% ***************************************************************** % AIM: Some properties of T, L and R % % T(x / (x / y),z) = x / (x / T(y,z)) # label("T property"). % L(x / (x / y),z,u) = x / (x / L(y,z,u)) # label("L property"). % R(x / (x / y),z,u) = x / (x / R(y,z,u)) # label("R property"). % % K(x \ 1,x) = K(T(x,y) \ 1,T(x,y)) # label("KinvT"). % K(x \ 1,x) = K(L(x,y,z) \ 1,L(x,y,z)) # label("KinvL"). % K(x \ 1,x) = K(R(x,y,z) \ 1,R(x,y,z)) # label("KinvR"). % ***************************************************************** 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. % associator (right associated * a = left associated) (x * (y * z)) \ ((x * y) * z) = a(x,y,z) # label("associator"). % commutator ( (x * y) * K(y,x) = y * x ) (x * y) \ (y * x) = K(y,x) # label("commutator"). % inner mappings (y * x) \ (y * (x * u)) = L(u,x,y). ((u * x) * y) / (x * y) = R(u,x,y). x \ (u * x) = T(u,x). % abelian inner mapping group T(T(u,x),y) = T(T(u,y),x). T(L(u,x,y),z) = L(T(u,z),x,y). T(R(u,x,y),z) = R(T(u,z),x,y). L(R(u,x,y),z,w) = R(L(u,z,w),x,y). L(L(u,x,y),z,w) = L(L(u,z,w),x,y). R(R(u,x,y),z,w) = R(R(u,z,w),x,y). end_of_list. formulas(goals). T(x / (x / y),z) = x / (x / T(y,z)) # label("T property"). L(x / (x / y),z,u) = x / (x / L(y,z,u)) # label("L property"). R(x / (x / y),z,u) = x / (x / R(y,z,u)) # label("R property"). K(x \ 1,x) = K(T(x,y) \ 1,T(x,y)) # label("KinvT"). K(x \ 1,x) = K(L(x,y,z) \ 1,L(x,y,z)) # label("KinvL"). K(x \ 1,x) = K(R(x,y,z) \ 1,R(x,y,z)) # label("KinvR"). end_of_list. % ********************* % AIM: Auxiliary Lemmas % ********************* formulas(assumptions). % cancellation laws (long form) x * y != u | x * z != u | y = z # label("*-Cancellation 1"). y * x != u | z * x != u | y = z # label("*-Cancellation 2"). x / y != u | x / z != u | y = z # label("/-Cancellation 1"). y / x != u | z / x != u | y = z # label("/-Cancellation 2"). x \ y != u | x \ z != u | y = z # label("\-Cancellation 1"). y \ x != u | z \ x != u | y = z # label("\-Cancellation 2"). T(x,y) != u | T(z,y) != u | x = z # label("T-Cancellation 1"). L(z,x,y) != u | L(w,x,y) != u | z = w # label("L-Cancellation 1"). R(z,x,y) != u | R(w,x,y) != u | z = w # label("R-Cancellation 1"). % cancellation laws (short form) x * y != x * z | y = z # label("*-Cancellation 3"). y * x != z * x | y = z # label("*-Cancellation 4"). x / y != x / z | y = z # label("/-Cancellation 3"). y / x != z / x | y = z # label("/-Cancellation 4"). x \ y != x \ z | y = z # label("\-Cancellation 3"). y \ x != z \ x | y = z # label("\-Cancellation 4"). T(x,y) != T(z,y) | x = z # label("T-Cancellation 2"). L(z,x,y) != L(w,x,y) | z = w # label("L-Cancellation 2"). R(z,x,y) != R(w,x,y) | z = w # label("R-Cancellation 2"). % compatibility a(x,y,z) != 1 | L(z,y,x) = z # label("Compat 1"). L(x,y,z) != x | a(z,y,x) = 1 # label("Compat 2"). T(x,y) != x | T(y,x) = y # label("Compat 3"). T(x,y) != x | K(x,y) = 1 # label("Compat 4"). K(x,y) != 1 | T(x,y) = x # label("Compat 5"). % sometimes helpful for demodulation-free proofs x != y | x * z = y * z # label("Aux 1"). x != y | z * x = z * y # label("Aux 2"). x != y | x / z = y / z # label("Aux 3"). x != y | z / x = z / y # label("Aux 4"). x != y | x \ z = y \ z # label("Aux 5"). x != y | z \ x = z \ y # label("Aux 6"). x != y | y != z | x = z # label("Transitivity ="). end_of_list. % % Hints extracted from previously found proofs. % formulas(hints). K(x \ 1,x) = K(T(x,y) \ 1,T(x,y)). 1 * x = x. x * 1 = x. x \ (x * y) = y. x * (x \ y) = y. (x * y) / y = x. (x / y) * y = x. (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). 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). x * y != z | x * u != z | y = u. x * y != z | u * y != z | x = u. x / y != z | x / u != z | y = u. x / y != z | u / y != z | x = u. x \ y != z | x \ u != z | y = u. T(x,y) != z | T(u,y) != z | x = u. x * y != x * z | y = z. x * y != z * y | x = z. x / y != x / z | y = z. x / y != z / y | x = z. x \ y != x \ z | y = z. x \ y != z \ y | x = z. T(x,y) != T(z,y) | x = z. T(x,y) != x | T(y,x) = y. T(x,y) != x | K(x,y) = 1. K(x,y) != 1 | T(x,y) = x. x != y | x * z = y * z. x != y | z * x = z * y. x != y | x / z = y / z. x != y | y != z | x = z. K(T(c12,c13) \ 1,T(c12,c13)) != K(c12 \ 1,c12). 1 \ x = x. x \ x = 1. x \ (y \ (y * (x * z))) = z. 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 / x = 1. x / 1 = x. x * (((x \ y) * z) / z) = y. x / (y \ x) = y. ((1 / x) * x) * y = y. (x / y) \ x = y. (x \ (x * (y / z))) * z = y. (((x / y) / z) * z) * y = x. (x * y) * K(y,x) = y * x. K(x \ y,x) = y \ ((x \ y) * x). x \ ((y \ x) * y) = K(y \ x,y). (x * y) * L(z,y,x) = x * (y * z). L(x \ y,x,z) = (z * x) \ (z * y). R(x,y,z) * (y * z) = (x * y) * z. R(x / y,y,z) = (x * z) / (y * z). T(1,x) = x \ x. T(x,x) = x. x * T(y,x) = y * x. T(x,x \ y) = (x \ y) \ y. T(x / y,y) = y \ x. T(x \ (y * x),z) = T(T(y,z),x). 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). 1 * x != y | z != y | x = z. 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 * z | y \ x = z. x * y != z | x \ z = y. x != y * 1 | x = y. x * 1 != y | y = x. x != y * z | x / z = y. x * y != z | z / y = x. x != y / z | x * z = y. x / y != z | z * y = x. x != y \ z | y * x = z. x \ y != z | x * z = y. ((x / y) * y) * z = x * z. (x * (x \ y)) * z = y * z. (x * (x \ y)) / z = y / z. x != y | (x / z) * z = y. (x / y) * y = (x * z) / z. (x * y) / y = (x / z) * z. (x / y) * y = z * (z \ x). (x / y) * y = 1 * x. x != y | (x * z) / z = y. (x * y) / y = x * 1. x != y | z * (z \ x) = y. x * (x \ y) = z \ (z * y). x \ (x * y) = z * (z \ y). x * (x \ y) = y * 1. x * (x \ y) = 1 * y. (x * (x \ 1)) \ y = y. ((1 / x) * x) \ y = y. x / (y * (y \ 1)) = x. x / ((1 / y) * y) = x. x != y / 1 | x = y. x / 1 != y | y = x. T(x,y) != T(T(z,y),u) | T(z,u) = x. T(x,T(x,y)) = x. (x / (y \ x)) * z = y * z. ((x * y) * z) / u != R(x,y,z) | y * z = u. x * y = R(z,x,y) \ ((z * x) * y). R(x,y,z) \ ((x * y) * z) = y * z. (x * y) / T(x,y) = y. x != y / z | x \ y = z. x / y != z | z \ x = y. x != y | (z / x) \ z = y. (x / (1 * y)) \ x = y. (x / y) \ x = y / 1. x * ((y / z) \ y) = x * z. ((x / y) \ x) * z = y * z. x != y \ z | z / x = y. x \ y != z | y / z = x. x \ x != y | T(1,x) = y. T(1,x) = 1. T(x,1) = x. x != T(y,1) | x = y. T(x,1) != y | y = x. x * (y * (y \ 1)) != z | z = x. 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). x * y != z | y * T(x,y) = z. x * T(y / x,x) = y. (x \ y) * T(x,x \ y) = y. (x * T(y,x)) * z = (y * x) * z. x * y != ((x * z) / u) * u | z = y. x = T((y * x) / y,y). T((x * y) / x,x) = y. (x * T(y,x)) / x = 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. 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 * T(y,x) != z * x | y = z. T(x,y) * x = x * T(x,y). x \ y != z | T(y / x,x) = z. T(x / (x / y),x / y) = y. 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). 1 * x != y * z | x / z = y. (x / y) * y != z | z = x. (x / y) * y != z | x = z. (x * y) / y != z | z = x. x * (x \ y) != z | z = y. (x * y) \ (x * (y * z)) != u | L(z,y,x) = u. L(x,y \ 1,y) = y * ((y \ 1) * x). x * ((x \ 1) * y) = L(y,x \ 1,x). (x * y) \ (y * x) != z | K(y,x) = z. K(x \ 1,x) = (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) = x * (1 / x). ((x * y) * z) / (y * z) != u | R(x,y,z) = u. 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). x / T(y,y \ x) = y \ x. (x / (1 * y)) * y = x. (x / y) \ x != z | z = y. (x * y) * T(R(z,x,y),x * y) = (z * x) * y. T(x,y) = (z * T(T(x,z),y)) / z. (x * T(T(y,x),z)) / x = T(y,z). T(x,y) = T(T((z * x) / z,y),z). T(T((x * y) / x,z),x) = T(y,z). x != T(y,z) | (z * x) / z = y. T(x,y) != z | (y * z) / y = x. (x / ((y / z) * z)) * y = x. (x / (y * (y \ z))) * z = x. R(x,y,z) * (y * z) != u | u = (x * y) * z. R(x,y,z) * (y * z) != u | (x * y) * z = u. x * T(y,x) != z | z = y * x. x * T(y,x) != z | y * x = z. x / (y \ x) != z | z = y. (x * T(y,x)) / x != z | z = y. x \ (x * y) != z | z = y. x \ (y * 1) != z | z = x \ y. x \ (y * 1) != z | x \ y = z. L(x \ (y \ z),x,y) = (y * x) \ z. R((x / y) / z,z,y) = x / (z * y). x * K(y \ x,y) = (y \ x) * y. x * K(y,x / y) = y * (x / y). T(x,x \ y) / z = ((x \ y) \ y) / z. x * T(y,y \ z) = x * ((y \ z) \ z). T(x,x \ y) * z = ((x \ y) \ y) * z. x != y | z != y | x = z. ((x / y) * y) * z != u | u = x * z. ((x / y) * y) * z != u | x * z = u. (x / y) * y != z * u | z \ x = u. x * (y * (y \ z)) != u | u = x * z. x * (y * (y \ z)) != u | x * z = u. x != (y / z) * z | y = x. x = (x / y) * ((z / y) \ z). (x / y) * ((z / y) \ z) = x. x * ((y / z) \ y) != u | u / z = x. x != y * (y \ z) | z = x. x = ((y / z) \ y) * (z \ x). ((x / y) \ x) * (y \ z) = z. x != y * z | z * T(y,z) = x. x * T(x \ 1,x) = K(x \ 1,x). (x \ 1) \ K(x \ 1,x) = x. R(x,y / z,z) * y = (x * (y / z)) * z. R(x,y,y \ z) * z = (x * y) * (y \ z). (x \ 1) * x != y | y = K(x \ 1,x). (x \ 1) * x != y | K(x \ 1,x) = y. x != ((1 / y) * y) \ z | z = x. 1 / x = L(x \ 1,x,1 / x). L(x \ 1,x,1 / x) = 1 / x. x * L(y \ 1,y,z) = x * ((z * y) \ z). x / L(y \ 1,y,x) = x * y. (x * y) * L(y \ 1,y,x) = x. L((x \ y) \ 1,x \ y,x) = y \ 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 * R(1 / y,y,z) = x * (z / (y * z)). R(1 / x,x,y) \ y = x * y. 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(L(1 / x,y,z),x,u) = L(u / (x * u),y,z). R(x / (y * x),z,u) = R(R(1 / y,z,u),y,x). R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z). 1 * x != y | T(y,1) = x. x != y | T(y,1) = x. x * T(T(y,x),z) != u * x | T(y,z) = u. ((1 / x) * x) * y != z * u | y / u = z. x * T(T(y,x),z) != u | T(y,z) * x = u. T(L(x \ 1,x,1 / x),x) = x \ 1. x * y != x / z | L(y \ 1,y,x) = z. x / y != x * z | L(z \ 1,z,x) = y. (x * y) \ x != z | z = L(y \ 1,y,x). (x * y) \ x != z | L(y \ 1,y,x) = 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. (x * y) \ ((x \ (x * y)) * x) = K(y,x). K(x,y) = (y * x) \ ((y \ (y * x)) * y). x * T(x \ (y * x),z) = T(y,z) * x. x * y != (z * u) \ (z * (u * w)) | x \ L(w,u,z) = y. x \ L(y,x \ 1,x) = (x \ 1) * y. 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 / y) * T(y,z) = T(x / (x / y),z) * (x / y). T(x / (x / y),z) * (x / y) = (x / y) * T(y,z). (x * T(x \ y,z)) / x = T(y / x,z). (x * T(y,z)) / x = T((x * y) / x,z). (x * ((T(y,x) \ z) \ z)) / x = T(y,T(y,x) \ z). T(x,T(x,y) \ z) = (y * ((T(x,y) \ z) \ z)) / y. x \ ((y \ x) * y) != z | z = K(y \ x,y). x \ ((y \ x) * y) != z | K(y \ x,y) = z. x \ (y * (x / y)) != z | z = K(y,x / y). x \ (y * (x / y)) != z | K(y,x / y) = z. (x * T(y,x)) * z != u | (y * x) * z = u. (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z). (x * (x \ y)) * z != u | y * z = u. x * L(y,z \ x,z) = z * ((z \ x) * y). x * L(y,z,x / z) = (x / z) * (z * y). x * y != (z * (z \ u)) * w | x \ (u * w) = y. x \ (y * L(z,x \ y,x)) = (x \ y) * z. (x * y) * T(L(z,y,x),u) = x * (y * T(z,u)). (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)). x * (y * z) != (x * y) * u | L(z,y,x) = u. (x * y) * z != x * (y * u) | L(u,y,x) = z. x != y \ (z * y) | T(z,y) = x. T(x,x * y) = L(y \ (x * y),y,x). L(x \ (y * x),x,y) = T(y,y * x). x != (y * (y \ 1)) \ z | z = x. x * y = L((x \ 1) \ y,x \ 1,x). L((x \ 1) \ y,x \ 1,x) = x * y. L((x \ y) \ z,x \ y,x) = y \ (x * z). L(x \ 1,x,y) != z | (y * x) \ y = z. T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z. (x * y) * z != u * (y * z) | R(x,y,z) = u. (x * y) * (y \ 1) != z | z = R(x,y,y \ 1). (x * y) * (y \ 1) != z | R(x,y,y \ 1) = z. x != y / ((1 / z) * z) | y = x. x * y = R(x / (1 / y),1 / y,y). R(x / (1 / y),1 / y,y) = x * y. x != y / (z * (z \ 1)) | y = x. x * (y \ 1) = R(x / y,y,y \ 1). R(x / y,y,y \ 1) = x * (y \ 1). R(x / y,y,y \ z) = (x * (y \ z)) / z. R(T(x / y,z),y,u) = T((x * u) / (y * u),z). T((x * y) / (z * y),u) = R(T(x / z,u),z,y). R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z)). R(x / (y \ 1),y \ 1,y) = (x * y) / K(y \ 1,y). R(x,x \ 1,x) = x / K(x \ 1,x). x / K(x \ 1,x) = R(x,x \ 1,x). 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). (1 / x) * (y * x) = L(T(y,x),x,1 / x). L(T(x,y),y,1 / y) = (1 / y) * (x * y). T(R(x,1 / y,y),1) = (x * (1 / y)) * 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). K(x,1 / x) * x = R(x,1 / x,x). x * y != z * u | z \ (x * y) = u. x * (y \ (y * z)) != u | x * z = u. 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(T(1 / (x / y),z),x / y,y) = T(y / x,z). T(L(x,y,z),u) != w | L(T(x,u),y,z) = w. L(T(x \ 1,x),x,1 / x) = x \ 1. (x \ 1) * y != x \ z | L(y,x \ 1,x) = z. x \ y != (x \ 1) * z | L(z,x \ 1,x) = y. L(T(x,y),y,x) = T(x,x * y). L(T(x,y),z,u) != w | T(L(x,z,u),y) = w. T(L(x,y,x),y) = T(x,x * y). L(T(T(x,y),z),y,x) = T(T(x,x * y),z). (x * T(y,y * x)) / x = L(y,x,y). T(x,y) != T(z,u) | T((y * z) / y,u) = x. T((x * y) / x,y * x) = L(y,x,y). x * T(y,y * x) = L(y,x,y) * x. x * ((y / z) \ y) != u | x * z = u. x * ((y \ z) \ z) != u | x * T(y,y \ z) = u. (x * y) * L(x,y,x) = ((y * x) / y) * (x * y). ((x * y) / x) * (y * x) = (y * x) * L(y,x,y). 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(y,z,u) = L((x * y) / x,z,u) * x. L((x * y) / x,z,u) * x = x * L(y,z,u). 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(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). ((x / y) \ x) * z != u | T(u / y,(x / y) \ x) = z. T(x / y,(z / y) \ z) = y \ x. (x * L(x \ y,z,u)) / x = L(y / x,z,u). T(L(R(x / y,y,z),u,w),y * z) = L((y * z) \ (x * z),u,w). (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). T(x / y,y / x) = R((y / x) \ 1,y / x,x). R((x / y) \ 1,x / y,y) = T(y / x,x / y). T(x * y,1 / y) = R((1 / y) \ x,1 / y,y). R((1 / x) \ y,1 / x,x) = T(y * x,1 / x). x * R(x \ 1,x,y) = (y / (x * y)) * x. (x / (y * x)) * y = y * R(y \ 1,y,x). x * R(x \ 1,x,y) != z | (y / (x * y)) * x = z. (1 / x) / K(x,1 / x) != y | R(1 / x,x,1 / x) = y. x != y \ ((z \ y) * z) | K(z \ y,z) = x. 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(L(y \ 1,y,x),z). K(L(x \ 1,x,y),z) = K((y * x) \ y,z). 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(x / y,y) != z | z = y \ x. T(x / y,y) != z | y \ x = z. 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. x * ((y * x) \ (y * (z * x))) = L(z,x,y) * x. 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)). T(x / (y * x),z) * (y * x) = (T(1 / y,z) * y) * x. x * ((T(y,x) \ z) \ z) != u * x | T(y,T(y,x) \ z) = u. x * T(L(y,z \ x,z),u) = z * ((z \ x) * T(y,u)). x * y != z * L(T(u,z),w,v5) | x \ (L(u,w,v5) * z) = y. (x / y) \ (L(z,y,x / y) * x) = y * T(z,x). L(x \ (y * z),u,w) = L(L((y \ x) \ z,u,w),y \ x,y). L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w). T(R(x / y,y,y \ z),z) = z \ (x * (y \ z)). L(T(x \ 1,x),x,1 / x) != y | x \ 1 = y. x \ 1 = (1 / x) * ((x \ 1) * x). (1 / x) * ((x \ 1) * x) = x \ 1. (1 / x) * K(x \ 1,x) = x \ 1. x * y != (1 / z) * K(z \ 1,z) | x \ (z \ 1) = y. x \ ((x \ 1) \ 1) = K((x \ 1) \ 1,x \ 1). K((x \ 1) \ 1,x \ 1) = x \ ((x \ 1) \ 1). (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),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),y) * (y * z) = ((y \ (x / z)) * y) * z. T(R(x,y,x),y * x) = T(x,y). R(x,y,x) * (y * x) = (y * x) * T(x,y). T(R(x,y,z),u) != w | R(T(x,u),y,z) = w. R(T(x,y * x),y,x) = T(x,y). T(R(x,y / x,x),y) = T(x,y / x). x != T(y,y \ z) | (y \ z) \ z = x. (x \ y) \ y = R(T(x,(x \ y) * x),x \ y,x). R(T(x,(x \ y) * x),x \ y,x) = (x \ y) \ y. T(x,1 / x) = R(x,1 / x,x). R(x,1 / x,x) = T(x,1 / x). T(R(x,1 / y,y),1) != z | (x * (1 / y)) * y = z. (x * (1 / x)) * x = T(x,1 / x). R(x,1 / x,x) != y | K(x,1 / x) * x = y. K(x,1 / x) * x = T(x,1 / x). R(L(x,y,z),1 / x,x) = L(T(x,1 / x),y,z). (x * y) * x = (y * x) * T(x,y). (x * y) * T(y,x) = (y * x) * y. x != (y * (y \ 1)) * z | z = x. x = ((x \ 1) * x) * T(x,x \ 1). ((x \ 1) * x) * T(x,x \ 1) = x. x * y != ((z / u) * u) * w | x \ (z * w) = y. (x * (y / x)) \ (y * (y / x)) = T(y / x,x). x * T(y,y \ z) != u | x * ((y \ z) \ z) = u. ((x \ 1) * x) * ((x \ 1) \ 1) = x. K(x \ 1,x) * ((x \ 1) \ 1) = x. x != T(R(y,z,u),w) | R(T(y,w),z,u) = x. R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y). L(1 / (x \ y),x \ y,x) * (x \ y) = (x \ y) * (y \ 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 * 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 != z * R(1 / u,u,w) | (z * (w / (u * w))) / y = x. (x * (y / (z * y))) / x = R((x * (1 / z)) / x,z,y). R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x. 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. 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. x * ((y * (x \ z)) / y) = ((y * (z / x)) / y) * x. ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x). (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y. x != T(y / z,z) | z \ y = x. x \ y = (x * (y / x)) \ (y * (y / x)). (x * (y / x)) \ (y * (y / x)) = x \ y. (x * (1 / x)) * (x \ 1) = 1 / x. (1 / (1 / x)) / x = (1 / x) * (1 / (1 / x)). (1 / x) * (1 / (1 / x)) = (1 / (1 / 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 * L(u,y,x)) / z) = x * (y * ((z * u) / z)). 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. ((x * R(y,z,u)) / x) * (z * u) = (((x * y) / x) * z) * u. R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x. T(R(x,y,T(x,y)),z) * (x * y) = (x * y) * T(T(x,y),z). (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u)). L(x / (y * x),z,u) * (y * x) = (L(1 / y,z,u) * y) * x. R(x / (y * x),z,u) * (y * x) = (R(1 / y,z,u) * y) * x. (x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u)). (x * y) * L((y * T(x,y)) \ y,z,u) = y * (T(x,y) * L(T(x,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)). T(R(x,y,T(z,y)),u) * (z * y) = (T(x,u) * y) * T(z,y). 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). R(T((x * y) / x,z),x,y) * (x * y) = (x * y) * T(y,z). x \ T(1 \ x,y) = (x \ 1) * T((x \ 1) \ 1,y). (x \ 1) * T((x \ 1) \ 1,y) = x \ T(1 \ x,y). 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 \ 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). T(x / y,z) * y = (T(1 / (y / x),z) * (y / x)) * x. (T(1 / (x / y),z) * (x / y)) * y = T(y / x,z) * x. R(x,y \ 1,(y \ 1) \ 1) != z | (x * (y \ 1)) * T(y,y \ 1) = z. x * y != y * L(z,u,w) | L((y * z) / y,u,w) = x. L(((x * y) * x) / (x * y),y,x) = (y * x) / y. T(x / y,y / x) * y = (((y / x) \ 1) * (y / x)) * x. x * y != R((1 / z) \ u,1 / z,z) | T(u * z,1 / z) / y = x. T(x * y,1 / y) / y = ((1 / y) \ x) * (1 / y). (x / y) \ ((x \ (x / y)) * x) = y * T(y \ 1,x). x * y != R(L(z,u,w),1 / z,z) | L(T(z,1 / z),u,w) / y = x. L(T(x,1 / x),y,z) / x = L(x,y,z) * (1 / x). L(((x * y) * x) / (x * y),y,x) * y = y * x. x * y != L(z,x,u) * x | (u * x) \ (u * (z * x)) = y. (x * y) \ (x * ((((x * y) * x) / (x * y)) * y)) = x. ((x * (y / z)) / x) * z != u | u = z * ((x * (z \ y)) / x). ((x * (y / z)) / x) * z != u | z * ((x * (z \ y)) / x) = u. T(x \ (y * (z \ x)),z) = R(T(z \ y,x),z,z \ x). R(T(x \ y,z),x,x \ z) = T(z \ (y * (x \ z)),x). (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y). (x \ y) * T((x \ y) \ y,z) != u | T(x,z) * (x \ y) = u. T(x,y) * (x \ 1) = x \ T(x,y). (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z). x * y != T(z / (1 / u),w) * (1 / u) | x \ (T(z * u,w) / u) = y. (1 / x) \ (T(y * x,z) / x) = T((1 / x) \ y,z). T(1 / (1 / x),y) * (1 / x) = T(x,y) / x. (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x. T(x / (x / y),z) * (x / y) != u | (x / y) * T(y,z) = u. (1 / x) * T(x,y) = T(x,y) / x. x * y != T(1 / (1 / z),u) * (1 / z) | (T(z,u) / z) / y = x. (T(x,y) / x) / T(x,y) = 1 / x. T(x,y) / x != z * (1 / x) | T(1 / (1 / x),y) = z. (1 / x) * ((x \ y) \ y) = T(x,x \ y) / x. T(x,x \ y) / x = (1 / x) * ((x \ y) \ y). (1 / (x / y)) * (y \ x) = T(x / y,y) / (x / y). T(x / y,y) / (x / y) = (1 / (x / y)) * (y \ x). T((T(x,y) * (1 / x)) / T(x,y),T(x,y) / x) = L(1 / x,T(x,y),1 / x). T(x,x \ y) / z != u | ((x \ y) \ y) / z = u. ((x \ y) \ y) / x = (1 / x) * ((x \ y) \ y). (1 / x) * ((x \ y) \ y) = ((x \ y) \ y) / x. T(x,1 / y) / y = ((1 / y) \ (x / y)) * (1 / y). ((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x. K(x \ (x / y),x) = y * T(y \ 1,x). x != (1 / y) * T((1 / y) \ 1,z) | T(y,z) / y = x. T(x,y) / x = K(y \ (y / (1 / x)),y). K(x \ (x / (1 / y)),x) = T(y,x) / y. 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(x \ (x / (1 / y)),x) * y = T(y,x). T(x,y) = K(y \ (y / (1 / x)),y) * x. K((x * y) \ x,x * y) / y = T(1 / y,x * y). T(L(x,y,z),1 / x) / x = L(x,y,z) * (1 / x). (x * y) * x = x * ((((x * y) * x) / (x * y)) * y). x * ((((x * y) * x) / (x * y)) * y) = (x * y) * x. x * y != (z \ 1) * T((z \ 1) \ (z \ u),w) | (z \ T(u,w)) / y = x. (x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z). (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 \ y) / (y / x) = (1 / (y / x)) * (x \ y). (1 / (x / y)) * (y \ x) = (y \ x) / (x / y). (x \ y) * z != (x \ y) / (y / x) | T(1 / (y / x),x \ y) = z. 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 * (1 / y) != T(z,1 / y) / y | (1 / y) \ (z / y) = x. (1 / x) \ (L(x,y,z) / x) = L(x,y,z). (L(x,y,z) / x) / L(x,y,z) = 1 / x. T(x * y,x) = (((x * y) * x) / (x * y)) * y. (((x * y) * x) / (x * y)) * y = T(x * y,x). T(x * y,x) / y = ((x * y) * x) / (x * y). ((x * y) * x) / (x * y) = T(x * y,x) / y. T(T(x * y,x) / y,x * y) = x. T(T(x,x / y) / y,(x / y) * y) = x / y. T(T(x,x / y) / y,x) = x / y. x != y / (z \ y) | z = x. x = T(T(y,y / (x \ y)) / (x \ y),y). T(T(x,x / (y \ x)) / (y \ x),x) = y. (x * (x / y)) / x = T(x,x / y) / y. T(x,x / y) / y = (x * (x / y)) / x. T(T(x,y) / (y \ x),x) = y. (x * y) / x = T(x,y) / (y \ x). T(x,y) / (y \ x) = (x * y) / x. ((x * y) / x) * (y \ x) = T(x,y). T(x,y) = ((x * y) / x) * (y \ x). 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)). x / y != (z * (u / y)) / z | y * ((z * (y \ u)) / z) = x. x * ((y * (x \ y)) / y) = T(y,y / x). (x * y) * ((x * L(y \ 1,y,x)) / x) = T(x,x / (x * y)). (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w)). x \ R(1 \ x,y,z) = (x \ 1) * R((x \ 1) \ 1,y,z). (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(1 \ x,y,z). R(x / 1,y,z) / x = R(1 / (1 / x),y,z) * (1 / x). R(1 / (1 / x),y,z) * (1 / x) = R(x / 1,y,z) / x. x * T(x \ y,z) = y * ((y \ x) * T((y \ x) \ 1,z)). x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z). ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y. (x * y) * T((x * y) \ y,z) = (T(1 / x,z) * x) * y. 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 != z * (u * (u \ 1)) | x \ z = y. T(x,y) \ x = x * (T(x,y) \ 1). x * (T(x,y) \ 1) = T(x,y) \ 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) \ 1) = x. (x / y) * ((y \ x) \ 1) = T(x / y,y) \ (x / y). T(x / y,y) \ (x / y) = (x / y) * ((y \ x) \ 1). T(x,T(x,y) \ 1) != z | (T(x,y) \ 1) \ (T(x,y) \ x) = z. (T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z). T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y). (x \ y) \ (y / x) = (y / x) * ((x \ y) \ 1). (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y). (1 / x) * ((x \ y) \ y) != z | ((x \ y) \ y) / x = z. ((x \ 1) \ 1) / x = (x \ 1) \ (1 / x). ((x * y) / x) * (y \ 1) = (x \ (x * y)) \ ((x * y) / x). (x \ (x * y)) \ ((x * y) / x) = ((x * y) / x) * (y \ 1). (x / (x / y)) * (y \ 1) = ((x / y) \ x) \ (x / (x / y)). ((x / y) \ x) \ (x / (x / y)) = (x / (x / y)) * (y \ 1). (x \ 1) * (((x \ 1) \ 1) / x) = 1 / x. (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * 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). x != T(y / z,u) * z | z * T(z \ y,u) = x. x * T(x \ y,z) = (T(1 / (x / y),z) * (x / y)) * y. (T(1 / (x / y),z) * (x / y)) * y = x * T(x \ y,z). x * T(x \ y,x / y) = (((x / y) \ 1) * (x / y)) * y. (((x / y) \ 1) * (x / y)) * y = x * T(x \ y,x / y). K(T(1 / (1 / x),x \ 1),x \ 1) = T(x,x \ 1) / x. (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z). (x \ y) * R((x \ y) \ y,z,u) != w | R(x,z,u) * (x \ y) = w. R(x,y,z) * (x \ 1) = x \ R(x,y,z). R(1 / x,y,z) * x = (1 / x) \ R(1 / x,y,z). (1 / x) \ R(1 / x,y,z) = R(1 / x,y,z) * x. x != R(y / z,u,w) * z | z * R(z \ y,u,w) = x. x * R(x \ 1,y,z) = (1 / x) \ R(1 / x,y,z). (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z). (1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z). (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y). x != R(1 / y,y,z) | z / (y * z) = x. x / (y * x) = (1 / y) * ((x / (y * x)) * y). (1 / x) * ((y / (x * y)) * x) = y / (x * y). ((x / (y * x)) * y) * z != x / (y * x) | T(1 / y,(x / (y * x)) * y) = z. T(1 / x,(y / (x * y)) * x) = ((y / (x * y)) * x) \ (y / (x * y)). ((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y). R(1 / (1 / x),y,z) * (1 / x) = R(x,y,z) / x. R(x / (x / y),z,u) * (x / y) != w | (x / y) * R(y,z,u) = w. (1 / x) * R(x,y,z) = R(x,y,z) / 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. 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)). K(x \ (x / T(y,z)),x) = z \ ((y * z) * T((y * z) \ z,x)). (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y. (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z). (x / y) * z = (y \ x) * ((x / y) * ((y \ x) \ z)). (x \ y) * ((y / x) * ((x \ y) \ z)) = (y / x) * z. (x \ y) \ ((y / x) * z) != u | u = (y / x) * ((x \ y) \ z). (x \ y) \ ((y / x) * z) != u | (y / x) * ((x \ y) \ z) = u. x \ ((y * x) / y) = ((y * x) / y) * (x \ 1). ((x * y) / x) * (y \ 1) = y \ ((x * y) / x). ((x * y) / x) * z != u | z * ((x * T(y,z)) / x) = u. (x \ 1) * ((y * T(x,x \ 1)) / y) = x \ ((y * x) / y). x \ (y / (y / x)) = (y / (y / x)) * (x \ 1). (x / (x / y)) * (y \ 1) = y \ (x / (x / y)). ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z). K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y). (x * T(x \ 1,y)) * z != (u * x) * T((u * x) \ u,y) | T(u,x * T(x \ 1,y)) = z. T(x,x * T(x \ 1,y)) = x. T(x,(x \ 1) * x) = x. T(x \ 1,T(x,y) * (x \ 1)) = x \ 1. T(x \ 1,x \ T(x,y)) = x \ 1. T(1 / x,T(x,y) / x) = 1 / x. ((x \ 1) * x) * x = x * ((x \ 1) * x). R(x,x \ 1,x) = T(x,x \ 1). R(x,x \ 1,x) = (x \ 1) \ 1. T(x,x \ 1) \ x = (x \ 1) * x. R(x,x \ 1,x) != y | x / K(x \ 1,x) = y. x / K(x \ 1,x) = (x \ 1) \ 1. (x * (1 / y)) / x = T((x * (1 / y)) / x,T(y,z) / y). T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x. 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 \ 1) \ 1) \ x = K(x \ 1,x). (x \ 1) \ 1 = T((1 / x) \ 1,1 / x). T((1 / x) \ 1,1 / x) = (x \ 1) \ 1. R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y)). x != y * ((y \ 1) * z) | L(z,y \ 1,y) = x. L(x,x \ 1,x) = ((x \ 1) * x) * x. ((x \ 1) * x) * x = L(x,x \ 1,x). T(x,1 / x) = (x \ 1) \ 1. x != (y \ z) \ z | T(y,y \ z) = x. T(x,x \ 1) = T(x,1 / x). T(x,1 / x) = T(x,x \ 1). x * y != T(z,1 / z) | ((z \ 1) \ 1) / y = x. ((x \ 1) \ 1) / x = K(x,1 / x). ((x \ 1) \ 1) / x = x * (1 / x). T(1 / x,1 / (1 / x)) = x \ 1. (x * ((T(y,x) \ 1) \ 1)) / x = T(y,1 / T(y,x)). T(x,1 / T(x,y)) = (y * ((T(x,y) \ 1) \ 1)) / y. x * y != T(z,1 / z) | T(z,z \ 1) / y = x. T(x,x \ 1) / x = K(x,1 / x). T(x,x \ 1) / x = x * (1 / x). ((x \ 1) \ 1) / x != y | (x \ 1) \ (1 / x) = y. (x \ 1) \ (1 / x) = K(x,1 / x). (x \ 1) * (x * (1 / x)) = 1 / x. (1 / (1 / x)) * L(x \ 1,y,z) = L(1 / x,y,z) * (1 / (1 / x)). L(1 / x,y,z) * (1 / (1 / x)) = (1 / (1 / x)) * L(x \ 1,y,z). L(x \ 1,y,z) / (1 / x) = L(1 / x,y,z) * (1 / (1 / x)). L(1 / x,y,z) * (1 / (1 / x)) = L(x \ 1,y,z) / (1 / x). T(1 / (1 / x),x \ 1) = x. T(x,y) = T(T(1 / (1 / x),y),x \ 1). T(T(1 / (1 / x),y),x \ 1) = T(x,y). (x \ 1) * x = (1 / (1 / x)) * (x \ 1). (1 / (1 / x)) * (x \ 1) = (x \ 1) * x. (x * (1 / x)) * ((1 / x) \ y) = y * T(y \ ((1 / x) \ y),x \ 1). K(x,x \ 1) = T(x,x \ 1) / x. T(x,x \ 1) / x = K(x,x \ 1). (1 / x) / K(x,1 / x) = x \ 1. R(x,y \ 1,y * (1 / y)) * (1 / y) = (x * (y \ 1)) * (y * (1 / y)). K(x,x \ 1) * x = T(x,x \ 1). T(x,x \ 1) / x != y | x * (1 / x) = y. x * (1 / x) = K(x,x \ 1). K(x,x \ 1) = x * (1 / x). T(x,x \ 1) / x != y | K(x,1 / x) = y. K(x,1 / x) = K(x,x \ 1). ((x \ 1) \ 1) / x = K(x,x \ 1). x * y != T(z,z \ 1) / z | x \ K(z,z \ 1) = y. x \ K(x,x \ 1) = 1 / x. K(1 / x,x) = (1 / x) * (1 / (1 / x)). (1 / x) * (1 / (1 / x)) = K(1 / x,x). K(x \ 1,x) = K(x \ 1,(x \ 1) \ 1). K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x). x * (1 / x) != y | y = K(x,x \ 1). x * (1 / x) != y | K(x,x \ 1) = y. 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). R(1 / x,x,1 / x) = x \ 1. R(x \ 1,x,y) = R(y / (x * y),x,1 / x). R(x / (y * x),y,1 / y) = R(y \ 1,y,x). T(x,x \ 1) * y != K(x,x \ 1) * (x * z) | L(z,x,K(x,x \ 1)) = y. (x / (x / y)) * (y \ 1) != z | y \ (x / (x / y)) = z. x \ (1 / (1 / x)) = (x \ 1) * x. (1 / (x / y)) * (y \ x) != z | (y \ x) / (x / y) = z. (x \ 1) / (1 / x) = (x \ 1) * x. L(x,x \ 1,x) = 1 / (1 / x). x != (y \ 1) * y | K(y \ 1,y) = x. K(x \ 1,x) = x \ (1 / (1 / x)). x \ (1 / (1 / x)) = K(x \ 1,x). x * y != L(z,z \ 1,z) | (1 / (1 / z)) / y = x. (1 / (1 / x)) / x = (x \ 1) * x. L(x \ 1,x,x \ 1) = 1 / x. K(x \ 1,x) = (x \ 1) / (1 / x). (x \ 1) / (1 / x) = K(x \ 1,x). x * K(x \ 1,x) = 1 / (1 / x). K(x \ 1,x) = (1 / (1 / x)) / x. (1 / (1 / x)) / x = K(x \ 1,x). K(x \ 1,x) * (1 / x) = x \ 1. (1 / (1 / x)) / x != y | (1 / x) * (1 / (1 / x)) = y. (1 / x) * (1 / (1 / x)) = K(x \ 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). (1 / x) * (1 / (1 / x)) != y | (1 / (1 / x)) / x = y. (1 / (1 / x)) / x = K(1 / x,x). (1 / (1 / x)) / x != y | K(x \ 1,x) = y. K(x \ 1,x) = K(1 / x,x). K(1 / x,x) = K(x \ 1,x). K(x,x \ 1) = K((x \ 1) \ 1,x \ 1). K((x \ 1) \ 1,x \ 1) = K(x,x \ 1). x * K(1 / x,x) = 1 / (1 / x). (x * y) * K(1 / y,y) != z * (1 / (1 / y)) | R(x,y,K(1 / y,y)) = z. K(1 / x,(1 / x) \ 1) = K(x \ 1,x). K((x \ 1) \ 1,x \ 1) != y | x \ ((x \ 1) \ 1) = y. x \ ((x \ 1) \ 1) = K(x,x \ 1). x * K(x,x \ 1) = (x \ 1) \ 1. R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = x * (1 / x). x != (y * ((T(z,y) \ u) \ u)) / y | T(z,T(z,y) \ u) = x. T(x,T(x,y) \ 1) = T(x,1 / T(x,y)). T(x,1 / T(x,y)) = T(x,T(x,y) \ 1). (x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y). K(x \ (x / (y / z)),x) * z = y * T(y \ z,x). (x * T(x \ y,z)) / y = K(z \ (z / (x / y)),z). K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z. K((x * (y / z)) \ x,x * (y / z)) = (y * T(y \ z,x * (y / z))) / z. x != y * T(y \ (z * y),u) | T(z,u) * y = x. T(x,y / (x * y)) * y = K((y / (x * y)) \ 1,y / (x * y)) * (x * y). K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x. L((x \ y) / y,z,u) * y = (L(1 / x,z,u) * x) * (x \ y). x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w). x * y != z * ((u / w) \ u) | (z * w) / y = x. ((x \ (x / y)) * y) / (x \ (x / y)) = L(1 / (x \ (x / y)),x \ (x / y),x). L(1 / (x \ (x / y)),x \ (x / y),x) = ((x \ (x / y)) * y) / (x \ (x / y)). 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 / w)) / z,w,w \ 1) | ((z * (u * (w \ 1))) / z) / y = x. ((x * (y * (z \ 1))) / x) / (z \ 1) = ((x * (y / z)) / x) * z. T(R(x,y,T(x,y)),z) * (x * y) != u | (x * y) * T(T(x,y),z) = u. (x * y) * T(T(x,y),z) = (T(x,z) * y) * T(x,y). (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y). x * y != (z * (z \ 1)) * u | u / y = x. T(T(x,x \ 1),y) / T(x,x \ 1) = T(x,y) * (x \ 1). x != T(y,z) * (y \ 1) | y \ T(y,z) = x. x \ T(x,y) = T(T(x,x \ 1),y) / T(x,x \ 1). T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y). (T((x * y) / x,z) * x) * y = (x * y) * T(y,z). (x * T(y,z)) * y = (x * y) * T(y,z). x / T(x,y) = (1 / T(x,y)) * x. (1 / T(x,y)) * x = x / T(x,y). 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. (1 / T(x,y)) \ (x / T(x,y)) = x. x * (1 / T(x,y)) = T(x,1 / T(x,y)) / T(x,y). T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y)). T(x,y) = (1 / T(x,z)) \ (T(x,y) / T(x,z)). (1 / T(x,y)) \ (T(x,z) / T(x,y)) = T(x,z). (T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z). T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y)). ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x. (x * y) * ((z * L(u,y,x)) / z) != w | x * (y * ((z * u) / z)) = w. x * (y * ((x * (y \ 1)) / x)) = T(x,x / (x * y)). (x * y) * L((x * y) \ y,z,u) = (L(1 / x,z,u) * x) * y. (x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y. (x * y) * T((x * y) \ z,x) != u | ((x \ (z / y)) * x) * y = u. ((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,x)). ((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 * (T((x \ y) * x,x) / x) = T(y,x). (x \ T(y,x)) * x != z | z = T((x \ y) * x,x). (x \ T(y,x)) * x != z | T((x \ y) * x,x) = z. x * (T(y,x) / x) = T(x * (y / x),x). T(x * (y / x),x) = x * (T(y,x) / x). (x * y) * T((x * y) \ z,u) = (T((z / y) / x,u) * x) * y. (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u). ((x * R(y,z,u)) / x) * (z * u) != w | (((x * y) / x) * z) * u = w. (((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)). K(x \ (x / T(y,z)),x) = z \ ((y * T(y \ 1,x)) * z). T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y). x != K(y \ (y / z),y) | z * T(z \ 1,y) = x. T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y). x * y != K(z \ (z / T(u,w)),z) | x \ T(u * T(u \ 1,z),w) = y. T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z). 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(x,y) \ 1) * T(x,y) = T(x * T(x \ 1,T(x,y)),y). T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y). T(x,y) \ T(x * (x \ 1),y) = T(T(x,y) \ 1,x \ T(x,z)). T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y). 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). x != ((y * (z / u)) / y) * u | u * ((y * (u \ z)) / y) = x. x * ((y * (x \ z)) / y) = ((y * (z * (x \ 1))) / y) / (x \ 1). ((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x). T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x. (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y. (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y. x != (y * z) * T((y * z) \ u,w) | y * (z * T(z \ (y \ u),w)) = x. x * (y * T(y \ (x \ z),u)) = (T((z / y) / x,u) * x) * y. (T((x / y) / z,u) * z) * y = z * (y * T(y \ (z \ x),u)). T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y). T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1. (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z). ((x * y) / x) / ((y \ 1) \ 1) = (y \ 1) * ((x * ((y \ 1) \ K(y \ 1,y))) / x). (x \ 1) * ((y * ((x \ 1) \ K(x \ 1,x))) / y) = ((y * x) / y) / ((x \ 1) \ 1). T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x. x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y))). (x * L(x \ 1,y,z)) * u != (w * x) * L((w * x) \ w,y,z) | T(w,x * L(x \ 1,y,z)) = u. T(x,x * L(x \ 1,y,z)) = x. T(x \ y,(x \ y) * (y \ x)) = x \ y. T(x,x * (y \ (y / x))) = x. (L(x \ 1,y,z) * x) / L(x \ 1,y,z) = L(x,L(x \ 1,y,z),x). ((x \ (x / y)) * y) / (x \ (x / y)) = L(y,x \ (x / y),y). (x \ y) * (y \ x) = L(y \ x,x \ y,y \ x) * (x \ y). L(x \ y,y \ x,x \ y) * (y \ x) = (y \ x) * (x \ y). x * (y \ z) != (y \ z) * (z \ y) | L(1 / (y \ z),y \ z,y) = x. L(1 / (x \ y),x \ y,x) = L(y \ x,x \ y,y \ x). L(x \ y,y \ x,x \ y) = L(1 / (y \ x),y \ x,y). x * L(x \ y,y \ x,x \ y) = y * ((y \ x) * (1 / (y \ x))). x \ (y * L(y \ x,x \ y,y \ x)) = (x \ y) * (1 / (x \ y)). 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),x) = x * R(x \ 1,y,z). T(x * ((x * R(x \ 1,y,z)) / x),x) = x * ((x * R(x \ 1,y,z)) / x). (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u)). (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 \ 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. T(R(L(x / y,z,u),y,w),y * w) = L((y * w) \ (x * w),z,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). x != R(T(1 / y,z),y,y \ z) | z \ (y \ z) = x. x \ (y \ x) = T(x \ (K(y,y \ 1) * (y \ x)),y). 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 * (1 / y) | K(y,y \ 1) = x. K(x,x \ 1) = R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)). R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = K(x,x \ 1). x * L(x \ y,y \ x,x \ y) = y * K(y \ x,(y \ x) \ 1). (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y. (x * y) * L((x * y) \ y,z,u) != w | (x * L(x \ 1,z,u)) * y = w. (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 * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y. x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y. x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y. (x \ 1) * (K(x \ 1,x) * ((x \ 1) \ y)) = K(x \ 1,(x \ 1) \ 1) * y. (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y. T(1 / x,(y / (x * y)) * x) != z | L(x \ 1,x,y / (x * y)) = z. L(1 / x,y,z) * (1 / (1 / x)) != u | L(x \ 1,y,z) / (1 / x) = u. L(x \ 1,y,z) / (1 / x) = (1 / (1 / x)) * L(x \ 1,y,z). (1 / (1 / x)) * L(x \ 1,y,z) = L(x \ 1,y,z) / (1 / x). (1 / (1 / (x \ y))) * (y \ x) = L((x \ y) \ 1,x \ y,x) / (1 / (x \ y)). L((x \ y) \ 1,x \ y,x) / (1 / (x \ y)) = (1 / (1 / (x \ y))) * (y \ x). K(x,x \ 1) * ((1 / x) \ y) = y * T(y \ ((1 / x) \ y),x \ 1). 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)). (x \ y) * z != x \ (y * L(y \ x,x \ y,y \ x)) | 1 / (x \ y) = z. 1 / (x \ y) = L((x \ y) \ 1,x \ y,y \ x). L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y). ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x). (x \ y) / (1 / (y \ x)) = (x \ y) * (y \ x). (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y)). (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y. ((x * y) \ x) / (1 / y) = ((x * y) \ x) * 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). (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z). (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y. (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y. (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) | y \ ((z * y) / z) = x. x \ ((y * x) / y) = K(y,(y / (x \ 1)) / y). K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x). K(T(x,y),1 / x) = x * ((T(x,y) * (x \ 1)) / T(x,y)). x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x). K(T(x,y),1 / T(x,z)) = T(x,z) * ((T(x,y) * (T(x,z) \ 1)) / T(x,y)). T(x,y) * ((T(x,z) * (T(x,y) \ 1)) / T(x,z)) = K(T(x,z),1 / T(x,y)). K(L(x \ 1,y,z),1 / (x \ 1)) = x \ ((L(x \ 1,y,z) * x) / L(x \ 1,y,z)). x \ ((L(x \ 1,y,z) * x) / L(x \ 1,y,z)) = K(L(x \ 1,y,z),1 / (x \ 1)). K(x,(x / ((T(x,y) \ 1) \ 1)) / x) = (T(x,y) \ 1) \ ((T(x,y) \ x) / x). x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)) = K(T(x,y),1 / x). (x * y) * L((x * y) \ x,z,u) != w | x * (y * L(y \ 1,z,u)) = w. (x * y) * (y * L(y \ 1,z,u)) = ((x * y) * L((x * y) \ x,z,u)) * y. ((x * y) * L((x * y) \ x,z,u)) * y = (x * y) * (y * L(y \ 1,z,u)). (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,T(x,y) \ 1) = T(x,x / (x * T(x,y))). T(x,x / (x * T(x,y))) = T(x,T(x,y) \ 1). T(x,x / (x * T(x,y))) != z | x * (T(x,T(x,y) \ 1) / x) = z. 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). T(x * ((x * R(x \ 1,y,z)) / x),x) = x * R(1 / x,y,z). T(x * R(1 / x,y,z),x) = x * R(1 / x,y,z). T(x * (y / (x * y)),x) = x * R(1 / x,x,y). x != y * R(1 / z,z,u) | y * (u / (z * u)) = x. x * (y / (x * y)) = T(x * (y / (x * y)),x). T(x * (y / (x * y)),x) = x * (y / (x * y)). T(x,x * (y / (x * y))) = x. T(x / y,(x / y) * (y / x)) = x / y. T(x / y,y) = T(y \ x,(x / y) * (y / x)). T(x \ y,(y / x) * (x / y)) = T(y / x,x). x \ y = T(x \ y,(y / x) * (x / y)). T(x \ y,(y / x) * (x / y)) = x \ y. K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = (y * (y \ x)) / x. (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) * (x * y),x) = (x \ 1) * (y * x). T((x \ 1) * (x * y),x) != (x \ 1) * 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) | z * ((y * (z \ 1)) / y) = x. T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y). T(x * (1 / x),y) = K(x,(x / T(x,y)) / x). K(x,(x / T(x,y)) / x) = T(x * (1 / x),y). K(x,(x / y) / x) != z | y * ((x * (y \ 1)) / x) = z. 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). T(x,T(x,y) \ 1) != x * z | T(K(x,x \ 1),y) = z. T(x,y) * (1 / T(x,y)) = T(x * ((T(x,y) * (x \ 1)) / T(x,y)),y). T(x * ((T(x,y) * (x \ 1)) / T(x,y)),y) = T(x,y) * (1 / T(x,y)). T(x,y) * ((T(x,z) * (T(x,y) \ 1)) / T(x,z)) = T(x * (((x \ 1) * T((x \ 1) \ 1,z)) / T(x,z)),y). T(x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)),z) = T(x,z) * ((T(x,y) * (T(x,z) \ 1)) / T(x,y)). K(T(x,y),T(x,y) \ 1) = T(x * ((T(x,y) * (x \ 1)) / T(x,y)),y). T(x * ((T(x,y) * (x \ 1)) / T(x,y)),y) = K(T(x,y),T(x,y) \ 1). T(K(T(x,y),1 / x),y) = K(T(x,y),T(x,y) \ 1). K(T(x,y),T(x,y) \ 1) = T(K(T(x,y),1 / x),y). K(T(x,y),T(x,y) \ 1) != T(z,y) | K(T(x,y),1 / x) = z. T(x,y) != K(T(z,y),T(z,y) \ 1) | K(T(z,y),1 / z) = x. (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 \ 1) \ (K(x \ 1,x) * y) != z | L((1 / x) \ y,1 / x,K(x \ 1,x)) = z. L((1 / x) \ y,1 / x,K(x \ 1,x)) = K(x \ 1,x) * ((x \ 1) \ y). T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) = K(T(x,z),1 / T(x,y)). (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 != (y * (y \ z)) / u | z / u = x. x / x = K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)). K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = x / x. x != y / y | 1 = x. 1 = K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)). 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). K(1 / (x / y),(y / x) * (x / y)) = 1. K(1 / x,(y / (x * y)) * ((x * y) / y)) = 1. K(1 / x,(y / (x * y)) * x) = 1. T(1 / x,(y / (x * y)) * x) = 1 / x. L(x \ 1,x,y / (x * y)) = 1 / x. L(x \ 1,x,R(1 / x,x,y)) = 1 / x. ((x / (y * x)) * y) * (1 / y) = x / (y * x). R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x. R(x \ 1,x,y) \ (y / (x * y)) = K(x,x \ 1). 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). (x \ 1) \ 1 = T(x,y / (x * y)). T(x,y / (x * y)) = (x \ 1) \ 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. T(x / (y * x),y) = ((x / (y * x)) \ 1) \ 1. T(x / (y * x),y) != z | R(y \ 1,y,x) = z. R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1. R(x \ 1,x,y) \ (y / (x * y)) = K((y / (x * y)) \ 1,y / (x * y)). K((x / (y * x)) \ 1,x / (y * x)) = R(y \ 1,y,x) \ (x / (y * x)). x != R(y \ 1,y,z) \ (z / (y * z)) | K(y,y \ 1) = x. K(x,x \ 1) = K((y / (x * y)) \ 1,y / (x * y)). K((x / (y * x)) \ 1,x / (y * x)) = K(y,y \ 1). K(x,x \ 1) * (x * y) = T(x,x \ 1) * y. L(x,y,K(y,y \ 1)) = x. L(x,1 / y,K(y \ 1,y)) = x. L((1 / x) \ y,1 / x,K(x \ 1,x)) != z | K(x \ 1,x) * ((x \ 1) \ y) = z. 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. T(x \ ((1 / y) \ x),y \ 1) = x \ ((y \ 1) \ x). x * y != z * (z \ u) | x \ u = y. K(x \ 1,x) \ y = (1 / x) * ((x \ 1) \ y). (1 / x) * ((x \ 1) \ y) = K(x \ 1,x) \ y. x * T(x \ ((1 / y) \ x),y \ 1) = (y \ 1) \ x. x * T(x \ ((1 / y) \ x),y \ 1) != z | K(y,y \ 1) * ((1 / y) \ x) = z. K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ 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. (1 / x) * ((x \ 1) \ y) != z | K(x \ 1,x) \ y = z. K(x \ 1,x) \ y = K(x,x \ 1) * y. K(x,x \ 1) * y != z | K(x \ 1,x) * z = y. T((x * (1 / y)) / x,T(y,z) / y) != u | (x * (1 / y)) / x = u. (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x). T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y). T(L(x / y,z,u),y) != w | L(y \ x,z,u) = w. L(x \ 1,T(x,y),1 / x) = (T(x,y) * (x \ 1)) / T(x,y). (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x). x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x). x != ((y \ (y / z)) * z) / (y \ (y / z)) | L(z,y \ (y / z),z) = x. L(x,y \ (y / x),x) = L(1 / (y \ (y / x)),y \ (y / x),y). L(1 / (x \ (x / y)),x \ (x / y),x) = L(y,x \ (x / y),y). (x \ y) / (1 / (y \ x)) = (1 / (1 / (y \ x))) * (x \ y). (1 / (1 / (x \ y))) * (y \ x) = (y \ x) / (1 / (x \ y)). x != (y \ z) / (1 / (z \ y)) | (y \ z) * (z \ y) = x. (x \ y) * (y \ x) = (1 / (1 / (y \ x))) * (x \ y). (1 / (1 / (x \ y))) * (y \ x) = (y \ x) * (x \ y). (x \ y) * z != (x \ y) / (1 / (y \ x)) | T(1 / (1 / (y \ x)),x \ y) = z. T(1 / (1 / (x \ y)),y \ x) = x \ y. T(1 / (1 / x),(y * x) \ y) = y \ (y * x). x != y \ (y * z) | z = x. x = T(1 / (1 / x),(y * x) \ y). 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). (x \ 1) \ 1 = T(x,(y * x) \ y). T(x,(y * x) \ y) = (x \ 1) \ 1. x * (y \ z) != (y \ z) * (z \ y) | L(z \ y,y \ z,z \ y) = x. L(x \ y,y \ x,x \ y) = 1 / (1 / (x \ y)). L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x)). x * (1 / (1 / (x \ y))) = y * K(y \ x,(y \ x) \ 1). x * K(x \ y,(x \ y) \ 1) = y * (1 / (1 / (y \ x))). L(1 / (x \ (x / y)),x \ (x / y),x) != z | L(y,x \ (x / y),y) = z. L(x,y \ (y / x),x) = 1 / (1 / ((y / x) \ y)). L(x,y \ (y / x),x) = 1 / (1 / x). L(x,(y * x) \ y,x) = 1 / (1 / x). (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). 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). (x / (T(y,z) * x)) * T(y,z) = T(y * R(y \ 1,T(y,z),x),z). T(x * R(x \ 1,T(x,y),z),y) = (z / (T(x,y) * z)) * T(x,y). T(x * R(x \ 1,T(x,y),x \ 1),y) = ((x \ 1) / (x \ T(x,y))) * T(x,y). T(x * T(x \ 1,T(x,y)),y) = ((x \ 1) / (x \ T(x,y))) * T(x,y). ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y). x * T(y,z) != T(y * T(y \ 1,T(y,z)),z) | T(y,z) \ 1 = x. T(x,y) \ 1 = (x \ 1) / (x \ T(x,y)). (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1. T(T(x,y) \ 1,x \ T(x,y)) = (x \ T(x,y)) \ (x \ 1). T(T(x,y) \ 1,x \ T(x,z)) != u | T(x,y) \ 1 = u. T(x,y) \ 1 = (x \ T(x,y)) \ (x \ 1). (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1. (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). x * y != (z * x) * L((z * x) \ x,u,w) | T(z * L(z \ 1,u,w),x) = y. 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). x * L(y \ 1,y,z) != u | x * ((z * y) \ z) = u. T(x,y) * ((z * T(x,y)) \ z) = T(x * L(x \ 1,T(x,y),z),y). T(x * L(x \ 1,T(x,y),z),y) = T(x,y) * ((z * T(x,y)) \ z). T(x * L(x \ 1,T(x,y),1 / x),y) = T(x,y) * ((T(x,y) / x) \ (1 / x)). T(K(T(x,y),1 / x),y) = T(x,y) * ((T(x,y) / x) \ (1 / x)). T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y). x != T(K(T(y,z),1 / y),z) | K(T(y,z),T(y,z) \ 1) = x. K(T(x,y),T(x,y) \ 1) = T(x,y) * ((T(x,y) / x) \ (1 / x)). T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1). x * y != K(x,x \ 1) | 1 / x = y. 1 / T(x,y) = (T(x,y) / x) \ (1 / x). (T(x,y) / x) \ (1 / x) = 1 / T(x,y). (T(T(x,x \ 1),y) / T(x,x \ 1)) \ (x \ 1) = 1 / T(T(x,x \ 1),y). (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y). (x \ T(x,y)) \ (x \ 1) != z | T(x,y) \ 1 = z. T(x,y) \ 1 = 1 / T(T(x,x \ 1),y). 1 / T(T(x,x \ 1),y) = T(x,y) \ 1. (T(x,y) \ 1) \ 1 = T(T(x,x \ 1),y). T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1. T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1. x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x. T(x,T(x,y) \ 1) = (x \ 1) \ 1. (T(x,y) \ 1) \ (T(x,y) \ x) = (x \ 1) \ 1. x != (y \ 1) \ 1 | y * K(y,y \ 1) = x. x * K(x,x \ 1) = T(x,T(x,y) \ 1). T(x,T(x,y) \ 1) = x * K(x,x \ 1). T(K(x,x \ 1),y) = K(x,x \ 1). K(T(x,y),1 / x) = K(T(x,y),T(x,y) \ 1). K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / x). K(K(x,x \ 1),y) = 1. T(x,K(y,y \ 1)) = x. x * y != T(K(z,z \ 1),u) | x \ K(z,z \ 1) = y. T(x,y) \ K(x,x \ 1) = (T(x,y) \ x) / x. x * K(y,y \ 1) = K(y,y \ 1) * x. K(x,x \ 1) * y = y * K(x,x \ 1). K(K(x \ 1,x),y) = 1. T(x,K(y \ 1,y)) = x. T(K(x \ 1,x),y) = K(x \ 1,x). x * K(y \ 1,y) = K(y \ 1,y) * x. K(x \ 1,x) * y = y * K(x \ 1,x). T(K(x \ 1,x),y) != z | K(x \ (x / T(x,y)),x) = z. K(x \ (x / T(x,y)),x) = K(x \ 1,x). K(x \ 1,x) * (y * K(x,x \ 1)) = y. K(x,x \ 1) * (x * y) != z | T(x,x \ 1) * y = z. T(x,x \ 1) * y = (x * y) * K(x,x \ 1). (x * y) * K(x,x \ 1) = T(x,x \ 1) * y. K(x \ 1,x) / T(x,y) = T(1 / T(x,y),x). x * y != K(z \ 1,z) * (u * K(z,z \ 1)) | u / y = x. x / K(y \ 1,y) = x * K(y,y \ 1). (x * y) / K(y \ 1,y) != z | R(x / (y \ 1),y \ 1,y) = z. R(x / (y \ 1),y \ 1,y) = (x * y) * K(y,y \ 1). (T(x,y) \ 1) * ((x \ 1) \ 1) = T(x,y) \ x. x != T(y,y \ z) * u | ((y \ z) \ z) * u = x. ((x \ 1) \ 1) * y = (x * y) * K(x,x \ 1). (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y. (x \ 1) * ((y * x) / y) = ((y * x) / y) / ((x \ 1) \ 1). ((x * y) / x) / ((y \ 1) \ 1) = (y \ 1) * ((x * y) / x). x / ((T(x,y) \ 1) \ 1) = (T(x,y) \ 1) * ((y * T(x,y)) / y). (T(x,y) \ 1) * ((y * T(x,y)) / y) = x / ((T(x,y) \ 1) \ 1). (T(x,y) \ 1) * x = x / ((T(x,y) \ 1) \ 1). x / ((T(x,y) \ 1) \ 1) = (T(x,y) \ 1) * x. K(x,((T(x,y) \ 1) * x) / x) = (T(x,y) \ 1) \ ((T(x,y) \ x) / x). (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,((T(x,y) \ 1) * x) / x). (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,T(x,y) \ 1). (T(x,y) \ 1) * K(x,T(x,y) \ 1) = (T(x,y) \ x) / x. 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 | K(y,y \ 1) = x. K(x,x \ 1) = K(x,(y * x) \ y). 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). x * K(x \ y,y \ x) = y * (1 / (1 / (y \ x))). (x * y) * K((x * y) \ x,x \ (x * y)) = x * (1 / (1 / y)). (x * y) * K((x * y) \ x,y) = x * (1 / (1 / y)). x \ ((L(x \ 1,y,z) * x) / L(x \ 1,y,z)) = K(L(x \ 1,y,z),x). x \ L(x,L(x \ 1,y,z),x) = K(L(x \ 1,y,z),x). x \ L(x,(y * x) \ y,x) = K(L(x \ 1,x,y),x). x \ (1 / (1 / x)) = K(L(x \ 1,x,y),x). K(L(x \ 1,x,y),x) = x \ (1 / (1 / x)). x != y \ (1 / (1 / y)) | K(y \ 1,y) = x. K(x \ 1,x) = K(L(x \ 1,x,y),x). K(L(x \ 1,x,y),x) = K(x \ 1,x). K(L(x \ 1,x,y),z) != u | K((y * x) \ y,z) = u. K((x * y) \ x,y) = K(y \ 1,y). x != K(y \ 1,y) | K(1 / y,y) = x. K(1 / x,x) = K((y * x) \ y,x). K((x * y) \ x,y) = K(1 / y,y). (x * y) * K(1 / y,y) = x * (1 / (1 / y)). R(x,y,K(1 / y,y)) = x. R(x,y \ 1,K(y,y \ 1)) = x. R(x,y \ 1,y * (1 / y)) = x. x * (1 / y) = (x * (y \ 1)) * (y * (1 / y)). (x * (y \ 1)) * (y * (1 / y)) = x * (1 / y). x * (y * z) != (u * y) * z | R(u,y,z) = x. R(x,y,1 / y) = (x * y) * (y \ 1). (x * y) * (y \ 1) = R(x,y,1 / y). R(x,y,y \ 1) = R(x,y,1 / y). R(x,y,1 / y) = R(x,y,y \ 1). R(x,y \ 1,y) = R(x,y \ 1,(y \ 1) \ 1). R(x,y \ 1,(y \ 1) \ 1) = R(x,y \ 1,y). (x * (y \ 1)) * T(y,y \ 1) = R(x,y \ 1,y). x * T(y,y \ 1) = R(x / (y \ 1),y \ 1,y). R(x / (y \ 1),y \ 1,y) = x * T(y,y \ 1). R(x / (y \ 1),y \ 1,y) != z | (x * y) * K(y,y \ 1) = z. (x * y) * K(y,y \ 1) = x * T(y,y \ 1). x != y * T(z,z \ u) | y * ((z \ u) \ u) = x. x * ((y \ 1) \ 1) = (x * y) * K(y,y \ 1). (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1). (x * y) * K(T(x,y),T(x,y) \ 1) = y * ((T(x,y) \ 1) \ 1). (x * y) * K(y,y \ 1) != z | (x * K(y,y \ 1)) * y = z. (x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1). x * y != (T(z,u) \ 1) * ((z \ 1) \ 1) | (T(z,u) \ z) / y = x. (T(x,y) \ x) / x = (T(x,y) \ 1) * K(x,x \ 1). (T(x,y) \ 1) * K(x,x \ 1) = (T(x,y) \ x) / x. (T(x,y) \ 1) * z != (T(x,y) \ x) / x | K(x,T(x,y) \ 1) = z. K(x,T(x,y) \ 1) = K(x,x \ 1). x != K(y,y \ 1) | T(K(y,y \ 1),z) = x. T(K(x,x \ 1),y) = K(x,T(x,z) \ 1). K(x,T(x,y) \ 1) != z | z = K(x,x \ 1). K(x,T(x,y) \ 1) != z | K(x,x \ 1) = z. T(K(T(x,y),1 / x),z) = K(T(x,y),T(T(x,y),u) \ 1). T(K(T(x,y),1 / x),z) != u | K(T(x,y),T(x,y) \ 1) = u. (x * y) * K(T(x,y),1 / x) = y * ((T(x,y) \ 1) \ 1). x != y * ((T(z,y) \ 1) \ 1) | ((z \ 1) \ 1) * y = x. ((x \ 1) \ 1) * y = (x * y) * K(T(x,y),1 / x). (x * y) * K(T(x,y),1 / x) = ((x \ 1) \ 1) * y. T(x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)),z) = T(x,z) * ((T(x,z) \ T(x,y)) / T(x,y)). T(K(T(x,y),1 / x),z) = T(x,z) * ((T(x,z) \ T(x,y)) / T(x,y)). T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) = T(K(T(x,z),1 / x),y). T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) != u | K(T(x,z),1 / T(x,y)) = u. K(T(x,y),1 / T(x,z)) = T(K(T(x,y),1 / x),z). K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / T(x,z)). K(T(x,y),T(x,y) \ 1) = K(T(x,y),x \ 1). K(T(x,y),T(x,y) \ 1) != z | K(T(x,y),1 / x) = z. K(T(x,y),1 / x) = K(T(x,y),x \ 1). (x * y) * K(T(x,y),x \ 1) = ((x \ 1) \ 1) * y. (x * y) * z != ((x \ 1) \ 1) * y | K(x,x \ 1) = z. K(x,x \ 1) = K(T(x,y),x \ 1). K(T(x,y),x \ 1) = K(x,x \ 1). K(T(x,y),x \ 1) != z | K(T(x,y),T(x,y) \ 1) = z. K(T(x,y),T(x,y) \ 1) = K(x,x \ 1). x * y != K(T(z,u),T(z,u) \ 1) | x \ K(z,z \ 1) = y. T(x,y) \ K(x,x \ 1) = 1 / T(x,y). T(x,y) \ K(x,x \ 1) != z | (T(x,y) \ x) / x = z. (T(x,y) \ x) / x = 1 / T(x,y). (1 / T(x,y)) * x = T(x,y) \ x. x * y != T(x,z) \ x | T(1 / T(x,z),x) = y. T(1 / T(x,y),x) = T(x,y) \ 1. T(1 / T(x,y),x) != z | K(x \ 1,x) / T(x,y) = z. 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) = K(L(x,y,z) \ 1,L(x,y,z)). (x * (y * z)) \ ((x * y) * z) = a(x,y,z). a(x,y,z) = (x * (y * z)) \ ((x * y) * z). x \ y != z | u \ y != z | x = u. R(x,y,z) != R(u,y,z) | x = u. x != y | z / x = z / y. x != y | z \ x = z \ y. K(L(c14,c15,c16) \ 1,L(c14,c15,c16)) != K(c14 \ 1,c14). x \ (y * (y \ (x * z))) = z. x * ((1 / y) * y) = x. ((x * (x \ y)) / z) * z = y. K(x / y,y) = (y * (x / y)) \ x. (x * (y / x)) \ y = K(y / x,x). L(x,y,z / y) = z \ ((z / y) * (y * x)). x \ ((x / y) * (y * z)) = L(z,y,x / y). R(1,x,y) = (x * y) / (x * y). (x * y) / (x * y) = R(1,x,y). x * y != z \ (z * (x * u)) | y = u. x \ (x * (y * z)) != y * u | u = z. (x / y) * z != x | z = y. x * 1 != y | x = y. x * y != z \ (z * (u * y)) | x = u. x \ (x * (y * z)) != u * z | u = y. x * y != ((z * y) * u) / u | x = z. ((x * y) * z) / z != u * y | u = x. x * (y * (y \ z)) = x * z. x * (y \ (y * z)) = x * z. ((x / y) * y) / z = x / z. x * (y / y) = x. T(x,y) = T(T(x,y),x). T(T(x,y),x) = T(x,y). R(x,y,z) = T(R(x,y,z),x). T(R(x,y,z),x) = R(x,y,z). x != y | z / (x \ z) = y. x / (y \ x) = (y * z) / z. (x * y) / y = z / (x \ z). (x * (y * z)) / L(z,y,x) = x * y. x / (y / ((z \ x) \ y)) = z. (x * (x \ 1)) * y != z | z = y. a(x,1 / y,y) = x \ ((x * (1 / y)) * y). x \ ((x * (1 / y)) * y) = a(x,1 / y,y). x * (y * (y \ T(z,x))) = z * x. x * 1 != y * z | y \ x = z. x * (x \ y) != z | y = z. K(T(x,y),x) = 1. (T(x,y) * z) / T(T(x,z),y) = z. x != (y * x) / z | T(y,x) = z. (x * y) / z != y | T(x,y) = z. K(x,(y * x) / y) = 1. T(x,(y * x) / y) = x. x * y != z | z = y * T(x,y). x / x != y | y = 1. x / x != y | 1 = y. (x * y) * L(z,y,x) != u | u = x * (y * z). (x * y) * L(z,y,x) != u | x * (y * z) = u. x \ (y * x) != z | z = T(y,x). x \ (y * x) != z | T(y,x) = z. x * (y * (y \ z)) = u * (u \ (x * z)). x * (x \ (y * z)) = y * (u * (u \ z)). x != y | y = z * (z \ x). ((x / y) * y) * (x \ z) = z. x * y != (y * x) * z | K(x,y) = z. (x * y) * z != y * x | K(y,x) = z. (x * y) / T(y * x,K(x,y)) = K(x,y). x * (x \ T(y,y \ z)) = (y \ z) \ z. (x \ y) \ y = z * (z \ T(x,x \ y)). x \ T(y,y \ z) = x \ ((y \ z) \ z). x / T(y,y \ z) = x / ((y \ z) \ z). R((x \ y) \ y,z,u) = T(R(x,z,u),x \ y). T(R(x,y,z),x \ u) = R((x \ u) \ u,y,z). x * (x \ y) != z * u | y / u = z. (x * (x \ y)) / z != u | u = y / z. (x * (x \ y)) / z != u | y / z = u. x \ (x * y) != z * u | z \ y = u. x \ (x * y) != z | y = z. x * R(x,y,z) = R(x,y,z) * x. R(x,y,z) * x = x * R(x,y,z). (x / (y \ x)) * z != u | u = y * z. (x / (y \ x)) * z != u | y * z = u. x = y * (((z / y) \ z) \ x). x * (((y / x) \ y) \ z) = z. T(x / (x / y),(z / (x / y)) \ z) = y. T(x \ 1,x) = x \ K(x \ 1,x). x \ K(x \ 1,x) = T(x \ 1,x). 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). R(x / y,y,x \ z) = z / (y * (x \ z)). T(x,x \ y) * (((x \ y) \ y) \ z) = z. 1 = R(1,x,y). R(1,x,y) = 1. x \ 1 = R(1 / x,x,x \ 1). R(1 / x,x,x \ 1) = x \ 1. (x / y) * y != z * u | x / u = z. x * (x \ y) != z * u | z \ y = u. x * L(T(y,x),z,u) != w | L(y,z,u) * x = w. L(T(x \ 1,y),x,1 / x) = T(1 / x,y). x / L(y,1 / y,x) = x * (1 / y). R(T(1 / x,y),x,x \ 1) = T(x \ 1,y). L(x \ T(y,z),x,z) = (z * x) \ (y * z). x != y | z \ (z * y) = x. x \ (x * T(y \ z,u)) = T(T(z / y,u),y). T(T(x / y,z),y) = u \ (u * T(y \ x,z)). x * T(x \ y,z) != u | T(y / x,z) * x = u. K(x \ y,x) * z != (x \ y) * x | T(y,K(x \ y,x)) = z. x * T(x \ 1,x) != y | y = K(x \ 1,x). x * T(x \ 1,x) != y | K(x \ 1,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). (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w)). (x * y) \ (x * (y * z)) != u | u = L(z,y,x). K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y). x * ((x \ 1) * y) != z | z = L(y,x \ 1,x). x * ((x \ 1) * y) != z | L(y,x \ 1,x) = z. (1 / x) * y = L(x \ y,x,1 / x). L(x \ y,x,1 / x) = (1 / x) * y. L(x \ y,x,z / x) = z \ ((z / x) * y). 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). x * y != ((z / u) * u) * (z \ w) | x \ w = y. R(x / y,y,x \ z) \ z = y * (x \ z). R(x,x \ y,z) \ (y * z) = (x \ 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. ((x * y) * z) / (y * z) != u | u = R(x,y,z). R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y. x * y != R(z,u,x) * (u * x) | T(z * u,x) = y. R(x,y,z) * (y * z) != z * u | T(x * y,z) = u. R(x / (y / z),y / z,z) = (x * z) / y. x \ (x * y) != z * u | z = y / u. x \ (x * y) != z * u | y / u = z. R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z. (x * y) / L(z,y / z,x) = x * (y / z). (x * (y * z)) / L(T(y,z),z,x) = x * z. 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 \ 1) * (T(x,x \ 1) * y) = L(y,(x \ 1) \ 1,x \ 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. T(R(x,y,y \ 1),z) / (y \ 1) = T(x,z) * y. 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). x * (y * (y \ z)) != u * w | (x * z) / w = u. ((x / y) * y) / z != u | x / z = u. x \ (y * (y \ (x * z))) != u * w | u \ z = w. x \ (y * (x / y)) != z * u | z \ K(y,x / 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). ((x / y) * y) * z != u * w | (x * z) / w = u. x * (y * (y \ z)) != u * w | u \ (x * z) = w. x * (1 / y) != x / z | L(y,1 / y,x) = z. x / y != x * (1 / z) | L(z,1 / z,x) = y. 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 * (y \ (y * z)) != u * w | u \ (x * z) = w. (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y). x != R(y,z,u) * (z * u) | (y * z) * u = x. (x * y) * z = (y * z) * R(T(x,y * z),y,z). (x * y) * R(T(z,x * y),x,y) = (z * x) * y. x * y != R(z,u,w) * (u * w) | x \ ((z * u) * w) = y. (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). (x * y) * R(L(T(x,y),y,x),z,u) = R(x,z,u) * (x * y). T((x \ y) / y,x) = R(x \ 1,x,x \ y). x \ ((y \ z) \ z) != u | u = x \ T(y,y \ z). x \ ((y \ z) \ z) != u | x \ T(y,y \ z) = u. (x / ((y \ z) \ z)) * T(y,y \ z) = x. x \ ((y \ z) \ z) != x \ u | T(y,y \ z) = u. x * T(y,y \ z) = ((y \ z) \ z) * T(x,T(y,y \ z)). ((x \ y) \ y) * T(z,T(x,x \ y)) = z * T(x,x \ 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). K((x / y) \ x,z) = K(y,z). T(x,x \ y) != z | (x \ y) \ y = z. x / T(y,y \ z) != u | u = x / ((y \ z) \ z). x / T(y,y \ z) != u | x / ((y \ z) \ z) = u. x \ ((x / y) * (z * y)) = L(T(z,y),y,x / y). L(T(x,y),y,z / y) = z \ ((z / y) * (x * y)). x \ R(x,1 / y,y) = a(x,1 / y,y). x * y != L(T(z \ 1,u),z,1 / z) | x \ T(1 / z,u) = y. (1 / x) \ T(1 / x,y) = x * T(x \ 1,y). x * y != R(T(1 / z,u),z,z \ 1) | T(z \ 1,u) / y = x. T(x \ 1,y) / (x \ 1) = T(1 / x,y) * x. x != (y * z) \ (z * y) | K(z,y) = x. 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). x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z). 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 \ (y * L(z,x \ y,x)) != (x \ y) * u | u = z. x * y != z * (u * (u \ x)) | T(z,x) = y. T(x / y,x) = L(y \ x,y,x / y). L(x \ y,x,y / x) = T(y / x,y). x * L(L(y,z,x / z),u,w) = (x / z) * (z * L(y,u,w)). 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). (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. (1 / x) \ T(L(y,x,1 / x),x) = y * x. (1 / (1 / x)) * (x * (1 / x)) = (1 / x) \ 1. (x \ 1) * L(y,K(x \ 1,x),1 / x) = (1 / x) * (K(x \ 1,x) * y). T((x \ y) / y,x) * y = ((x \ 1) * x) * (x \ y). (x / y) * (y / x) = (y / x) * R((y / x) \ 1,y / x,x). (x / y) * R((x / y) \ 1,x / y,y) = (y / x) * (x / y). K(L(x \ 1,x,y / x),z) = K(y \ (y / x),z). (1 / x) \ T((1 / x) * y,x) = (x \ y) * x. R(x,1 / y,y) = T(((1 / y) * x) * y,1 / y). T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x). T(R(x,y,z),y * z) = T((y * z) \ ((y * x) * z),y). T((x * y) \ ((x * z) * y),x) = T(R(z,x,y),x * y). T(x,y) != R(z,y,u) | ((y * z) * u) / (y * u) = x. ((x * T(y,x * y)) * y) / (x * y) = y. R(T(x,y),y / x,x) = T(x,y / x). R(T(x,1 / x),y,z) = R(R(x,y,z),1 / x,x). R(R(x,y,z),1 / x,x) = R(T(x,1 / x),y,z). T(x * T(y,x * y),y) = x * y. x = T((x / y) * T(y,(x / y) * y),y). T((x / y) * T(y,(x / y) * y),y) = x. T((x / y) * T(y,x),y) = x. (x * y) / x = (y / x) * T(x,y). (x / y) * T(y,x) = (y * x) / y. x * T(x \ y,y) = ((x \ y) * y) / (x \ y). ((x \ y) * y) / (x \ y) = x * T(x \ y,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). R(T(x,x \ y),z,u) = R((x \ y) \ y,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 != 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. K(1 / x,y) = L(x * T(x \ 1,y),1 / x,y). L(x * T(x \ 1,y),1 / x,y) = K(1 / x,y). x * T(x \ 1,y) = T(x \ 1,y) / (x \ 1). T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y). x != (y / z) \ y | z = x. x = (1 / (1 / x)) * (x * (1 / x)). (1 / (1 / x)) * (x * (1 / x)) = x. (1 / x) * ((x \ y) * x) = T((1 / x) * y,x). T(x,y * T(y \ x,x)) = x. T(x,(x * y) * L(T(y \ 1,x),y,x)) = x. T(x,x * (y * T(y \ 1,x))) = 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,1 / y) = (x * ((1 / y) * z)) / x. R((x * (y / (1 / z))) / x,1 / z,z) = (x * (y * z)) / x. (x * T(x \ 1,y)) \ T(x \ 1,y) = x \ 1. (1 / x) * (y * x) = T((1 / x) * (x * y),x). T((1 / x) * (x * y),x) = (1 / x) * (y * x). T(x \ 1,y) / (x \ 1) != z | z = x * T(x \ 1,y). T(x \ 1,y) / (x \ 1) != z | x * T(x \ 1,y) = z. R(x / (y * x),z,u) != R(w,y,x) | R(1 / y,z,u) = w. (x * y) * L(L(z,T(x,y),y),u,w) = y * (T(x,y) * L(z,u,w)). 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. x * y != T(z,z \ u) * w | (((z \ u) \ u) * w) / y = x. (((R(x,y,z) \ u) \ u) * (y * z)) / z = T(x,R(x,y,z) \ u) * y. (x * y) \ (z * y) = R(T(z / x,x * y),x,y). R(T(x / y,y * z),y,z) = (y * z) \ (x * z). T(R(T(x / y,z),y,u),y * u) = T((y * u) \ (x * u),z). T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y. (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u)). L(T(x \ 1,y),x,z / x) != u | T(z \ (z / x),y) = u. T(x \ (x / y),y) = x \ ((x / y) * ((y \ 1) * y)). x \ ((x / y) * ((y \ 1) * y)) = T(x \ (x / y),y). x \ ((y \ x) * y) = (x \ y) * T((x \ y) \ 1,y). (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y). R(T(x / y,z),y,y \ z) = z \ (x * (y \ z)). R(T(x / (y \ 1),K(y \ 1,y)),y \ 1,y) = ((y \ 1) * y) \ (x * y). (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x). (x * y) * z != z * u | T(x * y,z) = u. x * T(x \ (y \ x),y) = ((y \ 1) * y) * (y \ x). ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x). T(1 / (x \ 1),y) * (x \ 1) = x \ T(x,y). (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z). x * T(x \ y,z) = T(y * (x \ 1),z) / (x \ 1). T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z). (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x. T(x,y) / x != z | (1 / x) * T((1 / x) \ 1,y) = z. T(x,y) * z != T(x,y) / x | T(1 / x,T(x,y)) = z. 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)). x * T(x \ (x / y),y) = (x / y) * ((y \ 1) * y). (x / y) * ((y \ 1) * y) = x * T(x \ (x / y),y). x != (y * z) \ ((y \ (y * z)) * y) | K(z,y) = x. K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y). x != (y \ 1) * T((y \ 1) \ 1,z) | y \ T(y,z) = x. x \ T(x,y) = K(y \ (y / (x \ 1)),y). K(x \ (x / (y \ 1)),x) = y \ T(y,x). K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y)). K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x). (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. (x * T(x \ y,z)) * (x \ 1) = T(y * (x \ 1),z). (1 / (x / (x / y))) * y = ((x / y) \ x) / (x / (x / y)). ((x / y) \ x) / (x / (x / y)) = (1 / (x / (x / y))) * y. (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y). T(x,x * K(y,x)) = x. T(1 / x,L(x,y,z)) = L(x,y,z) \ (L(x,y,z) / x). L(x,y,z) \ (L(x,y,z) / x) = T(1 / x,L(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). T(x,T(y,x)) = y * (T(y,x) \ x). x * (T(x,y) \ y) = T(y,T(x,y)). 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)). x \ y = T(x \ T(y,y / x),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 / T(y,x)) * y = T(x,x / (x / T(y,x))). T(x,x / (x / T(y,x))) = (x / T(y,x)) * y. K(x,1 / x) \ (x * (T(x,y) / x)) = L(T(x,y),1 / x,x). x != y * (z * (z \ u)) | y * u = x. (x \ 1) * y = K(x \ 1,x) * L(x \ y,x,x \ 1). K(x \ 1,x) * L(x \ y,x,x \ 1) = (x \ 1) * y. L((x * y) / (z * y),u,w) * (z * y) = (L(x / z,u,w) * z) * y. L(x / (y * z),u,w) * (y * z) = (L((x / z) / y,u,w) * y) * z. (L((x / y) / z,u,w) * z) * y = L(x / (z * y),u,w) * (z * y). R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y. R(x \ T(x,y),K(x \ 1,T(x,y)),z) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z. x \ L(L(y,x \ 1,x),z,u) != (x \ 1) * w | L(y,z,u) = w. x \ L(x * y,z,u) = (x \ 1) * L((x \ 1) \ y,z,u). (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u). 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). L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y. 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) * L(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u)). 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). ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z). (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y. (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 \ y) \ y) * z != u * T(x,x \ y) | T(u,(x \ y) \ y) = z. T(x,(y \ z) \ z) = T(x,T(y,y \ z)). T(x,T(y,y \ z)) = T(x,(y \ z) \ z). x \ (T(x,y) * z) = T(x,y) * (x \ z). (T(x,y) * z) / (T(x,y) * (x \ z)) = x. T(x,y) * z = x * (T(x,y) * (x \ z)). x * (T(x,y) * (x \ z)) = T(x,y) * z. x * y = T(x,z) * (x * (T(x,z) \ y)). T(x,y) * (x * (T(x,y) \ z)) = x * z. (x * y) * z != x * (T(x,u) * y) | T(T(x,u),x * y) = z. T(T(x,y),x * (T(x,y) \ z)) = (x * (T(x,y) \ z)) \ (x * 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). (T(x,y) \ 1) * z != T(x,y) \ x | T(x,T(x,y) \ 1) = z. T(x,T(x,y) \ 1) = (T(x,y) \ 1) \ (T(x,y) \ x). (T(x,y) \ 1) \ (T(x,y) \ x) = T(x,T(x,y) \ 1). x \ (T(x,y) \ x) = T(x,y) \ 1. (1 / x) * (T(x,y) \ x) = L(T(x,y) \ 1,x,1 / x). L(T(x,y) \ 1,x,1 / x) = (1 / x) * (T(x,y) \ x). T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x). x \ y = T(x,x \ z) * (x \ (((x \ z) \ z) \ y)). T(x,x \ y) * (x \ (((x \ y) \ y) \ z)) = x \ z. x * y != T(x,z) * u | y = T(x,z) * (x \ u). T(x,z) * u != x * y | y = T(x,z) * (x \ u). T(x,y) * z != x * u | T(x,y) * (x \ z) = u. x \ (T(x,y) * z) != u | u = T(x,y) * (x \ z). x \ (T(x,y) * z) != u | T(x,y) * (x \ z) = u. x * y != z * ((z \ x) * u) | L(u,z \ x,z) = y. L(x,y \ T(y,z),y) = y * (T(y,z) \ ((y \ T(y,z)) * x)). x * (T(x,y) \ ((x \ T(x,y)) * z)) = L(z,x \ T(x,y),x). x * y != z * (x / z) | K(z,x / z) = y. K(x,T(x,y) / x) = x * (T(x,y) \ (T(x,y) / x)). 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. L(x,T(x,y) \ x,T(x,y)) = T(x,y) * T(T(x,y) \ x,x). T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,T(x,y)). x * K(x \ (x / T(x,y)),x) = T(x,y) * ((T(x,y) \ 1) * x). T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x). (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x. x * T(1 / x,T(x,y)) = K(x,T(x,y) / x). (x / y) \ (T(x / y,z) * x) != u * w | (y * T(y \ x,z)) / w = u. (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x). x / (y / (y / x)) = (1 / (y / (y / x))) * x. (1 / (x / (x / y))) * y = y / (x / (x / y)). (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z). (T(x,y) \ 1) * L(T(x,T(x,y) \ 1),z,u) = T(x,y) \ L(T(x,y) * (T(x,y) \ x),z,u). T(x,y) \ L(T(x,y) * (T(x,y) \ x),z,u) = (T(x,y) \ 1) * L(T(x,T(x,y) \ 1),z,u). x * y != (z \ 1) * L((z \ 1) \ 1,u,w) | x \ (z \ L(z,u,w)) = y. L(x,y,z) \ (x \ L(x,y,z)) = x \ 1. x * y != R(z,u,w) * (z \ 1) | (z \ R(z,u,w)) / y = x. (x \ R(x,y,z)) / R(T(x,x \ 1),y,z) = x \ 1. ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z) = R(x,y,z) * R(R(x,y,z) \ 1,R(x,y,z),x \ 1). R(x,y,z) * R(R(x,y,z) \ 1,R(x,y,z),x \ 1) = ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z). T((R(x,y,z) * (1 / x)) / R(x,y,z),x) = (x \ R(x,y,z)) / R(x,y,z). x != L(y / z,u,w) * z | z * L(z \ y,u,w) = x. x * L(x \ y,z,u) = L(y * (x \ 1),z,u) / (x \ 1). L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u). (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x. x * y != R(1 / (1 / z),u,w) * (1 / z) | (R(z,u,w) / z) / y = x. (R(x,y,z) / x) / R(x,y,z) = 1 / x. L(R(x,y,z) \ u,R(x,y,z),1 / x) = (R(x,y,z) / x) \ ((1 / x) * u). (1 / x) * R((1 / x) \ y,z,u) = R(y * x,z,u) / x. R(x * y,z,u) / y != w * (1 / y) | R(x / (1 / y),z,u) = w. (1 / x) * T((1 / x) \ y,z) != u | T(y * x,z) / x = u. T(x * y,z) / y = x * K(z \ (z / (x \ (1 / y))),z). (x * (y * z)) * T((x * (y * z)) \ (x * y),u) = (x * y) * K(u \ (u / L(z,y,x)),u). K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x)). T(x,x * (y \ (z * T(z \ y,x)))) = x. T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x. T(x,x * (T(x,y) \ x)) = x. T(x,y) = T(T(x,y),x * (T(x,z) \ x)). T(T(x,y),x * (T(x,z) \ x)) = T(x,y). x * ((y * (x \ 1)) / y) = (y * ((x \ y) / y)) / (x \ y). (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x). ((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) * T((x * y) \ x,z) != u | x * (y * T(y \ 1,z)) = u. x * (y * T(y \ 1,x)) = ((x \ (x / y)) * x) * y. ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x)). (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y). (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y). (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x). (x \ y) * z != (y \ (x \ y)) * y | T(x * T(x \ 1,y),x \ y) = z. T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y). T(x * T(x \ 1,L(x,y,z)),x \ L(x,y,z)) = K(x \ 1,L(x,y,z)). L(x * y,z,u) / ((1 / y) \ 1) = (1 / y) * L((1 / y) \ x,z,u). T(x,y) / z = (x / z) * K(y \ (y / ((x / z) \ (1 / z))),y). (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y. K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y). R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x). T(x \ T(x,y),x \ 1) = x \ T(x,y). 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). R(R(x,y,z),1 / x,x) = R(T(x,x \ 1),y,z). T(1 / (1 / (1 / x)),x) = 1 / x. x * (1 / x) = (1 / (1 / (1 / x))) * x. (1 / (1 / (1 / x))) * x = x * (1 / x). K(x,x \ 1) \ 1 = K(1 / x,x). (1 / (1 / x)) * K(x,x \ 1) = x. K(x,y) != z | K((u / x) \ u,y) = z. K((x / y) \ x,1 / y) = K(y,y \ 1). T(x,x \ 1) * L(y,x,K(x,x \ 1)) = K(x,x \ 1) * (x * y). x * L(y,K(x,x \ 1),1 / (1 / x)) = (1 / (1 / x)) * (K(x,x \ 1) * y). L(1 / (1 / x),y,z) = L(L(x,y,z),x \ 1,x). L(L(x,y,z),x \ 1,x) = L(1 / (1 / x),y,z). R((x / K(y \ 1,y)) / y,y,K(y \ 1,y)) = x / (1 / (1 / y)). R(x,x \ y,K(y \ 1,y)) \ (1 / (1 / y)) = (x \ y) * K(y \ 1,y). (1 / (x / (x / y))) * y != z | y / (x / (x / y)) = z. x / (1 / (1 / x)) = x * (1 / x). L(x,1 / x,x) = 1 / (1 / x). K(x,x \ 1) = x / (1 / (1 / x)). x / (1 / (1 / x)) = K(x,x \ 1). L(T(x,y),1 / x,x) = T(1 / (1 / x),y). K(x,x \ 1) \ x = 1 / (1 / x). K(1 / x,x) != y | K(x,x \ 1) \ 1 = y. K(x,x \ 1) \ 1 = K(x \ 1,x). K(x \ 1,x) != y | K(1 / x,x) = y. K(1 / (1 / x),1 / x) = K(x,x \ 1). x \ T(x,x \ 1) = K(x,x \ 1). x * K(x,x \ 1) = T(x,x \ 1). T(x,x \ 1) * L(y,K(x,x \ 1),x) = x * (K(x,x \ 1) * y). (T(x,x \ 1) * y) / (K(x,x \ 1) * y) != z | R(x,K(x,x \ 1),y) = z. K(1 / (1 / x),(y / (1 / x)) \ y) = K(x,x \ 1). R(x,y,z) \ R(T(x,x \ 1),y,z) = a(R(x,y,z),1 / x,x). x != L(y \ T(y,z),y,z) | K(y,z) = 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). T(x \ 1,K(x,y)) = x \ 1. x * T(x \ 1,K(x,y)) = 1. x * y != z * T(z \ 1,K(z,u)) | 1 / y = x. 1 / x = T(1 / x,K(x,y)). T(1 / x,K(x,y)) = 1 / x. R(1 / (x / y),x / y,y) = T(y / x,K(x / y,z)). T(x / y,K(y / x,z)) = R(1 / (y / x),y / x,x). x != R(1 / (y / z),y / z,z) | z / y = x. x / y = T(x / y,K(y / x,z)). 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). x \ y = T(x \ y,K(x / y,z)). T(x \ y,K(x / y,z)) = x \ y. (x * T(x \ (y \ x),z)) / (y \ x) != u | u = y * T(y \ 1,z). (x * T(x \ (y \ x),z)) / (y \ x) != u | y * T(y \ 1,z) = u. K(x \ (x / R(y,z,u)),x) = (((y * z) * u) * T(((y * z) * u) \ (z * u),x)) / (z * u). (x * y) * R(L(z,y,x),u,w) != v5 | x * (y * R(z,u,w)) = v5. 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). R(x,y,z) * u = x * (R(x,y,z) * (x \ u)). x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. 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). 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). 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 * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z)). (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z)). x * y != L((z * (u \ w)) / z,u,1 / u) | x \ ((z * ((1 / u) * w)) / z) = y. (1 / x) \ ((y * ((1 / x) * z)) / y) = x * ((y * (x \ z)) / y). ((x * ((y * z) / (u * z))) / x) * (u * z) = (((x * (y / u)) / x) * u) * z. ((x * (y / (z * u))) / x) * (z * u) = (((x * ((y / u) / z)) / x) * z) * u. (((x * ((y / z) / u)) / x) * u) * z = ((x * (y / (u * z))) / x) * (u * 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) / T(y,z) = (x / T(y,z)) * y. x * y = ((x / T(y,z)) * y) * T(y,z). ((x / T(y,z)) * y) * T(y,z) = x * 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). (1 / T(x,y)) * x != z | z = x / T(x,y). (1 / T(x,y)) * x != z | x / T(x,y) = z. x * y != (z * x) / T(x,u) | T(z / T(x,u),x) = y. (x * y) / T(y,z) != y * u | T(x / T(y,z),y) = u. T(x,x / (x / T(y,x))) * T(y,x) = x * y. x * (x * y) = T(x,x / (x / T(y,x))) * (y * x). T(x,x / (x / T(y,x))) * (y * x) = x * (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 \ z)) / (z / y) = (x / (z / y)) * (y \ z). ((x / (y \ z)) / (z / y)) * (y \ z) != u | x / (z / y) = u. x * y != (z * u) * ((z * L(u \ 1,u,z)) / z) | x \ T(z,z / (z * u)) = y. x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / 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 * ((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 != L(T(y,z),1 / y,y) | T(1 / (1 / y),z) = x. T(1 / (1 / x),y) = K(x,1 / x) \ (x * (T(x,y) / x)). 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 / z)) * (z \ y) != u | (x * (z \ y)) / (y / z) = u. ((x \ (y / z)) * x) * z = x * (z * T(z \ (x \ y),x)). x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y. T(x,y) / y = y \ T(y * (x / y),y). x \ T(x * (y / x),x) = T(y,x) / x. x * (y * T(y \ (x \ y),x)) = ((x \ 1) * x) * y. 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 \ 1) * x) * y. x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y. x * (K(x \ 1,x) * y) = K(x \ 1,x) * (x * y). K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y). x * (K(x \ 1,x) * y) != K(x \ 1,x) * z | x * y = z. K(x \ 1,x) * y != x * (K(x \ 1,x) * z) | x * z = y. x * (K(x \ 1,x) * (x \ y)) != z | K(x \ 1,x) * y = z. (x * y) * T((x * y) \ y,z) != u | (x * T(x \ 1,z)) * y = 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. x * ((y \ (x \ y)) * y) = (x * T(x \ 1,y)) * y. (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y). x * T(y * T(y \ 1,x),x) = y * ((x \ (y \ x)) * x). 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). L(x,y,z) \ x = x * (L(x,y,z) \ 1). x * (L(x,y,z) \ 1) = L(x,y,z) \ x. L(x,y,z) * (u * x) = x * (L(x,y,z) * T(u,x)). x * (L(x,y,z) * T(u,x)) = L(x,y,z) * (u * x). x \ (L(x,y,z) \ x) = L(x,y,z) \ 1. T(L(x,y,z) * T(L(x,y,z) \ 1,x),x * (L(x,y,z) \ 1)) = K(x \ (L(x,y,z) \ x),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. T(T(x,y),x * (T(x,z) \ x)) != u | T(x,y) = u. T(x,y) = (x * (T(x,y) \ x)) \ (x * x). (x * (T(x,y) \ x)) \ (x * x) = T(x,y). (x * x) / T(x,y) = x * (T(x,y) \ x). T(x / T(x,y),x) = T(x,y) \ x. T(((T(x,y) \ x) * x) / (T(x,y) \ x),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x). (T(x,y) \ x) * T(x,y) = T(x,y) * T(T(x,y) \ x,x). T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y). x * K(x \ (x / T(x,y)),x) != z | L(x,T(x,y) \ 1,T(x,y)) = 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). x * y != z * (u * (u \ w)) | x \ (z * w) = y. ((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 * (1 / (1 / y))) / x) * (1 / y) = ((x * y) / x) / y. (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x. (1 / x) * ((y * x) / y) = ((y * x) / y) / x. x * ((y * (x \ 1)) / y) = ((y * (x \ 1)) / y) / (x \ 1). ((x * (y \ 1)) / x) / (y \ 1) = y * ((x * (y \ 1)) / x). (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y. (x * y) * ((z * y) / z) = (x * ((z * y) / z)) * y. (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y). T(x,x / (x / y)) * y = ((x / y) * y) * ((x * y) / x). ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y. x * ((x * y) / x) = T(x,x / (x / y)) * y. T(x,x / (x / y)) * y = x * ((x * y) / x). T(x,x / (x / y)) * (x \ y) = (x * y) / x. (x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),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 * 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). T(x \ T(x * y,x),z) = x \ T(x * T(y,z),x). T(T(x,y) / y,z) = y \ T(y * T(x / y,z),y). 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). T(x * T(1 / x,y),x) = x * T(1 / x,y). (x * R(x \ 1,y,z)) * u != (w * x) * R((w * x) \ w,y,z) | T(w,x * R(x \ 1,y,z)) = u. T(x,x * R(x \ 1,y,z)) = x. T(1 / x,(1 / x) * R(x,y,z)) = 1 / x. T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1. T(x \ 1,x \ R(x,y,z)) = x \ 1. T(x / y,(y / x) * (x / y)) = x / y. T(x \ 1,y) = T(T(x \ 1,y),x \ R(x,z,u)). T(T(x \ 1,y),x \ R(x,z,u)) = T(x \ 1,y). T(x / (y * x),y * (x / (y * x))) = x / (y * x). (R(x,y,z) * (1 / x)) / R(x,y,z) = L(1 / x,R(x,y,z),1 / x). R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z)). R(x / (y * x),y,x / (y * x)) = T(x / (y * x),y). x != T(y / (z * y),z) | R(z \ 1,z,y) = x. R(x \ 1,x,y) = R(y / (x * y),x,y / (x * y)). R(x / (y * x),y,x / (y * x)) = R(y \ 1,y,x). R(1 / x,x,y / (x * y)) = x \ 1. R(1 / x,x,(x \ y) / y) = x \ 1. (x \ 1) \ ((x \ y) / y) = x * ((x \ y) / y). x * (y * T(y \ (x \ z),x)) != u | ((x \ (z / y)) * x) * y = u. ((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) | z * u = x. x * (y \ 1) = (R(x,y \ 1,y) / y) * K(y \ 1,y). (R(x,y \ 1,y) / y) * K(y \ 1,y) = x * (y \ 1). (x * K(y \ 1,y)) * y = (x * y) * K(y \ 1,y). x * y = ((x / K(y \ 1,y)) * y) * K(y \ 1,y). ((x / K(y \ 1,y)) * y) * K(y \ 1,y) = x * y. x * K(y \ 1,y) != (z * (y \ 1)) * y | R(z,y \ 1,y) = x. R(x,y \ 1,y) = ((x * (y \ 1)) / K(y \ 1,y)) * y. ((x * (y \ 1)) / K(y \ 1,y)) * y = R(x,y \ 1,y). (x * (y \ 1)) / K(y \ 1,y) != z | z = R(x,y \ 1,y) / y. (x * (y \ 1)) / K(y \ 1,y) != z | R(x,y \ 1,y) / y = z. (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)). T(x,T(1 / x,y)) * T(T(1 / x,y),x) = T(x * T(1 / x,y),x). x * (y \ T(y * (x \ z),x)) != u | ((x \ (z / (y \ 1))) * x) * (y \ 1) = u. (((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)) \ (x * x) = T(x,R(T(y,x),T(y,x) \ 1,x)). x * ((x * (1 / x)) * (x \ y)) = (x * (1 / x)) * y. x * ((x * (1 / x)) * y) = (x * (1 / x)) * (x * y). (x * (1 / x)) * (x * y) = x * ((x * (1 / x)) * y). x * y != (x * z) * L(u,z,x) | z * u = y. (1 / x) * y = K(x,x \ 1) * (x \ L(y,1 / x,x)). K(x,x \ 1) * (x \ L(y,1 / x,x)) = (1 / x) * y. x * (K(x,x \ 1) * y) = K(x,x \ 1) * (x * y). K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y). K(x,x \ 1) * (x * y) != z | T(x,x \ 1) * L(y,x,K(x,x \ 1)) = z. 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. T(x,x \ 1) * y != x * (K(x,x \ 1) * z) | L(z,K(x,x \ 1),x) = 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) * 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 * L(y,z,u)) * y = (x * y) * L(y,z,u). (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y. 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 * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u). L(x,y,z) / T(x,x \ 1) = (x \ 1) * L(x,y,z). (x * y) * L((x * y) \ z,u,w) = (L((z / y) / x,u,w) * x) * y. (L((x / y) / z,u,w) * z) * y = (z * y) * L((z * y) \ x,u,w). (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * 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). 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) * K(1 / x,y) = L(T(1 / x,y) * x,1 / x,y) / x. L(T(1 / x,y) * x,1 / x,y) / x = (1 / x) * K(1 / x,y). L(x * T(x \ 1,y),1 / x,y) / x = (1 / x) * K(1 / x,y). K(1 / x,y) / x = (1 / x) * K(1 / x,y). (1 / x) * K(1 / x,y) = K(1 / x,y) / x. x * K(1 / (x \ 1),y) = K(1 / (x \ 1),y) / (x \ 1). K(1 / (x \ 1),y) / (x \ 1) = x * K(1 / (x \ 1),y). K(1 / (x \ 1),y) / (x \ 1) = x * K(x,y). K(x,y) / (x \ 1) = x * K(x,y). (x / y) * (y * L(y \ ((x / y) \ z),u,w)) = x * L(x \ z,u,w). (R(1 / (x / y),z,u) * (x / y)) * y = R(y / x,z,u) * x. x * R(x \ y,z,u) = (R(1 / (x / y),z,u) * (x / y)) * y. (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). T(x,T(1 / x,y)) * T(x \ 1,y) = T(x * T(1 / x,y),x). x != T(y * T(1 / y,z),y) | y * T(1 / y,z) = x. x * T(1 / x,y) = T(x,T(1 / x,y)) * T(x \ 1,y). T(x,T(1 / x,y)) * T(x \ 1,y) = x * T(1 / x,y). (x * L(x \ (y / z),u,w)) * z = (x * z) * L((x * z) \ y,u,w). (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * 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. 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). x \ K(y,(y / x) / y) = (y * (x \ 1)) / y. x * ((y * (x \ 1)) / y) != z | K(y,(y / x) / y) = z. x \ K(R(x,y,z),1 / x) = (R(x,y,z) * (x \ 1)) / R(x,y,z). (R(x,y,z) * (x \ 1)) / R(x,y,z) = x \ K(R(x,y,z),1 / x). K(x,y / x) = (y \ x) * ((x * ((y \ x) \ 1)) / x). (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y). x * K(x,(x / y) / x) = T(x,x / (x * y)). (x \ R(x,y,z)) / R(x,y,z) = x \ K(R(x,y,z),1 / x). K(R(x,y,z),(R(x,y,z) / ((x \ 1) \ 1)) / R(x,y,z)) = (x \ 1) \ (x \ K(R(x,y,z),1 / x)). (x * y) * L((x * y) \ z,u,w) != v5 | x * (y * L(y \ (x \ z),u,w)) = v5. x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * 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). (x * R(y,z,u)) * y = (x * y) * R(y,z,u). x * y = ((x / R(y,z,u)) * y) * R(y,z,u). ((x / R(y,z,u)) * y) * R(y,z,u) = x * y. (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y. x * y != ((z / u) * u) * w | (z * w) / y = x. (x * R(y,z,u)) / y = (x / y) * R(y,z,u). T(1 * x,1 / R(x,y,z)) = R(x,1 / R(x,y,z),R(x,y,z)). R(x,1 / R(x,y,z),R(x,y,z)) = T(1 * x,1 / R(x,y,z)). T(x,y) = T(R(x,y,R(x,z,u)),y * R(x,z,u)). T(R(x,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). R(x,y,z) / T(x,x \ 1) = (x \ 1) * R(x,y,z). R(x,y,z) / ((x \ 1) \ 1) = (x \ 1) * R(x,y,z). R(x,1 / R(x,y,z),R(x,y,z)) = T(x,1 / R(x,y,z)). L(x \ L(y,1 / x,K(x \ 1,x)),x,x \ 1) = (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 * y) * ((z * ((x * y) \ y)) / z) != u | (x * ((z * (x \ 1)) / z)) * y = u. (x * ((y * (x \ 1)) / y)) * (x * z) = x * ((x * z) * ((y * ((x * z) \ z)) / y)). x * ((x * y) * ((z * ((x * y) \ y)) / z)) = (x * ((z * (x \ 1)) / z)) * (x * y). ((x * ((y * z) / (u * z))) / x) * (u * z) = (u * ((x * (u \ y)) / x)) * z. (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) * 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 * (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) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x * (z / z),y)) * z. (x \ T(x * (y / y),z)) * y = (x \ 1) * ((x \ T(x,z)) * ((x \ 1) \ y)). T(x \ T(x,x / (x * y)),z) = K(x,(x / T(y,z)) / x). 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). 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). (x * K(y,y \ 1)) / y = (x / y) * K(y,y \ 1). (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. (x * y) * ((z * ((x * y) \ u)) / z) != w | x * (y * ((z * (y \ (x \ u))) / z)) = w. 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. R(x \ 1,x,y) = (R(1 / x,x,y) \ 1) \ 1. (R(1 / x,x,y) \ 1) \ 1 = R(x \ 1,x,y). x * y != K(z,z \ 1) * (z * u) | (T(z,z \ 1) * u) / y = x. (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = x. (x * (1 / x)) * (x * y) = T(x,x \ 1) * y. L(x,y,K(y,y \ 1)) != z | L(x,K(y,y \ 1),y) = z. L(x,K(y,y \ 1),y) = x. L(x,1 / y,K(1 / y,(1 / y) \ 1)) != z | L(x,K(y \ 1,y),1 / y) = z. L(x,K(y \ 1,y),1 / y) = x. 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 \ y,x,x \ 1) = (1 / x) * y. L((x \ 1) * y,x,x \ 1) = (1 / x) * L(y,x \ 1,x). R(x,K(x,x \ 1),y) = x. R(1 / x,K(x \ 1,x),y) = 1 / x. (x * (1 / x)) * y = T(x,x \ 1) * (x \ y). T(x,x \ 1) * (x \ y) = (x * (1 / x)) * y. ((x \ 1) \ 1) * y = (x * (1 / x)) * (x * y). (x * (1 / x)) * (x * y) = ((x \ 1) \ 1) * y. (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y. R(x,K(y \ 1,y),(1 / y) * z) = ((x * K(y \ 1,y)) * ((1 / y) * z)) / ((y \ 1) * z). ((x * K(y \ 1,y)) * ((1 / y) * z)) / ((y \ 1) * z) = R(x,K(y \ 1,y),(1 / y) * z). ((x \ 1) * y) \ (K(x \ 1,x) * ((1 / x) * (y * z))) = L(L(z,y,1 / x),(1 / x) * y,K(x \ 1,x)). T(x,x \ y) * (x \ (((x \ y) \ y) \ z)) != u | x \ z = u. x \ y = (x * (1 / x)) * (((x \ 1) \ 1) \ y). (x * (1 / x)) * (((x \ 1) \ 1) \ y) = x \ y. (x * (1 / x)) * (x * y) != z | x * ((x * (1 / x)) * y) = z. x * ((x * (1 / x)) * y) = ((x \ 1) \ 1) * y. (x \ 1) * (x * ((y * (x \ z)) / y)) = K(x \ 1,x) * ((y * ((1 / x) * z)) / y). K(x \ 1,x) * ((y * ((1 / x) * z)) / y) = (x \ 1) * (x * ((y * (x \ z)) / y)). K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y. x * T(x \ ((1 / y) \ x),y \ 1) != z | (y * (1 / y)) * ((1 / y) \ x) = z. (x * (1 / x)) * ((1 / x) \ y) = (x \ 1) \ y. (1 / x) * y = K(x,x \ 1) * ((x \ 1) * y). K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y. 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 \ 1,x) * (K(x,x \ 1) * y) = y. K(x,x \ 1) * y != x \ z | ((x \ 1) \ 1) \ z = y. ((x \ 1) \ 1) \ y = K(x \ 1,x) * (x \ y). K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y. K(x,x \ 1) * y != T(x,x \ 1) * z | x * z = y. x * y = K(x \ 1,x) * (T(x,x \ 1) * y). K(x \ 1,x) * (T(x,x \ 1) * y) = x * y. (x * (1 / x)) * (K(x \ 1,x) * y) = y. K(x \ 1,x) * y != z | K(x,x \ 1) * z = y. K(x \ 1,x) * ((x * (1 / x)) * y) = 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) * z | (y * (1 / y)) * x = z. K(x \ 1,x) * y != z | (x * (1 / x)) * z = y. (1 / x) * y = (x \ 1) * ((x * (1 / x)) * y). (x \ 1) * ((x * (1 / x)) * y) = (1 / x) * y. x \ L(y,1 / x,x) = (x \ 1) * y. (x * ((1 / y) * z)) / L((y \ 1) * z,K(y,y \ 1),x) = x * K(y,y \ 1). (x * K(y,y \ 1)) \ (x * ((1 / y) * z)) != u | L((y \ 1) * z,K(y,y \ 1),x) = u. L(x,1 / y,y) = L(x,y \ 1,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) * (x \ y) != z | y * T(y \ (x \ y),x) = z. x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x. x * y = T(x,x \ 1) * (K(x \ 1,x) * y). T(x,x \ 1) * (K(x \ 1,x) * y) = x * y. K(x \ 1,x) * y = x * (T(x,x \ 1) \ y). x * (T(x,x \ 1) \ y) = K(x \ 1,x) * y. L(x,(y \ 1) \ 1,y \ 1) != z | (y \ 1) * (T(y,y \ 1) * x) = z. (x \ 1) * (T(x,x \ 1) * y) = L(y,x,x \ 1). (x \ 1) * (x * y) = L(K(x \ 1,x) * y,x,x \ 1). L(K(x \ 1,x) * y,x,x \ 1) = (x \ 1) * (x * y). L((x \ 1) * ((1 / x) \ y),x,x \ 1) = (x \ 1) * (x * y). (x \ T(x,y)) * z = (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)). (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x,y)) * z. x * y != z * (z \ x) | 1 = y. 1 = (x \ T(x,y)) * ((x \ 1) \ ((x \ T(x,y)) \ (x \ 1))). (x \ T(x,y)) * ((x \ 1) \ ((x \ T(x,y)) \ (x \ 1))) = 1. x * y = (1 / (1 / x)) * (K(x,x \ 1) * y). (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y. (1 / (1 / x)) * y = x * (K(x \ 1,x) * y). x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y. K(x \ 1,x) * y = (1 / (1 / x)) * (x \ y). (1 / (1 / x)) * (x \ y) = K(x \ 1,x) * y. K(x \ 1,x) * (x * y) != z | (1 / (1 / x)) * y = z. x != T(y,R(T(z,y),T(z,y) \ 1,y)) | (T(z,y) \ z) * y = x. (T(x,y) \ x) * y = (y * (((T(x,y) \ x) * y) \ y)) \ (y * y). (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = (T(y,x) \ y) * x. T(1 / (1 / K(x \ (x / (y \ 1)),x)),T(y,x) \ y) = y \ T(y,x). T(K(x,y),(x * y) \ (y * x)) = T(K(x,y),K(x,y) \ 1). T(x \ y,y \ x) = ((x \ y) \ 1) \ 1. T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = ((y \ T(y,x)) \ 1) \ 1. 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. T(K(x,y),K(z,x)) != u | K(x,y) = u. K(x,y) = (K(x,y) \ 1) \ 1. (K(x,y) \ 1) \ 1 = K(x,y). 1 / (1 / K(x,y)) = K(x,y). T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = y \ T(y,x). T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) != z | y \ T(y,x) = z. x \ T(x,y) = ((x \ T(x,y)) \ 1) \ 1. ((x \ T(x,y)) \ 1) \ 1 = x \ T(x,y). 1 / (x \ T(x,y)) = (x \ T(x,y)) \ 1. (x \ T(x,y)) * ((x \ 1) \ (T(x,y) \ 1)) = 1. (x \ T(x,y)) \ 1 = (x \ 1) \ (T(x,y) \ 1). (x \ 1) \ (T(x,y) \ 1) = (x \ T(x,y)) \ 1. x != (y \ T(y,z)) \ 1 | 1 / (y \ T(y,z)) = x. 1 / (x \ T(x,y)) = (x \ 1) \ (T(x,y) \ 1). (x \ 1) \ (T(x,y) \ 1) = 1 / (x \ T(x,y)). T(x,y) * L(T(x,y) \ 1,x,1 / x) = T(x * T(1 / x,1),y). T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * T(1 / x,1),y). T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * (1 / x),y). T(x,y) * z != T(x * (1 / x),y) | (T(x,y) \ x) / x = z. (T(x,y) \ x) / x = (1 / x) * (T(x,y) \ x). (1 / x) * (T(x,y) \ x) = (T(x,y) \ x) / x. T((T(x,y) \ x) / x,x) = (1 / x) * ((T(x,y) \ 1) * x). x \ (T(x,y) \ x) = (1 / x) * ((T(x,y) \ 1) * x). (1 / x) * ((T(x,y) \ 1) * x) = x \ (T(x,y) \ x). x != y \ (T(y,z) \ y) | T(y,z) \ 1 = x. T(x,y) \ 1 = (1 / x) * ((T(x,y) \ 1) * x). (1 / x) * ((T(x,y) \ 1) * x) = T(x,y) \ 1. 1 / T(x,y) = T(1 / (1 / x),y) \ 1. T(1 / (1 / x),y) \ 1 = 1 / T(x,y). 1 / (1 / T(x,y)) = T(1 / (1 / x),y). T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1. 1 / (1 / x) != y | x * K(x \ 1,x) = y. T(x,y) * K(T(x,y) \ 1,T(x,y)) = T(1 / (1 / x),y). T(x,y) * (K(T(x,y) \ 1,T(x,y)) * z) = T(1 / (1 / x),y) * z. x * (((x \ y) \ 1) \ 1) = (((y / x) \ 1) \ 1) * x. (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1). K(x,x \ 1) * y != z | y * K(x,x \ 1) = z. R(x / (y \ 1),y \ 1,y) = ((y \ 1) * y) \ (x * y). x * K(y \ 1,y) != z | K(y \ 1,y) * x = z. x != (y / z) * K(z,z \ 1) | (y * K(z,z \ 1)) / z = x. (x * K(y,y \ 1)) / y = K(y,y \ 1) * (x / y). x * y != z * K(u,u \ 1) | (K(u,u \ 1) * z) / y = x. (K(x,x \ 1) * (y * z)) / (z * K(x,x \ 1)) = R(y,z,K(x,x \ 1)). K(x,x \ 1) * y = y * (x * (1 / x)). (1 / (1 / x)) * y = (x * y) * K(x \ 1,x). (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y. K(x,x \ 1) * (y * K(x \ 1,x)) = y. x != (y * z) * u | R(y,z,u) * (z * u) = x. R(x,y,K(z \ 1,z)) * (y * K(z \ 1,z)) = K(z \ 1,z) * (x * y). K(x \ 1,x) * y != z | (x \ 1) * ((1 / x) \ y) = z. (x \ 1) * ((1 / x) \ y) = y * K(x \ 1,x). x * y != K(z \ 1,z) * u | x \ (u * K(z \ 1,z)) = y. x \ (y * K(x \ 1,x)) = T(x,x \ 1) \ y. (x * y) * L(K(z \ 1,z),y,x) = x * (K(z \ 1,z) * y). R(K(x \ 1,x),y,z) * (y * z) = (y * K(x \ 1,x)) * z. R(x,x \ y,K(z \ 1,z)) \ (K(z \ 1,z) * y) = (x \ y) * K(z \ 1,z). (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. (1 / x) * (y * K(x \ 1,x)) = (x \ 1) * y. x * (y * K(x \ 1,x)) = (1 / (1 / x)) * y. x * K(x \ (x / T(x,y)),x) = 1 / (1 / x). K(x \ 1,x) * y != z * K(x \ 1,x) | z = y. x = (x * K(y \ 1,y)) * K(y,y \ 1). (x * K(y \ 1,y)) * K(y,y \ 1) = x. L((x * K(y,y \ 1)) \ z,x * K(y,y \ 1),K(y \ 1,y)) = x \ (K(y \ 1,y) * z). K(x,x \ 1) * y != z * (x * (1 / x)) | z = y. x = (x * (y * (1 / y))) * K(y \ 1,y). (x * (y * (1 / y))) * K(y \ 1,y) = x. x * y != K(z,z \ 1) * (u * K(z \ 1,z)) | u / y = x. x / (y * (1 / y)) = x * K(y \ 1,y). x / K(y \ 1,y) = x * (y * (1 / y)). R((x * K(y,y \ 1)) / y,y,K(y \ 1,y)) = x / (1 / (1 / y)). T(T(x / y,y / x),y) = ((y \ x) \ 1) \ 1. (1 / x) * (y * K(1 / x,(1 / x) \ 1)) = (x \ 1) * y. x != (1 / (1 / y)) * z | (y * z) * K(y \ 1,y) = x. (x * y) * K(x \ 1,x) = x * (y * K(x \ 1,x)). L(x,T(x,y) \ 1,T(x,y)) = 1 / (1 / x). x * y != z * K(z \ (z / T(z,u)),z) | x \ (1 / (1 / z)) = y. T(x,y) \ (1 / (1 / x)) = (T(x,y) \ 1) * x. L(1 / (1 / x),y,z) = L(L(x,y,z),T(x,u) \ 1,T(x,u)). L(L(x,y,z),T(x,u) \ 1,T(x,u)) = L(1 / (1 / x),y,z). T(x \ y,x / y) = ((x \ y) \ 1) \ 1. T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1. x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x. (x * K(y,y \ 1)) / y != z | (x / y) * K(y,y \ 1) = z. R(x,y,K(x \ 1,x)) = x. R(T(x,y),z,K(x \ 1,x)) = T(x,y). T(x,y) \ (1 / (1 / x)) = (T(x,y) \ x) * K(x \ 1,x). (T(x,y) \ x) * K(x \ 1,x) = T(x,y) \ (1 / (1 / x)). x * (((x \ y) \ 1) \ 1) = (((x / y) \ 1) \ 1) \ x. (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1). x / (x * (((x \ y) \ 1) \ 1)) = ((x / y) \ 1) \ 1. x / ((((y / x) \ 1) \ 1) * x) = ((x / y) \ 1) \ 1. x / (((y \ 1) \ 1) * x) = ((x / (y * x)) \ 1) \ 1. x != ((y / (z * y)) \ 1) \ 1 | R(z \ 1,z,y) = x. R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y). x != y / ((z \ 1) * y) | R(z,z \ 1,y) = x. R(x \ 1,(x \ 1) \ 1,y) = R(x \ 1,x,y). (1 / x) * (T(x,y) \ (1 / (1 / x))) = (x \ 1) * (T(x,y) \ x). x * (K(y \ 1,y) * z) != u | x * (z * K(y \ 1,y)) = u. (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x). x * y != (1 / z) * ((T(z,u) \ 1) * z) | x \ (T(z,u) \ 1) = y. (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x. (x \ 1) \ (T(x,y) \ 1) != z | 1 / (x \ T(x,y)) = z. 1 / (x \ T(x,y)) = T(x,y) \ x. (x \ 1) \ (T(x,y) \ 1) != z | (x \ T(x,y)) \ 1 = z. (x \ T(x,y)) \ 1 = T(x,y) \ x. ((x / y) \ (y \ x)) \ 1 = T(x / y,y) \ (x / y). T(x / y,y) \ (x / y) = ((x / y) \ (y \ x)) \ 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. (K(x,x \ 1) * (y * z)) / (K(x,x \ 1) * z) = R(y,z,K(x,x \ 1)). ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z). x * y != (((z * (1 / u)) / z) * u) * (u \ w) | (((z * ((u \ w) / w)) / z) * w) / y = x. (((x * ((y \ z) / z)) / x) * z) / (y \ z) = ((x * (1 / y)) / x) * y. (((x * ((y \ z) / z)) / x) * z) / (y \ z) != u | u = ((x * (1 / y)) / x) * y. (((x * ((y \ z) / z)) / x) * z) / (y \ z) != u | ((x * (1 / y)) / x) * y = u. x != (y / z) * R(z,u,w) | (y * R(z,u,w)) / z = x. ((x * (1 / R(x,y,z))) * R(x,y,z)) / x = (((x * ((R(x,y,z) \ u) / u)) / x) * u) / (R(x,y,z) \ u). (((x * ((R(x,y,z) \ u) / u)) / x) * u) / (R(x,y,z) \ u) = ((x * (1 / R(x,y,z))) * R(x,y,z)) / x. x * y != (z * x) * L((z * x) \ u,w,v5) | T(z * L(z \ (u / x),w,v5),x) = y. T(x * L(x \ ((y * z) / y),u,w),y) = T(x,y) * L(T(x,y) \ z,u,w). T(L((x \ 1) * ((1 / x) \ ((y * z) / y)),x,x \ 1),y) = T(1 / x,y) * L(T(1 / x,y) \ z,x \ 1,x). K(x,y \ (y / x)) = K(x,x \ 1). K((x / y) \ x,z \ (z / y)) = K(y,y \ 1). (x / y) * K(y,y \ 1) = x * (1 / (1 / (x \ (x / y)))). 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). K(x,(x / y) / x) * (y * z) = y * ((y * ((x * (y \ 1)) / x)) * z). x != (y * z) * T(L(u,z,y),w) | y * (z * T(u,w)) = x. x * ((1 / y) * T(y,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(x,y)). (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (T(x,y) / x). (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). T(T(x,y) * T(T(x,y) \ x,x),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x). T(L(x,T(x,y) \ x,T(x,y)),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x). T(L(x,T(x,y) \ x,T(x,y)),x * (T(x,y) \ x)) = L(x,T(x,y) \ x,x). L(T(x,x * (T(x,y) \ x)),T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x). L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x). L(x,T(x,y) \ x,T(x,y)) != z | T(x,y) * T(T(x,y) \ x,x) = z. T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x). x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y). T(x,y) * T(T(x,y) \ x,x) != z | (T(x,y) \ x) * T(x,y) = z. (T(x,y) \ x) * T(x,y) = L(x,T(x,y) \ x,x). L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y). K(L(x \ 1,x,y / x),z) != u | K(y \ (y / x),z) = u. K(x \ (x / y),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). x != K(y \ 1,y) | (y \ 1) * y = x. (x \ 1) * x = K(y \ (y / x),x). K(x \ (x / y),y) = (y \ 1) * y. ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z. R(x,y,K(y \ 1,y)) = x. R((x * K(y,y \ 1)) / y,y,K(y \ 1,y)) != z | x / (1 / (1 / y)) = z. x / (1 / (1 / y)) = (x * K(y,y \ 1)) / y. (x * K(y,y \ 1)) / y = x / (1 / (1 / y)). (x / y) * K(y,y \ 1) = x / (1 / (1 / y)). x * y != (z / u) * u | z / y = x. x / (y * (1 / y)) = (x / (1 / y)) * (y \ 1). (x / (1 / y)) * (y \ 1) = x / (y * (1 / y)). x * (y * (1 / y)) != z | x / K(y \ 1,y) = z. (x * (y \ 1)) / K(y \ 1,y) = x * (1 / y). (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1). x * y != (z / u) * K(u,u \ 1) | x \ (z / (1 / (1 / u))) = y. x \ (x / (1 / (1 / y))) = 1 / (1 / (x \ (x / y))). 1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y))). x != y / (z * (1 / z)) | y * K(z \ 1,z) = x. x * K(y \ 1,y) = (x / (1 / y)) * (y \ 1). (x / (1 / y)) * (y \ 1) = x * K(y \ 1,y). R(x,y \ 1,y) / y = x * (1 / y). (x * (1 / y)) * y = R(x,y \ 1,y). R(x / (1 / y),y \ 1,y) = x * y. (x \ 1) * y != (z * (1 / x)) * K(x \ 1,x) | T(z,x \ 1) = y. T(x,y \ 1) = (1 / y) \ (x * (1 / y)). (1 / x) \ (y * (1 / x)) = T(y,x \ 1). T(x,1 / y) = T(x,y \ 1). T(x,y \ 1) != z | T(x,1 / y) = z. T(x,y) = T(x,(y \ 1) \ 1). T(x,(y \ 1) \ 1) = T(x,y). T(x,(y \ z) \ z) != u | T(x,T(y,y \ z)) = u. T(x,T(y,y \ 1)) = T(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)). T(x,x \ 1) * T(y,x) = y * T(x,x \ 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). R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y. R(x / (y \ 1),y \ 1,y) != z | ((y \ 1) * y) \ (x * y) = z. ((x \ 1) * x) \ (y * x) = y * T(x,x \ 1). x * K(y,y \ 1) = (x / y) * T(y,y \ 1). (x / y) * T(y,y \ 1) = x * K(y,y \ 1). K(x \ 1,x) \ (y * x) = y * T(x,x \ 1). (x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1). (x / T(y,z)) * T((y \ 1) \ 1,z) = x * K(T(y,z),T(y,z) \ 1). x * y = (x * K(y \ 1,y)) * ((y \ 1) \ 1). (x * K(y \ 1,y)) * ((y \ 1) \ 1) = x * y. x / ((y \ 1) \ 1) = (x / y) * K(y \ 1,y). (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1). (x / y) * K(y \ 1,y) != z | x * T(x \ (x / y),y) = z. x * T(x \ (x / y),y) = x / ((y \ 1) \ 1). x != y / ((z \ u) \ u) | y / T(z,z \ u) = x. x / T(y,y \ 1) = x * T(x \ (x / y),y). x * T(x \ (x / y),y) = x / T(y,y \ 1). x * (L(x,y,z) / T(x,x \ 1)) = L(x,y,z) * ((L(x,y,z) \ (L(x,y,z) / x)) * x). L(x,y,z) * ((L(x,y,z) \ (L(x,y,z) / x)) * x) = x * (L(x,y,z) / T(x,x \ 1)). 1 / (1 / (x \ (x / (y \ 1)))) = x \ (x / (1 / y)). R(((x \ (x / (y \ 1))) * x) * K(y \ 1,y),y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y. ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z. x * T((T(y,x) \ 1) \ 1,z) = (T(y,z) * x) * K(T(T(y,x),z),T(T(y,x),z) \ 1). (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = z * T((T(x,z) \ 1) \ 1,y). ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z. ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z. 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). L(x,y,z) * ((L(x,y,z) \ (L(x,y,z) / x)) * x) = x * ((x \ 1) * L(x,y,z)). L(L(x,y,z),x \ 1,x) = L(x,y,z) * ((L(x,y,z) \ (L(x,y,z) / x)) * x). L(x,y,z) * ((L(x,y,z) \ (L(x,y,z) / x)) * x) = L(L(x,y,z),x \ 1,x). x != L(L(y,z,u),y \ 1,y) | L(1 / (1 / y),z,u) = x. L(1 / (1 / x),y,z) = L(x,y,z) * ((L(x,y,z) \ (L(x,y,z) / x)) * x). L(x,y,z) * ((L(x,y,z) \ (L(x,y,z) / x)) * x) = L(1 / (1 / x),y,z). L(x,y,z) * (T(1 / x,L(x,y,z)) * x) = L(1 / (1 / x),y,z). L(x,y,z) * (x * T(x \ 1,L(x,y,z))) = L(1 / (1 / x),y,z). (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = z * T(T((x \ 1) \ 1,z),y). x != y * T(T(z,y),u) | T(z,u) * y = x. T((x \ 1) \ 1,y) * z = (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1). (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = T((x \ 1) \ 1,y) * z. 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). L(x,y,z) * T(L(x,y,z) \ 1,u) = L(x * T(x \ 1,u),y,z). L(x * T(x \ 1,L(x,y,z)),y,z) != u | K(L(x,y,z) \ 1,L(x,y,z)) = u. 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). x != ((y * z) * u) / (z * u) | R(y,z,u) = x. R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y). x != K(y \ (y / z),z) | (z \ 1) * z = x. (R(x,y,z) \ 1) * R(x,y,z) = R(x * T(x \ 1,R(x,y,z)),y,z). R(x * T(x \ 1,R(x,y,z)),y,z) = (R(x,y,z) \ 1) * R(x,y,z). R(x,y,z) * T(R(x,y,z) \ 1,u) = R(x * T(x \ 1,u),y,z). R(T(x,x \ 1) * T(T(x,x \ 1) \ 1,x \ R(x,y,z)),y,z) = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)). (1 / x) * T(R(1 / x,K(x \ 1,x),y) \ 1,z) = R((1 / x) * T((1 / x) \ 1,z),K(x \ 1,x),y). R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = (1 / x) * T(R(1 / x,K(x \ 1,x),z) \ 1,y). K(x \ 1,x) * L(K(x \ 1,x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u)). T(x,y) \ L(x,z,u) = (T(x,y) \ 1) * L(T(x,T(x,y) \ 1),z,u). (T(x,y) \ 1) * L(T(x,T(x,y) \ 1),z,u) = T(x,y) \ L(x,z,u). x * y != (T(z,u) \ 1) * L(T(z,T(z,u) \ 1),w,v5) | x \ (T(z,u) \ L(z,w,v5)) = y. L(x,y,z) \ (T(x,u) \ L(x,y,z)) = T(x,u) \ 1. T(L(x * T(x \ 1,x),y,z),x * (L(x,y,z) \ 1)) = K(x \ (L(x,y,z) \ x),x). T(L(K(x \ 1,x),y,z),x * (L(x,y,z) \ 1)) = K(x \ (L(x,y,z) \ x),x). T(L(K(x \ 1,x),y,z),L(x,y,z) \ x) = K(x \ (L(x,y,z) \ x),x). L(T(K(x \ 1,x),L(x,y,z) \ x),y,z) = K(x \ (L(x,y,z) \ x),x). L(T(K(x \ 1,x),L(x,y,z) \ x),y,z) = K(L(x,y,z) \ 1,x). L(K(x \ 1,x),y,z) = K(L(x,y,z) \ 1,x). (x * y) * K(L(z,y,x) \ 1,z) = x * (y * K(z \ 1,z)). x * (y * K(z \ 1,z)) != (x * y) * u | K(L(z,y,x) \ 1,z) = u. (x * y) * z != x * (y * K(u \ 1,u)) | K(L(u,y,x) \ 1,u) = z. x != y * (z * L(z \ (y \ (u * z)),w,v5)) | (y * L(y \ u,w,v5)) * z = x. ((x \ 1) * L((x \ 1) \ y,z,u)) * x = K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u). K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = ((x \ 1) * L((x \ 1) \ 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(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. 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)). K(R(x,y,z),((x \ 1) * R(x,y,z)) / R(x,y,z)) = (x \ 1) \ (x \ K(R(x,y,z),1 / x)). K(R(x,y,z),x \ 1) = (x \ 1) \ (x \ K(R(x,y,z),1 / x)). (x \ 1) \ (x \ K(R(x,y,z),1 / x)) = K(R(x,y,z),x \ 1). (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z)) = K(R(x,y,z),x \ 1). (x \ 1) \ ((x \ y) / y) != z | x * ((x \ y) / y) = z. x * ((x \ R(x,y,z)) / R(x,y,z)) = K(R(x,y,z),x \ 1). 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. 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) | y * K(y,z) = x. R(x,y,z) * K(R(x,y,z),x \ 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)) = 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))) = 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(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). R(x,y,z) \ R(T(x,x \ 1),y,z) != u | a(R(x,y,z),1 / x,x) = u. a(R(x,y,z),1 / x,x) = K(R(x,y,z),x \ 1). x != K(R(y,z,u),y \ 1) | y * ((y \ R(y,z,u)) / R(y,z,u)) = x. 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). (T(x,y) * z) * K(T(x,z),T(x,z) \ 1) = T((x \ 1) \ 1,y) * z. x / T(x,y) = T(x,y) \ x. (T(x,y) \ x) \ x = T(x,y). (T(x,y) \ x) * T(x,y) = x. (T(x,y) \ x) * T(x,y) != z | L(x,T(x,y) \ x,x) = z. L(x,T(x,y) \ x,x) = x. 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). K(K(x,y),y) = 1. T(x,K(y,x)) = x. K(x * T(x \ 1,y),y) = 1. T(x,y) = T(T(x,y),K(z,x)). T(T(x,y),K(z,x)) = T(x,y). T(x,y \ T(y,x)) = x. T(x,x \ ((y * x) / y)) = x. (x \ T(x,y)) * y = y * (x \ T(x,y)). (x \ T(x,y)) * T(y,z) != u | T(y,z) * (x \ T(x,y)) = u. T(x * T(x \ 1,y),y) = x * T(x \ 1,y). T(K(x,y),T(y,z)) = K(x,y). ((x * y) / x) / y = y \ ((x * y) / x). K(K(x,y),T(y,z)) = 1. K(x \ T(x,y),T(y,z)) = 1. T(x \ T(x,y),T(y,z)) = x \ T(x,y). x * (T(x,y) \ (y * (x \ T(x,y)))) = L(y,x \ T(x,y),x). x * (((y * x) / y) / x) = (y * x) / y. (x \ 1) * (x * ((y * (x \ 1)) / y)) = (y * (x \ 1)) / y. T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y). T(x,y) * (K(x \ 1,x) * z) = T(1 / (1 / x),y) * z. x * (y * T(y \ 1,x)) = y * ((x \ (y \ x)) * x). x * ((y \ (x \ y)) * y) = y * (x * T(x \ 1,y)). x * K(y \ 1,y) != T(1 / (1 / y),z) | y * (T(y,z) / 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). (x \ T(x,y)) * x = T(x,y). 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((1 / x) \ 1,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 / y != z \ x | T(z,z \ x) = y. T(x,x \ T(x,y)) = x. (x * (y \ T(y,x))) \ (x * z) = x * ((x * (T(y,x) / y)) \ z). K(x,x \ T(x,y)) = 1. K(x,T(x,y) / x) = 1. 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 \ T(x,x / (x * y))) * x != z | T(x,R(1 / y,y,x)) = z. 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)). T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z). x = T(1 / (1 / x),T(1 / 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). T(x / (y * x),T(y,z)) = R(y \ 1,y,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). (x \ 1) \ 1 = T(x,T(1 / x,y)). T(x,T(1 / x,y)) = (x \ 1) \ 1. T(x,x \ 1) * T(x \ 1,y) = x * T(1 / x,y). ((x \ 1) \ 1) * T(x \ 1,y) = x * T(1 / x,y). T(x,R(1 / y,y,z)) != u | T(x,R(y \ 1,y,z)) = u. T(x,R(y \ 1,y,x)) = T(x,x / (x * y)). 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) | K(y \ 1,y) = x. K(x \ 1,x) = K(x \ 1,T(x,y)). K(x \ 1,T(x,y)) = K(x \ 1,x). R(x \ T(x,y),K(x \ 1,x),z) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z. x \ ((y * x) / y) != y \ z | T(y,R(x,x \ 1,y)) = z. 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)). T(x,y \ ((x * y) / x)) = x. T(x,T(y,x) \ y) = x. (T(x,y) \ x) * y = y * (T(x,y) \ x). (T(x,y) \ x) * y != z | T(y,R(T(x,y),T(x,y) \ 1,y)) = z. T(x,R(T(y,x),T(y,x) \ 1,x)) = x * (T(y,x) \ y). (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = (T(y,x) \ y) * x. T(x,y) * ((T(x,y) \ 1) * L(x,z,u)) = L(x,z,u) * (T(x,y) * T(T(x,y) \ 1,L(x,z,u))). L(x,y,z) * (T(x,u) * T(T(x,u) \ 1,L(x,y,z))) = T(x,u) * ((T(x,u) \ 1) * L(x,y,z)). (x * T(1 / x,y)) \ (((x \ 1) \ 1) * (T(x \ 1,y) * z)) = L(z,T(x \ 1,y),(x \ 1) \ 1). x != 1 / (y \ ((z * y) / z)) | ((z * y) / z) \ y = x. ((x * y) / x) \ y = T(x,R(y,y \ 1,x)) \ x. 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). T(x \ 1,y) * (K((x \ 1) \ 1,x \ 1) * z) = T(1 / x,y) * z. 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 \ T(y,z),y) = y * L(y \ x,y,y \ T(y,z)). x * L(x \ y,x,x \ T(x,z)) = L(y,x \ T(x,z),x). T(x,y) * L(T(x,y) \ z,u,w) != v5 | T(x * L(x \ ((y * z) / y),u,w),y) = v5. T(x * L(x \ ((y * z) / y),x,x \ T(x,y)),y) = (x \ T(x,y)) * (x * (T(x,y) \ z)). (x * (y \ T(y,x))) \ (x * z) = x * ((x * (y \ T(y,x))) \ z). x != (T(y,z) \ y) * z | z * (T(y,z) \ y) = x. x * (T(y,x) \ y) = (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x). (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 != (x * (z \ T(z,x))) \ (x * u) | (x * (z \ T(z,x))) \ u = y. (x * (y \ T(y,x))) \ x = T(y,x) \ y. (T(x,y) * z) * K(x,x \ 1) = T((x \ 1) \ 1,y) * z. (1 / x) * (T(((1 / x) \ 1) \ 1,y) * z) = (x \ 1) * (T(1 / x,y) * z). T(x \ 1,y) * (K(x,x \ 1) * z) = T(1 / x,y) * z. T(x \ 1,y) * ((((x \ 1) \ 1) \ 1) \ z) = T(1 / x,y) * ((x \ 1) \ z). T(x \ 1,y) * ((x \ 1) \ z) = T(1 / x,y) * ((1 / x) \ z). T(1 / x,y) * ((1 / x) \ z) = T(x \ 1,y) * ((x \ 1) \ z). (1 / x) * (T(x \ 1,y) * ((x \ 1) \ z)) = T(1 / x,y) * z. (1 / x) * (T(x \ 1,y) * z) = (x \ 1) * (T(1 / x,y) * z). (1 / x) * y != (x \ 1) * z | K(x \ 1,x) * z = y. K(x \ 1,x) * (T(1 / x,y) * z) = T(x \ 1,y) * z. x * y != (1 / z) * (T(z \ 1,u) * ((z \ 1) \ w)) | (T(1 / z,u) * w) / y = x. (T(1 / x,y) * z) / (T(1 / x,y) * ((x \ 1) \ z)) = x \ 1. ((x \ 1) \ 1) * (T(x \ 1,y) * z) = x * (T(1 / x,y) * z). T(x \ 1,y) * (T(x \ 1,(x \ 1) \ 1) \ z) = T(1 / x,y) * ((x \ 1) \ z). T(L((x * y) / x,z \ T(z,x),z),x) = (z \ T(z,x)) * (z * (T(z,x) \ y)). L(x \ (x * y),z \ T(z,x),z) = (z \ T(z,x)) * (z * (T(z,x) \ y)). L(x,y \ T(y,z),y) = (y \ T(y,z)) * (y * (T(y,z) \ x)). (x \ T(x,y)) * (x * (T(x,y) \ z)) = L(z,x \ T(x,y),x). (x \ T(x,y)) * T(y,T(x,y)) = L(y,x \ T(x,y),x). T(x,T(y,x)) * (y \ T(y,x)) = L(x,y \ T(y,x),y). L(L(x,y,z),T(x,u) \ 1,T(x,u)) = L(x,y,z) * (T(x,u) * T(T(x,u) \ 1,L(x,y,z))). L(x,y,z) * (T(x,u) * T(T(x,u) \ 1,L(x,y,z))) = L(L(x,y,z),T(x,u) \ 1,T(x,u)). L(x,y,z) * T(x * T(x \ 1,L(x,y,z)),u) = L(L(x,y,z),T(x,u) \ 1,T(x,u)). L(L(x,y,z),T(x,u) \ 1,T(x,u)) = L(x,y,z) * T(x * T(x \ 1,L(x,y,z)),u). L(L(x,y,z),T(x,u) \ 1,T(x,u)) != w | L(1 / (1 / x),y,z) = w. L(1 / (1 / x),y,z) = L(x,y,z) * T(x * T(x \ 1,L(x,y,z)),u). L(x,y,z) * T(x * T(x \ 1,L(x,y,z)),u) = L(1 / (1 / x),y,z). L(x,y,z) * K(x \ 1,L(x,y,z)) = L(1 / (1 / x),y,z). L(x,y,z) * u != L(1 / (1 / x),y,z) | x * T(x \ 1,L(x,y,z)) = u. x * T(x \ 1,L(x,y,z)) = K(x \ 1,L(x,y,z)). L(K(x \ 1,L(x,y,z)),y,z) != u | K(L(x,y,z) \ 1,L(x,y,z)) = u. (x * T(1 / x,y)) \ (x * (T(1 / x,y) * z)) = L(z,T(x \ 1,y),(x \ 1) \ 1). L(x,T(y \ 1,z),(y \ 1) \ 1) != u | L(x,T(1 / y,z),y) = 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 * ((R(x,y,z) \ u) / u)) / x) * u) / (R(x,y,z) \ u) = R(x,1 / R(x,y,z),R(x,y,z)) / x. (((x * ((R(x,y,z) \ u) / u)) / x) * u) / (R(x,y,z) \ u) = T(x,1 / R(x,y,z)) / x. ((x * (1 / R(x,y,z))) / x) * R(x,y,z) = T(x,1 / R(x,y,z)) / x. R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = (1 / x) * T((1 / x) \ 1,y). x != (1 / y) * T((1 / y) \ 1,z) | y \ T(y,z) = x. x \ T(x,y) = R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z). R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = x \ T(x,y). R(x \ T(x,y),K(x \ 1,x),z) = x \ T(x,y). (x \ T(x,y)) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z. (x \ T(x,y)) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,x) * z. (x \ T(x,y)) * (K(x \ 1,x) * z) = ((x \ 1) * T(x,y)) * z. (x \ T(x,y)) * (z * K(x \ 1,x)) = ((x \ 1) * T(x,y)) * z. T((x \ 1) * (x * ((y * z) / y)),y) = T(1 / x,y) * L(T(1 / x,y) \ z,x \ 1,x). x != y * (z * ((y * (z \ (y \ u))) / y)) | (y * ((u / z) / y)) * z = x. (x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) = (x * (R(u / z,z,u \ y) / x)) * (z * (u \ y)). (x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u)). R(T(x,x \ 1) * T(T(x \ 1,x),x \ R(x,y,z)),y,z) = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)). R(T(x,x \ 1) * T(x \ 1,x),y,z) = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)). K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(T(x,x \ 1) * T(x \ 1,x),y,z). K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R((x \ 1) * T(x,x \ 1),y,z). K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(1,y,z). x != R(1,y,z) | 1 = x. 1 = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)). K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = 1. (x \ 1) * 1 = ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)). ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = (x \ 1) * 1. x != y * 1 | y = x. x \ 1 = ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)). ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = x \ 1. (x \ 1) / (x \ R(x,y,z)) != u | u = (x \ R(x,y,z)) \ (x \ 1). (x \ 1) / (x \ R(x,y,z)) != u | (x \ R(x,y,z)) \ (x \ 1) = u. ((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 != ((y * ((z * u) / (w * u))) / y) * (w * u) | (w * ((y * (w \ z)) / y)) * u = x. ((x * y) * ((z * ((x * y) \ y)) / z)) * u = (((z * (1 / R(x,y,u))) / z) * R(x,y,u)) * (y * u). (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u. x * y != ((z * ((u * w) / (v5 * w))) / z) * (v5 * w) | ((((z * (u / v5)) / z) * v5) * w) / y = x. ((((x * (y / (z * y))) / x) * (z * y)) * u) / (y * u) = ((x * (1 / R(z,y,u))) / x) * R(z,y,u). (R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u)) * (y * z) = ((x * y) * ((u * ((x * y) \ y)) / u)) * z. (((((x * (1 / y)) / x) * y) * z) * u) / (z * u) = ((x * (1 / R(y,z,u))) / x) * R(y,z,u). R(((x * (1 / y)) / x) * y,z,u) = ((x * (1 / R(y,z,u))) / x) * R(y,z,u). ((x * (1 / R(y,z,u))) / x) * R(y,z,u) = R(((x * (1 / y)) / x) * y,z,u). R(x,y,z) * (1 / R(x,y,z)) = R(((R(x,y,z) * (1 / x)) / R(x,y,z)) * x,y,z). R(((R(x,y,z) * (1 / x)) / R(x,y,z)) * x,y,z) = R(x,y,z) * (1 / R(x,y,z)). ((x * (1 / R(x,y,z))) / x) * R(x,y,z) != u | T(x,1 / R(x,y,z)) / x = u. T(x,1 / R(x,y,z)) / x = R(((x * (1 / x)) / x) * x,y,z). R(((x * (1 / x)) / x) * x,y,z) = T(x,1 / R(x,y,z)) / x. R((K(x,1 / x) / x) * x,y,z) = T(x,1 / R(x,y,z)) / x. R(K(x,1 / x),y,z) = T(x,1 / R(x,y,z)) / x. T(x,1 / R(x,y,z)) / x = R(K(x,1 / x),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)). K(R(x,y,z),R(x,y,z) \ 1) = 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) = 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). (R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u)) * (y * z) = ((x * ((u * (x \ 1)) / u)) * y) * z. R(x * ((y * (x \ 1)) / y),z,u) = R(x,z,u) * ((y * (R(x,z,u) \ 1)) / y). R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u) = R(x * ((u * (x \ 1)) / u),y,z). K(x,(x / R(y,z,u)) / x) = R(y * ((x * (y \ 1)) / x),z,u). R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y). R(K(x,(x / y) / x),z,u) = K(x,(x / R(y,z,u)) / x). (((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). R(x,y,z) * R(R(x,y,z) \ 1,R(x,y,z),x \ 1) != u | ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z) = u. ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z) = R(x * R(x \ 1,R(x,y,z),x \ 1),y,z). R(x * R(x \ 1,R(x,y,z),x \ 1),y,z) = ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z). R(x * T(x \ 1,R(x,y,z)),y,z) = ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z). ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z) = R(x * T(x \ 1,R(x,y,z)),y,z). x * R(y,z,u) != R(y * T(y \ 1,R(y,z,u)),z,u) | R(y,z,u) \ 1 = x. R(x,y,z) \ 1 = (x \ 1) / (x \ R(x,y,z)). (x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1. (x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1. ((1 / x) \ R(1 / x,y,z)) \ x = R(1 / x,y,z) \ 1. (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). (((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) | K(R(y,z,u),R(y,z,u) \ 1) = x. K(R(x,y,z),R(x,y,z) \ 1) = R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)). R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = K(R(x,y,z),R(x,y,z) \ 1). 1 / R(x,y,z) = (R(x,y,z) / x) \ (1 / x). (R(x,y,z) / x) \ (1 / x) = 1 / R(x,y,z). (R(x,y,z) / x) \ (1 / x) != u | R(1 / (1 / x),y,z) \ 1 = u. R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z). (R(1 / (1 / x),y,z) \ 1) \ 1 = R(x,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. ((R(x,y,z) \ 1) \ 1) * (y * z) = (((x \ 1) \ 1) * y) * z. ((((x \ 1) \ 1) * y) * z) / z = T(x,R(x,y,z) \ 1) * y. T(x,R(x,y,z) \ 1) = (x \ 1) \ 1. T(x,1 / R(x,y,z)) = (x \ 1) \ 1. ((x \ 1) \ 1) / x = R(K(x,1 / x),y,z). R(K(x,1 / x),y,z) = ((x \ 1) \ 1) / x. x != ((y \ 1) \ 1) / y | K(y,1 / y) = x. K(x,1 / x) = R(K(x,1 / x),y,z). R(K(x,1 / x),y,z) = K(x,1 / x). R(K(x \ 1,x),y,z) = K(x \ 1,1 / (x \ 1)). R(K(x \ 1,x),y,z) = K(x \ 1,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) = (y * K(x \ 1,x)) * z. (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z). L(x,y,K(z \ 1,z)) = x. K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * 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). L(x,y,z \ 1) = L(x,y,1 / z). L(x,y,1 / z) = L(x,y,z \ 1). L(T(x,y),y,K(z \ 1,z)) != u | R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) = u. R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) = T(x,y). L((x * K(y,y \ 1)) \ z,x * K(y,y \ 1),K(y \ 1,y)) != u | x \ (K(y \ 1,y) * z) = u. x \ (K(y \ 1,y) * z) = (x * K(y,y \ 1)) \ z. (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z). (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z). L(x,y,z) = L(x,y,(z \ 1) \ 1). L(x,y,(z \ 1) \ 1) = L(x,y,z). L(x,T(1 / y,z),y) = L(x,T(y \ 1,z),y). L(x \ y,x,z) != u | (z * x) \ (z * y) = u. (x * T(1 / x,y)) \ (x * z) = L(T(1 / x,y) \ z,T(x \ 1,y),x). L(T(1 / x,y) \ z,T(x \ 1,y),x) = (x * T(1 / x,y)) \ (x * z). (K(x \ 1,x) * (y * ((1 / x) * z))) / ((x \ 1) * z) = R(y,K(x \ 1,x),(1 / x) * z). K(x,x \ 1) * (y * z) = (y * K(x,x \ 1)) * z. (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z). x \ (K(y \ 1,y) * (x * ((1 / y) * z))) != u | L((y \ 1) * z,K(y,y \ 1),x) = u. x != K(y \ 1,y) * z | z * K(y \ 1,y) = x. (x / y) * K(z \ 1,z) = (K(z \ 1,z) * x) / y. (K(x \ 1,x) * y) / z = (y / z) * K(x \ 1,x). T(K(x \ 1,x) * (y / z),z) = z \ (K(x \ 1,x) * y). 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). (K(x \ 1,x) * y) / z != u | K(x \ 1,x) * (y / z) = u. R(T(x,y / (1 / z)),y / (z \ 1),K(z \ 1,z)) = T(x,y / (z \ 1)). T((x \ 1) * (x * ((y * (x \ z)) / y)),y) = y \ (K(x \ 1,x) * (y * ((1 / x) * z))). (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u). (K(x,x \ 1) * (y * z)) / (K(x,x \ 1) * z) != u | R(y,z,K(x,x \ 1)) = u. 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)). 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 * (1 / x)) * R(K(x \ 1,x) * y,z,u) = R(y,z,u). (x * (1 / x)) * R(y,z,u) = R((x * (1 / x)) * y,z,u). R((x * (1 / x)) * y,z,u) = (x * (1 / x)) * R(y,z,u). (x \ 1) * R((x * (1 / x)) * y,z,u) = (1 / x) * R(y,z,u). (x \ 1) * R((x \ 1) \ y,z,u) = (1 / x) * R((1 / x) \ y,z,u). (1 / x) * R((1 / x) \ y,z,u) = (x \ 1) * R((x \ 1) \ y,z,u). x != (y \ 1) * R((y \ 1) \ z,u,w) | y \ R(y * z,u,w) = x. x \ R(x * y,z,u) = (1 / x) * R((1 / x) \ y,z,u). (1 / x) * R((1 / x) \ y,z,u) = x \ R(x * y,z,u). (1 / x) * R((1 / x) \ y,z,u) != w | R(y * x,z,u) / x = w. R(x * y,z,u) / y = y \ R(y * x,z,u). x * (R(y * x,z,u) / x) = R(x * y,z,u). R((x \ y) * x,z,u) / x = x \ R(y,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). (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)). R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x. R((x \ (x / (1 / y))) * x,y \ 1,y) != z | (x * (y \ T(y,x))) * y = z. (x * (y \ T(y,x))) * y = (x \ (x * y)) * x. (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 * 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. x * y != y * T(z,y) | z = x. x = T(x,y) * (y \ T(y,T(x,y))). T(x,y) * (y \ T(y,T(x,y))) = x. x \ ((y * x) / y) = y \ T(y,x). x * y != (z * T(u,z)) / z | x \ u = y. T(x,y) \ x = y \ T(y,T(x,y)). x * y != ((z / u) * u) / w | x \ (z / w) = y. x \ (y / (y / x)) = (y / x) \ T(y / x,x). (x / y) \ T(x / y,y) = y \ (x / (x / y)). (x \ 1) * y != (z * (x \ 1)) / z | x * ((z * (x \ 1)) / z) = y. x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1). x * y != (z * x) / z | ((z * x) / z) / x = y. ((x * y) / x) / y = x \ T(x,y). ((x * y) / x) \ y = T(x,y) \ x. x \ T(x,y) = T(y,T(x,y)) \ y. T(x,T(y,x)) \ x = y \ T(y,x). T(x,R(y,y \ 1,x)) = T(x,y). T(x,R(y \ 1,y,x)) = T(x,y \ 1). R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z). (x / y) \ (y \ x) = T(y,y \ x) \ y. T(x,x \ y) \ x = (y / x) \ (x \ y). ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x). T(x,T(y,x)) * (y \ T(y,x)) = x. (x \ T(x,y)) \ y = T(y,T(x,y)). (x * (T(x,T(y,x)) \ x)) * y = y * x. T(x,T(y,x)) * (y \ T(y,x)) != z | L(x,y \ T(y,x),y) = z. L(x,y \ T(y,x),y) = x. x * y != L(z,u \ T(u,z),u) | x \ z = y. x \ y = T(x,y) \ (y * (x \ T(x,y))). T(x,y) \ (y * (x \ T(x,y))) = x \ y. (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y)). T(x,R(y \ 1,y,x)) != z | T(x,x / (x * y)) = z. T(x,x / (x * y)) = T(x,y \ 1). (x * ((x / y) / x)) * y = 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) * (x \ ((x \ y) \ y)) = y / x. T(x * (T(x,T(y,x)) \ x),y) = x. T(x,y) \ ((x * y) / x) = x \ y. T(x,y) * (x \ y) = (x * y) / x. x * (y \ z) != (y * z) / y | T(y,y / (y / z)) = x. T(x,x / (x / y)) = T(x,y). T(x,T(y,x)) * (y * x) = x * (x * y). R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x). (x \ y) \ (y / x) = x \ ((x \ y) \ y). (x / y) \ (y \ x) = y \ (x / (x / y)). (x / y) \ (y \ x) != z | T(y,y \ x) \ y = z. T(x,x \ y) \ x = x \ (y / (y / x)). x * ((y * (x \ 1)) / y) != z | (y * ((x \ y) / y)) / (x \ y) = z. (x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1). K(x,(x / y) / x) * (y * z) = y * ((x \ T(x,y \ 1)) * z). (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y)). x != K(y,(y / z) / y) | y \ T(y,z \ 1) = x. x \ T(x,T(y,z) \ 1) = T(x \ T(x,y \ 1),z). T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1). T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = x \ T(x,R(z \ 1,z,y) \ 1). x \ T(x,R(y,z,u) \ 1) = R(x \ T(x,y \ 1),z,u). R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1). ((x \ (y / (1 / z))) * x) * (1 / z) != u | x * (T((x \ y) * z,x) / z) = u. x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z. (x \ T(x,y \ 1)) * (y * z) = y * ((x \ T(x,y \ 1)) * z). x != y \ T(y,R(z,u,w) \ 1) | R(y \ T(y,z \ 1),u,w) = x. R(x \ T(x,(y \ 1) \ 1),y,z) = T(x \ T(x,(z / (y * z)) \ 1),T(y,u)). T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,(z \ 1) \ 1),z,y). T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y). ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x). T((x \ 1) * (x * ((y * (x \ z)) / y)),y) != u | L((x \ 1) * z,K(x,x \ 1),y) = u. K(x \ 1,x) * ((y * ((1 / x) * z)) / ((x \ 1) * z)) = R(y,K(x \ 1,x),(1 / x) * z). ((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 * (x \ y))) / x)) * (z * (x \ y)) != u | x * ((x \ T(x,z \ 1)) * (x \ y)) = u. x * ((x \ T(x,y \ 1)) * (x \ z)) = ((x * ((x / y) / x)) * y) * (x \ 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). x \ (T(x,y) * z) = (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. (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z). T(x,y) * (x \ z) = (x \ T(x,y)) * z. (x \ T(x,y)) * z = T(x,y) * (x \ z). L(x,y \ T(y,z),y) = x. (x \ T(x,y)) \ z = T(x,y) \ (x * z). x * y != L(z,u \ T(u,w),u) | x \ z = y. (x \ T(x,y)) \ z = x * (T(x,y) \ z). L(x,T(y,T(z,y)) \ y,z) = x. L(x,T(y,z) \ y,(y * z) / y) = x. 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. x * ((T(y,x) \ y) * z) = T(x,T(y,x)) * z. (x \ T(x,y \ 1)) * (y * z) != u | y * ((x \ T(x,y \ 1)) * z) = u. x * ((y \ T(y,x \ 1)) * z) = T(y,x \ 1) * (y \ (x * z)). T(x,y \ 1) * (x \ (y * z)) = y * ((x \ T(x,y \ 1)) * z). (x \ T(x,y)) * (z * K(x \ 1,x)) != u | ((x \ 1) * T(x,y)) * z = u. ((x \ 1) * T(x,y)) * z = T(x,y) * (x \ (z * K(x \ 1,x))). T(x,y) * (x \ (z * K(x \ 1,x))) = ((x \ 1) * T(x,y)) * z. (x \ T(x,y)) \ z != u | x * (T(x,y) \ z) = u. (x \ T(x,y)) \ (T(x,y) * z) != u | x * z = u. x * (((y * x) / y) \ z) = (T(y,x) \ y) * z. x * y != T(x,T(z,x)) * (z * x) | x * z = y. x * y = (T(y,x) \ y) * (y * x). (T(x,y) \ x) * (x * y) = y * x. (x * y) / (y * x) = T(y,x) \ y. (x * (y / x)) / y = T(y / x,x) \ (y / x). T(x / y,y) \ (x / y) = (y * (x / y)) / x. x * (((y * x) / y) \ z) != u | R(y \ T(y,x),x,((y * x) / y) \ z) \ z = u. R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z. (x \ y) \ (y / x) = (x * (y / x)) / y. (x * (y / x)) / y = (x \ y) \ (y / x). x != (y \ z) \ (z / y) | y \ ((y \ z) \ z) = x. x \ ((x \ y) \ y) = (x * (y / x)) / y. (x * (y / x)) / y = x \ ((x \ y) \ y). (x * ((y \ x) / x)) / (y \ x) != z | x \ T(x,y \ 1) = z. x \ T(x,y \ 1) = x \ ((x \ (y \ x)) \ (y \ x)). x \ ((x \ (y \ x)) \ (y \ x)) = x \ T(x,y \ 1). x * T(x \ 1,y) = ((x \ z) / z) \ T((x \ z) / z,y). ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z). T(x,x \ (y \ x)) = T(x,y \ 1). T(x,y \ 1) \ x = x \ ((y \ x) / ((y \ x) / x)). x \ ((y \ x) / ((y \ x) / x)) = T(x,y \ 1) \ x. (x / y) \ T(x / y,y) != z | y \ (x / (x / y)) = z. x \ ((y \ x) / ((y \ x) / x)) = y * T(y \ 1,x). (x * T(x \ 1,y)) \ y = T(y,T((x \ z) / z,y)). T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x. x \ ((y \ x) / ((y \ x) / x)) != z | T(x,y \ 1) \ x = z. T(x,y \ 1) \ x = y * T(y \ 1,x). x \ T(x,y) = T(y,(x \ 1) \ 1) \ y. T(x,(y \ 1) \ 1) \ x = y \ T(y,x). L(x,T(y \ 1,z),y) = (T(z,y \ 1) \ z) \ (y * (T(y \ 1,z) * x)). (T(x,y \ 1) \ x) \ (y * (T(y \ 1,x) * z)) = L(z,T(y \ 1,x),y). T(x,y) \ x = y \ T(y,x). x \ y != z \ T(z,y) | T(y,T(z,y)) = x. T(x,T(y,x)) = T(x,y). x * ((T(y,x) \ y) * z) = T(x,y) * z. (T(x,y) \ x) * z = T(y,x) * (y \ z). T(x,y) * (x \ z) = (T(y,x) \ y) * z. T(x * (T(x,y) \ x),y) = x. (x / y) * z != T(x / y,u) * x | y * T(y \ x,u) = z. x * T(x \ y,z) = (T(z,y / x) \ z) * y. (T(x,y / z) \ x) * y = z * T(z \ y,x). x != y * T(y \ z,u) | z * K(u \ (u / (z \ y)),u) = x. x * K(y \ (y / (x \ z)),y) = (T(y,x / z) \ y) * x. x != (y * T(y \ 1,z)) \ z | T(z,T(y \ 1,z)) = x. T(x,T(y \ 1,x)) = T(x,T((y \ z) / z,x)). T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x)). T(x,T(y,x)) != z | T(x,y) = z. T(x,(y \ z) / z) = T(x,T(y \ 1,x)). T(x,T(y \ 1,x)) = T(x,(y \ z) / z). T(x,y \ 1) = T(x,(y \ z) / z). T(x,(y \ z) / z) = T(x,y \ 1). T(x,y / z) = T(x,(z / y) \ 1). T(x,(y / z) \ 1) = T(x,z / y). T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z). (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) != u | T(x,z) / y = u. T(x,y) / z = (T(y,(x / z) / (1 / z)) \ y) * (x / z). (T(x,(y / z) / (1 / z)) \ x) * (y / z) = T(y,x) / z. T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u). T(x \ T(x,y),T(y,z)) != u | x \ T(x,y) = u. x \ T(x,y) = R(x \ T(x,y),y,z). R(x \ T(x,y),y,z) = x \ T(x,y). T(x,y \ 1) * (x \ (y * z)) = y * (T(x,y \ 1) * (x \ z)). T(x,y) * (T(x,x \ 1) \ z) = ((x \ 1) * T(x,y)) * z. T(x \ 1,y) * (T(x \ 1,(x \ 1) \ 1) \ z) != u | T(1 / x,y) * ((x \ 1) \ z) = u. T(1 / x,y) * ((x \ 1) \ z) = (((x \ 1) \ 1) * T(x \ 1,y)) * z. (((x \ 1) \ 1) * T(x \ 1,y)) * z = T(1 / x,y) * ((x \ 1) \ z). (x \ T(x,y)) \ z = (T(x,y) \ x) * z. x * y = (T(x,z) \ x) * (T(x,z) * y). (T(x,y) \ x) * (T(x,y) * z) = x * z. x * (T(x,y) \ z) = (T(x,y) \ x) * z. (T(x,y) \ x) * z = x * (T(x,y) \ z). (T(x,y) \ x) \ z = T(x,y) * (x \ z). (T(x,y) \ x) * z != u | T(y,x) * (y \ z) = u. T(x,y) * (x \ (T(y,x) * z)) = y * z. (T(x,(y / z) / (1 / z)) \ x) * (y / z) != u | T(y,x) / z = u. T(x,y) / z = y * (T(y,(x / z) / (1 / z)) \ (x / z)). x * (T(x,(y / z) / (1 / z)) \ (y / z)) = T(y,x) / z. (T(x,y / z) \ x) * y != u | z * T(z \ y,x) = u. x * T(x \ y,z) = z * (T(z,y / x) \ y). x * (T(x,y / (z \ 1)) \ y) != u | z \ T(z * y,x) = u. (x * T(1 / x,y)) * z = T(1 / x,y) * ((x \ 1) \ z). T(1 / x,y) * ((x \ 1) \ z) = (x * T(1 / x,y)) * z. (T(1 / x,y) * z) / ((x * T(1 / x,y)) * z) = x \ 1. (x \ 1) * y = T(1 / x,z) * ((x * T(1 / x,z)) \ y). T(1 / x,y) * ((x * T(1 / x,y)) \ z) = (x \ 1) * z. (T(x,y) \ x) \ z != u | T(x,y) * (x \ z) = u. T(x,y \ 1) * (x \ (y * (T(y \ 1,x) * z))) = L(z,T(y \ 1,x),y). T(x,y \ 1) * (x \ (y * z)) != u | y * (T(x,y \ 1) * (x \ z)) = u. x * (T(y,x \ 1) * (y \ (T(x \ 1,y) * z))) = L(z,T(x \ 1,y),x). x * ((x \ 1) * y) = L(y,T(x \ 1,z),x). L(x,T(y \ 1,z),y) = y * ((y \ 1) * x). L(x,y \ 1,y) = L(x,T(y \ 1,z),y). L(x,T(y \ 1,z),y) = L(x,y \ 1,y). L(T(1 / x,y) \ z,T(x \ 1,y),x) != u | (x * T(1 / x,y)) \ (x * z) = u. (x * T(1 / x,y)) \ (x * z) = L(T(1 / x,y) \ z,x \ 1,x). L(T(1 / x,y) \ z,x \ 1,x) = (x * T(1 / x,y)) \ (x * z). T((x \ 1) * (x * ((y * z) / y)),y) = T(1 / x,y) * ((x * T(1 / x,y)) \ (x * z)). x != T(1 / y,z) * ((y * T(1 / y,z)) \ u) | (y \ 1) * u = x. (x \ 1) * (x * y) = T((x \ 1) * (x * ((z * y) / z)),z). T((x \ 1) * (x * ((y * z) / y)),y) = (x \ 1) * (x * z). L((x \ 1) * y,K(x,x \ 1),z) = (x \ 1) * (x * (x \ y)). (x \ 1) * y = L((x \ 1) * y,K(x,x \ 1),z). L((x \ 1) * y,K(x,x \ 1),z) = (x \ 1) * y. (x * ((1 / y) * z)) / ((y \ 1) * z) = x * K(y,y \ 1). K(x \ 1,x) * (y * K(x,x \ 1)) = R(y,K(x \ 1,x),(1 / x) * z). R(x,K(y \ 1,y),(1 / y) * z) = K(y \ 1,y) * (x * K(y,y \ 1)). x != K(y \ 1,y) * (z * K(y,y \ 1)) | z = x. x = R(x,K(y \ 1,y),(1 / y) * z). R(x,K(y \ 1,y),(1 / y) * z) = x. R(x,K(y \ 1,y),z) = x. R(x,K(y \ 1,y),z) != u | R(x,z,K(y \ 1,y)) = u. R(x,y,K(z \ 1,z)) = x. 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(T(x,y / (1 / z)),y / (z \ 1),K(z \ 1,z)) != u | T(x,y / (z \ 1)) = u. T(x,y / (z \ 1)) = T(x,y / (1 / z)). T(x,y / (1 / z)) = T(x,y / (z \ 1)). 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 \ 1,z)) = K(z \ 1,z) * (x * y). K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x)). x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y). x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z. (x * K(y \ 1,y)) * z != u | K(y \ 1,y) * (x * z) = u. K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z). K(L(x,y,z) \ 1,x) = K(x \ 1,x). L(x * K(y \ 1,y),z,u) = (u * z) \ (u * (K(y \ 1,y) * (z * x))). (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u * K(z \ 1,z),y,x). L(K(x \ 1,x) * y,z,u) = (u * z) \ (u * (K(x \ 1,x) * (z * y))). (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(K(z \ 1,z) * u,y,x). x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z). x \ T(x * (y / x),z) = T(y,z) / x. (x \ T(x * (y / x),z)) * x = T(y,z). x \ T(x * y,z) = T(y * x,z) / x. T(x * y,z) / y = y \ T(y * x,z). (x \ T(y,z)) * x = T((x \ y) * x,z). T((x \ y) * x,z) = (x \ T(y,z)) * x. x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y. T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x. (x * ((y \ (x \ z)) * y)) / x = (y \ (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 / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z. (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y,x) * K(z \ 1,z). (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x. (x * y) \ (x * (K(z \ 1,z) * (y * u))) != w | L(K(z \ 1,z) * u,y,x) = w. L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x). (x * y) \ (x * (K(z \ 1,z) * (y * u))) != w | L(u * K(z \ 1,z),y,x) = w. L(x * K(y \ 1,y),z,u) = L(x,z,u) * K(y \ 1,y). x != y * K(z \ 1,z) | K(z \ 1,z) * y = x. K(x \ 1,x) * L(y,z,u) = L(K(x \ 1,x) * y,z,u). L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,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 \ 1,x) * L(y * K(x,x \ 1),z,u) != w | (x \ L(x * (y / x),z,u)) * x = w. (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. L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x. 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 \ 1) * ((y \ ((x \ 1) \ z)) * y) != u | ((y \ (z * x)) * y) / x = u. ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x). (x \ ((y \ (x * z)) * y)) * x = (y \ (z * x)) * y. (x \ ((y \ (x * 1)) * y)) * x = (y \ x) * y. (x \ ((y \ x) * y)) * x = (y \ x) * y. K(x \ y,x) * y = (x \ y) * x. T(x,K(y \ x,y)) = x. T(x * y,K(y,x)) = x * y. (x * y) / (y * x) = K(x,y). K(x,y) = (x * y) / (y * x). x != (y * z) / (z * y) | T(z,y) \ z = x. T(x,y) \ x = K(y,x). K(x,y) = T(y,x) \ y. x != T(y,z) \ y | z \ T(z,y) = x. x \ T(x,y) = K(x,y). K(x,y) = x \ T(x,y). T(x * K(y,x),y) = x. (x * K(y,x)) * y = y * x. 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 * y != y * z | z * K(y,z) = x. L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z). L(x,y,z) * u != L(x * K(w \ 1,w),y,z) | K(w \ 1,w) = u. K(x \ 1,x) = K(x \ 1,L(x,y,z)). K(x \ 1,L(x,y,z)) = K(x \ 1,x). L(K(x \ 1,L(x,y,z)),u,w) = K(L(x,u,w) \ 1,x). K(L(x,y,z) \ 1,L(x,y,z)) = K(L(x,y,z) \ 1,x). x != K(L(y,z,u) \ 1,y) | K(y \ 1,y) = x. K(L(x,y,z) \ 1,L(x,y,z)) = K(x \ 1,x). K(x \ 1,x) = K(R(x,y,z) \ 1,R(x,y,z)). K(R(c17,c18,c19) \ 1,R(c17,c18,c19)) != K(c17 \ 1,c17). R(x,x \ y,z) = (y * z) / ((x \ y) * z). R(x / y,y,z) \ (x * z) = y * z. R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u). 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). R(R(x,y,z) \ 1,R(x,y,z),y * z) = (((y * z) / ((x * y) * z)) \ 1) \ 1. x * (((x \ y) \ 1) \ 1) = y * K((y \ x) \ 1,y \ x). x * K((x \ y) \ 1,x \ y) = y * (((y \ x) \ 1) \ 1). ((((x * y) / ((z * x) * y)) \ 1) \ 1) * ((z * x) * y) = ((R(z,x,y) \ 1) * R(z,x,y)) * (x * y). (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 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. ((R(x / y,y,z) \ 1) \ 1) * (y * z) != u | (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1) = u. 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)). x * K(y \ x,x \ y) = y * (((y \ x) \ 1) \ 1). K(T(x,y) \ 1,T(x,y)) = K((x * y) \ y,y \ (x * y)). K((x * y) \ y,y \ (x * y)) = K(T(x,y) \ 1,T(x,y)). x * K(T(y,x) \ 1,T(y,x)) = (y * x) * ((((y * x) \ x) \ 1) \ 1). (x * y) * ((((x * y) \ y) \ 1) \ 1) = y * K(T(x,y) \ 1,T(x,y)). ((x * y) * z) * (((((x * y) * z) \ (y * z)) \ 1) \ 1) = ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z). (x * y) * ((((x * y) \ y) \ 1) \ 1) = y * K(x \ 1,x). (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) * (((((x * y) * z) \ (y * z)) \ 1) \ 1) != u | ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = u. ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z. ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = (y * K(x \ 1,x)) * z. x != y \ T(y,z \ 1) | z * ((y * (z \ 1)) / y) = x. x * ((y * (x \ 1)) / y) = K(y,x \ 1). K(x,(y \ z) / z) = x \ T(x,y \ 1). R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u) != w | R(x * ((u * (x \ 1)) / u),y,z) = w. R(x * ((y * (x \ 1)) / y),z,u) = K(y,R(x,z,u) \ 1). x != y \ T(y,z) | K(y,z) = x. K(x,y \ 1) = K(x,(y \ z) / z). K(x,(y \ z) / z) = K(x,y \ 1). K(x,y / z) = K(x,(z / y) \ 1). K(x,(y / z) \ 1) = K(x,z / y). K(x,(y * z) / (u * z)) = K(x,R(u / y,y,z) \ 1). K(x,R(y / z,z,u) \ 1) = K(x,(z * u) / (y * u)). R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1). 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). K(x,R(y / z,z,u) \ 1) != w | K(x,(z * u) / (y * u)) = w. 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) = K(x,(z * u) / ((y \ z) * u)). K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z). K(x,R(y,y \ z,u)) = R(K(x,y),z,u). 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)). R(K(x \ 1,x),y,z) != u | K(x \ 1,x) = u. K(x \ 1,x) = K(x \ 1,R(x,y,z)). K(x \ 1,R(x,y,z)) = K(x \ 1,x). (x * K(y \ 1,y)) * z = K(y \ 1,R(y,u,w)) * (x * z). K(x \ 1,R(x,y,z)) * (u * w) = (u * K(x \ 1,x)) * w. x * (y * z) != (y * K(u \ 1,u)) * z | (R(u,y,z) \ 1) * R(u,y,z) = x. (R(x,y,z) \ 1) * R(x,y,z) = K(x \ 1,R(x,u,w)). K(x \ 1,R(x,y,z)) = (R(x,u,w) \ 1) * R(x,u,w). K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,R(x,u,w)). x != K(y \ 1,R(y,z,u)) | K(y \ 1,y) = x. K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x). T(x / (x / y),z) = x / (x / T(y,z)). T(c1 / (c1 / c2),c3) != c1 / (c1 / T(c2,c3)). c1 / (c1 / T(c2,c3)) != T(c1 / (c1 / c2),c3). L(x,y / x,z) = (z * (y / x)) \ (z * y). x \ ((x * y) * L(z,y,x)) = y * z. 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 != z * (u * (u \ w)) | (z * w) / y = x. (x * y) / L(z \ y,z,x) = x * z. (x * (y * T(z,u))) / T(L(z,y,x),u) = x * y. x * (y * (y \ (x \ z))) != u * w | u \ z = w. 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). (x \ y) * T(x,y) = L(x,x \ y,x) * (x \ y). L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). 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). x \ (x / y) != z | L(y \ 1,y,x / y) = z. K(x \ (x / L(y \ 1,y,x)),z) = K(y,z). 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)). R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u). T(x,y) != R(z,y,x) | T(x,y * x) = z. R(x,y,z) != T(z,y) | T(z,y * z) = x. x * T(y,x / y) = (y * (x / y)) * y. (x * (y / x)) * x = y * T(x,y / x). x / (y * z) != u | R((x / z) / y,y,z) = u. x * y != z * L(u \ 1,u,w) | (z * ((w * u) \ w)) / y = x. (x * ((y * z) \ y)) / x = L((x * (z \ 1)) / x,z,y). L((x * (y \ 1)) / x,y,z) = (x * ((z * y) \ z)) / x. 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)). (x * K(x,y)) / x = L(T(x,y) / x,x,y). L(T(x,y) / x,x,y) = (x * K(x,y)) / x. L((x * (y \ z)) / x,y,u) = (x * ((u * y) \ (u * z))) / x. (x * T(y,z)) / x != u | T((x * y) / x,z) = u. T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y)). L(T(R(x,y,z),u),u,x) = R(T(x,x * u),y,z). x * R(T(y,y * x),z,u) = L(R(y,z,u),x,y) * x. T(x * y,z) = z \ ((x * y) * z). x \ ((y * z) * x) = T(y * z,x). L(x \ 1,x,T(x,y) / x) = T(1 / x,T(x,y)). K(x \ y,x) = (y \ x) * T((y \ x) \ 1,x). (x \ y) * T((x \ y) \ 1,y) = K(y \ x,y). x * y != (z * u) \ ((z \ (z * u)) * z) | x \ K(u,z) = y. ((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(x \ (x / L(y \ 1,y,x)),z) != u | K(y,z) = u. K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y). (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = ((x * y) \ x) * T(((x * y) \ x) \ 1,x). T(T(x * y,x) / y,y) = R(x,y,T(x,y)). x * R(y,x,T(y,x)) = T(y * x,y). x != T(y * z,u) | u \ ((y * z) * u) = x. x \ ((x * y) * x) = y * R(x,y,T(x,y)). x \ ((x * y) * x) != y * z | R(x,y,T(x,y)) = z. ((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) / 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 * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z)). x \ y = T(x,z) * (x \ (T(x,z) \ y)). T(x,y) * (x \ (T(x,y) \ z)) = x \ z. T(x,y) \ (x \ z) = x \ (T(x,y) \ z). x * (T(x,y) \ (x \ z)) != u | u = T(x,y) \ z. x * (T(x,y) \ (x \ z)) != u | T(x,y) \ z = u. 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 * y != (z \ u) * T((z \ u) \ u,w) | x \ (T(z,w) * (z \ u)) = y. x \ (T(y,z) * (y \ x)) = K(z \ (z / (x \ (y \ x))),z). K(x \ (x / (y \ (z \ y))),x) = y \ (T(z,x) * (z \ y)). (x * y) * ((z * ((x * y) \ (x * u))) / z) != w | x * (y * ((z * (y \ u)) / z)) = w. x != ((y / z) * z) * u | y * u = x. x * T(y,z) = ((x / y) * T(y,z)) * y. ((x / y) * T(y,z)) * y = x * T(y,z). (x * T(y,z)) \ ((x * y) * T(y,z)) = y. 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 * (x * y)) / (y * x) = T(x,x / (x / T(y,x))). T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x). T(x,x / (x / T(y,x))) != z | (x / T(y,x)) * y = z. (x / T(y,x)) * y = (x * (x * y)) / (y * x). (x * (x * y)) / (y * x) = (x / T(y,x)) * y. R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y. (x * y) * R((x * y) \ (x * z),u,w) != v5 | x * (y * R(y \ z,u,w)) = v5. x * T(x \ (y * z),u) = (T(y / (x / z),u) * (x / z)) * z. (T(x / (y / z),u) * (y / z)) * z = y * T(y \ (x * z),u). 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). 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,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). R(T(x,x / (1 / y)),y,x) = (x / T(y,x)) * y. (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y. ((x * y) / x) / (x \ y) = T(x,x / (x / y)). ((x * y) / x) / (x \ y) != z | T(x,x / (1 / (x \ y))) = z. T(x,x / (1 / (x \ y))) = T(x,x / (x / y)). T(x,x / (1 / y)) = T(x,x / (x / (x * y))). T(x,x / (x / (x * y))) = T(x,x / (1 / y)). ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u). (x * y) * T((x * y) \ z,u) != w | x * (y * T(y \ (x \ z),u)) = w. x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y. x * y != (z * u) * T((z * u) \ w,v5) | (z * (u * T(u \ (z \ w),v5))) / y = x. (x * (y * T(y \ (x \ (z * u)),w))) / u = ((x * y) / u) * T(((x * y) / u) \ z,w). x * ((y \ (x \ (z * y))) * y) = (x * T(x \ z,y)) * y. (x * y) * ((z \ L(y \ z,y,x)) * z) = ((x * y) * T((x * y) \ x,z)) * z. ((x * y) * T((x * y) \ x,z)) * z = (x * y) * ((z \ L(y \ z,y,x)) * z). T(x,R(y,y \ 1,x)) / x = y \ ((x * y) / x). L(x \ 1,x,y \ ((x * y) / x)) = T(1 / x,T(x,R(y,y \ 1,x))). T(1 / x,T(x,R(y,y \ 1,x))) = L(x \ 1,x,y \ ((x * y) / x)). (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)). 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). (x * (y * T(y \ 1,z))) * z = (x * y) * ((z \ L(y \ z,y,x)) * z). (x * y) * ((z \ L(y \ z,y,x)) * z) = (x * (y * T(y \ 1,z))) * z. 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). L((x * y) \ x,y,(x * y) \ x) = 1 / (1 / ((x * y) \ x)). L((x * y) \ x,y,(z * y) \ z) != u | L(1 / y,y,x) = u. L(1 / x,x,y) = 1 / (1 / ((y * x) \ y)). L(x,x \ 1,y) = 1 / (1 / ((y * (x \ 1)) \ y)). K(x \ (x / T(y \ x,z)),x) != u | T(K(x \ y,x),z) = u. T(K(x \ y,x),x \ y) = T(K(x \ y,x),(y \ x) \ 1). 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). 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 \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y). (x / y) * K(y,y \ 1) != z | x * (1 / (1 / (x \ (x / y)))) = z. x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y)). T(x,R(1 / y,y,x)) != z | (y * ((x * (y \ 1)) / x)) * x = z. (x * ((y * (x \ 1)) / y)) * y = T(y,R(x \ 1,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 / L(y,y \ 1,x) = x * (1 / (1 / (y \ 1))). x / L(y,y \ 1,x) = x * (1 / y). K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z). (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. T(x,R((y \ x) \ 1,((y \ x) \ 1) \ 1,x)) = K(x,y / x) * x. (x * (y * T(y \ T(z,x),u))) / x = ((x * y) / x) * T(((x * y) / x) \ z,u). ((x * y) / x) * T(((x * y) / x) \ z,u) = (x * (y * T(y \ T(z,x),u))) / x. x != T(R(y,z,u),w) * (z * u) | (T(y,w) * z) * u = x. (T(x,y) * z) * K(z,x) = (z * K(z,x)) * T((z * K(z,x)) \ (z * x),y). (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 != K(y \ (y / L(z,z \ 1,y)),u) | K(1 / z,u) = x. 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). L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y). L(T(x,y) / x,x,y) = K(1 / (1 / x),y). L(T(x,y) / x,x,y) != z | (x * K(x,y)) / x = z. (x * K(x,y)) / x = K(1 / (1 / x),y). K(1 / (1 / x),y) = (x * K(x,y)) / x. T(K(1 / (1 / x),y),x) = K(x,y). x != ((y * z) \ y) * T(((y * z) \ y) \ 1,y) | K(z,y) = x. K(x,y) = (((y * x) \ y) \ K(x,y)) / (((y * x) \ y) \ 1). (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = K(y,x). T(K(x,y),((y * x) \ y) \ 1) = (((y * x) \ y) \ 1) \ (((y * x) \ y) \ K(x,y)). (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = T(K(y,x),((x * y) \ x) \ 1). x != T(K(y,z),((z * y) \ z) \ 1) | T(K(y,z),y) = x. T(K(x,y),x) = (((y * x) \ y) \ 1) \ (((y * x) \ y) \ K(x,y)). (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = T(K(y,x),y). x != R(R(y,z,u),w,v5) * (z * u) | (R(y,w,v5) * z) * u = x. (R(x,y,z) * u) * K(u,x) = (u * K(u,x)) * R((u * K(u,x)) \ (u * x),y,z). (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(y,x) = K(y,x) * x. K(x,y) * y = y * K(x,y). (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 * K(y,z)) * z != u * (z * K(y,z)) | R(x,K(y,z),z) = u. ((x * K(y,z)) * z) / (z * K(y,z)) != u | R(x,K(y,z),z) = u. R(x,y \ T(y,z),y) * T(y,z) = (x * (y \ T(y,z))) * y. T(1 / x,T(x,R(y,y \ 1,x))) != z | L(x \ 1,x,y \ ((x * y) / x)) = z. L(x \ 1,x,y \ ((x * y) / x)) = x \ 1. L(x \ 1,x,T(y,x) \ y) = x \ 1. 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). (x * T(x \ 1,y)) \ 1 = T(x \ 1,y) \ (x \ 1). L(x * T(x \ 1,y),x \ 1,y) != z | K(1 / x,y) = z. K(1 / x,y) = K(x \ 1,y). x != K((y / z) \ y,u) | K(z,u) = x. K(x,y) = K(1 / (1 / x),y). K(1 / (1 / x),y) = K(x,y). K(x,y) = K((x \ 1) \ 1,y). K((x \ 1) \ 1,y) = K(x,y). T(K(x,y),x) = K(x,y). T(K(x,y),x) != z | (((y * x) \ y) \ 1) \ (((y * x) \ y) \ K(x,y)) = z. (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K(y,x). T(x,K(x,y)) = x. K(x,y) * x != z | x * K(x,y) = z. T(x,R((y \ x) \ 1,((y \ x) \ 1) \ 1,x)) != z | x * K(x,y / x) = z. x * y != (z * x) * K(x,z) | z = y. x = (K(y,x) \ x) * K(y,x). (K(x,y) \ y) * K(x,y) = y. x / K(y,x) = K(y,x) \ x. K(x,y) \ 1 = T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1). T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1. (x \ (y * T(y \ x,z))) \ 1 = T((x \ y) \ 1,z) \ ((x \ y) \ 1). T((x \ y) \ 1,z) \ ((x \ y) \ 1) = (x \ (y * T(y \ x,z))) \ 1. x / (y \ T(y,x)) = x * (T(y,x) \ y). x / ((((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x))) = x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)). L(x \ 1,x,K(y,x) \ 1) = x \ 1. T(x,K(y,x) \ 1) = x. (K(x,y) \ 1) * y = y * (K(x,y) \ 1). L(x \ 1,x,K(y,x) \ 1) = (x * (K(y,x) \ 1)) \ (K(y,x) \ 1). (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = L(x \ 1,x,K(y,x) \ 1). x != L(y \ 1,y,K(z,y) \ 1) | y \ 1 = x. x \ 1 = (x * (K(y,x) \ 1)) \ (K(y,x) \ 1). (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = x \ 1. 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 * (((x * y) \ (x * T(x \ (x * y),x))) \ 1) = x / K(y,x). x * (((x * y) \ (x * T(y,x))) \ 1) = x / K(y,x). x * (((x * y) \ (y * x)) \ 1) = x / K(y,x). x * (K(y,x) \ 1) = x / K(y,x). x != y / K(z,y) | K(z,y) \ y = x. K(x,y) \ y = y * (K(x,y) \ 1). x * (K(y,x) \ 1) = K(y,x) \ x. 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. (K(x,y) \ y) \ (K(x,y) \ 1) = y \ 1. (K(x,y) \ 1) * T(y,z) = K(x,y) \ T(y,z). (K(x,y) \ y) * (y \ 1) = K(x,y) \ 1. (K(x,y) \ 1) * ((y \ 1) \ 1) = R(K(x,y) \ y,y \ 1,y). R(K(x,y) \ y,y \ 1,y) = (K(x,y) \ 1) * ((y \ 1) \ 1). (K(x,y) \ 1) * ((y \ z) \ z) = K(x,y) \ T(y,y \ z). K(x,y) \ T(y,y \ z) = (K(x,y) \ 1) * ((y \ z) \ z). x \ T(y,y \ z) != u | x \ ((y \ z) \ z) = u. K(x,y) \ ((y \ z) \ z) = (K(x,y) \ 1) * ((y \ z) \ z). (K(x,y) \ 1) * ((y \ z) \ z) = K(x,y) \ ((y \ z) \ z). x != (K(y,z) \ 1) * ((z \ u) \ u) | K(y,z) \ ((z \ u) \ u) = x. K(x,y) \ ((y \ 1) \ 1) = R(K(x,y) \ y,y \ 1,y). R(K(x,y) \ y,y \ 1,y) = K(x,y) \ ((y \ 1) \ 1). 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)) | K(u,(y \ z) \ z) = x. K(x,(y \ 1) \ 1) = K(x,y). (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 != (z * (u \ T(u,z))) * u | (u * z) / y = x. (x * y) / T(x,y) = R(y,x \ T(x,y),x). R(x,y \ T(y,x),y) = (y * x) / T(y,x). T(x,(y \ x) \ 1) != z | x * K(x,y / x) = z. (x \ (y * (T(z,x) \ z))) * x = (((z * x) / z) * T(((z * x) / z) \ y,x)) * (((z * x) / z) \ x). (((x * y) / x) * T(((x * y) / x) \ z,y)) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y. T(x,x / (x / (x * y))) != z | T(x,x / (1 / y)) = z. T(x,x / (1 / y)) = T(x,x * y). (x / T(y,x)) * y = T(x,T(y,x)). R(T(x,x * y),y,x) = (x / T(y,x)) * y. x != (y * z) / T(y,z) | z = x. x = R(x,y \ T(y,x),y). R(x,y \ T(y,x),y) = x. R(T(x,y),z \ T(z,x),z) = T(x,y). T(x,y) * T(z,x) = (T(x,y) * (z \ T(z,x))) * z. (T(x,y) * (z \ T(z,x))) * z = T(x,y) * T(z,x). x != (y / T(z,y)) * z | T(y,T(z,y)) = x. T(x,T(y,x)) = R(T(x,x * y),y,x). R(T(x,x * y),y,x) = T(x,T(y,x)). x * T(y,T(x,y)) = L(R(y,x,y),x,y) * x. L(R(x,y,x),y,x) * y = y * T(x,T(y,x)). L(x,y,z) * ((u * (L(x,y,z) \ 1)) / u) != w | L(x * ((u * (x \ 1)) / u),y,z) = w. L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1). x * T(y,T(x,y)) != z * x | L(R(y,x,y),x,y) = z. L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1). ((x * (y * T(y \ T(z,x),y))) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y. ((x * ((y \ T(z,x)) * y)) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y. ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y. x != y * T(y \ 1,z) | K(z \ (z / y),z) = x. K(x \ (x / y),x) = T(x,y \ 1) \ x. T(T(x,y \ 1) \ x,z) = K(x \ (x / T(y,z)),x). x * ((y \ (x \ y)) * y) = y * (T(y,x \ 1) \ y). x * (T(x,y \ 1) \ x) = y * ((x \ (y \ x)) * x). K(x \ (x / y),x) \ x = T(x,y \ 1). T(x,y) * (y \ T(y,x)) = x. x \ y != z \ T(z,y) | y * (T(z,y) \ z) = x. x * (T(y,x) \ y) = T(x,y). x * (T(x,y) \ x) = (y * x) / y. (x * y) / x = y * (T(y,x) \ y). T(x,T(y,x)) != z | R(T(x,x * y),y,x) = z. R(T(x,x * y),y,x) = T(x,y). x * T(y,T(x,y)) = y * x. T(x,x \ y) = T(x,y / x). T(x,y / x) = T(x,x \ y). x * y = T(x,y) * T(y,x). T(x,y) * T(y,x) = x * y. L(R(x,y,x),y,x) = x. x \ ((x * y) * x) = y * R(x,y,x). x * (y * x) = (L(x,y,x) * y) * x. (L(x,y,x) * y) * x = x * (y * x). (x \ y) \ y = T(x,y / x). T(x,y / x) = (x \ y) \ y. R(x,T(y,z),T(z,y)) * (y * z) = (x * T(y,z)) * T(z,y). (x * (y / x)) * x = y * ((x \ y) \ y). T(x,y * x) = T(x,x * y). R(T(x,T(x * y,x)),y,x) = T(x,y). T(x,(x \ y) * x) = T(x,y). R(T(x,y),x \ y,x) = (x \ y) \ y. R(x,y,T(x,y)) = R(x,y,x). T(x * y,x) = y * R(x,y,x). x * R(y,x,y) = T(y * x,y). R(x,T(y,x),T(x,y)) = R(x,T(y,x),x). (x * y) \ (x * T(z * y,z)) != u | L(R(z,y,z),y,x) = u. T(L(x,y,x) * y,x) = y * x. T(x,y * x) = T(x,L(x,y,x) * y). T(x,L(x,y,x) * y) = T(x,y * x). 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). x * ((y \ x) \ x) = R(y,y \ x,y) * x. R(x,x \ y,x) * y = y * ((x \ y) \ y). T(x,(x \ y) * T(x,y)) = T(x,(x \ y) * x). K(x \ y,x) \ x = T(x,(y \ x) \ 1). T(x,(y \ x) \ 1) = K(x \ y,x) \ x. x * K(x,y / x) = K(x \ y,x) \ x. K(x \ y,x) \ x = x * K(x,y / x). 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). x != y * ((z \ y) \ y) | (z * (y / z)) * z = x. (x * (y / x)) * x = R(x,x \ y,x) * y. R(x,x \ y,x) * y = (x * (y / x)) * x. x * y != (z * (y / u)) * u | R(z,y / u,u) = x. R(x,y / x,x) = R(x,x \ y,x). R(x,(x * y) / x,x) = R(x,y,x). R(x,y,x) = R(x,T(y,x),x). R(x,T(y,x),x) = R(x,y,x). R(x,T(y,x),x) != z | R(x,T(y,x),T(x,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). x != T(y,(y \ z) * y) | T(y,z) = x. T(x,y) = T(x,(x \ y) * T(x,y)). T(x,(x \ y) * T(x,y)) = T(x,y). R(T(x,y),x \ y,T(x,y)) = T(x,x \ y). 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 * (T(z,u) \ x) | T(T(z,u) \ z,x) = y. T(T(x,y) \ x,z) = z \ (x * (T(x,y) \ z)). x \ (y * (T(y,z) \ x)) = T(T(y,z) \ y,x). T(x,y) * (x \ z) = y * (T(y,x) \ z). K(x \ (x / (y \ (z \ y))),x) = y \ (x * (T(x,z) \ y)). x != y \ (z * (T(z,u) \ y)) | T(T(z,u) \ z,y) = x. T(T(x,y) \ x,z) = K(x \ (x / (z \ (y \ z))),x). K(x \ (x / (y \ (z \ y))),x) = T(T(x,z) \ x,y). K(x \ (x / y),x) != z | T(x,y \ 1) \ x = z. T(x,(y \ (z \ y)) \ 1) \ x = T(T(x,z) \ x,y). (R(x,y,z) * u) * x = (R(x,y,z) * T(u,x)) * T(x,u). (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. x * y != T(z * u,z) * T(z,u) | x \ (R(z,u,z) * T(z * u,z)) = y. (R(x,y,x) * y) \ (R(x,y,x) * T(x * y,x)) = x. L(R(x,y,x),y,R(x,y,x)) = x. ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y. (x * y) * ((z \ L(u,y,x)) * z) = x * (y * ((z \ u) * z)). (x * y) * ((z \ L(y \ z,y,x)) * z) != u | (x * (y * T(y \ 1,z))) * z = u. (x * (y * T(y \ 1,z))) * z = x * (y * ((z \ (y \ z)) * z)). x != T(y,(z \ (u \ z)) \ 1) \ y | T(T(y,u) \ y,z) = x. T(T(x,y) \ x,z) = K((z \ (y \ z)) \ 1,x). x != T(y,z \ 1) \ y | z * T(z \ 1,y) = x. x * T(x \ 1,y) = K(x \ 1,y). x != T(y,T(z,y)) \ y | z \ T(z,y) = x. x \ T(x,y) = K(T(x,y),y). K(T(x,y),y) = x \ T(x,y). x / K(y,x) = T(x,y). T(x,y) = x / K(y,x). K(x,y) * T(y,x) = y. x * K(x,y) = T(x,y). T(x,y) = x * K(x,y). (x * y) / x = y * K(x,y). 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). x * K(y \ 1,x) = y * ((x \ (y \ x)) * x). x * ((y \ (x \ y)) * y) = y * K(x \ 1,y). K(x,y) * z = y * (T(y,x) \ z). x * (T(x,y) \ z) = K(y,x) * z. x != y \ T(y,L(z,u,w) \ 1) | L(y \ T(y,z \ 1),u,w) = x. L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1). x != y \ T(y,T(z,u) \ 1) | T(y \ T(y,z \ 1),u) = x. T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1). T(x,y) \ x != z | z = K(y,x). T(x,y) \ x != z | K(y,x) = z. (x * y) / T(L(y,K(z,y),x),z) = x * K(z,y). (x * y) * L(K(y,z),y,x) = x * T(y,z). x * L(K(y,z),y,x / y) = (x / y) * T(y,z). K(x,y) = K(T(x,y),y). K(T(x,y),y) = K(x,y). K(x,y) \ 1 = K(y,x). 1 / K(x,y) = K(y,x). K(x,y) != z \ 1 | K(y,x) = z. (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y. K(x \ (x / y),x) != z | K(y \ 1,x) = z. L(K(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y). K(x \ (x / L(y,z,u)),x) = L(K(y \ 1,x),z,u). (x * K(y \ 1,z)) * z = x * (y * ((z \ (y \ z)) * z)). x * (y * ((z \ (y \ z)) * z)) = (x * K(y \ 1,z)) * z. T(x,y) \ z = K(y,x) * (x \ z). K(x,y) * (y \ z) = T(y,x) \ z. K(x,y / z) * z = T(y / z,x) \ y. T(x / y,z) \ x = K(z,x / y) * y. x * T(K(y,z / x),x) = T(z / x,y) \ z. T(x / y,z) \ x = y * T(K(z,x / y),y). T(K(x,y),z) = K((z \ (x \ z)) \ 1,y). K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). K((x \ y) \ 1,z) = T(K(x / y,z),x). T(K(x / y,z),x) = K((x \ y) \ 1,z). T(K(x / y,z),x) \ 1 = K(z,(x \ y) \ 1). K(T(x,y) \ 1,z) = T(K(x \ 1,z),y). K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). T(K(x,y),z) \ 1 = K(y,T(x \ 1,z) \ 1). K(x,T(y \ 1,z) \ 1) = T(K(y,x),z) \ 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). K(x,T(y \ 1,z) \ 1) = T(K(x,y),z). K(x,T(y \ 1,z) \ 1) != u | T(K(x,y),z) = u. T(K(x,y),z) = T(K(y,x),z) \ 1. T(K(x,y),z) \ 1 = T(K(y,x),z). 1 / T(K(x,y),z) = T(K(y,x),z). T(K(x,y),z) \ 1 != u | u = T(K(y,x),z). T(K(x,y),z) \ 1 != u | T(K(y,x),z) = u. K(x,(y \ z) \ 1) != u | T(K(x,y / z),y) = u. L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1). 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). 1 / L(K(x,y),z,u) = K(L(y \ 1,z,u) \ 1,x). K(L(x \ 1,y,z) \ 1,u) = 1 / L(K(u,x),y,z). L(K(x,y \ (y / z)),y \ (y / z),y) = K(x,z \ 1). (x * y) / (y * K(z,y)) = (x / (y * K(z,y))) * y. 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). K(L(x \ 1,y,z) \ 1,u) != w | L(K(x,u),y,z) = 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 = L(K(y,x),z,u). 1 / L(K(x,y),z,u) != w | w = L(K(y,x),z,u). 1 / L(K(x,y),z,u) != w | L(K(y,x),z,u) = w. R(x,K(y,z),z) = ((x * K(y,z)) / (z * K(y,z))) * z. ((x * K(y,z)) / (z * K(y,z))) * z = R(x,K(y,z),z). R(x,y,K(z,y)) * y = R(x * y,K(z,y),y). R(x * y,K(z,y),y) = R(x,y,K(z,y)) * y. R(x * y,K(z,y),y) != u * y | R(x,y,K(z,y)) = u. x * (y * K(z \ 1,y)) = (x * K(z \ 1,y)) * y. (x * K(y \ 1,z)) * z = x * (z * K(y \ 1,z)). R(x,K(y \ 1,z),z) = x. R(x,K(y,z),z) = x. R(x,y,K(z,y)) = x. x * (K(y,z) * z) = (x * K(y,z)) * z. (x * K(y,z)) * z = x * (K(y,z) * z). x * (y * K(z,y)) = (x * y) * K(z,y). (x * y) * K(z,y) = x * (y * K(z,y)). L(x,K(y,x),z) = x. (x * y) / T(y,z) = x * K(z,y). x / T(y \ x,z) = y * K(z,y \ x). L(K(x,y),y,z) = K(x,y). L(K(x,y \ (y / z)),y \ (y / z),y) != u | K(x,z \ 1) = u. K(x,y \ 1) = K(x,z \ (z / y)). K(x,y \ (y / z)) = K(x,z \ 1). L(K(x,y \ z),y \ z,y) != u | K(x,(z \ y) \ 1) = u. K(x,(y \ z) \ 1) = K(x,z \ y). 1 / L(K(x,y),y,z) = K(y,x). L(K(x,y),x,z) = K(x,y). (x * y) * K(y,z) = x * T(y,z). x * K(y,z) = (x / y) * T(y,z). (x / y) * T(y,z) = x * K(y,z). K(x,(y * z) \ (y * u)) = K(x,L(u \ z,u,y) \ 1). K(x,L(y \ z,y,u) \ 1) = K(x,(u * z) \ (u * y)). T(K(x,y / z),y) = K(x,z \ y). L(K(x,y \ z),u,w) = K(x,L(z \ y,u,w) \ 1). K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w). (x * K(y,z)) * y = x * T(y,z). T(K(x,y),z) = K(x,(y \ z) \ z). K(x,(y \ z) \ z) = T(K(x,y),z). x != y * T(z,u) | (y * z) * K(z,u) = x. (x * y) * K(y,z) = (x * K(y,z)) * y. (x * K(y,z)) * y = (x * y) * K(y,z). K(x,T(y,y \ z)) = T(K(x,y),z). K(x,L(y \ z,u,w) \ 1) != v5 | L(K(x,z \ y),u,w) = v5. L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z)). L(K(x,y),z,u) = K(x,(u * (z / y)) \ (u * z)). K(x,(y * (z / u)) \ (y * z)) = L(K(x,u),z,y). K(x,L(y,z / y,u)) = L(K(x,y),z,u). x != L(K(y,z),u,w) | L(K(z,y),u,w) \ 1 = x. 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(L(x,y / x,z),u) = L(K(x,u),y,z). 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). ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * (T(z,x) \ z))) * x. (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z). (x \ (y * K(x,z))) * x = ((x \ y) * x) * (T(z,x) \ z). ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x. ((x \ y) * x) * K(x,z) = (x \ (y * K(x,z))) * x. (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z). x * y != (z * y) * K(y,u) | z * K(y,u) = x. (x \ y) * K(x,z) = x \ (y * K(x,z)). x \ (y * K(x,z)) = (x \ y) * K(x,z). x * ((x \ y) * K(x,z)) = y * K(x,z). x * (y * K(x,z)) = (x * y) * K(x,z). (x * y) * K(x,z) = x * (y * K(x,z)). L(K(x,y),z,x) = K(x,y). L(K(x,y),z * x,u) != w | K(L(x,z,u),y) = w. K(L(x,y,x),z) = K(x,z). K(x,y) = K(R(x,z,x),y). K(R(x,y,x),z) = K(x,z). 1 / K(x,y) = K(y,R(x,z,x)). K(x,R(y,z,y)) = 1 / K(y,x). x != 1 / K(y,z) | K(z,y) = x. K(x,y) = K(x,R(y,z,y)). K(x,R(y,z,y)) = K(x,y). K(x,T(y,y \ z)) = K(x,T(y,z)). K(x,T(y,y \ z)) != u | T(K(x,y),z) = u. T(K(x,y),z) = K(x,T(y,z)). K(x,T(y,z)) = T(K(x,y),z). K(x,y \ z) = T(K(x,z / y),y). T(K(x,y / z),z) = K(x,z \ y). T(x / y,z) \ x = y * K(z,y \ x). x != y * K(z,y \ u) | u / T(y \ u,z) = x. x / T(y \ x,z) = T(x / y,z) \ x. x / T(y,z) = T(x / (x / y),z) \ x. T(x / (x / y),z) \ x = x / T(y,z). x / (x / T(y,z)) = T(x / (x / y),z). L(x / (x / y),z,u) = x / (x / L(y,z,u)). L(c4 / (c4 / c5),c6,c7) != c4 / (c4 / L(c5,c6,c7)). 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). L(x,1,y) = (y * 1) \ (y * x). (x * 1) \ (x * y) = L(y,1,x). L(x,y \ z,y) = z \ (y * ((y \ z) * x)). x \ (y * ((y \ x) * z)) = L(z,y \ x,y). ((1 / x) * x) * y != z | y = z. K(T(x,y),y) = (x * y) \ (T(x,y) * y). (x * y) \ (T(x,y) * y) = K(T(x,y),y). 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). (x * y) \ (y * x) != z | z = K(y,x). (x * y) / y != z * u | x / u = z. ((x / y) \ x) * z != u | y \ u = z. x \ (x * y) = L(y,1,x). L(x,1,y) != z | z = x. x * (y * (y \ 1)) != z * u | z \ x = u. x * y != ((z * u) * w) / (u * w) | x \ R(z,u,w) = y. (x * y) \ R(x,y,y \ 1) = y \ 1. (x \ y) * x != y * z | K(x \ y,x) = z. (1 / x) * (x * y) != z | L(y,x,1 / x) = z. (x * y) * L(K(z \ y,z),y,x) = x * ((z \ y) * z). x != y \ (z * (y / z)) | K(z,y / z) = x. K(x,(x * y) / x) = L(y \ ((x * y) / x),y,x). L(x \ ((y * x) / y),x,y) = K(y,(y * x) / y). 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). (x * (y * z)) / L(K(y,z),z * y,x) = x * (z * y). (((x * y) / z) * z) / y != u * w | x / w = u. (x \ 1) * y != z \ y | R(x,x \ 1,y) = z. x \ y != (z \ 1) * y | R(z,z \ 1,y) = x. L(x * y,z,u) = L(L((x \ 1) \ y,z,u),x \ 1,x). L(L((x \ 1) \ y,z,u),x \ 1,x) = L(x * y,z,u). ((x \ y) * T(x,y)) / (x \ y) = L(x,x \ y,x). x * L(x \ (y * x),z,u) = L(y,z,u) * x. T(x,x \ y) \ (((x \ y) \ y) * z) = z. T(x,x \ y) * z != u | u = ((x \ y) \ y) * z. T(x,x \ y) * z != u | ((x \ y) \ y) * z = u. x \ (y * ((z \ (y \ x)) * z)) = L(K(z \ (y \ x),z),y \ x,y). L(K(x \ (y \ z),x),y \ z,y) = z \ (y * ((x \ (y \ z)) * x)). x != L(T(y,z),u,w) | T(L(y,u,w),z) = x. T(L(x,y,z),y) = (z * y) \ (z * (x * y)). (x * y) \ (x * (z * y)) = T(L(z,y,x),y). L(x \ T(x,y),x,y) != z | K(x,y) = z. T(x * T(T(y,x),y * x),T(y,x)) = y * x. (x * 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 * x) * T(L(x \ 1,x,y),y). ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y). (x * ((y * x) \ z)) / x = L((y \ z) / x,x,y). L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z. (1 / x) \ T(y,x) = (x \ ((1 / x) \ y)) * x. (x \ ((1 / x) \ y)) * x = (1 / x) \ T(y,x). T(T(x,x * y) * y,T(x,y)) = x * y. x = T(T(x / y,(x / y) * y) * y,T(x / y,y)). T(T(x / y,(x / y) * y) * y,T(x / y,y)) = x. x * y != (z \ ((1 / z) \ u)) * z | x \ ((1 / z) \ T(u,z)) = y. ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((1 / x) \ y),x). ((x \ T(x,y)) * x) / (x \ T(x,y)) = L(x,x \ T(x,y),x). L((x \ (T(x,y) * y)) / y,y,x) = (y * K(T(x,y),y)) / y. x * y != (z \ 1) * T((z \ 1) \ 1,u) | (z \ T(z,u)) / y = x. (x \ T(x,y)) / (x \ 1) = T(x,y). T(x,y) * (x \ 1) != z | z = x \ T(x,y). T(x,y) * (x \ 1) != z | x \ T(x,y) = z. (x \ 1) * T((x \ 1) \ 1,y) != z | x \ T(x,y) = z. K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y. (T(x,1 / y) / y) \ (x / y) = K(1 / y,(1 / y) \ (x / y)). K(1 / x,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x). T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y. (x * (y \ x)) / x = y \ T(x,x / y). x \ T(y,y / x) = (y * (x \ y)) / 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. L(K(x \ 1,y),x \ 1,x) = L(x * T(x \ 1,y),x \ 1,y). L(x * T(x \ 1,y),x \ 1,y) = L(K(x \ 1,y),x \ 1,x). x * (y * ((x \ y) / y)) = T(y,y / (x * y)). x \ (T(x,y) \ x) != z | z = T(x,y) \ 1. x \ (T(x,y) \ x) != z | T(x,y) \ 1 = z. ((x \ (y / z)) * x) * z != u | (x * z) * T((x * z) \ y,x) = u. T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) != z | (((x * y) / x) \ y) \ y = z. (x \ 1) * T((x \ 1) \ (x \ y),z) != u | x \ T(y,z) = u. x \ T(y,z) = (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z). (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). 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). K(1 / x,x) * (1 / x) = x \ 1. (x \ 1) * L(y,1 / x,K(1 / x,x)) = K(1 / x,x) * ((1 / x) * y). (x * y) / T(y,z) != u | u = (x / T(y,z)) * y. (x * y) / T(y,z) != u | (x / T(y,z)) * y = u. (x * T(y,z)) / y != u | u = (x / y) * T(y,z). (x * T(y,z)) / y != u | (x / y) * T(y,z) = u. T(x,y) / x != z | (1 / x) * T(x,y) = z. L((T(x,y) * (x \ y)) / y,y,x) = (y * K(T(x,y),y)) / y. x * y != z | (u / (x \ u)) * y = z. (x / ((y * z) \ x)) * T((y * z) \ u,w) = y * (z * T(z \ (y \ u),w)). L(x \ T(x,y),(x \ 1) \ 1,y) = L(K((x \ 1) \ 1,y),(x \ 1) \ 1,x \ 1). L(K((x \ 1) \ 1,y),(x \ 1) \ 1,x \ 1) = L(x \ T(x,y),(x \ 1) \ 1,y). T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y. T(x * y,z) = T(T(T(x,x * y) * y,z),R(x,y,y \ 1)). T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z). T(x,R(x / y,y,y \ 1)) = T((x / y) * y,T(x / y,y)). T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1)). T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1)). T(x,T(x / y,y)) = T(x,x * (y \ 1)). T(x,y \ x) = T(x,x * (y \ 1)). T(x,x * (y \ 1)) = T(x,y \ x). (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)). T((x \ 1) * y,x) = (x \ 1) * ((x \ y) * x). (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x). x * y != (z \ 1) * ((z \ u) * z) | x \ T((z \ 1) * u,z) = y. ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1). T(x,x / (x * y)) = (x * ((x / y) / x)) * y. (x * ((x / y) / x)) * y = T(x,x / (x * y)). L(x,1 / y,K(1 / y,y)) = x. (x \ 1) * y = K(1 / x,x) * ((1 / x) * y). K(1 / x,x) * ((1 / x) * y) = (x \ 1) * y. L(x,y,y \ 1) = (1 / y) * (y * x). (1 / x) * (x * y) = L(y,x,x \ 1). x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x. L(x,y,y \ 1) != z | L(x,y,1 / y) = z. L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y). K(1 / x,x) \ y = (1 / x) * ((x \ 1) \ y). (1 / x) * ((x \ 1) \ y) = K(1 / x,x) \ y. ((x \ 1) \ 1) * (x \ y) = (x * (1 / x)) * y. K(x,1 / x) * (x * y) = ((x \ 1) \ 1) * y. x * (K(x,1 / x) * y) = ((x \ 1) \ 1) * y. (K(x,1 / x) * y) \ (((x \ 1) \ 1) * y) = T(L(x,y,K(x,1 / x)),y). x != y | L(y,z,K(z,z \ 1)) = x. L(x \ y,z,K(z,z \ 1)) = K(x,x \ 1) * (((x \ 1) \ 1) \ y). (K(x,1 / x) * y) * z != ((x \ 1) \ 1) * y | T(x,K(x,1 / x) * y) = z. T(x,K(x,1 / x) * y) = (K(x,1 / x) * y) \ (((x \ 1) \ 1) * y). (K(x,1 / x) * y) \ (((x \ 1) \ 1) * y) = T(x,K(x,1 / x) * y). x * y != (z * (1 / z)) * ((1 / z) \ u) | x \ ((z \ 1) \ u) = y. ((x \ 1) \ 1) \ ((x \ 1) \ y) = x \ ((1 / x) \ y). (1 / x) * ((x \ 1) \ y) = K(x,1 / x) * y. (1 / x) * ((x \ 1) \ y) != z | K(1 / x,x) \ y = z. K(1 / x,x) \ y = K(x,1 / x) * y. x = K(y,1 / y) * (K(1 / y,y) * x). K(x,1 / x) * (K(1 / x,x) * y) = y. K(x,x \ 1) * (((x \ 1) \ 1) \ y) != z | z = x \ y. K(x,x \ 1) * (((x \ 1) \ 1) \ y) != z | x \ y = z. x * (y * T(y \ 1,x)) = (L(y \ 1,y,x) * x) / L(y \ 1,y,x). (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y)). (x * (y * T(y \ 1,x))) * (x \ 1) = x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x)). x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x)) = (x * (y * T(y \ 1,x))) * (x \ 1). (1 / x) * ((T(x,y) \ 1) * x) != z | T(x,y) \ 1 = z. x * K(y,y \ 1) != z | K(y,y \ 1) * x = z. x \ y = (((x \ 1) \ 1) \ y) * K(x,x \ 1). (((x \ 1) \ 1) \ y) * K(x,x \ 1) = x \ y. x * y != z * (((z \ (u \ z)) \ 1) \ 1) | (((u \ 1) \ 1) \ z) / y = x. (((x \ 1) \ 1) \ y) / y = (((x \ y) / y) \ 1) \ 1. ((x \ 1) \ y) / y = ((((1 / x) \ y) / y) \ 1) \ 1. ((((1 / x) \ y) / y) \ 1) \ 1 = ((x \ 1) \ y) / y. R(x \ 1,x,y) \ y = ((x \ 1) \ 1) * y. R(x,1 / x,y) \ y = (((1 / x) \ 1) \ 1) * y. R(x,1 / x,y) \ y = (x \ 1) * y. R(x,x \ 1,y) = R(x,1 / x,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). L(R(x,y,z),x \ 1,x) != u | R(1 / (1 / x),y,z) = u. R(1 / (1 / x),x \ 1,y) = R(1 / (1 / x),1 / x,y). R(1 / (1 / x),1 / x,y) = R(1 / (1 / x),x \ 1,y). R(1 / x,x,x \ y) != z | (x \ y) / y = z. ((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,y) \ 1 = (x \ 1) * (T(x,y) \ x). (x \ 1) * (T(x,y) \ x) = T(x,y) \ 1. x \ (T(1 / x,y) \ 1) = T(1 / x,y) \ (1 / x). T(1 / x,y) \ (1 / x) = x \ (T(1 / x,y) \ 1). (x * T(x \ 1,y)) \ 1 = T(1 / x,y) \ (1 / x). x != T(1 / y,z) \ (1 / y) | y \ (T(1 / y,z) \ 1) = x. x \ (T(1 / x,y) \ 1) = (x * T(x \ 1,y)) \ 1. (x * T(x \ 1,y)) \ 1 = x \ (T(1 / x,y) \ 1). L(x,(y \ 1) \ 1,y \ 1) != z | L(x,y,y \ 1) = z. L(K((x \ 1) \ 1,y),x,x \ 1) = L(x \ T(x,y),(x \ 1) \ 1,y). L(x \ T(x,y),(x \ 1) \ 1,y) != z | L(K((x \ 1) \ 1,y),x,1 / x) = z. (x * y) * K(y \ 1,y) = x * (1 / (1 / y)). x * y != (z * u) * K(u \ 1,u) | (z * (1 / (1 / u))) / y = x. (x * (1 / (1 / y))) / y = x * K(y \ 1,y). x / y = (x / (1 / (1 / y))) * K(y \ 1,y). (x / (1 / (1 / y))) * K(y \ 1,y) = x / y. (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y). x * (y / x) = (1 / (1 / x)) * (y / (1 / (1 / x))). (1 / (1 / x)) * (y / (1 / (1 / x))) = x * (y / x). ((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 != T((y \ 1) * z,y) | (y \ 1) * ((y \ z) * y) = x. (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,(x \ 1) \ 1). T((x \ 1) * y,(x \ 1) \ 1) = (x \ 1) * ((x \ y) * x). T(x,R(y \ 1,y,z)) = T(x,z / (y * z)). K(x,x \ 1) * (y * x) = y * T(x,x \ 1). x * ((y \ 1) \ 1) = K(y,y \ 1) * (x * y). K(x,x \ 1) * (y * x) = y * ((x \ 1) \ 1). (K(x,x \ 1) * y) * x = y * ((x \ 1) \ 1). (x \ y) * x = (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1). (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x. x != y * ((z \ 1) \ 1) | K(z,z \ 1) * (y * z) = x. K(x,x \ 1) * (y * x) = (K(x,x \ 1) * y) * x. (K(x,x \ 1) * y) * x = K(x,x \ 1) * (y * x). x != (y \ z) * y | z * K(y \ z,y) = x. x * K(y \ x,y) = (((y \ 1) \ 1) \ x) * ((y \ 1) \ 1). (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = y * K(x \ y,x). L(x,y,K(x,x \ 1)) = x. L(x,y,K(x,1 / x)) = x. (K(x,1 / x) * y) \ (((x \ 1) \ 1) * y) = T(x,y). T(x,y) = (K(x,1 / x) * y) \ (((x \ 1) \ 1) * y). x != (K(y,1 / y) * z) \ (((y \ 1) \ 1) * z) | T(y,K(y,1 / y) * z) = x. T(x,K(x,1 / x) * y) = T(x,y). T(x,y) = T(x,K(1 / x,x) * y). T(x,K(1 / x,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). 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). (x * ((y * (x \ 1)) / y)) * (x * z) != u | x * ((x * ((y * (x \ 1)) / y)) * z) = u. x * ((x * (((x * y) * (x \ 1)) / (x * y))) * y) = T(x * y,R(x \ 1,x,x * y)). K(((x \ 1) \ 1) \ y,(x \ 1) \ 1) = K(x \ y,x). 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))). x \ (x * (y * T(y \ 1,x))) = (x * (y * T(y \ 1,x))) * (x \ 1). (x * (y * T(y \ 1,x))) * (x \ 1) = x \ (x * (y * T(y \ 1,x))). x * T(x \ 1,y) = (y * (x * T(x \ 1,y))) * (y \ 1). (x * (y * T(y \ 1,x))) * (x \ 1) = y * T(y \ 1,x). (x * (y \ T(y,x))) * (x \ 1) = (y \ 1) * T((y \ 1) \ 1,x). (x \ 1) * T((x \ 1) \ 1,y) = (y * (x \ T(x,y))) * (y \ 1). x \ T(x,y) = (y * (x \ T(x,y))) * (y \ 1). (x * (y \ T(y,x))) * (x \ 1) = y \ T(y,x). L(x \ 1,x,y) * T(L(x \ 1,(x \ 1) \ 1,y) \ 1,z) = L((x \ 1) * T((x \ 1) \ 1,z),(x \ 1) \ 1,y). (x * K(y,x)) / x = K(y,x). (x * K(T(y,x),x)) / x != z | L((T(y,x) * (y \ x)) / x,x,y) = z. L((T(x,y) * (x \ y)) / y,y,x) = K(T(x,y),y). (1 / x) * T(x,y) = x \ T(x,y). T(x,K(y \ (y / (x \ 1)),y)) = x. T(x,y) / (x \ T(x,y)) = L(x,x \ T(x,y),x). L(x,x \ T(x,y),x) = T(x,y) / (x \ T(x,y)). (((x * y) / x) \ y) \ y = (x * y) / x. (((x * y) / x) \ y) * ((x * y) / x) = y. (((L(x,y,y \ 1) * y) / y) \ ((1 / y) * (x * y))) * ((y * ((1 / y) * (x * y))) / y) = (1 / y) * (x * y). x * y != T(z,z / (z * u)) | T(z,R(u \ 1,u,z)) / y = x. T(x,R(y \ 1,y,x)) / y = x * ((x / y) / x). x = L(x,x \ T(x,y),x). L(x,x \ T(x,y),x) = x. K(1 / x,(1 / x) \ (y / x)) != z | (T(y,1 / x) / x) \ (y / x) = z. (T(x,1 / y) / y) \ (x / y) = K(y \ 1,(1 / y) \ (x / y)). K(x \ 1,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x). (x * T(x \ 1,y)) \ 1 != z | x \ (T(1 / x,y) \ 1) = z. x \ (T(1 / x,y) \ 1) = T(x \ 1,y) \ (x \ 1). T(x \ 1,y) \ (x \ 1) = x \ (T(1 / x,y) \ 1). K(x \ 1,(1 / x) \ (y / x)) = (T(y,x \ 1) / x) \ (y / x). x * y != L(z,z \ T(z,u),z) | x \ z = y. (x \ T(x,y)) \ x = x * (T(x,y) \ 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. 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. ((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(x,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)) = R(x,y,1 / z). R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(z \ 1,(z \ 1) \ 1)) = R(x,y,1 / (z \ 1)). R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(z \ 1,z)) = R(x,y,1 / (z \ 1)). R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(z \ 1,z)) = R(x,y,z). (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. K(((x \ 1) \ 1) \ y,(x \ 1) \ 1) != z | K(x \ y,x) = z. K(x \ y,x) = K(((x \ 1) \ 1) \ y,x). K(((x \ 1) \ 1) \ y,x) = K(x \ y,x). K(x,((y \ 1) \ z) / z) = K(x,((1 / y) \ z) / z). K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z). K(x \ ((1 / x) \ y),x) = K(x \ ((x \ 1) \ y),x). K(x,((1 / y) \ x) / x) != z | ((1 / y) \ x) \ (x * R(1 / (1 / y),y \ 1,(1 / y) \ x)) = z. ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((x \ 1) \ y) / y). K(x \ ((1 / x) \ y),x) != z | ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = z. ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x). L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,z) = L((x \ 1) * T((x \ 1) \ 1,z),(x \ 1) \ 1,y). L((x \ 1) * T((x \ 1) \ 1,y),(x \ 1) \ 1,z) = L(x \ 1,x,z) * T(L(x \ 1,x,z) \ 1,y). x != L(y,z,u) * T(L(y,z,u) \ 1,w) | L(y * T(y \ 1,w),z,u) = x. L((x \ 1) * T((x \ 1) \ 1,y),x,z) = L((x \ 1) * T((x \ 1) \ 1,y),(x \ 1) \ 1,z). L((x \ 1) * T((x \ 1) \ 1,y),(x \ 1) \ 1,z) = L((x \ 1) * T((x \ 1) \ 1,y),x,z). L((x \ 1) * T((x \ 1) \ 1,y),(x \ 1) \ 1,z) = L(x \ T(x,y),x,z). L(x \ T(x,y),(x \ 1) \ 1,z) = L(x \ T(x,y),x,z). L(K((x \ 1) \ 1,y),x,1 / x) = L(x \ T(x,y),x,y). K(x,y) = L(K((x \ 1) \ 1,y),x,1 / x). L(K((x \ 1) \ 1,y),x,1 / x) = K(x,y). L(K((x \ 1) \ 1,y),x,1 / x) != z | K(x,y) = z. x != K(y,z) | K((y \ 1) \ 1,z) = x. K((x \ 1) \ 1,y) = L(K((x \ 1) \ 1,y),x,1 / x). L(K((x \ 1) \ 1,y),x,1 / x) = K((x \ 1) \ 1,y). K((x \ 1) \ 1,y) != z | K(x,y) = z. K(x \ 1,y) != z | K(1 / x,y) = z. (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z. L(K(x,y),y * x,1 / y) != z | L(x,y,y \ 1) \ ((1 / y) * (x * y)) = z. L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,y \ 1). (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * (y * x)) != u | K(y * K(z \ 1,z),x) = u. x * (y \ T(y,x)) != z | (y \ T(y,x)) * x = z. (x \ T(x,y)) * y = (x * y) / x. ((x * y) / x) * (y \ 1) = x \ T(x,y). (T(x,y) \ x) * ((x * y) / x) = y. L(x \ T(x,y),y,x) = K(x,(x * y) / x). x * K(x,y / x) = T(x,(y \ x) \ 1). T(x,(y \ x) \ 1) = x * K(x,y / x). R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z. L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y. T(x * y,R(x \ 1,x,x * y)) != z | x * ((x * y) * (y / (x * y))) = z. x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1). T(x,R(y \ 1,y,z)) != u | T(x,z / (y * z)) = u. T(x,x / (y * x)) = T(x,y \ 1). T(x,y \ 1) / y = x * ((x / y) / 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,T(y,y \ x) \ 1) = x * K(x,(y \ x) / x). L(((x * y) / x) / y,y,x) = K(T(x,y),y). T(x,(y \ x) \ 1) / (y \ x) = 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). L(x \ T(x,y),y,x) = K(T(x,y),y). L(x \ T(x,y),y,x) != z | K(x,(x * y) / x) = z. K(x,(x * y) / x) = K(T(x,y),y). K(T(x,y),y) = K(x,(x * y) / x). K(T(x,x \ y),x \ y) = K(x,y / x). K(T(x,T(y,x)),T(y,x)) = K(x,y). x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y). (x \ 1) * y != T((x \ 1) * z,(x \ 1) \ 1) | (x \ z) * x = y. (x \ y) * x = ((x \ 1) * y) * (y / ((x \ 1) * y)). ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x. T(x,T(y,y \ x) \ 1) != x * z | K(x,(y \ x) / x) = z. ((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 * 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)) | K(y \ ((y \ 1) \ z),y) = x. K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y). ((x * y) / x) * (y \ 1) != z | x \ T(x,y) = z. ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y. ((x \ 1) * y) \ T((x \ 1) * y,x) != z | L(K(x \ y,x),y,x \ 1) = z. 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). L(x,y,y \ 1) \ ((1 / y) * (x * y)) != z | L(K(x,y),y * x,y \ 1) = z. 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. L(K(x,y),y * x,y \ 1) != z | (x * y) / (y * x) = z. (x * y) / (y * x) = T(y,(y \ 1) * (x * y)) \ y. T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y). (x * y) / (y * x) != z \ y | T(y,(y \ 1) * (x * y)) = z. x \ y != (z * y) / (y * z) | T(y,(y \ 1) * (z * y)) = x. x * y != z * (u \ (u * w)) | (z * w) / y = x. (T(x,y) * z) / (x * z) = x \ T(x,y). (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). T(x,(x \ 1) * (y * x)) = T(x,y). T(x,T((x \ 1) * y,x)) = T(x,x \ y). K(x,y) = T(x \ T(x,y),y * x). T(x,T((x \ 1) * y,x)) != z | T(x,x \ y) = z. T(x,x \ y) = T(x,(x \ 1) * y). T(x,(x \ 1) * y) = T(x,x \ 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,y) * z != y * x | T(T(y,x),T(x,y)) = z. T(T(x,y),T(y,x)) = T(y,x) \ (x * y). x != T(y \ T(y,z \ 1),u) | y \ T(y,T(z,u) \ 1) = x. x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1). x != T(T(y,z),u) | T(T(y,u),z) = x. T(T(x,y),z) = T(T(x,y),T(z,x)). T(T(x,y),T(z,x)) = T(T(x,y),z). T(T(x,y),T(z,x)) != u | T(T(x,y),z) = u. T(T(x,y),y) = T(y,x) \ (x * y). T(x,y) \ (y * x) = T(T(y,x),x). T(x,y) * T(T(y,x),x) = y * x. K(T(x,y),y) * K(y,x) = 1. K(T(x,y),y) \ 1 != z | z = K(y,x). K(T(x,y),y) \ 1 != z | K(y,x) = z. 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). K(x,((y \ 1) \ x) / x) != z | K(y \ ((y \ 1) \ x),y) = z. K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1). x != K(y,(z \ 1) \ 1) | K(y,z) = x. K(x,y) = K(y \ ((y \ 1) \ x),y). K(x \ ((x \ 1) \ y),x) = K(y,x). (x \ T(x,y)) \ (((x * y) / x) * z) = y * z. x * (y * z) = T(x,y) * (T(y,x) * z). T(x,y) * (T(y,x) * z) = x * (y * z). x != y * (z * u) | (y * z) * L(u,z,y) = x. (x * y) * L(z,y,x) = T(x,y) * (T(y,x) * z). T(x,y) * (T(y,x) * z) = (x * y) * L(z,y,x). (x * y) \ T(x,y) = L(T(y,x) \ 1,y,x). L(T(x,y) \ 1,x,y) = (y * x) \ T(y,x). R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(z \ 1,z)) != u | R(x,y,z) = u. R(x,y,z) = R(x,y,(z \ 1) \ 1). R(x,y,(z \ 1) \ 1) = R(x,y,z). R(x,y,K(1 / z,z)) = x. x != R(y,z,K(1 / u,u)) | x = y. R(x,y,K(1 / z,z)) != u | u = x. R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1). (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * u) = (x * y) \ u. x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x. x * ((y \ (x \ z)) * y) = ((y \ (z / x)) * y) * x. ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x). (x * y) * T((x * y) \ z,x) = y * ((x \ (y \ z)) * x). (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1)) | R(x,y,z) = u. K(x * K(y \ 1,y),z) = (z * x) \ (x * z). K(x,y) = K(x * K(z \ 1,z),y). K(x * K(y \ 1,y),z) = K(x,z). K(x * (y \ 1),z) = K(x * (1 / y),z). K(x * (1 / y),z) = K(x * (y \ 1),z). (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z)). x != T(y,z \ 1) \ y | K(y \ (y / z),y) = x. K(x \ (x / y),x) = K(y \ 1,x). x != T(y,z) \ y | y * (T(y,z) \ 1) = x. x * (T(x,y) \ 1) = K(y,x). K(x,y) = y * (T(y,x) \ 1). x != T(y \ 1,z) \ (y \ 1) | y \ (T(1 / y,z) \ 1) = x. x \ (T(1 / x,y) \ 1) = K(y,x \ 1). K(x,y) \ y = T(y,x). T(x,y) = K(y,x) \ x. x * (K(x,y) * z) = T(x,y) * z. T(x,y) * (x \ z) = K(x,y) * z. x != y \ T(y,z) | (T(y,z) * u) / (y * u) = x. (T(x,y) * z) / (x * z) = K(x,y). x != y \ T(y,z) | (1 / y) * T(y,z) = x. (1 / x) * T(x,y) = K(x,y). K(x,y) = (1 / x) * T(x,y). x != y \ T(y,z) | T(y,z) * (y \ 1) = x. T(x,y) * (x \ 1) = K(x,y). K(x,y) = T(x,y) * (x \ 1). 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). L(K(x \ y,z),x \ y,x) = y \ (x * T(x \ y,z)). K(x,x * (y \ 1)) = x \ T(x,y \ x). K(x,y) * x = T(x,y). T(x,y) = K(x,y) * x. K(x,y) * y = (x * y) / x. (x * y) / x = K(x,y) * y. K(x,y) \ z = x * (T(x,y) \ z). x * (T(x,y) \ z) = K(x,y) \ z. K(x,y) \ (((x * y) / x) * z) = y * z. x != K(y \ z,y) \ y | T(y,(z \ y) \ 1) = x. T(x,(y \ x) \ 1) = T(x,x \ y). T(x,y) != x * z | K(x,y) = z. x \ T(x,y) != z | z = K(x,y). x \ T(x,y) != z | K(x,y) = z. x / (y * K(y,y \ x)) = y \ x. K(T(x,T(y,x)),T(y,x)) != z | K(x,y) = z. K(x,y) = K(x,T(y,x)). K(x,T(y,x)) = K(x,y). K(T(x,x \ y),x \ y) != z | K(x,y / x) = z. K(x,y / x) = K(x,x \ y). K(x \ y,x) = K(y / x,x). K(x / y,y) = K(y \ x,y). K(x,y) \ 1 != z | K(y,x) = z. K(x,x \ (y * x)) = K(x,y). 1 / K(x,y) != z | z = K(y,x). 1 / K(x,y) != z | K(y,x) = z. T((x * K(y,z)) \ x,u) = L(T(K(z,y),u),K(y,z),x). K(x,T(y,x)) != z | K(x,y) = z. T(x,y) * K(y,T(x,y)) != z | z = x. K(K(x,y),z) = K(y,x) * T(K(x,y),z). K(x,y) * T(K(y,x),z) = K(K(y,x),z). 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). x * K(y,y \ x) = y * (x / y). K(x / y,y) != z | (y * (x / y)) \ x = z. (x * (y / x)) \ y = K(x \ y,x). K(x,L(T(y,x),z,u)) != w | K(x,L(y,z,u)) = w. (x * y) * K(((x * y) \ x) \ 1,z) = x * T(y,z). x * y != T(x,z) * (u * x) | T(x,z) * T(u,x) = y. T(x,y) * T(z,x) = K(x,y) * (z * x). K(x,y) * (z * x) = T(x,y) * T(z,x). (K(x,y) * z) \ (T(x,y) * z) != u | T(x,K(x,y) * z) = u. x * T(K(x,y),z) = T(x,y) * K(K(x,y),z). T(x,y) * K(K(x,y),z) = x * T(K(x,y),z). K(x,y) * (x * z) != u | T(x,y) * z = u. (T(R(x,y,z),u) * (y * z)) / ((x * y) * z) = K(R(x,y,z),u). R(K(x,y),x * z,u) = ((T(x,y) * z) * u) / ((x * z) * u). ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u). x * (T(x,y) \ z) != u | K(y,x) * z = u. K(x,y) * z = K(y,x) \ z. K(x,y) \ z = K(y,x) * z. x / (K(y,z) * x) = K(z,y). x = K(y,z) * (K(z,y) * x). K(x,y) * (K(y,x) * z) = z. K(x,y) * z != u | K(y,x) * u = z. K(x,y) * (K(y,x) * z) != u | u = z. L((K(x,y) * z) \ u,K(x,y) * z,K(y,x)) = z \ (K(y,x) * u). T(x,x \ y) / (y \ x) = x * (y / x). (T(x,y \ 1) / y) \ (x / y) = K(x \ (x / y),x). K(x \ (x / y),x) = (T(x,y \ 1) / y) \ (x / y). x * K(y,x \ 1) = T(1 / x,y) \ 1. T(1 / x,y) \ 1 = x * K(y,x \ 1). K(x,y \ x) = K(x,x * (y \ 1)). K(x,x * (y \ 1)) = K(x,y \ x). K(x,(y \ z) / z) != u | K(x,y \ 1) = u. K(x,y) * (y * z) = ((x * y) / x) * z. x != T(y,z) * u | y * (K(y,z) * u) = x. x * (K(x,y) * T(z,x)) = K(x,y) * (z * x). T(x,x \ (y * x)) / ((y * x) \ x) = x * y. K(x,y) * (y * z) = (K(x,y) * y) * z. (K(x,y) * y) * z = K(x,y) * (y * z). R(K(x,y),y,z) = K(x,y). K(x,y) * T(x,z) != u | T(x,y) * K(x,z) = u. K(x,T(1 / y,z) \ 1) = T(K(x,y),z). x * K(y,T(z,x) \ 1) = K(y,z \ 1) * x. K(x,y * K(z,y \ 1)) = T(K(x,y),z). T(x,T(y,x)) / ((y * x) \ x) = x * y. T(x,y) / ((y * x) \ x) = x * y. (x * y) \ T(x,y) = (y * x) \ x. (x * y) \ T(x,y) != z | L(T(y,x) \ 1,y,x) = z. L(T(x,y) \ 1,x,y) = (x * y) \ y. K(x,K(y,z)) = K(y,z) * T(K(z,y),x). K(x,y) * T(K(y,x),z) = K(z,K(x,y)). L(T(K(x,y),z),K(y,x),z) = (K(y,x) * z) \ z. K(x,y) * K(z,K(y,x)) = T(K(x,y),z). K(x,y) * T(K(y,x),z) != u | K(K(y,x),z) = u. K(K(x,y),z) = K(z,K(y,x)). T(x,K(y,z)) = x * K(K(z,y),x). x * K(K(y,z),x) = T(x,K(z,y)). K(x,K(y,z)) \ 1 != u | K(x,K(z,y)) = u. T(T(x,K(y,z)),K(z,y)) = x. T(x,K(y,z)) * K(z,y) = K(z,y) * x. T(T(x,K(y,z)),K(z,y)) != u | u = x. K(x,y) * T(K(y,x),z) != u | u = K(z,K(x,y)). K(x,y) * T(K(y,x),z) != u | K(z,K(x,y)) = u. K(K(x,y),z) != u | K(z,K(y,x)) = u. T(K(x,y),z) * K(y,x) != u | K(z,K(y,x)) = u. x * K(y,(x \ z) \ 1) = K(y,(z / x) \ 1) * x. K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1). K(x \ 1,y) = (T(y,x \ 1) / x) \ (y / x). (T(x,y \ 1) / y) \ (x / y) = K(y \ 1,x). (T(x,y \ 1) / y) \ (x / y) != z | K(y \ 1,(1 / y) \ (x / y)) = z. K(x \ 1,(1 / x) \ (y / x)) = K(x \ 1,y). K(x \ 1,(1 / x) \ y) = K(x \ 1,y * x). K(1 / x,(1 / x) \ y) = K(x \ 1,y * x). x * K(y \ 1,x * y) = (1 / y) * (x / (1 / y)). (1 / x) * (y / (1 / x)) = y * K(x \ 1,y * x). (1 / (1 / x)) * (y / (1 / (1 / x))) != z | x * (y / x) = z. x * (y / x) = y * K((1 / x) \ 1,y * (1 / x)). x * K((1 / y) \ 1,x * (1 / y)) = y * (x / y). x * K(y,x * (1 / y)) = y * (x / y). x * y != z * (x / z) | K(z,z \ x) = y. K(x,x \ y) = K(x,y * (1 / x)). K(x,y * (1 / x)) = K(x,x \ y). 1 / K(x,x \ y) = K(y * (1 / x),x). K(x * (1 / y),y) = 1 / K(y,y \ x). K(x \ y,x) = K(y * (1 / x),x). K(x * (1 / y),y) = K(y \ x,y). K(x * (1 / y),z) != u | K(x * (y \ 1),z) = u. K(x * (y \ 1),y) = K(y \ x,y). x != K(y \ ((y \ 1) \ z),y) | K(z,y) = x. K(x,y) = K(((y \ 1) \ x) * (y \ 1),y). K(((x \ 1) \ y) * (x \ 1),x) = K(y,x). K((x \ y) * x,x \ 1) = K(y,x \ 1). K(x * y,y \ 1) = K(y * x,y \ 1). K(x,y * K(y * z,y \ 1)) = T(K(x,y),z * y). K(x,y * K(z,y \ 1)) != u | T(K(x,y),z) = u. T(K(x,y),y * z) = T(K(x,y),z * y). 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). 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 != L(T(K(y,z),u),K(z,y),u) | (K(z,y) * u) \ u = x. (K(x,y) * z) \ z = T((z * K(x,y)) \ z,z). T((x * K(y,z)) \ x,x) = (K(y,z) * x) \ x. (x / T(y,z)) * y = x * K(z,y). x / K(y,z) = (x * T(z,y)) / z. (x * T(y,z)) / y = x / K(z,y). (x * K(y,z)) * T(z,y) = x * z. x * y = (x * T(y,z)) * K(z,y). (x * T(y,z)) * K(z,y) = x * y. (x * K(y,z)) * z = (x * z) * K(y,z). (x / y) * T(y,z) = x / K(z,y). x * T(y / z,z) != (u * (z \ y)) * (y / z) | u * (y / z) = x. x * (y / z) = (x * (z \ y)) * K(z,y / z). (x * (y \ z)) * K(y,z / y) = x * (z / y). x * y != (z / u) * u | x \ z = y. ((x / y) * T(y,z)) \ x = K(z,y). (x * T(x \ y,z)) \ y = K(z,x \ y). (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z). K(x,y) \ 1 = L(K(y,x),y,z). L(K(x,y),x,z) = K(y,x) \ 1. L(K(x \ y,z),x \ y,x) != u | y \ (x * T(x \ y,z)) = u. x \ (y * T(y \ x,z)) = K(y \ x,z). L(K(x,y),x,z) != u | K(x,y) = u. x != K(y,z) | K(z,y) \ 1 = x. K(x \ y,z) \ 1 = K(z,(y \ x) \ 1). K(x,(y \ z) \ 1) = K(z \ y,x) \ 1. (x * y) * z != x * T(y,u) | K(((x * y) \ x) \ 1,u) = z. K(((x * y) \ x) \ 1,z) = K(y,z). (x / y) * T(y,z) != u | x / K(z,y) = u. x / K(y,z) = x * K(z,y). (x * K(y,z)) \ x = K(z,y). (x * K(y,z)) * K(z,y) = x. (x * K(y,z)) \ x != u | u = K(z,y). (x * K(y,z)) \ x != u | K(z,y) = u. x != K(y,L(z \ 1,u,w) \ 1) | L(K(y,z),u,w) = x. L(K(x,y),z,u) = (w * K(L(y \ 1,z,u) \ 1,x)) \ w. (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u). x / K(y,z) != u | u = x * K(z,y). x / K(y,z) != u | x * K(z,y) = u. T(K(x,y),z) = (K(y,x) * z) \ z. (K(x,y) * z) \ z = T(K(y,x),z). (x * (y * K(z,y))) \ (x * y) = K(y,z). K((x \ y) \ 1,z) = K(y \ x,z). x * y != z * T(T(u,z),w) | x \ (T(u,w) * z) = y. (x * K(T(y,x),z)) \ (T(y,z) * x) = T(y,x). (K(x,y) * z) * x = T(z,K(y,x)) * T(x,y). T(x,K(y,z)) * T(z,y) = (K(z,y) * x) * z. (K(x,y) * z) * T(K(y,x),z) = z. K((x \ (y \ x)) \ 1,z) != u | T(K(y,z),x) = u. T(K(x,y),z) = K((x \ z) \ z,y). K((x \ y) \ y,z) = T(K(x,z),y). K(x,T(y,z)) = T(K(x,y),y * z). T(K(x,y),y * z) = K(x,T(y,z)). K(T(x,x \ y),z) = T(K(x,z),y). K(x,y) * K(y,T(x,z)) != u | K(x * z,K(x,y)) = u. (x * (y * K(z,y))) \ (x * y) != u | K(y,z) = u. ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u)). (x * ((y \ (x \ z)) * y)) \ z = K(y,(y * x) \ z). x \ (y * ((z \ (y \ x)) * z)) = K((z * y) \ x,z). K(x,(y \ z) \ 1) != u | K(x,z \ y) = u. K(x,T(y,z) \ 1) != u | K(x,(y * z) \ z) = u. T(x,y) * z != (K(x,y) * u) * x | T(T(u,K(y,x)),T(x,y)) = z. K(x,y \ x) = K(x,(z * y) \ (z * x)). K(x,(y * z) \ (y * x)) = K(x,z \ x). L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u). L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u)). K(x,y \ (z * x)) = K(x,(z \ y) \ x). K(x,(y \ z) \ x) = K(x,z \ (y * x)). L(K(x,y \ z),z,u) != w | K(x,(u * y) \ (u * z)) = w. K(x,(y * z) \ (y * u)) = K(x,L(z \ u,z,y)). K(x,L(y \ z,y,u)) = K(x,(u * y) \ (u * z)). 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(L(x \ y,x,z),u) = L(K(x \ y,u),y,z). L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z). (x * (y * z)) / K(L(y,z,x),z) = x * (z * y). L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u). (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y). L(K(x \ (y \ z),x),y \ z,y) != u | z \ (y * ((x \ (y \ z)) * x)) = u. x \ (y * ((z \ (y \ x)) * z)) = K((y * z) \ x,z). 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 \ (y * ((z \ (y \ x)) * z)) != u | K((z * y) \ x,z) = u. K((x * y) \ z,x) = K((y * x) \ z,x). K((x * y) \ z,y) = K((y * x) \ z,y). 1 / K((x * y) \ z,x) = K(x,(y * x) \ z). K(x,(x * y) \ z) = K(x,(y * x) \ z). K(x,(y * x) \ z) = K(x,(x * y) \ z). K(x,(y * x) \ z) != u | K(x,(x * y) \ z) = u. (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u). (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). ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y). ((T(x,y) * z) * u) / ((x * z) * u) != w | R(K(x,y),x * z,u) = w. R(K(x,y),x * z,u) = K(R(x,z,u),y). R(K(x,y),z,u) = K(R(x,x \ z,u),y). K(R(x,x \ y,z),u) = R(K(x,u),y,z). K(R(x,x \ y,z),u) * (y * z) = (K(x,u) * y) * z. (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u)). (x * ((x \ y) * K(z \ (x \ y),u))) \ y != w | K(u,(x * z) \ y) = w. ((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). ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u. (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). K((x * y) \ (z * y),u) = (z * y) \ ((z * K(x \ z,u)) * y). (x * y) \ ((x * K(z \ x,u)) * y) = K((z * y) \ (x * y),u). (x * y) * K((z * y) \ (x * y),u) = (x * K(z \ x,u)) * y. (x * y) * z != (x * K(u,y)) * y | K(u,y) = z. K(x \ y,z) = K((x * z) \ (y * z),z). K((x * y) \ (z * y),y) = K(x \ z,y). (x * (y * K(z \ u,y))) \ (x * y) = K(y,(z * y) \ (u * y)). K(x,y \ z) = K(x,(y * x) \ (z * x)). K(x,(y * x) \ (z * x)) = K(x,y \ z). K(x,(x * y) \ (z * x)) = K(x,y \ z). K(x,y \ (z * x)) = K(x,(y / x) \ z). K(x,(y / x) \ z) = K(x,y \ (z * x)). K(x,y \ (z * x)) = K(x,(x \ y) \ z). K(x,(x \ y) \ z) = K(x,y \ (z * x)). L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (y / x)) \ u). K(x,y) = K(x,z \ (((x \ z) * y) * x)). K(x,y \ (((x \ y) * z) * x)) = K(x,z). L(K(x,y \ (z \ u)),z \ u,z) != w | K(x,(z * y) \ u) = w. (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u). ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u). K(x,(x * y) \ z) = K(x,y \ (x \ z)). K(T(x,x \ y),z) = K(T(x,y),z). K(x,y) * (z * x) = (K(x,y) * z) * x. (K(x,y) * z) * x = K(x,y) * (z * x). K(x,R(y,z,y)) != u | K(x,y) = u. K(T(x,x \ y),z) != u | T(K(x,z),y) = u. T(K(x,y),z) = K(T(x,z),y). K(T(x,y),z) = T(K(x,z),y). x != T(K(y,z),K(z,u)) | K(y,z) = x. K(x,y) = K(T(x,K(y,z)),y). K(T(x,K(y,z)),y) = K(x,y). x * K(T(y,x),z) = K(y,z) * x. 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). K(x,T(y,y \ z)) != u | K(x,T(y,z)) = u. x != T(K(y,z),u) | K(T(y,u),z) = x. K(T(x,y),z) = K(x,T(z,y)). x != T(K(y,z),u) | K(y,z) * K(u,K(z,y)) = x. K(x,y) * K(z,K(y,x)) = K(x,T(y,z)). x != T(K(y,z \ 1),u) | K(y,T(z,u) \ 1) = x. K(x,T(y,z) \ 1) = K(x,T(y \ 1,z)). K(x,T(y \ 1,z)) = K(x,T(y,z) \ 1). x * K(y,T(z,x)) = K(y,z) * x. T(x,T(y,z)) = x * T(K(x,y),z). x * T(K(x,y),z) = T(x,T(y,z)). K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). (K(x,y) * z) * K(y,T(x,z)) = z. K(T(x,y),z / y) = K(x,y \ z). x * K(y,z) = K((x * y) / x,z) * x. K((x * y) / x,z) * x = x * K(y,z). (K(x,y) * z) \ (T(x,y) * z) = T(x,z). x * y != K(z,(u / x) \ 1) * x | K(z,(x \ u) \ 1) = y. K(x,(y \ z) \ 1) = K(x,T((z / y) \ 1,y)). K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1). x * T(K(x,y),z) != u | T(x,y) * K(K(x,y),z) = u. T(x,y) * K(K(x,y),z) = T(x,T(y,z)). K(T(x,y),z \ 1) = K(x,y \ (z \ y)). K(x,(x * y) \ z) != u | K(x,(y * x) \ z) = u. K(x,(y * x) \ z) = K(x,y \ (x \ z)). K(x,(x * y) \ z) != u | (y * ((x \ (y \ z)) * x)) \ z = u. (x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z)). L(x,y,K(x,z)) = x. x != K(y,z) * (u * y) | T(y,z) * T(u,y) = x. T(x,y) * T(z,x) = (K(x,y) * z) * x. (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) * z,x) = K(x,y) * T(z,x). K(x,y) = L(K(x,y),z,K(x,u)). L(K(x,y),z,K(x,u)) = K(x,y). L(K(x,y),z * y,u) != w | K(x,L(y,z,u)) = w. K(x,L(y,z,K(x,u))) = K(x,y). K(x,y \ (K(x,z) * u)) = K(x,(K(z,x) * y) \ u). K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u)). K(x,(y * z) \ z) = K(x,T(y \ 1,z)). K(x,T(y \ 1,z)) = K(x,(y * z) \ z). K(x * y,K(x,z)) = K(y,K(x,z)). x != K(y,K(z,u)) | K(K(u,z),y) = x. K(K(x,y),z) = K(y * z,K(y,x)). K(x * y,K(x,z)) = K(K(z,x),y). K(x * y,K(x,z)) != u | K(y * x,K(x,z)) = u. K(x * y,K(y,z)) = K(x,K(y,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,K(y \ x,z)) = K(y,K(y \ x,z)). T(x,K(x,y) * z) = T(x,z). T(x,y) = T(x,K(z,x) * y). T(x,K(y,x) * z) = T(x,z). T(x,y * K(z,x)) = T(x,y). T(x,y) = T(x,y * K(x,z)). T(x,y * K(x,z)) = T(x,y). x != T(y,z) | y * K(y,z) = x. x * K(x,y) = T(x,y * K(x,z)). T(x,y * K(x,z)) = x * K(x,y). T(x,y * (z / x)) = T(x,y * (x \ z)). K(T(x,y),z) = K(x,T(z,y * K(x,u))). K(x,T(y,z * K(x,u))) = K(T(x,z),y). K(x,y * K(x,z)) = K(x,y). K(x,y) = K(x,y * K(z,x)). K(x,y * K(z,x)) = K(x,y). R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x)). K(T(x,y),z) != u | K(x,T(z,y)) = u. K(x,T(y \ 1,z)) = K(x,z \ (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)). L(K(x,y \ (x \ z)),u * x,w) = K(L(x,u,w),(y * x) \ z). T(T(x,K(y,z)),T(z,y)) = T(x,z). T(x,T(y,z)) = T(T(x,K(y,z)),y). T(T(x,K(y,z)),y) = T(x,T(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). x != K(T(y,z),u) | K(y,T(u,z)) = x. K(x,T(y,z)) = K(x,T(y,z * K(x,u))). K(x,T(y,z * K(x,u))) = K(x,T(y,z)). K(x,T(y \ 1,z)) != u | K(x,(y * z) \ z) = u. K(x,(y * z) \ z) = K(x,z \ (y \ z)). (x * T(x \ y,z)) \ y = K(z,(x * K(z,u)) \ y). K(x,(y * K(x,z)) \ u) = (y * T(y \ u,x)) \ u. K(x,T(y,z * (u / x))) = K(x,T(y,z * (x \ u))). T(K(x,y),z) != u | K(x,T(y,z)) = u. K(x,y \ (z \ y)) != u | K(x,T(z \ 1,y)) = u. x != T(T(y,K(z,u)),z) | T(y,T(z,u)) = x. 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)). T(x,y) * K(x,K(y,z)) = T(x,T(y,z)). T(x,y) * z != T(x,T(y,u)) | K(K(x,y),u) = z. K(K(x,y),z) = K(x,K(y,z)). K(x,K(y,z)) = K(z,K(y,x)). K(K(x,y),z) != u | K(y * z,K(y,x)) = u. K(x * y,K(x,z)) = K(z,K(x,y)). K(x,K(y,z)) \ 1 = K(z,K(x,y)). x * K(y,K(z,x)) = T(x,K(z,y)). K(x,K(y,z)) != u | K(z,K(y,x)) = u. K(x,K(y,y * z)) = K(x,K(y,z)). K(x,K(y,z)) = K(y,K(x,z)). x != K(y,K(z,u)) | K(u,K(z,y)) = x. K(x,K(y,z)) = K(y,K(z,x)). K(x,K(y,z)) = K(z,K(x,y)). x != K(y \ z,K(y,u)) | K(z,K(y,u)) = x. K(x,K(y,z)) = K(y,K(y \ x,z)). K(x,K(x \ y,z)) = K(y,K(x,z)). T(x,K(y,z)) = x * K(y,K(z,x)). x * K(y,K(z,x)) = T(x,K(y,z)). K(x,y) * K(x,K(z,y)) = T(K(x,y),z). K(x,y) * K(x,K(z,y)) = K(x,T(y,z)). K(x,K(y,z \ y)) = K(x,K(y,z \ 1)). K(x,K(y,z \ 1)) = K(x,K(y,z \ y)). K(x,K(y,z)) = K(y,K(y \ z,x)). K(x,K(x \ y,z)) = K(z,K(x,y)). x * K(y,K(z,x)) != u | T(x,K(z,y)) = u. T(x,K(y,z)) = T(x,K(z,y)). T(T(x,K(y,z)),K(y,z)) = x. T(K(x,y),z) * z = z * K(x,y). K(x,K(x \ y,z)) != u | K(y,K(x \ y,z)) = u. K(x,K(y \ x,z)) = K(z,K(y,x)). K(x,T(y,z)) * z = z * K(x,y). K(x,K(y,z)) != u | K(z,K(x,y)) = u. K(x,K(y,z \ y)) = K(x,K(z,y)). K(x,K(y,z \ (u * y))) = K(x,K(u \ z,y)). K(x,y) * K(x,K(z,y)) != u | K(x,T(y,z)) = u. x != K(y,K(z,u \ z)) | K(y,K(u,z)) = x. K(x,K(y,z)) = K(x,K(z,y \ 1)). K(x,K(y,z \ 1)) = K(x,K(z,y)). K(x,K(y,z \ u)) = K(x,K(u \ z,y)). K(x,K(y \ z,u)) = K(x,K(u,z \ y)). K(x,T((y / z) \ 1,z)) != u | K(x,y \ z) = u. x != K(y,K(z \ u,w)) | K(y,K(w,u \ z)) = x. K(x,K(y,z \ u)) = K(x,K(y,z \ (u * y))). K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u)). K(x,y * K(z,x)) != u | u = K(x,y). K(x,y * K(z,x)) != u | K(x,y) = u. K(x,y \ T(z,x)) != u | K(x,y \ z) = u. K(x,y \ (x \ (z * x))) != u | K(x,y \ z) = u. ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u != w | K(z,(x * (y * z)) \ u) = w. K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u)). x != (y * T(y \ z,u)) \ z | K(u,y \ z) = x. 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)) \ u) = K(x,(y * (z * x)) \ u). K(x,(y * (z * x)) \ u) = K(x,(y * (x * z)) \ u). K(x,y \ z) = K(x,(K(u,x) * y) \ z). K(x,(K(y,x) * z) \ u) = K(x,z \ u). K(x,(K(y,x) * z) \ u) != w | K(x,z \ (K(x,y) * u)) = w. K(x,y \ (K(x,z) * u)) = K(x,y \ u). K(x,y \ (z * K(x,u))) = K(x,y \ z). K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u))). K(x,(y * z) \ u) = K(x,(y * (z / x)) \ (x \ u)). K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u). K(x,(y * (z * x)) \ u) != w | K(x,(y * z) \ (x \ u)) = w. 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 * (x * z)) \ u),w * x,v5) = K(L(x,w,v5),(y * (z * x)) \ u). K(x,(y * z) \ z) != u | K(x,z \ (y \ z)) = u. 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 / x)) \ u) = K(x,(y * z) \ (u * x)). L(K(x,(y * z) \ (x \ u)),w * x,v5) = K(L(x,w,v5),(y * (x * z)) \ u). K(x,(y * (z / x)) \ u) != w | L(K(x,z \ ((y \ u) * x)),y \ u,y) = w. L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x)). L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w). K(x,K(y,(z * u) \ (y * y))) = K(x,K(z * (u / y),y)). K(x,y \ (x \ (y * (z * x)))) != u | K(x,L(z,x,y)) = u. K(x,K(y,z \ (u * y))) != w | K(x,K(y,z \ u)) = w. K(x,K(y,(z * u) \ y)) = K(x,K(z * (u / y),y)). K(x,K(y * (z / u),u)) = K(x,K(u,(y * z) \ u)). K(x,K(y * z,u)) = K(x,K(y * (z / u),u)). K(x,K(y * (z / u),u)) = K(x,K(y * z,u)). K(x,y) * K(x,K(z * u,y)) = K(x,T(y,z * (u / y))). K(x,T(y,z * u)) = K(x,T(y,z * (u / y))). K(x,T(y,z * (u / y))) = K(x,T(y,z * u)). K(x,T(y,z * (y \ u))) = K(x,T(y,z * u)). x / (K(y,T(z,u * w)) * x) = K(T(z,u * (z \ w)),y). K(T(x,y * (x \ z)),u) = w / (K(u,T(x,y * z)) * w). x != y / (K(z,u) * y) | K(u,z) = x. K(T(x,y * z),u) = K(T(x,y * (x \ z)),u). K(T(x,y * (x \ z)),u) = K(T(x,y * z),u). K(x,T(y,z * u)) = K(T(x,z * (x \ u)),y). K(T(x,y * (x \ z)),u) = K(x,T(u,y * z)). K(x,T(y,z * (x \ u))) = K(x,T(y,z * u)). K(x,T(y,z * (x \ u))) != w | K(x,T(y,z * (u / x))) = w. K(x,T(y,z * (u / x))) = K(x,T(y,z * u)). K(L(x,y,z),u \ (x \ w)) = K(L(x,y,z),(u * x) \ w). K(L(x,y,z),(u * x) \ w) = K(L(x,y,z),u \ (x \ w)). K(L(x,y,z),(u * (x * w)) \ v5) = K(L(x,y,z),(u * (w * x)) \ v5). K(L(x,y,z),(u * (w * x)) \ v5) = K(L(x,y,z),(u * (x * w)) \ v5). K(L(x,y,z),(u * w) \ (x \ v5)) = K(L(x,y,z),(u * (x * w)) \ v5). K(L(x,y,z),(u * (x * w)) \ v5) = K(L(x,y,z),(u * w) \ (x \ v5)). K(L(x,y,z),(u * (x * w)) \ v5) != v6 | K(L(x,y,z),(u * (w * x)) \ v5) = v6. K(L(x,y,z),(u * (w * x)) \ v5) = K(L(x,y,z),(u * w) \ (x \ v5)). L(K(x,y \ ((z \ u) * x)),z \ u,z) != w | K(x,(z * y) \ (u * x)) = w. K(x,(y * (z * u)) \ (w * x)) = K(x,(y * (z * (u / x))) \ w). K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x)). K(x,(y * (z * (u / x))) \ w) != v5 | K(x,(y * (z * u)) \ (w * x)) = v5. 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))) | K(y,T(z,u * w)) = x. K(x,T(y \ 1,z * u)) = 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)). 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 \ y) * z) * x)) != u | K(x,z) = u. K(x,x \ y) = K(x,z \ ((x \ z) * y)). K(x,y \ ((x \ y) * z)) = K(x,x \ z). K(x,y \ z) = K(x,x \ ((x \ y) \ z)). K(x,x \ ((x \ y) \ z)) = K(x,y \ z). K(x,x \ (y \ z)) = K(x,(x * y) \ z). K(x,(x * y) \ z) = K(x,x \ (y \ z)). K(x,(y * x) \ z) = K(x,x \ (y \ z)). K(x,(x * y) \ z) != u | K(x,y \ (x \ z)) = u. K(x,y \ (x \ z)) = K(x,x \ (y \ z)). K(x,(y * x) \ (y * z)) = K(x,x \ z). K(x,y \ (x \ (y * z))) = K(x,x \ z). K(L(x,y,z),(z * (y * x)) \ ((z * y) * u)) = K(L(x,y,z),L(x,y,z) \ u). x != K(y,y \ (z * y)) | K(y,z) = x. K(x,y) = K(x,z \ (x \ (z * (y * x)))). K(x,y \ (x \ (y * (z * x)))) = K(x,z). K(x,L(y,x,z)) = K(x,y). L(K(x,y),z * x,u) = K(L(x,z,u),L(y,x,w)). K(L(x,y,z),L(u,x,w)) = L(K(x,u),y * x,z). x != L(K(y,z),u * y,w) | K(L(y,u,w),z) = x. K(L(x,y,z),u) = K(L(x,y,z),L(u,x,w)). K(L(x,y,z),L(u,x,w)) = K(L(x,y,z),u). K(x,L(y \ z,y,u)) != w | K(x,(u * y) \ (u * z)) = w. K(L(x,y,z),(u * x) \ (u * w)) = K(L(x,y,z),x \ w). K(L(x,y,z),(u * x) \ w) != v5 | K(L(x,y,z),u \ (x \ w)) = v5. K(L(x,y,z),u \ (x \ (u * w))) = K(L(x,y,z),x \ w). K(L(x,y,z),(u * (w * x)) \ v5) != v6 | K(L(x,y,z),(u * w) \ (x \ v5)) = v6. K(L(x,y,z),(z * y) \ (x \ ((z * y) * u))) = K(L(x,y,z),L(x,y,z) \ u). K(L(x,y,z),u \ (x \ (u * w))) != v5 | K(L(x,y,z),x \ w) = v5. K(L(x,y,z),x \ u) = K(L(x,y,z),L(x,y,z) \ u). K(L(x,y,z),L(x,y,z) \ u) = K(L(x,y,z),x \ u). x != K(L(y,z,u),w) | L(y,z,u) \ L(T(y,w),z,u) = x. L(x,y,z) \ L(T(x,x \ u),y,z) = K(L(x,y,z),L(x,y,z) \ u). L(x,y,z) * K(L(x,y,z),L(x,y,z) \ u) = L(T(x,x \ u),y,z). x / L(T(y,y \ x),z,u) = L(y,z,u) \ x. x / L(y,z,u) = L(x / (x / y),z,u) \ x. L(x / (x / y),z,u) \ x = x / L(y,z,u). x / (x / L(y,z,u)) = L(x / (x / y),z,u). R(x / (x / y),z,u) = x / (x / R(y,z,u)). R(c8 / (c8 / c9),c10,c11) != c8 / (c8 / R(c9,c10,c11)). x / (y * (y \ 1)) != z | z = x. 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). R(1 / x,x,y) * z = (y / (x * y)) * z. T(x,x \ y) \ y != z | T(x \ y,T(x,x \ y)) = z. x * T(x \ (y * x),z) != u | T(y,z) * x = u. R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u). x * y != (z * u) * (u \ 1) | x \ R(z,u,u \ 1) = y. (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1). T((x * y) / (y * x),y * x) != z | K(x,y) = z. R((x / y) / z,z,y) != u | x / (z * y) = u. T(x,x \ y) \ z != u | u = ((x \ y) \ y) \ z. T(x,x \ y) \ z != u | ((x \ y) \ y) \ z = u. T(x,y) / (x * y) != z | R(1 / y,y,T(x,y)) = z. R(T(x,R(x,y,z) \ u),y,z) != w | (R(x,y,z) \ u) \ u = w. x = (y / (z * y)) * (R(1 / z,z,y) \ x). (x / (y * x)) * (R(1 / y,y,x) \ z) = z. L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u). ((x \ y) / y) * (R(1 / x,x,x \ y) \ z) = z. x * y != (z * u) * L(w,u,z) | (z * (u * w)) / y = 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((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x. L((x * y) \ (y * z),u,w) = L(L(T(x,y) \ z,u,w),T(x,y),y). L(L(T(x,y) \ z,u,w),T(x,y),y) = L((x * y) \ (y * z),u,w). T(x,y) * (x \ z) != u | (x \ z) * T((x \ z) \ z,y) = u. x \ ((y \ (x * z)) * y) = (x \ y) * T((x \ y) \ z,y). (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y). R(R(x,1 / y,y),z,u) / y != w * (1 / y) | R(x,z,u) = w. x \ T(x * y,z) = y * K(z \ (z / (y \ (x \ 1))),z). ((x \ 1) \ 1) \ 1 = T(x \ 1,x). T(x \ 1,x) = ((x \ 1) \ 1) \ 1. T(x \ 1,T(x,x \ 1)) = T(x \ 1,x). K(x \ (x / ((y \ x) / T(x,y))),x) = ((y \ x) * ((y \ x) \ x)) / T(x,y). T(x,y) \ T(x * T(x \ 1,z),y) != u | u = T(T(x,y) \ 1,z). T(x,y) \ T(x * T(x \ 1,z),y) != u | T(T(x,y) \ 1,z) = u. T(x,y) \ T(x * T(x \ 1,x),y) = T(T(x,y) \ 1,T(x,x \ 1)). (x * T(x \ (y / z),u)) * z = (x * z) * T((x * z) \ y,u). x * y != z * T(u,z) | (u * z) / y = x. ((x \ (y * z)) * x) / z = (x / z) * T((x / z) \ y,x). (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y. T(T(x,y) \ 1,x) = T(T(x,y) \ 1,T(x,x \ 1)). T(T(x,y) \ 1,T(x,x \ 1)) = T(T(x,y) \ 1,x). T(x,T(y,y \ z)) != u | T(x,(y \ z) \ z) = u. T(T(x,y) \ 1,(x \ 1) \ 1) = T(T(x,y) \ 1,x). ((x \ 1) \ 1) * T(T(x,y) \ 1,x) = (T(x,y) \ 1) * ((x \ 1) \ 1). (x * y) * ((z * ((x * y) \ x)) / z) != u | x * (y * ((z * (y \ 1)) / z)) = u. x * (x * ((y * (x \ 1)) / y)) = (x * ((y * (x \ 1)) / y)) * x. (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y)). (((x * y) / x) / y) * (1 / y) = (1 / y) * ((1 / y) * ((x * ((1 / y) \ 1)) / x)). (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x). x / T(x,y) = K(x \ (x / ((y \ x) / T(x,y))),x). K(x \ (x / ((y \ x) / T(x,y))),x) = x / T(x,y). (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y. x * ((x \ 1) * (y * x)) = ((x \ 1) * (x * y)) * x. ((x \ 1) * (x * y)) * x = x * ((x \ 1) * (y * x)). L(x * y,y \ 1,y) = ((y \ 1) * (y * x)) * y. ((x \ 1) * (x * y)) * x = L(y * x,x \ 1,x). (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y. 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). (T(x,y) \ 1) * ((x \ 1) \ 1) != z | ((x \ 1) \ 1) * T(T(x,y) \ 1,x) = z. ((x \ 1) \ 1) * T(T(x,y) \ 1,x) = T(x,y) \ x. x * (y * K(x \ 1,x)) != z | (x * y) * K(x \ 1,x) = z. (1 / x) * (((y * x) / y) / x) = (((y * x) / y) / x) * (1 / x). (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y). ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x. R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y). (x * y) / (y * x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y). ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y). T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y). K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y). K(x,y) = ((1 / y) * K(x,y)) / (1 / y). ((1 / x) * K(y,x)) / (1 / x) = K(y,x). T(1 / x,K(y,x)) = 1 / x. K(x,y) * (1 / y) = (1 / y) * K(x,y). T(1 / x,x) = T(x \ 1,K(y,x)). T(x \ 1,K(y,x)) = T(1 / x,x). x \ 1 = T(x \ 1,K(y,x)). T(x \ 1,K(y,x)) = x \ 1. R(x,y \ 1,y) = R(x,1 / y,y). R(x,1 / y,y) = R(x,y \ 1,y). ((1 / x) * K(y,x)) * x = R(K(y,x),x \ 1,x). T(((1 / x) * y) * x,1 / x) != z | R(y,1 / x,x) = z. R(x,1 / y,y) = T(((1 / y) * x) * y,y \ 1). T(((1 / x) * y) * x,x \ 1) = R(y,1 / x,x). T(x,T(y \ 1,y)) = T(x,y \ 1). ((x \ 1) \ 1) * T(y,x) = y * T(x,x \ 1). x != R(y,z \ 1,z) | R(y,1 / z,z) = x. R(x,1 / y,y) = R(x,y \ 1,(y \ 1) \ 1). R(x,y \ 1,(y \ 1) \ 1) = R(x,1 / y,y). (T(x,x \ 1) \ 1) \ R(y,T(x,x \ 1),T(x,x \ 1) \ 1) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1). R(x,(y \ 1) \ 1,T(y \ 1,y)) = R(x,1 / (y \ 1),y \ 1). T((K(x,x \ 1) * y) * x,x \ 1) = R((x \ 1) \ y,1 / x,x). x != y * ((z \ u) \ u) | y * T(z,z \ u) = x. x * T(y,y \ 1) = (K(y,y \ 1) * x) * y. (K(x,x \ 1) * y) * x = y * T(x,x \ 1). R(x,(y \ 1) \ 1,T(y \ 1,y)) = R(x,y,y \ 1). R(x,T(y,y \ 1),T(y \ 1,y)) = R(x,y,y \ 1). T(x * T(y,y \ 1),y \ 1) = R((y \ 1) \ x,1 / y,y). ((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. K(x \ (x / R(y,z,u)),x) != w | R(y * T(y \ 1,x),z,u) = w. x / T(x,y) != z | K(x \ (x / ((y \ x) / T(x,y))),x) = z. K(x \ (x / ((y \ x) / T(x,y))),x) = T(x,y) \ x. (1 / T(x,y)) * K(x \ 1,x) = T(x,y) \ 1. x * ((1 / T(x,y)) * K(x \ 1,x)) = T(x,y) \ x. K(L(x,x \ 1,y),z) = K((y * (x \ 1)) \ y,z). T(x,y) = T(T(x,y),K(x,z)). T(T(x,y),K(x,z)) = T(x,y). T(K(x,y),T(x,z)) = K(x,y). T(x,y) * K(x,z) != u | K(x,z) * T(x,y) = u. T(x \ 1,T(x,y) \ x) = x \ 1. ((1 / x) * (T(x,y) \ x)) * x = R(K(x \ (x / ((y \ x) / T(x,y))),x),x \ 1,x). R(K(x \ (x / ((y \ x) / T(x,y))),x),x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x. T(T(x,y) \ x,x \ 1) = T(x,y) \ x. (x * (1 / T(x,y))) * K(x \ 1,x) = T(x,y) \ x. (1 / x) * (T(x,y) \ x) = (x \ 1) * (x * (1 / T(x,y))). (x \ 1) * (x * (1 / T(x,y))) = (1 / x) * (T(x,y) \ x). ((1 / x) * (T(x,y) \ x)) * x = L((1 / T(x,y)) * x,x \ 1,x). L((1 / T(x,y)) * x,x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x. L(T(x,y) \ x,x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x. ((1 / x) * (T(x,y) \ x)) * x = L(T(x,y) \ x,x \ 1,x). x != ((1 / y) * (T(y,z) \ y)) * y | L(T(y,z) \ y,y \ 1,y) = x. L(T(x,y) \ x,x \ 1,x) = R(K(x \ (x / ((y \ x) / T(x,y))),x),x \ 1,x). R(K(x \ (x / ((y \ x) / T(x,y))),x),x \ 1,x) = L(T(x,y) \ x,x \ 1,x). R(T(x,y) \ x,x \ 1,x) = L(T(x,y) \ x,x \ 1,x). T(x \ 1,x) \ R(y,T(x,x \ 1),T(x,x \ 1) \ 1) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1). T(x \ 1,x) \ R(y,T(x,x \ 1),T(x \ 1,x)) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1). T(x \ 1,x) \ R(y,x,x \ 1) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1). T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1) = T(x \ 1,x) \ R(y,x,x \ 1). T(T(x,y) \ x,T(x,x \ 1) \ 1) = T(x \ 1,x) \ R(T(x,y) \ 1,x,x \ 1). T(x \ 1,x) \ R(T(x,y) \ 1,x,x \ 1) = T(T(x,y) \ x,T(x,x \ 1) \ 1). T(x * T(y,y \ 1),T(y,y \ 1) \ 1) = T(y \ 1,y) \ R(x,y,y \ 1). T(x * T(y,y \ 1),T(y \ 1,y)) = T(y \ 1,y) \ R(x,y,y \ 1). T(x,T(y \ 1,y)) != z | T(x,y \ 1) = z. T(x * T(y,y \ 1),y \ 1) = T(y \ 1,y) \ R(x,y,y \ 1). T(x \ 1,x) \ R(y,x,x \ 1) = T(y * T(x,x \ 1),x \ 1). x != T(y * T(z,z \ 1),z \ 1) | R((z \ 1) \ y,1 / z,z) = x. R((x \ 1) \ y,1 / x,x) = T(x \ 1,x) \ R(y,x,x \ 1). T(x \ 1,x) \ R(y,x,x \ 1) = R((x \ 1) \ y,1 / x,x). x != R(y,1 / z,z) | R(y,z \ 1,z) = x. R((x \ 1) \ y,x \ 1,x) = T(x \ 1,x) \ R(y,x,x \ 1). T(x \ 1,x) \ R(y,x,x \ 1) = R((x \ 1) \ y,x \ 1,x). T(x \ 1,x) \ R(y,x,x \ 1) != z | R((x \ 1) \ y,x \ 1,x) = z. R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,T(x,x \ 1) \ 1). R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,T(x \ 1,x)). x != T(y,T(z \ 1,z)) | T(y,z \ 1) = x. T(T(x,y) \ x,x \ 1) = R((x \ 1) \ (T(x,y) \ 1),x \ 1,x). R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,x \ 1). x != T(T(y,z) \ y,y \ 1) | T(y,z) \ y = x. T(x,y) \ x = R((x \ 1) \ (T(x,y) \ 1),x \ 1,x). R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(x,y) \ x. R(T(x,y) \ x,x \ 1,x) = T(x,y) \ x. R(T(x,y) \ x,x \ 1,x) != z | L(T(x,y) \ x,x \ 1,x) = z. L(T(x,y) \ x,x \ 1,x) = T(x,y) \ x. L(T(x,y) \ x,T(x,y),y) = L((x * y) \ (y * x),x \ 1,x). L(T(x,y) \ z,T(x,y),y) != u | (x * y) \ (y * z) = u. (x * y) \ (y * x) = L((x * y) \ (y * x),x \ 1,x). L((x * y) \ (y * x),x \ 1,x) = (x * y) \ (y * x). K(x,y) = L((y * x) \ (x * y),y \ 1,y). K(x,y) = L(K(x,y),y \ 1,y). L(K(x,y),y \ 1,y) = K(x,y). R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x. 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 / y) \ T(x,(x / y) \ 1) = x * (y / x). x * (T(x,x \ y) \ x) = y / (y / x). x / (x / y) = y * (T(y,y \ x) \ y). T(x,x \ y) = T(x,(x / y) \ 1). T(x,(x / y) \ 1) = T(x,x \ y). (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. T(x / (x / y),y \ x) = y. T(x,y) / (x * y) = x / (y * x). x != y / (z * y) | R(1 / z,z,y) = x. R(1 / x,x,y) = T(y,x) / (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. x * (y * (T(z,x) / y)) = (y * (z / y)) * x. x * (y * ((x \ z) / y)) = (y * ((z / x) / y)) * x. (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x)). (x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) != w | ((x * ((u / z) / x)) * z) * (u \ y) = w. ((x * ((y / z) / x)) * z) * (y \ u) = (z * (y \ u)) * (x * (((z * (y \ u)) \ u) / x)). (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z). ((x \ (y / z)) * x) * z != u | ((x \ (y * (z \ 1))) * x) / (z \ 1) = u. ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x). ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x). K(x / y,z) * x = y * T(y \ x,z). x != y \ T(y,z) | (1 / y) * T((1 / y) \ 1,z) = x. (1 / x) * T((1 / x) \ 1,y) = K(x,y). K(x,y) = (1 / x) * T((1 / x) \ 1,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),x) = K(y,x). 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)). (x * ((y * z) / y)) / L(z,K(y,z),x) = x * K(y,z). R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y). K(x \ (x / (y \ z)),x) != u | y \ (z * T(z \ y,x)) = u. x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z). x * T(x \ y,z) = y * K((y \ x) \ 1,z). x \ T(x * y,z) = y * K((y \ (x \ 1)) \ 1,z). K((x * y) \ 1,x) != z | ((x \ (1 / y)) * x) * y = z. (x \ y) * T((x \ y) \ y,z) = K(x,z) * 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) != z | z = K(y,x) \ 1. K(x,y) != z | K(y,x) \ 1 = z. L(x,K(y,y \ z),z) = (y * (z / y)) \ (z * (K(y,y \ z) * x)). (x * (y / x)) \ (y * (K(x,x \ y) * z)) = L(z,K(x,x \ y),y). 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 * T(y \ x,z)) = K(z,x / y). (x / y) * ((z * ((x / y) \ 1)) / z) != u | (x * ((z * (x \ y)) / z)) / y = u. (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1). K(x,y) * T(x,z) != u | K(x,z) * T(x,y) = u. x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z)). x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z * y)). T(x,y) * z = (x * z) * K(((x * z) \ z) \ 1,y). (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y. 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). 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),z,u) \ 1 = K(y,R(1 / x,z,u) \ 1). K(x,R(1 / y,z,u) \ 1) = R(K(y,x),z,u) \ 1. x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z). L(K(x,y),z,u) \ w = K(y,L(x \ 1,z,u) \ 1) * w. K(x,L(y \ 1,z,u) \ 1) * w = L(K(y,x),z,u) \ w. (x * (y * ((z * (y \ (x \ u))) / z))) / u = K(z,((x * y) / u) \ 1). x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1))). 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. K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u). (x * ((y * z) / y)) / z = x * K(y,z). L(K(x,y),x,z) != u | (z * x) \ (z * T(x,y)) = u. (x * y) \ (x * T(y,z)) = K(y,z). (x * y) * K(y,z) != u | u = x * T(y,z). (x * y) * K(y,z) != u | x * T(y,z) = u. x \ (y * T(y \ x,z)) != u | K(y \ x,z) = u. K(x,y \ z) != T(u,z) | K(x,z / y) = u. T(x,y) != K(z,u \ y) | K(z,y / u) = x. K((x \ y) \ 1,z) != u | T(K(x / y,z),x) = u. T(K(x / y,z),x) = K(y \ x,z). K(x \ 1,y) = K((z * x) \ z,y). K((x * y) \ x,z) = K(y \ 1,z). x != K((y \ 1) \ 1,z) | K(y,z) = x. K(x,y) = K((z * (x \ 1)) \ z,y). K((x * (y \ 1)) \ x,z) = K(y,z). K((x * (y \ 1)) \ x,z) != u | K(L(y,y \ 1,x),z) = u. K(L(x,x \ 1,y),z) = K(x,z). x / y = (x / ((z * y) / z)) * K(z,y). (x / ((y * z) / y)) * K(y,z) = x / z. x \ (y \ ((z \ (y * x)) * z)) = K((y \ z) \ x,z). x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y). (x / (y / z)) * K(z,z \ y) = x / (z \ y). K((x \ y) \ 1,z) != u | K(y \ x,z) = u. T(K(x / y,z),x) != u | K(y \ x,z) = u. x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z). x \ (y \ ((z \ (y * x)) * z)) != u | K((y \ z) \ x,z) = u. K((x \ y) \ z,y) = K((y / x) \ z,y). K((x / y) \ z,x) = K((y \ x) \ z,x). K(x,L(y,z / y,u)) != w | L(K(x,y),z,u) = w. x != L(y,z,u) | (u * z) \ (u * (z * y)) = x. (x * y) \ (x * (y * K(z,u))) = K(L(z,y / z,x),u). K(L(x,y / x,z),u) = (z * y) \ (z * (y * K(x,u))). K(L(x,y / x,z),u) != w | L(K(x,u),y,z) = w. K(L(x \ y,x,z),u) != w | L(K(x \ y,u),y,z) = w. L(K(x,y),y \ 1,y) != z | K(x,y) = z. K(x \ (y \ 1),y) = K((y * x) \ 1,y). K((x * y) \ 1,x) = K(y \ (x \ 1),x). L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y). ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x). K((x * y) \ (x * z),u) != w | L(K(y \ z,u),z,x) = w. 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(1 / y,z,u) \ 1) != w | R(K(y,x),z,u) \ 1 = w. R(K(x,y),z,u) \ 1 = R(K(y,x),z,u). R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z)). L(K(x,y),z,u) * w = L(K(y,x),z,u) \ w. L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w. x / (y * ((z \ (y \ x)) * z)) != u | K(z,x / (z * y)) = u. K(x,y / (x * z)) = K(x,y / (x / (z \ 1))). K(x,y / (x / (z \ 1))) = K(x,y / (x * z)). 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). (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). 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)). T(K(x,y) * (z * K(y,x)),u) != K(x,y) * w | T(z,u) * K(y,x) = w. (x * (y / x)) \ (y * z) = L(K(x \ y,x) * z,K(x,x \ y),y). L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z). L(K(x \ (y \ z),u),y \ z,y) != w | K((y * x) \ z,u) = 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). K((x * (y / x)) \ z,y) = K(y \ z,y). (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1). x != K(y,(z / u) \ 1) | K(y,u / z) = x. K(x,y / (z * x)) = (z * (x * ((z \ y) / x))) / y. (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y)). R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y. R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x). (((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). K(x,y \ (x \ 1)) = K(x,z / (x / ((y * z) \ 1))). K(x,y / (x / ((z * y) \ 1))) = K(x,z \ (x \ 1)). K(x,y / (x / (z \ 1))) != u | K(x,y / (x * z)) = u. K(x,y / (x * (z * y))) = K(x,z \ (x \ 1)). K(x,L(y,z,x)) = K(x,y). T(x,L(y,z,y)) = x / K(y,x). K(x,T(y \ (x * z),u)) = K(x,T((x \ y) \ z,u)). K(x,T((x \ y) \ z,u)) = K(x,T(y \ (x * z),u)). T(x,y) = x * K(R(x,z,x),y). x * K(R(x,y,x),z) = T(x,z). x != y / K(z,u) | y * K(u,z) = x. x * K(x,y) = T(x,L(y,z,y)). T(x,L(y,z,y)) = x * K(x,y). K(x,L(y,z,y)) = K(x,y). L(K(x,y),z,y) = K(x,y). K(L(x,y,z),z) = K(x,z). K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y). x != T(K(y,z),u) | K((y \ u) \ u,z) = x. K((x \ y) \ y,z) = K(x,T(z,y)). x != T(K(y,z),u) | K(u,K(z,y)) * K(y,z) = x. K(x,K(y,z)) * K(z,y) = K(z,T(y,x)). x != T(K(y / z,u),y) | K(z \ y,u) = x. K(x \ y,z) = K(y / x,T(z,y)). K(x / y,T(z,x)) = K(y \ x,z). K(x,T(T(y,z),u)) = T(K(x,T(y,u)),z). K(x,T(y,z)) \ 1 = K(y,T(x,z)). T(K(x,y),z) = K(x,T(y,x \ z)). K(x,T(y,x \ z)) = T(K(x,y),z). K(T(x,y),T(z,u)) = K(x,T(T(z,y),u)). K(x,y) = K((z * x) / z,T(y,z)). K((x * y) / x,T(z,x)) = K(y,z). 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). 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,z)) != u | K(T(x,z),y) = u. x != T(K(y,z),u) | K(y,T(z,u)) = x. K(x,T(y,z)) = K(x,T(y,x \ z)). K(x,T(y,x \ z)) = K(x,T(y,z)). K(x,T(y,z)) = K(x,T(y,x * z)). K(x,T(y,x * z)) = K(x,T(y,z)). R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z)). x != K(y,T(z,u)) | K(T(y,u),z) = x. K(T(x,y),z) = K(x,T(z,x * y)). K(x,T(y,x * z)) = K(T(x,z),y). T(K(x,y),z) != u | K(T(x,z),y) = u. (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w)). x * y != T(z,u * K(z,w)) | x \ T(z,u) = y. x \ T(x,y) = K(x,y * K(x,z)). K(x,y * K(x,z)) = x \ T(x,y). K(x,K(x,y) * z) = K(x,z). K(x,R(K(x,y),z,u) * w) = K(x,w). K(x,y * K(x,z)) != u | K(x,y) = u. K(x,K(R(x,y,z),u) * w) = K(x,w). K(x,y / (x \ z)) != u | K(x,y / (z / x)) = u. K(x,T(y,x * z)) != u | K(x,T(y,z)) = u. K(x,K(y,z)) * T(x,y) = T(x,T(y,z)). K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). K(x,K(y,z)) * K(y,x) = T(K(y,x),z). K(x,K(y,z)) * K(y,x) = K(y,T(x,z)). x * y != y * K(z,T(u,y)) | K(z,u) = x. K(x,y) = T(K(x,T(y,z)),z). T(K(x,T(y,z)),z) = K(x,y). K(T(x,y),T(z,y)) = K(x,z). K(x \ y,T(z,y)) = K(y / x,z). K(x,y / z) = K(x,T(z \ y,y)). K(x,T(y \ z,z)) = K(x,z / y). (x * K(y,z)) / x = K(y,T(z,x)). K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w). K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w). K(T(x,y),y \ z) = K(x,z / y). L(K(x,y),z * T(x,u),w) = K(L(T(x,u),z,w),T(y,u)). R(K(x,y),T(y,z) * u,w) = K(T(x,z),R(T(y,z),u,w)). (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). L(K(x \ y,T(z,u * y)),y,u) = K((u * y) / (u * x),z). K(x,T(y \ (x * z),z)) = K(x,(x * z) / y). 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(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x))). K(x,K(y,z)) * T(z,y) = T(z,T(y,x)). K(x,T(y,z)) != K(x,y) * u | K(x,K(y,z)) = u. K(x,K(y,z)) * K(y,x) != u | K(y,T(x,z)) = u. K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z)). 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)). K(L(x,x \ 1,y),z) != u | K(x,z) = u. K(T(x,y),T(z,y)) = K(L(x,T(x,y) \ 1,u),z). 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(x,T(y \ z,z)) != u | K(x,z / y) = u. K(x,y / (x \ z)) = K(x,T(z \ (x * y),y)). K(x,T(y \ (x * z),z)) = K(x,z / (x \ y)). K(x,T(y \ (x * z),z)) != u | K(x,(x * z) / y) = u. K(x,(x * y) / z) = K(x,y / (x \ z)). K(x,y / z) = K(x,(x \ y) / (x \ z)). K(x,(x \ y) / (x \ z)) = K(x,y / z). K(x,(x \ y) / (z / x)) = K(x,y / z). K(x,(x \ y) / z) = K(x,y / (z * x)). K(x,(x \ y) / (x \ z)) != u | K(x,y / z) = u. K(x,y / z) = K(x,y / ((x \ z) * x)). K(x,y / ((x \ z) * x)) = K(x,y / z). K(x,y / (z * x)) = K(x,y / (x * z)). x != K(y,z / (y * (u * z))) | K(y,u \ (y \ 1)) = x. 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) / (z * x)) = K(x,R(y / x,x,z)). K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x)). 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)). K(x,R(y / x,z,u)) != w | K(x,R(x \ y,z,u)) = w. K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x)). K(x,y \ z) = K(x,(y * K(u,x)) \ z). K(x,(y * K(z,x)) \ u) = K(x,y \ u). K(T(x,y),(z * K(u,x)) \ w) = K(T(x,y),z \ w). x != K(y,L(T(z,y),u,w)) | K(y,L(z,u,w)) = x. K(x,L(y,x,z)) = K(x,z \ (x \ (z * (y * x)))). K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y)). K((x * (y / x)) \ z,y) != u | K(y \ z,y) = u. K(x \ (x * y),x) = K(K(z \ x,z) * y,x). K(x \ (x * y),z) != u | K(y,z) = u. 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). R(K(x,y),x * z,u) != w | K(R(x,z,u),y) = w. K(R(x,y,z),T(u,w)) = K(R(x,y,z),T(u,x \ w)). K(R(x,y,z),T(u,x \ w)) = K(R(x,y,z),T(u,w)). R(K(x,y),z,R(x,u,w)) = K(x,y). K(R(x,y,R(x,z,u)),w) = K(x,w). x != K(L(T(y,z),u,w),T(v5,z)) | K(L(y,u,w),v5) = x. K(L(x,y,z),u) = L(K(x,u),y * T(x,w),z). 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),T(x,z) * u,w) = K(L(T(x,z),u,w),T(y,z)). K(T(x,y),(z * K(u,x)) \ w) != v5 | K(T(x,y),z \ w) = v5. K(T(x,y),y \ z) = K(x,z / (y * K(u,x))). K(T(x,y),y \ z) != u | K(x,z / y) = u. K(x,y / z) = K(x,y / (z * K(u,x))). K(x,y / (z * K(u,x))) = K(x,y / z). K(x,y / z) = K(x,y / (z * K(x,u))). K(x,y / (z * K(x,u))) = K(x,y / 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 * x) * u)) = K(x,y / ((x * z) * u)). x != K(R(y,z,u),T(w,y \ v5)) | K(R(y,z,u),T(w,v5)) = x. K(R(x,y,z),T(u,w)) = K(R(w / (w / x),y,z),u). 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(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). K(L(x,y,z),u) = L(K(x,u),T(x,w) * y,z). L(K(x,y),T(x,z) * u,w) = K(L(x,u,w),y). L(K(x,y),z,u) = K(L(x,T(x,w) \ z,u),y). K(L(x,T(x,y) \ z,u),w) = L(K(x,w),z,u). K(L(x,T(x,y) \ 1,z),u) != w | w = K(x,u). K(L(x,T(x,y) \ 1,z),u) != w | K(x,u) = w. K(T(x,y),T(z,y)) != u | K(x,z) = u. K(T(x,y),R(T(z,y),u,w)) != v5 | K(x,R(z,u,w)) = v5. K(x,T(T(y,z),z)) != u | K(x,y) = u. R(K(x,y),T(y,z) * u,w) != v5 | K(x,R(y,u,w)) = v5. R(K(x,y),y * z,u) != w | K(x,R(y,z,u)) = w. K(x,T(y,z)) = K(R(x,z,R(x,u,w)),T(y,z * R(x,u,w))). K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) = K(x,T(w,y)). L(K(x,T(T(y,z * u),u)),u,z) = K((z * u) / (z * (x \ u)),y). (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(R(x,y / x,z),u) = K((y * z) / ((y / x) * z),T(u,y)). K(R(x,y,R(x,z,u)),w) != v5 | K(x,w) = v5. 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)). K(x,T(y,z / R(x,u,w))) != v5 | K(x,T(y,R(x,u,w) \ z)) = v5. 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)) | K(y,z) * K(y,K(z,u)) = x. K(x,y) * K(x,K(y,z)) = K(x,T(y,R(x,u,w) * z)). 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,(x * z) * u)) = K(x,K(y,z * u)). K(x,K(y,z * u)) * K(y,x) = K(y,T(x,(x * 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((y * z) / (u * z),T(w,y)) | R(K(u \ y,w),y,z) = x. 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(x,R(y,x,z)) = K(R(x,y,z),y). K(R(x,y,z),y) = K(x,R(y,x,z)). T(x,R(y,x,z)) = x * K(R(x,y,z),y). x * K(R(x,y,z),y) = T(x,R(y,x,z)). 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). R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * 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 * 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. 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). x != K(y,(z / u) \ (y \ 1)) | K(y,u / (z * y)) = x. K(x,y / ((z \ y) * x)) = K(x,(z * (y / z)) / ((y / z) * x)). K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x)). K(x,(y * z) / (z * x)) != u | K(x,R(x \ y,x,z)) = u. 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)). R(K(T(x,y),T(z,y * u)),y,u) = ((y * u) \ ((y * K(z,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). R(K(x,T(T(y,z),z * u)),z,u) = ((z * u) \ ((z * K(y,x)) * u)) \ 1. R(K(x,T(T(y,z),z * u)),z,u) != w | (z * u) \ ((z * K(x,y)) * u) = w. (x * y) \ ((x * K(z,u)) * y) = ((x * y) \ ((x * K(u,z)) * y)) \ 1. ((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. x != K(y,z) \ u | K(z,y) * u = x. K(x,(y * z) / (y * (u \ z))) * w = L(K(T(T(x,z),y * z),u),z,y) * w. L(K(T(T(x,y),z * y),u),y,z) * w = K(x,(z * y) / (z * (u \ y))) * w. 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) != 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. L(K(T(x,y),T(z,u * y)),y,u) * w = K(x,(u * y) / (u * (z \ y))) * w. L(K(x,T(T(y,z * u),u)),u,z) * w = K(x,(z * u) / (z * (y \ u))) * 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))). K((x * y) / (x * (z \ y)),u) != w | (x * (K(z,u) * y)) / (x * y) = w. (x * (K(y,z) * u)) / (x * u) = K(y,(x * u) / (x * (z \ u))). K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z). K(x,((y * x) * z) / ((y * x) * (y \ z))) != u | L(K(x,y),z,y * x) = u. R(K(x,(y / z) / u),y / z,z) != w | K(x,y / (u * z)) = w. K(x,y / ((z * x) * u)) = ((z * (x * ((z \ (y / u)) / x))) * u) / y. ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u)). (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z). (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)). (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)))) | K(y,L(u,y,z)) = x. K(x,L(y,x,z)) = L(K(x,y),T(z,y * x),y * x). 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). K(x,L(y,x,z)) != u | K(x,y) = u. K(x,y) = L(K(x,y),z,y * x). L(K(x,y),z,y * x) = K(x,y). (x * (y * z)) * K(z,L(y,z,x)) = (y * z) * T(x * K(z,y),y * z). (x * (y * z)) * K(z,L(y,z,x)) != u | x * (z * y) = u. 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 * K(y,z)) * (z * y) = x * (y * z). x / (y * z) = (x / (z * y)) * K(z,y). (x / (y * z)) * K(y,z) = x / (z * y). K(x,y / (z * x)) != u | K(x,y / (x * z)) = u. (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)). (x * (y * ((x \ z) / y))) / z != u | K(y,z / (x * y)) = u. 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). K(x,y / ((z * x) * u)) != w | K(x,y / ((x * z) * u)) = w. 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)). L(K(x,y),z,y * x) != u | K(x,y) = u. K(x,y) = K(x,R(y,x,z)). K(x,R(y,x,z)) = K(x,y). K(x,R(y,x,z)) != u | K(R(x,y,z),y) = u. K(R(x,y,z),y) = K(x,y). K(x,R(x \ (y / z),x,y / (y / z))) != u | K(x,y / (z * x)) = u. K(x,y / (z * x)) = K(x,x \ (y / z)). x != K(y,z) | K(R(y,z,u),z) = x. K(R(x,y,z),y) = K(R(x,y,u),y). x * K(R(x,y,z),y) = T(x,R(y,x,u)). T(x,R(y,x,z)) = x * K(R(x,y,u),y). K(x,y / (x * z)) = K(x,x \ (y / z)). x != y * K(R(y,z,y),u) | T(y,u) = x. T(x,y) = T(x,R(y,x,z)). 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 * K(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u)). 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(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) | T(y,y \ z) = x. T(R(x,y,z),R(x,y,z) \ u) = 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),R(x,z,u) \ y). R(T(x,R(x,y,z) \ u),y,z) = R(T(x,(u * (y * z)) / ((x * y) * z)),y,z). 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(y / x,z,u) \ y) \ y. (R(x / y,z,u) \ x) \ x = R(y \ x,z,u). x / (x / R(y \ x,z,u)) = R(x / y,z,u). x / (x / R(y,z,u)) = R(x / (x / y),z,u). end_of_list.