============================== Prover9 =============================== Prover9 (64) version 2017-09A, September 2017. Process 17600 was started by veroff on theorem, Mon Jan 20 20:57:41 2020 The command was "prover9 -f lbol_to_aK1.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file lbol_to_aK1.in assign(order,kbo). set(lex_order_vars). set(para_from_small). clear(back_demod). set(restrict_denials). assign(max_weight,5). formulas(assumptions). 1 * x = x. x * 1 = x. x \ (x * y) = y. x * (x \ y) = y. (x * y) / y = x. (x / y) * y = x. x * y = u & x * z = u -> y = z. y * x = u & z * x = u -> y = z. x * y = x * z -> y = z. y * x = z * x -> y = z. x != y | z * x = z * y. x != y | x * z = y * z. (x * (y * z)) \ ((x * y) * z) = a(x,y,z) # label("associator"). (x * y) \ (y * x) = K(y,x) # label("commutator"). (y * x) \ (y * (x * u)) = L(u,x,y). ((u * x) * y) / (x * y) = R(u,x,y). x \ (u * x) = T(u,x). a(x,y,z) = 1 -> L(z,y,x) = z. L(x,y,z) = x -> a(z,y,x) = 1. T(x,y) = x -> T(y,x) = y. T(x,y) = x -> K(x,y) = 1. K(x,y) = 1 -> T(x,y) = x. T(T(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). (x * (y * x)) * z = x * (y * (x * z)) # label("left Bol"). end_of_list. formulas(goals). a(K(x,y),z,u) = 1 # label("aK1"). end_of_list. formulas(hints). a(K(x,y),z,u) = 1. 1 * x = x. x * 1 = x. x \ (x * y) = y. x * (x \ y) = y. (x * y) / y = x. (x / y) * y = x. x * y != z | x * u != z | u = y. x * y != z | u * y != z | u = x. x * y != x * z | y = z. x * y != z * y | x = z. (x * (y * z)) \ ((x * y) * z) = a(x,y,z). a(x,y,z) = (x * (y * z)) \ ((x * y) * z). (x * y) \ (y * x) = K(y,x). K(x,y) = (y * x) \ (x * y). (x * y) \ (x * (y * z)) = L(z,y,x). L(x,y,z) = (z * y) \ (z * (y * x)). ((x * y) * z) / (y * z) = R(x,y,z). R(x,y,z) = ((x * y) * z) / (y * z). x \ (y * x) = T(y,x). T(x,y) = y \ (x * y). a(x,y,z) != 1 | L(z,y,x) = z. L(x,y,z) != x | a(z,y,x) = 1. T(x,y) != x | T(y,x) = y. T(x,y) != x | K(x,y) = 1. K(x,y) != 1 | T(x,y) = x. T(T(x,y),z) = T(T(x,z),y). T(L(x,y,z),u) = L(T(x,u),y,z). L(T(x,y),z,u) = T(L(x,z,u),y). T(R(x,y,z),u) = R(T(x,u),y,z). R(T(x,y),z,u) = T(R(x,z,u),y). L(R(x,y,z),u,w) = R(L(x,u,w),y,z). R(L(x,y,z),u,w) = L(R(x,u,w),y,z). L(L(x,y,z),u,w) = L(L(x,u,w),y,z). R(R(x,y,z),u,w) = R(R(x,u,w),y,z). (x * (y * x)) * z = x * (y * (x * z)). a(K(c1,c2),c3,c4) != 1. 1 \ x = x. x \ x = 1. x / 1 = x. x / (y \ x) = y. (x / y) \ x = y. 1 * x != y | x = y. x != y * z | y \ x = z. x * y != z | x \ z = y. x * y != z * (z \ (x * u)) | y = u. x * (x \ (y * z)) != y * u | u = z. x * 1 != y | x = y. x * y != ((z * y) * u) / u | x = z. ((x * y) * z) / z != u * y | u = x. x != y * z | x / z = y. x * y != z | z / y = x. (x * (y * z)) * a(x,y,z) = (x * y) * z. a(x,y,y \ z) = (x * z) \ ((x * y) * (y \ z)). (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y). a(x / y,y,z) = ((x / y) * (y * z)) \ (x * z). ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). (x * y) * K(y,x) = y * x. K(x \ y,x) = y \ ((x \ y) * x). x \ ((y \ x) * y) = K(y \ x,y). K(x,y / x) = y \ (x * (y / x)). x \ (y * (x / y)) = K(y,x / y). K(x / y,y) = (y * (x / y)) \ x. (x * (y / x)) \ y = K(y / x,x). (x * y) * L(z,y,x) = x * (y * z). L(x,y \ z,y) = z \ (y * ((y \ z) * x)). x \ (y * ((y \ x) * z)) = L(z,y \ x,y). L(x \ y,x,z) = (z * x) \ (z * y). L(x,y,z / y) = z \ ((z / y) * (y * x)). x \ ((x / y) * (y * z)) = L(z,y,x / y). R(x,x \ y,z) = (y * z) / ((x \ y) * z). R(x,y,y \ z) = ((x * y) * (y \ z)) / z. ((x * y) * (y \ z)) / z = R(x,y,y \ z). R(x,y,z) * (y * z) = (x * y) * z. R(x / y,y,z) = (x * z) / (y * z). R(x,y / z,z) = ((x * (y / z)) * z) / y. ((x * (y / z)) * z) / y = R(x,y / z,z). T(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. x * y != z | x = z / y. x * (y * x) = (x * (y * (x * z))) / z. (x * (y * (x * z))) / z = x * (y * x). (x * x) * y = x * (1 * (x * y)). x * (1 * (x * y)) = (x * x) * y. (x * y) * z = x * ((y / x) * (x * z)). x * ((y / x) * (x * z)) = (x * y) * z. T(x,y) = T(T(x,y),x). T(T(x,y),x) = T(x,y). (x * y) / K(x,y) = y * x. (x * (y * z)) / L(z,y,x) = x * y. (x * y) / T(x,y) = y. R(x,y,z) \ ((x * y) * z) = y * z. T(1,x) = 1. x * y != (x * (z * x)) * u | y = z * (x * u). T(x * (y * x),x) = y * (x * x). x * y != y * z | T(x,y) = z. x * y != z * x | T(z,x) = y. K(x,T(y,x)) = (T(y,x) * x) \ (y * x). (T(x,y) * y) \ (x * y) = K(y,T(x,y)). 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). T(x,T(y,x)) = T(y,x) \ (y * x). T(x,y) \ (x * y) = T(y,T(x,y)). x * T(T(y,x),z) = T(y,z) * x. x * L(T(y,x),z,u) = L(y,z,u) * x. x * R(T(y,x),z,u) = R(y,z,u) * x. T(R(x,y,z),y * z) = (y * z) \ ((x * y) * z). (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y). K(T(x,y),x) = 1. x * T(x,y) = T(x,y) * x. T(x,y) * x = x * T(x,y). K(x \ y,y / x) = 1. x / T(y,y \ x) = y \ x. x * K(y \ x,y) = (y \ x) * y. L(x,K(y,z),z * y) = (y * z) \ ((z * y) * (K(y,z) * x)). (x * y) \ ((y * x) * (K(x,y) * z)) = L(z,K(x,y),y * x). ((x / y) * (y \ x)) * 1 = (y \ x) * (x / y). T((x \ y) \ y,z) = T(T(x,z),x \ y). T(T(x,y),x \ z) = T((x \ z) \ z,y). (x * y) / K(y,T(x,y)) = T(x,y) * y. K(x \ 1,x) = (x \ 1) * x. a(x,y \ 1,y) = (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y). (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y). R(x,y \ 1,y) = ((x * (y \ 1)) * y) / K(y \ 1,y). ((x * (y \ 1)) * y) / K(y \ 1,y) = R(x,y \ 1,y). K(x,1 / x) = x * (1 / x). x * (x * y) = (x * x) * y. (x * x) * y = x * (x * y). (x * (x * y)) / y = x * x. (x * y) / (x \ y) = x * x. x / (x \ 1) = x * x. x / ((x / y) \ y) = (x / y) * (x / y). (1 / x) / x = (1 / x) * (1 / x). (1 / x) * (1 / x) = (1 / x) / x. T(x * y,x) = (y / x) * (x * x). (x / y) * (y * y) = T(y * x,y). x * T(x \ y,z) = T(y / x,z) * x. T(x / y,z) * y = y * T(y \ x,z). T(x * y,x) / (x * x) = y / x. T(x,x) / (x * x) = 1 / x. T(x,y) / (y * y) = (y \ x) / y. x / (x * x) = 1 / x. (1 / x) \ x = x * x. 1 / (x * x) = (x \ 1) / x. (x \ 1) / x = 1 / (x * x). (1 / (x * x)) * x = x \ 1. (x * y) * L(z,y,x) != x * u | u = y * z. (x * y) * L(z,y,x) != x * u | y * z = u. x * L(y,z \ x,z) = z * ((z \ x) * y). x * (y * z) != (x * y) * u | L(z,y,x) = u. (x * y) * z != x * (y * u) | L(u,y,x) = z. L(x \ 1,x,y) = (y * x) \ y. L((x \ y) \ z,x \ y,x) = y \ (x * z). L(x \ (y \ z),x,y) = (y * x) \ z. L(x \ y,x,z / y) = ((z / y) * x) \ z. T(x,x * y) = L(y \ (x * y),y,x). L(x \ (y * x),x,y) = T(y,y * x). (x * y) / L(z \ y,z,x) = x * z. L(x \ T(y,z),x,z) = (z * x) \ (y * z). x / L(y \ 1,y,x) = x * y. x / L(y,1 / y,x) = x * (1 / y). x * (y * z) != (y * y) * z | x = y. R(x,x,y) = x. L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. R(T(x,y),x,z) = T(x,y). R(x,y,z) = R(R(x,y,z),x,u). R(R(x,y,z),x,u) = R(x,y,z). R(T(x,y),z,u) = R(R(T(x,y),z,u),x,w). R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u). T(x,y) * (x * z) = (T(x,y) * x) * z. (T(x,y) * x) * z = T(x,y) * (x * z). R(x,y,z) * (x * u) = (R(x,y,z) * x) * u. (R(x,y,z) * x) * u = R(x,y,z) * (x * u). R(1 / x,x,y) = y / (x * y). R((x / y) / z,z,y) = x / (z * y). R(x / (y / z),y / z,z) = (x * z) / y. R(x / y,y,z) \ (x * z) = y * z. T(R(x / y,y,z),y * z) = (y * z) \ (x * z). R(x,x \ y,z) \ (y * z) = (x \ y) * z. R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z. L(x \ (y \ ((y * x) * z)),x,y) = z. L(T(x,y),y,x) = T(x,x * y). (x * (y * z)) / (x \ z) = x * (y * x). x \ ((x * y) * z) = (y / x) * (x * z). x * y != (x * z) * L(u,z,x) | y = z * u. (x / y) * (y * L(z,x,y)) = x * z. x * ((y / x) * z) = (x * y) * (x \ z). (x * y) * (x \ z) = x * ((y / x) * z). (x / y) \ (x * z) = y * L(z,x,y). (x / y) \ z = y * L(x \ z,x,y). x * L(y \ z,y,x) = (y / x) \ z. x \ ((y / x) \ z) = L(y \ z,y,x). L(x \ y,x,z) = z \ ((x / z) \ y). x * ((x * y) \ z) = (y / x) \ (x \ z). (x / y) \ (y \ z) = y * ((y * x) \ z). L(x \ ((x / y) * z),x,y) = y \ z. L((x * y) \ z,x * y,y) = y \ (x \ z). L(x \ (x / y),x,y) = y \ 1. L(x \ y,x,z \ x) = (z \ x) \ (z \ y). L((x * y) \ z,x * y,K(x,y)) = K(x,y) \ ((y * x) \ z). x \ ((y / x) \ z) = (x * y) \ (x * z). (x * y) \ (x * z) = x \ ((y / x) \ z). x \ 1 = (x * y) \ (x * (y / x)). (x * y) \ (x * (y / x)) = x \ 1. (x * y) * (x \ 1) = x * (y / x). (x * (y * x)) \ (x * y) = x \ 1. (x * y) * (x \ 1) != x * z | z = y / x. (x * y) * (x \ 1) != x * z | y / x = z. x * (y \ 1) = y * ((y \ x) / y). x * ((x \ y) / x) = y * (x \ 1). R(x,y,x \ 1) = (x * (y / x)) / (y * (x \ 1)). (x * (y / x)) / (y * (x \ 1)) = R(x,y,x \ 1). (x * y) * (y \ 1) = y * (T(x,y) / y). (x * y) / (x \ 1) = x * (y * x). x \ (y * (x \ 1)) = (x \ y) / x. x * (y \ 1) != y * z | (y \ x) / y = z. x / (y \ 1) = y * ((y \ x) * y). x * ((x \ y) * x) = y / (x \ 1). (x * y) / (y \ 1) = y * (T(x,y) * y). x \ (y / (x \ 1)) = (x \ y) * x. a(x,x \ y,x) = (y / (x \ 1)) \ ((x * (x \ y)) * x). (x / (y \ 1)) \ ((y * (y \ x)) * y) = a(y,y \ x,y). x * L(x,y,z) = L(x,y,z) * x. L(x,y,z) * x = x * L(x,y,z). 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 * T(y,y * x) = L(y,x,y) * x. (x \ y) * T(x,y) = L(x,x \ y,x) * (x \ y). L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). x * R(x,y,z) = R(x,y,z) * x. R(x,y,z) * x = x * R(x,y,z). x * R(x \ y,z,u) = R(y / x,z,u) * x. R(x / y,z,u) * y = y * R(y \ x,z,u). a(x,R(y,z,u),y) = (x * (y * R(y,z,u))) \ ((x * R(y,z,u)) * y). (x * (y * R(y,z,u))) \ ((x * R(y,z,u)) * y) = a(x,R(y,z,u),y). R(x,R(y,z,u),y) * (y * R(y,z,u)) = (x * R(y,z,u)) * y. 1 / ((1 / x) \ x) = (1 / x) / x. 1 / (x * x) = (1 / x) / x. (1 / x) / x = 1 / (x * x). (1 / (x * x)) * x = 1 / x. 1 / x = x \ 1. x * (1 / x) = 1. (x \ 1) \ 1 = x. T(x \ 1,x) = x \ 1. x / L(1 / y,y,x) = x * y. R(x \ 1,x,y) = y / (x * y). R((1 / x) / y,y,x) = (y * x) \ 1. x * ((x \ 1) * (x * y)) = (x * 1) * y. (x * y) * (1 / x) = x * (y / x). a(x,y,1 / y) = (x * 1) \ ((x * y) * (1 / y)). (x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y). K(x,1 / x) = 1. T(x,x \ 1) = x. T(T(x,y),x \ 1) = T(x,y). T(x,1 / x) = x. K(x \ 1,x) = 1. (x \ 1) * L(x,y,z) = L(x,y,z) * (x \ 1). L(x,y,z) * (x \ 1) = (x \ 1) * L(x,y,z). T(x,y) = T(T(x,y),1 / x). T(T(x,y),1 / x) = T(x,y). (1 / x) * L(x,y,z) = L(x,y,z) * (1 / x). L(x,y,z) * (1 / x) = (1 / x) * L(x,y,z). x * L(x \ 1,y,z) = L(x \ 1,y,z) * x. L(x \ 1,y,z) * x = x * L(x \ 1,y,z). T(x \ 1,T(x,y)) = x \ 1. T(1 / x,T(x,y)) = 1 / x. T(x \ 1,(x \ y) \ y) = x \ 1. T(1 / (x \ 1),T(x \ 1,y)) = x. (x * y) * (1 / y) = y * (T(x,y) / y). T((x \ y) \ y,x \ 1) = (x \ y) \ y. T(x,T(x \ 1,y)) = x. T(x,T(1 / x,y)) = x. T(x,((1 / x) \ y) \ y) = x. R((x \ 1) / y,y,x) = (y * x) \ 1. (x * T(x \ y,z)) / x = T(y / x,z). (x * y) * z != x * (y * u) | z = L(u,y,x). x = L(x,y,T(y,z)). L(x,y,T(y,z)) = x. x * y != (x * z) * (x \ 1) | y = z / x. x * (T(x,y) \ 1) = x / T(x,y). (x * T(x,y)) * z = T(x,y) * (x * z). L(x,y / z,z \ y) = x. L(x,y,(y \ z) \ z) = x. T(x,y) * (x \ z) = (x / T(x,y)) \ z. (x / T(x,y)) \ z = T(x,y) * (x \ z). x \ (x / T(x,y)) = T(x,y) \ 1. (x * y) / (x \ z) = x * ((y / z) * x). x \ (y * z) = ((x \ y) / x) * (x * z). ((x \ y) / x) * (x * z) = x \ (y * z). T(x,y) * z != (T(x,y) * x) * u | z = x * u. (x / T(x,y)) * z = x * (T(x,y) \ z). x * (y \ z) = y * (((y \ x) / y) * z). x * (((x \ y) / x) * z) = y * (x \ z). (x / y) \ (y \ (x * y)) = y * K(x,y). x \ (y * z) = y \ (((y \ x) / y) \ z). x \ (((x \ y) / x) \ z) = y \ (x * z). x * ((x \ 1) * (x * y)) = x * y. (x \ 1) * (x * y) = y. x / (y * x) = y \ 1. (x \ 1) \ y = x * y. (x \ 1) * y = x \ y. x != (y \ 1) * z | y * x = z. (x \ 1) * y != z | x * z = y. R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). T(x \ 1,x * y) = (x * y) \ y. (1 / x) * (x * y) = y. (x \ y) / y = x \ 1. x / y = (y / x) \ 1. (x / y) \ 1 = y / x. (x * y) / ((z * x) * y) = R(z,x,y) \ 1. R(x \ 1,x,y) = x \ 1. x \ y = (1 / x) * y. (1 / x) * y = x \ y. (1 / x) \ y = x * y. a(x \ 1,y,z) = (x \ (y * z)) \ (((x \ 1) * y) * z). (x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z). T(x \ 1,y) = y \ (x \ y). x \ T(y,x \ 1) = y * (x \ 1). T(x,1 / y) = y * (x * (1 / y)). x * (y * (1 / x)) = T(y,1 / x). T(1 / x,x * y) = (x * y) \ y. L(x \ 1,x,y) / y = (y * x) \ 1. (x * y) / (z * y) = R(z / x,x,y) \ 1. R(x / y,y,z) \ 1 = (y * z) / (x * z). 1 / x = (x \ y) / y. (x \ y) / y = 1 / x. (x / y) * (y / x) = 1. 1 / (x / y) = y / x. x * L(y \ 1,y,x) = x / y. L(x \ 1,x,y) = y \ (y / x). (x / y) * ((y / x) * z) = z. (x / y) \ z = (y / x) * z. T(1 / x,y) = y \ (x \ y). x \ T(y,1 / x) = y * (1 / x). T(x,(x * y) \ y) = x. T(x,x \ y) / y = 1 / (x \ y). T(x / y,x \ y) = x / y. ((x * y) \ y) * x = x * ((x * y) \ y). T(x \ 1,x / T(x,y)) = (x / T(x,y)) \ (T(x,y) \ 1). (x / T(x,y)) \ (T(x,y) \ 1) = T(x \ 1,x / T(x,y)). T(x / y,z) = z \ ((y / x) \ z). x \ ((y / z) \ x) = T(z / y,x). (x / y) * z != x * u | z = y * L(u,x,y). (x / y) * (y * z) = x * L(z,y,x). (x / y) * z != T(y * x,y) | z = y * y. (x / y) * T(x * y,x) = x * x. x != (y / z) * u | (z / y) * x = u. (x / y) * z != u | (y / x) * u = z. L(x \ y,x,z) = z \ ((z / x) * y). (x / y) \ (x * L(z,y,x)) = y * z. x * L(y \ z,y,x) = (x / y) * z. x \ ((x * y) * z) = (x / y) \ (x * z). (x / y) \ (x * z) = x \ ((x * y) * z). (x * y) * (x \ z) = x * ((x / y) \ z). (x / y) * (x \ z) = x * ((x * y) \ z). (x * y) \ (x * z) = x \ ((x / y) * z). T(1 / (x * y),y * x) = (y * x) \ K(y,x). T((x / y) / x,y) = (x / y) / x. (x \ y) * (x / y) = (x / y) * (x \ y). (x / y) * (x \ y) = (x \ y) * (x / y). (x / y) / L(y \ 1,y,x) = x. x * ((x * y) \ x) = x / y. x * L(1 / y,y,x) = x / y. x * L(y,y \ 1,x) = x / (y \ 1). ((x \ y) \ y) * (x \ 1) = ((x \ y) \ y) / x. x \ (x / y) = (x * y) \ x. (x * y) \ x = x \ (x / y). x * (y \ x) = x / (x \ y). x / (x \ y) = x * (y \ x). x * ((y * x) \ x) = x / T(y,x). x / (x \ (x / y)) = x * y. (x * y) \ (y * x) = (y * x) \ ((y * x) / K(x,y)). (x * y) \ ((x * y) / K(y,x)) = (y * x) \ (x * y). x / T(y \ 1,x) = x * ((y \ x) \ x). (x * (y \ x)) \ z = ((x \ y) / x) * z. L(T(x \ 1,y),x,z) = T(z \ (z / x),y). T(x \ (x / y),z) = L(T(y \ 1,z),y,x). T(x,y) * (1 / x) = T(x,y) / x. x \ T(x,y) = T(x,y) * (x \ 1). T(x,y) * (x \ 1) = x \ T(x,y). x * (x * (y / x)) = T(x * y,1 / x). T(x * y,1 / x) = x * (x * (y / x)). x \ T(x,y) = T(x,y) * (1 / x). T(x,y) * (1 / x) = x \ T(x,y). L(x \ y,x,y) = T(y / x,y). L(x,y,y * x) = T((y * x) / y,y * x). T((x * y) / x,x * y) = L(y,x,x * y). T(x * y,x) = y * L(x,x,y). x * L(y,y,x) = T(y * x,y). x \ T(y * x,y) = L(y,y,x). (x \ y) \ T(y,x) = L(x,x,x \ y). L(x,x,x \ y) = (x \ y) \ T(y,x). x * ((y / x) / y) = ((y / x) / y) * x. ((x / y) / x) * y = y * ((x / y) / x). x \ (x \ T(x,y)) = (x \ T(x,y)) / x. (x \ T(x,y)) / x = x \ (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). T(T(x,y) / x,x) = T(x,y) / x. T(x / y,y) / (x / y) = (x / y) \ (y \ x). (x \ T(x,y)) \ z = (x / T(x,y)) * z. T(x,y) != x * z | T(x,y) / x = z. T(x,T(x,y) / x) = x. ((x / y) \ 1) / (y \ x) = ((y \ x) * (x / y)) \ 1. x \ ((x / y) * (y * z)) = L(z,y,x). L(x,y,z) = z \ ((z / y) * (y * x)). x * y != (x / z) * (z * L(u,x,z)) | y = u. L(L(x,y,z),z,y) = x. x * (y * L(z,x,y)) = (x * y) * z. x \ ((x * y) * z) = y * L(z,x,y). L((x * y) \ z,x,y) = y \ (x \ z). L(T(x,x * y),x,y) = T(x,y). L(x,y,z) = z \ (y \ ((y * z) * x)). x = L(x,T(y,z),y). L(x,T(y,z),y) = x. x = L(x,y \ z,z / y). L(x,y \ z,z / y) = x. (x * T(x,y)) * z = x * (T(x,y) * z). (T(x,y) / x) \ (T(x,y) * z) = x * z. ((x \ y) \ 1) / (y / x) = ((y / x) * (x \ y)) \ 1. L(T(x,y),x,x \ y) = T(x,x \ y). L((x \ y) \ z,x \ y,y) = y \ (x * z). L(x,y / x,z) = z \ ((z / (y / x)) * y). x \ (y * L(z,x \ y,y)) = (x \ y) * z. T(x,y) / L(y,y,y \ x) = y \ x. (x * y) * z != x * (y * L(u,x,y)) | z = u. x * (L(y,x,z) * z) = (x * z) * T(y,z). x \ (y * z) = (x \ y) * L(z,x,x \ y). (x \ y) * L(z,x,x \ y) = x \ (y * z). x \ ((x * y) * T(z,y)) = L(z,x,y) * y. x * T(y,y \ x) = L(y,y,y \ x) * x. L(x,x,x \ y) * y = y * T(x,x \ y). x \ ((x \ y) \ y) = ((x \ y) \ y) * (x \ 1). ((x \ y) \ y) * (x \ 1) = x \ ((x \ y) \ y). (x * T(y,z)) / x = T((x * y) / x,z). (x * T(x,y)) * (x \ z) = T(x,y) * z. x / (y \ z) = y * (((y \ x) / z) * y). x * (((x \ y) / z) * x) = y / (x \ z). ((x \ 1) * y) / ((x \ 1) \ z) = x \ ((y / z) * (x \ 1)). (x / y) \ T(x,y) = y * K(x,y). x * (y \ (x * z)) = ((x \ y) / x) \ z. ((x \ y) / x) \ z = x * (y \ (x * z)). (x * y) \ (y * z) = y \ ((y / T(x,y)) * z). x \ ((x / T(y,x)) * z) = (y * x) \ (x * z). (x \ y) * (x / y) = x * ((x * y) \ y). T(x * (y * x),1 / x) = x * (x * y). T(x * y,1 / x) != x * z | x * (y / x) = z. (x \ T(x,y)) \ z = x * (T(x,y) \ z). x * (T(x,y) * z) = T(x,y) * (x * z). T(x,y) * (x * z) = x * (T(x,y) * z). (T(x,y) * z) / (x * z) = T(x,y) / x. T(x,y) * z = x * ((T(x,y) / x) * z). x * ((T(x,y) / x) * z) = T(x,y) * z. T(x,y) * z = x * ((x / T(x,y)) \ z). x * ((x / T(x,y)) \ z) = T(x,y) * z. T(x,y) * z = x * (T(x,y) * (x \ z)). x * (T(x,y) * (x \ z)) = T(x,y) * z. (x / (y \ z)) * (y \ u) = y * (((((y \ x) / z) * y) / y) * u). x * (((((x \ y) / z) * x) / x) * u) = (y / (x \ z)) * (x \ u). ((x \ (y * x)) / x) \ y = x * K(x,y). T(x,y) \ (x * (T(x,y) * z)) = x * z. x * (T(x,y) * z) != T(x,y) * u | x * z = u. T(x,y) * z != x * (T(x,y) * u) | x * u = z. (T(x,y) * z) / (x * z) = x \ T(x,y). x \ (T(x,y) * z) = (T(x,y) / x) * z. x * ((x \ T(x,y)) * z) = T(x,y) * z. x \ (T(x,y) * z) = T(x,y) * (x \ z). x * y != z * (x \ u) | y = ((x \ z) / x) * u. T(x,y) * (x \ (x \ z)) = ((x \ T(x,y)) / x) * z. ((x \ T(x,y)) / x) * z = T(x,y) * (x \ (x \ z)). (T(x,y) / y) \ x = y * K(y,x). T(x,y) \ (x * z) = x * (T(x,y) \ z). (T(R(x,y,z),u) * (y * z)) / ((x * y) * z) = R(x,y,z) \ T(R(x,y,z),u). R(x \ T(x,y),x * z,u) = ((T(x,y) * z) * u) / ((x * z) * u). x * y != T(x,z) * u | y = T(x,z) * (x \ u). (x \ T(x,y)) * z = T(x,y) * (x \ z). T(x,y) * z != x * u | (x \ T(x,y)) * z = u. x \ y = T(x,z) * (x \ (T(x,z) \ y)). T(x,y) * (x \ (T(x,y) \ z)) = x \ z. x \ (T(x,y) \ (x * z)) = T(x,y) \ z. T(x,y) \ x = x * (T(x,y) \ 1). x * (T(x,y) \ 1) = T(x,y) \ x. x * (T(x,y) \ y) = T(y,T(x,y)). (x \ T(x,y)) \ z = T(x,y) \ (x * z). x \ (T(x,y) \ x) = T(x,y) \ 1. T(x,y) \ x = x / T(x,y). x / T(x,y) = T(x,y) \ x. x / (x / T(x,y)) = T(x,y). (x / y) / (y \ x) = T(x / y,y) \ (x / y). T(x / y,y) \ (x / y) = (x / y) / (y \ x). (x / y) / T(x / y,y) = (y \ x) \ (x / y). (T(x,y) \ x) \ z = T(x,y) * (x \ z). (T(x,y) \ x) * z = x * (T(x,y) \ z). (x / y) * ((y \ x) \ y) = T(y,T(x / y,y)). T(T(x,y) \ 1,x) = T(x,y) \ 1. T(x,T(x,y) \ 1) = x. T(x / y,(y \ x) \ 1) = x / y. (x \ y) \ (y / x) = (y / x) * ((x \ y) \ 1). (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y). (x \ ((x \ y) \ y)) * z = T(x,x \ y) * (x \ z). T(x,x \ y) * (x \ z) = (x \ ((x \ y) \ y)) * z. ((x \ 1) \ T(x \ 1,x * y)) * z = ((x * y) \ y) * ((x \ 1) \ z). (T(x,y) / x) \ z = T(x,y) \ (x * z). T(x,T(x,y) \ x) = x. T(x,x / T(x,y)) = x. T(x * (y * z),a(x,y,z)) = a(x,y,z) \ ((x * y) * z). a(x,y,z) \ ((x * y) * z) = T(x * (y * z),a(x,y,z)). x \ (x / (y \ 1)) = L(y,y \ x,y). L(x,x \ y,x) = y \ (y / (x \ 1)). x / L(y,y \ x,y) = x * (y \ 1). L(x,y,z) = L(x,y,z / y). L(x,y,z / y) = L(x,y,z). L(x,y,z) = L(x,y,z * y). L(x,y,z * y) = L(x,y,z). L(x,y \ z,y) = L(x,y \ z,z). L(x,y \ z,z) = L(x,y \ z,y). L(x,y,z \ 1) = L(x,y,z \ y). L(x,y,1 / z) = L(x,y,z \ y). L(x,y,z \ y) = L(x,y,1 / z). L(L(x,y,z / y),z,y) = x. L(L(x,y,z),z,y / z) = x. L(x,T(y,z),y / T(y,z)) = x. L((x * (y / x)) \ z,x,y) = (y / x) \ (x \ z). L(L(x,y,z),z * y,y) = x. L(L(x,y,z \ 1),z \ y,y) = x. L(L(x,y,1 / z),z \ y,y) = x. L(x,y,z) = L(x,y / z,z). L(x,y / z,z) = L(x,y,z). L(T(x,y / x),y,x) = T(x,x * (y / x)). L(L(x,y * z,K(y,z)),K(y,z),z * y) = x. L(x,y * z,z) = L(x,y,z). L(x,y,y \ z) = L(x,z,y \ z). L(x,y,z \ y) = L(x,z,z \ y). L(x,y \ 1,z) = L(x,y \ z,z). L(x,1 / (y \ z),z) = L(x,T(y,y \ z),z). L(x,T(y,y \ z),z) = L(x,1 / (y \ z),z). L(x,T(y,z),T(y,z) \ y) = x. x = L(L(x,y,z \ 1),z \ y,z). L(L(x,y,z \ 1),z \ y,z) = x. L(x,y,T(y,z) \ y) = x. L(x,y,z \ 1) = L(x,z,z \ y). L(x,y,y \ z) = L(x,z,1 / y). L(x,y,y / T(y,z)) = x. L(x,y,T(y,z) \ 1) = x. L(x,T(y,z) \ 1,y) = x. L(x,(y \ z) \ 1,z / y) = x. ((x \ y) \ 1) \ (((x \ y) \ 1) / (y / x)) = (y / x) \ 1. ((x \ y) \ 1) \ ((((x \ y) \ 1) / (y / x)) * z) = (y / x) \ z. L(x,y \ 1,z) = L(x,y \ z,y). L((x \ 1) \ y,x \ z,x) = z \ ((z / (x \ 1)) * y). L(x,y * z,y \ 1) = L(x,y,z). L(x,y \ 1,y * z) = L(x,z,y). L(x,y \ 1,z * y) = L(x,T(z,y),y). (x * (y \ 1)) * L(z,y \ x,y) = x * ((y \ 1) * z). R(x,x \ y,y \ z) = z / ((x \ y) * (y \ z)). R(x,y,y \ 1) = (x * y) * (y \ 1). (x * y) * (y \ 1) = R(x,y,y \ 1). R(x,y,y \ 1) / (y \ 1) = x * y. (x * y) \ R(x,y,y \ 1) = y \ 1. x * (y \ 1) = R(x / y,y,y \ 1). R(x / y,y,y \ 1) = x * (y \ 1). (x * L(x,y,z)) * (x \ 1) = R(L(x,y,z),x,x \ 1). R(x,y,y \ 1) = y * (T(x,y) / y). x * (T(y,x) / x) = R(y,x,x \ 1). x \ R(y,x,x \ 1) = T(y,x) / x. x * (T(R(x,y,z),x) / x) = R(x,y,z). x * (T(y,x) / x) = R(y,x,1 / x). x \ R(y,x,1 / x) = T(y,x) / x. (x * y) * (1 / y) = R(x,y,1 / y). (x * y) \ R(x,y,1 / y) = 1 / y. x * (1 / y) = R(x / y,y,1 / y). R(x / y,y,1 / y) = x * (1 / y). (R(x,y,z) * x) \ R(x,y,z) = 1 / x. R(T(x / y,z),y,1 / y) = T(x * (1 / y),z). R(T((x * y) / x,z),x,1 / x) = (x * T(y,z)) * (1 / x). x * (R(T(x,x),y,z) / x) = R(x,y,z). 1 / x = R(x,y,z) \ (R(x,y,z) / x). R(x,y,z) \ (R(x,y,z) / x) = 1 / x. x * (R(x,y,z) / x) = R(x,y,z). x \ R(x,y,z) = R(x,y,z) / x. R(x,y,z) / x = x \ R(x,y,z). (x \ R(x,y,z)) * x = R(x,y,z). T(x \ R(x,y,z),x) = x \ R(x,y,z). (x \ R(x,y,z)) \ u = (x / R(x,y,z)) * u. L(L(x,R(y,z,u),y),y,y \ R(y,z,u)) = x. R(x,y,z) \ (R(x,y,z) / x) = x \ 1. K(x \ R(x,y,z),x) = 1. R(x,y,z) \ (x \ R(x,y,z)) = x \ 1. R(x,y,z) * (x \ 1) = x \ R(x,y,z). R(x,1 / y,y) = (x * (1 / y)) * y. (x * (1 / y)) * y = R(x,1 / y,y). R(x,1 / y,y) / y = x * (1 / y). x * y = R(x / (1 / y),1 / y,y). R(x / (1 / y),1 / y,y) = x * y. T(x * (1 / y),y) = y \ R(x,1 / y,y). x \ R(y,1 / x,x) = T(y * (1 / x),x). R(T(x / (1 / y),z),1 / y,y) / y = (1 / y) * T((1 / y) \ x,z). R(T(x / (1 / y),z),1 / y,y) = T(x * y,z). T(x,y) * z != x * ((x \ T(x,y)) * u) | z = u. L(x,y \ T(y,z),y) = x. L(x,T(y,z),y \ 1) = x. L(x,T(1 / y,z),y) = x. L(x,y \ (z \ y),z) = x. L(x,(y * z) \ z,y) = x. L(x,y \ z,y / z) = x. (x * ((x * y) \ y)) * z = x * (((x * y) \ y) * z). ((x * y) \ y) \ (x \ z) = (x * ((x * y) \ y)) \ z. (x * ((x * y) \ y)) \ z = ((x * y) \ y) \ (x \ z). x / (1 / ((x * y) \ y)) = x * ((x * y) \ y). ((x * y) \ y) * (x * z) = (((x * y) \ y) * x) * z. (((x * y) \ y) * x) * z = ((x * y) \ y) * (x * z). L(x,y,(z / y) / z) = x. (x / y) * ((x \ y) \ z) = ((x / y) / (x \ y)) * z. ((x / y) / (x \ y)) * z = (x / y) * ((x \ y) \ z). (x \ y) * ((x / y) * z) = ((x \ y) * (x / y)) * z. ((x \ y) * (x / y)) * z = (x \ y) * ((x / y) * z). ((x \ y) * (x / y)) \ z = (x / y) \ ((x \ y) \ z). x * (((y / x) / y) * z) = (x * ((y / x) / y)) * z. (x * ((y / x) / y)) * z = x * (((y / x) / y) * z). 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). x \ (y \ (x \ z)) = (x * (y * x)) \ z. (x * (y * x)) \ z = x \ (y \ (x \ z)). a(x,y,x) = x \ (y \ (x \ ((x * y) * x))). x \ (y \ (x \ ((x * y) * x))) = a(x,y,x). K(x * y,y) = y \ (x \ (y \ ((x * y) * y))). x \ (y \ (x \ ((y * x) * x))) = K(y * x,x). T(x \ 1,x * (y * x)) = x \ (y \ (x \ (y * x))). L(x \ y,x,z \ 1) = (z \ x) \ (z \ y). R(x / y,y,z) = R(y / x,x,z) \ 1. x \ (y * z) = (x \ y) * L(z,y,x \ 1). (x \ y) * L(z,y,x \ 1) = x \ (y * z). x \ (y * T(y \ (y / (x \ y)),z)) = (x \ y) * T((x \ y) \ 1,z). x * T(y,y \ x) != z * x | L(y,y,y \ x) = z. x \ L(x,x,y) = a(x,y,x). x * a(x,y,x) = L(x,x,y). L(x,y,z \ 1) = (z \ y) \ (z \ (y * x)). (x \ y) \ (x \ (y * z)) = L(z,y,x \ 1). (x / y) * (y \ x) = (y \ x) * (x / y). (x * y) * L(L(z,y,x),u,w) != x * v5 | y * L(z,u,w) = v5. x / R(x,y,z) = x * (R(x,y,z) \ 1). x * (R(x,y,z) \ 1) = x / R(x,y,z). L(x,y,R(y,z,u)) = x. L(x,R(y,z,u),y) = x. (x * R(x,y,z)) * u = R(x,y,z) * (x * u). L(x,y / z,(y * u) / (z * u)) = x. x * (R(x,y,z) * u) = (x * R(x,y,z)) * u. (x * R(x,y,z)) * u = x * (R(x,y,z) * u). L(x,R(y,z,u),y / R(y,z,u)) = x. ((x * y) / (z * y)) * z = z * R(z \ x,z,y). L(x,y,z) * (x \ 1) = x \ L(x,y,z). L(x,y,z) * (1 / x) = x \ L(x,y,z). T(1 / x,L(x,y,z)) = 1 / x. K(1 / x,L(x,y,z)) = 1. K(x \ 1,L(x,y,z)) = 1. K(L(x,y,z) \ 1,x) = 1. (x * (L(x,y,z) \ 1)) * 1 = (L(x,y,z) \ 1) * x. (x \ y) / (y / x) = (y / x) \ (x \ y). x \ ((x \ y) \ y) = ((x \ y) \ y) / x. ((x \ y) \ y) / x = x \ ((x \ y) \ y). (x \ y) \ (y / x) = (y / x) / (x \ y). (x / y) / (y \ x) = (y \ x) \ (x / y). (x / y) * ((y \ x) \ y) = T(y,y \ x). L(x,y,y \ R(y,z,u)) = x. L(x,y \ R(y,z,u),y) = x. R(x,y,z) * u = x * ((x \ R(x,y,z)) * u). x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u. (x \ R(x,y,z)) \ u = R(x,y,z) \ (x * u). (x / y) \ (y \ x) = y / (1 / ((y * x) \ x)). x / (1 / ((x * y) \ y)) = (y / x) \ (x \ y). x \ (y \ T(y * x,x)) = K(y * x,x). x * (R(x,y,z) * u) = R(x,y,z) * (x * u). R(x,y,z) * (x * u) = x * (R(x,y,z) * u). (x \ y) / (y / x) = x / (1 / ((x * y) \ y)). x / (1 / ((x * y) \ y)) = (x \ y) / (y / x). R(x,y,z) * u = x * (R(x,y,z) * (x \ u)). x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. 1 / ((x \ y) / (y / x)) = (1 / ((x * y) \ y)) / x. (1 / ((x * y) \ y)) / x = 1 / ((x \ y) / (y / x)). x * y != R(x,z,u) * w | y = (x \ R(x,z,u)) * w. R(x,y,z) * (x \ u) = (x \ R(x,y,z)) * u. (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u). R(x,y,z) * u != x * w | R(x,y,z) * (x \ u) = w. (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). R(x \ R(x,y,z),u,w) = ((R(x,y,z) * (x \ u)) * w) / (u * w). ((R(x,y,z) * (x \ u)) * w) / (u * w) = R(x \ R(x,y,z),u,w). (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). (R(R(x,x \ y,z),u,w) * ((x \ y) * z)) / (y * z) = R(x,x \ y,z) \ R(R(x,x \ y,z),u,w). R(x,x \ y,z) \ R(R(x,x \ y,z),u,w) = (R(R(x,x \ y,z),u,w) * ((x \ y) * z)) / (y * z). x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). T(x \ R(x,y,z),x * u) = (x * u) \ (R(x,y,z) * u). (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). (x * y) / ((x / z) * (z * y)) = (x / z) \ R(x / z,z,y). (x / y) \ R(x / y,y,z) = (x * z) / ((x / y) * (y * z)). 1 / ((x / y) * ((y * z) / (x * z))) = (x / y) \ R(x / y,y,z). (x / y) \ R(x / y,y,z) = 1 / ((x / y) * ((y * z) / (x * z))). 1 / ((x / y) * R(y / x,x,z)) = (x / y) \ R(x / y,y,z). (x / y) \ R(x / y,y,z) = 1 / ((x / y) * R(y / x,x,z)). 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) \ x = x * (R(x,y,z) \ 1). x * (R(x,y,z) \ 1) = R(x,y,z) \ x. (x * y) / (x * (R(x,z,u) \ y)) = R(x,z,u). R(x,y,z) \ x = x / R(x,y,z). x / R(x,y,z) = R(x,y,z) \ x. (R(x,y,z) \ x) * R(x,y,z) = x. (R(x,y,z) \ x) \ x = R(x,y,z). 1 / (R(x,y,z) \ x) = R(x,y,z) / x. (R(x,y,z) \ x) \ u = (R(x,y,z) / x) * u. L(x,R(y,z,u),R(y,z,u) \ y) = x. (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. L(x,y,R(y,z,u) \ 1) = x. (R(x,y,z) \ x) * u = R(x,y,z) \ (x * u). R(x,y,z) \ (x * u) = (R(x,y,z) \ x) * u. ((R(x,y,z) \ 1) * u) / (x \ u) = (R(x,y,z) \ 1) * x. (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u. (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). (x * y) / ((R(x,z,u) \ x) * y) = R(x,z,u). (R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u). x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). x \ R(x,y,y \ 1) = a(x,y,y \ 1). x * a(x,y,y \ 1) = R(x,y,y \ 1). (x * L(y,z,x)) \ (x * y) = a(x / z,z,y). a(x / y,y,z) = (x * L(z,y,x)) \ (x * z). (x \ (y * z)) \ ((x \ y) * z) = a((x \ y) / x,x,z). a((x \ y) / x,x,z) = (x \ (y * z)) \ ((x \ y) * z). a(x / y,y,z) = x \ ((x / L(z,y,x)) * z). R(T(x,y * z),y,z) = (y * z) \ ((x * y) * z). (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). x \ ((x * y) * (1 / y)) = a(x,y,1 / y). a(x,y,1 / y) = y * L(1 / y,x,y). x * L(1 / x,y,x) = a(y,x,1 / x). x \ R(x,y,1 / y) = a(x,y,1 / y). x * L(1 / x,y,x) = a(y / x,x,1 / x). a(x / y,y,1 / y) = y * L(1 / y,x,y). R(x,y,1 / y) / x = a(x,y,1 / y). a(x,y,1 / y) * x = R(x,y,1 / y). a(x / y,y,1 / y) = a(x,y,1 / y). a(x,y,1 / y) = a(x * y,y,1 / y). a(x * y,y,1 / y) = a(x,y,1 / y). R(x \ 1,x * y,z) = R(x,y,z) \ 1. R(x \ 1,y,z) = R(x,x \ y,z) \ 1. R(x,x \ y,z) \ 1 = R(x \ 1,y,z). x * R(x \ 1,y,z) = R(x,x \ y,z) \ x. R(x,x \ y,z) \ x = x * R(x \ 1,y,z). L((x * (y / x)) \ z,x,y) = x * ((x * y) \ z). K(x,y) = (x * y) \ ((x * y) / K(y,x)). (x * y) \ ((x * y) / K(y,x)) = K(x,y). (x / y) / (x \ y) = ((x \ y) * (y / x)) \ 1. ((x \ y) * (y / x)) \ 1 = (x / y) / (x \ y). (x * (T(x,y) \ x)) \ z = T(x,y) * (x \ (x \ z)). (x \ (x \ T(x,y))) * z = T(x,y) * (x \ (x \ z)). (x * ((x * y) \ y)) * z = ((x * y) \ y) * (x * z). (x * ((x * y) \ y)) * z = (x \ y) * ((x / y) * z). ((x \ y) * (x / y)) \ z = (y / x) * ((x \ y) \ z). T(x \ 1,x * (y * x)) = x \ (y \ T(y,x)). x * (L(x,y,z) \ 1) = (L(x,y,z) \ 1) * x. (L(x,y,z) \ 1) * x = x * (L(x,y,z) \ 1). x * (L(x,y,z) \ 1) = L(x,y,z) \ x. x * (1 / L(x,y,z)) = L(x,y,z) \ x. (1 / ((x * y) \ y)) / x = (y / x) / (x \ y). ((x * y) \ y) * (x * z) = x * (((x * y) \ y) * z). (x \ y) * ((x / y) * z) = x * (((x * y) \ y) * z). (x * ((x * y) \ y)) \ z = (y / x) * ((x \ y) \ z). (x / y) * ((y \ x) \ z) = ((y * x) \ x) \ (y \ z). ((x * y) \ y) \ (x \ z) = (y / x) * ((x \ y) \ z). ((x * y) \ y) \ 1 = (y / x) * ((x \ y) \ x). (x / y) * ((y \ x) \ y) = ((y * x) \ x) \ 1. ((x * y) \ y) \ 1 = T(x,x \ y). T(x,x \ y) = ((x * y) \ y) \ 1. T(x / y,(x / y) \ y) = (x \ y) \ 1. 1 / T(x,x \ y) = (x * y) \ y. (x * y) \ y = 1 / T(x,x \ y). ((x * y) \ y) \ 1 = (x \ y) \ y. T(x,x \ y) \ 1 = (x * y) \ y. (x * (x * y)) \ (x * y) = 1 / T(x,y). 1 / ((x * y) \ y) = (x \ y) \ y. ((x \ y) \ y) \ 1 = (x * y) \ y. ((x \ y) \ y) * z = ((x * y) \ y) \ z. ((x * y) \ y) \ z = ((x \ y) \ y) * z. T(x,y) \ 1 = (x * (x * y)) \ (x * y). (x * (x * y)) \ (x * y) = T(x,y) \ 1. T(x \ 1,x * y) = T(x,x \ y) \ 1. T(x,x \ y) \ 1 = T(x \ 1,x * y). x * ((x * y) \ y) = T(x,x \ y) \ x. T(x,x \ y) \ x = x * ((x * y) \ y). 1 / (x \ y) = ((x / y) \ y) \ y. ((x / y) \ y) \ y = 1 / (x \ y). ((x \ y) \ y) / x = (y / x) / (x \ y). (x \ y) \ 1 = ((y / x) * y) \ y. ((x / y) * x) \ x = (y \ x) \ 1. (((T(x,y) * y) / (x * y)) \ (x * y)) \ (x * y) = 1 / K(y,T(x,y)). x / ((y \ x) \ 1) = (x / y) * x. L(x \ y,x,x / y) = (y \ x) \ 1. x / (y \ 1) = (x / (x / y)) * x. (x / (x / y)) * x = x / (y \ 1). (x * y) / ((K(x,y) \ (x * y)) \ 1) = (y * x) * (x * y). (x / (y \ 1)) / x = x / (x / y). (x / y) * ((y \ x) \ 1) = ((x / y) / x) * y. (x * y) * (1 / T(x,y)) = (x * y) / T(x,x * y). (x * y) / T(x,x * y) = (x * y) * (1 / T(x,y)). ((x \ y) \ y) * (x \ z) = (y / x) * ((x \ y) \ z). (x * y) / (T(x,y) \ 1) = x * (x * y). x * T(x \ 1,x * y) = T(x,x \ y) \ x. (x / y) * (x \ y) = T(x,x \ y) \ x. T(x,x \ y) \ x = (x / y) * (x \ y). ((x \ y) \ y) / x = (x \ y) \ (y / x). (x / y) * (T(y,y \ x) \ y) = y \ x. (x \ y) \ (y / x) = x \ ((x \ y) \ y). (x / y) * ((y \ x) \ 1) = y \ ((y \ x) \ x). (x / y) * ((y \ x) \ 1) = y * ((x / y) / x). x * ((y / x) / y) = x \ ((x \ y) \ y). x \ ((x \ y) \ y) = x * ((y / x) / y). T(x,x \ y) * (x \ z) = (x * ((y / x) / y)) * z. T(x / y,(y \ x) \ x) = y \ x. T(x / y,T(y,y \ x)) = y \ x. T((x * y) / x,T(x,x \ (x * y))) = y. T((x * y) / x,T(x,y)) = y. T(R((x * y) / x,x,y),T(x * y,y)) = y. R(T((x * y) / x,T(x * y,y)),x,y) = y. T(x,x \ y) * (x \ z) = x * (((y / x) / y) * z). T(x,x \ y) * (x \ y) = x * (y / x). T(x,y) * (x \ (x * y)) = x * ((x * y) / x). T(x,y) * y = x * ((x * y) / x). T(x,y) \ (x * ((x * y) / x)) = y. x \ (T(x,y) * y) = (x * y) / x. T(x / y,y) * y = (x / y) * (x / (x / y)). (T(x,y) * y) \ (x * y) = K((x * y) / x,x). K((x * y) / x,x) = (T(x,y) * y) \ (x * y). x \ y = T(x,y) \ ((x * y) / x). T(x,y) \ ((x * y) / x) = x \ y. (x \ y) * x = (y / x) * (y / (y / x)). (x / y) * (x / (x / y)) = (y \ x) * y. ((x \ y) * x) \ y = K(y / (y / x),y / x). K(x / (x / y),x / y) = ((y \ x) * y) \ x. K((x * y) / x,x) = K(y,T(x,y)). K(x / y,y) = K(y \ x,T(y,y \ x)). K(x \ y,T(x,x \ y)) = K(y / x,x). ((x * (y \ 1)) * y) / 1 = R(x,y \ 1,y). R(x,y \ 1,y) = (x * (y \ 1)) * y. (x * (y \ 1)) * y = R(x,y \ 1,y). R(x,y \ 1,y) / y = x * (y \ 1). x * y = R(x / (y \ 1),y \ 1,y). R(x / (y \ 1),y \ 1,y) = x * y. x * (((y \ 1) / x) * (x * y)) = R(x,y \ 1,y). L(x,y / (z \ 1),y * z) = x. L(x \ 1,y,z) * (x * u) = (L(x \ 1,y,z) * x) * u. (L(x \ 1,y,z) * x) * u = L(x \ 1,y,z) * (x * u). (x / (y \ 1)) \ (x * y) = a(y,y \ x,y). a(x,x \ y,x) = (y / (x \ 1)) \ (y * x). a(x,x \ y,x) = (y / (1 / x)) \ (y * x). a(x,x \ y,x) = ((x \ 1) / y) * (y * x). a(x,x \ y,x) = y \ ((y * (1 / x)) * x). a(x,x \ y,x) = y \ R(y,1 / x,x). (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). L(x * y,x \ z,x) = z \ ((z / (x \ 1)) * y). (x * (y \ 1)) * L(z,y \ x,y) = x * (y \ z). R(L(x,y,z),x,x \ 1) = x * (L(x,y,z) / x). x * (L(x,y,z) / x) = L(R(x,x,x \ 1),y,z). L(R(x,x,x \ 1),y,z) = x * (L(x,y,z) / x). L(x,y,z) = x * (L(x,y,z) / x). x * (L(x,y,z) / x) = L(x,y,z). x \ L(x,y,z) = L(x,y,z) / x. L(x,y,z) / x = x \ L(x,y,z). x * y != L(x,x,z) | y = a(x,z,x). L(x,x,y) / x = a(x,y,x). a(x,y,x) * x = L(x,x,y). (x \ L(x,y,z)) * x = L(x,y,z). (x \ L(x,y,z)) \ u = (x / L(x,y,z)) * u. L(x,y,z) * (1 / x) = L(x,y,z) / x. L(x,y,z) != u * x | x \ L(x,y,z) = u. a((x \ y) / x,x,z) = a(x \ 1,y,z). a((x \ y) / x,x,z) = a(1 / x,y,z). T(x \ 1,x / T(x,y)) = T(x,y) * (x \ (T(x,y) \ 1)). T(x,y) * (x \ (T(x,y) \ 1)) = T(x \ 1,x / T(x,y)). (x \ y) / ((x \ 1) \ z) = x \ ((y / z) * (x \ 1)). (x \ y) / (x * z) = x \ ((y / z) * (x \ 1)). x \ ((y / z) * (x \ 1)) = (x \ y) / (x * z). (x \ y) / (x * z) = (x \ (y / z)) / x. (x \ (y / z)) / x = (x \ y) / (x * z). (x / y) \ 1 = (y \ x) * (((y \ x) \ 1) / (x / y)). (x \ y) * (((x \ y) \ 1) / (y / x)) = (y / x) \ 1. (x \ y) * (((x \ y) \ 1) / (y / x)) = x / y. (x \ y) \ (x / y) = ((x \ y) \ 1) / (y / x). ((x \ y) \ 1) / (y / x) = (x \ y) \ (x / y). (x \ y) \ (x / y) = ((y / x) * (x \ y)) \ 1. ((x / y) * (y \ x)) \ 1 = (y \ x) \ (y / x). ((x \ y) * (y / x)) \ 1 = (x \ y) \ (x / y). (x \ y) \ (x / y) = (x / y) / (x \ y). (x / y) / (x \ y) = (x \ y) \ (x / y). ((x \ y) \ (x / y)) * z = (x / y) * ((x \ y) \ z). (R(x,y,z) \ u) / (x \ u) = (R(x,y,z) \ 1) * x. (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. (x * y) / ((x / z) * (z * y)) = R(z,x,y) \ z. L(x,L(y \ 1,z,u),y) = x. L(x,y,L(y \ 1,z,u)) = x. L(x,L(y,z,u),y \ 1) = x. L(x,1 / y,L(y,z,u)) = x. (L(x,y,z) * (x \ 1)) \ u = (x \ 1) \ (L(x,y,z) \ u). L(x,y \ L(y,z,u),y) = x. (x \ L(x,y,z)) * u = x \ (L(x,y,z) * u). x \ (L(x,y,z) * u) = (x \ L(x,y,z)) * u. (L(x,y,z) * u) / ((1 / x) \ u) = L(x,y,z) * (1 / x). L(x,1 / L(y,z,u),y) = x. (x * y) / ((x \ L(x,z,u)) \ y) = x * (x \ L(x,z,u)). x / L(x,y,z) = x * (1 / L(x,y,z)). x * (1 / L(x,y,z)) = x / L(x,y,z). L(x,y,1 / L(y,z,u)) = x. x / L(x,y,z) = L(x,y,z) \ x. L(x,y,z) * (x / L(x,y,z)) = x. (L(x,y,z) \ x) * L(x,y,z) = x. x / (x / L(x,y,z)) = L(x,y,z). L(L(x,y,1 / L(y,z,u)),y / L(y,z,u),y) = x. (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. x != y * L(x,z,u) | L(x,z,u) \ x = y. x * L(y,z,u) != y | L(y,z,u) \ y = x. L(x,y / L(y,z,u),y) = x. T(x \ 1,x / T(x,y)) = x \ 1. T(x \ 1,T(x,y) \ x) = x \ 1. T((x \ 1) \ 1,((x * y) \ y) \ (x \ 1)) = (x \ 1) \ 1. (L(x,y,z) * (x \ 1)) \ u = x * (L(x,y,z) \ u). (x \ L(x,y,z)) \ u = x * (L(x,y,z) \ u). x * (L(x,y,z) \ u) = (L(x,y,z) \ x) * u. (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). T(x,L(x,y,z) \ x) = x. (L(x,y,z) * u) / (x * u) = L(x,y,z) * (1 / x). (L(x,y,z) * u) / (x * u) = L(x,y,z) / x. (x * y) / ((L(x,z,u) \ x) * y) = x * (x \ L(x,z,u)). T(x,((x * y) \ y) \ (x \ 1)) = (x \ 1) \ 1. T(x,((x * y) \ y) \ (x \ 1)) = x. T(x,(y / x) * ((x \ y) \ 1)) = x. T(x,(x \ y) \ (y / x)) = x. T(x,(x \ (y * x)) \ y) = x. T(x,T(y,x) \ y) = x. (T(x,y) \ x) * y = y * (T(x,y) \ x). x * (T(y,x) \ y) = y * (T(y,x) \ x). x * (T(y,x) \ y) = T(x,T(y,x)). x \ T(x,T(y,x)) = T(y,x) \ y. T(x,y) \ x = y \ T(y,T(x,y)). x * y != T(x,z) | y = T(x,z) / x. T(x,y) \ x = T(y,T(x,y)) / y. T(x,y) * (y \ T(y,T(x,y))) = x. L(x,T(y,z) \ y,z) = x. ((T(x,y) \ x) * y) \ z = y \ ((T(x,y) \ x) \ z). (T(x,y) \ x) \ 1 = y / T(y,T(x,y)). x / T(x,y) = T(y,T(x,y)) / y. T(x,T(y,x)) / x = y / T(y,x). (T(x,T(y,x)) / x) \ y = T(y,x). 1 / (x / T(x,y)) = y / T(y,T(x,y)). T(x,y) = T(y,T(x,y)) \ (y * x). T(x,T(y,x)) \ (x * y) = T(y,x). T(x,T(y,x)) * T(y,x) = x * y. (x * T(y,x)) / (T(y,x) \ 1) = T(y,x) * (x * y). (T(x,y) \ x) \ 1 = T(y,T(x,y)) \ y. T(x,T(y,x)) \ x = (T(y,x) \ y) \ 1. x / T(x,T(y,x)) = T(y,x) / y. T(x,y) / x = y / T(y,T(x,y)). x / (T(y,x) / y) = T(x,T(y,x)). T(x,T(y,x) / y) = x. L(x,y,T(z,y) / z) = x. (T(x,y) / x) * y = y * (T(x,y) / x). ((T(x,y) / x) / y) \ ((T(x,y) / x) * z) = y * z. ((T(x,y) / x) / y) \ z = T(y,T(x,y)) * z. T(x,T(y,x)) \ x = T(y,x) * (y \ 1). x \ (T(x,y) * y) = y * (T(x,y) / x). T(x,T(y,x)) \ x = y \ T(y,x). x \ (y \ T(y,x)) = T(x,T(y,x)) \ 1. T(x,T(y,x)) \ 1 = x \ (y \ T(y,x)). x * (T(y,x) / y) = (y * x) / y. x * (y \ T(y,x)) = (y * x) / y. ((T(x,y) \ x) * y) \ z = y \ (T(x,y) * (x \ z)). (x * y) / (T(x,y) \ 1) = T(x,y) * (y * x). T(x,y) * (y * x) = x * (x * y). (x * (x * y)) / (y * x) = T(x,y). T(x,y) = (x * (x * y)) / (y * x). T(x,y) \ (x * (x * y)) = y * x. K(T(x,y),y * x) = ((y * x) * T(x,y)) \ (x * (x * y)). ((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y). x * y = y * (T(y,x) \ (y * x)). x * (T(x,y) \ (x * y)) = y * x. T(x,y) = T(y,x) \ (y * x). T(x,y) \ (x * y) = T(y,x). T(x,y) * T(y,x) = x * y. T(x,y) = T(x,T(y,x)). T(x,T(y,x)) = T(x,y). x \ T(y,x) = T(x,y) \ y. T(x,y) \ y = x \ T(y,x). 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,x \ y) = T(x,y / x). T(x,y / x) = T(x,x \ y). (x * T(y,z)) / x = T((x * y) / x,T(z,y)). T((x * y) / x,T(z,y)) = (x * T(y,z)) / x. T(x,y) \ x = y \ T(y,x). T(x,y) * (y \ T(y,x)) = x. T(x,y) / x = y / T(y,x). T(x,y) \ 1 = x \ (y \ T(y,x)). x \ (y \ T(y,x)) = T(x,y) \ 1. (x \ T(x,y)) * T(y,x) = y. L(x,T(y,z),T(z,y)) = (z * y) \ (T(z,y) * (T(y,z) * x)). (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). T(x,y) * (x \ (x \ T(y,x))) = x \ y. T(x,(x * y) / x) = T(x,y). (x * (y / x)) / T(x,x \ y) = y / x. T(x,y / x) = (x \ y) \ y. x / T(y,x / y) = y \ x. T(x,y / x) / y = 1 / (x \ y). L(T(x,x \ y),y,x) = T(x,x * (y / x)). L(x,T(y,z / y),z) = L(x,1 / (y \ z),z). T(T(x,y),((x * y) / x) / T(x,y)) = T(T(x,y),x \ y). x * (T(x,y) \ x) = (y * x) / y. (x * y) / x = y * (T(y,x) \ y). (x \ y) * T(x,y / x) = y. T(T(x,y),((x * y) / x) / T(x,y)) = (x \ y) \ ((x * y) / x). L(x,T(y,z / y),y \ z) = L(x,T(y,z / y),z). L(x,y \ z,T(y,z / y)) = L(x,z,T(y,z / y)). ((x \ y) \ y) * T(x \ y,x) = y. T(T(x,y),T(z,x)) = T(T(x,y),z). T(x \ 1,x * (y * x)) = T(x,y) \ 1. (1 / (x \ y)) \ T(T(x,y / x),y) = y * K(T(x,y / x),y). x \ ((y * x) / y) = T(x,y) \ x. T(x * (T(x,y) \ x),y) = y \ (y * x). ((x * y) \ y) \ T(x \ y,x) = y. T(T(x,y),x \ z) = T(T(x,y),z / x). T(T(x,y),z / x) = T(T(x,y),x \ z). T(x \ y,x) / y = (x * y) \ y. (x * (T(x,y) \ x)) \ T(y,x) = x \ y. (x \ (x \ T(x,y))) * T(y,x) = x \ y. T(x * (T(x,y) \ x),y) = x. ((x * y) / x) \ T(x,y) = y \ x. T(x,y) / (y \ x) = (x * y) / x. x \ y = (y / (y * x)) * T(y,x). (x / (x * y)) * T(x,y) = y \ x. T(x * y,x) / y = ((x * y) * x) / (x * y). ((x * y) * x) / (x * y) = T(x * y,x) / y. x * T(y,z) != z \ y | x = y / (y * z). x \ (x \ T(x,y)) = y / (y * x). x * (y / (y * x)) = x \ T(x,y). T((x * y) / x,T(z,y)) = T((x * y) / x,z). R(T((x * y) / x,x * y),x,y) = y. R(L(x,y,y * x),y,x) = x. x = L(R(x,y,x),y,y * x). L(R(x,y,x),y,y * x) = x. L(x,y * x,y) = R(x,y,x). ((T(x,y) / x) / y) \ (x \ (T(x,y) * z)) = y * z. (x * (T(x,y) \ y)) \ z = y \ (T(x,y) * (x \ z)). x * y = T(x,T(z,x)) * (z \ (T(z,x) * y)). T(x,T(y,x)) * (y \ (T(y,x) * z)) = x * z. T(x,y) * (y \ (T(y,x) * z)) = x * z. x * y = z \ (T(z,x) * (T(x,z) * y)). x \ (T(x,y) * (T(y,x) * z)) = y * z. T(x,y) * (y \ z) = x * (T(y,x) \ z). x * (y * z) = T(x,y) * (T(y,x) * z). T(x,y) * (T(y,x) * z) = x * (y * z). T(x,y) * (1 / y) = x * (T(y,x) \ 1). T(x,y) * (1 / y) = x * (1 / T(y,x)). T(x,T(y,x)) \ z = x \ (T(y,x) * (y \ z)). x \ (T(y,x) * (y \ z)) = T(x,T(y,x)) \ z. x \ (T(y,x) * (y \ z)) = T(x,y) \ z. (x * y) / ((L(x,z,u) \ x) * y) = L(x,z,u). L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u). L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u). 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). T(T(x,y),y / x) = T(T(x,y),((x * y) / x) / T(x,y)). T(T(x,y),((x * y) / x) / T(x,y)) = T(T(x,y),y / x). (x * 1) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y). x \ ((x * (y \ 1)) * y) = a(x,y \ 1,y). x \ ((x * (1 / y)) * y) = a(x,y \ 1,y). x \ R(x,1 / y,y) = a(x,y \ 1,y). x \ R(x,1 / y,y) = a(x,1 / y,y). a(x,1 / y,y) * x = R(x,1 / y,y). a(x,x \ y,x) = a(y,1 / x,x). (x * T(y,z)) * (1 / x) = T((x * y) * (1 / x),z). T((x * y) * (1 / x),z) = (x * T(y,z)) * (1 / x). T(x * (y / x),z) = (x * T(y,z)) * (1 / x). (x * T(y,z)) * (1 / x) = T(x * (y / x),z). T(x * (y / x),z) = x * (T(y,z) / x). x * ((y / x) / x) = T(y,1 / x) / x. T(x,1 / y) / y = y * ((x / y) / y). T(x * (y / x),x) = R(y,x,x \ 1). T(x * (y / x),x) = R(y,x,1 / x). T(x * ((y \ x) / x),y) = x * ((y * x) \ x). T(x * y,x) = R(y * x,x,x \ 1). R(x * y,y,y \ 1) = T(y * x,y). T(T(x,y) * y,x) = R(x * y,x,1 / x). T(x * y,x) / (x \ 1) = (y * x) * x. T(x * y,1 / y) / y = y * (x / y). T(x,y) / (y \ 1) = ((y \ x) * y) * y. (x * (y / x)) * x = T(y * x,1 / x). T(x * y,1 / y) = (y * (x / y)) * y. T((x * y) * y,1 / y) = (y * x) * y. T(x * y,y \ 1) = (y * (x / y)) * y. T(x * ((y \ x) / x),y) = x / T(y,x). T(x * (1 / y),y) = x / T(y,x). T(x * (1 / y),y) \ x = T(y,x). T((x * y) * (1 / x),x) = (x * y) * (1 / T(x,y)). T(x * (y / x),x) = (x * y) * (1 / T(x,y)). (x * y) * (1 / T(x,y)) = R(y,x,1 / x). (x * y) / T(x,x * y) = R(y,x,1 / x). (x * y) / T(x,x * y) = R(y,x,x \ 1). (x / y) \ R(x / y,y,z) = R(y,x,z) \ y. R(x,y,z) \ x = (x / y) * R(y / x,x,z). (x / y) * R(y / x,x,z) = R(x,y,z) \ x. (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). L(x,y,z) = L(x,T(y,z),T(z,y)). L(x,T(y,z),T(z,y)) = L(x,y,z). L(x,y \ z,T(y,z / y)) = L(x,z / y,y). L(x,T(y,z / y),y \ z) = L(x,y,z / y). L(T(x,y),T(y,x),T(x,y)) = T(x,x * y). L(x,y / z,z) = L(x,y,T(z,y / z)). L(x,y,T(z,y / z)) = L(x,y / z,z). L(x,y,T(z,y / z)) = L(x,y,z). L(x,y,(z \ y) \ y) = L(x,y,z). L(x,y,z \ y) = L(x,y,y / z). L(x,y,y / z) = L(x,y,z \ y). L(x,y,y / z) = L(x,z,z \ y). L(x,y,y \ z) = L(x,z,z / y). L(x,T(y,z / y),y \ z) = L(x,y,z). L(x,T(y,y \ z),y \ z) = L(x,y,z). L(x,y,z) = L(x,T(y,z / y),z). L(x,T(y,z / y),z) = L(x,y,z). L(x,y,z) = L(x,1 / (y \ z),z). L(x,1 / (y \ z),z) = L(x,y,z). L(x,(y \ z) \ 1,z) = L(x,y,z). L(x,y \ 1,z * y) = L(x,z,z * y). L(x,((y \ z) \ 1) \ 1,z) = L(x,(z / y) * z,z). L(x,y,y * z) = L(x,T(y,z),z). L(x,T(y,z),z) = L(x,y,y * z). L(L(x,y * z,y),T(y,z),z) = x. L(x,y,T(z,y)) = L(x,z * y,z). L(x,y * z,y) = L(x,z,T(y,z)). L(x,x,T(y,x)) = R(x,y,x). R(x,y,x) / x = a(x,T(y,x),x). a(x,T(y,x),x) = R(x,y,x) / x. L(x,y \ z,z) = L(x,(z / y) * z,z). L(x,(y / z) * y,y) = L(x,z \ y,y). L(x,y \ z,z) = L(x,z / y,z). L(x,y / z,y) = L(x,z \ y,y). L(x,y / z,z * (y / z)) = L(x,T(z,z \ y) \ (z * (y / z)),z * (y / z)). L(x,T(y,y \ z) \ (y * (z / y)),y * (z / y)) = L(x,z / y,y * (z / y)). x * (((x \ y) / z) * u) = (y / (x \ z)) * (x \ u). (x / (y \ z)) * (y \ u) = y * (((y \ x) / z) * u). ((x \ y) \ 1) \ ((((x \ y) \ 1) / (y / x)) * z) = (x / y) * z. (x / y) \ R(x / y,y,z) = 1 / (R(x,y,z) \ x). (x / y) \ R(x / y,y,z) = (R(x,y,z) \ x) \ 1. (x / y) \ R(x / y,y,z) = R(x,y,z) * (x \ 1). (x / y) \ R(x / y,y,z) = x \ R(x,y,z). x \ R(x,y,z) = R(y,x,z) \ y. R(x,y,z) \ x = y \ R(y,x,z). x * (R(y,x,z) \ y) = R(x,y,z). x / (y \ R(y,x,z)) = R(x,y,z). (R(x,y,z) \ x) * y = R(y,x,z). K(R(x,y,z) \ x,y) = 1. (x \ R(x,y,z)) * u = y * (R(y,x,z) \ u). x * (((y * z) / (x * z)) \ (y / x)) = R(x,y / x,z). R(x,y,z) = y * (R(y,x,z) \ x). x * (R(x,y,z) \ y) = R(y,x,z). (x * y) / R(y,x,z) = R(x,y,z). x * (R(x,y,z) \ u) = R(y,x,z) * (y \ u). R(x,y,z) * (x \ u) = y * (R(y,x,z) \ u). x * (((x * y) / (z * y)) * (z / x)) = R(x,z / x,y). (x \ y) \ ((x * y) / x) = T(T(x,y),y / x). (x \ y) * T(T(x,y),y / x) = (x * y) / x. (1 / (x \ y)) \ T(T(x,y),y / x) = y * K(T(x,y / x),y). (x / y) * z = (x \ y) * ((((x \ y) \ 1) / (y / x)) * z). (x \ y) * ((((x \ y) \ 1) / (y / x)) * z) = (x / y) * z. (x \ y) * (((x \ y) \ (x / y)) * z) = (x / y) * z. (x \ y) * ((x / y) * ((x \ y) \ z)) = (x / y) * z. (x / y) * z = x * (((x * y) \ y) * ((x \ y) \ z)). x * (((x * y) \ y) * ((x \ y) \ z)) = (x / y) * z. x * K(T(y,x / y),x) = (y \ x) * T(T(y,x),x / y). (x \ y) * T(T(x,y),y / x) = y * K(T(x,y / x),y). x * K(T(y,x / y),x) = (y * x) / y. x * y != (z * x) / z | y = T(z,x) / z. K(T(x,y / x),y) = T(x,y) / x. (x / y) \ R(x / y,y,z) = ((x / y) * ((y * z) / (x * z))) \ 1. (x * T(x \ 1,x * y)) * z = ((x * y) \ y) * ((x \ 1) \ z). ((x * y) \ y) * ((x \ 1) \ z) = (x * T(x \ 1,x * y)) * z. ((x * y) \ y) * ((x \ 1) \ z) = (T(x,x \ y) \ x) * z. (T(x,x \ y) \ x) * z = ((x * y) \ y) * ((x \ 1) \ z). ((x * y) \ y) * ((x \ 1) \ z) = x * (T(x,x \ y) \ z). ((x * y) \ y) * (x * z) = x * (T(x,x \ y) \ z). x * (T(x,x \ y) \ z) = x * (((x * y) \ y) * z). x \ (y * T(y \ x,z)) = (x \ y) * T((x \ y) \ 1,z). (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). ((T(x,y) / x) \ (x * y)) \ (x * y) = 1 / K(y,T(x,y)). (T(x,y) \ (x * (x * y))) \ (x * y) = 1 / K(y,T(x,y)). (x * y) \ (y * x) = 1 / K(x,T(y,x)). K(x,y) = 1 / K(y,T(x,y)). 1 / K(x,T(y,x)) = K(y,x). K(x,y) \ 1 = K(y,T(x,y)). K(x,T(y,x)) = K(y,x) \ 1. K(x,y) * z = K(y,T(x,y)) \ z. K(x,T(y,x)) \ z = K(y,x) * z. K(x,T(T(y,x),z)) = K(T(y,z),x) \ 1. (x * y) / (K(x,y) \ 1) = T(x,y) * y. K((x * y) / x,x) = K(x,y) \ 1. (T(x,y) * y) / (x * y) = (x * y) / ((x * y) / K(x,y)). (x * y) / ((x * y) / K(x,y)) = (T(x,y) * y) / (x * y). (x * y) / (y * x) = (T(x,y) * y) / (x * y). (T(x,y) * y) / (x * y) = (x * y) / (y * x). (x * y) / (y * x) = T(x,y) / x. T(x * y,z) / y = (1 / y) * T((1 / y) \ x,z). (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x. (1 / x) * T(x * y,z) = T(y * x,z) / x. T(x * y,z) / y = y \ T(y * x,z). T((x \ y) * x,z) / x = x \ T(y,z). ((x * y) * x) / (x * y) = y \ T(y * x,x). T(x * (y * x),1 / x) / (y * x) = (y * x) \ ((x * y) * x). (x \ T(y,z)) * x = T((x \ y) * x,z). T((x \ y) * x,z) = (x \ T(y,z)) * x. T((x \ y) * x,1 / y) = (x \ y) * x. T(1 / x,(y \ x) * y) = 1 / x. T(1 / (x * y),y * x) = 1 / (x * y). 1 / (x * y) = (y * x) \ K(y,x). (x * y) \ K(x,y) = 1 / (y * x). (x * y) * (1 / (y * x)) = K(x,y). K(x,y) = (x * y) * (1 / (y * x)). K(x,y) = (x * y) * ((y * x) \ 1). ((x * y) / ((y * x) \ 1)) * ((x * y) \ z) = (x * y) * (K(x,y) \ z). x \ (y \ T(y * x,x)) = T(x,x * y) \ x. T(x,x * y) \ x = K(y * x,x). L(x,y,K(z * y,y)) = x. L(x,y,K(z,y)) = x. L(x,K(y,z),z) = x. x * (K(y,x) * z) = (x * K(y,x)) * z. (x * K(y,x)) * z = x * (K(y,x) * z). L(x,K(y,z) \ 1,y) = x. x * ((K(x,y) \ 1) \ z) = (x / (K(x,y) \ 1)) * z. (x / (K(x,y) \ 1)) * z = x * ((K(x,y) \ 1) \ z). x * K(x,y) = x / (K(x,y) \ 1). x / (K(x,y) \ 1) = x * K(x,y). (x / (K(x,y) \ 1)) * z = x * (K(x,y) * z). (x * K(x,y)) * z = x * (K(x,y) * z). T(x * (y * x),1 / x) / (y * x) = R(T(x,y * x),y,x). (x * (x * y)) / (y * x) = R(T(x,y * x),y,x). T(x,y) = R(T(x,y * x),y,x). R(T(x,y * x),y,x) = T(x,y). (x * y) * T(y,x) = R(y,x,y) * (x * y). R(x,y,x) * (y * x) = (y * x) * T(x,y). (x * y) * T(y,x) = (y * x) * y. x * T(y,x / y) = (y * (x / y)) * y. (x * (y / x)) * x = y * T(x,y / x). ((x * y) * x) \ (x * (x * y)) = K(T(x,y),y * x). (T(x,y) * y) * x = (x * y) * T(x,(x * y) / x). (x * y) * T(x,(x * y) / x) = (T(x,y) * y) * x. K(x,x * y) = K(T(x,y),y * x). K(T(x,y),y * x) = K(x,x * y). K(T(x,y / x),y) = K(x,x * (y / x)). K(x,x * (y / x)) = T(x,y) / x. K(x,x * y) = T(x,y * x) / x. T(x,y * x) / x = K(x,x * y). x * K(x,x * y) = T(x,y * x). T(x,K(x,x * y)) = x. T(x,K(x,y)) = x. (x * y) * T(x,y) = (T(x,y) * y) * x. (T(x,y) * y) * x = (x * y) * T(x,y). T(T(x,y) * y,x) = x \ ((x * y) * T(x,y)). x \ ((x * y) * T(x,y)) = T(T(x,y) * y,x). T(T(x,y) * y,x) = L(x,x,y) * y. L(x,x,y) * y = R(x * y,x,1 / x). R(x * y,x,1 / x) = L(x,x,y) * y. (L(x,x,y) * y) / (x * y) = a(x * y,x,1 / x). a(x * y,x,1 / x) = L(x,x,y) / x. a(x * y,x,1 / x) = a(x,y,x). a(x * y,y,1 / y) = a(y,T(x,y),y). a(x * (x \ y),x,1 / x) = a(y,1 / x,x). a(x,T(y,x),x) = a(y,x,1 / x). a(x,y,1 / y) = a(x,1 / y,y). a(x,1 / y,y) = a(x,y,1 / y). a(x,y,1 / y) * x = R(x,1 / y,y). R(x,1 / y,y) = R(x,y,1 / y). x \ R(y,x,1 / x) = T(y * (1 / x),x). T(x * (1 / y),y) = T(x,y) / y. T(x * y,y \ 1) = T(x,y \ 1) / (y \ 1). T(x,y \ 1) / (y \ 1) = T(x * y,y \ 1). T(x * (y \ 1),y) = T(x,y) / y. T(x,y) / y = x / T(y,x). (T(x,y) / y) \ x = T(y,x). (x / T(y,x)) * y = T(x,y). T(x,y \ 1) / (y \ 1) = x * ((y \ x) \ x). T(x,y) = x * K(x,y). T(x,y) / x = K(x,y). K(x,y) = T(x,y) / x. x * T(x \ 1,y) = K(x \ 1,y). x \ T(x,y) = K(x,y). K(x,y) = x \ T(x,y). (x / y) * T(y,z) = x * L(K(y,z),y,x). x * L(K(y,z),y,x) = (x / y) * T(y,z). L(K(x,y),x,z) = z \ ((z / x) * T(x,y)). x \ ((x / y) * T(y,z)) = L(K(y,z),y,x). T(x,y) * z = x * (K(x,y) * z). x * (K(x,y) * z) = T(x,y) * z. T(x,x * y) = T(x,y * x). T(x,y * x) = T(x,x * y). K(x,y) * x = T(x,y). T(x,y) = K(x,y) * x. R(K(x,y) / z,z,x) = T(x,y) / (z * x). K(x,y) \ 1 = x / T(x,y). K(x,y) \ (T(x,y) * z) = x * z. K(x,y) \ z = T(x,y) \ (x * z). T(x,y) \ (x * z) = K(x,y) \ z. x * K(y,x) = (y * x) / y. (x * y) / x = y * K(x,y). K(x,y) = y / T(y,x). (x * y) / (y * x) = K(x,y). K(x,y) = (x * y) / (y * x). K(T(x,y),z) = T(x,y) \ T(T(x,z),y). T(x,y) \ T(T(x,z),y) = K(T(x,y),z). K(R(x,y,z),u) = R(x,y,z) \ R(T(x,u),y,z). R(x,y,z) \ R(T(x,u),y,z) = K(R(x,y,z),u). K(x,y) * z = T(x,y) * (x \ z). T(x,y) * (x \ z) = K(x,y) * z. T(x,y) \ x = K(y,x). K(x,y) = T(y,x) \ y. T(x,y) * K(y,x) = x. K(x,y) * T(y,x) = y. x \ K(y,x) = T(x,y) \ 1. T(x,y) \ 1 = x \ K(y,x). x * (y / (y * x)) = K(x,y). K(x,y) = x * (y / (y * x)). R(x,K(y,z),y) * T(y,z) = (x * K(y,z)) * y. R(x / K(y,z),K(y,z),y) = (x * y) / T(y,z). K(x,y) \ y = T(y,x). T(x,y) = K(y,x) \ x. K(x,y) * z = y * (T(y,x) \ z). x * (T(x,y) \ z) = K(y,x) * z. x * (K(y,x) \ z) = T(x,y) * z. K(x,y / x) = (x \ y) \ (y / x). (x \ y) \ (y / x) = K(x,y / x). (x / y) * K(y \ x,y) = y \ x. T(x * K(y,x),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). R(x,y,y \ 1) * y = T(y * x,y). T(x,y) = T(x,x * (y / x)). T(x,x * (y / x)) = T(x,y). K(x,y) = K(y,x) \ 1. K(x,y) \ 1 = K(y,x). K(x,y) * K(y,x) = 1. 1 / K(x,y) = K(y,x). K(x,y) \ (z / K(y,x)) = (K(x,y) \ z) * K(x,y). K(x,y) * (K(y,x) * z) = z. K(x,y) \ z = K(y,x) * z. x * L(K(y,z),K(z,y),x) = x / K(z,y). L(K(x,y),K(y,x),z) = z \ (z / K(y,x)). (x / K(y,z)) / L(K(z,y),K(y,z),x) = x. K(x,T(y,x)) = K(x,y). K(x,T(T(y,x),z)) = K(x,T(y,z)). R(x,K(y,z),K(z,y)) = ((x * K(y,z)) * K(z,y)) / 1. ((x * K(y,z)) * K(z,y)) / 1 = R(x,K(y,z),K(z,y)). T(x,K(y,z)) * K(z,y) = x * (1 / T(K(y,z),x)). K(x \ y,x) = K(y / x,x). K(x / y,y) = K(y \ x,y). R((x * y) / x,x,y) = y * K(x * y,y). K(x,y) \ (x * y) = y * x. (x \ K(y,x)) * z = T(x,y) \ z. T(x,x \ K(y,x)) = x. T(x,y) = T(T(x,y),x \ K(z,x)). T(T(x,y),x \ K(z,x)) = T(x,y). (x \ K(y,x)) * T(x,z) = T(x,z) * (x \ K(y,x)). T(x,y) * (x \ K(z,x)) = (x \ K(z,x)) * T(x,y). T(x,y * (x \ 1)) = T(x,x \ y). L(T(x,x \ y),y,x) = T(x,y). (x * (y / x)) / T(x,y) = R(y / x,x,x \ 1). T(x,K(y,z)) = K(z,y) * (x * K(y,z)). K(x,y) * (z * K(y,x)) = T(z,K(y,x)). K(x,K(y,z)) = (K(z,y) \ x) \ (x * K(y,z)). (K(x,y) \ z) \ (z * K(y,x)) = K(z,K(y,x)). K(x / (x / y),x / y) = K(y,x / y). (x * y) / ((y * x) \ 1) = (y * x) * (x * y). (x \ y) * T(x,y) = L(x,y,x) * (x \ y). L(x,y,x) * (x \ y) = (x \ y) * T(x,y). L(T(x,y),x,y) = T(x,x \ y). L(x \ y,y / x,x) = T(y / x,(y / x) \ x). T(x / y,(x / y) \ y) = L(y \ x,x / y,y). x * T(y,y \ x) = L(y,y,x) * x. L(T(x,y),x,T(y,x)) = T(x,x \ T(y,x)). L(T(x,y),T(x,y),T(y,x)) = T(x,x \ y). T((x * (y * x)) * (x \ 1),x) = (y * (x * x)) / x. x * y != T(x,z) * (T(z,x) * u) | y = z * u. K(x,y) * (T(y,x) * z) = y * z. x * y != T(x,z) * (x * u) | y = T(x,z) * u. K(x,y) * (x * z) = T(x,y) * z. x * y = T(x,z) * (K(z,x) * y). T(x,y) * (K(y,x) * z) = x * z. R(K(x,y),x * z,u) \ 1 = R(K(x,y) \ 1,T(x,y) * z,u). R(K(x,y) \ 1,T(x,y) * z,u) = R(K(x,y),x * z,u) \ 1. T(x,y) \ (x * z) = K(y,x) * z. T(x,y) \ (K(x,y) * z) = x \ z. T(T(x,y),x \ z) = (x \ z) \ (K(x,y) * z). (x \ y) \ (K(x,z) * y) = T(T(x,z),x \ y). T(x / y,z) * y = K(x / y,z) * x. x \ (K(y,x) * z) = T(x,y) \ z. K(x \ y,x) * z = x * (((x * y) \ y) * z). x * (((x * y) \ y) * z) = K(x \ y,x) * z. T(x,y) * z != x * u | K(y,x) \ z = u. K(x,T(y,x)) = K(x,T(y,K(T(y,x),z))). K(x,T(y,K(T(y,x),z))) = K(x,T(y,x)). R(K(x,y),T(y,x) * z,u) = ((y * z) * u) / ((T(y,x) * z) * u). K(x,y) * (y * z) = y * (K(x,y) * z). T(x * y,x) != z * x | R(y,x,x \ 1) = z. (x * (T(y,x) / x)) * x = T(x * y,x). L(x,x,x \ y) = L(x,x,y). x * ((y \ x) \ x) = L(y,y,x) * x. L(x,x,y) * y = y * ((x \ y) \ y). T(x,y) / L(y,y,x) = y \ x. x \ L(x,x,y) = a(x,x \ y,x). a(x,x \ y,x) = x \ L(x,x,y). L(x,x,y) = L(x,y,y / x). L(x,y,y / x) = L(x,x,y). a(x,x \ y,x) = a(x,y,x). a(x,y,x) = a(x,x * y,x). a(x,x * y,x) = a(x,y,x). a(x,y,x) = ((x \ 1) / y) * (y * x). ((x \ 1) / y) * (y * x) = a(x,y,x). x * a(y,x,y) = R(x,y \ 1,y). R(x,y \ 1,y) = x * a(y,x,y). R(x,y \ 1,y) != x * z | a(y,x,y) = z. K(x / y,z) * x = y * T(y \ x,z). K(x,T(y,K(T(y,x),z))) = K(x,y). T(T(x,K(T(x,y),z)),y) * K(y,x) = T(x,K(T(x,y),z)). T(K(x / y,z),x) = x \ (y * T(y \ x,z)). x \ (y * T(y \ x,z)) = T(K(x / y,z),x). x / ((K(y,z) / x) \ (T(y,z) / (x * y))) = R(x,K(y,z) / x,y). x * (y \ z) != (y \ z) * T(y,z) | x = L(y,y \ z,y). L(x,y,x) = L(x,x \ y,x). L(x,x \ y,x) = L(x,y,x). L(x,y,x) = L(x,x * y,x). L(x,x * y,x) = L(x,y,x). x / L(y,x,y) = x * (y \ 1). T(L(x,y,x),y * (x \ 1)) = T(L(x,y,x),L(x,y,x) \ y). T(L(x,y,x),L(x,y,x) \ y) = T(L(x,y,x),y * (x \ 1)). x * ((y \ x) \ x) = T(x * y,y \ 1). T(x * y,y \ 1) = x * ((y \ x) \ x). L(x,x,y) * y = T(y * x,x \ 1). T(x * y,y \ 1) = L(y,y,x) * x. L(x,x,y) * y = (x * (y / x)) * x. L(x,x,y * x) * (y * x) = (x * y) * x. L(x,x,y) * (y * x) = (x * y) * x. x * (y * z) != (u * y) * z | x = R(u,y,z). L(x,x,y) = R(x,y,x). R(x,y,x) = L(x,x,y). R(L(x,x,y),z,u) = R(R(x,z,u),y,x). R(R(x,y,z),u,x) = R(L(x,x,u),y,z). L(x \ 1,x \ 1,x * y) = R(x,y,x \ 1) \ 1. L(x,x,T(y,x)) = L(x,x,y). a(x,T(y,x),x) = L(x,x,y) / x. L(T(x,y),x,T(z,x)) = T(L(x,x,z),y). L(x,x,y) * T(y,x) = (x * (T(y,x) / x)) * x. a(x,T(y,x),x) = a(x,y,x). a(x,y,x) = a(y,x,1 / x). a(x,y,1 / y) = a(y,x,y). a(x,y \ 1,y) = a(y \ 1,x,y \ 1). a(x \ 1,y,x \ 1) = a(y,x \ 1,x). a(x,y,y \ 1) = a(y,x,y). x * L(1 / x,y,x) = a(x,y,x). x * a(y,x,y) = R(x,y,y \ 1). R(x,y,y \ 1) = x * a(y,x,y). x * L(x \ 1,y,x) = a(x,y,x). R(x,y \ 1,y) = R(x,y,y \ 1). R(x,y,y \ 1) / y = x * (y \ 1). R(x / (y \ 1),y,y \ 1) = x * y. R(L(x / (y \ 1),z,u),y,y \ 1) / y = (y \ 1) * L((y \ 1) \ x,z,u). R(R(x,y,z),u,x) = L(R(x,y,z),x,u). L(T(x,y),x,z) = L(T(x,y),x,T(z,x)). L(T(x,y),x,T(z,x)) = L(T(x,y),x,z). (x * R(y,z,u)) / L(R(y,z,u),y,x) = R(x,R(y,z,u),y). L(T(x,y),x,y) = T(x,x \ T(y,x)). T(x,x \ T(y,x)) = L(T(x,y),x,y). T(x,x \ T(y,x)) = T(x,x \ y). L(R((x * y) / x,x,y),z,u) * (x * y) = (x * y) * L(y,z,u). K(x \ y,x) * ((x \ y) \ z) = (x / y) * z. (x \ y) * T((x \ y) \ 1,z) = T(K(x / y,z),x). (x * (y / x)) / T(x,y) = y * (x \ 1). T(x / y,(x / y) \ y) = L(y \ x,x,y). L(x \ y,y,x) = (y \ x) \ 1. L((x / y) \ x,x,x / y) = L(y \ 1,y,x) \ 1. L((x \ y) \ 1,y,x) = y \ x. ((x / y) \ ((x * z) / (y * z))) \ 1 = ((x * z) / (y * z)) \ (x / y). (x / (y \ 1)) \ (x * y) = ((x * y) \ (x / (y \ 1))) \ 1. ((x * y) \ (x / (y \ 1))) \ 1 = (x / (y \ 1)) \ (x * y). L(x,x,y) * T(y,x) = T(x * y,x). x * L(y,y,x) = L(y,y,x) * T(x,y). L(x,x,y) * T(y,x) = y * L(x,x,y). T(x,L(y,y,x)) = T(x,y). K(x / (x / K(y,z)),x / K(y,z)) = (K(y,z) \ (x / K(z,y))) \ x. K(K(x,y),z) \ K(y,x) = 1 / T(K(x,y),z). T(x,y) * (x \ K(z,x)) = T(x,z) \ T(x,y). T(x,y) \ T(x,z) = K(x,z) * K(y,x). T(x * (((y * x) / x) * 1),x) = (y * (x * x)) / x. R(x,y,x \ 1) \ 1 = L(x \ 1,y,x). T(K(x / y,z),x) = K((x \ y) \ 1,z). 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) / y) * (x \ y)) \ (x \ y),z) = T(K(x,z),y). L(x,y,y / x) = L(x \ 1,x,y) \ 1. L(x \ 1,x,y) \ 1 = L(x,x,y). (x \ (x / y)) \ 1 = L(y,y,x). L(x,x,y) = (y \ (y / x)) \ 1. L(x,x,y) \ z = (y \ (y / x)) * z. x \ ((y \ (y / x)) \ 1) = a(x,y,x). (x \ (x / y)) * T(L(y,y,x),z) = K((x \ (x / y)) \ 1,z). T(x * (y * 1),x) = (y * (x * x)) / x. T(x * y,x) = (y * (x * x)) / x. (x * (y * y)) / y = T(y * x,y). T(x * y,x) * x = y * (x * x). x * y != R(z,u,y) * (u * y) | x = z * u. T(x * R(y,x,x),x) = y * x. R(R(x,y,y),y,y \ 1) = x. x = R(R(x,y,y \ 1),y,y). R(R(x,y,y \ 1),y,y) = x. x / (y \ 1) = R(x,y,y) * y. R(x,y,y) * y = x / (y \ 1). x / y = R(x,y,y) * (y \ 1). R(x,y,y) * (y \ 1) = x / y. R(x * (y \ 1),y,y) = x / y. R(T(x * y,x),x,x) = y * x. R(x * y,y,y) = x / (y \ 1). (x / (y \ 1)) / y = R(x,y,y). x * y != T(z,y) / (y \ 1) | x = (y \ z) * y. R(T(x,y),y,y) = (y \ x) * y. (x / y) / (y \ 1) = R(x,y,y). R(x,y,y) \ (x / y) = y \ 1. (x \ 1) / (y / x) = R(y,x,x) \ 1. K(R(x,y,y),z) * (x / y) = T(R(x,y,y),z) * (y \ 1). T(R(x,y,y),z) * (y \ 1) = K(R(x,y,y),z) * (x / y). (x / y) / (y \ 1) = R(x,y \ 1,y \ 1). R(x,y \ 1,y \ 1) = (x / y) / (y \ 1). R(R(T(x,y),y,y),x,z) = (y \ x) * y. (x / K(y,z)) / K(z,y) = R(x,K(y,z),K(y,z)). R(x * y,y * x,z) = (y \ (y * x)) * y. R(x,y \ 1,y \ 1) = R(x,y,y). R(x * y,y * x,z) = x * y. (x * y) * ((y * x) * z) = ((x * y) * (y * x)) * z. ((x * y) * (y * x)) * z = (x * y) * ((y * x) * z). R(x,K(y,z),K(z,y)) = (x * K(y,z)) * K(z,y). (x * K(y,z)) * K(z,y) = R(x,K(y,z),K(z,y)). T(T(x,y),K(T(x,y),z)) * K(y,x) = T(x,K(T(x,y),z)). ((x * y) \ (x / (y \ 1))) \ 1 = ((y \ 1) / x) * (x * y). K(((x \ 1) * (x \ y)) \ (x \ y),z) = T(K(x,z),y). K((x \ (x \ y)) \ (x \ y),z) = T(K(x,z),y). K(T(x,x \ (x \ y)),z) = T(K(x,z),y). R(T(x,y),z,z) * (z \ 1) = K(R(x,z,z),y) * (x / z). T(x,y) * K(y,x) = T(x,K(T(x,y),z)). T(x,K(T(x,y),z)) = T(x,y) * K(y,x). T(x,K(T(x,y),z)) = x. K(T(x,y),z) * x = x * K(T(x,y),z). K(x \ y,z) * (y / x) = (y / x) * K(T(y / x,x),z). (x / y) * K(T(x / y,y),z) = K(y \ x,z) * (x / y). ((x * y) \ (x / (y \ 1))) \ 1 = a(y,x,y). ((x * (y * y)) \ (T(y * x,y) / (y \ 1))) \ 1 = a(y,T(y * x,y),y). K(R(x,y,y),z) * (x / y) = T(x,z) / y. (x / y) * K(y \ x,z) = K(y \ x,z) * (x / y). K(x \ y,z) * (y / x) = (y / x) * K(x \ y,z). L(T(x,y * (x \ 1)),y,x) = T(L(x,y,x),L(x,y,x) \ y). T(L(x,y,x),L(x,y,x) \ y) = L(T(x,y * (x \ 1)),y,x). (x \ (x / y)) * L(T(y,z),y,x) = K((x \ (x / y)) \ 1,z). T(L(x,y,x),L(x,y,x) \ y) = L(T(x,x \ y),y,x). T(L(x,y,x),L(x,y,x) \ y) = T(x,y). x / T(y,x) = L(y,x,y) \ x. L(x,y,x) \ y = y / T(x,y). x / (x / T(y,x)) = L(y,x,y). L(x,y,x) = y / (y / T(x,y)). L(x,y,x) = y / (T(y,x) / x). x / (T(x,y) / y) = L(y,x,y). L(x,x * (y / x),x) = (x * (y / x)) / ((x * (y / x)) / T(x,y)). (x * (y / x)) / ((x * (y / x)) / T(x,y)) = L(x,x * (y / x),x). x / (T(x,y) / L(y,y,x)) = L(L(y,y,x),x,L(y,y,x)). L(L(x,x,y),y,L(x,x,y)) = y / (T(y,x) / L(x,x,y)). L(L(x,x,y),y,L(x,x,y)) = y / (x \ y). L(L(x,x,y),y,L(x,x,y)) = x. R(K(x,y),T(y,x) * z,u) = R(K(y,x),y * z,u) \ 1. x / ((x / K(y,z)) * (T(y,z) / (x * y))) = R(x,K(y,z) / x,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(x \ (x * y),z,u)) * y = (x * y) * L(y,z,u). (x * L(y,z,u)) * y = (x * y) * L(y,z,u). ((x * y) * L(y,z,u)) / y = x * L(y,z,u). x * y = ((x / L(y,z,u)) * y) * L(y,z,u). ((x / L(y,z,u)) * y) * L(y,z,u) = x * y. (x * L(y,z,u)) / y = (x / y) * L(y,z,u). (x * y) / L(y,z,u) = (x / L(y,z,u)) * y. (x * (y / x)) / ((x * (y / x)) / T(x,y)) = L(x,y / x,x). (x * (y / x)) / ((x * (y / x)) / T(x,y)) = L(x,y,x). (x * (y / x)) / (y * (x \ 1)) = L(x,y,x). L(x,y,x) = R(x,y,x \ 1). R(x,y,x \ 1) = L(x,y,x). L(x,y,x) \ 1 = L(x \ 1,y,x). L(x \ 1,y,x) = L(x,y,x) \ 1. x * (L(x,y,x) \ 1) = a(x,y,x). a(x,y,x) = L(x,y,x) \ x. L(x,y,x) \ x = a(x,y,x). ((x * y) * (y * x)) * ((y * x) \ z) = (y * x) * (K(y,x) \ z). ((x * y) * (y * x)) * ((y * x) \ z) = (y * x) * (K(x,y) * z). (x * y) * (K(y,x) * z) = (y * x) * ((x * y) * ((x * y) \ z)). (x * y) * ((y * x) * ((y * x) \ z)) = (y * x) * (K(x,y) * z). (x * y) * z = (y * x) * (K(x,y) * z). (x * y) * (K(y,x) * z) = (y * x) * z. (x * y) \ ((x * y) * z) = L(z,K(x,y),y * x). L(x,K(y,z),z * y) = x. K(x,y) * ((y * x) * z) = (K(x,y) * (y * x)) * z. (K(x,y) * (y * x)) * z = K(x,y) * ((y * x) * z). L(x,y * z,K(y,z)) = x. (x * y) \ z = K(x,y) \ ((y * x) \ z). K(x,y) \ ((y * x) \ z) = (x * y) \ z. x * ((y * x) \ z) = T(x,y) * ((x * y) \ z). T(x,y) * ((x * y) \ z) = x * ((y * x) \ z). T(x,y) * (y * ((x * y) \ z)) = x * (y * ((y * x) \ z)). (x * (K(y,x) * y)) * z = K(y,x) * ((x * y) * z). (x * T(y,x)) * z = K(y,x) * ((x * y) * z). K(x,y) * ((y * x) * z) = (y * T(x,y)) * z. K(x,y) * ((y * x) * z) = (x * y) * z. ((x * y) * z) / ((y * x) * z) = K(x,y). K(x,y) * (y * (x * z)) = (x * y) * L(z,x,y). ((x * y) * z) / ((T(x,y) * y) * z) = K(y,T(x,y)). (x * y) * L(z,x,y) = y * (K(x,y) * (x * z)). x * (K(y,x) * (y * z)) = (y * x) * L(z,y,x). x * (T(y,x) * z) = (y * x) * L(z,y,x). (x * y) * L(z,x,y) = y * (T(x,y) * z). (x * y) \ (y * (T(x,y) * z)) = L(z,x,y). L(x,y,z) = (y * z) \ (z * (T(y,z) * x)). L(T(x,y) \ z,x,y) = (x * y) \ (y * z). L(x,y,z) = L(x,T(y,z),z). L(x,T(y,z),z) = L(x,y,z). L(x,T(y,z),T(z,y)) = L(x,y,T(z,y)). L(x,y,y \ z) = L(x,y,z). L(x,y,z \ y) = L(x,z,y). L(x,y,z \ 1) = L(x,z,y). L(x,y,z) = L(x,z,1 / y). L(x,y,1 / z) = L(x,z,y). (x \ y) * L(z,x,y) = x \ (y * z). L(x,y,z) = L(x,z,z / y). L(x,y,y / z) = L(x,z,y). L(x,y \ z,z) = L(x,z,y). L(x,y,z) = L(x,z \ 1,y). L(x,y \ 1,z) = L(x,z,y). L(x,y,z) = L(x,z \ y,z). L(x,y \ z,y) = L(x,z,y). L((x \ y) \ z,y,x) = y \ (x * z). x \ (y * L(z,y,x)) = (x \ y) * z. x \ (y * ((y \ x) * z)) = L(z,x,y). L(x,y,z) = y \ (z * ((z \ y) * x)). x * L(y,x,z) = z * ((z \ x) * y). L(x * y,z,x) = z \ ((z / (x \ 1)) * y). (x * (y \ 1)) * L(z,x,y) = x * (y \ z). L(L((x \ y) \ z,u,w),y,x) = L(y \ (x * z),u,w). (x \ y) * ((z / (x \ y)) * (x \ (y * u))) = ((x \ y) * z) * L(u,x,y). (x \ (x / y)) * L(z,y,x) = x \ ((x / y) * z). L((x \ y) \ 1,z,u) * (x \ y) = x \ (y * L(L((x \ y) \ 1,z,u),y,x)). x \ (y * L(L((x \ y) \ 1,z,u),y,x)) = L((x \ y) \ 1,z,u) * (x \ y). L(x,y,T(z,y)) = L(x,y,z). x \ ((x / y) * T(y,z)) = K((x \ (x / y)) \ 1,z). K((x \ (x / y)) \ 1,z) = x \ ((x / y) * T(y,z)). K((x \ (x / y)) \ 1,z) = L(K(y,z),y,x). L(K(x,y),x,z) = K((z \ (z / x)) \ 1,y). (x * y) * K((x \ (x / y)) \ 1,z) = x * (y * K(y,z)). L(K(x,y),x,z) = K(L(x,x,z),y). x * K(L(y,y,x),z) = (x / y) * T(y,z). K(L(x,x,y \ x),z) = L(K(x,z),y,x). K(L(x,y,x),z) = L(K(x,z),y,x). L(K(x,y),z,x) = K(L(x,z,x),y). (x \ y) * K(L(y,x,y),z) = x \ (y * K(y,z)). (x \ y) * K(L(y,x,y),z) = x \ T(y,z). T(x / y,y) * (y * (((x / y) * y) \ z)) = x * L((y * (x / y)) \ z,y,x). (x * y) * K((x \ (x / y)) \ 1,z) = x * T(y,z). ((x / y) * ((y * z) / (x * z))) \ 1 = ((y * z) / (x * z)) \ (y / x). (K(x,y) \ (z / K(y,x))) \ z = K(K(x,y),z / K(x,y)). ((x / y) * ((y * z) / (x * z))) \ 1 = ((x * z) / (y * z)) * (y / x). (x / y) \ R(x / y,y,z) = ((x * z) / (y * z)) * (y / x). ((x * y) / (z * y)) * (z / x) = R(z,x,y) \ z. x * (R(y,x,z) \ y) = R(x,y / x,z). R(x,y / x,z) = R(x,y,z). R(x,y,z) = R(x,y * x,z). R(x,y * x,z) = R(x,y,z). x / ((x / K(y,z)) * (T(y,z) / (x * y))) = R(x,K(y,z),y). R(T(x,y),z * x,u) = T(R(x,z,u),y). R(T(x,y),z,u) = R(T(x,y),z * x,u). R(T(x,y),z * x,u) = R(T(x,y),z,u). ((x * (y * y)) \ ((x * y) * y)) \ 1 = a(y,T(y * x,y),y). a(x,y,y) \ 1 = a(y,T(y * x,y),y). a(x,T(x * y,x),x) = a(y,x,x) \ 1. a(x,y,y) \ 1 = a(y,y * x,y). a(x,x * y,x) = a(y,x,x) \ 1. a(x,y,y) \ 1 = a(y,x,y). a(x,y,x) \ z = a(y,x,x) * z. a(x,y,x) * z = a(y,x,x) \ z. a(x,y,y) \ z = a(y,x,y) * z. x / (a(y,z,z) * R(a(z,y,z),x,u)) = R(x,a(z,y,z),u). (x \ y) * (x * (((x \ z) / y) * (y * u))) = ((x \ y) * z) * L(u,x,y). (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = R(x,z,u) \ T(R(x,z,u),y). L(R(x / (y \ 1),y,y \ 1),z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u). x \ (y * L(y \ (x * 1),z,u)) = L((x \ y) \ 1,z,u) * (x \ y). x \ (y * L(y \ x,z,u)) = L((x \ y) \ 1,z,u) * (x \ y). L((x \ y) \ 1,z,u) * (x \ y) = x \ (y * L(y \ x,z,u)). 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) * (x * (((y / x) * x) \ z)) = y * L((x * (y / x)) \ z,x,y). (x \ y) * (x * (y \ z)) = y * L((x * (y / x)) \ z,x,y). x * L((y * (x / y)) \ z,y,x) = (y \ x) * (y * (x \ z)). x * (y * ((y * x) \ z)) = (y \ x) * (y * (x \ z)). (x \ y) * (x * (y \ z)) = y * (x * ((x * y) \ z)). (x \ y) * (x * (((x \ (x * (y \ z))) / y) * (y * u))) = (y * (x * ((x * y) \ z))) * L(u,x,y). ((T(x,y) * z) * u) / ((x * z) * u) = R(x,z,u) \ T(R(x,z,u),y). ((T(x,y) * z) * u) / ((x * z) * u) = R(x,z,u) \ R(T(x,y),z,u). R(x \ T(x,y),x * z,u) = R(x,z,u) \ R(T(x,y),z,u). R(K(x,y),x * z,u) = R(x,z,u) \ R(T(x,y),z,u). R(x,y,z) \ R(T(x,u),y,z) = R(K(x,u),x * y,z). 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). R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1. R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)). K(x,R(y,z,u)) = ((y * z) * u) / ((T(y,x) * z) * u). ((x * y) * z) / ((T(x,u) * y) * z) = K(u,R(x,y,z)). K(x,R(y,x,z)) = K(x,T(y,x)). K(x,R(y,x,z)) = K(x,y). K(x,y) * T(R(y,x,z),x) = R(y,x,z). K(x,y) * R(T(y,x),x,z) = R(y,x,z). x \ R(x,y,z) = T(x,y) \ R(T(x,y),y,z). T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). x / (y \ R(y,x,z)) = R(x,T(y,x),z). R(x,T(y,x),z) = R(x,y,z). R(x,x \ y,z) = R(x,y / x,z). R(x,y / x,z) = R(x,x \ y,z). R(x,x \ y,z) = R(x,y,z). R(x,y,z) = R(x,x * y,z). R(x,x * y,z) = R(x,y,z). R(x,y,z) \ (y * z) = (x \ y) * z. R(x,y,z) \ 1 = R(x \ 1,y,z). R(x \ 1,y,z) = R(x,y,z) \ 1. R(x,y,z) \ x = x * R(x \ 1,y,z). x * R(x \ 1,y,z) = R(x,y,z) \ x. R(x,y,y \ z) = z / ((x \ y) * (y \ z)). x / ((y \ z) * (z \ x)) = R(y,z,z \ x). K(R(x,y,z),u) = R(K(x,u),y,z). R(K(x,y),z,u) = K(R(x,z,u),y). R(T(x,y),x * z,u) = T(R(x,z,u),y). x * (R(x,y,z) \ (x * y)) = R(x * y,x,z). (x \ 1) / (y / x) = R(y \ 1,x,x). K(R(x,y,y),z) \ (K(x,z) / y) = y \ 1. R(K(x,y) \ 1,z,u) = K(R(x,z,u),y) \ 1. R(x,y,z) * (x \ (x * z)) = y * ((y \ x) * z). (x \ 1) / y = R((y * x) \ 1,x,x). R((x * y) \ 1,y,y) = (y \ 1) / x. R((x * (y \ 1)) \ 1,y \ 1,y \ 1) = T(y,y \ 1) / x. R(T(x,y),z,u) = R(T(x,y),x * z,u). R(T(x,y),x * z,u) = R(T(x,y),z,u). R(x,(x * K(y,x)) * z,u) = R(T(x * K(y,x),y),z,u). R(T(x * K(y,x),y),z,u) = R(x,(x * K(y,x)) * z,u). T(x,y) / ((z \ x) * K(x,y)) = R(z,x,x \ T(x,y)). x \ 1 = K(y,R(z,x,x)) * (K(z,y) / x). K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1. x * (x * (R(x,y,z) \ y)) = R(x * y,x,z). R(K(x,y) \ 1,z,u) = K(y,R(x,z,u)). R(K(x,y),z,u) = K(x,R(y,z,u)). K(x,R(y,z,u)) = K(R(x,z,u),y). K(R(x,y,z),u) = K(x,R(u,y,z)). K(L(x,x,y),z) = K(x,R(z,y,x)). K((x \ (x / y)) \ 1,z) = K(y,R(z,x,y)). x * K(y,R(z,x,y)) = (x / y) * T(y,z). x * R(y,x,z) = R(x * y,x,z). R(x * y,x,z) = x * R(y,x,z). ((x * y) / (z * y)) * z = R(z * (z \ x),z,y). R(x * (x \ y),x,z) = ((y * z) / (x * z)) * x. R(x,y,z) * z = y * ((y \ x) * z). (x * ((x \ y) * z)) / z = R(y,x,z). R(x,y,z) = (y * ((y \ x) * z)) / z. R(x * y,x,z) * z = x * (y * z). x * L(y,x,z) = R(x,z,y) * y. R(x,y,z) * z = x * L(z,x,y). R(x,y,z) * (x \ z) = L(z,x,y). L(x,y,z) = R(y,z,x) * (y \ x). T(x,L(y,x,z)) = L(y,x,z) \ (R(x,z,y) * y). L(x,y,z) \ (R(y,z,x) * x) = T(y,L(x,y,z)). L(x,y,z) = z * (R(z,y,x) \ x). x \ L(y,z,x) = R(x,z,y) \ y. R(x,y,z) \ z = x \ L(z,y,x). (x * y) / L(y,z,x) = R(x,z,y). R(x,y,z) = (x * z) / L(z,y,x). L(x,y * z,T(z,u)) = T(z,u) * (R(T(z,u),y,x) \ x). T(x,y) * (R(T(x,y),z,u) \ u) = L(u,z * x,T(x,y)). R(x,y,z) * (x \ L(z,y,x)) = z. R(x,y,z) * L(z,y,x) = x * z. R(x,y,R(y,z,u)) = R(x,R(y,z,u),y). R(x,R(y,z,u),y) = R(x,y,R(y,z,u)). R(x,y,z) = (x / L(z,y,x)) * z. x = y * (R(y,z,x) \ L(x,y,z)). x * (R(x,y,z) \ L(z,x,y)) = z. K(R(x,y,z),L(z,y,x)) = (L(z,y,x) * R(x,y,z)) \ (x * z). (L(x,y,z) * R(z,y,x)) \ (z * x) = K(R(z,y,x),L(x,y,z)). (L(x,y,z) / z) * R(z,y,x) = x. a(x / y,y,z) = x \ R(x,y,z). (R(x,y,z) \ x) * L(z,x,y) = z. (x / y) * R(y,z,L(x,y,z)) = L(x,y,z). a(x,y,z) = (x * y) \ R(x * y,y,z). R(x,y,z) \ x = a(y / x,x,z). a(x / y,y,z) = R(y,x,z) \ y. L(x,y,z) \ x = R(y,z,x) \ y. R(x,y,z) \ x = L(z,x,y) \ z. a(x,y,z) = R(y,x * y,z) \ y. T(x,R(y,z,x) \ y) = x. R(x,y,y) \ x = a(y,x,y). T(x,a(y / z,z,x)) = x. T(x,a(y,z,x)) = x. a(x,y,z) * z = z * a(x,y,z). R(x,y,y) * a(y,x,y) = x. a(x,y,z) = R(y,x,z) \ y. x / a(y,x,z) = R(x,y,z). R(x,y,z) = x / a(y,x,z). a(x,y,z) * R(y,x,z) = y. a(x,y,z) \ y = R(y,x,z). R(x,y,z) = a(y,x,z) \ x. 1 / a(x,y,z) = R(y,x,z) / y. R(x,y,z) / x = 1 / a(y,x,z). R(x,y,z) \ (x * u) = a(y,x,z) * u. a(x,y,z) * u = y * (R(y,x,z) \ u). x * (R(x,y,z) \ u) = a(y,x,z) * u. a(x,y,z) = x \ R(x,y,z). K(a(x,y,z),x) = 1. x * a(x,y,z) = R(x,y,z). R(x,y,z) = x * a(x,y,z). a(x,y,z) * x = R(x,y,z). R(x,y,z) = a(x,y,z) * x. x * R(x \ 1,y,z) = a(y,x,z). a(x,y,z) = y * R(y \ 1,x,z). a(x,K(y,z),u) = K(y,R(z,x,u)) \ K(y,z). K(x,R(y,z,u)) \ K(x,y) = a(z,K(x,y),u). a(x,y,z) * L(z,y,x) = z. a(x / y,y,z) = a(x,y,z). a(x,y,z) = a(x * y,y,z). a(x * y,y,z) = a(x,y,z). T(a(x,y,z),x) = a(x,y,z). L(a(x,y,z),x,u) = u \ ((u / x) * R(x,y,z)). x \ ((x / y) * R(y,z,u)) = L(a(y,z,u),y,x). R(x,y,z) / x = a(x,y,z). a(x,y,z) = R(x,y,z) / x. R(x,y,z) \ a(x,y,z) = x \ 1. L(x,y,a(y,z,u)) = x. x * (a(x,y,z) * u) = R(x,y,z) * u. a(x,y,z) * u = R(x,y,z) * (x \ u). R(x,y,z) * (x \ u) = a(x,y,z) * u. a(x,y,z) \ u = x * (R(x,y,z) \ u). x * (R(x,y,z) \ u) = a(x,y,z) \ u. T(a(x,y,z),x * u) = (x * u) \ (R(x,y,z) * u). (x * y) \ (R(x,z,u) * y) = T(a(x,z,u),x * y). a(L(x,x,y),z,u) = (y \ (y / x)) * R(L(x,x,y),z,u). (x \ (x / y)) * R(L(y,y,x),z,u) = a(L(y,y,x),z,u). L(a(T(x,y),z,u),x,y) = (x * y) \ (y * R(T(x,y),z,u)). (x * y) \ (y * R(T(x,y),z,u)) = L(a(T(x,y),z,u),x,y). x \ T(y,a(x,z,u)) = (a(x,z,u) * x) \ (y * a(x,z,u)). (a(x,y,z) * x) \ (u * a(x,y,z)) = x \ T(u,a(x,y,z)). a(x,y,x) = a(y,x \ 1,x). a(x,y \ 1,y) = a(y,x,y). R(x,y,a(y,z,u)) * R(y,z,u) = (x * y) * a(y,z,u). L(x,a(x,y,z),u) = u \ ((u / a(x,y,z)) * R(x,y,z)). x \ ((x / a(y,z,u)) * R(y,z,u)) = L(y,a(y,z,u),x). x / L(x,y,z) = a(z,y,x). a(x,y,z) = z / L(z,y,x). R(x,a(y,z,u),L(u,z,y)) = ((x * a(y,z,u)) * L(u,z,y)) / u. ((x * a(y,z,u)) * L(u,z,y)) / u = R(x,a(y,z,u),L(u,z,y)). K(a(x,y,z),u) * z = T(a(x,y,z),u) * L(z,y,x). T(a(x,y,z),u) * L(z,y,x) = K(a(x,y,z),u) * z. a(x \ 1,y,x \ 1) = a(x,y,x). R(x / a(y,z,u),u / L(u,z,y),L(u,z,y)) = (x * L(u,z,y)) / u. L(x,y,z) * a(z,y,x) = x. x / a(y,z,x) = L(x,z,y). L(x,y,z) = x / a(z,y,x). L(x,a(y,z,u),u) = x. a(1 / x,y,z) = z / L(z,x,y). a(x,y,z) * (u * z) = (a(x,y,z) * z) * T(u,z). (a(x,y,z) * z) * T(u,z) = a(x,y,z) * (u * z). a(x,y,z) = 1 / a(y,x,z). 1 / a(x,y,z) = a(y,x,z). a(x,y,z) * a(y,x,z) = 1. a(x,y,z) \ 1 = a(y,x,z). a(x,y,z) * (a(y,x,z) * u) = u. a(x,y,z) * u = a(y,x,z) \ u. a(x,y,z) \ u = a(y,x,z) * u. K(a(x,y,z),u) * 1 = T(a(x,y,z),u) * a(y,x,z). T(a(x,y,z),u) * a(y,x,z) = K(a(x,y,z),u) * 1. a(x,y,z) = a(1 / y,x,z). a(1 / x,y,z) = a(y,x,z). a(x,y,z) = a(y,x \ 1,z). a(x,y \ 1,z) = a(y,x,z). a(x \ 1,y,z) = a(y,x,z). a((x \ y) / x,x,z) = a(y,x,z). a(x,y \ 1,y \ 1) = a(y,x \ 1,y). T(x,a(y,z,u)) = a(z,y,u) * (x * a(y,z,u)). a(x,y,z) * (u * a(y,x,z)) = T(u,a(y,x,z)). a(x,y,z) * u != z | u = L(z,y,x). a(x,y,z) * z = L(z,x,y). L(x,y,z) = a(y,z,x) * x. K(a(x,y,z) * u,a(y,x,z)) = u \ ((a(x,y,z) * u) * a(y,x,z)). x \ ((a(y,z,u) * x) * a(z,y,u)) = K(a(y,z,u) * x,a(z,y,u)). x \ L(x,y,z) = a(y,z,x). a(x,y,z) = z \ L(z,x,y). L(x,y,z) / x = a(y,z,x). a(x,y,z) = L(z,x,y) / z. L(x,y,z) = x * a(y,z,x). a(x,y,z \ 1) = z * L(z \ 1,x,y). x * L(x \ 1,y,z) = a(y,z,x \ 1). a(x,y,x \ z) = (x \ z) \ (y \ ((y / x) * z)). (x \ y) \ (z \ ((z / x) * y)) = a(x,z,x \ y). x * L(a(y,z,u),u,x) = (x / u) * L(u,y,z). ((L(x,y,z) / x) * L(x,y,z)) \ L(x,y,z) = a(y,z,x) \ 1. x \ (L(x,y,z) * u) = a(y,z,x) * u. a(x,y,z) \ u = z * (L(z,x,y) \ u). x * (L(x,y,z) \ u) = a(y,z,x) \ u. a(x,y,K(z,u)) = K(u,z) * L(K(z,u),x,y). K(x,y) * L(K(y,x),z,u) = a(z,u,K(y,x)). L(a(x,y,z \ u),u,z) = u \ (z * L(z \ u,x,y)). x \ (y * L(y \ x,z,u)) = L(a(z,u,y \ x),x,y). R(a(x,y,z) * 1,u,w) = R(a(y,x,z),u,w) \ 1. a(x,y,z) = a(y \ x,y,z). a(x \ y,x,z) = a(y,x,z). a(x,y,z) = a(y * x,y,z). a(x * y,x,z) = a(y,x,z). R(x,y,R(y,z,u)) * (y * R(y,z,u)) = (x * R(y,z,u)) * y. a(R(x,y,z) / u,u,x) = R(u,x,R(x,y,z)) \ u. a(x,y,y) = (x * y) \ (x / (y \ 1)). (x * y) \ (x / (y \ 1)) = a(x,y,y). (x * (y \ 1)) \ (x / y) = a(x,y \ 1,y \ 1). x * y = a(z,x,u) * (R(x,z,u) * y). a(x,y,z) * (R(y,x,z) * u) = y * u. x * (y * z) = a(y,x,z) * ((x * y) * z). a(x,y,z) * ((y * x) * z) = y * (x * z). x * (a(y,x,z) * u) = a(y,x,z) * (x * u). a(x,y,z) * (y * u) = y * (a(x,y,z) * u). (R(x,y,z) * u) / (a(x,y,z) * u) = x. x * y != R(x,z,u) * (x * w) | y = R(x,z,u) * w. a(x,y,z) * (x * u) = R(x,y,z) * u. R(x,a(x,y,z) * u,w) = ((R(x,y,z) * u) * w) / ((a(x,y,z) * u) * w). ((R(x,y,z) * u) * w) / ((a(x,y,z) * u) * w) = R(x,a(x,y,z) * u,w). x * (y * z) = a(x,y,z) \ ((x * y) * z). a(x,y,z) \ ((x * y) * z) = x * (y * z). a(x,y \ 1,y \ 1) = a(x,y,y). a(x,y,y) = a(y,x,y \ 1). a(x,y,x \ 1) = a(y,x,x). a(x,y,(z \ u) \ 1) = z \ (u * L(u \ z,x,y)). x \ (y * L(y \ x,z,u)) = a(z,u,(x \ y) \ 1). x * (a(y,z,x) * u) = L(x,y,z) * u. R(x,y,z) = z * (L(z,y,x) \ x). x * (L(x,y,z) \ u) = a(z,y,x) * u. (x * y) / R(y,z,x) = L(x,z,y). L(x,y,z) = (x * z) / R(z,y,x). L(x,y,z) * R(z,y,x) = x * z. a(L(x,y,z),R(z,y,x),u) = (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u). (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). x * R(y,z,L(x,y,z)) = L(x,y,z) * y. ((R(x,y,z) * u) * w) / (a(R(x,u,w),y,z) * (u * w)) = R(x,u,w). x * R(y,z,x) = L(x,y,z) * y. L(x,y,z) * y = x * R(y,z,x). x * (y * z) = L(x,u,y) * (R(y,u,x) * z). L(x,y,z) * (R(z,y,x) * u) = x * (z * u). x * T(y,L(x,z,u)) = a(u,z,x) * (y * L(x,z,u)). a(x,y,z) * (u * L(z,y,x)) = z * T(u,L(z,y,x)). (x * y) / (a(z,u,x) * y) = L(x,u,z). a(x,y,z) * T(u,z) = L(z,y,x) \ (u * z). L(x,y,z) \ (u * x) = a(z,y,x) * T(u,x). x * (y * z) = T(x * (y * z),a(x,y,z)). T(x * (y * z),a(x,y,z)) = x * (y * z). x * y != L(x,z,u) * z | y = R(z,u,x). R(x,y,L(z,x,y)) = R(x,y,z). R(x * y,y,L(z,x,y)) = R(x * y,y,z). (x / y) * R(y,z,x) = L(x,y,z). L(x,y,z) = (x / y) * R(y,z,x). x \ L(x,T(y,x),z) = (y * x) \ (x * R(T(y,x),z,x)). (x * y) \ (y * R(T(x,y),z,y)) = y \ L(y,T(x,y),z). L(x * R(x \ 1,y,z),z,x) = z \ L(z,x \ 1,y). K(x * (y * z),a(x,y,z)) = 1. K(x * y,a(x / z,z,L(y,x,z))) = 1. K(x * y,a(x,z,L(y,x,z))) = 1. a(x,y,L(z,x,y)) = (x * y) \ R(x * y,y,z). (x * y) \ R(x * y,y,z) = a(x,y,L(z,x,y)). a(x,K(y,z),u) = K(R(z,x,u),y) * K(y,z). K(R(x,y,z),u) * K(u,x) = a(y,K(u,x),z). (x * (a(y,x,z) * u)) / a(y,x,z) = (x * u) * K(a(y,x,z),x * u). K(x,R(y,z,u)) * K(y,x) = a(z,K(y,x),u). R(x,y,z) = ((x * z) / (y * z)) * y. R(x,y,z) / y = (x * z) / (y * z). R(x / y,z,y) = (x / (z * y)) * z. R(K(x,y),z,x) / z = T(x,y) / (z * x). (x / (y * z)) * y = ((x / z) * z) / L(z,y,x / z). ((x / y) * y) / L(y,z,x / y) = (x / (z * y)) * z. K(x,R(y,z,x)) / z = T(x,y) / (z * x). T(x,L(y,x,z)) = a(z,x,y) * T(R(x,z,y),y). a(x,y,z) * T(R(y,x,z),z) = T(y,L(z,y,x)). T(x,a(y,z,u)) != a(z,y,u) * w | x * a(y,z,u) = w. L(a(x,y,x \ z),x \ z,y) = (y * (x \ z)) \ ((y / x) * z). (x * (y \ 1)) \ (x / y) = a(x,y,y). a(x,y,z) = a(x,y,L(z,x,y)). a(x,y,L(z,x,y)) = a(x,y,z). K(x * y,a(x,z,y)) = 1. T(a(x,y,z),x * z) * 1 = a(x,y,z). K((x * y) * z,a(y,x,z)) = 1. T(a(x,y,z),(y * x) * z) * 1 = a(x,y,z). T(a(x,y,z),x * z) = a(x,y,z). T(a(x,y,z),(y * x) * z) = a(x,y,z). a(x,y,z) = ((y * x) * z) \ (a(x,y,z) * ((y * x) * z)). ((x * y) * z) \ (a(y,x,z) * ((x * y) * z)) = a(y,x,z). a(x,y,z) * R(T(y,z),x,z) = T(y,L(z,y,x)). L(x,y,z) * T(u,x) = a(y,z,x) * (u * x). a(x,y,z) * (u * z) = L(z,x,y) * T(u,z). a(x,y,R(x,z,u)) = a(R(x,z,u) / y,y,x). a(R(x,y,z) / u,u,x) = a(x,u,R(x,y,z)). a(x,y,R(x,z,u)) = a(R(x,z,u),y,x). a(R(x,y,z),u,x) = a(x,u,R(x,y,z)). T(x,y) / ((z \ x) * K(x,y)) = R(z,x,K(x,y)). K(a(x,y,z),u) = T(a(x,y,z),u) * a(y,x,z). T(a(x,y,z),u) * a(y,x,z) = K(a(x,y,z),u). L(a(x,y,z \ u),u,z) = a(x,y,(u \ z) \ 1). L(a(x,y,(z / u) \ z),z,z / u) = a(x,y,L(u \ 1,u,z) \ 1). L(a(x,y,z),z,y) = z \ L(z,y \ 1,x). L(a(x,y,z),z,y) = z \ L(z,x,y). a(x,y,z) = L(a(x,y,z),z,y). L(a(x,y,z),z,y) = a(x,y,z). x / L(y,z,x / y) = (x / (z * y)) * z. R(T(x * K(y,x),y),z,u) = R(x,x * (K(y,x) * z),u). L(x,y,T(z,u)) = L(x,y * z,T(z,u)). L(x,y * z,T(z,u)) = L(x,y,T(z,u)). (x \ (x / y)) * L(R(y,z,u),y,x) = a(L(y,y,x),z,u). a(T(x,y),z,y) = (x * y) \ (y * R(T(x,y),z,y)). (x * y) \ (y * R(T(x,y),z,y)) = a(T(x,y),z,y). (x * y) \ (R(x,z,y) * y) = a(T(x,y),z,y). a(T(x,y),z,y) = T(a(x,z,y),x * y). T(a(x,y,z),x * z) = a(T(x,z),y,z). a(T(x,y),z,y) = a(x,z,y). a(x,y \ 1,z) = a(y,T(x,z),z). a(x,T(y,z),z) = a(y,x \ 1,z). L(x,T(y,x),z) = x * a(y,z,x). a(x,T(y,z),z) = a(x,y,z). a(x,y,z) * R(T(y,z),x,z) = T(y,z). L(x,y,z) = L(x,T(y,x),z). L(x,T(y,x),z) = L(x,y,z). L(x,T(y / x,x),z) = z \ ((z / (y / x)) * y). T(x,y) = T(x,L(y,x,z)). T(x,L(y,x,z)) = T(x,y). K(L(x,y,z),y) = T(y,x) \ y. K(x,y) = K(L(x,y,z),y). K(L(x,y,z),y) = K(x,y). L(x,x \ y,z) = z \ ((z / (y / x)) * y). ((x * y) * z) \ (x * (y * z)) = a(y,x,z). a(x,y,z) = ((y * x) * z) \ (y * (x * z)). a(x \ y,x,z) = (y * z) \ (x * ((x \ y) * z)). (x * y) \ (z * ((z \ x) * y)) = a(z \ x,z,y). (x * y) \ (z * ((z \ x) * y)) = a(x,z,y). a(x,y,z) = (x * z) \ (y * ((y \ x) * z)). R(T(x * K(y,x),y),z,u) = R(x,K(y,x) * z,u). R(x,y,z) = R(x,K(u,x) * y,z). R(x,K(y,x) * z,u) = R(x,z,u). R(x,y,z) = R(x,K(x,u) * y,z). R(x,K(x,y) * z,u) = R(x,z,u). L(x,y,K(z,y) * u) = R(y,u,x) * (y \ x). L(x,K(y,z) * u,y) = y * (R(y,u,x) \ x). L(x,y,z) = L(x,y,K(u,y) * z). L(x,y,K(z,y) * u) = L(x,y,u). L(x,y,z) = L(x,y,K(y,u) * z). L(x,y,K(y,z) * u) = L(x,y,u). L(x,y,z \ 1) = L(x,y,K(u,y) / z). L(x,y,K(z,y) / u) = L(x,y,u \ 1). L(x,y,K(z,y) / u) = L(x,u,y). L(x,y,K(z,y) * (u \ K(z,y))) = L(x,K(z,y) \ u,y). L(x,y,z) = L(x,K(z,u) * y,z). L(x,K(y,z) * u,y) = L(x,u,y). a(L(x,x,y),z,u) = y \ ((y / x) * R(x,z,u)). x \ ((x / y) * R(y,z,u)) = a(L(y,y,x),z,u). a(L(x,x,y),z,u) = L(a(x,z,u),x,y). a(L(T(x,y),T(x,y),T(y,x)),z,u) = L(a(T(x,y),z,u),x,y). L(x,K(y,z) \ u,z) = L(x,z,u \ K(y,z)). L(x,K(y,z) * u,y) = L(x,y,u \ K(z,y)). L(x,y,z \ K(u,y)) = L(x,z,y). a(x,y \ K(z,x),u) = u \ L(u,y,x). a(x,y,z) = a(y,x \ K(u,y),z). a(x,y \ K(z,x),u) = a(y,x,u). T(x,x \ 1) / y = R((y * (x \ 1)) \ 1,x,x). R((x * (y \ 1)) \ 1,y,y) = T(y,y \ 1) / x. R((x * (y \ 1)) \ 1,y,y) = y / x. (x * y) \ (R(x,z,u) * y) = L(a(T(x,y),z,u),x,y). L(a(T(x,y),z,u),x,y) = T(a(x,z,u),x * y). R(x,y,z) \ (u * a(x,y,z)) = x \ T(u,a(x,y,z)). (L(x,y,z) * R(z,y,x)) \ (z * x) = K(z,R(L(x,y,z),y,x)). (a(x,y,z) * L(z,x,y)) \ L(z,x,y) = a(x,y,z) \ 1. (a(x,y,z) * L(z,x,y)) \ L(z,x,y) = a(y,x,z). (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 * (y * R(y,z,u))) \ ((x * y) * R(y,z,u)) = a(x,R(y,z,u),y). (x * (y \ z)) \ ((x / y) * z) = a(y,x,y \ z). (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(R(y,z,u),x,R(y,z,u) \ a(y,z,u)). a(R(x,y,z),u,R(x,y,z) \ a(x,y,z)) = (u * (x \ 1)) \ ((u / R(x,y,z)) * a(x,y,z)). a(T(x,x \ y),z,u) = L(a(T(x,y),z,u),x,y). L(a(T(x,y),z,u),x,y) = a(T(x,x \ y),z,u). a(T(x,x \ y),z,u) = T(a(x,z,u),x * y). a(T(x,x \ T(y,x)),z,u) = T(a(x,z,u),y * x). a(T(x,x \ y),z,u) = T(a(x,z,u),y * x). a(T(x \ 1,(x \ 1) \ (y * x)),z,u) = T(a(x \ 1,z,u),R(y,x,x \ 1)). (L(x,y,z) * R(z,y,x)) \ (z * x) = K(z,L(R(x,y,x),y,z)). (L(x,y,z) * R(z,y,x)) \ (z * x) = K(z,L(L(x,x,y),y,z)). (x * y) \ (y * x) = K(y,L(L(x,x,z),z,y)). K(x,L(L(y,y,z),z,x)) = (y * x) \ (x * y). K(x,y) = K(x,L(L(y,y,z),z,x)). K(x,L(L(y,y,z),z,x)) = K(x,y). T(x,L(L(y,y,z),z,x)) = x * K(x,y). K(x,y) \ 1 = K(L(L(y,y,z),z,x),x). K(L(L(x,x,y),y,z),z) = K(z,x) \ 1. T(x,y) = T(x,L(L(y,y,z),z,x)). T(x,L(L(y,y,z),z,x)) = T(x,y). T(x,L(L(y,y,z \ 1),x,z)) = T(x,y). K(L(L(x,x,y),y,z),z) = K(x,z). K(L(L(x,x,y \ 1),z,y),z) = K(x,z). T(x,L(L(y,z,y),x,z)) = T(x,y). T(x,y) = T(x,L(y,z,y)). T(x,L(y,z,y)) = T(x,y). L(x,y,x) * T(z,x) = z * L(x,y,x). K(L(L(x,y,x),z,y),z) = K(x,z). K(L(x,y,z),y) = K(L(x,x,z),y). K(x,y) = K(L(x,z,x),y). K(L(x,y,x),z) = K(x,z). K(T(x,x * y),z) = K(T(x,y),z). (x \ y) * K(y,z) = x \ T(y,z). K(L(x,y,z),y) = K(x,R(y,z,x)). K(T(x,y),z) = K(T(x,x \ y),z). K(T(x,x \ y),z) = K(T(x,y),z). L(K(x,y),z \ x,u) = u \ ((u / (z \ x)) * (z \ T(x,y))). x \ ((x / (y \ z)) * (y \ T(z,u))) = L(K(z,u),y \ z,x). T(x,y) / (z \ T(x,y)) = R(z,x,K(x,y)). K(x,R(y,z,x)) = K(x,y). K((x \ (x / y)) \ 1,z) = K(y,z). x * K(y,z) = (x / y) * T(y,z). (x / y) * T(y,z) = x * K(y,z). K(x,y) / z = T(x,y) / (z * x). T(x,y) / (z * x) = K(x,y) / z. K(T(x,x \ y),z) = T(K(x,z),y). (x * y) * K(y,z) = x * T(y,z). (x * y) * T(L(z,y,x),u) = (x * (y * z)) * K(L(z,y,x),u). (x * (y * z)) * K(L(z,y,x),u) = (x * y) * T(L(z,y,x),u). x / ((x / K(y,z)) * (K(y,z) / x)) = R(x,K(y,z),y). T(K(x,y),z) = K(T(x,z),y). K(T(x,y),z) = T(K(x,z),y). 1 / T(K(x,y),z) = K(y,T(x,z)). L(K(x,y),z * x,u) = u \ ((u / (z * x)) * (z * T(x,y))). x \ ((x / (y * z)) * (y * T(z,u))) = L(K(z,u),y * z,x). a(x,y,y) * (z * y) = z * L(y,x,y). x * y != ((x * z) / u) * u | y = z. ((a(x,y,y) * z) / L(y,x,y)) * y = z. (x \ ((a(y,x \ 1,x \ 1) * (x * z)) / L(x \ 1,y,x \ 1))) / x = z. R(x,y,K(y,z)) = x. (x * y) / y = R(x,y,K(x,z)). R(x,y,K(x,z)) = (x * y) / y. R(x,y,K(x,z)) = x. x \ ((y * x) * K(x,z)) = T(y,x) * K(x,z). x \ (y * T(x,z)) = T(y,x) * K(x,z). x / 1 = R(x,K(y,z),y). R(x,K(y,z),y) = x / 1. R(x,K(y,z),y) = x. x * T(y,z) = (x * K(y,z)) * y. (x * K(y,z)) * y = x * T(y,z). x / K(y,z) = (x * y) / T(y,z). (x * y) / T(y,z) = x / K(y,z). L(x,K(x,y),z) = (x * z) / z. L(x,K(x,y),z) = x. L(x,y,K(x,z)) = x. L(x,y,K(x,z) \ y) = x. (x \ K(y,z)) \ (x \ (K(y,z) * y)) = y. L(x,y,K(z,x) * y) = x. x = L(x,y,K(z,x)). L(x,y,K(z,x)) = x. T(x * K(y,z),y) = y \ (x * T(y,z)). x \ (y * T(x,z)) = T(y * K(x,z),x). (x \ K(y,z)) \ (x \ T(y,z)) = y. T(x * K(y,z),y) = T(x,y) * K(y,z). x \ (y * (((y \ x) / z) * T(z,u))) = L(K(z,u),y \ z,x). x \ (y * ((y \ x) * K(z,u))) = L(K(z,u),y \ z,x). L(K(x,y),z \ x,u) = u \ (z * ((z \ u) * K(x,y))). L(K(x,y),z,u) = L(K(x,y),u \ x,z). L(K(x,y),z \ x,u) = L(K(x,y),u,z). (x * (y * z)) * K(L(z,y,x),u) = (x * y) * L(T(z,u),y,x). (x * (y * z)) * K(L(z,y,x),u) = x * (y * T(z,u)). (x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u). K(L(x,y,z),u) = z \ ((z / (y * x)) * (y * T(x,u))). x \ ((x / (y * z)) * (y * T(z,u))) = K(L(z,y,x),u). K(L(x,y,z),u) = L(K(x,u),y * x,z). L(K(x,y),z * x,u) = K(L(x,z,u),y). L(K(x,y),z \ x,u) = K(L(x,z \ 1,u),y). K(L(x,y \ 1,z),u) = L(K(x,u),z,y). K(L(x,y,z),u) = L(K(x,u),y,z). L(K(x,y),z,u) = K(L(x,z,u),y). K(x,y) = L(K(x,y),K(z,x),u). L(K(x,y),K(z,x),u) = K(x,y). x * K(y,z) = x / K(z,y). x / K(y,z) = x * K(z,y). K(x,y) = z \ (z / K(y,x)). x \ (x / K(y,z)) = K(z,y). (x / K(y,z)) / K(z,y) = x. T(x,K(y,z)) = K(y,z) \ (x / K(z,y)). K(x,y) \ (z / K(y,x)) = T(z,K(x,y)). (x \ K(y,z)) * K(z,y) = x \ 1. (K(x,y) \ z) \ (z / K(x,y)) = K(z,K(y,x)). (x * K(y,z)) / K(y,z) = R(x,K(z,y),K(z,y)). (x * y) / T(y,z) = x * K(z,y). x = R(x,K(y,z),K(y,z)). R(x,K(y,z),K(y,z)) = x. (x * y) * K(L(z,y,x),u) = x * (y * K(z,u)). (x / y) * (y * K(z,u)) = x * K(L(z,y,x),u). K(x,y) * K(L(y,z,u),x) = a(z,u,K(y,x)). K(L(x,K(x,y) \ z,u),y) = u \ ((u / (z / K(x,y))) * z). a(x \ 1,K(y,z),u) = a(x \ K(z,y),K(y,z),u). a(x \ K(y,z),K(z,y),u) = a(x \ 1,K(z,y),u). (x * K(y,z)) * T(z,y) = x * z. L(x,y,z) / T(a(y,z,x),u) = x * K(u,a(y,z,x)). T(x,K(y,z)) \ x = K(K(y,z),x / K(y,z)). K(K(x,y),z / K(x,y)) = T(z,K(x,y)) \ z. K(x,K(y,z)) = K(K(z,y),x / K(z,y)). K(K(x,y),z / K(x,y)) = K(z,K(y,x)). K(K(x,y),z) = K(K(x,y),z / K(x,y)). K(K(x,y),z / K(x,y)) = K(K(x,y),z). K(K(x,y),z) = K(z,K(y,x)). K(x,K(y,z)) \ K(y,z) = 1 / T(K(z,y),x). 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) = K(x,T(y,z)). K(x,T(y,z)) = T(K(x,y),z). x * K(y,T(z,x)) = K(y,z) * x. K(T(x,y),z) = K(x,T(z,y)). K(x,y) * z != z * u | K(x,T(y,z)) = u. R(x,K(y,z),K(y,z)) = (x * K(z,y)) * K(y,z). (x * K(y,z)) * K(z,y) = R(x,K(z,y),K(z,y)). (x * (y * K(z,u))) \ R(x * y,K(L(z,y,x),u),K(L(z,y,x),u) \ 1) = K(L(z,y,x),u) \ 1. R(x,K(y,z),K(y,z)) = R(x,K(z,y),K(y,z)). R(x,K(y,z),K(z,y)) = R(x,K(z,y),K(z,y)). R(x,K(y,z),K(z,y)) = x. a(x \ K(y,z),K(z,y),u) = a(K(z,y),x,u). K(L(x,K(y,x) * z,u),y) = u \ ((u / (z / K(x,y))) * z). R(x,a(y,z,u),L(u,z,y)) = ((x * a(y,z,u)) / u) * L(u,z,y). ((x * a(y,z,u)) / u) * L(u,z,y) = R(x,a(y,z,u),L(u,z,y)). L(a(x,y,z),u,u / z) = a(x,y,L(z \ 1,z,u) \ 1). a(x,y,L(z \ 1,z,u) \ 1) = L(a(x,y,z),z,u). a(x,y,L(z,z,u)) = L(a(x,y,z),z,u). x * a(y,z,L(u,u,x)) = (x / u) * L(u,y,z). a(x,y,R(y,z,u)) = a(x,R(y,z,u),y). a(x,R(y,z,u),y) = a(x,y,R(y,z,u)). (x \ ((a(y,x,x) * (x * z)) / L(x \ 1,y,x \ 1))) / x = z. (x \ ((x * (a(y,x,x) * z)) / L(x \ 1,y,x \ 1))) / x = z. (x \ ((L(x,y,x) * z) / L(x \ 1,y,x \ 1))) / x = z. (x \ ((L(x,y,x) * z) / L(x \ 1,x,y))) / x = z. x = (y \ (L(y,z,y) * x)) / (y * L(y \ 1,y,z)). (x \ (L(x,y,x) * z)) / (x * L(x \ 1,x,y)) = z. (a(x,y,y) * z) / (y * L(y \ 1,y,x)) = z. (a(x,y,y) * z) / a(y,x,y \ 1) = z. (a(x,y,y) * z) / a(x,y,y) = z. x * a(y,z,z) = a(y,z,z) * x. a(x,y,y) * z = z * a(x,y,y). T(x,a(y,z,z)) = x. a(x,y,y) * (z \ 1) = z \ a(x,y,y). x * (y * a(x,z,z)) = R(x,z,z) * y. (x * y) * a(x,z,z) = R(x,z,z) * y. K(x,a(y,z,z)) = 1. T(x,a(y,z,y)) = x. 1 * ((a(x,y,y) \ z) \ u) = (a(x,y,y) / z) * u. (a(x,y,y) * z) * a(y,x,y) = z. x / a(y,z,y) = a(z,y,y) * x. R(x,y,a(y,z,z)) = (R(y,z,z) * (y \ x)) / a(y,z,z). (R(x,y,y) * (x \ z)) / a(x,y,y) = R(z,x,a(x,y,y)). (R(x,y,y) * z) / ((z * x) * a(x,y,y)) = K(x,z). 1 * ((a(x,y,x) * z) \ u) = (a(y,x,x) / z) * u. (a(x,y,x) * z) \ u = (a(y,x,x) / z) * u. (a(x,y,y) * z) / a(x,y,y) = R(z,x,a(x,y,y)). R(x,y,a(y,z,z)) = x. x * R(y,z,z) = (x * y) * a(y,z,z). (x * y) * a(y,z,z) = x * R(y,z,z). (R(x,y,y) * z) / (z * R(x,y,y)) = K(x,z). K(R(x,y,y),z) = K(x,z). K(x,y) * (x / z) = T(x,y) / z. K(x,y) \ (K(x,y) / z) = z \ 1. K(x,y) = K(x,R(y,z,z)). K(x,R(y,z,z)) = K(x,y). T(x,R(y,z,z)) = x * K(x,y). T(x,y) = T(x,R(y,z,z)). T(x,R(y,z,z)) = T(x,y). T(x,y) = T(x,R(y,z,z \ 1)). T(x,R(y,z,z \ 1)) = T(x,y). T(x,y) \ (T(x,y) / z) = x \ (x / z). (K(x,y) * z) \ K(x,y) = z \ 1. x \ K(y,z) = (K(z,y) * x) \ 1. (K(x,y) * z) \ 1 = z \ K(y,x). (x \ K(y,z)) \ u = (K(z,y) * x) * u. x \ ((y \ (y / x)) \ 1) = a(x,T(y,z),x). a(x,T(y,z),x) = x \ ((y \ (y / x)) \ 1). (K(x,y) * z) * (z \ T(y,x)) = y. L(x,y,K(z,x) * u) = y \ ((y / ((K(z,x) * u) \ 1)) * (u \ T(x,z))). x \ ((x / ((K(y,z) * u) \ 1)) * (u \ T(z,y))) = L(z,x,K(y,z) * u). a(x,T(y,z),x) = a(x,y,x). x \ ((x / (y \ K(z,u))) * (y \ T(z,u))) = L(z,x,K(u,z) * y). x \ (y * (((y \ x) / K(z,u)) * T(z,u))) = L(z,x,K(u,z) * y). x \ (y * (((y \ x) * K(z,u)) * T(u,z))) = L(u,x,K(z,u) * y). x \ (y * ((y \ x) * z)) = L(z,x,K(u,z) * y). L(x,y,K(z,x) * u) = y \ (u * ((u \ y) * x)). L(x,y,z) = L(x,y,K(u,x) * z). L(x,y,K(z,x) * u) = L(x,y,u). L(x,y \ 1,z) = L(x,K(u,x) * z,y). L(x,K(y,x) * z,u) = L(x,u \ 1,z). L(x,K(y,x) * z,u) = L(x,z,u). K(L(x,y,z),u) = z \ ((z / (y / K(x,u))) * y). x \ ((x / (y / K(z,u))) * y) = K(L(z,y,x),u). x \ ((x / (y * K(z,u))) * y) = K(L(u,y,x),z). L(x * y,z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u). (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x. (x \ 1) * L(x * y,z,u) = L(y * x,z,u) / x. L(x * y,z,u) / y = y \ L(y * x,z,u). L(x,y,z) / a(u,w,x) = a(u,w,x) \ L(a(u,w,x) * L(x,w,u),y,z). a(x,y,z) \ L(a(x,y,z) * L(z,y,x),u,w) = L(z,u,w) / a(x,y,z). a(x,y,z) \ L(z,u,w) = L(z,u,w) / a(x,y,z). L(x,y,z) / a(u,w,x) = a(u,w,x) \ L(x,y,z). L(x,y,z) / a(u,w,x) = a(w,u,x) * L(x,y,z). (x * (y * z)) \ ((x * y) * z) = a(L(x,u,y),R(y,u,x),z). a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u). a(x,y,z) = a(L(x,u,y),R(y,u,x),z). a(L(x,y,z),R(z,y,x),u) = a(x,z,u). a(x,R(y,z,L(x,y,z)),u) = a(L(x,y,z),y,u). L(x,R(y,z,u),L(u,z,y)) = x / a(u,y,x). L(x,y,z) = L(x,R(y,u,z),L(z,u,y)). L(x,R(y,z,u),L(u,z,y)) = L(x,y,u). a(x,R(y,z,x),u) = a(L(x,y,z),y,u). a(L(x,y,z),y,u) = a(x,R(y,z,x),u). a(T(x \ 1,(x \ 1) \ (y * x)),z,u) = T(a(z,x,u),R(y,x,x \ 1)). a(T(x \ 1,(x \ 1) \ (y * x)),z,u) = T(a(z,x,u),y). a(T(x \ 1,x * (y * x)),z,u) = T(a(z,x,u),y). a(T(x,y) \ 1,z,u) = T(a(z,x,u),y). T(a(x,y,z),u) = a(x,T(y,u),z). a(x,T(y,z),u) = T(a(x,y,u),z). x * a(y,T(z,x),u) = a(y,z,u) * x. K(x,a(y,z,u)) = a(y,T(z,x),u) \ a(y,z,u). a(x,T(y,z),u) \ a(x,y,u) = K(z,a(x,y,u)). T(a(x \ 1,y,z),u) = a(T(y,u),x,z). a(x,T(y,z),u) * L(u,y,x) = K(a(x,y,u),z) * u. a(x,T(y,z),u) * a(y,x,u) = K(a(x,y,u),z). L(x,y,z) / a(y,T(z,u),x) = x * K(u,a(y,z,x)). T(a(x,y,z),u) = a(T(x,u),y,z). a(T(x,y),z,u) = T(a(x,z,u),y). a(x,T(y,z),u) = a(T(x,z),y,u). a(T(x,y),z,u) = a(x,T(z,y),u). K(x,a(y,z,u)) = a(T(z,x),y,u) * a(y,z,u). a(T(x,y),z,u) * a(z,x,u) = K(y,a(z,x,u)). a(x,T(y,z),u) * a(y,x,u) = K(z,a(y,x,u)). K(x,a(y,z,u)) = K(a(z,y,u),x). K(a(x,y,z),u) = K(u,a(y,x,z)). T(x,a(y,z,u)) = x * K(a(z,y,u),x). x * K(a(y,z,u),x) = T(x,a(z,y,u)). (x * (a(y,x,z) * u)) / a(y,x,z) = T(x * u,a(x,y,z)). x * K(y,a(z,u,x)) = a(T(u,y),z,x) * L(x,z,u). a(T(x,y),z,u) * L(u,z,x) = u * K(y,a(z,x,u)). a(x,T(y,z),u) * L(u,y,x) = u * K(z,a(y,x,u)). x * K(y,a(z,u,x)) = K(a(u,z,x),y) * x. K(a(x,y,z),u) * z = z * K(u,a(y,x,z)). K(a(x,y,z),T(u,z)) = K(u,a(y,x,z)). L(x,T(y,y \ z) \ (y * (z / y)),y * (z / y)) = L(x,z / y,y). L(x,T(y,y \ z) \ (y * (z / y)),y * (z / y)) = L(x,z,y). L(x,K(y \ z,y) * (z / y),y * (z / y)) = L(x,z,y). L(x,(y / z) * K(z \ y,z),z * (y / z)) = L(x,y,z). L(x,y \ z,y * (z / y)) = L(x,z,y). a(R(x,y,z),u,x \ 1) = (u * (x \ 1)) \ ((u / R(x,y,z)) * a(x,y,z)). (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(R(y,z,u),x,y \ 1). (x \ y) * (x * (((y \ z) / y) * (y * u))) = (y * (x * ((x * y) \ z))) * L(u,x,y). (x \ y) * (x * (y \ (z * u))) = (y * (x * ((x * y) \ z))) * L(u,x,y). (x * (y * ((y * x) \ z))) * L(u,y,x) = (y \ x) * (y * (x \ (z * u))). (x * (y * ((y * x) \ z))) * L(u,y,x) = x * (y * ((y * x) \ (z * u))). (x * (y * ((y * x) \ 1))) * L(z,y,x) = x * (y * ((y * x) \ z)). (x * (y * ((y * x) \ z))) * L(u,y,x) = (x * (y * ((y * x) \ 1))) * L(z * u,y,x). (x * (y * ((y * x) \ 1))) * L(z * u,y,x) = (x * (y * ((y * x) \ z))) * L(u,y,x). (x * (y * ((y * x) \ 1))) * L(z * u,y,x) = ((x * (y * ((y * x) \ 1))) * L(z,y,x)) * L(u,y,x). ((x * (y * ((y * x) \ 1))) * L(z,y,x)) * L(u,y,x) = (x * (y * ((y * x) \ 1))) * L(z * u,y,x). (x * (y * K(z,u))) \ R(x * y,K(L(z,y,x),u),K(u,L(z,y,x))) = K(L(z,y,x),u) \ 1. (x * (y * K(z,u))) \ (x * y) = K(L(z,y,x),u) \ 1. K(L(x,y,z),u) \ 1 = z \ ((z / (y * K(x,u))) * y). x \ ((x / (y * K(z,u))) * y) = K(L(z,y,x),u) \ 1. K(L(x,y,z),u) \ 1 = K(L(u,y,z),x). K(L(x,y,z),u) = K(x,L(u,y,z)). L(K(x,y),z,u) = K(x,L(y,z,u)). (x / y) * (y * K(z,u)) = x * K(z,L(u,y,x)). R(x,x \ y,z) \ R(R(x,x \ y,z),u,w) = ((R(x,u,w) * (x \ y)) * z) / (y * z). R(x,x \ y,z) \ R(R(x,x \ y,z),u,w) = R(x \ R(x,u,w),y,z). R(x,y,z) \ R(R(x,x \ y,z),u,w) = R(x \ R(x,u,w),y,z). R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). a(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z). R(a(x,y,z),u,w) = a(R(x,u,w),y,z). a(R(x,y,z),u,w) = R(a(x,u,w),y,z). a(R(x,y,z),u,w) * (y * z) = (a(x,u,w) * y) * z. x / (a(y,z,z) * a(R(z,x,u),y,z)) = R(x,a(z,y,z),u). R(a(x,y,z) * 1,u,w) = a(R(y,u,w),x,z) \ 1. R(a(x,y,z) * 1,u,w) = a(x,R(y,u,w),z). R(a(x,y,z),u,w) = a(x,R(y,u,w),z). a(x,R(y,z,u),w) = R(a(x,y,w),z,u). a(R(x,y,z),u,w) = a(x,R(u,y,z),w). (x * y) / (a(z,R(u,w,v5),x) * y) = L(x,u,R(z,w,v5)). (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(y,R(x,z,u),y \ 1). ((R(x,y,z) * u) * w) / ((a(x,y,z) * u) * w) = R(x,u,w). L(x,y,R(z,u,w)) = L(x,R(y,u,w),z). L(x,R(y,z,u),w) = L(x,y,R(w,z,u)). L(x,y,R(L(z,u,y),u,z)) = L(x,y,z). L(x,y,L(R(z,u,z),u,y)) = L(x,y,z). L(x,y,L(L(z,z,u),u,y)) = L(x,y,z). x / (a(y,z,z) * a(z,y,R(z,x,u))) = R(x,a(z,y,z),u). R(x,y,z) = R(x,a(x,u,w) * y,z). R(x,a(x,y,z) * u,w) = R(x,u,w). R(x,y,z) = R(x,L(y,u,x),z). R(x,L(y,z,x),u) = R(x,y,u). a(x,L(y,z,x),u) = x \ R(x,y,u). L(x,y,L(z,u,y)) = (x / y) * R(y,z,x). a(x,y,z) = a(x,L(y,u,x),z). a(x,L(y,z,x),u) = a(x,y,u). a(x \ 1,L(y,x,z),u) = a(x \ 1,y,u). L(x,y,z) = L(x,y,L(z,u,y)). L(x,y,L(z,u,y)) = L(x,y,z). L(x,y,L(z,z,u)) = L(x,y,z). L(x,y,L(z,u,z)) = L(x,y,z). (a(x,L(y,z,y),u) * L(u,x,y)) \ L(u,x,L(y,z,y)) = a(L(y,z,y),x,u). a(x \ 1,y,z) = a(L(y,x,u),x,z). a(L(x,y,z),y,u) = a(y \ 1,x,u). a(L(x,y,z),y,u) = a(x,y,u). a(x,y,z) = a(x,R(y,u,x),z). a(x,R(y,z,x),u) = a(x,y,u). a(x \ 1,y,z) = a(R(y,u,x \ 1),x,z). a(R(x,y,z \ 1),z,u) = a(z \ 1,x,u). a(R(x,y,z \ 1),z,u) = a(x,z,u). a(x,y,z) = a(x,R(y,u,y \ 1),z). a(x,R(y,z,y \ 1),u) = a(x,y,u). a(x,L(y,z,y),u) = a(x,y,u). (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(R(x,z,u),y,y). (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(x,R(y,z,u),y). (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(x,y,R(y,z,u)). (a(x,y,z) * L(z,x,y)) \ L(z,x,L(y,u,y)) = a(L(y,u,y),x,z). (a(x,y,z) * L(z,x,y)) \ L(z,x,y) = a(L(y,u,y),x,z). a(L(x,y,x),z,u) = (a(z,x,u) * L(u,z,x)) \ L(u,z,x). a(L(x,y,x),z,u) = a(x,z,u). a(T(x,x * y),z,u) = a(T(x,y),z,u). a(T(x,y),z,u) = a(x,T(z,x * y),u). a(x,T(y,x * z),u) = a(T(x,z),y,u). a(x,T(y,x * z),u) = a(x,T(y,z),u). (x * y) * a(x,T(z,y),u) = a(x,z,u) * (x * y). (x * y) * a(x,T(z,y),u) = R(x,z,u) * y. a(x,y,a(x,T(z,y),u)) = (x * (y * a(x,T(z,y),u))) \ (R(x,z,u) * y). (x * (y * a(x,T(z,y),u))) \ (R(x,z,u) * y) = a(x,y,a(x,T(z,y),u)). (x * (a(x,y,z) * u)) \ (R(x,y,z) * u) = a(x,u,a(x,T(y,u),z)). (R(x,y,z) * u) \ (R(x,y,z) * u) = a(x,u,a(x,T(y,u),z)). a(x,y,a(x,T(z,y),u)) = 1. a(x,y,a(x,z,u)) = 1. R(x,y,a(y,z,u)) = x / 1. a(x,y,a(z,x,u)) = 1. 1 = a(x,y,a(z,y,u)). a(x,y,a(z,y,u)) = 1. L(a(x,y,z),y,u) = a(x,y,z). R(x,y,a(y,z,u)) = x. T(x / y,y * a(y,z,u)) = (y * a(y,z,u)) \ (x * a(y,z,u)). (x * a(x,y,z)) \ (u * a(x,y,z)) = T(u / x,x * a(x,y,z)). (x * y) * a(x,z,u) = x * (y * a(x,z,u)). x / a(y,z,u) = (x / (y * a(y,z,u))) * y. (x / (y * a(y,z,u))) * y = x / a(y,z,u). (x / R(y,z,u)) * y = x / a(y,z,u). x * L(R(y,z,u) \ y,R(y,z,u),x) = x / a(y,z,u). (x / a(y,z,u)) * R(y,z,u) = x * y. x \ (x * y) = L(y,a(y,z,u),x). L(x,a(x,y,z),u) = u \ (u * x). L(x,a(x,y,z),u) = x. x / y = (x / (a(y,z,u) * y)) * a(y,z,u). (x / (a(y,z,u) * y)) * a(y,z,u) = x / y. (x / R(y,z,u)) * a(y,z,u) = x / y. (x * (y \ 1)) \ (x / y) = a(x,y,R(y,z,u)). a(x,y,R(y,z,u)) = (x * (y \ 1)) \ (x / y). a(x,y,R(y,z,u)) = a(x,y,y). a(x \ 1,y,y) = a(y,x,R(y,z,u)). a(x,y,R(x,z,u)) = a(y \ 1,x,x). a(x,y,R(x,z,u)) = a(x,y,x). x / (a(y,z,z) * a(z,y,z)) = R(x,a(z,y,z),u). R(x,a(y,z,y),u) = x / (a(z,y,y) * a(y,z,y)). R(x,a(y,z,y),u) = x / 1. R(x,a(y,z,y),u) = x. x * (a(y,z,y) * u) = (x * a(y,z,y)) * u. (x * a(y,z,y)) * u = x * (a(y,z,y) * u). (x \ 1) / a(y,z,y) = (a(y,z,y) * x) \ 1. R(x,a(y,z,z),u) = x. (a(x,y,x) * z) * u = a(x,y,x) * (z * u). a(x,a(y,z,z),u) = x \ x. (a(x,y,y) * z) * u = a(x,y,y) * (z * u). a(x,a(y,z,z),u) = 1. L(x,a(y,z,z),u) = x. (a(x,y,y) * (z \ 1)) * u = a(x,y,y) * (z \ u). a(x,y * a(z,u,z),w) = (x * w) \ (y * (a(z,u,z) * (((y * a(z,u,z)) \ x) * w))). (x * y) \ (z * (a(u,w,u) * (((z * a(u,w,u)) \ x) * y))) = a(x,z * a(u,w,u),y). (a(x,y,x) * z) * u = z * (a(x,T(y,z),x) * u). x * (a(y,T(z,x),y) * u) = (a(y,z,y) * x) * u. (a(x,y,x) * z) \ 1 = a(y,x,x) * (z \ 1). (a(x,y,x) * z) \ 1 = z \ a(y,x,x). x \ a(y,z,z) = (a(y,z,z) / x) * 1. (a(x,y,y) / z) * 1 = z \ a(x,y,y). a(x,y,y) / z = z \ a(x,y,y). (x \ a(y,z,z)) * u = a(y,z,z) * (x \ u). x * (a(y,z,y) * u) = (a(y,z,y) * x) * u. (a(x,y,x) * z) * u = z * (a(x,y,x) * u). x * (a(y,z,y) * u) = a(y,z,y) * (x * u). a(x,y,x) * (z * u) = z * (a(x,y,x) * u). a(x,a(y,z,y) * u,w) = (x * ((a(y,z,y) * u) * w)) \ ((a(y,z,y) * (x * u)) * w). (x * ((a(y,z,y) * u) * w)) \ ((a(y,z,y) * (x * u)) * w) = a(x,a(y,z,y) * u,w). x * L(a(y,z,u),R(z,y,u),x) = x / a(z,y,u). x * L(a(y,z,u),z,R(x,y,u)) = x / a(z,y,u). x * a(y,z,u) = x / a(z,y,u). x / a(y,z,u) = x * a(z,y,u). (x * a(y,z,u)) * a(z,y,u) = x. (x * a(y,z,u)) \ w = (a(z,y,u) / x) * w. (a(x,y,z) * u) * a(y,x,z) = u * K(a(x,y,z),u). (x * (a(y,x,z) * u)) * a(x,y,z) = T(x * u,a(x,y,z)). (a(x,y,z) * u) * a(y,x,z) = T(u,a(y,x,z)). x \ T(x,a(y,z,u)) = K(a(z,y,u) * x,a(y,z,u)). K(a(x,y,z) * u,a(y,x,z)) = u \ T(u,a(y,x,z)). K(x,a(y,z,u)) = K(a(z,y,u) * x,a(y,z,u)). K(a(x,y,z) * u,a(y,x,z)) = K(u,a(y,x,z)). T(x * y,a(x,z,u)) = x * ((a(z,x,u) * y) * a(x,z,u)). x * ((a(y,x,z) * u) * a(x,y,z)) = T(x * u,a(x,y,z)). x * T(y,a(x,z,u)) = T(x * y,a(x,z,u)). T(x * y,a(x,z,u)) = x * T(y,a(x,z,u)). T(x * T(y,x),a(x,z,u)) = T(y,a(x,z,u)) * x. T(x * y,a(y,z,u)) = T(x,a(y,z,u)) * y. T(T(x,a(y,z,u)),y) = y \ T(x * y,a(y,z,u)). x \ T(y * x,a(x,z,u)) = T(T(y,a(x,z,u)),x). (x * a(x,y,z)) \ (u * a(x,y,z)) = T(u / x,R(x,y,z)). R(x,y,z) \ (u * a(x,y,z)) = T(u / x,R(x,y,z)). T(x / y,R(y,z,u)) = y \ T(x,a(y,z,u)). x \ T(y,a(x,z,u)) = T(y / x,R(x,z,u)). T((x * y) / y,R(y,z,u)) = T(T(x,a(y,z,u)),y). T(x,R(y,z,u)) = T(T(x,a(y,z,u)),y). T(T(x,a(y,z,u)),y) = T(x,R(y,z,u)). T(x,y) \ T(x,R(y,z,u)) = K(T(x,y),a(y,z,u)). K(T(x,y),a(y,z,u)) = K(x,R(y,z,u)) * K(y,x). K(x,R(y,z,u)) * K(y,x) = K(T(x,y),a(y,z,u)). K(T(x,y),a(y,z,u)) = a(z,K(y,x),u). a(x,K(y,z),u) = K(z,T(a(y,x,u),y)). K(x,T(a(y,z,u),y)) = a(z,K(y,x),u). K(x,a(y,z,u)) = a(z,K(y,x),u). a(x,K(y,z),u) = K(z,a(y,x,u)). L(x,y,K(z,u)) = x * K(u,a(z,y,x)). x * K(y,a(z,u,x)) = L(x,u,K(z,y)). K(x,a(y,z \ K(x,y),u)) = a(K(y,x),z,u). K(x,a(y,z,u)) = a(K(z,x),y,u). a(K(x,y),z,u) = K(y,a(z,x,u)). L(x,K(y,z),u) = x * K(z,a(u,y,x)). x * K(y,a(z,u,x)) = L(x,K(u,y),z). L(x,K(y,z),u) = L(x,y,K(u,z)). (x * y) \ (z * (a(u,w,u) * (((a(w,u,u) / z) * x) * y))) = a(x,z * a(u,w,u),y). (x * (y * (a(z,u,z) * w))) \ ((a(z,u,z) * (x * y)) * w) = a(x,a(z,u,z) * y,w). (x * y) \ (z * (a(u,w,u) * (((z \ a(w,u,u)) * x) * y))) = a(x,z * a(u,w,u),y). (x * (y * (a(z,u,z) * w))) \ ((x * y) * (a(z,u,z) * w)) = a(x,a(z,u,z) * y,w). (x * y) \ (z * (a(u,w,u) * ((a(w,u,u) * (z \ x)) * y))) = a(x,z * a(u,w,u),y). a(x,y,a(z,u,z) * w) = a(x,a(z,u,z) * y,w). a(x,a(y,z,y) * u,w) = a(x,u,a(y,z,y) * w). (x * y) \ (z * (a(u,w,u) * (a(w,u,u) * ((z \ x) * y)))) = a(x,z * a(u,w,u),y). (x * y) \ (z * ((z \ x) * y)) = a(x,z * a(u,w,u),y). a(x,y * a(z,u,z),w) = (x * w) \ (y * ((y \ x) * w)). a(x,y,z) = a(x,y * a(u,w,u),z). a(x,y * a(z,u,z),w) = a(x,y,w). a(x,y,z) = a(x,R(y,u,u),z). a(x,R(y,z,z),u) = a(x,y,u). L(x,y,z * a(u,w,u)) = x * a(y,z,x). a(x,a(y,z,y) * u,w) = a(x,u,w). L(x,y,R(z,u,u)) = x * a(y,z,x). a(x,y,z) = a(x,y,a(u,w,u) * z). a(x,y,a(z,u,z) * w) = a(x,y,w). L(x,y,z) = L(x,y,R(z,u,u)). L(x,y,R(z,u,u)) = L(x,y,z). L(x,y,z / u) = L(x,y,z * (u \ 1)). L(x,y,z * (u \ 1)) = L(x,y,z / u). L(x,y,z / (u \ 1)) = L(x,y,z * u). a(x,y,L(z,z,u)) = a(x,y,z). x * a(y,z,u) = (x / u) * L(u,y,z). (x / y) * L(y,z,u) = x * a(z,u,y). L(x,y,z * (u / w)) = L(x,y,z / (w / u)). L(x,y,z / (u / w)) = L(x,y,z * (w / u)). L(x,y,(z / R(u \ 1,w,v5)) * a(u \ 1,w,v5)) = L(x,y,z * u). (x * a(y,z,u)) * a(z,y,u) = R(x,a(y,z,u),L(u,z,y)). L(x,y,z) = L(x,y,z * a(u,w,u)). L(x,y,z * a(u,w,u)) = L(x,y,z). R(x,a(y,z,u),L(u,z,y)) = x. T(x / a(y,z,u),a(y,z,u) * L(u,z,y)) = (a(y,z,u) * L(u,z,y)) \ (x * L(u,z,y)). (a(x,y,z) * L(z,y,x)) \ (u * L(z,y,x)) = T(u / a(x,y,z),a(x,y,z) * L(z,y,x)). R(x,y / L(y,z,u),L(y,z,u)) = x. (a(x,y,z) * u) * L(z,y,x) = a(x,y,z) * (u * L(z,y,x)). x / a(y,z,u) = (x * L(u,z,y)) / u. (x * L(y,z,u)) / y = x / a(u,z,y). x / y = (x / L(y,z,u)) / a(u,z,y). (x / L(y,z,u)) / a(u,z,y) = x / y. (x / y) \ (x / L(y,z,u)) = a(u,z,y). a(x,y,z) = (z / u) * (u / L(z,y,x)). (x / y) * (y / L(x,z,u)) = a(u,z,x). (L(x,y,z) / u) * (u / x) = a(y,z,L(x,y,z)). a(x,y,L(z,x,y)) = (L(z,x,y) / u) * (u / z). (L(x,y,z) / u) * (u / x) = a(y,z,x). (L(x \ y,z,u) / y) * x = a(z,u,x \ y). a(x,y,(z * K(u,w)) \ z) = L((z * K(u,w)) \ z,x,y) * K(u,L(w,z,L((z * K(u,w)) \ z,x,y))). L((x * K(y,z)) \ x,u,w) * K(y,L(z,x,L((x * K(y,z)) \ x,u,w))) = a(u,w,(x * K(y,z)) \ x). (a(x,y,z) * u) * L(z,y,x) = z * T(u,L(z,y,x)). L(x,y,(z / R(u \ 1,w,v5)) * a(w,u,v5)) = L(x,y,z * u). L(x,y,(z / (u / w)) * a(u,w * (u \ 1),u)) = L(x,y,z * (w * (u \ 1))). L(x,y,z * (u * (w \ 1))) = L(x,y,z / (w / u)). L(x,y,z * (u * (w \ 1))) = L(x,y,z * (u / w)). (a(x,y,z) * L(z,y,x)) \ (u * L(z,y,x)) = T(u * a(y,x,z),a(x,y,z) * L(z,y,x)). (a(x,y,z) * L(z,y,x)) \ (u * L(z,y,x)) = T(u * a(y,x,z),z). x \ (y * L(x,z,u)) = T(y * a(z,u,x),x). x \ ((a(y,z,x) \ u) * L(x,y,z)) = T(u * K(a(y,z,x) \ u,a(y,z,x)),x). T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = u \ ((a(y,z,u) \ x) * L(u,y,z)). T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = u \ ((a(z,y,u) * x) * L(u,y,z)). T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = u \ (u * T(x,L(u,y,z))). T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = T(x,L(u,y,z)). T(x * K(a(y,z,u) * x,a(z,y,u)),u) = T(x,L(u,z,y)). T(x * K(x,a(y,z,u)),u) = T(x,L(u,y,z)). T(T(x,a(y,z,u)),u) = T(x,L(u,y,z)). T(x,L(y,z,u)) = T(T(x,y),a(z,u,y)). T(T(x,y),a(z,u,y)) = T(x,L(y,z,u)). K(a(x,y,z),T(u,z)) = T(u,L(z,x,y)) \ T(u,z). T(x,L(y,z,u)) \ T(x,y) = K(a(z,u,y),T(x,y)). K(a(x,y,z),T(u,z)) = K(u,z) * K(L(z,x,y),u). K(x,y) * K(L(y,z,u),x) = K(a(z,u,y),T(x,y)). K(x,y) * K(L(y,z,u),x) = K(x,a(u,z,y)). K(x,a(y,z,u)) = a(z,y,K(u,x)). a(x,y,K(z,u)) = K(u,a(y,x,z)). L(x,y,z) * L(u,y,z) = L(x * L(u,L(x,y,z),z * (y * ((y * z) \ 1))),y,z). L(x * L(y,L(x,z,u),u * (z * ((z * u) \ 1))),z,u) = L(x,z,u) * L(y,z,u). L(x * L(y,L(x,z,u),u * (z / (z * u))),z,u) = L(x,z,u) * L(y,z,u). L(x * L(y,L(x,z,u),K(u,z)),z,u) = L(x,z,u) * L(y,z,u). L(x * L(T(y,L(x,z,u)),L(x,z,u),K(u,z)),z,u) = L(y,z,u) * L(x,z,u). L(x \ (x / K(y,z)),u,w) * K(y,L(z,x,L((x * K(y,z)) \ x,u,w))) = a(u,w,(x * K(y,z)) \ x). L(K(x,y),z,u) * K(y,L(x,w,L((w * K(y,x)) \ w,z,u))) = a(z,u,(w * K(y,x)) \ w). K(x,L(y,z,u)) * K(y,L(x,w,L((w * K(y,x)) \ w,z,u))) = a(z,u,(w * K(y,x)) \ w). K(x,L(y,z,u)) * K(y,L(x,w,L(w \ (w / K(y,x)),z,u))) = a(z,u,(w * K(y,x)) \ w). K(x,L(y,z,u)) * K(y,L(x,w,L(K(x,y),z,u))) = a(z,u,(w * K(y,x)) \ w). a(x,y,(z * K(u,w)) \ z) = K(w,L(u,x,y)) * K(u,L(w,z,L(K(w,u),x,y))). a(x,y,(z * K(u,w)) \ z) = K(w,L(u,x,y)) * K(u,L(w,z,K(w,L(u,x,y)))). a(x,y,(z * K(u,w)) \ z) = K(w,L(u,x,y)) * K(u,w). a(x,y,z \ (z / K(u,w))) = K(w,L(u,x,y)) * K(u,w). a(x,y,K(z,u)) = K(z,L(u,x,y)) * K(u,z). K(x,L(y,z,u)) * K(y,x) = a(z,u,K(x,y)). K(x,L(y,z,u)) * K(y,x) = K(y,a(u,z,x)). (x \ K(y,x)) \ K(y,a(z,u,x)) = T(T(x,L(y,u,z)),x \ K(y,x)). T(T(x,L(y,z,u)),x \ K(y,x)) = (K(x,y) * x) * K(y,a(u,z,x)). T(T(x,L(y,z,u)),x \ K(y,x)) = T(x,y) * K(y,a(u,z,x)). T(x * K(y,a(z,u,x)),y) = T(T(x,L(y,u,z)),x \ K(y,x)). T(T(x,L(y,z,u)),x \ K(y,x)) = T(x * K(y,a(u,z,x)),y). T(T(x,L(y,z,u)),x \ K(y,x)) = T(L(x,z,K(u,y)),y). L(T(x,y),z,K(u,y)) = T(T(x,L(y,z,u)),x \ K(y,x)). T(T(x,L(y,z,u)),x \ K(y,x)) = L(T(x,y),z,K(u,y)). L(T(x,y),z,K(u,y)) = T(x,L(y,z,u)). L(T(x,y),K(z,y) \ u,K(z,y) * (u / K(z,y))) = T(x,L(y,u,z)). L(T(x,y),K(y,z) * u,K(z,y) * (u / K(z,y))) = T(x,L(y,u,z)). L(T(x,y),K(y,z) * u,K(z,y) * (u * K(y,z))) = T(x,L(y,u,z)). L(T(x,y),K(y,z) * u,T(u,K(y,z))) = T(x,L(y,u,z)). T(x,L(y,z,u)) = L(T(x,y),K(y,u),T(z,K(y,u))). L(T(x,y),K(y,z),T(u,K(y,z))) = T(x,L(y,u,z)). T(x,L(y,z,u)) = L(T(x,y),K(y,u),z). L(T(x,y),K(y,z),u) = T(x,L(y,u,z)). T(x,L(y,z,u)) = L(T(x,y),y,K(z,u)). L(T(x,y),y,K(z,u)) = T(x,L(y,z,u)). L(x * T(y,L(L(x,z,u),u,z)),z,u) = L(y,z,u) * L(x,z,u). L(x * T(y,x),z,u) = L(y,z,u) * L(x,z,u). L(x * y,z,u) = L(x,z,u) * L(y,z,u). L(x,y,z) * L(u,y,z) = L(x * u,y,z). x * L(y,z,u) = L(L(x,u,z) * y,z,u). L(L(x,y,z) * u,z,y) = x * L(u,z,y). L(x,y,z) * u = L(x * L(u,z,y),y,z). L(x * L(y,z,u),u,z) = L(x,u,z) * y. L(L(x,y,z) * u,z,y) = L(u,z,y) * T(x,u). L(x,y,z) * T(u,x) = u * L(x,y,z). T(x,L(y,z,u)) = T(x,y). K(x,L(y,z,u)) = T(x,y) / x. K(x,y) = K(x,L(y,z,u)). K(x,L(y,z,u)) = K(x,y). L(K(x,y),z,u) = K(x,y). a(x,y,K(z,u)) = 1. 1 = K(x,a(y,z,u)). K(x,a(y,z,u)) = 1. 1 = a(K(x,y),z,u). end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: 1 x * y = u & x * z = u -> y = z # label(non_clause). [assumption]. 2 y * x = u & z * x = u -> y = z # label(non_clause). [assumption]. 3 x * y = x * z -> y = z # label(non_clause). [assumption]. 4 y * x = z * x -> y = z # label(non_clause). [assumption]. 5 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 6 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 7 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 8 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 9 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 10 a(K(x,y),z,u) = 1 # label("aK1") # label(non_clause) # label(goal). [goal]. ============================== end of process non-clausal formulas === ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). 1 * x = x. [assumption]. x * 1 = x. [assumption]. x \ (x * y) = y. [assumption]. x * (x \ y) = y. [assumption]. (x * y) / y = x. [assumption]. (x / y) * y = x. [assumption]. x * y != z | x * u != z | u = y. [clausify(1)]. x * y != z | u * y != z | u = x. [clausify(2)]. x * y != x * z | y = z. [clausify(3)]. x * y != z * y | x = z. [clausify(4)]. x != y | z * x = z * y. [assumption]. x != y | x * z = y * z. [assumption]. (x * (y * z)) \ ((x * y) * z) = a(x,y,z) # label("associator"). [assumption]. (x * y) \ (y * x) = K(y,x) # label("commutator"). [assumption]. (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. x \ (y * x) = T(y,x). [assumption]. a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. T(x,y) != x | T(y,x) = y. [clausify(7)]. T(x,y) != x | K(x,y) = 1. [clausify(8)]. K(x,y) != 1 | T(x,y) = x. [clausify(9)]. T(T(x,y),z) = T(T(x,z),y). [assumption]. T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. (x * (y * x)) * z = x * (y * (x * z)) # label("left Bol"). [assumption]. a(K(c1,c2),c3,c4) != 1 # label("aK1"). [deny(10)]. end_of_list. formulas(demodulators). end_of_list. % 2687 hints input. ============================== PREDICATE ELIMINATION ================= No predicates eliminated. ============================== end predicate elimination ============= Auto_denials: % copying label "aK1" to answer in negative clause Term ordering decisions: Function symbol KB weights: 1=1. c1=1. c2=1. c3=1. c4=1. *=1. T=1. \=1. /=1. K=1. L=1. R=1. a=1. Predicate symbol precedence: predicate_order([ = ]). Function symbol precedence: function_order([ 1, c1, c2, c3, c4, *, T, \, /, K, L, R, a ]). Skipping inverse_order, because term ordering is KBO. Unfolding symbols: K/2 T/2 L/3 R/3 a/3. Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(hyper_resolution). % (nonunit Horn with equality) % set(hyper_resolution) -> set(pos_hyper_resolution). % set(neg_ur_resolution). % (nonunit Horn with equality) % assign(para_lit_limit, 3). % (nonunit Horn with equality) Auto_process settings: (no changes). kept: 11 1 * x = x. [assumption]. kept: 12 x * 1 = x. [assumption]. kept: 13 x \ (x * y) = y. [assumption]. kept: 14 x * (x \ y) = y. [assumption]. kept: 15 (x * y) / y = x. [assumption]. kept: 16 (x / y) * y = x. [assumption]. kept: 17 x * y != z | x * u != z | u = y. [clausify(1)]. kept: 18 x * y != z | u * y != z | u = x. [clausify(2)]. kept: 19 x * y != x * z | y = z. [clausify(3)]. kept: 20 x * y != z * y | x = z. [clausify(4)]. kept: 21 x != y | z * x = z * y. [assumption]. kept: 22 x != y | x * z = y * z. [assumption]. 23 (x * (y * z)) \ ((x * y) * z) = a(x,y,z) # label("associator"). [assumption]. kept: 24 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(23),flip(a)]. 25 (x * y) \ (y * x) = K(y,x) # label("commutator"). [assumption]. kept: 26 K(x,y) = (y * x) \ (x * y). [copy(25),flip(a)]. 27 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. kept: 28 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(27),flip(a)]. 29 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. kept: 30 R(x,y,z) = ((x * y) * z) / (y * z). [copy(29),flip(a)]. 31 x \ (y * x) = T(y,x). [assumption]. kept: 32 T(x,y) = y \ (x * y). [copy(31),flip(a)]. kept: 33 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. kept: 34 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. kept: 35 T(x,y) != x | T(y,x) = y. [clausify(7)]. kept: 36 T(x,y) != x | K(x,y) = 1. [clausify(8)]. kept: 37 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. kept: 38 T(T(x,y),z) = T(T(x,z),y). [assumption]. 39 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. kept: 40 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(39),flip(a)]. 41 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. kept: 42 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(41),flip(a)]. 43 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. kept: 44 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(43),flip(a)]. kept: 45 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. kept: 46 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. kept: 47 (x * (y * x)) * z = x * (y * (x * z)) # label("left Bol"). [assumption]. kept: 48 a(K(c1,c2),c3,c4) != 1 # label("aK1") # answer("aK1"). [deny(10)]. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). 48 a(K(c1,c2),c3,c4) != 1 # label("aK1") # answer("aK1"). [deny(10)]. end_of_list. formulas(sos). 11 1 * x = x. [assumption]. 12 x * 1 = x. [assumption]. 13 x \ (x * y) = y. [assumption]. 14 x * (x \ y) = y. [assumption]. 15 (x * y) / y = x. [assumption]. 16 (x / y) * y = x. [assumption]. 17 x * y != z | x * u != z | u = y. [clausify(1)]. 18 x * y != z | u * y != z | u = x. [clausify(2)]. 19 x * y != x * z | y = z. [clausify(3)]. 20 x * y != z * y | x = z. [clausify(4)]. 21 x != y | z * x = z * y. [assumption]. 22 x != y | x * z = y * z. [assumption]. 24 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(23),flip(a)]. 26 K(x,y) = (y * x) \ (x * y). [copy(25),flip(a)]. 28 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(27),flip(a)]. 30 R(x,y,z) = ((x * y) * z) / (y * z). [copy(29),flip(a)]. 32 T(x,y) = y \ (x * y). [copy(31),flip(a)]. 33 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. 34 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. 35 T(x,y) != x | T(y,x) = y. [clausify(7)]. 36 T(x,y) != x | K(x,y) = 1. [clausify(8)]. 37 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. 38 T(T(x,y),z) = T(T(x,z),y). [assumption]. 40 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(39),flip(a)]. 42 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(41),flip(a)]. 44 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(43),flip(a)]. 45 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 46 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 47 (x * (y * x)) * z = x * (y * (x * z)) # label("left Bol"). [assumption]. end_of_list. formulas(demodulators). end_of_list. % 2002 hints (2687 processed, 685 redundant). ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.11 seconds. given #1 (I,wt=5): 11 1 * x = x. [assumption]. given #2 (I,wt=5): 12 x * 1 = x. [assumption]. given #3 (I,wt=7): 13 x \ (x * y) = y. [assumption]. given #4 (I,wt=7): 14 x * (x \ y) = y. [assumption]. given #5 (I,wt=7): 15 (x * y) / y = x. [assumption]. given #6 (I,wt=7): 16 (x / y) * y = x. [assumption]. given #7 (I,wt=13): 17 x * y != z | x * u != z | u = y. [clausify(1)]. given #8 (I,wt=13): 18 x * y != z | u * y != z | u = x. [clausify(2)]. given #9 (I,wt=10): 19 x * y != x * z | y = z. [clausify(3)]. given #10 (I,wt=10): 20 x * y != z * y | x = z. [clausify(4)]. given #11 (I,wt=10): 21 x != y | z * x = z * y. [assumption]. given #12 (I,wt=10): 22 x != y | x * z = y * z. [assumption]. given #13 (I,wt=16): 24 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(23),flip(a)]. given #14 (I,wt=11): 26 K(x,y) = (y * x) \ (x * y). [copy(25),flip(a)]. given #15 (I,wt=14): 28 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(27),flip(a)]. given #16 (I,wt=14): 30 R(x,y,z) = ((x * y) * z) / (y * z). [copy(29),flip(a)]. given #17 (I,wt=9): 32 T(x,y) = y \ (x * y). [copy(31),flip(a)]. given #18 (I,wt=12): 33 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. given #19 (I,wt=12): 34 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. given #20 (I,wt=10): 35 T(x,y) != x | T(y,x) = y. [clausify(7)]. given #21 (I,wt=10): 36 T(x,y) != x | K(x,y) = 1. [clausify(8)]. given #22 (I,wt=10): 37 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. given #23 (I,wt=11): 38 T(T(x,y),z) = T(T(x,z),y). [assumption]. given #24 (I,wt=13): 40 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(39),flip(a)]. given #25 (I,wt=13): 42 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(41),flip(a)]. given #26 (I,wt=15): 44 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(43),flip(a)]. given #27 (I,wt=15): 45 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. given #28 (I,wt=15): 46 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. given #29 (I,wt=15): 47 (x * (y * x)) * z = x * (y * (x * z)) # label("left Bol"). [assumption]. given #30 (H,wt=5): 49 1 \ x = x. [para(11(a,1),13(a,1,2))]. given #31 (H,wt=5): 50 x \ x = 1. [para(12(a,1),13(a,1,2))]. given #32 (H,wt=5): 52 x / 1 = x. [para(12(a,1),15(a,1,1))]. given #33 (H,wt=5): 79 T(x,x) = x. [para(32(a,2),13(a,1))]. given #34 (H,wt=7): 53 x / (y \ x) = y. [para(14(a,1),15(a,1,1))]. given #35 (H,wt=7): 54 (x / y) \ x = y. [para(16(a,1),13(a,1,2))]. given #36 (H,wt=7): 78 T(1,x) = x \ x. [para(11(a,1),32(a,2,2))]. given #37 (H,wt=5): 93 T(1,x) = 1. [para(78(a,2),50(a,1))]. => 96 back subsumes hint matchers not on Sos. Reset weight to 507.000. given #38 (H,wt=8): 55 1 * x != y | x = y. [para(11(a,1),19(a,2))]. given #39 (H,wt=8): 59 x * 1 != y | x = y. [para(12(a,1),20(a,2))]. given #40 (H,wt=9): 80 x * T(y,x) = y * x. [para(32(a,2),14(a,1,2))]. given #41 (H,wt=9): 82 T(x / y,y) = y \ x. [para(16(a,1),32(a,2,2))]. given #42 (H,wt=9): 88 T(T(x,y),x) = T(x,y). [para(79(a,1),38(a,1,1)),flip(a)]. given #43 (H,wt=7): 106 K(T(x,y),x) = 1. [hyper(36,a,88,a)]. given #44 (H,wt=9): 91 (x * y) / T(x,y) = y. [para(32(a,2),53(a,1,2))]. given #45 (H,wt=9): 108 K(x \ y,y / x) = 1. [para(82(a,1),106(a,1,1))]. given #46 (H,wt=10): 56 x * y != z | x \ z = y. [para(14(a,1),19(a,1)),flip(a)]. given #47 (H,wt=10): 61 x * y != z | z / y = x. [para(16(a,1),20(a,1)),flip(a)]. given #48 (H,wt=11): 65 (x * y) * K(y,x) = y * x. [para(26(a,2),14(a,1,2))]. given #49 (H,wt=11): 81 T(x,x \ y) = (x \ y) \ y. [para(14(a,1),32(a,2,2))]. given #50 (H,wt=11): 89 (x * y) / K(x,y) = y * x. [para(26(a,2),53(a,1,2))]. given #51 (H,wt=11): 107 T(x,y) * x = x * T(x,y). [para(88(a,1),80(a,1,2)),flip(a)]. given #52 (H,wt=11): 109 x / T(y,y \ x) = y \ x. [para(14(a,1),91(a,1,1))]. given #53 (H,wt=12): 98 x * y != z * x | T(z,x) = y. [para(80(a,1),19(a,1)),flip(a)]. given #54 (H,wt=13): 66 x \ ((y \ x) * y) = K(y \ x,y). [para(14(a,1),26(a,2,1)),flip(a)]. given #55 (H,wt=11): 115 K(x \ 1,x) = (x \ 1) * x. [para(66(a,1),49(a,1))]. given #56 (H,wt=13): 67 x \ (y * (x / y)) = K(y,x / y). [para(16(a,1),26(a,2,1)),flip(a)]. given #57 (H,wt=11): 118 K(x,1 / x) = x * (1 / x). [para(67(a,1),49(a,1))]. given #58 (H,wt=13): 68 (x * (y / x)) \ y = K(y / x,x). [para(16(a,1),26(a,2,2)),flip(a)]. given #59 (H,wt=13): 84 x * (1 * (x * y)) = (x * x) * y. [para(11(a,1),47(a,1,1,2)),flip(a)]. given #60 (H,wt=11): 119 (x * x) * y = x * (x * y). [para(11(a,1),84(a,1,2)),flip(a)]. given #61 (H,wt=11): 120 (x * (x * y)) / y = x * x. [hyper(61,a,119,a)]. given #62 (H,wt=11): 122 (x * y) / (x \ y) = x * x. [para(14(a,1),120(a,1,1,2))]. given #63 (H,wt=9): 123 x / (x \ 1) = x * x. [para(12(a,1),122(a,1,1))]. given #64 (H,wt=13): 97 T(x * (y * x),x) = y * (x * x). [hyper(17,a,47,a(flip),b,80,a)]. given #65 (H,wt=13): 101 T(x,y) \ (x * y) = T(y,T(x,y)). [para(80(a,1),32(a,2,2)),flip(a)]. given #66 (H,wt=13): 102 x * T(T(y,x),z) = T(y,z) * x. [para(38(a,1),80(a,1,2))]. given #67 (H,wt=13): 110 x * K(y \ x,y) = (y \ x) * y. [para(14(a,1),65(a,1,1))]. given #68 (H,wt=13): 125 (1 / x) * (1 / x) = (1 / x) / x. [para(54(a,1),123(a,1,2)),flip(a)]. given #69 (H,wt=13): 126 (x / y) * (y * y) = T(y * x,y). [para(16(a,1),97(a,1,1,2)),flip(a)]. given #70 (H,wt=13): 128 T(x * y,x) / (x * x) = y / x. [hyper(61,a,126,a)]. given #71 (H,wt=11): 130 T(x,x) / (x * x) = 1 / x. [para(12(a,1),128(a,1,1,1))]. given #72 (H,wt=9): 132 x / (x * x) = 1 / x. [para(79(a,1),130(a,1,1))]. given #73 (H,wt=9): 133 (1 / x) \ x = x * x. [para(132(a,1),54(a,1,1))]. given #74 (H,wt=13): 131 T(x,y) / (y * y) = (y \ x) / y. [para(14(a,1),128(a,1,1,1))]. given #75 (H,wt=11): 134 (x \ 1) / x = 1 / (x * x). [para(93(a,1),131(a,1,1)),flip(a)]. given #76 (H,wt=11): 135 (1 / (x * x)) * x = x \ 1. [para(134(a,1),16(a,1,1))]. given #77 (H,wt=14): 57 x * (x \ (y * z)) != y * u | u = z. [para(14(a,2),19(a,2)),flip(a)]. given #78 (H,wt=14): 58 ((x * y) / z) * z != x * u | u = y. [para(16(a,2),19(a,2)),flip(a)]. given #79 (H,wt=14): 60 ((x * y) * z) / z != u * y | u = x. [para(15(a,2),20(a,2)),flip(a)]. given #80 (H,wt=14): 69 (x * y) * L(z,y,x) = x * (y * z). [para(28(a,2),14(a,1,2))]. given #81 (H,wt=14): 71 L(x \ y,x,z) = (z * x) \ (z * y). [para(14(a,1),28(a,2,2,2))]. given #82 (H,wt=12): 139 L(x \ 1,x,y) = (y * x) \ y. [para(12(a,1),71(a,2,2))]. given #83 (H,wt=12): 146 x / L(y \ 1,y,x) = x * y. [para(139(a,2),53(a,1,2))]. given #84 (H,wt=14): 75 R(x,y,z) * (y * z) = (x * y) * z. [para(30(a,2),16(a,1,1))]. given #85 (H,wt=6): 148 R(x,x,y) = x. [hyper(18,a,119,a(flip),b,75,a)]. given #86 (H,wt=10): 153 R(T(x,y),x,z) = T(x,y). [para(148(a,1),42(a,2,1))]. given #87 (H,wt=12): 154 R(R(x,y,z),x,u) = R(x,y,z). [para(148(a,1),46(a,1,1)),flip(a)]. given #88 (H,wt=14): 76 R(x / y,y,z) = (x * z) / (y * z). [para(16(a,1),30(a,2,1,1))]. given #89 (H,wt=12): 158 R(1 / x,x,y) = y / (x * y). [para(11(a,1),76(a,2,1))]. given #90 (H,wt=14): 90 (x * (y * z)) / L(z,y,x) = x * y. [para(28(a,2),53(a,1,2))]. given #91 (H,wt=14): 92 R(x,y,z) \ ((x * y) * z) = y * z. [para(30(a,2),54(a,1,1))]. given #92 (H,wt=14): 121 (x * x) * y != z * (x * y) | z = x. [para(119(a,2),20(a,2)),flip(a)]. given #93 (H,wt=14): 141 L(x \ (y \ z),x,y) = (y * x) \ z. [para(14(a,1),71(a,2,2))]. given #94 (H,wt=14): 143 L(x \ (y * x),x,y) = T(y,y * x). [para(71(a,2),32(a,2)),flip(a)]. given #95 (H,wt=12): 166 L(T(x,y),y,x) = T(x,x * y). [para(32(a,2),143(a,1,1))]. given #96 (H,wt=14): 144 (x * y) / L(z \ y,z,x) = x * z. [para(71(a,2),53(a,1,2))]. given #97 (H,wt=14): 147 x / L(y,1 / y,x) = x * (1 / y). [para(54(a,1),146(a,1,2,1))]. given #98 (H,wt=14): 159 R((x / y) / z,z,y) = x / (z * y). [para(16(a,1),76(a,2,1))]. given #99 (H,wt=14): 161 R(x / y,y,z) \ (x * z) = y * z. [para(76(a,2),54(a,1,1))]. given #100 (H,wt=14): 165 L(x \ (y \ ((y * x) * z)),x,y) = z. [para(141(a,2),13(a,1))]. given #101 (H,wt=15): 83 (x * (y * (x * z))) / z = x * (y * x). [hyper(18,a,16,a,b,47,a),flip(a)]. given #102 (H,wt=15): 85 x * ((y / x) * (x * z)) = (x * y) * z. [para(16(a,1),47(a,1,1,2)),flip(a)]. given #103 (H,wt=14): 169 (x / y) * (y * L(z,x,y)) = x * z. [hyper(17,a,69,a(flip),b,85,a)]. given #104 (H,wt=14): 171 (x / y) \ (x * z) = y * L(z,x,y). [hyper(56,a,169,a)]. given #105 (H,wt=14): 174 x * L(y \ z,y,x) = (y / x) \ z. [para(14(a,1),171(a,1,2)),flip(a)]. given #106 (H,wt=14): 175 L(x \ y,x,z) = z \ ((x / z) \ y). [hyper(56,a,174,a),flip(a)]. given #107 (H,wt=12): 179 L(x \ (x / y),x,y) = y \ 1. [para(50(a,1),175(a,2,2))]. given #108 (H,wt=13): 183 (x * y) \ (x * (y / x)) = x \ 1. [para(179(a,1),71(a,1)),flip(a)]. given #109 (H,wt=13): 184 (x * y) * (x \ 1) = x * (y / x). [para(183(a,1),14(a,1,2))]. given #110 (H,wt=13): 185 (x * (y * x)) \ (x * y) = x \ 1. [para(15(a,1),183(a,1,2,2))]. given #111 (H,wt=13): 187 x * ((x \ y) / x) = y * (x \ 1). [para(14(a,1),184(a,1,1)),flip(a)]. given #112 (H,wt=13): 190 (x * y) / (x \ 1) = x * (y * x). [para(185(a,1),53(a,1,2))]. given #113 (H,wt=13): 191 x \ (y * (x \ 1)) = (x \ y) / x. [hyper(56,a,187,a)]. given #114 (H,wt=13): 193 x * ((x \ y) * x) = y / (x \ 1). [para(14(a,1),190(a,1,1)),flip(a)]. given #115 (H,wt=13): 195 x \ (y / (x \ 1)) = (x \ y) * x. [hyper(56,a,193,a)]. given #116 (H,wt=14): 177 L(x \ ((x / y) * z),x,y) = y \ z. [para(13(a,1),175(a,2,2))]. given #117 (H,wt=15): 99 (T(x,y) * y) \ (x * y) = K(y,T(x,y)). [para(80(a,1),26(a,2,2)),flip(a)]. given #118 (H,wt=15): 103 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(40(a,2),80(a,1,2))]. given #119 (H,wt=13): 197 L(x,y,z) * x = x * L(x,y,z). [para(79(a,1),103(a,1,2,1)),flip(a)]. given #120 (H,wt=14): 199 x * T(y,y * x) = L(y,x,y) * x. [para(166(a,1),103(a,1,2))]. given #121 (H,wt=15): 104 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(42(a,2),80(a,1,2))]. given #122 (H,wt=13): 201 R(x,y,z) * x = x * R(x,y,z). [para(79(a,1),104(a,1,2,1)),flip(a)]. given #123 (H,wt=15): 113 T(T(x,y),x \ z) = T((x \ z) \ z,y). [para(81(a,1),38(a,1,1)),flip(a)]. given #124 (H,wt=15): 114 (x * y) / K(y,T(x,y)) = T(x,y) * y. [para(80(a,1),89(a,1,1))]. given #125 (H,wt=15): 124 x / ((x / y) \ y) = (x / y) * (x / y). [para(16(a,1),122(a,1,1))]. given #126 (H,wt=13): 205 1 / ((1 / x) \ x) = (1 / x) / x. [para(124(a,2),125(a,1))]. given #127 (H,wt=11): 206 (1 / x) / x = 1 / (x * x). [para(133(a,1),205(a,1,2)),flip(a)]. given #128 (H,wt=11): 207 (1 / (x * x)) * x = 1 / x. [para(206(a,1),16(a,1,1))]. given #129 (H,wt=7): 208 1 / x = x \ 1. [para(207(a,1),135(a,1))]. given #130 (H,wt=7): 209 x * (1 / x) = 1. [para(208(a,2),14(a,1,2))]. given #131 (H,wt=7): 210 (x \ 1) \ 1 = x. [para(208(a,1),53(a,1))]. given #132 (H,wt=7): 218 K(x,1 / x) = 1. [para(209(a,1),118(a,2))]. => 223 back subsumes hint matchers not on Sos. Reset weight to 511.000. given #133 (H,wt=7): 219 T(x,x \ 1) = x. [para(210(a,1),81(a,2))]. given #134 (H,wt=7): 221 T(x,1 / x) = x. [hyper(37,a,218,a)]. given #135 (H,wt=7): 222 K(x \ 1,x) = 1. [para(53(a,1),218(a,1,2))]. given #136 (H,wt=9): 211 T(x \ 1,x) = x \ 1. [para(208(a,1),82(a,1,1))]. given #137 (H,wt=11): 220 T(T(x,y),x \ 1) = T(x,y). [para(210(a,1),113(a,2,1))]. given #138 (H,wt=11): 225 T(T(x,y),1 / x) = T(x,y). [para(221(a,1),38(a,1,1)),flip(a)]. given #139 (H,wt=11): 228 T(x \ 1,T(x,y)) = x \ 1. [hyper(35,a,220,a)]. given #140 (H,wt=11): 229 T(1 / x,T(x,y)) = 1 / x. [hyper(35,a,225,a)]. given #141 (H,wt=12): 212 x / L(1 / y,y,x) = x * y. [para(208(a,2),146(a,1,2,1))]. given #142 (H,wt=12): 213 R(x \ 1,x,y) = y / (x * y). [para(208(a,1),158(a,1,1))]. given #143 (H,wt=13): 216 (x * y) * (1 / x) = x * (y / x). [para(208(a,2),184(a,1,2))]. given #144 (H,wt=13): 230 T(x \ 1,(x \ y) \ y) = x \ 1. [para(81(a,1),228(a,1,2))]. given #145 (H,wt=13): 231 T(1 / (x \ 1),T(x \ 1,y)) = x. [para(229(a,2),53(a,1))]. given #146 (H,wt=9): 234 T(x,T(x \ 1,y)) = x. [para(53(a,1),231(a,1,1))]. given #147 (H,wt=9): 235 T(x,T(1 / x,y)) = x. [para(208(a,2),234(a,1,2,1))]. given #148 (H,wt=11): 236 T(x,((1 / x) \ y) \ y) = x. [para(81(a,1),235(a,1,2))]. given #149 (H,wt=14): 214 R((1 / x) / y,y,x) = (y * x) \ 1. [para(208(a,1),159(a,2))]. given #150 (H,wt=14): 237 R((x \ 1) / y,y,x) = (y * x) \ 1. [para(208(a,1),214(a,1,1,1))]. given #151 (H,wt=15): 127 T(x / y,z) * y = y * T(y \ x,z). [para(82(a,1),102(a,1,2,1)),flip(a)]. given #152 (H,wt=15): 156 (T(x,y) * x) * z = T(x,y) * (x * z). [para(153(a,1),75(a,1,1)),flip(a)]. given #153 (H,wt=8): 239 L(x,y,T(y,z)) = x. [hyper(17,a,69,a,b,156,a),flip(a)]. given #154 (H,wt=10): 243 L(x,y / z,z \ y) = x. [para(82(a,1),239(a,1,3))]. given #155 (H,wt=10): 244 L(x,y,(y \ z) \ z) = x. [para(81(a,1),239(a,1,3))]. given #156 (H,wt=13): 240 x * (T(x,y) \ 1) = x / T(x,y). [hyper(17,a,184,a(flip),b,156,a(flip))]. given #157 (H,wt=13): 246 x \ (x / T(x,y)) = T(x,y) \ 1. [para(239(a,1),179(a,1))]. given #158 (H,wt=15): 167 (x * (y * z)) / (x \ z) = x * (y * x). [para(14(a,1),83(a,1,1,2,2))]. given #159 (H,wt=15): 168 x \ ((x * y) * z) = (y / x) * (x * z). [hyper(56,a,85,a)]. given #160 (H,wt=15): 170 (x * y) * (x \ z) = x * ((y / x) * z). [para(14(a,1),85(a,1,2,2)),flip(a)]. given #161 (H,wt=15): 176 (x / y) \ (y \ z) = y * ((y * x) \ z). [para(141(a,1),174(a,1,2)),flip(a)]. given #162 (H,wt=15): 182 (x * y) \ (x * z) = x \ ((y / x) \ z). [para(175(a,1),71(a,1)),flip(a)]. given #163 (H,wt=15): 189 (x * y) * (y \ 1) = y * (T(x,y) / y). [para(80(a,1),184(a,1,1))]. given #164 (H,wt=15): 194 (x * y) / (y \ 1) = y * (T(x,y) * y). [para(80(a,1),190(a,1,1))]. given #165 (H,wt=15): 215 x * ((x \ 1) * (x * y)) = (x * 1) * y. [para(208(a,1),85(a,1,2,1))]. given #166 (H,wt=13): 253 x * ((x \ 1) * (x * y)) = x * y. [para(12(a,1),215(a,2,1))]. given #167 (H,wt=9): 254 (x \ 1) * (x * y) = y. [hyper(19,a,253,a)]. => 257 back subsumes hint matchers not on Sos. Reset weight to 513.000. given #168 (H,wt=9): 255 x / (y * x) = y \ 1. [hyper(61,a,254,a)]. => 267 back subsumes hint matchers not on Sos. Reset weight to 509.000. given #169 (H,wt=9): 256 (x \ 1) \ y = x * y. [hyper(56,a,254,a)]. given #170 (H,wt=9): 259 (x \ 1) * y = x \ y. [para(14(a,1),254(a,1,2))]. given #171 (H,wt=9): 263 (1 / x) * (x * y) = y. [para(208(a,2),254(a,1,1))]. given #172 (H,wt=9): 264 (x \ y) / y = x \ 1. [para(14(a,1),255(a,1,2))]. given #173 (H,wt=9): 265 (x / y) \ 1 = y / x. [para(16(a,1),255(a,1,2)),flip(a)]. given #174 (H,wt=9): 269 (1 / x) * y = x \ y. [para(54(a,1),256(a,1,1)),flip(a)]. given #175 (H,wt=9): 270 (1 / x) \ y = x * y. [para(208(a,2),256(a,1,1))]. given #176 (H,wt=9): 278 (x \ y) / y = 1 / x. [para(264(a,2),208(a,2)),flip(a)]. => 288 back subsumes hint matchers not on Sos. Reset weight to 511.000. given #177 (H,wt=9): 279 (x / y) * (y / x) = 1. [para(265(a,1),14(a,1,2))]. given #178 (H,wt=9): 280 1 / (x / y) = y / x. [para(265(a,1),53(a,1,2))]. given #179 (H,wt=9): 287 T(x,(x * y) \ y) = x. [para(270(a,1),236(a,1,2,1))]. given #180 (H,wt=10): 268 R(x \ 1,x,y) = x \ 1. [para(255(a,1),213(a,2))]. => 292 back subsumes hint matchers not on Sos. Reset weight to 512.000. given #181 (H,wt=11): 272 T(x \ 1,y) = y \ (x \ y). [para(259(a,1),32(a,2,2))]. given #182 (H,wt=11): 283 (x / y) * ((y / x) * z) = z. [para(265(a,1),254(a,1,1))]. given #183 (H,wt=11): 284 (x / y) \ z = (y / x) * z. [para(265(a,1),256(a,1,1))]. given #184 (H,wt=11): 285 T(1 / x,y) = y \ (x \ y). [para(269(a,1),32(a,2,2))]. given #185 (H,wt=11): 290 T(x / y,x \ y) = x / y. [para(16(a,1),287(a,1,2,1))]. given #186 (H,wt=12): 260 (x \ 1) * y != z | x * z = y. [para(254(a,1),19(a,1)),flip(a)]. given #187 (H,wt=12): 281 x * L(y \ 1,y,x) = x / y. [para(265(a,1),174(a,2))]. given #188 (H,wt=11): 309 x * ((x * y) \ x) = x / y. [para(139(a,1),281(a,1,2))]. given #189 (H,wt=11): 313 (x * y) \ x = x \ (x / y). [hyper(56,a,309,a),flip(a)]. given #190 (H,wt=11): 314 x / (x \ y) = x * (y \ x). [para(14(a,1),309(a,1,2,1)),flip(a)]. given #191 (H,wt=11): 316 x / (x \ (x / y)) = x * y. [para(313(a,1),53(a,1,2))]. given #192 (H,wt=12): 282 L(x \ 1,x,y) = y \ (y / x). [para(265(a,1),175(a,2,2))]. given #193 (H,wt=12): 308 (x / y) / L(y \ 1,y,x) = x. [hyper(61,a,281,a)]. given #194 (H,wt=12): 310 x * L(1 / y,y,x) = x / y. [para(208(a,2),281(a,1,2,1))]. given #195 (H,wt=13): 262 T(x \ 1,x * y) = (x * y) \ y. [para(254(a,1),32(a,2,2))]. given #196 (H,wt=13): 273 x \ T(y,x \ 1) = y * (x \ 1). [para(259(a,1),80(a,1))]. given #197 (H,wt=13): 274 x * (y * (1 / x)) = T(y,1 / x). [hyper(98,a,263,a),flip(a)]. given #198 (H,wt=13): 275 T(1 / x,x * y) = (x * y) \ y. [para(263(a,1),32(a,2,2))]. given #199 (H,wt=13): 286 x \ T(y,1 / x) = y * (1 / x). [para(269(a,1),80(a,1))]. given #200 (H,wt=13): 289 T(x,x \ y) / y = 1 / (x \ y). [para(81(a,2),278(a,1,1))]. given #201 (H,wt=13): 294 x \ ((y / z) \ x) = T(z / y,x). [para(265(a,1),272(a,1,1)),flip(a)]. given #202 (H,wt=12): 325 L(x \ y,x,y) = T(y / x,y). [para(294(a,1),175(a,2))]. given #203 (H,wt=13): 296 (x / y) * T(x * y,x) = x * x. [hyper(17,a,126,a,b,283,a)]. given #204 (H,wt=12): 327 x * L(y,y,x) = T(y * x,y). [hyper(17,a,169,a,b,296,a),flip(a)]. given #205 (H,wt=12): 328 x \ T(y * x,y) = L(y,y,x). [hyper(56,a,327,a)]. given #206 (H,wt=13): 306 T((x / y) / x,y) = (x / y) / x. [para(54(a,1),290(a,1,2))]. given #207 (H,wt=13): 315 x * ((y * x) \ x) = x / T(y,x). [para(80(a,1),309(a,1,2,1))]. given #208 (H,wt=13): 321 T(x,y) * (1 / x) = T(x,y) / x. [para(239(a,1),310(a,1,2))]. given #209 (H,wt=13): 322 T(x,y) * (x \ 1) = x \ T(x,y). [para(220(a,1),273(a,1,2)),flip(a)]. given #210 (H,wt=13): 324 T(x,y) * (1 / x) = x \ T(x,y). [para(225(a,1),286(a,1,2)),flip(a)]. given #211 (H,wt=11): 332 T(x,y) / x = x \ T(x,y). [para(324(a,1),321(a,1)),flip(a)]. given #212 (H,wt=11): 333 x * (T(x,y) / x) = T(x,y). [para(332(a,2),14(a,1,2))]. given #213 (H,wt=13): 334 T(T(x,y) / x,x) = T(x,y) / x. [para(332(a,2),82(a,2))]. given #214 (H,wt=9): 338 T(x,T(x,y) / x) = x. [hyper(35,a,334,a)]. given #215 (H,wt=14): 276 L(x \ 1,x,y) / y = (y * x) \ 1. [para(139(a,2),264(a,1,1))]. given #216 (H,wt=14): 295 (x / y) * (y * z) = x * L(z,y,x). [hyper(17,a,169,a,b,283,a)]. given #217 (H,wt=9): 341 L(L(x,y,z),z,y) = x. [hyper(17,a,169,a(flip),b,295,a(flip))]. given #218 (H,wt=8): 347 L(x,T(y,z),y) = x. [para(341(a,1),239(a,1)),flip(a)]. given #219 (H,wt=10): 348 L(x,y \ z,z / y) = x. [para(341(a,1),243(a,1)),flip(a)]. given #220 (H,wt=12): 345 L(T(x,x * y),x,y) = T(x,y). [para(166(a,1),341(a,1,1))]. given #221 (H,wt=14): 297 (x / y) * z != u | (y / x) * u = z. [para(283(a,1),19(a,1)),flip(a)]. given #222 (H,wt=14): 298 L(x \ y,x,z) = z \ ((z / x) * y). [para(283(a,1),177(a,1,1,2))]. given #223 (H,wt=14): 299 (x / y) \ (x * L(z,y,x)) = y * z. [para(284(a,2),169(a,1))]. given #224 (H,wt=14): 300 x * L(y \ z,y,x) = (x / y) * z. [para(284(a,1),174(a,2))]. given #225 (H,wt=14): 311 x * L(y,y \ 1,x) = x / (y \ 1). [para(210(a,1),281(a,1,2,1))]. given #226 (H,wt=14): 329 L(x,x,x \ y) = (x \ y) \ T(y,x). [para(14(a,1),328(a,1,2,1)),flip(a)]. given #227 (H,wt=14): 337 T(x,y) != x * z | T(x,y) / x = z. [para(333(a,1),19(a,1))]. given #228 (H,wt=14): 340 L(x,y,z) = z \ ((z / y) * (y * x)). [hyper(56,a,295,a(flip)),flip(a)]. given #229 (H,wt=14): 342 x * (y * L(z,x,y)) = (x * y) * z. [para(295(a,1),85(a,1,2))]. given #230 (H,wt=14): 343 x \ ((x * y) * z) = y * L(z,x,y). [para(295(a,1),168(a,2))]. given #231 (H,wt=14): 344 L((x * y) \ z,x,y) = y \ (x \ z). [para(141(a,1),341(a,1,1))]. given #232 (H,wt=14): 346 L(x,y,z) = z \ (y \ ((y * z) * x)). [para(165(a,1),341(a,1,1))]. given #233 (H,wt=14): 352 L(T(x,y),x,x \ y) = T(x,x \ y). [para(14(a,1),345(a,1,1,2))]. given #234 (H,wt=14): 356 T(x,y) / L(y,y,y \ x) = y \ x. [para(329(a,2),53(a,1,2))]. given #235 (H,wt=15): 232 (x * y) * (1 / y) = y * (T(x,y) / y). [para(80(a,1),216(a,1,1))]. given #236 (H,wt=15): 233 T((x \ y) \ y,x \ 1) = (x \ y) \ y. [hyper(35,a,230,a)]. given #237 (H,wt=15): 238 (x * T(x \ y,z)) / x = T(y / x,z). [hyper(61,a,127,a)]. given #238 (H,wt=15): 242 (x * T(x,y)) * z = T(x,y) * (x * z). [para(107(a,1),156(a,1,1))]. given #239 (H,wt=15): 245 (x / T(x,y)) \ z = T(x,y) * (x \ z). [para(239(a,1),174(a,1,2)),flip(a)]. given #240 (H,wt=15): 247 (x * y) / (x \ z) = x * ((y / z) * x). [para(16(a,1),167(a,1,1,2))]. given #241 (H,wt=15): 248 ((x \ y) / x) * (x * z) = x \ (y * z). [para(14(a,1),168(a,1,2,1)),flip(a)]. given #242 (H,wt=15): 249 (x / T(x,y)) * z = x * (T(x,y) \ z). [hyper(17,a,156,a(flip),b,170,a(flip))]. given #243 (H,wt=15): 250 x * (((x \ y) / x) * z) = y * (x \ z). [para(14(a,1),170(a,1,1)),flip(a)]. given #244 (H,wt=15): 251 (x / y) \ (y \ (x * y)) = y * K(x,y). [para(26(a,2),176(a,2,2))]. given #245 (H,wt=13): 368 (x / y) \ T(x,y) = y * K(x,y). [para(32(a,2),251(a,1,2))]. given #246 (H,wt=15): 252 x \ (((x \ y) / x) \ z) = y \ (x * z). [para(14(a,1),182(a,1,1)),flip(a)]. given #247 (H,wt=15): 291 ((x * y) \ y) * x = x * ((x * y) \ y). [para(287(a,1),80(a,1,2))]. given #248 (H,wt=15): 301 (x / y) \ (x * z) = x \ ((x * y) * z). [para(284(a,2),168(a,2)),flip(a)]. given #249 (H,wt=15): 302 (x * y) * (x \ z) = x * ((x / y) \ z). [para(284(a,2),170(a,2,2))]. given #250 (H,wt=15): 303 (x / y) * (x \ z) = x * ((x * y) \ z). [para(284(a,1),176(a,1))]. given #251 (H,wt=15): 304 (x * y) \ (x * z) = x \ ((x / y) * z). [para(284(a,1),182(a,2,2))]. given #252 (H,wt=15): 307 (x / y) * (x \ y) = (x \ y) * (x / y). [para(290(a,1),80(a,1,2)),flip(a)]. given #253 (H,wt=15): 318 x / T(y \ 1,x) = x * ((y \ x) \ x). [para(272(a,2),314(a,1,2))]. given #254 (H,wt=15): 319 (x * (y \ x)) \ z = ((x \ y) / x) * z. [para(314(a,1),284(a,1,1))]. given #255 (H,wt=15): 323 T(x * y,1 / x) = x * (x * (y / x)). [para(216(a,1),274(a,1,2)),flip(a)]. given #256 (H,wt=15): 330 ((x / y) / x) * y = y * ((x / y) / x). [para(306(a,1),80(a,1,2)),flip(a)]. given #257 (H,wt=15): 331 (x \ T(x,y)) / x = x \ (x \ T(x,y)). [para(322(a,1),191(a,1,2)),flip(a)]. given #258 (H,wt=15): 336 (x \ T(x,y)) \ z = (x / T(x,y)) * z. [para(332(a,1),284(a,1,1))]. given #259 (H,wt=15): 349 (x * T(x,y)) * z = x * (T(x,y) * z). [para(347(a,1),69(a,1,2))]. given #260 (H,wt=15): 350 (T(x,y) / x) \ (T(x,y) * z) = x * z. [para(347(a,1),171(a,2,2))]. given #261 (H,wt=15): 363 (x * T(y,z)) / x = T((x * y) / x,z). [para(13(a,1),238(a,1,1,2,1))]. given #262 (H,wt=15): 364 (x * T(x,y)) * (x \ z) = T(x,y) * z. [para(14(a,1),242(a,2,2))]. given #263 (H,wt=15): 365 x * (((x \ y) / z) * x) = y / (x \ z). [para(14(a,1),247(a,1,1)),flip(a)]. given #264 (H,wt=15): 369 ((x \ y) / x) \ z = x * (y \ (x * z)). [para(252(a,1),14(a,1,2)),flip(a)]. given #265 (H,wt=15): 371 (x \ y) * (x / y) = x * ((x * y) \ y). [para(307(a,1),303(a,1))]. given #266 (H,wt=15): 372 T(x * (y * x),1 / x) = x * (x * y). [para(15(a,1),323(a,2,2,2))]. given #267 (H,wt=15): 374 (x \ T(x,y)) \ z = x * (T(x,y) \ z). [para(336(a,2),249(a,1))]. given #268 (H,wt=15): 375 T(x,y) * (x * z) = x * (T(x,y) * z). [para(349(a,1),242(a,1)),flip(a)]. given #269 (H,wt=15): 376 (T(x,y) * z) / (x * z) = T(x,y) / x. [para(350(a,1),53(a,1,2))]. given #270 (H,wt=15): 377 x * ((T(x,y) / x) * z) = T(x,y) * z. [para(364(a,1),170(a,1)),flip(a)]. given #271 (H,wt=15): 378 x * ((x / T(x,y)) \ z) = T(x,y) * z. [para(364(a,1),302(a,1)),flip(a)]. given #272 (H,wt=15): 379 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(364(a,1),349(a,1)),flip(a)]. given #273 (H,wt=15): 381 ((x \ (y * x)) / x) \ y = x * K(x,y). [para(26(a,2),369(a,2,2))]. given #274 (H,wt=13): 391 (T(x,y) / y) \ x = y * K(y,x). [para(32(a,2),381(a,1,1,1))]. given #275 (H,wt=15): 382 T(x,y) \ (x * (T(x,y) * z)) = x * z. [hyper(56,a,375,a)]. given #276 (H,wt=15): 385 (T(x,y) * z) / (x * z) = x \ T(x,y). [para(376(a,2),332(a,1))]. given #277 (H,wt=15): 386 x \ (T(x,y) * z) = (T(x,y) / x) * z. [hyper(56,a,377,a)]. given #278 (H,wt=15): 387 x * ((x \ T(x,y)) * z) = T(x,y) * z. [para(332(a,1),377(a,1,2,1))]. given #279 (H,wt=15): 388 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(56,a,379,a)]. given #280 (H,wt=15): 392 T(x,y) \ (x * z) = x * (T(x,y) \ z). [para(14(a,1),382(a,1,2,2))]. given #281 (H,wt=13): 400 x * (T(x,y) \ 1) = T(x,y) \ x. [para(12(a,1),392(a,1,2)),flip(a)]. given #282 (H,wt=11): 404 x / T(x,y) = T(x,y) \ x. [para(400(a,1),240(a,1)),flip(a)]. given #283 (H,wt=11): 405 x / (x / T(x,y)) = T(x,y). [para(404(a,2),53(a,1,2))]. given #284 (H,wt=13): 401 x * (T(x,y) \ y) = T(y,T(x,y)). [para(392(a,1),101(a,1))]. given #285 (H,wt=13): 403 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(56,a,400,a)]. given #286 (H,wt=13): 411 T(T(x,y) \ 1,x) = T(x,y) \ 1. [para(403(a,1),272(a,2))]. given #287 (H,wt=9): 412 T(x,T(x,y) \ 1) = x. [hyper(35,a,411,a)]. given #288 (H,wt=13): 413 T(x / y,(y \ x) \ 1) = x / y. [para(82(a,1),412(a,1,2,1))]. given #289 (H,wt=15): 395 (x \ T(x,y)) * z = T(x,y) * (x \ z). [hyper(17,a,379,a,b,387,a)]. given #290 (H,wt=15): 398 T(x,y) * (x \ (T(x,y) \ z)) = x \ z. [para(14(a,1),388(a,1,2)),flip(a)]. given #291 (H,wt=15): 399 x \ (T(x,y) \ (x * z)) = T(x,y) \ z. [hyper(56,a,392,a(flip))]. given #292 (H,wt=15): 402 (x \ T(x,y)) \ z = T(x,y) \ (x * z). [para(392(a,2),374(a,2))]. given #293 (H,wt=15): 408 (T(x,y) \ x) \ z = T(x,y) * (x \ z). [para(404(a,1),245(a,1,1))]. given #294 (H,wt=15): 409 (T(x,y) \ x) * z = x * (T(x,y) \ z). [para(404(a,1),249(a,1,1))]. given #295 (H,wt=9): 418 T(x,T(x,y) \ x) = x. [hyper(98,a,409,a)]. given #296 (H,wt=9): 419 T(x,x / T(x,y)) = x. [para(404(a,2),418(a,1,2))]. given #297 (H,wt=15): 417 (T(x,y) / x) \ z = T(x,y) \ (x * z). [para(332(a,2),402(a,1,1))]. given #298 (H,wt=16): 62 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(24(a,2),14(a,1,2))]. given #299 (H,wt=16): 70 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(14(a,1),28(a,2,1)),flip(a)]. given #300 (H,wt=14): 421 L(x,x \ y,x) = y \ (y / (x \ 1)). [para(193(a,1),70(a,1,2)),flip(a)]. given #301 (H,wt=14): 422 x / L(y,y \ x,y) = x * (y \ 1). [para(421(a,2),316(a,1,2))]. given #302 (H,wt=16): 72 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(16(a,1),28(a,2,1)),flip(a)]. given #303 (H,wt=11): 423 L(x,y,z / y) = L(x,y,z). [para(72(a,1),340(a,2)),flip(a)]. given #304 (H,wt=11): 424 L(x,y,z * y) = L(x,y,z). [para(15(a,1),423(a,1,3)),flip(a)]. given #305 (H,wt=11): 428 L(L(x,y,z / y),z,y) = x. [para(423(a,2),341(a,1,1))]. given #306 (H,wt=11): 429 L(L(x,y,z),z,y / z) = x. [para(423(a,2),341(a,1))]. given #307 (H,wt=11): 432 L(L(x,y,z),z * y,y) = x. [para(424(a,1),341(a,1,1))]. given #308 (H,wt=11): 435 L(x,y / z,z) = L(x,y,z). [para(341(a,1),428(a,1,1)),flip(a)]. given #309 (H,wt=11): 438 L(x,y * z,z) = L(x,y,z). [para(341(a,1),432(a,1,1))]. given #310 (H,wt=12): 430 L(x,T(y,z),y / T(y,z)) = x. [para(423(a,2),347(a,1))]. given #311 (H,wt=12): 442 L(x,T(y,z),T(y,z) \ y) = x. [para(404(a,1),430(a,1,3))]. given #312 (H,wt=13): 425 L(x,y \ z,z) = L(x,y \ z,y). [para(53(a,1),423(a,1,3)),flip(a)]. given #313 (H,wt=13): 426 L(x,y,z \ 1) = L(x,y,z \ y). [para(264(a,1),423(a,1,3))]. given #314 (H,wt=13): 427 L(x,y,z \ y) = L(x,y,1 / z). [para(278(a,1),423(a,1,3)),flip(a)]. given #315 (H,wt=13): 433 L(L(x,y,z \ 1),z \ y,y) = x. [para(264(a,1),428(a,1,1,3))]. given #316 (H,wt=13): 434 L(L(x,y,1 / z),z \ y,y) = x. [para(278(a,1),428(a,1,1,3))]. given #317 (H,wt=13): 439 L(x,y,z \ y) = L(x,z,z \ y). [para(53(a,1),435(a,1,2)),flip(a)]. given #318 (H,wt=10): 444 L(x,y,T(y,z) \ y) = x. [para(439(a,2),442(a,1))]. given #319 (H,wt=10): 447 L(x,y,y / T(y,z)) = x. [para(404(a,2),444(a,1,3))]. given #320 (H,wt=10): 448 L(x,y,T(y,z) \ 1) = x. [para(444(a,1),426(a,2))]. given #321 (H,wt=10): 449 L(x,T(y,z) \ 1,y) = x. [para(448(a,1),341(a,1,1))]. given #322 (H,wt=12): 450 L(x,(y \ z) \ 1,z / y) = x. [para(82(a,1),449(a,1,2,1))]. given #323 (H,wt=13): 440 L(x,y \ 1,z) = L(x,y \ z,z). [para(264(a,1),435(a,1,2))]. given #324 (H,wt=13): 443 L(L(x,y,z \ 1),z \ y,z) = x. [para(433(a,1),425(a,1)),flip(a)]. given #325 (H,wt=13): 445 L(x,y,z \ 1) = L(x,z,z \ y). [para(439(a,1),426(a,2))]. given #326 (H,wt=13): 446 L(x,y,y \ z) = L(x,z,1 / y). [para(439(a,1),427(a,1))]. given #327 (H,wt=13): 453 L(x,y \ 1,z) = L(x,y \ z,y). [para(440(a,2),425(a,1))]. given #328 (H,wt=13): 455 L(x,y * z,y \ 1) = L(x,y,z). [para(13(a,1),445(a,2,3))]. given #329 (H,wt=13): 456 L(x,y \ 1,y * z) = L(x,z,y). [para(13(a,1),453(a,2,2))]. given #330 (H,wt=15): 457 L(x,y \ 1,z * y) = L(x,T(z,y),y). [para(32(a,2),453(a,2,2))]. given #331 (H,wt=16): 73 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(14(a,1),30(a,2,1,1))]. given #332 (H,wt=16): 74 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(14(a,1),30(a,2,2)),flip(a)]. given #333 (H,wt=14): 460 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(74(a,1),52(a,1)),flip(a)]. given #334 (H,wt=14): 461 R(x,y,y \ 1) / (y \ 1) = x * y. [hyper(61,a,460,a)]. given #335 (H,wt=14): 462 (x * y) \ R(x,y,y \ 1) = y \ 1. [hyper(56,a,460,a)]. given #336 (H,wt=14): 463 R(x / y,y,y \ 1) = x * (y \ 1). [para(16(a,1),460(a,1,1)),flip(a)]. given #337 (H,wt=14): 465 x * (T(y,x) / x) = R(y,x,x \ 1). [para(460(a,1),189(a,1)),flip(a)]. given #338 (H,wt=14): 466 x \ R(y,x,x \ 1) = T(y,x) / x. [hyper(56,a,465,a)]. given #339 (H,wt=14): 468 x * (T(y,x) / x) = R(y,x,1 / x). [para(208(a,2),465(a,2,3))]. given #340 (H,wt=14): 469 x \ R(y,x,1 / x) = T(y,x) / x. [para(208(a,2),466(a,1,2,3))]. given #341 (H,wt=14): 470 (x * y) * (1 / y) = R(x,y,1 / y). [para(468(a,1),232(a,2))]. given #342 (H,wt=14): 471 (x * y) \ R(x,y,1 / y) = 1 / y. [hyper(56,a,470,a)]. given #343 (H,wt=14): 472 R(x / y,y,1 / y) = x * (1 / y). [para(16(a,1),470(a,1,1)),flip(a)]. given #344 (H,wt=15): 467 x * (T(R(x,y,z),x) / x) = R(x,y,z). [para(465(a,2),154(a,1))]. given #345 (H,wt=15): 473 (R(x,y,z) * x) \ R(x,y,z) = 1 / x. [para(154(a,1),471(a,1,2))]. given #346 (H,wt=15): 476 x * (R(T(x,x),y,z) / x) = R(x,y,z). [para(42(a,2),467(a,1,2,1))]. given #347 (H,wt=13): 478 x * (R(x,y,z) / x) = R(x,y,z). [para(79(a,1),476(a,1,2,1,1))]. given #348 (H,wt=13): 479 R(x,y,z) / x = x \ R(x,y,z). [hyper(56,a,478,a),flip(a)]. given #349 (H,wt=13): 480 (x \ R(x,y,z)) * x = R(x,y,z). [para(479(a,1),16(a,1,1))]. given #350 (H,wt=15): 477 R(x,y,z) \ (R(x,y,z) / x) = 1 / x. [para(473(a,1),313(a,1)),flip(a)]. given #351 (H,wt=15): 481 T(x \ R(x,y,z),x) = x \ R(x,y,z). [para(479(a,1),82(a,1,1))]. given #352 (H,wt=10): 485 K(x \ R(x,y,z),x) = 1. [hyper(36,a,481,a)]. given #353 (H,wt=15): 484 R(x,y,z) \ (R(x,y,z) / x) = x \ 1. [para(477(a,2),208(a,1))]. given #354 (H,wt=15): 486 R(x,y,z) \ (x \ R(x,y,z)) = x \ 1. [para(479(a,1),484(a,1,2))]. given #355 (H,wt=15): 487 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(486(a,1),14(a,1,2))]. given #356 (H,wt=16): 77 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(16(a,1),30(a,2,2)),flip(a)]. given #357 (H,wt=14): 488 (x * (1 / y)) * y = R(x,1 / y,y). [para(77(a,1),52(a,1)),flip(a)]. given #358 (H,wt=14): 489 R(x,1 / y,y) / y = x * (1 / y). [hyper(61,a,488,a)]. given #359 (H,wt=14): 490 R(x / (1 / y),1 / y,y) = x * y. [para(16(a,1),488(a,1,1)),flip(a)]. given #360 (H,wt=16): 129 T(x * y,x) != (y / x) * z | x * x = z. [para(126(a,1),19(a,1))]. given #361 (H,wt=16): 137 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(14(a,1),69(a,1,1))]. given #362 (H,wt=10): 494 L(x,y \ T(y,z),y) = x. [hyper(17,a,387,a(flip),b,137,a)]. given #363 (H,wt=10): 495 L(x,T(y,z),y \ 1) = x. [para(494(a,1),443(a,1))]. given #364 (H,wt=10): 496 L(x,T(1 / y,z),y) = x. [para(54(a,1),495(a,1,3))]. given #365 (H,wt=10): 497 L(x,y \ (z \ y),z) = x. [para(285(a,1),496(a,1,2))]. given #366 (H,wt=10): 498 L(x,(y * z) \ z,y) = x. [para(275(a,1),496(a,1,2))]. given #367 (H,wt=10): 499 L(x,y \ z,y / z) = x. [para(54(a,1),497(a,1,2,2))]. given #368 (H,wt=10): 504 L(x,y,(z / y) / z) = x. [para(54(a,1),499(a,1,2))]. given #369 (H,wt=16): 140 L((x \ y) \ z,x \ y,x) = y \ (x * z). [para(14(a,1),71(a,2,1))]. given #370 (H,wt=16): 142 L(x \ y,x,z / y) = ((z / y) * x) \ z. [para(16(a,1),71(a,2,2))]. given #371 (H,wt=16): 145 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(80(a,1),71(a,2,2))]. given #372 (H,wt=16): 155 R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u). [para(153(a,1),46(a,1,1)),flip(a)]. given #373 (H,wt=16): 160 R(x / (y / z),y / z,z) = (x * z) / y. [para(16(a,1),76(a,2,2))]. given #374 (H,wt=16): 163 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(14(a,1),92(a,1,2,1))]. given #375 (H,wt=16): 178 L((x * y) \ z,x * y,y) = y \ (x \ z). [para(15(a,1),175(a,2,2,1))]. given #376 (H,wt=15): 510 (x * (y * x)) \ z = x \ (y \ (x \ z)). [para(178(a,1),141(a,1)),flip(a)]. given #377 (H,wt=16): 180 L(x \ y,x,z \ x) = (z \ x) \ (z \ y). [para(53(a,1),175(a,2,2,1))]. given #378 (H,wt=16): 186 (x * y) * (x \ 1) != x * z | y / x = z. [para(183(a,1),57(a,1,2)),flip(b)]. given #379 (H,wt=16): 192 x * (y \ 1) != y * z | (y \ x) / y = z. [para(187(a,1),19(a,1))]. given #380 (H,wt=16): 266 (x * y) / ((z * x) * y) = R(z,x,y) \ 1. [para(75(a,1),255(a,1,2))]. given #381 (H,wt=16): 277 R(x / y,y,z) \ 1 = (y * z) / (x * z). [para(161(a,1),264(a,1,1)),flip(a)]. given #382 (H,wt=15): 515 R(x / y,y,z) = R(y / x,x,z) \ 1. [para(277(a,2),76(a,2))]. given #383 (H,wt=16): 320 T(x \ (x / y),z) = L(T(y \ 1,z),y,x). [para(282(a,1),40(a,2,1)),flip(a)]. given #384 (H,wt=16): 326 T((x * y) / x,x * y) = L(y,x,x * y). [para(13(a,1),325(a,1,1)),flip(a)]. given #385 (H,wt=16): 353 L((x \ y) \ z,x \ y,y) = y \ (x * z). [para(53(a,1),298(a,2,2,1))]. given #386 (H,wt=16): 354 L(x,y / x,z) = z \ ((z / (y / x)) * y). [para(54(a,1),298(a,1,1))]. given #387 (H,wt=16): 355 x \ (y * L(z,x \ y,y)) = (x \ y) * z. [para(53(a,1),299(a,1,1))]. given #388 (H,wt=16): 358 x * (L(y,x,z) * z) = (x * z) * T(y,z). [para(103(a,1),342(a,1,2))]. given #389 (H,wt=16): 359 (x \ y) * L(z,x,x \ y) = x \ (y * z). [para(14(a,1),343(a,1,2,1)),flip(a)]. given #390 (H,wt=16): 360 x \ ((x * y) * T(z,y)) = L(z,x,y) * y. [para(343(a,2),103(a,1))]. given #391 (H,wt=16): 361 L(x,x,x \ y) * y = y * T(x,x \ y). [para(352(a,1),103(a,1,2)),flip(a)]. given #392 (H,wt=16): 436 L(T(x,y / x),y,x) = T(x,x * (y / x)). [para(345(a,1),428(a,1,1))]. given #393 (H,wt=16): 491 x \ R(y,1 / x,x) = T(y * (1 / x),x). [para(488(a,1),32(a,2,2)),flip(a)]. given #394 (H,wt=16): 511 x \ (y \ (x \ ((x * y) * x))) = a(x,y,x). [para(510(a,1),24(a,2)),flip(a)]. given #395 (H,wt=11): 519 x \ L(x,x,y) = a(x,y,x). [para(346(a,2),511(a,1,2))]. given #396 (H,wt=11): 520 x * a(x,y,x) = L(x,x,y). [para(519(a,1),14(a,1,2))]. given #397 (H,wt=14): 521 L(x,x,y) != x * z | a(x,y,x) = z. [para(520(a,1),19(a,1))]. given #398 (H,wt=16): 514 L(x \ y,x,z \ 1) = (z \ x) \ (z \ y). [para(180(a,1),426(a,2))]. given #399 (H,wt=16): 516 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(433(a,1),355(a,1,2,2)),flip(a)]. given #400 (H,wt=16): 522 (x \ y) \ (x \ (y * z)) = L(z,y,x \ 1). [para(13(a,1),514(a,1,1)),flip(a)]. given #401 (H,wt=17): 112 ((x / y) * (y \ x)) * 1 = (y \ x) * (x / y). [para(108(a,1),65(a,1,2))]. given #402 (H,wt=15): 523 (x / y) * (y \ x) = (y \ x) * (x / y). [hyper(59,a,112,a)]. given #403 (H,wt=17): 136 (x * y) * L(z,y,x) != x * u | y * z = u. [para(28(a,2),57(a,1,2)),flip(b)]. given #404 (H,wt=17): 138 (x * y) * z != x * (y * u) | L(u,y,x) = z. [para(69(a,1),19(a,1)),flip(a)]. given #405 (H,wt=17): 149 (x * y) * z != u * (y * z) | R(x,y,z) = u. [para(75(a,1),20(a,1))]. given #406 (H,wt=17): 150 R(x,y,z) * (y * z) != u * z | x * y = u. [para(75(a,2),20(a,1))]. given #407 (H,wt=17): 157 (R(x,y,z) * x) * u = R(x,y,z) * (x * u). [para(154(a,1),75(a,1,1)),flip(a)]. given #408 (H,wt=9): 526 L(x,y,R(y,z,u)) = x. [hyper(138,a,157,a)]. given #409 (H,wt=9): 527 L(x,R(y,z,u),y) = x. [hyper(17,a,342,a(flip),b,157,a)]. given #410 (H,wt=14): 529 L(x,y / z,(y * u) / (z * u)) = x. [para(76(a,1),526(a,1,3))]. given #411 (H,wt=14): 531 L(x,R(y,z,u),y / R(y,z,u)) = x. [para(526(a,1),428(a,1))]. given #412 (H,wt=15): 525 x * (R(x,y,z) \ 1) = x / R(x,y,z). [hyper(186,a,157,a),flip(a)]. given #413 (H,wt=17): 172 (x / y) * z != x * u | y * L(u,x,y) = z. [para(169(a,1),19(a,1)),flip(a)]. given #414 (H,wt=17): 173 (x / y) * (y * L(z,x,y)) != x * u | u = z. [para(169(a,2),19(a,2)),flip(a)]. given #415 (H,wt=17): 198 L(x / y,z,u) * y = y * L(y \ x,z,u). [para(82(a,1),103(a,1,2,1)),flip(a)]. given #416 (H,wt=17): 202 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(82(a,1),104(a,1,2,1)),flip(a)]. given #417 (H,wt=17): 224 L(x,y,z) * (x \ 1) = (x \ 1) * L(x,y,z). [para(219(a,1),103(a,1,2,1)),flip(a)]. given #418 (H,wt=15): 533 L(x,y,z) * (x \ 1) = x \ L(x,y,z). [para(224(a,2),259(a,1))]. given #419 (H,wt=15): 534 L(x,y,z) * (1 / x) = x \ L(x,y,z). [para(208(a,2),533(a,1,2))]. given #420 (H,wt=17): 226 L(x,y,z) * (1 / x) = (1 / x) * L(x,y,z). [para(221(a,1),103(a,1,2,1)),flip(a)]. given #421 (H,wt=12): 535 T(1 / x,L(x,y,z)) = 1 / x. [hyper(98,a,226,a)]. given #422 (H,wt=10): 536 K(1 / x,L(x,y,z)) = 1. [hyper(36,a,535,a)]. given #423 (H,wt=10): 537 K(x \ 1,L(x,y,z)) = 1. [para(208(a,1),536(a,1,1))]. given #424 (H,wt=10): 538 K(L(x,y,z) \ 1,x) = 1. [para(341(a,1),537(a,1,2))]. given #425 (H,wt=17): 227 L(x \ 1,y,z) * x = x * L(x \ 1,y,z). [para(211(a,1),103(a,1,2,1)),flip(a)]. given #426 (H,wt=17): 305 T(1 / (x * y),y * x) = (y * x) \ K(y,x). [para(26(a,2),285(a,2,2))]. given #427 (H,wt=17): 312 ((x \ y) \ y) * (x \ 1) = ((x \ y) \ y) / x. [para(244(a,1),281(a,1,2))]. given #428 (H,wt=17): 335 T(x / y,y) / (x / y) = (x / y) \ (y \ x). [para(82(a,1),332(a,2,2))]. given #429 (H,wt=15): 540 (x \ y) / (y / x) = (y / x) \ (x \ y). [para(82(a,1),335(a,1,1))]. given #430 (H,wt=17): 357 (x * y) * z != x * (y * L(u,x,y)) | z = u. [para(342(a,2),19(a,2))]. given #431 (H,wt=17): 362 ((x \ y) \ y) * (x \ 1) = x \ ((x \ y) \ y). [para(233(a,1),273(a,1,2)),flip(a)]. given #432 (H,wt=15): 541 ((x \ y) \ y) / x = x \ ((x \ y) \ y). [para(362(a,1),312(a,1)),flip(a)]. given #433 (H,wt=17): 370 x \ ((x / T(y,x)) * z) = (y * x) \ (x * z). [para(80(a,1),304(a,1,1)),flip(a)]. given #434 (H,wt=17): 406 T(x / y,y) \ (x / y) = (x / y) / (y \ x). [para(82(a,1),404(a,1,2)),flip(a)]. given #435 (H,wt=15): 542 (x / y) / (y \ x) = (y \ x) \ (x / y). [para(82(a,1),406(a,1,1)),flip(a)]. given #436 (H,wt=17): 407 (x / y) / T(x / y,y) = (y \ x) \ (x / y). [para(82(a,1),404(a,2,1))]. given #437 (H,wt=17): 410 (x / y) * ((y \ x) \ y) = T(y,T(x / y,y)). [para(82(a,1),401(a,1,2,1))]. given #438 (H,wt=15): 543 (x / y) * ((y \ x) \ y) = T(y,y \ x). [para(82(a,1),410(a,2,2))]. given #439 (H,wt=17): 414 (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y). [para(413(a,1),273(a,1,2)),flip(a)]. given #440 (H,wt=17): 437 L(L(x,y * z,K(y,z)),K(y,z),z * y) = x. [para(89(a,1),429(a,1,3))]. given #441 (H,wt=17): 441 L(x,T(y,y \ z),z) = L(x,1 / (y \ z),z). [para(289(a,1),435(a,1,2)),flip(a)]. given #442 (H,wt=17): 482 (x \ R(x,y,z)) \ u = (x / R(x,y,z)) * u. [para(479(a,1),284(a,1,1))]. given #443 (H,wt=17): 483 L(L(x,R(y,z,u),y),y,y \ R(y,z,u)) = x. [para(479(a,1),429(a,1,3))]. given #444 (H,wt=11): 544 L(x,y,y \ R(y,z,u)) = x. [para(527(a,1),483(a,1,1))]. => 546 back subsumes hint matchers not on Sos. Reset weight to 517.000. given #445 (H,wt=11): 545 L(x,y \ R(y,z,u),y) = x. [para(544(a,1),341(a,1,1))]. given #446 (H,wt=17): 502 x / (1 / ((x * y) \ y)) = x * ((x * y) \ y). [para(498(a,1),212(a,1,2))]. given #447 (H,wt=17): 512 x \ (y \ (x \ ((y * x) * x))) = K(y * x,x). [para(510(a,1),26(a,2)),flip(a)]. given #448 (H,wt=15): 550 x \ (y \ T(y * x,x)) = K(y * x,x). [para(32(a,2),512(a,1,2,2))]. given #449 (H,wt=17): 528 (x * R(x,y,z)) * u = R(x,y,z) * (x * u). [para(201(a,1),157(a,1,1))]. given #450 (H,wt=17): 530 (x * R(x,y,z)) * u = x * (R(x,y,z) * u). [para(526(a,1),342(a,1,2,2)),flip(a)]. given #451 (H,wt=17): 547 x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u. [para(545(a,1),137(a,1,2)),flip(a)]. given #452 (H,wt=17): 548 (x \ R(x,y,z)) \ u = R(x,y,z) \ (x * u). [para(545(a,1),140(a,1))]. given #453 (H,wt=17): 549 x / (1 / ((x * y) \ y)) = (y / x) \ (x \ y). [para(502(a,2),176(a,2)),flip(a)]. given #454 (H,wt=17): 551 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(530(a,1),528(a,1)),flip(a)]. given #455 (H,wt=17): 553 x / (1 / ((x * y) \ y)) = (x \ y) / (y / x). [para(549(a,2),540(a,2)),flip(a)]. given #456 (H,wt=17): 554 x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. [para(14(a,1),551(a,1,2)),flip(a)]. given #457 (H,wt=17): 557 (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u). [hyper(17,a,547,a,b,554,a),flip(a)]. given #458 (H,wt=17): 559 (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). [hyper(61,a,557,a)]. given #459 (H,wt=17): 561 (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). [para(13(a,1),559(a,1,1,2))]. given #460 (H,wt=17): 563 x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). [para(14(a,1),561(a,1,1))]. given #461 (H,wt=17): 565 (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). [para(563(a,1),54(a,1,1))]. given #462 (H,wt=17): 569 R(x,y,z) \ (x * u) = x * (R(x,y,z) \ u). [para(565(a,1),548(a,1)),flip(a)]. given #463 (H,wt=15): 570 x * (R(x,y,z) \ 1) = R(x,y,z) \ x. [para(12(a,1),569(a,1,2)),flip(a)]. given #464 (H,wt=13): 572 x / R(x,y,z) = R(x,y,z) \ x. [para(570(a,1),525(a,1)),flip(a)]. given #465 (H,wt=13): 573 (R(x,y,z) \ x) * R(x,y,z) = x. [para(572(a,1),16(a,1,1))]. given #466 (H,wt=13): 574 (R(x,y,z) \ x) \ x = R(x,y,z). [para(572(a,1),54(a,1,1))]. given #467 (H,wt=14): 577 L(x,R(y,z,u),R(y,z,u) \ y) = x. [para(572(a,1),531(a,1,3))]. given #468 (H,wt=11): 579 L(x,y,R(y,z,u) \ 1) = x. [para(577(a,1),445(a,2))]. given #469 (H,wt=15): 575 1 / (R(x,y,z) \ x) = R(x,y,z) / x. [para(572(a,1),280(a,1,2))]. given #470 (H,wt=17): 571 (x * y) / (x * (R(x,z,u) \ y)) = R(x,z,u). [para(569(a,1),53(a,1,2))]. given #471 (H,wt=17): 576 (R(x,y,z) \ x) \ u = (R(x,y,z) / x) * u. [para(572(a,1),284(a,1,1))]. given #472 (H,wt=17): 578 (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. [para(572(a,1),482(a,2,1))]. given #473 (H,wt=17): 580 R(x,y,z) \ (x * u) = (R(x,y,z) \ x) * u. [para(577(a,1),359(a,1,2)),flip(a)]. given #474 (H,wt=17): 582 (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u. [para(479(a,1),576(a,2,1))]. given #475 (H,wt=17): 583 (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). [para(578(a,1),565(a,1))]. given #476 (H,wt=17): 584 (x * y) / ((R(x,z,u) \ x) * y) = R(x,z,u). [para(580(a,1),53(a,1,2))]. given #477 (H,wt=17): 585 (R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u). [para(582(a,2),557(a,1))]. given #478 (H,wt=18): 63 (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y). [para(14(a,1),24(a,2,1,2)),flip(a)]. given #479 (H,wt=16): 586 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(12(a,1),63(a,1,1))]. given #480 (H,wt=15): 587 x \ R(x,y,y \ 1) = a(x,y,y \ 1). [para(460(a,1),586(a,1,2))]. given #481 (H,wt=15): 588 x * a(x,y,y \ 1) = R(x,y,y \ 1). [para(587(a,1),14(a,1,2))]. given #482 (H,wt=18): 64 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(16(a,1),24(a,2,2,1)),flip(a)]. given #483 (H,wt=17): 589 a(x / y,y,z) = (x * L(z,y,x)) \ (x * z). [para(295(a,1),64(a,1,1)),flip(a)]. given #484 (H,wt=17): 591 a(x / y,y,z) = x \ ((x / L(z,y,x)) * z). [para(589(a,2),304(a,1))]. given #485 (H,wt=18): 86 (x * (y * x)) * z != x * u | y * (x * z) = u. [para(47(a,2),19(a,1))]. given #486 (H,wt=18): 100 (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y). [para(80(a,1),28(a,2,1)),flip(a)]. given #487 (H,wt=18): 105 (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y). [para(30(a,2),82(a,1,1)),flip(a)]. given #488 (H,wt=18): 162 T(R(x / y,y,z),y * z) = (y * z) \ (x * z). [para(76(a,2),82(a,1,1))]. given #489 (H,wt=18): 164 R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z. [para(80(a,1),92(a,1,2,1))]. given #490 (H,wt=18): 188 (x * (y / x)) / (y * (x \ 1)) = R(x,y,x \ 1). [para(184(a,1),30(a,2,1)),flip(a)]. given #491 (H,wt=18): 200 L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). [para(14(a,1),199(a,1,2,2)),flip(a)]. given #492 (H,wt=18): 217 (x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(209(a,1),24(a,2,1,2)),flip(a)]. given #493 (H,wt=16): 594 x \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(12(a,1),217(a,1,1))]. given #494 (H,wt=15): 595 x * L(1 / x,y,x) = a(y,x,1 / x). [para(594(a,1),343(a,1)),flip(a)]. given #495 (H,wt=15): 596 x \ R(x,y,1 / y) = a(x,y,1 / y). [para(470(a,1),594(a,1,2))]. given #496 (H,wt=15): 598 R(x,y,1 / y) / x = a(x,y,1 / y). [para(596(a,1),479(a,2))]. given #497 (H,wt=15): 599 a(x,y,1 / y) * x = R(x,y,1 / y). [para(596(a,1),480(a,1,1))]. given #498 (H,wt=17): 597 a(x / y,y,1 / y) = y * L(1 / y,x,y). [para(435(a,1),595(a,1,2)),flip(a)]. given #499 (H,wt=15): 600 a(x / y,y,1 / y) = a(x,y,1 / y). [para(597(a,2),595(a,1))]. NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 72 (0.00 of 3.35 sec). given #500 (H,wt=15): 601 a(x * y,y,1 / y) = a(x,y,1 / y). [para(15(a,1),600(a,1,1)),flip(a)]. given #501 (H,wt=18): 241 T(x,y) * z != (T(x,y) * x) * u | x * u = z. [para(156(a,2),19(a,1)),flip(a)]. given #502 (H,wt=18): 261 R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). [para(254(a,1),30(a,2,1,1))]. given #503 (H,wt=15): 602 R(x \ 1,x * y,z) = R(x,y,z) \ 1. [para(261(a,2),266(a,1))]. given #504 (H,wt=15): 603 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(14(a,1),602(a,1,2)),flip(a)]. given #505 (H,wt=17): 604 R(x,x \ y,z) \ x = x * R(x \ 1,y,z). [para(603(a,1),570(a,1,2)),flip(a)]. given #506 (H,wt=18): 367 x * (y \ z) != y * u | ((y \ x) / y) * z = u. [para(250(a,1),19(a,1))]. given #507 (H,wt=18): 373 T(x * y,1 / x) != x * z | x * (y / x) = z. [para(323(a,2),19(a,1))]. given #508 (H,wt=18): 383 T(x,y) * z != x * (T(x,y) * u) | x * u = z. [para(375(a,1),19(a,1)),flip(a)]. given #509 (H,wt=18): 384 T(x,y) * (x * z) != x * u | T(x,y) * z = u. [para(375(a,2),19(a,1))]. given #510 (H,wt=18): 390 T(x,y) * z != x * u | T(x,y) * (x \ z) = u. [para(379(a,1),19(a,1))]. given #511 (H,wt=18): 396 T(x,y) * z != x * u | (x \ T(x,y)) * z = u. [para(387(a,1),19(a,1))]. given #512 (H,wt=18): 397 T(x,y) * z != x * ((x \ T(x,y)) * u) | z = u. [para(387(a,2),19(a,2))]. given #513 (H,wt=18): 431 L((x * (y / x)) \ z,x,y) = (y / x) \ (x \ z). [para(423(a,1),344(a,1))]. given #514 (H,wt=18): 459 R(x,x \ y,y \ z) = z / ((x \ y) * (y \ z)). [para(14(a,1),73(a,2,1))]. given #515 (H,wt=18): 474 R(T(x / y,z),y,1 / y) = T(x * (1 / y),z). [para(472(a,1),42(a,2,1))]. given #516 (H,wt=18): 493 R(T(x / (1 / y),z),1 / y,y) = T(x * y,z). [para(490(a,1),42(a,2,1))]. given #517 (H,wt=18): 532 ((x * y) / (z * y)) * z = z * R(z \ x,z,y). [para(76(a,1),202(a,1,1))]. given #518 (H,wt=18): 592 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(105(a,2),42(a,2)),flip(a)]. given #519 (H,wt=18): 605 L((x * (y / x)) \ z,x,y) = x * ((x * y) \ z). [para(431(a,2),176(a,1))]. given #520 (H,wt=19): 317 (x * y) \ ((x * y) / K(y,x)) = (y * x) \ (x * y). [para(65(a,1),313(a,1,1)),flip(a)]. given #521 (H,wt=15): 606 (x * y) \ ((x * y) / K(y,x)) = K(x,y). [para(317(a,2),26(a,2)),flip(a)]. given #522 (H,wt=19): 339 ((x / y) \ 1) / (y \ x) = ((y \ x) * (x / y)) \ 1. [para(243(a,1),276(a,1,1))]. given #523 (H,wt=17): 607 ((x \ y) * (y / x)) \ 1 = (x / y) / (x \ y). [para(265(a,1),339(a,1,1)),flip(a)]. given #524 (H,wt=19): 351 ((x \ y) \ 1) / (y / x) = ((y / x) * (x \ y)) \ 1. [para(348(a,1),276(a,1,1))]. given #525 (H,wt=19): 389 ((x \ T(x,y)) / x) * z = T(x,y) * (x \ (x \ z)). [hyper(17,a,250,a,b,379,a),flip(a)]. given #526 (H,wt=19): 415 T(x,x \ y) * (x \ z) = (x \ ((x \ y) \ y)) * z. [para(81(a,1),395(a,1,1,2)),flip(a)]. given #527 (H,wt=19): 500 (x * ((x * y) \ y)) * z = x * (((x * y) \ y) * z). [para(498(a,1),69(a,1,2))]. given #528 (H,wt=19): 501 (x * ((x * y) \ y)) \ z = ((x * y) \ y) \ (x \ z). [para(498(a,1),141(a,1)),flip(a)]. given #529 (H,wt=19): 503 (((x * y) \ y) * x) * z = ((x * y) \ y) * (x * z). [para(498(a,1),342(a,1,2,2)),flip(a)]. given #530 (H,wt=19): 505 ((x / y) / (x \ y)) * z = (x / y) * ((x \ y) \ z). [para(499(a,1),300(a,1,2)),flip(a)]. given #531 (H,wt=19): 506 ((x \ y) * (x / y)) * z = (x \ y) * ((x / y) * z). [para(499(a,1),342(a,1,2,2)),flip(a)]. given #532 (H,wt=19): 507 ((x \ y) * (x / y)) \ z = (x / y) \ ((x \ y) \ z). [para(499(a,1),344(a,1))]. given #533 (H,wt=19): 508 (x * ((y / x) / y)) * z = x * (((y / x) / y) * z). [para(504(a,1),342(a,1,2,2)),flip(a)]. given #534 (H,wt=19): 513 T(x \ 1,x * (y * x)) = x \ (y \ (x \ (y * x))). [para(510(a,1),262(a,2))]. given #535 (H,wt=17): 613 T(x \ 1,x * (y * x)) = x \ (y \ T(y,x)). [para(32(a,2),513(a,2,2,2))]. given #536 (H,wt=19): 518 x * T(y,y \ x) != z * x | L(y,y,y \ x) = z. [para(361(a,1),20(a,1))]. given #537 (H,wt=19): 539 (x * (L(x,y,z) \ 1)) * 1 = (L(x,y,z) \ 1) * x. [para(538(a,1),65(a,1,2))]. given #538 (H,wt=17): 614 (L(x,y,z) \ 1) * x = x * (L(x,y,z) \ 1). [hyper(59,a,539,a),flip(a)]. given #539 (H,wt=15): 615 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(614(a,1),259(a,1))]. given #540 (H,wt=15): 616 x * (1 / L(x,y,z)) = L(x,y,z) \ x. [para(208(a,2),615(a,1,2))]. given #541 (H,wt=19): 556 (1 / ((x * y) \ y)) / x = 1 / ((x \ y) / (y / x)). [para(553(a,1),280(a,1,2)),flip(a)]. given #542 (H,wt=17): 617 (1 / ((x * y) \ y)) / x = (y / x) / (x \ y). [para(556(a,2),280(a,1))]. given #543 (H,wt=19): 608 (x * (T(x,y) \ x)) \ z = T(x,y) * (x \ (x \ z)). [para(389(a,1),319(a,2))]. given #544 (H,wt=19): 609 (x \ (x \ T(x,y))) * z = T(x,y) * (x \ (x \ z)). [para(331(a,1),389(a,1,1))]. given #545 (H,wt=19): 610 (x * ((x * y) \ y)) * z = ((x * y) \ y) * (x * z). [para(291(a,1),503(a,1,1))]. given #546 (H,wt=19): 611 (x * ((x * y) \ y)) * z = (x \ y) * ((x / y) * z). [para(371(a,1),506(a,1,1))]. given #547 (H,wt=19): 612 ((x \ y) * (x / y)) \ z = (y / x) * ((x \ y) \ z). [para(507(a,2),284(a,1))]. given #548 (H,wt=19): 618 ((x * y) \ y) * (x * z) = x * (((x * y) \ y) * z). [para(610(a,1),500(a,1))]. given #549 (H,wt=19): 619 (x \ y) * ((x / y) * z) = x * (((x * y) \ y) * z). [para(611(a,1),500(a,1))]. given #550 (H,wt=19): 620 (x * ((x * y) \ y)) \ z = (y / x) * ((x \ y) \ z). [para(371(a,1),612(a,1,1))]. given #551 (H,wt=19): 621 ((x * y) \ y) \ (x \ z) = (y / x) * ((x \ y) \ z). [para(620(a,1),501(a,1)),flip(a)]. given #552 (H,wt=17): 622 (x / y) * ((y \ x) \ y) = ((y * x) \ x) \ 1. [para(50(a,1),621(a,1,2)),flip(a)]. given #553 (H,wt=13): 623 T(x,x \ y) = ((x * y) \ y) \ 1. [para(622(a,1),543(a,1)),flip(a)]. given #554 (H,wt=13): 625 (x * y) \ y = 1 / T(x,x \ y). [para(623(a,2),53(a,1,2)),flip(a)]. given #555 (H,wt=13): 626 ((x * y) \ y) \ 1 = (x \ y) \ y. [para(623(a,1),81(a,1))]. given #556 (H,wt=13): 627 T(x,x \ y) \ 1 = (x * y) \ y. [para(623(a,2),210(a,1,1))]. given #557 (H,wt=13): 629 1 / ((x * y) \ y) = (x \ y) \ y. [para(626(a,1),208(a,2))]. given #558 (H,wt=13): 630 ((x \ y) \ y) \ 1 = (x * y) \ y. [para(626(a,1),210(a,1,1))]. given #559 (H,wt=13): 635 ((x / y) \ y) \ y = 1 / (x \ y). [para(16(a,1),629(a,1,2,1)),flip(a)]. given #560 (H,wt=13): 637 ((x / y) * x) \ x = (y \ x) \ 1. [para(54(a,1),630(a,1,1,1)),flip(a)]. given #561 (H,wt=13): 639 x / ((y \ x) \ 1) = (x / y) * x. [para(637(a,1),53(a,1,2))]. given #562 (H,wt=13): 641 (x / (x / y)) * x = x / (y \ 1). [para(54(a,1),639(a,1,2,1)),flip(a)]. given #563 (H,wt=13): 643 (x / (y \ 1)) / x = x / (x / y). [hyper(61,a,641,a)]. given #564 (H,wt=14): 640 L(x \ y,x,x / y) = (y \ x) \ 1. [para(637(a,1),142(a,2))]. given #565 (H,wt=15): 624 T(x / y,(x / y) \ y) = (x \ y) \ 1. [para(16(a,1),623(a,2,1,1))]. given #566 (H,wt=15): 628 (x * (x * y)) \ (x * y) = 1 / T(x,y). [para(13(a,1),625(a,2,2,2))]. given #567 (H,wt=15): 631 ((x * y) \ y) \ z = ((x \ y) \ y) * z. [para(626(a,1),259(a,1,1)),flip(a)]. given #568 (H,wt=15): 632 (x * (x * y)) \ (x * y) = T(x,y) \ 1. [para(13(a,1),627(a,1,1,2)),flip(a)]. given #569 (H,wt=15): 633 T(x,x \ y) \ 1 = T(x \ 1,x * y). [para(627(a,2),262(a,2)),flip(a)]. given #570 (H,wt=15): 634 T(x,x \ y) \ x = x * ((x * y) \ y). [para(627(a,1),400(a,1,2)),flip(a)]. given #571 (H,wt=15): 636 ((x \ y) \ y) / x = (y / x) / (x \ y). [para(629(a,1),617(a,1,1))]. given #572 (H,wt=15): 647 (x * y) / (T(x,y) \ 1) = x * (x * y). [para(632(a,1),53(a,1,2))]. given #573 (H,wt=15): 649 T(x,x \ y) \ x = (x / y) * (x \ y). [para(634(a,2),303(a,2)),flip(a)]. given #574 (H,wt=15): 650 ((x \ y) \ y) / x = (x \ y) \ (y / x). [para(636(a,2),542(a,1))]. given #575 (H,wt=15): 651 (x / y) * (T(y,y \ x) \ y) = y \ x. [hyper(297,a,649,a(flip))]. given #576 (H,wt=15): 652 (x \ y) \ (y / x) = x \ ((x \ y) \ y). [para(650(a,1),541(a,1))]. given #577 (H,wt=17): 644 (x / y) * ((y \ x) \ 1) = ((x / y) / x) * y. [para(640(a,1),300(a,1,2))]. given #578 (H,wt=17): 648 x * T(x \ 1,x * y) = T(x,x \ y) \ x. [para(633(a,1),400(a,1,2))]. given #579 (H,wt=17): 653 (x / y) * ((y \ x) \ 1) = y \ ((y \ x) \ x). [para(652(a,1),414(a,2))]. given #580 (H,wt=17): 654 (x / y) * ((y \ x) \ 1) = y * ((x / y) / x). [para(644(a,2),330(a,1))]. given #581 (H,wt=15): 655 x \ ((x \ y) \ y) = x * ((y / x) / y). [para(654(a,1),653(a,1)),flip(a)]. given #582 (H,wt=19): 645 (x * y) / T(x,x * y) = (x * y) * (1 / T(x,y)). [para(628(a,1),315(a,1,2)),flip(a)]. given #583 (H,wt=19): 646 ((x \ y) \ y) * (x \ z) = (y / x) * ((x \ y) \ z). [para(631(a,1),621(a,1))]. given #584 (H,wt=13): 657 T(x / y,(y \ x) \ x) = y \ x. [hyper(98,a,646,a)]. given #585 (H,wt=13): 658 T(x / y,T(y,y \ x)) = y \ x. [para(81(a,2),657(a,1,2))]. given #586 (H,wt=15): 659 T((x * y) / x,T(x,x \ (x * y))) = y. [para(658(a,2),13(a,1))]. given #587 (H,wt=11): 660 T((x * y) / x,T(x,y)) = y. [para(13(a,1),659(a,1,2,2))]. given #588 (H,wt=16): 661 T(R((x * y) / x,x,y),T(x * y,y)) = y. [para(76(a,2),660(a,1,1))]. given #589 (H,wt=16): 662 R(T((x * y) / x,T(x * y,y)),x,y) = y. [para(661(a,1),42(a,2))]. given #590 (H,wt=19): 656 T(x,x \ y) * (x \ z) = (x * ((y / x) / y)) * z. [para(655(a,1),415(a,2,1))]. given #591 (H,wt=19): 663 T(x,x \ y) * (x \ z) = x * (((y / x) / y) * z). [para(656(a,2),508(a,1))]. given #592 (H,wt=15): 664 T(x,x \ y) * (x \ y) = x * (y / x). [para(16(a,1),663(a,2,2))]. given #593 (H,wt=17): 665 T(x,y) * (x \ (x * y)) = x * ((x * y) / x). [para(13(a,1),664(a,1,1,2))]. given #594 (H,wt=13): 666 T(x,y) * y = x * ((x * y) / x). [para(13(a,1),665(a,1,2))]. given #595 (H,wt=13): 667 T(x,y) \ (x * ((x * y) / x)) = y. [hyper(56,a,666,a)]. given #596 (H,wt=13): 668 x \ (T(x,y) * y) = (x * y) / x. [hyper(56,a,666,a(flip))]. given #597 (H,wt=13): 671 T(x,y) \ ((x * y) / x) = x \ y. [para(667(a,1),399(a,1,2)),flip(a)]. given #598 (H,wt=17): 669 T(x / y,y) * y = (x / y) * (x / (x / y)). [para(16(a,1),666(a,2,2,1))]. given #599 (H,wt=15): 672 (x / y) * (x / (x / y)) = (y \ x) * y. [para(82(a,1),669(a,1,1)),flip(a)]. given #600 (H,wt=17): 670 K((x * y) / x,x) = (T(x,y) * y) \ (x * y). [para(666(a,2),68(a,1,1)),flip(a)]. given #601 (H,wt=13): 674 K((x * y) / x,x) = K(y,T(x,y)). [para(670(a,2),99(a,1))]. given #602 (H,wt=15): 675 K(x \ y,T(x,x \ y)) = K(y / x,x). [para(14(a,1),674(a,1,1,1)),flip(a)]. given #603 (H,wt=17): 673 K(x / (x / y),x / y) = ((y \ x) * y) \ x. [para(672(a,1),68(a,1,1)),flip(a)]. given #604 (H,wt=20): 117 ((x * (y \ 1)) * y) / K(y \ 1,y) = R(x,y \ 1,y). [para(115(a,2),30(a,2,2)),flip(a)]. given #605 (H,wt=16): 676 ((x * (y \ 1)) * y) / 1 = R(x,y \ 1,y). [para(222(a,1),117(a,1,2))]. given #606 (H,wt=14): 677 (x * (y \ 1)) * y = R(x,y \ 1,y). [para(676(a,1),52(a,1)),flip(a)]. given #607 (H,wt=14): 679 R(x,y \ 1,y) / y = x * (y \ 1). [hyper(61,a,677,a)]. given #608 (H,wt=14): 680 R(x / (y \ 1),y \ 1,y) = x * y. [para(16(a,1),677(a,1,1)),flip(a)]. given #609 (H,wt=12): 682 L(x,y / (z \ 1),y * z) = x. [para(680(a,1),526(a,1,3))]. given #610 (H,wt=18): 681 x * (((y \ 1) / x) * (x * y)) = R(x,y \ 1,y). [para(677(a,1),85(a,2))]. given #611 (H,wt=20): 151 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(44(a,1),75(a,1,1))]. given #612 (H,wt=20): 152 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(46(a,1),75(a,1,1))]. given #613 (H,wt=20): 196 (x / (y \ 1)) \ ((y * (y \ x)) * y) = a(y,y \ x,y). [para(193(a,1),24(a,2,1)),flip(a)]. given #614 (H,wt=16): 684 a(x,x \ y,x) = (y / (x \ 1)) \ (y * x). [para(14(a,1),196(a,1,2,1)),flip(a)]. given #615 (H,wt=16): 685 a(x,x \ y,x) = (y / (1 / x)) \ (y * x). [para(208(a,2),684(a,2,1,2))]. given #616 (H,wt=16): 686 a(x,x \ y,x) = ((x \ 1) / y) * (y * x). [para(684(a,2),284(a,1))]. given #617 (H,wt=16): 687 a(x,x \ y,x) = y \ ((y * (1 / x)) * x). [para(685(a,2),301(a,1))]. given #618 (H,wt=15): 688 a(x,x \ y,x) = y \ R(y,1 / x,x). [para(488(a,1),687(a,2,2))]. given #619 (H,wt=20): 271 (x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z). [para(259(a,1),24(a,2,1)),flip(a)]. given #620 (H,wt=18): 689 (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). [para(259(a,1),271(a,1,2,1))]. given #621 (H,wt=20): 454 L((x \ 1) \ y,x \ z,x) = z \ ((z / (x \ 1)) * y). [para(177(a,1),443(a,1,1))]. given #622 (H,wt=18): 690 L(x * y,x \ z,x) = z \ ((z / (x \ 1)) * y). [para(256(a,1),454(a,1,1))]. given #623 (H,wt=20): 458 (x * (y \ 1)) * L(z,y \ x,y) = x * ((y \ 1) * z). [para(453(a,1),69(a,1,2))]. given #624 (H,wt=18): 691 (x * (y \ 1)) * L(z,y \ x,y) = x * (y \ z). [para(259(a,1),458(a,2,2))]. given #625 (H,wt=20): 464 (x * L(x,y,z)) * (x \ 1) = R(L(x,y,z),x,x \ 1). [para(197(a,1),460(a,1,1))]. given #626 (H,wt=18): 692 R(L(x,y,z),x,x \ 1) = x * (L(x,y,z) / x). [para(464(a,1),184(a,1))]. given #627 (H,wt=18): 693 L(R(x,x,x \ 1),y,z) = x * (L(x,y,z) / x). [para(692(a,1),44(a,1)),flip(a)]. given #628 (H,wt=13): 694 x * (L(x,y,z) / x) = L(x,y,z). [para(148(a,1),693(a,1,1)),flip(a)]. given #629 (H,wt=11): 696 L(x,x,y) / x = a(x,y,x). [hyper(17,a,520,a,b,694,a)]. given #630 (H,wt=11): 697 a(x,y,x) * x = L(x,x,y). [para(696(a,1),16(a,1,1))]. given #631 (H,wt=13): 695 L(x,y,z) / x = x \ L(x,y,z). [hyper(56,a,694,a),flip(a)]. given #632 (H,wt=13): 698 (x \ L(x,y,z)) * x = L(x,y,z). [para(695(a,1),16(a,1,1))]. given #633 (H,wt=15): 700 L(x,y,z) * (1 / x) = L(x,y,z) / x. [para(695(a,2),534(a,2))]. given #634 (H,wt=16): 701 L(x,y,z) != u * x | x \ L(x,y,z) = u. [para(698(a,1),20(a,1))]. given #635 (H,wt=17): 699 (x \ L(x,y,z)) \ u = (x / L(x,y,z)) * u. [para(695(a,1),284(a,1,1))]. given #636 (H,wt=20): 552 R(x,y,z) * u != x * w | (x \ R(x,y,z)) * u = w. [para(547(a,1),19(a,1))]. given #637 (H,wt=20): 555 R(x,y,z) * (x * u) != x * w | R(x,y,z) * u = w. [para(551(a,2),19(a,1))]. given #638 (H,wt=20): 558 R(x,y,z) * u != x * w | R(x,y,z) * (x \ u) = w. [para(554(a,1),19(a,1))]. given #639 (H,wt=20): 590 a((x \ y) / x,x,z) = (x \ (y * z)) \ ((x \ y) * z). [para(248(a,1),64(a,1,1)),flip(a)]. given #640 (H,wt=15): 702 a((x \ y) / x,x,z) = a(x \ 1,y,z). [para(590(a,2),689(a,1))]. given #641 (H,wt=15): 703 a((x \ y) / x,x,z) = a(1 / x,y,z). [para(208(a,2),702(a,2,1))]. given #642 (H,wt=21): 293 (x / T(x,y)) \ (T(x,y) \ 1) = T(x \ 1,x / T(x,y)). [para(246(a,1),272(a,2,2)),flip(a)]. given #643 (H,wt=21): 366 ((x \ 1) * y) / ((x \ 1) \ z) = x \ ((y / z) * (x \ 1)). [para(247(a,2),259(a,1))]. given #644 (H,wt=19): 705 (x \ y) / ((x \ 1) \ z) = x \ ((y / z) * (x \ 1)). [para(259(a,1),366(a,1,1))]. given #645 (H,wt=17): 706 x \ ((y / z) * (x \ 1)) = (x \ y) / (x * z). [para(256(a,1),705(a,1,2)),flip(a)]. given #646 (H,wt=15): 707 (x \ (y / z)) / x = (x \ y) / (x * z). [para(706(a,1),191(a,1)),flip(a)]. given #647 (H,wt=21): 420 a(x,y,z) \ ((x * y) * z) = T(x * (y * z),a(x,y,z)). [para(62(a,1),32(a,2,2)),flip(a)]. given #648 (H,wt=21): 451 ((x \ y) \ 1) \ (((x \ y) \ 1) / (y / x)) = (y / x) \ 1. [para(450(a,1),179(a,1))]. given #649 (H,wt=19): 708 (x \ y) * (((x \ y) \ 1) / (y / x)) = (y / x) \ 1. [para(451(a,1),256(a,1)),flip(a)]. given #650 (H,wt=17): 709 (x \ y) * (((x \ y) \ 1) / (y / x)) = x / y. [para(708(a,2),265(a,1))]. given #651 (H,wt=17): 710 ((x \ y) \ 1) / (y / x) = (x \ y) \ (x / y). [hyper(56,a,709,a),flip(a)]. given #652 (H,wt=17): 711 ((x / y) * (y \ x)) \ 1 = (y \ x) \ (y / x). [para(710(a,1),351(a,1)),flip(a)]. given #653 (H,wt=17): 712 ((x \ y) * (y / x)) \ 1 = (x \ y) \ (x / y). [para(523(a,1),711(a,1,1))]. given #654 (H,wt=15): 713 (x / y) / (x \ y) = (x \ y) \ (x / y). [para(712(a,1),607(a,1)),flip(a)]. given #655 (H,wt=19): 714 ((x \ y) \ (x / y)) * z = (x / y) * ((x \ y) \ z). [para(713(a,1),505(a,1,1))]. given #656 (H,wt=21): 564 T(x \ R(x,y,z),x * u) = (x * u) \ (R(x,y,z) * u). [para(561(a,1),82(a,1,1))]. given #657 (H,wt=21): 581 ((R(x,y,z) \ 1) * u) / (x \ u) = (R(x,y,z) \ 1) * x. [para(579(a,1),144(a,1,2))]. given #658 (H,wt=19): 715 (R(x,y,z) \ u) / (x \ u) = (R(x,y,z) \ 1) * x. [para(259(a,1),581(a,1,1))]. given #659 (H,wt=17): 716 (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. [para(715(a,2),259(a,1))]. given #660 (H,wt=18): 717 (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. [para(92(a,1),716(a,1,1))]. given #661 (H,wt=18): 718 (x * y) / ((x / z) * (z * y)) = R(z,x,y) \ z. [para(168(a,1),717(a,1,2))]. given #662 (H,wt=21): 593 (x \ y) * T(x,y) != z * (x \ y) | L(x,x \ y,x) = z. [para(200(a,1),20(a,1))]. given #663 (H,wt=21): 642 (x * y) / ((K(x,y) \ (x * y)) \ 1) = (y * x) * (x * y). [para(89(a,1),639(a,2,1))]. given #664 (H,wt=21): 683 (L(x \ 1,y,z) * x) * u = L(x \ 1,y,z) * (x * u). [para(268(a,1),151(a,1,1,1)),flip(a)]. given #665 (H,wt=11): 719 L(x,L(y \ 1,z,u),y) = x. [hyper(357,a,683,a)]. given #666 (H,wt=11): 720 L(x,y,L(y \ 1,z,u)) = x. [hyper(138,a,683,a)]. given #667 (H,wt=11): 721 L(x,L(y,z,u),y \ 1) = x. [para(210(a,1),719(a,1,2,1))]. given #668 (H,wt=11): 722 L(x,1 / y,L(y,z,u)) = x. [para(54(a,1),720(a,1,3,1))]. given #669 (H,wt=11): 724 L(x,y \ L(y,z,u),y) = x. [para(721(a,1),443(a,1,1))]. given #670 (H,wt=11): 727 L(x,1 / L(y,z,u),y) = x. [para(341(a,1),722(a,1,3))]. given #671 (H,wt=11): 730 L(x,y,1 / L(y,z,u)) = x. [para(727(a,1),341(a,1,1))]. given #672 (H,wt=15): 729 x * (1 / L(x,y,z)) = x / L(x,y,z). [para(727(a,1),147(a,1,2)),flip(a)]. given #673 (H,wt=13): 731 x / L(x,y,z) = L(x,y,z) \ x. [para(729(a,1),616(a,1))]. given #674 (H,wt=13): 732 L(x,y,z) * (x / L(x,y,z)) = x. [para(731(a,2),14(a,1,2))]. given #675 (H,wt=13): 733 (L(x,y,z) \ x) * L(x,y,z) = x. [para(731(a,1),16(a,1,1))]. given #676 (H,wt=13): 734 x / (x / L(x,y,z)) = L(x,y,z). [para(731(a,2),53(a,1,2))]. given #677 (H,wt=16): 737 x * L(y,z,u) != y | L(y,z,u) \ y = x. [para(733(a,1),20(a,1)),flip(a)]. given #678 (H,wt=17): 725 x \ (L(x,y,z) * u) = (x \ L(x,y,z)) * u. [para(721(a,1),516(a,1,2)),flip(a)]. given #679 (H,wt=17): 736 (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. [para(731(a,1),699(a,2,1))]. given #680 (H,wt=19): 735 L(L(x,y,1 / L(y,z,u)),y / L(y,z,u),y) = x. [para(731(a,2),434(a,1,2))]. given #681 (H,wt=11): 738 L(x,y / L(y,z,u),y) = x. [para(730(a,1),735(a,1,1))]. given #682 (H,wt=21): 704 T(x,y) * (x \ (T(x,y) \ 1)) = T(x \ 1,x / T(x,y)). [para(293(a,1),245(a,1)),flip(a)]. given #683 (H,wt=13): 740 T(x \ 1,x / T(x,y)) = x \ 1. [para(704(a,1),398(a,1))]. given #684 (H,wt=13): 741 T(x \ 1,T(x,y) \ x) = x \ 1. [para(404(a,1),740(a,1,2))]. given #685 (H,wt=21): 723 (L(x,y,z) * (x \ 1)) \ u = (x \ 1) \ (L(x,y,z) \ u). [para(721(a,1),344(a,1))]. given #686 (H,wt=19): 744 (L(x,y,z) * (x \ 1)) \ u = x * (L(x,y,z) \ u). [para(723(a,2),256(a,1))]. given #687 (H,wt=17): 745 (x \ L(x,y,z)) \ u = x * (L(x,y,z) \ u). [para(533(a,1),744(a,1,1))]. given #688 (H,wt=17): 746 (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). [para(745(a,1),736(a,1)),flip(a)]. given #689 (H,wt=10): 747 T(x,L(x,y,z) \ x) = x. [hyper(98,a,746,a)]. given #690 (H,wt=21): 726 (L(x,y,z) * u) / ((1 / x) \ u) = L(x,y,z) * (1 / x). [para(722(a,1),144(a,1,2))]. given #691 (H,wt=19): 748 (L(x,y,z) * u) / (x * u) = L(x,y,z) * (1 / x). [para(270(a,1),726(a,1,2))]. given #692 (H,wt=17): 749 (L(x,y,z) * u) / (x * u) = L(x,y,z) / x. [para(748(a,2),700(a,1))]. given #693 (H,wt=21): 728 (x * y) / ((x \ L(x,z,u)) \ y) = x * (x \ L(x,z,u)). [para(724(a,1),144(a,1,2))]. given #694 (H,wt=21): 743 T((x \ 1) \ 1,((x * y) \ y) \ (x \ 1)) = (x \ 1) \ 1. [para(262(a,1),741(a,1,2,1))]. given #695 (H,wt=17): 751 T(x,((x * y) \ y) \ (x \ 1)) = (x \ 1) \ 1. [para(210(a,1),743(a,1,1))]. given #696 (H,wt=13): 752 T(x,((x * y) \ y) \ (x \ 1)) = x. [para(751(a,2),210(a,1))]. given #697 (H,wt=13): 753 T(x,(y / x) * ((x \ y) \ 1)) = x. [para(621(a,1),752(a,1,2))]. given #698 (H,wt=11): 754 T(x,(x \ y) \ (y / x)) = x. [para(414(a,1),753(a,1,2))]. given #699 (H,wt=11): 755 T(x,(x \ (y * x)) \ y) = x. [para(15(a,1),754(a,1,2,2))]. given #700 (H,wt=9): 756 T(x,T(y,x) \ y) = x. [para(32(a,2),755(a,1,2,1))]. given #701 (H,wt=15): 757 (T(x,y) \ x) * y = y * (T(x,y) \ x). [para(756(a,1),80(a,1,2))]. given #702 (H,wt=15): 758 x * (T(y,x) \ y) = y * (T(y,x) \ x). [para(757(a,1),409(a,1))]. given #703 (H,wt=13): 759 x * (T(y,x) \ y) = T(x,T(y,x)). [para(758(a,2),401(a,1))]. given #704 (H,wt=13): 760 T(x,y) \ x = y \ T(y,T(x,y)). [hyper(56,a,759,a),flip(a)]. given #705 (H,wt=10): 763 L(x,T(y,z) \ y,z) = x. [para(760(a,2),494(a,1,2))]. given #706 (H,wt=13): 761 T(x,y) \ x = T(y,T(x,y)) / y. [hyper(17,a,333,a,b,759,a)]. given #707 (H,wt=13): 762 T(x,y) * (y \ T(y,T(x,y))) = x. [para(760(a,1),14(a,1,2))]. given #708 (H,wt=13): 766 T(x,T(y,x)) / x = y / T(y,x). [para(761(a,1),404(a,2)),flip(a)]. given #709 (H,wt=13): 767 (T(x,T(y,x)) / x) \ y = T(y,x). [para(766(a,2),54(a,1,1))]. given #710 (H,wt=13): 769 T(x,T(y,x)) \ (x * y) = T(y,x). [para(767(a,1),417(a,1)),flip(a)]. given #711 (H,wt=13): 770 T(x,T(y,x)) * T(y,x) = x * y. [para(769(a,1),14(a,1,2))]. given #712 (H,wt=15): 765 (T(x,y) \ x) \ 1 = y / T(y,T(x,y)). [para(761(a,2),265(a,1,1))]. given #713 (H,wt=15): 768 1 / (x / T(x,y)) = y / T(y,T(x,y)). [para(766(a,1),280(a,1,2))]. given #714 (H,wt=13): 773 T(x,y) / x = y / T(y,T(x,y)). [para(768(a,1),280(a,1)),flip(a)]. given #715 (H,wt=9): 775 T(x,T(y,x) / y) = x. [para(773(a,2),419(a,1,2))]. given #716 (H,wt=10): 776 L(x,y,T(z,y) / z) = x. [para(773(a,2),447(a,1,3))]. given #717 (H,wt=13): 774 x / (T(y,x) / y) = T(x,T(y,x)). [para(773(a,2),405(a,1,2))]. given #718 (H,wt=15): 772 T(x,T(y,x)) \ x = (T(y,x) \ y) \ 1. [para(765(a,2),404(a,1)),flip(a)]. given #719 (H,wt=15): 777 (T(x,y) / x) * y = y * (T(x,y) / x). [para(775(a,1),80(a,1,2))]. given #720 (H,wt=15): 780 T(x,T(y,x)) \ x = T(y,x) * (y \ 1). [para(772(a,2),408(a,1))]. given #721 (H,wt=13): 782 T(x,T(y,x)) \ x = y \ T(y,x). [para(780(a,2),322(a,1))]. given #722 (H,wt=15): 781 x \ (T(x,y) * y) = y * (T(x,y) / x). [para(777(a,1),386(a,2))]. given #723 (H,wt=13): 784 x * (T(y,x) / y) = (y * x) / y. [para(781(a,1),668(a,1))]. given #724 (H,wt=13): 786 x * (y \ T(y,x)) = (y * x) / y. [para(332(a,1),784(a,1,2))]. given #725 (H,wt=15): 783 T(x,T(y,x)) \ 1 = x \ (y \ T(y,x)). [para(782(a,1),403(a,1,2)),flip(a)]. given #726 (H,wt=16): 785 (x * y) / x != y * z | T(x,y) / x = z. [para(784(a,1),19(a,1))]. given #727 (H,wt=17): 779 ((T(x,y) / x) / y) \ z = T(y,T(x,y)) * z. [para(774(a,1),284(a,2,1))]. given #728 (H,wt=19): 764 ((T(x,y) \ x) * y) \ z = y \ ((T(x,y) \ x) \ z). [para(763(a,1),344(a,1))]. given #729 (H,wt=19): 771 (x * T(y,x)) / (T(y,x) \ 1) = T(y,x) * (x * y). [para(770(a,1),194(a,2,2))]. given #730 (H,wt=17): 788 (x * y) / (T(x,y) \ 1) = T(x,y) * (y * x). [para(80(a,1),771(a,1,1))]. given #731 (H,wt=13): 789 T(x,y) * (y * x) = x * (x * y). [para(788(a,1),647(a,1))]. given #732 (H,wt=13): 790 T(x,y) = (x * (x * y)) / (y * x). [hyper(61,a,789,a),flip(a)]. given #733 (H,wt=13): 791 T(x,y) \ (x * (x * y)) = y * x. [hyper(56,a,789,a)]. given #734 (H,wt=13): 793 x * (T(x,y) \ (x * y)) = y * x. [para(791(a,1),392(a,1)),flip(a)]. given #735 (H,wt=11): 794 T(x,y) \ (x * y) = T(y,x). [hyper(98,a,793,a),flip(a)]. given #736 (H,wt=9): 796 T(x,T(y,x)) = T(x,y). [para(794(a,1),101(a,1)),flip(a)]. given #737 (H,wt=11): 795 T(x,y) * T(y,x) = x * y. [para(794(a,1),14(a,1,2))]. given #738 (H,wt=11): 797 T(x,y) \ y = x \ T(y,x). [para(794(a,1),399(a,1,2)),flip(a)]. given #739 (H,wt=11): 799 T(x,y / x) = T(x,x \ y). [para(82(a,1),796(a,1,2)),flip(a)]. given #740 (H,wt=11): 801 T(x,y) \ x = y \ T(y,x). [para(796(a,1),760(a,2,2))]. given #741 (H,wt=11): 802 T(x,y) * (y \ T(y,x)) = x. [para(796(a,1),762(a,1,2,2))]. given #742 (H,wt=11): 803 T(x,y) / x = y / T(y,x). [para(796(a,1),766(a,1,1))]. given #743 (H,wt=11): 805 (x \ T(x,y)) * T(y,x) = y. [hyper(396,a,795,a)]. given #744 (H,wt=11): 808 T(x,(x * y) / x) = T(x,y). [para(13(a,1),799(a,2,2))]. given #745 (H,wt=11): 810 T(x,y / x) = (x \ y) \ y. [para(799(a,2),81(a,1))]. given #746 (H,wt=11): 811 x / T(y,x / y) = y \ x. [para(799(a,2),109(a,1,2))]. given #747 (H,wt=11): 817 (x \ y) * T(x,y / x) = y. [para(810(a,2),14(a,1,2))]. given #748 (H,wt=13): 798 T(T(x,y),T(z,x)) = T(T(x,z),y). [para(796(a,1),38(a,1,1)),flip(a)]. given #749 (H,wt=13): 804 x \ (y \ T(y,x)) = T(x,y) \ 1. [para(796(a,1),783(a,1,1)),flip(a)]. given #750 (H,wt=13): 812 T(x,y / x) / y = 1 / (x \ y). [para(799(a,2),289(a,1,1))]. given #751 (H,wt=13): 816 (x * y) / x = y * (T(y,x) \ y). [para(801(a,2),786(a,1,2)),flip(a)]. given #752 (H,wt=13): 821 ((x \ y) \ y) * T(x \ y,x) = y. [para(53(a,1),817(a,1,2,2))]. given #753 (H,wt=13): 822 T(T(x,y),T(z,x)) = T(T(x,y),z). [para(798(a,2),38(a,1))]. given #754 (H,wt=13): 825 x \ ((y * x) / y) = T(x,y) \ x. [hyper(56,a,816,a(flip))]. given #755 (H,wt=13): 827 ((x * y) \ y) \ T(x \ y,x) = y. [para(821(a,1),631(a,2))]. given #756 (H,wt=13): 829 T(x \ y,x) / y = (x * y) \ y. [para(827(a,1),53(a,1,2))]. given #757 (H,wt=15): 807 T(x,y) * (x \ (x \ T(y,x))) = x \ y. [para(797(a,1),398(a,1,2,2))]. given #758 (H,wt=15): 809 (x * (y / x)) / T(x,x \ y) = y / x. [para(799(a,1),91(a,1,2))]. given #759 (H,wt=15): 823 T(x \ 1,x * (y * x)) = T(x,y) \ 1. [para(804(a,1),613(a,2))]. given #760 (H,wt=15): 826 T(x * (T(x,y) \ x),y) = y \ (y * x). [para(816(a,1),82(a,1,1))]. given #761 (H,wt=11): 832 T(x * (T(x,y) \ x),y) = x. [para(826(a,2),13(a,1))]. given #762 (H,wt=15): 828 T(T(x,y),z / x) = T(T(x,y),x \ z). [para(82(a,1),822(a,1,2)),flip(a)]. given #763 (H,wt=15): 830 (x * (T(x,y) \ x)) \ T(y,x) = x \ y. [para(807(a,1),608(a,2))]. given #764 (H,wt=13): 833 ((x * y) / x) \ T(x,y) = y \ x. [para(816(a,2),830(a,1,1))]. given #765 (H,wt=13): 834 T(x,y) / (y \ x) = (x * y) / x. [para(833(a,1),53(a,1,2))]. given #766 (H,wt=13): 835 (x / (x * y)) * T(x,y) = y \ x. [para(833(a,1),284(a,1)),flip(a)]. given #767 (H,wt=15): 831 (x \ (x \ T(x,y))) * T(y,x) = x \ y. [para(807(a,1),609(a,2))]. given #768 (H,wt=13): 838 x \ (x \ T(x,y)) = y / (y * x). [hyper(18,a,835,a,b,831,a)]. given #769 (H,wt=13): 839 x * (y / (y * x)) = x \ T(x,y). [para(838(a,1),14(a,1,2))]. given #770 (H,wt=16): 813 L(T(x,x \ y),y,x) = T(x,x * (y / x)). [para(799(a,1),436(a,1,1))]. given #771 (H,wt=16): 837 x * T(y,z) != z \ y | y / (y * z) = x. [para(835(a,1),20(a,1)),flip(a)]. given #772 (H,wt=17): 800 T((x * y) / x,T(z,y)) = (x * T(y,z)) / x. [para(796(a,1),363(a,1,1,2)),flip(a)]. given #773 (H,wt=17): 814 L(x,T(y,z / y),z) = L(x,1 / (y \ z),z). [para(799(a,2),441(a,1,2))]. given #774 (H,wt=17): 836 ((x * y) * x) / (x * y) = T(x * y,x) / y. [para(13(a,1),834(a,1,2)),flip(a)]. given #775 (H,wt=17): 840 T((x * y) / x,T(z,y)) = T((x * y) / x,z). [para(800(a,2),363(a,1))]. given #776 (H,wt=14): 841 R(T((x * y) / x,x * y),x,y) = y. [para(840(a,1),662(a,1,1))]. given #777 (H,wt=11): 842 R(L(x,y,y * x),y,x) = x. [para(326(a,1),841(a,1,1))]. given #778 (H,wt=11): 843 L(R(x,y,x),y,y * x) = x. [para(842(a,1),44(a,1)),flip(a)]. given #779 (H,wt=11): 844 L(x,y * x,y) = R(x,y,x). [para(843(a,1),341(a,1,1))]. given #780 (H,wt=19): 778 ((T(x,y) / x) / y) \ ((T(x,y) / x) * z) = y * z. [para(776(a,1),299(a,1,2,2))]. given #781 (H,wt=19): 787 ((T(x,y) \ x) * y) \ z = y \ (T(x,y) * (x \ z)). [para(408(a,1),764(a,2,2))]. given #782 (H,wt=19): 819 L(x,T(y,z / y),y \ z) = L(x,T(y,z / y),z). [para(811(a,1),423(a,1,3))]. given #783 (H,wt=19): 820 L(x,y \ z,T(y,z / y)) = L(x,z,T(y,z / y)). [para(811(a,1),435(a,1,2))]. given #784 (H,wt=19): 845 ((T(x,y) / x) / y) \ (x \ (T(x,y) * z)) = y * z. [para(386(a,2),778(a,1,2))]. given #785 (H,wt=17): 847 T(x,T(y,x)) * (y \ (T(y,x) * z)) = x * z. [para(845(a,1),779(a,1)),flip(a)]. given #786 (H,wt=15): 848 T(x,y) * (y \ (T(y,x) * z)) = x * z. [para(796(a,1),847(a,1,1))]. given #787 (H,wt=15): 849 x \ (T(x,y) * (T(y,x) * z)) = y * z. [hyper(383,a,848,a),flip(a)]. given #788 (H,wt=15): 850 T(x,y) * (y \ z) = x * (T(y,x) \ z). [para(14(a,1),848(a,1,2,2))]. given #789 (H,wt=15): 851 T(x,y) * (T(y,x) * z) = x * (y * z). [para(849(a,1),14(a,1,2)),flip(a)]. given #790 (H,wt=15): 852 T(x,y) * (1 / y) = x * (T(y,x) \ 1). [para(208(a,2),850(a,1,2))]. given #791 (H,wt=15): 854 T(x,y) * (1 / y) = x * (1 / T(y,x)). [para(208(a,2),852(a,2,2))]. given #792 (H,wt=18): 853 T(x,y) * (T(y,x) * z) != x * u | y * z = u. [para(851(a,2),19(a,1))]. given #793 (H,wt=19): 846 (x * (T(x,y) \ y)) \ z = y \ (T(x,y) * (x \ z)). [para(409(a,1),787(a,1,1))]. given #794 (H,wt=17): 855 x \ (T(y,x) * (y \ z)) = T(x,T(y,x)) \ z. [para(401(a,1),846(a,1,1)),flip(a)]. given #795 (H,wt=15): 856 x \ (T(y,x) * (y \ z)) = T(x,y) \ z. [para(796(a,1),855(a,2,1))]. given #796 (H,wt=21): 750 (x * y) / ((L(x,z,u) \ x) * y) = x * (x \ L(x,z,u)). [para(736(a,1),728(a,1,2))]. given #797 (H,wt=17): 857 (x * y) / ((L(x,z,u) \ x) * y) = L(x,z,u). [para(750(a,2),14(a,1))]. given #798 (H,wt=17): 858 L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. [para(857(a,1),54(a,1,1))]. given #799 (H,wt=17): 859 (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u). [para(746(a,1),857(a,1,2))]. given #800 (H,wt=17): 860 L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u). [para(858(a,2),746(a,1))]. given #801 (H,wt=19): 861 x * (L(x,y,z) \ T(u,x)) = L(x,y,z) \ (u * x). [para(80(a,1),860(a,1,2)),flip(a)]. given #802 (H,wt=21): 792 ((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y). [para(789(a,1),26(a,2,2)),flip(a)]. given #803 (H,wt=21): 815 T(T(x,y),((x * y) / x) / T(x,y)) = T(T(x,y),x \ y). [para(671(a,1),799(a,2,2))]. given #804 (H,wt=21): 862 T(T(x,y),((x * y) / x) / T(x,y)) = T(T(x,y),y / x). [para(815(a,2),828(a,2)),flip(a)]. given #805 (H,wt=22): 111 (x * y) \ ((y * x) * (K(x,y) * z)) = L(z,K(x,y),y * x). [para(65(a,1),28(a,2,1)),flip(a)]. given #806 (H,wt=22): 116 (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y). [para(115(a,2),24(a,2,1,2)),flip(a)]. given #807 (H,wt=18): 863 (x * 1) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y). [para(222(a,1),116(a,1,1,2))]. given #808 (H,wt=16): 864 x \ ((x * (y \ 1)) * y) = a(x,y \ 1,y). [para(12(a,1),863(a,1,1))]. given #809 (H,wt=16): 866 x \ ((x * (1 / y)) * y) = a(x,y \ 1,y). [para(208(a,2),864(a,1,2,1,2))]. given #810 (H,wt=15): 867 x \ R(x,1 / y,y) = a(x,y \ 1,y). [para(488(a,1),866(a,1,2))]. given #811 (H,wt=15): 868 x \ R(x,1 / y,y) = a(x,1 / y,y). [para(208(a,2),867(a,2,2))]. given #812 (H,wt=13): 870 a(x,x \ y,x) = a(y,1 / x,x). [para(868(a,1),688(a,2))]. given #813 (H,wt=15): 869 a(x,1 / y,y) * x = R(x,1 / y,y). [para(868(a,1),480(a,1,1))]. given #814 (H,wt=22): 181 L((x * y) \ z,x * y,K(x,y)) = K(x,y) \ ((y * x) \ z). [para(89(a,1),175(a,2,2,1))]. given #815 (H,wt=22): 475 R(T((x * y) / x,z),x,1 / x) = (x * T(y,z)) * (1 / x). [para(363(a,1),472(a,1,1))]. given #816 (H,wt=19): 871 T((x * y) * (1 / x),z) = (x * T(y,z)) * (1 / x). [para(475(a,1),474(a,1)),flip(a)]. given #817 (H,wt=17): 872 (x * T(y,z)) * (1 / x) = T(x * (y / x),z). [para(216(a,1),871(a,1,1)),flip(a)]. given #818 (H,wt=15): 873 T(x * (y / x),z) = x * (T(y,z) / x). [para(872(a,1),216(a,1))]. given #819 (H,wt=14): 875 T(x * (y / x),x) = R(y,x,x \ 1). [para(873(a,2),465(a,1))]. given #820 (H,wt=14): 876 T(x * (y / x),x) = R(y,x,1 / x). [para(873(a,2),468(a,1))]. given #821 (H,wt=14): 878 R(x * y,y,y \ 1) = T(y * x,y). [para(15(a,1),875(a,1,1,2)),flip(a)]. given #822 (H,wt=15): 874 T(x,1 / y) / y = y * ((x / y) / y). [hyper(373,a,873,a),flip(a)]. given #823 (H,wt=15): 880 T(x * y,x) / (x \ 1) = (y * x) * x. [para(878(a,1),461(a,1,1))]. given #824 (H,wt=15): 881 T(x * y,1 / y) / y = y * (x / y). [para(15(a,1),874(a,2,2,1))]. given #825 (H,wt=15): 882 T(x,y) / (y \ 1) = ((y \ x) * y) * y. [para(14(a,1),880(a,1,1,1))]. given #826 (H,wt=15): 883 T(x * y,1 / y) = (y * (x / y)) * y. [para(881(a,1),16(a,1,1)),flip(a)]. given #827 (H,wt=15): 885 T((x * y) * y,1 / y) = (y * x) * y. [para(15(a,1),883(a,2,1,2))]. given #828 (H,wt=15): 886 T(x * y,y \ 1) = (y * (x / y)) * y. [para(208(a,1),883(a,1,2))]. given #829 (H,wt=16): 879 T(T(x,y) * y,x) = R(x * y,x,1 / x). [para(666(a,2),876(a,1,1))]. given #830 (H,wt=17): 877 T(x * ((y \ x) / x),y) = x * ((y * x) \ x). [para(829(a,1),873(a,2,2))]. given #831 (H,wt=15): 887 T(x * ((y \ x) / x),y) = x / T(y,x). [para(877(a,2),315(a,1))]. given #832 (H,wt=13): 888 T(x * (1 / y),y) = x / T(y,x). [para(278(a,1),887(a,1,1,2))]. given #833 (H,wt=13): 889 T(x * (1 / y),y) \ x = T(y,x). [para(888(a,2),54(a,1,1))]. given #834 (H,wt=18): 884 T(x,y) / (y \ 1) != z * y | (y \ x) * y = z. [para(882(a,2),20(a,1))]. given #835 (H,wt=19): 891 T((x * y) * (1 / x),x) = (x * y) * (1 / T(x,y)). [para(888(a,2),645(a,1))]. given #836 (H,wt=17): 892 T(x * (y / x),x) = (x * y) * (1 / T(x,y)). [para(216(a,1),891(a,1,1))]. given #837 (H,wt=16): 893 (x * y) * (1 / T(x,y)) = R(y,x,1 / x). [para(892(a,1),876(a,1))]. given #838 (H,wt=16): 894 (x * y) / T(x,x * y) = R(y,x,1 / x). [para(893(a,1),645(a,2))]. given #839 (H,wt=16): 895 (x * y) / T(x,x * y) = R(y,x,x \ 1). [para(208(a,1),894(a,2,3))]. given #840 (H,wt=22): 509 L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w). [para(140(a,1),45(a,1,1)),flip(a)]. given #841 (H,wt=22): 566 (x / y) \ R(x / y,y,z) = (x * z) / ((x / y) * (y * z)). [para(161(a,1),563(a,1,2,2)),flip(a)]. given #842 (H,wt=17): 896 (x / y) \ R(x / y,y,z) = R(y,x,z) \ y. [para(566(a,2),718(a,1))]. given #843 (H,wt=17): 897 (x / y) * R(y / x,x,z) = R(x,y,z) \ x. [para(896(a,1),284(a,1)),flip(a)]. given #844 (H,wt=22): 806 (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). [para(795(a,1),28(a,2,1)),flip(a)]. given #845 (H,wt=18): 898 (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). [para(851(a,1),806(a,1,2))]. given #846 (H,wt=13): 899 L(x,T(y,z),T(z,y)) = L(x,y,z). [para(898(a,1),28(a,2)),flip(a)]. given #847 (H,wt=16): 902 L(T(x,y),T(y,x),T(x,y)) = T(x,x * y). [para(899(a,2),166(a,1))]. given #848 (H,wt=17): 900 L(x,y \ z,T(y,z / y)) = L(x,z / y,y). [para(82(a,1),899(a,1,2))]. given #849 (H,wt=15): 903 L(x,y,T(z,y / z)) = L(x,y / z,z). [para(900(a,1),820(a,1)),flip(a)]. given #850 (H,wt=13): 904 L(x,y,T(z,y / z)) = L(x,y,z). [para(903(a,2),435(a,1))]. given #851 (H,wt=13): 905 L(x,y,(z \ y) \ y) = L(x,y,z). [para(810(a,1),904(a,1,3))]. given #852 (H,wt=13): 906 L(x,y,y / z) = L(x,y,z \ y). [para(54(a,1),905(a,1,3,1)),flip(a)]. given #853 (H,wt=13): 907 L(x,y,y \ z) = L(x,z,z / y). [para(906(a,2),439(a,1)),flip(a)]. given #854 (H,wt=17): 901 L(x,T(y,z / y),y \ z) = L(x,y,z / y). [para(82(a,1),899(a,1,3))]. given #855 (H,wt=15): 908 L(x,T(y,z / y),y \ z) = L(x,y,z). [para(901(a,2),423(a,1))]. given #856 (H,wt=13): 910 L(x,T(y,z / y),z) = L(x,y,z). [para(908(a,1),819(a,1)),flip(a)]. given #857 (H,wt=13): 911 L(x,1 / (y \ z),z) = L(x,y,z). [para(910(a,1),814(a,1)),flip(a)]. given #858 (H,wt=13): 912 L(x,(y \ z) \ 1,z) = L(x,y,z). [para(208(a,1),911(a,1,2))]. given #859 (H,wt=15): 909 L(x,T(y,y \ z),y \ z) = L(x,y,z). [para(799(a,1),908(a,1,2))]. given #860 (H,wt=15): 913 L(x,y \ 1,z * y) = L(x,z,z * y). [para(13(a,1),912(a,1,2,1))]. given #861 (H,wt=13): 915 L(x,T(y,z),z) = L(x,y,y * z). [para(913(a,1),457(a,1)),flip(a)]. given #862 (H,wt=13): 916 L(L(x,y * z,y),T(y,z),z) = x. [para(915(a,2),341(a,1))]. given #863 (H,wt=13): 917 L(x,y * z,y) = L(x,z,T(y,z)). [para(916(a,1),341(a,1,1)),flip(a)]. given #864 (H,wt=11): 918 L(x,x,T(y,x)) = R(x,y,x). [para(917(a,1),844(a,1))]. given #865 (H,wt=13): 919 a(x,T(y,x),x) = R(x,y,x) / x. [para(918(a,1),696(a,1,1)),flip(a)]. given #866 (H,wt=19): 914 L(x,((y \ z) \ 1) \ 1,z) = L(x,(z / y) * z,z). [para(637(a,1),912(a,1,2,1))]. given #867 (H,wt=15): 920 L(x,(y / z) * y,y) = L(x,z \ y,y). [para(210(a,1),914(a,1,2)),flip(a)]. given #868 (H,wt=13): 921 L(x,y / z,y) = L(x,z \ y,y). [para(920(a,1),438(a,1)),flip(a)]. given #869 (H,wt=23): 204 R(x,R(y,z,u),y) * (y * R(y,z,u)) = (x * R(y,z,u)) * y. [para(201(a,1),75(a,1,2))]. given #870 (H,wt=23): 380 x * (((((x \ y) / z) * x) / x) * u) = (y / (x \ z)) * (x \ u). [para(365(a,1),170(a,1,1)),flip(a)]. given #871 (H,wt=19): 924 (x / (y \ z)) * (y \ u) = y * (((y \ x) / z) * u). [para(15(a,1),380(a,1,2,1)),flip(a)]. given #872 (H,wt=23): 452 ((x \ y) \ 1) \ ((((x \ y) \ 1) / (y / x)) * z) = (y / x) \ z. [para(450(a,1),177(a,1))]. given #873 (H,wt=23): 524 (x * y) * L(L(z,y,x),u,w) != x * v5 | y * L(z,u,w) = v5. [para(45(a,1),136(a,1,2))]. given #874 (H,wt=23): 568 (x / y) \ R(x / y,y,z) = 1 / ((x / y) * R(y / x,x,z)). [para(515(a,2),563(a,1,2,2)),flip(a)]. given #875 (H,wt=19): 927 (x / y) \ R(x / y,y,z) = 1 / (R(x,y,z) \ x). [para(897(a,1),568(a,2,2))]. given #876 (H,wt=19): 928 (x / y) \ R(x / y,y,z) = (R(x,y,z) \ x) \ 1. [para(927(a,2),208(a,1))]. given #877 (H,wt=19): 929 (x / y) \ R(x / y,y,z) = R(x,y,z) * (x \ 1). [para(928(a,2),585(a,1))]. given #878 (H,wt=17): 930 (x / y) \ R(x / y,y,z) = x \ R(x,y,z). [para(929(a,2),487(a,1))]. given #879 (H,wt=13): 931 R(x,y,z) \ x = y \ R(y,x,z). [para(930(a,1),896(a,1)),flip(a)]. given #880 (H,wt=10): 935 K(R(x,y,z) \ x,y) = 1. [para(931(a,2),485(a,1,1))]. given #881 (H,wt=13): 932 x * (R(y,x,z) \ y) = R(x,y,z). [para(931(a,2),14(a,1,2))]. given #882 (H,wt=13): 933 x / (y \ R(y,x,z)) = R(x,y,z). [para(931(a,1),53(a,1,2))]. given #883 (H,wt=13): 934 (R(x,y,z) \ x) * y = R(y,x,z). [para(931(a,2),480(a,1,1))]. given #884 (H,wt=13): 938 x * (R(x,y,z) \ y) = R(y,x,z). [para(934(a,1),583(a,1)),flip(a)]. given #885 (H,wt=13): 939 (x * y) / R(y,x,z) = R(x,y,z). [para(934(a,1),584(a,1,2))]. given #886 (H,wt=17): 936 (x \ R(x,y,z)) * u = y * (R(y,x,z) \ u). [para(931(a,1),583(a,1,1))]. given #887 (H,wt=17): 940 R(x,y,z) * (x \ u) = y * (R(y,x,z) \ u). [para(936(a,1),557(a,1)),flip(a)]. given #888 (H,wt=20): 937 x * (((y * z) / (x * z)) \ (y / x)) = R(x,y / x,z). [para(76(a,1),932(a,1,2,1))]. given #889 (H,wt=20): 941 x * (((x * y) / (z * y)) * (z / x)) = R(x,z / x,y). [para(284(a,1),937(a,1,2))]. given #890 (H,wt=23): 818 T(T(x,y),((x * y) / x) / T(x,y)) = (x \ y) \ ((x * y) / x). [para(671(a,1),810(a,2,1))]. given #891 (H,wt=17): 942 (x \ y) \ ((x * y) / x) = T(T(x,y),y / x). [para(818(a,1),862(a,1))]. given #892 (H,wt=17): 943 (x \ y) * T(T(x,y),y / x) = (x * y) / x. [para(942(a,1),14(a,1,2))]. given #893 (H,wt=23): 824 (1 / (x \ y)) \ T(T(x,y / x),y) = y * K(T(x,y / x),y). [para(812(a,1),368(a,1,1))]. given #894 (H,wt=23): 926 ((x \ y) \ 1) \ ((((x \ y) \ 1) / (y / x)) * z) = (x / y) * z. [para(452(a,2),284(a,1))]. given #895 (H,wt=21): 945 (x \ y) * ((((x \ y) \ 1) / (y / x)) * z) = (x / y) * z. [para(926(a,1),256(a,1)),flip(a)]. given #896 (H,wt=19): 946 (x \ y) * (((x \ y) \ (x / y)) * z) = (x / y) * z. [para(710(a,1),945(a,1,2,1))]. given #897 (H,wt=19): 947 (x \ y) * ((x / y) * ((x \ y) \ z)) = (x / y) * z. [para(714(a,1),946(a,1,2))]. given #898 (H,wt=19): 948 x * (((x * y) \ y) * ((x \ y) \ z)) = (x / y) * z. [para(947(a,1),619(a,1)),flip(a)]. given #899 (H,wt=23): 944 (1 / (x \ y)) \ T(T(x,y),y / x) = y * K(T(x,y / x),y). [para(38(a,1),824(a,1,2))]. given #900 (H,wt=21): 949 (x \ y) * T(T(x,y),y / x) = y * K(T(x,y / x),y). [para(944(a,1),270(a,1)),flip(a)]. given #901 (H,wt=15): 950 x * K(T(y,x / y),x) = (y * x) / y. [para(949(a,1),943(a,1))]. given #902 (H,wt=13): 951 K(T(x,y / x),y) = T(x,y) / x. [hyper(17,a,784,a,b,950,a)]. given #903 (H,wt=24): 394 R(x \ T(x,y),x * z,u) = ((T(x,y) * z) * u) / ((x * z) * u). [para(385(a,1),76(a,1,1))]. given #904 (H,wt=24): 560 ((R(x,y,z) * (x \ u)) * w) / (u * w) = R(x \ R(x,y,z),u,w). [para(557(a,1),30(a,2,1,1)),flip(a)]. given #905 (H,wt=24): 567 (x / y) \ R(x / y,y,z) = 1 / ((x / y) * ((y * z) / (x * z))). [para(277(a,1),563(a,1,2,2)),flip(a)]. given #906 (H,wt=24): 952 (x / y) \ R(x / y,y,z) = ((x / y) * ((y * z) / (x * z))) \ 1. [para(567(a,2),208(a,1))]. given #907 (H,wt=25): 203 (x * (y * R(y,z,u))) \ ((x * R(y,z,u)) * y) = a(x,R(y,z,u),y). [para(201(a,1),24(a,2,1,2)),flip(a)]. given #908 (H,wt=25): 416 ((x \ 1) \ T(x \ 1,x * y)) * z = ((x * y) \ y) * ((x \ 1) \ z). [para(262(a,1),395(a,2,1))]. given #909 (H,wt=23): 953 ((x * y) \ y) * ((x \ 1) \ z) = (x * T(x \ 1,x * y)) * z. [para(256(a,1),416(a,1,1)),flip(a)]. given #910 (H,wt=21): 954 (T(x,x \ y) \ x) * z = ((x * y) \ y) * ((x \ 1) \ z). [para(648(a,1),953(a,2,1)),flip(a)]. given #911 (H,wt=21): 955 ((x * y) \ y) * ((x \ 1) \ z) = x * (T(x,x \ y) \ z). [para(954(a,1),409(a,1))]. given #912 (H,wt=19): 956 ((x * y) \ y) * (x * z) = x * (T(x,x \ y) \ z). [para(256(a,1),955(a,1,2))]. given #913 (H,wt=19): 957 x * (T(x,x \ y) \ z) = x * (((x * y) \ y) * z). [para(956(a,1),618(a,1))]. given #914 (H,wt=25): 517 x \ (y * T(y \ (y / (x \ y)),z)) = (x \ y) * T((x \ y) \ 1,z). [para(320(a,2),355(a,1,2,2))]. given #915 (H,wt=21): 958 (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). [para(53(a,1),517(a,1,2,2,1,2)),flip(a)]. given #916 (H,wt=25): 638 (((T(x,y) * y) / (x * y)) \ (x * y)) \ (x * y) = 1 / K(y,T(x,y)). [para(99(a,1),635(a,2,2))]. given #917 (H,wt=21): 959 ((T(x,y) / x) \ (x * y)) \ (x * y) = 1 / K(y,T(x,y)). [para(376(a,1),638(a,1,1,1))]. given #918 (H,wt=21): 961 (T(x,y) \ (x * (x * y))) \ (x * y) = 1 / K(y,T(x,y)). [para(417(a,1),959(a,1,1))]. given #919 (H,wt=15): 962 (x * y) \ (y * x) = 1 / K(x,T(y,x)). [para(791(a,1),961(a,1,1))]. given #920 (H,wt=11): 963 1 / K(x,T(y,x)) = K(y,x). [para(962(a,1),26(a,2)),flip(a)]. given #921 (H,wt=11): 964 K(x,T(y,x)) = K(y,x) \ 1. [para(963(a,1),54(a,1,1)),flip(a)]. given #922 (H,wt=13): 965 K(x,T(y,x)) \ z = K(y,x) * z. [para(963(a,1),269(a,1,1)),flip(a)]. given #923 (H,wt=13): 968 K((x * y) / x,x) = K(x,y) \ 1. [para(964(a,1),674(a,2))]. given #924 (H,wt=15): 966 K(x,T(T(y,x),z)) = K(T(y,z),x) \ 1. [para(38(a,1),964(a,1,2))]. given #925 (H,wt=15): 967 (x * y) / (K(x,y) \ 1) = T(x,y) * y. [para(964(a,1),114(a,1,2))]. given #926 (H,wt=21): 969 (x * y) / ((x * y) / K(x,y)) = (T(x,y) * y) / (x * y). [para(967(a,1),643(a,1,1)),flip(a)]. given #927 (H,wt=17): 970 (T(x,y) * y) / (x * y) = (x * y) / (y * x). [para(89(a,1),969(a,1,2)),flip(a)]. given #928 (H,wt=13): 971 (x * y) / (y * x) = T(x,y) / x. [para(970(a,1),376(a,1))]. given #929 (H,wt=26): 492 R(T(x / (1 / y),z),1 / y,y) / y = (1 / y) * T((1 / y) \ x,z). [para(489(a,2),127(a,1))]. given #930 (H,wt=19): 973 (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x. [para(493(a,1),492(a,1,1)),flip(a)]. given #931 (H,wt=17): 974 (1 / x) * T(x * y,z) = T(y * x,z) / x. [para(270(a,1),973(a,1,2,1))]. given #932 (H,wt=15): 975 T(x * y,z) / y = y \ T(y * x,z). [para(974(a,1),269(a,1))]. given #933 (H,wt=15): 976 T((x \ y) * x,z) / x = x \ T(y,z). [para(14(a,1),975(a,2,2,1))]. given #934 (H,wt=15): 979 T((x \ y) * x,z) = (x \ T(y,z)) * x. [para(976(a,1),16(a,1,1)),flip(a)]. given #935 (H,wt=15): 980 T((x \ y) * x,1 / y) = (x \ y) * x. [para(221(a,1),979(a,2,1,2))]. given #936 (H,wt=13): 981 T(1 / x,(y \ x) * y) = 1 / x. [hyper(35,a,980,a)]. given #937 (H,wt=15): 982 T(1 / (x * y),y * x) = 1 / (x * y). [para(13(a,1),981(a,1,2,1))]. given #938 (H,wt=13): 983 (x * y) \ K(x,y) = 1 / (y * x). [para(982(a,1),305(a,1)),flip(a)]. given #939 (H,wt=13): 984 K(x,y) = (x * y) * (1 / (y * x)). [para(983(a,1),14(a,1,2)),flip(a)]. given #940 (H,wt=13): 985 K(x,y) = (x * y) * ((y * x) \ 1). [para(208(a,1),984(a,2,2))]. given #941 (H,wt=17): 977 ((x * y) * x) / (x * y) = y \ T(y * x,x). [para(975(a,1),836(a,2))]. given #942 (H,wt=17): 987 x \ (y \ T(y * x,x)) = T(x,x * y) \ x. [para(977(a,1),825(a,1,2))]. given #943 (H,wt=13): 988 T(x,x * y) \ x = K(y * x,x). [para(987(a,1),550(a,1))]. given #944 (H,wt=10): 989 L(x,y,K(z * y,y)) = x. [para(988(a,1),444(a,1,3))]. given #945 (H,wt=8): 990 L(x,y,K(z,y)) = x. [para(16(a,1),989(a,1,3,1))]. given #946 (H,wt=8): 991 L(x,K(y,z),z) = x. [para(990(a,1),341(a,1,1))]. given #947 (H,wt=10): 993 L(x,K(y,z) \ 1,y) = x. [para(968(a,1),991(a,1,2))]. given #948 (H,wt=13): 995 x / (K(x,y) \ 1) = x * K(x,y). [para(993(a,1),311(a,1,2)),flip(a)]. given #949 (H,wt=15): 992 (x * K(y,x)) * z = x * (K(y,x) * z). [para(990(a,1),342(a,1,2,2)),flip(a)]. given #950 (H,wt=19): 994 (x / (K(x,y) \ 1)) * z = x * ((K(x,y) \ 1) \ z). [para(993(a,1),300(a,1,2)),flip(a)]. given #951 (H,wt=17): 996 (x / (K(x,y) \ 1)) * z = x * (K(x,y) * z). [para(256(a,1),994(a,2,2))]. given #952 (H,wt=15): 997 (x * K(x,y)) * z = x * (K(x,y) * z). [para(995(a,1),996(a,1,1))]. given #953 (H,wt=23): 978 T(x * (y * x),1 / x) / (y * x) = (y * x) \ ((x * y) * x). [para(885(a,1),975(a,2,2))]. given #954 (H,wt=22): 998 T(x * (y * x),1 / x) / (y * x) = R(T(x,y * x),y,x). [para(978(a,2),592(a,1))]. given #955 (H,wt=18): 999 (x * (x * y)) / (y * x) = R(T(x,y * x),y,x). [para(372(a,1),998(a,1,1))]. given #956 (H,wt=12): 1000 R(T(x,y * x),y,x) = T(x,y). [para(999(a,1),790(a,2)),flip(a)]. given #957 (H,wt=16): 1001 R(x,y,x) * (y * x) = (y * x) * T(x,y). [para(1000(a,1),104(a,1,2)),flip(a)]. given #958 (H,wt=13): 1002 (x * y) * T(y,x) = (y * x) * y. [para(1001(a,1),75(a,1))]. given #959 (H,wt=15): 1003 (x * (y / x)) * x = y * T(x,y / x). [para(16(a,1),1002(a,1,1)),flip(a)]. given #960 (H,wt=19): 1004 ((x * y) * x) \ (x * (x * y)) = K(T(x,y),y * x). [para(1002(a,1),792(a,1,1))]. given #961 (H,wt=13): 1006 K(T(x,y),y * x) = K(x,x * y). [para(1004(a,1),26(a,2)),flip(a)]. given #962 (H,wt=15): 1007 K(T(x,y / x),y) = K(x,x * (y / x)). [para(16(a,1),1006(a,1,2))]. given #963 (H,wt=13): 1008 K(x,x * (y / x)) = T(x,y) / x. [para(1007(a,1),951(a,1))]. given #964 (H,wt=13): 1009 T(x,y * x) / x = K(x,x * y). [para(15(a,1),1008(a,1,2,2)),flip(a)]. given #965 (H,wt=9): 1011 T(x,K(x,x * y)) = x. [para(1009(a,1),338(a,1,2))]. given #966 (H,wt=7): 1012 T(x,K(x,y)) = x. [para(14(a,1),1011(a,1,2,2))]. given #967 (H,wt=13): 1010 x * K(x,x * y) = T(x,y * x). [para(1009(a,1),333(a,1,2))]. given #968 (H,wt=19): 1005 (x * y) * T(x,(x * y) / x) = (T(x,y) * y) * x. [para(666(a,2),1003(a,1,1)),flip(a)]. given #969 (H,wt=15): 1013 (T(x,y) * y) * x = (x * y) * T(x,y). [para(808(a,1),1005(a,1,2)),flip(a)]. given #970 (H,wt=17): 1014 x \ ((x * y) * T(x,y)) = T(T(x,y) * y,x). [para(1013(a,1),32(a,2,2)),flip(a)]. given #971 (H,wt=14): 1015 T(T(x,y) * y,x) = L(x,x,y) * y. [para(1014(a,1),360(a,1))]. given #972 (H,wt=15): 1016 R(x * y,x,1 / x) = L(x,x,y) * y. [para(1015(a,1),879(a,1)),flip(a)]. given #973 (H,wt=19): 1017 (L(x,x,y) * y) / (x * y) = a(x * y,x,1 / x). [para(1016(a,1),598(a,1,1))]. given #974 (H,wt=15): 1018 a(x * y,x,1 / x) = L(x,x,y) / x. [para(1017(a,1),749(a,1))]. given #975 (H,wt=13): 1019 a(x * y,x,1 / x) = a(x,y,x). [para(1018(a,2),696(a,1))]. given #976 (H,wt=15): 1021 a(x * y,y,1 / y) = a(y,T(x,y),y). [para(80(a,1),1019(a,1,1))]. given #977 (H,wt=13): 1023 a(x,T(y,x),x) = a(y,x,1 / x). [para(1021(a,1),601(a,1))]. given #978 (H,wt=17): 1022 a(x * (x \ y),x,1 / x) = a(y,1 / x,x). [para(1019(a,2),870(a,1))]. given #979 (H,wt=13): 1024 a(x,1 / y,y) = a(x,y,1 / y). [para(14(a,1),1022(a,1,1)),flip(a)]. given #980 (H,wt=15): 1025 a(x,y,1 / y) * x = R(x,1 / y,y). [para(1024(a,1),869(a,1,1))]. given #981 (H,wt=13): 1026 R(x,1 / y,y) = R(x,y,1 / y). [para(1025(a,1),599(a,1))]. given #982 (H,wt=16): 1027 x \ R(y,x,1 / x) = T(y * (1 / x),x). [para(1026(a,1),491(a,1,2))]. given #983 (H,wt=13): 1028 T(x * (1 / y),y) = T(x,y) / y. [para(1027(a,1),469(a,1))]. given #984 (H,wt=11): 1031 T(x,y) / y = x / T(y,x). [para(1028(a,1),888(a,1))]. given #985 (H,wt=11): 1032 (T(x,y) / y) \ x = T(y,x). [para(1028(a,1),889(a,1,1))]. given #986 (H,wt=9): 1035 T(x,y) = x * K(x,y). [para(1032(a,1),391(a,1))]. given #987 (H,wt=9): 1036 K(x,y) = T(x,y) / x. [hyper(337,a,1035,a),flip(a)]. given #988 (H,wt=9): 1038 K(x,y) = x \ T(x,y). [hyper(56,a,1035,a(flip)),flip(a)]. given #989 (H,wt=9): 1043 T(x,y) = K(x,y) * x. [para(1036(a,2),16(a,1,1)),flip(a)]. given #990 (H,wt=9): 1049 K(x,y) = y / T(y,x). [para(1036(a,2),803(a,1))]. given #991 (H,wt=9): 1054 K(x,y) = T(y,x) \ y. [para(1038(a,2),801(a,2)),flip(a)]. given #992 (H,wt=9): 1055 T(x,y) * K(y,x) = x. [para(1038(a,2),802(a,1,2))]. given #993 (H,wt=9): 1056 K(x,y) * T(y,x) = y. [para(1038(a,2),805(a,1,1))]. given #994 (H,wt=9): 1061 T(x,y) = K(y,x) \ x. [para(1049(a,2),54(a,1,1)),flip(a)]. given #995 (H,wt=9): 1066 T(x * K(y,x),y) = x. [para(1054(a,2),832(a,1,1,2))]. given #996 (H,wt=11): 1033 (x / T(y,x)) * y = T(x,y). [para(1031(a,1),16(a,1,1))]. given #997 (H,wt=11): 1042 T(x,y * x) = T(x,x * y). [para(1035(a,2),1010(a,1)),flip(a)]. given #998 (H,wt=11): 1045 K(x,y) \ 1 = x / T(x,y). [para(1036(a,2),265(a,1,1))]. given #999 (H,wt=9): 1070 K(x,y) \ 1 = K(y,x). [para(1045(a,2),1049(a,2)),flip(a)]. given #1000 (H,wt=9): 1071 K(x,y) * K(y,x) = 1. [para(1070(a,1),14(a,1,2))]. given #1001 (H,wt=9): 1072 1 / K(x,y) = K(y,x). [para(1070(a,1),53(a,1,2))]. given #1002 (H,wt=9): 1079 K(x,T(y,x)) = K(x,y). [para(1070(a,1),964(a,2))]. given #1003 (H,wt=11): 1048 (x * y) / x = y * K(x,y). [para(1036(a,2),784(a,1,2)),flip(a)]. given #1004 (H,wt=11): 1050 K(x,y) = (x * y) / (y * x). [para(1036(a,2),971(a,2)),flip(a)]. given #1005 (H,wt=11): 1057 T(x,y) \ 1 = x \ K(y,x). [para(1038(a,2),804(a,1,2)),flip(a)]. given #1006 (H,wt=9): 1087 T(x,x \ K(y,x)) = x. [para(1057(a,1),412(a,1,2))]. given #1007 (H,wt=11): 1058 K(x,y) = x * (y / (y * x)). [para(1038(a,2),839(a,2)),flip(a)]. given #1008 (H,wt=11): 1069 T(x,x * (y / x)) = T(x,y). [para(16(a,1),1042(a,1,2)),flip(a)]. given #1009 (H,wt=11): 1074 K(x,y) * (K(y,x) * z) = z. [para(1070(a,1),254(a,1,1))]. given #1010 (H,wt=11): 1075 K(x,y) \ z = K(y,x) * z. [para(1070(a,1),256(a,1,1))]. given #1011 (H,wt=11): 1083 K(x / y,y) = K(y \ x,y). [para(1079(a,1),675(a,1)),flip(a)]. given #1012 (H,wt=11): 1085 K(x,y) \ (x * y) = y * x. [para(1050(a,2),54(a,1,1))]. given #1013 (H,wt=12): 1091 L(T(x,x \ y),y,x) = T(x,y). [para(1069(a,1),813(a,2))]. given #1014 (H,wt=12): 1098 L(T(x,y),x,y) = T(x,x \ y). [para(1091(a,1),341(a,1,1))]. given #1015 (H,wt=13): 1030 T(x * (y \ 1),y) = T(x,y) / y. [para(208(a,1),1028(a,1,1,2))]. given #1016 (H,wt=13): 1037 x * T(x \ 1,y) = K(x \ 1,y). [hyper(260,a,1035,a(flip))]. given #1017 (H,wt=13): 1041 x * (K(x,y) * z) = T(x,y) * z. [para(1035(a,2),997(a,1,1)),flip(a)]. given #1018 (H,wt=13): 1046 K(x,y) \ (T(x,y) * z) = x * z. [para(1036(a,2),350(a,1,1))]. given #1019 (H,wt=13): 1047 T(x,y) \ (x * z) = K(x,y) \ z. [para(1036(a,2),417(a,1,1)),flip(a)]. given #1020 (H,wt=13): 1053 T(x,y) * (x \ z) = K(x,y) * z. [para(1038(a,2),395(a,1,1)),flip(a)]. given #1021 (H,wt=13): 1062 x * (T(x,y) \ z) = K(y,x) * z. [para(1049(a,2),249(a,1,1)),flip(a)]. given #1022 (H,wt=13): 1063 x * (K(y,x) \ z) = T(x,y) * z. [para(1049(a,2),378(a,1,2,1))]. given #1023 (H,wt=13): 1064 (x \ y) \ (y / x) = K(x,y / x). [para(1049(a,2),407(a,1)),flip(a)]. given #1024 (H,wt=13): 1065 (x / y) * K(y \ x,y) = y \ x. [para(1054(a,2),651(a,1,2))]. given #1025 (H,wt=13): 1080 K(x,T(T(y,x),z)) = K(x,T(y,z)). [para(1070(a,1),966(a,2))]. given #1026 (H,wt=13): 1086 (x \ K(y,x)) * z = T(x,y) \ z. [para(1057(a,1),259(a,1,1))]. given #1027 (H,wt=13): 1088 T(T(x,y),x \ K(z,x)) = T(x,y). [para(1087(a,1),38(a,1,1)),flip(a)]. given #1028 (H,wt=13): 1090 T(x,y * (x \ 1)) = T(x,x \ y). [para(187(a,1),1069(a,1,2))]. given #1029 (H,wt=13): 1104 K(x,y) * (T(y,x) * z) = y * z. [hyper(17,a,851,a(flip),b,1041,a)]. given #1030 (H,wt=13): 1105 K(x,y) * (x * z) = T(x,y) * z. [hyper(17,a,375,a(flip),b,1041,a)]. given #1031 (H,wt=13): 1106 T(x,y) * (K(y,x) * z) = x * z. [para(1074(a,1),1041(a,1,2)),flip(a)]. given #1032 (H,wt=13): 1108 T(x,y) \ (x * z) = K(y,x) * z. [para(1047(a,2),1075(a,1))]. given #1033 (H,wt=13): 1109 T(x,y) \ (K(x,y) * z) = x \ z. [hyper(56,a,1053,a)]. given #1034 (H,wt=13): 1112 x \ (K(y,x) * z) = T(x,y) \ z. [para(1053(a,1),856(a,1,2))]. given #1035 (H,wt=14): 1068 R(x,y,y \ 1) * y = T(y * x,y). [para(895(a,1),1033(a,1,1))]. given #1036 (H,wt=14): 1100 x * T(y,y \ x) = L(y,y,x) * x. [para(1098(a,1),103(a,1,2))]. given #1037 (H,wt=11): 1120 L(x,x,x \ y) = L(x,x,y). [hyper(518,a,1100,a)]. given #1038 (H,wt=11): 1124 L(x,y,y / x) = L(x,x,y). [para(1120(a,1),907(a,1)),flip(a)]. given #1039 (H,wt=12): 1122 T(x,y) / L(y,y,x) = y \ x. [para(1120(a,1),356(a,1,2))]. given #1040 (H,wt=13): 1123 a(x,x \ y,x) = x \ L(x,x,y). [para(1120(a,1),519(a,1,2)),flip(a)]. given #1041 (H,wt=11): 1125 a(x,x \ y,x) = a(x,y,x). [para(1123(a,2),519(a,1))]. given #1042 (H,wt=11): 1126 a(x,x * y,x) = a(x,y,x). [para(13(a,1),1125(a,1,2)),flip(a)]. given #1043 (H,wt=14): 1121 L(x,x,y) * y = y * ((x \ y) \ y). [para(81(a,1),1100(a,1,2)),flip(a)]. given #1044 (H,wt=14): 1127 ((x \ 1) / y) * (y * x) = a(x,y,x). [para(1125(a,1),686(a,1)),flip(a)]. given #1045 (H,wt=13): 1128 R(x,y \ 1,y) = x * a(y,x,y). [para(1127(a,1),681(a,1,2)),flip(a)]. given #1046 (H,wt=15): 1051 T(x,y) \ T(T(x,z),y) = K(T(x,y),z). [para(38(a,1),1038(a,2,2)),flip(a)]. given #1047 (H,wt=15): 1093 K(x,y) * (z * K(y,x)) = T(z,K(y,x)). [hyper(98,a,1074,a),flip(a)]. given #1048 (H,wt=15): 1095 K(x / (x / y),x / y) = K(y,x / y). [para(54(a,1),1083(a,2,1))]. given #1049 (H,wt=15): 1111 T(x / y,z) * y = K(x / y,z) * x. [para(54(a,1),1053(a,1,2))]. given #1050 (H,wt=15): 1115 K(x,T(y,K(T(y,x),z))) = K(x,T(y,x)). [para(1012(a,1),1080(a,1,2)),flip(a)]. given #1051 (H,wt=13): 1131 K(x,T(y,K(T(y,x),z))) = K(x,y). [para(1115(a,2),1079(a,1))]. given #1052 (H,wt=15): 1117 K(x,y) * (y * z) = y * (K(x,y) * z). [para(1106(a,1),1104(a,1,2))]. given #1053 (H,wt=15): 1119 (x * (T(y,x) / x)) * x = T(x * y,x). [para(465(a,2),1068(a,1,1))]. given #1054 (H,wt=15): 1130 K(x / y,z) * x = y * T(y \ x,z). [para(1111(a,1),127(a,1))]. given #1055 (H,wt=16): 1039 x * L(K(y,z),y,x) = (x / y) * T(y,z). [para(1035(a,2),295(a,1,2)),flip(a)]. given #1056 (H,wt=16): 1040 x \ ((x / y) * T(y,z)) = L(K(y,z),y,x). [para(1035(a,2),340(a,2,2,2)),flip(a)]. given #1057 (H,wt=16): 1044 R(K(x,y) / z,z,x) = T(x,y) / (z * x). [para(1036(a,2),159(a,1,1,1))]. given #1058 (H,wt=16): 1076 x * L(K(y,z),K(z,y),x) = x / K(z,y). [para(1070(a,1),281(a,1,2,1))]. given #1059 (H,wt=16): 1077 L(K(x,y),K(y,x),z) = z \ (z / K(y,x)). [para(1070(a,1),282(a,1,1))]. given #1060 (H,wt=16): 1078 (x / K(y,z)) / L(K(z,y),K(y,z),x) = x. [para(1070(a,1),308(a,1,2,1))]. given #1061 (H,wt=16): 1084 R((x * y) / x,x,y) = y * K(x * y,y). [para(1048(a,1),76(a,2))]. given #1062 (H,wt=16): 1097 L(x,y,x) * (x \ y) = (x \ y) * T(x,y). [para(1091(a,1),103(a,1,2)),flip(a)]. given #1063 (H,wt=11): 1135 L(x,x \ y,x) = L(x,y,x). [hyper(18,a,200,a,b,1097,a),flip(a)]. given #1064 (H,wt=11): 1136 L(x,x * y,x) = L(x,y,x). [para(13(a,1),1135(a,1,2)),flip(a)]. given #1065 (H,wt=12): 1137 x / L(y,x,y) = x * (y \ 1). [para(1135(a,1),422(a,1,2))]. given #1066 (H,wt=16): 1101 L(T(x,y),x,T(y,x)) = T(x,x \ T(y,x)). [para(796(a,1),1098(a,1,1))]. given #1067 (H,wt=16): 1102 L(T(x,y),T(x,y),T(y,x)) = T(x,x \ y). [para(1098(a,1),899(a,2))]. given #1068 (H,wt=16): 1114 T(x,y) * z != x * u | K(y,x) \ z = u. [para(1063(a,1),19(a,1))]. given #1069 (H,wt=16): 1129 R(x,y \ 1,y) != x * z | a(y,x,y) = z. [para(1128(a,2),19(a,1))]. given #1070 (H,wt=17): 1029 T(x,y \ 1) / (y \ 1) = T(x * y,y \ 1). [para(53(a,1),1028(a,1,1,2)),flip(a)]. given #1071 (H,wt=17): 1034 T(x,y \ 1) / (y \ 1) = x * ((y \ x) \ x). [para(1031(a,2),318(a,1))]. given #1072 (H,wt=15): 1139 T(x * y,y \ 1) = x * ((y \ x) \ x). [para(1034(a,1),1029(a,1)),flip(a)]. given #1073 (H,wt=14): 1140 T(x * y,y \ 1) = L(y,y,x) * x. [para(1139(a,2),1121(a,2)),flip(a)]. given #1074 (H,wt=14): 1141 L(x,x,y) * y = (x * (y / x)) * x. [para(1140(a,1),886(a,1))]. given #1075 (H,wt=16): 1142 L(x,x,y * x) * (y * x) = (x * y) * x. [para(15(a,1),1141(a,2,1,2))]. given #1076 (H,wt=14): 1143 L(x,x,y) * (y * x) = (x * y) * x. [para(424(a,1),1142(a,1,1))]. given #1077 (H,wt=9): 1144 R(x,y,x) = L(x,x,y). [hyper(18,a,75,a,b,1143,a),flip(a)]. given #1078 (H,wt=11): 1147 L(x,x,T(y,x)) = L(x,x,y). [para(1144(a,1),918(a,2))]. given #1079 (H,wt=13): 1148 a(x,T(y,x),x) = L(x,x,y) / x. [para(1144(a,1),919(a,2,1))]. given #1080 (H,wt=11): 1151 a(x,T(y,x),x) = a(x,y,x). [para(1148(a,2),696(a,1))]. given #1081 (H,wt=11): 1152 a(x,y,1 / y) = a(y,x,y). [para(1151(a,1),1023(a,1)),flip(a)]. given #1082 (H,wt=11): 1154 a(x,y,y \ 1) = a(y,x,y). [para(208(a,1),1152(a,1,3))]. given #1083 (H,wt=13): 1155 x * L(1 / x,y,x) = a(x,y,x). [para(1152(a,1),595(a,2))]. given #1084 (H,wt=13): 1156 R(x,y,y \ 1) = x * a(y,x,y). [para(1154(a,1),588(a,1,2)),flip(a)]. given #1085 (H,wt=13): 1157 x * L(x \ 1,y,x) = a(x,y,x). [para(208(a,1),1155(a,1,2,1))]. given #1086 (H,wt=13): 1158 R(x,y \ 1,y) = R(x,y,y \ 1). [para(1156(a,2),1128(a,2))]. given #1087 (H,wt=14): 1159 R(x,y,y \ 1) / y = x * (y \ 1). [para(1158(a,1),679(a,1,1))]. given #1088 (H,wt=14): 1160 R(x / (y \ 1),y,y \ 1) = x * y. [para(1158(a,1),680(a,1))]. given #1089 (H,wt=15): 1145 R(R(x,y,z),u,x) = R(L(x,x,u),y,z). [para(1144(a,1),46(a,1,1)),flip(a)]. given #1090 (H,wt=15): 1149 L(T(x,y),x,T(z,x)) = T(L(x,x,z),y). [para(1147(a,1),40(a,2,1))]. given #1091 (H,wt=15): 1153 a(x \ 1,y,x \ 1) = a(y,x \ 1,x). [para(53(a,1),1152(a,1,3)),flip(a)]. given #1092 (H,wt=15): 1162 R(R(x,y,z),u,x) = L(R(x,y,z),x,u). [para(1145(a,2),44(a,1))]. given #1093 (H,wt=15): 1163 L(T(x,y),x,T(z,x)) = L(T(x,y),x,z). [para(1149(a,2),40(a,2)),flip(a)]. given #1094 (H,wt=14): 1165 T(x,x \ T(y,x)) = L(T(x,y),x,y). [para(1163(a,1),1101(a,1)),flip(a)]. given #1095 (H,wt=13): 1166 T(x,x \ T(y,x)) = T(x,x \ y). [para(1165(a,2),1098(a,1))]. given #1096 (H,wt=17): 1067 L(x * K(y,x),z,u) * y = y * L(x,z,u). [para(1066(a,1),103(a,1,2,1)),flip(a)]. given #1097 (H,wt=17): 1094 (K(x,y) \ z) \ (z * K(y,x)) = K(z,K(y,x)). [para(1075(a,2),26(a,2,1)),flip(a)]. given #1098 (H,wt=17): 1096 (x * y) / ((y * x) \ 1) = (y * x) * (x * y). [para(1085(a,1),642(a,1,2,1))]. given #1099 (H,wt=17): 1110 (x \ y) \ (K(x,z) * y) = T(T(x,z),x \ y). [para(1053(a,1),32(a,2,2)),flip(a)]. given #1100 (H,wt=17): 1113 x * (((x * y) \ y) * z) = K(x \ y,x) * z. [para(1062(a,1),957(a,1)),flip(a)]. given #1101 (H,wt=17): 1118 T(x * y,x) != z * x | R(y,x,x \ 1) = z. [para(1068(a,1),20(a,1))]. given #1102 (H,wt=17): 1133 x \ (y * T(y \ x,z)) = T(K(x / y,z),x). [para(1130(a,1),32(a,2,2)),flip(a)]. given #1103 (H,wt=17): 1168 K(x \ y,x) * ((x \ y) \ z) = (x / y) * z. [para(1113(a,1),948(a,1))]. given #1104 (H,wt=18): 1052 R(x,y,z) \ R(T(x,u),y,z) = K(R(x,y,z),u). [para(42(a,2),1038(a,2,2)),flip(a)]. given #1105 (H,wt=18): 1059 R(x,K(y,z),y) * T(y,z) = (x * K(y,z)) * y. [para(1043(a,2),75(a,1,2))]. given #1106 (H,wt=18): 1060 R(x / K(y,z),K(y,z),y) = (x * y) / T(y,z). [para(1043(a,2),76(a,2,2))]. given #1107 (H,wt=18): 1092 (x * (y / x)) / T(x,y) = R(y / x,x,x \ 1). [para(1069(a,1),895(a,1,2))]. given #1108 (H,wt=15): 1170 (x * (y / x)) / T(x,y) = y * (x \ 1). [para(1092(a,2),463(a,1))]. given #1109 (H,wt=18): 1099 T(x / y,(x / y) \ y) = L(y \ x,x / y,y). [para(82(a,1),1098(a,1,1)),flip(a)]. given #1110 (H,wt=16): 1171 T(x / y,(x / y) \ y) = L(y \ x,x,y). [para(1099(a,2),435(a,1))]. given #1111 (H,wt=12): 1172 L(x \ y,y,x) = (y \ x) \ 1. [para(1171(a,1),624(a,1))]. given #1112 (H,wt=12): 1174 L((x \ y) \ 1,y,x) = y \ x. [para(1172(a,1),341(a,1,1))]. given #1113 (H,wt=18): 1150 L(x,x,y) * T(y,x) = (x * (T(y,x) / x)) * x. [para(1147(a,1),1141(a,1,1))]. given #1114 (H,wt=14): 1177 L(x,x,y) * T(y,x) = T(x * y,x). [para(1150(a,2),1119(a,1))]. given #1115 (H,wt=15): 1178 L(x,x,y) * T(y,x) = y * L(x,x,y). [para(1177(a,2),327(a,2)),flip(a)]. given #1116 (H,wt=10): 1179 T(x,L(y,y,x)) = T(x,y). [hyper(98,a,1178,a)]. given #1117 (H,wt=19): 1073 K(x,y) \ (z / K(y,x)) = (K(x,y) \ z) * K(x,y). [para(1070(a,1),195(a,1,2,2))]. given #1118 (H,wt=19): 1082 T(x,K(y,z)) * K(z,y) = x * (1 / T(K(y,z),x)). [para(1072(a,1),854(a,1,2))]. given #1119 (H,wt=17): 1181 K(K(x,y),z) \ K(y,x) = 1 / T(K(x,y),z). [hyper(1114,a,1082,a)]. given #1120 (H,wt=19): 1089 T(x,y) * (x \ K(z,x)) = (x \ K(z,x)) * T(x,y). [para(1087(a,1),102(a,1,2,1)),flip(a)]. given #1121 (H,wt=17): 1182 T(x,y) * (x \ K(z,x)) = T(x,z) \ T(x,y). [para(1089(a,2),1086(a,1))]. given #1122 (H,wt=15): 1183 T(x,y) \ T(x,z) = K(x,z) * K(y,x). [para(1182(a,1),1053(a,1))]. given #1123 (H,wt=19): 1103 T((x * (y * x)) * (x \ 1),x) = (y * (x * x)) / x. [para(97(a,1),1030(a,2,1))]. given #1124 (H,wt=19): 1146 L(x \ 1,x \ 1,x * y) = R(x,y,x \ 1) \ 1. [para(1144(a,1),602(a,1))]. given #1125 (H,wt=15): 1185 R(x,y,x \ 1) \ 1 = L(x \ 1,y,x). [para(1146(a,1),456(a,1))]. given #1126 (H,wt=19): 1169 (x \ y) * T((x \ y) \ 1,z) = T(K(x / y,z),x). [para(1133(a,1),958(a,2))]. given #1127 (H,wt=15): 1186 T(K(x / y,z),x) = K((x \ y) \ 1,z). [para(1169(a,1),1037(a,1))]. given #1128 (H,wt=15): 1187 K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). [para(53(a,1),1186(a,1,1,1)),flip(a)]. given #1129 (H,wt=19): 1173 L((x / y) \ x,x,x / y) = L(y \ 1,y,x) \ 1. [para(282(a,2),1172(a,2,1))]. given #1130 (H,wt=15): 1189 L(x,y,y / x) = L(x \ 1,x,y) \ 1. [para(54(a,1),1173(a,1,1))]. given #1131 (H,wt=13): 1190 L(x \ 1,x,y) \ 1 = L(x,x,y). [para(1189(a,1),1124(a,1))]. given #1132 (H,wt=12): 1191 L(x,x,y) = (y \ (y / x)) \ 1. [para(282(a,1),1190(a,1,1)),flip(a)]. given #1133 (H,wt=14): 1192 L(x,x,y) \ z = (y \ (y / x)) * z. [para(1191(a,2),256(a,1,1))]. given #1134 (H,wt=14): 1193 x \ ((y \ (y / x)) \ 1) = a(x,y,x). [para(1191(a,1),519(a,1,2))]. given #1135 (H,wt=19): 1184 T(x * (((y * x) / x) * 1),x) = (y * (x * x)) / x. [para(170(a,1),1103(a,1,1))]. given #1136 (H,wt=15): 1195 T(x * (y * 1),x) = (y * (x * x)) / x. [para(15(a,1),1184(a,1,1,2,1))]. given #1137 (H,wt=13): 1196 (x * (y * y)) / y = T(y * x,y). [para(12(a,1),1195(a,1,1,2)),flip(a)]. given #1138 (H,wt=13): 1197 T(x * y,x) * x = y * (x * x). [para(1196(a,1),16(a,1,1))]. given #1139 (H,wt=12): 1198 T(x * R(y,x,x),x) = y * x. [hyper(18,a,75,a(flip),b,1197,a)]. given #1140 (H,wt=11): 1199 R(R(x,y,y),y,y \ 1) = x. [hyper(1118,a,1198,a)]. given #1141 (H,wt=11): 1200 R(R(x,y,y \ 1),y,y) = x. [para(1199(a,1),46(a,1)),flip(a)]. given #1142 (H,wt=12): 1201 R(x,y,y) * y = x / (y \ 1). [para(1199(a,1),461(a,1,1)),flip(a)]. given #1143 (H,wt=12): 1202 R(x,y,y) * (y \ 1) = x / y. [para(1199(a,1),1159(a,1,1)),flip(a)]. given #1144 (H,wt=12): 1203 R(x * (y \ 1),y,y) = x / y. [para(463(a,1),1200(a,1,1))]. given #1145 (H,wt=12): 1204 R(T(x * y,x),x,x) = y * x. [para(878(a,1),1200(a,1,1))]. given #1146 (H,wt=12): 1205 R(x * y,y,y) = x / (y \ 1). [para(1160(a,1),1200(a,1,1))]. given #1147 (H,wt=12): 1206 (x / (y \ 1)) / y = R(x,y,y). [hyper(61,a,1201,a)]. given #1148 (H,wt=12): 1207 R(T(x,y),y,y) = (y \ x) * y. [hyper(18,a,882,a(flip),b,1201,a)]. given #1149 (H,wt=12): 1208 (x / y) / (y \ 1) = R(x,y,y). [hyper(61,a,1202,a)]. given #1150 (H,wt=12): 1209 R(x,y,y) \ (x / y) = y \ 1. [hyper(56,a,1202,a)]. given #1151 (H,wt=14): 1210 (x \ 1) / (y / x) = R(y,x,x) \ 1. [para(1202(a,1),255(a,1,2))]. given #1152 (H,wt=15): 1213 R(R(T(x,y),y,y),x,z) = (y \ x) * y. [para(1207(a,1),155(a,2))]. given #1153 (H,wt=16): 1212 R(x,y \ 1,y \ 1) = (x / y) / (y \ 1). [para(210(a,1),1206(a,1,1,2)),flip(a)]. given #1154 (H,wt=13): 1216 R(x,y \ 1,y \ 1) = R(x,y,y). [para(1212(a,2),1208(a,1))]. given #1155 (H,wt=16): 1215 R(x * y,y * x,z) = (y \ (y * x)) * y. [para(1204(a,1),1213(a,1,1))]. given #1156 (H,wt=12): 1217 R(x * y,y * x,z) = x * y. [para(13(a,1),1215(a,2,1))]. given #1157 (H,wt=18): 1214 (x / K(y,z)) / K(z,y) = R(x,K(y,z),K(y,z)). [para(1070(a,1),1208(a,1,2))]. given #1158 (H,wt=19): 1218 ((x * y) * (y * x)) * z = (x * y) * ((y * x) * z). [para(1217(a,1),75(a,1,1)),flip(a)]. given #1159 (H,wt=20): 1081 ((x * K(y,z)) * K(z,y)) / 1 = R(x,K(y,z),K(z,y)). [para(1071(a,1),30(a,2,2)),flip(a)]. given #1160 (H,wt=18): 1219 (x * K(y,z)) * K(z,y) = R(x,K(y,z),K(z,y)). [para(1081(a,1),52(a,1)),flip(a)]. given #1161 (H,wt=21): 1132 T(T(x,K(T(x,y),z)),y) * K(y,x) = T(x,K(T(x,y),z)). [para(1131(a,1),1055(a,1,2))]. given #1162 (H,wt=21): 1176 ((x * y) \ (x / (y \ 1))) \ 1 = (x / (y \ 1)) \ (x * y). [para(1174(a,1),682(a,1)),flip(a)]. given #1163 (H,wt=21): 1188 K((((x \ y) / y) * (x \ y)) \ (x \ y),z) = T(K(x,z),y). [para(637(a,2),1187(a,1,1))]. given #1164 (H,wt=19): 1222 K(((x \ 1) * (x \ y)) \ (x \ y),z) = T(K(x,z),y). [para(264(a,1),1188(a,1,1,1,1))]. given #1165 (H,wt=17): 1223 K((x \ (x \ y)) \ (x \ y),z) = T(K(x,z),y). [para(259(a,1),1222(a,1,1,1))]. given #1166 (H,wt=15): 1225 K(T(x,x \ (x \ y)),z) = T(K(x,z),y). [para(81(a,2),1223(a,1,1))]. given #1167 (H,wt=21): 1211 T(R(x,y,y),z) * (y \ 1) = K(R(x,y,y),z) * (x / y). [para(1202(a,1),1105(a,1,2)),flip(a)]. given #1168 (H,wt=21): 1220 T(T(x,y),K(T(x,y),z)) * K(y,x) = T(x,K(T(x,y),z)). [para(38(a,1),1132(a,1,1))]. given #1169 (H,wt=15): 1227 T(x,K(T(x,y),z)) = T(x,y) * K(y,x). [para(1012(a,1),1220(a,1,1)),flip(a)]. given #1170 (H,wt=9): 1229 T(x,K(T(x,y),z)) = x. [para(1227(a,2),1055(a,1))]. given #1171 (H,wt=15): 1230 K(T(x,y),z) * x = x * K(T(x,y),z). [para(1229(a,1),80(a,1,2))]. given #1172 (H,wt=21): 1221 ((x * y) \ (x / (y \ 1))) \ 1 = ((y \ 1) / x) * (x * y). [para(1176(a,2),284(a,1))]. given #1173 (H,wt=16): 1232 ((x * y) \ (x / (y \ 1))) \ 1 = a(y,x,y). [para(1221(a,2),1127(a,1))]. given #1174 (H,wt=21): 1226 R(T(x,y),z,z) * (z \ 1) = K(R(x,z,z),y) * (x / z). [para(42(a,2),1211(a,1,1))]. given #1175 (H,wt=16): 1234 K(R(x,y,y),z) * (x / y) = T(x,z) / y. [para(1226(a,1),1202(a,1))]. given #1176 (H,wt=21): 1231 (x / y) * K(T(x / y,y),z) = K(y \ x,z) * (x / y). [para(82(a,1),1230(a,1,1,1)),flip(a)]. given #1177 (H,wt=19): 1235 K(x \ y,z) * (y / x) = (y / x) * K(x \ y,z). [para(82(a,1),1231(a,1,2,1)),flip(a)]. given #1178 (H,wt=22): 1138 T(L(x,y,x),L(x,y,x) \ y) = T(L(x,y,x),y * (x \ 1)). [para(1137(a,1),799(a,1,2)),flip(a)]. given #1179 (H,wt=22): 1164 (x * R(y,z,u)) / L(R(y,z,u),y,x) = R(x,R(y,z,u),y). [para(1162(a,1),939(a,1,2))]. given #1180 (H,wt=22): 1194 (x \ (x / y)) * T(L(y,y,x),z) = K((x \ (x / y)) \ 1,z). [para(1191(a,2),1037(a,1,2,1))]. given #1181 (H,wt=22): 1236 T(L(x,y,x),L(x,y,x) \ y) = L(T(x,y * (x \ 1)),y,x). [para(1138(a,2),40(a,2)),flip(a)]. given #1182 (H,wt=20): 1238 T(L(x,y,x),L(x,y,x) \ y) = L(T(x,x \ y),y,x). [para(1090(a,1),1236(a,2,1))]. given #1183 (H,wt=15): 1239 T(L(x,y,x),L(x,y,x) \ y) = T(x,y). [para(1238(a,2),1091(a,1))]. given #1184 (H,wt=12): 1240 L(x,y,x) \ y = y / T(x,y). [para(1239(a,1),109(a,1,2)),flip(a)]. given #1185 (H,wt=12): 1241 L(x,y,x) = y / (y / T(x,y)). [para(1240(a,1),53(a,1,2)),flip(a)]. given #1186 (H,wt=12): 1242 x / (T(x,y) / y) = L(y,x,y). [para(1031(a,2),1241(a,2,2)),flip(a)]. given #1187 (H,wt=21): 1244 L(L(x,x,y),y,L(x,x,y)) = y / (T(y,x) / L(x,x,y)). [para(1179(a,1),1242(a,1,2,1)),flip(a)]. given #1188 (H,wt=16): 1245 L(L(x,x,y),y,L(x,x,y)) = y / (x \ y). [para(1122(a,1),1244(a,2,2))]. given #1189 (H,wt=12): 1246 L(L(x,x,y),y,L(x,x,y)) = x. [para(1245(a,2),53(a,1))]. given #1190 (H,wt=22): 1237 (x \ (x / y)) * L(T(y,z),y,x) = K((x \ (x / y)) \ 1,z). [para(40(a,2),1194(a,1,2))]. given #1191 (H,wt=23): 1107 R(K(x,y) \ 1,T(x,y) * z,u) = R(K(x,y),x * z,u) \ 1. [para(1046(a,1),603(a,1,1,2)),flip(a)]. given #1192 (H,wt=21): 1247 R(K(x,y),T(y,x) * z,u) = R(K(y,x),y * z,u) \ 1. [para(1070(a,1),1107(a,1,1))]. given #1193 (H,wt=24): 1116 R(K(x,y),T(y,x) * z,u) = ((y * z) * u) / ((T(y,x) * z) * u). [para(1104(a,1),30(a,2,1,1))]. given #1194 (H,wt=24): 1134 x / ((K(y,z) / x) \ (T(y,z) / (x * y))) = R(x,K(y,z) / x,y). [para(1044(a,1),933(a,1,2,2))]. given #1195 (H,wt=24): 1167 L(R((x * y) / x,x,y),z,u) * (x * y) = (x * y) * L(y,z,u). [para(1084(a,2),1067(a,1,1,1))]. given #1196 (H,wt=21): 1249 (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u). [para(1167(a,1),151(a,1)),flip(a)]. given #1197 (H,wt=21): 1250 (x * L(x \ (x * y),z,u)) * y = (x * y) * L(y,z,u). [para(198(a,1),1249(a,1,1))]. given #1198 (H,wt=17): 1251 (x * L(y,z,u)) * y = (x * y) * L(y,z,u). [para(13(a,1),1250(a,1,1,2,1))]. given #1199 (H,wt=17): 1252 ((x * y) * L(y,z,u)) / y = x * L(y,z,u). [hyper(61,a,1251,a)]. given #1200 (H,wt=17): 1253 ((x / L(y,z,u)) * y) * L(y,z,u) = x * y. [para(16(a,1),1251(a,1,1)),flip(a)]. given #1201 (H,wt=17): 1254 (x * L(y,z,u)) / y = (x / y) * L(y,z,u). [para(16(a,1),1252(a,1,1,1))]. given #1202 (H,wt=17): 1255 (x * y) / L(y,z,u) = (x / L(y,z,u)) * y. [hyper(61,a,1253,a)]. given #1203 (H,wt=24): 1243 (x * (y / x)) / ((x * (y / x)) / T(x,y)) = L(x,x * (y / x),x). [para(1069(a,1),1241(a,2,2,2)),flip(a)]. given #1204 (H,wt=22): 1256 (x * (y / x)) / ((x * (y / x)) / T(x,y)) = L(x,y / x,x). [para(1243(a,2),1136(a,1))]. given #1205 (H,wt=20): 1257 (x * (y / x)) / ((x * (y / x)) / T(x,y)) = L(x,y,x). [para(1256(a,2),435(a,1))]. given #1206 (H,wt=16): 1258 (x * (y / x)) / (y * (x \ 1)) = L(x,y,x). [para(1170(a,1),1257(a,1,2))]. given #1207 (H,wt=11): 1259 R(x,y,x \ 1) = L(x,y,x). [para(1258(a,1),188(a,1)),flip(a)]. given #1208 (H,wt=13): 1260 L(x \ 1,y,x) = L(x,y,x) \ 1. [para(1259(a,1),1185(a,1,1)),flip(a)]. given #1209 (H,wt=13): 1261 x * (L(x,y,x) \ 1) = a(x,y,x). [para(1260(a,1),1157(a,1,2))]. given #1210 (H,wt=11): 1262 L(x,y,x) \ x = a(x,y,x). [para(1261(a,1),615(a,1)),flip(a)]. given #1211 (H,wt=24): 1248 x / ((x / K(y,z)) * (T(y,z) / (x * y))) = R(x,K(y,z) / x,y). [para(284(a,1),1134(a,1,2))]. given #1212 (H,wt=25): 986 ((x * y) / ((y * x) \ 1)) * ((x * y) \ z) = (x * y) * (K(x,y) \ z). [para(985(a,2),303(a,2,2,1))]. given #1213 (H,wt=23): 1263 ((x * y) * (y * x)) * ((y * x) \ z) = (y * x) * (K(y,x) \ z). [para(1096(a,1),986(a,1,1))]. given #1214 (H,wt=23): 1264 ((x * y) * (y * x)) * ((y * x) \ z) = (y * x) * (K(x,y) * z). [para(1075(a,1),1263(a,2,2))]. given #1215 (H,wt=23): 1265 (x * y) * ((y * x) * ((y * x) \ z)) = (y * x) * (K(x,y) * z). [para(1264(a,1),1218(a,1)),flip(a)]. given #1216 (H,wt=15): 1266 (x * y) * (K(y,x) * z) = (y * x) * z. [para(14(a,1),1265(a,1,2)),flip(a)]. given #1217 (H,wt=18): 1267 (x * y) \ ((x * y) * z) = L(z,K(x,y),y * x). [para(1266(a,1),111(a,1,2))]. given #1218 (H,wt=10): 1268 L(x,K(y,z),z * y) = x. [para(1267(a,1),13(a,1))]. given #1219 (H,wt=10): 1270 L(x,y * z,K(y,z)) = x. [para(1268(a,1),437(a,1))]. given #1220 (H,wt=15): 1271 K(x,y) \ ((y * x) \ z) = (x * y) \ z. [para(1270(a,1),181(a,1)),flip(a)]. given #1221 (H,wt=17): 1272 T(x,y) * ((x * y) \ z) = x * ((y * x) \ z). [para(1271(a,1),1063(a,1,2)),flip(a)]. given #1222 (H,wt=19): 1269 (K(x,y) * (y * x)) * z = K(x,y) * ((y * x) * z). [para(1268(a,1),342(a,1,2,2)),flip(a)]. given #1223 (H,wt=19): 1274 (x * (K(y,x) * y)) * z = K(y,x) * ((x * y) * z). [para(1117(a,1),1269(a,1,1))]. given #1224 (H,wt=17): 1275 K(x,y) * ((y * x) * z) = (y * T(x,y)) * z. [para(1043(a,2),1274(a,1,1,2)),flip(a)]. given #1225 (H,wt=15): 1276 K(x,y) * ((y * x) * z) = (x * y) * z. [para(80(a,1),1275(a,2,1))]. given #1226 (H,wt=15): 1277 ((x * y) * z) / ((y * x) * z) = K(x,y). [hyper(61,a,1276,a)]. given #1227 (H,wt=18): 1278 K(x,y) * (y * (x * z)) = (x * y) * L(z,x,y). [para(69(a,1),1276(a,1,2))]. given #1228 (H,wt=18): 1280 x * (K(y,x) * (y * z)) = (y * x) * L(z,y,x). [para(1278(a,1),1117(a,1)),flip(a)]. given #1229 (H,wt=16): 1281 (x * y) * L(z,x,y) = y * (T(x,y) * z). [para(1105(a,1),1280(a,1,2)),flip(a)]. given #1230 (H,wt=16): 1282 L(x,y,z) = (y * z) \ (z * (T(y,z) * x)). [hyper(56,a,1281,a),flip(a)]. given #1231 (H,wt=11): 1284 L(x,T(y,z),z) = L(x,y,z). [para(1282(a,2),100(a,1)),flip(a)]. given #1232 (H,wt=11): 1286 L(x,y,y \ z) = L(x,y,z). [para(1284(a,1),909(a,1))]. given #1233 (H,wt=11): 1288 L(x,y,z \ y) = L(x,z,y). [para(1286(a,1),439(a,2))]. given #1234 (H,wt=11): 1289 L(x,y,z \ 1) = L(x,z,y). [para(1286(a,1),445(a,2))]. given #1235 (H,wt=11): 1290 L(x,y,1 / z) = L(x,z,y). [para(1286(a,1),446(a,1)),flip(a)]. given #1236 (H,wt=11): 1292 L(x,y,y / z) = L(x,z,y). [para(1286(a,1),907(a,1)),flip(a)]. given #1237 (H,wt=11): 1293 L(x,y \ z,z) = L(x,z,y). [para(1288(a,1),905(a,1))]. given #1238 (H,wt=11): 1294 L(x,y \ 1,z) = L(x,z,y). [para(210(a,1),1289(a,1,3)),flip(a)]. given #1239 (H,wt=11): 1295 L(x,y \ z,y) = L(x,z,y). [para(1293(a,1),425(a,1)),flip(a)]. given #1240 (H,wt=14): 1291 (x \ y) * L(z,x,y) = x \ (y * z). [para(1286(a,1),359(a,1,2))]. given #1241 (H,wt=14): 1296 L((x \ y) \ z,y,x) = y \ (x * z). [para(1293(a,1),353(a,1))]. given #1242 (H,wt=14): 1297 x \ (y * L(z,y,x)) = (x \ y) * z. [para(1293(a,1),355(a,1,2,2))]. given #1243 (H,wt=14): 1299 L(x,y,z) = y \ (z * ((z \ y) * x)). [para(1295(a,1),70(a,2)),flip(a)]. given #1244 (H,wt=14): 1300 x * L(y,x,z) = z * ((z \ x) * y). [para(1295(a,1),137(a,1,2))]. given #1245 (H,wt=15): 1285 L(x,T(y,z),T(z,y)) = L(x,y,T(z,y)). [para(796(a,1),1284(a,1,2))]. given #1246 (H,wt=11): 1307 L(x,y,T(z,y)) = L(x,y,z). [para(1285(a,1),899(a,1))]. given #1247 (H,wt=16): 1283 L(T(x,y) \ z,x,y) = (x * y) \ (y * z). [para(14(a,1),1282(a,2,2,2))]. given #1248 (H,wt=16): 1301 L(x * y,z,x) = z \ ((z / (x \ 1)) * y). [para(1295(a,1),690(a,1))]. given #1249 (H,wt=16): 1302 (x * (y \ 1)) * L(z,x,y) = x * (y \ z). [para(1295(a,1),691(a,1,2))]. given #1250 (H,wt=18): 1305 (x \ (x / y)) * L(z,y,x) = x \ ((x / y) * z). [para(1292(a,1),1291(a,1,2))]. given #1251 (H,wt=19): 1279 ((x * y) * z) / ((T(x,y) * y) * z) = K(y,T(x,y)). [para(80(a,1),1277(a,1,1,1))]. given #1252 (H,wt=19): 1309 K((x \ (x / y)) \ 1,z) = x \ ((x / y) * T(y,z)). [para(1305(a,1),1237(a,1)),flip(a)]. given #1253 (H,wt=16): 1310 L(K(x,y),x,z) = K((z \ (z / x)) \ 1,y). [para(1309(a,2),1040(a,1)),flip(a)]. given #1254 (H,wt=13): 1312 L(K(x,y),x,z) = K(L(x,x,z),y). [para(1191(a,2),1310(a,2,1))]. given #1255 (H,wt=15): 1314 K(L(x,x,y \ x),z) = L(K(x,z),y,x). [para(1312(a,1),1288(a,1))]. given #1256 (H,wt=13): 1315 L(K(x,y),z,x) = K(L(x,z,x),y). [para(1288(a,1),1314(a,1,1)),flip(a)]. given #1257 (H,wt=16): 1313 x * K(L(y,y,x),z) = (x / y) * T(y,z). [para(1312(a,1),1039(a,1,2))]. given #1258 (H,wt=18): 1316 (x \ y) * K(L(y,x,y),z) = x \ (y * K(y,z)). [para(1315(a,1),1291(a,1,2))]. given #1259 (H,wt=16): 1317 (x \ y) * K(L(y,x,y),z) = x \ T(y,z). [para(1035(a,2),1316(a,2,2))]. given #1260 (H,wt=20): 1303 L(L((x \ y) \ z,u,w),y,x) = L(y \ (x * z),u,w). [para(1295(a,1),509(a,1))]. given #1261 (H,wt=21): 1273 T(x,y) * (y * ((x * y) \ z)) = x * (y * ((y * x) \ z)). [para(1272(a,1),851(a,1,2))]. given #1262 (H,wt=21): 1311 (x * y) * K((x \ (x / y)) \ 1,z) = x * (y * K(y,z)). [para(1310(a,1),69(a,1,2))]. given #1263 (H,wt=19): 1319 (x * y) * K((x \ (x / y)) \ 1,z) = x * T(y,z). [para(1035(a,2),1311(a,2,2))]. given #1264 (H,wt=25): 1175 ((x / y) \ ((x * z) / (y * z))) \ 1 = ((x * z) / (y * z)) \ (x / y). [para(1172(a,1),529(a,1))]. given #1265 (H,wt=25): 1180 K(x / (x / K(y,z)),x / K(y,z)) = (K(y,z) \ (x / K(z,y))) \ x. [para(1073(a,2),673(a,2,1))]. given #1266 (H,wt=21): 1321 (K(x,y) \ (z / K(y,x))) \ z = K(K(x,y),z / K(x,y)). [para(1180(a,1),1095(a,1))]. given #1267 (H,wt=25): 1320 ((x / y) * ((y * z) / (x * z))) \ 1 = ((y * z) / (x * z)) \ (y / x). [para(284(a,1),1175(a,1,1))]. given #1268 (H,wt=25): 1322 ((x / y) * ((y * z) / (x * z))) \ 1 = ((x * z) / (y * z)) * (y / x). [para(1320(a,2),284(a,1))]. given #1269 (H,wt=22): 1323 (x / y) \ R(x / y,y,z) = ((x * z) / (y * z)) * (y / x). [para(1322(a,1),952(a,2))]. given #1270 (H,wt=18): 1324 ((x * y) / (z * y)) * (z / x) = R(z,x,y) \ z. [para(1323(a,1),896(a,1))]. given #1271 (H,wt=15): 1325 x * (R(y,x,z) \ y) = R(x,y / x,z). [para(1324(a,1),941(a,1,2))]. given #1272 (H,wt=11): 1326 R(x,y / x,z) = R(x,y,z). [para(1325(a,1),932(a,1))]. given #1273 (H,wt=11): 1327 R(x,y * x,z) = R(x,y,z). [para(15(a,1),1326(a,1,2)),flip(a)]. given #1274 (H,wt=15): 1329 R(T(x,y),z * x,u) = T(R(x,z,u),y). [para(1327(a,1),42(a,2,1))]. given #1275 (H,wt=15): 1330 R(T(x,y),z * x,u) = R(T(x,y),z,u). [para(1329(a,2),42(a,2)),flip(a)]. given #1276 (H,wt=22): 1328 x / ((x / K(y,z)) * (T(y,z) / (x * y))) = R(x,K(y,z),y). [para(1326(a,1),1248(a,2))]. given #1277 (H,wt=26): 1233 ((x * (y * y)) \ (T(y * x,y) / (y \ 1))) \ 1 = a(y,T(y * x,y),y). [para(1197(a,1),1232(a,1,1,1))]. given #1278 (H,wt=22): 1331 ((x * (y * y)) \ ((x * y) * y)) \ 1 = a(y,T(y * x,y),y). [para(880(a,1),1233(a,1,1,2))]. given #1279 (H,wt=15): 1332 a(x,T(x * y,x),x) = a(y,x,x) \ 1. [para(24(a,2),1331(a,1,1)),flip(a)]. given #1280 (H,wt=13): 1333 a(x,x * y,x) = a(y,x,x) \ 1. [para(1332(a,1),1151(a,1)),flip(a)]. given #1281 (H,wt=11): 1334 a(x,y,y) \ 1 = a(y,x,y). [para(1333(a,1),1126(a,1))]. given #1282 (H,wt=13): 1335 a(x,y,x) \ z = a(y,x,x) * z. [para(1334(a,1),256(a,1,1))]. given #1283 (H,wt=13): 1336 a(x,y,y) \ z = a(y,x,y) * z. [para(1334(a,1),259(a,1,1)),flip(a)]. given #1284 (H,wt=22): 1337 x / (a(y,z,z) * R(a(z,y,z),x,u)) = R(x,a(z,y,z),u). [para(1335(a,1),933(a,1,2))]. given #1285 (H,wt=26): 1304 (x \ y) * ((z / (x \ y)) * (x \ (y * u))) = ((x \ y) * z) * L(u,x,y). [para(1291(a,1),85(a,1,2,2))]. given #1286 (H,wt=26): 1338 (x \ y) * (x * (((x \ z) / y) * (y * u))) = ((x \ y) * z) * L(u,x,y). [para(924(a,1),1304(a,1,2))]. given #1287 (H,wt=28): 393 (T(R(x,y,z),u) * (y * z)) / ((x * y) * z) = R(x,y,z) \ T(R(x,y,z),u). [para(75(a,1),385(a,1,2))]. given #1288 (H,wt=28): 1161 R(L(x / (y \ 1),z,u),y,y \ 1) / y = (y \ 1) * L((y \ 1) \ x,z,u). [para(1159(a,2),198(a,1))]. given #1289 (H,wt=28): 1306 x \ (y * L(L((x \ y) \ 1,z,u),y,x)) = L((x \ y) \ 1,z,u) * (x \ y). [para(1297(a,2),227(a,2)),flip(a)]. given #1290 (H,wt=25): 1341 x \ (y * L(y \ (x * 1),z,u)) = L((x \ y) \ 1,z,u) * (x \ y). [para(1303(a,1),1306(a,1,2,2))]. given #1291 (H,wt=23): 1342 L((x \ y) \ 1,z,u) * (x \ y) = x \ (y * L(y \ x,z,u)). [para(12(a,1),1341(a,1,2,2,1,2)),flip(a)]. given #1292 (H,wt=23): 1343 (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u)). [para(1342(a,1),227(a,1)),flip(a)]. given #1293 (H,wt=28): 1318 T(x / y,y) * (y * (((x / y) * y) \ z)) = x * L((y * (x / y)) \ z,y,x). [para(1273(a,2),295(a,1))]. given #1294 (H,wt=26): 1344 (x \ y) * (x * (((y / x) * x) \ z)) = y * L((x * (y / x)) \ z,x,y). [para(82(a,1),1318(a,1,1))]. given #1295 (H,wt=22): 1345 x * L((y * (x / y)) \ z,y,x) = (y \ x) * (y * (x \ z)). [para(16(a,1),1344(a,1,2,2,1)),flip(a)]. given #1296 (H,wt=19): 1346 (x \ y) * (x * (y \ z)) = y * (x * ((x * y) \ z)). [para(605(a,1),1345(a,1,2)),flip(a)]. given #1297 (H,wt=28): 1339 (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = R(x,z,u) \ T(R(x,z,u),y). [para(42(a,2),393(a,1,1,1))]. given #1298 (H,wt=25): 1348 ((T(x,y) * z) * u) / ((x * z) * u) = R(x,z,u) \ T(R(x,z,u),y). [para(75(a,1),1339(a,1,1))]. given #1299 (H,wt=25): 1349 ((T(x,y) * z) * u) / ((x * z) * u) = R(x,z,u) \ R(T(x,y),z,u). [para(42(a,2),1348(a,2,2))]. given #1300 (H,wt=22): 1350 R(x \ T(x,y),x * z,u) = R(x,z,u) \ R(T(x,y),z,u). [para(1349(a,1),394(a,2))]. given #1301 (H,wt=20): 1351 R(x,y,z) \ R(T(x,u),y,z) = R(K(x,u),x * y,z). [para(1038(a,2),1350(a,1,1)),flip(a)]. given #1302 (H,wt=15): 1352 R(K(x,y),x * z,u) = K(R(x,z,u),y). [para(1351(a,1),1052(a,1))]. given #1303 (H,wt=15): 1353 K(R(x,x \ y,z),u) = R(K(x,u),y,z). [para(14(a,1),1352(a,1,2)),flip(a)]. given #1304 (H,wt=19): 1354 R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1. [para(1352(a,1),1247(a,2,1))]. given #1305 (H,wt=17): 1355 R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)). [para(1354(a,2),1070(a,1))]. given #1306 (H,wt=20): 1356 ((x * y) * z) / ((T(x,u) * y) * z) = K(u,R(x,y,z)). [para(1355(a,1),1116(a,1)),flip(a)]. given #1307 (H,wt=12): 1357 K(x,R(y,x,z)) = K(x,T(y,x)). [para(1356(a,1),1279(a,1))]. given #1308 (H,wt=10): 1358 K(x,R(y,x,z)) = K(x,y). [para(1357(a,2),1079(a,1))]. given #1309 (H,wt=15): 1359 K(x,y) * T(R(y,x,z),x) = R(y,x,z). [para(1358(a,1),1056(a,1,1))]. given #1310 (H,wt=15): 1360 K(x,y) * R(T(y,x),x,z) = R(y,x,z). [para(42(a,2),1359(a,1,2))]. given #1311 (H,wt=17): 1361 T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). [para(1360(a,1),1112(a,1,2)),flip(a)]. given #1312 (H,wt=15): 1362 x / (y \ R(y,x,z)) = R(x,T(y,x),z). [para(1361(a,1),933(a,1,2))]. given #1313 (H,wt=11): 1363 R(x,T(y,x),z) = R(x,y,z). [para(1362(a,1),933(a,1))]. given #1314 (H,wt=13): 1364 R(x,y / x,z) = R(x,x \ y,z). [para(82(a,1),1363(a,1,2)),flip(a)]. given #1315 (H,wt=11): 1365 R(x,x \ y,z) = R(x,y,z). [para(1364(a,1),1326(a,1))]. given #1316 (H,wt=11): 1366 R(x,x * y,z) = R(x,y,z). [para(13(a,1),1365(a,1,2)),flip(a)]. given #1317 (H,wt=13): 1368 R(x \ 1,y,z) = R(x,y,z) \ 1. [para(1365(a,1),603(a,1,1)),flip(a)]. given #1318 (H,wt=13): 1371 R(K(x,y),z,u) = K(R(x,z,u),y). [para(1365(a,1),1353(a,1,1)),flip(a)]. given #1319 (H,wt=14): 1367 R(x,y,z) \ (y * z) = (x \ y) * z. [para(1365(a,1),163(a,1,1))]. given #1320 (H,wt=14): 1374 (x \ 1) / (y / x) = R(y \ 1,x,x). [para(1368(a,2),1210(a,2))]. given #1321 (H,wt=14): 1378 R((x * y) \ 1,y,y) = (y \ 1) / x. [para(15(a,1),1374(a,1,2)),flip(a)]. given #1322 (H,wt=15): 1369 x * R(x \ 1,y,z) = R(x,y,z) \ x. [para(1365(a,1),604(a,1,1)),flip(a)]. given #1323 (H,wt=15): 1372 R(T(x,y),x * z,u) = T(R(x,z,u),y). [para(1366(a,1),42(a,2,1))]. given #1324 (H,wt=15): 1380 R(T(x,y),x * z,u) = R(T(x,y),z,u). [para(1372(a,2),42(a,2)),flip(a)]. given #1325 (H,wt=16): 1370 x / ((y \ z) * (z \ x)) = R(y,z,z \ x). [para(1365(a,1),459(a,1)),flip(a)]. given #1326 (H,wt=16): 1375 K(R(x,y,y),z) \ (K(x,z) / y) = y \ 1. [para(1371(a,1),1209(a,1,1))]. given #1327 (H,wt=16): 1383 K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1. [para(1375(a,1),1075(a,1)),flip(a)]. given #1328 (H,wt=17): 1373 x * (R(x,y,z) \ (x * y)) = R(x * y,x,z). [para(1366(a,1),938(a,1,2,1))]. given #1329 (H,wt=17): 1376 R(K(x,y) \ 1,z,u) = K(R(x,z,u),y) \ 1. [para(1371(a,1),1368(a,2,1))]. given #1330 (H,wt=15): 1385 R(K(x,y) \ 1,z,u) = K(y,R(x,z,u)). [para(1376(a,2),1070(a,1))]. given #1331 (H,wt=13): 1386 R(K(x,y),z,u) = K(x,R(y,z,u)). [para(1070(a,1),1385(a,1,1))]. given #1332 (H,wt=13): 1387 K(R(x,y,z),u) = K(x,R(u,y,z)). [para(1386(a,1),1371(a,1)),flip(a)]. given #1333 (H,wt=13): 1388 K(L(x,x,y),z) = K(x,R(z,y,x)). [para(1144(a,1),1387(a,1,1))]. given #1334 (H,wt=16): 1389 K((x \ (x / y)) \ 1,z) = K(y,R(z,x,y)). [para(1191(a,1),1388(a,1,1))]. given #1335 (H,wt=16): 1390 x * K(y,R(z,x,y)) = (x / y) * T(y,z). [para(1388(a,1),1313(a,1,2))]. given #1336 (H,wt=17): 1384 x * (x * (R(x,y,z) \ y)) = R(x * y,x,z). [para(569(a,1),1373(a,1,2))]. given #1337 (H,wt=13): 1391 R(x * y,x,z) = x * R(y,x,z). [para(938(a,1),1384(a,1,2)),flip(a)]. given #1338 (H,wt=18): 1377 R(x,y,z) * (x \ (x * z)) = y * ((y \ x) * z). [para(1367(a,1),940(a,2,2))]. given #1339 (H,wt=14): 1393 R(x,y,z) * z = y * ((y \ x) * z). [para(13(a,1),1377(a,1,2))]. given #1340 (H,wt=13): 1396 R(x,y,z) * z = x * L(z,x,y). [para(1393(a,2),1300(a,2)),flip(a)]. given #1341 (H,wt=13): 1397 L(x,y,z) = R(y,z,x) * (y \ x). [hyper(558,a,1396,a),flip(a)]. given #1342 (H,wt=13): 1399 L(x,y,z) = z * (R(z,y,x) \ x). [para(1397(a,2),940(a,1))]. given #1343 (H,wt=13): 1400 R(x,y,z) \ z = x \ L(z,y,x). [hyper(56,a,1399,a(flip)),flip(a)]. given #1344 (H,wt=13): 1401 R(x,y,z) = (x * z) / L(z,y,x). [para(1399(a,2),571(a,1,2)),flip(a)]. given #1345 (H,wt=13): 1403 R(x,y,z) * (x \ L(z,y,x)) = z. [para(1400(a,1),14(a,1,2))]. given #1346 (H,wt=13): 1404 R(x,y,z) * L(z,y,x) = x * z. [para(1401(a,2),16(a,1,1))]. given #1347 (H,wt=13): 1406 R(x,y,z) = (x / L(z,y,x)) * z. [para(1401(a,2),1255(a,1))]. given #1348 (H,wt=13): 1407 x * (R(x,y,z) \ L(z,x,y)) = z. [para(1403(a,1),940(a,1)),flip(a)]. given #1349 (H,wt=13): 1409 (L(x,y,z) / z) * R(z,y,x) = x. [hyper(297,a,1406,a(flip))]. given #1350 (H,wt=13): 1410 a(x / y,y,z) = x \ R(x,y,z). [para(1406(a,2),591(a,2,2))]. given #1351 (H,wt=13): 1411 (R(x,y,z) \ x) * L(z,x,y) = z. [para(1407(a,1),583(a,2))]. given #1352 (H,wt=13): 1414 a(x / y,y,z) = R(y,x,z) \ y. [para(1410(a,2),931(a,2)),flip(a)]. given #1353 (H,wt=13): 1415 R(x,y,z) \ x = L(z,x,y) \ z. [hyper(737,a,1411,a),flip(a)]. given #1354 (H,wt=10): 1417 T(x,R(y,z,x) \ y) = x. [para(1415(a,2),747(a,1,2))]. given #1355 (H,wt=10): 1419 T(x,a(y / z,z,x)) = x. [para(1414(a,2),1417(a,1,2))]. given #1356 (H,wt=8): 1420 T(x,a(y,z,x)) = x. [para(15(a,1),1419(a,1,2,1))]. given #1357 (H,wt=11): 1418 R(x,y,y) \ x = a(y,x,y). [para(1415(a,2),1262(a,1))]. given #1358 (H,wt=11): 1422 R(x,y,y) * a(y,x,y) = x. [para(1418(a,1),14(a,1,2))]. given #1359 (H,wt=13): 1416 a(x,y,z) = R(y,x * y,z) \ y. [para(15(a,1),1414(a,1,1))]. given #1360 (H,wt=11): 1423 a(x,y,z) = R(y,x,z) \ y. [para(1327(a,1),1416(a,2,1))]. given #1361 (H,wt=8): 1432 K(a(x,y,z),x) = 1. [para(1423(a,2),935(a,1,1))]. given #1362 (H,wt=11): 1425 R(x,y,z) = x / a(y,x,z). [para(1423(a,2),53(a,1,2)),flip(a)]. given #1363 (H,wt=11): 1426 a(x,y,z) * R(y,x,z) = y. [para(1423(a,2),573(a,1,1))]. given #1364 (H,wt=11): 1427 R(x,y,z) = a(y,x,z) \ x. [para(1423(a,2),574(a,1,1)),flip(a)]. given #1365 (H,wt=11): 1431 a(x,y,z) = x \ R(x,y,z). [para(1423(a,2),931(a,1))]. given #1366 (H,wt=9): 1444 L(x,y,a(y,z,u)) = x. [para(1431(a,2),544(a,1,3))]. given #1367 (H,wt=11): 1433 R(x,y,z) = x * a(x,y,z). [para(1423(a,2),932(a,1,2)),flip(a)]. given #1368 (H,wt=11): 1434 R(x,y,z) = a(x,y,z) * x. [para(1423(a,2),934(a,1,1)),flip(a)]. given #1369 (H,wt=11): 1437 a(x,y,z) * L(z,y,x) = z. [para(1423(a,2),1411(a,1,1))]. given #1370 (H,wt=11): 1438 a(x / y,y,z) = a(x,y,z). [para(1423(a,2),1414(a,2))]. given #1371 (H,wt=11): 1439 a(x * y,y,z) = a(x,y,z). [para(1423(a,2),1416(a,2)),flip(a)]. given #1372 (H,wt=11): 1440 T(a(x,y,z),x) = a(x,y,z). [hyper(37,a,1432,a)]. given #1373 (H,wt=11): 1442 a(x,y,z) = R(x,y,z) / x. [para(1431(a,2),479(a,2)),flip(a)]. given #1374 (H,wt=11): 1452 a(x,y \ 1,y) = a(y,x,y). [hyper(1129,a,1433,a),flip(a)]. given #1375 (H,wt=11): 1455 a(x,y,z) = z / L(z,y,x). [hyper(61,a,1437,a),flip(a)]. given #1376 (H,wt=9): 1465 L(x,a(y,z,u),u) = x. [para(1455(a,2),738(a,1,2))]. given #1377 (H,wt=11): 1463 L(x,y,z) * a(z,y,x) = x. [para(1455(a,2),732(a,1,2))]. given #1378 (H,wt=11): 1464 L(x,y,z) = x / a(z,y,x). [para(1455(a,2),734(a,1,2)),flip(a)]. given #1379 (H,wt=13): 1421 a(x,y,z) * z = z * a(x,y,z). [para(1420(a,1),80(a,1,2))]. given #1380 (H,wt=13): 1428 R(x,y,z) / x = 1 / a(y,x,z). [para(1423(a,2),575(a,1,2)),flip(a)]. given #1381 (H,wt=11): 1468 1 / a(x,y,z) = a(y,x,z). [para(1428(a,1),1442(a,2)),flip(a)]. given #1382 (H,wt=11): 1469 a(x,y,z) * a(y,x,z) = 1. [para(1468(a,1),16(a,1,1))]. given #1383 (H,wt=11): 1470 a(x,y,z) \ 1 = a(y,x,z). [para(1468(a,1),54(a,1,1))]. given #1384 (H,wt=13): 1435 a(x,y,z) = y * R(y \ 1,x,z). [para(1423(a,2),1369(a,2)),flip(a)]. given #1385 (H,wt=13): 1443 R(x,y,z) \ a(x,y,z) = x \ 1. [para(1431(a,2),486(a,1,2))]. given #1386 (H,wt=13): 1461 a(x \ 1,y,x \ 1) = a(x,y,x). [para(1452(a,1),1153(a,2))]. given #1387 (H,wt=13): 1466 a(1 / x,y,z) = z / L(z,x,y). [para(1290(a,1),1455(a,2,2))]. given #1388 (H,wt=11): 1474 a(1 / x,y,z) = a(y,x,z). [para(1466(a,2),1455(a,2)),flip(a)]. given #1389 (H,wt=11): 1475 a(x,y \ 1,z) = a(y,x,z). [para(53(a,1),1474(a,1,1)),flip(a)]. given #1390 (H,wt=11): 1476 a(x \ 1,y,z) = a(y,x,z). [para(208(a,1),1474(a,1,1))]. given #1391 (H,wt=13): 1471 a(x,y,z) * (a(y,x,z) * u) = u. [para(1468(a,1),263(a,1,1))]. given #1392 (H,wt=11): 1481 L(x,y,z) = a(y,z,x) * x. [hyper(17,a,1437,a,b,1471,a),flip(a)]. given #1393 (H,wt=11): 1483 a(x,y,z) = z \ L(z,x,y). [hyper(701,a,1481,a),flip(a)]. given #1394 (H,wt=11): 1484 a(x,y,z) = L(z,x,y) / z. [hyper(61,a,1481,a(flip)),flip(a)]. given #1395 (H,wt=11): 1485 L(x,y,z) = x * a(y,z,x). [para(1481(a,2),1421(a,1))]. given #1396 (H,wt=13): 1472 a(x,y,z) \ u = a(y,x,z) * u. [para(1468(a,1),269(a,1,1)),flip(a)]. given #1397 (H,wt=13): 1477 a((x \ y) / x,x,z) = a(y,x,z). [para(1474(a,1),703(a,2))]. given #1398 (H,wt=11): 1500 a(x \ y,x,z) = a(y,x,z). [para(1477(a,1),1438(a,1)),flip(a)]. given #1399 (H,wt=11): 1501 a(x * y,x,z) = a(y,x,z). [para(13(a,1),1500(a,1,1)),flip(a)]. given #1400 (H,wt=14): 1394 R(x,y,z) = (y * ((y \ x) * z)) / z. [hyper(61,a,1393,a),flip(a)]. given #1401 (H,wt=14): 1395 R(x * y,x,z) * z = x * (y * z). [para(13(a,1),1393(a,2,2,1))]. given #1402 (H,wt=14): 1456 a(x,y,z) * u != z | L(z,y,x) = u. [para(1437(a,1),19(a,1)),flip(a)]. given #1403 (H,wt=15): 1405 R(x,R(y,z,u),y) = R(x,y,R(y,z,u)). [para(1401(a,2),1164(a,1)),flip(a)]. given #1404 (H,wt=15): 1413 a(x,y,z) = (x * y) \ R(x * y,y,z). [para(15(a,1),1410(a,1,1))]. given #1405 (H,wt=14): 1505 (x * y) \ (x / (y \ 1)) = a(x,y,y). [para(1205(a,1),1413(a,2,2)),flip(a)]. given #1406 (H,wt=15): 1429 R(x,y,z) \ (x * u) = a(y,x,z) * u. [para(1423(a,2),580(a,2,1))]. given #1407 (H,wt=15): 1430 x * (R(x,y,z) \ u) = a(y,x,z) * u. [para(1423(a,2),583(a,1,1)),flip(a)]. given #1408 (H,wt=15): 1445 x * (a(x,y,z) * u) = R(x,y,z) * u. [para(1431(a,2),547(a,1,2,1))]. given #1409 (H,wt=15): 1446 R(x,y,z) * (x \ u) = a(x,y,z) * u. [para(1431(a,2),557(a,1,1)),flip(a)]. given #1410 (H,wt=15): 1447 x * (R(x,y,z) \ u) = a(x,y,z) \ u. [para(1431(a,2),565(a,1,1)),flip(a)]. given #1411 (H,wt=15): 1479 a(x,y \ 1,y \ 1) = a(y,x \ 1,y). [para(1475(a,1),1461(a,1))]. given #1412 (H,wt=13): 1514 a(x,y \ 1,y \ 1) = a(x,y,y). [para(1479(a,2),1475(a,1))]. given #1413 (H,wt=11): 1515 a(x,y,x \ 1) = a(y,x,x). [para(1514(a,1),1475(a,1)),flip(a)]. given #1414 (H,wt=15): 1486 x * L(x \ 1,y,z) = a(y,z,x \ 1). [para(1483(a,2),256(a,1)),flip(a)]. given #1415 (H,wt=15): 1491 x \ (L(x,y,z) * u) = a(y,z,x) * u. [para(1483(a,2),725(a,2,1))]. given #1416 (H,wt=15): 1492 x * (L(x,y,z) \ u) = a(y,z,x) \ u. [para(1483(a,2),745(a,1,1)),flip(a)]. given #1417 (H,wt=13): 1518 R(x,y,z) = z * (L(z,y,x) \ x). [para(1492(a,2),1427(a,2))]. given #1418 (H,wt=13): 1520 L(x,y,z) = (x * z) / R(z,y,x). [para(1518(a,2),859(a,1,2)),flip(a)]. given #1419 (H,wt=13): 1521 L(x,y,z) * R(z,y,x) = x * z. [para(1520(a,2),16(a,1,1))]. given #1420 (H,wt=15): 1507 a(x,y,z) * (R(y,x,z) * u) = y * u. [para(13(a,1),1430(a,1,2)),flip(a)]. given #1421 (H,wt=15): 1510 (R(x,y,z) * u) / (a(x,y,z) * u) = x. [hyper(61,a,1445,a)]. given #1422 (H,wt=15): 1511 a(x,y,z) * (x * u) = R(x,y,z) * u. [hyper(17,a,551,a(flip),b,1445,a)]. given #1423 (H,wt=15): 1517 x * (a(y,z,x) * u) = L(x,y,z) * u. [para(1491(a,1),14(a,1,2))]. given #1424 (H,wt=13): 1525 L(x,y,z) * y = x * R(y,z,x). [para(1434(a,2),1517(a,1,2)),flip(a)]. given #1425 (H,wt=15): 1519 x * (L(x,y,z) \ u) = a(z,y,x) * u. [para(1492(a,2),1472(a,1))]. given #1426 (H,wt=15): 1529 (x * y) / (a(z,u,x) * y) = L(x,u,z). [para(1519(a,1),859(a,1,2))]. given #1427 (H,wt=16): 1412 (x / y) * R(y,z,L(x,y,z)) = L(x,y,z). [para(341(a,1),1409(a,1,1,1))]. given #1428 (H,wt=16): 1508 a(x,y,z) * ((y * x) * z) = y * (x * z). [para(92(a,1),1430(a,1,2)),flip(a)]. given #1429 (H,wt=16): 1513 a(x,y,z) \ ((x * y) * z) = x * (y * z). [para(92(a,1),1447(a,1,2)),flip(a)]. given #1430 (H,wt=16): 1523 x * R(y,z,L(x,y,z)) = L(x,y,z) * y. [para(341(a,1),1521(a,1,1))]. given #1431 (H,wt=12): 1532 R(x,y,L(z,x,y)) = R(x,y,z). [hyper(17,a,1525,a(flip),b,1523,a)]. given #1432 (H,wt=13): 1534 L(x,y,z) = (x / y) * R(y,z,x). [para(1532(a,1),1412(a,1,2)),flip(a)]. given #1433 (H,wt=16): 1527 L(x,y,z) * y != x * u | R(y,z,x) = u. [para(1525(a,2),19(a,1))]. given #1434 (H,wt=16): 1531 T(x * (y * z),a(x,y,z)) = x * (y * z). [para(1513(a,1),420(a,1)),flip(a)]. given #1435 (H,wt=12): 1537 K(x * (y * z),a(x,y,z)) = 1. [hyper(36,a,1531,a)]. given #1436 (H,wt=15): 1538 K(x * y,a(x / z,z,L(y,x,z))) = 1. [para(169(a,1),1537(a,1,1))]. given #1437 (H,wt=13): 1539 K(x * y,a(x,z,L(y,x,z))) = 1. [para(1438(a,1),1538(a,1,2))]. given #1438 (H,wt=16): 1533 R(x * y,y,L(z,x,y)) = R(x * y,y,z). [para(438(a,1),1532(a,1,3))]. given #1439 (H,wt=17): 1436 K(x,R(y,z,u)) \ K(x,y) = a(z,K(x,y),u). [para(1386(a,1),1423(a,2,1)),flip(a)]. given #1440 (H,wt=17): 1493 K(x,y) * L(K(y,x),z,u) = a(z,u,K(y,x)). [para(1483(a,2),1075(a,1)),flip(a)]. given #1441 (H,wt=17): 1509 a(x,y,z) * (y * u) = y * (a(x,y,z) * u). [para(1429(a,1),1430(a,1,2)),flip(a)]. given #1442 (H,wt=17): 1526 L(x,y,z) * (R(z,y,x) * u) = x * (z * u). [para(1507(a,1),1517(a,1,2)),flip(a)]. given #1443 (H,wt=17): 1530 L(x,y,z) \ (u * x) = a(z,y,x) * T(u,x). [para(1519(a,1),861(a,1)),flip(a)]. given #1444 (H,wt=17): 1541 K(R(x,y,z),u) * K(u,x) = a(y,K(u,x),z). [para(1436(a,1),1075(a,1)),flip(a)]. given #1445 (H,wt=17): 1543 K(x,R(y,z,u)) * K(y,x) = a(z,K(y,x),u). [para(1387(a,1),1541(a,1,1))]. given #1446 (H,wt=18): 1392 R(x * (x \ y),x,z) = ((y * z) / (x * z)) * x. [para(1391(a,2),532(a,2)),flip(a)]. given #1447 (H,wt=14): 1544 R(x,y,z) = ((x * z) / (y * z)) * y. [para(14(a,1),1392(a,1,1))]. given #1448 (H,wt=14): 1545 R(x,y,z) / y = (x * z) / (y * z). [hyper(61,a,1544,a(flip))]. given #1449 (H,wt=14): 1546 R(x / y,z,y) = (x / (z * y)) * z. [para(16(a,1),1544(a,2,1,1))]. given #1450 (H,wt=16): 1547 R(K(x,y),z,x) / z = T(x,y) / (z * x). [para(1043(a,2),1545(a,2,1))]. given #1451 (H,wt=16): 1549 K(x,R(y,z,x)) / z = T(x,y) / (z * x). [para(1386(a,1),1547(a,1,1))]. given #1452 (H,wt=18): 1398 L(x,y,z) \ (R(y,z,x) * x) = T(y,L(x,y,z)). [para(1396(a,2),32(a,2,2)),flip(a)]. given #1453 (H,wt=18): 1441 x \ ((x / y) * R(y,z,u)) = L(a(y,z,u),y,x). [para(1431(a,2),298(a,1,1)),flip(a)]. given #1454 (H,wt=18): 1480 a(x,y,z) * (u * a(y,x,z)) = T(u,a(y,x,z)). [hyper(98,a,1471,a),flip(a)]. given #1455 (H,wt=18): 1488 (x \ y) \ (z \ ((z / x) * y)) = a(x,z,x \ y). [para(298(a,1),1483(a,2,2)),flip(a)]. given #1456 (H,wt=18): 1489 x * L(a(y,z,u),u,x) = (x / u) * L(u,y,z). [para(1483(a,2),300(a,1,2,1))]. given #1457 (H,wt=18): 1506 (x * (y \ 1)) \ (x / y) = a(x,y \ 1,y \ 1). [para(210(a,1),1505(a,1,2,2))]. given #1458 (H,wt=14): 1553 (x * (y \ 1)) \ (x / y) = a(x,y,y). [para(1506(a,2),1514(a,1))]. given #1459 (H,wt=18): 1540 (x * y) \ R(x * y,y,z) = a(x,y,L(z,x,y)). [para(1533(a,1),1413(a,2,2)),flip(a)]. given #1460 (H,wt=12): 1554 a(x,y,L(z,x,y)) = a(x,y,z). [para(1540(a,1),1413(a,2)),flip(a)]. given #1461 (H,wt=10): 1555 K(x * y,a(x,z,y)) = 1. [para(1554(a,1),1539(a,1,2))]. given #1462 (H,wt=12): 1557 K((x * y) * z,a(y,x,z)) = 1. [para(1501(a,1),1555(a,1,2))]. given #1463 (H,wt=15): 1556 T(a(x,y,z),x * z) * 1 = a(x,y,z). [para(1555(a,1),1055(a,1,2))]. given #1464 (H,wt=13): 1559 T(a(x,y,z),x * z) = a(x,y,z). [hyper(59,a,1556,a)]. given #1465 (H,wt=17): 1558 T(a(x,y,z),(y * x) * z) * 1 = a(x,y,z). [para(1557(a,1),1055(a,1,2))]. given #1466 (H,wt=15): 1560 T(a(x,y,z),(y * x) * z) = a(x,y,z). [hyper(59,a,1558,a)]. given #1467 (H,wt=18): 1550 a(x,y,z) * T(R(y,x,z),z) = T(y,L(z,y,x)). [para(1398(a,1),1530(a,1)),flip(a)]. given #1468 (H,wt=18): 1562 a(x,y,z) * R(T(y,z),x,z) = T(y,L(z,y,x)). [para(42(a,2),1550(a,1,2))]. given #1469 (H,wt=19): 1448 (x * y) \ (R(x,z,u) * y) = T(a(x,z,u),x * y). [para(1431(a,2),564(a,1,1)),flip(a)]. given #1470 (H,wt=19): 1467 (a(x,y,z) * z) * T(u,z) = a(x,y,z) * (u * z). [para(1465(a,1),358(a,1,2,1)),flip(a)]. given #1471 (H,wt=17): 1563 a(x,y,z) * (u * z) = L(z,x,y) * T(u,z). [para(1481(a,2),1467(a,1,1)),flip(a)]. given #1472 (H,wt=19): 1499 R(a(x,y,z) * 1,u,w) = R(a(y,x,z),u,w) \ 1. [para(1472(a,1),1368(a,1,1))]. given #1473 (H,wt=19): 1504 a(R(x,y,z) / u,u,x) = R(u,x,R(x,y,z)) \ u. [para(1405(a,1),1414(a,2,1))]. given #1474 (H,wt=17): 1564 a(R(x,y,z) / u,u,x) = a(x,u,R(x,y,z)). [para(1504(a,2),1423(a,2)),flip(a)]. given #1475 (H,wt=15): 1565 a(R(x,y,z),u,x) = a(x,u,R(x,y,z)). [para(1564(a,1),1438(a,1)),flip(a)]. given #1476 (H,wt=19): 1516 x \ (y * L(y \ x,z,u)) = a(z,u,(x \ y) \ 1). [para(1486(a,1),1343(a,1)),flip(a)]. given #1477 (H,wt=20): 1382 T(x,y) / ((z \ x) * K(x,y)) = R(z,x,x \ T(x,y)). [para(1038(a,2),1370(a,1,2,2))]. given #1478 (H,wt=18): 1566 T(x,y) / ((z \ x) * K(x,y)) = R(z,x,K(x,y)). [para(1038(a,2),1382(a,2,3))]. given #1479 (H,wt=20): 1459 T(a(x,y,z),u) * L(z,y,x) = K(a(x,y,z),u) * z. [para(1437(a,1),1105(a,1,2)),flip(a)]. given #1480 (H,wt=20): 1473 T(a(x,y,z),u) * a(y,x,z) = K(a(x,y,z),u) * 1. [para(1469(a,1),1105(a,1,2)),flip(a)]. given #1481 (H,wt=18): 1567 T(a(x,y,z),u) * a(y,x,z) = K(a(x,y,z),u). [hyper(59,a,1473,a(flip)),flip(a)]. given #1482 (H,wt=20): 1495 x \ (y * L(y \ x,z,u)) = L(a(z,u,y \ x),x,y). [para(1483(a,2),1296(a,1,1)),flip(a)]. given #1483 (H,wt=18): 1568 L(a(x,y,z \ u),u,z) = a(x,y,(u \ z) \ 1). [para(1495(a,1),1516(a,1))]. given #1484 (H,wt=20): 1528 a(x,y,z) * (u * L(z,y,x)) = z * T(u,L(z,y,x)). [para(32(a,2),1519(a,1,2)),flip(a)]. given #1485 (H,wt=20): 1536 L(x * R(x \ 1,y,z),z,x) = z \ L(z,x \ 1,y). [para(1534(a,2),1301(a,2,2))]. given #1486 (H,wt=16): 1570 L(a(x,y,z),z,y) = z \ L(z,y \ 1,x). [para(1435(a,2),1536(a,1,1))]. given #1487 (H,wt=14): 1571 L(a(x,y,z),z,y) = z \ L(z,x,y). [para(1294(a,1),1570(a,2,2))]. given #1488 (H,wt=12): 1572 L(a(x,y,z),z,y) = a(x,y,z). [para(1571(a,2),1483(a,2)),flip(a)]. given #1489 (H,wt=20): 1548 ((x / y) * y) / L(y,z,x / y) = (x / (z * y)) * z. [para(1546(a,1),1401(a,1)),flip(a)]. given #1490 (H,wt=16): 1573 x / L(y,z,x / y) = (x / (z * y)) * z. [para(16(a,1),1548(a,1,1))]. given #1491 (H,wt=21): 1381 R(T(x * K(y,x),y),z,u) = R(x,(x * K(y,x)) * z,u). [para(1066(a,1),1380(a,1,1)),flip(a)]. given #1492 (H,wt=21): 1402 T(x,y) * (R(T(x,y),z,u) \ u) = L(u,z * x,T(x,y)). [para(1330(a,1),1399(a,2,2,1)),flip(a)]. given #1493 (H,wt=15): 1575 L(x,y * z,T(z,u)) = L(x,y,T(z,u)). [para(1402(a,1),1399(a,2)),flip(a)]. given #1494 (H,wt=21): 1449 (x \ (x / y)) * R(L(y,y,x),z,u) = a(L(y,y,x),z,u). [para(1431(a,2),1192(a,1)),flip(a)]. given #1495 (H,wt=21): 1453 R(x,y,a(y,z,u)) * R(y,z,u) = (x * y) * a(y,z,u). [para(1433(a,2),75(a,1,2))]. given #1496 (H,wt=21): 1454 x \ ((x / a(y,z,u)) * R(y,z,u)) = L(y,a(y,z,u),x). [para(1434(a,2),340(a,2,2,2)),flip(a)]. given #1497 (H,wt=21): 1535 (x * y) \ (y * R(T(x,y),z,y)) = y \ L(y,T(x,y),z). [para(1534(a,2),370(a,1,2)),flip(a)]. given #1498 (H,wt=19): 1577 (x * y) \ (y * R(T(x,y),z,y)) = a(T(x,y),z,y). [para(1535(a,2),1483(a,2)),flip(a)]. given #1499 (H,wt=17): 1578 (x * y) \ (R(x,z,y) * y) = a(T(x,y),z,y). [para(104(a,1),1577(a,1,2))]. given #1500 (H,wt=15): 1579 T(a(x,y,z),x * z) = a(T(x,z),y,z). [para(1578(a,1),1448(a,1)),flip(a)]. given #1501 (H,wt=11): 1580 a(T(x,y),z,y) = a(x,z,y). [para(1579(a,1),1559(a,1))]. given #1502 (H,wt=13): 1581 a(x,T(y,z),z) = a(y,x \ 1,z). [para(1580(a,1),1475(a,1)),flip(a)]. given #1503 (H,wt=11): 1583 a(x,T(y,z),z) = a(x,y,z). [para(1581(a,2),1475(a,1))]. given #1504 (H,wt=13): 1582 L(x,T(y,x),z) = x * a(y,z,x). [para(1580(a,1),1485(a,2,2))]. given #1505 (H,wt=11): 1587 L(x,T(y,x),z) = L(x,y,z). [para(1582(a,2),1485(a,2)),flip(a)]. given #1506 (H,wt=15): 1584 a(x,y,z) * R(T(y,z),x,z) = T(y,z). [para(1583(a,1),1426(a,1,1))]. given #1507 (H,wt=10): 1589 T(x,L(y,x,z)) = T(x,y). [para(1584(a,1),1562(a,1)),flip(a)]. given #1508 (H,wt=12): 1591 K(L(x,y,z),y) = T(y,x) \ y. [para(1589(a,1),1054(a,2,1))]. given #1509 (H,wt=10): 1593 K(L(x,y,z),y) = K(x,y). [para(1591(a,2),1054(a,2)),flip(a)]. given #1510 (H,wt=18): 1588 L(x,T(y / x,x),z) = z \ ((z / (y / x)) * y). [para(1587(a,2),354(a,1))]. given #1511 (H,wt=16): 1594 L(x,x \ y,z) = z \ ((z / (y / x)) * y). [para(82(a,1),1588(a,1,2))]. given #1512 (H,wt=21): 1551 T(x,a(y,z,u)) != a(z,y,u) * w | x * a(y,z,u) = w. [para(1480(a,1),19(a,1))]. given #1513 (H,wt=21): 1561 ((x * y) * z) \ (a(y,x,z) * ((x * y) * z)) = a(y,x,z). [para(1560(a,1),32(a,1)),flip(a)]. given #1514 (H,wt=16): 1595 a(x,y,z) = ((y * x) * z) \ (y * (x * z)). [para(1508(a,1),1561(a,1,2)),flip(a)]. given #1515 (H,wt=18): 1596 (x * y) \ (z * ((z \ x) * y)) = a(z \ x,z,y). [para(14(a,1),1595(a,2,1,1)),flip(a)]. given #1516 (H,wt=16): 1597 a(x,y,z) = (x * z) \ (y * ((y \ x) * z)). [para(1596(a,2),1500(a,1)),flip(a)]. given #1517 (H,wt=21): 1574 R(T(x * K(y,x),y),z,u) = R(x,x * (K(y,x) * z),u). [para(992(a,1),1381(a,2,2))]. given #1518 (H,wt=19): 1598 R(T(x * K(y,x),y),z,u) = R(x,K(y,x) * z,u). [para(1574(a,2),1366(a,1))]. given #1519 (H,wt=13): 1599 R(x,K(y,x) * z,u) = R(x,z,u). [para(1066(a,1),1598(a,1,1)),flip(a)]. given #1520 (H,wt=13): 1600 R(x,K(x,y) * z,u) = R(x,z,u). [para(1074(a,1),1599(a,1,2)),flip(a)]. given #1521 (H,wt=17): 1601 L(x,y,K(z,y) * u) = R(y,u,x) * (y \ x). [para(1599(a,1),1397(a,2,1))]. given #1522 (H,wt=13): 1603 L(x,y,K(z,y) * u) = L(x,y,u). [para(1601(a,2),1397(a,2)),flip(a)]. given #1523 (H,wt=13): 1604 L(x,y,K(y,z) * u) = L(x,y,u). [para(1074(a,1),1603(a,1,3)),flip(a)]. given #1524 (H,wt=15): 1605 L(x,y,K(z,y) / u) = L(x,y,u \ 1). [para(1383(a,1),1604(a,1,3)),flip(a)]. given #1525 (H,wt=13): 1606 L(x,y,K(z,y) / u) = L(x,u,y). [para(1605(a,2),1289(a,1))]. given #1526 (H,wt=17): 1602 L(x,K(y,z) * u,y) = y * (R(y,u,x) \ x). [para(1600(a,1),1399(a,2,2,1))]. given #1527 (H,wt=13): 1608 L(x,K(y,z) * u,y) = L(x,u,y). [para(1602(a,2),1399(a,2)),flip(a)]. given #1528 (H,wt=21): 1576 (x \ (x / y)) * L(R(y,z,u),y,x) = a(L(y,y,x),z,u). [para(44(a,1),1449(a,1,2))]. given #1529 (H,wt=18): 1609 x \ ((x / y) * R(y,z,u)) = a(L(y,y,x),z,u). [para(1576(a,1),1305(a,1)),flip(a)]. given #1530 (H,wt=15): 1610 a(L(x,x,y),z,u) = L(a(x,z,u),x,y). [para(1609(a,1),1441(a,1))]. given #1531 (H,wt=21): 1607 L(x,y,K(z,y) * (u \ K(z,y))) = L(x,K(z,y) \ u,y). [para(314(a,1),1606(a,1,3))]. given #1532 (H,wt=17): 1612 L(x,K(y,z) \ u,z) = L(x,z,u \ K(y,z)). [para(1607(a,1),1603(a,1))]. given #1533 (H,wt=17): 1613 L(x,K(y,z) * u,y) = L(x,y,u \ K(z,y)). [para(1075(a,1),1612(a,1,2))]. given #1534 (H,wt=13): 1615 L(x,y,z \ K(u,y)) = L(x,z,y). [para(1613(a,1),1608(a,1))]. given #1535 (H,wt=15): 1616 a(x,y \ K(z,x),u) = u \ L(u,y,x). [para(1615(a,1),1483(a,2,2))]. given #1536 (H,wt=13): 1618 a(x,y \ K(z,x),u) = a(y,x,u). [para(1616(a,2),1483(a,2)),flip(a)]. given #1537 (H,wt=22): 1379 R((x * (y \ 1)) \ 1,y \ 1,y \ 1) = T(y,y \ 1) / x. [para(81(a,2),1378(a,2,1))]. given #1538 (H,wt=18): 1619 R((x * (y \ 1)) \ 1,y,y) = T(y,y \ 1) / x. [para(1379(a,1),1216(a,1)),flip(a)]. given #1539 (H,wt=14): 1620 R((x * (y \ 1)) \ 1,y,y) = y / x. [para(219(a,1),1619(a,2,1))]. given #1540 (H,wt=22): 1450 (x * y) \ (y * R(T(x,y),z,u)) = L(a(T(x,y),z,u),x,y). [para(1431(a,2),1283(a,1,1)),flip(a)]. given #1541 (H,wt=20): 1621 (x * y) \ (R(x,z,u) * y) = L(a(T(x,y),z,u),x,y). [para(104(a,1),1450(a,1,2))]. given #1542 (H,wt=18): 1622 L(a(T(x,y),z,u),x,y) = T(a(x,z,u),x * y). [para(1621(a,1),1448(a,1))]. given #1543 (H,wt=22): 1451 (a(x,y,z) * x) \ (u * a(x,y,z)) = x \ T(u,a(x,y,z)). [para(1444(a,1),145(a,1)),flip(a)]. given #1544 (H,wt=20): 1623 R(x,y,z) \ (u * a(x,y,z)) = x \ T(u,a(x,y,z)). [para(1434(a,2),1451(a,1,1))]. given #1545 (H,wt=23): 1408 (L(x,y,z) * R(z,y,x)) \ (z * x) = K(R(z,y,x),L(x,y,z)). [para(1404(a,1),26(a,2,2)),flip(a)]. given #1546 (H,wt=23): 1490 ((L(x,y,z) / x) * L(x,y,z)) \ L(x,y,z) = a(y,z,x) \ 1. [para(1483(a,2),637(a,2,1))]. given #1547 (H,wt=21): 1625 (a(x,y,z) * L(z,x,y)) \ L(z,x,y) = a(x,y,z) \ 1. [para(1484(a,2),1490(a,1,1,1))]. given #1548 (H,wt=19): 1626 (a(x,y,z) * L(z,x,y)) \ L(z,x,y) = a(y,x,z). [para(1625(a,2),1470(a,1))]. given #1549 (H,wt=23): 1503 R(x,y,R(y,z,u)) * (y * R(y,z,u)) = (x * R(y,z,u)) * y. [para(1405(a,1),204(a,1,1))]. given #1550 (H,wt=17): 1627 (x * R(y,z,u)) * y = (x * y) * R(y,z,u). [para(1503(a,1),75(a,1))]. given #1551 (H,wt=17): 1628 ((x / R(y,z,u)) * y) * R(y,z,u) = x * y. [para(16(a,1),1627(a,1,1)),flip(a)]. given #1552 (H,wt=23): 1552 L(a(x,y,x \ z),x \ z,y) = (y * (x \ z)) \ ((y / x) * z). [para(1488(a,1),141(a,1,1))]. given #1553 (H,wt=18): 1630 (x * (y \ z)) \ ((x / y) * z) = a(y,x,y \ z). [para(1552(a,1),1572(a,1))]. given #1554 (H,wt=23): 1611 a(L(T(x,y),T(x,y),T(y,x)),z,u) = L(a(T(x,y),z,u),x,y). [para(1610(a,2),899(a,1))]. given #1555 (H,wt=18): 1632 L(a(T(x,y),z,u),x,y) = a(T(x,x \ y),z,u). [para(1102(a,1),1611(a,1,1)),flip(a)]. given #1556 (H,wt=17): 1633 a(T(x,x \ y),z,u) = T(a(x,z,u),x * y). [para(1632(a,1),1622(a,1))]. given #1557 (H,wt=19): 1634 a(T(x,x \ T(y,x)),z,u) = T(a(x,z,u),y * x). [para(80(a,1),1633(a,2,2))]. given #1558 (H,wt=17): 1635 a(T(x,x \ y),z,u) = T(a(x,z,u),y * x). [para(1166(a,1),1634(a,1,1))]. given #1559 (H,wt=23): 1624 (L(x,y,z) * R(z,y,x)) \ (z * x) = K(z,R(L(x,y,z),y,x)). [para(1408(a,2),1387(a,1))]. given #1560 (H,wt=23): 1637 (L(x,y,z) * R(z,y,x)) \ (z * x) = K(z,L(R(x,y,x),y,z)). [para(44(a,1),1624(a,2,2))]. given #1561 (H,wt=23): 1638 (L(x,y,z) * R(z,y,x)) \ (z * x) = K(z,L(L(x,x,y),y,z)). [para(1144(a,1),1637(a,2,2,1))]. given #1562 (H,wt=17): 1639 K(x,L(L(y,y,z),z,x)) = (y * x) \ (x * y). [para(1521(a,1),1638(a,1,1)),flip(a)]. given #1563 (H,wt=13): 1640 K(x,L(L(y,y,z),z,x)) = K(x,y). [para(1639(a,2),26(a,2)),flip(a)]. given #1564 (H,wt=15): 1642 T(x,L(L(y,y,z),z,x)) = x * K(x,y). [para(1640(a,1),1035(a,2,2))]. given #1565 (H,wt=13): 1644 T(x,L(L(y,y,z),z,x)) = T(x,y). [para(1642(a,2),1035(a,2)),flip(a)]. given #1566 (H,wt=15): 1643 K(L(L(x,x,y),y,z),z) = K(z,x) \ 1. [para(1640(a,1),1070(a,1,1)),flip(a)]. given #1567 (H,wt=13): 1646 K(L(L(x,x,y),y,z),z) = K(x,z). [para(1643(a,2),1070(a,1))]. given #1568 (H,wt=15): 1645 T(x,L(L(y,y,z \ 1),x,z)) = T(x,y). [para(1294(a,1),1644(a,1,2))]. given #1569 (H,wt=13): 1648 T(x,L(L(y,z,y),x,z)) = T(x,y). [para(1289(a,1),1645(a,1,2,1))]. given #1570 (H,wt=10): 1649 T(x,L(y,z,y)) = T(x,y). [para(1648(a,1),1589(a,1)),flip(a)]. given #1571 (H,wt=15): 1647 K(L(L(x,x,y \ 1),z,y),z) = K(x,z). [para(1294(a,1),1646(a,1,1))]. given #1572 (H,wt=13): 1653 K(L(L(x,y,x),z,y),z) = K(x,z). [para(1289(a,1),1647(a,1,1,1))]. given #1573 (H,wt=10): 1655 K(L(x,y,x),z) = K(x,z). [para(1653(a,1),1593(a,1)),flip(a)]. given #1574 (H,wt=13): 1654 K(L(x,y,z),y) = K(L(x,x,z),y). [para(1246(a,1),1653(a,1,1,1))]. given #1575 (H,wt=13): 1656 K(T(x,x * y),z) = K(T(x,y),z). [para(902(a,1),1655(a,1,1))]. given #1576 (H,wt=13): 1657 (x \ y) * K(y,z) = x \ T(y,z). [para(1655(a,1),1317(a,1,2))]. given #1577 (H,wt=13): 1659 K(L(x,y,z),y) = K(x,R(y,z,x)). [para(1654(a,2),1388(a,1))]. given #1578 (H,wt=10): 1665 K(x,R(y,z,x)) = K(x,y). [para(1659(a,1),1593(a,1))]. given #1579 (H,wt=13): 1660 K(T(x,x \ y),z) = K(T(x,y),z). [para(14(a,1),1656(a,1,1,2)),flip(a)]. given #1580 (H,wt=13): 1666 K((x \ (x / y)) \ 1,z) = K(y,z). [para(1665(a,1),1389(a,2))]. given #1581 (H,wt=13): 1667 (x / y) * T(y,z) = x * K(y,z). [para(1665(a,1),1390(a,1,2)),flip(a)]. given #1582 (H,wt=13): 1668 T(x,y) / (z * x) = K(x,y) / z. [para(1665(a,1),1549(a,1,1)),flip(a)]. given #1583 (H,wt=13): 1670 K(T(x,x \ y),z) = T(K(x,z),y). [para(1660(a,1),1225(a,1))]. given #1584 (H,wt=11): 1677 K(T(x,y),z) = T(K(x,z),y). [para(1670(a,1),1660(a,1)),flip(a)]. given #1585 (H,wt=13): 1671 (x * y) * K(y,z) = x * T(y,z). [para(1666(a,1),1319(a,1,2))]. given #1586 (H,wt=13): 1678 1 / T(K(x,y),z) = K(y,T(x,z)). [para(1677(a,1),1072(a,1,2))]. given #1587 (H,wt=15): 1650 L(x,y,x) * T(z,x) = z * L(x,y,x). [para(1649(a,1),80(a,1,2))]. given #1588 (H,wt=15): 1681 a(x,y,y) * (z * y) = z * L(y,x,y). [para(1650(a,1),1563(a,2))]. given #1589 (H,wt=15): 1682 ((a(x,y,y) * z) / L(y,x,y)) * y = z. [hyper(17,a,16,a(flip),b,1681,a)]. given #1590 (H,wt=16): 1663 T(x,y) / (z \ T(x,y)) = R(z,x,K(x,y)). [para(1657(a,1),1566(a,1,2))]. given #1591 (H,wt=8): 1684 R(x,y,K(y,z)) = x. [para(1663(a,1),53(a,1))]. given #1592 (H,wt=12): 1685 R(x,y,K(x,z)) = (x * y) / y. [para(1684(a,1),939(a,1,2)),flip(a)]. given #1593 (H,wt=8): 1686 R(x,y,K(x,z)) = x. [para(1685(a,2),15(a,1))]. given #1594 (H,wt=17): 1687 x \ ((y * x) * K(x,z)) = T(y,x) * K(x,z). [para(1686(a,1),164(a,1,1))]. given #1595 (H,wt=15): 1688 x \ (y * T(x,z)) = T(y,x) * K(x,z). [para(1671(a,1),1687(a,1,2))]. given #1596 (H,wt=20): 1675 x / ((x / K(y,z)) * (K(y,z) / x)) = R(x,K(y,z),y). [para(1668(a,1),1328(a,1,2,2))]. given #1597 (H,wt=10): 1689 R(x,K(y,z),y) = x / 1. [para(279(a,1),1675(a,1,2)),flip(a)]. given #1598 (H,wt=8): 1690 R(x,K(y,z),y) = x. [para(1689(a,2),52(a,1))]. given #1599 (H,wt=12): 1694 L(x,K(x,y),z) = (x * z) / z. [para(1690(a,1),1520(a,2,2))]. given #1600 (H,wt=8): 1695 L(x,K(x,y),z) = x. [para(1694(a,2),15(a,1))]. given #1601 (H,wt=8): 1696 L(x,y,K(x,z)) = x. [para(1695(a,1),341(a,1,1))]. given #1602 (H,wt=10): 1697 L(x,y,K(x,z) \ y) = x. [para(1695(a,1),439(a,2))]. given #1603 (H,wt=10): 1699 L(x,y,K(z,x) * y) = x. [para(965(a,1),1697(a,1,3))]. given #1604 (H,wt=8): 1700 L(x,y,K(z,x)) = x. [para(1699(a,1),424(a,1)),flip(a)]. given #1605 (H,wt=13): 1692 (x * K(y,z)) * y = x * T(y,z). [para(1690(a,1),1059(a,1,1)),flip(a)]. given #1606 (H,wt=13): 1693 (x * y) / T(y,z) = x / K(y,z). [para(1690(a,1),1060(a,1)),flip(a)]. given #1607 (H,wt=15): 1698 (x \ K(y,z)) \ (x \ (K(y,z) * y)) = y. [para(1695(a,1),522(a,2))]. given #1608 (H,wt=13): 1702 (x \ K(y,z)) \ (x \ T(y,z)) = y. [para(1043(a,2),1698(a,1,2,2))]. given #1609 (H,wt=15): 1701 x \ (y * T(x,z)) = T(y * K(x,z),x). [para(1692(a,1),32(a,2,2)),flip(a)]. given #1610 (H,wt=15): 1703 T(x * K(y,z),y) = T(x,y) * K(y,z). [para(1701(a,1),1688(a,1))]. given #1611 (H,wt=22): 1662 x \ ((x / (y \ z)) * (y \ T(z,u))) = L(K(z,u),y \ z,x). [para(1657(a,1),340(a,2,2,2)),flip(a)]. given #1612 (H,wt=22): 1679 x \ ((x / (y * z)) * (y * T(z,u))) = L(K(z,u),y * z,x). [para(1671(a,1),340(a,2,2,2)),flip(a)]. given #1613 (H,wt=22): 1704 x \ (y * (((y \ x) / z) * T(z,u))) = L(K(z,u),y \ z,x). [para(924(a,1),1662(a,1,2))]. given #1614 (H,wt=20): 1705 L(K(x,y),z \ x,u) = u \ (z * ((z \ u) * K(x,y))). [para(1667(a,1),1704(a,1,2,2)),flip(a)]. given #1615 (H,wt=15): 1706 L(K(x,y),z \ x,u) = L(K(x,y),u,z). [para(1705(a,2),1299(a,2)),flip(a)]. given #1616 (H,wt=23): 1673 (x * (y * z)) * K(L(z,y,x),u) = (x * y) * T(L(z,y,x),u). [para(90(a,1),1667(a,1,1)),flip(a)]. given #1617 (H,wt=23): 1707 (x * (y * z)) * K(L(z,y,x),u) = (x * y) * L(T(z,u),y,x). [para(40(a,2),1673(a,2,2))]. given #1618 (H,wt=20): 1708 (x * (y * z)) * K(L(z,y,x),u) = x * (y * T(z,u)). [para(1707(a,2),69(a,1))]. given #1619 (H,wt=20): 1709 (x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u). [hyper(56,a,1708,a)]. given #1620 (H,wt=20): 1710 x \ ((x / (y * z)) * (y * T(z,u))) = K(L(z,y,x),u). [para(1709(a,1),304(a,1)),flip(a)]. given #1621 (H,wt=15): 1711 L(K(x,y),z * x,u) = K(L(x,z,u),y). [para(1710(a,1),1679(a,1)),flip(a)]. given #1622 (H,wt=17): 1712 L(K(x,y),z \ x,u) = K(L(x,z \ 1,u),y). [para(259(a,1),1711(a,1,2))]. given #1623 (H,wt=15): 1713 K(L(x,y \ 1,z),u) = L(K(x,u),z,y). [para(1712(a,1),1706(a,1))]. given #1624 (H,wt=12): 1715 L(K(x,y),K(z,x),u) = K(x,y). [para(1700(a,1),1713(a,1,1)),flip(a)]. given #1625 (H,wt=11): 1716 x / K(y,z) = x * K(z,y). [para(1715(a,1),1076(a,1,2)),flip(a)]. given #1626 (H,wt=11): 1717 x \ (x / K(y,z)) = K(z,y). [para(1715(a,1),1077(a,1)),flip(a)]. given #1627 (H,wt=11): 1718 (x / K(y,z)) / K(z,y) = x. [para(1715(a,1),1078(a,1,2))]. given #1628 (H,wt=10): 1728 R(x,K(y,z),K(y,z)) = x. [para(1718(a,1),1214(a,1)),flip(a)]. given #1629 (H,wt=13): 1714 L(K(x,y),z,u) = K(L(x,z,u),y). [para(1294(a,1),1713(a,1,1)),flip(a)]. given #1630 (H,wt=13): 1720 (x \ K(y,z)) * K(z,y) = x \ 1. [para(1716(a,1),264(a,1))]. given #1631 (H,wt=13): 1724 (x * y) / T(y,z) = x * K(z,y). [para(1716(a,1),1693(a,2))]. given #1632 (H,wt=13): 1737 (x * K(y,z)) * T(z,y) = x * z. [para(1724(a,1),16(a,1,1))]. given #1633 (H,wt=15): 1719 K(x,y) \ (z / K(y,x)) = T(z,K(x,y)). [para(1716(a,2),32(a,2,2)),flip(a)]. given #1634 (H,wt=17): 1722 (K(x,y) \ z) \ (z / K(x,y)) = K(z,K(y,x)). [para(1716(a,2),1094(a,1,2))]. given #1635 (H,wt=15): 1740 K(K(x,y),z / K(x,y)) = K(z,K(y,x)). [para(1722(a,1),1064(a,1)),flip(a)]. given #1636 (H,wt=17): 1734 K(x,y) * K(L(y,z,u),x) = a(z,u,K(y,x)). [para(1714(a,1),1493(a,1,2))]. given #1637 (H,wt=17): 1739 K(K(x,y),z / K(x,y)) = T(z,K(x,y)) \ z. [para(1719(a,1),1321(a,1,1)),flip(a)]. given #1638 (H,wt=15): 1741 K(K(x,y),z / K(x,y)) = K(K(x,y),z). [para(1739(a,2),1054(a,2)),flip(a)]. given #1639 (H,wt=11): 1742 K(K(x,y),z) = K(z,K(y,x)). [para(1741(a,1),1740(a,1))]. given #1640 (H,wt=17): 1743 K(x,K(y,z)) \ K(y,z) = 1 / T(K(z,y),x). [para(1742(a,1),1181(a,1,1))]. given #1641 (H,wt=13): 1744 1 / T(K(x,y),z) = T(K(y,x),z). [para(1743(a,1),1061(a,2)),flip(a)]. given #1642 (H,wt=11): 1745 K(x,T(y,z)) = T(K(x,y),z). [para(1744(a,1),1678(a,1)),flip(a)]. given #1643 (H,wt=11): 1747 K(T(x,y),z) = K(x,T(z,y)). [para(1745(a,2),1677(a,2))]. given #1644 (H,wt=13): 1746 x * K(y,T(z,x)) = K(y,z) * x. [para(1745(a,2),80(a,1,2))]. given #1645 (H,wt=16): 1748 K(x,y) * z != z * u | K(x,T(y,z)) = u. [para(1746(a,1),19(a,1))]. given #1646 (H,wt=18): 1723 (x * K(y,z)) / K(y,z) = R(x,K(z,y),K(z,y)). [para(1716(a,1),1214(a,1,1))]. given #1647 (H,wt=18): 1730 (x * y) * K(L(z,y,x),u) = x * (y * K(z,u)). [para(1714(a,1),69(a,1,2))]. given #1648 (H,wt=18): 1731 (x / y) * (y * K(z,u)) = x * K(L(z,y,x),u). [para(1714(a,1),295(a,2,2))]. given #1649 (H,wt=18): 1749 (x * K(y,z)) * K(z,y) = R(x,K(z,y),K(z,y)). [para(1723(a,1),1716(a,1)),flip(a)]. given #1650 (H,wt=17): 1751 R(x,K(y,z),K(z,y)) = R(x,K(z,y),K(z,y)). [para(1749(a,1),1219(a,1)),flip(a)]. given #1651 (H,wt=10): 1752 R(x,K(y,z),K(z,y)) = x. [para(1751(a,2),1728(a,1))]. given #1652 (H,wt=19): 1736 a(x \ K(y,z),K(z,y),u) = a(x \ 1,K(z,y),u). [para(1720(a,1),1439(a,1,1)),flip(a)]. given #1653 (H,wt=17): 1753 a(x \ K(y,z),K(z,y),u) = a(K(z,y),x,u). [para(1736(a,2),1476(a,1))]. given #1654 (H,wt=20): 1738 L(x,y,z) / T(a(y,z,x),u) = x * K(u,a(y,z,x)). [para(1485(a,2),1724(a,1,1))]. given #1655 (H,wt=22): 1735 K(L(x,K(x,y) \ z,u),y) = u \ ((u / (z / K(x,y))) * z). [para(1714(a,1),1594(a,1))]. given #1656 (H,wt=22): 1754 K(L(x,K(y,x) * z,u),y) = u \ ((u / (z / K(x,y))) * z). [para(1075(a,1),1735(a,1,1,2))]. given #1657 (H,wt=24): 1457 ((x * a(y,z,u)) * L(u,z,y)) / u = R(x,a(y,z,u),L(u,z,y)). [para(1437(a,1),30(a,2,2)),flip(a)]. given #1658 (H,wt=24): 1755 ((x * a(y,z,u)) / u) * L(u,z,y) = R(x,a(y,z,u),L(u,z,y)). [para(1457(a,1),1254(a,1)),flip(a)]. given #1659 (H,wt=25): 1482 x \ ((a(y,z,u) * x) * a(z,y,u)) = K(a(y,z,u) * x,a(z,y,u)). [para(1471(a,1),26(a,2,1)),flip(a)]. given #1660 (H,wt=25): 1524 ((R(x,y,z) * u) * w) / (a(R(x,u,w),y,z) * (u * w)) = R(x,u,w). [para(152(a,1),1510(a,1,1))]. given #1661 (H,wt=25): 1569 L(a(x,y,(z / u) \ z),z,z / u) = a(x,y,L(u \ 1,u,z) \ 1). [para(282(a,2),1568(a,2,3,1))]. given #1662 (H,wt=21): 1756 L(a(x,y,z),u,u / z) = a(x,y,L(z \ 1,z,u) \ 1). [para(54(a,1),1569(a,1,1,3))]. given #1663 (H,wt=19): 1757 a(x,y,L(z \ 1,z,u) \ 1) = L(a(x,y,z),z,u). [para(1756(a,1),1292(a,1))]. given #1664 (H,wt=15): 1758 a(x,y,L(z,z,u)) = L(a(x,y,z),z,u). [para(1190(a,1),1757(a,1,3))]. given #1665 (H,wt=18): 1759 x * a(y,z,L(u,u,x)) = (x / u) * L(u,y,z). [para(1758(a,2),1489(a,1,2))]. given #1666 (H,wt=25): 1629 (x * (y * R(y,z,u))) \ ((x * y) * R(y,z,u)) = a(x,R(y,z,u),y). [para(1627(a,1),203(a,1,2))]. given #1667 (H,wt=15): 1760 a(x,R(y,z,u),y) = a(x,y,R(y,z,u)). [para(1629(a,1),24(a,2)),flip(a)]. given #1668 (H,wt=26): 1462 R(x / a(y,z,u),u / L(u,z,y),L(u,z,y)) = (x * L(u,z,y)) / u. [para(1455(a,2),160(a,1,1,2))]. given #1669 (H,wt=26): 1542 (x * (a(y,x,z) * u)) / a(y,x,z) = (x * u) * K(a(y,x,z),x * u). [para(1509(a,1),1048(a,1,1))]. given #1670 (H,wt=27): 1512 ((R(x,y,z) * u) * w) / ((a(x,y,z) * u) * w) = R(x,a(x,y,z) * u,w). [para(1445(a,1),30(a,2,1,1)),flip(a)]. given #1671 (H,wt=27): 1683 (x \ ((a(y,x \ 1,x \ 1) * (x * z)) / L(x \ 1,y,x \ 1))) / x = z. [hyper(192,a,1682,a)]. given #1672 (H,wt=23): 1761 (x \ ((a(y,x,x) * (x * z)) / L(x \ 1,y,x \ 1))) / x = z. [para(1514(a,1),1683(a,1,1,2,1,1))]. given #1673 (H,wt=23): 1762 (x \ ((x * (a(y,x,x) * z)) / L(x \ 1,y,x \ 1))) / x = z. [para(1509(a,1),1761(a,1,1,2,1))]. given #1674 (H,wt=21): 1763 (x \ ((L(x,y,x) * z) / L(x \ 1,y,x \ 1))) / x = z. [para(1517(a,1),1762(a,1,1,2,1))]. given #1675 (H,wt=19): 1764 (x \ ((L(x,y,x) * z) / L(x \ 1,x,y))) / x = z. [para(1289(a,1),1763(a,1,1,2,2))]. given #1676 (H,wt=19): 1765 (x \ (L(x,y,x) * z)) / (x * L(x \ 1,x,y)) = z. [para(1764(a,1),707(a,1)),flip(a)]. given #1677 (H,wt=17): 1766 (a(x,y,y) * z) / (y * L(y \ 1,y,x)) = z. [para(1491(a,1),1765(a,1,1))]. given #1678 (H,wt=15): 1767 (a(x,y,y) * z) / a(y,x,y \ 1) = z. [para(1486(a,1),1766(a,1,2))]. given #1679 (H,wt=13): 1768 (a(x,y,y) * z) / a(x,y,y) = z. [para(1515(a,1),1767(a,1,2))]. given #1680 (H,wt=13): 1769 a(x,y,y) * z = z * a(x,y,y). [para(1768(a,1),16(a,1,1)),flip(a)]. given #1681 (H,wt=8): 1770 T(x,a(y,z,z)) = x. [hyper(98,a,1769,a)]. given #1682 (H,wt=8): 1774 K(x,a(y,z,z)) = 1. [hyper(36,a,1770,a)]. given #1683 (H,wt=8): 1775 T(x,a(y,z,y)) = x. [para(1474(a,1),1770(a,1,2))]. given #1684 (H,wt=13): 1777 (a(x,y,y) * z) * a(y,x,y) = z. [hyper(1551,a,1775,a)]. given #1685 (H,wt=13): 1778 x / a(y,z,y) = a(z,y,y) * x. [hyper(61,a,1777,a)]. given #1686 (H,wt=15): 1771 a(x,y,y) * (z \ 1) = z \ a(x,y,y). [para(1769(a,2),259(a,1))]. given #1687 (H,wt=15): 1772 x * (y * a(x,z,z)) = R(x,z,z) * y. [para(1769(a,1),1445(a,1,2))]. given #1688 (H,wt=15): 1773 (x * y) * a(x,z,z) = R(x,z,z) * y. [para(1769(a,1),1511(a,1))]. given #1689 (H,wt=19): 1776 1 * ((a(x,y,y) \ z) \ u) = (a(x,y,y) / z) * u. [para(1774(a,1),1168(a,1,1))]. given #1690 (H,wt=19): 1780 (R(x,y,y) * z) / ((z * x) * a(x,y,y)) = K(x,z). [para(1773(a,1),1277(a,1,1))]. given #1691 (H,wt=19): 1781 1 * ((a(x,y,x) * z) \ u) = (a(y,x,x) / z) * u. [para(1336(a,1),1776(a,1,2,1))]. given #1692 (H,wt=17): 1782 (a(x,y,x) * z) \ u = (a(y,x,x) / z) * u. [hyper(55,a,1781,a)]. given #1693 (H,wt=21): 1779 (R(x,y,y) * (x \ z)) / a(x,y,y) = R(z,x,a(x,y,y)). [para(1772(a,1),1394(a,2,1)),flip(a)]. given #1694 (H,wt=19): 1783 (a(x,y,y) * z) / a(x,y,y) = R(z,x,a(x,y,y)). [para(1446(a,1),1779(a,1,1))]. given #1695 (H,wt=9): 1784 R(x,y,a(y,z,z)) = x. [para(1783(a,1),1768(a,1))]. given #1696 (H,wt=15): 1785 (x * y) * a(y,z,z) = x * R(y,z,z). [para(1784(a,1),1453(a,1,1)),flip(a)]. given #1697 (H,wt=17): 1786 (R(x,y,y) * z) / (z * R(x,y,y)) = K(x,z). [para(1785(a,1),1780(a,1,2))]. given #1698 (H,wt=10): 1787 K(R(x,y,y),z) = K(x,z). [para(1786(a,1),1050(a,2))]. given #1699 (H,wt=10): 1790 K(x,R(y,z,z)) = K(x,y). [para(1787(a,1),1387(a,1)),flip(a)]. given #1700 (H,wt=12): 1791 T(x,R(y,z,z)) = x * K(x,y). [para(1790(a,1),1035(a,2,2))]. given #1701 (H,wt=10): 1792 T(x,R(y,z,z)) = T(x,y). [para(1791(a,2),1035(a,2)),flip(a)]. given #1702 (H,wt=12): 1793 T(x,R(y,z,z \ 1)) = T(x,y). [para(1200(a,1),1792(a,1,2)),flip(a)]. given #1703 (H,wt=13): 1788 K(x,y) * (x / z) = T(x,y) / z. [para(1787(a,1),1234(a,1,1))]. given #1704 (H,wt=13): 1789 K(x,y) \ (K(x,y) / z) = z \ 1. [para(1787(a,1),1375(a,1,1))]. given #1705 (H,wt=13): 1796 (K(x,y) * z) \ K(x,y) = z \ 1. [para(1789(a,1),313(a,2))]. given #1706 (H,wt=13): 1798 (K(x,y) * z) \ 1 = z \ K(y,x). [para(1074(a,1),1796(a,1,1)),flip(a)]. given #1707 (H,wt=15): 1794 T(x,y) \ (T(x,y) / z) = x \ (x / z). [para(1788(a,1),1109(a,1,2))]. given #1708 (H,wt=15): 1799 (x \ K(y,z)) \ u = (K(z,y) * x) * u. [para(1798(a,1),256(a,1,1))]. given #1709 (H,wt=13): 1802 (K(x,y) * z) * (z \ T(y,x)) = y. [para(1799(a,1),1702(a,1))]. given #1710 (H,wt=16): 1801 a(x,T(y,z),x) = x \ ((y \ (y / x)) \ 1). [para(1794(a,1),1193(a,1,2,1)),flip(a)]. given #1711 (H,wt=11): 1804 a(x,T(y,z),x) = a(x,y,x). [para(1801(a,2),1193(a,1))]. given #1712 (H,wt=26): 1803 x \ ((x / ((K(y,z) * u) \ 1)) * (u \ T(z,y))) = L(z,x,K(y,z) * u). [para(1802(a,1),1301(a,1,1)),flip(a)]. given #1713 (H,wt=24): 1809 x \ ((x / (y \ K(z,u))) * (y \ T(z,u))) = L(z,x,K(u,z) * y). [para(1798(a,1),1803(a,1,2,1,2))]. given #1714 (H,wt=24): 1810 x \ (y * (((y \ x) / K(z,u)) * T(z,u))) = L(z,x,K(u,z) * y). [para(924(a,1),1809(a,1,2))]. given #1715 (H,wt=24): 1811 x \ (y * (((y \ x) * K(z,u)) * T(u,z))) = L(u,x,K(z,u) * y). [para(1716(a,1),1810(a,1,2,2,1))]. given #1716 (H,wt=18): 1812 L(x,y,K(z,x) * u) = y \ (u * ((u \ y) * x)). [para(1737(a,1),1811(a,1,2,2)),flip(a)]. given #1717 (H,wt=13): 1813 L(x,y,K(z,x) * u) = L(x,y,u). [para(1812(a,2),1299(a,2)),flip(a)]. given #1718 (H,wt=15): 1816 L(x,K(y,x) * z,u) = L(x,u \ 1,z). [para(1813(a,1),1294(a,1)),flip(a)]. given #1719 (H,wt=13): 1817 L(x,K(y,x) * z,u) = L(x,z,u). [para(1816(a,2),1294(a,1))]. given #1720 (H,wt=18): 1818 x \ ((x / (y / K(z,u))) * y) = K(L(z,y,x),u). [para(1817(a,1),1754(a,1,1)),flip(a)]. given #1721 (H,wt=18): 1819 x \ ((x / (y * K(z,u))) * y) = K(L(u,y,x),z). [para(1716(a,1),1818(a,1,2,1,2))]. given #1722 (H,wt=28): 1340 L(R(x / (y \ 1),y,y \ 1),z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u). [para(44(a,1),1161(a,1,1))]. given #1723 (H,wt=21): 1821 (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x. [para(1160(a,1),1340(a,1,1,1)),flip(a)]. given #1724 (H,wt=19): 1822 (x \ 1) * L(x * y,z,u) = L(y * x,z,u) / x. [para(256(a,1),1821(a,1,2,1))]. given #1725 (H,wt=17): 1823 L(x * y,z,u) / y = y \ L(y * x,z,u). [para(1822(a,1),259(a,1))]. given #1726 (H,wt=27): 1824 a(x,y,z) \ L(a(x,y,z) * L(z,y,x),u,w) = L(z,u,w) / a(x,y,z). [para(1463(a,1),1823(a,1,1,1)),flip(a)]. given #1727 (H,wt=19): 1825 L(x,y,z) / a(u,w,x) = a(u,w,x) \ L(x,y,z). [para(1437(a,1),1824(a,1,2,1)),flip(a)]. given #1728 (H,wt=19): 1826 L(x,y,z) / a(u,w,x) = a(w,u,x) * L(x,y,z). [para(1825(a,2),1472(a,1))]. given #1729 (H,wt=28): 1522 (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). [para(1521(a,1),24(a,2,2,1)),flip(a)]. given #1730 (H,wt=22): 1828 a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u). [para(1526(a,1),1522(a,1,1)),flip(a)]. given #1731 (H,wt=15): 1829 a(L(x,y,z),R(z,y,x),u) = a(x,z,u). [para(1828(a,2),24(a,2)),flip(a)]. given #1732 (H,wt=17): 1832 L(x,R(y,z,u),L(u,z,y)) = x / a(u,y,x). [para(1829(a,1),1464(a,2,2))]. given #1733 (H,wt=15): 1833 L(x,R(y,z,u),L(u,z,y)) = L(x,y,u). [para(1832(a,2),1464(a,2)),flip(a)]. given #1734 (H,wt=18): 1831 a(x,R(y,z,L(x,y,z)),u) = a(L(x,y,z),y,u). [para(341(a,1),1829(a,1,1))]. given #1735 (H,wt=15): 1834 a(L(x,y,z),y,u) = a(x,R(y,z,x),u). [para(1532(a,1),1831(a,1,2)),flip(a)]. given #1736 (H,wt=28): 1636 a(T(x \ 1,(x \ 1) \ (y * x)),z,u) = T(a(x \ 1,z,u),R(y,x,x \ 1)). [para(460(a,1),1635(a,2,2))]. given #1737 (H,wt=26): 1835 a(T(x \ 1,(x \ 1) \ (y * x)),z,u) = T(a(z,x,u),R(y,x,x \ 1)). [para(1476(a,1),1636(a,2,1))]. given #1738 (H,wt=21): 1836 a(T(x \ 1,(x \ 1) \ (y * x)),z,u) = T(a(z,x,u),y). [para(1835(a,2),1793(a,1))]. given #1739 (H,wt=19): 1837 a(T(x \ 1,x * (y * x)),z,u) = T(a(z,x,u),y). [para(256(a,1),1836(a,1,1,2))]. given #1740 (H,wt=15): 1839 a(T(x,y) \ 1,z,u) = T(a(z,x,u),y). [para(823(a,1),1837(a,1,1))]. given #1741 (H,wt=13): 1840 a(x,T(y,z),u) = T(a(x,y,u),z). [para(1839(a,1),1476(a,1)),flip(a)]. given #1742 (H,wt=15): 1841 x * a(y,T(z,x),u) = a(y,z,u) * x. [para(1840(a,2),80(a,1,2))]. given #1743 (H,wt=15): 1844 T(a(x \ 1,y,z),u) = a(T(y,u),x,z). [para(1840(a,1),1476(a,1))]. given #1744 (H,wt=13): 1848 a(T(x,y),z,u) = T(a(x,z,u),y). [para(1476(a,1),1844(a,1,1)),flip(a)]. given #1745 (H,wt=13): 1849 a(T(x,y),z,u) = a(x,T(z,y),u). [para(1848(a,2),1840(a,2)),flip(a)]. given #1746 (H,wt=18): 1842 a(x,T(y,z),u) \ a(x,y,u) = K(z,a(x,y,u)). [para(1840(a,2),1054(a,2,1)),flip(a)]. given #1747 (H,wt=18): 1846 a(x,T(y,z),u) * a(y,x,u) = K(a(x,y,u),z). [para(1840(a,2),1567(a,1,1))]. given #1748 (H,wt=18): 1850 a(T(x,y),z,u) * a(z,x,u) = K(y,a(z,x,u)). [para(1842(a,1),1472(a,1)),flip(a)]. given #1749 (H,wt=18): 1851 a(x,T(y,z),u) * a(y,x,u) = K(z,a(y,x,u)). [para(1849(a,1),1850(a,1,1))]. given #1750 (H,wt=13): 1852 K(a(x,y,z),u) = K(u,a(y,x,z)). [para(1851(a,1),1846(a,1)),flip(a)]. given #1751 (H,wt=15): 1853 x * K(a(y,z,u),x) = T(x,a(z,y,u)). [para(1852(a,2),1035(a,2,2)),flip(a)]. given #1752 (H,wt=20): 1845 a(x,T(y,z),u) * L(u,y,x) = K(a(x,y,u),z) * u. [para(1840(a,2),1459(a,1,1))]. given #1753 (H,wt=20): 1847 L(x,y,z) / a(y,T(z,u),x) = x * K(u,a(y,z,x)). [para(1840(a,2),1738(a,1,2))]. given #1754 (H,wt=20): 1855 a(T(x,y),z,u) * L(u,z,x) = u * K(y,a(z,x,u)). [para(1847(a,1),1826(a,1)),flip(a)]. given #1755 (H,wt=20): 1856 a(x,T(y,z),u) * L(u,y,x) = u * K(z,a(y,x,u)). [para(1849(a,1),1855(a,1,1))]. given #1756 (H,wt=17): 1857 K(a(x,y,z),u) * z = z * K(u,a(y,x,z)). [para(1856(a,1),1845(a,1)),flip(a)]. given #1757 (H,wt=15): 1858 K(a(x,y,z),T(u,z)) = K(u,a(y,x,z)). [hyper(1748,a,1857,a)]. given #1758 (H,wt=22): 1854 (x * (a(y,x,z) * u)) / a(y,x,z) = T(x * u,a(x,y,z)). [para(1853(a,1),1542(a,2))]. given #1759 (H,wt=29): 923 L(x,T(y,y \ z) \ (y * (z / y)),y * (z / y)) = L(x,z / y,y * (z / y)). [para(809(a,1),921(a,1,2)),flip(a)]. given #1760 (H,wt=25): 1859 L(x,T(y,y \ z) \ (y * (z / y)),y * (z / y)) = L(x,z / y,y). [para(923(a,2),424(a,1))]. given #1761 (H,wt=23): 1860 L(x,T(y,y \ z) \ (y * (z / y)),y * (z / y)) = L(x,z,y). [para(1859(a,2),435(a,1))]. given #1762 (H,wt=21): 1861 L(x,K(y \ z,y) * (z / y),y * (z / y)) = L(x,z,y). [para(1108(a,1),1860(a,1,2))]. given #1763 (H,wt=21): 1862 L(x,(y / z) * K(z \ y,z),z * (y / z)) = L(x,y,z). [para(1235(a,1),1861(a,1,2))]. given #1764 (H,wt=15): 1863 L(x,y \ z,y * (z / y)) = L(x,z,y). [para(1065(a,1),1862(a,1,2))]. given #1765 (H,wt=33): 1631 a(R(x,y,z),u,R(x,y,z) \ a(x,y,z)) = (u * (x \ 1)) \ ((u / R(x,y,z)) * a(x,y,z)). [para(1443(a,1),1630(a,1,1,2)),flip(a)]. given #1766 (H,wt=27): 1864 (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(R(y,z,u),x,y \ 1). [para(1443(a,1),1631(a,1,3)),flip(a)]. given #1767 (H,wt=34): 1347 (x \ y) * (x * (((x \ (x * (y \ z))) / y) * (y * u))) = (y * (x * ((x * y) \ z))) * L(u,x,y). [para(1346(a,1),1338(a,2,1))]. given #1768 (H,wt=30): 1866 (x \ y) * (x * (((y \ z) / y) * (y * u))) = (y * (x * ((x * y) \ z))) * L(u,x,y). [para(13(a,1),1347(a,1,2,2,1,1))]. given #1769 (H,wt=26): 1868 (x * (y * ((y * x) \ z))) * L(u,y,x) = (y \ x) * (y * (x \ (z * u))). [para(248(a,1),1866(a,1,2,2)),flip(a)]. given #1770 (H,wt=26): 1869 (x * (y * ((y * x) \ z))) * L(u,y,x) = x * (y * ((y * x) \ (z * u))). [para(1868(a,2),1346(a,1))]. given #1771 (H,wt=24): 1870 (x * (y * ((y * x) \ 1))) * L(z,y,x) = x * (y * ((y * x) \ z)). [para(11(a,1),1869(a,2,2,2,2))]. given #1772 (H,wt=31): 1871 (x * (y * ((y * x) \ 1))) * L(z * u,y,x) = (x * (y * ((y * x) \ z))) * L(u,y,x). [para(1870(a,2),1869(a,2)),flip(a)]. given #1773 (H,wt=35): 1750 (x * (y * K(z,u))) \ R(x * y,K(L(z,y,x),u),K(L(z,y,x),u) \ 1) = K(L(z,y,x),u) \ 1. [para(1730(a,1),462(a,1,1))]. given #1774 (H,wt=33): 1873 (x * (y * K(z,u))) \ R(x * y,K(L(z,y,x),u),K(u,L(z,y,x))) = K(L(z,y,x),u) \ 1. [para(1070(a,1),1750(a,1,2,3))]. given #1775 (H,wt=20): 1874 (x * (y * K(z,u))) \ (x * y) = K(L(z,y,x),u) \ 1. [para(1752(a,1),1873(a,1,2))]. given #1776 (H,wt=20): 1875 x \ ((x / (y * K(z,u))) * y) = K(L(z,y,x),u) \ 1. [para(1874(a,1),304(a,1)),flip(a)]. given #1777 (H,wt=15): 1877 K(L(x,y,z),u) \ 1 = K(L(u,y,z),x). [para(1875(a,1),1819(a,1))]. given #1778 (H,wt=13): 1878 K(L(x,y,z),u) = K(x,L(u,y,z)). [para(1877(a,1),1070(a,1))]. given #1779 (H,wt=13): 1879 L(K(x,y),z,u) = K(x,L(y,z,u)). [para(1878(a,1),1714(a,2))]. given #1780 (H,wt=18): 1880 (x / y) * (y * K(z,u)) = x * K(z,L(u,y,x)). [para(1878(a,1),1731(a,2,2))]. given #1781 (H,wt=36): 562 R(x,x \ y,z) \ R(R(x,x \ y,z),u,w) = (R(R(x,x \ y,z),u,w) * ((x \ y) * z)) / (y * z). [para(163(a,1),559(a,1,1,2)),flip(a)]. given #1782 (H,wt=31): 1881 R(x,x \ y,z) \ R(R(x,x \ y,z),u,w) = ((R(x,u,w) * (x \ y)) * z) / (y * z). [para(152(a,1),562(a,2,1))]. given #1783 (H,wt=26): 1882 R(x,x \ y,z) \ R(R(x,x \ y,z),u,w) = R(x \ R(x,u,w),y,z). [para(1881(a,2),560(a,1))]. given #1784 (H,wt=24): 1883 R(x,y,z) \ R(R(x,x \ y,z),u,w) = R(x \ R(x,u,w),y,z). [para(1365(a,1),1882(a,1,1))]. given #1785 (H,wt=22): 1884 R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). [para(1365(a,1),1883(a,1,2,1))]. given #1786 (H,wt=17): 1885 R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z). [para(1884(a,1),1431(a,2)),flip(a)]. given #1787 (H,wt=15): 1886 a(R(x,y,z),u,w) = R(a(x,u,w),y,z). [para(1431(a,2),1885(a,1,1)),flip(a)]. given #1788 (H,wt=19): 1889 R(a(x,y,z) * 1,u,w) = a(R(y,u,w),x,z) \ 1. [para(1886(a,2),1499(a,2,1))]. given #1789 (H,wt=17): 1890 R(a(x,y,z) * 1,u,w) = a(x,R(y,u,w),z). [para(1889(a,2),1470(a,1))]. given #1790 (H,wt=15): 1891 a(x,R(y,z,u),w) = R(a(x,y,w),z,u). [para(12(a,1),1890(a,1,1)),flip(a)]. given #1791 (H,wt=15): 1892 a(R(x,y,z),u,w) = a(x,R(u,y,z),w). [para(1891(a,2),1886(a,2))]. given #1792 (H,wt=20): 1887 a(R(x,y,z),u,w) * (y * z) = (a(x,u,w) * y) * z. [para(1886(a,2),75(a,1,1))]. given #1793 (H,wt=21): 1893 (x * y) / (a(z,R(u,w,v5),x) * y) = L(x,u,R(z,w,v5)). [para(1892(a,1),1529(a,1,2,1))]. given #1794 (H,wt=15): 1896 L(x,R(y,z,u),w) = L(x,y,R(w,z,u)). [para(1893(a,1),1529(a,1)),flip(a)]. given #1795 (H,wt=15): 1897 L(x,y,R(L(z,u,y),u,z)) = L(x,y,z). [para(1896(a,1),1833(a,1))]. given #1796 (H,wt=15): 1898 L(x,y,L(R(z,u,z),u,y)) = L(x,y,z). [para(44(a,1),1897(a,1,3))]. given #1797 (H,wt=15): 1899 L(x,y,L(L(z,z,u),u,y)) = L(x,y,z). [para(1144(a,1),1898(a,1,3,1))]. given #1798 (H,wt=22): 1888 x / (a(y,z,z) * a(R(z,x,u),y,z)) = R(x,a(z,y,z),u). [para(1886(a,2),1337(a,1,2,2))]. given #1799 (H,wt=22): 1895 ((R(x,y,z) * u) * w) / ((a(x,y,z) * u) * w) = R(x,u,w). [para(1887(a,1),1524(a,1,2))]. given #1800 (H,wt=14): 1901 R(x,a(x,y,z) * u,w) = R(x,u,w). [para(1895(a,1),1512(a,1)),flip(a)]. given #1801 (H,wt=12): 1902 R(x,L(y,z,x),u) = R(x,y,u). [para(1437(a,1),1901(a,1,2)),flip(a)]. given #1802 (H,wt=14): 1904 a(x,L(y,z,x),u) = x \ R(x,y,u). [para(1902(a,1),1431(a,2,2))]. given #1803 (H,wt=12): 1906 a(x,L(y,z,x),u) = a(x,y,u). [para(1904(a,2),1431(a,2)),flip(a)]. given #1804 (H,wt=16): 1905 L(x,y,L(z,u,y)) = (x / y) * R(y,z,x). [para(1902(a,1),1534(a,2,2))]. given #1805 (H,wt=12): 1908 L(x,y,L(z,u,y)) = L(x,y,z). [para(1905(a,2),1534(a,2)),flip(a)]. given #1806 (H,wt=12): 1910 L(x,y,L(z,z,u)) = L(x,y,z). [para(1908(a,1),1899(a,1))]. given #1807 (H,wt=12): 1912 L(x,y,L(z,u,z)) = L(x,y,z). [para(1288(a,1),1910(a,1,3))]. given #1808 (H,wt=16): 1907 a(x \ 1,L(y,x,z),u) = a(x \ 1,y,u). [para(455(a,1),1906(a,1,2))]. given #1809 (H,wt=14): 1915 a(L(x,y,z),y,u) = a(y \ 1,x,u). [para(1907(a,1),1476(a,1)),flip(a)]. given #1810 (H,wt=12): 1916 a(L(x,y,z),y,u) = a(x,y,u). [para(1915(a,2),1476(a,1))]. given #1811 (H,wt=12): 1917 a(x,R(y,z,x),u) = a(x,y,u). [para(1916(a,1),1834(a,1)),flip(a)]. given #1812 (H,wt=16): 1918 a(R(x,y,z \ 1),z,u) = a(z \ 1,x,u). [para(1917(a,1),1476(a,1)),flip(a)]. given #1813 (H,wt=14): 1920 a(R(x,y,z \ 1),z,u) = a(x,z,u). [para(1918(a,2),1476(a,1))]. given #1814 (H,wt=14): 1921 a(x,R(y,z,y \ 1),u) = a(x,y,u). [para(1920(a,1),1892(a,1)),flip(a)]. given #1815 (H,wt=12): 1922 a(x,L(y,z,y),u) = a(x,y,u). [para(1259(a,1),1921(a,1,2))]. given #1816 (H,wt=22): 1900 x / (a(y,z,z) * a(z,y,R(z,x,u))) = R(x,a(z,y,z),u). [para(1565(a,1),1888(a,1,2,2))]. given #1817 (H,wt=27): 1894 (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(y,R(x,z,u),y \ 1). [para(1892(a,1),1864(a,2))]. given #1818 (H,wt=25): 1923 (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(R(x,z,u),y,y). [para(1894(a,2),1515(a,1))]. given #1819 (H,wt=25): 1924 (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(x,R(y,z,u),y). [para(1923(a,2),1892(a,1))]. given #1820 (H,wt=25): 1925 (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(x,y,R(y,z,u)). [para(1924(a,2),1760(a,1))]. given #1821 (H,wt=28): 1914 (a(x,L(y,z,y),u) * L(u,x,y)) \ L(u,x,L(y,z,y)) = a(L(y,z,y),x,u). [para(1912(a,1),1626(a,1,1,2))]. given #1822 (H,wt=25): 1926 (a(x,y,z) * L(z,x,y)) \ L(z,x,L(y,u,y)) = a(L(y,u,y),x,z). [para(1922(a,1),1914(a,1,1,1))]. given #1823 (H,wt=22): 1927 a(L(x,y,x),z,u) = (a(z,x,u) * L(u,z,x)) \ L(u,z,x). [para(1912(a,1),1926(a,1,2)),flip(a)]. given #1824 (H,wt=12): 1929 a(L(x,y,x),z,u) = a(x,z,u). [para(1927(a,2),1626(a,1))]. given #1825 (H,wt=15): 1931 a(T(x,x * y),z,u) = a(T(x,y),z,u). [para(902(a,1),1929(a,1,1))]. given #1826 (H,wt=15): 1933 a(x,T(y,x * z),u) = a(T(x,z),y,u). [para(1931(a,1),1849(a,1)),flip(a)]. given #1827 (H,wt=15): 1934 a(x,T(y,x * z),u) = a(x,T(y,z),u). [para(1933(a,2),1849(a,1))]. given #1828 (H,wt=19): 1935 (x * y) * a(x,T(z,y),u) = a(x,z,u) * (x * y). [para(1934(a,1),1841(a,1,2))]. given #1829 (H,wt=17): 1936 (x * y) * a(x,T(z,y),u) = R(x,z,u) * y. [para(1935(a,2),1511(a,1))]. given #1830 (H,wt=27): 1937 (x * (y * a(x,T(z,y),u))) \ (R(x,z,u) * y) = a(x,y,a(x,T(z,y),u)). [para(1936(a,1),24(a,2,2)),flip(a)]. given #1831 (H,wt=25): 1938 (x * (a(x,y,z) * u)) \ (R(x,y,z) * u) = a(x,u,a(x,T(y,u),z)). [para(1841(a,1),1937(a,1,1,2))]. given #1832 (H,wt=23): 1939 (R(x,y,z) * u) \ (R(x,y,z) * u) = a(x,u,a(x,T(y,u),z)). [para(1445(a,1),1938(a,1,1))]. given #1833 (H,wt=11): 1940 a(x,y,a(x,T(z,y),u)) = 1. [para(1939(a,1),50(a,1))]. given #1834 (H,wt=9): 1942 a(x,y,a(x,z,u)) = 1. [para(832(a,1),1940(a,1,3,2))]. given #1835 (H,wt=9): 1945 a(x,y,a(z,x,u)) = 1. [para(1475(a,1),1942(a,1,3))]. given #1836 (H,wt=9): 1948 a(x,y,a(z,y,u)) = 1. [para(1945(a,1),1475(a,1)),flip(a)]. given #1837 (H,wt=11): 1944 R(x,y,a(y,z,u)) = x / 1. [para(1942(a,1),1425(a,2,2))]. given #1838 (H,wt=9): 1950 R(x,y,a(y,z,u)) = x. [para(1944(a,2),52(a,1))]. given #1839 (H,wt=12): 1949 L(a(x,y,z),y,u) = a(x,y,z). [hyper(33,a,1948,a)]. given #1840 (H,wt=17): 1952 (x * y) * a(x,z,u) = x * (y * a(x,z,u)). [para(1950(a,1),1395(a,1,1))]. given #1841 (H,wt=17): 1953 (x / (y * a(y,z,u))) * y = x / a(y,z,u). [para(1950(a,1),1546(a,1)),flip(a)]. given #1842 (H,wt=15): 1955 (x / R(y,z,u)) * y = x / a(y,z,u). [para(1433(a,2),1953(a,1,1,2))]. given #1843 (H,wt=15): 1957 (x / a(y,z,u)) * R(y,z,u) = x * y. [para(1955(a,1),1628(a,1,1))]. given #1844 (H,wt=13): 1958 L(x,a(x,y,z),u) = u \ (u * x). [para(1957(a,1),1454(a,1,2)),flip(a)]. given #1845 (H,wt=9): 1959 L(x,a(x,y,z),u) = x. [para(1958(a,2),13(a,1))]. given #1846 (H,wt=17): 1961 (x / (a(y,z,u) * y)) * a(y,z,u) = x / y. [para(1959(a,1),1573(a,1,2)),flip(a)]. given #1847 (H,wt=15): 1962 (x / R(y,z,u)) * a(y,z,u) = x / y. [para(1434(a,2),1961(a,1,1,2))]. given #1848 (H,wt=17): 1963 a(x,y,R(y,z,u)) = (x * (y \ 1)) \ (x / y). [para(1962(a,1),1925(a,1,2)),flip(a)]. given #1849 (H,wt=12): 1964 a(x,y,R(y,z,u)) = a(x,y,y). [para(1963(a,2),1553(a,1))]. given #1850 (H,wt=14): 1966 a(x,y,R(x,z,u)) = a(y \ 1,x,x). [para(1964(a,1),1476(a,1)),flip(a)]. given #1851 (H,wt=12): 1967 a(x,y,R(x,z,u)) = a(x,y,x). [para(1966(a,2),1476(a,1))]. given #1852 (H,wt=19): 1968 R(x,a(y,z,y),u) = x / (a(z,y,y) * a(y,z,y)). [para(1967(a,1),1900(a,1,2,2)),flip(a)]. given #1853 (H,wt=11): 1969 R(x,a(y,z,y),u) = x / 1. [para(1469(a,1),1968(a,2,2))]. given #1854 (H,wt=9): 1971 R(x,a(y,z,y),u) = x. [para(1969(a,2),52(a,1))]. given #1855 (H,wt=9): 1975 R(x,a(y,z,z),u) = x. [para(1475(a,1),1971(a,1,2))]. given #1856 (H,wt=11): 1977 a(x,a(y,z,z),u) = x \ x. [para(1975(a,1),1431(a,2,2))]. given #1857 (H,wt=9): 1979 a(x,a(y,z,z),u) = 1. [para(1977(a,2),50(a,1))]. given #1858 (H,wt=9): 1980 L(x,a(y,z,z),u) = x. [hyper(33,a,1979,a)]. given #1859 (H,wt=17): 1973 (x * a(y,z,y)) * u = x * (a(y,z,y) * u). [para(1971(a,1),75(a,1,1)),flip(a)]. given #1860 (H,wt=17): 1974 (x \ 1) / a(y,z,y) = (a(y,z,y) * x) \ 1. [para(1971(a,1),237(a,1))]. given #1861 (H,wt=17): 1976 (a(x,y,x) * z) * u = a(x,y,x) * (z * u). [para(1971(a,1),1395(a,1,1))]. given #1862 (H,wt=17): 1978 (a(x,y,y) * z) * u = a(x,y,y) * (z * u). [para(1975(a,1),1395(a,1,1))]. given #1863 (H,wt=17): 1985 (a(x,y,x) * z) \ 1 = a(y,x,x) * (z \ 1). [para(1974(a,1),1778(a,1))]. given #1864 (H,wt=15): 1986 (a(x,y,x) * z) \ 1 = z \ a(y,x,x). [para(1985(a,2),1771(a,1))]. given #1865 (H,wt=15): 1987 (a(x,y,y) / z) * 1 = z \ a(x,y,y). [para(1986(a,1),1782(a,1)),flip(a)]. given #1866 (H,wt=13): 1988 a(x,y,y) / z = z \ a(x,y,y). [hyper(59,a,1987,a)]. given #1867 (H,wt=19): 1982 (a(x,y,y) * (z \ 1)) * u = a(x,y,y) * (z \ u). [para(1980(a,1),1302(a,1,2))]. given #1868 (H,wt=17): 1989 (x \ a(y,z,z)) * u = a(y,z,z) * (x \ u). [para(1771(a,1),1982(a,1,1))]. given #1869 (H,wt=19): 1984 x * (a(y,T(z,x),y) * u) = (a(y,z,y) * x) * u. [para(1841(a,1),1973(a,1,1)),flip(a)]. given #1870 (H,wt=17): 1990 (a(x,y,x) * z) * u = z * (a(x,y,x) * u). [para(1804(a,1),1984(a,1,2,1)),flip(a)]. given #1871 (H,wt=17): 1992 a(x,y,x) * (z * u) = z * (a(x,y,x) * u). [para(1990(a,1),1976(a,1)),flip(a)]. given #1872 (H,wt=21): 1956 x * L(R(y,z,u) \ y,R(y,z,u),x) = x / a(y,z,u). [para(1955(a,1),300(a,2))]. given #1873 (H,wt=19): 1994 x * L(a(y,z,u),R(z,y,u),x) = x / a(z,y,u). [para(1423(a,2),1956(a,1,2,1))]. given #1874 (H,wt=19): 1995 x * L(a(y,z,u),z,R(x,y,u)) = x / a(z,y,u). [para(1896(a,1),1994(a,1,2))]. given #1875 (H,wt=13): 1996 x / a(y,z,u) = x * a(z,y,u). [para(1949(a,1),1995(a,1,2)),flip(a)]. given #1876 (H,wt=13): 1997 (x * a(y,z,u)) * a(z,y,u) = x. [hyper(60,a,1996,a)]. given #1877 (H,wt=17): 1998 (x * a(y,z,u)) \ w = (a(z,y,u) / x) * w. [para(1996(a,1),284(a,1,1))]. given #1878 (H,wt=20): 1999 (a(x,y,z) * u) * a(y,x,z) = u * K(a(x,y,z),u). [para(1996(a,1),1048(a,1))]. given #1879 (H,wt=18): 2002 (a(x,y,z) * u) * a(y,x,z) = T(u,a(y,x,z)). [para(1999(a,2),1853(a,1))]. given #1880 (H,wt=20): 2003 K(a(x,y,z) * u,a(y,x,z)) = u \ T(u,a(y,x,z)). [para(2002(a,1),1482(a,1,2)),flip(a)]. given #1881 (H,wt=18): 2004 K(a(x,y,z) * u,a(y,x,z)) = K(u,a(y,x,z)). [para(2003(a,2),1038(a,2)),flip(a)]. given #1882 (H,wt=22): 2000 (x * (a(y,x,z) * u)) * a(x,y,z) = T(x * u,a(x,y,z)). [para(1996(a,1),1854(a,1))]. given #1883 (H,wt=22): 2005 x * ((a(y,x,z) * u) * a(x,y,z)) = T(x * u,a(x,y,z)). [para(2000(a,1),1952(a,1)),flip(a)]. given #1884 (H,wt=17): 2006 T(x * y,a(x,z,u)) = x * T(y,a(x,z,u)). [para(2002(a,1),2005(a,1,2)),flip(a)]. given #1885 (H,wt=19): 2007 T(x * T(y,x),a(x,z,u)) = T(y,a(x,z,u)) * x. [para(2006(a,2),102(a,1))]. given #1886 (H,wt=17): 2008 T(x * y,a(y,z,u)) = T(x,a(y,z,u)) * y. [para(80(a,1),2007(a,1,1))]. given #1887 (H,wt=19): 2009 x \ T(y * x,a(x,z,u)) = T(T(y,a(x,z,u)),x). [para(2008(a,2),32(a,2,2)),flip(a)]. given #1888 (H,wt=24): 1951 (x * a(x,y,z)) \ (u * a(x,y,z)) = T(u / x,x * a(x,y,z)). [para(1950(a,1),162(a,1,1)),flip(a)]. given #1889 (H,wt=22): 2010 (x * a(x,y,z)) \ (u * a(x,y,z)) = T(u / x,R(x,y,z)). [para(1433(a,2),1951(a,2,2))]. given #1890 (H,wt=20): 2011 R(x,y,z) \ (u * a(x,y,z)) = T(u / x,R(x,y,z)). [para(1433(a,2),2010(a,1,1))]. given #1891 (H,wt=17): 2012 x \ T(y,a(x,z,u)) = T(y / x,R(x,z,u)). [para(2011(a,1),1623(a,1)),flip(a)]. given #1892 (H,wt=19): 2013 T((x * y) / y,R(y,z,u)) = T(T(x,a(y,z,u)),y). [para(2012(a,1),2009(a,1))]. given #1893 (H,wt=15): 2014 T(T(x,a(y,z,u)),y) = T(x,R(y,z,u)). [para(15(a,1),2013(a,1,1)),flip(a)]. given #1894 (H,wt=19): 2015 T(x,y) \ T(x,R(y,z,u)) = K(T(x,y),a(y,z,u)). [para(2014(a,1),1051(a,1,2))]. given #1895 (H,wt=19): 2016 K(x,R(y,z,u)) * K(y,x) = K(T(x,y),a(y,z,u)). [para(2015(a,1),1183(a,1)),flip(a)]. given #1896 (H,wt=15): 2017 K(T(x,y),a(y,z,u)) = a(z,K(y,x),u). [para(2016(a,1),1543(a,1))]. given #1897 (H,wt=15): 2018 K(x,T(a(y,z,u),y)) = a(z,K(y,x),u). [para(2017(a,1),1747(a,1)),flip(a)]. given #1898 (H,wt=13): 2019 a(x,K(y,z),u) = K(z,a(y,x,u)). [para(1440(a,1),2018(a,1,2)),flip(a)]. given #1899 (H,wt=15): 2020 x * K(y,a(z,u,x)) = L(x,u,K(z,y)). [para(2019(a,1),1485(a,2,2)),flip(a)]. given #1900 (H,wt=17): 2021 K(x,a(y,z \ K(x,y),u)) = a(K(y,x),z,u). [para(2019(a,1),1753(a,1))]. given #1901 (H,wt=13): 2022 a(K(x,y),z,u) = K(y,a(z,x,u)). [para(1618(a,1),2021(a,1,2)),flip(a)]. given #1902 (H,wt=15): 2023 x * K(y,a(z,u,x)) = L(x,K(u,y),z). [para(2022(a,1),1485(a,2,2)),flip(a)]. given #1903 (H,wt=13): 2025 L(x,K(y,z),u) = L(x,y,K(u,z)). [para(2023(a,1),2020(a,1))]. given #1904 (H,wt=31): 1983 (x * y) \ (z * (a(u,w,u) * (((z * a(u,w,u)) \ x) * y))) = a(x,z * a(u,w,u),y). [para(1973(a,1),1597(a,2,2)),flip(a)]. given #1905 (H,wt=31): 1993 (x * ((a(y,z,y) * u) * w)) \ ((a(y,z,y) * (x * u)) * w) = a(x,a(y,z,y) * u,w). [para(1992(a,2),24(a,2,2,1)),flip(a)]. given #1906 (H,wt=31): 2026 (x * y) \ (z * (a(u,w,u) * (((a(w,u,u) / z) * x) * y))) = a(x,z * a(u,w,u),y). [para(1998(a,1),1983(a,1,2,2,2,1))]. given #1907 (H,wt=31): 2027 (x * (y * (a(z,u,z) * w))) \ ((a(z,u,z) * (x * y)) * w) = a(x,a(z,u,z) * y,w). [para(1990(a,1),1993(a,1,1,2))]. given #1908 (H,wt=31): 2028 (x * y) \ (z * (a(u,w,u) * (((z \ a(w,u,u)) * x) * y))) = a(x,z * a(u,w,u),y). [para(1988(a,1),2026(a,1,2,2,2,1,1))]. given #1909 (H,wt=31): 2029 (x * (y * (a(z,u,z) * w))) \ ((x * y) * (a(z,u,z) * w)) = a(x,a(z,u,z) * y,w). [para(1990(a,1),2027(a,1,2))]. given #1910 (H,wt=19): 2031 a(x,a(y,z,y) * u,w) = a(x,u,a(y,z,y) * w). [para(2029(a,1),24(a,2)),flip(a)]. given #1911 (H,wt=31): 2030 (x * y) \ (z * (a(u,w,u) * ((a(w,u,u) * (z \ x)) * y))) = a(x,z * a(u,w,u),y). [para(1989(a,1),2028(a,1,2,2,2,1))]. given #1912 (H,wt=31): 2032 (x * y) \ (z * (a(u,w,u) * (a(w,u,u) * ((z \ x) * y)))) = a(x,z * a(u,w,u),y). [para(1978(a,1),2030(a,1,2,2,2))]. given #1913 (H,wt=21): 2033 a(x,y * a(z,u,z),w) = (x * w) \ (y * ((y \ x) * w)). [para(1471(a,1),2032(a,1,2,2)),flip(a)]. given #1914 (H,wt=14): 2035 a(x,y * a(z,u,z),w) = a(x,y,w). [para(2033(a,2),1597(a,2)),flip(a)]. given #1915 (H,wt=12): 2036 a(x,R(y,z,z),u) = a(x,y,u). [para(1422(a,1),2035(a,1,2)),flip(a)]. given #1916 (H,wt=14): 2038 a(x,a(y,z,y) * u,w) = a(x,u,w). [para(1841(a,1),2035(a,1,2))]. given #1917 (H,wt=14): 2039 L(x,y,R(z,u,u)) = x * a(y,z,x). [para(2036(a,1),1485(a,2,2))]. given #1918 (H,wt=12): 2041 L(x,y,R(z,u,u)) = L(x,y,z). [para(2039(a,2),1485(a,2)),flip(a)]. given #1919 (H,wt=14): 2040 a(x,y,a(z,u,z) * w) = a(x,y,w). [para(2038(a,1),2031(a,1)),flip(a)]. given #1920 (H,wt=12): 2044 a(x,y,L(z,z,u)) = a(x,y,z). [para(697(a,1),2040(a,1,3))]. given #1921 (H,wt=15): 2042 L(x,y,z * (u \ 1)) = L(x,y,z / u). [para(1203(a,1),2041(a,1,3)),flip(a)]. given #1922 (H,wt=15): 2043 L(x,y,z / (u \ 1)) = L(x,y,z * u). [para(1205(a,1),2041(a,1,3))]. given #1923 (H,wt=15): 2047 (x / y) * L(y,z,u) = x * a(z,u,y). [para(2044(a,1),1759(a,1,2)),flip(a)]. given #1924 (H,wt=16): 2037 L(x,y,z * a(u,w,u)) = x * a(y,z,x). [para(2035(a,1),1485(a,2,2))]. given #1925 (H,wt=14): 2052 L(x,y,z * a(u,w,u)) = L(x,y,z). [para(2037(a,2),1485(a,2)),flip(a)]. given #1926 (H,wt=17): 2048 L(x,y,z / (u / w)) = L(x,y,z * (w / u)). [para(265(a,1),2042(a,1,3,2)),flip(a)]. given #1927 (H,wt=22): 2050 (x * a(y,z,u)) * a(z,y,u) = R(x,a(y,z,u),L(u,z,y)). [para(2047(a,1),1755(a,1))]. given #1928 (H,wt=12): 2053 R(x,a(y,z,u),L(u,z,y)) = x. [para(2050(a,1),1997(a,1))]. given #1929 (H,wt=14): 2055 R(x,y / L(y,z,u),L(y,z,u)) = x. [para(1455(a,1),2053(a,1,2))]. given #1930 (H,wt=15): 2057 (x * L(y,z,u)) / y = x / a(u,z,y). [para(2055(a,1),1462(a,1)),flip(a)]. given #1931 (H,wt=15): 2058 (x / L(y,z,u)) / a(u,z,y) = x / y. [para(16(a,1),2057(a,1,1)),flip(a)]. given #1932 (H,wt=15): 2059 (x / y) \ (x / L(y,z,u)) = a(u,z,y). [para(2058(a,1),54(a,1,1))]. given #1933 (H,wt=15): 2060 (x / y) * (y / L(x,z,u)) = a(u,z,x). [para(2059(a,1),284(a,1)),flip(a)]. given #1934 (H,wt=18): 2061 a(x,y,L(z,x,y)) = (L(z,x,y) / u) * (u / z). [para(341(a,1),2060(a,1,2,2)),flip(a)]. given #1935 (H,wt=15): 2062 (L(x,y,z) / u) * (u / x) = a(y,z,x). [para(2061(a,1),1554(a,1))]. given #1936 (H,wt=17): 2063 (L(x \ y,z,u) / y) * x = a(z,u,x \ y). [para(53(a,1),2062(a,1,2))]. given #1937 (H,wt=23): 2056 (a(x,y,z) * u) * L(z,y,x) = a(x,y,z) * (u * L(z,y,x)). [para(2053(a,1),1395(a,1,1))]. given #1938 (H,wt=20): 2065 (a(x,y,z) * u) * L(z,y,x) = z * T(u,L(z,y,x)). [para(2056(a,2),1528(a,1))]. given #1939 (H,wt=25): 2049 L(x,y,(z / R(u \ 1,w,v5)) * a(u \ 1,w,v5)) = L(x,y,z * u). [para(1962(a,2),2043(a,1,3))]. given #1940 (H,wt=23): 2066 L(x,y,(z / R(u \ 1,w,v5)) * a(w,u,v5)) = L(x,y,z * u). [para(1476(a,1),2049(a,1,3,2))]. given #1941 (H,wt=28): 2067 L(x,y,(z / (u / w)) * a(u,w * (u \ 1),u)) = L(x,y,z * (w * (u \ 1))). [para(1620(a,1),2066(a,1,3,1,2))]. given #1942 (H,wt=19): 2068 L(x,y,z * (u * (w \ 1))) = L(x,y,z / (w / u)). [para(2067(a,1),2052(a,1))]. given #1943 (H,wt=19): 2070 L(x,y,z * (u * (w \ 1))) = L(x,y,z * (u / w)). [para(2068(a,2),2048(a,1))]. given #1944 (H,wt=33): 2054 (a(x,y,z) * L(z,y,x)) \ (u * L(z,y,x)) = T(u / a(x,y,z),a(x,y,z) * L(z,y,x)). [para(2053(a,1),162(a,1,1)),flip(a)]. given #1945 (H,wt=33): 2071 (a(x,y,z) * L(z,y,x)) \ (u * L(z,y,x)) = T(u * a(y,x,z),a(x,y,z) * L(z,y,x)). [para(1996(a,1),2054(a,2,1))]. given #1946 (H,wt=25): 2072 (a(x,y,z) * L(z,y,x)) \ (u * L(z,y,x)) = T(u * a(y,x,z),z). [para(1437(a,1),2071(a,2,2))]. given #1947 (H,wt=17): 2073 x \ (y * L(x,z,u)) = T(y * a(z,u,x),x). [para(1437(a,1),2072(a,1,1))]. given #1948 (H,wt=29): 2074 T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = u \ ((a(y,z,u) \ x) * L(u,y,z)). [para(110(a,2),2073(a,2,1)),flip(a)]. given #1949 (H,wt=29): 2075 T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = u \ ((a(z,y,u) * x) * L(u,y,z)). [para(1472(a,1),2074(a,2,2,1))]. given #1950 (H,wt=26): 2076 T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = u \ (u * T(x,L(u,y,z))). [para(2065(a,1),2075(a,2,2))]. given #1951 (H,wt=22): 2077 T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = T(x,L(u,y,z)). [para(2076(a,2),13(a,1))]. given #1952 (H,wt=22): 2078 T(x * K(a(y,z,u) * x,a(z,y,u)),u) = T(x,L(u,z,y)). [para(1472(a,1),2077(a,1,1,2,1))]. given #1953 (H,wt=17): 2079 T(x * K(x,a(y,z,u)),u) = T(x,L(u,y,z)). [para(2004(a,1),2078(a,1,1,2))]. given #1954 (H,wt=15): 2080 T(T(x,a(y,z,u)),u) = T(x,L(u,y,z)). [para(1035(a,2),2079(a,1,1))]. given #1955 (H,wt=15): 2081 T(T(x,y),a(z,u,y)) = T(x,L(y,z,u)). [para(2080(a,1),38(a,1)),flip(a)]. given #1956 (H,wt=19): 2082 T(x,L(y,z,u)) \ T(x,y) = K(a(z,u,y),T(x,y)). [para(2081(a,1),1054(a,2,1)),flip(a)]. given #1957 (H,wt=19): 2083 K(x,y) * K(L(y,z,u),x) = K(a(z,u,y),T(x,y)). [para(2082(a,1),1183(a,1)),flip(a)]. given #1958 (H,wt=17): 2084 K(x,y) * K(L(y,z,u),x) = K(x,a(u,z,y)). [para(2083(a,2),1858(a,1))]. given #1959 (H,wt=13): 2085 a(x,y,K(z,u)) = K(u,a(y,x,z)). [para(2084(a,1),1734(a,1)),flip(a)]. given #1960 (H,wt=36): 1872 ((x * (y * ((y * x) \ 1))) * L(z,y,x)) * L(u,y,x) = (x * (y * ((y * x) \ 1))) * L(z * u,y,x). [para(1870(a,2),1871(a,2,1)),flip(a)]. given #1961 (H,wt=30): 2086 L(x * L(y,L(x,z,u),u * (z * ((z * u) \ 1))),z,u) = L(x,z,u) * L(y,z,u). [hyper(524,a,1872,a),flip(a)]. given #1962 (H,wt=28): 2087 L(x * L(y,L(x,z,u),u * (z / (z * u))),z,u) = L(x,z,u) * L(y,z,u). [para(2070(a,1),2086(a,1,1,2))]. given #1963 (H,wt=24): 2088 L(x * L(y,L(x,z,u),K(u,z)),z,u) = L(x,z,u) * L(y,z,u). [para(1058(a,2),2087(a,1,1,2,3))]. given #1964 (H,wt=29): 2089 L(x * L(T(y,L(x,z,u)),L(x,z,u),K(u,z)),z,u) = L(y,z,u) * L(x,z,u). [para(2088(a,2),103(a,1))]. given #1965 (H,wt=37): 2064 L((x * K(y,z)) \ x,u,w) * K(y,L(z,x,L((x * K(y,z)) \ x,u,w))) = a(u,w,(x * K(y,z)) \ x). [para(2063(a,1),1880(a,1)),flip(a)]. given #1966 (H,wt=37): 2090 L(x \ (x / K(y,z)),u,w) * K(y,L(z,x,L((x * K(y,z)) \ x,u,w))) = a(u,w,(x * K(y,z)) \ x). [para(313(a,1),2064(a,1,1,1))]. given #1967 (H,wt=33): 2091 L(K(x,y),z,u) * K(y,L(x,w,L((w * K(y,x)) \ w,z,u))) = a(z,u,(w * K(y,x)) \ w). [para(1717(a,1),2090(a,1,1,1))]. given #1968 (H,wt=33): 2093 K(x,L(y,z,u)) * K(y,L(x,w,L((w * K(y,x)) \ w,z,u))) = a(z,u,(w * K(y,x)) \ w). [para(1879(a,1),2091(a,1,1))]. given #1969 (H,wt=33): 2094 K(x,L(y,z,u)) * K(y,L(x,w,L(w \ (w / K(y,x)),z,u))) = a(z,u,(w * K(y,x)) \ w). [para(313(a,1),2093(a,1,2,2,3,1))]. given #1970 (H,wt=29): 2095 a(x,y,(z * K(u,w)) \ z) = K(w,L(u,x,y)) * K(u,L(w,z,L(K(w,u),x,y))). [para(1717(a,1),2094(a,1,2,2,3,1)),flip(a)]. given #1971 (H,wt=29): 2097 a(x,y,(z * K(u,w)) \ z) = K(w,L(u,x,y)) * K(u,L(w,z,K(w,L(u,x,y)))). [para(1879(a,1),2095(a,2,2,2,3))]. given #1972 (H,wt=21): 2098 a(x,y,(z * K(u,w)) \ z) = K(w,L(u,x,y)) * K(u,w). [para(1696(a,1),2097(a,2,2,2))]. given #1973 (H,wt=21): 2099 a(x,y,z \ (z / K(u,w))) = K(w,L(u,x,y)) * K(u,w). [para(16(a,1),2098(a,1,3,1))]. given #1974 (H,wt=17): 2100 K(x,L(y,z,u)) * K(y,x) = a(z,u,K(x,y)). [para(606(a,1),2099(a,1,3)),flip(a)]. given #1975 (H,wt=17): 2101 K(x,L(y,z,u)) * K(y,x) = K(y,a(u,z,x)). [para(2100(a,2),2085(a,1))]. given #1976 (H,wt=25): 2102 (x \ K(y,x)) \ K(y,a(z,u,x)) = T(T(x,L(y,u,z)),x \ K(y,x)). [para(2101(a,1),1110(a,1,2))]. given #1977 (H,wt=25): 2103 T(T(x,L(y,z,u)),x \ K(y,x)) = (K(x,y) * x) * K(y,a(u,z,x)). [para(2102(a,1),1799(a,1))]. given #1978 (H,wt=23): 2104 T(T(x,L(y,z,u)),x \ K(y,x)) = T(x,y) * K(y,a(u,z,x)). [para(1043(a,2),2103(a,2,1))]. given #1979 (H,wt=23): 2105 T(T(x,L(y,z,u)),x \ K(y,x)) = T(x * K(y,a(u,z,x)),y). [para(2104(a,2),1703(a,2)),flip(a)]. given #1980 (H,wt=21): 2106 T(T(x,L(y,z,u)),x \ K(y,x)) = T(L(x,z,K(u,y)),y). [para(2020(a,1),2105(a,2,1))]. given #1981 (H,wt=21): 2107 T(T(x,L(y,z,u)),x \ K(y,x)) = L(T(x,y),z,K(u,y)). [para(2106(a,2),40(a,2)),flip(a)]. given #1982 (H,wt=15): 2108 L(T(x,y),z,K(u,y)) = T(x,L(y,z,u)). [para(2107(a,1),1088(a,1))]. given #1983 (H,wt=25): 2110 L(T(x,y),K(z,y) \ u,K(z,y) * (u / K(z,y))) = T(x,L(y,u,z)). [para(2108(a,1),1863(a,2))]. given #1984 (H,wt=25): 2111 L(T(x,y),K(y,z) * u,K(z,y) * (u / K(z,y))) = T(x,L(y,u,z)). [para(1075(a,1),2110(a,1,2))]. given #1985 (H,wt=25): 2112 L(T(x,y),K(y,z) * u,K(z,y) * (u * K(y,z))) = T(x,L(y,u,z)). [para(1716(a,1),2111(a,1,3,2))]. given #1986 (H,wt=21): 2113 L(T(x,y),K(y,z) * u,T(u,K(y,z))) = T(x,L(y,u,z)). [para(1093(a,1),2112(a,1,3))]. given #1987 (H,wt=19): 2114 L(T(x,y),K(y,z),T(u,K(y,z))) = T(x,L(y,u,z)). [para(2113(a,1),1575(a,1)),flip(a)]. given #1988 (H,wt=15): 2115 L(T(x,y),K(y,z),u) = T(x,L(y,u,z)). [para(2114(a,1),1307(a,1)),flip(a)]. given #1989 (H,wt=15): 2116 L(T(x,y),y,K(z,u)) = T(x,L(y,z,u)). [para(2115(a,1),2025(a,1)),flip(a)]. given #1990 (H,wt=24): 2117 L(x * T(y,L(L(x,z,u),u,z)),z,u) = L(y,z,u) * L(x,z,u). [para(2116(a,1),2089(a,1,1,2))]. given #1991 (H,wt=18): 2118 L(x * T(y,x),z,u) = L(y,z,u) * L(x,z,u). [para(341(a,1),2117(a,1,1,2,2))]. given #1992 (H,wt=16): 2119 L(x,y,z) * L(u,y,z) = L(x * u,y,z). [para(80(a,1),2118(a,1,1)),flip(a)]. given #1993 (H,wt=16): 2120 L(L(x,y,z) * u,z,y) = x * L(u,z,y). [para(341(a,1),2119(a,1,1)),flip(a)]. given #1994 (H,wt=16): 2121 L(x * L(y,z,u),u,z) = L(x,u,z) * y. [para(341(a,1),2119(a,1,2)),flip(a)]. given #1995 (H,wt=18): 2122 L(L(x,y,z) * u,z,y) = L(u,z,y) * T(x,u). [para(103(a,1),2121(a,1,1))]. given #1996 (H,wt=15): 2123 L(x,y,z) * T(u,x) = u * L(x,y,z). [para(2122(a,1),2120(a,1))]. given #1997 (H,wt=10): 2124 T(x,L(y,z,u)) = T(x,y). [hyper(98,a,2123,a)]. given #1998 (H,wt=12): 2126 K(x,L(y,z,u)) = T(x,y) / x. [para(2124(a,1),1036(a,2,1))]. given #1999 (H,wt=10): 2133 K(x,L(y,z,u)) = K(x,y). [para(2126(a,2),1036(a,2)),flip(a)]. given #2000 (H,wt=10): 2135 L(K(x,y),z,u) = K(x,y). [para(2133(a,1),1879(a,2))]. given #2001 (H,wt=8): 2138 a(x,y,K(z,u)) = 1. [hyper(34,a,2135,a)]. given #2002 (H,wt=8): 2147 K(x,a(y,z,u)) = 1. [para(2138(a,1),2085(a,1)),flip(a)]. -------- Proof 1 -------- "aK1". ============================== PROOF ================================= % Proof 1 at 50.72 (+ 2.20) seconds: "aK1". % Length of proof is 1998. % Level of proof is 253. % Maximum clause weight is 37.000. % Given clauses 2002 (7.913 givens/level). 1 x * y = u & x * z = u -> y = z # label(non_clause). [assumption]. 2 y * x = u & z * x = u -> y = z # label(non_clause). [assumption]. 3 x * y = x * z -> y = z # label(non_clause). [assumption]. 4 y * x = z * x -> y = z # label(non_clause). [assumption]. 5 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 6 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 7 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 8 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 9 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 10 a(K(x,y),z,u) = 1 # label("aK1") # label(non_clause) # label(goal). [goal]. 11 1 * x = x. [assumption]. 12 x * 1 = x. [assumption]. 13 x \ (x * y) = y. [assumption]. 14 x * (x \ y) = y. [assumption]. 15 (x * y) / y = x. [assumption]. 16 (x / y) * y = x. [assumption]. 17 x * y != z | x * u != z | u = y. [clausify(1)]. 18 x * y != z | u * y != z | u = x. [clausify(2)]. 19 x * y != x * z | y = z. [clausify(3)]. 20 x * y != z * y | x = z. [clausify(4)]. 23 (x * (y * z)) \ ((x * y) * z) = a(x,y,z) # label("associator"). [assumption]. 24 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(23),flip(a)]. 25 (x * y) \ (y * x) = K(y,x) # label("commutator"). [assumption]. 26 K(x,y) = (y * x) \ (x * y). [copy(25),flip(a)]. 27 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 28 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(27),flip(a)]. 29 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 30 R(x,y,z) = ((x * y) * z) / (y * z). [copy(29),flip(a)]. 31 x \ (y * x) = T(y,x). [assumption]. 32 T(x,y) = y \ (x * y). [copy(31),flip(a)]. 33 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. 34 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. 35 T(x,y) != x | T(y,x) = y. [clausify(7)]. 36 T(x,y) != x | K(x,y) = 1. [clausify(8)]. 37 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. 38 T(T(x,y),z) = T(T(x,z),y). [assumption]. 39 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 40 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(39),flip(a)]. 41 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 42 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(41),flip(a)]. 43 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 44 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(43),flip(a)]. 45 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 46 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 47 (x * (y * x)) * z = x * (y * (x * z)) # label("left Bol"). [assumption]. 48 a(K(c1,c2),c3,c4) != 1 # label("aK1") # answer("aK1"). [deny(10)]. 49 1 \ x = x. [para(11(a,1),13(a,1,2))]. 50 x \ x = 1. [para(12(a,1),13(a,1,2))]. 52 x / 1 = x. [para(12(a,1),15(a,1,1))]. 53 x / (y \ x) = y. [para(14(a,1),15(a,1,1))]. 54 (x / y) \ x = y. [para(16(a,1),13(a,1,2))]. 55 1 * x != y | x = y. [para(11(a,1),19(a,2))]. 56 x * y != z | x \ z = y. [para(14(a,1),19(a,1)),flip(a)]. 57 x * (x \ (y * z)) != y * u | u = z. [para(14(a,2),19(a,2)),flip(a)]. 59 x * 1 != y | x = y. [para(12(a,1),20(a,2))]. 60 ((x * y) * z) / z != u * y | u = x. [para(15(a,2),20(a,2)),flip(a)]. 61 x * y != z | z / y = x. [para(16(a,1),20(a,1)),flip(a)]. 62 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(24(a,2),14(a,1,2))]. 63 (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y). [para(14(a,1),24(a,2,1,2)),flip(a)]. 64 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(16(a,1),24(a,2,2,1)),flip(a)]. 65 (x * y) * K(y,x) = y * x. [para(26(a,2),14(a,1,2))]. 66 x \ ((y \ x) * y) = K(y \ x,y). [para(14(a,1),26(a,2,1)),flip(a)]. 67 x \ (y * (x / y)) = K(y,x / y). [para(16(a,1),26(a,2,1)),flip(a)]. 68 (x * (y / x)) \ y = K(y / x,x). [para(16(a,1),26(a,2,2)),flip(a)]. 69 (x * y) * L(z,y,x) = x * (y * z). [para(28(a,2),14(a,1,2))]. 70 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(14(a,1),28(a,2,1)),flip(a)]. 71 L(x \ y,x,z) = (z * x) \ (z * y). [para(14(a,1),28(a,2,2,2))]. 72 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(16(a,1),28(a,2,1)),flip(a)]. 73 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(14(a,1),30(a,2,1,1))]. 74 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(14(a,1),30(a,2,2)),flip(a)]. 75 R(x,y,z) * (y * z) = (x * y) * z. [para(30(a,2),16(a,1,1))]. 76 R(x / y,y,z) = (x * z) / (y * z). [para(16(a,1),30(a,2,1,1))]. 77 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(16(a,1),30(a,2,2)),flip(a)]. 78 T(1,x) = x \ x. [para(11(a,1),32(a,2,2))]. 79 T(x,x) = x. [para(32(a,2),13(a,1))]. 80 x * T(y,x) = y * x. [para(32(a,2),14(a,1,2))]. 81 T(x,x \ y) = (x \ y) \ y. [para(14(a,1),32(a,2,2))]. 82 T(x / y,y) = y \ x. [para(16(a,1),32(a,2,2))]. 83 (x * (y * (x * z))) / z = x * (y * x). [hyper(18,a,16,a,b,47,a),flip(a)]. 84 x * (1 * (x * y)) = (x * x) * y. [para(11(a,1),47(a,1,1,2)),flip(a)]. 85 x * ((y / x) * (x * z)) = (x * y) * z. [para(16(a,1),47(a,1,1,2)),flip(a)]. 88 T(T(x,y),x) = T(x,y). [para(79(a,1),38(a,1,1)),flip(a)]. 89 (x * y) / K(x,y) = y * x. [para(26(a,2),53(a,1,2))]. 90 (x * (y * z)) / L(z,y,x) = x * y. [para(28(a,2),53(a,1,2))]. 91 (x * y) / T(x,y) = y. [para(32(a,2),53(a,1,2))]. 92 R(x,y,z) \ ((x * y) * z) = y * z. [para(30(a,2),54(a,1,1))]. 93 T(1,x) = 1. [para(78(a,2),50(a,1))]. 97 T(x * (y * x),x) = y * (x * x). [hyper(17,a,47,a(flip),b,80,a)]. 98 x * y != z * x | T(z,x) = y. [para(80(a,1),19(a,1)),flip(a)]. 99 (T(x,y) * y) \ (x * y) = K(y,T(x,y)). [para(80(a,1),26(a,2,2)),flip(a)]. 100 (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y). [para(80(a,1),28(a,2,1)),flip(a)]. 101 T(x,y) \ (x * y) = T(y,T(x,y)). [para(80(a,1),32(a,2,2)),flip(a)]. 102 x * T(T(y,x),z) = T(y,z) * x. [para(38(a,1),80(a,1,2))]. 103 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(40(a,2),80(a,1,2))]. 104 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(42(a,2),80(a,1,2))]. 105 (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y). [para(30(a,2),82(a,1,1)),flip(a)]. 106 K(T(x,y),x) = 1. [hyper(36,a,88,a)]. 107 T(x,y) * x = x * T(x,y). [para(88(a,1),80(a,1,2)),flip(a)]. 108 K(x \ y,y / x) = 1. [para(82(a,1),106(a,1,1))]. 109 x / T(y,y \ x) = y \ x. [para(14(a,1),91(a,1,1))]. 110 x * K(y \ x,y) = (y \ x) * y. [para(14(a,1),65(a,1,1))]. 111 (x * y) \ ((y * x) * (K(x,y) * z)) = L(z,K(x,y),y * x). [para(65(a,1),28(a,2,1)),flip(a)]. 112 ((x / y) * (y \ x)) * 1 = (y \ x) * (x / y). [para(108(a,1),65(a,1,2))]. 113 T(T(x,y),x \ z) = T((x \ z) \ z,y). [para(81(a,1),38(a,1,1)),flip(a)]. 114 (x * y) / K(y,T(x,y)) = T(x,y) * y. [para(80(a,1),89(a,1,1))]. 115 K(x \ 1,x) = (x \ 1) * x. [para(66(a,1),49(a,1))]. 116 (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y). [para(115(a,2),24(a,2,1,2)),flip(a)]. 117 ((x * (y \ 1)) * y) / K(y \ 1,y) = R(x,y \ 1,y). [para(115(a,2),30(a,2,2)),flip(a)]. 118 K(x,1 / x) = x * (1 / x). [para(67(a,1),49(a,1))]. 119 (x * x) * y = x * (x * y). [para(11(a,1),84(a,1,2)),flip(a)]. 120 (x * (x * y)) / y = x * x. [hyper(61,a,119,a)]. 122 (x * y) / (x \ y) = x * x. [para(14(a,1),120(a,1,1,2))]. 123 x / (x \ 1) = x * x. [para(12(a,1),122(a,1,1))]. 124 x / ((x / y) \ y) = (x / y) * (x / y). [para(16(a,1),122(a,1,1))]. 125 (1 / x) * (1 / x) = (1 / x) / x. [para(54(a,1),123(a,1,2)),flip(a)]. 126 (x / y) * (y * y) = T(y * x,y). [para(16(a,1),97(a,1,1,2)),flip(a)]. 127 T(x / y,z) * y = y * T(y \ x,z). [para(82(a,1),102(a,1,2,1)),flip(a)]. 128 T(x * y,x) / (x * x) = y / x. [hyper(61,a,126,a)]. 130 T(x,x) / (x * x) = 1 / x. [para(12(a,1),128(a,1,1,1))]. 131 T(x,y) / (y * y) = (y \ x) / y. [para(14(a,1),128(a,1,1,1))]. 132 x / (x * x) = 1 / x. [para(79(a,1),130(a,1,1))]. 133 (1 / x) \ x = x * x. [para(132(a,1),54(a,1,1))]. 134 (x \ 1) / x = 1 / (x * x). [para(93(a,1),131(a,1,1)),flip(a)]. 135 (1 / (x * x)) * x = x \ 1. [para(134(a,1),16(a,1,1))]. 136 (x * y) * L(z,y,x) != x * u | y * z = u. [para(28(a,2),57(a,1,2)),flip(b)]. 137 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(14(a,1),69(a,1,1))]. 138 (x * y) * z != x * (y * u) | L(u,y,x) = z. [para(69(a,1),19(a,1)),flip(a)]. 139 L(x \ 1,x,y) = (y * x) \ y. [para(12(a,1),71(a,2,2))]. 140 L((x \ y) \ z,x \ y,x) = y \ (x * z). [para(14(a,1),71(a,2,1))]. 141 L(x \ (y \ z),x,y) = (y * x) \ z. [para(14(a,1),71(a,2,2))]. 142 L(x \ y,x,z / y) = ((z / y) * x) \ z. [para(16(a,1),71(a,2,2))]. 143 L(x \ (y * x),x,y) = T(y,y * x). [para(71(a,2),32(a,2)),flip(a)]. 144 (x * y) / L(z \ y,z,x) = x * z. [para(71(a,2),53(a,1,2))]. 145 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(80(a,1),71(a,2,2))]. 146 x / L(y \ 1,y,x) = x * y. [para(139(a,2),53(a,1,2))]. 147 x / L(y,1 / y,x) = x * (1 / y). [para(54(a,1),146(a,1,2,1))]. 148 R(x,x,y) = x. [hyper(18,a,119,a(flip),b,75,a)]. 151 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(44(a,1),75(a,1,1))]. 152 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(46(a,1),75(a,1,1))]. 153 R(T(x,y),x,z) = T(x,y). [para(148(a,1),42(a,2,1))]. 154 R(R(x,y,z),x,u) = R(x,y,z). [para(148(a,1),46(a,1,1)),flip(a)]. 155 R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u). [para(153(a,1),46(a,1,1)),flip(a)]. 156 (T(x,y) * x) * z = T(x,y) * (x * z). [para(153(a,1),75(a,1,1)),flip(a)]. 157 (R(x,y,z) * x) * u = R(x,y,z) * (x * u). [para(154(a,1),75(a,1,1)),flip(a)]. 158 R(1 / x,x,y) = y / (x * y). [para(11(a,1),76(a,2,1))]. 159 R((x / y) / z,z,y) = x / (z * y). [para(16(a,1),76(a,2,1))]. 160 R(x / (y / z),y / z,z) = (x * z) / y. [para(16(a,1),76(a,2,2))]. 161 R(x / y,y,z) \ (x * z) = y * z. [para(76(a,2),54(a,1,1))]. 162 T(R(x / y,y,z),y * z) = (y * z) \ (x * z). [para(76(a,2),82(a,1,1))]. 163 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(14(a,1),92(a,1,2,1))]. 164 R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z. [para(80(a,1),92(a,1,2,1))]. 165 L(x \ (y \ ((y * x) * z)),x,y) = z. [para(141(a,2),13(a,1))]. 166 L(T(x,y),y,x) = T(x,x * y). [para(32(a,2),143(a,1,1))]. 167 (x * (y * z)) / (x \ z) = x * (y * x). [para(14(a,1),83(a,1,1,2,2))]. 168 x \ ((x * y) * z) = (y / x) * (x * z). [hyper(56,a,85,a)]. 169 (x / y) * (y * L(z,x,y)) = x * z. [hyper(17,a,69,a(flip),b,85,a)]. 170 (x * y) * (x \ z) = x * ((y / x) * z). [para(14(a,1),85(a,1,2,2)),flip(a)]. 171 (x / y) \ (x * z) = y * L(z,x,y). [hyper(56,a,169,a)]. 174 x * L(y \ z,y,x) = (y / x) \ z. [para(14(a,1),171(a,1,2)),flip(a)]. 175 L(x \ y,x,z) = z \ ((x / z) \ y). [hyper(56,a,174,a),flip(a)]. 176 (x / y) \ (y \ z) = y * ((y * x) \ z). [para(141(a,1),174(a,1,2)),flip(a)]. 177 L(x \ ((x / y) * z),x,y) = y \ z. [para(13(a,1),175(a,2,2))]. 178 L((x * y) \ z,x * y,y) = y \ (x \ z). [para(15(a,1),175(a,2,2,1))]. 179 L(x \ (x / y),x,y) = y \ 1. [para(50(a,1),175(a,2,2))]. 180 L(x \ y,x,z \ x) = (z \ x) \ (z \ y). [para(53(a,1),175(a,2,2,1))]. 181 L((x * y) \ z,x * y,K(x,y)) = K(x,y) \ ((y * x) \ z). [para(89(a,1),175(a,2,2,1))]. 182 (x * y) \ (x * z) = x \ ((y / x) \ z). [para(175(a,1),71(a,1)),flip(a)]. 183 (x * y) \ (x * (y / x)) = x \ 1. [para(179(a,1),71(a,1)),flip(a)]. 184 (x * y) * (x \ 1) = x * (y / x). [para(183(a,1),14(a,1,2))]. 185 (x * (y * x)) \ (x * y) = x \ 1. [para(15(a,1),183(a,1,2,2))]. 186 (x * y) * (x \ 1) != x * z | y / x = z. [para(183(a,1),57(a,1,2)),flip(b)]. 187 x * ((x \ y) / x) = y * (x \ 1). [para(14(a,1),184(a,1,1)),flip(a)]. 188 (x * (y / x)) / (y * (x \ 1)) = R(x,y,x \ 1). [para(184(a,1),30(a,2,1)),flip(a)]. 189 (x * y) * (y \ 1) = y * (T(x,y) / y). [para(80(a,1),184(a,1,1))]. 190 (x * y) / (x \ 1) = x * (y * x). [para(185(a,1),53(a,1,2))]. 191 x \ (y * (x \ 1)) = (x \ y) / x. [hyper(56,a,187,a)]. 192 x * (y \ 1) != y * z | (y \ x) / y = z. [para(187(a,1),19(a,1))]. 193 x * ((x \ y) * x) = y / (x \ 1). [para(14(a,1),190(a,1,1)),flip(a)]. 194 (x * y) / (y \ 1) = y * (T(x,y) * y). [para(80(a,1),190(a,1,1))]. 195 x \ (y / (x \ 1)) = (x \ y) * x. [hyper(56,a,193,a)]. 196 (x / (y \ 1)) \ ((y * (y \ x)) * y) = a(y,y \ x,y). [para(193(a,1),24(a,2,1)),flip(a)]. 197 L(x,y,z) * x = x * L(x,y,z). [para(79(a,1),103(a,1,2,1)),flip(a)]. 198 L(x / y,z,u) * y = y * L(y \ x,z,u). [para(82(a,1),103(a,1,2,1)),flip(a)]. 199 x * T(y,y * x) = L(y,x,y) * x. [para(166(a,1),103(a,1,2))]. 200 L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). [para(14(a,1),199(a,1,2,2)),flip(a)]. 201 R(x,y,z) * x = x * R(x,y,z). [para(79(a,1),104(a,1,2,1)),flip(a)]. 202 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(82(a,1),104(a,1,2,1)),flip(a)]. 203 (x * (y * R(y,z,u))) \ ((x * R(y,z,u)) * y) = a(x,R(y,z,u),y). [para(201(a,1),24(a,2,1,2)),flip(a)]. 204 R(x,R(y,z,u),y) * (y * R(y,z,u)) = (x * R(y,z,u)) * y. [para(201(a,1),75(a,1,2))]. 205 1 / ((1 / x) \ x) = (1 / x) / x. [para(124(a,2),125(a,1))]. 206 (1 / x) / x = 1 / (x * x). [para(133(a,1),205(a,1,2)),flip(a)]. 207 (1 / (x * x)) * x = 1 / x. [para(206(a,1),16(a,1,1))]. 208 1 / x = x \ 1. [para(207(a,1),135(a,1))]. 209 x * (1 / x) = 1. [para(208(a,2),14(a,1,2))]. 210 (x \ 1) \ 1 = x. [para(208(a,1),53(a,1))]. 211 T(x \ 1,x) = x \ 1. [para(208(a,1),82(a,1,1))]. 212 x / L(1 / y,y,x) = x * y. [para(208(a,2),146(a,1,2,1))]. 213 R(x \ 1,x,y) = y / (x * y). [para(208(a,1),158(a,1,1))]. 214 R((1 / x) / y,y,x) = (y * x) \ 1. [para(208(a,1),159(a,2))]. 215 x * ((x \ 1) * (x * y)) = (x * 1) * y. [para(208(a,1),85(a,1,2,1))]. 216 (x * y) * (1 / x) = x * (y / x). [para(208(a,2),184(a,1,2))]. 217 (x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(209(a,1),24(a,2,1,2)),flip(a)]. 218 K(x,1 / x) = 1. [para(209(a,1),118(a,2))]. 219 T(x,x \ 1) = x. [para(210(a,1),81(a,2))]. 220 T(T(x,y),x \ 1) = T(x,y). [para(210(a,1),113(a,2,1))]. 221 T(x,1 / x) = x. [hyper(37,a,218,a)]. 222 K(x \ 1,x) = 1. [para(53(a,1),218(a,1,2))]. 224 L(x,y,z) * (x \ 1) = (x \ 1) * L(x,y,z). [para(219(a,1),103(a,1,2,1)),flip(a)]. 225 T(T(x,y),1 / x) = T(x,y). [para(221(a,1),38(a,1,1)),flip(a)]. 226 L(x,y,z) * (1 / x) = (1 / x) * L(x,y,z). [para(221(a,1),103(a,1,2,1)),flip(a)]. 227 L(x \ 1,y,z) * x = x * L(x \ 1,y,z). [para(211(a,1),103(a,1,2,1)),flip(a)]. 228 T(x \ 1,T(x,y)) = x \ 1. [hyper(35,a,220,a)]. 229 T(1 / x,T(x,y)) = 1 / x. [hyper(35,a,225,a)]. 230 T(x \ 1,(x \ y) \ y) = x \ 1. [para(81(a,1),228(a,1,2))]. 231 T(1 / (x \ 1),T(x \ 1,y)) = x. [para(229(a,2),53(a,1))]. 232 (x * y) * (1 / y) = y * (T(x,y) / y). [para(80(a,1),216(a,1,1))]. 233 T((x \ y) \ y,x \ 1) = (x \ y) \ y. [hyper(35,a,230,a)]. 234 T(x,T(x \ 1,y)) = x. [para(53(a,1),231(a,1,1))]. 235 T(x,T(1 / x,y)) = x. [para(208(a,2),234(a,1,2,1))]. 236 T(x,((1 / x) \ y) \ y) = x. [para(81(a,1),235(a,1,2))]. 237 R((x \ 1) / y,y,x) = (y * x) \ 1. [para(208(a,1),214(a,1,1,1))]. 238 (x * T(x \ y,z)) / x = T(y / x,z). [hyper(61,a,127,a)]. 239 L(x,y,T(y,z)) = x. [hyper(17,a,69,a,b,156,a),flip(a)]. 240 x * (T(x,y) \ 1) = x / T(x,y). [hyper(17,a,184,a(flip),b,156,a(flip))]. 242 (x * T(x,y)) * z = T(x,y) * (x * z). [para(107(a,1),156(a,1,1))]. 243 L(x,y / z,z \ y) = x. [para(82(a,1),239(a,1,3))]. 244 L(x,y,(y \ z) \ z) = x. [para(81(a,1),239(a,1,3))]. 245 (x / T(x,y)) \ z = T(x,y) * (x \ z). [para(239(a,1),174(a,1,2)),flip(a)]. 246 x \ (x / T(x,y)) = T(x,y) \ 1. [para(239(a,1),179(a,1))]. 247 (x * y) / (x \ z) = x * ((y / z) * x). [para(16(a,1),167(a,1,1,2))]. 248 ((x \ y) / x) * (x * z) = x \ (y * z). [para(14(a,1),168(a,1,2,1)),flip(a)]. 249 (x / T(x,y)) * z = x * (T(x,y) \ z). [hyper(17,a,156,a(flip),b,170,a(flip))]. 250 x * (((x \ y) / x) * z) = y * (x \ z). [para(14(a,1),170(a,1,1)),flip(a)]. 251 (x / y) \ (y \ (x * y)) = y * K(x,y). [para(26(a,2),176(a,2,2))]. 252 x \ (((x \ y) / x) \ z) = y \ (x * z). [para(14(a,1),182(a,1,1)),flip(a)]. 253 x * ((x \ 1) * (x * y)) = x * y. [para(12(a,1),215(a,2,1))]. 254 (x \ 1) * (x * y) = y. [hyper(19,a,253,a)]. 255 x / (y * x) = y \ 1. [hyper(61,a,254,a)]. 256 (x \ 1) \ y = x * y. [hyper(56,a,254,a)]. 259 (x \ 1) * y = x \ y. [para(14(a,1),254(a,1,2))]. 260 (x \ 1) * y != z | x * z = y. [para(254(a,1),19(a,1)),flip(a)]. 261 R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). [para(254(a,1),30(a,2,1,1))]. 262 T(x \ 1,x * y) = (x * y) \ y. [para(254(a,1),32(a,2,2))]. 263 (1 / x) * (x * y) = y. [para(208(a,2),254(a,1,1))]. 264 (x \ y) / y = x \ 1. [para(14(a,1),255(a,1,2))]. 265 (x / y) \ 1 = y / x. [para(16(a,1),255(a,1,2)),flip(a)]. 266 (x * y) / ((z * x) * y) = R(z,x,y) \ 1. [para(75(a,1),255(a,1,2))]. 268 R(x \ 1,x,y) = x \ 1. [para(255(a,1),213(a,2))]. 269 (1 / x) * y = x \ y. [para(54(a,1),256(a,1,1)),flip(a)]. 270 (1 / x) \ y = x * y. [para(208(a,2),256(a,1,1))]. 271 (x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z). [para(259(a,1),24(a,2,1)),flip(a)]. 272 T(x \ 1,y) = y \ (x \ y). [para(259(a,1),32(a,2,2))]. 273 x \ T(y,x \ 1) = y * (x \ 1). [para(259(a,1),80(a,1))]. 274 x * (y * (1 / x)) = T(y,1 / x). [hyper(98,a,263,a),flip(a)]. 275 T(1 / x,x * y) = (x * y) \ y. [para(263(a,1),32(a,2,2))]. 276 L(x \ 1,x,y) / y = (y * x) \ 1. [para(139(a,2),264(a,1,1))]. 277 R(x / y,y,z) \ 1 = (y * z) / (x * z). [para(161(a,1),264(a,1,1)),flip(a)]. 278 (x \ y) / y = 1 / x. [para(264(a,2),208(a,2)),flip(a)]. 279 (x / y) * (y / x) = 1. [para(265(a,1),14(a,1,2))]. 280 1 / (x / y) = y / x. [para(265(a,1),53(a,1,2))]. 281 x * L(y \ 1,y,x) = x / y. [para(265(a,1),174(a,2))]. 282 L(x \ 1,x,y) = y \ (y / x). [para(265(a,1),175(a,2,2))]. 283 (x / y) * ((y / x) * z) = z. [para(265(a,1),254(a,1,1))]. 284 (x / y) \ z = (y / x) * z. [para(265(a,1),256(a,1,1))]. 285 T(1 / x,y) = y \ (x \ y). [para(269(a,1),32(a,2,2))]. 286 x \ T(y,1 / x) = y * (1 / x). [para(269(a,1),80(a,1))]. 287 T(x,(x * y) \ y) = x. [para(270(a,1),236(a,1,2,1))]. 289 T(x,x \ y) / y = 1 / (x \ y). [para(81(a,2),278(a,1,1))]. 290 T(x / y,x \ y) = x / y. [para(16(a,1),287(a,1,2,1))]. 291 ((x * y) \ y) * x = x * ((x * y) \ y). [para(287(a,1),80(a,1,2))]. 293 (x / T(x,y)) \ (T(x,y) \ 1) = T(x \ 1,x / T(x,y)). [para(246(a,1),272(a,2,2)),flip(a)]. 294 x \ ((y / z) \ x) = T(z / y,x). [para(265(a,1),272(a,1,1)),flip(a)]. 295 (x / y) * (y * z) = x * L(z,y,x). [hyper(17,a,169,a,b,283,a)]. 296 (x / y) * T(x * y,x) = x * x. [hyper(17,a,126,a,b,283,a)]. 297 (x / y) * z != u | (y / x) * u = z. [para(283(a,1),19(a,1)),flip(a)]. 298 L(x \ y,x,z) = z \ ((z / x) * y). [para(283(a,1),177(a,1,1,2))]. 299 (x / y) \ (x * L(z,y,x)) = y * z. [para(284(a,2),169(a,1))]. 300 x * L(y \ z,y,x) = (x / y) * z. [para(284(a,1),174(a,2))]. 301 (x / y) \ (x * z) = x \ ((x * y) * z). [para(284(a,2),168(a,2)),flip(a)]. 302 (x * y) * (x \ z) = x * ((x / y) \ z). [para(284(a,2),170(a,2,2))]. 303 (x / y) * (x \ z) = x * ((x * y) \ z). [para(284(a,1),176(a,1))]. 304 (x * y) \ (x * z) = x \ ((x / y) * z). [para(284(a,1),182(a,2,2))]. 305 T(1 / (x * y),y * x) = (y * x) \ K(y,x). [para(26(a,2),285(a,2,2))]. 306 T((x / y) / x,y) = (x / y) / x. [para(54(a,1),290(a,1,2))]. 307 (x / y) * (x \ y) = (x \ y) * (x / y). [para(290(a,1),80(a,1,2)),flip(a)]. 308 (x / y) / L(y \ 1,y,x) = x. [hyper(61,a,281,a)]. 309 x * ((x * y) \ x) = x / y. [para(139(a,1),281(a,1,2))]. 310 x * L(1 / y,y,x) = x / y. [para(208(a,2),281(a,1,2,1))]. 311 x * L(y,y \ 1,x) = x / (y \ 1). [para(210(a,1),281(a,1,2,1))]. 312 ((x \ y) \ y) * (x \ 1) = ((x \ y) \ y) / x. [para(244(a,1),281(a,1,2))]. 313 (x * y) \ x = x \ (x / y). [hyper(56,a,309,a),flip(a)]. 314 x / (x \ y) = x * (y \ x). [para(14(a,1),309(a,1,2,1)),flip(a)]. 315 x * ((y * x) \ x) = x / T(y,x). [para(80(a,1),309(a,1,2,1))]. 316 x / (x \ (x / y)) = x * y. [para(313(a,1),53(a,1,2))]. 317 (x * y) \ ((x * y) / K(y,x)) = (y * x) \ (x * y). [para(65(a,1),313(a,1,1)),flip(a)]. 318 x / T(y \ 1,x) = x * ((y \ x) \ x). [para(272(a,2),314(a,1,2))]. 319 (x * (y \ x)) \ z = ((x \ y) / x) * z. [para(314(a,1),284(a,1,1))]. 320 T(x \ (x / y),z) = L(T(y \ 1,z),y,x). [para(282(a,1),40(a,2,1)),flip(a)]. 321 T(x,y) * (1 / x) = T(x,y) / x. [para(239(a,1),310(a,1,2))]. 322 T(x,y) * (x \ 1) = x \ T(x,y). [para(220(a,1),273(a,1,2)),flip(a)]. 323 T(x * y,1 / x) = x * (x * (y / x)). [para(216(a,1),274(a,1,2)),flip(a)]. 324 T(x,y) * (1 / x) = x \ T(x,y). [para(225(a,1),286(a,1,2)),flip(a)]. 325 L(x \ y,x,y) = T(y / x,y). [para(294(a,1),175(a,2))]. 326 T((x * y) / x,x * y) = L(y,x,x * y). [para(13(a,1),325(a,1,1)),flip(a)]. 327 x * L(y,y,x) = T(y * x,y). [hyper(17,a,169,a,b,296,a),flip(a)]. 328 x \ T(y * x,y) = L(y,y,x). [hyper(56,a,327,a)]. 329 L(x,x,x \ y) = (x \ y) \ T(y,x). [para(14(a,1),328(a,1,2,1)),flip(a)]. 330 ((x / y) / x) * y = y * ((x / y) / x). [para(306(a,1),80(a,1,2)),flip(a)]. 331 (x \ T(x,y)) / x = x \ (x \ T(x,y)). [para(322(a,1),191(a,1,2)),flip(a)]. 332 T(x,y) / x = x \ T(x,y). [para(324(a,1),321(a,1)),flip(a)]. 333 x * (T(x,y) / x) = T(x,y). [para(332(a,2),14(a,1,2))]. 334 T(T(x,y) / x,x) = T(x,y) / x. [para(332(a,2),82(a,2))]. 335 T(x / y,y) / (x / y) = (x / y) \ (y \ x). [para(82(a,1),332(a,2,2))]. 336 (x \ T(x,y)) \ z = (x / T(x,y)) * z. [para(332(a,1),284(a,1,1))]. 337 T(x,y) != x * z | T(x,y) / x = z. [para(333(a,1),19(a,1))]. 338 T(x,T(x,y) / x) = x. [hyper(35,a,334,a)]. 339 ((x / y) \ 1) / (y \ x) = ((y \ x) * (x / y)) \ 1. [para(243(a,1),276(a,1,1))]. 340 L(x,y,z) = z \ ((z / y) * (y * x)). [hyper(56,a,295,a(flip)),flip(a)]. 341 L(L(x,y,z),z,y) = x. [hyper(17,a,169,a(flip),b,295,a(flip))]. 342 x * (y * L(z,x,y)) = (x * y) * z. [para(295(a,1),85(a,1,2))]. 343 x \ ((x * y) * z) = y * L(z,x,y). [para(295(a,1),168(a,2))]. 344 L((x * y) \ z,x,y) = y \ (x \ z). [para(141(a,1),341(a,1,1))]. 345 L(T(x,x * y),x,y) = T(x,y). [para(166(a,1),341(a,1,1))]. 346 L(x,y,z) = z \ (y \ ((y * z) * x)). [para(165(a,1),341(a,1,1))]. 347 L(x,T(y,z),y) = x. [para(341(a,1),239(a,1)),flip(a)]. 348 L(x,y \ z,z / y) = x. [para(341(a,1),243(a,1)),flip(a)]. 349 (x * T(x,y)) * z = x * (T(x,y) * z). [para(347(a,1),69(a,1,2))]. 350 (T(x,y) / x) \ (T(x,y) * z) = x * z. [para(347(a,1),171(a,2,2))]. 351 ((x \ y) \ 1) / (y / x) = ((y / x) * (x \ y)) \ 1. [para(348(a,1),276(a,1,1))]. 352 L(T(x,y),x,x \ y) = T(x,x \ y). [para(14(a,1),345(a,1,1,2))]. 353 L((x \ y) \ z,x \ y,y) = y \ (x * z). [para(53(a,1),298(a,2,2,1))]. 354 L(x,y / x,z) = z \ ((z / (y / x)) * y). [para(54(a,1),298(a,1,1))]. 355 x \ (y * L(z,x \ y,y)) = (x \ y) * z. [para(53(a,1),299(a,1,1))]. 356 T(x,y) / L(y,y,y \ x) = y \ x. [para(329(a,2),53(a,1,2))]. 357 (x * y) * z != x * (y * L(u,x,y)) | z = u. [para(342(a,2),19(a,2))]. 358 x * (L(y,x,z) * z) = (x * z) * T(y,z). [para(103(a,1),342(a,1,2))]. 359 (x \ y) * L(z,x,x \ y) = x \ (y * z). [para(14(a,1),343(a,1,2,1)),flip(a)]. 360 x \ ((x * y) * T(z,y)) = L(z,x,y) * y. [para(343(a,2),103(a,1))]. 361 L(x,x,x \ y) * y = y * T(x,x \ y). [para(352(a,1),103(a,1,2)),flip(a)]. 362 ((x \ y) \ y) * (x \ 1) = x \ ((x \ y) \ y). [para(233(a,1),273(a,1,2)),flip(a)]. 363 (x * T(y,z)) / x = T((x * y) / x,z). [para(13(a,1),238(a,1,1,2,1))]. 364 (x * T(x,y)) * (x \ z) = T(x,y) * z. [para(14(a,1),242(a,2,2))]. 365 x * (((x \ y) / z) * x) = y / (x \ z). [para(14(a,1),247(a,1,1)),flip(a)]. 366 ((x \ 1) * y) / ((x \ 1) \ z) = x \ ((y / z) * (x \ 1)). [para(247(a,2),259(a,1))]. 368 (x / y) \ T(x,y) = y * K(x,y). [para(32(a,2),251(a,1,2))]. 369 ((x \ y) / x) \ z = x * (y \ (x * z)). [para(252(a,1),14(a,1,2)),flip(a)]. 370 x \ ((x / T(y,x)) * z) = (y * x) \ (x * z). [para(80(a,1),304(a,1,1)),flip(a)]. 371 (x \ y) * (x / y) = x * ((x * y) \ y). [para(307(a,1),303(a,1))]. 372 T(x * (y * x),1 / x) = x * (x * y). [para(15(a,1),323(a,2,2,2))]. 373 T(x * y,1 / x) != x * z | x * (y / x) = z. [para(323(a,2),19(a,1))]. 374 (x \ T(x,y)) \ z = x * (T(x,y) \ z). [para(336(a,2),249(a,1))]. 375 T(x,y) * (x * z) = x * (T(x,y) * z). [para(349(a,1),242(a,1)),flip(a)]. 376 (T(x,y) * z) / (x * z) = T(x,y) / x. [para(350(a,1),53(a,1,2))]. 377 x * ((T(x,y) / x) * z) = T(x,y) * z. [para(364(a,1),170(a,1)),flip(a)]. 378 x * ((x / T(x,y)) \ z) = T(x,y) * z. [para(364(a,1),302(a,1)),flip(a)]. 379 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(364(a,1),349(a,1)),flip(a)]. 380 x * (((((x \ y) / z) * x) / x) * u) = (y / (x \ z)) * (x \ u). [para(365(a,1),170(a,1,1)),flip(a)]. 381 ((x \ (y * x)) / x) \ y = x * K(x,y). [para(26(a,2),369(a,2,2))]. 382 T(x,y) \ (x * (T(x,y) * z)) = x * z. [hyper(56,a,375,a)]. 383 T(x,y) * z != x * (T(x,y) * u) | x * u = z. [para(375(a,1),19(a,1)),flip(a)]. 385 (T(x,y) * z) / (x * z) = x \ T(x,y). [para(376(a,2),332(a,1))]. 386 x \ (T(x,y) * z) = (T(x,y) / x) * z. [hyper(56,a,377,a)]. 387 x * ((x \ T(x,y)) * z) = T(x,y) * z. [para(332(a,1),377(a,1,2,1))]. 388 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(56,a,379,a)]. 389 ((x \ T(x,y)) / x) * z = T(x,y) * (x \ (x \ z)). [hyper(17,a,250,a,b,379,a),flip(a)]. 391 (T(x,y) / y) \ x = y * K(y,x). [para(32(a,2),381(a,1,1,1))]. 392 T(x,y) \ (x * z) = x * (T(x,y) \ z). [para(14(a,1),382(a,1,2,2))]. 393 (T(R(x,y,z),u) * (y * z)) / ((x * y) * z) = R(x,y,z) \ T(R(x,y,z),u). [para(75(a,1),385(a,1,2))]. 394 R(x \ T(x,y),x * z,u) = ((T(x,y) * z) * u) / ((x * z) * u). [para(385(a,1),76(a,1,1))]. 395 (x \ T(x,y)) * z = T(x,y) * (x \ z). [hyper(17,a,379,a,b,387,a)]. 396 T(x,y) * z != x * u | (x \ T(x,y)) * z = u. [para(387(a,1),19(a,1))]. 398 T(x,y) * (x \ (T(x,y) \ z)) = x \ z. [para(14(a,1),388(a,1,2)),flip(a)]. 399 x \ (T(x,y) \ (x * z)) = T(x,y) \ z. [hyper(56,a,392,a(flip))]. 400 x * (T(x,y) \ 1) = T(x,y) \ x. [para(12(a,1),392(a,1,2)),flip(a)]. 401 x * (T(x,y) \ y) = T(y,T(x,y)). [para(392(a,1),101(a,1))]. 402 (x \ T(x,y)) \ z = T(x,y) \ (x * z). [para(392(a,2),374(a,2))]. 403 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(56,a,400,a)]. 404 x / T(x,y) = T(x,y) \ x. [para(400(a,1),240(a,1)),flip(a)]. 405 x / (x / T(x,y)) = T(x,y). [para(404(a,2),53(a,1,2))]. 406 T(x / y,y) \ (x / y) = (x / y) / (y \ x). [para(82(a,1),404(a,1,2)),flip(a)]. 407 (x / y) / T(x / y,y) = (y \ x) \ (x / y). [para(82(a,1),404(a,2,1))]. 408 (T(x,y) \ x) \ z = T(x,y) * (x \ z). [para(404(a,1),245(a,1,1))]. 409 (T(x,y) \ x) * z = x * (T(x,y) \ z). [para(404(a,1),249(a,1,1))]. 410 (x / y) * ((y \ x) \ y) = T(y,T(x / y,y)). [para(82(a,1),401(a,1,2,1))]. 411 T(T(x,y) \ 1,x) = T(x,y) \ 1. [para(403(a,1),272(a,2))]. 412 T(x,T(x,y) \ 1) = x. [hyper(35,a,411,a)]. 413 T(x / y,(y \ x) \ 1) = x / y. [para(82(a,1),412(a,1,2,1))]. 414 (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y). [para(413(a,1),273(a,1,2)),flip(a)]. 415 T(x,x \ y) * (x \ z) = (x \ ((x \ y) \ y)) * z. [para(81(a,1),395(a,1,1,2)),flip(a)]. 416 ((x \ 1) \ T(x \ 1,x * y)) * z = ((x * y) \ y) * ((x \ 1) \ z). [para(262(a,1),395(a,2,1))]. 417 (T(x,y) / x) \ z = T(x,y) \ (x * z). [para(332(a,2),402(a,1,1))]. 418 T(x,T(x,y) \ x) = x. [hyper(98,a,409,a)]. 419 T(x,x / T(x,y)) = x. [para(404(a,2),418(a,1,2))]. 420 a(x,y,z) \ ((x * y) * z) = T(x * (y * z),a(x,y,z)). [para(62(a,1),32(a,2,2)),flip(a)]. 421 L(x,x \ y,x) = y \ (y / (x \ 1)). [para(193(a,1),70(a,1,2)),flip(a)]. 422 x / L(y,y \ x,y) = x * (y \ 1). [para(421(a,2),316(a,1,2))]. 423 L(x,y,z / y) = L(x,y,z). [para(72(a,1),340(a,2)),flip(a)]. 424 L(x,y,z * y) = L(x,y,z). [para(15(a,1),423(a,1,3)),flip(a)]. 425 L(x,y \ z,z) = L(x,y \ z,y). [para(53(a,1),423(a,1,3)),flip(a)]. 426 L(x,y,z \ 1) = L(x,y,z \ y). [para(264(a,1),423(a,1,3))]. 427 L(x,y,z \ y) = L(x,y,1 / z). [para(278(a,1),423(a,1,3)),flip(a)]. 428 L(L(x,y,z / y),z,y) = x. [para(423(a,2),341(a,1,1))]. 429 L(L(x,y,z),z,y / z) = x. [para(423(a,2),341(a,1))]. 430 L(x,T(y,z),y / T(y,z)) = x. [para(423(a,2),347(a,1))]. 431 L((x * (y / x)) \ z,x,y) = (y / x) \ (x \ z). [para(423(a,1),344(a,1))]. 432 L(L(x,y,z),z * y,y) = x. [para(424(a,1),341(a,1,1))]. 433 L(L(x,y,z \ 1),z \ y,y) = x. [para(264(a,1),428(a,1,1,3))]. 434 L(L(x,y,1 / z),z \ y,y) = x. [para(278(a,1),428(a,1,1,3))]. 435 L(x,y / z,z) = L(x,y,z). [para(341(a,1),428(a,1,1)),flip(a)]. 436 L(T(x,y / x),y,x) = T(x,x * (y / x)). [para(345(a,1),428(a,1,1))]. 437 L(L(x,y * z,K(y,z)),K(y,z),z * y) = x. [para(89(a,1),429(a,1,3))]. 438 L(x,y * z,z) = L(x,y,z). [para(341(a,1),432(a,1,1))]. 439 L(x,y,z \ y) = L(x,z,z \ y). [para(53(a,1),435(a,1,2)),flip(a)]. 440 L(x,y \ 1,z) = L(x,y \ z,z). [para(264(a,1),435(a,1,2))]. 441 L(x,T(y,y \ z),z) = L(x,1 / (y \ z),z). [para(289(a,1),435(a,1,2)),flip(a)]. 442 L(x,T(y,z),T(y,z) \ y) = x. [para(404(a,1),430(a,1,3))]. 443 L(L(x,y,z \ 1),z \ y,z) = x. [para(433(a,1),425(a,1)),flip(a)]. 444 L(x,y,T(y,z) \ y) = x. [para(439(a,2),442(a,1))]. 445 L(x,y,z \ 1) = L(x,z,z \ y). [para(439(a,1),426(a,2))]. 446 L(x,y,y \ z) = L(x,z,1 / y). [para(439(a,1),427(a,1))]. 447 L(x,y,y / T(y,z)) = x. [para(404(a,2),444(a,1,3))]. 448 L(x,y,T(y,z) \ 1) = x. [para(444(a,1),426(a,2))]. 449 L(x,T(y,z) \ 1,y) = x. [para(448(a,1),341(a,1,1))]. 450 L(x,(y \ z) \ 1,z / y) = x. [para(82(a,1),449(a,1,2,1))]. 451 ((x \ y) \ 1) \ (((x \ y) \ 1) / (y / x)) = (y / x) \ 1. [para(450(a,1),179(a,1))]. 452 ((x \ y) \ 1) \ ((((x \ y) \ 1) / (y / x)) * z) = (y / x) \ z. [para(450(a,1),177(a,1))]. 453 L(x,y \ 1,z) = L(x,y \ z,y). [para(440(a,2),425(a,1))]. 454 L((x \ 1) \ y,x \ z,x) = z \ ((z / (x \ 1)) * y). [para(177(a,1),443(a,1,1))]. 455 L(x,y * z,y \ 1) = L(x,y,z). [para(13(a,1),445(a,2,3))]. 456 L(x,y \ 1,y * z) = L(x,z,y). [para(13(a,1),453(a,2,2))]. 457 L(x,y \ 1,z * y) = L(x,T(z,y),y). [para(32(a,2),453(a,2,2))]. 458 (x * (y \ 1)) * L(z,y \ x,y) = x * ((y \ 1) * z). [para(453(a,1),69(a,1,2))]. 459 R(x,x \ y,y \ z) = z / ((x \ y) * (y \ z)). [para(14(a,1),73(a,2,1))]. 460 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(74(a,1),52(a,1)),flip(a)]. 461 R(x,y,y \ 1) / (y \ 1) = x * y. [hyper(61,a,460,a)]. 462 (x * y) \ R(x,y,y \ 1) = y \ 1. [hyper(56,a,460,a)]. 463 R(x / y,y,y \ 1) = x * (y \ 1). [para(16(a,1),460(a,1,1)),flip(a)]. 464 (x * L(x,y,z)) * (x \ 1) = R(L(x,y,z),x,x \ 1). [para(197(a,1),460(a,1,1))]. 465 x * (T(y,x) / x) = R(y,x,x \ 1). [para(460(a,1),189(a,1)),flip(a)]. 466 x \ R(y,x,x \ 1) = T(y,x) / x. [hyper(56,a,465,a)]. 467 x * (T(R(x,y,z),x) / x) = R(x,y,z). [para(465(a,2),154(a,1))]. 468 x * (T(y,x) / x) = R(y,x,1 / x). [para(208(a,2),465(a,2,3))]. 469 x \ R(y,x,1 / x) = T(y,x) / x. [para(208(a,2),466(a,1,2,3))]. 470 (x * y) * (1 / y) = R(x,y,1 / y). [para(468(a,1),232(a,2))]. 471 (x * y) \ R(x,y,1 / y) = 1 / y. [hyper(56,a,470,a)]. 472 R(x / y,y,1 / y) = x * (1 / y). [para(16(a,1),470(a,1,1)),flip(a)]. 473 (R(x,y,z) * x) \ R(x,y,z) = 1 / x. [para(154(a,1),471(a,1,2))]. 474 R(T(x / y,z),y,1 / y) = T(x * (1 / y),z). [para(472(a,1),42(a,2,1))]. 475 R(T((x * y) / x,z),x,1 / x) = (x * T(y,z)) * (1 / x). [para(363(a,1),472(a,1,1))]. 476 x * (R(T(x,x),y,z) / x) = R(x,y,z). [para(42(a,2),467(a,1,2,1))]. 477 R(x,y,z) \ (R(x,y,z) / x) = 1 / x. [para(473(a,1),313(a,1)),flip(a)]. 478 x * (R(x,y,z) / x) = R(x,y,z). [para(79(a,1),476(a,1,2,1,1))]. 479 R(x,y,z) / x = x \ R(x,y,z). [hyper(56,a,478,a),flip(a)]. 480 (x \ R(x,y,z)) * x = R(x,y,z). [para(479(a,1),16(a,1,1))]. 481 T(x \ R(x,y,z),x) = x \ R(x,y,z). [para(479(a,1),82(a,1,1))]. 482 (x \ R(x,y,z)) \ u = (x / R(x,y,z)) * u. [para(479(a,1),284(a,1,1))]. 483 L(L(x,R(y,z,u),y),y,y \ R(y,z,u)) = x. [para(479(a,1),429(a,1,3))]. 484 R(x,y,z) \ (R(x,y,z) / x) = x \ 1. [para(477(a,2),208(a,1))]. 485 K(x \ R(x,y,z),x) = 1. [hyper(36,a,481,a)]. 486 R(x,y,z) \ (x \ R(x,y,z)) = x \ 1. [para(479(a,1),484(a,1,2))]. 487 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(486(a,1),14(a,1,2))]. 488 (x * (1 / y)) * y = R(x,1 / y,y). [para(77(a,1),52(a,1)),flip(a)]. 489 R(x,1 / y,y) / y = x * (1 / y). [hyper(61,a,488,a)]. 490 R(x / (1 / y),1 / y,y) = x * y. [para(16(a,1),488(a,1,1)),flip(a)]. 491 x \ R(y,1 / x,x) = T(y * (1 / x),x). [para(488(a,1),32(a,2,2)),flip(a)]. 492 R(T(x / (1 / y),z),1 / y,y) / y = (1 / y) * T((1 / y) \ x,z). [para(489(a,2),127(a,1))]. 493 R(T(x / (1 / y),z),1 / y,y) = T(x * y,z). [para(490(a,1),42(a,2,1))]. 494 L(x,y \ T(y,z),y) = x. [hyper(17,a,387,a(flip),b,137,a)]. 495 L(x,T(y,z),y \ 1) = x. [para(494(a,1),443(a,1))]. 496 L(x,T(1 / y,z),y) = x. [para(54(a,1),495(a,1,3))]. 497 L(x,y \ (z \ y),z) = x. [para(285(a,1),496(a,1,2))]. 498 L(x,(y * z) \ z,y) = x. [para(275(a,1),496(a,1,2))]. 499 L(x,y \ z,y / z) = x. [para(54(a,1),497(a,1,2,2))]. 500 (x * ((x * y) \ y)) * z = x * (((x * y) \ y) * z). [para(498(a,1),69(a,1,2))]. 501 (x * ((x * y) \ y)) \ z = ((x * y) \ y) \ (x \ z). [para(498(a,1),141(a,1)),flip(a)]. 502 x / (1 / ((x * y) \ y)) = x * ((x * y) \ y). [para(498(a,1),212(a,1,2))]. 503 (((x * y) \ y) * x) * z = ((x * y) \ y) * (x * z). [para(498(a,1),342(a,1,2,2)),flip(a)]. 504 L(x,y,(z / y) / z) = x. [para(54(a,1),499(a,1,2))]. 505 ((x / y) / (x \ y)) * z = (x / y) * ((x \ y) \ z). [para(499(a,1),300(a,1,2)),flip(a)]. 506 ((x \ y) * (x / y)) * z = (x \ y) * ((x / y) * z). [para(499(a,1),342(a,1,2,2)),flip(a)]. 507 ((x \ y) * (x / y)) \ z = (x / y) \ ((x \ y) \ z). [para(499(a,1),344(a,1))]. 508 (x * ((y / x) / y)) * z = x * (((y / x) / y) * z). [para(504(a,1),342(a,1,2,2)),flip(a)]. 509 L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w). [para(140(a,1),45(a,1,1)),flip(a)]. 510 (x * (y * x)) \ z = x \ (y \ (x \ z)). [para(178(a,1),141(a,1)),flip(a)]. 511 x \ (y \ (x \ ((x * y) * x))) = a(x,y,x). [para(510(a,1),24(a,2)),flip(a)]. 512 x \ (y \ (x \ ((y * x) * x))) = K(y * x,x). [para(510(a,1),26(a,2)),flip(a)]. 513 T(x \ 1,x * (y * x)) = x \ (y \ (x \ (y * x))). [para(510(a,1),262(a,2))]. 514 L(x \ y,x,z \ 1) = (z \ x) \ (z \ y). [para(180(a,1),426(a,2))]. 515 R(x / y,y,z) = R(y / x,x,z) \ 1. [para(277(a,2),76(a,2))]. 516 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(433(a,1),355(a,1,2,2)),flip(a)]. 517 x \ (y * T(y \ (y / (x \ y)),z)) = (x \ y) * T((x \ y) \ 1,z). [para(320(a,2),355(a,1,2,2))]. 518 x * T(y,y \ x) != z * x | L(y,y,y \ x) = z. [para(361(a,1),20(a,1))]. 519 x \ L(x,x,y) = a(x,y,x). [para(346(a,2),511(a,1,2))]. 520 x * a(x,y,x) = L(x,x,y). [para(519(a,1),14(a,1,2))]. 522 (x \ y) \ (x \ (y * z)) = L(z,y,x \ 1). [para(13(a,1),514(a,1,1)),flip(a)]. 523 (x / y) * (y \ x) = (y \ x) * (x / y). [hyper(59,a,112,a)]. 524 (x * y) * L(L(z,y,x),u,w) != x * v5 | y * L(z,u,w) = v5. [para(45(a,1),136(a,1,2))]. 525 x * (R(x,y,z) \ 1) = x / R(x,y,z). [hyper(186,a,157,a),flip(a)]. 526 L(x,y,R(y,z,u)) = x. [hyper(138,a,157,a)]. 527 L(x,R(y,z,u),y) = x. [hyper(17,a,342,a(flip),b,157,a)]. 528 (x * R(x,y,z)) * u = R(x,y,z) * (x * u). [para(201(a,1),157(a,1,1))]. 529 L(x,y / z,(y * u) / (z * u)) = x. [para(76(a,1),526(a,1,3))]. 530 (x * R(x,y,z)) * u = x * (R(x,y,z) * u). [para(526(a,1),342(a,1,2,2)),flip(a)]. 531 L(x,R(y,z,u),y / R(y,z,u)) = x. [para(526(a,1),428(a,1))]. 532 ((x * y) / (z * y)) * z = z * R(z \ x,z,y). [para(76(a,1),202(a,1,1))]. 533 L(x,y,z) * (x \ 1) = x \ L(x,y,z). [para(224(a,2),259(a,1))]. 534 L(x,y,z) * (1 / x) = x \ L(x,y,z). [para(208(a,2),533(a,1,2))]. 535 T(1 / x,L(x,y,z)) = 1 / x. [hyper(98,a,226,a)]. 536 K(1 / x,L(x,y,z)) = 1. [hyper(36,a,535,a)]. 537 K(x \ 1,L(x,y,z)) = 1. [para(208(a,1),536(a,1,1))]. 538 K(L(x,y,z) \ 1,x) = 1. [para(341(a,1),537(a,1,2))]. 539 (x * (L(x,y,z) \ 1)) * 1 = (L(x,y,z) \ 1) * x. [para(538(a,1),65(a,1,2))]. 540 (x \ y) / (y / x) = (y / x) \ (x \ y). [para(82(a,1),335(a,1,1))]. 541 ((x \ y) \ y) / x = x \ ((x \ y) \ y). [para(362(a,1),312(a,1)),flip(a)]. 542 (x / y) / (y \ x) = (y \ x) \ (x / y). [para(82(a,1),406(a,1,1)),flip(a)]. 543 (x / y) * ((y \ x) \ y) = T(y,y \ x). [para(82(a,1),410(a,2,2))]. 544 L(x,y,y \ R(y,z,u)) = x. [para(527(a,1),483(a,1,1))]. 545 L(x,y \ R(y,z,u),y) = x. [para(544(a,1),341(a,1,1))]. 547 x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u. [para(545(a,1),137(a,1,2)),flip(a)]. 548 (x \ R(x,y,z)) \ u = R(x,y,z) \ (x * u). [para(545(a,1),140(a,1))]. 549 x / (1 / ((x * y) \ y)) = (y / x) \ (x \ y). [para(502(a,2),176(a,2)),flip(a)]. 550 x \ (y \ T(y * x,x)) = K(y * x,x). [para(32(a,2),512(a,1,2,2))]. 551 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(530(a,1),528(a,1)),flip(a)]. 553 x / (1 / ((x * y) \ y)) = (x \ y) / (y / x). [para(549(a,2),540(a,2)),flip(a)]. 554 x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. [para(14(a,1),551(a,1,2)),flip(a)]. 556 (1 / ((x * y) \ y)) / x = 1 / ((x \ y) / (y / x)). [para(553(a,1),280(a,1,2)),flip(a)]. 557 (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u). [hyper(17,a,547,a,b,554,a),flip(a)]. 558 R(x,y,z) * u != x * w | R(x,y,z) * (x \ u) = w. [para(554(a,1),19(a,1))]. 559 (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). [hyper(61,a,557,a)]. 560 ((R(x,y,z) * (x \ u)) * w) / (u * w) = R(x \ R(x,y,z),u,w). [para(557(a,1),30(a,2,1,1)),flip(a)]. 561 (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). [para(13(a,1),559(a,1,1,2))]. 562 R(x,x \ y,z) \ R(R(x,x \ y,z),u,w) = (R(R(x,x \ y,z),u,w) * ((x \ y) * z)) / (y * z). [para(163(a,1),559(a,1,1,2)),flip(a)]. 563 x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). [para(14(a,1),561(a,1,1))]. 564 T(x \ R(x,y,z),x * u) = (x * u) \ (R(x,y,z) * u). [para(561(a,1),82(a,1,1))]. 565 (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). [para(563(a,1),54(a,1,1))]. 566 (x / y) \ R(x / y,y,z) = (x * z) / ((x / y) * (y * z)). [para(161(a,1),563(a,1,2,2)),flip(a)]. 567 (x / y) \ R(x / y,y,z) = 1 / ((x / y) * ((y * z) / (x * z))). [para(277(a,1),563(a,1,2,2)),flip(a)]. 568 (x / y) \ R(x / y,y,z) = 1 / ((x / y) * R(y / x,x,z)). [para(515(a,2),563(a,1,2,2)),flip(a)]. 569 R(x,y,z) \ (x * u) = x * (R(x,y,z) \ u). [para(565(a,1),548(a,1)),flip(a)]. 570 x * (R(x,y,z) \ 1) = R(x,y,z) \ x. [para(12(a,1),569(a,1,2)),flip(a)]. 571 (x * y) / (x * (R(x,z,u) \ y)) = R(x,z,u). [para(569(a,1),53(a,1,2))]. 572 x / R(x,y,z) = R(x,y,z) \ x. [para(570(a,1),525(a,1)),flip(a)]. 573 (R(x,y,z) \ x) * R(x,y,z) = x. [para(572(a,1),16(a,1,1))]. 574 (R(x,y,z) \ x) \ x = R(x,y,z). [para(572(a,1),54(a,1,1))]. 575 1 / (R(x,y,z) \ x) = R(x,y,z) / x. [para(572(a,1),280(a,1,2))]. 576 (R(x,y,z) \ x) \ u = (R(x,y,z) / x) * u. [para(572(a,1),284(a,1,1))]. 577 L(x,R(y,z,u),R(y,z,u) \ y) = x. [para(572(a,1),531(a,1,3))]. 578 (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. [para(572(a,1),482(a,2,1))]. 579 L(x,y,R(y,z,u) \ 1) = x. [para(577(a,1),445(a,2))]. 580 R(x,y,z) \ (x * u) = (R(x,y,z) \ x) * u. [para(577(a,1),359(a,1,2)),flip(a)]. 581 ((R(x,y,z) \ 1) * u) / (x \ u) = (R(x,y,z) \ 1) * x. [para(579(a,1),144(a,1,2))]. 582 (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u. [para(479(a,1),576(a,2,1))]. 583 (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). [para(578(a,1),565(a,1))]. 584 (x * y) / ((R(x,z,u) \ x) * y) = R(x,z,u). [para(580(a,1),53(a,1,2))]. 585 (R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u). [para(582(a,2),557(a,1))]. 586 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(12(a,1),63(a,1,1))]. 587 x \ R(x,y,y \ 1) = a(x,y,y \ 1). [para(460(a,1),586(a,1,2))]. 588 x * a(x,y,y \ 1) = R(x,y,y \ 1). [para(587(a,1),14(a,1,2))]. 589 a(x / y,y,z) = (x * L(z,y,x)) \ (x * z). [para(295(a,1),64(a,1,1)),flip(a)]. 590 a((x \ y) / x,x,z) = (x \ (y * z)) \ ((x \ y) * z). [para(248(a,1),64(a,1,1)),flip(a)]. 591 a(x / y,y,z) = x \ ((x / L(z,y,x)) * z). [para(589(a,2),304(a,1))]. 592 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(105(a,2),42(a,2)),flip(a)]. 594 x \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(12(a,1),217(a,1,1))]. 595 x * L(1 / x,y,x) = a(y,x,1 / x). [para(594(a,1),343(a,1)),flip(a)]. 596 x \ R(x,y,1 / y) = a(x,y,1 / y). [para(470(a,1),594(a,1,2))]. 597 a(x / y,y,1 / y) = y * L(1 / y,x,y). [para(435(a,1),595(a,1,2)),flip(a)]. 598 R(x,y,1 / y) / x = a(x,y,1 / y). [para(596(a,1),479(a,2))]. 599 a(x,y,1 / y) * x = R(x,y,1 / y). [para(596(a,1),480(a,1,1))]. 600 a(x / y,y,1 / y) = a(x,y,1 / y). [para(597(a,2),595(a,1))]. 601 a(x * y,y,1 / y) = a(x,y,1 / y). [para(15(a,1),600(a,1,1)),flip(a)]. 602 R(x \ 1,x * y,z) = R(x,y,z) \ 1. [para(261(a,2),266(a,1))]. 603 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(14(a,1),602(a,1,2)),flip(a)]. 604 R(x,x \ y,z) \ x = x * R(x \ 1,y,z). [para(603(a,1),570(a,1,2)),flip(a)]. 605 L((x * (y / x)) \ z,x,y) = x * ((x * y) \ z). [para(431(a,2),176(a,1))]. 606 (x * y) \ ((x * y) / K(y,x)) = K(x,y). [para(317(a,2),26(a,2)),flip(a)]. 607 ((x \ y) * (y / x)) \ 1 = (x / y) / (x \ y). [para(265(a,1),339(a,1,1)),flip(a)]. 608 (x * (T(x,y) \ x)) \ z = T(x,y) * (x \ (x \ z)). [para(389(a,1),319(a,2))]. 609 (x \ (x \ T(x,y))) * z = T(x,y) * (x \ (x \ z)). [para(331(a,1),389(a,1,1))]. 610 (x * ((x * y) \ y)) * z = ((x * y) \ y) * (x * z). [para(291(a,1),503(a,1,1))]. 611 (x * ((x * y) \ y)) * z = (x \ y) * ((x / y) * z). [para(371(a,1),506(a,1,1))]. 612 ((x \ y) * (x / y)) \ z = (y / x) * ((x \ y) \ z). [para(507(a,2),284(a,1))]. 613 T(x \ 1,x * (y * x)) = x \ (y \ T(y,x)). [para(32(a,2),513(a,2,2,2))]. 614 (L(x,y,z) \ 1) * x = x * (L(x,y,z) \ 1). [hyper(59,a,539,a),flip(a)]. 615 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(614(a,1),259(a,1))]. 616 x * (1 / L(x,y,z)) = L(x,y,z) \ x. [para(208(a,2),615(a,1,2))]. 617 (1 / ((x * y) \ y)) / x = (y / x) / (x \ y). [para(556(a,2),280(a,1))]. 618 ((x * y) \ y) * (x * z) = x * (((x * y) \ y) * z). [para(610(a,1),500(a,1))]. 619 (x \ y) * ((x / y) * z) = x * (((x * y) \ y) * z). [para(611(a,1),500(a,1))]. 620 (x * ((x * y) \ y)) \ z = (y / x) * ((x \ y) \ z). [para(371(a,1),612(a,1,1))]. 621 ((x * y) \ y) \ (x \ z) = (y / x) * ((x \ y) \ z). [para(620(a,1),501(a,1)),flip(a)]. 622 (x / y) * ((y \ x) \ y) = ((y * x) \ x) \ 1. [para(50(a,1),621(a,1,2)),flip(a)]. 623 T(x,x \ y) = ((x * y) \ y) \ 1. [para(622(a,1),543(a,1)),flip(a)]. 624 T(x / y,(x / y) \ y) = (x \ y) \ 1. [para(16(a,1),623(a,2,1,1))]. 625 (x * y) \ y = 1 / T(x,x \ y). [para(623(a,2),53(a,1,2)),flip(a)]. 626 ((x * y) \ y) \ 1 = (x \ y) \ y. [para(623(a,1),81(a,1))]. 627 T(x,x \ y) \ 1 = (x * y) \ y. [para(623(a,2),210(a,1,1))]. 628 (x * (x * y)) \ (x * y) = 1 / T(x,y). [para(13(a,1),625(a,2,2,2))]. 629 1 / ((x * y) \ y) = (x \ y) \ y. [para(626(a,1),208(a,2))]. 630 ((x \ y) \ y) \ 1 = (x * y) \ y. [para(626(a,1),210(a,1,1))]. 631 ((x * y) \ y) \ z = ((x \ y) \ y) * z. [para(626(a,1),259(a,1,1)),flip(a)]. 632 (x * (x * y)) \ (x * y) = T(x,y) \ 1. [para(13(a,1),627(a,1,1,2)),flip(a)]. 633 T(x,x \ y) \ 1 = T(x \ 1,x * y). [para(627(a,2),262(a,2)),flip(a)]. 634 T(x,x \ y) \ x = x * ((x * y) \ y). [para(627(a,1),400(a,1,2)),flip(a)]. 635 ((x / y) \ y) \ y = 1 / (x \ y). [para(16(a,1),629(a,1,2,1)),flip(a)]. 636 ((x \ y) \ y) / x = (y / x) / (x \ y). [para(629(a,1),617(a,1,1))]. 637 ((x / y) * x) \ x = (y \ x) \ 1. [para(54(a,1),630(a,1,1,1)),flip(a)]. 638 (((T(x,y) * y) / (x * y)) \ (x * y)) \ (x * y) = 1 / K(y,T(x,y)). [para(99(a,1),635(a,2,2))]. 639 x / ((y \ x) \ 1) = (x / y) * x. [para(637(a,1),53(a,1,2))]. 640 L(x \ y,x,x / y) = (y \ x) \ 1. [para(637(a,1),142(a,2))]. 641 (x / (x / y)) * x = x / (y \ 1). [para(54(a,1),639(a,1,2,1)),flip(a)]. 642 (x * y) / ((K(x,y) \ (x * y)) \ 1) = (y * x) * (x * y). [para(89(a,1),639(a,2,1))]. 643 (x / (y \ 1)) / x = x / (x / y). [hyper(61,a,641,a)]. 644 (x / y) * ((y \ x) \ 1) = ((x / y) / x) * y. [para(640(a,1),300(a,1,2))]. 645 (x * y) / T(x,x * y) = (x * y) * (1 / T(x,y)). [para(628(a,1),315(a,1,2)),flip(a)]. 646 ((x \ y) \ y) * (x \ z) = (y / x) * ((x \ y) \ z). [para(631(a,1),621(a,1))]. 647 (x * y) / (T(x,y) \ 1) = x * (x * y). [para(632(a,1),53(a,1,2))]. 648 x * T(x \ 1,x * y) = T(x,x \ y) \ x. [para(633(a,1),400(a,1,2))]. 649 T(x,x \ y) \ x = (x / y) * (x \ y). [para(634(a,2),303(a,2)),flip(a)]. 650 ((x \ y) \ y) / x = (x \ y) \ (y / x). [para(636(a,2),542(a,1))]. 651 (x / y) * (T(y,y \ x) \ y) = y \ x. [hyper(297,a,649,a(flip))]. 652 (x \ y) \ (y / x) = x \ ((x \ y) \ y). [para(650(a,1),541(a,1))]. 653 (x / y) * ((y \ x) \ 1) = y \ ((y \ x) \ x). [para(652(a,1),414(a,2))]. 654 (x / y) * ((y \ x) \ 1) = y * ((x / y) / x). [para(644(a,2),330(a,1))]. 655 x \ ((x \ y) \ y) = x * ((y / x) / y). [para(654(a,1),653(a,1)),flip(a)]. 656 T(x,x \ y) * (x \ z) = (x * ((y / x) / y)) * z. [para(655(a,1),415(a,2,1))]. 657 T(x / y,(y \ x) \ x) = y \ x. [hyper(98,a,646,a)]. 658 T(x / y,T(y,y \ x)) = y \ x. [para(81(a,2),657(a,1,2))]. 659 T((x * y) / x,T(x,x \ (x * y))) = y. [para(658(a,2),13(a,1))]. 660 T((x * y) / x,T(x,y)) = y. [para(13(a,1),659(a,1,2,2))]. 661 T(R((x * y) / x,x,y),T(x * y,y)) = y. [para(76(a,2),660(a,1,1))]. 662 R(T((x * y) / x,T(x * y,y)),x,y) = y. [para(661(a,1),42(a,2))]. 663 T(x,x \ y) * (x \ z) = x * (((y / x) / y) * z). [para(656(a,2),508(a,1))]. 664 T(x,x \ y) * (x \ y) = x * (y / x). [para(16(a,1),663(a,2,2))]. 665 T(x,y) * (x \ (x * y)) = x * ((x * y) / x). [para(13(a,1),664(a,1,1,2))]. 666 T(x,y) * y = x * ((x * y) / x). [para(13(a,1),665(a,1,2))]. 667 T(x,y) \ (x * ((x * y) / x)) = y. [hyper(56,a,666,a)]. 668 x \ (T(x,y) * y) = (x * y) / x. [hyper(56,a,666,a(flip))]. 669 T(x / y,y) * y = (x / y) * (x / (x / y)). [para(16(a,1),666(a,2,2,1))]. 670 K((x * y) / x,x) = (T(x,y) * y) \ (x * y). [para(666(a,2),68(a,1,1)),flip(a)]. 671 T(x,y) \ ((x * y) / x) = x \ y. [para(667(a,1),399(a,1,2)),flip(a)]. 672 (x / y) * (x / (x / y)) = (y \ x) * y. [para(82(a,1),669(a,1,1)),flip(a)]. 673 K(x / (x / y),x / y) = ((y \ x) * y) \ x. [para(672(a,1),68(a,1,1)),flip(a)]. 674 K((x * y) / x,x) = K(y,T(x,y)). [para(670(a,2),99(a,1))]. 675 K(x \ y,T(x,x \ y)) = K(y / x,x). [para(14(a,1),674(a,1,1,1)),flip(a)]. 676 ((x * (y \ 1)) * y) / 1 = R(x,y \ 1,y). [para(222(a,1),117(a,1,2))]. 677 (x * (y \ 1)) * y = R(x,y \ 1,y). [para(676(a,1),52(a,1)),flip(a)]. 679 R(x,y \ 1,y) / y = x * (y \ 1). [hyper(61,a,677,a)]. 680 R(x / (y \ 1),y \ 1,y) = x * y. [para(16(a,1),677(a,1,1)),flip(a)]. 681 x * (((y \ 1) / x) * (x * y)) = R(x,y \ 1,y). [para(677(a,1),85(a,2))]. 682 L(x,y / (z \ 1),y * z) = x. [para(680(a,1),526(a,1,3))]. 683 (L(x \ 1,y,z) * x) * u = L(x \ 1,y,z) * (x * u). [para(268(a,1),151(a,1,1,1)),flip(a)]. 684 a(x,x \ y,x) = (y / (x \ 1)) \ (y * x). [para(14(a,1),196(a,1,2,1)),flip(a)]. 685 a(x,x \ y,x) = (y / (1 / x)) \ (y * x). [para(208(a,2),684(a,2,1,2))]. 686 a(x,x \ y,x) = ((x \ 1) / y) * (y * x). [para(684(a,2),284(a,1))]. 687 a(x,x \ y,x) = y \ ((y * (1 / x)) * x). [para(685(a,2),301(a,1))]. 688 a(x,x \ y,x) = y \ R(y,1 / x,x). [para(488(a,1),687(a,2,2))]. 689 (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). [para(259(a,1),271(a,1,2,1))]. 690 L(x * y,x \ z,x) = z \ ((z / (x \ 1)) * y). [para(256(a,1),454(a,1,1))]. 691 (x * (y \ 1)) * L(z,y \ x,y) = x * (y \ z). [para(259(a,1),458(a,2,2))]. 692 R(L(x,y,z),x,x \ 1) = x * (L(x,y,z) / x). [para(464(a,1),184(a,1))]. 693 L(R(x,x,x \ 1),y,z) = x * (L(x,y,z) / x). [para(692(a,1),44(a,1)),flip(a)]. 694 x * (L(x,y,z) / x) = L(x,y,z). [para(148(a,1),693(a,1,1)),flip(a)]. 695 L(x,y,z) / x = x \ L(x,y,z). [hyper(56,a,694,a),flip(a)]. 696 L(x,x,y) / x = a(x,y,x). [hyper(17,a,520,a,b,694,a)]. 697 a(x,y,x) * x = L(x,x,y). [para(696(a,1),16(a,1,1))]. 698 (x \ L(x,y,z)) * x = L(x,y,z). [para(695(a,1),16(a,1,1))]. 699 (x \ L(x,y,z)) \ u = (x / L(x,y,z)) * u. [para(695(a,1),284(a,1,1))]. 700 L(x,y,z) * (1 / x) = L(x,y,z) / x. [para(695(a,2),534(a,2))]. 701 L(x,y,z) != u * x | x \ L(x,y,z) = u. [para(698(a,1),20(a,1))]. 702 a((x \ y) / x,x,z) = a(x \ 1,y,z). [para(590(a,2),689(a,1))]. 703 a((x \ y) / x,x,z) = a(1 / x,y,z). [para(208(a,2),702(a,2,1))]. 704 T(x,y) * (x \ (T(x,y) \ 1)) = T(x \ 1,x / T(x,y)). [para(293(a,1),245(a,1)),flip(a)]. 705 (x \ y) / ((x \ 1) \ z) = x \ ((y / z) * (x \ 1)). [para(259(a,1),366(a,1,1))]. 706 x \ ((y / z) * (x \ 1)) = (x \ y) / (x * z). [para(256(a,1),705(a,1,2)),flip(a)]. 707 (x \ (y / z)) / x = (x \ y) / (x * z). [para(706(a,1),191(a,1)),flip(a)]. 708 (x \ y) * (((x \ y) \ 1) / (y / x)) = (y / x) \ 1. [para(451(a,1),256(a,1)),flip(a)]. 709 (x \ y) * (((x \ y) \ 1) / (y / x)) = x / y. [para(708(a,2),265(a,1))]. 710 ((x \ y) \ 1) / (y / x) = (x \ y) \ (x / y). [hyper(56,a,709,a),flip(a)]. 711 ((x / y) * (y \ x)) \ 1 = (y \ x) \ (y / x). [para(710(a,1),351(a,1)),flip(a)]. 712 ((x \ y) * (y / x)) \ 1 = (x \ y) \ (x / y). [para(523(a,1),711(a,1,1))]. 713 (x / y) / (x \ y) = (x \ y) \ (x / y). [para(712(a,1),607(a,1)),flip(a)]. 714 ((x \ y) \ (x / y)) * z = (x / y) * ((x \ y) \ z). [para(713(a,1),505(a,1,1))]. 715 (R(x,y,z) \ u) / (x \ u) = (R(x,y,z) \ 1) * x. [para(259(a,1),581(a,1,1))]. 716 (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. [para(715(a,2),259(a,1))]. 717 (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. [para(92(a,1),716(a,1,1))]. 718 (x * y) / ((x / z) * (z * y)) = R(z,x,y) \ z. [para(168(a,1),717(a,1,2))]. 719 L(x,L(y \ 1,z,u),y) = x. [hyper(357,a,683,a)]. 720 L(x,y,L(y \ 1,z,u)) = x. [hyper(138,a,683,a)]. 721 L(x,L(y,z,u),y \ 1) = x. [para(210(a,1),719(a,1,2,1))]. 722 L(x,1 / y,L(y,z,u)) = x. [para(54(a,1),720(a,1,3,1))]. 723 (L(x,y,z) * (x \ 1)) \ u = (x \ 1) \ (L(x,y,z) \ u). [para(721(a,1),344(a,1))]. 724 L(x,y \ L(y,z,u),y) = x. [para(721(a,1),443(a,1,1))]. 725 x \ (L(x,y,z) * u) = (x \ L(x,y,z)) * u. [para(721(a,1),516(a,1,2)),flip(a)]. 726 (L(x,y,z) * u) / ((1 / x) \ u) = L(x,y,z) * (1 / x). [para(722(a,1),144(a,1,2))]. 727 L(x,1 / L(y,z,u),y) = x. [para(341(a,1),722(a,1,3))]. 728 (x * y) / ((x \ L(x,z,u)) \ y) = x * (x \ L(x,z,u)). [para(724(a,1),144(a,1,2))]. 729 x * (1 / L(x,y,z)) = x / L(x,y,z). [para(727(a,1),147(a,1,2)),flip(a)]. 730 L(x,y,1 / L(y,z,u)) = x. [para(727(a,1),341(a,1,1))]. 731 x / L(x,y,z) = L(x,y,z) \ x. [para(729(a,1),616(a,1))]. 732 L(x,y,z) * (x / L(x,y,z)) = x. [para(731(a,2),14(a,1,2))]. 733 (L(x,y,z) \ x) * L(x,y,z) = x. [para(731(a,1),16(a,1,1))]. 734 x / (x / L(x,y,z)) = L(x,y,z). [para(731(a,2),53(a,1,2))]. 735 L(L(x,y,1 / L(y,z,u)),y / L(y,z,u),y) = x. [para(731(a,2),434(a,1,2))]. 736 (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. [para(731(a,1),699(a,2,1))]. 737 x * L(y,z,u) != y | L(y,z,u) \ y = x. [para(733(a,1),20(a,1)),flip(a)]. 738 L(x,y / L(y,z,u),y) = x. [para(730(a,1),735(a,1,1))]. 740 T(x \ 1,x / T(x,y)) = x \ 1. [para(704(a,1),398(a,1))]. 741 T(x \ 1,T(x,y) \ x) = x \ 1. [para(404(a,1),740(a,1,2))]. 743 T((x \ 1) \ 1,((x * y) \ y) \ (x \ 1)) = (x \ 1) \ 1. [para(262(a,1),741(a,1,2,1))]. 744 (L(x,y,z) * (x \ 1)) \ u = x * (L(x,y,z) \ u). [para(723(a,2),256(a,1))]. 745 (x \ L(x,y,z)) \ u = x * (L(x,y,z) \ u). [para(533(a,1),744(a,1,1))]. 746 (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). [para(745(a,1),736(a,1)),flip(a)]. 747 T(x,L(x,y,z) \ x) = x. [hyper(98,a,746,a)]. 748 (L(x,y,z) * u) / (x * u) = L(x,y,z) * (1 / x). [para(270(a,1),726(a,1,2))]. 749 (L(x,y,z) * u) / (x * u) = L(x,y,z) / x. [para(748(a,2),700(a,1))]. 750 (x * y) / ((L(x,z,u) \ x) * y) = x * (x \ L(x,z,u)). [para(736(a,1),728(a,1,2))]. 751 T(x,((x * y) \ y) \ (x \ 1)) = (x \ 1) \ 1. [para(210(a,1),743(a,1,1))]. 752 T(x,((x * y) \ y) \ (x \ 1)) = x. [para(751(a,2),210(a,1))]. 753 T(x,(y / x) * ((x \ y) \ 1)) = x. [para(621(a,1),752(a,1,2))]. 754 T(x,(x \ y) \ (y / x)) = x. [para(414(a,1),753(a,1,2))]. 755 T(x,(x \ (y * x)) \ y) = x. [para(15(a,1),754(a,1,2,2))]. 756 T(x,T(y,x) \ y) = x. [para(32(a,2),755(a,1,2,1))]. 757 (T(x,y) \ x) * y = y * (T(x,y) \ x). [para(756(a,1),80(a,1,2))]. 758 x * (T(y,x) \ y) = y * (T(y,x) \ x). [para(757(a,1),409(a,1))]. 759 x * (T(y,x) \ y) = T(x,T(y,x)). [para(758(a,2),401(a,1))]. 760 T(x,y) \ x = y \ T(y,T(x,y)). [hyper(56,a,759,a),flip(a)]. 761 T(x,y) \ x = T(y,T(x,y)) / y. [hyper(17,a,333,a,b,759,a)]. 762 T(x,y) * (y \ T(y,T(x,y))) = x. [para(760(a,1),14(a,1,2))]. 763 L(x,T(y,z) \ y,z) = x. [para(760(a,2),494(a,1,2))]. 764 ((T(x,y) \ x) * y) \ z = y \ ((T(x,y) \ x) \ z). [para(763(a,1),344(a,1))]. 765 (T(x,y) \ x) \ 1 = y / T(y,T(x,y)). [para(761(a,2),265(a,1,1))]. 766 T(x,T(y,x)) / x = y / T(y,x). [para(761(a,1),404(a,2)),flip(a)]. 767 (T(x,T(y,x)) / x) \ y = T(y,x). [para(766(a,2),54(a,1,1))]. 768 1 / (x / T(x,y)) = y / T(y,T(x,y)). [para(766(a,1),280(a,1,2))]. 769 T(x,T(y,x)) \ (x * y) = T(y,x). [para(767(a,1),417(a,1)),flip(a)]. 770 T(x,T(y,x)) * T(y,x) = x * y. [para(769(a,1),14(a,1,2))]. 771 (x * T(y,x)) / (T(y,x) \ 1) = T(y,x) * (x * y). [para(770(a,1),194(a,2,2))]. 772 T(x,T(y,x)) \ x = (T(y,x) \ y) \ 1. [para(765(a,2),404(a,1)),flip(a)]. 773 T(x,y) / x = y / T(y,T(x,y)). [para(768(a,1),280(a,1)),flip(a)]. 774 x / (T(y,x) / y) = T(x,T(y,x)). [para(773(a,2),405(a,1,2))]. 775 T(x,T(y,x) / y) = x. [para(773(a,2),419(a,1,2))]. 776 L(x,y,T(z,y) / z) = x. [para(773(a,2),447(a,1,3))]. 777 (T(x,y) / x) * y = y * (T(x,y) / x). [para(775(a,1),80(a,1,2))]. 778 ((T(x,y) / x) / y) \ ((T(x,y) / x) * z) = y * z. [para(776(a,1),299(a,1,2,2))]. 779 ((T(x,y) / x) / y) \ z = T(y,T(x,y)) * z. [para(774(a,1),284(a,2,1))]. 780 T(x,T(y,x)) \ x = T(y,x) * (y \ 1). [para(772(a,2),408(a,1))]. 781 x \ (T(x,y) * y) = y * (T(x,y) / x). [para(777(a,1),386(a,2))]. 782 T(x,T(y,x)) \ x = y \ T(y,x). [para(780(a,2),322(a,1))]. 783 T(x,T(y,x)) \ 1 = x \ (y \ T(y,x)). [para(782(a,1),403(a,1,2)),flip(a)]. 784 x * (T(y,x) / y) = (y * x) / y. [para(781(a,1),668(a,1))]. 786 x * (y \ T(y,x)) = (y * x) / y. [para(332(a,1),784(a,1,2))]. 787 ((T(x,y) \ x) * y) \ z = y \ (T(x,y) * (x \ z)). [para(408(a,1),764(a,2,2))]. 788 (x * y) / (T(x,y) \ 1) = T(x,y) * (y * x). [para(80(a,1),771(a,1,1))]. 789 T(x,y) * (y * x) = x * (x * y). [para(788(a,1),647(a,1))]. 790 T(x,y) = (x * (x * y)) / (y * x). [hyper(61,a,789,a),flip(a)]. 791 T(x,y) \ (x * (x * y)) = y * x. [hyper(56,a,789,a)]. 792 ((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y). [para(789(a,1),26(a,2,2)),flip(a)]. 793 x * (T(x,y) \ (x * y)) = y * x. [para(791(a,1),392(a,1)),flip(a)]. 794 T(x,y) \ (x * y) = T(y,x). [hyper(98,a,793,a),flip(a)]. 795 T(x,y) * T(y,x) = x * y. [para(794(a,1),14(a,1,2))]. 796 T(x,T(y,x)) = T(x,y). [para(794(a,1),101(a,1)),flip(a)]. 797 T(x,y) \ y = x \ T(y,x). [para(794(a,1),399(a,1,2)),flip(a)]. 798 T(T(x,y),T(z,x)) = T(T(x,z),y). [para(796(a,1),38(a,1,1)),flip(a)]. 799 T(x,y / x) = T(x,x \ y). [para(82(a,1),796(a,1,2)),flip(a)]. 800 T((x * y) / x,T(z,y)) = (x * T(y,z)) / x. [para(796(a,1),363(a,1,1,2)),flip(a)]. 801 T(x,y) \ x = y \ T(y,x). [para(796(a,1),760(a,2,2))]. 802 T(x,y) * (y \ T(y,x)) = x. [para(796(a,1),762(a,1,2,2))]. 803 T(x,y) / x = y / T(y,x). [para(796(a,1),766(a,1,1))]. 804 x \ (y \ T(y,x)) = T(x,y) \ 1. [para(796(a,1),783(a,1,1)),flip(a)]. 805 (x \ T(x,y)) * T(y,x) = y. [hyper(396,a,795,a)]. 806 (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). [para(795(a,1),28(a,2,1)),flip(a)]. 807 T(x,y) * (x \ (x \ T(y,x))) = x \ y. [para(797(a,1),398(a,1,2,2))]. 808 T(x,(x * y) / x) = T(x,y). [para(13(a,1),799(a,2,2))]. 809 (x * (y / x)) / T(x,x \ y) = y / x. [para(799(a,1),91(a,1,2))]. 810 T(x,y / x) = (x \ y) \ y. [para(799(a,2),81(a,1))]. 811 x / T(y,x / y) = y \ x. [para(799(a,2),109(a,1,2))]. 812 T(x,y / x) / y = 1 / (x \ y). [para(799(a,2),289(a,1,1))]. 813 L(T(x,x \ y),y,x) = T(x,x * (y / x)). [para(799(a,1),436(a,1,1))]. 814 L(x,T(y,z / y),z) = L(x,1 / (y \ z),z). [para(799(a,2),441(a,1,2))]. 815 T(T(x,y),((x * y) / x) / T(x,y)) = T(T(x,y),x \ y). [para(671(a,1),799(a,2,2))]. 816 (x * y) / x = y * (T(y,x) \ y). [para(801(a,2),786(a,1,2)),flip(a)]. 817 (x \ y) * T(x,y / x) = y. [para(810(a,2),14(a,1,2))]. 818 T(T(x,y),((x * y) / x) / T(x,y)) = (x \ y) \ ((x * y) / x). [para(671(a,1),810(a,2,1))]. 819 L(x,T(y,z / y),y \ z) = L(x,T(y,z / y),z). [para(811(a,1),423(a,1,3))]. 820 L(x,y \ z,T(y,z / y)) = L(x,z,T(y,z / y)). [para(811(a,1),435(a,1,2))]. 821 ((x \ y) \ y) * T(x \ y,x) = y. [para(53(a,1),817(a,1,2,2))]. 822 T(T(x,y),T(z,x)) = T(T(x,y),z). [para(798(a,2),38(a,1))]. 823 T(x \ 1,x * (y * x)) = T(x,y) \ 1. [para(804(a,1),613(a,2))]. 824 (1 / (x \ y)) \ T(T(x,y / x),y) = y * K(T(x,y / x),y). [para(812(a,1),368(a,1,1))]. 825 x \ ((y * x) / y) = T(x,y) \ x. [hyper(56,a,816,a(flip))]. 826 T(x * (T(x,y) \ x),y) = y \ (y * x). [para(816(a,1),82(a,1,1))]. 827 ((x * y) \ y) \ T(x \ y,x) = y. [para(821(a,1),631(a,2))]. 828 T(T(x,y),z / x) = T(T(x,y),x \ z). [para(82(a,1),822(a,1,2)),flip(a)]. 829 T(x \ y,x) / y = (x * y) \ y. [para(827(a,1),53(a,1,2))]. 830 (x * (T(x,y) \ x)) \ T(y,x) = x \ y. [para(807(a,1),608(a,2))]. 831 (x \ (x \ T(x,y))) * T(y,x) = x \ y. [para(807(a,1),609(a,2))]. 832 T(x * (T(x,y) \ x),y) = x. [para(826(a,2),13(a,1))]. 833 ((x * y) / x) \ T(x,y) = y \ x. [para(816(a,2),830(a,1,1))]. 834 T(x,y) / (y \ x) = (x * y) / x. [para(833(a,1),53(a,1,2))]. 835 (x / (x * y)) * T(x,y) = y \ x. [para(833(a,1),284(a,1)),flip(a)]. 836 ((x * y) * x) / (x * y) = T(x * y,x) / y. [para(13(a,1),834(a,1,2)),flip(a)]. 838 x \ (x \ T(x,y)) = y / (y * x). [hyper(18,a,835,a,b,831,a)]. 839 x * (y / (y * x)) = x \ T(x,y). [para(838(a,1),14(a,1,2))]. 840 T((x * y) / x,T(z,y)) = T((x * y) / x,z). [para(800(a,2),363(a,1))]. 841 R(T((x * y) / x,x * y),x,y) = y. [para(840(a,1),662(a,1,1))]. 842 R(L(x,y,y * x),y,x) = x. [para(326(a,1),841(a,1,1))]. 843 L(R(x,y,x),y,y * x) = x. [para(842(a,1),44(a,1)),flip(a)]. 844 L(x,y * x,y) = R(x,y,x). [para(843(a,1),341(a,1,1))]. 845 ((T(x,y) / x) / y) \ (x \ (T(x,y) * z)) = y * z. [para(386(a,2),778(a,1,2))]. 846 (x * (T(x,y) \ y)) \ z = y \ (T(x,y) * (x \ z)). [para(409(a,1),787(a,1,1))]. 847 T(x,T(y,x)) * (y \ (T(y,x) * z)) = x * z. [para(845(a,1),779(a,1)),flip(a)]. 848 T(x,y) * (y \ (T(y,x) * z)) = x * z. [para(796(a,1),847(a,1,1))]. 849 x \ (T(x,y) * (T(y,x) * z)) = y * z. [hyper(383,a,848,a),flip(a)]. 850 T(x,y) * (y \ z) = x * (T(y,x) \ z). [para(14(a,1),848(a,1,2,2))]. 851 T(x,y) * (T(y,x) * z) = x * (y * z). [para(849(a,1),14(a,1,2)),flip(a)]. 852 T(x,y) * (1 / y) = x * (T(y,x) \ 1). [para(208(a,2),850(a,1,2))]. 854 T(x,y) * (1 / y) = x * (1 / T(y,x)). [para(208(a,2),852(a,2,2))]. 855 x \ (T(y,x) * (y \ z)) = T(x,T(y,x)) \ z. [para(401(a,1),846(a,1,1)),flip(a)]. 856 x \ (T(y,x) * (y \ z)) = T(x,y) \ z. [para(796(a,1),855(a,2,1))]. 857 (x * y) / ((L(x,z,u) \ x) * y) = L(x,z,u). [para(750(a,2),14(a,1))]. 858 L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. [para(857(a,1),54(a,1,1))]. 859 (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u). [para(746(a,1),857(a,1,2))]. 860 L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u). [para(858(a,2),746(a,1))]. 861 x * (L(x,y,z) \ T(u,x)) = L(x,y,z) \ (u * x). [para(80(a,1),860(a,1,2)),flip(a)]. 862 T(T(x,y),((x * y) / x) / T(x,y)) = T(T(x,y),y / x). [para(815(a,2),828(a,2)),flip(a)]. 863 (x * 1) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y). [para(222(a,1),116(a,1,1,2))]. 864 x \ ((x * (y \ 1)) * y) = a(x,y \ 1,y). [para(12(a,1),863(a,1,1))]. 866 x \ ((x * (1 / y)) * y) = a(x,y \ 1,y). [para(208(a,2),864(a,1,2,1,2))]. 867 x \ R(x,1 / y,y) = a(x,y \ 1,y). [para(488(a,1),866(a,1,2))]. 868 x \ R(x,1 / y,y) = a(x,1 / y,y). [para(208(a,2),867(a,2,2))]. 869 a(x,1 / y,y) * x = R(x,1 / y,y). [para(868(a,1),480(a,1,1))]. 870 a(x,x \ y,x) = a(y,1 / x,x). [para(868(a,1),688(a,2))]. 871 T((x * y) * (1 / x),z) = (x * T(y,z)) * (1 / x). [para(475(a,1),474(a,1)),flip(a)]. 872 (x * T(y,z)) * (1 / x) = T(x * (y / x),z). [para(216(a,1),871(a,1,1)),flip(a)]. 873 T(x * (y / x),z) = x * (T(y,z) / x). [para(872(a,1),216(a,1))]. 874 T(x,1 / y) / y = y * ((x / y) / y). [hyper(373,a,873,a),flip(a)]. 875 T(x * (y / x),x) = R(y,x,x \ 1). [para(873(a,2),465(a,1))]. 876 T(x * (y / x),x) = R(y,x,1 / x). [para(873(a,2),468(a,1))]. 877 T(x * ((y \ x) / x),y) = x * ((y * x) \ x). [para(829(a,1),873(a,2,2))]. 878 R(x * y,y,y \ 1) = T(y * x,y). [para(15(a,1),875(a,1,1,2)),flip(a)]. 879 T(T(x,y) * y,x) = R(x * y,x,1 / x). [para(666(a,2),876(a,1,1))]. 880 T(x * y,x) / (x \ 1) = (y * x) * x. [para(878(a,1),461(a,1,1))]. 881 T(x * y,1 / y) / y = y * (x / y). [para(15(a,1),874(a,2,2,1))]. 882 T(x,y) / (y \ 1) = ((y \ x) * y) * y. [para(14(a,1),880(a,1,1,1))]. 883 T(x * y,1 / y) = (y * (x / y)) * y. [para(881(a,1),16(a,1,1)),flip(a)]. 885 T((x * y) * y,1 / y) = (y * x) * y. [para(15(a,1),883(a,2,1,2))]. 886 T(x * y,y \ 1) = (y * (x / y)) * y. [para(208(a,1),883(a,1,2))]. 887 T(x * ((y \ x) / x),y) = x / T(y,x). [para(877(a,2),315(a,1))]. 888 T(x * (1 / y),y) = x / T(y,x). [para(278(a,1),887(a,1,1,2))]. 889 T(x * (1 / y),y) \ x = T(y,x). [para(888(a,2),54(a,1,1))]. 891 T((x * y) * (1 / x),x) = (x * y) * (1 / T(x,y)). [para(888(a,2),645(a,1))]. 892 T(x * (y / x),x) = (x * y) * (1 / T(x,y)). [para(216(a,1),891(a,1,1))]. 893 (x * y) * (1 / T(x,y)) = R(y,x,1 / x). [para(892(a,1),876(a,1))]. 894 (x * y) / T(x,x * y) = R(y,x,1 / x). [para(893(a,1),645(a,2))]. 895 (x * y) / T(x,x * y) = R(y,x,x \ 1). [para(208(a,1),894(a,2,3))]. 896 (x / y) \ R(x / y,y,z) = R(y,x,z) \ y. [para(566(a,2),718(a,1))]. 897 (x / y) * R(y / x,x,z) = R(x,y,z) \ x. [para(896(a,1),284(a,1)),flip(a)]. 898 (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). [para(851(a,1),806(a,1,2))]. 899 L(x,T(y,z),T(z,y)) = L(x,y,z). [para(898(a,1),28(a,2)),flip(a)]. 900 L(x,y \ z,T(y,z / y)) = L(x,z / y,y). [para(82(a,1),899(a,1,2))]. 901 L(x,T(y,z / y),y \ z) = L(x,y,z / y). [para(82(a,1),899(a,1,3))]. 902 L(T(x,y),T(y,x),T(x,y)) = T(x,x * y). [para(899(a,2),166(a,1))]. 903 L(x,y,T(z,y / z)) = L(x,y / z,z). [para(900(a,1),820(a,1)),flip(a)]. 904 L(x,y,T(z,y / z)) = L(x,y,z). [para(903(a,2),435(a,1))]. 905 L(x,y,(z \ y) \ y) = L(x,y,z). [para(810(a,1),904(a,1,3))]. 906 L(x,y,y / z) = L(x,y,z \ y). [para(54(a,1),905(a,1,3,1)),flip(a)]. 907 L(x,y,y \ z) = L(x,z,z / y). [para(906(a,2),439(a,1)),flip(a)]. 908 L(x,T(y,z / y),y \ z) = L(x,y,z). [para(901(a,2),423(a,1))]. 909 L(x,T(y,y \ z),y \ z) = L(x,y,z). [para(799(a,1),908(a,1,2))]. 910 L(x,T(y,z / y),z) = L(x,y,z). [para(908(a,1),819(a,1)),flip(a)]. 911 L(x,1 / (y \ z),z) = L(x,y,z). [para(910(a,1),814(a,1)),flip(a)]. 912 L(x,(y \ z) \ 1,z) = L(x,y,z). [para(208(a,1),911(a,1,2))]. 913 L(x,y \ 1,z * y) = L(x,z,z * y). [para(13(a,1),912(a,1,2,1))]. 914 L(x,((y \ z) \ 1) \ 1,z) = L(x,(z / y) * z,z). [para(637(a,1),912(a,1,2,1))]. 915 L(x,T(y,z),z) = L(x,y,y * z). [para(913(a,1),457(a,1)),flip(a)]. 916 L(L(x,y * z,y),T(y,z),z) = x. [para(915(a,2),341(a,1))]. 917 L(x,y * z,y) = L(x,z,T(y,z)). [para(916(a,1),341(a,1,1)),flip(a)]. 918 L(x,x,T(y,x)) = R(x,y,x). [para(917(a,1),844(a,1))]. 919 a(x,T(y,x),x) = R(x,y,x) / x. [para(918(a,1),696(a,1,1)),flip(a)]. 920 L(x,(y / z) * y,y) = L(x,z \ y,y). [para(210(a,1),914(a,1,2)),flip(a)]. 921 L(x,y / z,y) = L(x,z \ y,y). [para(920(a,1),438(a,1)),flip(a)]. 923 L(x,T(y,y \ z) \ (y * (z / y)),y * (z / y)) = L(x,z / y,y * (z / y)). [para(809(a,1),921(a,1,2)),flip(a)]. 924 (x / (y \ z)) * (y \ u) = y * (((y \ x) / z) * u). [para(15(a,1),380(a,1,2,1)),flip(a)]. 926 ((x \ y) \ 1) \ ((((x \ y) \ 1) / (y / x)) * z) = (x / y) * z. [para(452(a,2),284(a,1))]. 927 (x / y) \ R(x / y,y,z) = 1 / (R(x,y,z) \ x). [para(897(a,1),568(a,2,2))]. 928 (x / y) \ R(x / y,y,z) = (R(x,y,z) \ x) \ 1. [para(927(a,2),208(a,1))]. 929 (x / y) \ R(x / y,y,z) = R(x,y,z) * (x \ 1). [para(928(a,2),585(a,1))]. 930 (x / y) \ R(x / y,y,z) = x \ R(x,y,z). [para(929(a,2),487(a,1))]. 931 R(x,y,z) \ x = y \ R(y,x,z). [para(930(a,1),896(a,1)),flip(a)]. 932 x * (R(y,x,z) \ y) = R(x,y,z). [para(931(a,2),14(a,1,2))]. 933 x / (y \ R(y,x,z)) = R(x,y,z). [para(931(a,1),53(a,1,2))]. 934 (R(x,y,z) \ x) * y = R(y,x,z). [para(931(a,2),480(a,1,1))]. 935 K(R(x,y,z) \ x,y) = 1. [para(931(a,2),485(a,1,1))]. 936 (x \ R(x,y,z)) * u = y * (R(y,x,z) \ u). [para(931(a,1),583(a,1,1))]. 937 x * (((y * z) / (x * z)) \ (y / x)) = R(x,y / x,z). [para(76(a,1),932(a,1,2,1))]. 938 x * (R(x,y,z) \ y) = R(y,x,z). [para(934(a,1),583(a,1)),flip(a)]. 939 (x * y) / R(y,x,z) = R(x,y,z). [para(934(a,1),584(a,1,2))]. 940 R(x,y,z) * (x \ u) = y * (R(y,x,z) \ u). [para(936(a,1),557(a,1)),flip(a)]. 941 x * (((x * y) / (z * y)) * (z / x)) = R(x,z / x,y). [para(284(a,1),937(a,1,2))]. 942 (x \ y) \ ((x * y) / x) = T(T(x,y),y / x). [para(818(a,1),862(a,1))]. 943 (x \ y) * T(T(x,y),y / x) = (x * y) / x. [para(942(a,1),14(a,1,2))]. 944 (1 / (x \ y)) \ T(T(x,y),y / x) = y * K(T(x,y / x),y). [para(38(a,1),824(a,1,2))]. 945 (x \ y) * ((((x \ y) \ 1) / (y / x)) * z) = (x / y) * z. [para(926(a,1),256(a,1)),flip(a)]. 946 (x \ y) * (((x \ y) \ (x / y)) * z) = (x / y) * z. [para(710(a,1),945(a,1,2,1))]. 947 (x \ y) * ((x / y) * ((x \ y) \ z)) = (x / y) * z. [para(714(a,1),946(a,1,2))]. 948 x * (((x * y) \ y) * ((x \ y) \ z)) = (x / y) * z. [para(947(a,1),619(a,1)),flip(a)]. 949 (x \ y) * T(T(x,y),y / x) = y * K(T(x,y / x),y). [para(944(a,1),270(a,1)),flip(a)]. 950 x * K(T(y,x / y),x) = (y * x) / y. [para(949(a,1),943(a,1))]. 951 K(T(x,y / x),y) = T(x,y) / x. [hyper(17,a,784,a,b,950,a)]. 952 (x / y) \ R(x / y,y,z) = ((x / y) * ((y * z) / (x * z))) \ 1. [para(567(a,2),208(a,1))]. 953 ((x * y) \ y) * ((x \ 1) \ z) = (x * T(x \ 1,x * y)) * z. [para(256(a,1),416(a,1,1)),flip(a)]. 954 (T(x,x \ y) \ x) * z = ((x * y) \ y) * ((x \ 1) \ z). [para(648(a,1),953(a,2,1)),flip(a)]. 955 ((x * y) \ y) * ((x \ 1) \ z) = x * (T(x,x \ y) \ z). [para(954(a,1),409(a,1))]. 956 ((x * y) \ y) * (x * z) = x * (T(x,x \ y) \ z). [para(256(a,1),955(a,1,2))]. 957 x * (T(x,x \ y) \ z) = x * (((x * y) \ y) * z). [para(956(a,1),618(a,1))]. 958 (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). [para(53(a,1),517(a,1,2,2,1,2)),flip(a)]. 959 ((T(x,y) / x) \ (x * y)) \ (x * y) = 1 / K(y,T(x,y)). [para(376(a,1),638(a,1,1,1))]. 961 (T(x,y) \ (x * (x * y))) \ (x * y) = 1 / K(y,T(x,y)). [para(417(a,1),959(a,1,1))]. 962 (x * y) \ (y * x) = 1 / K(x,T(y,x)). [para(791(a,1),961(a,1,1))]. 963 1 / K(x,T(y,x)) = K(y,x). [para(962(a,1),26(a,2)),flip(a)]. 964 K(x,T(y,x)) = K(y,x) \ 1. [para(963(a,1),54(a,1,1)),flip(a)]. 965 K(x,T(y,x)) \ z = K(y,x) * z. [para(963(a,1),269(a,1,1)),flip(a)]. 966 K(x,T(T(y,x),z)) = K(T(y,z),x) \ 1. [para(38(a,1),964(a,1,2))]. 967 (x * y) / (K(x,y) \ 1) = T(x,y) * y. [para(964(a,1),114(a,1,2))]. 968 K((x * y) / x,x) = K(x,y) \ 1. [para(964(a,1),674(a,2))]. 969 (x * y) / ((x * y) / K(x,y)) = (T(x,y) * y) / (x * y). [para(967(a,1),643(a,1,1)),flip(a)]. 970 (T(x,y) * y) / (x * y) = (x * y) / (y * x). [para(89(a,1),969(a,1,2)),flip(a)]. 971 (x * y) / (y * x) = T(x,y) / x. [para(970(a,1),376(a,1))]. 973 (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x. [para(493(a,1),492(a,1,1)),flip(a)]. 974 (1 / x) * T(x * y,z) = T(y * x,z) / x. [para(270(a,1),973(a,1,2,1))]. 975 T(x * y,z) / y = y \ T(y * x,z). [para(974(a,1),269(a,1))]. 976 T((x \ y) * x,z) / x = x \ T(y,z). [para(14(a,1),975(a,2,2,1))]. 977 ((x * y) * x) / (x * y) = y \ T(y * x,x). [para(975(a,1),836(a,2))]. 978 T(x * (y * x),1 / x) / (y * x) = (y * x) \ ((x * y) * x). [para(885(a,1),975(a,2,2))]. 979 T((x \ y) * x,z) = (x \ T(y,z)) * x. [para(976(a,1),16(a,1,1)),flip(a)]. 980 T((x \ y) * x,1 / y) = (x \ y) * x. [para(221(a,1),979(a,2,1,2))]. 981 T(1 / x,(y \ x) * y) = 1 / x. [hyper(35,a,980,a)]. 982 T(1 / (x * y),y * x) = 1 / (x * y). [para(13(a,1),981(a,1,2,1))]. 983 (x * y) \ K(x,y) = 1 / (y * x). [para(982(a,1),305(a,1)),flip(a)]. 984 K(x,y) = (x * y) * (1 / (y * x)). [para(983(a,1),14(a,1,2)),flip(a)]. 985 K(x,y) = (x * y) * ((y * x) \ 1). [para(208(a,1),984(a,2,2))]. 986 ((x * y) / ((y * x) \ 1)) * ((x * y) \ z) = (x * y) * (K(x,y) \ z). [para(985(a,2),303(a,2,2,1))]. 987 x \ (y \ T(y * x,x)) = T(x,x * y) \ x. [para(977(a,1),825(a,1,2))]. 988 T(x,x * y) \ x = K(y * x,x). [para(987(a,1),550(a,1))]. 989 L(x,y,K(z * y,y)) = x. [para(988(a,1),444(a,1,3))]. 990 L(x,y,K(z,y)) = x. [para(16(a,1),989(a,1,3,1))]. 991 L(x,K(y,z),z) = x. [para(990(a,1),341(a,1,1))]. 992 (x * K(y,x)) * z = x * (K(y,x) * z). [para(990(a,1),342(a,1,2,2)),flip(a)]. 993 L(x,K(y,z) \ 1,y) = x. [para(968(a,1),991(a,1,2))]. 994 (x / (K(x,y) \ 1)) * z = x * ((K(x,y) \ 1) \ z). [para(993(a,1),300(a,1,2)),flip(a)]. 995 x / (K(x,y) \ 1) = x * K(x,y). [para(993(a,1),311(a,1,2)),flip(a)]. 996 (x / (K(x,y) \ 1)) * z = x * (K(x,y) * z). [para(256(a,1),994(a,2,2))]. 997 (x * K(x,y)) * z = x * (K(x,y) * z). [para(995(a,1),996(a,1,1))]. 998 T(x * (y * x),1 / x) / (y * x) = R(T(x,y * x),y,x). [para(978(a,2),592(a,1))]. 999 (x * (x * y)) / (y * x) = R(T(x,y * x),y,x). [para(372(a,1),998(a,1,1))]. 1000 R(T(x,y * x),y,x) = T(x,y). [para(999(a,1),790(a,2)),flip(a)]. 1001 R(x,y,x) * (y * x) = (y * x) * T(x,y). [para(1000(a,1),104(a,1,2)),flip(a)]. 1002 (x * y) * T(y,x) = (y * x) * y. [para(1001(a,1),75(a,1))]. 1003 (x * (y / x)) * x = y * T(x,y / x). [para(16(a,1),1002(a,1,1)),flip(a)]. 1004 ((x * y) * x) \ (x * (x * y)) = K(T(x,y),y * x). [para(1002(a,1),792(a,1,1))]. 1005 (x * y) * T(x,(x * y) / x) = (T(x,y) * y) * x. [para(666(a,2),1003(a,1,1)),flip(a)]. 1006 K(T(x,y),y * x) = K(x,x * y). [para(1004(a,1),26(a,2)),flip(a)]. 1007 K(T(x,y / x),y) = K(x,x * (y / x)). [para(16(a,1),1006(a,1,2))]. 1008 K(x,x * (y / x)) = T(x,y) / x. [para(1007(a,1),951(a,1))]. 1009 T(x,y * x) / x = K(x,x * y). [para(15(a,1),1008(a,1,2,2)),flip(a)]. 1010 x * K(x,x * y) = T(x,y * x). [para(1009(a,1),333(a,1,2))]. 1011 T(x,K(x,x * y)) = x. [para(1009(a,1),338(a,1,2))]. 1012 T(x,K(x,y)) = x. [para(14(a,1),1011(a,1,2,2))]. 1013 (T(x,y) * y) * x = (x * y) * T(x,y). [para(808(a,1),1005(a,1,2)),flip(a)]. 1014 x \ ((x * y) * T(x,y)) = T(T(x,y) * y,x). [para(1013(a,1),32(a,2,2)),flip(a)]. 1015 T(T(x,y) * y,x) = L(x,x,y) * y. [para(1014(a,1),360(a,1))]. 1016 R(x * y,x,1 / x) = L(x,x,y) * y. [para(1015(a,1),879(a,1)),flip(a)]. 1017 (L(x,x,y) * y) / (x * y) = a(x * y,x,1 / x). [para(1016(a,1),598(a,1,1))]. 1018 a(x * y,x,1 / x) = L(x,x,y) / x. [para(1017(a,1),749(a,1))]. 1019 a(x * y,x,1 / x) = a(x,y,x). [para(1018(a,2),696(a,1))]. 1021 a(x * y,y,1 / y) = a(y,T(x,y),y). [para(80(a,1),1019(a,1,1))]. 1022 a(x * (x \ y),x,1 / x) = a(y,1 / x,x). [para(1019(a,2),870(a,1))]. 1023 a(x,T(y,x),x) = a(y,x,1 / x). [para(1021(a,1),601(a,1))]. 1024 a(x,1 / y,y) = a(x,y,1 / y). [para(14(a,1),1022(a,1,1)),flip(a)]. 1025 a(x,y,1 / y) * x = R(x,1 / y,y). [para(1024(a,1),869(a,1,1))]. 1026 R(x,1 / y,y) = R(x,y,1 / y). [para(1025(a,1),599(a,1))]. 1027 x \ R(y,x,1 / x) = T(y * (1 / x),x). [para(1026(a,1),491(a,1,2))]. 1028 T(x * (1 / y),y) = T(x,y) / y. [para(1027(a,1),469(a,1))]. 1029 T(x,y \ 1) / (y \ 1) = T(x * y,y \ 1). [para(53(a,1),1028(a,1,1,2)),flip(a)]. 1030 T(x * (y \ 1),y) = T(x,y) / y. [para(208(a,1),1028(a,1,1,2))]. 1031 T(x,y) / y = x / T(y,x). [para(1028(a,1),888(a,1))]. 1032 (T(x,y) / y) \ x = T(y,x). [para(1028(a,1),889(a,1,1))]. 1033 (x / T(y,x)) * y = T(x,y). [para(1031(a,1),16(a,1,1))]. 1034 T(x,y \ 1) / (y \ 1) = x * ((y \ x) \ x). [para(1031(a,2),318(a,1))]. 1035 T(x,y) = x * K(x,y). [para(1032(a,1),391(a,1))]. 1036 K(x,y) = T(x,y) / x. [hyper(337,a,1035,a),flip(a)]. 1037 x * T(x \ 1,y) = K(x \ 1,y). [hyper(260,a,1035,a(flip))]. 1038 K(x,y) = x \ T(x,y). [hyper(56,a,1035,a(flip)),flip(a)]. 1039 x * L(K(y,z),y,x) = (x / y) * T(y,z). [para(1035(a,2),295(a,1,2)),flip(a)]. 1040 x \ ((x / y) * T(y,z)) = L(K(y,z),y,x). [para(1035(a,2),340(a,2,2,2)),flip(a)]. 1041 x * (K(x,y) * z) = T(x,y) * z. [para(1035(a,2),997(a,1,1)),flip(a)]. 1042 T(x,y * x) = T(x,x * y). [para(1035(a,2),1010(a,1)),flip(a)]. 1043 T(x,y) = K(x,y) * x. [para(1036(a,2),16(a,1,1)),flip(a)]. 1044 R(K(x,y) / z,z,x) = T(x,y) / (z * x). [para(1036(a,2),159(a,1,1,1))]. 1045 K(x,y) \ 1 = x / T(x,y). [para(1036(a,2),265(a,1,1))]. 1046 K(x,y) \ (T(x,y) * z) = x * z. [para(1036(a,2),350(a,1,1))]. 1047 T(x,y) \ (x * z) = K(x,y) \ z. [para(1036(a,2),417(a,1,1)),flip(a)]. 1048 (x * y) / x = y * K(x,y). [para(1036(a,2),784(a,1,2)),flip(a)]. 1049 K(x,y) = y / T(y,x). [para(1036(a,2),803(a,1))]. 1050 K(x,y) = (x * y) / (y * x). [para(1036(a,2),971(a,2)),flip(a)]. 1051 T(x,y) \ T(T(x,z),y) = K(T(x,y),z). [para(38(a,1),1038(a,2,2)),flip(a)]. 1052 R(x,y,z) \ R(T(x,u),y,z) = K(R(x,y,z),u). [para(42(a,2),1038(a,2,2)),flip(a)]. 1053 T(x,y) * (x \ z) = K(x,y) * z. [para(1038(a,2),395(a,1,1)),flip(a)]. 1054 K(x,y) = T(y,x) \ y. [para(1038(a,2),801(a,2)),flip(a)]. 1055 T(x,y) * K(y,x) = x. [para(1038(a,2),802(a,1,2))]. 1056 K(x,y) * T(y,x) = y. [para(1038(a,2),805(a,1,1))]. 1057 T(x,y) \ 1 = x \ K(y,x). [para(1038(a,2),804(a,1,2)),flip(a)]. 1058 K(x,y) = x * (y / (y * x)). [para(1038(a,2),839(a,2)),flip(a)]. 1059 R(x,K(y,z),y) * T(y,z) = (x * K(y,z)) * y. [para(1043(a,2),75(a,1,2))]. 1060 R(x / K(y,z),K(y,z),y) = (x * y) / T(y,z). [para(1043(a,2),76(a,2,2))]. 1061 T(x,y) = K(y,x) \ x. [para(1049(a,2),54(a,1,1)),flip(a)]. 1062 x * (T(x,y) \ z) = K(y,x) * z. [para(1049(a,2),249(a,1,1)),flip(a)]. 1063 x * (K(y,x) \ z) = T(x,y) * z. [para(1049(a,2),378(a,1,2,1))]. 1064 (x \ y) \ (y / x) = K(x,y / x). [para(1049(a,2),407(a,1)),flip(a)]. 1065 (x / y) * K(y \ x,y) = y \ x. [para(1054(a,2),651(a,1,2))]. 1066 T(x * K(y,x),y) = x. [para(1054(a,2),832(a,1,1,2))]. 1067 L(x * K(y,x),z,u) * y = y * L(x,z,u). [para(1066(a,1),103(a,1,2,1)),flip(a)]. 1068 R(x,y,y \ 1) * y = T(y * x,y). [para(895(a,1),1033(a,1,1))]. 1069 T(x,x * (y / x)) = T(x,y). [para(16(a,1),1042(a,1,2)),flip(a)]. 1070 K(x,y) \ 1 = K(y,x). [para(1045(a,2),1049(a,2)),flip(a)]. 1071 K(x,y) * K(y,x) = 1. [para(1070(a,1),14(a,1,2))]. 1072 1 / K(x,y) = K(y,x). [para(1070(a,1),53(a,1,2))]. 1073 K(x,y) \ (z / K(y,x)) = (K(x,y) \ z) * K(x,y). [para(1070(a,1),195(a,1,2,2))]. 1074 K(x,y) * (K(y,x) * z) = z. [para(1070(a,1),254(a,1,1))]. 1075 K(x,y) \ z = K(y,x) * z. [para(1070(a,1),256(a,1,1))]. 1076 x * L(K(y,z),K(z,y),x) = x / K(z,y). [para(1070(a,1),281(a,1,2,1))]. 1077 L(K(x,y),K(y,x),z) = z \ (z / K(y,x)). [para(1070(a,1),282(a,1,1))]. 1078 (x / K(y,z)) / L(K(z,y),K(y,z),x) = x. [para(1070(a,1),308(a,1,2,1))]. 1079 K(x,T(y,x)) = K(x,y). [para(1070(a,1),964(a,2))]. 1080 K(x,T(T(y,x),z)) = K(x,T(y,z)). [para(1070(a,1),966(a,2))]. 1081 ((x * K(y,z)) * K(z,y)) / 1 = R(x,K(y,z),K(z,y)). [para(1071(a,1),30(a,2,2)),flip(a)]. 1082 T(x,K(y,z)) * K(z,y) = x * (1 / T(K(y,z),x)). [para(1072(a,1),854(a,1,2))]. 1083 K(x / y,y) = K(y \ x,y). [para(1079(a,1),675(a,1)),flip(a)]. 1084 R((x * y) / x,x,y) = y * K(x * y,y). [para(1048(a,1),76(a,2))]. 1085 K(x,y) \ (x * y) = y * x. [para(1050(a,2),54(a,1,1))]. 1086 (x \ K(y,x)) * z = T(x,y) \ z. [para(1057(a,1),259(a,1,1))]. 1087 T(x,x \ K(y,x)) = x. [para(1057(a,1),412(a,1,2))]. 1088 T(T(x,y),x \ K(z,x)) = T(x,y). [para(1087(a,1),38(a,1,1)),flip(a)]. 1089 T(x,y) * (x \ K(z,x)) = (x \ K(z,x)) * T(x,y). [para(1087(a,1),102(a,1,2,1)),flip(a)]. 1090 T(x,y * (x \ 1)) = T(x,x \ y). [para(187(a,1),1069(a,1,2))]. 1091 L(T(x,x \ y),y,x) = T(x,y). [para(1069(a,1),813(a,2))]. 1092 (x * (y / x)) / T(x,y) = R(y / x,x,x \ 1). [para(1069(a,1),895(a,1,2))]. 1093 K(x,y) * (z * K(y,x)) = T(z,K(y,x)). [hyper(98,a,1074,a),flip(a)]. 1094 (K(x,y) \ z) \ (z * K(y,x)) = K(z,K(y,x)). [para(1075(a,2),26(a,2,1)),flip(a)]. 1095 K(x / (x / y),x / y) = K(y,x / y). [para(54(a,1),1083(a,2,1))]. 1096 (x * y) / ((y * x) \ 1) = (y * x) * (x * y). [para(1085(a,1),642(a,1,2,1))]. 1097 L(x,y,x) * (x \ y) = (x \ y) * T(x,y). [para(1091(a,1),103(a,1,2)),flip(a)]. 1098 L(T(x,y),x,y) = T(x,x \ y). [para(1091(a,1),341(a,1,1))]. 1099 T(x / y,(x / y) \ y) = L(y \ x,x / y,y). [para(82(a,1),1098(a,1,1)),flip(a)]. 1100 x * T(y,y \ x) = L(y,y,x) * x. [para(1098(a,1),103(a,1,2))]. 1101 L(T(x,y),x,T(y,x)) = T(x,x \ T(y,x)). [para(796(a,1),1098(a,1,1))]. 1102 L(T(x,y),T(x,y),T(y,x)) = T(x,x \ y). [para(1098(a,1),899(a,2))]. 1103 T((x * (y * x)) * (x \ 1),x) = (y * (x * x)) / x. [para(97(a,1),1030(a,2,1))]. 1104 K(x,y) * (T(y,x) * z) = y * z. [hyper(17,a,851,a(flip),b,1041,a)]. 1105 K(x,y) * (x * z) = T(x,y) * z. [hyper(17,a,375,a(flip),b,1041,a)]. 1106 T(x,y) * (K(y,x) * z) = x * z. [para(1074(a,1),1041(a,1,2)),flip(a)]. 1107 R(K(x,y) \ 1,T(x,y) * z,u) = R(K(x,y),x * z,u) \ 1. [para(1046(a,1),603(a,1,1,2)),flip(a)]. 1108 T(x,y) \ (x * z) = K(y,x) * z. [para(1047(a,2),1075(a,1))]. 1109 T(x,y) \ (K(x,y) * z) = x \ z. [hyper(56,a,1053,a)]. 1110 (x \ y) \ (K(x,z) * y) = T(T(x,z),x \ y). [para(1053(a,1),32(a,2,2)),flip(a)]. 1111 T(x / y,z) * y = K(x / y,z) * x. [para(54(a,1),1053(a,1,2))]. 1112 x \ (K(y,x) * z) = T(x,y) \ z. [para(1053(a,1),856(a,1,2))]. 1113 x * (((x * y) \ y) * z) = K(x \ y,x) * z. [para(1062(a,1),957(a,1)),flip(a)]. 1114 T(x,y) * z != x * u | K(y,x) \ z = u. [para(1063(a,1),19(a,1))]. 1115 K(x,T(y,K(T(y,x),z))) = K(x,T(y,x)). [para(1012(a,1),1080(a,1,2)),flip(a)]. 1116 R(K(x,y),T(y,x) * z,u) = ((y * z) * u) / ((T(y,x) * z) * u). [para(1104(a,1),30(a,2,1,1))]. 1117 K(x,y) * (y * z) = y * (K(x,y) * z). [para(1106(a,1),1104(a,1,2))]. 1118 T(x * y,x) != z * x | R(y,x,x \ 1) = z. [para(1068(a,1),20(a,1))]. 1119 (x * (T(y,x) / x)) * x = T(x * y,x). [para(465(a,2),1068(a,1,1))]. 1120 L(x,x,x \ y) = L(x,x,y). [hyper(518,a,1100,a)]. 1121 L(x,x,y) * y = y * ((x \ y) \ y). [para(81(a,1),1100(a,1,2)),flip(a)]. 1122 T(x,y) / L(y,y,x) = y \ x. [para(1120(a,1),356(a,1,2))]. 1123 a(x,x \ y,x) = x \ L(x,x,y). [para(1120(a,1),519(a,1,2)),flip(a)]. 1124 L(x,y,y / x) = L(x,x,y). [para(1120(a,1),907(a,1)),flip(a)]. 1125 a(x,x \ y,x) = a(x,y,x). [para(1123(a,2),519(a,1))]. 1126 a(x,x * y,x) = a(x,y,x). [para(13(a,1),1125(a,1,2)),flip(a)]. 1127 ((x \ 1) / y) * (y * x) = a(x,y,x). [para(1125(a,1),686(a,1)),flip(a)]. 1128 R(x,y \ 1,y) = x * a(y,x,y). [para(1127(a,1),681(a,1,2)),flip(a)]. 1129 R(x,y \ 1,y) != x * z | a(y,x,y) = z. [para(1128(a,2),19(a,1))]. 1130 K(x / y,z) * x = y * T(y \ x,z). [para(1111(a,1),127(a,1))]. 1131 K(x,T(y,K(T(y,x),z))) = K(x,y). [para(1115(a,2),1079(a,1))]. 1132 T(T(x,K(T(x,y),z)),y) * K(y,x) = T(x,K(T(x,y),z)). [para(1131(a,1),1055(a,1,2))]. 1133 x \ (y * T(y \ x,z)) = T(K(x / y,z),x). [para(1130(a,1),32(a,2,2)),flip(a)]. 1134 x / ((K(y,z) / x) \ (T(y,z) / (x * y))) = R(x,K(y,z) / x,y). [para(1044(a,1),933(a,1,2,2))]. 1135 L(x,x \ y,x) = L(x,y,x). [hyper(18,a,200,a,b,1097,a),flip(a)]. 1136 L(x,x * y,x) = L(x,y,x). [para(13(a,1),1135(a,1,2)),flip(a)]. 1137 x / L(y,x,y) = x * (y \ 1). [para(1135(a,1),422(a,1,2))]. 1138 T(L(x,y,x),L(x,y,x) \ y) = T(L(x,y,x),y * (x \ 1)). [para(1137(a,1),799(a,1,2)),flip(a)]. 1139 T(x * y,y \ 1) = x * ((y \ x) \ x). [para(1034(a,1),1029(a,1)),flip(a)]. 1140 T(x * y,y \ 1) = L(y,y,x) * x. [para(1139(a,2),1121(a,2)),flip(a)]. 1141 L(x,x,y) * y = (x * (y / x)) * x. [para(1140(a,1),886(a,1))]. 1142 L(x,x,y * x) * (y * x) = (x * y) * x. [para(15(a,1),1141(a,2,1,2))]. 1143 L(x,x,y) * (y * x) = (x * y) * x. [para(424(a,1),1142(a,1,1))]. 1144 R(x,y,x) = L(x,x,y). [hyper(18,a,75,a,b,1143,a),flip(a)]. 1145 R(R(x,y,z),u,x) = R(L(x,x,u),y,z). [para(1144(a,1),46(a,1,1)),flip(a)]. 1146 L(x \ 1,x \ 1,x * y) = R(x,y,x \ 1) \ 1. [para(1144(a,1),602(a,1))]. 1147 L(x,x,T(y,x)) = L(x,x,y). [para(1144(a,1),918(a,2))]. 1148 a(x,T(y,x),x) = L(x,x,y) / x. [para(1144(a,1),919(a,2,1))]. 1149 L(T(x,y),x,T(z,x)) = T(L(x,x,z),y). [para(1147(a,1),40(a,2,1))]. 1150 L(x,x,y) * T(y,x) = (x * (T(y,x) / x)) * x. [para(1147(a,1),1141(a,1,1))]. 1151 a(x,T(y,x),x) = a(x,y,x). [para(1148(a,2),696(a,1))]. 1152 a(x,y,1 / y) = a(y,x,y). [para(1151(a,1),1023(a,1)),flip(a)]. 1153 a(x \ 1,y,x \ 1) = a(y,x \ 1,x). [para(53(a,1),1152(a,1,3)),flip(a)]. 1154 a(x,y,y \ 1) = a(y,x,y). [para(208(a,1),1152(a,1,3))]. 1155 x * L(1 / x,y,x) = a(x,y,x). [para(1152(a,1),595(a,2))]. 1156 R(x,y,y \ 1) = x * a(y,x,y). [para(1154(a,1),588(a,1,2)),flip(a)]. 1157 x * L(x \ 1,y,x) = a(x,y,x). [para(208(a,1),1155(a,1,2,1))]. 1158 R(x,y \ 1,y) = R(x,y,y \ 1). [para(1156(a,2),1128(a,2))]. 1159 R(x,y,y \ 1) / y = x * (y \ 1). [para(1158(a,1),679(a,1,1))]. 1160 R(x / (y \ 1),y,y \ 1) = x * y. [para(1158(a,1),680(a,1))]. 1161 R(L(x / (y \ 1),z,u),y,y \ 1) / y = (y \ 1) * L((y \ 1) \ x,z,u). [para(1159(a,2),198(a,1))]. 1162 R(R(x,y,z),u,x) = L(R(x,y,z),x,u). [para(1145(a,2),44(a,1))]. 1163 L(T(x,y),x,T(z,x)) = L(T(x,y),x,z). [para(1149(a,2),40(a,2)),flip(a)]. 1164 (x * R(y,z,u)) / L(R(y,z,u),y,x) = R(x,R(y,z,u),y). [para(1162(a,1),939(a,1,2))]. 1165 T(x,x \ T(y,x)) = L(T(x,y),x,y). [para(1163(a,1),1101(a,1)),flip(a)]. 1166 T(x,x \ T(y,x)) = T(x,x \ y). [para(1165(a,2),1098(a,1))]. 1167 L(R((x * y) / x,x,y),z,u) * (x * y) = (x * y) * L(y,z,u). [para(1084(a,2),1067(a,1,1,1))]. 1168 K(x \ y,x) * ((x \ y) \ z) = (x / y) * z. [para(1113(a,1),948(a,1))]. 1169 (x \ y) * T((x \ y) \ 1,z) = T(K(x / y,z),x). [para(1133(a,1),958(a,2))]. 1170 (x * (y / x)) / T(x,y) = y * (x \ 1). [para(1092(a,2),463(a,1))]. 1171 T(x / y,(x / y) \ y) = L(y \ x,x,y). [para(1099(a,2),435(a,1))]. 1172 L(x \ y,y,x) = (y \ x) \ 1. [para(1171(a,1),624(a,1))]. 1173 L((x / y) \ x,x,x / y) = L(y \ 1,y,x) \ 1. [para(282(a,2),1172(a,2,1))]. 1174 L((x \ y) \ 1,y,x) = y \ x. [para(1172(a,1),341(a,1,1))]. 1175 ((x / y) \ ((x * z) / (y * z))) \ 1 = ((x * z) / (y * z)) \ (x / y). [para(1172(a,1),529(a,1))]. 1176 ((x * y) \ (x / (y \ 1))) \ 1 = (x / (y \ 1)) \ (x * y). [para(1174(a,1),682(a,1)),flip(a)]. 1177 L(x,x,y) * T(y,x) = T(x * y,x). [para(1150(a,2),1119(a,1))]. 1178 L(x,x,y) * T(y,x) = y * L(x,x,y). [para(1177(a,2),327(a,2)),flip(a)]. 1179 T(x,L(y,y,x)) = T(x,y). [hyper(98,a,1178,a)]. 1180 K(x / (x / K(y,z)),x / K(y,z)) = (K(y,z) \ (x / K(z,y))) \ x. [para(1073(a,2),673(a,2,1))]. 1181 K(K(x,y),z) \ K(y,x) = 1 / T(K(x,y),z). [hyper(1114,a,1082,a)]. 1182 T(x,y) * (x \ K(z,x)) = T(x,z) \ T(x,y). [para(1089(a,2),1086(a,1))]. 1183 T(x,y) \ T(x,z) = K(x,z) * K(y,x). [para(1182(a,1),1053(a,1))]. 1184 T(x * (((y * x) / x) * 1),x) = (y * (x * x)) / x. [para(170(a,1),1103(a,1,1))]. 1185 R(x,y,x \ 1) \ 1 = L(x \ 1,y,x). [para(1146(a,1),456(a,1))]. 1186 T(K(x / y,z),x) = K((x \ y) \ 1,z). [para(1169(a,1),1037(a,1))]. 1187 K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). [para(53(a,1),1186(a,1,1,1)),flip(a)]. 1188 K((((x \ y) / y) * (x \ y)) \ (x \ y),z) = T(K(x,z),y). [para(637(a,2),1187(a,1,1))]. 1189 L(x,y,y / x) = L(x \ 1,x,y) \ 1. [para(54(a,1),1173(a,1,1))]. 1190 L(x \ 1,x,y) \ 1 = L(x,x,y). [para(1189(a,1),1124(a,1))]. 1191 L(x,x,y) = (y \ (y / x)) \ 1. [para(282(a,1),1190(a,1,1)),flip(a)]. 1192 L(x,x,y) \ z = (y \ (y / x)) * z. [para(1191(a,2),256(a,1,1))]. 1193 x \ ((y \ (y / x)) \ 1) = a(x,y,x). [para(1191(a,1),519(a,1,2))]. 1194 (x \ (x / y)) * T(L(y,y,x),z) = K((x \ (x / y)) \ 1,z). [para(1191(a,2),1037(a,1,2,1))]. 1195 T(x * (y * 1),x) = (y * (x * x)) / x. [para(15(a,1),1184(a,1,1,2,1))]. 1196 (x * (y * y)) / y = T(y * x,y). [para(12(a,1),1195(a,1,1,2)),flip(a)]. 1197 T(x * y,x) * x = y * (x * x). [para(1196(a,1),16(a,1,1))]. 1198 T(x * R(y,x,x),x) = y * x. [hyper(18,a,75,a(flip),b,1197,a)]. 1199 R(R(x,y,y),y,y \ 1) = x. [hyper(1118,a,1198,a)]. 1200 R(R(x,y,y \ 1),y,y) = x. [para(1199(a,1),46(a,1)),flip(a)]. 1201 R(x,y,y) * y = x / (y \ 1). [para(1199(a,1),461(a,1,1)),flip(a)]. 1202 R(x,y,y) * (y \ 1) = x / y. [para(1199(a,1),1159(a,1,1)),flip(a)]. 1203 R(x * (y \ 1),y,y) = x / y. [para(463(a,1),1200(a,1,1))]. 1204 R(T(x * y,x),x,x) = y * x. [para(878(a,1),1200(a,1,1))]. 1205 R(x * y,y,y) = x / (y \ 1). [para(1160(a,1),1200(a,1,1))]. 1206 (x / (y \ 1)) / y = R(x,y,y). [hyper(61,a,1201,a)]. 1207 R(T(x,y),y,y) = (y \ x) * y. [hyper(18,a,882,a(flip),b,1201,a)]. 1208 (x / y) / (y \ 1) = R(x,y,y). [hyper(61,a,1202,a)]. 1209 R(x,y,y) \ (x / y) = y \ 1. [hyper(56,a,1202,a)]. 1210 (x \ 1) / (y / x) = R(y,x,x) \ 1. [para(1202(a,1),255(a,1,2))]. 1211 T(R(x,y,y),z) * (y \ 1) = K(R(x,y,y),z) * (x / y). [para(1202(a,1),1105(a,1,2)),flip(a)]. 1212 R(x,y \ 1,y \ 1) = (x / y) / (y \ 1). [para(210(a,1),1206(a,1,1,2)),flip(a)]. 1213 R(R(T(x,y),y,y),x,z) = (y \ x) * y. [para(1207(a,1),155(a,2))]. 1214 (x / K(y,z)) / K(z,y) = R(x,K(y,z),K(y,z)). [para(1070(a,1),1208(a,1,2))]. 1215 R(x * y,y * x,z) = (y \ (y * x)) * y. [para(1204(a,1),1213(a,1,1))]. 1216 R(x,y \ 1,y \ 1) = R(x,y,y). [para(1212(a,2),1208(a,1))]. 1217 R(x * y,y * x,z) = x * y. [para(13(a,1),1215(a,2,1))]. 1218 ((x * y) * (y * x)) * z = (x * y) * ((y * x) * z). [para(1217(a,1),75(a,1,1)),flip(a)]. 1219 (x * K(y,z)) * K(z,y) = R(x,K(y,z),K(z,y)). [para(1081(a,1),52(a,1)),flip(a)]. 1220 T(T(x,y),K(T(x,y),z)) * K(y,x) = T(x,K(T(x,y),z)). [para(38(a,1),1132(a,1,1))]. 1221 ((x * y) \ (x / (y \ 1))) \ 1 = ((y \ 1) / x) * (x * y). [para(1176(a,2),284(a,1))]. 1222 K(((x \ 1) * (x \ y)) \ (x \ y),z) = T(K(x,z),y). [para(264(a,1),1188(a,1,1,1,1))]. 1223 K((x \ (x \ y)) \ (x \ y),z) = T(K(x,z),y). [para(259(a,1),1222(a,1,1,1))]. 1225 K(T(x,x \ (x \ y)),z) = T(K(x,z),y). [para(81(a,2),1223(a,1,1))]. 1226 R(T(x,y),z,z) * (z \ 1) = K(R(x,z,z),y) * (x / z). [para(42(a,2),1211(a,1,1))]. 1227 T(x,K(T(x,y),z)) = T(x,y) * K(y,x). [para(1012(a,1),1220(a,1,1)),flip(a)]. 1229 T(x,K(T(x,y),z)) = x. [para(1227(a,2),1055(a,1))]. 1230 K(T(x,y),z) * x = x * K(T(x,y),z). [para(1229(a,1),80(a,1,2))]. 1231 (x / y) * K(T(x / y,y),z) = K(y \ x,z) * (x / y). [para(82(a,1),1230(a,1,1,1)),flip(a)]. 1232 ((x * y) \ (x / (y \ 1))) \ 1 = a(y,x,y). [para(1221(a,2),1127(a,1))]. 1233 ((x * (y * y)) \ (T(y * x,y) / (y \ 1))) \ 1 = a(y,T(y * x,y),y). [para(1197(a,1),1232(a,1,1,1))]. 1234 K(R(x,y,y),z) * (x / y) = T(x,z) / y. [para(1226(a,1),1202(a,1))]. 1235 K(x \ y,z) * (y / x) = (y / x) * K(x \ y,z). [para(82(a,1),1231(a,1,2,1)),flip(a)]. 1236 T(L(x,y,x),L(x,y,x) \ y) = L(T(x,y * (x \ 1)),y,x). [para(1138(a,2),40(a,2)),flip(a)]. 1237 (x \ (x / y)) * L(T(y,z),y,x) = K((x \ (x / y)) \ 1,z). [para(40(a,2),1194(a,1,2))]. 1238 T(L(x,y,x),L(x,y,x) \ y) = L(T(x,x \ y),y,x). [para(1090(a,1),1236(a,2,1))]. 1239 T(L(x,y,x),L(x,y,x) \ y) = T(x,y). [para(1238(a,2),1091(a,1))]. 1240 L(x,y,x) \ y = y / T(x,y). [para(1239(a,1),109(a,1,2)),flip(a)]. 1241 L(x,y,x) = y / (y / T(x,y)). [para(1240(a,1),53(a,1,2)),flip(a)]. 1242 x / (T(x,y) / y) = L(y,x,y). [para(1031(a,2),1241(a,2,2)),flip(a)]. 1243 (x * (y / x)) / ((x * (y / x)) / T(x,y)) = L(x,x * (y / x),x). [para(1069(a,1),1241(a,2,2,2)),flip(a)]. 1244 L(L(x,x,y),y,L(x,x,y)) = y / (T(y,x) / L(x,x,y)). [para(1179(a,1),1242(a,1,2,1)),flip(a)]. 1245 L(L(x,x,y),y,L(x,x,y)) = y / (x \ y). [para(1122(a,1),1244(a,2,2))]. 1246 L(L(x,x,y),y,L(x,x,y)) = x. [para(1245(a,2),53(a,1))]. 1247 R(K(x,y),T(y,x) * z,u) = R(K(y,x),y * z,u) \ 1. [para(1070(a,1),1107(a,1,1))]. 1248 x / ((x / K(y,z)) * (T(y,z) / (x * y))) = R(x,K(y,z) / x,y). [para(284(a,1),1134(a,1,2))]. 1249 (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u). [para(1167(a,1),151(a,1)),flip(a)]. 1250 (x * L(x \ (x * y),z,u)) * y = (x * y) * L(y,z,u). [para(198(a,1),1249(a,1,1))]. 1251 (x * L(y,z,u)) * y = (x * y) * L(y,z,u). [para(13(a,1),1250(a,1,1,2,1))]. 1252 ((x * y) * L(y,z,u)) / y = x * L(y,z,u). [hyper(61,a,1251,a)]. 1253 ((x / L(y,z,u)) * y) * L(y,z,u) = x * y. [para(16(a,1),1251(a,1,1)),flip(a)]. 1254 (x * L(y,z,u)) / y = (x / y) * L(y,z,u). [para(16(a,1),1252(a,1,1,1))]. 1255 (x * y) / L(y,z,u) = (x / L(y,z,u)) * y. [hyper(61,a,1253,a)]. 1256 (x * (y / x)) / ((x * (y / x)) / T(x,y)) = L(x,y / x,x). [para(1243(a,2),1136(a,1))]. 1257 (x * (y / x)) / ((x * (y / x)) / T(x,y)) = L(x,y,x). [para(1256(a,2),435(a,1))]. 1258 (x * (y / x)) / (y * (x \ 1)) = L(x,y,x). [para(1170(a,1),1257(a,1,2))]. 1259 R(x,y,x \ 1) = L(x,y,x). [para(1258(a,1),188(a,1)),flip(a)]. 1260 L(x \ 1,y,x) = L(x,y,x) \ 1. [para(1259(a,1),1185(a,1,1)),flip(a)]. 1261 x * (L(x,y,x) \ 1) = a(x,y,x). [para(1260(a,1),1157(a,1,2))]. 1262 L(x,y,x) \ x = a(x,y,x). [para(1261(a,1),615(a,1)),flip(a)]. 1263 ((x * y) * (y * x)) * ((y * x) \ z) = (y * x) * (K(y,x) \ z). [para(1096(a,1),986(a,1,1))]. 1264 ((x * y) * (y * x)) * ((y * x) \ z) = (y * x) * (K(x,y) * z). [para(1075(a,1),1263(a,2,2))]. 1265 (x * y) * ((y * x) * ((y * x) \ z)) = (y * x) * (K(x,y) * z). [para(1264(a,1),1218(a,1)),flip(a)]. 1266 (x * y) * (K(y,x) * z) = (y * x) * z. [para(14(a,1),1265(a,1,2)),flip(a)]. 1267 (x * y) \ ((x * y) * z) = L(z,K(x,y),y * x). [para(1266(a,1),111(a,1,2))]. 1268 L(x,K(y,z),z * y) = x. [para(1267(a,1),13(a,1))]. 1269 (K(x,y) * (y * x)) * z = K(x,y) * ((y * x) * z). [para(1268(a,1),342(a,1,2,2)),flip(a)]. 1270 L(x,y * z,K(y,z)) = x. [para(1268(a,1),437(a,1))]. 1271 K(x,y) \ ((y * x) \ z) = (x * y) \ z. [para(1270(a,1),181(a,1)),flip(a)]. 1272 T(x,y) * ((x * y) \ z) = x * ((y * x) \ z). [para(1271(a,1),1063(a,1,2)),flip(a)]. 1273 T(x,y) * (y * ((x * y) \ z)) = x * (y * ((y * x) \ z)). [para(1272(a,1),851(a,1,2))]. 1274 (x * (K(y,x) * y)) * z = K(y,x) * ((x * y) * z). [para(1117(a,1),1269(a,1,1))]. 1275 K(x,y) * ((y * x) * z) = (y * T(x,y)) * z. [para(1043(a,2),1274(a,1,1,2)),flip(a)]. 1276 K(x,y) * ((y * x) * z) = (x * y) * z. [para(80(a,1),1275(a,2,1))]. 1277 ((x * y) * z) / ((y * x) * z) = K(x,y). [hyper(61,a,1276,a)]. 1278 K(x,y) * (y * (x * z)) = (x * y) * L(z,x,y). [para(69(a,1),1276(a,1,2))]. 1279 ((x * y) * z) / ((T(x,y) * y) * z) = K(y,T(x,y)). [para(80(a,1),1277(a,1,1,1))]. 1280 x * (K(y,x) * (y * z)) = (y * x) * L(z,y,x). [para(1278(a,1),1117(a,1)),flip(a)]. 1281 (x * y) * L(z,x,y) = y * (T(x,y) * z). [para(1105(a,1),1280(a,1,2)),flip(a)]. 1282 L(x,y,z) = (y * z) \ (z * (T(y,z) * x)). [hyper(56,a,1281,a),flip(a)]. 1283 L(T(x,y) \ z,x,y) = (x * y) \ (y * z). [para(14(a,1),1282(a,2,2,2))]. 1284 L(x,T(y,z),z) = L(x,y,z). [para(1282(a,2),100(a,1)),flip(a)]. 1285 L(x,T(y,z),T(z,y)) = L(x,y,T(z,y)). [para(796(a,1),1284(a,1,2))]. 1286 L(x,y,y \ z) = L(x,y,z). [para(1284(a,1),909(a,1))]. 1288 L(x,y,z \ y) = L(x,z,y). [para(1286(a,1),439(a,2))]. 1289 L(x,y,z \ 1) = L(x,z,y). [para(1286(a,1),445(a,2))]. 1290 L(x,y,1 / z) = L(x,z,y). [para(1286(a,1),446(a,1)),flip(a)]. 1291 (x \ y) * L(z,x,y) = x \ (y * z). [para(1286(a,1),359(a,1,2))]. 1292 L(x,y,y / z) = L(x,z,y). [para(1286(a,1),907(a,1)),flip(a)]. 1293 L(x,y \ z,z) = L(x,z,y). [para(1288(a,1),905(a,1))]. 1294 L(x,y \ 1,z) = L(x,z,y). [para(210(a,1),1289(a,1,3)),flip(a)]. 1295 L(x,y \ z,y) = L(x,z,y). [para(1293(a,1),425(a,1)),flip(a)]. 1296 L((x \ y) \ z,y,x) = y \ (x * z). [para(1293(a,1),353(a,1))]. 1297 x \ (y * L(z,y,x)) = (x \ y) * z. [para(1293(a,1),355(a,1,2,2))]. 1299 L(x,y,z) = y \ (z * ((z \ y) * x)). [para(1295(a,1),70(a,2)),flip(a)]. 1300 x * L(y,x,z) = z * ((z \ x) * y). [para(1295(a,1),137(a,1,2))]. 1301 L(x * y,z,x) = z \ ((z / (x \ 1)) * y). [para(1295(a,1),690(a,1))]. 1302 (x * (y \ 1)) * L(z,x,y) = x * (y \ z). [para(1295(a,1),691(a,1,2))]. 1303 L(L((x \ y) \ z,u,w),y,x) = L(y \ (x * z),u,w). [para(1295(a,1),509(a,1))]. 1304 (x \ y) * ((z / (x \ y)) * (x \ (y * u))) = ((x \ y) * z) * L(u,x,y). [para(1291(a,1),85(a,1,2,2))]. 1305 (x \ (x / y)) * L(z,y,x) = x \ ((x / y) * z). [para(1292(a,1),1291(a,1,2))]. 1306 x \ (y * L(L((x \ y) \ 1,z,u),y,x)) = L((x \ y) \ 1,z,u) * (x \ y). [para(1297(a,2),227(a,2)),flip(a)]. 1307 L(x,y,T(z,y)) = L(x,y,z). [para(1285(a,1),899(a,1))]. 1309 K((x \ (x / y)) \ 1,z) = x \ ((x / y) * T(y,z)). [para(1305(a,1),1237(a,1)),flip(a)]. 1310 L(K(x,y),x,z) = K((z \ (z / x)) \ 1,y). [para(1309(a,2),1040(a,1)),flip(a)]. 1311 (x * y) * K((x \ (x / y)) \ 1,z) = x * (y * K(y,z)). [para(1310(a,1),69(a,1,2))]. 1312 L(K(x,y),x,z) = K(L(x,x,z),y). [para(1191(a,2),1310(a,2,1))]. 1313 x * K(L(y,y,x),z) = (x / y) * T(y,z). [para(1312(a,1),1039(a,1,2))]. 1314 K(L(x,x,y \ x),z) = L(K(x,z),y,x). [para(1312(a,1),1288(a,1))]. 1315 L(K(x,y),z,x) = K(L(x,z,x),y). [para(1288(a,1),1314(a,1,1)),flip(a)]. 1316 (x \ y) * K(L(y,x,y),z) = x \ (y * K(y,z)). [para(1315(a,1),1291(a,1,2))]. 1317 (x \ y) * K(L(y,x,y),z) = x \ T(y,z). [para(1035(a,2),1316(a,2,2))]. 1318 T(x / y,y) * (y * (((x / y) * y) \ z)) = x * L((y * (x / y)) \ z,y,x). [para(1273(a,2),295(a,1))]. 1319 (x * y) * K((x \ (x / y)) \ 1,z) = x * T(y,z). [para(1035(a,2),1311(a,2,2))]. 1320 ((x / y) * ((y * z) / (x * z))) \ 1 = ((y * z) / (x * z)) \ (y / x). [para(284(a,1),1175(a,1,1))]. 1321 (K(x,y) \ (z / K(y,x))) \ z = K(K(x,y),z / K(x,y)). [para(1180(a,1),1095(a,1))]. 1322 ((x / y) * ((y * z) / (x * z))) \ 1 = ((x * z) / (y * z)) * (y / x). [para(1320(a,2),284(a,1))]. 1323 (x / y) \ R(x / y,y,z) = ((x * z) / (y * z)) * (y / x). [para(1322(a,1),952(a,2))]. 1324 ((x * y) / (z * y)) * (z / x) = R(z,x,y) \ z. [para(1323(a,1),896(a,1))]. 1325 x * (R(y,x,z) \ y) = R(x,y / x,z). [para(1324(a,1),941(a,1,2))]. 1326 R(x,y / x,z) = R(x,y,z). [para(1325(a,1),932(a,1))]. 1327 R(x,y * x,z) = R(x,y,z). [para(15(a,1),1326(a,1,2)),flip(a)]. 1328 x / ((x / K(y,z)) * (T(y,z) / (x * y))) = R(x,K(y,z),y). [para(1326(a,1),1248(a,2))]. 1329 R(T(x,y),z * x,u) = T(R(x,z,u),y). [para(1327(a,1),42(a,2,1))]. 1330 R(T(x,y),z * x,u) = R(T(x,y),z,u). [para(1329(a,2),42(a,2)),flip(a)]. 1331 ((x * (y * y)) \ ((x * y) * y)) \ 1 = a(y,T(y * x,y),y). [para(880(a,1),1233(a,1,1,2))]. 1332 a(x,T(x * y,x),x) = a(y,x,x) \ 1. [para(24(a,2),1331(a,1,1)),flip(a)]. 1333 a(x,x * y,x) = a(y,x,x) \ 1. [para(1332(a,1),1151(a,1)),flip(a)]. 1334 a(x,y,y) \ 1 = a(y,x,y). [para(1333(a,1),1126(a,1))]. 1335 a(x,y,x) \ z = a(y,x,x) * z. [para(1334(a,1),256(a,1,1))]. 1336 a(x,y,y) \ z = a(y,x,y) * z. [para(1334(a,1),259(a,1,1)),flip(a)]. 1337 x / (a(y,z,z) * R(a(z,y,z),x,u)) = R(x,a(z,y,z),u). [para(1335(a,1),933(a,1,2))]. 1338 (x \ y) * (x * (((x \ z) / y) * (y * u))) = ((x \ y) * z) * L(u,x,y). [para(924(a,1),1304(a,1,2))]. 1339 (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = R(x,z,u) \ T(R(x,z,u),y). [para(42(a,2),393(a,1,1,1))]. 1340 L(R(x / (y \ 1),y,y \ 1),z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u). [para(44(a,1),1161(a,1,1))]. 1341 x \ (y * L(y \ (x * 1),z,u)) = L((x \ y) \ 1,z,u) * (x \ y). [para(1303(a,1),1306(a,1,2,2))]. 1342 L((x \ y) \ 1,z,u) * (x \ y) = x \ (y * L(y \ x,z,u)). [para(12(a,1),1341(a,1,2,2,1,2)),flip(a)]. 1343 (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u)). [para(1342(a,1),227(a,1)),flip(a)]. 1344 (x \ y) * (x * (((y / x) * x) \ z)) = y * L((x * (y / x)) \ z,x,y). [para(82(a,1),1318(a,1,1))]. 1345 x * L((y * (x / y)) \ z,y,x) = (y \ x) * (y * (x \ z)). [para(16(a,1),1344(a,1,2,2,1)),flip(a)]. 1346 (x \ y) * (x * (y \ z)) = y * (x * ((x * y) \ z)). [para(605(a,1),1345(a,1,2)),flip(a)]. 1347 (x \ y) * (x * (((x \ (x * (y \ z))) / y) * (y * u))) = (y * (x * ((x * y) \ z))) * L(u,x,y). [para(1346(a,1),1338(a,2,1))]. 1348 ((T(x,y) * z) * u) / ((x * z) * u) = R(x,z,u) \ T(R(x,z,u),y). [para(75(a,1),1339(a,1,1))]. 1349 ((T(x,y) * z) * u) / ((x * z) * u) = R(x,z,u) \ R(T(x,y),z,u). [para(42(a,2),1348(a,2,2))]. 1350 R(x \ T(x,y),x * z,u) = R(x,z,u) \ R(T(x,y),z,u). [para(1349(a,1),394(a,2))]. 1351 R(x,y,z) \ R(T(x,u),y,z) = R(K(x,u),x * y,z). [para(1038(a,2),1350(a,1,1)),flip(a)]. 1352 R(K(x,y),x * z,u) = K(R(x,z,u),y). [para(1351(a,1),1052(a,1))]. 1353 K(R(x,x \ y,z),u) = R(K(x,u),y,z). [para(14(a,1),1352(a,1,2)),flip(a)]. 1354 R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1. [para(1352(a,1),1247(a,2,1))]. 1355 R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)). [para(1354(a,2),1070(a,1))]. 1356 ((x * y) * z) / ((T(x,u) * y) * z) = K(u,R(x,y,z)). [para(1355(a,1),1116(a,1)),flip(a)]. 1357 K(x,R(y,x,z)) = K(x,T(y,x)). [para(1356(a,1),1279(a,1))]. 1358 K(x,R(y,x,z)) = K(x,y). [para(1357(a,2),1079(a,1))]. 1359 K(x,y) * T(R(y,x,z),x) = R(y,x,z). [para(1358(a,1),1056(a,1,1))]. 1360 K(x,y) * R(T(y,x),x,z) = R(y,x,z). [para(42(a,2),1359(a,1,2))]. 1361 T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). [para(1360(a,1),1112(a,1,2)),flip(a)]. 1362 x / (y \ R(y,x,z)) = R(x,T(y,x),z). [para(1361(a,1),933(a,1,2))]. 1363 R(x,T(y,x),z) = R(x,y,z). [para(1362(a,1),933(a,1))]. 1364 R(x,y / x,z) = R(x,x \ y,z). [para(82(a,1),1363(a,1,2)),flip(a)]. 1365 R(x,x \ y,z) = R(x,y,z). [para(1364(a,1),1326(a,1))]. 1366 R(x,x * y,z) = R(x,y,z). [para(13(a,1),1365(a,1,2)),flip(a)]. 1367 R(x,y,z) \ (y * z) = (x \ y) * z. [para(1365(a,1),163(a,1,1))]. 1368 R(x \ 1,y,z) = R(x,y,z) \ 1. [para(1365(a,1),603(a,1,1)),flip(a)]. 1369 x * R(x \ 1,y,z) = R(x,y,z) \ x. [para(1365(a,1),604(a,1,1)),flip(a)]. 1370 x / ((y \ z) * (z \ x)) = R(y,z,z \ x). [para(1365(a,1),459(a,1)),flip(a)]. 1371 R(K(x,y),z,u) = K(R(x,z,u),y). [para(1365(a,1),1353(a,1,1)),flip(a)]. 1372 R(T(x,y),x * z,u) = T(R(x,z,u),y). [para(1366(a,1),42(a,2,1))]. 1373 x * (R(x,y,z) \ (x * y)) = R(x * y,x,z). [para(1366(a,1),938(a,1,2,1))]. 1374 (x \ 1) / (y / x) = R(y \ 1,x,x). [para(1368(a,2),1210(a,2))]. 1375 K(R(x,y,y),z) \ (K(x,z) / y) = y \ 1. [para(1371(a,1),1209(a,1,1))]. 1376 R(K(x,y) \ 1,z,u) = K(R(x,z,u),y) \ 1. [para(1371(a,1),1368(a,2,1))]. 1377 R(x,y,z) * (x \ (x * z)) = y * ((y \ x) * z). [para(1367(a,1),940(a,2,2))]. 1378 R((x * y) \ 1,y,y) = (y \ 1) / x. [para(15(a,1),1374(a,1,2)),flip(a)]. 1379 R((x * (y \ 1)) \ 1,y \ 1,y \ 1) = T(y,y \ 1) / x. [para(81(a,2),1378(a,2,1))]. 1380 R(T(x,y),x * z,u) = R(T(x,y),z,u). [para(1372(a,2),42(a,2)),flip(a)]. 1381 R(T(x * K(y,x),y),z,u) = R(x,(x * K(y,x)) * z,u). [para(1066(a,1),1380(a,1,1)),flip(a)]. 1382 T(x,y) / ((z \ x) * K(x,y)) = R(z,x,x \ T(x,y)). [para(1038(a,2),1370(a,1,2,2))]. 1383 K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1. [para(1375(a,1),1075(a,1)),flip(a)]. 1384 x * (x * (R(x,y,z) \ y)) = R(x * y,x,z). [para(569(a,1),1373(a,1,2))]. 1385 R(K(x,y) \ 1,z,u) = K(y,R(x,z,u)). [para(1376(a,2),1070(a,1))]. 1386 R(K(x,y),z,u) = K(x,R(y,z,u)). [para(1070(a,1),1385(a,1,1))]. 1387 K(R(x,y,z),u) = K(x,R(u,y,z)). [para(1386(a,1),1371(a,1)),flip(a)]. 1388 K(L(x,x,y),z) = K(x,R(z,y,x)). [para(1144(a,1),1387(a,1,1))]. 1389 K((x \ (x / y)) \ 1,z) = K(y,R(z,x,y)). [para(1191(a,1),1388(a,1,1))]. 1390 x * K(y,R(z,x,y)) = (x / y) * T(y,z). [para(1388(a,1),1313(a,1,2))]. 1391 R(x * y,x,z) = x * R(y,x,z). [para(938(a,1),1384(a,1,2)),flip(a)]. 1392 R(x * (x \ y),x,z) = ((y * z) / (x * z)) * x. [para(1391(a,2),532(a,2)),flip(a)]. 1393 R(x,y,z) * z = y * ((y \ x) * z). [para(13(a,1),1377(a,1,2))]. 1394 R(x,y,z) = (y * ((y \ x) * z)) / z. [hyper(61,a,1393,a),flip(a)]. 1395 R(x * y,x,z) * z = x * (y * z). [para(13(a,1),1393(a,2,2,1))]. 1396 R(x,y,z) * z = x * L(z,x,y). [para(1393(a,2),1300(a,2)),flip(a)]. 1397 L(x,y,z) = R(y,z,x) * (y \ x). [hyper(558,a,1396,a),flip(a)]. 1398 L(x,y,z) \ (R(y,z,x) * x) = T(y,L(x,y,z)). [para(1396(a,2),32(a,2,2)),flip(a)]. 1399 L(x,y,z) = z * (R(z,y,x) \ x). [para(1397(a,2),940(a,1))]. 1400 R(x,y,z) \ z = x \ L(z,y,x). [hyper(56,a,1399,a(flip)),flip(a)]. 1401 R(x,y,z) = (x * z) / L(z,y,x). [para(1399(a,2),571(a,1,2)),flip(a)]. 1402 T(x,y) * (R(T(x,y),z,u) \ u) = L(u,z * x,T(x,y)). [para(1330(a,1),1399(a,2,2,1)),flip(a)]. 1403 R(x,y,z) * (x \ L(z,y,x)) = z. [para(1400(a,1),14(a,1,2))]. 1404 R(x,y,z) * L(z,y,x) = x * z. [para(1401(a,2),16(a,1,1))]. 1405 R(x,R(y,z,u),y) = R(x,y,R(y,z,u)). [para(1401(a,2),1164(a,1)),flip(a)]. 1406 R(x,y,z) = (x / L(z,y,x)) * z. [para(1401(a,2),1255(a,1))]. 1407 x * (R(x,y,z) \ L(z,x,y)) = z. [para(1403(a,1),940(a,1)),flip(a)]. 1408 (L(x,y,z) * R(z,y,x)) \ (z * x) = K(R(z,y,x),L(x,y,z)). [para(1404(a,1),26(a,2,2)),flip(a)]. 1409 (L(x,y,z) / z) * R(z,y,x) = x. [hyper(297,a,1406,a(flip))]. 1410 a(x / y,y,z) = x \ R(x,y,z). [para(1406(a,2),591(a,2,2))]. 1411 (R(x,y,z) \ x) * L(z,x,y) = z. [para(1407(a,1),583(a,2))]. 1412 (x / y) * R(y,z,L(x,y,z)) = L(x,y,z). [para(341(a,1),1409(a,1,1,1))]. 1413 a(x,y,z) = (x * y) \ R(x * y,y,z). [para(15(a,1),1410(a,1,1))]. 1414 a(x / y,y,z) = R(y,x,z) \ y. [para(1410(a,2),931(a,2)),flip(a)]. 1415 R(x,y,z) \ x = L(z,x,y) \ z. [hyper(737,a,1411,a),flip(a)]. 1416 a(x,y,z) = R(y,x * y,z) \ y. [para(15(a,1),1414(a,1,1))]. 1417 T(x,R(y,z,x) \ y) = x. [para(1415(a,2),747(a,1,2))]. 1418 R(x,y,y) \ x = a(y,x,y). [para(1415(a,2),1262(a,1))]. 1419 T(x,a(y / z,z,x)) = x. [para(1414(a,2),1417(a,1,2))]. 1420 T(x,a(y,z,x)) = x. [para(15(a,1),1419(a,1,2,1))]. 1421 a(x,y,z) * z = z * a(x,y,z). [para(1420(a,1),80(a,1,2))]. 1422 R(x,y,y) * a(y,x,y) = x. [para(1418(a,1),14(a,1,2))]. 1423 a(x,y,z) = R(y,x,z) \ y. [para(1327(a,1),1416(a,2,1))]. 1425 R(x,y,z) = x / a(y,x,z). [para(1423(a,2),53(a,1,2)),flip(a)]. 1426 a(x,y,z) * R(y,x,z) = y. [para(1423(a,2),573(a,1,1))]. 1427 R(x,y,z) = a(y,x,z) \ x. [para(1423(a,2),574(a,1,1)),flip(a)]. 1428 R(x,y,z) / x = 1 / a(y,x,z). [para(1423(a,2),575(a,1,2)),flip(a)]. 1429 R(x,y,z) \ (x * u) = a(y,x,z) * u. [para(1423(a,2),580(a,2,1))]. 1430 x * (R(x,y,z) \ u) = a(y,x,z) * u. [para(1423(a,2),583(a,1,1)),flip(a)]. 1431 a(x,y,z) = x \ R(x,y,z). [para(1423(a,2),931(a,1))]. 1432 K(a(x,y,z),x) = 1. [para(1423(a,2),935(a,1,1))]. 1433 R(x,y,z) = x * a(x,y,z). [para(1423(a,2),932(a,1,2)),flip(a)]. 1434 R(x,y,z) = a(x,y,z) * x. [para(1423(a,2),934(a,1,1)),flip(a)]. 1435 a(x,y,z) = y * R(y \ 1,x,z). [para(1423(a,2),1369(a,2)),flip(a)]. 1436 K(x,R(y,z,u)) \ K(x,y) = a(z,K(x,y),u). [para(1386(a,1),1423(a,2,1)),flip(a)]. 1437 a(x,y,z) * L(z,y,x) = z. [para(1423(a,2),1411(a,1,1))]. 1438 a(x / y,y,z) = a(x,y,z). [para(1423(a,2),1414(a,2))]. 1439 a(x * y,y,z) = a(x,y,z). [para(1423(a,2),1416(a,2)),flip(a)]. 1440 T(a(x,y,z),x) = a(x,y,z). [hyper(37,a,1432,a)]. 1441 x \ ((x / y) * R(y,z,u)) = L(a(y,z,u),y,x). [para(1431(a,2),298(a,1,1)),flip(a)]. 1442 a(x,y,z) = R(x,y,z) / x. [para(1431(a,2),479(a,2)),flip(a)]. 1443 R(x,y,z) \ a(x,y,z) = x \ 1. [para(1431(a,2),486(a,1,2))]. 1444 L(x,y,a(y,z,u)) = x. [para(1431(a,2),544(a,1,3))]. 1445 x * (a(x,y,z) * u) = R(x,y,z) * u. [para(1431(a,2),547(a,1,2,1))]. 1446 R(x,y,z) * (x \ u) = a(x,y,z) * u. [para(1431(a,2),557(a,1,1)),flip(a)]. 1447 x * (R(x,y,z) \ u) = a(x,y,z) \ u. [para(1431(a,2),565(a,1,1)),flip(a)]. 1448 (x * y) \ (R(x,z,u) * y) = T(a(x,z,u),x * y). [para(1431(a,2),564(a,1,1)),flip(a)]. 1449 (x \ (x / y)) * R(L(y,y,x),z,u) = a(L(y,y,x),z,u). [para(1431(a,2),1192(a,1)),flip(a)]. 1450 (x * y) \ (y * R(T(x,y),z,u)) = L(a(T(x,y),z,u),x,y). [para(1431(a,2),1283(a,1,1)),flip(a)]. 1451 (a(x,y,z) * x) \ (u * a(x,y,z)) = x \ T(u,a(x,y,z)). [para(1444(a,1),145(a,1)),flip(a)]. 1452 a(x,y \ 1,y) = a(y,x,y). [hyper(1129,a,1433,a),flip(a)]. 1453 R(x,y,a(y,z,u)) * R(y,z,u) = (x * y) * a(y,z,u). [para(1433(a,2),75(a,1,2))]. 1454 x \ ((x / a(y,z,u)) * R(y,z,u)) = L(y,a(y,z,u),x). [para(1434(a,2),340(a,2,2,2)),flip(a)]. 1455 a(x,y,z) = z / L(z,y,x). [hyper(61,a,1437,a),flip(a)]. 1457 ((x * a(y,z,u)) * L(u,z,y)) / u = R(x,a(y,z,u),L(u,z,y)). [para(1437(a,1),30(a,2,2)),flip(a)]. 1459 T(a(x,y,z),u) * L(z,y,x) = K(a(x,y,z),u) * z. [para(1437(a,1),1105(a,1,2)),flip(a)]. 1461 a(x \ 1,y,x \ 1) = a(x,y,x). [para(1452(a,1),1153(a,2))]. 1462 R(x / a(y,z,u),u / L(u,z,y),L(u,z,y)) = (x * L(u,z,y)) / u. [para(1455(a,2),160(a,1,1,2))]. 1463 L(x,y,z) * a(z,y,x) = x. [para(1455(a,2),732(a,1,2))]. 1464 L(x,y,z) = x / a(z,y,x). [para(1455(a,2),734(a,1,2)),flip(a)]. 1465 L(x,a(y,z,u),u) = x. [para(1455(a,2),738(a,1,2))]. 1466 a(1 / x,y,z) = z / L(z,x,y). [para(1290(a,1),1455(a,2,2))]. 1467 (a(x,y,z) * z) * T(u,z) = a(x,y,z) * (u * z). [para(1465(a,1),358(a,1,2,1)),flip(a)]. 1468 1 / a(x,y,z) = a(y,x,z). [para(1428(a,1),1442(a,2)),flip(a)]. 1469 a(x,y,z) * a(y,x,z) = 1. [para(1468(a,1),16(a,1,1))]. 1470 a(x,y,z) \ 1 = a(y,x,z). [para(1468(a,1),54(a,1,1))]. 1471 a(x,y,z) * (a(y,x,z) * u) = u. [para(1468(a,1),263(a,1,1))]. 1472 a(x,y,z) \ u = a(y,x,z) * u. [para(1468(a,1),269(a,1,1)),flip(a)]. 1473 T(a(x,y,z),u) * a(y,x,z) = K(a(x,y,z),u) * 1. [para(1469(a,1),1105(a,1,2)),flip(a)]. 1474 a(1 / x,y,z) = a(y,x,z). [para(1466(a,2),1455(a,2)),flip(a)]. 1475 a(x,y \ 1,z) = a(y,x,z). [para(53(a,1),1474(a,1,1)),flip(a)]. 1476 a(x \ 1,y,z) = a(y,x,z). [para(208(a,1),1474(a,1,1))]. 1477 a((x \ y) / x,x,z) = a(y,x,z). [para(1474(a,1),703(a,2))]. 1479 a(x,y \ 1,y \ 1) = a(y,x \ 1,y). [para(1475(a,1),1461(a,1))]. 1480 a(x,y,z) * (u * a(y,x,z)) = T(u,a(y,x,z)). [hyper(98,a,1471,a),flip(a)]. 1481 L(x,y,z) = a(y,z,x) * x. [hyper(17,a,1437,a,b,1471,a),flip(a)]. 1482 x \ ((a(y,z,u) * x) * a(z,y,u)) = K(a(y,z,u) * x,a(z,y,u)). [para(1471(a,1),26(a,2,1)),flip(a)]. 1483 a(x,y,z) = z \ L(z,x,y). [hyper(701,a,1481,a),flip(a)]. 1484 a(x,y,z) = L(z,x,y) / z. [hyper(61,a,1481,a(flip)),flip(a)]. 1485 L(x,y,z) = x * a(y,z,x). [para(1481(a,2),1421(a,1))]. 1486 x * L(x \ 1,y,z) = a(y,z,x \ 1). [para(1483(a,2),256(a,1)),flip(a)]. 1488 (x \ y) \ (z \ ((z / x) * y)) = a(x,z,x \ y). [para(298(a,1),1483(a,2,2)),flip(a)]. 1489 x * L(a(y,z,u),u,x) = (x / u) * L(u,y,z). [para(1483(a,2),300(a,1,2,1))]. 1490 ((L(x,y,z) / x) * L(x,y,z)) \ L(x,y,z) = a(y,z,x) \ 1. [para(1483(a,2),637(a,2,1))]. 1491 x \ (L(x,y,z) * u) = a(y,z,x) * u. [para(1483(a,2),725(a,2,1))]. 1492 x * (L(x,y,z) \ u) = a(y,z,x) \ u. [para(1483(a,2),745(a,1,1)),flip(a)]. 1493 K(x,y) * L(K(y,x),z,u) = a(z,u,K(y,x)). [para(1483(a,2),1075(a,1)),flip(a)]. 1495 x \ (y * L(y \ x,z,u)) = L(a(z,u,y \ x),x,y). [para(1483(a,2),1296(a,1,1)),flip(a)]. 1499 R(a(x,y,z) * 1,u,w) = R(a(y,x,z),u,w) \ 1. [para(1472(a,1),1368(a,1,1))]. 1500 a(x \ y,x,z) = a(y,x,z). [para(1477(a,1),1438(a,1)),flip(a)]. 1501 a(x * y,x,z) = a(y,x,z). [para(13(a,1),1500(a,1,1)),flip(a)]. 1503 R(x,y,R(y,z,u)) * (y * R(y,z,u)) = (x * R(y,z,u)) * y. [para(1405(a,1),204(a,1,1))]. 1504 a(R(x,y,z) / u,u,x) = R(u,x,R(x,y,z)) \ u. [para(1405(a,1),1414(a,2,1))]. 1505 (x * y) \ (x / (y \ 1)) = a(x,y,y). [para(1205(a,1),1413(a,2,2)),flip(a)]. 1506 (x * (y \ 1)) \ (x / y) = a(x,y \ 1,y \ 1). [para(210(a,1),1505(a,1,2,2))]. 1507 a(x,y,z) * (R(y,x,z) * u) = y * u. [para(13(a,1),1430(a,1,2)),flip(a)]. 1508 a(x,y,z) * ((y * x) * z) = y * (x * z). [para(92(a,1),1430(a,1,2)),flip(a)]. 1509 a(x,y,z) * (y * u) = y * (a(x,y,z) * u). [para(1429(a,1),1430(a,1,2)),flip(a)]. 1510 (R(x,y,z) * u) / (a(x,y,z) * u) = x. [hyper(61,a,1445,a)]. 1511 a(x,y,z) * (x * u) = R(x,y,z) * u. [hyper(17,a,551,a(flip),b,1445,a)]. 1512 ((R(x,y,z) * u) * w) / ((a(x,y,z) * u) * w) = R(x,a(x,y,z) * u,w). [para(1445(a,1),30(a,2,1,1)),flip(a)]. 1513 a(x,y,z) \ ((x * y) * z) = x * (y * z). [para(92(a,1),1447(a,1,2)),flip(a)]. 1514 a(x,y \ 1,y \ 1) = a(x,y,y). [para(1479(a,2),1475(a,1))]. 1515 a(x,y,x \ 1) = a(y,x,x). [para(1514(a,1),1475(a,1)),flip(a)]. 1516 x \ (y * L(y \ x,z,u)) = a(z,u,(x \ y) \ 1). [para(1486(a,1),1343(a,1)),flip(a)]. 1517 x * (a(y,z,x) * u) = L(x,y,z) * u. [para(1491(a,1),14(a,1,2))]. 1518 R(x,y,z) = z * (L(z,y,x) \ x). [para(1492(a,2),1427(a,2))]. 1519 x * (L(x,y,z) \ u) = a(z,y,x) * u. [para(1492(a,2),1472(a,1))]. 1520 L(x,y,z) = (x * z) / R(z,y,x). [para(1518(a,2),859(a,1,2)),flip(a)]. 1521 L(x,y,z) * R(z,y,x) = x * z. [para(1520(a,2),16(a,1,1))]. 1522 (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). [para(1521(a,1),24(a,2,2,1)),flip(a)]. 1523 x * R(y,z,L(x,y,z)) = L(x,y,z) * y. [para(341(a,1),1521(a,1,1))]. 1524 ((R(x,y,z) * u) * w) / (a(R(x,u,w),y,z) * (u * w)) = R(x,u,w). [para(152(a,1),1510(a,1,1))]. 1525 L(x,y,z) * y = x * R(y,z,x). [para(1434(a,2),1517(a,1,2)),flip(a)]. 1526 L(x,y,z) * (R(z,y,x) * u) = x * (z * u). [para(1507(a,1),1517(a,1,2)),flip(a)]. 1528 a(x,y,z) * (u * L(z,y,x)) = z * T(u,L(z,y,x)). [para(32(a,2),1519(a,1,2)),flip(a)]. 1529 (x * y) / (a(z,u,x) * y) = L(x,u,z). [para(1519(a,1),859(a,1,2))]. 1530 L(x,y,z) \ (u * x) = a(z,y,x) * T(u,x). [para(1519(a,1),861(a,1)),flip(a)]. 1531 T(x * (y * z),a(x,y,z)) = x * (y * z). [para(1513(a,1),420(a,1)),flip(a)]. 1532 R(x,y,L(z,x,y)) = R(x,y,z). [hyper(17,a,1525,a(flip),b,1523,a)]. 1533 R(x * y,y,L(z,x,y)) = R(x * y,y,z). [para(438(a,1),1532(a,1,3))]. 1534 L(x,y,z) = (x / y) * R(y,z,x). [para(1532(a,1),1412(a,1,2)),flip(a)]. 1535 (x * y) \ (y * R(T(x,y),z,y)) = y \ L(y,T(x,y),z). [para(1534(a,2),370(a,1,2)),flip(a)]. 1536 L(x * R(x \ 1,y,z),z,x) = z \ L(z,x \ 1,y). [para(1534(a,2),1301(a,2,2))]. 1537 K(x * (y * z),a(x,y,z)) = 1. [hyper(36,a,1531,a)]. 1538 K(x * y,a(x / z,z,L(y,x,z))) = 1. [para(169(a,1),1537(a,1,1))]. 1539 K(x * y,a(x,z,L(y,x,z))) = 1. [para(1438(a,1),1538(a,1,2))]. 1540 (x * y) \ R(x * y,y,z) = a(x,y,L(z,x,y)). [para(1533(a,1),1413(a,2,2)),flip(a)]. 1541 K(R(x,y,z),u) * K(u,x) = a(y,K(u,x),z). [para(1436(a,1),1075(a,1)),flip(a)]. 1542 (x * (a(y,x,z) * u)) / a(y,x,z) = (x * u) * K(a(y,x,z),x * u). [para(1509(a,1),1048(a,1,1))]. 1543 K(x,R(y,z,u)) * K(y,x) = a(z,K(y,x),u). [para(1387(a,1),1541(a,1,1))]. 1544 R(x,y,z) = ((x * z) / (y * z)) * y. [para(14(a,1),1392(a,1,1))]. 1545 R(x,y,z) / y = (x * z) / (y * z). [hyper(61,a,1544,a(flip))]. 1546 R(x / y,z,y) = (x / (z * y)) * z. [para(16(a,1),1544(a,2,1,1))]. 1547 R(K(x,y),z,x) / z = T(x,y) / (z * x). [para(1043(a,2),1545(a,2,1))]. 1548 ((x / y) * y) / L(y,z,x / y) = (x / (z * y)) * z. [para(1546(a,1),1401(a,1)),flip(a)]. 1549 K(x,R(y,z,x)) / z = T(x,y) / (z * x). [para(1386(a,1),1547(a,1,1))]. 1550 a(x,y,z) * T(R(y,x,z),z) = T(y,L(z,y,x)). [para(1398(a,1),1530(a,1)),flip(a)]. 1551 T(x,a(y,z,u)) != a(z,y,u) * w | x * a(y,z,u) = w. [para(1480(a,1),19(a,1))]. 1552 L(a(x,y,x \ z),x \ z,y) = (y * (x \ z)) \ ((y / x) * z). [para(1488(a,1),141(a,1,1))]. 1553 (x * (y \ 1)) \ (x / y) = a(x,y,y). [para(1506(a,2),1514(a,1))]. 1554 a(x,y,L(z,x,y)) = a(x,y,z). [para(1540(a,1),1413(a,2)),flip(a)]. 1555 K(x * y,a(x,z,y)) = 1. [para(1554(a,1),1539(a,1,2))]. 1556 T(a(x,y,z),x * z) * 1 = a(x,y,z). [para(1555(a,1),1055(a,1,2))]. 1557 K((x * y) * z,a(y,x,z)) = 1. [para(1501(a,1),1555(a,1,2))]. 1558 T(a(x,y,z),(y * x) * z) * 1 = a(x,y,z). [para(1557(a,1),1055(a,1,2))]. 1559 T(a(x,y,z),x * z) = a(x,y,z). [hyper(59,a,1556,a)]. 1560 T(a(x,y,z),(y * x) * z) = a(x,y,z). [hyper(59,a,1558,a)]. 1561 ((x * y) * z) \ (a(y,x,z) * ((x * y) * z)) = a(y,x,z). [para(1560(a,1),32(a,1)),flip(a)]. 1562 a(x,y,z) * R(T(y,z),x,z) = T(y,L(z,y,x)). [para(42(a,2),1550(a,1,2))]. 1563 a(x,y,z) * (u * z) = L(z,x,y) * T(u,z). [para(1481(a,2),1467(a,1,1)),flip(a)]. 1564 a(R(x,y,z) / u,u,x) = a(x,u,R(x,y,z)). [para(1504(a,2),1423(a,2)),flip(a)]. 1565 a(R(x,y,z),u,x) = a(x,u,R(x,y,z)). [para(1564(a,1),1438(a,1)),flip(a)]. 1566 T(x,y) / ((z \ x) * K(x,y)) = R(z,x,K(x,y)). [para(1038(a,2),1382(a,2,3))]. 1567 T(a(x,y,z),u) * a(y,x,z) = K(a(x,y,z),u). [hyper(59,a,1473,a(flip)),flip(a)]. 1568 L(a(x,y,z \ u),u,z) = a(x,y,(u \ z) \ 1). [para(1495(a,1),1516(a,1))]. 1569 L(a(x,y,(z / u) \ z),z,z / u) = a(x,y,L(u \ 1,u,z) \ 1). [para(282(a,2),1568(a,2,3,1))]. 1570 L(a(x,y,z),z,y) = z \ L(z,y \ 1,x). [para(1435(a,2),1536(a,1,1))]. 1571 L(a(x,y,z),z,y) = z \ L(z,x,y). [para(1294(a,1),1570(a,2,2))]. 1572 L(a(x,y,z),z,y) = a(x,y,z). [para(1571(a,2),1483(a,2)),flip(a)]. 1573 x / L(y,z,x / y) = (x / (z * y)) * z. [para(16(a,1),1548(a,1,1))]. 1574 R(T(x * K(y,x),y),z,u) = R(x,x * (K(y,x) * z),u). [para(992(a,1),1381(a,2,2))]. 1575 L(x,y * z,T(z,u)) = L(x,y,T(z,u)). [para(1402(a,1),1399(a,2)),flip(a)]. 1576 (x \ (x / y)) * L(R(y,z,u),y,x) = a(L(y,y,x),z,u). [para(44(a,1),1449(a,1,2))]. 1577 (x * y) \ (y * R(T(x,y),z,y)) = a(T(x,y),z,y). [para(1535(a,2),1483(a,2)),flip(a)]. 1578 (x * y) \ (R(x,z,y) * y) = a(T(x,y),z,y). [para(104(a,1),1577(a,1,2))]. 1579 T(a(x,y,z),x * z) = a(T(x,z),y,z). [para(1578(a,1),1448(a,1)),flip(a)]. 1580 a(T(x,y),z,y) = a(x,z,y). [para(1579(a,1),1559(a,1))]. 1581 a(x,T(y,z),z) = a(y,x \ 1,z). [para(1580(a,1),1475(a,1)),flip(a)]. 1582 L(x,T(y,x),z) = x * a(y,z,x). [para(1580(a,1),1485(a,2,2))]. 1583 a(x,T(y,z),z) = a(x,y,z). [para(1581(a,2),1475(a,1))]. 1584 a(x,y,z) * R(T(y,z),x,z) = T(y,z). [para(1583(a,1),1426(a,1,1))]. 1587 L(x,T(y,x),z) = L(x,y,z). [para(1582(a,2),1485(a,2)),flip(a)]. 1588 L(x,T(y / x,x),z) = z \ ((z / (y / x)) * y). [para(1587(a,2),354(a,1))]. 1589 T(x,L(y,x,z)) = T(x,y). [para(1584(a,1),1562(a,1)),flip(a)]. 1591 K(L(x,y,z),y) = T(y,x) \ y. [para(1589(a,1),1054(a,2,1))]. 1593 K(L(x,y,z),y) = K(x,y). [para(1591(a,2),1054(a,2)),flip(a)]. 1594 L(x,x \ y,z) = z \ ((z / (y / x)) * y). [para(82(a,1),1588(a,1,2))]. 1595 a(x,y,z) = ((y * x) * z) \ (y * (x * z)). [para(1508(a,1),1561(a,1,2)),flip(a)]. 1596 (x * y) \ (z * ((z \ x) * y)) = a(z \ x,z,y). [para(14(a,1),1595(a,2,1,1)),flip(a)]. 1597 a(x,y,z) = (x * z) \ (y * ((y \ x) * z)). [para(1596(a,2),1500(a,1)),flip(a)]. 1598 R(T(x * K(y,x),y),z,u) = R(x,K(y,x) * z,u). [para(1574(a,2),1366(a,1))]. 1599 R(x,K(y,x) * z,u) = R(x,z,u). [para(1066(a,1),1598(a,1,1)),flip(a)]. 1600 R(x,K(x,y) * z,u) = R(x,z,u). [para(1074(a,1),1599(a,1,2)),flip(a)]. 1601 L(x,y,K(z,y) * u) = R(y,u,x) * (y \ x). [para(1599(a,1),1397(a,2,1))]. 1602 L(x,K(y,z) * u,y) = y * (R(y,u,x) \ x). [para(1600(a,1),1399(a,2,2,1))]. 1603 L(x,y,K(z,y) * u) = L(x,y,u). [para(1601(a,2),1397(a,2)),flip(a)]. 1604 L(x,y,K(y,z) * u) = L(x,y,u). [para(1074(a,1),1603(a,1,3)),flip(a)]. 1605 L(x,y,K(z,y) / u) = L(x,y,u \ 1). [para(1383(a,1),1604(a,1,3)),flip(a)]. 1606 L(x,y,K(z,y) / u) = L(x,u,y). [para(1605(a,2),1289(a,1))]. 1607 L(x,y,K(z,y) * (u \ K(z,y))) = L(x,K(z,y) \ u,y). [para(314(a,1),1606(a,1,3))]. 1608 L(x,K(y,z) * u,y) = L(x,u,y). [para(1602(a,2),1399(a,2)),flip(a)]. 1609 x \ ((x / y) * R(y,z,u)) = a(L(y,y,x),z,u). [para(1576(a,1),1305(a,1)),flip(a)]. 1610 a(L(x,x,y),z,u) = L(a(x,z,u),x,y). [para(1609(a,1),1441(a,1))]. 1611 a(L(T(x,y),T(x,y),T(y,x)),z,u) = L(a(T(x,y),z,u),x,y). [para(1610(a,2),899(a,1))]. 1612 L(x,K(y,z) \ u,z) = L(x,z,u \ K(y,z)). [para(1607(a,1),1603(a,1))]. 1613 L(x,K(y,z) * u,y) = L(x,y,u \ K(z,y)). [para(1075(a,1),1612(a,1,2))]. 1615 L(x,y,z \ K(u,y)) = L(x,z,y). [para(1613(a,1),1608(a,1))]. 1616 a(x,y \ K(z,x),u) = u \ L(u,y,x). [para(1615(a,1),1483(a,2,2))]. 1618 a(x,y \ K(z,x),u) = a(y,x,u). [para(1616(a,2),1483(a,2)),flip(a)]. 1619 R((x * (y \ 1)) \ 1,y,y) = T(y,y \ 1) / x. [para(1379(a,1),1216(a,1)),flip(a)]. 1620 R((x * (y \ 1)) \ 1,y,y) = y / x. [para(219(a,1),1619(a,2,1))]. 1621 (x * y) \ (R(x,z,u) * y) = L(a(T(x,y),z,u),x,y). [para(104(a,1),1450(a,1,2))]. 1622 L(a(T(x,y),z,u),x,y) = T(a(x,z,u),x * y). [para(1621(a,1),1448(a,1))]. 1623 R(x,y,z) \ (u * a(x,y,z)) = x \ T(u,a(x,y,z)). [para(1434(a,2),1451(a,1,1))]. 1624 (L(x,y,z) * R(z,y,x)) \ (z * x) = K(z,R(L(x,y,z),y,x)). [para(1408(a,2),1387(a,1))]. 1625 (a(x,y,z) * L(z,x,y)) \ L(z,x,y) = a(x,y,z) \ 1. [para(1484(a,2),1490(a,1,1,1))]. 1626 (a(x,y,z) * L(z,x,y)) \ L(z,x,y) = a(y,x,z). [para(1625(a,2),1470(a,1))]. 1627 (x * R(y,z,u)) * y = (x * y) * R(y,z,u). [para(1503(a,1),75(a,1))]. 1628 ((x / R(y,z,u)) * y) * R(y,z,u) = x * y. [para(16(a,1),1627(a,1,1)),flip(a)]. 1629 (x * (y * R(y,z,u))) \ ((x * y) * R(y,z,u)) = a(x,R(y,z,u),y). [para(1627(a,1),203(a,1,2))]. 1630 (x * (y \ z)) \ ((x / y) * z) = a(y,x,y \ z). [para(1552(a,1),1572(a,1))]. 1631 a(R(x,y,z),u,R(x,y,z) \ a(x,y,z)) = (u * (x \ 1)) \ ((u / R(x,y,z)) * a(x,y,z)). [para(1443(a,1),1630(a,1,1,2)),flip(a)]. 1632 L(a(T(x,y),z,u),x,y) = a(T(x,x \ y),z,u). [para(1102(a,1),1611(a,1,1)),flip(a)]. 1633 a(T(x,x \ y),z,u) = T(a(x,z,u),x * y). [para(1632(a,1),1622(a,1))]. 1634 a(T(x,x \ T(y,x)),z,u) = T(a(x,z,u),y * x). [para(80(a,1),1633(a,2,2))]. 1635 a(T(x,x \ y),z,u) = T(a(x,z,u),y * x). [para(1166(a,1),1634(a,1,1))]. 1636 a(T(x \ 1,(x \ 1) \ (y * x)),z,u) = T(a(x \ 1,z,u),R(y,x,x \ 1)). [para(460(a,1),1635(a,2,2))]. 1637 (L(x,y,z) * R(z,y,x)) \ (z * x) = K(z,L(R(x,y,x),y,z)). [para(44(a,1),1624(a,2,2))]. 1638 (L(x,y,z) * R(z,y,x)) \ (z * x) = K(z,L(L(x,x,y),y,z)). [para(1144(a,1),1637(a,2,2,1))]. 1639 K(x,L(L(y,y,z),z,x)) = (y * x) \ (x * y). [para(1521(a,1),1638(a,1,1)),flip(a)]. 1640 K(x,L(L(y,y,z),z,x)) = K(x,y). [para(1639(a,2),26(a,2)),flip(a)]. 1642 T(x,L(L(y,y,z),z,x)) = x * K(x,y). [para(1640(a,1),1035(a,2,2))]. 1643 K(L(L(x,x,y),y,z),z) = K(z,x) \ 1. [para(1640(a,1),1070(a,1,1)),flip(a)]. 1644 T(x,L(L(y,y,z),z,x)) = T(x,y). [para(1642(a,2),1035(a,2)),flip(a)]. 1645 T(x,L(L(y,y,z \ 1),x,z)) = T(x,y). [para(1294(a,1),1644(a,1,2))]. 1646 K(L(L(x,x,y),y,z),z) = K(x,z). [para(1643(a,2),1070(a,1))]. 1647 K(L(L(x,x,y \ 1),z,y),z) = K(x,z). [para(1294(a,1),1646(a,1,1))]. 1648 T(x,L(L(y,z,y),x,z)) = T(x,y). [para(1289(a,1),1645(a,1,2,1))]. 1649 T(x,L(y,z,y)) = T(x,y). [para(1648(a,1),1589(a,1)),flip(a)]. 1650 L(x,y,x) * T(z,x) = z * L(x,y,x). [para(1649(a,1),80(a,1,2))]. 1653 K(L(L(x,y,x),z,y),z) = K(x,z). [para(1289(a,1),1647(a,1,1,1))]. 1654 K(L(x,y,z),y) = K(L(x,x,z),y). [para(1246(a,1),1653(a,1,1,1))]. 1655 K(L(x,y,x),z) = K(x,z). [para(1653(a,1),1593(a,1)),flip(a)]. 1656 K(T(x,x * y),z) = K(T(x,y),z). [para(902(a,1),1655(a,1,1))]. 1657 (x \ y) * K(y,z) = x \ T(y,z). [para(1655(a,1),1317(a,1,2))]. 1659 K(L(x,y,z),y) = K(x,R(y,z,x)). [para(1654(a,2),1388(a,1))]. 1660 K(T(x,x \ y),z) = K(T(x,y),z). [para(14(a,1),1656(a,1,1,2)),flip(a)]. 1662 x \ ((x / (y \ z)) * (y \ T(z,u))) = L(K(z,u),y \ z,x). [para(1657(a,1),340(a,2,2,2)),flip(a)]. 1663 T(x,y) / (z \ T(x,y)) = R(z,x,K(x,y)). [para(1657(a,1),1566(a,1,2))]. 1665 K(x,R(y,z,x)) = K(x,y). [para(1659(a,1),1593(a,1))]. 1666 K((x \ (x / y)) \ 1,z) = K(y,z). [para(1665(a,1),1389(a,2))]. 1667 (x / y) * T(y,z) = x * K(y,z). [para(1665(a,1),1390(a,1,2)),flip(a)]. 1668 T(x,y) / (z * x) = K(x,y) / z. [para(1665(a,1),1549(a,1,1)),flip(a)]. 1670 K(T(x,x \ y),z) = T(K(x,z),y). [para(1660(a,1),1225(a,1))]. 1671 (x * y) * K(y,z) = x * T(y,z). [para(1666(a,1),1319(a,1,2))]. 1673 (x * (y * z)) * K(L(z,y,x),u) = (x * y) * T(L(z,y,x),u). [para(90(a,1),1667(a,1,1)),flip(a)]. 1675 x / ((x / K(y,z)) * (K(y,z) / x)) = R(x,K(y,z),y). [para(1668(a,1),1328(a,1,2,2))]. 1677 K(T(x,y),z) = T(K(x,z),y). [para(1670(a,1),1660(a,1)),flip(a)]. 1678 1 / T(K(x,y),z) = K(y,T(x,z)). [para(1677(a,1),1072(a,1,2))]. 1679 x \ ((x / (y * z)) * (y * T(z,u))) = L(K(z,u),y * z,x). [para(1671(a,1),340(a,2,2,2)),flip(a)]. 1681 a(x,y,y) * (z * y) = z * L(y,x,y). [para(1650(a,1),1563(a,2))]. 1682 ((a(x,y,y) * z) / L(y,x,y)) * y = z. [hyper(17,a,16,a(flip),b,1681,a)]. 1683 (x \ ((a(y,x \ 1,x \ 1) * (x * z)) / L(x \ 1,y,x \ 1))) / x = z. [hyper(192,a,1682,a)]. 1684 R(x,y,K(y,z)) = x. [para(1663(a,1),53(a,1))]. 1685 R(x,y,K(x,z)) = (x * y) / y. [para(1684(a,1),939(a,1,2)),flip(a)]. 1686 R(x,y,K(x,z)) = x. [para(1685(a,2),15(a,1))]. 1687 x \ ((y * x) * K(x,z)) = T(y,x) * K(x,z). [para(1686(a,1),164(a,1,1))]. 1688 x \ (y * T(x,z)) = T(y,x) * K(x,z). [para(1671(a,1),1687(a,1,2))]. 1689 R(x,K(y,z),y) = x / 1. [para(279(a,1),1675(a,1,2)),flip(a)]. 1690 R(x,K(y,z),y) = x. [para(1689(a,2),52(a,1))]. 1692 (x * K(y,z)) * y = x * T(y,z). [para(1690(a,1),1059(a,1,1)),flip(a)]. 1693 (x * y) / T(y,z) = x / K(y,z). [para(1690(a,1),1060(a,1)),flip(a)]. 1694 L(x,K(x,y),z) = (x * z) / z. [para(1690(a,1),1520(a,2,2))]. 1695 L(x,K(x,y),z) = x. [para(1694(a,2),15(a,1))]. 1696 L(x,y,K(x,z)) = x. [para(1695(a,1),341(a,1,1))]. 1697 L(x,y,K(x,z) \ y) = x. [para(1695(a,1),439(a,2))]. 1698 (x \ K(y,z)) \ (x \ (K(y,z) * y)) = y. [para(1695(a,1),522(a,2))]. 1699 L(x,y,K(z,x) * y) = x. [para(965(a,1),1697(a,1,3))]. 1700 L(x,y,K(z,x)) = x. [para(1699(a,1),424(a,1)),flip(a)]. 1701 x \ (y * T(x,z)) = T(y * K(x,z),x). [para(1692(a,1),32(a,2,2)),flip(a)]. 1702 (x \ K(y,z)) \ (x \ T(y,z)) = y. [para(1043(a,2),1698(a,1,2,2))]. 1703 T(x * K(y,z),y) = T(x,y) * K(y,z). [para(1701(a,1),1688(a,1))]. 1704 x \ (y * (((y \ x) / z) * T(z,u))) = L(K(z,u),y \ z,x). [para(924(a,1),1662(a,1,2))]. 1705 L(K(x,y),z \ x,u) = u \ (z * ((z \ u) * K(x,y))). [para(1667(a,1),1704(a,1,2,2)),flip(a)]. 1706 L(K(x,y),z \ x,u) = L(K(x,y),u,z). [para(1705(a,2),1299(a,2)),flip(a)]. 1707 (x * (y * z)) * K(L(z,y,x),u) = (x * y) * L(T(z,u),y,x). [para(40(a,2),1673(a,2,2))]. 1708 (x * (y * z)) * K(L(z,y,x),u) = x * (y * T(z,u)). [para(1707(a,2),69(a,1))]. 1709 (x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u). [hyper(56,a,1708,a)]. 1710 x \ ((x / (y * z)) * (y * T(z,u))) = K(L(z,y,x),u). [para(1709(a,1),304(a,1)),flip(a)]. 1711 L(K(x,y),z * x,u) = K(L(x,z,u),y). [para(1710(a,1),1679(a,1)),flip(a)]. 1712 L(K(x,y),z \ x,u) = K(L(x,z \ 1,u),y). [para(259(a,1),1711(a,1,2))]. 1713 K(L(x,y \ 1,z),u) = L(K(x,u),z,y). [para(1712(a,1),1706(a,1))]. 1714 L(K(x,y),z,u) = K(L(x,z,u),y). [para(1294(a,1),1713(a,1,1)),flip(a)]. 1715 L(K(x,y),K(z,x),u) = K(x,y). [para(1700(a,1),1713(a,1,1)),flip(a)]. 1716 x / K(y,z) = x * K(z,y). [para(1715(a,1),1076(a,1,2)),flip(a)]. 1717 x \ (x / K(y,z)) = K(z,y). [para(1715(a,1),1077(a,1)),flip(a)]. 1718 (x / K(y,z)) / K(z,y) = x. [para(1715(a,1),1078(a,1,2))]. 1719 K(x,y) \ (z / K(y,x)) = T(z,K(x,y)). [para(1716(a,2),32(a,2,2)),flip(a)]. 1720 (x \ K(y,z)) * K(z,y) = x \ 1. [para(1716(a,1),264(a,1))]. 1722 (K(x,y) \ z) \ (z / K(x,y)) = K(z,K(y,x)). [para(1716(a,2),1094(a,1,2))]. 1723 (x * K(y,z)) / K(y,z) = R(x,K(z,y),K(z,y)). [para(1716(a,1),1214(a,1,1))]. 1724 (x * y) / T(y,z) = x * K(z,y). [para(1716(a,1),1693(a,2))]. 1728 R(x,K(y,z),K(y,z)) = x. [para(1718(a,1),1214(a,1)),flip(a)]. 1730 (x * y) * K(L(z,y,x),u) = x * (y * K(z,u)). [para(1714(a,1),69(a,1,2))]. 1731 (x / y) * (y * K(z,u)) = x * K(L(z,y,x),u). [para(1714(a,1),295(a,2,2))]. 1734 K(x,y) * K(L(y,z,u),x) = a(z,u,K(y,x)). [para(1714(a,1),1493(a,1,2))]. 1735 K(L(x,K(x,y) \ z,u),y) = u \ ((u / (z / K(x,y))) * z). [para(1714(a,1),1594(a,1))]. 1736 a(x \ K(y,z),K(z,y),u) = a(x \ 1,K(z,y),u). [para(1720(a,1),1439(a,1,1)),flip(a)]. 1737 (x * K(y,z)) * T(z,y) = x * z. [para(1724(a,1),16(a,1,1))]. 1738 L(x,y,z) / T(a(y,z,x),u) = x * K(u,a(y,z,x)). [para(1485(a,2),1724(a,1,1))]. 1739 K(K(x,y),z / K(x,y)) = T(z,K(x,y)) \ z. [para(1719(a,1),1321(a,1,1)),flip(a)]. 1740 K(K(x,y),z / K(x,y)) = K(z,K(y,x)). [para(1722(a,1),1064(a,1)),flip(a)]. 1741 K(K(x,y),z / K(x,y)) = K(K(x,y),z). [para(1739(a,2),1054(a,2)),flip(a)]. 1742 K(K(x,y),z) = K(z,K(y,x)). [para(1741(a,1),1740(a,1))]. 1743 K(x,K(y,z)) \ K(y,z) = 1 / T(K(z,y),x). [para(1742(a,1),1181(a,1,1))]. 1744 1 / T(K(x,y),z) = T(K(y,x),z). [para(1743(a,1),1061(a,2)),flip(a)]. 1745 K(x,T(y,z)) = T(K(x,y),z). [para(1744(a,1),1678(a,1)),flip(a)]. 1746 x * K(y,T(z,x)) = K(y,z) * x. [para(1745(a,2),80(a,1,2))]. 1747 K(T(x,y),z) = K(x,T(z,y)). [para(1745(a,2),1677(a,2))]. 1748 K(x,y) * z != z * u | K(x,T(y,z)) = u. [para(1746(a,1),19(a,1))]. 1749 (x * K(y,z)) * K(z,y) = R(x,K(z,y),K(z,y)). [para(1723(a,1),1716(a,1)),flip(a)]. 1750 (x * (y * K(z,u))) \ R(x * y,K(L(z,y,x),u),K(L(z,y,x),u) \ 1) = K(L(z,y,x),u) \ 1. [para(1730(a,1),462(a,1,1))]. 1751 R(x,K(y,z),K(z,y)) = R(x,K(z,y),K(z,y)). [para(1749(a,1),1219(a,1)),flip(a)]. 1752 R(x,K(y,z),K(z,y)) = x. [para(1751(a,2),1728(a,1))]. 1753 a(x \ K(y,z),K(z,y),u) = a(K(z,y),x,u). [para(1736(a,2),1476(a,1))]. 1754 K(L(x,K(y,x) * z,u),y) = u \ ((u / (z / K(x,y))) * z). [para(1075(a,1),1735(a,1,1,2))]. 1755 ((x * a(y,z,u)) / u) * L(u,z,y) = R(x,a(y,z,u),L(u,z,y)). [para(1457(a,1),1254(a,1)),flip(a)]. 1756 L(a(x,y,z),u,u / z) = a(x,y,L(z \ 1,z,u) \ 1). [para(54(a,1),1569(a,1,1,3))]. 1757 a(x,y,L(z \ 1,z,u) \ 1) = L(a(x,y,z),z,u). [para(1756(a,1),1292(a,1))]. 1758 a(x,y,L(z,z,u)) = L(a(x,y,z),z,u). [para(1190(a,1),1757(a,1,3))]. 1759 x * a(y,z,L(u,u,x)) = (x / u) * L(u,y,z). [para(1758(a,2),1489(a,1,2))]. 1760 a(x,R(y,z,u),y) = a(x,y,R(y,z,u)). [para(1629(a,1),24(a,2)),flip(a)]. 1761 (x \ ((a(y,x,x) * (x * z)) / L(x \ 1,y,x \ 1))) / x = z. [para(1514(a,1),1683(a,1,1,2,1,1))]. 1762 (x \ ((x * (a(y,x,x) * z)) / L(x \ 1,y,x \ 1))) / x = z. [para(1509(a,1),1761(a,1,1,2,1))]. 1763 (x \ ((L(x,y,x) * z) / L(x \ 1,y,x \ 1))) / x = z. [para(1517(a,1),1762(a,1,1,2,1))]. 1764 (x \ ((L(x,y,x) * z) / L(x \ 1,x,y))) / x = z. [para(1289(a,1),1763(a,1,1,2,2))]. 1765 (x \ (L(x,y,x) * z)) / (x * L(x \ 1,x,y)) = z. [para(1764(a,1),707(a,1)),flip(a)]. 1766 (a(x,y,y) * z) / (y * L(y \ 1,y,x)) = z. [para(1491(a,1),1765(a,1,1))]. 1767 (a(x,y,y) * z) / a(y,x,y \ 1) = z. [para(1486(a,1),1766(a,1,2))]. 1768 (a(x,y,y) * z) / a(x,y,y) = z. [para(1515(a,1),1767(a,1,2))]. 1769 a(x,y,y) * z = z * a(x,y,y). [para(1768(a,1),16(a,1,1)),flip(a)]. 1770 T(x,a(y,z,z)) = x. [hyper(98,a,1769,a)]. 1771 a(x,y,y) * (z \ 1) = z \ a(x,y,y). [para(1769(a,2),259(a,1))]. 1772 x * (y * a(x,z,z)) = R(x,z,z) * y. [para(1769(a,1),1445(a,1,2))]. 1773 (x * y) * a(x,z,z) = R(x,z,z) * y. [para(1769(a,1),1511(a,1))]. 1774 K(x,a(y,z,z)) = 1. [hyper(36,a,1770,a)]. 1775 T(x,a(y,z,y)) = x. [para(1474(a,1),1770(a,1,2))]. 1776 1 * ((a(x,y,y) \ z) \ u) = (a(x,y,y) / z) * u. [para(1774(a,1),1168(a,1,1))]. 1777 (a(x,y,y) * z) * a(y,x,y) = z. [hyper(1551,a,1775,a)]. 1778 x / a(y,z,y) = a(z,y,y) * x. [hyper(61,a,1777,a)]. 1779 (R(x,y,y) * (x \ z)) / a(x,y,y) = R(z,x,a(x,y,y)). [para(1772(a,1),1394(a,2,1)),flip(a)]. 1780 (R(x,y,y) * z) / ((z * x) * a(x,y,y)) = K(x,z). [para(1773(a,1),1277(a,1,1))]. 1781 1 * ((a(x,y,x) * z) \ u) = (a(y,x,x) / z) * u. [para(1336(a,1),1776(a,1,2,1))]. 1782 (a(x,y,x) * z) \ u = (a(y,x,x) / z) * u. [hyper(55,a,1781,a)]. 1783 (a(x,y,y) * z) / a(x,y,y) = R(z,x,a(x,y,y)). [para(1446(a,1),1779(a,1,1))]. 1784 R(x,y,a(y,z,z)) = x. [para(1783(a,1),1768(a,1))]. 1785 (x * y) * a(y,z,z) = x * R(y,z,z). [para(1784(a,1),1453(a,1,1)),flip(a)]. 1786 (R(x,y,y) * z) / (z * R(x,y,y)) = K(x,z). [para(1785(a,1),1780(a,1,2))]. 1787 K(R(x,y,y),z) = K(x,z). [para(1786(a,1),1050(a,2))]. 1788 K(x,y) * (x / z) = T(x,y) / z. [para(1787(a,1),1234(a,1,1))]. 1789 K(x,y) \ (K(x,y) / z) = z \ 1. [para(1787(a,1),1375(a,1,1))]. 1790 K(x,R(y,z,z)) = K(x,y). [para(1787(a,1),1387(a,1)),flip(a)]. 1791 T(x,R(y,z,z)) = x * K(x,y). [para(1790(a,1),1035(a,2,2))]. 1792 T(x,R(y,z,z)) = T(x,y). [para(1791(a,2),1035(a,2)),flip(a)]. 1793 T(x,R(y,z,z \ 1)) = T(x,y). [para(1200(a,1),1792(a,1,2)),flip(a)]. 1794 T(x,y) \ (T(x,y) / z) = x \ (x / z). [para(1788(a,1),1109(a,1,2))]. 1796 (K(x,y) * z) \ K(x,y) = z \ 1. [para(1789(a,1),313(a,2))]. 1798 (K(x,y) * z) \ 1 = z \ K(y,x). [para(1074(a,1),1796(a,1,1)),flip(a)]. 1799 (x \ K(y,z)) \ u = (K(z,y) * x) * u. [para(1798(a,1),256(a,1,1))]. 1801 a(x,T(y,z),x) = x \ ((y \ (y / x)) \ 1). [para(1794(a,1),1193(a,1,2,1)),flip(a)]. 1802 (K(x,y) * z) * (z \ T(y,x)) = y. [para(1799(a,1),1702(a,1))]. 1803 x \ ((x / ((K(y,z) * u) \ 1)) * (u \ T(z,y))) = L(z,x,K(y,z) * u). [para(1802(a,1),1301(a,1,1)),flip(a)]. 1804 a(x,T(y,z),x) = a(x,y,x). [para(1801(a,2),1193(a,1))]. 1809 x \ ((x / (y \ K(z,u))) * (y \ T(z,u))) = L(z,x,K(u,z) * y). [para(1798(a,1),1803(a,1,2,1,2))]. 1810 x \ (y * (((y \ x) / K(z,u)) * T(z,u))) = L(z,x,K(u,z) * y). [para(924(a,1),1809(a,1,2))]. 1811 x \ (y * (((y \ x) * K(z,u)) * T(u,z))) = L(u,x,K(z,u) * y). [para(1716(a,1),1810(a,1,2,2,1))]. 1812 L(x,y,K(z,x) * u) = y \ (u * ((u \ y) * x)). [para(1737(a,1),1811(a,1,2,2)),flip(a)]. 1813 L(x,y,K(z,x) * u) = L(x,y,u). [para(1812(a,2),1299(a,2)),flip(a)]. 1816 L(x,K(y,x) * z,u) = L(x,u \ 1,z). [para(1813(a,1),1294(a,1)),flip(a)]. 1817 L(x,K(y,x) * z,u) = L(x,z,u). [para(1816(a,2),1294(a,1))]. 1818 x \ ((x / (y / K(z,u))) * y) = K(L(z,y,x),u). [para(1817(a,1),1754(a,1,1)),flip(a)]. 1819 x \ ((x / (y * K(z,u))) * y) = K(L(u,y,x),z). [para(1716(a,1),1818(a,1,2,1,2))]. 1821 (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x. [para(1160(a,1),1340(a,1,1,1)),flip(a)]. 1822 (x \ 1) * L(x * y,z,u) = L(y * x,z,u) / x. [para(256(a,1),1821(a,1,2,1))]. 1823 L(x * y,z,u) / y = y \ L(y * x,z,u). [para(1822(a,1),259(a,1))]. 1824 a(x,y,z) \ L(a(x,y,z) * L(z,y,x),u,w) = L(z,u,w) / a(x,y,z). [para(1463(a,1),1823(a,1,1,1)),flip(a)]. 1825 L(x,y,z) / a(u,w,x) = a(u,w,x) \ L(x,y,z). [para(1437(a,1),1824(a,1,2,1)),flip(a)]. 1826 L(x,y,z) / a(u,w,x) = a(w,u,x) * L(x,y,z). [para(1825(a,2),1472(a,1))]. 1828 a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u). [para(1526(a,1),1522(a,1,1)),flip(a)]. 1829 a(L(x,y,z),R(z,y,x),u) = a(x,z,u). [para(1828(a,2),24(a,2)),flip(a)]. 1831 a(x,R(y,z,L(x,y,z)),u) = a(L(x,y,z),y,u). [para(341(a,1),1829(a,1,1))]. 1832 L(x,R(y,z,u),L(u,z,y)) = x / a(u,y,x). [para(1829(a,1),1464(a,2,2))]. 1833 L(x,R(y,z,u),L(u,z,y)) = L(x,y,u). [para(1832(a,2),1464(a,2)),flip(a)]. 1834 a(L(x,y,z),y,u) = a(x,R(y,z,x),u). [para(1532(a,1),1831(a,1,2)),flip(a)]. 1835 a(T(x \ 1,(x \ 1) \ (y * x)),z,u) = T(a(z,x,u),R(y,x,x \ 1)). [para(1476(a,1),1636(a,2,1))]. 1836 a(T(x \ 1,(x \ 1) \ (y * x)),z,u) = T(a(z,x,u),y). [para(1835(a,2),1793(a,1))]. 1837 a(T(x \ 1,x * (y * x)),z,u) = T(a(z,x,u),y). [para(256(a,1),1836(a,1,1,2))]. 1839 a(T(x,y) \ 1,z,u) = T(a(z,x,u),y). [para(823(a,1),1837(a,1,1))]. 1840 a(x,T(y,z),u) = T(a(x,y,u),z). [para(1839(a,1),1476(a,1)),flip(a)]. 1841 x * a(y,T(z,x),u) = a(y,z,u) * x. [para(1840(a,2),80(a,1,2))]. 1842 a(x,T(y,z),u) \ a(x,y,u) = K(z,a(x,y,u)). [para(1840(a,2),1054(a,2,1)),flip(a)]. 1844 T(a(x \ 1,y,z),u) = a(T(y,u),x,z). [para(1840(a,1),1476(a,1))]. 1845 a(x,T(y,z),u) * L(u,y,x) = K(a(x,y,u),z) * u. [para(1840(a,2),1459(a,1,1))]. 1846 a(x,T(y,z),u) * a(y,x,u) = K(a(x,y,u),z). [para(1840(a,2),1567(a,1,1))]. 1847 L(x,y,z) / a(y,T(z,u),x) = x * K(u,a(y,z,x)). [para(1840(a,2),1738(a,1,2))]. 1848 a(T(x,y),z,u) = T(a(x,z,u),y). [para(1476(a,1),1844(a,1,1)),flip(a)]. 1849 a(T(x,y),z,u) = a(x,T(z,y),u). [para(1848(a,2),1840(a,2)),flip(a)]. 1850 a(T(x,y),z,u) * a(z,x,u) = K(y,a(z,x,u)). [para(1842(a,1),1472(a,1)),flip(a)]. 1851 a(x,T(y,z),u) * a(y,x,u) = K(z,a(y,x,u)). [para(1849(a,1),1850(a,1,1))]. 1852 K(a(x,y,z),u) = K(u,a(y,x,z)). [para(1851(a,1),1846(a,1)),flip(a)]. 1853 x * K(a(y,z,u),x) = T(x,a(z,y,u)). [para(1852(a,2),1035(a,2,2)),flip(a)]. 1854 (x * (a(y,x,z) * u)) / a(y,x,z) = T(x * u,a(x,y,z)). [para(1853(a,1),1542(a,2))]. 1855 a(T(x,y),z,u) * L(u,z,x) = u * K(y,a(z,x,u)). [para(1847(a,1),1826(a,1)),flip(a)]. 1856 a(x,T(y,z),u) * L(u,y,x) = u * K(z,a(y,x,u)). [para(1849(a,1),1855(a,1,1))]. 1857 K(a(x,y,z),u) * z = z * K(u,a(y,x,z)). [para(1856(a,1),1845(a,1)),flip(a)]. 1858 K(a(x,y,z),T(u,z)) = K(u,a(y,x,z)). [hyper(1748,a,1857,a)]. 1859 L(x,T(y,y \ z) \ (y * (z / y)),y * (z / y)) = L(x,z / y,y). [para(923(a,2),424(a,1))]. 1860 L(x,T(y,y \ z) \ (y * (z / y)),y * (z / y)) = L(x,z,y). [para(1859(a,2),435(a,1))]. 1861 L(x,K(y \ z,y) * (z / y),y * (z / y)) = L(x,z,y). [para(1108(a,1),1860(a,1,2))]. 1862 L(x,(y / z) * K(z \ y,z),z * (y / z)) = L(x,y,z). [para(1235(a,1),1861(a,1,2))]. 1863 L(x,y \ z,y * (z / y)) = L(x,z,y). [para(1065(a,1),1862(a,1,2))]. 1864 (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(R(y,z,u),x,y \ 1). [para(1443(a,1),1631(a,1,3)),flip(a)]. 1866 (x \ y) * (x * (((y \ z) / y) * (y * u))) = (y * (x * ((x * y) \ z))) * L(u,x,y). [para(13(a,1),1347(a,1,2,2,1,1))]. 1868 (x * (y * ((y * x) \ z))) * L(u,y,x) = (y \ x) * (y * (x \ (z * u))). [para(248(a,1),1866(a,1,2,2)),flip(a)]. 1869 (x * (y * ((y * x) \ z))) * L(u,y,x) = x * (y * ((y * x) \ (z * u))). [para(1868(a,2),1346(a,1))]. 1870 (x * (y * ((y * x) \ 1))) * L(z,y,x) = x * (y * ((y * x) \ z)). [para(11(a,1),1869(a,2,2,2,2))]. 1871 (x * (y * ((y * x) \ 1))) * L(z * u,y,x) = (x * (y * ((y * x) \ z))) * L(u,y,x). [para(1870(a,2),1869(a,2)),flip(a)]. 1872 ((x * (y * ((y * x) \ 1))) * L(z,y,x)) * L(u,y,x) = (x * (y * ((y * x) \ 1))) * L(z * u,y,x). [para(1870(a,2),1871(a,2,1)),flip(a)]. 1873 (x * (y * K(z,u))) \ R(x * y,K(L(z,y,x),u),K(u,L(z,y,x))) = K(L(z,y,x),u) \ 1. [para(1070(a,1),1750(a,1,2,3))]. 1874 (x * (y * K(z,u))) \ (x * y) = K(L(z,y,x),u) \ 1. [para(1752(a,1),1873(a,1,2))]. 1875 x \ ((x / (y * K(z,u))) * y) = K(L(z,y,x),u) \ 1. [para(1874(a,1),304(a,1)),flip(a)]. 1877 K(L(x,y,z),u) \ 1 = K(L(u,y,z),x). [para(1875(a,1),1819(a,1))]. 1878 K(L(x,y,z),u) = K(x,L(u,y,z)). [para(1877(a,1),1070(a,1))]. 1879 L(K(x,y),z,u) = K(x,L(y,z,u)). [para(1878(a,1),1714(a,2))]. 1880 (x / y) * (y * K(z,u)) = x * K(z,L(u,y,x)). [para(1878(a,1),1731(a,2,2))]. 1881 R(x,x \ y,z) \ R(R(x,x \ y,z),u,w) = ((R(x,u,w) * (x \ y)) * z) / (y * z). [para(152(a,1),562(a,2,1))]. 1882 R(x,x \ y,z) \ R(R(x,x \ y,z),u,w) = R(x \ R(x,u,w),y,z). [para(1881(a,2),560(a,1))]. 1883 R(x,y,z) \ R(R(x,x \ y,z),u,w) = R(x \ R(x,u,w),y,z). [para(1365(a,1),1882(a,1,1))]. 1884 R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). [para(1365(a,1),1883(a,1,2,1))]. 1885 R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z). [para(1884(a,1),1431(a,2)),flip(a)]. 1886 a(R(x,y,z),u,w) = R(a(x,u,w),y,z). [para(1431(a,2),1885(a,1,1)),flip(a)]. 1887 a(R(x,y,z),u,w) * (y * z) = (a(x,u,w) * y) * z. [para(1886(a,2),75(a,1,1))]. 1888 x / (a(y,z,z) * a(R(z,x,u),y,z)) = R(x,a(z,y,z),u). [para(1886(a,2),1337(a,1,2,2))]. 1889 R(a(x,y,z) * 1,u,w) = a(R(y,u,w),x,z) \ 1. [para(1886(a,2),1499(a,2,1))]. 1890 R(a(x,y,z) * 1,u,w) = a(x,R(y,u,w),z). [para(1889(a,2),1470(a,1))]. 1891 a(x,R(y,z,u),w) = R(a(x,y,w),z,u). [para(12(a,1),1890(a,1,1)),flip(a)]. 1892 a(R(x,y,z),u,w) = a(x,R(u,y,z),w). [para(1891(a,2),1886(a,2))]. 1893 (x * y) / (a(z,R(u,w,v5),x) * y) = L(x,u,R(z,w,v5)). [para(1892(a,1),1529(a,1,2,1))]. 1894 (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(y,R(x,z,u),y \ 1). [para(1892(a,1),1864(a,2))]. 1895 ((R(x,y,z) * u) * w) / ((a(x,y,z) * u) * w) = R(x,u,w). [para(1887(a,1),1524(a,1,2))]. 1896 L(x,R(y,z,u),w) = L(x,y,R(w,z,u)). [para(1893(a,1),1529(a,1)),flip(a)]. 1897 L(x,y,R(L(z,u,y),u,z)) = L(x,y,z). [para(1896(a,1),1833(a,1))]. 1898 L(x,y,L(R(z,u,z),u,y)) = L(x,y,z). [para(44(a,1),1897(a,1,3))]. 1899 L(x,y,L(L(z,z,u),u,y)) = L(x,y,z). [para(1144(a,1),1898(a,1,3,1))]. 1900 x / (a(y,z,z) * a(z,y,R(z,x,u))) = R(x,a(z,y,z),u). [para(1565(a,1),1888(a,1,2,2))]. 1901 R(x,a(x,y,z) * u,w) = R(x,u,w). [para(1895(a,1),1512(a,1)),flip(a)]. 1902 R(x,L(y,z,x),u) = R(x,y,u). [para(1437(a,1),1901(a,1,2)),flip(a)]. 1904 a(x,L(y,z,x),u) = x \ R(x,y,u). [para(1902(a,1),1431(a,2,2))]. 1905 L(x,y,L(z,u,y)) = (x / y) * R(y,z,x). [para(1902(a,1),1534(a,2,2))]. 1906 a(x,L(y,z,x),u) = a(x,y,u). [para(1904(a,2),1431(a,2)),flip(a)]. 1907 a(x \ 1,L(y,x,z),u) = a(x \ 1,y,u). [para(455(a,1),1906(a,1,2))]. 1908 L(x,y,L(z,u,y)) = L(x,y,z). [para(1905(a,2),1534(a,2)),flip(a)]. 1910 L(x,y,L(z,z,u)) = L(x,y,z). [para(1908(a,1),1899(a,1))]. 1912 L(x,y,L(z,u,z)) = L(x,y,z). [para(1288(a,1),1910(a,1,3))]. 1914 (a(x,L(y,z,y),u) * L(u,x,y)) \ L(u,x,L(y,z,y)) = a(L(y,z,y),x,u). [para(1912(a,1),1626(a,1,1,2))]. 1915 a(L(x,y,z),y,u) = a(y \ 1,x,u). [para(1907(a,1),1476(a,1)),flip(a)]. 1916 a(L(x,y,z),y,u) = a(x,y,u). [para(1915(a,2),1476(a,1))]. 1917 a(x,R(y,z,x),u) = a(x,y,u). [para(1916(a,1),1834(a,1)),flip(a)]. 1918 a(R(x,y,z \ 1),z,u) = a(z \ 1,x,u). [para(1917(a,1),1476(a,1)),flip(a)]. 1920 a(R(x,y,z \ 1),z,u) = a(x,z,u). [para(1918(a,2),1476(a,1))]. 1921 a(x,R(y,z,y \ 1),u) = a(x,y,u). [para(1920(a,1),1892(a,1)),flip(a)]. 1922 a(x,L(y,z,y),u) = a(x,y,u). [para(1259(a,1),1921(a,1,2))]. 1923 (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(R(x,z,u),y,y). [para(1894(a,2),1515(a,1))]. 1924 (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(x,R(y,z,u),y). [para(1923(a,2),1892(a,1))]. 1925 (x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(x,y,R(y,z,u)). [para(1924(a,2),1760(a,1))]. 1926 (a(x,y,z) * L(z,x,y)) \ L(z,x,L(y,u,y)) = a(L(y,u,y),x,z). [para(1922(a,1),1914(a,1,1,1))]. 1927 a(L(x,y,x),z,u) = (a(z,x,u) * L(u,z,x)) \ L(u,z,x). [para(1912(a,1),1926(a,1,2)),flip(a)]. 1929 a(L(x,y,x),z,u) = a(x,z,u). [para(1927(a,2),1626(a,1))]. 1931 a(T(x,x * y),z,u) = a(T(x,y),z,u). [para(902(a,1),1929(a,1,1))]. 1933 a(x,T(y,x * z),u) = a(T(x,z),y,u). [para(1931(a,1),1849(a,1)),flip(a)]. 1934 a(x,T(y,x * z),u) = a(x,T(y,z),u). [para(1933(a,2),1849(a,1))]. 1935 (x * y) * a(x,T(z,y),u) = a(x,z,u) * (x * y). [para(1934(a,1),1841(a,1,2))]. 1936 (x * y) * a(x,T(z,y),u) = R(x,z,u) * y. [para(1935(a,2),1511(a,1))]. 1937 (x * (y * a(x,T(z,y),u))) \ (R(x,z,u) * y) = a(x,y,a(x,T(z,y),u)). [para(1936(a,1),24(a,2,2)),flip(a)]. 1938 (x * (a(x,y,z) * u)) \ (R(x,y,z) * u) = a(x,u,a(x,T(y,u),z)). [para(1841(a,1),1937(a,1,1,2))]. 1939 (R(x,y,z) * u) \ (R(x,y,z) * u) = a(x,u,a(x,T(y,u),z)). [para(1445(a,1),1938(a,1,1))]. 1940 a(x,y,a(x,T(z,y),u)) = 1. [para(1939(a,1),50(a,1))]. 1942 a(x,y,a(x,z,u)) = 1. [para(832(a,1),1940(a,1,3,2))]. 1944 R(x,y,a(y,z,u)) = x / 1. [para(1942(a,1),1425(a,2,2))]. 1945 a(x,y,a(z,x,u)) = 1. [para(1475(a,1),1942(a,1,3))]. 1948 a(x,y,a(z,y,u)) = 1. [para(1945(a,1),1475(a,1)),flip(a)]. 1949 L(a(x,y,z),y,u) = a(x,y,z). [hyper(33,a,1948,a)]. 1950 R(x,y,a(y,z,u)) = x. [para(1944(a,2),52(a,1))]. 1951 (x * a(x,y,z)) \ (u * a(x,y,z)) = T(u / x,x * a(x,y,z)). [para(1950(a,1),162(a,1,1)),flip(a)]. 1952 (x * y) * a(x,z,u) = x * (y * a(x,z,u)). [para(1950(a,1),1395(a,1,1))]. 1953 (x / (y * a(y,z,u))) * y = x / a(y,z,u). [para(1950(a,1),1546(a,1)),flip(a)]. 1955 (x / R(y,z,u)) * y = x / a(y,z,u). [para(1433(a,2),1953(a,1,1,2))]. 1956 x * L(R(y,z,u) \ y,R(y,z,u),x) = x / a(y,z,u). [para(1955(a,1),300(a,2))]. 1957 (x / a(y,z,u)) * R(y,z,u) = x * y. [para(1955(a,1),1628(a,1,1))]. 1958 L(x,a(x,y,z),u) = u \ (u * x). [para(1957(a,1),1454(a,1,2)),flip(a)]. 1959 L(x,a(x,y,z),u) = x. [para(1958(a,2),13(a,1))]. 1961 (x / (a(y,z,u) * y)) * a(y,z,u) = x / y. [para(1959(a,1),1573(a,1,2)),flip(a)]. 1962 (x / R(y,z,u)) * a(y,z,u) = x / y. [para(1434(a,2),1961(a,1,1,2))]. 1963 a(x,y,R(y,z,u)) = (x * (y \ 1)) \ (x / y). [para(1962(a,1),1925(a,1,2)),flip(a)]. 1964 a(x,y,R(y,z,u)) = a(x,y,y). [para(1963(a,2),1553(a,1))]. 1966 a(x,y,R(x,z,u)) = a(y \ 1,x,x). [para(1964(a,1),1476(a,1)),flip(a)]. 1967 a(x,y,R(x,z,u)) = a(x,y,x). [para(1966(a,2),1476(a,1))]. 1968 R(x,a(y,z,y),u) = x / (a(z,y,y) * a(y,z,y)). [para(1967(a,1),1900(a,1,2,2)),flip(a)]. 1969 R(x,a(y,z,y),u) = x / 1. [para(1469(a,1),1968(a,2,2))]. 1971 R(x,a(y,z,y),u) = x. [para(1969(a,2),52(a,1))]. 1973 (x * a(y,z,y)) * u = x * (a(y,z,y) * u). [para(1971(a,1),75(a,1,1)),flip(a)]. 1974 (x \ 1) / a(y,z,y) = (a(y,z,y) * x) \ 1. [para(1971(a,1),237(a,1))]. 1975 R(x,a(y,z,z),u) = x. [para(1475(a,1),1971(a,1,2))]. 1976 (a(x,y,x) * z) * u = a(x,y,x) * (z * u). [para(1971(a,1),1395(a,1,1))]. 1977 a(x,a(y,z,z),u) = x \ x. [para(1975(a,1),1431(a,2,2))]. 1978 (a(x,y,y) * z) * u = a(x,y,y) * (z * u). [para(1975(a,1),1395(a,1,1))]. 1979 a(x,a(y,z,z),u) = 1. [para(1977(a,2),50(a,1))]. 1980 L(x,a(y,z,z),u) = x. [hyper(33,a,1979,a)]. 1982 (a(x,y,y) * (z \ 1)) * u = a(x,y,y) * (z \ u). [para(1980(a,1),1302(a,1,2))]. 1983 (x * y) \ (z * (a(u,w,u) * (((z * a(u,w,u)) \ x) * y))) = a(x,z * a(u,w,u),y). [para(1973(a,1),1597(a,2,2)),flip(a)]. 1984 x * (a(y,T(z,x),y) * u) = (a(y,z,y) * x) * u. [para(1841(a,1),1973(a,1,1)),flip(a)]. 1985 (a(x,y,x) * z) \ 1 = a(y,x,x) * (z \ 1). [para(1974(a,1),1778(a,1))]. 1986 (a(x,y,x) * z) \ 1 = z \ a(y,x,x). [para(1985(a,2),1771(a,1))]. 1987 (a(x,y,y) / z) * 1 = z \ a(x,y,y). [para(1986(a,1),1782(a,1)),flip(a)]. 1988 a(x,y,y) / z = z \ a(x,y,y). [hyper(59,a,1987,a)]. 1989 (x \ a(y,z,z)) * u = a(y,z,z) * (x \ u). [para(1771(a,1),1982(a,1,1))]. 1990 (a(x,y,x) * z) * u = z * (a(x,y,x) * u). [para(1804(a,1),1984(a,1,2,1)),flip(a)]. 1992 a(x,y,x) * (z * u) = z * (a(x,y,x) * u). [para(1990(a,1),1976(a,1)),flip(a)]. 1993 (x * ((a(y,z,y) * u) * w)) \ ((a(y,z,y) * (x * u)) * w) = a(x,a(y,z,y) * u,w). [para(1992(a,2),24(a,2,2,1)),flip(a)]. 1994 x * L(a(y,z,u),R(z,y,u),x) = x / a(z,y,u). [para(1423(a,2),1956(a,1,2,1))]. 1995 x * L(a(y,z,u),z,R(x,y,u)) = x / a(z,y,u). [para(1896(a,1),1994(a,1,2))]. 1996 x / a(y,z,u) = x * a(z,y,u). [para(1949(a,1),1995(a,1,2)),flip(a)]. 1997 (x * a(y,z,u)) * a(z,y,u) = x. [hyper(60,a,1996,a)]. 1998 (x * a(y,z,u)) \ w = (a(z,y,u) / x) * w. [para(1996(a,1),284(a,1,1))]. 1999 (a(x,y,z) * u) * a(y,x,z) = u * K(a(x,y,z),u). [para(1996(a,1),1048(a,1))]. 2000 (x * (a(y,x,z) * u)) * a(x,y,z) = T(x * u,a(x,y,z)). [para(1996(a,1),1854(a,1))]. 2002 (a(x,y,z) * u) * a(y,x,z) = T(u,a(y,x,z)). [para(1999(a,2),1853(a,1))]. 2003 K(a(x,y,z) * u,a(y,x,z)) = u \ T(u,a(y,x,z)). [para(2002(a,1),1482(a,1,2)),flip(a)]. 2004 K(a(x,y,z) * u,a(y,x,z)) = K(u,a(y,x,z)). [para(2003(a,2),1038(a,2)),flip(a)]. 2005 x * ((a(y,x,z) * u) * a(x,y,z)) = T(x * u,a(x,y,z)). [para(2000(a,1),1952(a,1)),flip(a)]. 2006 T(x * y,a(x,z,u)) = x * T(y,a(x,z,u)). [para(2002(a,1),2005(a,1,2)),flip(a)]. 2007 T(x * T(y,x),a(x,z,u)) = T(y,a(x,z,u)) * x. [para(2006(a,2),102(a,1))]. 2008 T(x * y,a(y,z,u)) = T(x,a(y,z,u)) * y. [para(80(a,1),2007(a,1,1))]. 2009 x \ T(y * x,a(x,z,u)) = T(T(y,a(x,z,u)),x). [para(2008(a,2),32(a,2,2)),flip(a)]. 2010 (x * a(x,y,z)) \ (u * a(x,y,z)) = T(u / x,R(x,y,z)). [para(1433(a,2),1951(a,2,2))]. 2011 R(x,y,z) \ (u * a(x,y,z)) = T(u / x,R(x,y,z)). [para(1433(a,2),2010(a,1,1))]. 2012 x \ T(y,a(x,z,u)) = T(y / x,R(x,z,u)). [para(2011(a,1),1623(a,1)),flip(a)]. 2013 T((x * y) / y,R(y,z,u)) = T(T(x,a(y,z,u)),y). [para(2012(a,1),2009(a,1))]. 2014 T(T(x,a(y,z,u)),y) = T(x,R(y,z,u)). [para(15(a,1),2013(a,1,1)),flip(a)]. 2015 T(x,y) \ T(x,R(y,z,u)) = K(T(x,y),a(y,z,u)). [para(2014(a,1),1051(a,1,2))]. 2016 K(x,R(y,z,u)) * K(y,x) = K(T(x,y),a(y,z,u)). [para(2015(a,1),1183(a,1)),flip(a)]. 2017 K(T(x,y),a(y,z,u)) = a(z,K(y,x),u). [para(2016(a,1),1543(a,1))]. 2018 K(x,T(a(y,z,u),y)) = a(z,K(y,x),u). [para(2017(a,1),1747(a,1)),flip(a)]. 2019 a(x,K(y,z),u) = K(z,a(y,x,u)). [para(1440(a,1),2018(a,1,2)),flip(a)]. 2020 x * K(y,a(z,u,x)) = L(x,u,K(z,y)). [para(2019(a,1),1485(a,2,2)),flip(a)]. 2021 K(x,a(y,z \ K(x,y),u)) = a(K(y,x),z,u). [para(2019(a,1),1753(a,1))]. 2022 a(K(x,y),z,u) = K(y,a(z,x,u)). [para(1618(a,1),2021(a,1,2)),flip(a)]. 2023 x * K(y,a(z,u,x)) = L(x,K(u,y),z). [para(2022(a,1),1485(a,2,2)),flip(a)]. 2025 L(x,K(y,z),u) = L(x,y,K(u,z)). [para(2023(a,1),2020(a,1))]. 2026 (x * y) \ (z * (a(u,w,u) * (((a(w,u,u) / z) * x) * y))) = a(x,z * a(u,w,u),y). [para(1998(a,1),1983(a,1,2,2,2,1))]. 2027 (x * (y * (a(z,u,z) * w))) \ ((a(z,u,z) * (x * y)) * w) = a(x,a(z,u,z) * y,w). [para(1990(a,1),1993(a,1,1,2))]. 2028 (x * y) \ (z * (a(u,w,u) * (((z \ a(w,u,u)) * x) * y))) = a(x,z * a(u,w,u),y). [para(1988(a,1),2026(a,1,2,2,2,1,1))]. 2029 (x * (y * (a(z,u,z) * w))) \ ((x * y) * (a(z,u,z) * w)) = a(x,a(z,u,z) * y,w). [para(1990(a,1),2027(a,1,2))]. 2030 (x * y) \ (z * (a(u,w,u) * ((a(w,u,u) * (z \ x)) * y))) = a(x,z * a(u,w,u),y). [para(1989(a,1),2028(a,1,2,2,2,1))]. 2031 a(x,a(y,z,y) * u,w) = a(x,u,a(y,z,y) * w). [para(2029(a,1),24(a,2)),flip(a)]. 2032 (x * y) \ (z * (a(u,w,u) * (a(w,u,u) * ((z \ x) * y)))) = a(x,z * a(u,w,u),y). [para(1978(a,1),2030(a,1,2,2,2))]. 2033 a(x,y * a(z,u,z),w) = (x * w) \ (y * ((y \ x) * w)). [para(1471(a,1),2032(a,1,2,2)),flip(a)]. 2035 a(x,y * a(z,u,z),w) = a(x,y,w). [para(2033(a,2),1597(a,2)),flip(a)]. 2036 a(x,R(y,z,z),u) = a(x,y,u). [para(1422(a,1),2035(a,1,2)),flip(a)]. 2037 L(x,y,z * a(u,w,u)) = x * a(y,z,x). [para(2035(a,1),1485(a,2,2))]. 2038 a(x,a(y,z,y) * u,w) = a(x,u,w). [para(1841(a,1),2035(a,1,2))]. 2039 L(x,y,R(z,u,u)) = x * a(y,z,x). [para(2036(a,1),1485(a,2,2))]. 2040 a(x,y,a(z,u,z) * w) = a(x,y,w). [para(2038(a,1),2031(a,1)),flip(a)]. 2041 L(x,y,R(z,u,u)) = L(x,y,z). [para(2039(a,2),1485(a,2)),flip(a)]. 2042 L(x,y,z * (u \ 1)) = L(x,y,z / u). [para(1203(a,1),2041(a,1,3)),flip(a)]. 2043 L(x,y,z / (u \ 1)) = L(x,y,z * u). [para(1205(a,1),2041(a,1,3))]. 2044 a(x,y,L(z,z,u)) = a(x,y,z). [para(697(a,1),2040(a,1,3))]. 2047 (x / y) * L(y,z,u) = x * a(z,u,y). [para(2044(a,1),1759(a,1,2)),flip(a)]. 2048 L(x,y,z / (u / w)) = L(x,y,z * (w / u)). [para(265(a,1),2042(a,1,3,2)),flip(a)]. 2049 L(x,y,(z / R(u \ 1,w,v5)) * a(u \ 1,w,v5)) = L(x,y,z * u). [para(1962(a,2),2043(a,1,3))]. 2050 (x * a(y,z,u)) * a(z,y,u) = R(x,a(y,z,u),L(u,z,y)). [para(2047(a,1),1755(a,1))]. 2052 L(x,y,z * a(u,w,u)) = L(x,y,z). [para(2037(a,2),1485(a,2)),flip(a)]. 2053 R(x,a(y,z,u),L(u,z,y)) = x. [para(2050(a,1),1997(a,1))]. 2054 (a(x,y,z) * L(z,y,x)) \ (u * L(z,y,x)) = T(u / a(x,y,z),a(x,y,z) * L(z,y,x)). [para(2053(a,1),162(a,1,1)),flip(a)]. 2055 R(x,y / L(y,z,u),L(y,z,u)) = x. [para(1455(a,1),2053(a,1,2))]. 2056 (a(x,y,z) * u) * L(z,y,x) = a(x,y,z) * (u * L(z,y,x)). [para(2053(a,1),1395(a,1,1))]. 2057 (x * L(y,z,u)) / y = x / a(u,z,y). [para(2055(a,1),1462(a,1)),flip(a)]. 2058 (x / L(y,z,u)) / a(u,z,y) = x / y. [para(16(a,1),2057(a,1,1)),flip(a)]. 2059 (x / y) \ (x / L(y,z,u)) = a(u,z,y). [para(2058(a,1),54(a,1,1))]. 2060 (x / y) * (y / L(x,z,u)) = a(u,z,x). [para(2059(a,1),284(a,1)),flip(a)]. 2061 a(x,y,L(z,x,y)) = (L(z,x,y) / u) * (u / z). [para(341(a,1),2060(a,1,2,2)),flip(a)]. 2062 (L(x,y,z) / u) * (u / x) = a(y,z,x). [para(2061(a,1),1554(a,1))]. 2063 (L(x \ y,z,u) / y) * x = a(z,u,x \ y). [para(53(a,1),2062(a,1,2))]. 2064 L((x * K(y,z)) \ x,u,w) * K(y,L(z,x,L((x * K(y,z)) \ x,u,w))) = a(u,w,(x * K(y,z)) \ x). [para(2063(a,1),1880(a,1)),flip(a)]. 2065 (a(x,y,z) * u) * L(z,y,x) = z * T(u,L(z,y,x)). [para(2056(a,2),1528(a,1))]. 2066 L(x,y,(z / R(u \ 1,w,v5)) * a(w,u,v5)) = L(x,y,z * u). [para(1476(a,1),2049(a,1,3,2))]. 2067 L(x,y,(z / (u / w)) * a(u,w * (u \ 1),u)) = L(x,y,z * (w * (u \ 1))). [para(1620(a,1),2066(a,1,3,1,2))]. 2068 L(x,y,z * (u * (w \ 1))) = L(x,y,z / (w / u)). [para(2067(a,1),2052(a,1))]. 2070 L(x,y,z * (u * (w \ 1))) = L(x,y,z * (u / w)). [para(2068(a,2),2048(a,1))]. 2071 (a(x,y,z) * L(z,y,x)) \ (u * L(z,y,x)) = T(u * a(y,x,z),a(x,y,z) * L(z,y,x)). [para(1996(a,1),2054(a,2,1))]. 2072 (a(x,y,z) * L(z,y,x)) \ (u * L(z,y,x)) = T(u * a(y,x,z),z). [para(1437(a,1),2071(a,2,2))]. 2073 x \ (y * L(x,z,u)) = T(y * a(z,u,x),x). [para(1437(a,1),2072(a,1,1))]. 2074 T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = u \ ((a(y,z,u) \ x) * L(u,y,z)). [para(110(a,2),2073(a,2,1)),flip(a)]. 2075 T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = u \ ((a(z,y,u) * x) * L(u,y,z)). [para(1472(a,1),2074(a,2,2,1))]. 2076 T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = u \ (u * T(x,L(u,y,z))). [para(2065(a,1),2075(a,2,2))]. 2077 T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = T(x,L(u,y,z)). [para(2076(a,2),13(a,1))]. 2078 T(x * K(a(y,z,u) * x,a(z,y,u)),u) = T(x,L(u,z,y)). [para(1472(a,1),2077(a,1,1,2,1))]. 2079 T(x * K(x,a(y,z,u)),u) = T(x,L(u,y,z)). [para(2004(a,1),2078(a,1,1,2))]. 2080 T(T(x,a(y,z,u)),u) = T(x,L(u,y,z)). [para(1035(a,2),2079(a,1,1))]. 2081 T(T(x,y),a(z,u,y)) = T(x,L(y,z,u)). [para(2080(a,1),38(a,1)),flip(a)]. 2082 T(x,L(y,z,u)) \ T(x,y) = K(a(z,u,y),T(x,y)). [para(2081(a,1),1054(a,2,1)),flip(a)]. 2083 K(x,y) * K(L(y,z,u),x) = K(a(z,u,y),T(x,y)). [para(2082(a,1),1183(a,1)),flip(a)]. 2084 K(x,y) * K(L(y,z,u),x) = K(x,a(u,z,y)). [para(2083(a,2),1858(a,1))]. 2085 a(x,y,K(z,u)) = K(u,a(y,x,z)). [para(2084(a,1),1734(a,1)),flip(a)]. 2086 L(x * L(y,L(x,z,u),u * (z * ((z * u) \ 1))),z,u) = L(x,z,u) * L(y,z,u). [hyper(524,a,1872,a),flip(a)]. 2087 L(x * L(y,L(x,z,u),u * (z / (z * u))),z,u) = L(x,z,u) * L(y,z,u). [para(2070(a,1),2086(a,1,1,2))]. 2088 L(x * L(y,L(x,z,u),K(u,z)),z,u) = L(x,z,u) * L(y,z,u). [para(1058(a,2),2087(a,1,1,2,3))]. 2089 L(x * L(T(y,L(x,z,u)),L(x,z,u),K(u,z)),z,u) = L(y,z,u) * L(x,z,u). [para(2088(a,2),103(a,1))]. 2090 L(x \ (x / K(y,z)),u,w) * K(y,L(z,x,L((x * K(y,z)) \ x,u,w))) = a(u,w,(x * K(y,z)) \ x). [para(313(a,1),2064(a,1,1,1))]. 2091 L(K(x,y),z,u) * K(y,L(x,w,L((w * K(y,x)) \ w,z,u))) = a(z,u,(w * K(y,x)) \ w). [para(1717(a,1),2090(a,1,1,1))]. 2093 K(x,L(y,z,u)) * K(y,L(x,w,L((w * K(y,x)) \ w,z,u))) = a(z,u,(w * K(y,x)) \ w). [para(1879(a,1),2091(a,1,1))]. 2094 K(x,L(y,z,u)) * K(y,L(x,w,L(w \ (w / K(y,x)),z,u))) = a(z,u,(w * K(y,x)) \ w). [para(313(a,1),2093(a,1,2,2,3,1))]. 2095 a(x,y,(z * K(u,w)) \ z) = K(w,L(u,x,y)) * K(u,L(w,z,L(K(w,u),x,y))). [para(1717(a,1),2094(a,1,2,2,3,1)),flip(a)]. 2097 a(x,y,(z * K(u,w)) \ z) = K(w,L(u,x,y)) * K(u,L(w,z,K(w,L(u,x,y)))). [para(1879(a,1),2095(a,2,2,2,3))]. 2098 a(x,y,(z * K(u,w)) \ z) = K(w,L(u,x,y)) * K(u,w). [para(1696(a,1),2097(a,2,2,2))]. 2099 a(x,y,z \ (z / K(u,w))) = K(w,L(u,x,y)) * K(u,w). [para(16(a,1),2098(a,1,3,1))]. 2100 K(x,L(y,z,u)) * K(y,x) = a(z,u,K(x,y)). [para(606(a,1),2099(a,1,3)),flip(a)]. 2101 K(x,L(y,z,u)) * K(y,x) = K(y,a(u,z,x)). [para(2100(a,2),2085(a,1))]. 2102 (x \ K(y,x)) \ K(y,a(z,u,x)) = T(T(x,L(y,u,z)),x \ K(y,x)). [para(2101(a,1),1110(a,1,2))]. 2103 T(T(x,L(y,z,u)),x \ K(y,x)) = (K(x,y) * x) * K(y,a(u,z,x)). [para(2102(a,1),1799(a,1))]. 2104 T(T(x,L(y,z,u)),x \ K(y,x)) = T(x,y) * K(y,a(u,z,x)). [para(1043(a,2),2103(a,2,1))]. 2105 T(T(x,L(y,z,u)),x \ K(y,x)) = T(x * K(y,a(u,z,x)),y). [para(2104(a,2),1703(a,2)),flip(a)]. 2106 T(T(x,L(y,z,u)),x \ K(y,x)) = T(L(x,z,K(u,y)),y). [para(2020(a,1),2105(a,2,1))]. 2107 T(T(x,L(y,z,u)),x \ K(y,x)) = L(T(x,y),z,K(u,y)). [para(2106(a,2),40(a,2)),flip(a)]. 2108 L(T(x,y),z,K(u,y)) = T(x,L(y,z,u)). [para(2107(a,1),1088(a,1))]. 2110 L(T(x,y),K(z,y) \ u,K(z,y) * (u / K(z,y))) = T(x,L(y,u,z)). [para(2108(a,1),1863(a,2))]. 2111 L(T(x,y),K(y,z) * u,K(z,y) * (u / K(z,y))) = T(x,L(y,u,z)). [para(1075(a,1),2110(a,1,2))]. 2112 L(T(x,y),K(y,z) * u,K(z,y) * (u * K(y,z))) = T(x,L(y,u,z)). [para(1716(a,1),2111(a,1,3,2))]. 2113 L(T(x,y),K(y,z) * u,T(u,K(y,z))) = T(x,L(y,u,z)). [para(1093(a,1),2112(a,1,3))]. 2114 L(T(x,y),K(y,z),T(u,K(y,z))) = T(x,L(y,u,z)). [para(2113(a,1),1575(a,1)),flip(a)]. 2115 L(T(x,y),K(y,z),u) = T(x,L(y,u,z)). [para(2114(a,1),1307(a,1)),flip(a)]. 2116 L(T(x,y),y,K(z,u)) = T(x,L(y,z,u)). [para(2115(a,1),2025(a,1)),flip(a)]. 2117 L(x * T(y,L(L(x,z,u),u,z)),z,u) = L(y,z,u) * L(x,z,u). [para(2116(a,1),2089(a,1,1,2))]. 2118 L(x * T(y,x),z,u) = L(y,z,u) * L(x,z,u). [para(341(a,1),2117(a,1,1,2,2))]. 2119 L(x,y,z) * L(u,y,z) = L(x * u,y,z). [para(80(a,1),2118(a,1,1)),flip(a)]. 2120 L(L(x,y,z) * u,z,y) = x * L(u,z,y). [para(341(a,1),2119(a,1,1)),flip(a)]. 2121 L(x * L(y,z,u),u,z) = L(x,u,z) * y. [para(341(a,1),2119(a,1,2)),flip(a)]. 2122 L(L(x,y,z) * u,z,y) = L(u,z,y) * T(x,u). [para(103(a,1),2121(a,1,1))]. 2123 L(x,y,z) * T(u,x) = u * L(x,y,z). [para(2122(a,1),2120(a,1))]. 2124 T(x,L(y,z,u)) = T(x,y). [hyper(98,a,2123,a)]. 2126 K(x,L(y,z,u)) = T(x,y) / x. [para(2124(a,1),1036(a,2,1))]. 2133 K(x,L(y,z,u)) = K(x,y). [para(2126(a,2),1036(a,2)),flip(a)]. 2135 L(K(x,y),z,u) = K(x,y). [para(2133(a,1),1879(a,2))]. 2138 a(x,y,K(z,u)) = 1. [hyper(34,a,2135,a)]. 2147 K(x,a(y,z,u)) = 1. [para(2138(a,1),2085(a,1)),flip(a)]. 2152 a(K(x,y),z,u) = 1. [para(2147(a,1),2021(a,1)),flip(a)]. 2153 $F # answer("aK1"). [resolve(2152,a,48,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=2002. Generated=4914760. Kept=2134. proofs=1. Usable=1995. Sos=126. Demods=0. Limbo=4, Disabled=38. Hints=2687. Kept_by_rule=0, Deleted_by_rule=4891273. Forward_subsumed=21353. Back_subsumed=8. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. Demod_attempts=0. Demod_rewrites=0. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=352. Nonunit_bsub_feature_tests=68. Megabytes=7.30. User_CPU=50.76, System_CPU=2.21, Wall_clock=53. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED THEOREM PROVED Exiting with 1 proof. ------ process 17600 exit (max_proofs) ------  Process 17600 exit (max_proofs) Mon Jan 20 20:58:34 2020