)). x != ((y \ 1) * z) \ ((y \ 1) * u) | x = (z \ y) / (u \ y). L(x,y,K(T(z,u) \ 1,(u \ 1) \ ((T(z,u) \ 1) \ 1))) = ((T(z,u) / (x * y)) \ z) / ((T(z,u) / y) \ z). L(x,y,K(T(z,u) \ 1,(u \ 1) \ ((T(z,u) \ 1) \ 1))) = ((x * y) * K(u,z)) / ((T(z,u) / y) \ z). L(x,y,K(T(z,u) \ 1,(u \ 1) \ ((T(z,u) \ 1) \ 1))) = ((x * y) * K(u,z)) / (y * K(u,z)). L(x,y,K(T(z,u) \ 1,(u \ 1) \ ((T(z,u) \ 1) \ 1))) = R(x,y,K(u,z)). L(x,y,K(T(z,u) \ 1,(u \ 1) \ ((T(z,u) \ 1) \ 1))) = L(x,y,K(u,z)). L(x,y,K(T(z,u) \ 1,(u \ 1) \ T((z \ 1) \ 1,u))) = L(x,y,K(u,z)). L(x,y,K(T(z,u) \ 1,((z \ 1) \ 1) / (1 / u))) = L(x,y,K(u,z)). L(x,y,K(T(z,u) \ 1,(z \ 1) \ (1 / (1 / u)))) = L(x,y,K(u,z)). L(x,y,K(T(z,u) \ 1,(z \ 1) \ u)) = L(x,y,K(u,z)). L(x,y,K(T(z,u) \ 1,z * u)) = L(x,y,K(u,z)). L(x,y,K(T(z,u),(z * u) \ 1)) = L(x,y,K(u,z)). L(x,y,K(T(z,u),u \ (z \ 1))) = L(x,y,K(u,z)). L(x,y,K(z,(z \ 1) / u)) = L(x,y,K(u,z)). L(x,y,K(z,z \ (u \ 1))) = L(x,y,K(u,z)). x != L(y,z,K(u,u \ (w \ 1))) | x = L(y,K(z,u),w * u). L(x,y,K(z,u)) = L(x,K(y,u),z * u). L(x,K(y,z),u * z) = L(x,y,K(u,z)). L(x,y,K(z,u * y)) = L(x,z,K(u,y)). x != L(L(y,z,u * w),u,K(z,w * u)) | x = L(y,z,w * u). L(L(x,y,z * u),y,K(u,z)) = L(x,y,u * z). L(L(x,y,z * u),z,K(y,u)) = L(x,y,u * z). x != L(L(y,z,u),w,v5) | x = L(L(y,w,v5),z,u). L(x,y,z * u) = L(L(x,u,K(y,z)),y,u * z). L(L(x,y,K(z,u)),z,y * u) = L(x,z,u * y). L(L(x,y,K(z,u)),u,z * y) = L(x,u,y * z). ((K(x,x \ K(y,z)) \ (u / w)) \ v5) * (((u / w) \ 1) * K(x,x \ K(y,z))) = (w * (u \ K(x,x \ K(y,z)))) * (v5 * ((u / w) \ K(x,x \ K(y,z)))). ((K(x \ K(y,z),x) * (u / w)) \ v5) * (((u / w) \ 1) * K(x,x \ K(y,z))) = (w * (u \ K(x,x \ K(y,z)))) * (v5 * ((u / w) \ K(x,x \ K(y,z)))). ((K(x,x \ K(y,z)) * (u / w)) \ v5) * (((u / w) \ 1) * K(x,x \ K(y,z))) = (w * (u \ K(x,x \ K(y,z)))) * (v5 * ((u / w) \ K(x,x \ K(y,z)))). (((x / y) \ z) * K(u,u \ K(w,v5))) * (((x / y) \ 1) * K(u,u \ K(w,v5))) = (y * (x \ K(u,u \ K(w,v5)))) * (z * ((x / y) \ K(u,u \ K(w,v5)))). (((x / y) \ z) * K(u,u \ K(w,v5))) * ((y * (x \ 1)) * K(u,u \ K(w,v5))) = (y * (x \ K(u,u \ K(w,v5)))) * (z * ((x / y) \ K(u,u \ K(w,v5)))). (((x / y) \ z) * K(u,u \ K(w,v5))) * (y * ((x \ 1) * K(u,u \ K(w,v5)))) = (y * (x \ K(u,u \ K(w,v5)))) * (z * ((x / y) \ K(u,u \ K(w,v5)))). (((x / y) \ z) * K(u,u \ K(w,v5))) * (y * (x \ K(u,u \ K(w,v5)))) = (y * (x \ K(u,u \ K(w,v5)))) * (z * ((x / y) \ K(u,u \ K(w,v5)))). (x * (y \ K(z,z \ K(u,w)))) * (v5 * ((y / x) \ K(z,z \ K(u,w)))) = ((y / x) \ v5) * (K(z,z \ K(u,w)) * (x * (y \ K(z,z \ K(u,w))))). ((x / y) \ z) * (K(u,u \ K(w,v5)) * (y * (x \ K(u,u \ K(w,v5))))) = (y * (x \ K(u,u \ K(w,v5)))) * (z * ((x / y) \ K(u,u \ K(w,v5)))). ((x / y) \ z) * (y * (x \ 1)) = (y * (x \ K(u,u \ K(w,v5)))) * (z * ((x / y) \ K(u,u \ K(w,v5)))). (x * (y \ K(z,z \ K(u,w)))) * (v5 * ((y / x) \ K(z,z \ K(u,w)))) = ((y / x) \ v5) * (x * (y \ 1)). x != ((y / z) \ u) * (z * (y \ 1)) | x = (z / y) * (u * (z / y)). (x * (y \ K(z,z \ K(u,w)))) * (v5 * ((y / x) \ K(z,z \ K(u,w)))) = (x / y) * (v5 * (x / y)). (x * (y \ K(z,z \ K(u,w)))) * (v5 * (x * (y \ K(z,z \ K(u,w))))) = (x / y) * (v5 * (x / y)). x != (y * z) * (u * (y * z)) | x = y * (z * ((u * y) * z)). (x / y) * (z * (x / y)) = x * ((y \ K(u,u \ K(w,v5))) * ((z * x) * (y \ K(u,u \ K(w,v5))))). x * ((y \ K(z,z \ K(u,w))) * ((v5 * x) * (y \ K(z,z \ K(u,w))))) = (x / y) * (v5 * (x / y)). x * (y \ ((z * x) / y)) = (x / y) * (z * (x / y)). (x / y) * (z * (x / y)) = x * (y \ ((z * x) / y)). x != (y / z) * (u * (y / z)) | x = (z / y) \ (u / (z / y)). x * (y \ ((z * x) / y)) = (y / x) \ (z / (y / x)). (x / y) \ (z / (x / y)) = y * (x \ ((z * y) / x)). (x / y) * (((x / y) \ 1) * z) = x * (y \ ((((x / y) \ (z / (x / y))) * x) / y)). x * (y \ ((((x / y) \ (z / (x / y))) * x) / y)) = (x / y) * (((x / y) \ 1) * z). x * (y \ ((((x / y) \ (z / (x / y))) * x) / y)) = (x / y) * ((y * (x \ 1)) * z). x != (y / z) * ((z * (y \ 1)) * u) | x = L(u,z \ y,z \ y). x * (y \ ((((x / y) \ (z / (x / y))) * x) / y)) = L(z,y \ x,y \ x). x * (y \ (((y * (x \ ((z * y) / x))) * x) / y)) = L(z,y \ x,y \ x). x * ((x \ ((y * z) / x)) * (x * (z \ 1))) = L(y,z \ x,z \ x). x != L(y,z \ u,z \ u) | x = L(y,u * z,u * z). x * ((x \ ((y * z) / x)) * (x * (z \ 1))) = L(y,x * z,x * z). x * ((x \ 1) * ((y * z) * (z \ 1))) = L(y,x * z,x * z). x * ((x \ 1) * L(y,z,z)) = L(y,x * z,x * z). L(L(x,y,y),z,z) = L(x,z * y,z * y). L(x,y * z,y * z) = L(L(x,z,z),y,y). x != L(y,z * u,z * u) | x = L(y,u \ z,u \ z). L(L(x,y,y),z,z) = L(x,y \ z,y \ z). L(x,y \ z,y \ z) = L(L(x,y,y),z,z). x != L(1 / y,z \ u,z \ u) | x = ((1 / u) * z) \ (((1 / u) * z) / y). L(L(1 / x,y,y),z,z) = ((1 / z) * y) \ (((1 / z) * y) / x). ((1 / x) * y) \ (((1 / x) * y) / z) = L(L(1 / z,y,y),x,x). ((1 / x) * y) \ (((1 / x) * y) / z) = L(y \ (y / z),x,x). ((1 / x) * y) \ (1 / (z * (y \ x))) = L(y \ (y / z),x,x). (x \ y) / (z * (x \ y)) = L(x \ (x / z),y,y). (x \ y) \ ((x \ y) / z) = L(x \ (x / z),y,y). x != (y \ z) \ ((y \ z) / u) | x = (y * z) \ ((y * z) / u). L(x \ (x / y),z,z) = (x * z) \ ((x * z) / y). (x * y) \ ((x * y) / z) = L(x \ (x / z),y,y). x / L(y \ (y / ((y / (x * (1 / z))) * x)),x,x) = (x * y) * z. x * (1 / (y \ (y / ((y / (x * (1 / z))) * x)))) = (x * y) * z. x * ((1 / (y / ((y / (x * (1 / z))) * x))) * y) = (x * y) * z. x * (y * ((((y / (x * (1 / z))) * x) \ y) \ 1)) = (x * y) * z. x * (y * (((y * x) \ (y * (x * (1 / z)))) \ 1)) = (x * y) * z. x * (y * (L(1 / z,x,y) \ 1)) = (x * y) * z. x * (y * L(z,x,y)) = (x * y) * z. L(L(x,y,z),z,y) = x. (1 / x) * (y * L(z,y,x)) = ((1 / x) * y) * z. x * (y * (z * a(x,y,z))) = (x * y) * z. x * (y * (z * (((u / T(x,y)) / y) / z))) = (x * y) * (z * ((u / (x * y)) / z)). x * ((y * (z * u)) * a(y,z,u)) = (x * (y * (z * u))) * a(y,z,u). (x * (y * (z * u))) * a(y,z,u) = x * ((y * (z * u)) * a(y,z,u)). L(x,y,z) = L(L(L(x,u,w),y,z),w,u). L(L(L(x,y,z),u,w),z,y) = L(x,u,w). x \ ((x * y) * z) = y * (z * a(x,y,z)). x * y != z * (u * a(w,z,u)) | x \ (w \ ((w * z) * u)) = y. x \ (y \ ((y * x) * z)) = z * a(y,x,z). x != y * a(z,u,y) | x = R(1 / y,z,u) \ 1. x \ (y \ ((y * x) * z)) = R(1 / z,y,x) \ 1. x \ (y \ ((y * x) * z)) = a(y,x,z) * z. x \ (y \ (x * (T(y,x) * z))) = a(y,x,L(z,y,x)) * L(z,y,x). a(x,y,L(z,x,y)) * L(z,x,y) = y \ (x \ (y * (T(x,y) * z))). (1 / x) \ ((((1 / x) * y) * z) / (1 / x)) = (y * L(z,y,x)) * ((1 / x) \ 1). x != a(y,z,u) * u | x = L(u,y,z). x \ (y \ (x * (T(y,x) * z))) = L(L(z,y,x),y,x). L(x,y * (z * u),a(y,z,u)) = x. (x / (y * (z * u))) / a(y,z,u) = x / (a(y,z,u) * (y * (z * u))). x != L(y * z,u,y) | x = T(u,y \ 1) \ ((y * u) * z). a(x,y,z) * u = T(x * (y * z),a(x,y,z) \ 1) \ ((a(x,y,z) * (x * (y * z))) * u). T(x * (y * z),a(x,y,z) \ 1) \ ((a(x,y,z) * (x * (y * z))) * u) = a(x,y,z) * u. x != y / a(z,u,w) | x = y * a(z,w,u). x / (a(y,z,u) * (y * (z * u))) = (x / (y * (z * u))) * a(y,u,z). x / ((y * z) * u) = (x / (y * (z * u))) * a(y,u,z). (x / (y * (z * u))) * a(y,u,z) = x / ((y * z) * u). T(x * (y * z),a(x,z,y)) = (1 / ((x * y) * z)) \ a(x,z,y). (1 / ((x * y) * z)) \ a(x,z,y) = T(x * (y * z),a(x,z,y)). L(x / ((y * z) * u),y,K(z,u)) = a(y,u,z) * (x / (y * (z * u))). ((x * y) * z) * a(x,z,y) = T(x * (y * z),a(x,z,y)). T(x * (y * z),a(x,z,y)) = ((x * y) * z) * a(x,z,y). x * (y * z) = T(x * (y * z),a(x,z,y)). T(x * (y * z),a(x,z,y)) = x * (y * z). (1 / x) \ (1 / ((1 / x) * (y \ (z \ x)))) = (z * L(y,z,x)) * ((1 / x) \ 1). (1 / x) \ (1 / ((y * (z * x)) \ x)) = (y * L(z,y,x)) * ((1 / x) \ 1). (1 / x) \ ((1 / x) * (y * (z * x))) = (y * L(z,y,x)) * ((1 / x) \ 1). (x * L(y,x,z)) * ((1 / z) \ 1) = x * (y * z). (x * L(y,x,z)) * z = x * (y * z). (x * (y * z)) \ ((x * y) * (z * ((u / (x * y)) / z))) = L(L(((u / T(x,y)) / y) / z,z,y),y * z,x). L(L(((x / T(y,z)) / z) / u,u,z),z * u,y) = (y * (z * u)) \ ((y * z) * (u * ((x / (y * z)) / u))). T(x * (y * z),a(x,z,y)) \ ((a(x,y,z) * (x * (y * z))) * u) = a(x,y,z) * u. (x * (y * z)) \ ((a(x,y,z) * (x * (y * z))) * u) = a(x,y,z) * u. (x * (y * z)) \ (((x * y) * z) * u) = a(x,y,z) * u. (x * (y * z)) \ ((x * y) * (z * u)) = a(x,y,z) * L(u,z,x * y). L((x / T(y,z)) / (u * z),z * u,y) = (y * (z * u)) \ ((y * z) * (u * ((x / (y * z)) / u))). (x * (y * z)) \ ((x * y) * (z * ((u / (x * y)) / z))) = L((u / T(x,y)) / (z * y),y * z,x). x != (y * (z * u)) \ ((y * z) * (u * w)) | x = a(y,z,u) * L(w,u,y * z). L((x / T(y,z)) / (u * z),z * u,y) = a(y,z,u) * L((x / (y * z)) / u,u,y * z). a(x,y,z) * L((u / (x * y)) / z,z,x * y) = L((u / T(x,y)) / (z * y),y * z,x). a(x,y,z) * (u / (z * (x * y))) = L((u / T(x,y)) / (z * y),y * z,x). L((x / T(y,z)) / (u * z),z * u,y) = a(y,z,u) * (x / (u * (y * z))). L((x / T(y,z)) / (u * T(z,y)),T(z,y) * u,y) = a(y,T(z,y),u) * (x / (u * (y * T(z,y)))). L((x / T(y,z)) / (u * T(z,y)),z * u,y) = a(y,T(z,y),u) * (x / (u * (y * T(z,y)))). L((x / T(y,z)) / (u * T(z,y)),z * u,y) = a(y,z,u) * (x / (u * (y * T(z,y)))). L((x / T(y,z)) / (u * T(z,y)),z * u,y) = a(y,z,u) * (x / (u * (z * y))). L(a(x,y,z) * (u / (z * (y * x))),x,y * z) = (u / T(x,y)) / (z * T(y,x)). L(a(x,y,z) * (u / (x * (z * y))),y,z * x) = (u / T(y,z)) / (x * T(z,y)). L(L(x / ((y * z) * u),y,K(z,u)),u,z * y) = (x / T(u,z)) / (y * T(z,u)). x != L(L(y,z,K(u,w)),w,u * z) | x = L(y,w,z * u). (x / T(y,z)) / (u * T(z,y)) = L(x / ((u * z) * y),y,u * z). L(x / ((y * z) * u),u,y * z) = (x / T(u,z)) / (y * T(z,u)). (x / y) / (z * u) = (x / T(y,u)) / (z * T(u,y)). (x / T(y,z)) / (u * T(z,y)) = (x / y) / (u * z). (x * ((y / z) / (u * w))) / (x * ((y / z) / (u * w))) = a(u,w,K(z,y)). 1 = a(x,y,K(z,u)). a(x,y,K(z,u)) = 1. a(K(x,y),z,u) = 1. L(K(x,y),z,u) = K(x,y). L(x,y,K(z,u)) = x. L(x,y,T(z,u)) = L(x,y,z). L(x,K(y,z),u) = x. x != y | x = L(y,z,K(u,w)). L(x,y,K(z,u)) = L(x,w,K(v5,v6)). x != L(y * a(z,u,w),z,K(w,u)) | x = a(z,u,w) * y. x * a(y,z,u) = a(y,z,u) * x. a(x,y,z) * u = u * a(x,y,z). x != L(y,z,K(u,w)) | x = T(y,a(w,z,u)). x = T(x,a(y,z,u)). T(x,a(y,z,u)) = x. x != L(y \ (K(z,u) * w),y,K(u,z)) | x = (K(u,z) * y) \ w. x \ (K(y,z) * u) = (K(z,y) * x) \ u. (K(x,y) * z) \ u = z \ (K(y,x) * u). x * y != L(x * a(z,u,w),z,K(w,u)) | T(a(z,u,w),x) = y. T(a(x,y,z),u) = a(x,y,z). (K(x,y) * z) * u = K(x,y) * (z * u). (K(x,y) * (z * u)) / u != w | K(x,y) * z = w. L(x,y,T(z,u)) != w | L(x,y,z) = w. x * (y * K(z,u)) = (x * y) * K(z,u). (x * y) * K(z,u) = x * (y * K(z,u)). x * (K(y,z) * u) = (x * K(y,z)) * u. (x * K(y,z)) * u = x * (K(y,z) * u). K(x,y) * (z \ u) = (z * K(y,x)) \ u. (x * K(y,z)) \ u = K(z,y) * (x \ u). a(x,y,z) \ u = u / a(x,y,z). x / a(y,z,u) = a(y,z,u) \ x. x != T(y,a(z,u,w)) | x = T(y,L(w,u,z) \ w). x = T(x,L(y,z,u) \ y). T(x,L(y,z,u) \ y) = x. x * (a(y,z,u) \ 1) = a(y,z,u) \ x. K(x,L(y,z,u)) = K(x,y). x / (L(y,z,u) \ y) = (y \ L(y,z,u)) * x. T(x,L(y,z,u)) = x * K(x,y). x != L(y,z,T(u,w)) | x = L(y,T(z,w),u). L(x,y,z) = L(x,T(y,u),z). L(x,T(y,z),u) = L(x,y,u). L(x,y,z \ u) = L(x,y,u / z). L(x,y,z / u) = L(x,y,u \ z). L(x,y,z * (u \ 1)) = L(x,y,u \ z). x != T(a(y,z,u),w) | x = a(y,z,T(u,w)). a(x,y,z) = a(x,y,T(z,u)). a(x,y,T(z,u)) = a(x,y,z). x != T(a(y,z,u),w) | x = a(T(y,w),z,u). a(x,y,z) = a(T(x,u),y,z). a(T(x,y),z,u) = a(x,z,u). x * a(y,z,u) = (a(y,z,u) \ 1) \ x. (a(x,y,z) \ 1) \ u = u * a(x,y,z). x != L(y,T(z,u),w) | x = L(y,(z \ u) \ u,w). L(x,y,z) = L(x,(y \ u) \ u,z). L(x,(y \ z) \ z,u) = L(x,y,u). L(x,y * (z \ 1),u) = L(x,z \ y,u). L(x,y * (z \ u),w) = L(x,((1 / u) * z) \ y,w). L(x,((1 / y) * z) \ u,w) = L(x,u * (z \ y),w). L(x,y \ z,u) = L(x,(y / z) \ 1,u). L(x,(y / z) \ 1,u) = L(x,y \ z,u). L(x,(y * z) \ u,w) = L(x,u * (z \ (y \ 1)),w). L(x,y * (z \ (u \ 1)),w) = L(x,(u * z) \ y,w). a(x,y,(z \ u) \ u) = a(x,y,z). a(x,y,z * (u \ w)) = a(x,y,((1 / w) * u) \ z). a(x,y,((1 / z) * u) \ w) = a(x,y,w * (u \ z)). a(x,y,(z * u) \ u) = a(x,y,z \ 1). a(x,y,(z * u) \ w) = a(x,y,w * (u \ (z \ 1))). a(x,y,z * (u \ (w \ 1))) = a(x,y,(w * u) \ z). a(T(x,y),z,u) = L(a(x,z,u),w,K(v5,v6)). L(a(x,y,z),u,K(w,v5)) = a(T(x,v6),y,z). a(x \ y,z,u) = a(y / x,z,u). a(x / y,z,u) = a(y \ x,z,u). T(x,L(y,z,u)) = T(x,y). L(x,y,z) \ u = T(u / L(x,y,z),x). T(x / L(y,z,u),y) = L(y,z,u) \ x. x != T(y,L(z,u,w)) | x = T(y,R(z,u,w)). T(x,y) = T(x,R(y,z,u)). T(x,R(y,z,u)) = T(x,y). R(x,y,z) * T(u,x) = u * R(x,y,z). K(x,T(y,z)) * R(z,u,w) = R(z,u,w) * K(x,y). L(x,y,K(z,u)) != w | w = x. L(x,y,z * u) != w | w = L(x,y,u * z). L(x,y,z * u) != w | L(x,y,u * z) = w. x * (a(y,z,u) * w) = x * (w * a(y,z,u)). (a(x,y,z) \ u) \ u != w | w = a(x,y,z). (a(x,y,z) \ u) \ u != w | a(x,y,z) = w. x != L(y,z,u \ w) | x = L(y,z,(u \ 1) * w). L(x,y,z / u) = L(x,y,(u \ 1) * z). L(x,y,(z \ 1) * u) = L(x,y,u / z). x != a(y,z \ 1,(u \ 1) \ 1) | x = (u \ (z / y)) \ ((u \ z) / y). a(x,y \ 1,z) = (z \ (y / x)) \ ((z \ y) / x). (x \ (y / z)) \ ((x \ y) / z) = a(z,y \ 1,x). a(x,y,L(z \ 1,u,w) \ 1) = a(x,y,L(z,u,w)). L(x,y,z \ u) != w | L(x,y,u / z) = w. L(x,y,z * (u \ 1)) != w | L(x,y,u \ z) = w. (x * y) \ z = (T(x,u) * y) \ (K(x,u) * z). (T(x,y) * z) \ (K(x,y) * u) = (x * z) \ u. L(x,y,K(z,u) * w) = (K(z,u) * (w * y)) \ ((K(z,u) * w) * (y * x)). (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,u,K(x,y) * z). R(K(x,y) * z,u,w) = ((K(x,y) * (z * u)) * w) / (u * w). ((K(x,y) * (z * u)) * w) / (u * w) = R(K(x,y) * z,u,w). R(x,K(y,z) * u,w) * (K(y,z) * (u * w)) = (x * (K(y,z) * u)) * w. (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) != v5 | a(x,K(y,z) * u,w) = v5. (x \ y) * z = K(x,u) * ((T(x,u) \ y) * z). K(x,y) * ((T(x,y) \ z) * u) = (x \ z) * u. (T(x,y) * z) * u = K(x,y) * ((x * z) * u). K(x,y) * ((x * z) * u) = (T(x,y) * z) * u. (x * (y \ 1)) * z = K(y,x) * ((y \ x) * z). K(x,y) * ((x \ y) * z) = (y * (x \ 1)) * z. x * y != (z * K(u,w)) * v5 | x \ (z * (K(u,w) * v5)) = y. ((x * K(y,z)) * u) \ (x * (K(y,z) * (u * w))) = L(w,u,x * K(y,z)). a(x,y * K(z,u),w) = (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w). (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y * K(z,u),w). a(x * K(y,z),u,w) = (x * (K(y,z) * (u * w))) \ (((x * K(y,z)) * u) * w). (x * (K(y,z) * (u * w))) \ (((x * K(y,z)) * u) * w) = a(x * K(y,z),u,w). (x \ 1) * y = (x \ K(z,u)) * (K(u,z) * y). (x \ K(y,z)) * (K(z,y) * u) = (x \ 1) * u. (x \ y) * z = (x \ T(y,u)) * (K(u,y) * z). (x \ T(y,z)) * (K(z,y) * u) = (x \ y) * u. (x * (y * K(z,u))) * w = (x * y) * (K(z,u) * w). (K(x,y) * z) \ u = K(y,T(x,z)) * (z \ u). K(x,T(y,z)) * (z \ u) = (K(y,x) * z) \ u. x * a(y \ 1,z,u) = a(z,u,y) \ x. (x \ L(x,y,z)) \ u = u * a(z,y,x). a(x,y,((z * u) * w) \ (u * w)) = a(x,y,R(z,u,w) \ 1). x * (L(x,y,z) \ u) != w | (u / L(x,y,z)) * x = w. R(x,y,z) * u = ((x * u) / x) * R(x,y,z). ((x * y) / x) * R(x,z,u) = R(x,z,u) * y. a(T(x,y),z,u) != w | w = a(x,z,u). a(T(x,y),z,u) != w | a(x,z,u) = w. (x \ L(x,y,z)) * (u * (L(x,y,z) \ x)) = u. ((x \ y) * (z * u)) \ (K(x,w) * (((T(x,w) \ y) * z) * u)) = L(a(T(x,w) \ y,z,u),(T(x,w) \ y) * (z * u),K(x,w)). L(a(T(x,y) \ z,u,w),(T(x,y) \ z) * (u * w),K(x,y)) = ((x \ z) * (u * w)) \ (K(x,y) * (((T(x,y) \ z) * u) * w)). ((x \ y) * z) * u = K(x,w) * (((T(x,w) \ y) * z) * u). K(x,y) * (((T(x,y) \ z) * u) * w) = ((x \ z) * u) * w. x != (K(y,z) * u) \ w | x = u \ (K(z,y) * w). K(x,T(y,z)) * (z \ u) = z \ (K(x,y) * u). L(x \ R(x,y,z),x,x \ (x * u)) = (x * u) \ (R(x,y,z) * u). x * y != (z \ L(z,u,w)) * (v5 * (L(z,u,w) \ z)) | x \ v5 = y. L(x,y,z) \ u = x \ (u * (L(x,y,z) \ x)). x \ (y * (L(x,z,u) \ x)) = L(x,z,u) \ y. x * (L(x,y,z) \ u) = u * (L(x,y,z) \ x). x * (L(y,z,u) \ y) = y * (L(y,z,u) \ x). x * a(y,z,u) = u * (L(u,z,y) \ x). x * (L(x,y,z) \ u) = u * a(z,y,x). L(x,y,z) \ (x * u) = u * a(z,y,x). L(x,y,z) \ u = (x \ u) * a(z,y,x). (x \ y) * a(z,u,x) = L(x,u,z) \ y. (x \ y) * a(z,u,x) != w | L(x,u,z) \ y = w. x * (y * a(z,u,x)) = (x * y) * a(z,u,x). (x * y) * a(z,u,x) = x * (y * a(z,u,x)). L(a(x,y,z),u,z) = a(x,y,z). x * (y * a(z,u,y)) = (x * y) * a(z,u,y). (x * y) * a(z,u,y) = x * (y * a(z,u,y)). (x * a(y,z,u)) * u = x * (a(y,z,u) * u). x != y * (z * a(u,w,v5)) | x = y * (a(u,w,v5) * z). (x * y) * a(z,u,y) = x * (a(z,u,y) * y). (x * a(y,z,u)) * u = x * L(u,y,z). (x * a(y,z,u)) * u = x * (z \ (y \ ((y * z) * u))). (L(x,y,z) \ u) * x = (x \ u) * L(x,z,y). x != y * (a(z,u,w) * w) | x = (y * a(z,u,w)) * w. (x * y) * a(z,u,y) = (x * a(z,u,y)) * y. (x * a(y,z,u)) * u = (x * u) * a(y,z,u). (L(x,y,z) \ u) * x = ((x \ u) * x) * a(z,y,x). ((x \ y) * x) * a(z,u,x) = (L(x,u,z) \ y) * x. (K(x,y) * z) / u != w | K(x,y) * (z / u) = w. (x \ (y / z)) * a(z,y \ 1,x) = (x \ y) / z. L(x,y \ 1,z) \ (y / z) = (x \ y) / z. L(L(x,y \ 1,z),u,w) \ (y / z) = (L(x,u,w) \ y) / z. a(x,y,(T(z / u,z) * w) \ v5) = a(x,y,v5 * (w \ (z \ u))). a(x,y,(T(z \ u,z) * w) \ v5) = a(x,y,v5 * (w \ T(u \ z,z))). L(a(x,y,z),(z \ u) * z,w) = (w * ((z \ u) * z)) \ (w * ((L(z,y,x) \ u) * z)). (x * ((y \ z) * y)) \ (x * ((L(y,u,w) \ z) * y)) = L(a(w,u,y),(y \ z) * y,x). (x / L(y,z,u)) * y = x * a(u,z,y). x * y != (z * y) * a(u,w,y) | x = z * a(u,w,y). (x * y) / L(y,z,u) = x * a(u,z,y). x / L(y,z,u) = (x / y) * a(u,z,y). (x / y) * a(z,u,y) = x / L(y,u,z). x != y * a(z,u,w) | x = (w \ L(w,u,z)) \ y. x / L(y,z,u) = (y \ L(y,z,u)) \ (x / y). (x \ L(x,y,z)) \ (u / x) = u / L(x,y,z). a(x,y,z) \ (u / z) = u / L(z,x,y). x * y != (z * a(u,w,v5)) * v5 | x \ (z * (w \ (u \ ((u * w) * v5)))) = y. (x * y) \ (x * (z \ (u \ ((u * z) * y)))) = a(u,z,y). (x * y) \ (x * (R(1 / y,z,u) \ 1)) = a(z,u,y). (x * (y * z)) \ ((x * y) * (R(1 / L(z,y,x),u,w) \ 1)) = a(u,w,L(z,y,x)). (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w). a(x,y,(((z \ u) \ 1) * w) \ (((z \ 1) \ 1) * w)) = a(x,y,R(u \ 1,(z \ 1) \ 1,w) \ 1). L(L(x,y,z),u,w) \ (z / y) = (L(x,u,w) \ z) / y. x * y != L(L(z,u,w),v5,v6) \ (w / u) | x \ ((L(z,v5,v6) \ w) / u) = y. x \ ((L(y,x,z / u) \ z) / u) = (L(y,u,z) * x) \ (z / u). K(x,y) * (((z * u) * w) / (u * w)) = R(K(x,y) * z,u,w). K(x,y) * R(z,u,w) = R(K(x,y) * z,u,w). R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w). x != K(y,T(z,u)) * R(u,w,v5) | x = R(u,w,v5) * K(y,z). R(K(x,T(y,z)) * z,u,w) = R(z,u,w) * K(x,y). R(x * K(y,z),u,w) = R(x,u,w) * K(y,z). R(x * K(y,z),u,w) * v5 = R(x,u,w) * (K(y,z) * v5). ((x * K(y,z)) * u) * w = R(x,u,w) * (K(y,z) * (u * w)). R(x,y,z) * (K(u,w) * (y * z)) = ((x * K(u,w)) * y) * z. R(x,y,z) * (K(u,w) * (y * z)) = (x * (K(u,w) * y)) * z. x \ ((L(y,x,z \ u) \ u) / z) = (L(y,z,u) * x) \ (u / z). L(x \ R(x,y,z),x,u) = (x * u) \ (R(x,y,z) * u). L(a(x,y,z),x,u) = (x * u) \ (R(x,y,z) * u). (x * y) \ (R(x,z,u) * y) = L(a(x,z,u),x,y). (x * y) \ (R(x,z,u) * y) = a(x,z,u). (x * y) * a(x,z,u) = R(x,z,u) * y. x / a(y,z,u) = y * (R(y,z,u) \ x). x * (R(x,y,z) \ u) = u / a(x,y,z). (x / y) * a(K(y,x) / y,z,u) = R(K(y,x) / y,z,u) * x. x != y / a(z,u,w) | x = a(z,u,w) \ y. x * (R(x,y,z) \ u) = a(x,y,z) \ u. x * ((x \ (y / z)) * z) = a(x,x \ (y / z),z) \ y. a(x,x \ (y / z),z) \ y = x * ((x \ (y / z)) * z). (x * ((x \ (y / z)) * z)) \ y != u | a(x,x \ (y / z),z) = u. (x / y) * a(y \ K(y,x),z,u) = R(K(y,x) / y,z,u) * x. (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z). x * (K(y,z) * (u * w)) != (v5 * (K(y,z) * u)) * w | x = R(v5,u,w). R(x,K(y,z) * u,w) = R(x,u,w). R(x,y / z,u) = R(x,z \ y,u). R(x,y / z,u) = R(x,(1 / z) * y,u). R(x,(1 / y) * z,u) = R(x,z / y,u). x != R(y,z / u,w) | x = R(y,u \ z,w). R(x,(1 / y) * z,u) = R(x,y \ z,u). R(x,1 / y,z) = R(x,(u * y) \ u,z). R(x,(y * z) \ y,u) = R(x,1 / z,u). R(x,(y * z) \ y,u) = R(x,z \ 1,u). R(x,y \ z,u) = R(x,(z \ y) \ 1,u). R(x,(y \ z) \ 1,u) = R(x,z \ y,u). (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,u,x * K(y,z)). L(L(x,y,z),z * y,K(u,w)) = L(x,y,K(u,w) * z). L(x,y,K(z,u) * w) = L(x,y,w). L(x,y,K(z,u) * w) != v5 | v5 = L(x,y,w). L(x,y,K(z,u) * w) != v5 | L(x,y,w) = v5. L(x,y,z * K(u,w)) = L(x,y,z). L(x,y,z * T(u,w)) = L(x,y,z * u). L(x,y,T(z,u) * w) = L(x,y,z * w). L(x,y,(z / u) * w) = L(x,y,(u \ z) * w). L(x,y,z * u) = L(x,y,z * (K(w,v5) * u)). L(x,y,z * (K(u,w) * v5)) = L(x,y,z * v5). L(x,y,(z * u) \ w) = L(x,y,(u * z) \ w). L(x,y,(T(z,u) * w) * v5) = L(x,y,(z * w) * v5). L(x,y,z \ (K(u,w) * v5)) = L(x,y,z \ v5). L(x,y,z / u) = L(x,y,z / T(u,w)). L(x,y,z / T(u,w)) = L(x,y,z / u). L(x,y,z \ (u * w)) = L(x,y,z \ (w * u)). L(x,y,z * T(u,w)) != v5 | L(x,y,u * z) = v5. L(x,y,((1 / z) * u) * w) = L(x,y,(u / z) * w). x != L(y,z,u / w) | x = L(y,z,(w \ 1) * u). L(x,y,z / u) = L(x,y,(T(u,w) \ 1) * z). L(x,y,(T(z,u) \ 1) * w) = L(x,y,w / z). L(x,y,z / u) != w | L(x,y,u \ z) = w. L(x,y,(z * u) \ w) != v5 | L(x,y,(u * z) \ w) = v5. L(x,y,(z * (u \ 1)) * w) != v5 | L(x,y,(u \ z) * w) = v5. L(x,y,(z \ 1) * u) = L(x,y,(z \ K(w,v5)) * u). L(x,y,(z \ K(u,w)) * v5) = L(x,y,(z \ 1) * v5). L(x,y,(z \ u) * w) = L(x,y,(z \ T(u,v5)) * w). L(x,y,(z \ T(u,w)) * v5) = L(x,y,(z \ u) * v5). L(x,y,z / (u * w)) = L(x,y,(w * u) \ z). L(x,y,z \ (u / w)) = L(x,y,z \ (w \ u)). L(x,y,z \ (u * (w \ 1))) = L(x,y,z \ (w \ u)). L(x,y,z \ (u / w)) = L(x,y,z \ ((1 / w) * u)). L(x,y,z \ ((1 / u) * w)) = L(x,y,z \ (w / u)). L(x,y,(z * u) \ w) = L(x,y,(T(z,v5) * u) \ w). L(x,y,(T(z,u) * w) \ v5) = L(x,y,(z * w) \ v5). L(x,y,L(z,u,w)) = L(x,y,(w * u) \ ((u * z) * w)). L(x,y,(z * u) \ ((u * w) * z)) = L(x,y,L(w,u,z)). L(x,y,(z \ (u \ z)) * w) = L(x,y,w / u). L(x,y,R(z,u,w)) = L(x,y,(w * u) \ ((z * u) * w)). L(x,y,(z * u) \ ((w * u) * z)) = L(x,y,R(w,u,z)). L(x,y,z \ ((1 / u) * w)) = L(x,y,z \ ((w \ u) \ 1)). L(x,y,z \ ((u \ w) \ 1)) = L(x,y,z \ ((1 / w) * u)). L(x,y,R(z,u,w \ 1)) = L(x,y,(w / (z * u)) \ (u \ w)). L(x,y,(z / (u * w)) \ (w \ z)) = L(x,y,R(u,w,z \ 1)). x != L(y,z,u / w) | x = L(y,z,w \ u). L(x,y,(z \ (u \ z)) * w) = L(x,y,u \ w). L(x,y,(z \ (u \ z)) * w) != v5 | L(x,y,u \ w) = v5. L(x,y,(z \ u) * w) = L(x,y,(z / u) \ w). L(x,y,(z / u) \ w) = L(x,y,(z \ u) * w). L(x,y,(((1 / z) * u) * w) * v5) = L(x,y,((u / z) * w) * v5). x != L(y,z,(u / w) * v5) | x = L(y,z,(w \ u) * v5). L(x,y,((1 / z) * u) * w) = L(x,y,(z \ u) * w). L(x,y,(z \ K(u,w)) * v5) = L(x,y,z \ v5). L(x,y,(z * (u \ 1)) * w) = L(x,y,(z \ u) \ w). L(x,y,(z \ (u \ w)) * v5) = L(x,y,(z \ (w / u)) * v5). L(x,y,(z \ (u / w)) * v5) = L(x,y,(z \ (w \ u)) * v5). L(x,y,(z \ (u * w)) * v5) = L(x,y,(z \ ((1 / w) \ u)) * v5). L(x,y,(z \ ((1 / u) \ w)) * v5) = L(x,y,(z \ (w * u)) * v5). x != L(y,z,u \ (w * v5)) | x = L(y,z,u \ (v5 * w)). L(x,y,z \ (u \ w)) = L(x,y,z \ ((u \ 1) * w)). L(x,y,z \ ((u \ 1) * w)) = L(x,y,z \ (u \ w)). x != L(y,z,u \ (w / v5)) | x = L(y,z,u \ (v5 \ w)). L(x,y,z \ ((1 / u) * w)) = L(x,y,z \ (u \ w)). x != L(y,z,(u * w) \ v5) | x = L(y,z,(w * u) \ v5). L(x,y,(z * u) \ w) = L(x,y,(u * T(z,v5)) \ w). L(x,y,(z * T(u,w)) \ v5) = L(x,y,(u * z) \ v5). L(x,y,L(z,u,w \ 1)) = L(x,y,((w \ 1) * u) \ (w \ (u * z))). L(x,y,((z \ 1) * u) \ (z \ (u * w))) = L(x,y,L(w,u,z \ 1)). x != L(y,z,(u * w) \ v5) | x = L(y,z,(T(u,v6) * w) \ v5). L(x,y,(z * T(u,w)) \ v5) = L(x,y,(T(u,v6) * z) \ v5). L(x,y,(T(z,u) * w) \ v5) = L(x,y,(w * T(z,v6)) \ v5). L(x,y,(z * (1 / (u * w))) \ ((1 / w) * z)) = L(x,y,L(u,1 / (u * w),z)). L(x,y,L(z,1 / (z * u),w)) = L(x,y,(w * (1 / (z * u))) \ ((1 / u) * w)). L(x,y,(z * u) \ ((w * u) * z)) = L(x,y,L(w,u,z)). x != L(y,z,(u * w) \ ((v5 * w) * u)) | x = L(y,z,R(v5,w,u)). L(x,y,L(z,u,w)) = L(x,y,R(z,u,w)). L(x,y,R(z,u,w)) = L(x,y,L(z,u,w)). L(x,y,L(z,u,w \ 1)) = L(x,y,L(z,w,u)). L(x,y,L(z,u \ 1,w)) = L(x,y,L(z,w,u)). x != L(y,z,u \ ((1 / w) * v5)) | x = L(y,z,u \ (w \ v5)). L(x,y,z \ ((u \ w) \ 1)) = L(x,y,z \ (w \ u)). L(x,y,(((1 / z) * u) * w) \ v5) = L(x,y,(w * T(u / z,v6)) \ v5). L(x,y,(z \ u) * w) = L(x,y,(u \ z) \ w). L(x,y,(z \ u) \ w) = L(x,y,(u \ z) * w). L(x,y,z \ u) = L(x,y,((w * z) \ w) * u). L(x,y,((z * u) \ z) * w) = L(x,y,u \ w). L(x,y,L(z \ 1,z,u) * w) = L(x,y,z \ w). x != L(y,z,(u / w) \ v5) | x = L(y,z,(u \ w) * v5). L(x,y,R(z,u,w \ 1)) = L(x,y,(w \ (z * u)) * (u \ w)). L(x,y,(z \ (u * w)) * (w \ z)) = L(x,y,R(u,w,z \ 1)). x != L(y,z,R(u,w,v5)) | x = L(y,z,L(u,w,v5)). L(x,y,(z \ (u * w)) * (w \ z)) = L(x,y,L(u,w,z \ 1)). L(x,y,z \ (u * (w * z))) = L(x,y,((u / z) * w) * z). L(x,y,z * ((u * z) \ ((1 / w) \ 1))) = L(x,y,(u \ (z * w)) * (z \ 1)). x != L(y,z,(((1 / u) * w) * v5) \ v6) | x = L(y,z,(v5 \ (w \ u)) * v6). L(x,y,(z * T(u / w,v5)) \ v6) = L(x,y,(z \ (u \ w)) * v6). L(x,y,(z * (u / w)) \ v5) = L(x,y,(z \ (u \ w)) * v5). L(x,y,(z * (u \ w)) \ v5) = L(x,y,(z \ (w \ u)) * v5). L(x,y,((z \ u) * w) \ v5) = L(x,y,(w \ (u \ z)) * v5). x != L(y,z,((u \ 1) * w) \ (u \ (w * v5))) | x = L(y,z,L(v5,w,u \ 1)). L(x,y,(z \ (1 \ u)) * (u \ (z * w))) = L(x,y,L(w,z,u \ 1)). L(x,y,(z \ u) * (u \ (z * w))) = L(x,y,L(w,z,u \ 1)). L(x,y,(z \ (u * w)) * (u \ z)) = L(x,y,L(w,u,z \ 1)). x != L(y,z,((u * w) \ u) * v5) | x = L(y,z,w \ v5). L(x,y,L(z,u * w,u \ 1)) = L(x,y,w \ (u \ ((u * w) * z))). L(x,y,z \ (u \ ((u * z) * w))) = L(x,y,L(w,u * z,u \ 1)). L(x,y,L(z,u,((u * z) * w) \ 1)) = L(x,y,w \ (u \ ((u * z) * w))). L(x,y,(z \ u) * ((u / w) \ z)) = L(x,y,L(w,u / w,z \ 1)). L(x,y,L(z,u / z,w \ 1)) = L(x,y,(w \ u) * ((u / z) \ w)). L(x,y,((z * u) \ (u * w)) * T(z,u)) = L(x,y,L(w,u,(z * u) \ 1)). L(x,y,z * a(u,w,z)) = L(x,y,L(z,u * w,u \ 1)). L(x,y,L(z,u * w,u \ 1)) = L(x,y,z * a(u,w,z)). L(L(x,y,K(z,u)),K(z,u) * y,w) = L(x,y,w * K(z,u)). L(x,K(y,z) * u,w) = L(x,u,w * K(y,z)). x != L(y,z,u * K(w,v5)) | x = L(y,z,u). L(x,K(y,z) * u,w) = L(x,u,w). x != L(y,K(z,u) * w,v5) | x = L(y,w * K(z,u),v5). L(x,y,z) = L(x,y * K(u,w),z). L(x,y * K(z,u),w) = L(x,y,w). L(x,(y \ z) * y,u) = L(x,z,u). L(x,y * z,u) = L(x,z * y,u). L(x,y * T(z,u),w) = L(x,y * z,w). L(x,y \ z,u) = L(x,T(y,w) \ z,u). L(x,T(y,z) \ u,w) = L(x,y \ u,w). L(x,(y / z) \ u,w) = L(x,(z \ y) \ u,w). L(x,(y / z) * u,w) = L(x,(z \ y) * u,w). L(x,y * (z * K(u,w)),v5) = L(x,y * z,v5). x != L(y,z * (u \ 1),w) | x = L(y,u \ z,w). L(x,(y \ 1) * z,u) = L(x,y \ z,u). L(x,y * (z * u),w) = L(x,y * ((1 / u) \ z),w). L(x,y * ((1 / z) \ u),w) = L(x,y * (u * z),w). L(x,(y \ 1) \ z,u) = L(x,z * y,u). L(x,((1 / y) * z) \ u,w) = L(x,(z / y) \ u,w). L(x,(y \ z) \ u,w) = L(x,u * ((1 / z) * y),w). L(x,y * ((1 / z) * u),w) = L(x,(u \ z) \ y,w). x != L(y,(z \ 1) * u,w) | x = L(y,z \ u,w). L(x,(1 / y) * z,u) = L(x,y \ z,u). L(x,(y / z) * (u \ 1),w) = L(x,u \ (z \ y),w). L(x,y * (z \ T(u,w)),v5) = L(x,y * (z \ u),v5). x != L(y,z * (u \ (w \ 1)),v5) | x = L(y,(w * u) \ z,v5). L(x,y * ((z \ 1) * u),w) = L(x,(z * (1 / u)) \ y,w). L(x,(y * (1 / z)) \ u,w) = L(x,u * ((y \ 1) * z),w). x != L(y,(z / u) \ w,v5) | x = L(y,(u \ z) \ w,v5). L(x,((1 / y) * z) \ u,w) = L(x,(y \ z) \ u,w). x != L(y,((1 / z) * u) \ w,v5) | x = L(y,w * (u \ z),v5). L(x,(y \ z) \ u,w) = L(x,u * (z \ y),w). x != L(y,z * u,w) | x = L(y,u * z,w). L(x,(y \ z) \ u,w) = L(x,(z \ y) * u,w). L(x,(T(y,z) * (1 / z)) \ u,w) = L(x,u * (y \ T(z,z \ 1)),w). x != L(y,(z \ u) \ w,v5) | x = L(y,w * ((1 / u) * z),v5). L(x,(y \ z) * u,w) = L(x,u * ((1 / y) * z),w). L(x,y * ((1 / z) * u),w) = L(x,(z \ u) * y,w). L(x,y * (z * u),w) = L(x,((z \ 1) \ u) * y,w). L(x,((y \ 1) \ z) * u,w) = L(x,u * (y * z),w). L(x,y * (z * u),w) = L(x,y * ((z \ 1) \ u),w). L(x,y * ((z \ 1) \ u),w) = L(x,y * (z * u),w). x != L(y,(z * (1 / u)) \ w,v5) | x = L(y,w * ((z \ 1) * u),v5). L(x,y * (z \ T(u,u \ 1)),w) = L(x,y * ((T(z,u) \ 1) * u),w). L(x,y * (z \ T(u,u \ 1)),w) = L(x,y * T((z \ 1) * u,u),w). x != L(y,z * T(u,w),v5) | x = L(y,z * u,v5). L(x,y * (z \ T(u,u \ 1)),w) = L(x,y * ((z \ 1) * u),w). x != L(y,z * (u \ T(w,v5)),v6) | x = L(y,z * (u \ w),v6). L(x,y * ((z \ 1) * u),w) = L(x,y * (z \ u),w). L(x,y,L(z,u,w \ ((u * z) \ 1))) = L(x,y,w \ (u \ ((u * z) * w))). L(x,y,z * ((z * u) \ (u * w))) = L(x,y,L(w,u,(z * u) \ 1)). L(x,y,z * ((z * u) \ (u * w))) = L(x,y,L(w,u,u \ (z \ 1))). L(x,y,((z * u) \ (u * w)) * z) = L(x,y,L(w,u,u \ (z \ 1))). L(x,y,L(z,u,u \ (w \ 1))) != v5 | L(x,y,w * ((w * u) \ (u * z))) = v5. L(x,y,L(z,u,w \ (z \ (u \ 1)))) = L(x,y,w \ (u \ ((u * z) * w))). x != L(y,z,u \ (w \ v5)) | x = L(y,z,u \ ((1 / w) * v5)). L(x,y,L(z,u,w \ (z \ (u \ 1)))) = L(x,y,w \ ((1 / u) * ((u * z) * w))). L(x,y,z * ((u * z) \ w)) = L(x,y,(u \ (z * w)) * (z \ 1)). L(x,y,(z \ (u * w)) * (u \ 1)) = L(x,y,u * ((z * u) \ w)). L(x,y,z \ (u \ (z * w))) = L(x,y,z * ((u * z) \ w)). (x * (y * (K(z,u) * w))) \ ((x * y) * (K(z,u) * w)) = a(x,y * K(z,u),w). (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x * K(y,z),u,w). L(x,y,L(z,1 / (z * u),w)) = L(x,y,(w * (1 / (z * u))) \ (u \ w)). x != L(y,z,(u * (w / v5)) \ v6) | x = L(y,z,(u \ (w \ v5)) * v6). L(x,y,L(z,1 / (z * u),w)) = L(x,y,(w \ (1 \ (z * u))) * (u \ w)). L(x,y,L(z,1 / (z * u),w)) = L(x,y,(w \ (z * u)) * (u \ w)). x != L(y,z,(u \ (w * v5)) * (v5 \ u)) | x = L(y,z,L(w,v5,u \ 1)). L(x,y,L(z,1 / (z * u),w)) = L(x,y,L(z,u,w \ 1)). L(x,y,L(z,(z * u) \ 1,w)) = L(x,y,L(z,u,w \ 1)). L(x,y,L(z,u \ 1,w)) = L(x,y,L(z,z \ u,w \ 1)). L(x,y,L(z,z \ u,w \ 1)) = L(x,y,L(z,u \ 1,w)). L(x,y,L(z,u \ (z \ 1),w)) = L(x,y,L(z,u,w \ 1)). L(x,y,L(z,z \ u,w)) = L(x,y,L(z,u \ 1,w \ 1)). L(x,y,L(z,u \ 1,w \ 1)) = L(x,y,L(z,z \ u,w)). L(x,y,L(z,u / z,w \ 1)) = L(x,y,L(z,u \ 1,w)). x != L(y,z,L(u,w,v5 \ 1)) | x = L(y,z,L(u,v5,w)). L(x,y,L(z,z \ u,w)) = L(x,y,L(z,w,u \ 1)). L(x,y,L(z,u,w \ 1)) = L(x,y,L(z,z \ (u \ 1),w)). L(x,y,L(z,z \ (u \ 1),w)) = L(x,y,L(z,u,w \ 1)). L(x,y,L(z,z \ u,w)) = L(x,y,L(z,u,w)). x != L(y,z,L(u,w / u,v5 \ 1)) | x = L(y,z,(v5 \ w) * ((w / u) \ v5)). L(x,y,L(z,u \ 1,w)) = L(x,y,(w \ u) * ((u / z) \ w)). L(x,y,(z \ u) * ((u / w) \ z)) = L(x,y,L(w,u \ 1,z)). L(x,y,L(z,z \ (u \ (w \ 1)),v5)) = L(x,y,L(z,w * u,v5 \ 1)). L(x,y,(z \ (z / u)) * (z \ ((z * w) * u))) = L(x,y,L(w,(z / u) \ 1,z)). x != L(y,z,u \ (w * (v5 * u))) | x = L(y,z,((w / u) * v5) * u). L(x,y,L(z,u,w \ (z \ (u \ 1)))) = L(x,y,(((1 / u) / w) * (u * z)) * w). a(x,y,K(z,u) * w) = a(x,y * K(z,u),w). a(x,y * K(z,u),w) = a(x,y,K(z,u) * w). a(x,T(y,K(z,u)),w) = a(x,K(u,z) * y,K(z,u) * w). a(x,K(y,z) * u,K(z,y) * w) = a(x,T(u,K(z,y)),w). x != L(y,z,(u \ (w / v5)) * v6) | x = L(y,z,(u \ (v5 \ w)) * v6). L(x,y,L(z,(u / w) \ 1,u)) = L(x,y,(u \ (w \ u)) * (u \ ((u * z) * w))). L(x,y,(z \ (u \ z)) * (z \ ((z * w) * u))) = L(x,y,L(w,(z / u) \ 1,z)). L(x,y,L(z,u,w \ (z \ (u \ 1)))) = L(x,y,((1 / (w * u)) * (u * z)) * w). L(x,y,z \ (u \ ((u * w) * z))) = L(x,y,L(w,(u / z) \ 1,u)). L(x,y,z \ (u \ ((u * w) * z))) = L(x,y,L(w,u \ z,u)). x != L(y,z,u \ (w \ ((w * v5) * u))) | x = L(y,z,L(v5,w,u \ (v5 \ (w \ 1)))). L(x,y,L(z,u \ w,u)) = L(x,y,L(z,u,w \ (z \ (u \ 1)))). L(x,y,L(z,u,w \ (z \ (u \ 1)))) = L(x,y,L(z,u \ w,u)). x != L(y,z,((1 / u) * w) * v5) | x = L(y,z,(u \ w) * v5). L(x,y,L(z,u,w \ (z \ (u \ 1)))) = L(x,y,((w * u) \ (u * z)) * w). x != L(y,z,((u * w) \ (w * v5)) * u) | x = L(y,z,L(v5,w,w \ (u \ 1))). L(x,y,L(z,u,w \ (z \ (u \ 1)))) = L(x,y,L(z,u,u \ (w \ 1))). x != L(y,z,L(u,w,v5 \ (u \ (w \ 1)))) | x = L(y,z,L(u,w \ v5,w)). L(x,y,L(z,u,u \ (w \ 1))) = L(x,y,L(z,u \ w,u)). L(x,y,L(z,u,u \ (w \ v5))) = L(x,y,L(z,u \ (v5 \ w),u)). L(x,y,L(z,u \ (w \ v5),u)) = L(x,y,L(z,u,u \ (v5 \ w))). L(x,y,L(z,u \ w,u)) != v5 | L(x,y,w * ((w * u) \ (u * z))) = v5. L(x,y,L(z,(1 / u) * (w \ v5),u)) = L(x,y,L(z,u,u \ (v5 \ w))). L(x,y,L(z,(1 / u) * (w \ 1),u)) = L(x,y,L(z,u,u \ w)). L(x,y,L(z,u \ (w \ 1),w)) = L(x,y,L(z,w,w \ u)). x != L(y,z,L(u,w,v5 \ 1)) | x = L(y,z,L(u,w \ (u \ 1),v5)). L(x,y,L(z,u \ 1,(u \ 1) \ w)) = L(x,y,L(z,(w \ ((u \ 1) \ 1)) \ (z \ 1),u)). L(x,y,L(z,(u \ ((w \ 1) \ 1)) \ (z \ 1),w)) = L(x,y,L(z,w \ 1,(w \ 1) \ u)). (x * (y * z)) \ ((x * y) * R(L(z,y,x),u,w)) = a(u,w,L(z,y,x)). (x * (y * z)) \ (x * (y * R(z,u,w))) = a(u,w,L(z,y,x)). (x * (y * z)) \ (x * (y * L(z,u,w))) = a(u,w,L(z,y,x)). x != L(y,(z \ u) * z,w) | x = L(y,u,w). (x * ((y \ z) * y)) \ (x * ((L(y,u,w) \ z) * y)) = L(a(w,u,y),z,x). (x * ((y \ z) * y)) \ (x * ((y \ z) * L(y,u,w))) = L(a(u,w,y),z,x). x != (y * (z * u)) \ (y * (z * L(u,w,v5))) | x = a(w,v5,L(u,z,y)). L(a(x,y,z),u,w) = a(x,y,L(z,z \ u,w)). a(x,y,L(z,z \ u,w)) = L(a(x,y,z),u,w). a(x * K(y,z),u,w) != v5 | a(x,K(y,z) * u,w) = v5. L(x,y,L(z,(z \ 1) * (((u \ 1) \ 1) \ w),u)) = L(x,y,L(z,u \ 1,(u \ 1) \ w)). L(x,y,L(z,(z \ 1) * ((u \ 1) * w),u)) = L(x,y,L(z,u \ 1,(u \ 1) \ w)). L(x,y,L(z,(z \ 1) * (u \ w),u)) = L(x,y,L(z,u \ 1,(u \ 1) \ w)). L(x,y,L(z,u \ 1,(u \ 1) \ w)) = L(x,y,L(z,(z \ 1) * (u \ w),u)). L(x,y,L(z,u \ 1,(u \ 1) \ w)) = L(x,y,L(z,z \ (u \ w),u)). L(x,y,L(z,u \ 1,u * w)) = L(x,y,L(z,z \ (u \ w),u)). x != L(y,z,L(u,u \ (w \ (v5 \ 1)),v6)) | x = L(y,z,L(u,v5 * w,v6 \ 1)). L(x,y,L(z,u \ 1,u * (w \ 1))) = L(x,y,L(z,w * u,u \ 1)). x != L(y,z,L(u,w \ 1,v5)) | x = L(y,z,L(u,v5,w)). L(x,y,L(z,z \ (u \ w),u)) = L(x,y,L(z,u * w,u)). x != L(y,z,L(u,u \ w,v5)) | x = L(y,z,L(u,w,v5)). L(x,y,L(z,u * w,u)) = L(x,y,L(z,u \ w,u)). L(x,y,L(z,u \ w,u)) = L(x,y,L(z,u * w,u)). L(x,y,z * ((z * u) \ (u * w))) = L(x,y,L(w,u * z,u)). L(x,y,L(z,u \ 1,w \ u)) = L(x,y,L(z,w * u,u \ 1)). L(x,y,L(z,u * w,w \ 1)) = L(x,y,L(z,u \ w,w)). L(x,y,L(z,u \ w,w)) = L(x,y,L(z,w,u * w)). L(x,y,L(z,u * w,u \ 1)) = L(x,y,L(z,w \ u,u)). L(x,y,L(z,u,w)) = L(x,y,L(z,w,(u \ w) * w)). L(x,y,L(z,u,(w \ u) * u)) = L(x,y,L(z,w,u)). L(x,y,L(z,u,w \ u)) = L(x,y,L(z,u * w,u)). L(x,y,L(z,u * w,u)) = L(x,y,L(z,u,w \ u)). x != L(y,z,L(u,w * v5,w)) | x = L(y,z,v5 * ((v5 * w) \ (w * u))). L(x,y,L(z,u,w \ u)) = L(x,y,w * ((w * u) \ (u * z))). L(x,y,z * ((z * u) \ (u * w))) = L(x,y,L(w,u,z \ u)). x != L(y,z,L(u,w * v5,w \ 1)) | x = L(y,z,u * a(w,v5,u)). L(x,y,L(z,u \ w,w)) = L(x,y,z * a(w,u,z)). x != L(y,z,L(u,w \ v5,v5)) | x = L(y,z,L(u,v5,w * v5)). L(x,y,z * a(u,w,z)) = L(x,y,L(z,u,w * u)). L(x,y,L(z,u,w * u)) = L(x,y,z * a(u,w,z)). L(x,y,L(z,u,w * u)) = L(x,y,L(z,u,w)). x != L(y,z,L(u,w,(v5 \ w) * w)) | x = L(y,z,L(u,v5,w)). L(x,y,L(z,u,w \ u)) = L(x,y,L(z,w,u)). x != L(y,z,L(u,w,v5 \ w)) | x = L(y,z,L(u,v5,w)). L(x,y,z * ((z * u) \ (u * w))) = L(x,y,L(w,z,u)). L(a(T(x,y) \ z,u,w),(T(x,y) \ z) * (u * w),K(x,y)) = ((x \ z) * (u * w)) \ (((x \ z) * u) * w). L(a(T(x,y) \ z,u,w),(T(x,y) \ z) * (u * w),K(x,y)) = a(x \ z,u,w). a(x \ y,z,u) = a(T(x,w) \ y,z,u). a(T(x,y) \ z,u,w) = a(x \ z,u,w). a(T(x,T(y,z)),u,w) = a(y \ (x * T(y,z)),u,w). a(x \ (y * T(x,z)),u,w) = a(T(y,T(x,z)),u,w). x != a(T(y,z),u,w) | x = a(y,u,w). a(x \ (y * T(x,z)),u,w) = a(y,u,w). a(T(x * K(y,z),y),u,w) = a(x,u,w). a(x * K(y,z),u,w) = a(x,u,w). a(x,K(y,z) * u,w) = a(x,u,w). a(x \ 1,y,z) = a(x \ K(u,w),y,z). a(x \ K(y,z),u,w) = a(x \ 1,u,w). a(x,K(y,z) * u,w) = a(T(x,v5),u,w). a(T(x,y),z,u) = a(x,K(w,v5) * z,u). x != a(y,K(z,u) * w,K(u,z) * v5) | x = a(y,T(w,K(u,z)),v5). a(x,y,K(z,u) * w) = a(x,T(y,K(z,u)),w). a(x,T(y,K(z,u)),w) = a(x,y,K(z,u) * w). a(x,((y \ z) \ z) * u,w) = a(x,y * u,w). (x / y) * a(y \ 1,z,u) = R(K(y,x) / y,z,u) * x. R(K(x,y) / x,z,u) * y = (y / x) * a(x \ 1,z,u). a(x,K(y,z) * u,w) != v5 | a(x,u,w) = v5. a(x,T(y,z),u) != w | a(x,y,u) = w. a(x,y / z,u) != w | a(x,z \ y,u) = w. a(x,y,z) = a(x,y,K(u,w) * z). a(x,y,K(z,u) * w) = a(x,y,w). a(x,y,K(z,u) * w) != v5 | a(x,y,w) = v5. a(x,y,z \ u) = a(x,y,T(z,w) \ u). a(x,y,T(z,u) \ w) = a(x,y,z \ w). a(x,y,z * K(u,w)) = a(x,y,z). a(x,y,z \ u) = a(x,y,z \ T(u,w)). a(x,y,z \ T(u,w)) = a(x,y,z \ u). a(x,y,z \ (K(u,w) * v5)) = a(x,y,z \ v5). a(x,y,z * (u * w)) = a(x,y,z * (w * u)). a(x,y,z * (u * K(w,v5))) = a(x,y,z * u). a(x,y,((1 / z) * u) \ w) = a(x,y,(u / z) \ w). a(x,y,z \ (u \ w)) = a(x,y,z \ (w / u)). a(x,y,z \ (u / w)) = a(x,y,z \ (w \ u)). a(x,y,z \ (u * w)) = a(x,y,z \ ((1 / w) \ u)). a(x,y,z \ ((1 / u) \ w)) = a(x,y,z \ (w * u)). a(x,y,z \ (u / (u * (1 / w)))) = a(x,y,z \ w). a(x,y,z * u) != w | a(x,y,u * z) = w. a(x,y,(z \ u) \ u) != w | a(x,y,z) = w. a(x,y,T(z,u) \ w) != v5 | a(x,y,z \ w) = v5. a(x,y,(z * u) \ w) != v5 | a(x,y,(u * z) \ w) = v5. a(x,y,(z * (u \ 1)) * w) != v5 | a(x,y,(u \ z) * w) = v5. a(x,y,((z \ u) * w) \ (u * w)) != v5 | a(x,y,R(z,z \ u,w)) = v5. a(x,(y \ 1) \ z,u) = a(x,y * z,u). a(x,y,z) = a(x,u * ((u \ 1) * y),z). a(x,y * ((y \ 1) * z),u) = a(x,z,u). a(x,(y * z) \ y,u) = a(x,z \ 1,u). a(x,L(y \ 1,y,z),u) = a(x,y \ 1,u). x \ (a(x,y \ 1,(x * L(y \ 1,y,z)) \ u) \ u) = L(y \ 1,z,y) * ((x * L(y \ 1,y,z)) \ u). a(x,y,z \ ((u / w) * v5)) = a(x,y,z \ ((w \ u) * v5)). a(x,y,(z * u) \ w) = a(x,y,(T(z,v5) * u) \ w). a(x,y,(T(z,u) * w) \ v5) = a(x,y,(z * w) \ v5). a(x,y,(z * u) * w) = a(x,y,w * (u * z)). a(x,y,z * (u \ T(w,v5))) = a(x,y,z * (u \ w)). a(x,y,((1 / z) \ u) \ w) != v5 | a(x,y,(u * z) \ w) = v5. x != a(y,z,((1 / u) * w) \ v5) | x = a(y,z,v5 * (w \ u)). a(x,y,(z / u) \ w) = a(x,y,w * (z \ u)). a(x,y,((1 / z) / u) \ w) = a(x,y,w * (1 \ (u * z))). a(x,y,R(z,u \ 1,1 / w)) = a(x,y,((1 / w) \ (u / z)) \ (u * w)). a(x,y,((1 / z) \ (u / w)) \ (u * z)) = a(x,y,R(w,u \ 1,1 / z)). x != a(y,z,u \ (w / v5)) | x = a(y,z,u \ (v5 \ w)). a(x,y,z \ u) = a(x,y,z \ ((w * (1 / u)) \ w)). a(x,y,z \ ((u * (1 / w)) \ u)) = a(x,y,z \ w). x != a(y,z,(T(u / w,u) * v5) \ v6) | x = a(y,z,v6 * (v5 \ (u \ w))). a(x,y,((z / u) * w) \ v5) = a(x,y,v5 * (w \ (z \ u))). x != a(y,z,u * (w \ T(v5 \ v6,v6))) | x = a(y,z,(T(v6 \ v5,v6) * w) \ u). a(x,y,z * (u \ (w \ v5))) = a(x,y,(T(v5 \ w,v5) * u) \ z). a(x,y,(T(z \ u,z) * w) \ v5) = a(x,y,v5 * (w \ (u \ z))). a(x,y,z \ ((u \ 1) \ w)) = a(x,y,z \ (u * w)). a(x,y,z \ (u \ w)) = a(x,y,z \ ((1 / u) * w)). a(x,y,z \ ((1 / u) * w)) = a(x,y,z \ (u \ w)). x != y * a(z \ 1,u,w) | x = a(u,w,z) \ y. R(K(x,y) / x,z,u) * y = a(z,u,x) \ (y / x). L(K(x,y) / x,z,u) * y = a(z,u,x) \ (y / x). x != a(y,z,u) \ (w / u) | x = w / L(u,y,z). L(K(x,y) / x,z,u) * y = y / L(x,z,u). x != a(y,z,u \ ((1 / w) * v5)) | x = a(y,z,u \ (w \ v5)). a(x,y,z \ ((u \ 1) * w)) = a(x,y,z \ (u \ w)). x != a(y,z,(((u \ w) \ 1) * v5) \ (((u \ 1) \ 1) * v5)) | x = a(y,z,R(w \ 1,(u \ 1) \ 1,v5) \ 1). a(x,y,(((z \ u) \ 1) * w) \ ((z \ 1) \ w)) = a(x,y,R(u \ 1,(z \ 1) \ 1,w) \ 1). a(x,y,((1 / z) / u) \ w) = a(x,y,w * (u * z)). x != a(y,z,(u / w) \ v5) | x = a(y,z,v5 * (u \ w)). a(x,y,z * (u * w)) = a(x,y,z * ((1 / w) \ u)). a(x,y,z * ((1 / u) \ w)) = a(x,y,z * (w * u)). x != a(y,z,u * (w \ (v5 \ 1))) | x = a(y,z,(v5 * w) \ u). a(x,y,z * ((u \ 1) * w)) = a(x,y,(u * (1 / w)) \ z). a(x,y,(z * (1 / u)) \ w) = a(x,y,w * ((z \ 1) * u)). x != a(y,1 / z,(y * (1 / z)) \ u) | x = (y * ((y \ (u / z)) * z)) \ u. a(x,1 / y,z * ((x \ 1) * y)) = (x * ((x \ (z / y)) * y)) \ z. a(x,y,z * ((u \ 1) * w)) != v5 | a(x,y,(u \ w) * z) = v5. x != a(y,z,(T(u,w) * v5) \ v6) | x = a(y,z,(u * v5) \ v6). a(x,y,z * (u \ (w \ v5))) = a(x,y,((v5 \ w) * u) \ z). a(x,y,((z \ u) * w) \ v5) = a(x,y,v5 * (w \ (u \ z))). a(x,y,(z * (u \ w)) \ v5) = a(x,y,v5 * (z \ (w \ u))). a(x,y,(z * L(u \ 1,u,w)) \ v5) = a(x,y,v5 * (z \ (w \ (w * u)))). a(x,y \ 1,z * ((x \ 1) * y)) = (x * ((x \ (z / y)) * y)) \ z. a(x,y \ 1,(x \ y) * z) = (x * ((x \ (z / y)) * y)) \ z. (x * ((x \ (y / z)) * z)) \ y = a(x,z \ 1,(x \ z) * y). a(x,x \ (y / z),z) = a(x,z \ 1,(x \ z) * y). a(x,y \ 1,(x \ y) * z) = a(x,x \ (z / y),y). a(x,y \ 1,z * (x \ y)) = a(x,x \ (z / y),y). a(x,y,(z * u) * (u \ (z \ w))) != v5 | a(x,y,R(w,w \ z,u)) = v5. a(x,y,((1 / z) \ (u / w)) \ (u * z)) = a(x,y,R(w,u \ 1,z \ 1)). a(x,y,(z * L(u \ 1,u,w)) \ v5) = a(x,y,v5 * (z \ u)). a(x,y,((z / u) * w) \ (z * w)) = a(x,y,R(u,z \ 1,w \ 1)). x != a(y,z,((u / w) * v5) \ v6) | x = a(y,z,v6 * (v5 \ (u \ w))). a(x,y,R(z,u \ 1,w \ 1)) = a(x,y,(u * w) * (w \ (u \ z))). a(x,y,(z * u) * (u \ (z \ w))) = a(x,y,R(w,z \ 1,u \ 1)). a(x,y,R(z,z \ u,w)) = a(x,y,R(z,u \ 1,w \ 1)). a(x,y,R(z,u \ 1,w \ 1)) = a(x,y,R(z,z \ u,w)). a(x,y,R(z,u \ w,v5 \ 1)) = a(x,y,R(z,z \ (w \ u),v5)). a(x,y,L(z,u \ w,v5 \ 1)) = a(x,y,R(z,z \ (w \ u),v5)). a(x,y,R(z,z \ (u \ w),v5)) = a(x,y,L(z,w \ u,v5 \ 1)). a(x,y,L(z,z \ (u \ w),v5)) = a(x,y,L(z,w \ u,v5 \ 1)). a(x,y,L(z,u \ w,v5 \ 1)) = a(x,y,L(z,z \ (w \ u),v5)). a(x,y,L(z,u \ 1,w \ 1)) = a(x,y,L(z,z \ u,w)). x != a(y,z,u \ ((w \ 1) \ v5)) | x = a(y,z,u \ (w * v5)). a(x,y,R(z \ 1,(u \ 1) \ 1,w) \ 1) = a(x,y,(((u \ z) \ 1) * w) \ (u * w)). x != a(y,z,((u \ w) * v5) \ v6) | x = a(y,z,v6 * (v5 \ (w \ u))). a(x,y,R(z \ 1,(u \ 1) \ 1,w) \ 1) = a(x,y,(u * w) * (w \ (1 \ (u \ z)))). a(x,y,R(z \ 1,(u \ 1) \ 1,w) \ 1) = a(x,y,(u * w) * (w \ (u \ z))). x != a(y,z,(u * w) * (w \ (u \ v5))) | x = a(y,z,R(v5,u \ 1,w \ 1)). a(x,y,R(z \ 1,(u \ 1) \ 1,w) \ 1) = a(x,y,R(z,u \ 1,w \ 1)). a(x,y,R(z \ 1,u,w) \ 1) = a(x,y,R(z,u \ 1,w \ 1)). a(x,y,R(z,u \ 1,w \ 1)) = a(x,y,R(z \ 1,u,w) \ 1). a(x,y,R(z,u \ 1,w \ 1)) = a(x,y,L(z \ 1,u,w) \ 1). a(x,y,L(z,u \ 1,w \ 1)) = a(x,y,L(z \ 1,u,w) \ 1). x != a(y,z,L(u \ 1,w,v5) \ 1) | x = a(y,z,L(u,w,v5)). a(x,y,L(z,u \ 1,w \ 1)) = a(x,y,L(z,u,w)). x != a(y,z,L(u,w \ 1,v5 \ 1)) | x = a(y,z,L(u,u \ w,v5)). a(x,y,L(z,u,w)) = a(x,y,L(z,z \ u,w)). a(x,y,L(z,z \ u,w)) = a(x,y,L(z,u,w)). x != a(y,z,L(u,u \ w,v5)) | x = L(a(y,z,u),w,v5). a(x,y,L(z,u,w)) = L(a(x,y,z),u,w). a(x,L(y,z,u),w) = L(a(w,x,y),z,u). a(x,y,L(z,x,u)) = a(x,y,z). a(x,y,L(z,u,w)) = L(a(z,x,y),u,w). L(L(x,y,z),y,u) = a(y,u,x) * L(x,y,z). a(x,y,z) * L(z,x,u) = L(L(z,x,u),x,y). x != L(a(y,z,u),w,v5) | x = a(z,L(u,w,v5),y). a(x,y,L(z,u,w)) = a(x,L(y,u,w),z). a(x,L(y,z,u),w) = a(x,y,L(w,z,u)). L(x,L(y,z,u),w) = a(x,y,L(w,z,u)) * x. a(x,y,L(z,u,w)) * x = L(x,L(y,u,w),z). a(x,y,z) * L(y,z,u) = L(L(y,z,u),z,x). L(x,y,L(z,u,w)) = L(x,L(y,u,w),z). L(x,L(y,z,u),w) = L(x,y,L(w,z,u)). L(x,L(y,z,u),w) != v5 | L(x,y,L(w,z,u)) = v5. L(x,y,L(z * u,z,u)) * ((y * z) * u) = (x * L(y,z,u)) * (z * u). x != L(L(y,z,u),z,u) | x = u \ (z \ (u * (T(z,u) * y))). a(x,y,z) * L(y,z,x) = x \ (z \ (x * (T(z,x) * y))). x \ (y \ (x * (T(y,x) * z))) = a(x,z,y) * L(z,y,x). L(x,y,a(z,u,w) * L(u,w,z)) = L(x,y,z * ((w * z) \ (T(w,z) * u))). L(x,y,z * u) * ((y * z) * u) = (x * L(y,z,u)) * (z * u). x * y != (z * L(u,w,v5)) * (w * v5) | (L(z,u,w * v5) * ((u * w) * v5)) / y = x. (L(x,y,L(z \ 1,z,u) * w) * ((y * L(z \ 1,z,u)) * w)) / (L(z \ 1,u,z) * w) = x * L(y,L(z \ 1,z,u),w). L(x,y,a(z,u,w) * L(u,w,z)) = L(x,y,z * ((z * w) \ (w * u))). x != L(y,z,u * ((u * w) \ (w * v5))) | x = L(y,z,L(v5,u,w)). L(x,y,a(z,u,w) * L(u,w,z)) = L(x,y,L(u,z,w)). L(x,y,L(L(z,u,w),u,w)) = L(x,y,L(z,w,u)). x \ (a(x,y \ 1,z * (x \ y)) \ z) = L(y \ 1,u,y) * ((x * L(y \ 1,y,u)) \ z). x \ (a(x,x \ (y / z),z) \ y) = L(z \ 1,u,z) * ((x * L(z \ 1,z,u)) \ y). x \ (x * ((x \ (y / z)) * z)) = L(z \ 1,u,z) * ((x * L(z \ 1,z,u)) \ y). L(x \ 1,y,x) * ((z * L(x \ 1,x,y)) \ u) = (z \ (u / x)) * x. (L(x,y,z \ u) * ((y * L(z \ 1,z,w)) * u)) / (L(z \ 1,w,z) * u) = x * L(y,L(z \ 1,z,w),u). x / (L(y \ 1,z,y) * ((u * L(y \ 1,y,z)) \ (L(w,u,y \ x) \ x))) = w * L(u,L(y \ 1,y,z),x). x / ((y \ ((L(z,y,u \ x) \ x) / u)) * u) = z * L(y,L(u \ 1,u,w),x). x / ((y \ ((L(z,y,u \ x) \ x) / u)) * u) = z * L(y,x,L(u,u,w)). x / ((y \ ((L(z,y,u \ x) \ x) / u)) * u) = z * L(y,x,u). x / (((L(y,z,x) * u) \ (x / z)) * z) = y * L(u,x,z). L(L(x,y,z) * u,z,y) = x * L(u,z,y). L(x * y,z,u) = L(x,z,u) * L(y,z,u). L(x,y,z) * L(u,y,z) = L(x * u,y,z). x != L(K(y,z) / y,u,w) * z | x = z / L(y,u,w). L((K(x,L(y,z,u)) / x) * y,z,u) = L(y,z,u) / L(x,z,u). (x * L(y,z,u)) * L(w,z,u) = L((L(x,u,z) * y) * w,z,u). L((L(x,y,z) * u) * w,z,y) = (x * L(u,z,y)) * L(w,z,y). L((K(x,y) / x) * y,z,u) = L(y,z,u) / L(x,z,u). L(x / y,z,u) = L(x,z,u) / L(y,z,u). L(x,y,z) / L(u,y,z) = L(x / u,y,z). x * y != (z * L(u,w,v5)) * L(v6,w,v5) | L((L(z,v5,w) * u) * v6,w,v5) / y = x. L((L(x,y,z) * u) * w,z,y) / (L(u,z,y) * L(w,z,y)) = L(x,L(u,z,y),L(w,z,y)). L((L(x,y,z) * u) * w,z,y) / L(u * w,z,y) = L(x,L(u,z,y),L(w,z,y)). x != L(y,z,u) / L(w,z,u) | x = L(y / w,z,u). L(x,L(y,z,u),L(w,z,u)) = L(((L(x,u,z) * y) * w) / (y * w),z,u). L(((L(x,y,z) * u) * w) / (u * w),z,y) = L(x,L(u,z,y),L(w,z,y)). L(x / (y * ((L(z,u,w) * y) \ x)),w,u) = L(z,L(y,w,u),L(x,w,u)). L(L(L(x,y,z),u,w),z,y) = L(x,L(u,z,y),L(w,z,y)). x != L(L(L(y,z,u),w,v5),u,z) | x = L(y,w,v5). L(x,L(y,z,u),L(w,z,u)) = L(x,y,w). L(x,y,L(L(z,u,w),u,w)) = L(x,y,z). x != L(y,z,L(L(u,w,v5),w,v5)) | x = L(y,z,L(u,v5,w)). L(x,y,z) = L(x,y,L(z,u,w)). L(x,y,L(z,u,w)) = L(x,y,z). x != L(y,z,L(u,w,v5)) | x = L(y,z,u). L(x,y,L(L(z,u,w),v5,v6)) = L(x,y,z). x != L(y,L(z,u,w),L(v5,u,w)) | x = L(y,z,v5). L(x,L(y,z,u),w) = L(x,y,L(w,v5,v6)). x != L(y,z,u) | x = a(y,z,u) * y. L(x,L(y,z,u),w) = a(x,y,L(w,v5,v6)) * x. a(x,L(y,z,u),w) = a(x,y,L(w,v5,v6)). a(x,y,z) = a(x,y,L(z,u,w)). a(x,y,L(z,u,w)) = a(x,y,z). x != a(y,z,L(u,w,v5)) | x = L(a(y,z,u),w,v5). a(x,y,z) = L(a(x,y,z),u,w). L(a(x,y,z),u,w) = a(x,y,z). a(x,y,z) * u != L(a(x,y,z),w,v5) | 1 = u. 1 = a(a(x,y,z),u,w). end_of_list.