============================== Prover9 =============================== Prover9 (64) version 2017-09A, September 2017. Process 28884 was started by veroff on theorem, Wed Jan 29 20:28:02 2020 The command was "prover9 -f moufang_to_aa1.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file moufang_to_aa1.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("Moufang"). end_of_list. formulas(goals). a(a(x,y,z),u,w) = 1 # label("aa1"). end_of_list. formulas(hints). a(a(x,y,z),u,w) = 1. 1 * x = x. x * 1 = x. x \ (x * y) = y. x * (x \ y) = y. (x * y) / y = x. (x / y) * y = x. x * y != z | x * u != z | u = y. x * y != z | u * y != z | u = x. x * y != x * z | y = z. x * y != z * y | x = z. (x * (y * z)) \ ((x * 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(L(x,y,z),u,w) = L(L(x,u,w),y,z). ((x * y) * x) * z = x * (y * (x * z)). a(a(c1,c2,c3),c4,c5) != 1. 1 \ x = x. x \ x = 1. x / (y \ x) = y. (x / y) \ x = y. x != x * y | 1 = y. x * y != x | 1 = y. x != y * z | y \ x = z. x * y != z | x \ z = y. x * 1 != y | x = y. 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). (x * y) * K(y,x) = y * x. K(x \ y,x) = y \ ((x \ y) * x). x \ ((y \ x) * y) = K(y \ x,y). K(x,x \ y) = ((x \ y) * x) \ y. ((x \ y) * x) \ y = K(x,x \ y). K(x / y,y) = (y * (x / y)) \ x. (x * (y / x)) \ y = K(y / x,x). L(x,y,1) = y \ (1 * (y * x)). x \ (1 * (x * y)) = L(y,x,1). L(x,1,y) = (y * 1) \ (y * x). (x * 1) \ (x * y) = L(y,1,x). (x * y) * L(z,y,x) = x * (y * z). L(x \ y,x,z) = (z * x) \ (z * y). L(x,y,z / y) = z \ ((z / y) * (y * x)). x \ ((x / y) * (y * z)) = L(z,y,x / y). L(x,y / x,z) = (z * (y / x)) \ (z * y). R(x,x \ y,z) = (y * z) / ((x \ y) * z). R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)). R(x,y,z) * (y * z) = (x * y) * z. R(x / y,y,z) = (x * z) / (y * z). R(x,y / z,z) = ((x * (y / z)) * z) / y. ((x * (y / z)) * z) / y = R(x,y / z,z). T(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) * x = x * (y * (x * 1)). x * (y * (x * 1)) = (x * y) * x. ((x * 1) * x) * y = x * (x * y). (x * y) * z = y * ((y \ x) * (y * z)). x * ((x \ y) * (x * z)) = (y * x) * z. a(x * y,x,z) = ((x * y) * (x * z)) \ (x * (y * (x * z))). ((x * y) * (x * z)) \ (x * (y * (x * z))) = a(x * y,x,z). T(x,y) = T(T(x,y),x). T(T(x,y),x) = T(x,y). (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 != y * z | T(x,y) = z. x * y != z * x | T(z,x) = 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. T(x \ y,z) = T(T(y / x,z),x). T(T(x / y,z),y) = T(y \ x,z). K(T(x,y),x) = 1. T(x,T(x,y)) = x. K(x \ y,y / x) = 1. T(x,y) = T(T(x,y),T(x,z)). T(T(x,y),T(x,z)) = T(x,y). x / T(y,y \ x) = y \ x. (x * y) / T(y,T(x,y)) = T(x,y). T(x \ y,y / x) = x \ y. x * K(y,x / y) = y * (x / y). L(K(x,y),y * x,z) = (z * (y * x)) \ (z * (x * y)). (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x). (x * y) / T(y * x,K(x,y)) = K(x,y). x \ (x * y) = L(y,x,1). L(x,y,1) = x. x \ (x * y) = L(y,1,x). L(x,1,y) = x. x * (y * x) = (x * y) * x. (x * y) * x = x * (y * x). (x * (y * x)) / x = x * y. (x * y) \ (x * (y * x)) = x. T(x * y,x) = y * x. (x * y) * x != x * z | y * x = z. (x * (y * x)) * z = x * (y * (x * z)). T((x \ y) * x,x \ y) = y. T(x,y) = (y \ x) * y. T(x,x / y) = y * (x / y). T(x * y,y) = T(x,y) * y. T(x,y) / y = y \ x. (x \ y) \ T(y,x) = x. T(x \ y,x) = x \ T(y,x). x \ T(y,x) = T(x \ y,x). (x \ T(x,y)) * x = T(x,y). x \ T(x,y) = K(y \ x,y). K(x \ y,x) = y \ T(y,x). T(x,y) \ x = K(y,y \ x). K(x,x \ y) = T(y,x) \ y. 1 / x = x \ 1. (x \ y) / x = x \ (y / x). T(x,y) / x = x \ T(x,y). x / T(x,y) = T(x,y) \ x. T(x,y) / T(x,z) = T(x,z) \ T(x,y). (x \ y) / (y / x) = (y / x) \ (x \ y). (x \ 1) \ 1 = x. (x \ T(x,y)) \ T(x,y) = x. (x * y) / x = x * (y / x). (x * (y / x)) \ (x * y) = x. L(x,y,x) = x. L(T(x,y),z,x) = T(x,y). L(x,y,z) = L(L(x,y,z),u,x). L(L(x,y,z),u,x) = L(x,y,z). L(T(T(x,y),z),u,x) = T(T(x,y),z). T(T(x,y),y \ x) = x. T(x,y) = T(T(T(x,z),y),z \ x). T(T(T(x,y),z),y \ x) = T(x,z). T(T(x,x / y),y) = x. T(x,T(x,y) \ x) = x. L(x,y,T(x,z)) = T(T(x,z),z \ x). T(T(x,y),y \ x) = L(x,z,T(x,y)). x = T(T(x,y),x / y). T(T(x,y),x / y) = x. x * y = T(y,y / x) * x. T(x,x / y) * y = y * x. K(x,T(x,y) \ x) = 1. T(x,y) = T(T(T(x,z),y),x / z). T(T(T(x,y),z),x / y) = T(x,z). T(x,(y * (x / y)) \ x) = x. x \ (x \ y) = T(x \ (y / x),x). T(x \ (y / x),x) = x \ (x \ y). x * K(y \ x,y) = T(x,y). T(x,y) = x * K(y \ x,y). K(x \ y,x) * y = T(y,x). T(x,y) = K(y \ x,y) * x. T(x,y) * K(y,y \ x) = x. T(x,x \ T(x,y)) = x. T(x,K(y \ x,y)) = x. T(x * y,K(y,x)) = x * y. T(x,K(x / y,y)) = x. T(K(x / y,y),x) = K(x / y,y). T(x,y) != x * z | K(y \ x,y) = z. T(T(x,y),y) = T(x,y) * K(T(y \ x,y),y). T(x,y) * K(T(y \ x,y),y) = T(T(x,y),y). (x * x) * y = x * (x * y). (x * (x * y)) / y = x * x. L(x,y,z * z) = (z * (z * y)) \ ((z * z) * (y * x)). (x * (x * y)) \ ((x * x) * (y * z)) = L(z,y,x * x). (x * y) / (x \ y) = x * x. x / (y \ (y \ x)) = y * y. (x * x) \ y = x \ (x \ y). T(x,y * y) = (y \ (y \ x)) * (y * y). (x \ (x \ y)) * (x * x) = T(y,x * x). (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y). x * y = T(y,x \ y) * x. T(x,y \ x) * y = y * x. x * y != y * z | x = T(z,z / y). T(x,y \ x) = T(x,x / y). T(x,x / y) = T(x,y \ x). x * y != z * x | T(y,x \ y) = z. T(x,y) = T(x,(y \ x) \ x). T(x,(y \ x) \ x) = T(x,y). T(x,y \ x) = y * (x / y). T(x,T(y,y \ x)) = T(x,y). T(x * y,y) = x * ((x * y) / x). R(x,y,z / (x * y)) = T(z,(x * y) \ z) / (y * (z / (x * y))). T(x,(y * z) \ x) / (z * (x / (y * z))) = R(y,z,x / (y * z)). T(x * (y / x),z) = T(T(y,z),x \ y). T(T(x,y),z \ x) = T(z * (x / z),y). T(x * y,T(x,y)) = T(x * y,x). T(x,y \ x) = x * K(y,x / y). x * K(y,x / y) = T(x,y \ x). T(T(T(x,y),z),z \ x) = T(x,y). T(T(T(x,y \ x),z),y) = T(x,z). T(T(T(T(x,y),z),y \ x),T(x,y) / z) = x. K(x / y,y) / x = x \ K(x / y,y). T(x * y,y) = x * (x * (y / x)). T(x * y,T(x,y)) = y * x. K(T(x,y) \ (x * y),T(x,y)) = (x * y) \ (y * x). x * T(y,z) = T(T(y,z),x \ y) * x. T(T(x,y),z \ x) * z = z * T(x,y). T(x,y) / z = z \ T(T(x,z \ x),y). x \ T(T(y,x \ y),z) = T(y,z) / x. T(x * y,y) = x * T(y,x \ y). x * T(y,x \ y) = T(x * y,y). x * L(y,z,x / z) = (x / z) * (z * y). x * (y * z) != (x * y) * u | L(z,y,x) = u. (x * y) * z != x * (y * u) | L(u,y,x) = z. a(x,y,L(z,y,x)) = (x * (y * L(z,y,x))) \ (x * (y * z)). (x * (y * L(z,y,x))) \ (x * (y * z)) = a(x,y,L(z,y,x)). L(L(x,y,z),z * y,u) = (u * (z * y)) \ (u * (z * (y * x))). (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z). (x * y) * L(x,z,u) = x * (y * L(x,z,u)). 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. T(x,x * y) = L(y \ (x * y),y,x). L(x \ (y * x),x,y) = T(y,y * x). L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z). T(x * y,x * z) = L(z \ y,z,x) * (x * z). L(x \ y,x,z) * (z * x) = T(z * y,z * x). x / L(y \ 1,y,x) = x * y. x / L(y,y \ 1,x) = x * (y \ 1). R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y). R(1 / x,x,y) = y / (x * y). R((x / y) / z,z,y) = x / (z * y). R((x * y) / z,z,x) = (x * (y * x)) / (z * x). R(x \ 1,x,y) = y / (x * y). R(x,x \ y,z) \ (y * z) = (x \ y) * z. R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z). (x * y) * T(T(x,z),u) = x * (y * T(T(x,z),u)). L(x,y,T(x,z)) = x. L(x,y,z) = L(L(x,y,z),u,T(x,w)). L(L(x,y,z),u,T(x,w)) = L(x,y,z). L(T(x,y),y,x) = T(x,x * y). T(x,x * y) = T(x,y). T(x,y) = T(x,x \ y). T(x,x \ y) = T(x,y). T(x,y * x) = T(x,T(y,x)). T(x,T(y,x)) = T(x,y * x). T(T(x,y),(x * y) \ x) = x. (x * y) * T(T(x,y),z) = T(x,z) * (x * y). T(T(T(x,y),z),y \ x) = T(x,T(x,y) * z). T(x,y) = (x \ y) \ y. x / T(y,x) = y \ x. T(x,T(y,x)) = T(x,y). (x \ y) * T(x,y) = y. T(x / y,x) = y \ x. T(x \ y,y) = T(x,y) \ y. T(x,y) \ y = T(x \ y,y). x / T(T(y,x),z) = T(y,z) \ x. x / L(T(y,x),z,u) = L(y,z,u) \ x. (x * y) / T(y,x) = T(x,y). ((x * y) \ x) * (y * x) = x. x * (y \ x) = (x / y) * x. (x / y) * x = x * (y \ x). (x \ y) / y = y \ (y / x). T(x \ y,y \ (y / x)) = y / x. K(x \ (x / y),x) = (x / y) \ (y \ x). K(x,x \ (x / y)) = (y \ x) \ (x / y). (x \ y) * K(y,y \ (y / x)) = y / x. T(x \ y,x) = T(x \ y,y). T(x \ y,y) = T(x \ y,x). T(x,y * x) = T(x,y). T(x,y) = T(x,y / x). T(x,y / x) = T(x,y). (x / y) * T(y,x) = y * (x / y). T(x * (y / x),y / x) = T(x,y) * (y / x). (x * y) \ y = T((y * x) \ y,y). T((x * y) \ x,x) = (y * x) \ x. T(x,y) * T(y,x) = x * y. x != y * (z * x) | (x * z) \ x = y. x * (y * z) != z | (z * y) \ z = x. T(x \ y,x) = ((x \ y) \ y) \ 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(L(x \ 1,x,y),y) = (x * y) \ y. x * (((x \ y) \ y) \ y) = (x \ y) * x. x / L(x,y,z) = x * (L(x,y,z) \ 1). x * (L(x,y,z) \ 1) = x / L(x,y,z). L(T(x \ 1,y),x,y) = (x * y) \ y. (x * y) * ((y * x) \ x) = x * (y * T(y \ 1,x)). T(x * y,y) = (y \ x) * (y * y). (x \ y) * (x * x) = T(y * x,x). x \ ((y * x) * z) = (x \ y) * (x * z). x * ((x \ y) * z) = (y * x) * (x \ z). (x * y) * (y \ z) = y * ((y \ x) * z). 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). T(x,L(x,y,z) \ x) = x. T(x,L(x,y,z)) = x. K(x,L(x,y,z)) = 1. 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) = L(x,y,z) \ x. L(x,y,z) / x = x \ L(x,y,z). (x * y) / (y * x) = K(x,y). K(x,y) = (x * y) / (y * x). K(x,T(y,x \ y)) = (x * T(y,x \ y)) / (x * y). (x * T(y,x \ y)) / (x * y) = K(x,T(y,x \ y)). (x * y) * y = x * (y * y). x * y != (x * z) * L(u,z,x) | y = z * u. x * (y * L(z,x * y,y)) = (x * y) * z. (x * y) * z != x * (y * u) | z = L(u,y,x). x = L(x,x,y). L(x,x,y) = x. x * (y * z) != (u * y) * z | x = R(u,y,z). x = R(x,y,y). R(x,y,y) = x. L(x,y,z) = L(L(x,y,z),x,u). L(L(x,y,z),x,u) = L(x,y,z). x / y = (x * y) / (y * y). (x * y) / (y * y) = x / y. (x / y) / y = x / (y * y). T(x / (y * y),y) = y \ (x / y). T(x,y / (x * x)) = T(x,y / x). T(x,y / (x * x)) = T(x,y). T(x,y * y) = T((y \ x) * y,y). T((x \ y) * x,x) = T(y,x * x). T(x * (y / x),y / x) = T(y,(y / x) * (y / x)). T(T(x,y),y) = T(x,y * y). T(x * (y / x),z) = T(T(y,x \ y),z). T(T(x,y \ x),z) = T(y * (x / y),z). x * (T(y,z) / x) = T(T(y,x \ y),z). T(T(x,y \ x),z) = y * (T(x,z) / y). T(T(T(x,y \ x),z),T(x,z) / y) = y * (T(T(x,y \ x),z) / y). T(x,y) = y * (((y \ x) \ x) \ x). T(x,y) = y * (T(y,x) \ x). x * (T(x,y) \ y) = T(y,x). (x * y) * ((y * x) \ x) = T(x,x * y). x * (L(x,y,z) \ 1) = L(x,y,z) \ x. T(T(x,(y * y) \ x),z) = T(y * (y * (x / (y * y))),z). T(x * (y / x),z) = x * (T(y,z) / x). (x * y) * ((y * x) \ x) = T(x,y). T(x,y) = (x * y) * ((y * x) \ x). ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). L(x,y,1 / y) = (1 / y) * (y * x). (1 / x) * (x * y) = L(y,x,1 / x). L(x,y,1 / y) / (y * x) = 1 / y. (1 / x) \ L(y,x,1 / x) = x * y. (1 / x) * y = L(x \ y,x,1 / x). L(x \ y,x,1 / x) = (1 / x) * y. L(x \ y,x,x \ 1) = (1 / x) * y. L(x \ y,x,x \ 1) = (x \ 1) * y. L(x,y,y \ 1) = (y \ 1) * (y * x). (x \ 1) * (x * y) = L(y,x,x \ 1). x = L(L(x,y * z,z),z,y). L(L(x,y * z,z),z,y) = x. L(L(x,y,z),z,y / z) = x. x = L(L(x,y,z),z * y,y). L(L(x,y,z),z * y,y) = x. x = L(L(x,y,z / y),z,y). L(L(x,y,z / y),z,y) = x. L(x,y,1 / y) = x. K(L(x,y,z),x) = 1. L(x,y,z / y) = L(x,y * z,z). L(x,y * z,z) = L(x,y,z / y). L(x,y,y \ 1) = x. x / (y * x) = 1 / y. (1 / x) \ y = x * y. x \ y = (x \ 1) * y. (x \ 1) * y = x \ y. (x \ 1) * (x * y) = y. x / (y * x) = y \ 1. (x \ 1) \ y = x * y. (x \ y) / y = x \ 1. L(x,y \ 1,z) = (z * (y \ 1)) \ (z * (y \ x)). (x * (y \ 1)) \ (x * (y \ z)) = L(z,y \ 1,x). T(x \ 1,y) = y \ (x \ y). ((x * (y / x)) \ 1) * y = K(y / x,x). (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). L(x \ y,x,z \ 1) = (z \ x) \ ((z \ 1) * y). T(x,y \ x) = T(x,y \ 1). T(x,y \ 1) = T(x,y \ x). (x * y) \ x = y \ 1. R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). x / y = (y / x) \ 1. (x / y) \ 1 = y / x. (x * y) / ((z * x) * y) = R(z,x,y) \ 1. T(x \ 1,y) = (x * y) \ y. x / (x * y) = (x * (y / x)) \ 1. (x * (y / x)) \ 1 = x / (x * y). T(x \ (y \ 1),x) = x \ (x \ (y \ x)). x \ 1 = y \ (y / x). x \ (x / y) = y \ 1. x \ y = (y \ x) \ 1. (x \ y) \ 1 = y \ x. x / (y \ 1) = x * y. (x * y) \ y = T(x,y) \ 1. T(x,y) \ 1 = (x * y) \ y. (x * y) \ (y * x) = K(x,y) \ 1. x \ (y \ x) = T(y,x) \ 1. T(x,y) \ 1 = y \ (x \ y). T(T(x,y),y \ 1) = x. ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. x \ (y \ 1) = (y * x) \ 1. (x * y) \ 1 = y \ (x \ 1). L(x / y,y / x,z) = (z * (y / x)) \ z. (x / y) * z = (y / x) \ z. (x / y) \ z = (y / x) * z. (x / y) * ((y / x) * z) = z. x * (y \ 1) = x / y. x \ (T(x,y) \ x) = T(x,y) \ 1. T(x \ y,x \ 1) = y / x. K(x \ 1,y) = (y / x) \ (x \ y). (x / y) \ (y \ x) = K(y \ 1,x). K(x,y \ 1) = (y \ x) \ (x / y). (x \ y) \ (y / x) = K(y,x \ 1). (x \ y) * K(y,x \ 1) = y / x. R(x \ y,y \ x,z) = z / ((y \ x) * z). (x \ y) * z = (y \ x) \ z. (x \ y) \ z = (y \ x) * z. (x \ y) * ((y \ x) * z) = z. (x * (y \ z)) \ x = z \ y. x \ (x / (y \ z)) = z \ y. x / (y / z) = x * (z / y). x / (y \ z) = x * (z \ y). T(x * y,y \ 1) = y * x. x * y = T(y,x \ 1) * x. T(x,y \ 1) * y = y * x. T(x \ y,y \ 1) = y / x. x / y = T(y,x \ 1) \ x. T(x,y \ 1) \ y = y / x. x * (T(x,y) \ 1) = T(x,y) \ x. R(x,y,z \ 1) * (y / z) = (x * y) * (z \ 1). (x * (y * x)) / z = x * (y * (x * (z \ 1))). x * (y * (x * (z \ 1))) = (x * (y * x)) / z. (x \ 1) / y = x \ (y \ 1). L(L(x,y,y \ z),T(z,y),y) = x. L(x,y,L(x,z,u)) = L(L(x,z,u),u * z,z). L(L(x,y,z),z * y,y) = L(x,u,L(x,y,z)). L((x * y) \ z,x * y,y) = y \ (x \ z). L(L(x,y,z \ 1),z \ y,y) = x. T(x,y \ 1) = y * (x / y). (x * y) \ y = y \ (x \ y). T(x \ 1,y) = T(x,y) \ 1. T(x,y) \ 1 = T(x \ 1,y). (x \ (y \ x)) * z = T(y,x) \ z. x * (y \ (z \ y)) = x / T(z,y). (x \ (y \ 1)) * z = (y * x) \ z. x * (y \ (z \ 1)) = x / (z * y). (x / y) \ y = y * (x \ y). x != (y / z) * u | (z / y) * x = u. (x / y) * z != u | (y / x) * u = z. T(x,y \ 1) = (y * x) / y. T(x,y \ z) = ((z \ y) * x) * (y \ z). ((x \ y) * z) * (y \ x) = T(z,y \ x). L((x \ y) * z,y \ x,y) = x \ (y * z). ((x \ y) * z) \ u = (z \ (y \ x)) * u. x != (y \ z) * u | (z \ y) * x = u. (x \ y) * z != u | (y \ x) * u = z. x \ (y * y) = (y \ x) \ y. (x \ y) \ x = y \ (x * x). (x * (y / z)) \ u = ((z / y) / x) * u. x / (y * (z / u)) = x * ((u / z) / y). (x * y) * (y \ x) = x * x. (x * (y \ z)) \ u = ((z \ y) / x) * u. x / ((y \ z) * u) = x * (u \ (z \ y)). x / (y * (z \ u)) = x * ((u \ z) / y). x * y != y * T(z,u) | x = T(T(z,u),y \ z). T(T(x,y),z \ 1) = T(T(x,y),z \ x). T(x,y \ z) * (z \ y) = (z \ y) * x. T(x / y,x \ 1) = x / T(y,x \ 1). x / T(y,x \ 1) = T(x / y,x \ 1). T(x \ (y \ 1),y) = y \ (x \ 1). (x \ (y \ 1)) / z = (y * x) \ (z \ 1). T(x \ 1,y) * z = T(x,y) \ z. x \ (y * y) = (x \ y) * y. x * (y \ (x / y)) = (x / y) * (x / y). (x / y) * (x / y) = x * (y \ (x / y)). L(x,(y \ z) * z,z) = L(x,y \ z,y). L(x,y \ z,y) = L(x,(y \ z) * z,z). K(x,y) = K(y,x) \ 1. K(x,y) \ 1 = K(y,x). K(x,y) * K(y,x) = 1. K(x,y) * z = K(y,x) \ z. K(x,y) \ z = K(y,x) * z. K(x,y) * (K(y,x) * z) = z. (x * K(y,z)) \ x = K(z,y). x / K(y,z) = x * K(z,y). T(x,K(y,z)) = (K(z,y) * x) / K(z,y). (K(x,y) * z) / K(x,y) = T(z,K(y,x)). T(x,K(y,z)) = K(z,y) * (x * K(y,z)). K(x,y) * (z * K(y,x)) = T(z,K(y,x)). (K(x,y) * z) \ u = (z \ K(y,x)) * u. x != K(y,z) * u | K(z,y) * x = u. K(x,y) * z != u | K(y,x) * u = z. (x * K(y,z)) * K(z,y) = x. x != y * K(z,u) | x * K(u,z) = y. x * K(y,z) != u | u * K(z,y) = x. x \ (T(x,y) \ x) = T(x \ 1,y). (x / y) * K(y \ 1,x) = y \ x. (x \ y) / (y / x) = K(x \ 1,y). K(x,y \ 1) = (x \ y) * (x / y). (x \ y) * (x / y) = K(x,y \ 1). x * T(x \ 1,y) = T(x,y) \ x. (x * (y \ x)) * z = x * ((y \ x) * L(z,x,y \ 1)). x * ((y \ x) * L(z,x,y \ 1)) = (x * (y \ x)) * z. (x \ 1) * (T(x,y) \ x) = T(x \ 1,y). K(x \ 1,y) = (x \ y) * (x / y). (x \ y) * (x / y) = K(x \ 1,y). K(x \ 1,y) = K(x,y \ 1). K(x \ 1,y \ z) = K(x,z \ y). (x / y) * K(y,x \ 1) = y \ x. (x / (x * y)) * y = K(y / x,x). K(x / y,y) / x = y / (y * x). x / (x * y) = y \ K(y / x,x). x \ K(x / y,y) = y / (y * x). T((x \ y) \ (z \ 1),x \ y) = (y \ x) * ((x \ y) \ (z \ (x \ y))). (x \ y) * ((y \ x) \ (z \ (y \ x))) = T((y \ x) \ (z \ 1),y \ x). L(x,y / x,z) = ((x / y) / z) * (z * y). R(x,x \ y,z) = (y * z) * (z \ (y \ x)). T(x \ 1,y) \ (x \ 1) = x \ T(x,y). L(x / y,y / x,z) = (y / x) \ 1. L(x / y,y / x,z) = x / y. L(x,y / (x * y),z) = (x * y) / y. L(x,x \ 1,y) = (x * z) / z. L(x,x \ 1,y) = x. L(T(x,y),x \ 1,z) = T(x,y). L(x,y,x \ 1) = x. L(x \ 1,y,x) = x \ 1. L(x \ 1,y,z) = L(L(x \ 1,y,z),u,x). L(L(x \ 1,y,z),u,x) = L(x \ 1,y,z). R(x \ y,y \ x,z) = (y \ x) \ 1. R(x \ y,y \ x,z) = x \ y. R(x,(y * x) \ y,z) = y \ (y * x). R(x,x \ 1,y) = z \ (z * x). R(x,x \ 1,y) = x. R(T(x,y),x \ 1,z) = T(x,y). T(x,y) * ((x \ 1) * z) = (T(x,y) * (x \ 1)) * z. (T(x,y) * (x \ 1)) * z = T(x,y) * ((x \ 1) * z). L(x,y * z,z) = z \ (y \ ((y * z) * x)). x \ (y \ ((y * x) * z)) = L(z,y * x,x). x \ (y \ (x \ z)) = (x * (y * x)) \ z. (x * (y * x)) \ z = x \ (y \ (x \ z)). R(x,x \ y,z) = z * ((z \ y) * (y \ x)). (x * y) * L(x \ 1,z,u) = x * (y * L(x \ 1,z,u)). T(x,y) * K(T(y \ x,y),y) = T(x,y * y). T(T(x,y),T(x,z) / y) = x. T(x,(T(x,y) / z) \ x) = T(x,z). T(x,(y / T(x,z)) * x) = T(x,y). T(x,y) = T(x,y / T(x,z)). T(x,y / T(x,z)) = T(x,y). x = R(x,y,L(x,z,u)). R(x,y,L(x,z,u)) = x. x \ (y * L(x,z,u)) = (x \ y) * L(x,z,u). T(x,T(x,y) * z) = T(x,z). (x * L(x \ y,z,u)) / x = L(y / x,z,u). x * (y * (x / z)) = (x * (y * x)) / z. (x * (y * x)) / z = x * (y * (x / z)). L(x,y,L(x,z,u)) = x. (x * y) \ (z * ((z \ x) * y)) = a(x,z,z \ y). R(x,y,(x * y) \ z) = z * ((z \ (x * y)) / y). R((x * y) / z,z,x) = x * (y * (x / (z * x))). (x / y) \ (x * (y \ z)) = L(z,y \ 1,x). (x / y) \ (x * z) = L(y * z,y \ 1,x). L(x * y,x \ 1,z) = (z / x) \ (z * y). (x / y) * L(z,y \ 1,x) = x * (y \ z). L(x,y \ 1,z) = (y / z) * (z * (y \ x)). (x / y) * (y * (x \ z)) = L(z,x \ 1,y). L(x * y,x \ 1,z) = (x / z) * (z * y). x * (y \ z) != (x / y) * u | L(z,y \ 1,x) = u. (x / y) * z != x * (y \ u) | L(u,y \ 1,x) = z. (x / y) * T(y,z) = x * (y \ T(y,z)). (x \ y) * L(z,y,x \ 1) = x \ (y * z). x * L(y,z * x,z \ 1) = z \ ((z * x) * y). L(x \ y,x,z \ 1) = (z \ x) \ (z \ y). L(x \ (y * z),x,y \ 1) = (y \ x) \ z. L(x \ y,x,z \ 1) = (x \ z) * (z \ y). L(x \ (y * z),x,y \ 1) = (x \ y) * z. R(x \ 1,x * y,z) = R(x,y,z) \ 1. R(x,y,z \ 1) * (y / z) = (x * y) / z. R((x * y) / z,z,x) = x * (y * (z \ 1)). R((x * y) / z,z,x) = x * (y / z). R(x / y,y,z) = z * ((z \ x) / y). x \ R(y / z,z,x) = (x \ y) / z. R(x,y,z) = z * ((z \ (x * y)) / y). R(x,y / x,z) = z * ((z \ T(y,x \ y)) / (y / x)). x * ((x \ T(y,z \ y)) / (y / z)) = R(z,y / z,x). R(x,y,(x * y) \ z) = R(x,y,z). R(x,y,z) = R(x,y,(x * y) * z). R(x,y,(x * y) * z) = R(x,y,z). R(x,x \ y,y \ z) = R(x,x \ y,z). R(x,y,z) \ z = y * ((x * y) \ z). R(x * y,x,z) \ z = x * ((x * (y * x)) \ z). x \ (y \ ((y * x) * z)) = L(z,y * x,y \ 1). R(x * y,x,z) \ z = x * (x \ (y \ (x \ z))). L(x,y * z,y \ 1) = L(x,y * z,z). R(x * y,x,z) \ z = y \ (x \ z). K(T(x,T(y,x)),T(y,x)) = (y * x) \ (x * y). K(x,y) = K(T(x,T(y,x)),T(y,x)). K(T(x,T(y,x)),T(y,x)) = K(x,y). K(T(x,y),T(y,x)) = K(x,y). K(T(x,y),T(y,T(x,y))) = K(x,y). K(T(x,y),T(y / (x * x),x)) = K(x,y / (x * x)). x * (y * T(T(x,y),z)) = T(x,z) * (x * y). x * (T(x,y) * z) = T(x,y) * (x * z). T(x,y) * (x * z) = x * (T(x,y) * z). T(x,y) * z = x * (T(x,y) * (x \ z)). x * (T(x,y) * (x \ z)) = T(x,y) * z. T(x,y) = x * (y * T(y \ 1,x)). x * (y * T(y \ 1,x)) = T(x,y). x * (T(y,x) \ y) = T(x,y). x * y != T(x,z) | y = K(z \ x,z). T(x,y) \ x = K(x \ y,x). K(x \ y,x) = T(x,y) \ x. T(x,y) != x * z | T(y,x) \ y = z. x * ((y * x) \ (x * y)) = T(x,x * y). K(x,K(x \ y,x)) = 1. K(x,K(y,x)) = 1. T(x,K(y,x)) = x. K(x,y) / y = y \ K(x,y). x * K(x,y) = T(x,x * y). T(x,x * y) = x * K(x,y). x * K(x,y) = T(x,y). T(x,y) = x * K(x,y). T(x,y) \ x = K(y,x). K(x,y) = T(y,x) \ y. K(x \ y,x) = K(y,x). T(x,y) * K(y,x) = x. x \ T(x,y) = K(x,y). K(x,y) = x \ T(x,y). x * y != T(x,z) | y = z * T(z \ 1,x). K(x,y) = y * T(y \ 1,x). T(x,y) * L(z,K(x,y),x) = x * (K(x,y) * z). x / K(y,x) = T(x,y). T(x,y) = x / K(y,x). K(x,x \ y) = K(x,y). x / T(x,y) = K(y,x). K(x,y) = y / T(y,x). x \ K(y,x) = T(x \ 1,y). T(x \ 1,y) = x \ K(y,x). K(x,y \ 1) = y \ T(y,x). K(x,y) = K(y * x,y). K(x * y,x) = K(y,x). T(x,K(x,y)) = x. T(x,y) = K(x,y) * x. T(K(x,y),x) = K(x,y). K(x,y * x) = x \ T(x,y). K(x,y / T(x,z)) = x \ T(x,y). K(x,T(x,y) * z) = x \ T(x,z). (x / y) * T(y,z) = x * K(y,z). T(x,y) \ z = (K(y,x) / x) * z. (K(x,y) / y) * z = T(y,x) \ z. K(x,y) \ y = T(y,x). T(x,y) = K(y,x) \ x. T(K(x,y),z) * K(y,x) = K(K(x,y),z). K(x,y / x) * x = T(x,y). T(x,y) = K(x,y / x) * x. x / T(y,z) = x * (y \ K(z,y)). x * (y \ K(z,y)) = x / T(y,z). K(x,K(y,z)) = K(y,z) * T(K(z,y),x). K(x,y) * T(K(y,x),z) = K(z,K(x,y)). K(x,y) / y = T(y \ 1,x). T(x \ 1,y) = K(y,x) / x. x * K(y,x \ 1) = T(x,y). T(x,y) = x * K(y,x \ 1). K(x,y \ 1) * y = T(y,x). T(x,y) = K(y,x \ 1) * x. K(x,y) = K(y,x \ 1). K(x,y \ 1) = K(y,x). K(x,y) = K(y \ 1,x). K(x \ 1,y) = K(y,x). K(x,y / z) = K(z / y,x). K(x / y,z) = K(z,y / x). K(x,y \ z) = K(z \ y,x). K(x \ y,z) = K(z,y \ x). K(x,y \ (z \ 1)) = K(z * y,x). K(x,T(y \ 1,z)) = K(T(y,z),x). K(x,K(y,z)) = K(K(z,y),x). K(K(x,y),z) = K(z,K(y,x)). (x \ y) * K(x,y) = y / x. K(x * y,x) = K(x,y \ 1). T(x \ 1,y \ 1) = x \ K(x,y). K(x,y) = K(x,y * x). K(x,y * x) = K(x,y). K(x,y) = K(x,y / x). K(x,y / x) = K(x,y). K(x,T(y,x)) = K(x,x \ y). K(x,x \ y) = K(x,T(y,x)). x * K(y,x) = y * (x / y). x * K(y,x) = T(x,y \ x). T(x,y \ x) = x * K(y,x). L(L(x,y,T(y \ 1,z)),K(z,y),y) = x. T(K(x,y),z) = K(x,y) * K(z,K(y,x)). K(x,y) * K(z,K(y,x)) = T(K(x,y),z). K(x * y,x \ 1) * x = T(x,y). T(x,y) = K(x * y,x \ 1) * x. K(x,y \ x) = K(y,x). K(x \ y,y) = K(y,x). K(x,y) = K(y,y / x). K(x,x / y) = K(y,x). K(x / y,y) = K(x,y). K(x,y) = K(x * y,y). K(x * y,y) = K(x,y). x \ K(x,y) = y / (y * x). K(x,x / (x * y)) = K(x,y \ 1). K(x,T(y,x)) = K(x,y). K(T(x,y),y) = K(x,y). T(x,y) * K(y \ x,y) = T(x,y * y). (x * (y / x)) * K(y,x) = y. (x / y) \ K(x / y,y) = y / T(x,y \ x). T(x \ K(x,y),y) = (y * x) \ y. x / (K(x,y) * K(x,y)) = (y * (x / y)) / K(x,y). (x * (y / x)) / K(y,x) = y / (K(y,x) * K(y,x)). K(x,y) = K(x,y / T(x,z)). K(x,y / T(x,z)) = K(x,y). K(x,y) = K(x,y * T(x,z)). K(x,y * T(x,z)) = K(x,y). K(x,(y / x) * T(x,z)) = K(x,y). K(x,y) = K(x,T(x,z) * y). K(x,T(x,y) * z) = K(x,z). K(x,y) = K(x,T(x,z) \ y). K(x,T(x,y) \ z) = K(x,z). K(T(x,y),x \ z) = K(T(x,y),z). x * T(y,z) = (x * y) * K(y,z). (x * y) * K(y,z) = x * T(y,z). (x / y) \ T(x,z) = y * K(x,z). T(x,y) \ T(x,z) = K(y,x) * K(x,z). x * (y \ K(y,z)) = x / T(y,z \ y). x / T(y,z \ y) = x * (y \ K(y,z)). K(x,y \ K(y,z)) = K(T(y,z \ 1),x). K(T(x,y \ 1),z) = K(z,x \ K(x,y)). x * y != T(y,z) | x = K(y,z / y). K(x * y,x \ 1) = K(x,y / x). T(x \ K(x,y),y) = x \ 1. K(x,y * K(x,z)) = K(x,y). (x * T(y,z)) * K(z,y) = x * y. (x * y) \ (x * T(y,z)) = K(y,z). (x * T(y,z)) \ (x * y) = K(z,y). x \ T(y,z) = (x \ y) * K(y,z). (x \ y) * K(y,z) = x \ T(y,z). x * K(y,z) = (x / T(z,y)) * z. (x / T(y,z)) * y = x * K(z,y). L(K(x,y),z * T(y,x),u) = (u * (z * T(y,x))) \ (u * (z * y)). x \ (y * T(y \ x,z)) = K(y \ x,z). ((x * y) * T(L(z,y,x),u)) \ (x * (y * z)) = K(u,L(z,y,x)). (x \ T(y,z)) * K(z,y) = x \ y. (x \ y) * K(z,y) = x \ T(y,z \ y). x \ T(y,z \ y) = (x \ y) * K(z,y). (x * K(y,z)) / z = x / T(z,y). T(x,y * K(z,x)) = T(x,y). K(x * K(y,z),z) = T(z,x) \ z. (T(x,y) \ z) * (z \ x) = K(y,x). (x * K(y,z / y)) / (z / y) = x / (y \ z). K(x,y) = K(x * K(z,y),y). K(x * K(y,z),z) = K(x,z). K(x,y) = K(x / K(z,y),y). K(x / K(y,z),z) = K(x,z). K(T(x,K(y,z)),y) = K(K(z,y) * x,y). K(x,y) = K(y,K(z,y) / x). K(x,K(y,x) / z) = K(z,x). K(x,K(x,y) / z) = K(z,x). K(x,y \ K(x,z)) = K(T(y,K(x,z)),x). K(T(x,K(y,z)),y) = K(y,x \ K(y,z)). K(x,K(x,y) * z) = K(z \ 1,x). K(T(x,y) \ z,z \ x) = ((z \ x) * (T(x,y) \ z)) \ K(y,x). ((x \ y) * (T(y,z) \ x)) \ K(z,y) = K(T(y,z) \ x,x \ y). K(K(x,y),z \ y) = K(T(y,x) \ z,z \ y). K(T(x,y) \ z,z \ x) = K(K(y,x),z \ x). K(x,K(x,y) * z) = K(x,z). K(x,y * K(x,z)) = K(x,T(y,K(x,z))). K(x,T(y,K(x,z))) = K(x,y * K(x,z)). T(x,K(x,y) * z) = x * K(x,z). T(x,y) = T(x,K(x,z) * y). T(x,K(x,y) * z) = T(x,z). T(x,y) = T(x,K(z,x) * y). T(x,K(y,x) * z) = T(x,z). K(K(x,y) * z,y) = T(y,z) \ y. K(x,y) = K(K(z,y) * x,y). K(K(x,y) * z,y) = K(z,y). T(K(x,y) * z,y) = (K(x,y) * z) * K(z,y). (K(x,y) * z) * K(z,y) = T(K(x,y) * z,y). T(K(x,y),z) * K(y,x) = K(z,K(y,x)). T(x,y) * K(x,y) = T(x,y * y). x \ (T(y,z) * (y \ x)) = K((y \ x) \ x,z). K(T(x,K(y,z)),y) = K(x,y). K(x,y \ K(x,z)) = K(y,x). K(x,y \ K(z,x)) = K(y,x). K(x,T(y,K(x,z))) = K(x,y). T(T(x,K(y,z)),y) * K(y,x) = T(x,K(y,z)). (x / y) \ K(x,y) = y / T(x,y \ x). x / T(y,x \ y) = (y / x) \ K(y,x). x / T(y,x \ y) = (x / y) * K(y,x). (x / y) * K(y,x) = x * (y \ K(y,x)). (x * K(y,z)) / (z / y) = x / (y \ z). x / (y \ z) = (x * K(y,z)) * (y / z). (x * K(y,z)) * (y / z) = x / (y \ z). (x * K(y,z)) * (y / z) = x * (z \ y). T(K(x,y) * z,y) = K(x,y) * T(z,y). x \ (T(y,z) * (y \ x)) = K(T(y,x),z). x * K(T(y,x),z) = T(y,z) * (y \ x). T(x,y) * (x \ z) = z * K(T(x,z),y). T(x * y,y) / (x * y) = K(x,T(y,x \ y)). K(x,T(y,x \ y)) = (x * y) \ T(x * y,y). (x * y) \ T(x * y,y) = K(x,T(y,x \ y)). K(x \ (y * x),x) = K(y,T(x,y \ x)). K(T(x,y),y) = K(x,T(y,x \ y)). K(x,T(y,x \ y)) = K(T(x,y),y). K(x,x * (y / x)) = K(T(x,y),y). K(T(x,y),y) = K(x,x * (y / x)). K(x * (y / x),x \ 1) = K(y,y * ((x \ 1) / y)). T(x,(x / y) * (x / y)) = T(y,x) * (x / y). T(x,x * (y \ (x / y))) = T(y,x) * (x / y). T(x,y) * (y / x) = T(y,x \ (y / x)). T(x,y \ (x / y)) = T(y,x) * (x / y). L(x,y \ 1,T(y,z)) = x. L(x,y,T(y \ 1,z)) = x. L(x,K(y,z),z) = x. L(x,K(y,z),y) = x. T(x,y) * z = x * (K(x,y) * z). x * (K(x,y) * z) = T(x,y) * z. x \ (T(x,y) * z) = K(x,y) * z. x * y != T(x,z) * u | y = T(x,z) * (x \ u). K(x,y) * z = T(x,y) * (x \ z). T(x,y) * (x \ z) = K(x,y) * z. x * y != T(x,z) * (x * u) | y = 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. x * (K(y,x) * z) = T(x,y \ x) * z. T(x,y \ x) * z = x * (K(y,x) * z). x \ y = K(x,z) * (T(x,z) \ y). K(x,y) * (T(x,y) \ z) = x \ z. x \ T(x,y * y) = K(x,y) * K(x,y). K(x,y) * K(z,x) = T(x,y) / T(x,z). T(x,y) / T(x,z) = K(x,y) * K(z,x). K(x,y) * z = z * K(T(x,z),y). x * K(T(y,x),z) = K(y,z) * x. K(x,y) * (T(y,x) * z) = y * z. T(x,y) * (T(y,x) * z) = x * (y * z). K(x,y) * (y \ z) = T(y,x) \ z. T(K(x,y),z) = K(T(x,z),y). K(T(x,y),z) = T(K(x,z),y). K(T(x,y),z) \ 1 = y \ (K(x,z) \ y). K(x,y) * z = y * (T(y,x) \ z). x * (T(x,y) \ z) = K(y,x) * z. K(x,y / x) * ((x \ y) * z) = (y / x) * z. K(x,y \ (x \ 1)) * ((x \ (y \ 1)) * z) = (y \ (x \ 1)) * z. K(x,y \ K(y,x)) * ((y \ 1) * z) = (y \ K(y,x)) * z. T(x,T(y,z)) = K(z,y) * (y \ (x * T(y,z))). K(x,y) * (y \ (z * T(y,x))) = T(z,T(y,x)). x \ (K(y,x) * z) = T(x,y) \ z. T(K(x,y) * z,y) = (T(y,x) \ z) * y. (K(x,y) * z) \ y = z \ T(y,x). x / (y \ T(x,z)) = K(z,x) * y. x \ T(y,z) = (x \ K(y,z)) * y. (x \ K(y,z)) * y = x \ T(y,z). x / y = K(z,x) * (T(x,z) / y). K(x,y) * (T(y,x) / z) = y / z. (x \ T(y,z)) / y = x \ K(y,z). K(x,y) * (x / z) = T(x,y) / z. (x / y) / (T(x,z) / y) = K(z,x). K(x \ 1,x \ y) * ((y / x) / z) = (x \ y) / z. x / y = (T(y,z) / x) \ K(y,z). (T(x,y) / z) \ K(x,y) = z / x. K(x,y) * (y / z) = T(y,x \ y) / z. T(x,y \ x) / z = K(y,x) * (x / z). K(x,y) = (y / z) * (z / T(y,x)). (x / y) * (y / T(x,z)) = K(z,x). x / y = (x / T(y,z)) * K(y,z). (x / T(y,z)) * K(y,z) = x / y. (x \ y) * (x / T(T(y,x),z)) = K(z,T(y,x)). ((x \ (y \ 1)) / z) * (z / (y \ (x \ 1))) = K(y,x \ (y \ 1)). x * K(y,z) = (x * T(y,z)) / y. (x * T(y,z)) / y = x * K(y,z). (x / (y \ z)) * K(z / y,y) = x / (z / y). T(x * K(y,z),y) = y \ (x * T(y,z)). x \ (y * T(x,z)) = T(y * K(x,z),x). K(x,y * y) = K(x,y) * K(x,y). K(x,y) * K(x,y) = K(x,y * y). K(x,y) * K(z,x) = T(x,z) \ T(x,y). T(x,y) \ T(x,z) = K(x,z) * K(y,x). K(T(x,y),z) \ 1 = y \ (K(z,x) * y). x * (T(y,x \ y) / z) = T(x,y) * (y / z). T(K(x,y),z) = K(T(y,z),x) \ 1. K(T(x,y),z) \ 1 = T(K(z,x),y). T(K(x,y),z) = K(x,T(y,z)). K(x,T(y,z)) = T(K(x,y),z). K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). K(x,y) * K(z,K(y,x)) = K(x,T(y,z)). K(x,T(y,z)) * K(y,x) = K(z,K(y,x)). K(T(x,y),z) = K(x,T(z,y)). K(x \ y,z) = K(y / x,T(z,y)). K(x / y,T(z,x)) = K(y \ x,z). K(x,T(y,z \ 1)) = K(y,x \ K(x,z)). K(x / y,T(z,x)) = K(z,x \ y). K(x,y) * ((x \ y) * z) = (y / x) * z. K(x,y) * (y / x) = (y / x) * K(x,y). K(x,y) * (y / x) = y * (x \ K(x,y)). T(x,y \ x) / y = x * (y \ K(y,x)). K(x,y) * T(z * K(y,x),y) = T(z,T(y,x)). (x \ y) * (T(y,z) \ x) = K(z,T(y,x)). (x * (y \ z)) * K(y / z,z) = x / (y / z). T(x,y \ (x / y)) = y * (T(x,y \ x) / y). x * (T(y,x \ y) / x) = T(y,x \ (y / x)). T(K(x,y) * (z * K(y,x)),y) = T(z,T(y,x)). (x * (y \ z)) * K(y,z) = x / (y / z). (x * (y \ z)) * K(y,z) = x * (z / y). x \ ((y * (x \ z)) * T(x,z)) = T(y * (z / x),x). x * (y * (x \ K(x,y))) = T(y,x \ (y / x)). T(T(x,K(y,z)),y) = T(x,T(y,z)). T(x,T(y,z)) = T(T(x,y),K(y,z)). T(T(x,y),K(y,z)) = T(x,T(y,z)). T(x,T(y,z)) * K(y,x) = T(x,K(y,z)). K(T(x,y),K(y,z)) = T(x,y) \ T(x,T(y,z)). T(x,y) \ T(x,T(y,z)) = K(T(x,y),K(y,z)). K(T(x,y),K(y,z)) = K(y,x) * K(x,T(y,z)). K(x,y) * K(y,T(x,z)) = K(T(y,x),K(x,z)). K(T(x,y),K(y,z)) = K(z,K(y,x)). K(x,K(y,z)) = K(z,T(K(y,x),y)). K(x,T(K(y,z),y)) = K(z,K(y,x)). K(x,K(y,z)) = K(z,K(y,x)). K(K(x,y),z) = K(x,K(y,z)). K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). K(x,y) * K(x,K(z,y)) = K(x,T(y,z \ 1)). K(T(x,y),x \ (y / x)) = K(x,y / (x * x)). (x * (y / x)) / K(y,x) = y / K(y,x * x). (x * (y / x)) / K(y,x) = y * K(x * x,y). T(x,(y * y) \ x) = (y * (x / y)) / K(x,y). (x * (y / x)) / K(y,x) = T(y,(x * x) \ y). (x * (y / x)) / K(y,x) = T(y,x \ (x \ y)). T(x,y \ (y \ x)) = (y * (x / y)) * K(y,x). (x * (y / x)) * K(x,y) = T(y,x \ (x \ y)). K(x,x * ((y \ 1) / x)) = K(y,(x / y) / y). K(x,(y / x) / x) = K(y,y * ((x \ 1) / y)). K(x,y / (x * x)) = K(y,y * ((x \ 1) / y)). K(x,y / (x * x)) = K(y,y * (x \ (y \ 1))). K(x,y / (x * x)) = K(y,y / (y * x)). K(x,y / (x * x)) = K(y,x \ 1). K(T(x,y),x \ (y / x)) = K(y,x \ 1). K(x,y \ 1) = K(T(y,x),x / y). K(T(x,y),y / x) = K(y,x \ 1). K(T(x,y),y / x) = K(x,y). ((x / y) * T(y,x)) * K(y,x) = T(y,x) * (x / y). K(x,y \ x) * ((y / x) / z) = (x \ y) / z. K(x,y) * ((x / y) / z) = (y \ x) / z. (x * (y / x)) * K(x,y) = T(x,y) * (y / x). T(x,y \ (x / y)) = (y * (x / y)) * K(y,x). (x * (y / x)) * K(x,y) = T(y,x \ (y / x)). T(x,y \ (x / y)) = T(x,y \ (y \ x)). x * (y * (x \ K(x,y))) = T(y,x \ (x \ y)). (x * (x * y)) \ (x * (x * (y * z))) = L(z,y,x * x). x * (y \ (x * z)) = (x * (y \ x)) * z. (x * (y \ x)) * z = x * (y \ (x * z)). x * (((x \ y) * K(z,y)) / (y / z)) = R(z,y / z,x). x * (((x \ y) * K(z,y)) * (z / y)) = R(z,y / z,x). x * ((x \ y) * (y \ z)) = R(z,y / z,x). R(x,y / x,z) = z * ((z \ y) * (y \ x)). T(T(x,y \ (y \ x)),z) = T(y * (y * (x / (y * y))),z). K(x,y) * ((x \ 1) * z) = (x \ K(x,y)) * z. K(x,y) * (x \ z) = (x \ K(x,y)) * z. (x \ K(x,y)) * z = K(x,y) * (x \ z). a(x * y,x,z) = a(x,y,x * z) \ 1. a(x,y,x * z) \ 1 = a(x * y,x,z). (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(z,z * y)) = L(x,z * y,z). L(L(x,T(y,z) * T(z,y),T(z,y)),z,y) = x. L(x,y * z,T(z,y)) = L(x,z * y,z). L(L(x,y * z,T(z,y)),z,y) = x. L(L(x,y * z,y),y,z) = x. L(L(x,y,z),z,z \ y) = x. L(x,y * z,z) = L(x,z * y,z). x = L(L(x,y,y \ z),z,y). L(L(x,y,y \ z),z,y) = x. L(x,y,y \ z) = L(x,y * z,z). L(x,y * z,z) = L(x,y,y \ z). L(x,(y \ z) * y,y) = L(x,z,y). L(x,y,y \ (z * y)) = L(x,y,z). L(x,y,y \ z) = L(x,y,z / y). L(x,y,z / y) = L(x,y,y \ z). L(x,T(y,z),z) = L(x,y,z). L(x,y,y \ (z \ y)) = L(x,y,z \ 1). L(x,y,y \ z) = L(x,z * y,z). L(x,y * z,y) = L(x,z,z \ y). L(((x \ y) * x) \ z,y,x) = x \ ((x \ y) \ z). L(x,y \ z,y) = L(x,z / y,y). L(x,y / z,z) = L(x,z \ y,z). L(x,y * (z / y),z / y) = L(x,z,z / 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 / y),y \ 1) = L(x,z,y \ 1). (x * y) * L(z,x,y) = y * (T(x,y) * z). L(T(x,y) \ z,x,y) = (x * y) \ (y * z). L(x,y * z,y \ 1) = L(x,y,y \ z). L(x,y,T(z,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). x \ ((x / y) * (y * z)) = L(z,y,y \ x). x * L(y,z,z \ x) = (x / z) * (z * y). x * L(y,z,z \ x) = z \ ((z * x) * y). x \ ((x * y) * z) = (y / x) * (x * z). T(x,y \ z) \ (((z \ y) * x) * u) = ((z \ y) / T(x,y \ z)) * (T(x,y \ z) * u). ((x \ y) / T(z,y \ x)) * (T(z,y \ x) * u) = T(z,y \ x) \ (((x \ y) * z) * u). L(x,y * (z / y),z / y) = L(x,z,y \ z). L(x,y,z \ 1) = L(x,z * (y / z),y / z). L(x,y * (z / y),z / y) = L(x,z,y \ 1). L(x,y,z \ 1) = L(x,y,z \ y). L(x,y,(z * y) \ 1) = L(x,y,y \ (z \ y)). L(x,y,y \ (z \ 1)) = L(x,y,y \ (z \ y)). L(x,y,y \ (z \ 1)) = L(x,y,z \ 1). L(L(x,y \ 1,z),z,y \ 1) = x. L(x,y \ z,z) = L(x,y \ 1,z). L(x,y \ 1,z) = L(x,y \ z,z). L(x,y \ z,u) = L(x,(z \ y) \ u,u). L(x,(y \ z) \ u,u) = L(x,z \ y,u). L(x,(y \ z) * u,u) = L(x,y \ z,u). L(x,y \ z,y) = L(x,y \ z,z). L(x,y \ z,z) = L(x,y \ z,y). L(x,y \ z,y) = 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,x,y) = x \ (y * z). L(L(x,y,z),z,y) = x. L(x,y * z,z) = L(x,y,z). L(x,y,z) = L(x,y,y \ z). L(x,y,y \ z) = L(x,y,z). L(x,y,z) = L(L(L(x,u,w),y,z),w,u). L(L(L(x,y,z),u,w),z,y) = L(x,u,w). (x * y) * z = x * (y * L(z,x,y)). x * (y * L(z,x,y)) = (x * y) * z. L((x * y) \ z,x,y) = y \ (x \ 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). L(x,y,z) = L(x,y,y * z). L(x,y,y * z) = L(x,y,z). x \ ((x / y) * (y * z)) = L(z,y,x). L(x,y,z) = z \ ((z / y) * (y * x)). L(x \ y,x,z) = ((x * z) * x) \ ((x * z) * y). ((x * y) * x) \ ((x * y) * z) = L(x \ z,x,y). L(x,y \ z,z) = L(x,z,y). L(L(x,y,z \ 1),y,z) = x. L(x,y / z,y) = L(x,y,z). L(x,y \ 1,z) = L(x,z,y). L(x,y,z) = L(x,z,y \ 1). L(x,y,z \ 1) = 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 \ 1),u) = L(x,u,z * y). L(x,K(y,z),u) = L(x,u,K(z,y)). (x / y) * L(z,x,y) = x * (y \ z). (x / y) * (y * (x \ z)) = L(z,y,x). L(x,y,z) = (z / y) * (y * (z \ x)). L(x * y,z,x) = (x / z) * (z * y). (x \ y) * L(z,x,y) = x \ (y * z). L(x \ y,z,x) = (x \ z) * (z \ y). L(x \ (y * z),y,x) = (x \ y) * z. L(x \ (y * z),u,w) = L(L((x \ y) * z,u,w),x,y). L(L((x \ y) * z,u,w),x,y) = L(x \ (y * z),u,w). (x / y) * L(y,z,u) = x * (y \ L(y,z,u)). R(x,y,z) \ z = (y / (x * y)) * L(z,y,x * y). L(x \ y,z,x) = x \ L(y,z,x). L(x,y,z) = z \ L(z * x,y,z). x \ L(x * y,z,x) = L(y,z,x). L(x \ L(x,y,z),u,x) = x \ L(x,y,z). L((x * y) \ z,x,x * y) = (x * y) \ L(z,x,y). x * L(y,z,x) = L(x * y,z,x). L(x * y,z,x) = x * L(y,z,x). x * L(y * z,x,y) = (x * y) * z. L(x * ((y * x) \ z),y,x) = x * (x \ (y \ z)). L((x * y) * z,y,x * y) = x * (y * z). L(x * y,y \ z,x) = (x / (y \ z)) * T(z,y). L(x \ (y * z),z,x) = (x \ z) * T(y,z). L(x \ y,z * z,x) = (x \ (z * z)) * (z \ (z \ y)). L(x \ L(x,y,z),x,u) = x \ L(x,y,z). x * (y * z) = L((x * y) * z,y,x). L((x * y) * z,y,x) = x * (y * z). L(x,y,z) = z * (y * ((z * y) \ x)). L((x * y) * z,x * y,x) = x * (y * z). L(x * (y * z),x,y) = (x * y) * z. L(L(x,y,z \ u),z,u) = z \ (u * (y * (((z \ u) * y) \ x))). x \ (y * (z * (((x \ y) * z) \ u))) = L(L(u,z,x \ y),x,y). L(T(x,y) \ z,x,y) = y \ ((y \ x) \ z). x \ ((x \ y) \ z) = (y * x) \ (x * z). (x * y) \ (y * z) = y \ ((y \ x) \ z). (x * y) \ (y * z) = y \ ((x \ y) * z). (x * (y * x)) \ ((x * y) * z) = L(x \ z,x,y). L(x * ((y * x) \ z),y,x) = y \ z. L(x \ y,x,z) = x \ (z \ (x \ ((x * z) * y))). x \ (y \ (x \ ((x * y) * z))) = L(x \ z,x,y). x \ (y \ ((y / x) * (x * z))) = L(x \ z,x,y). x \ L(y,x,z) = L(x \ y,x,z). L(x \ y,x,z) = x \ L(y,x,z). L(x,y,z) = y \ L(y * x,y,z). x \ L(x * y,x,z) = L(y,x,z). x * L(x \ y,x,z) = L(y,x,z). x * L(y,x,z) = L(x * y,x,z). L(x * y,x,z) = x * L(y,x,z). T(L(x * y,x,z),x) = L(y,x,z) * x. (x * y) * (y \ (x \ z)) = L(z,x * y,y). L(x,y,z) / y = L(x / y,y,z). L(x / y,y,z) = L(x,y,z) / y. L(x * y,x,z) != x * u | L(y,x,z) = u. (x * L(y * z,y,x)) \ (x * (y * z)) = a(x,y,L(z,y,x)). L(x / (y \ 1),y \ 1,z) = L(x,z,y) / (y \ 1). L(T(x * y,x),x,z) = L(y,x,z) * x. L(x * y,y,z) = L(x,y,z) * y. L(x,y * z,z) = z * ((z \ y) * (y \ x)). x * ((x \ y) * (y \ z)) = L(z,y * x,x). x * ((x \ y) * (y \ z)) = L(z,y,x). L(x,y,z) = z * ((z \ y) * (y \ x)). R(x,x \ y,z) = L(x,y,z). L(x,y,z) = R(x,x \ y,z). R(x,y / x,z) = L(x,y,z). L(x,y,z) = R(x,y / x,z). L(x,y * x,z) = R(x,T(y,x),z). R(x,T(y,x),z) = L(x,y * x,z). L(x,y * x,z) = R(x,y,z). R(x,y,z) = L(x,y * x,z). L(x \ y,y,z) = R(x \ y,x,z). R(x \ y,x,z) = L(x \ y,y,z). R(x,y \ (z \ 1),u) = L(x,(z * y) \ x,u). R(x,y,z) = R(x,T(y,x),z). R(x,T(y,x),z) = R(x,y,z). R(x \ 1,x * y,z) = R(x \ 1,y * x,z). R(x \ 1,y * x,z) = R(x \ 1,x * y,z). R(x \ 1,y * x,z) = L((y * x) \ y,y,z). R(x,x \ (y \ 1),z) = L(x,x \ (y \ x),z). R(x \ 1,y * x,z) = R(x,y,z) \ 1. R(x \ 1,y,z) = R(x,y / x,z) \ 1. R(x,y / x,z) \ 1 = R(x \ 1,y,z). L(x,y,z) \ 1 = R(x \ 1,y,z). R(x \ 1,y,z) = L(x,y,z) \ 1. R(x \ 1,y,z) \ u = L(x,y,z) * u. L((x * y) \ x,x,z) = R(y,x,z) \ 1. L(x \ 1,y,z) = R(x,y,z) \ 1. L(x,y \ 1,z) = L(x,x \ (y \ x),z). L(x,x \ (y \ x),z) = L(x,y \ 1,z). L(x,x \ (y \ x),z) = L(x,z,y). R(x,y,z) \ z = (x \ 1) * L(z,y,x * y). R(x,y,z) \ z = (x \ 1) * L(z,y,x). R(x,y,z) \ z = x \ L(z,y,x). L(x \ y,z,x) = R(x,z,y) \ y. (R(x,y,z) \ 1) * z = L(x \ z,y,x). L(x \ y,z,x) = (R(x,z,y) \ 1) * y. R(x \ 1,y,z) \ z = L((x \ 1) \ z,x,y). L((x \ 1) \ y,x,z) = R(x \ 1,z,y) \ y. L(x \ y,z,x) = L(x \ 1,z,y) * y. L((x \ 1) \ y,x,z) = L(x,z,y) * y. (x * y) \ L(z,x,y) = L((x * y) \ z,x,y). L((x * y) \ z,x,y) = (x * y) \ L(z,x,y). (x * y) \ L(z,x,y) = y \ (x \ z). L(x / (y \ 1),y \ 1,z) = L(x,z,y) * y. L(x * y,y \ 1,z) = 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,x) = L((x \ 1) * y,z,y). L((x \ 1) \ y,x,z) = L(x * y,z,y). L(x \ y,z,x) = L(x \ y,z,y). L(x \ y,z,y) = L(x \ y,z,x). L(L(x \ y,z,y),x,z) = x \ y. L(x \ y,z \ y,x) = L(x \ y,y,z). L(x \ y,z,y) = x \ L(y,z,x). L(x \ y,y,z) = L(x \ y,x,z). x * L(x \ y,z,y) = L(y,z,x). L(x \ y,z * y,y) = x \ R(y,z,x). L(x \ (y \ z),y \ z,y) = (y * x) \ z. x * L(x \ y,y,z) = L(y,x,z). L(x * y,x,z) = L(x * y,z,y). L(x * y,z,y) = L(x * y,x,z). L((x * y) * z,x,z) = x * (y * z). x \ L(x * y,z,y) = L(y,x,z). (x / y) \ L(x,z,y) = L(y,x / y,z). L(x * y,z,y) = z * ((z \ x) * y). x * (y * z) = L(x * y,x,z) * z. L(x * y,x,z) * z = x * (y * z). L(x,y,z) = y * ((y \ (x / z)) * z). (x * y) * (y \ z) = L(x * z,y,z). L(x * y,z,y) = (x * z) * (z \ y). (x \ y) * (x * ((x \ z) * y)) = x \ (y * (z * y)). ((x * y) * z) * y = x * ((y * z) * y). x * y != L(z,x,u) | y = L(x \ z,z,u). (x \ (y / z)) * z = L(x \ y,y,z). L(x \ y,y,z) = (x \ (y / z)) * z. L((x / y) * z,y,z) = x * (y \ z). L(x * (y \ z),z,y) = (x / y) * z. x \ R(y,z,x) = L(x \ y,z,y). L(x \ y,z,y) = x \ R(y,z,x). x * L(x \ y,z,y) = R(y,z,x). R(x,y,z) = z * L(z \ x,y,x). R(x,y,z) = L(x,y,z). L(x,y,z) * (y * z) = (x * y) * z. L((x / y) / z,z,y) = x / (z * y). ((x * (y / z)) * z) / y = L(x,y / z,z). L((x * y) / z,z,x) = x * (y / z). L(x / y,y,z) = z * ((z \ x) / y). L(x,y,(x * y) * z) = R(x,y,z). R(x,y,z) = L(x,y,(x * y) * z). L(x * y,x,z) \ z = y \ (x \ z). L(x,y,z) = L(x,x \ y,z). L(x,x \ y,z) = L(x,y,z). R(x,y,z) = R(x,x \ y,z). R(x,x \ y,z) = R(x,y,z). L(x,y,z) = L(x,y / x,z). L(x,y / x,z) = L(x,y,z). L(x,y,z) = L(x,y * x,z). L(x,y * x,z) = L(x,y,z). R(x,y,z) = R(x,y * x,z). R(x,y * x,z) = R(x,y,z). L(x \ 1,y,z) = L(x,y,z) \ 1. L(x \ 1,y,z) \ u = L(x,y,z) * u. L(x \ y,z,x) = L(x,z,y) \ y. R((x / y) * z,y,z) = x * (y \ z). R(x \ y,z,y) = x \ R(y,z,x). L(x,y,z) = L(x,x * y,z). L(x,x * y,z) = L(x,y,z). L(T(x,y),x \ z,u) = T(L(x,z,u),y). L(x / y,y,z) = L(x / y,x,z). L(x,T(x,y) \ z,u) = L(x,K(y,x) * z,u). L(L(L(x,y,z),u,w),z,y) = L(x,L(x,y,z) \ u,w). L(x,y \ x,z) = L(x,z,y). R(x,y,y \ z) = R(x,x \ y,z). R(x,x \ y,z) = R(x,y,y \ z). L(L(x,y,z),u,w) = L(L(x,u,w),y / x,z). L(L(x,y,z),u / x,w) = L(L(x,u,w),y,z). L(x,y,z) = ((x / y) / z) * (z * y). L(L(x,y,z),z,y / x) = x. L(K(x,y),z * y,u) = L(K(x,y),z * T(y,x),u). L(K(x,y),z * T(y,x),u) = L(K(x,y),z * y,u). L(x * y,y,z) = L(x * y,z,x). L(x * y,z,x) = L(x * y,y,z). L(L(x,y,z),u,w) = L(L(x,u,w),z \ x,y). L(L(x,y,z),u \ x,w) = L(L(x,w,u),y,z). L(x,y,z) = L(x,z,x / y). L(x,y,x / z) = L(x,z,y). L(x,y,(x * y) * z) = L(x,y,z). x * L(x \ 1,y,z) = L(x,y,z) \ x. L(x \ 1,y,z) * u = L(x,y,z) \ u. x * L(y \ 1,z,u) = x / L(y,z,u). K(x,L(y \ 1,z,u)) = K(L(y,z,u),x). L(x \ y,z \ y,x) = L(x,y,z) \ y. L(x \ y,z,y) = L(x,z,y) \ y. R(x,y,y \ z) = R(x,y,z). R(x,y,z) = R(x,y,y * z). R(x,y,y * z) = R(x,y,z). (x * y) \ R(z / x,x,y) = ((x * y) \ z) / x. R(x,y * x,z) = R(x,y,(y * x) * z). R(x,y,(y * x) * z) = R(x,y * x,z). L(L(x * y,z,x),z,y) = x * y. L(x * y,y \ z,x) = L(x * y,y,z). L((x \ y) * z,z,y) = L((x \ y) * z,x,y). x * (y * L(z * x,y,z)) = (x * y) * (z * x). x \ L(x * y,y,z) = L(y,z,x). L(x * (y * z),y,z) = (x * y) * z. x \ L(x * (y \ z),y \ z,z) = (y \ (z / x)) * x. (x * y) * z != u * (y * z) | L(x,y,z) = u. T((x * y) * z,L(x,y,z)) = (y * z) * L(x,y,z). ((x * y) * z) * ((y * z) \ u) = (y * z) * (((y * z) \ L(x,y,z)) * u). (x * y) * (((x * y) \ L(z,x,y)) * u) = ((z * x) * y) * ((x * y) \ u). L(x * (y / z),x,z) = (x * y) / z. x * ((x \ y) / z) = L(y / z,y,x). L(x / y,x,z) = z * ((z \ x) / y). L((x * y) \ z,x,z) = y \ (x \ z). x * (y * ((z * x) * y)) = (x * y) * (z * (x * y)). (x * y) * (z * (x * y)) = x * (y * ((z * x) * y)). ((x * y) * z) / x = x * (y * (z / x)). L(L(x / y,x,z) * u,z,u) = z * (((z \ x) / y) * u). L(((x * y) \ z) * x,x,z) = (y \ (x \ z)) * x. L(L(x / y,y,z) \ u,z,u) = ((z \ x) / y) \ (z \ u). L(x,y / x,z) = (x / y) * L(y,z,x). (x / y) * L(y,z,x) = L(x,y / x,z). x * L(y \ 1,z,u) != y * (w * L(y \ 1,z,u)) | x = y * w. (x * L(x \ 1,y,z)) * u = x * (L(x \ 1,y,z) * u). ((x * y) * z) * y = x * (y * (z * y)). L(x / y,z,u) \ w = L(y / x,z,u) * w. L(T(x,y),z,u) = L(T(x,y),x \ z,u). L(T(x,y),x \ z,u) = L(T(x,y),z,u). L(x,y,z) \ y = L(x \ y,y,z). L(x \ y,y,z) = L(x,y,z) \ y. L(x \ (y \ z),y \ z,y) = L(x,z,y) \ (y \ z). L(x,y,L(z \ y,y,u)) = L(x,L(z,y,u),y). R(x,y,(y * x) * z) = R(x,y,z). R(x,y,z) = L(x,y,(y * x) * z). L(x,y,(y * x) * z) = L(x,y,z). L(x * y,y,z) = (x / (y \ z)) * T(z,y). (x / (y \ z)) * T(z,y) = L(x * y,y,z). (x / y) * L(y,z,x) = L(x,y,z). (x / y) * L(y,x,z) = L(x,z,y). L(x,y,z) = x * (y \ L(y,z,x)). x * (y \ L(y,z,x)) = L(x,y,z). (x / L(y,z,u)) * L(y,z,u) = L(x,T(y,w),L(y,z,u)). L(x,T(y,z),L(y,u,w)) = (x / L(y,u,w)) * L(y,u,w). (x / y) * y = L(x,L(y,z,u),y). L(x,L(y,z,u),y) = (x / y) * y. L(x,y,z) = x * (z \ L(z,x,y)). x * (y \ L(y,x,z)) = L(x,z,y). x \ L(x,y,z) = y \ L(y,z,x). x \ L(x,y,z) = z \ L(z,x,y). L(x,L(y,z,u),y) = x. x = L(x,y,L(y \ 1,z,u)). L(x,y,L(y \ 1,z,u)) = x. (L(x,y,z) \ x) * u = L(x,y,z) \ (x * u). L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. x * y != L(x * ((z * x) \ u),z,x) | y = x \ (z \ u). (x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u). L(x,y,z) / (z \ L(z,x,y)) = x. K(L(x,y,z),x) = K(z \ L(z,x,y),x). K(x \ L(x,y,z),y) = K(L(y,z,x),y). x * (((y * x) * z) \ L((y * x) * z,x,y)) = L(x,y,z). x = L(x,y,z) * (L(z,x,y) \ z). L(x,y,z) * (L(z,x,y) \ z) = x. x != L(x,y,z) * u | L(z,x,y) \ z = u. L(x,y,z) * u != x | L(z,x,y) \ z = u. (x * y) * z = (x / z) * (z * (y * z)). (x / y) * (y * (z * y)) = (x * z) * y. ((x \ y) * z) * y = (x \ 1) * (y * (z * y)). (x \ 1) * (y * (z * y)) = ((x \ y) * z) * y. ((x / y) * z) * (y \ 1) = x * ((y \ 1) * (z * (y \ 1))). x * ((y \ 1) * (z * (y \ 1))) = ((x / y) * z) * (y \ 1). L(x,T(x,y) \ z,u) = L(T(T(x,y),y \ x),z,u). L(T(T(x,y),y \ x),z,u) = L(x,T(x,y) \ z,u). K(x \ L(x,y,z),y) = 1. 1 = K(x,L(y,x,z) \ y). K(x,L(y,x,z) \ y) = 1. (x / y) * (y * z) = (x * (z / y)) * y. (x * (y / z)) * z = (x / z) * (z * y). ((x * (y / z)) * z) / y = L(x,z \ y,z). (x * (y \ z)) * T(y,z) = L(x * z,z,y). x \ L(y * z,z,x) = T(y * (z / x),x). L(x \ (y * z),z,x) = T(y * (z / x),x). T(x * (y / z),z) = (z \ y) * T(x,y). L((x \ y) * z,z,y) = x \ (y * z). ((x \ y) * z) * y = x \ (y * (z * y)). x \ (y * (z * y)) = ((x \ y) * z) * y. L(x * (y * x),z,u) = u * (z * ((((u * z) \ x) * y) * x)). x * (y * ((((x * y) \ z) * u) * z)) = L(z * (u * z),y,x). (x * y) \ L(z / x,x,y) = ((x * y) \ z) / x. x * ((y * z) * x) = (x * y) * (z * x). (x * y) * (z * x) = x * ((y * z) * x). x * (y * z) = z * (((z \ x) * y) * z). x * (((x \ y) * z) * x) = y * (z * x). (x \ (y \ z)) * y = (y * x) \ (z * y). (x * y) \ (z * x) = (y \ (x \ z)) * x. (x * y) \ (z * x) != u * x | y \ (x \ z) = u. ((x * y) \ z) / x = y \ (x \ (z / x)). (x \ ((y \ x) * z)) / y = x \ (y \ ((x * z) / y)). (x \ y) * (x * ((x \ z) * y)) = ((x \ y) * z) * y. T((x * y) * z,L(x,y,z)) = z * (T(y,z) * x). L(x,y,z) * (u * (z * (y * ((z * y) \ x)))) = z * ((y * ((z * y) \ x)) * ((u * z) * (y * ((z * y) \ x)))). x * ((y * ((x * y) \ z)) * ((u * x) * (y * ((x * y) \ z)))) = L(z,y,x) * (u * (x * (y * ((x * y) \ z)))). L(x,y,z) \ (z \ y) = (z * x) \ y. L(T(T(x,y),y \ x),z,u) = L(x,K(y,x) * z,u). ((x * y) \ z) * ((x * y) * ((y \ (x \ u)) * z)) = (((x * y) \ z) * L(u,x,y)) * z. L(x,y,z) = L(x,K(u,x) * y,z). L(x,K(y,x) * z,u) = L(x,z,u). L(x,K(y,x) / z,u) = L(x,z \ 1,u). L(x,K(y,x) / z,u) = L(x,u,z). L(x,y,(K(z,x) / u) \ y) = L(x,y,u). L(x,y,(z / K(u,x)) * y) = L(x,y,z). L(x,y,(z * K(x,u)) * y) = L(x,y,z). L(x,y,z) = L(x,y,z * K(x,u)). L(x,y,z * K(x,u)) = L(x,y,z). L(x \ y,z,u) = L(z \ (u * ((x * (z \ u)) \ y)),x,z \ u). L(x \ (y * ((z * (x \ y)) \ u)),z,x \ y) = L(z \ u,x,y). L(x \ y,z * z,x) = ((x \ z) * z) * (z \ (z \ y)). L(x,L(x,y,z) \ u,w) = L(x,u,w). L(x,y,z) = L(x,L(x,u,w) * y,z). L(x,L(x,y,z) * u,w) = L(x,u,w). L(x,(y * x) \ z,u) = L(x,y \ z,u). x \ L(x * (y \ z),z,y) = (y \ (z / x)) * x. x \ ((x / y) * z) = (y \ (z / x)) * x. L(x \ y,z * z,x) = z * ((z \ (x \ z)) * (z \ y)). L(x \ y,z * z,x) = z * (T(x,z) \ (z \ y)). L(x,y * y,z) = y * (T(z,y) \ (y \ (z * x))). x * (T(y,x) \ (x \ (y * z))) = L(z,x * x,y). (x \ 1) * (y \ ((x \ 1) \ (T(y,x) * z))) = L(z,(x \ 1) * (x \ 1),T(y,x)). L(L(x / y,x,z) * u,z,u) = ((z \ y) / x) \ (z \ u). (L(x,y,z) \ x) * u = x * (L(x \ 1,y,z) * u). x * (L(x \ 1,y,z) * u) = (L(x,y,z) \ x) * 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). L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u). L(x,y,z) \ u = x * (L(x,y,z) \ (x \ u)). x * (L(x,y,z) \ (x \ u)) = L(x,y,z) \ u. x \ (L(x,y,z) \ u) = L(x,y,z) \ (x \ u). L(x,y,z) \ (x \ u) = x \ (L(x,y,z) \ u). L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u. L(x,y,z) * (x \ u) = x \ (L(x,y,z) * u). x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u). x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. L(x,T(y,z),L(y,u,w)) = x. L(x,T(L(y,z,u),w),y) = x. L(x,L(T(y,z),u,w),y) = x. (x * y) / L(T(x,z),u,w) = x * (y / L(T(x,z),u,w)). (x * L(x \ 1,y,z)) \ u = L(x,y,z) * (x \ u). (x / L(x,y,z)) \ u = L(x,y,z) * (x \ u). x * (((y * x) * z) \ (y * (x * z))) = L(x,y,z). L(x,y,z) = x * (((y * x) * z) \ (y * (x * z))). L(x,y,z) = x * (a(y,x,z) \ 1). x \ L(x,y,z) = a(y,x,z) \ 1. a(x,y,z) \ 1 = y \ L(y,x,z). L(x,y,z) = x / a(y,x,z). L(x,y,z) * a(y,x,z) = x. L(x,y,z) \ x = a(y,x,z). a(x,y,z) = L(y,x,z) \ y. L(x,y,L(x,z,u)) = L(x,a(z,x,u),y). L(x,a(y,x,z),u) = L(x,u,L(x,y,z)). L(x,y,z) \ x = a(z,y,x). a(x,y,z) = L(z,y,x) \ z. a(x,y,z) * L(y,x,z) = y. x / L(x,y,z) = a(y,x,z). a(x,y,z) = y / L(y,x,z). K(x,a(x,y,z)) = 1. T(x,a(x,y,z)) = x. 1 * K(a(x,y,z),x) = 1. a(x,y,z) * x = x * a(x,y,z). 1 = K(a(x,y,z),x). K(a(x,y,z),x) = 1. K(a(x,y,z),u) = K(u,z \ L(z,y,x)). K(x,y \ L(y,z,u)) = K(a(u,z,y),x). a(x,y,z) = a(z,x,y). a(x,y,z) = L(x,z,y) \ x. K(a(x,y,z),z) = 1. T(a(x,y,z),z) = a(x,y,z). (x * y) / L(L(y,z,u),a(z,y,u),x) = x * a(z,y,u). a(x,y,z) = x / L(x,z,y). a(x,y,z \ 1) = L(x,y,z) \ x. a(x,y,z) * u = x * (L(x,z,y) \ u). x * (L(x,y,z) \ u) = a(x,z,y) * u. T(a(x,y,z) * (z / u),u) = (u \ z) * a(x,y,z). a(x,y,z) \ u = L(x,z,y) * (x \ u). L(x,y,z) * (x \ u) = a(x,z,y) \ u. a(x,y,z) = a(z,y,x \ 1). a(x,y,z \ 1) = a(z,y,x). a(x,y,K(z,u)) = a(K(u,z),y,x). a(K(x,y),z,u) = a(u,z,K(y,x)). a(x,y \ 1,z) = a(y,x,z). a(x,T(y \ 1,z),u) = a(T(y,z),x,u). a(x,y,K(z,u)) = a(x,K(u,z),y). a(x,K(y,z),u) = a(x,u,K(z,y)). L(x,a(y,x,z),u) = x. L(x,a(x,y,z),u) = x. L(x,y,z) = L(L(x,y,z),a(x,u,w),v5). L(L(x,y,z),a(x,u,w),v5) = L(x,y,z). (x * a(y,z,u)) * y = x * (a(y,z,u) * y). L(x,y,a(x,z,u)) = x. a(x,y,z) * (u * x) = (a(x,y,z) * u) * x. (a(x,y,z) * u) * x = a(x,y,z) * (u * x). L(x,y,a(y * x,z,u)) = x. L(x,y / x,a(y,z,u)) = x. x = L(x,y,a(y,z,u)). L(x,y,a(y,z,u)) = x. x * (y * a(y,z,u)) = (x * y) * a(y,z,u). (x * y) * a(y,z,u) = x * (y * a(y,z,u)). L(x,y,a(z,u,y)) = x. (a(x,y,z) / u) * u = L(a(x,y,z),u,z). L(a(x,y,z),u,z) = (a(x,y,z) / u) * u. x \ (a(x,y,z) * u) = L(x,z,y) \ u. T(a(x,y,z) * u,x) = (L(x,z,y) \ u) * x. a(x,y,T(z,u)) = a(x,T(z \ 1,u),y). a(x,T(y \ 1,z),u) = a(x,u,T(y,z)). x \ y = L(x,z,y) \ L(y,x,z). L(x,y,z) \ L(z,x,y) = x \ z. L(x,x \ y,z) = L(x,L(y,x,u),z). L(x,L(y,x,z),u) = L(x,x \ y,u). L(x,L(y,x,z),u) = L(x,y,u). L(x,y,z) = L(x,L(y,u,x),z). L(x,L(y,z,x),u) = L(x,y,u). L(x,y,z \ 1) = L(x,z,L(y,x,u)). L(x,y,L(z,x,u)) = L(x,z,y \ 1). x * L(x \ y,z,y) = L(y,L(z,x \ y,u),x). L(x,L(y,z \ x,u),z) = z * L(z \ x,y,x). L(x,(x * y) / z,u) = L(x,x * (y / z),u). L(x,y,L(z,x,u)) = L(x,y,z). a(x,y \ (z \ y),u) = a(x,u,T(z,y)). L(a(x,y,z),u,z) = a(x,y,z). L(a(x,y,z),u,x) = a(x,y,z). L(a(x,y,z),x,u) = a(x,y,z). L(x,(x * y) / z,u) = L(x,y / z,u). L(x,L(y,z \ x,u),z) = L(x,y,z). L(x,y,x / z) = L(x,z,L(y,(x / z) \ x,u)). L(x,y,L(z,(x / y) \ x,u)) = L(x,z,x / y). L(x,y,L(z,(x / y) \ x,u)) = L(x,y,z). L(x,y,L(z,y,u)) = L(x,y,z). L(x,y,z \ y) = L(x,L(z,y,u),y). L(x,L(y,z,u),z) = L(x,z,y \ z). L(x,L(y,z,u),z) = L(x,y,z). L(x,y,z) = L(x,L(y,u,z),z). L(x,L(y,z,u),u) = L(x,y,u). L(x,L(y,z,u),u / z) = L(x,y,u / z). x * ((y \ 1) * (z * (y \ 1))) = ((x / y) * z) / y. x * ((y \ 1) * (z / y)) = ((x / y) * z) / y. x * (y \ (z / y)) = ((x / y) * z) / y. ((x / y) * z) / y = x * (y \ (z / y)). (((((x / y) \ y) * z) / y) * x) / y = T(z,y \ (x / y)). ((x \ y) / z) \ (x \ u) = x * (((x \ z) / y) * u). x * (((x \ y) / z) * u) = (y / (x \ z)) * (x \ u). (x / (y \ z)) * (y \ u) = y * (((y \ x) / z) * u). (x * (y \ z)) * (z \ u) = z * (((z \ x) / y) * u). x \ (y * (((y \ x) / z) * u)) = ((z \ y) / x) * (x * (y \ u)). (x * y) / L(L(y,z,u),a(y,u,z),x) = x * a(z,y,u). ((((x * (y \ x)) * z) / x) * y) / x = T(z,x \ (y / x)). (x * y) / L(y,z,u) = x * a(z,y,u). (x * y) / L(y,z,u) = x * a(y,u,z). x / L(y,z,u) = (x / y) * a(y,u,z). (x / y) * a(y,z,u) = x / L(y,u,z). (x * y) / L(T(x,y),z,u) = y * a(T(x,y),u,z). (x / y) * (y / L(x,z,u)) = a(x,u,z). (x / y) * (y / L(x,z,u)) = a(x,u * K(x,w),z). a(x,y * K(x,z),u) = (x / w) * (w / L(x,u,y)). (x / y) * (y / L(x,z,u)) = a(x,u,L(x,w,v5) * z). a(x,y,L(x,z,u) * w) = (x / v5) * (v5 / L(x,w,y)). (x / y) * (y / L(x,z,u)) = a(x,u,L(z,w,x)). a(x,y,L(z,u,x)) = (x / w) * (w / L(x,z,y)). (x / y) * (y / L(x,z,u)) = a(x,L(u,x,w),z). a(x,L(y,x,z),u) = (x / w) * (w / L(x,u,y)). a(x,y,L(z,u,x)) = a(x,y,z). a(x,L(y,x,z),u) = a(x,y,u). x * a(T(y,x),z,u) = y * (x / L(T(y,x),u,z)). x * (y / L(T(x,y),z,u)) = y * a(T(x,y),u,z). a(x,y * K(x,z),u) = a(x,y,u). a(x,x \ y,z) = a(x,y / x,z). a(x,y / x,z) = a(x,x \ y,z). x * (L(x,y,z) \ u) = u * a(T(x,u),z,y). x * a(T(y,x),z,u) = y * (L(y,u,z) \ x). x * a(T(y,x),z,u) = a(y,z,u) * x. x * a(y,T(z,x),u) = a(z,u,y) * x. T(a(x,y,z),u) = a(z,T(x,u),y). a(x,T(y,z),u) = T(a(y,u,x),z). a(x,T(y,z),u) = T(a(x,y,u),z). a(x,y \ (z \ y),u) = T(a(x,z \ 1,u),y). T(a(x,y \ 1,z),u) = a(x,u \ (y \ u),z). a(x,T(y,z),z) = a(x,y,z). a(x,y \ z,y) = a(x,z / y,y). a(x,y / z,z) = a(x,z \ y,z). T(a(x,y,z),u) = a(y,u \ (x \ u),z). a(x,y \ (z \ y),u) = T(a(z,x,u),y). a(x,y \ (z \ y),u) = T(a(x,u,z),y). T(a(x,y,z),u) = a(x,y,T(z,u)). a(x,y,T(z,u)) = T(a(x,y,z),u). a(x,T(y,z),u) = a(x,y,T(u,z)). a(x,y,L(x,z,u) * w) = a(x,y,w). a(x,y,x * z) = a(x,y,z). ((x * ((y \ x) * (z / x))) * y) / x = T(z,x \ (y / x)). T(x,y \ (z / y)) = y * (((z \ y) * (x / y)) * (z / y)). x * (((y \ x) * (z / x)) * (y / x)) = T(z,x \ (y / x)). L(x * (y * z),y,x) \ (x * (y * z)) = a(x,y,L(z,y,x)). L(x * (y * z),y,x) \ (x * (y * z)) = a(x,y,z). a(x,y,z) = L(x * (y * z),y,x) \ (x * (y * z)). T(x * (y * z),a(x,y,z)) = x * (y * z). a(x,y,x * (y * z)) = a(x,y,z). a(x,y,z) = a(x,y,y * 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). (x * y) \ (z * ((z \ x) * y)) = a(x,z,y). a(x,y,z) = (x * z) \ (y * ((y \ x) * z)). ((x * y) * z) / (x * (y * z)) = a(x,y,z). a(x,y,z) = ((x * y) * z) / (x * (y * z)). a(x,y / z,z) = ((x * (y / z)) * z) / (x * y). ((x * (y / z)) * z) / (x * y) = a(x,y / z,z). ((x * (y / z)) * z) / (x * y) = a(x,z \ y,z). L((((x * (y / z)) * z) / y) / x,x,y) = a(x,z \ y,z). L(L(x,y \ z,y) / x,x,z) = a(x,y \ z,y). L(x \ L(x,y \ z,y),x,z) = a(x,y \ z,y). L(x \ L(x,y,z),x,z * y) = a(x,z \ (z * y),z). L(x \ L(x,y,z),x,z * y) = a(x,y,z). a(x,y,z) = L(x \ L(x,y,z),x,z * y). a(x,y,z) = x \ L(x,y,z). x * a(x,y,z) = L(x,y,z). L(x,y,z) = x * a(x,y,z). (x / y) * L(y,z,u) = x * a(y,z,u). x * a(y,z,x) = L(x,y,z). L(x,y,z) = x * a(y,z,x). x \ L(x,y,z) = a(z,x,y). a(x,y,z) = y \ L(y,z,x). a(x,y,z) * x = L(x,y,z). L(x,y,z) = a(x,y,z) * x. (x * y) * a(y,z,u) = x * L(y,z,u). L(x,T(y,z),u) = x * a(x,y,T(u,z)). x * a(x,y,T(z,u)) = L(x,T(y,u),z). K(x,y) * L(K(y,x),z,u) = a(z,u,K(y,x)). a(x,y,z) \ 1 = a(z,y,x). K(x,a(y,z,u)) = K(a(y,u,z),x). K(a(x,y,z),u) = K(u,a(x,z,y)). L(x,y,z) = a(z,x,y) * x. L(x,y,z) = a(y,z,x) * x. (x * a(y,z,u)) * y = x * L(y,z,u). a(x,y,z) * u = a(z,y,x) \ u. a(x,y,z) \ u = a(z,y,x) * u. x / a(y,z,u) = x * a(u,z,y). L(L(x,y,z),u,y) = a(y,x,u) * L(x,y,z). a(x,y,z) * L(y,x,u) = L(L(y,x,u),z,x). L(x,y,z * K(y,u)) = a(y,z,x) * x. a(x,y,z) \ u = a(x,z,y) * u. x / a(y,z,u) = x * a(y,u,z). T(x,a(y,z,u)) = (a(y,u,z) * x) * a(y,z,u). (a(x,y,z) * u) * a(x,z,y) = T(u,a(x,z,y)). a(x,x * y,z) * 1 = a(x * z,x,y). L(x,y,z) * (x \ u) = a(x,y,z) * u. T(x * a(y,z,u),a(y,u,z)) = a(y,u,z) \ x. (x \ (y / x)) * L(x,z,u) = (x \ y) * a(x,z,u). (x * (y / z)) * L(L(z,u,w),y / z,x) = x * (y * a(z,u,w)). T(x,L(y,z,u)) = ((L(y,z,u) \ x) * y) * a(y,z,u). ((L(x,y,z) \ u) * x) * a(x,y,z) = T(u,L(x,y,z)). L(x,y,T(z,u)) = L(x,T(y,u),z). L(x,T(y,z),u) = L(x,y,T(u,z)). T(x * a(y,z,u),y) = y \ (x * L(y,z,u)). x \ (y * L(x,z,u)) = T(y * a(x,z,u),x). L(x,y,z) = L(x,y,z * K(y,u)). L(x,y,z * K(y,u)) = L(x,y,z). L(x,y,z \ u) = L(x,y,z \ T(u,y)). L(x,y,z \ T(u,y)) = L(x,y,z \ u). a(x,x * y,z) = a(x * z,x,y). a(x * y,x,z) = a(x,x * z,y). a(x,y,x * z) = a(x,x * y,z). a(x,x * y,z) = a(x,y,x * z). a(x,x * y,z) = a(x,y,z). a(x,y,z) = a(x,x \ y,z). a(x,x \ y,z) = a(x,y,z). a(x,y / x,z) = a(x,y,z). x \ (L(x,y,z) * u) = a(x,y,z) * u. x * (a(x,y,z) * u) = L(x,y,z) * u. x \ (y \ L(y * x,z,u)) = a(y * x,z,u). T(x * a(y,z,u),y) = (y \ x) * L(y,z,u). a(x,y,z * u) = u \ (z \ L(z * u,x,y)). x \ (y \ L(y * x,z,u)) = a(z,u,y * x). (x * y) \ (((z / y) / x) \ L(L(z,y,x),u,w)) = a(u,w,((z / y) / x) * (x * y)). T(x * a(y,z,u),a(y,u,z)) = a(y,z,u) * x. T((x / y) * a(y,z,u),y) = (y \ x) * a(y,z,u). T(x / L(y,z,u),y) = (y \ x) * a(y,u,z). T((x * y) / L(y,z,u),y) = T(x,y) * a(y,u,z). T(x * a(y,z,u),y) = T(x,y) * a(y,z,u). T(a(x,y,z) * u,x) * a(x,z,y) = T(u,L(x,z,y)). T((a(x,y,z) * u) * a(x,z,y),x) = T(u,L(x,z,y)). T(T(x,a(y,z,u)),y) = T(x,L(y,z,u)). T(x,L(y,z,u)) = T(T(x,y),a(y,z,u)). T(T(x,y),a(y,z,u)) = T(x,L(y,z,u)). K(a(x,y,z),T(u,x)) = T(u,L(x,y,z)) \ T(u,x). T(x,L(y,z,u)) \ T(x,y) = K(a(y,z,u),T(x,y)). K(a(x,y,z),T(u,x)) = K(u,x) * K(L(x,y,z),u). K(x,y) * K(L(y,z,u),x) = K(a(y,z,u),T(x,y)). L(L(x,y,z),z * y,z) = L(x,y,z * z). L(x,y,z * z) = L(L(x,y,z),y,z). L(L(x,y,z),y,z) = L(x,y,z * z). ((x * y) * L(T(z,u),y,x)) \ (x * (y * z)) = K(u,L(z,y,x)). K(x,T(y,z)) \ K(x,y) = K(T(y,x) \ z,z \ y). K(T(x,y) \ z,z \ x) = K(y,T(x,z)) \ K(y,x). K(T(x,y) \ z,z \ x) = K(T(x,z),y) * K(y,x). K(T(x,y) \ z,z \ x) = K(x,T(y,z)) * K(y,x). K(T(x,y) \ z,z \ x) = K(z,K(y,x)). K(x,K(y,z)) = K(K(y,z),x \ z). K(K(x,y),z \ y) = K(z,K(x,y)). K(x,K(y,z)) = K(y,K(z,x \ z)). K(x,K(y,z \ y)) = K(z,K(x,y)). K(x,K(y,z)) = K(y,K(x,z)). K(x,K(y,z)) = K(z,K(x,y)). K(x,K(y,z)) = K(x,K(z,y)). K(x,y) * K(x,K(y,z)) = K(x,T(y,z \ 1)). K(x,T(y,z \ 1)) = K(x,T(y,z)). K(x,T(y,z \ y)) = K(x,T(y,z)). K(x,T(y,z \ (u \ 1))) = K(x,T(y,u * z)). K(x,T(y,z)) = K(y,x \ K(x,z)). K(x,y \ K(y,z)) = K(y,T(x,z)). K(x,T(T(T(y,z \ y),u),z \ T(T(y,z \ y),u))) = K(x,T(y,u)). K(x,a(y,z,u) \ 1) = K(a(y,z,u),T(x,y)). K(a(x,y,z),T(u,x)) = K(u,a(x,y,z) \ 1). K(x,T(y,z \ (u / w))) = K(x,T(y,(w / u) * z)). K(a(x,y,z),T(u,x)) = K(u,a(x,z,y) * 1). K(a(x,y,z),T(u,x)) = K(u,a(x,z,y)). K(x * y,x) * ((x \ (y \ 1)) * z) = (y \ (x \ 1)) * z. K(x,y) * ((y \ (x \ 1)) * z) = (x \ (y \ 1)) * z. K(x,y) * ((x * y) \ z) = (x \ (y \ 1)) * z. K(x,y) * ((x * y) \ z) = (y * x) \ z. L(x,(x * y) \ z,u) = L(x,(y * x) \ z,u). L(x,(y * x) \ z,u) = L(x,(x * y) \ z,u). L(x,(x * y) \ z,u) = L(x,y \ z,u). ((x * y) \ (z \ 1)) * (z / (x \ (y \ 1))) = K(x,y \ (x \ 1)). x \ (y * (z * ((z \ (y \ x)) * u))) = L(L(u,z,x \ y),x,y). L(x \ (y * (((y \ x) / z) * u)),z,x \ y) = L(z \ u,x,y). ((x \ y) * z) \ (y * (((y \ ((x \ y) * z)) / x) * u)) = (z \ K(z,x \ y)) * (((x \ y) * z) * (y \ u)). (x * (y * T(z,u))) \ (x * (y * z)) = K(u,L(z,y,x)). ((x * y) \ (z \ 1)) * (z * ((y \ 1) \ x)) = K(x,y \ (x \ 1)). L(((x \ y) / z) * (z * (y \ u)),x,z \ y) = L(x \ u,z,y). ((x * y) \ (z \ 1)) * (z * (y * x)) = K(x,y \ (x \ 1)). K(x,y \ (x \ 1)) = (z * (x * y)) \ (z * (y * x)). (x * (y * z)) \ (x * (z * y)) = K(y,z \ (y \ 1)). K(x,y \ (x \ 1)) = L(K(y,x),x * y,z). L(K(x,y),y * x,z) = K(y,x \ (y \ 1)). L(K(x,y),y * x,z) = K(y * x,y). L(K(x,y),y * x,z) = K(x,y). L(K(x,y),(x \ y) * y,z) = K(y,x \ y). L(K(x,y),(x \ y) * y,z) = K(x,y). L(T((x \ y) / z,(x \ y) \ 1) * (T(z,(x \ y) \ 1) * (y \ u)),x,T(z,(x \ y) \ 1) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). R(x,y,z / (x * y)) = T(z,(x * y) \ z) * (((x * y) / z) / y). T(x,(y * z) \ x) * (((y * z) / x) / z) = R(y,z,x / (y * z)). L(K(x,y),z * T(y,x),u) = K(x,L(y,z,u)). K(x,L(y,z,u)) = L(K(x,y),z * y,u). L(K(x,y),z * y,u) = K(x,L(y,z,u)). L(K(x,y),z,u) = K(x,L(y,z / y,u)). K(x,L(y,z / y,u)) = L(K(x,y),z,u). K(x,L(y,x \ y,z)) = K(x,y). K(x,L(y,z,x)) = K(x,y). T(x,L(y,z,x)) = x * K(x,y). T(x,y) = T(x,L(y,z,x)). T(x,L(y,z,x)) = T(x,y). T((x * y) * z,L(x,y,z)) = T((x * y) * z,x). K(x,L(y,z,u)) = L(K(x,y),z,u). L(K(x,y),z,u) = K(x,L(y,z,u)). L(K(x,y),z,u) = K(y,L(x \ 1,z,u)). K(x,L(y \ 1,z,u)) = L(K(y,x),z,u). a(x,y,K(z,u)) = K(z,L(u,y,x)) \ K(z,u). K(x,L(y,z,u)) \ K(x,y) = a(u,z,K(x,y)). K(x,y) * K(y,L(x,z,u)) = a(z,u,K(y,x)). L(K(x,y),z,u) = K(L(x,z,u),y). K(L(x,y,z),u) = K(x,L(u,y,z)). K(x,y) * K(y,L(x,z,u)) = K(a(y,z,u),T(x,y)). K(x,K(y,L(z,u,w))) \ K(x,K(y,z)) = a(w,u,K(x,K(y,z))). T((x * y) * z,x) = z * (T(y,z) * x). T((x * (y / z)) * z,x) = z * ((z \ y) * x). T((x / y) * (y * z),x) = y * ((y \ z) * x). K(a(x,y,z),T(u,x)) = a(y,z,K(x,u)). a(x,y,K(z,u)) = K(u,a(z,y,x)). a(x,y,K(z,u)) = K(u,a(x,z,y)). K(a(x,y,z),u) = a(y,z,K(x,u)). a(x,y,K(z,u)) = K(a(z,x,y),u). T(x,a(y,z,u)) = a(y,u,K(z,x)) * x. a(x,y,K(z,u)) * u = T(u,a(x,z,y)). a(x,y,K(z,u)) = a(z,x,K(y,u)). a(x,K(y,z),u) = a(x,y,K(u,z)). L(x,y,K(z,u)) = a(z,x,K(y,u)) * x. a(x,y,K(z,u)) * y = L(y,z,K(x,u)). a(x,y,K(z,u)) = a(x,z,K(u,y)). a(x,y,K(z,u)) = a(x,u,K(y,z)). L(x,K(y,z),u) = a(u,y,K(z,x)) * x. a(x,y,K(z,u)) * u = L(u,K(y,z),x). L(x,K(y,z),u) = L(x,y,K(u,z)). L(x,y,K(z,u)) = L(x,z,K(u,y)). L(x,y,K(z,u)) = L(x,u,K(y,z)). L(x,y,K(z,u)) = L(x,z \ u,K(y,u)). L(x,y \ z,K(u,z)) = L(x,u,K(y,z)). L(x,y \ z,K(z,u)) = L(x,u,K(z,y)). L(x,K(y,z),u) = T(x,a(u,z,y)). T(x,a(y,z,u)) = L(x,u,K(y,z)). L(x,y,K(z,u)) = T(x,a(z,u,y)). T(L(x,y,K(z,u)),K(a(z,u,y),w)) = T(x,T(a(z,u,y),w)). L(x * a(y,z,u),z,K(y,u)) = a(y,z,u) * x. L(x,(y / z) \ T(u,y),K(w,T(u,y))) = L(x,w,K(u,y \ z)). L(x,y \ z,K((x * u) / w,z)) = L(x,u / w,K(y,z)). L(x,y \ z,K(z,u / (x * w))) = L(x,w / u,K(y,z)). T(L(x,y,K(z,u)),K(a(y,z,u),w)) = T(x,T(a(z,u,y),w)). T(L(x,y,K(z,u)),a(z,u,K(y,w))) = T(x,T(a(z,u,y),w)). L(L(x,y,K(z,u)),K(y,w),K(z,u)) = T(x,T(a(z,u,y),w)). T(x,T(a(y,z,u),w)) = L(L(x,u,K(y,z)),u,K(K(y,z),w)). L(L(x,y,K(z,u)),y,K(K(z,u),w)) = T(x,T(a(z,u,y),w)). L(L(x,y,K(z,u)),y,K(z,K(u,w))) = T(x,T(a(z,u,y),w)). L(L(x,y,K(z,u)),y,K(z,K(u,w))) = T(x,T(a(y,z,u),w)). L(L(x,y,K(z,u)),y,K(z,K(u,w))) = T(x,a(y,z,T(u,w))). L(x,T(y,z),K(u,w)) = L(L(x,u,K(w,y)),u,K(w,K(y,z))). L(L(x,y,K(z,u)),y,K(z,K(u,w))) = L(x,T(u,w),K(y,z)). L(L(x,y,K(z,u)),y,K(z,K(u,w))) = L(x,u,T(K(y,z),w)). L(L(x,y,K(z,u)),y,K(z,K(u,w))) = L(x,u,K(y,T(z,w))). L(x,(y / z) * T(u,z),K(w,T(u,z))) = L(x,w,K(u,z \ y)). (x * (y / z)) * L(L(z,y,x),u,w) = x * (y * a(z,u,w)). R(x,y,z / (x * y)) = z * (K(x * y,z) * (((x * y) / z) / y)). x * (K(y * z,x) * (((y * z) / x) / z)) = R(y,z,x / (y * z)). x * ((x \ (y * z)) / z) = R(y,z,x / (y * z)). R(x,y,z / (x * y)) = z * ((z \ (x * y)) / y). R(x,y,z) = R(x,y,z / (x * y)). R(x,y,z / (x * y)) = R(x,y,z). R(x,x \ y,z / y) = R(x,x \ y,z). R(x,x \ y,z) = R(x,y,z / y). R(x,y,z / y) = R(x,y,z). R(x,y,y \ z) = R(x,y,T(z,y)). R(x,y,z \ 1) = R(x,y,z \ y). R(x,y,T(z,y)) = R(x,y,z). R(x,y,z \ y) = R(x,y,y / z). R(x,y,y / z) = R(x,y,z \ y). R(x,y,z) * (z * y) = (x * y) * T(z,y). R((x / y) \ z,x,z) = (x / y) \ R(z,x,y \ x). L(x,y,z) * (z * y) = (x * y) * T(z,y). ((x \ y) * x) * T(z,x) = T(z * y,z * x). T(x * y,x * z) = ((z \ y) * z) * T(x,z). T(x * y,x * z) = T(y,z) * T(x,z). T(x * y,z) = T(y,x \ z) * T(x,x \ z). T(x,y \ z) * T(y,y \ z) = T(y * x,z). T(x * y,x * a(x,z,u)) = T(y,a(x,z,u)) * x. T(x,y \ z) * T(y,z) = T(y * x,z). T(x * (y \ 1),z) = T(y,x \ z) \ T(x,z). T(x,y \ z) \ T(y,z) = T(y * (x \ 1),z). T(x,y \ z) \ T(y,z) = T(y / x,z). L(x,y,T(z / u,y)) = L(x,y,T(u,z \ y) \ z). L(x,y,T(z,u \ y) \ u) = L(x,y,T(u / z,y)). R((x / y) * z,y,z) = (y / x) \ R(z,y,x \ y). T(x * y,L(x,z,u)) = T(y,a(x,z,u)) * x. T(x * y,L(x,z,u)) = T(y,a(z,u,x)) * x. T(x * y,L(x,z,u)) = L(y,x,K(z,u)) * x. L(x * y,y,K(z,u)) = T(y * x,L(y,z,u)). L(x / y,y \ 1,K(z,u)) = T((y \ 1) * x,L(y \ 1,z,u)). T((x \ 1) * y,L(x \ 1,z,u)) = L(y / x,x \ 1,K(z,u)). L(x,y,T(z,u \ y) \ u) = L(x,y,u / z). R((x / y) * z,y,z) = (x / y) * R(z,y,x \ y). (x / y) * R(z,y,x \ y) = x * (y \ z). L(x,y \ 1,z) = R(x,y,z \ y). R(x,y,z \ y) = L(x,y \ 1,z). R(x,y,z \ 1) = L(x,y \ 1,z). L(x,y \ 1,z) * (y / z) = (x * y) / z. L(x,y,z) * (z / y) = (x * z) / 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) = (L(x \ y,z,y) * z) / x. (L(x \ y,z,y) * z) / x = (x \ y) * (z / x). ((x \ 1) * y) / z = L(x,z,y) \ (y / z). L(x,y,z) \ (z / y) = ((x \ 1) * z) / y. L(a(x,y,z),u,z) * (z / u) = L(z,x,y) / u. L(x,y,z) \ (z / y) = (x \ z) / y. L(((x \ y) / z) * u,L(x,z,y),y / z) = L(x,z,y) \ ((y / z) * u). L((x \ y) * z,z,y) / x = (x \ y) * (z / x). a(x,y,z) * (z / u) = L(z,x,y) / u. T(L(x,y,z) / u,u) = (u \ x) * a(y,z,x). (x \ y) * a(z,u,y) = x \ L(y,z,u). T(K(x,a(y,z,u)) * u,a(y,z,u)) = T(a(y,z,u),x) \ L(u,y,z). (x \ (y * z)) / x = (x \ y) * (z / x). (x \ y) * (z / x) = x \ ((y * z) / x). x \ ((y * z) / x) = (x \ y) * (z / x). (x \ ((y \ x) * z)) / y = x \ ((y \ x) * (z / y)). T(x * y,z) / x = ((z \ x) * y) * (z / x). ((x \ y) * z) * (x / y) = T(y * z,x) / y. x * (T(x * (y / x),z) / x) = T(y,x \ (z / x)). T(x * ((x * (y / x)) / x),z) = T(y,x \ (z / x)). T(x * (x * ((y / x) / x)),z) = T(y,x \ (z / x)). T(x * (x * (y / (x * x))),z) = T(y,x \ (z / x)). T(T(x,y \ (y \ x)),z) = T(x,y \ (z / y)). T(x \ y,L(x \ 1,z,u)) = L(y / x,x \ 1,K(z,u)). L(x / y,y \ 1,K(z,u)) = T(y \ x,L(y \ 1,z,u)). T(x \ y,L(x \ 1,z,u)) = L(y / x,K(z,u),x). T(x \ y,L(x \ 1,z,u)) = L(y / x,z,K(x,u)). T(x * (T(y,x \ y) / x),z) = T(T(T(y,x \ y),z),T(y,z) / x). T(T(T(x,y \ x),z),T(x,z) / y) = T(y * (T(x,y \ x) / y),z). (x \ y) * ((y \ x) \ (z \ (y \ x))) = T((x \ y) * (z \ 1),y \ x). K(x,T(T(T(y,z \ y),u),T(y,u) / z)) = K(x,T(y,u)). T(K(x,a(y,z,u)) * u,a(y,z,u)) = a(y,z,T(u,x)) \ L(u,y,z). T(T(T(x,y \ x),z),T(x,z) / y) = T(y * (x * (y \ K(y,x))),z). (x \ y) * ((y \ x) \ (z \ (y \ x))) = T((x \ y) / z,y \ x). T((x \ y) / z,y \ x) = (x \ y) / T(z,y \ x). (x \ y) / T(z,y \ x) = T((x \ y) / z,y \ x). T(K(x,a(y,z,u)) * u,a(y,z,u)) = a(y,T(u,x),z) * L(u,y,z). T(T(T(x,y \ x),z),T(x,z) / y) = T(T(x,y \ (y \ x)),z). K(x,T(T(y,z \ (z \ y)),u)) = K(x,T(y,u)). K(x,T(y,z \ (u / z))) = K(x,T(y,u)). K(x,T(y,z)) = K(x,T(y,(u / z) * u)). K(x,T(y,(z / u) * z)) = K(x,T(y,u)). K(x,T(y,z * u)) = K(x,T(y,z \ u)). K(x,T(y,z \ u)) = K(x,T(y,z * u)). K(x,T(y,(z / u) \ (u * (w * u)))) = K(x,T(y,(z * w) * u)). K(x,T(y,z * (u \ 1))) = K(x,T(y,u * z)). K(x,T(y,z / u)) = K(x,T(y,u * z)). K(x,T(y,z)) = K(x,T(y,u * (z * u))). K(x,T(y,z * (u * z))) = K(x,T(y,u)). K(x,T(y,(z * u) / ((w / u) / z))) = K(x,T(y,L(w,u,z))). K(x,T(y,(z \ u) * (z * ((z \ w) * u)))) = K(x,T(y,w * z)). K(x,T(y,z * (u * w))) = K(x,T(y,(w \ z) * u)). K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (w * z))). K(x,T(y,(z * u) * (z / (w / u)))) = K(x,T(y,L(w,u,z))). K(x,T(y,(z * u) * (z * (u / w)))) = K(x,T(y,L(w,u,z))). K(x,T(y,(((z / u) \ u) * w) * u)) = K(x,T(y,(z * w) * u)). K(x,T(y,((z \ u) * w) * u)) = K(x,T(y,w * z)). K(x,T(y,((z * (u \ z)) * w) * z)) = K(x,T(y,(u * w) * z)). K(x,T(y,(z * (u \ (z * w))) * z)) = K(x,T(y,(u * w) * z)). K(x,T(y,z * ((u \ (z * w)) * z))) = K(x,T(y,(u * w) * z)). K(x,T(y,(z * u) * w)) = K(x,T(y,z \ (w * u))). K(x,T(y,z \ (u * w))) = K(x,T(y,(z * w) * u)). K(x,T(y,(z * u) * w)) = K(x,T(y,z * (w * u))). K(x,T(y,z * ((z * (u / w)) * u))) = K(x,T(y,L(w,u,z))). K(x,T(y,(z \ u) * (u * w))) = K(x,T(y,w * z)). K(x,T(y,z * u)) = K(x,T(y,w * ((w * z) * u))). K(x,T(y,z * ((z * u) * w))) = K(x,T(y,u * w)). K(x,T(y,L(z,u,w))) = K(x,T(y,(u / z) * u)). K(x,T(y,L(z,u,w))) = K(x,T(y,z)). T(x,T(y,L(z,u,w))) = x * K(x,T(y,z)). T(x,T(y,z)) = T(x,T(y,L(z,u,w))). T(x,T(y,L(z,u,w))) = T(x,T(y,z)). T(x,T(y,z)) * K(y,x) = T(x,K(y,L(z,u,w))). T(x,K(y,L(z,u,w))) = T(x,T(y,z)) * K(y,x). T(x,K(y,L(z,u,w))) = T(x,K(y,z)). K(K(x,L(y,z,u)),w) = T(w,K(x,y)) \ w. K(K(x,y),z) = K(K(x,L(y,u,w)),z). K(K(x,L(y,z,u)),w) = K(K(x,y),w). K(K(x,L(y,z,u)),w) = K(x,K(y,w)). K(K(x,L(y,z,u)),w) = K(w,K(x,y)). K(x,K(y,z)) = K(y,K(L(z,u,w),x)). K(x,K(L(y,z,u),w)) = K(w,K(x,y)). K(x,K(y,L(z,u,w))) = K(z,K(x,y)). K(x,K(y,z)) \ K(y,K(z,x)) = a(u,w,K(y,K(z,x))). a(x,y,K(z,K(u,w))) = K(w,K(z,u)) \ K(z,K(u,w)). a(x,y,K(z,K(u,w))) = K(z,K(u,w)) \ K(z,K(u,w)). a(x,y,K(z,K(u,w))) = 1. 1 = a(K(x,K(y,z)),u,w). a(K(x,K(y,z)),u,w) = 1. L(x,y,K(z,K(u,w))) = x. L(x,y,K(z,u)) = L(x,u,K(y,T(z,w))). L(x,y,K(z,T(u,w))) = L(x,z,K(u,y)). L(x,y,K(z,(u / w) * T(z,w))) = L(x,y,K(z,w \ u)). L(x,y,K(z,u / w)) = L(x,y,K(z,w \ u)). L(x,y \ z,K(z,(x * u) \ w)) = L(x,u / w,K(y,z)). L(x,y / z,K(u,w)) = L(x,(x * y) \ z,K(w,u)). L(x,(x * y) \ z,K(u,w)) = L(x,y / z,K(w,u)). L(x,y / z,K(u,w)) = L(x,y \ z,K(w,u)). T(K(x,a(y,z,u)) * u,a(y,z,u)) = a(y,u,T(z,x)) * L(u,y,z). T(K(x,a(y,z,u)) * u,a(y,z,u)) = L(L(u,y,z),T(z,x),y). T(K(x,a(y,z,u)) * u,a(y,z,u)) = L(L(u,y,z),z,T(y,x)). T(a(x,y,K(z,u)) * x,a(z,y,x)) = L(L(x,z,y),y,T(z,u)). T(L(x,y,K(z,u)),a(z,y,x)) = L(L(x,z,y),y,T(z,u)). L(L(x,y,K(z,u)),x,K(z,y)) = L(L(x,z,y),y,T(z,u)). L(L(x,y,z),z,T(y,u)) = L(x,z,K(y,u)). L(x,y,K(z,u)) = L(L(x,y,T(z,u)),z,y). L(L(x,y,T(z,u)),z,y) = L(x,y,K(z,u)). L(x,y / x,T(z,u)) = L(L(x,y,z),y / x,K(z,u)). L(L(x,y,z),y / x,K(z,u)) = L(x,y / x,T(z,u)). L(L(x,y,z),y / x,K(z,u)) = L(x,y,T(z,u)). L(x,y,T(z,u)) = L(L(x,y,z),y \ x,K(u,z)). L(L(x,y,z),y \ x,K(u,z)) = L(x,y,T(z,u)). L(x,y,T(z,u)) = L(L(x,K(u,z),y),y,z). L(L(x,K(y,z),u),u,z) = L(x,u,T(z,y)). L(L(x,y,K(z,u)),z,u) = L(x,z,T(u,y)). L(L(x,y \ z,K(u,T(z,w))),u,T(z,w)) = L(x,u,T(T(z,w),y \ 1)). (x * y) * ((y \ (x \ z)) * u) = ((z * x) * y) * ((x * y) \ u). ((x * y) * z) * ((y * z) \ u) = (y * z) * ((z \ (y \ x)) * u). L(x,y,z) \ ((z / y) * u) = L(((x \ z) / y) * u,x,z / y). L(((x \ y) / z) * u,x,y / z) = L(x,z,y) \ ((y / z) * u). L(L(x,y,K(z,u \ z)),y,T(z,w)) = L(x,y,T(T(z,w),u \ 1)). L(L(x,y,K(z,u)),y,T(u,w)) = L(x,y,T(T(u,w),z \ 1)). (x \ 1) * (y \ (x * (T(y,x) * z))) = L(z,(x \ 1) * (x \ 1),T(y,x)). L(x,(y \ 1) * (y \ 1),T(z,y)) = y \ (z \ (y * (T(z,y) * x))). L(x,y \ (y \ 1),T(z,y)) = y \ (z \ (y * (T(z,y) * x))). x \ (y \ (x * (T(y,x) * z))) = L(z,x \ (x \ 1),T(y,x)). x \ (y \ (x * (T(y,x) * z))) = L(z,T(y,x),x * x). x \ (y \ (x * (T(y,x) * z))) = L(z,y,T(x * x,x)). x \ (y \ (x * (T(y,x) * z))) = L(z,y,x * x). (x * y) \ ((x / (z / y)) * L(L(z,y,x),u,w)) = a(u,w,((z / y) / x) * (x * y)). (x * y) \ ((x * (y / z)) * L(L(z,y,x),u,w)) = a(u,w,((z / y) / x) * (x * y)). (x * y) \ (x * (y * a(z,u,w))) = a(u,w,((z / y) / x) * (x * y)). a(x,y,((z / u) / w) * (w * u)) = (w * u) \ (w * (u * a(z,x,y))). L(a(x,y,z),u,w) = a(y,z,((x / u) / w) * (w * u)). a(x,y,((z / u) / w) * (w * u)) = L(a(z,x,y),u,w). a(x,y,L(z,u,w)) = L(a(z,x,y),u,w). a(x,y,L(z,u,w)) = L(a(y,z,x),u,w). a(x,y,L(z,u,w)) = L(a(x,y,z),u,w). a(x,y,L(z,u,w)) = a(y,z,L(x,u,w)). a(x,y,L(z,u,w)) = a(z,x,L(y,u,w)). T((x \ y) / z,y \ x) * (T(z,y \ x) * u) = T(z,y \ x) \ (((x \ y) * z) * u). ((x \ y) * z) \ (y * ((y \ ((x \ y) * (z / x))) * u)) = (z \ K(z,x \ y)) * (((x \ y) * z) * (y \ u)). (x \ K(x,y \ z)) * (((y \ z) * x) * (z \ u)) = (x \ (z \ y)) * (z * ((z \ ((y \ z) * (x / y))) * u)). T(x \ 1,(y \ z) \ 1) * (((y \ z) * x) * (z \ u)) = (x \ (z \ y)) * (z * ((z \ ((y \ z) * (x / y))) * u)). (x \ (y \ z)) * (y * ((y \ ((z \ y) * (x / z))) * u)) = K(x,z \ y) * (x \ (((z \ y) * x) * (y \ u))). K(x,y \ z) * (x \ (((y \ z) * x) * (z \ u))) = (x \ (z \ y)) * (z * ((z \ ((y \ z) * (x / y))) * u)). K(x,y \ z) * ((x \ (y \ z)) * (x * (z \ u))) = (x \ (z \ y)) * (z * ((z \ ((y \ z) * (x / y))) * u)). (x \ (y \ z)) * (y * ((y \ ((z \ y) * (x / z))) * u)) = ((z \ y) / x) * (x * (y \ u)). x * ((y * ((x * y) \ z)) * ((u * x) * (y * ((x * y) \ z)))) = L(z,y,x) * (u * L(z,y,x)). x * (y * (((x * y) \ z) * (((u * x) * y) * ((x * y) \ z)))) = L(z,y,x) * (u * L(z,y,x)). x * (y * (((x * y) \ z) * ((x * y) * ((y \ (x \ u)) * z)))) = L(z,y,x) * (u * L(z,y,x)). x * (y * ((((x * y) \ z) * L(u,x,y)) * z)) = L(z,y,x) * (u * L(z,y,x)). L(x,y,z) * (u * L(x,y,z)) = L(x * (L(u,z,y) * x),y,z). L(x * (L(y,z,u) * x),u,z) = L(x,u,z) * (y * L(x,u,z)). T(x \ 1,(y \ z) \ 1) * (((y \ z) * x) * (z \ u)) = ((y \ z) / x) * (x * (z \ u)). T(x \ 1,y \ z) * (((z \ y) * x) * (y \ u)) = ((z \ y) / x) * (x * (y \ u)). ((x \ y) / z) * (z * (y \ u)) = T(z,y \ x) \ (((x \ y) * z) * (y \ u)). T(x,y \ z) \ (((z \ y) * x) * (y \ u)) = ((z \ y) / x) * (x * (y \ u)). L(T((x \ y) / z,y \ x) * (T(z,(x \ y) \ 1) * (y \ u)),x,T(z,(x \ y) \ 1) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). L(T((x \ y) / z,y \ x) * (T(z,y \ x) * (y \ u)),x,T(z,(x \ y) \ 1) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). L(T(x,y \ z) \ (((z \ y) * x) * (y \ u)),z,T(x,(z \ y) \ 1) \ y) = L(z \ u,T(x,(z \ y) \ 1),y). L(((x \ y) / z) * (z * (y \ u)),x,T(z,(x \ y) \ 1) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). L(((x \ y) / z) * (z * (y \ u)),x,T(z,y \ x) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). L(x \ y,T(z,(x \ u) \ 1),u) = L(((x \ u) / z) * (z * (u \ y)),x,u / z). L(((x \ y) / z) * (z * (y \ u)),x,y / z) = L(x \ u,T(z,(x \ y) \ 1),y). L(x \ y,T(z,(x \ u) \ 1),u) = L(x,z,u) \ ((u / z) * (z * (u \ y))). L(x \ y,T(z,(x \ u) \ 1),u) = L(x,z,u) \ L(y,z,u). L(x \ y,T(z,u \ x),u) = L(x,z,u) \ L(y,z,u). L(x,y,z) \ L(u,y,z) = L(x \ u,y,T(z,z \ x)). L(x \ y,z,T(u,u \ x)) = L(x,z,u) \ L(y,z,u). L(x \ y,z,T(u,x)) = L(x,z,u) \ L(y,z,u). T(L(x \ y,z,T(u,x)),L(x,z,u) \ 1) = L(y,z,u) / L(x,z,u). T(L(x \ y,z,T(u,x)),L(x \ 1,z,u)) = L(y,z,u) / L(x,z,u). L(T(x \ y,L(x \ 1,z,u)),z,T(u,x)) = L(y,z,u) / L(x,z,u). L(L(x / y,z,K(y,u)),z,T(u,y)) = L(x,z,u) / L(y,z,u). L(x,y,z) / L(u,y,z) = L(x / u,y,T(T(z,u),u \ 1)). L(x / y,z,T(T(u,y),y \ 1)) = L(x,z,u) / L(y,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). L(x * y,z,u) / L(y,z,u) = L(x,z,u). L(x,y,z) \ (L(x / u,y,z) * w) = (L(u,y,z) \ (w / L(x,y,z))) * L(x,y,z). (L(x,y,z) \ (u / L(w,y,z))) * L(w,y,z) = L(w,y,z) \ (L(w / x,y,z) * u). L(x,y,z) * L(u,y,z) = L(x * u,y,z). L(x,y,z) \ L(x * u,y,z) = L(u,y,z). L(x,y,z) * u != L(x * (L(w,z,y) * x),y,z) | u = w * L(x,y,z). L(L(x,y,z) * u,z,y) = x * L(u,z,y). T(L(x * y,z,u),L(x,z,u)) = L(y,z,u) * L(x,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(w,y,z)) = L(x / (L(u,z,y) \ w),y,z). L(x / (L(y,z,u) \ w),u,z) = L(x,u,z) / (y \ L(w,u,z)). L(T(x * y,L(x,z,u)),z,u) = L(y,z,u) * L(x,z,u). L(L(x * y,y,K(z,u)),z,u) = L(x,z,u) * L(y,z,u). L(x,y,z) * L(u,y,z) = L(x * u,y,T(z,u)). L(x * y,z,T(u,y)) = L(x,z,u) * L(y,z,u). L(x * y,z,T(u,y)) = L(x * y,z,u). L(x,y,T(z,u)) = L((x / u) * u,y,z). L((x / y) * y,z,u) = L(x,z,T(u,y)). L(x,y,z) = L(x,y,T(z,u)). L(x,y,T(z,u)) = L(x,y,z). L(L(x,y,z),z,y) = L(x,y,K(z,u)). L(x,y,K(z,u)) = x. x = T(x,a(y,z,u)). T(x,a(y,z,u)) = x. x * a(y,z,u) = a(y,z,u) * x. a(x,y,z) * u = u * a(x,y,z). T(a(x,y,z),u) = a(x,y,z). a(x,y,z) / u = u \ a(x,y,z). x * (y * a(x,z,u)) = L(x,z,u) * y. T((a(x,y,z) / u) * (u * w),a(x,y,z)) = u * (a(x,y,z) * (u \ w)). T(a(x,y,z),u \ w) * T(u,w) = T(a(x,y,z) * u,w). x \ (y \ (x * (a(z,u,w) * T(y,x)))) = L(a(z,u,w),y,x * x). x \ (y * (L(z,u,w) * (z \ (y \ x)))) = L(L(a(z,u,w),z,x \ y),x,y). a(x,y,z) * T(u,w) = T(a(x,y,z) * u,w). T(a(x,y,z) * u,w) = a(x,y,z) * T(u,w). L(x / (L(y,z,u) \ w),u,z) = L(x,u,z) * (L(w,u,z) \ y). L(x * (y \ L(z,u,w)),w,u) = L(x,w,u) * (L(y,w,u) \ z). x \ (y \ (x * T(a(z,u,w) * y,x))) = L(a(z,u,w),y,x * x). x \ (y \ ((a(z,u,w) * y) * x)) = L(a(z,u,w),y,x * x). x \ ((y \ a(z,u,w)) * (y * x)) = L(a(z,u,w),y,x * x). T((x \ a(y,z,u)) * (x * w),a(y,z,u)) = x * (a(y,z,u) * (x \ w)). x * (a(y,z,u) * (x \ w)) = (x \ a(y,z,u)) * (x * w). (x \ a(y,z,u)) * (x * w) = x * (a(y,z,u) * (x \ w)). x \ (y * (a(z,u,w) * (y \ x))) = L(a(z,u,w),y,x * x). a(x,y,L(z,u,w * w)) = w \ (u * (a(z,x,y) * (u \ w))). x \ (y * (a(z,u,w) * (y \ x))) = a(u,w,L(z,y,x * x)). x \ (y * (a(z,u,w) * (y \ x))) = L(L(a(z,u,w),z,x \ y),x,y). L(L(a(x,y,z),x,u \ w),u,w) = u \ (w * (a(x,y,z) * (w \ u))). L(L(a(x,y,z),x,u \ w),u,w) = a(y,z,L(x,w,u * u)). L(a(x,y,z),u,w) = a(y,z,L(x,w,u * u)). a(x,y,L(z,u,w * w)) = L(a(z,x,y),w,u). a(x,y,L(z,u,w)) = a(x,y,L(z,w,u * u)). a(x,y,L(z,u,w * w)) = a(x,y,L(z,w,u)). a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = ((x / L(y,z,u)) * L(y,z,u)) \ (L(w,z,u) * (L(y,z,u) \ (L(y / w,z,u) * x))). ((x / L(y,z,u)) * L(y,z,u)) \ (L(w,z,u) * (L(y,z,u) \ (L(y / w,z,u) * x))) = a(x / L(y,z,u),L(w,z,u),L(y,z,u)). x \ (L(y,z,u) * (L(w,z,u) \ (L(w / y,z,u) * x))) = a(x / L(w,z,u),L(y,z,u),L(w,z,u)). x \ L(y * (z \ L(L(z / y,u,w) * x,w,u)),u,w) = a(x / L(z,u,w),L(y,u,w),L(z,u,w)). x \ L(y * (z \ ((z / y) * L(x,u,w))),w,u) = a(x / L(z,w,u),L(y,w,u),L(z,w,u)). a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = x \ L(w * (y \ ((y / w) * L(x,u,z))),z,u). a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = x \ L(w * ((w \ (L(x,u,z) / y)) * y),z,u). a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = x \ L(L(L(x,u,z),w,y),z,u). a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = x \ L(x,w,y). a(x,y,z) = a(x / L(z,u,w),L(y,u,w),L(z,u,w)). a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = a(x,w,y). a(x,y,z) = a(L(z,u,w),x / L(z,u,w),L(y,u,w)). a(L(x,y,z),u / L(x,y,z),L(w,y,z)) = a(u,w,x). a(x,y,z) = a(L(z,u,w),x,L(y,u,w)). a(L(x,y,z),u,L(w,y,z)) = a(u,w,x). a(x,y,L(L(z,u,w),u,w)) = a(x,y,z). a(x,y,L(z,u,w * w)) = a(x,y,z). a(x,y,z) = a(x,y,L(z,u,w)). a(x,y,L(z,u,w)) = a(x,y,z). a(x,y,z) = L(a(x,y,z),u,w). L(a(x,y,z),u,w) = a(x,y,z). a(x,y,a(z,u,w)) = 1. 1 = a(a(x,y,z),u,w). 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(a(x,y,z),u,w) = 1 # label("aa1") # 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("Moufang"). [assumption]. a(a(c1,c2,c3),c4,c5) != 1 # label("aa1"). [deny(10)]. end_of_list. formulas(demodulators). end_of_list. % 2076 hints input. ============================== PREDICATE ELIMINATION ================= No predicates eliminated. ============================== end predicate elimination ============= Auto_denials: % copying label "aa1" to answer in negative clause Term ordering decisions: Function symbol KB weights: 1=1. c1=1. c2=1. c3=1. c4=1. c5=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, c5, *, 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("Moufang"). [assumption]. kept: 48 a(a(c1,c2,c3),c4,c5) != 1 # label("aa1") # answer("aa1"). [deny(10)]. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). 48 a(a(c1,c2,c3),c4,c5) != 1 # label("aa1") # answer("aa1"). [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("Moufang"). [assumption]. end_of_list. formulas(demodulators). end_of_list. % 1554 hints (2076 processed, 522 redundant). ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.08 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("Moufang"). [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): 77 T(x,x) = x. [para(32(a,2),13(a,1))]. given #33 (H,wt=7): 53 x / (y \ x) = y. [para(14(a,1),15(a,1,1))]. given #34 (H,wt=7): 54 (x / y) \ x = y. [para(16(a,1),13(a,1,2))]. given #35 (H,wt=7): 76 T(1,x) = x \ x. [para(11(a,1),32(a,2,2))]. given #36 (H,wt=5): 90 T(1,x) = 1. [para(76(a,2),50(a,1))]. => 93 back subsumes hint matchers not on Sos. Reset weight to 507.000. given #37 (H,wt=8): 55 x * y != x | 1 = y. [para(12(a,1),19(a,1)),flip(a)]. given #38 (H,wt=8): 57 x * 1 != y | x = y. [para(12(a,1),20(a,2))]. given #39 (H,wt=9): 78 x * T(y,x) = y * x. [para(32(a,2),14(a,1,2))]. given #40 (H,wt=9): 80 T(x / y,y) = y \ x. [para(16(a,1),32(a,2,2))]. given #41 (H,wt=9): 86 T(T(x,y),x) = T(x,y). [para(77(a,1),38(a,1,1)),flip(a)]. given #42 (H,wt=7): 99 K(T(x,y),x) = 1. [hyper(36,a,86,a)]. given #43 (H,wt=7): 100 T(x,T(x,y)) = x. [hyper(35,a,86,a)]. given #44 (H,wt=9): 88 (x * y) / T(x,y) = y. [para(32(a,2),53(a,1,2))]. given #45 (H,wt=9): 101 K(x \ y,y / x) = 1. [para(80(a,1),99(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): 58 x * y != z | z / y = x. [para(16(a,1),20(a,1)),flip(a)]. given #48 (H,wt=11): 61 (x * y) * K(y,x) = y * x. [para(26(a,2),14(a,1,2))]. given #49 (H,wt=11): 79 T(x,x \ y) = (x \ y) \ y. [para(14(a,1),32(a,2,2))]. given #50 (H,wt=11): 102 T(T(x,y),T(x,z)) = T(x,y). [para(100(a,1),38(a,1,1)),flip(a)]. given #51 (H,wt=11): 103 x / T(y,y \ x) = y \ x. [para(14(a,1),88(a,1,1))]. given #52 (H,wt=11): 105 T(x \ y,y / x) = x \ y. [hyper(37,a,101,a)]. given #53 (H,wt=12): 65 x \ (1 * (x * y)) = L(y,x,1). [para(11(a,1),28(a,2,1)),flip(a)]. given #54 (H,wt=10): 109 x \ (x * y) = L(y,x,1). [para(11(a,1),65(a,1,2))]. given #55 (H,wt=6): 110 L(x,y,1) = x. [para(109(a,1),13(a,1))]. given #56 (H,wt=12): 66 (x * 1) \ (x * y) = L(y,1,x). [para(11(a,1),28(a,2,2,2)),flip(a)]. given #57 (H,wt=10): 111 x \ (x * y) = L(y,1,x). [para(12(a,1),66(a,1,1))]. given #58 (H,wt=6): 112 L(x,1,y) = x. [para(111(a,1),13(a,1))]. given #59 (H,wt=12): 94 x * y != z * x | T(z,x) = y. [para(78(a,1),19(a,1)),flip(a)]. given #60 (H,wt=13): 62 x \ ((y \ x) * y) = K(y \ x,y). [para(14(a,1),26(a,2,1)),flip(a)]. given #61 (H,wt=13): 63 ((x \ y) * x) \ y = K(x,x \ y). [para(14(a,1),26(a,2,2)),flip(a)]. given #62 (H,wt=13): 64 (x * (y / x)) \ y = K(y / x,x). [para(16(a,1),26(a,2,2)),flip(a)]. given #63 (H,wt=13): 81 x * (y * (x * 1)) = (x * y) * x. [hyper(18,a,12,a,b,47,a),flip(a)]. given #64 (H,wt=11): 113 (x * y) * x = x * (y * x). [para(12(a,1),81(a,1,2,2)),flip(a)]. given #65 (H,wt=9): 116 T(x * y,x) = y * x. [hyper(94,a,113,a(flip))]. given #66 (H,wt=9): 120 T(x,y) = (y \ x) * y. [para(14(a,1),116(a,1,1))]. given #67 (H,wt=9): 123 T(x,y) / y = y \ x. [hyper(58,a,120,a(flip))]. given #68 (H,wt=7): 129 1 / x = x \ 1. [para(90(a,1),123(a,1,1))]. given #69 (H,wt=7): 135 (x \ 1) \ 1 = x. [para(129(a,1),53(a,1))]. given #70 (H,wt=9): 124 (x \ y) \ T(y,x) = x. [hyper(56,a,120,a(flip))]. given #71 (H,wt=11): 114 (x * (y * x)) / x = x * y. [hyper(58,a,113,a)]. given #72 (H,wt=11): 115 (x * y) \ (x * (y * x)) = x. [hyper(56,a,113,a)]. given #73 (H,wt=6): 139 L(x,y,x) = x. [para(115(a,1),28(a,2))]. given #74 (H,wt=10): 140 L(T(x,y),z,x) = T(x,y). [para(139(a,1),40(a,2,1))]. given #75 (H,wt=11): 119 T((x \ y) * x,x \ y) = y. [para(116(a,2),14(a,1))]. given #76 (H,wt=9): 143 T(T(x,y),y \ x) = x. [para(120(a,2),119(a,1,1))]. given #77 (H,wt=9): 145 T(T(x,x / y),y) = x. [para(54(a,1),143(a,1,2))]. given #78 (H,wt=9): 146 T(x,T(x,y) \ x) = x. [para(100(a,1),143(a,1,1))]. given #79 (H,wt=9): 148 T(T(x,y),x / y) = x. [para(145(a,1),38(a,1)),flip(a)]. given #80 (H,wt=9): 150 K(x,T(x,y) \ x) = 1. [hyper(36,a,146,a)]. given #81 (H,wt=11): 121 T(x,x / y) = y * (x / y). [para(16(a,1),116(a,1,1))]. given #82 (H,wt=11): 122 T(x * y,y) = T(x,y) * y. [para(78(a,1),116(a,1,1))]. given #83 (H,wt=11): 125 x \ T(y,x) = T(x \ y,x). [para(120(a,2),32(a,2,2)),flip(a)]. given #84 (H,wt=11): 126 (x \ T(x,y)) * x = T(x,y). [para(120(a,1),86(a,1))]. given #85 (H,wt=11): 127 K(x \ y,x) = y \ T(y,x). [para(120(a,2),62(a,1,2)),flip(a)]. given #86 (H,wt=11): 128 K(x,x \ y) = T(y,x) \ y. [para(120(a,2),63(a,1,1)),flip(a)]. given #87 (H,wt=11): 130 (x \ y) / x = x \ (y / x). [para(80(a,1),123(a,1,1))]. given #88 (H,wt=11): 131 T(x,y) / x = x \ T(x,y). [para(86(a,1),123(a,1,1))]. given #89 (H,wt=11): 132 x / T(x,y) = T(x,y) \ x. [para(100(a,1),123(a,1,1))]. given #90 (H,wt=11): 136 (x \ T(x,y)) \ T(x,y) = x. [para(86(a,1),124(a,1,2))]. given #91 (H,wt=9): 157 T(x,x \ T(x,y)) = x. [para(136(a,1),79(a,2))]. given #92 (H,wt=9): 158 T(x,K(y \ x,y)) = x. [para(127(a,2),157(a,1,2))]. given #93 (H,wt=11): 137 (x * y) / x = x * (y / x). [para(16(a,1),114(a,1,1,2))]. given #94 (H,wt=11): 138 (x * (y / x)) \ (x * y) = x. [para(16(a,1),115(a,1,2,2))]. given #95 (H,wt=11): 149 T(x,x / y) * y = y * x. [para(145(a,1),78(a,1,2)),flip(a)]. given #96 (H,wt=11): 152 T(x,(y * (x / y)) \ x) = x. [para(121(a,1),146(a,1,2,1))]. given #97 (H,wt=9): 161 T(x,K(x / y,y)) = x. [para(64(a,1),152(a,1,2))]. given #98 (H,wt=11): 154 T(x,y) = x * K(y \ x,y). [para(127(a,2),14(a,1,2)),flip(a)]. given #99 (H,wt=11): 155 T(x,y) = K(y \ x,y) * x. [para(127(a,2),126(a,1,1)),flip(a)]. given #100 (H,wt=11): 156 T(x,y) * K(y,y \ x) = x. [para(128(a,2),14(a,1,2))]. given #101 (H,wt=11): 159 T(x * y,K(y,x)) = x * y. [para(13(a,1),158(a,1,2,1))]. given #102 (H,wt=12): 141 L(L(x,y,z),u,x) = L(x,y,z). [para(139(a,1),45(a,1,1)),flip(a)]. given #103 (H,wt=13): 82 ((x * 1) * x) * y = x * (x * y). [para(11(a,1),47(a,2,2))]. given #104 (H,wt=11): 165 (x * x) * y = x * (x * y). [para(12(a,1),82(a,1,1,1))]. given #105 (H,wt=11): 166 (x * (x * y)) / y = x * x. [hyper(58,a,165,a)]. given #106 (H,wt=11): 168 (x * y) / (x \ y) = x * x. [para(14(a,1),166(a,1,1,2))]. given #107 (H,wt=11): 169 x / (y \ (y \ x)) = y * y. [para(14(a,1),168(a,1,1))]. given #108 (H,wt=11): 170 (x * x) \ y = x \ (x \ y). [para(169(a,1),54(a,1,1))]. given #109 (H,wt=13): 95 T(x,y) \ (x * y) = T(y,T(x,y)). [para(78(a,1),32(a,2,2)),flip(a)]. given #110 (H,wt=13): 96 x * T(T(y,x),z) = T(y,z) * x. [para(38(a,1),78(a,1,2))]. given #111 (H,wt=11): 173 T(x,y \ x) * y = y * x. [para(143(a,1),96(a,1,2)),flip(a)]. given #112 (H,wt=11): 174 T(x,x / y) = T(x,y \ x). [hyper(18,a,149,a,b,173,a),flip(a)]. given #113 (H,wt=11): 176 T(x,(y \ x) \ x) = T(x,y). [para(53(a,1),174(a,1,2)),flip(a)]. given #114 (H,wt=11): 177 T(x,y \ x) = y * (x / y). [para(174(a,1),121(a,1))]. given #115 (H,wt=11): 178 T(x,T(y,y \ x)) = T(x,y). [para(79(a,2),176(a,1,2))]. given #116 (H,wt=13): 98 T(T(x / y,z),y) = T(y \ x,z). [para(80(a,1),38(a,1,1)),flip(a)]. given #117 (H,wt=13): 104 (x * y) / T(y,T(x,y)) = T(x,y). [para(78(a,1),88(a,1,1))]. given #118 (H,wt=13): 106 x * K(y,x / y) = y * (x / y). [para(16(a,1),61(a,1,1))]. given #119 (H,wt=13): 144 T(T(T(x,y),z),y \ x) = T(x,z). [para(143(a,1),38(a,1,1)),flip(a)]. given #120 (H,wt=13): 151 T(T(T(x,y),z),x / y) = T(x,z). [para(148(a,1),38(a,1,1)),flip(a)]. given #121 (H,wt=13): 153 T(x \ (y / x),x) = x \ (x \ y). [para(80(a,1),125(a,1,2)),flip(a)]. given #122 (H,wt=13): 162 T(K(x / y,y),x) = K(x / y,y). [hyper(35,a,161,a)]. given #123 (H,wt=13): 179 T(x * y,y) = x * ((x * y) / x). [para(13(a,1),177(a,1,2))]. given #124 (H,wt=13): 182 T(x * y,T(x,y)) = T(x * y,x). [para(13(a,1),178(a,1,2,2))]. given #125 (H,wt=11): 189 T(x * y,T(x,y)) = y * x. [para(182(a,2),116(a,1))]. given #126 (H,wt=13): 183 x * K(y,x / y) = T(x,y \ x). [para(106(a,2),177(a,2)),flip(a)]. given #127 (H,wt=13): 184 T(T(T(x,y),z),z \ x) = T(x,y). [para(38(a,1),144(a,1,1))]. given #128 (H,wt=13): 185 T(T(T(x,y \ x),z),y) = T(x,z). [para(53(a,1),151(a,1,2))]. given #129 (H,wt=13): 188 T(x * y,y) = x * (x * (y / x)). [para(137(a,1),179(a,2,2))]. given #130 (H,wt=13): 193 x * T(y,x \ y) = T(x * y,y). [para(177(a,2),188(a,2,2)),flip(a)]. given #131 (H,wt=14): 67 (x * y) * L(z,y,x) = x * (y * z). [para(28(a,2),14(a,1,2))]. given #132 (H,wt=14): 68 L(x \ y,x,z) = (z * x) \ (z * y). [para(14(a,1),28(a,2,2,2))]. given #133 (H,wt=12): 201 L(x \ 1,x,y) = (y * x) \ y. [para(12(a,1),68(a,2,2))]. given #134 (H,wt=12): 207 x / L(y \ 1,y,x) = x * y. [para(201(a,2),53(a,1,2))]. given #135 (H,wt=14): 73 R(x,y,z) * (y * z) = (x * y) * z. [para(30(a,2),16(a,1,1))]. given #136 (H,wt=14): 74 R(x / y,y,z) = (x * z) / (y * z). [para(16(a,1),30(a,2,1,1))]. given #137 (H,wt=12): 211 R(1 / x,x,y) = y / (x * y). [para(11(a,1),74(a,2,1))]. given #138 (H,wt=12): 214 R(x \ 1,x,y) = y / (x * y). [para(129(a,1),211(a,1,1))]. given #139 (H,wt=14): 87 (x * (y * z)) / L(z,y,x) = x * y. [para(28(a,2),53(a,1,2))]. given #140 (H,wt=14): 89 R(x,y,z) \ ((x * y) * z) = y * z. [para(30(a,2),54(a,1,1))]. given #141 (H,wt=14): 117 (x * y) * x != x * z | y * x = z. [para(113(a,2),19(a,1))]. given #142 (H,wt=14): 142 L(T(T(x,y),z),u,x) = T(T(x,y),z). [para(140(a,1),40(a,2,1))]. given #143 (H,wt=14): 147 T(T(x,y),y \ x) = L(x,z,T(x,y)). [para(143(a,1),140(a,1,1)),flip(a)]. given #144 (H,wt=8): 218 L(x,y,T(x,z)) = x. [para(147(a,1),143(a,1))]. given #145 (H,wt=14): 160 x * y != z * x | T(y,y / x) = z. [para(149(a,1),20(a,1))]. given #146 (H,wt=14): 163 T(x,y) != x * z | K(y \ x,y) = z. [para(154(a,2),19(a,1))]. given #147 (H,wt=14): 175 x * y != z * x | T(y,x \ y) = z. [para(173(a,1),20(a,1))]. given #148 (H,wt=14): 203 L(x \ (y \ z),x,y) = (y * x) \ z. [para(14(a,1),68(a,2,2))]. given #149 (H,wt=14): 204 L(x \ (y * x),x,y) = T(y,y * x). [para(68(a,2),32(a,2)),flip(a)]. given #150 (H,wt=12): 220 L(T(x,y),y,x) = T(x,x * y). [para(32(a,2),204(a,1,1))]. given #151 (H,wt=9): 221 T(x,x * y) = T(x,y). [para(220(a,1),140(a,1))]. => 224 back subsumes hint matchers not on Sos. Reset weight to 512.000. given #152 (H,wt=9): 222 T(x,x \ y) = T(x,y). [para(14(a,1),221(a,1,2)),flip(a)]. given #153 (H,wt=9): 228 T(x,y) = (x \ y) \ y. [para(222(a,1),79(a,1))]. given #154 (H,wt=9): 229 x / T(y,x) = y \ x. [para(222(a,1),103(a,1,2))]. given #155 (H,wt=9): 230 T(x,T(y,x)) = T(x,y). [para(222(a,1),178(a,1,2))]. given #156 (H,wt=9): 231 (x \ y) * T(x,y) = y. [para(228(a,2),14(a,1,2))]. given #157 (H,wt=9): 232 T(x / y,x) = y \ x. [para(54(a,1),228(a,2,1))]. given #158 (H,wt=11): 223 T(x,T(y,x)) = T(x,y * x). [para(78(a,1),221(a,1,2)),flip(a)]. given #159 (H,wt=9): 245 T(x,y * x) = T(x,y). [para(223(a,1),230(a,1))]. given #160 (H,wt=9): 246 T(x,y / x) = T(x,y). [para(16(a,1),245(a,1,2)),flip(a)]. given #161 (H,wt=11): 225 T(T(x,y),(x * y) \ x) = x. [para(221(a,1),143(a,1,1))]. given #162 (H,wt=11): 233 T(x,y) \ y = T(x \ y,y). [para(228(a,2),228(a,2,1)),flip(a)]. given #163 (H,wt=11): 236 (x * y) / T(y,x) = T(x,y). [para(230(a,1),104(a,1,2))]. given #164 (H,wt=11): 237 ((x * y) \ x) * (y * x) = x. [para(116(a,1),231(a,1,2))]. given #165 (H,wt=11): 238 (x / y) * x = x * (y \ x). [para(232(a,1),78(a,1,2)),flip(a)]. given #166 (H,wt=11): 239 (x \ y) / y = y \ (y / x). [para(232(a,1),123(a,1,1))]. given #167 (H,wt=11): 244 T(x \ y,y) = T(x \ y,x). [para(232(a,1),98(a,1,1)),flip(a)]. given #168 (H,wt=11): 250 T(x,y) * T(y,x) = x * y. [para(236(a,1),16(a,1,1))]. given #169 (H,wt=13): 234 x / T(T(y,x),z) = T(y,z) \ x. [para(38(a,1),229(a,1,2))]. given #170 (H,wt=13): 240 T(x \ y,y \ (y / x)) = y / x. [para(232(a,1),143(a,1,1))]. given #171 (H,wt=13): 247 (x / y) * T(y,x) = y * (x / y). [para(246(a,1),78(a,1,2))]. given #172 (H,wt=13): 249 T((x * y) \ x,x) = (y * x) \ x. [para(116(a,1),233(a,1,1)),flip(a)]. given #173 (H,wt=13): 252 T(x \ y,x) = ((x \ y) \ y) \ y. [para(244(a,1),228(a,1))]. given #174 (H,wt=14): 208 x / L(y,y \ 1,x) = x * (y \ 1). [para(135(a,1),207(a,1,2,1))]. given #175 (H,wt=14): 212 R((x / y) / z,z,y) = x / (z * y). [para(16(a,1),74(a,2,1))]. given #176 (H,wt=14): 219 L(L(x,y,z),u,T(x,w)) = L(x,y,z). [para(218(a,1),45(a,1,1)),flip(a)]. given #177 (H,wt=14): 251 x * (y * z) != z | (z * y) \ z = x. [para(237(a,1),20(a,1)),flip(a)]. given #178 (H,wt=14): 254 T(L(x \ 1,x,y),y) = (x * y) \ y. [para(201(a,2),249(a,1,1))]. given #179 (H,wt=14): 257 L(T(x \ 1,y),x,y) = (x * y) \ y. [para(254(a,1),40(a,2))]. given #180 (H,wt=15): 83 x * ((x \ y) * (x * z)) = (y * x) * z. [para(14(a,1),47(a,1,1,1)),flip(a)]. given #181 (H,wt=13): 259 (x \ y) * (x * x) = T(y * x,x). [hyper(94,a,83,a),flip(a)]. given #182 (H,wt=15): 97 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(40(a,2),78(a,1,2))]. given #183 (H,wt=13): 262 L(x,y,z) * x = x * L(x,y,z). [para(77(a,1),97(a,1,2,1)),flip(a)]. given #184 (H,wt=8): 265 T(x,L(x,y,z)) = x. [hyper(94,a,262,a)]. given #185 (H,wt=8): 266 K(x,L(x,y,z)) = 1. [hyper(36,a,265,a)]. given #186 (H,wt=10): 264 T(x,L(x,y,z) \ x) = x. [hyper(175,a,262,a)]. given #187 (H,wt=13): 267 (L(x,y,z) \ x) * L(x,y,z) = x. [para(265(a,1),120(a,1)),flip(a)]. given #188 (H,wt=13): 268 x / L(x,y,z) = L(x,y,z) \ x. [para(265(a,1),123(a,1,1))]. given #189 (H,wt=13): 269 L(x,y,z) / x = x \ L(x,y,z). [para(265(a,1),229(a,1,2))]. given #190 (H,wt=15): 108 (x * y) / T(y * x,K(x,y)) = K(x,y). [para(61(a,1),88(a,1,1))]. given #191 (H,wt=11): 270 K(x,y) = (x * y) / (y * x). [para(159(a,1),108(a,1,2)),flip(a)]. given #192 (H,wt=15): 118 (x * (y * x)) * z = x * (y * (x * z)). [para(113(a,1),47(a,1,1))]. given #193 (H,wt=11): 272 (x * y) * y = x * (y * y). [hyper(117,a,118,a)]. given #194 (H,wt=6): 274 L(x,x,y) = x. [hyper(17,a,67,a,b,272,a),flip(a)]. given #195 (H,wt=6): 275 R(x,y,y) = x. [hyper(18,a,73,a,b,272,a(flip)),flip(a)]. given #196 (H,wt=11): 277 (x * y) / (y * y) = x / y. [para(275(a,1),74(a,1)),flip(a)]. given #197 (H,wt=11): 278 (x / y) / y = x / (y * y). [para(275(a,1),212(a,1))]. given #198 (H,wt=12): 276 L(L(x,y,z),x,u) = L(x,y,z). [para(274(a,1),45(a,1,1)),flip(a)]. given #199 (H,wt=13): 279 T(x / (y * y),y) = y \ (x / y). [para(278(a,1),80(a,1,1))]. given #200 (H,wt=13): 280 T(x,y / (x * x)) = T(x,y / x). [para(278(a,1),246(a,1,2))]. given #201 (H,wt=11): 281 T(x,y / (x * x)) = T(x,y). [para(280(a,2),246(a,1))]. given #202 (H,wt=15): 133 T(x,y) / T(x,z) = T(x,z) \ T(x,y). [para(102(a,1),123(a,1,1))]. given #203 (H,wt=15): 134 (x \ y) / (y / x) = (y / x) \ (x \ y). [para(105(a,1),123(a,1,1))]. given #204 (H,wt=15): 171 (x \ (x \ y)) * (x * x) = T(y,x * x). [para(170(a,1),120(a,2,1)),flip(a)]. given #205 (H,wt=13): 282 T((x \ y) * x,x) = T(y,x * x). [para(171(a,1),259(a,1)),flip(a)]. given #206 (H,wt=11): 284 T(T(x,y),y) = T(x,y * y). [para(120(a,2),282(a,1,1))]. given #207 (H,wt=15): 181 T(T(x,y),z \ x) = T(z * (x / z),y). [para(177(a,1),38(a,1,1)),flip(a)]. given #208 (H,wt=15): 187 K(x / y,y) / x = x \ K(x / y,y). [para(162(a,1),123(a,1,1))]. given #209 (H,wt=15): 191 T(T(x,y),z \ x) * z = z * T(x,y). [para(184(a,1),96(a,1,2)),flip(a)]. given #210 (H,wt=15): 192 x \ T(T(y,x \ y),z) = T(y,z) / x. [para(185(a,1),123(a,1,1)),flip(a)]. given #211 (H,wt=15): 235 x / L(T(y,x),z,u) = L(y,z,u) \ x. [para(40(a,2),229(a,1,2))]. given #212 (H,wt=15): 241 K(x \ (x / y),x) = (x / y) \ (y \ x). [para(232(a,1),127(a,2,2))]. given #213 (H,wt=15): 242 K(x,x \ (x / y)) = (y \ x) \ (x / y). [para(232(a,1),128(a,2,1))]. given #214 (H,wt=15): 243 (x \ y) * K(y,y \ (y / x)) = y / x. [para(232(a,1),156(a,1,1))]. given #215 (H,wt=15): 255 x * (((x \ y) \ y) \ y) = (x \ y) * x. [para(252(a,1),78(a,1,2))]. given #216 (H,wt=13): 289 T(x,y) = y * (((y \ x) \ x) \ x). [para(255(a,2),120(a,2))]. given #217 (H,wt=11): 290 x * (T(x,y) \ y) = T(y,x). [para(228(a,2),289(a,2,2,1)),flip(a)]. given #218 (H,wt=15): 256 x * (L(x,y,z) \ 1) = x / L(x,y,z). [para(141(a,1),208(a,1,2)),flip(a)]. given #219 (H,wt=15): 260 x \ ((y * x) * z) = (x \ y) * (x * z). [hyper(56,a,83,a)]. given #220 (H,wt=15): 261 (x * y) * (y \ z) = y * ((y \ x) * z). [para(14(a,1),83(a,1,2,2)),flip(a)]. given #221 (H,wt=15): 285 T(T(x,y \ x),z) = T(y * (x / y),z). [para(181(a,1),38(a,1)),flip(a)]. given #222 (H,wt=15): 287 T(T(x,y \ x),z) = y * (T(x,z) / y). [para(192(a,1),14(a,1,2)),flip(a)]. given #223 (H,wt=15): 291 (x * y) * ((y * x) \ x) = T(x,x * y). [para(116(a,1),290(a,1,2,1))]. given #224 (H,wt=13): 295 T(x,y) = (x * y) * ((y * x) \ x). [para(291(a,2),221(a,1)),flip(a)]. given #225 (H,wt=15): 292 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(256(a,2),268(a,1))]. given #226 (H,wt=15): 294 T(x * (y / x),z) = x * (T(y,z) / x). [para(177(a,1),287(a,1,1))]. given #227 (H,wt=16): 59 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(24(a,2),14(a,1,2))]. given #228 (H,wt=16): 69 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(16(a,1),28(a,2,1)),flip(a)]. given #229 (H,wt=14): 297 (1 / x) * (x * y) = L(y,x,1 / x). [para(69(a,1),49(a,1)),flip(a)]. given #230 (H,wt=14): 298 L(x,y,1 / y) / (y * x) = 1 / y. [hyper(58,a,297,a)]. given #231 (H,wt=14): 299 (1 / x) \ L(y,x,1 / x) = x * y. [hyper(56,a,297,a)]. given #232 (H,wt=14): 300 L(x \ y,x,1 / x) = (1 / x) * y. [para(14(a,1),297(a,1,2)),flip(a)]. given #233 (H,wt=14): 301 L(x \ y,x,x \ 1) = (1 / x) * y. [para(129(a,1),300(a,1,3))]. given #234 (H,wt=14): 302 L(x \ y,x,x \ 1) = (x \ 1) * y. [para(129(a,1),301(a,2,1))]. given #235 (H,wt=14): 303 (x \ 1) * (x * y) = L(y,x,x \ 1). [para(13(a,1),302(a,1,1)),flip(a)]. given #236 (H,wt=16): 70 L(x,y / x,z) = (z * (y / x)) \ (z * y). [para(16(a,1),28(a,2,2,2))]. given #237 (H,wt=16): 71 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(14(a,1),30(a,2,1,1))]. given #238 (H,wt=16): 75 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(16(a,1),30(a,2,2)),flip(a)]. given #239 (H,wt=16): 194 x * L(y,z,x / z) = (x / z) * (z * y). [para(16(a,1),67(a,1,1))]. given #240 (H,wt=16): 202 L((x \ y) \ z,x \ y,x) = y \ (x * z). [para(14(a,1),68(a,2,1))]. given #241 (H,wt=16): 215 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(14(a,1),89(a,1,2,1))]. given #242 (H,wt=16): 273 x * (y * L(z,x * y,y)) = (x * y) * z. [hyper(17,a,67,a(flip),b,118,a(flip))]. given #243 (H,wt=11): 304 L(L(x,y * z,z),z,y) = x. [hyper(17,a,67,a,b,273,a(flip)),flip(a)]. given #244 (H,wt=11): 305 L(L(x,y,z),z,y / z) = x. [para(16(a,1),304(a,1,1,2))]. given #245 (H,wt=8): 308 L(x,y,1 / y) = x. [para(112(a,1),305(a,1,1))]. given #246 (H,wt=8): 309 K(L(x,y,z),x) = 1. [para(305(a,1),266(a,1,2))]. given #247 (H,wt=8): 311 L(x,y,y \ 1) = x. [para(129(a,1),308(a,1,3))]. given #248 (H,wt=9): 312 x / (y * x) = 1 / y. [para(308(a,1),298(a,1,1))]. given #249 (H,wt=9): 313 (1 / x) \ y = x * y. [para(308(a,1),299(a,1,2))]. given #250 (H,wt=9): 314 (x \ 1) * y = x \ y. [para(311(a,1),302(a,1)),flip(a)]. given #251 (H,wt=9): 315 (x \ 1) * (x * y) = y. [para(311(a,1),303(a,2))]. given #252 (H,wt=9): 316 x / (y * x) = y \ 1. [para(312(a,2),129(a,1))]. given #253 (H,wt=9): 317 (x \ 1) \ y = x * y. [para(129(a,1),313(a,1,1))]. given #254 (H,wt=9): 318 (x \ y) / y = x \ 1. [hyper(58,a,314,a)]. given #255 (H,wt=9): 325 (x * y) \ x = y \ 1. [hyper(251,a,315,a)]. => 340 back subsumes hint matchers not on Sos. Reset weight to 511.000. given #256 (H,wt=9): 327 (x / y) \ 1 = y / x. [para(16(a,1),316(a,1,2)),flip(a)]. given #257 (H,wt=9): 332 x \ (x / y) = y \ 1. [para(318(a,1),239(a,1)),flip(a)]. given #258 (H,wt=9): 333 (x \ y) \ 1 = y \ x. [para(14(a,1),325(a,1,1)),flip(a)]. given #259 (H,wt=9): 334 x / (y \ 1) = x * y. [para(325(a,1),53(a,1,2))]. given #260 (H,wt=9): 338 T(T(x,y),y \ 1) = x. [para(325(a,1),225(a,1,2))]. => 363 back subsumes hint matchers not on Sos. Reset weight to 511.000. given #261 (H,wt=9): 345 x * (y \ 1) = x / y. [para(332(a,1),14(a,1,2))]. given #262 (H,wt=11): 306 L(L(x,y,z),z * y,y) = x. [para(304(a,1),45(a,1)),flip(a)]. given #263 (H,wt=11): 307 L(L(x,y,z / y),z,y) = x. [para(305(a,1),45(a,1)),flip(a)]. given #264 (H,wt=11): 320 T(x \ 1,y) = y \ (x \ y). [para(314(a,1),32(a,2,2))]. given #265 (H,wt=11): 324 T(x,y \ 1) = T(x,y \ x). [para(314(a,1),245(a,1,2)),flip(a)]. given #266 (H,wt=11): 329 T(x \ 1,y) = (x * y) \ y. [para(316(a,1),232(a,1,1))]. => 373 back subsumes hint matchers not on Sos. Reset weight to 513.000. given #267 (H,wt=11): 335 T(x,y) \ 1 = (x * y) \ y. [para(78(a,1),325(a,1,1)),flip(a)]. given #268 (H,wt=11): 337 T(x,y) \ 1 = y \ (x \ y). [para(231(a,1),325(a,1,1)),flip(a)]. given #269 (H,wt=11): 341 (x * y) \ 1 = y \ (x \ 1). [para(315(a,1),325(a,1,1)),flip(a)]. given #270 (H,wt=11): 343 (x / y) \ z = (y / x) * z. [para(327(a,1),314(a,1,1)),flip(a)]. given #271 (H,wt=11): 344 (x / y) * ((y / x) * z) = z. [para(327(a,1),315(a,1,1))]. given #272 (H,wt=11): 347 T(x \ y,x \ 1) = y / x. [para(332(a,1),240(a,1,2))]. => 383 back subsumes hint matchers not on Sos. Reset weight to 513.000. given #273 (H,wt=11): 353 (x \ y) \ z = (y \ x) * z. [para(333(a,1),314(a,1,1)),flip(a)]. given #274 (H,wt=11): 354 (x \ y) * ((y \ x) * z) = z. [para(333(a,1),315(a,1,1))]. given #275 (H,wt=11): 355 (x * (y \ z)) \ x = z \ y. [para(333(a,1),325(a,2))]. given #276 (H,wt=11): 356 x \ (x / (y \ z)) = z \ y. [para(333(a,1),332(a,2))]. given #277 (H,wt=11): 357 x / (y / z) = x * (z / y). [para(327(a,1),334(a,1,2))]. given #278 (H,wt=11): 358 x / (y \ z) = x * (z \ y). [para(333(a,1),334(a,1,2))]. given #279 (H,wt=11): 359 T(x * y,y \ 1) = y * x. [para(116(a,1),338(a,1,1))]. given #280 (H,wt=11): 360 T(x,y \ 1) * y = y * x. [para(338(a,1),96(a,1,2)),flip(a)]. given #281 (H,wt=11): 361 T(x \ y,y \ 1) = y / x. [para(232(a,1),338(a,1,1))]. given #282 (H,wt=11): 362 T(x,y \ 1) \ y = y / x. [para(338(a,1),234(a,1,2)),flip(a)]. given #283 (H,wt=11): 367 (x \ 1) / y = x \ (y \ 1). [para(345(a,1),314(a,1))]. given #284 (H,wt=11): 372 T(x,y \ 1) = y * (x / y). [para(324(a,2),177(a,1))]. given #285 (H,wt=11): 374 (x * y) \ y = y \ (x \ y). [para(329(a,1),320(a,1))]. given #286 (H,wt=11): 375 T(x,y) \ 1 = T(x \ 1,y). [para(335(a,2),329(a,2)),flip(a)]. given #287 (H,wt=11): 380 (x / y) \ y = y * (x \ y). [para(343(a,2),238(a,1))]. given #288 (H,wt=11): 382 T(x,y \ 1) = (y * x) / y. [para(13(a,1),347(a,1,1))]. given #289 (H,wt=11): 388 (x \ y) \ x = y \ (x * x). [para(169(a,1),356(a,1,2)),flip(a)]. given #290 (H,wt=11): 391 (x * y) * (y \ x) = x * x. [para(358(a,1),168(a,1))]. given #291 (H,wt=11): 401 x \ (y * y) = (x \ y) * y. [para(388(a,1),353(a,1))]. given #292 (H,wt=13): 310 L(x,y * z,z) = L(x,y,z / y). [para(304(a,1),305(a,1,1)),flip(a)]. given #293 (H,wt=13): 330 (x * (y / x)) \ 1 = x / (x * y). [para(138(a,1),318(a,1,1)),flip(a)]. given #294 (H,wt=13): 336 (x * y) \ (y * x) = K(x,y) \ 1. [para(61(a,1),325(a,1,1))]. given #295 (H,wt=9): 404 K(x,y) \ 1 = K(y,x). [para(336(a,1),26(a,2)),flip(a)]. given #296 (H,wt=9): 405 K(x,y) * K(y,x) = 1. [para(404(a,1),14(a,1,2))]. given #297 (H,wt=11): 406 K(x,y) \ z = K(y,x) * z. [para(404(a,1),314(a,1,1)),flip(a)]. given #298 (H,wt=11): 407 K(x,y) * (K(y,x) * z) = z. [para(404(a,1),315(a,1,1))]. given #299 (H,wt=11): 408 (x * K(y,z)) \ x = K(z,y). [para(404(a,1),325(a,2))]. given #300 (H,wt=11): 409 x / K(y,z) = x * K(z,y). [para(404(a,1),334(a,1,2))]. given #301 (H,wt=11): 414 (x * K(y,z)) * K(z,y) = x. [para(408(a,1),14(a,1,2))]. given #302 (H,wt=13): 346 x \ (T(x,y) \ x) = T(x,y) \ 1. [para(132(a,1),332(a,1,2))]. given #303 (H,wt=13): 348 (x / y) \ (y \ x) = K(y \ 1,x). [para(332(a,1),241(a,1,1)),flip(a)]. => 419 back subsumes hint matchers not on Sos. Reset weight to 515.000. given #304 (H,wt=13): 349 (x \ y) \ (y / x) = K(y,x \ 1). [para(332(a,1),242(a,1,2)),flip(a)]. => 420 back subsumes hint matchers not on Sos. Reset weight to 515.000. given #305 (H,wt=13): 350 (x \ y) * K(y,x \ 1) = y / x. [para(332(a,1),243(a,1,2,2))]. => 422 back subsumes hint matchers not on Sos. Reset weight to 515.000. given #306 (H,wt=13): 364 x * (T(x,y) \ 1) = T(x,y) \ x. [para(345(a,2),132(a,1))]. given #307 (H,wt=13): 368 L(L(x,y,y \ z),T(z,y),y) = x. [para(120(a,2),306(a,1,2))]. given #308 (H,wt=13): 371 L(L(x,y,z \ 1),z \ y,y) = x. [para(314(a,1),306(a,1,2))]. given #309 (H,wt=13): 376 (x \ (y \ x)) * z = T(y,x) \ z. [para(337(a,1),314(a,1,1))]. given #310 (H,wt=13): 377 x * (y \ (z \ y)) = x / T(z,y). [para(337(a,1),345(a,1,2))]. given #311 (H,wt=13): 378 (x \ (y \ 1)) * z = (y * x) \ z. [para(341(a,1),314(a,1,1))]. given #312 (H,wt=13): 379 x * (y \ (z \ 1)) = x / (z * y). [para(341(a,1),345(a,1,2))]. given #313 (H,wt=13): 398 T(x \ (y \ 1),y) = y \ (x \ 1). [para(367(a,1),80(a,1,1))]. given #314 (H,wt=13): 400 T(x \ 1,y) * z = T(x,y) \ z. [para(375(a,1),314(a,1,1))]. given #315 (H,wt=13): 416 x \ (T(x,y) \ x) = T(x \ 1,y). [para(346(a,2),375(a,1))]. given #316 (H,wt=13): 417 (x / y) * K(y \ 1,x) = y \ x. [para(348(a,1),14(a,1,2))]. given #317 (H,wt=13): 418 (x \ y) / (y / x) = K(x \ 1,y). [para(348(a,1),134(a,2))]. given #318 (H,wt=13): 421 (x \ y) * (x / y) = K(x,y \ 1). [para(349(a,1),353(a,1)),flip(a)]. given #319 (H,wt=13): 423 x * T(x \ 1,y) = T(x,y) \ x. [para(375(a,1),364(a,1,2))]. given #320 (H,wt=13): 426 (x \ y) * (x / y) = K(x \ 1,y). [para(418(a,1),357(a,1)),flip(a)]. given #321 (H,wt=11): 427 K(x \ 1,y) = K(x,y \ 1). [para(426(a,1),421(a,1))]. given #322 (H,wt=13): 428 K(x \ 1,y \ z) = K(x,z \ y). [para(333(a,1),427(a,2,2))]. given #323 (H,wt=13): 429 (x / y) * K(y,x \ 1) = y \ x. [para(427(a,1),417(a,1,2))]. given #324 (H,wt=14): 381 (x / y) * z != u | (y / x) * u = z. [para(344(a,1),19(a,1)),flip(a)]. given #325 (H,wt=14): 387 (x \ y) * z != u | (y \ x) * u = z. [para(354(a,1),19(a,1)),flip(a)]. given #326 (H,wt=14): 413 K(x,y) * z != u | K(y,x) * u = z. [para(407(a,1),19(a,1)),flip(a)]. given #327 (H,wt=14): 415 x * K(y,z) != u | u * K(z,y) = x. [para(414(a,1),20(a,1)),flip(a)]. given #328 (H,wt=15): 321 ((x * (y / x)) \ 1) * y = K(y / x,x). [para(314(a,2),64(a,1))]. given #329 (H,wt=13): 430 (x / (x * y)) * y = K(y / x,x). [para(330(a,1),321(a,1,1))]. given #330 (H,wt=13): 431 K(x / y,y) / x = y / (y * x). [hyper(58,a,430,a)]. given #331 (H,wt=13): 432 x \ K(x / y,y) = y / (y * x). [para(431(a,1),187(a,1)),flip(a)]. given #332 (H,wt=15): 331 T(x \ (y \ 1),x) = x \ (x \ (y \ x)). [para(318(a,1),153(a,1,1,2))]. given #333 (H,wt=15): 384 ((x \ y) * z) * (y \ x) = T(z,y \ x). [para(353(a,1),120(a,2,1)),flip(a)]. given #334 (H,wt=15): 386 ((x \ y) * z) \ u = (z \ (y \ x)) * u. [para(353(a,1),353(a,1,1))]. given #335 (H,wt=15): 389 (x * (y / z)) \ u = ((z / y) / x) * u. [para(357(a,1),343(a,1,1))]. given #336 (H,wt=15): 390 x / (y * (z / u)) = x * ((u / z) / y). [para(357(a,1),357(a,1,2))]. given #337 (H,wt=15): 392 (x * (y \ z)) \ u = ((z \ y) / x) * u. [para(358(a,1),343(a,1,1))]. given #338 (H,wt=15): 393 x / ((y \ z) * u) = x * (u \ (z \ y)). [para(353(a,1),358(a,1,2))]. given #339 (H,wt=15): 394 x / (y * (z \ u)) = x * ((u \ z) / y). [para(358(a,1),357(a,1,2))]. given #340 (H,wt=15): 395 T(T(x,y),z \ 1) = T(T(x,y),z \ x). [hyper(18,a,191,a,b,360,a)]. given #341 (H,wt=15): 396 T(x,y \ z) * (z \ y) = (z \ y) * x. [para(333(a,1),360(a,1,1,2))]. given #342 (H,wt=15): 397 x / T(y,x \ 1) = T(x / y,x \ 1). [para(362(a,1),361(a,1,1)),flip(a)]. given #343 (H,wt=15): 399 (x \ (y \ 1)) / z = (y * x) \ (z \ 1). [para(341(a,1),367(a,1,1))]. given #344 (H,wt=15): 402 (x / y) * (x / y) = x * (y \ (x / y)). [para(16(a,1),391(a,1,1)),flip(a)]. given #345 (H,wt=15): 403 L(x,y \ z,y) = L(x,(y \ z) * z,z). [para(53(a,1),310(a,2,3)),flip(a)]. given #346 (H,wt=15): 410 (K(x,y) * z) / K(x,y) = T(z,K(y,x)). [para(404(a,1),382(a,1,2)),flip(a)]. given #347 (H,wt=15): 411 K(x,y) * (z * K(y,x)) = T(z,K(y,x)). [para(406(a,1),32(a,2)),flip(a)]. given #348 (H,wt=15): 412 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(406(a,1),353(a,1,1))]. given #349 (H,wt=15): 425 (x \ 1) * (T(x,y) \ x) = T(x \ 1,y). [para(416(a,1),314(a,2))]. given #350 (H,wt=15): 436 T(x \ 1,y) \ (x \ 1) = x \ T(x,y). [para(425(a,1),355(a,1,1))]. given #351 (H,wt=16): 328 (x * y) / ((z * x) * y) = R(z,x,y) \ 1. [para(73(a,1),316(a,1,2))]. given #352 (H,wt=16): 342 L(x / y,y / x,z) = (z * (y / x)) \ z. [para(327(a,1),201(a,1,1))]. given #353 (H,wt=14): 437 L(x / y,y / x,z) = (y / x) \ 1. [para(342(a,2),325(a,1))]. => 438 back subsumes hint matchers not on Sos. Reset weight to 516.000. given #354 (H,wt=12): 439 L(x / y,y / x,z) = x / y. [para(437(a,2),327(a,1))]. given #355 (H,wt=14): 440 L(x,y / (x * y),z) = (x * y) / y. [para(15(a,1),439(a,1,1))]. given #356 (H,wt=12): 441 L(x,x \ 1,y) = (x * z) / z. [para(316(a,1),440(a,1,2))]. => 443 back subsumes hint matchers not on Sos. Reset weight to 514.000. given #357 (H,wt=8): 442 L(x,x \ 1,y) = x. [para(441(a,2),15(a,1))]. given #358 (H,wt=8): 445 L(x,y,x \ 1) = x. [para(442(a,1),307(a,1,1))]. given #359 (H,wt=10): 446 L(x \ 1,y,x) = x \ 1. [para(135(a,1),445(a,1,3))]. given #360 (H,wt=12): 444 L(T(x,y),x \ 1,z) = T(x,y). [para(442(a,1),40(a,2,1))]. given #361 (H,wt=16): 352 R(x \ y,y \ x,z) = z / ((y \ x) * z). [para(333(a,1),214(a,1,1))]. given #362 (H,wt=14): 448 R(x \ y,y \ x,z) = (y \ x) \ 1. [para(352(a,2),316(a,1))]. => 449 back subsumes hint matchers not on Sos. Reset weight to 516.000. given #363 (H,wt=12): 450 R(x \ y,y \ x,z) = x \ y. [para(448(a,2),333(a,1))]. given #364 (H,wt=14): 451 R(x,(y * x) \ y,z) = y \ (y * x). [para(13(a,1),450(a,1,1))]. given #365 (H,wt=12): 452 R(x,x \ 1,y) = z \ (z * x). [para(325(a,1),451(a,1,2))]. => 454 back subsumes hint matchers not on Sos. Reset weight to 514.000. given #366 (H,wt=8): 453 R(x,x \ 1,y) = x. [para(452(a,2),13(a,1))]. given #367 (H,wt=12): 455 R(T(x,y),x \ 1,z) = T(x,y). [para(453(a,1),42(a,2,1))]. given #368 (H,wt=16): 370 L((x * y) \ z,x * y,y) = y \ (x \ z). [para(203(a,1),306(a,1,1))]. given #369 (H,wt=15): 458 (x * (y * x)) \ z = x \ (y \ (x \ z)). [para(370(a,1),203(a,1)),flip(a)]. given #370 (H,wt=16): 385 L((x \ y) * z,y \ x,y) = x \ (y * z). [para(353(a,1),202(a,1,1))]. given #371 (H,wt=16): 434 L(x,y / x,z) = ((x / y) / z) * (z * y). [para(389(a,1),70(a,2))]. given #372 (H,wt=16): 435 R(x,x \ y,z) = (y * z) * (z \ (y \ x)). [para(393(a,1),71(a,2))]. given #373 (H,wt=16): 447 L(L(x \ 1,y,z),u,x) = L(x \ 1,y,z). [para(446(a,1),45(a,1,1)),flip(a)]. given #374 (H,wt=16): 457 x \ (y \ ((y * x) * z)) = L(z,y * x,x). [para(13(a,1),370(a,1,1)),flip(a)]. given #375 (H,wt=16): 459 R(x,x \ y,z) = z * ((z \ y) * (y \ x)). [para(435(a,2),261(a,1))]. given #376 (H,wt=17): 164 T(x,y) * K(T(y \ x,y),y) = T(T(x,y),y). [para(125(a,1),154(a,2,2,1)),flip(a)]. given #377 (H,wt=17): 186 T(T(T(T(x,y),z),y \ x),T(x,y) / z) = x. [para(151(a,2),143(a,1))]. given #378 (H,wt=11): 462 T(T(x,y),T(x,z) / y) = x. [para(144(a,1),186(a,1,1))]. => 463 back subsumes hint matchers not on Sos. Reset weight to 517.000. given #379 (H,wt=13): 464 T(x,(T(x,y) / z) \ x) = T(x,z). [para(462(a,1),184(a,1,1))]. given #380 (H,wt=13): 465 T(x,(y / T(x,z)) * x) = T(x,y). [para(343(a,1),464(a,1,2))]. given #381 (H,wt=11): 466 T(x,y / T(x,z)) = T(x,y). [para(465(a,1),245(a,1)),flip(a)]. given #382 (H,wt=17): 195 (x * y) * z != x * (y * u) | L(u,y,x) = z. [para(67(a,1),19(a,1)),flip(a)]. given #383 (H,wt=17): 196 (x * y) * L(z,y,x) != x * u | y * z = u. [para(67(a,2),19(a,1))]. given #384 (H,wt=17): 200 (x * y) * L(x,z,u) = x * (y * L(x,z,u)). [para(141(a,1),67(a,1,2))]. given #385 (H,wt=9): 467 R(x,y,L(x,z,u)) = x. [hyper(18,a,73,a,b,200,a(flip)),flip(a)]. given #386 (H,wt=17): 209 (x * y) * z != u * (y * z) | R(x,y,z) = u. [para(73(a,1),20(a,1))]. given #387 (H,wt=17): 226 (x * y) * T(T(x,y),z) = T(x,z) * (x * y). [para(221(a,1),96(a,1,2,1))]. given #388 (H,wt=17): 227 T(T(T(x,y),z),y \ x) = T(x,T(x,y) * z). [para(221(a,1),144(a,1,1))]. given #389 (H,wt=11): 469 T(x,T(x,y) * z) = T(x,z). [para(227(a,1),144(a,1))]. => 470 back subsumes hint matchers not on Sos. Reset weight to 517.000. given #390 (H,wt=17): 248 T(x * (y / x),y / x) = T(x,y) * (y / x). [para(246(a,1),122(a,2,1))]. given #391 (H,wt=17): 263 L(x / y,z,u) * y = y * L(y \ x,z,u). [para(80(a,1),97(a,1,2,1)),flip(a)]. given #392 (H,wt=17): 366 x * (y * (x * (z \ 1))) = (x * (y * x)) / z. [para(345(a,1),118(a,1)),flip(a)]. given #393 (H,wt=15): 472 (x * (y * x)) / z = x * (y * (x / z)). [para(345(a,1),366(a,1,2,2)),flip(a)]. given #394 (H,wt=17): 369 L(L(x,y,z),z * y,y) = L(x,u,L(x,y,z)). [para(306(a,1),141(a,1,1)),flip(a)]. given #395 (H,wt=9): 473 L(x,y,L(x,z,u)) = x. [para(369(a,1),306(a,1))]. given #396 (H,wt=17): 461 T(x,y) * K(T(y \ x,y),y) = T(x,y * y). [para(164(a,2),284(a,1))]. given #397 (H,wt=17): 468 x \ (y * L(x,z,u)) = (x \ y) * L(x,z,u). [para(467(a,1),215(a,1,1))]. given #398 (H,wt=17): 471 (x * L(x \ y,z,u)) / x = L(y / x,z,u). [hyper(58,a,263,a)]. given #399 (H,wt=18): 60 (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y). [para(14(a,1),24(a,2,1,2)),flip(a)]. given #400 (H,wt=18): 72 R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)). [para(14(a,1),30(a,2,1))]. given #401 (H,wt=18): 199 (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z). [para(78(a,1),67(a,1,1))]. given #402 (H,wt=18): 205 L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z). [para(78(a,1),68(a,2,1))]. given #403 (H,wt=18): 206 L(x \ y,x,z) * (z * x) = T(z * y,z * x). [para(68(a,2),120(a,2,1)),flip(a)]. given #404 (H,wt=18): 210 R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y). [para(78(a,1),73(a,1,2))]. given #405 (H,wt=18): 213 R((x * y) / z,z,x) = (x * (y * x)) / (z * x). [para(113(a,1),74(a,2,1))]. given #406 (H,wt=18): 216 R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z). [para(14(a,1),89(a,1,2))]. given #407 (H,wt=18): 286 x * T(y,z) != u * x | T(T(y,z),x \ y) = u. [para(191(a,1),20(a,1))]. given #408 (H,wt=18): 319 (x * (y \ 1)) \ (x * (y \ z)) = L(z,y \ 1,x). [para(314(a,1),28(a,2,2,2)),flip(a)]. given #409 (H,wt=16): 477 (x / y) \ (x * (y \ z)) = L(z,y \ 1,x). [para(345(a,1),319(a,1,1))]. given #410 (H,wt=16): 478 L(x * y,x \ 1,z) = (z / x) \ (z * y). [para(13(a,1),477(a,1,2,2)),flip(a)]. given #411 (H,wt=16): 479 (x / y) * L(z,y \ 1,x) = x * (y \ z). [para(477(a,1),14(a,1,2))]. given #412 (H,wt=15): 483 (x / y) * T(y,z) = x * (y \ T(y,z)). [para(444(a,1),479(a,1,2))]. given #413 (H,wt=16): 480 (x / y) * (y * (x \ z)) = L(z,x \ 1,y). [para(477(a,1),343(a,1)),flip(a)]. given #414 (H,wt=16): 481 L(x * y,x \ 1,z) = (x / z) * (z * y). [para(478(a,2),343(a,1))]. given #415 (H,wt=18): 322 (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). [para(314(a,1),67(a,1,1))]. given #416 (H,wt=16): 484 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(322(a,2),314(a,1))]. given #417 (H,wt=18): 323 L(x \ y,x,z \ 1) = (z \ x) \ ((z \ 1) * y). [para(314(a,1),68(a,2,1))]. given #418 (H,wt=16): 486 L(x \ y,x,z \ 1) = (z \ x) \ (z \ y). [para(314(a,1),323(a,2,2))]. given #419 (H,wt=16): 487 L(x \ (y * z),x,y \ 1) = (y \ x) \ z. [para(315(a,1),323(a,2,2))]. given #420 (H,wt=16): 488 L(x \ y,x,z \ 1) = (x \ z) * (z \ y). [para(486(a,2),353(a,1))]. given #421 (H,wt=16): 489 L(x \ (y * z),x,y \ 1) = (x \ y) * z. [para(487(a,2),353(a,1))]. given #422 (H,wt=18): 326 R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). [para(315(a,1),30(a,2,1,1))]. given #423 (H,wt=15): 490 R(x \ 1,x * y,z) = R(x,y,z) \ 1. [para(326(a,2),328(a,1))]. given #424 (H,wt=18): 339 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(59(a,1),325(a,1,1))]. given #425 (H,wt=18): 365 R(x,y,z \ 1) * (y / z) = (x * y) * (z \ 1). [para(345(a,1),73(a,1,2))]. given #426 (H,wt=16): 491 R(x,y,z \ 1) * (y / z) = (x * y) / z. [para(365(a,2),345(a,1))]. given #427 (H,wt=18): 474 (x * y) \ (z * ((z \ x) * y)) = a(x,z,z \ y). [para(261(a,1),60(a,1,2))]. given #428 (H,wt=18): 475 R(x,y,(x * y) \ z) = z * ((z \ (x * y)) / y). [para(72(a,2),394(a,1))]. given #429 (H,wt=18): 476 R((x * y) / z,z,x) = x * (y * (x / (z * x))). [para(213(a,2),472(a,1))]. given #430 (H,wt=16): 492 R((x * y) / z,z,x) = x * (y * (z \ 1)). [para(316(a,1),476(a,2,2,2))]. => 493 back subsumes hint matchers not on Sos. Reset weight to 518.000. given #431 (H,wt=14): 494 R((x * y) / z,z,x) = x * (y / z). [para(345(a,1),492(a,2,2))]. given #432 (H,wt=14): 495 R(x / y,y,z) = z * ((z \ x) / y). [para(14(a,1),494(a,1,1,1))]. given #433 (H,wt=14): 496 x \ R(y / z,z,x) = (x \ y) / z. [hyper(56,a,495,a(flip))]. given #434 (H,wt=14): 497 R(x,y,z) = z * ((z \ (x * y)) / y). [para(15(a,1),495(a,1,1))]. given #435 (H,wt=13): 499 R(x,y,(x * y) \ z) = R(x,y,z). [para(497(a,2),475(a,2))]. given #436 (H,wt=13): 500 R(x,y,(x * y) * z) = R(x,y,z). [para(13(a,1),499(a,1,3)),flip(a)]. given #437 (H,wt=14): 502 R(x,y,z) \ z = y * ((x * y) \ z). [para(499(a,1),216(a,1,1))]. given #438 (H,wt=15): 501 R(x,x \ y,y \ z) = R(x,x \ y,z). [para(14(a,1),499(a,1,3,1))]. given #439 (H,wt=18): 485 x * L(y,z * x,z \ 1) = z \ ((z * x) * y). [para(13(a,1),484(a,1,1))]. given #440 (H,wt=18): 503 R(x * y,x,z) \ z = x * ((x * (y * x)) \ z). [para(113(a,1),502(a,2,2,1))]. given #441 (H,wt=18): 504 x \ (y \ ((y * x) * z)) = L(z,y * x,y \ 1). [hyper(56,a,485,a)]. given #442 (H,wt=15): 506 L(x,y * z,y \ 1) = L(x,y * z,z). [para(504(a,1),457(a,1))]. given #443 (H,wt=18): 505 R(x * y,x,z) \ z = x * (x \ (y \ (x \ z))). [para(458(a,1),503(a,2,2))]. given #444 (H,wt=14): 507 R(x * y,x,z) \ z = y \ (x \ z). [para(505(a,2),14(a,1))]. given #445 (H,wt=19): 172 (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y). [para(79(a,1),96(a,1,2,1))]. given #446 (H,wt=19): 190 K(T(x,y) \ (x * y),T(x,y)) = (x * y) \ (y * x). [para(189(a,1),127(a,2,2))]. given #447 (H,wt=17): 508 K(T(x,T(y,x)),T(y,x)) = (y * x) \ (x * y). [para(95(a,1),190(a,1,1))]. given #448 (H,wt=13): 509 K(T(x,T(y,x)),T(y,x)) = K(x,y). [para(508(a,2),26(a,2)),flip(a)]. given #449 (H,wt=11): 510 K(T(x,y),T(y,x)) = K(x,y). [para(230(a,1),509(a,1,1))]. given #450 (H,wt=13): 511 K(T(x,y),T(y,T(x,y))) = K(x,y). [para(230(a,2),510(a,1,2))]. given #451 (H,wt=19): 217 (x * y) * T(T(x,z),u) = x * (y * T(T(x,z),u)). [para(142(a,1),67(a,1,2))]. given #452 (H,wt=17): 513 x * (y * T(T(x,y),z)) = T(x,z) * (x * y). [para(217(a,1),226(a,1))]. given #453 (H,wt=15): 514 T(x,y) * (x * z) = x * (T(x,y) * z). [para(96(a,1),513(a,1,2)),flip(a)]. given #454 (H,wt=15): 515 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(14(a,1),514(a,1,2)),flip(a)]. given #455 (H,wt=18): 516 T(x,y) * (x * z) != x * u | T(x,y) * z = u. [para(514(a,2),19(a,1))]. given #456 (H,wt=18): 517 T(x,y) * z != x * u | T(x,y) * (x \ z) = u. [para(515(a,1),19(a,1))]. given #457 (H,wt=19): 258 (x * y) * ((y * x) \ x) = x * (y * T(y \ 1,x)). [para(257(a,1),67(a,1,2))]. given #458 (H,wt=13): 518 x * (y * T(y \ 1,x)) = T(x,y). [para(258(a,1),295(a,2)),flip(a)]. given #459 (H,wt=11): 520 x * (T(y,x) \ y) = T(x,y). [para(423(a,1),518(a,1,2))]. given #460 (H,wt=11): 521 K(x \ y,x) = T(x,y) \ x. [hyper(17,a,154,a(flip),b,520,a),flip(a)]. given #461 (H,wt=9): 524 K(x,K(x \ y,x)) = 1. [para(521(a,2),150(a,1,2))]. given #462 (H,wt=7): 525 K(x,K(y,x)) = 1. [para(13(a,1),524(a,1,2,1))]. given #463 (H,wt=7): 526 T(x,K(y,x)) = x. [hyper(37,a,525,a)]. given #464 (H,wt=11): 528 K(x,y) / y = y \ K(x,y). [para(526(a,1),229(a,1,2))]. given #465 (H,wt=14): 522 T(x,y) != x * z | T(y,x) \ y = z. [para(520(a,1),19(a,1))]. given #466 (H,wt=15): 523 x * ((y * x) \ (x * y)) = T(x,x * y). [para(116(a,1),520(a,1,2,1))]. given #467 (H,wt=11): 529 T(x,x * y) = x * K(x,y). [para(26(a,2),523(a,1,2)),flip(a)]. given #468 (H,wt=9): 530 T(x,y) = x * K(x,y). [para(529(a,1),221(a,1)),flip(a)]. given #469 (H,wt=9): 531 K(x,y) = T(y,x) \ y. [hyper(522,a,530,a),flip(a)]. given #470 (H,wt=9): 532 K(x \ y,x) = K(y,x). [hyper(163,a,530,a)]. given #471 (H,wt=7): 543 T(x,K(x,y)) = x. [para(532(a,1),158(a,1,2))]. given #472 (H,wt=9): 533 T(x,y) * K(y,x) = x. [hyper(415,a,530,a(flip))]. given #473 (H,wt=9): 534 K(x,y) = x \ T(x,y). [hyper(56,a,530,a(flip)),flip(a)]. given #474 (H,wt=9): 537 T(x,y) = x / K(y,x). [para(530(a,2),409(a,2)),flip(a)]. given #475 (H,wt=9): 538 K(x,x \ y) = K(x,y). [para(531(a,2),128(a,2))]. given #476 (H,wt=9): 539 K(x,y) = y / T(y,x). [para(531(a,2),132(a,2)),flip(a)]. given #477 (H,wt=9): 542 K(x * y,x) = K(y,x). [para(13(a,1),532(a,1,1)),flip(a)]. given #478 (H,wt=9): 544 T(x,y) = K(x,y) * x. [para(532(a,1),155(a,2,1))]. given #479 (H,wt=9): 545 T(K(x,y),x) = K(x,y). [hyper(35,a,543,a)]. given #480 (H,wt=9): 551 T(x,y) = K(y,x) \ x. [para(539(a,2),54(a,1,1)),flip(a)]. given #481 (H,wt=11): 535 K(x,y) = y * T(y \ 1,x). [hyper(17,a,518,a,b,530,a(flip))]. given #482 (H,wt=11): 540 T(x \ 1,y) = x \ K(y,x). [para(531(a,2),416(a,1,2)),flip(a)]. given #483 (H,wt=11): 541 K(x,y \ 1) = y \ T(y,x). [para(531(a,2),436(a,1))]. given #484 (H,wt=9): 559 K(x,y \ 1) = K(y,x). [para(541(a,2),534(a,2)),flip(a)]. given #485 (H,wt=9): 560 K(x \ 1,y) = K(y,x). [para(135(a,1),559(a,1,2)),flip(a)]. given #486 (H,wt=11): 546 K(x,y * x) = x \ T(x,y). [para(245(a,1),534(a,2,2))]. given #487 (H,wt=9): 569 K(x,y * x) = K(x,y). [para(546(a,2),534(a,2)),flip(a)]. given #488 (H,wt=9): 570 K(x,y / x) = K(x,y). [para(16(a,1),569(a,1,2)),flip(a)]. given #489 (H,wt=11): 553 T(x,y) = K(x,y / x) * x. [para(544(a,1),246(a,1)),flip(a)]. given #490 (H,wt=11): 556 T(x \ 1,y) = K(y,x) / x. [para(540(a,2),528(a,2)),flip(a)]. given #491 (H,wt=11): 557 T(x,y) = x * K(y,x \ 1). [para(541(a,2),14(a,1,2)),flip(a)]. given #492 (H,wt=11): 558 T(x,y) = K(y,x \ 1) * x. [para(541(a,2),126(a,1,1)),flip(a)]. given #493 (H,wt=11): 561 K(x / y,z) = K(z,y / x). [para(327(a,1),559(a,1,2)),flip(a)]. given #494 (H,wt=11): 562 K(x \ y,z) = K(z,y \ x). [para(333(a,1),559(a,1,2)),flip(a)]. given #495 (H,wt=9): 578 K(x,y \ x) = K(y,x). [para(562(a,1),532(a,1))]. given #496 (H,wt=9): 579 K(x \ y,y) = K(y,x). [para(562(a,2),538(a,1))]. given #497 (H,wt=9): 580 K(x,x / y) = K(y,x). [para(54(a,1),579(a,1,1)),flip(a)]. given #498 (H,wt=9): 581 K(x / y,y) = K(x,y). [para(580(a,1),561(a,2))]. given #499 (H,wt=9): 582 K(x * y,y) = K(x,y). [para(15(a,1),581(a,1,1)),flip(a)]. NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 31 (0.00 of 2.85 sec). given #500 (H,wt=11): 565 K(K(x,y),z) = K(z,K(y,x)). [para(404(a,1),559(a,1,2)),flip(a)]. given #501 (H,wt=11): 566 (x \ y) * K(x,y) = y / x. [para(559(a,1),350(a,1,2))]. given #502 (H,wt=11): 567 K(x * y,x) = K(x,y \ 1). [para(559(a,2),542(a,2))]. given #503 (H,wt=11): 571 K(x,x \ y) = K(x,T(y,x)). [para(120(a,2),569(a,1,2)),flip(a)]. given #504 (H,wt=9): 585 K(x,T(y,x)) = K(x,y). [para(571(a,1),538(a,1))]. given #505 (H,wt=9): 586 K(T(x,y),y) = K(x,y). [para(585(a,1),511(a,1))]. given #506 (H,wt=11): 572 x * K(y,x) = y * (x / y). [para(570(a,1),106(a,1,2))]. given #507 (H,wt=11): 573 T(x,y \ x) = x * K(y,x). [para(570(a,1),183(a,1,2)),flip(a)]. given #508 (H,wt=11): 583 x \ K(x,y) = y / (y * x). [para(581(a,1),432(a,1,2))]. given #509 (H,wt=11): 588 (x * (y / x)) * K(y,x) = y. [hyper(415,a,572,a)]. given #510 (H,wt=13): 547 K(x,y / T(x,z)) = x \ T(x,y). [para(466(a,1),534(a,2,2))]. given #511 (H,wt=11): 592 K(x,y / T(x,z)) = K(x,y). [para(547(a,2),534(a,2)),flip(a)]. given #512 (H,wt=11): 593 K(x,y * T(x,z)) = K(x,y). [para(15(a,1),592(a,1,2)),flip(a)]. given #513 (H,wt=13): 548 K(x,T(x,y) * z) = x \ T(x,z). [para(469(a,1),534(a,2,2))]. given #514 (H,wt=11): 595 K(x,T(x,y) * z) = K(x,z). [para(548(a,2),534(a,2)),flip(a)]. given #515 (H,wt=11): 596 K(x,T(x,y) \ z) = K(x,z). [para(14(a,1),595(a,1,2)),flip(a)]. given #516 (H,wt=13): 549 (x / y) * T(y,z) = x * K(y,z). [para(534(a,2),483(a,2,2))]. given #517 (H,wt=13): 550 (K(x,y) / y) * z = T(y,x) \ z. [para(537(a,2),343(a,1,1)),flip(a)]. given #518 (H,wt=13): 554 x * (y \ K(z,y)) = x / T(y,z). [para(551(a,2),358(a,1,2)),flip(a)]. given #519 (H,wt=13): 563 K(x,y \ (z \ 1)) = K(z * y,x). [para(341(a,1),559(a,1,2))]. given #520 (H,wt=13): 564 K(x,T(y \ 1,z)) = K(T(y,z),x). [para(375(a,1),559(a,1,2))]. given #521 (H,wt=13): 568 T(x \ 1,y \ 1) = x \ K(x,y). [para(560(a,1),540(a,2,2))]. given #522 (H,wt=13): 577 T(x,y) = K(x * y,x \ 1) * x. [para(558(a,1),221(a,1)),flip(a)]. given #523 (H,wt=13): 584 K(x,x / (x * y)) = K(x,y \ 1). [para(567(a,1),580(a,2))]. given #524 (H,wt=13): 590 T(x \ K(x,y),y) = (y * x) \ y. [para(583(a,2),232(a,1,1))]. given #525 (H,wt=11): 604 T(x \ K(x,y),y) = x \ 1. [para(590(a,2),325(a,1))]. given #526 (H,wt=13): 594 K(x,(y / x) * T(x,z)) = K(x,y). [para(593(a,2),570(a,1))]. given #527 (H,wt=11): 606 K(x,y * K(x,z)) = K(x,y). [para(549(a,1),594(a,1,2))]. given #528 (H,wt=13): 597 K(T(x,y),x \ z) = K(T(x,y),z). [para(143(a,1),596(a,1,2,1))]. given #529 (H,wt=13): 598 (x * y) * K(y,z) = x * T(y,z). [para(15(a,1),549(a,1,1)),flip(a)]. given #530 (H,wt=13): 599 (x / y) \ T(x,z) = y * K(x,z). [para(549(a,1),343(a,2))]. given #531 (H,wt=13): 603 K(x * y,x \ 1) = K(x,y / x). [hyper(18,a,553,a(flip),b,577,a(flip))]. given #532 (H,wt=13): 607 (x * T(y,z)) * K(z,y) = x * y. [hyper(415,a,598,a)]. given #533 (H,wt=13): 608 (x * y) \ (x * T(y,z)) = K(y,z). [hyper(56,a,598,a)]. given #534 (H,wt=13): 609 (x * T(y,z)) \ (x * y) = K(z,y). [para(598(a,1),408(a,1,1))]. given #535 (H,wt=13): 610 (x \ y) * K(y,z) = x \ T(y,z). [para(53(a,1),599(a,1,1)),flip(a)]. given #536 (H,wt=13): 611 (x / T(y,z)) * y = x * K(z,y). [para(16(a,1),607(a,1,1)),flip(a)]. given #537 (H,wt=11): 618 T(x,y * K(z,x)) = T(x,y). [para(611(a,1),465(a,1,2))]. given #538 (H,wt=13): 615 (x \ T(y,z)) * K(z,y) = x \ y. [hyper(415,a,610,a)]. given #539 (H,wt=13): 617 (x * K(y,z)) / z = x / T(z,y). [hyper(58,a,611,a)]. given #540 (H,wt=13): 619 K(x * K(y,z),z) = T(z,x) \ z. [para(618(a,1),531(a,2,1))]. given #541 (H,wt=11): 622 K(x * K(y,z),z) = K(x,z). [para(619(a,2),531(a,2)),flip(a)]. given #542 (H,wt=11): 623 K(x / K(y,z),z) = K(x,z). [para(16(a,1),622(a,1,1)),flip(a)]. given #543 (H,wt=11): 625 K(x,K(y,x) / z) = K(z,x). [para(623(a,1),561(a,1)),flip(a)]. given #544 (H,wt=11): 626 K(x,K(x,y) / z) = K(z,x). [para(560(a,1),625(a,1,2,1))]. given #545 (H,wt=13): 620 (T(x,y) \ z) * (z \ x) = K(y,x). [hyper(387,a,615,a)]. given #546 (H,wt=13): 628 K(x,K(x,y) * z) = K(z \ 1,x). [para(334(a,1),626(a,1,2))]. given #547 (H,wt=11): 631 K(x,K(x,y) * z) = K(x,z). [para(628(a,2),560(a,1))]. given #548 (H,wt=13): 633 T(x,K(x,y) * z) = x * K(x,z). [para(631(a,1),530(a,2,2))]. given #549 (H,wt=11): 634 T(x,K(x,y) * z) = T(x,z). [para(633(a,2),530(a,2)),flip(a)]. given #550 (H,wt=11): 635 T(x,K(y,x) * z) = T(x,z). [para(407(a,1),634(a,1,2)),flip(a)]. given #551 (H,wt=13): 636 K(K(x,y) * z,y) = T(y,z) \ y. [para(635(a,1),531(a,2,1))]. given #552 (H,wt=11): 637 K(K(x,y) * z,y) = K(z,y). [para(636(a,2),531(a,2)),flip(a)]. given #553 (H,wt=14): 574 T(x,y) != z * x | K(x,y / x) = z. [para(553(a,2),20(a,1))]. given #554 (H,wt=15): 552 T(K(x,y),z) * K(y,x) = K(K(x,y),z). [hyper(415,a,544,a(flip))]. given #555 (H,wt=15): 555 K(x,y) * T(K(y,x),z) = K(z,K(x,y)). [para(404(a,1),535(a,2,2,1)),flip(a)]. given #556 (H,wt=15): 575 L(L(x,y,T(y \ 1,z)),K(z,y),y) = x. [para(556(a,2),307(a,1,1,3))]. given #557 (H,wt=15): 576 K(x,y) * K(z,K(y,x)) = T(K(x,y),z). [para(404(a,1),557(a,2,2,2)),flip(a)]. given #558 (H,wt=15): 587 T(x,y) * K(y \ x,y) = T(x,y * y). [para(586(a,1),461(a,1,2))]. given #559 (H,wt=13): 640 T(x,y) * K(x,y) = T(x,y * y). [para(532(a,1),587(a,1,2))]. given #560 (H,wt=15): 600 T(x,y) \ T(x,z) = K(y,x) * K(x,z). [para(550(a,1),549(a,1))]. given #561 (H,wt=15): 601 x / T(y,z \ y) = x * (y \ K(y,z)). [para(579(a,1),554(a,1,2,2)),flip(a)]. given #562 (H,wt=15): 602 K(T(x,y \ 1),z) = K(z,x \ K(x,y)). [para(568(a,1),564(a,1,2)),flip(a)]. given #563 (H,wt=15): 613 x \ (y * T(y \ x,z)) = K(y \ x,z). [para(14(a,1),608(a,1,1))]. given #564 (H,wt=15): 616 x \ T(y,z \ y) = (x \ y) * K(z,y). [para(578(a,1),610(a,1,2)),flip(a)]. given #565 (H,wt=15): 624 K(T(x,K(y,z)),y) = K(K(z,y) * x,y). [para(410(a,1),623(a,1,1))]. given #566 (H,wt=11): 642 K(T(x,K(y,z)),y) = K(x,y). [para(624(a,2),637(a,1))]. given #567 (H,wt=15): 627 K(T(x,K(y,z)),y) = K(y,x \ K(y,z)). [para(229(a,1),626(a,1,2)),flip(a)]. given #568 (H,wt=11): 644 K(x,y \ K(x,z)) = K(y,x). [para(627(a,1),642(a,1))]. given #569 (H,wt=11): 645 K(x,y \ K(z,x)) = K(y,x). [para(559(a,1),644(a,1,2,2))]. given #570 (H,wt=15): 632 K(x,T(y,K(x,z))) = K(x,y * K(x,z)). [para(78(a,1),631(a,1,2)),flip(a)]. given #571 (H,wt=11): 647 K(x,T(y,K(x,z))) = K(x,y). [para(632(a,2),606(a,1))]. given #572 (H,wt=15): 639 T(K(x,y),z) * K(y,x) = K(z,K(y,x)). [para(552(a,2),565(a,1))]. given #573 (H,wt=16): 519 T(x,y) != x * z | y * T(y \ 1,x) = z. [para(518(a,1),19(a,1))]. given #574 (H,wt=17): 589 (x / y) \ K(x / y,y) = y / T(x,y \ x). [para(177(a,2),583(a,2,2))]. given #575 (H,wt=15): 650 x / T(y,x \ y) = (y / x) \ K(y,x). [para(581(a,1),589(a,1,2)),flip(a)]. given #576 (H,wt=15): 651 x / T(y,x \ y) = (x / y) * K(y,x). [para(650(a,2),343(a,1))]. given #577 (H,wt=15): 652 (x / y) * K(y,x) = x * (y \ K(y,x)). [para(651(a,1),601(a,1))]. given #578 (H,wt=17): 621 (x * K(y,z / y)) / (z / y) = x / (y \ z). [para(80(a,1),617(a,2,2))]. given #579 (H,wt=15): 653 (x * K(y,z)) / (z / y) = x / (y \ z). [para(570(a,1),621(a,1,1,2))]. given #580 (H,wt=15): 654 (x * K(y,z)) * (y / z) = x / (y \ z). [para(653(a,1),357(a,1)),flip(a)]. given #581 (H,wt=15): 655 (x * K(y,z)) * (y / z) = x * (z \ y). [para(654(a,2),358(a,1))]. given #582 (H,wt=17): 630 K(T(x,y) \ z,z \ x) = K(K(y,x),z \ x). [para(620(a,1),582(a,1,1)),flip(a)]. given #583 (H,wt=17): 638 (K(x,y) * z) * K(z,y) = T(K(x,y) * z,y). [para(637(a,1),530(a,2,2)),flip(a)]. given #584 (H,wt=15): 656 T(K(x,y) * z,y) = K(x,y) * T(z,y). [para(638(a,1),598(a,1))]. given #585 (H,wt=17): 641 x \ (T(y,z) * (y \ x)) = K((y \ x) \ x,z). [para(172(a,1),613(a,1,2))]. given #586 (H,wt=15): 657 x \ (T(y,z) * (y \ x)) = K(T(y,x),z). [para(228(a,2),641(a,2,1))]. given #587 (H,wt=15): 658 T(x,y) * (x \ z) = z * K(T(x,z),y). [para(657(a,1),14(a,1,2)),flip(a)]. given #588 (H,wt=17): 648 T(T(x,K(y,z)),y) * K(y,x) = T(x,K(y,z)). [para(647(a,1),533(a,1,2))]. given #589 (H,wt=18): 536 T(x,y) * L(z,K(x,y),x) = x * (K(x,y) * z). [para(530(a,2),67(a,1,1))]. given #590 (H,wt=19): 271 (x * T(y,x \ y)) / (x * y) = K(x,T(y,x \ y)). [para(173(a,1),270(a,2,2)),flip(a)]. given #591 (H,wt=17): 659 T(x * y,y) / (x * y) = K(x,T(y,x \ y)). [para(193(a,1),271(a,1,1))]. given #592 (H,wt=17): 660 (x * y) \ T(x * y,y) = K(x,T(y,x \ y)). [para(659(a,1),131(a,1)),flip(a)]. given #593 (H,wt=15): 661 K(x \ (y * x),x) = K(y,T(x,y \ x)). [para(660(a,1),127(a,2))]. given #594 (H,wt=13): 662 K(x,T(y,x \ y)) = K(T(x,y),y). [para(32(a,2),661(a,1,1)),flip(a)]. given #595 (H,wt=13): 663 K(T(x,y),y) = K(x,x * (y / x)). [para(177(a,1),662(a,1,2)),flip(a)]. given #596 (H,wt=19): 283 T(x * (y / x),y / x) = T(y,(y / x) * (y / x)). [para(54(a,1),282(a,1,1,1))]. given #597 (H,wt=17): 665 T(x,(x / y) * (x / y)) = T(y,x) * (x / y). [para(283(a,1),248(a,1))]. given #598 (H,wt=17): 666 T(x,x * (y \ (x / y))) = T(y,x) * (x / y). [para(402(a,1),665(a,1,2))]. given #599 (H,wt=15): 667 T(x,y \ (x / y)) = T(y,x) * (x / y). [para(666(a,1),221(a,1)),flip(a)]. given #600 (H,wt=19): 456 (T(x,y) * (x \ 1)) * z = T(x,y) * ((x \ 1) * z). [para(455(a,1),73(a,1,1)),flip(a)]. given #601 (H,wt=10): 668 L(x,y \ 1,T(y,z)) = x. [hyper(195,a,456,a)]. given #602 (H,wt=10): 669 L(x,y,T(y \ 1,z)) = x. [para(135(a,1),668(a,1,2))]. given #603 (H,wt=8): 670 L(x,K(y,z),z) = x. [para(669(a,1),575(a,1,1))]. given #604 (H,wt=8): 671 L(x,K(y,z),y) = x. [para(560(a,1),670(a,1,2))]. given #605 (H,wt=13): 673 x * (K(x,y) * z) = T(x,y) * z. [para(671(a,1),536(a,1,2)),flip(a)]. given #606 (H,wt=13): 674 x \ (T(x,y) * z) = K(x,y) * z. [hyper(56,a,673,a)]. given #607 (H,wt=13): 675 T(x,y) * (x \ z) = K(x,y) * z. [hyper(17,a,515,a,b,673,a),flip(a)]. given #608 (H,wt=13): 676 K(x,y) * (x * z) = T(x,y) * z. [hyper(17,a,514,a(flip),b,673,a)]. given #609 (H,wt=13): 677 T(x,y) * (K(y,x) * z) = x * z. [para(407(a,1),673(a,1,2)),flip(a)]. given #610 (H,wt=13): 679 K(x,y) * (T(x,y) \ z) = x \ z. [para(14(a,1),674(a,1,2)),flip(a)]. given #611 (H,wt=13): 682 x * K(T(y,x),z) = K(y,z) * x. [para(675(a,1),658(a,1)),flip(a)]. given #612 (H,wt=11): 686 K(T(x,y),z) = T(K(x,z),y). [hyper(94,a,682,a),flip(a)]. given #613 (H,wt=13): 683 K(x,y) * (T(y,x) * z) = y * z. [hyper(413,a,676,a)]. given #614 (H,wt=13): 685 K(x,y) * (y \ z) = T(y,x) \ z. [hyper(413,a,679,a)]. given #615 (H,wt=13): 688 x * (T(x,y) \ z) = K(y,x) * z. [para(14(a,1),683(a,1,2)),flip(a)]. given #616 (H,wt=13): 693 x \ (K(y,x) * z) = T(x,y) \ z. [hyper(56,a,688,a)]. given #617 (H,wt=13): 695 (K(x,y) * z) \ y = z \ T(y,x). [para(688(a,1),355(a,1,1))]. given #618 (H,wt=13): 696 x / (y \ T(x,z)) = K(z,x) * y. [para(688(a,1),358(a,2))]. given #619 (H,wt=13): 697 (x \ K(y,z)) * y = x \ T(y,z). [para(695(a,1),412(a,1)),flip(a)]. given #620 (H,wt=13): 698 K(x,y) * (T(y,x) / z) = y / z. [para(54(a,1),696(a,1,2)),flip(a)]. given #621 (H,wt=13): 699 (x \ T(y,z)) / y = x \ K(y,z). [hyper(58,a,697,a)]. given #622 (H,wt=13): 700 K(x,y) * (x / z) = T(x,y) / z. [hyper(413,a,698,a)]. given #623 (H,wt=13): 701 (x / y) / (T(x,z) / y) = K(z,x). [hyper(58,a,698,a)]. given #624 (H,wt=13): 703 (T(x,y) / z) \ K(x,y) = z / x. [para(54(a,1),699(a,1,1)),flip(a)]. given #625 (H,wt=13): 705 (x / y) * (y / T(x,z)) = K(z,x). [para(701(a,1),357(a,1)),flip(a)]. given #626 (H,wt=13): 706 (x / T(y,z)) * K(y,z) = x / y. [para(703(a,1),343(a,1)),flip(a)]. given #627 (H,wt=13): 709 (x * T(y,z)) / y = x * K(y,z). [para(15(a,1),706(a,1,1)),flip(a)]. given #628 (H,wt=15): 678 T(x,y \ x) * z = x * (K(y,x) * z). [para(578(a,1),673(a,1,2,1)),flip(a)]. given #629 (H,wt=15): 680 x \ T(x,y * y) = K(x,y) * K(x,y). [para(640(a,1),674(a,1,2))]. given #630 (H,wt=13): 712 K(x,y) * K(x,y) = K(x,y * y). [para(680(a,1),534(a,2)),flip(a)]. given #631 (H,wt=15): 681 T(x,y) / T(x,z) = K(x,y) * K(z,x). [para(675(a,1),554(a,1)),flip(a)]. given #632 (H,wt=15): 684 T(x,y) * (T(y,x) * z) = x * (y * z). [para(676(a,1),677(a,1,2))]. given #633 (H,wt=15): 687 K(T(x,y),z) \ 1 = y \ (K(x,z) \ y). [para(686(a,2),337(a,1,1))]. given #634 (H,wt=15): 694 T(K(x,y) * z,y) = (T(y,x) \ z) * y. [para(688(a,1),116(a,1,1))]. given #635 (H,wt=15): 704 T(x,y \ x) / z = K(y,x) * (x / z). [para(578(a,1),700(a,1,1)),flip(a)]. given #636 (H,wt=15): 711 x \ (y * T(x,z)) = T(y * K(x,z),x). [para(709(a,1),80(a,1,1)),flip(a)]. given #637 (H,wt=15): 713 T(x,y) \ T(x,z) = K(x,z) * K(y,x). [para(681(a,1),133(a,1)),flip(a)]. given #638 (H,wt=15): 714 K(T(x,y),z) \ 1 = y \ (K(z,x) * y). [para(406(a,1),687(a,2,2))]. given #639 (H,wt=13): 716 K(T(x,y),z) \ 1 = T(K(z,x),y). [para(714(a,2),32(a,2)),flip(a)]. given #640 (H,wt=11): 717 K(x,T(y,z)) = T(K(x,y),z). [para(716(a,1),404(a,1)),flip(a)]. given #641 (H,wt=11): 721 K(T(x,y),z) = K(x,T(z,y)). [para(717(a,2),686(a,2))]. given #642 (H,wt=13): 723 K(x / y,T(z,x)) = K(y \ x,z). [para(232(a,1),721(a,1,1)),flip(a)]. given #643 (H,wt=13): 725 K(x / y,T(z,x)) = K(z,x \ y). [para(723(a,2),562(a,1))]. given #644 (H,wt=15): 718 K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). [para(717(a,2),555(a,1,2))]. given #645 (H,wt=15): 719 K(x,y) * K(z,K(y,x)) = K(x,T(y,z)). [para(717(a,2),576(a,2))]. given #646 (H,wt=15): 720 K(x,T(y,z)) * K(y,x) = K(z,K(y,x)). [para(717(a,2),639(a,1,1))]. given #647 (H,wt=15): 724 K(x,T(y,z \ 1)) = K(y,x \ K(x,z)). [para(721(a,1),602(a,1))]. given #648 (H,wt=17): 689 K(x,y / x) * ((x \ y) * z) = (y / x) * z. [para(80(a,1),683(a,1,2,1))]. given #649 (H,wt=15): 726 K(x,y) * ((x \ y) * z) = (y / x) * z. [para(570(a,1),689(a,1,1))]. given #650 (H,wt=15): 727 K(x,y) * (y / x) = (y / x) * K(x,y). [para(566(a,1),726(a,1,2))]. given #651 (H,wt=15): 728 K(x,y) * (y / x) = y * (x \ K(x,y)). [para(727(a,2),652(a,1))]. given #652 (H,wt=15): 729 T(x,y \ x) / y = x * (y \ K(y,x)). [para(728(a,1),704(a,2))]. given #653 (H,wt=17): 692 K(x,y) * (y \ (z * T(y,x))) = T(z,T(y,x)). [para(685(a,2),32(a,2)),flip(a)]. given #654 (H,wt=17): 707 (x \ y) * (x / T(T(y,x),z)) = K(z,T(y,x)). [para(123(a,1),705(a,1,1))]. given #655 (H,wt=15): 731 (x \ y) * (T(y,z) \ x) = K(z,T(y,x)). [para(234(a,1),707(a,1,2))]. given #656 (H,wt=17): 710 (x / (y \ z)) * K(z / y,y) = x / (z / y). [para(80(a,1),706(a,1,1,2))]. given #657 (H,wt=17): 715 x * (T(y,x \ y) / z) = T(x,y) * (y / z). [para(704(a,2),673(a,1,2))]. given #658 (H,wt=17): 730 K(x,y) * T(z * K(y,x),y) = T(z,T(y,x)). [para(711(a,1),692(a,1,2))]. given #659 (H,wt=17): 732 (x * (y \ z)) * K(y / z,z) = x / (y / z). [para(358(a,1),710(a,1,1))]. given #660 (H,wt=15): 735 (x * (y \ z)) * K(y,z) = x / (y / z). [para(581(a,1),732(a,1,2))]. given #661 (H,wt=15): 736 (x * (y \ z)) * K(y,z) = x * (z / y). [para(735(a,2),357(a,1))]. given #662 (H,wt=17): 733 x * (T(y,x \ y) / x) = T(y,x \ (y / x)). [para(715(a,2),667(a,2)),flip(a)]. given #663 (H,wt=17): 734 T(K(x,y) * (z * K(y,x)),y) = T(z,T(y,x)). [para(730(a,1),656(a,2))]. given #664 (H,wt=13): 739 T(T(x,K(y,z)),y) = T(x,T(y,z)). [para(411(a,1),734(a,1,1))]. given #665 (H,wt=13): 740 T(T(x,y),K(y,z)) = T(x,T(y,z)). [para(739(a,1),38(a,1)),flip(a)]. given #666 (H,wt=15): 741 T(x,T(y,z)) * K(y,x) = T(x,K(y,z)). [para(739(a,1),648(a,1,1))]. given #667 (H,wt=17): 738 x * (y * (x \ K(x,y))) = T(y,x \ (y / x)). [para(729(a,1),733(a,1,2))]. given #668 (H,wt=17): 742 T(x,y) \ T(x,T(y,z)) = K(T(x,y),K(y,z)). [para(740(a,1),534(a,2,2)),flip(a)]. given #669 (H,wt=17): 743 K(x,y) * K(y,T(x,z)) = K(T(y,x),K(x,z)). [para(742(a,1),600(a,1)),flip(a)]. given #670 (H,wt=13): 744 K(T(x,y),K(y,z)) = K(z,K(y,x)). [para(743(a,1),718(a,1))]. given #671 (H,wt=13): 745 K(x,T(K(y,z),y)) = K(z,K(y,x)). [para(744(a,1),721(a,1)),flip(a)]. given #672 (H,wt=11): 746 K(x,K(y,z)) = K(z,K(y,x)). [para(545(a,1),745(a,1,2))]. given #673 (H,wt=11): 747 K(K(x,y),z) = K(x,K(y,z)). [para(746(a,1),565(a,2))]. given #674 (H,wt=15): 748 K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). [para(746(a,1),719(a,1,2))]. given #675 (H,wt=17): 749 K(x,y) * K(x,K(z,y)) = K(x,T(y,z \ 1)). [para(559(a,1),748(a,1,2,2))]. given #676 (H,wt=19): 482 (x / y) * z != x * (y \ u) | L(u,y \ 1,x) = z. [para(479(a,1),19(a,1)),flip(a)]. given #677 (H,wt=19): 512 K(T(x,y),T(y / (x * x),x)) = K(x,y / (x * x)). [para(281(a,1),510(a,1,1))]. given #678 (H,wt=17): 750 K(T(x,y),x \ (y / x)) = K(x,y / (x * x)). [para(279(a,1),512(a,1,2))]. given #679 (H,wt=19): 591 (x * (y / x)) / K(y,x) = y / (K(y,x) * K(y,x)). [para(588(a,1),277(a,1,1)),flip(a)]. given #680 (H,wt=17): 751 (x * (y / x)) / K(y,x) = y / K(y,x * x). [para(712(a,1),591(a,2,2))]. given #681 (H,wt=17): 752 (x * (y / x)) / K(y,x) = y * K(x * x,y). [para(751(a,2),409(a,1))]. given #682 (H,wt=17): 753 (x * (y / x)) / K(y,x) = T(y,(x * x) \ y). [para(752(a,2),573(a,2)),flip(a)]. given #683 (H,wt=17): 754 (x * (y / x)) / K(y,x) = T(y,x \ (x \ y)). [para(170(a,1),753(a,2,2))]. given #684 (H,wt=17): 755 (x * (y / x)) * K(x,y) = T(y,x \ (x \ y)). [para(754(a,1),409(a,1)),flip(a)]. given #685 (H,wt=19): 664 K(x * (y / x),x \ 1) = K(y,y * ((x \ 1) / y)). [para(372(a,1),663(a,1,1))]. given #686 (H,wt=17): 756 K(x,(y / x) / x) = K(y,y * ((x \ 1) / y)). [para(664(a,1),603(a,1)),flip(a)]. given #687 (H,wt=17): 757 K(x,y / (x * x)) = K(y,y * ((x \ 1) / y)). [para(278(a,1),756(a,1,2))]. given #688 (H,wt=17): 758 K(x,y / (x * x)) = K(y,y * (x \ (y \ 1))). [para(367(a,1),757(a,2,2,2))]. given #689 (H,wt=15): 759 K(x,y / (x * x)) = K(y,y / (y * x)). [para(379(a,1),758(a,2,2))]. given #690 (H,wt=13): 760 K(x,y / (x * x)) = K(y,x \ 1). [para(759(a,2),584(a,1))]. given #691 (H,wt=15): 761 K(T(x,y),x \ (y / x)) = K(y,x \ 1). [para(760(a,1),750(a,2))]. given #692 (H,wt=13): 762 K(T(x,y),y / x) = K(y,x \ 1). [para(761(a,1),597(a,1)),flip(a)]. given #693 (H,wt=11): 763 K(T(x,y),y / x) = K(x,y). [para(762(a,2),559(a,1))]. given #694 (H,wt=19): 702 K(x \ 1,x \ y) * ((y / x) / z) = (x \ y) / z. [para(347(a,1),698(a,1,2,1))]. given #695 (H,wt=17): 765 K(x,y \ x) * ((y / x) / z) = (x \ y) / z. [para(428(a,1),702(a,1,1))]. given #696 (H,wt=15): 766 K(x,y) * ((x / y) / z) = (y \ x) / z. [para(578(a,1),765(a,1,1))]. given #697 (H,wt=19): 737 x \ ((y * (x \ z)) * T(x,z)) = T(y * (z / x),x). [para(736(a,1),711(a,2,1))]. given #698 (H,wt=19): 764 ((x / y) * T(y,x)) * K(y,x) = T(y,x) * (x / y). [para(763(a,1),61(a,1,2))]. given #699 (H,wt=17): 767 (x * (y / x)) * K(x,y) = T(x,y) * (y / x). [para(247(a,1),764(a,1,1))]. given #700 (H,wt=17): 768 (x * (y / x)) * K(x,y) = T(y,x \ (y / x)). [para(767(a,2),667(a,2)),flip(a)]. given #701 (H,wt=15): 769 T(x,y \ (x / y)) = T(x,y \ (y \ x)). [para(768(a,1),755(a,1))]. given #702 (H,wt=17): 770 x * (y * (x \ K(x,y))) = T(y,x \ (x \ y)). [para(769(a,1),738(a,2))]. given #703 (H,wt=20): 107 (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x). [para(61(a,1),28(a,2,2,2)),flip(a)]. given #704 (H,wt=20): 167 (x * (x * y)) \ ((x * x) * (y * z)) = L(z,y,x * x). [para(165(a,1),28(a,2,1)),flip(a)]. given #705 (H,wt=20): 424 x * ((y \ x) * L(z,x,y \ 1)) = (x * (y \ x)) * z. [para(371(a,1),67(a,1,2)),flip(a)]. given #706 (H,wt=15): 772 (x * (y \ x)) * z = x * (y \ (x * z)). [para(484(a,1),424(a,1,2)),flip(a)]. given #707 (H,wt=20): 498 x * ((x \ T(y,z \ y)) / (y / z)) = R(z,y / z,x). [para(177(a,2),497(a,2,2,1,2)),flip(a)]. given #708 (H,wt=20): 771 (x * (x * y)) \ (x * (x * (y * z))) = L(z,y,x * x). [para(165(a,1),167(a,1,2))]. given #709 (H,wt=20): 773 x * (((x \ y) * K(z,y)) / (y / z)) = R(z,y / z,x). [para(616(a,1),498(a,1,2,1))]. given #710 (H,wt=20): 774 x * (((x \ y) * K(z,y)) * (z / y)) = R(z,y / z,x). [para(357(a,1),773(a,1,2))]. given #711 (H,wt=16): 775 R(x,y / x,z) = z * ((z \ y) * (y \ x)). [para(655(a,1),774(a,1,2)),flip(a)]. given #712 (H,wt=21): 293 T(T(x,(y * y) \ x),z) = T(y * (y * (x / (y * y))),z). [para(165(a,1),285(a,2,1))]. given #713 (H,wt=21): 296 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(59(a,1),88(a,1,1))]. given #714 (H,wt=21): 460 (x * y) * L(x \ 1,z,u) = x * (y * L(x \ 1,z,u)). [para(447(a,1),67(a,1,2))]. given #715 (H,wt=21): 691 K(x,y \ K(y,x)) * ((y \ 1) * z) = (y \ K(y,x)) * z. [para(604(a,1),683(a,1,2,1))]. given #716 (H,wt=17): 778 K(x,y) * ((x \ 1) * z) = (x \ K(x,y)) * z. [para(645(a,1),691(a,1,1))]. given #717 (H,wt=15): 779 (x \ K(x,y)) * z = K(x,y) * (x \ z). [para(314(a,1),778(a,1,2)),flip(a)]. given #718 (H,wt=21): 776 T(T(x,y \ (y \ x)),z) = T(y * (y * (x / (y * y))),z). [para(170(a,1),293(a,1,1,2))]. given #719 (H,wt=22): 84 ((x * y) * (x * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [para(47(a,1),24(a,2,2)),flip(a)]. given #720 (H,wt=15): 781 a(x,y,x * z) \ 1 = a(x * y,x,z). [para(84(a,1),339(a,1)),flip(a)]. given #721 (H,wt=22): 197 (x * (y * L(z,y,x))) \ (x * (y * z)) = a(x,y,L(z,y,x)). [para(67(a,1),24(a,2,2)),flip(a)]. given #722 (H,wt=22): 253 (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). [para(250(a,1),28(a,2,1)),flip(a)]. given #723 (H,wt=18): 782 (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). [para(684(a,1),253(a,1,2))]. given #724 (H,wt=13): 783 L(x,T(y,z),T(z,y)) = L(x,y,z). [para(782(a,1),28(a,2)),flip(a)]. given #725 (H,wt=17): 784 L(x,y * z,T(z,z * y)) = L(x,z * y,z). [para(116(a,1),783(a,1,2))]. given #726 (H,wt=15): 786 L(x,y * z,T(z,y)) = L(x,z * y,z). [para(221(a,1),784(a,1,3))]. given #727 (H,wt=17): 785 L(L(x,T(y,z) * T(z,y),T(z,y)),z,y) = x. [para(783(a,1),304(a,1))]. given #728 (H,wt=13): 787 L(L(x,y * z,T(z,y)),z,y) = x. [para(250(a,1),785(a,1,1,2))]. given #729 (H,wt=11): 788 L(L(x,y * z,y),y,z) = x. [para(786(a,1),787(a,1,1))]. given #730 (H,wt=11): 789 L(L(x,y,z),z,z \ y) = x. [para(14(a,1),788(a,1,1,2))]. given #731 (H,wt=11): 791 L(L(x,y,y \ z),z,y) = x. [para(789(a,1),45(a,1)),flip(a)]. given #732 (H,wt=11): 796 L(x,T(y,z),z) = L(x,y,z). [para(789(a,1),368(a,1,1))]. given #733 (H,wt=13): 790 L(x,y * z,z) = L(x,z * y,z). [para(788(a,1),306(a,1,1))]. given #734 (H,wt=13): 792 L(x,y * z,z) = L(x,y,y \ z). [para(304(a,1),789(a,1,1)),flip(a)]. given #735 (H,wt=13): 793 L(x,(y \ z) * y,y) = L(x,z,y). [para(789(a,1),306(a,1,1))]. given #736 (H,wt=13): 794 L(x,y,y \ (z * y)) = L(x,y,z). [para(306(a,1),789(a,1,1))]. given #737 (H,wt=11): 807 L(x,y,T(z,y)) = L(x,y,z). [para(32(a,2),794(a,1,3))]. given #738 (H,wt=13): 795 L(x,y,z / y) = L(x,y,y \ z). [para(307(a,1),789(a,1,1)),flip(a)]. given #739 (H,wt=13): 798 L(x,y * z,y) = L(x,z,z \ y). [para(788(a,1),789(a,1,1)),flip(a)]. given #740 (H,wt=13): 800 L(x,y / z,z) = L(x,z \ y,z). [para(80(a,1),796(a,1,2)),flip(a)]. given #741 (H,wt=13): 802 L(x,y / z,y) = L(x,z \ y,y). [para(232(a,1),796(a,1,2)),flip(a)]. given #742 (H,wt=13): 808 L(x,y,y / z) = L(x,y,z \ y). [para(232(a,1),807(a,1,3)),flip(a)]. given #743 (H,wt=15): 797 L(x,y,y \ (z \ y)) = L(x,y,z \ 1). [para(371(a,1),789(a,1,1))]. given #744 (H,wt=15): 806 L(x,y * z,y \ 1) = L(x,y,y \ z). [para(792(a,1),506(a,2))]. given #745 (H,wt=16): 804 (x * y) * L(z,x,y) = y * (T(x,y) * z). [para(796(a,1),199(a,1,2))]. given #746 (H,wt=16): 805 L(T(x,y) \ z,x,y) = (x * y) \ (y * z). [para(796(a,1),205(a,1))]. given #747 (H,wt=16): 809 x \ ((x / y) * (y * z)) = L(z,y,y \ x). [para(795(a,1),69(a,2))]. given #748 (H,wt=16): 810 x * L(y,z,z \ x) = (x / z) * (z * y). [para(795(a,1),194(a,1,2))]. given #749 (H,wt=16): 811 x * L(y,z,z \ x) = z \ ((z * x) * y). [para(806(a,1),485(a,1,2))]. given #750 (H,wt=15): 812 x \ ((x * y) * z) = (y / x) * (x * z). [para(811(a,1),810(a,1))]. given #751 (H,wt=17): 801 L(x,y * (z / y),z / y) = L(x,z,z / y). [para(121(a,1),796(a,1,2))]. given #752 (H,wt=17): 803 L(x,y * (z / y),y \ 1) = L(x,z,y \ 1). [para(372(a,1),796(a,1,2))]. given #753 (H,wt=17): 814 L(x,y * (z / y),z / y) = L(x,z,y \ z). [para(801(a,2),808(a,1))]. given #754 (H,wt=17): 815 L(x,y * (z / y),z / y) = L(x,z,y \ 1). [para(803(a,1),506(a,1)),flip(a)]. given #755 (H,wt=13): 816 L(x,y,z \ 1) = L(x,y,z \ y). [para(815(a,1),814(a,1))]. given #756 (H,wt=17): 817 L(x,y,(z * y) \ 1) = L(x,y,y \ (z \ y)). [para(374(a,1),816(a,2,3))]. given #757 (H,wt=17): 818 L(x,y,y \ (z \ 1)) = L(x,y,y \ (z \ y)). [para(341(a,1),817(a,1,3))]. given #758 (H,wt=15): 819 L(x,y,y \ (z \ 1)) = L(x,y,z \ 1). [para(818(a,2),797(a,1))]. given #759 (H,wt=13): 820 L(L(x,y \ 1,z),z,y \ 1) = x. [para(819(a,1),789(a,1))]. given #760 (H,wt=13): 821 L(x,y \ 1,z) = L(x,y \ z,z). [para(820(a,1),371(a,1,1)),flip(a)]. given #761 (H,wt=15): 822 L(x,(y \ z) \ u,u) = L(x,z \ y,u). [para(333(a,1),821(a,1,2)),flip(a)]. given #762 (H,wt=15): 823 L(x,(y \ z) * u,u) = L(x,y \ z,u). [para(353(a,1),822(a,1,2))]. given #763 (H,wt=11): 826 L(x,y \ z,y) = L(x,z,y). [para(823(a,1),793(a,1))]. given #764 (H,wt=11): 827 L(x,y * z,y) = L(x,z,y). [para(13(a,1),826(a,1,2)),flip(a)]. given #765 (H,wt=9): 829 L(L(x,y,z),z,y) = x. [para(827(a,1),788(a,1,1))]. given #766 (H,wt=11): 830 L(x,y * z,z) = L(x,y,z). [para(827(a,1),790(a,2))]. given #767 (H,wt=11): 831 L(x,y,y \ z) = L(x,y,z). [para(827(a,1),798(a,1)),flip(a)]. given #768 (H,wt=11): 835 L(x,y,z * y) = L(x,y,z). [para(829(a,1),304(a,1,1)),flip(a)]. given #769 (H,wt=11): 836 L(x,y,z / y) = L(x,y,z). [para(829(a,1),305(a,1,1))]. given #770 (H,wt=11): 837 L(x,y,y * z) = L(x,y,z). [para(829(a,1),788(a,1,1)),flip(a)]. given #771 (H,wt=13): 825 L(x,y \ z,z) = L(x,y \ z,y). [para(823(a,1),403(a,2)),flip(a)]. given #772 (H,wt=11): 840 L(x,y \ z,z) = L(x,z,y). [para(825(a,2),826(a,1))]. given #773 (H,wt=11): 841 L(L(x,y,z \ 1),y,z) = x. [para(840(a,1),371(a,1))]. given #774 (H,wt=11): 842 L(x,y / z,y) = L(x,y,z). [para(840(a,1),802(a,2))]. given #775 (H,wt=11): 843 L(x,y \ 1,z) = L(x,z,y). [para(840(a,1),821(a,2))]. given #776 (H,wt=11): 844 L(x,y,z \ 1) = L(x,z,y). [para(841(a,1),829(a,1,1)),flip(a)]. given #777 (H,wt=11): 845 L(x,y,z \ y) = L(x,z,y). [para(53(a,1),842(a,1,2)),flip(a)]. given #778 (H,wt=13): 847 L(x,K(y,z),u) = L(x,u,K(z,y)). [para(404(a,1),843(a,1,2))]. given #779 (H,wt=14): 828 L((x \ y) * z,x,y) = x \ (y * z). [para(826(a,1),385(a,1))]. given #780 (H,wt=14): 833 x * (y * L(z,x,y)) = (x * y) * z. [para(829(a,1),67(a,1,2)),flip(a)]. given #781 (H,wt=14): 834 L((x * y) \ z,x,y) = y \ (x \ z). [para(203(a,1),829(a,1,1))]. given #782 (H,wt=14): 838 L(x,y,z) = z \ ((z / y) * (y * x)). [para(831(a,1),809(a,2)),flip(a)]. given #783 (H,wt=14): 848 (x / y) * L(z,x,y) = x * (y \ z). [para(843(a,1),479(a,1,2))]. given #784 (H,wt=14): 849 L(x,y,z) = (z / y) * (y * (z \ x)). [para(843(a,1),480(a,2)),flip(a)]. given #785 (H,wt=13): 857 L(x \ y,z,x) = x \ L(y,z,x). [para(849(a,2),838(a,2,2))]. given #786 (H,wt=13): 858 x \ L(x * y,z,x) = L(y,z,x). [para(13(a,1),857(a,1,1)),flip(a)]. given #787 (H,wt=13): 861 L(x * y,z,x) = x * L(y,z,x). [para(858(a,1),14(a,1,2)),flip(a)]. given #788 (H,wt=14): 850 L(x * y,z,x) = (x / z) * (z * y). [para(843(a,1),481(a,1))]. given #789 (H,wt=14): 851 (x \ y) * L(z,x,y) = x \ (y * z). [para(844(a,1),484(a,1,2))]. given #790 (H,wt=14): 852 L(x \ y,z,x) = (x \ z) * (z \ y). [para(844(a,1),488(a,1))]. given #791 (H,wt=14): 853 L(x \ (y * z),y,x) = (x \ y) * z. [para(844(a,1),489(a,1))]. given #792 (H,wt=14): 862 x * L(y * z,x,y) = (x * y) * z. [para(861(a,2),833(a,1,2))]. given #793 (H,wt=15): 832 L(L(L(x,y,z),u,w),z,y) = L(x,u,w). [para(829(a,1),45(a,1,1)),flip(a)]. given #794 (H,wt=15): 846 L(x,y \ (z \ 1),u) = L(x,u,z * y). [para(341(a,1),843(a,1,2))]. given #795 (H,wt=16): 859 L(x \ L(x,y,z),u,x) = x \ L(x,y,z). [para(141(a,1),857(a,2,2))]. given #796 (H,wt=16): 864 L((x * y) * z,y,x * y) = x * (y * z). [para(15(a,1),850(a,2,1))]. given #797 (H,wt=14): 869 L((x * y) * z,y,x) = x * (y * z). [para(864(a,1),835(a,1)),flip(a)]. given #798 (H,wt=14): 870 L(x,y,z) = z * (y * ((z * y) \ x)). [para(14(a,1),869(a,1,1))]. given #799 (H,wt=14): 872 L(x * (y * z),x,y) = (x * y) * z. [para(869(a,1),829(a,1,1))]. given #800 (H,wt=16): 866 L(x \ (y * z),z,x) = (x \ z) * T(y,z). [para(32(a,2),852(a,2,2))]. given #801 (H,wt=16): 868 L(x \ L(x,y,z),x,u) = x \ L(x,y,z). [para(859(a,1),304(a,1,1))]. given #802 (H,wt=16): 871 L((x * y) * z,x * y,x) = x * (y * z). [para(869(a,1),827(a,2))]. given #803 (H,wt=17): 855 (x / y) * L(y,z,u) = x * (y \ L(y,z,u)). [para(141(a,1),848(a,1,2))]. given #804 (H,wt=18): 799 L(((x \ y) * x) \ z,y,x) = x \ ((x \ y) \ z). [para(203(a,1),791(a,1,1))]. given #805 (H,wt=16): 874 L(T(x,y) \ z,x,y) = y \ ((y \ x) \ z). [para(120(a,2),799(a,1,1,1))]. given #806 (H,wt=15): 875 (x * y) \ (y * z) = y \ ((y \ x) \ z). [para(874(a,1),805(a,1)),flip(a)]. given #807 (H,wt=15): 876 (x * y) \ (y * z) = y \ ((x \ y) * z). [para(353(a,1),875(a,2,2))]. given #808 (H,wt=18): 839 ((x * y) * x) \ ((x * y) * z) = L(x \ z,x,y). [para(837(a,1),68(a,1)),flip(a)]. given #809 (H,wt=18): 863 L(x * ((y * x) \ z),y,x) = x * (x \ (y \ z)). [para(834(a,1),861(a,2,2))]. given #810 (H,wt=14): 878 L(x * ((y * x) \ z),y,x) = y \ z. [para(863(a,2),14(a,1))]. given #811 (H,wt=18): 865 L(x * y,y \ z,x) = (x / (y \ z)) * T(z,y). [para(120(a,2),850(a,2,2))]. given #812 (H,wt=18): 877 (x * (y * x)) \ ((x * y) * z) = L(x \ z,x,y). [para(113(a,1),839(a,1,1))]. given #813 (H,wt=18): 880 x \ (y \ (x \ ((x * y) * z))) = L(x \ z,x,y). [para(877(a,1),458(a,1)),flip(a)]. given #814 (H,wt=18): 881 x \ (y \ ((y / x) * (x * z))) = L(x \ z,x,y). [para(812(a,1),880(a,1,2,2))]. given #815 (H,wt=13): 882 L(x \ y,x,z) = x \ L(y,x,z). [para(838(a,2),881(a,1,2)),flip(a)]. given #816 (H,wt=13): 883 x \ L(x * y,x,z) = L(y,x,z). [para(13(a,1),882(a,1,1)),flip(a)]. given #817 (H,wt=13): 884 x * L(x \ y,x,z) = L(y,x,z). [para(882(a,2),14(a,1,2))]. given #818 (H,wt=13): 885 L(x * y,x,z) = x * L(y,x,z). [para(883(a,1),14(a,1,2)),flip(a)]. given #819 (H,wt=13): 888 L(x / y,y,z) = L(x,y,z) / y. [para(884(a,1),471(a,1,1)),flip(a)]. given #820 (H,wt=15): 886 T(L(x * y,x,z),x) = L(y,x,z) * x. [para(883(a,1),120(a,2,1))]. given #821 (H,wt=15): 892 L(T(x * y,x),x,z) = L(y,x,z) * x. [para(886(a,1),40(a,2))]. given #822 (H,wt=13): 893 L(x * y,y,z) = L(x,y,z) * y. [para(116(a,1),892(a,1,1))]. given #823 (H,wt=16): 887 (x * y) * (y \ (x \ z)) = L(z,x * y,y). [para(370(a,1),884(a,1,2))]. given #824 (H,wt=16): 889 L(x * y,x,z) != x * u | L(y,x,z) = u. [para(885(a,2),19(a,1))]. given #825 (H,wt=16): 894 x * ((x \ y) * (y \ z)) = L(z,y * x,x). [para(887(a,1),261(a,1)),flip(a)]. given #826 (H,wt=14): 895 L(x,y,z) = z * ((z \ y) * (y \ x)). [para(894(a,2),830(a,1)),flip(a)]. given #827 (H,wt=11): 896 L(x,y,z) = R(x,x \ y,z). [para(895(a,2),459(a,2)),flip(a)]. given #828 (H,wt=11): 897 L(x,y,z) = R(x,y / x,z). [para(895(a,2),775(a,2)),flip(a)]. given #829 (H,wt=11): 900 R(x,y,z) = L(x,y * x,z). [para(15(a,1),897(a,2,2)),flip(a)]. given #830 (H,wt=13): 898 R(x,T(y,x),z) = L(x,y * x,z). [para(32(a,2),896(a,2,2)),flip(a)]. given #831 (H,wt=11): 903 R(x,T(y,x),z) = R(x,y,z). [para(898(a,2),900(a,2)),flip(a)]. given #832 (H,wt=13): 901 R(x \ y,x,z) = L(x \ y,y,z). [para(53(a,1),897(a,2,2)),flip(a)]. given #833 (H,wt=17): 902 R(x,y \ (z \ 1),u) = L(x,(z * y) \ x,u). [para(378(a,1),900(a,2,2))]. given #834 (H,wt=17): 904 R(x \ 1,y * x,z) = R(x \ 1,x * y,z). [para(359(a,1),903(a,1,2)),flip(a)]. given #835 (H,wt=15): 907 R(x \ 1,y * x,z) = R(x,y,z) \ 1. [para(904(a,2),490(a,1))]. given #836 (H,wt=15): 908 R(x,y / x,z) \ 1 = R(x \ 1,y,z). [para(16(a,1),907(a,1,2)),flip(a)]. given #837 (H,wt=13): 909 R(x \ 1,y,z) = L(x,y,z) \ 1. [para(897(a,2),908(a,1,1)),flip(a)]. given #838 (H,wt=15): 910 R(x \ 1,y,z) \ u = L(x,y,z) * u. [para(909(a,2),317(a,1,1))]. given #839 (H,wt=17): 905 R(x \ 1,y * x,z) = L((y * x) \ y,y,z). [para(325(a,1),901(a,1,1))]. given #840 (H,wt=15): 911 L((x * y) \ x,x,z) = R(y,x,z) \ 1. [para(905(a,1),907(a,1))]. given #841 (H,wt=13): 912 L(x \ 1,y,z) = R(x,y,z) \ 1. [para(325(a,1),911(a,1,1))]. given #842 (H,wt=17): 906 R(x,x \ (y \ 1),z) = L(x,x \ (y \ x),z). [para(374(a,1),902(a,2,2))]. given #843 (H,wt=15): 914 L(x,x \ (y \ x),z) = L(x,y \ 1,z). [para(906(a,1),896(a,2)),flip(a)]. given #844 (H,wt=13): 915 L(x,x \ (y \ x),z) = L(x,z,y). [para(914(a,2),843(a,1))]. given #845 (H,wt=19): 856 R(x,y,z) \ z = (y / (x * y)) * L(z,y,x * y). [para(848(a,2),502(a,2))]. given #846 (H,wt=17): 916 R(x,y,z) \ z = (x \ 1) * L(z,y,x * y). [para(316(a,1),856(a,2,1))]. given #847 (H,wt=15): 918 R(x,y,z) \ z = (x \ 1) * L(z,y,x). [para(835(a,1),916(a,2,2))]. given #848 (H,wt=13): 919 R(x,y,z) \ z = x \ L(z,y,x). [para(918(a,2),314(a,1))]. given #849 (H,wt=13): 920 L(x \ y,z,x) = R(x,z,y) \ y. [para(919(a,2),857(a,2))]. given #850 (H,wt=15): 921 L(x \ y,z,x) = (R(x,z,y) \ 1) * y. [para(920(a,2),314(a,2)),flip(a)]. given #851 (H,wt=15): 923 L(x \ y,z,x) = L(x \ 1,z,y) * y. [para(912(a,2),921(a,2,1))]. given #852 (H,wt=17): 922 L((x \ 1) \ y,x,z) = R(x \ 1,z,y) \ y. [para(920(a,1),844(a,1)),flip(a)]. given #853 (H,wt=15): 924 L((x \ 1) \ y,x,z) = L(x,z,y) * y. [para(922(a,2),910(a,1))]. given #854 (H,wt=19): 860 L((x * y) \ z,x,x * y) = (x * y) \ L(z,x,y). [para(837(a,1),857(a,2,2))]. given #855 (H,wt=17): 925 L((x * y) \ z,x,y) = (x * y) \ L(z,x,y). [para(860(a,1),837(a,1)),flip(a)]. given #856 (H,wt=14): 926 (x * y) \ L(z,x,y) = y \ (x \ z). [para(925(a,1),834(a,1))]. given #857 (H,wt=19): 891 L(x / (y \ 1),y \ 1,z) = L(x,z,y) / (y \ 1). [para(843(a,1),888(a,2,1))]. given #858 (H,wt=17): 927 L(x / (y \ 1),y \ 1,z) = L(x,z,y) * y. [para(891(a,2),334(a,1))]. given #859 (H,wt=15): 928 L(x * y,y \ 1,z) = L(x,z,y) * y. [para(334(a,1),927(a,1,1))]. given #860 (H,wt=13): 929 L(x * y,z,y) = L(x,z,y) * y. [para(928(a,1),843(a,1)),flip(a)]. given #861 (H,wt=15): 930 L(x \ y,z,x) = L((x \ 1) * y,z,y). [para(929(a,2),923(a,2))]. given #862 (H,wt=13): 932 L(x \ y,z,y) = L(x \ y,z,x). [para(314(a,1),930(a,2,1)),flip(a)]. given #863 (H,wt=13): 933 L(L(x \ y,z,y),x,z) = x \ y. [para(932(a,2),829(a,1,1))]. given #864 (H,wt=13): 935 L(x \ y,z,y) = x \ L(y,z,x). [para(932(a,2),857(a,1))]. given #865 (H,wt=13): 936 L(x \ y,y,z) = L(x \ y,x,z). [para(933(a,1),832(a,1,1))]. given #866 (H,wt=13): 937 x * L(x \ y,z,y) = L(y,z,x). [para(935(a,2),14(a,1,2))]. given #867 (H,wt=13): 940 x * L(x \ y,y,z) = L(y,x,z). [para(936(a,2),884(a,1,2))]. given #868 (H,wt=15): 931 L((x \ 1) \ y,x,z) = L(x * y,z,y). [para(929(a,2),924(a,2))]. given #869 (H,wt=13): 942 L(x * y,z,y) = L(x * y,x,z). [para(317(a,1),931(a,1,1)),flip(a)]. given #870 (H,wt=13): 944 x \ L(x * y,z,y) = L(y,x,z). [para(942(a,2),883(a,1,2))]. given #871 (H,wt=14): 943 L((x * y) * z,x,z) = x * (y * z). [para(942(a,2),871(a,1))]. given #872 (H,wt=14): 946 L(x * y,z,y) = z * ((z \ x) * y). [para(14(a,1),943(a,1,1,1))]. given #873 (H,wt=14): 947 L(x * y,x,z) * z = x * (y * z). [para(943(a,1),929(a,1)),flip(a)]. given #874 (H,wt=14): 948 L(x,y,z) = y * ((y \ (x / z)) * z). [para(16(a,1),946(a,1,1))]. given #875 (H,wt=14): 949 L(x * y,z,y) = (x * z) * (z \ y). [para(946(a,2),261(a,2)),flip(a)]. given #876 (H,wt=14): 952 L(x \ y,y,z) = (x \ (y / z)) * z. [hyper(17,a,940,a,b,948,a(flip)),flip(a)]. given #877 (H,wt=14): 953 L((x / y) * z,y,z) = x * (y \ z). [para(16(a,1),949(a,2,1))]. given #878 (H,wt=14): 954 L(x * (y \ z),z,y) = (x / y) * z. [para(953(a,1),829(a,1,1))]. given #879 (H,wt=15): 934 L(x \ y,z \ y,x) = L(x \ y,y,z). [para(932(a,1),840(a,1))]. given #880 (H,wt=15): 938 L(x \ y,z * y,y) = x \ R(y,z,x). [para(900(a,2),935(a,2,2))]. given #881 (H,wt=13): 956 L(x \ y,z,y) = x \ R(y,z,x). [para(938(a,1),830(a,1)),flip(a)]. given #882 (H,wt=13): 957 R(x,y,z) = z * L(z \ x,y,x). [para(956(a,2),14(a,1,2)),flip(a)]. given #883 (H,wt=9): 958 R(x,y,z) = L(x,y,z). [para(957(a,2),937(a,1))]. given #884 (H,wt=11): 966 L(x,x \ y,z) = L(x,y,z). [para(958(a,1),896(a,2)),flip(a)]. given #885 (H,wt=11): 967 R(x,x \ y,z) = R(x,y,z). [para(958(a,2),896(a,1)),flip(a)]. given #886 (H,wt=11): 968 L(x,y / x,z) = L(x,y,z). [para(958(a,1),897(a,2)),flip(a)]. given #887 (H,wt=11): 969 L(x,y * x,z) = L(x,y,z). [para(958(a,1),900(a,1)),flip(a)]. given #888 (H,wt=11): 970 R(x,y * x,z) = R(x,y,z). [para(958(a,2),900(a,2)),flip(a)]. given #889 (H,wt=11): 976 L(x,x * y,z) = L(x,y,z). [para(13(a,1),966(a,1,2)),flip(a)]. given #890 (H,wt=11): 981 L(x,y \ x,z) = L(x,z,y). [para(966(a,1),915(a,1))]. given #891 (H,wt=11): 985 L(L(x,y,z),z,y / x) = x. [para(968(a,1),829(a,1,1))]. given #892 (H,wt=11): 989 L(x,y,x / z) = L(x,z,y). [para(54(a,1),981(a,1,2)),flip(a)]. given #893 (H,wt=13): 964 R(x,y,z) = L(x,y,(x * y) * z). [para(958(a,1),500(a,1)),flip(a)]. given #894 (H,wt=13): 971 L(x \ 1,y,z) = L(x,y,z) \ 1. [para(958(a,1),909(a,1))]. given #895 (H,wt=13): 973 L(x \ y,z,x) = L(x,z,y) \ y. [para(958(a,1),920(a,2,1))]. given #896 (H,wt=13): 975 R(x \ y,z,y) = x \ R(y,z,x). [para(958(a,2),956(a,1))]. given #897 (H,wt=13): 978 L(x / y,y,z) = L(x / y,x,z). [para(54(a,1),966(a,1,2))]. given #898 (H,wt=13): 982 R(x,x \ y,z) = R(x,y,y \ z). [para(967(a,1),501(a,1)),flip(a)]. given #899 (H,wt=11): 997 R(x,y,y \ z) = R(x,y,z). [para(982(a,1),967(a,1))]. given #900 (H,wt=11): 998 R(x,y,y * z) = R(x,y,z). [para(13(a,1),997(a,1,3)),flip(a)]. given #901 (H,wt=13): 987 L(x * y,z,x) = L(x * y,y,z). [para(13(a,1),981(a,1,2)),flip(a)]. given #902 (H,wt=13): 990 L(x,y,(x * y) * z) = L(x,y,z). [para(964(a,1),958(a,1))]. given #903 (H,wt=13): 996 L(x \ y,z,y) = L(x,z,y) \ y. [para(973(a,1),932(a,2))]. given #904 (H,wt=13): 1001 L(L(x * y,z,x),z,y) = x * y. [para(987(a,2),829(a,1,1))]. given #905 (H,wt=13): 1005 x \ L(x * y,y,z) = L(y,z,x). [para(987(a,1),858(a,1,2))]. given #906 (H,wt=14): 959 L(x,y,z) * (y * z) = (x * y) * z. [para(958(a,1),73(a,1,1))]. given #907 (H,wt=14): 960 L((x / y) / z,z,y) = x / (z * y). [para(958(a,1),212(a,1))]. given #908 (H,wt=14): 962 L((x * y) / z,z,x) = x * (y / z). [para(958(a,1),494(a,1))]. given #909 (H,wt=14): 963 L(x / y,y,z) = z * ((z \ x) / y). [para(958(a,1),495(a,1))]. given #910 (H,wt=14): 965 L(x * y,x,z) \ z = y \ (x \ z). [para(958(a,1),507(a,1,1))]. given #911 (H,wt=14): 974 R((x / y) * z,y,z) = x * (y \ z). [para(958(a,2),953(a,1))]. given #912 (H,wt=14): 984 L(x,y,z) = ((x / y) / z) * (z * y). [para(968(a,1),434(a,1))]. given #913 (H,wt=14): 1006 L(x * (y * z),y,z) = (x * y) * z. [para(864(a,1),1001(a,1,1))]. given #914 (H,wt=14): 1011 L(x * (y / z),x,z) = (x * y) / z. [para(962(a,1),829(a,1,1))]. given #915 (H,wt=14): 1012 L(x / y,x,z) = z * ((z \ x) / y). [para(963(a,1),978(a,1)),flip(a)]. given #916 (H,wt=14): 1013 L((x * y) \ z,x,z) = y \ (x \ z). [para(965(a,1),996(a,2))]. given #917 (H,wt=15): 945 (x / y) \ L(x,z,y) = L(y,x / y,z). [para(16(a,1),944(a,1,2,1))]. given #918 (H,wt=15): 951 ((x * y) * z) * y = x * ((y * z) * y). [para(872(a,1),947(a,1,1))]. given #919 (H,wt=15): 972 L(x \ 1,y,z) \ u = L(x,y,z) * u. [para(958(a,1),910(a,1,1))]. given #920 (H,wt=15): 977 L(T(x,y),x \ z,u) = T(L(x,z,u),y). [para(966(a,1),40(a,2,1))]. given #921 (H,wt=15): 991 x * L(x \ 1,y,z) = L(x,y,z) \ x. [para(971(a,2),292(a,1,2))]. given #922 (H,wt=15): 992 L(x \ 1,y,z) * u = L(x,y,z) \ u. [para(971(a,2),314(a,1,1))]. given #923 (H,wt=15): 993 x * L(y \ 1,z,u) = x / L(y,z,u). [para(971(a,2),345(a,1,2))]. given #924 (H,wt=15): 994 K(x,L(y \ 1,z,u)) = K(L(y,z,u),x). [para(971(a,2),559(a,1,2))]. given #925 (H,wt=15): 995 L(x \ y,z \ y,x) = L(x,y,z) \ y. [para(840(a,1),973(a,2,1))]. given #926 (H,wt=13): 1025 L(x \ y,y,z) = L(x,y,z) \ y. [para(995(a,1),934(a,1)),flip(a)]. given #927 (H,wt=15): 1000 R(x,y,(y * x) * z) = R(x,y * x,z). [para(998(a,1),970(a,1)),flip(a)]. given #928 (H,wt=13): 1028 R(x,y,(y * x) * z) = R(x,y,z). [para(1000(a,2),970(a,1))]. given #929 (H,wt=13): 1029 R(x,y,z) = L(x,y,(y * x) * z). [para(1028(a,1),958(a,1))]. given #930 (H,wt=13): 1030 L(x,y,(y * x) * z) = L(x,y,z). [para(1029(a,1),958(a,1))]. given #931 (H,wt=15): 1002 L(x * y,y \ z,x) = L(x * y,y,z). [para(987(a,2),831(a,1))]. given #932 (H,wt=15): 1015 ((x * y) * z) / x = x * (y * (z / x)). [para(1011(a,1),871(a,1))]. given #933 (H,wt=15): 1019 (x / y) * L(y,z,x) = L(x,y / x,z). [para(945(a,1),343(a,1)),flip(a)]. given #934 (H,wt=13): 1032 (x / y) * L(y,z,x) = L(x,y,z). [para(1019(a,2),968(a,1))]. given #935 (H,wt=13): 1033 (x / y) * L(y,x,z) = L(x,z,y). [hyper(381,a,1032,a)]. given #936 (H,wt=13): 1034 x * (y \ L(y,z,x)) = L(x,y,z). [para(1032(a,1),855(a,1)),flip(a)]. given #937 (H,wt=13): 1036 L(x,L(y,z,u),y) = (x / y) * y. [para(473(a,1),1033(a,1,2)),flip(a)]. given #938 (H,wt=9): 1039 L(x,L(y,z,u),y) = x. [para(1036(a,2),16(a,1))]. given #939 (H,wt=11): 1040 L(x,y,L(y \ 1,z,u)) = x. [para(1039(a,1),844(a,1)),flip(a)]. given #940 (H,wt=13): 1037 x * (y \ L(y,x,z)) = L(x,z,y). [para(1033(a,1),855(a,1)),flip(a)]. given #941 (H,wt=13): 1038 x \ L(x,y,z) = z \ L(z,x,y). [hyper(56,a,1034,a),flip(a)]. given #942 (H,wt=13): 1043 L(x,y,z) / (z \ L(z,x,y)) = x. [hyper(58,a,1037,a)]. given #943 (H,wt=13): 1046 L(x,y,z) * (L(z,x,y) \ z) = x. [para(1043(a,1),358(a,1)),flip(a)]. given #944 (H,wt=15): 1021 ((x * y) * z) * y = x * (y * (z * y)). [para(113(a,1),951(a,2,2))]. given #945 (H,wt=15): 1023 L(T(x,y),x \ z,u) = L(T(x,y),z,u). [para(977(a,2),40(a,2)),flip(a)]. given #946 (H,wt=15): 1044 K(x \ L(x,y,z),y) = K(L(y,z,x),y). [para(1037(a,1),542(a,1,1)),flip(a)]. given #947 (H,wt=10): 1052 K(x \ L(x,y,z),y) = 1. [para(1044(a,2),309(a,1))]. given #948 (H,wt=10): 1054 K(x,L(y,x,z) \ y) = 1. [para(1052(a,1),562(a,1)),flip(a)]. given #949 (H,wt=15): 1048 (x / y) * (y * (z * y)) = (x * z) * y. [para(16(a,1),1021(a,1,1,1)),flip(a)]. given #950 (H,wt=15): 1055 (x * (y / z)) * z = (x / z) * (z * y). [para(16(a,1),1048(a,1,2,2)),flip(a)]. given #951 (H,wt=16): 939 L(x \ (y \ z),y \ z,y) = (y * x) \ z. [para(936(a,2),203(a,1))]. given #952 (H,wt=16): 941 L(x,y,z) != y * u | L(y \ x,x,z) = u. [para(940(a,1),19(a,1))]. given #953 (H,wt=16): 961 ((x * (y / z)) * z) / y = L(x,y / z,z). [para(958(a,1),75(a,2))]. given #954 (H,wt=16): 1031 (x / (y \ z)) * T(z,y) = L(x * y,y,z). [para(1002(a,1),865(a,1)),flip(a)]. given #955 (H,wt=16): 1047 L(x,y,z) * u != x | L(z,x,y) \ z = u. [para(1046(a,1),19(a,1)),flip(a)]. given #956 (H,wt=16): 1056 ((x * (y / z)) * z) / y = L(x,z \ y,z). [para(961(a,2),800(a,1))]. given #957 (H,wt=16): 1057 (x * (y \ z)) * T(y,z) = L(x * z,z,y). [para(358(a,1),1031(a,1,1))]. given #958 (H,wt=16): 1058 x \ L(y * z,z,x) = T(y * (z / x),x). [para(1057(a,1),737(a,1,2))]. given #959 (H,wt=16): 1059 L(x \ (y * z),z,x) = T(y * (z / x),x). [para(1058(a,1),857(a,2))]. given #960 (H,wt=15): 1060 T(x * (y / z),z) = (z \ y) * T(x,y). [para(1059(a,1),866(a,1))]. given #961 (H,wt=17): 979 L(x,T(x,y) \ z,u) = L(x,K(y,x) * z,u). [para(693(a,1),966(a,1,2))]. given #962 (H,wt=17): 983 L(L(x,y,z),u / x,w) = L(L(x,u,w),y,z). [para(968(a,1),45(a,1,1)),flip(a)]. given #963 (H,wt=17): 988 L(L(x,y,z),u \ x,w) = L(L(x,w,u),y,z). [para(981(a,1),45(a,1,1)),flip(a)]. given #964 (H,wt=17): 1003 L((x \ y) * z,z,y) = L((x \ y) * z,x,y). [para(987(a,1),845(a,1))]. given #965 (H,wt=14): 1061 L((x \ y) * z,z,y) = x \ (y * z). [para(1003(a,2),828(a,1))]. given #966 (H,wt=17): 1008 (x * y) * z != u * (y * z) | L(x,y,z) = u. [para(959(a,1),20(a,1))]. given #967 (H,wt=17): 1022 L(x / y,z,u) \ w = L(y / x,z,u) * w. [para(327(a,1),972(a,1,1,1))]. given #968 (H,wt=17): 1027 L(x,y,L(z \ y,y,u)) = L(x,L(z,y,u),y). [para(1025(a,2),845(a,1,3))]. given #969 (H,wt=17): 1041 L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. [para(1039(a,1),828(a,1)),flip(a)]. given #970 (H,wt=17): 1049 (x \ 1) * (y * (z * y)) = ((x \ y) * z) * y. [para(314(a,1),1021(a,1,1,1)),flip(a)]. given #971 (H,wt=15): 1062 x \ (y * (z * y)) = ((x \ y) * z) * y. [para(1049(a,1),314(a,1)),flip(a)]. given #972 (H,wt=18): 999 (x * y) \ R(z / x,x,y) = ((x * y) \ z) / x. [para(998(a,1),496(a,1,2))]. given #973 (H,wt=18): 1004 x * (y * L(z * x,y,z)) = (x * y) * (z * x). [para(987(a,2),833(a,1,2,2))]. given #974 (H,wt=15): 1065 (x * y) * (z * x) = x * ((y * z) * x). [para(862(a,1),1004(a,1,2)),flip(a)]. given #975 (H,wt=15): 1066 x * (((x \ y) * z) * x) = y * (z * x). [para(14(a,1),1065(a,1,1)),flip(a)]. given #976 (H,wt=18): 1017 L(((x * y) \ z) * x,x,z) = (y \ (x \ z)) * x. [para(1013(a,1),893(a,2,1))]. given #977 (H,wt=15): 1067 (x * y) \ (z * x) = (y \ (x \ z)) * x. [para(1017(a,1),1061(a,1)),flip(a)]. given #978 (H,wt=18): 1064 (x * y) \ L(z / x,x,y) = ((x * y) \ z) / x. [para(958(a,1),999(a,1,2))]. given #979 (H,wt=15): 1069 ((x * y) \ z) / x = y \ (x \ (z / x)). [para(1064(a,1),926(a,1))]. given #980 (H,wt=18): 1068 (x * y) \ (z * x) != u * x | y \ (x \ z) = u. [para(1067(a,2),20(a,1))]. given #981 (H,wt=19): 950 (x \ y) * (x * ((x \ z) * y)) = x \ (y * (z * y)). [para(946(a,1),851(a,1,2))]. given #982 (H,wt=19): 986 L(K(x,y),z * T(y,x),u) = L(K(x,y),z * y,u). [para(607(a,1),969(a,1,2)),flip(a)]. given #983 (H,wt=19): 1009 T((x * y) * z,L(x,y,z)) = (y * z) * L(x,y,z). [para(959(a,1),116(a,1,1))]. given #984 (H,wt=18): 1072 T((x * y) * z,L(x,y,z)) = z * (T(y,z) * x). [para(1009(a,2),804(a,1))]. given #985 (H,wt=19): 1014 (x * y) * (z * (x * y)) = x * (y * ((z * x) * y)). [para(1006(a,1),833(a,1,2,2)),flip(a)]. given #986 (H,wt=19): 1026 L(x \ (y \ z),y \ z,y) = L(x,z,y) \ (y \ z). [para(826(a,1),1025(a,2,1))]. given #987 (H,wt=14): 1074 L(x,y,z) \ (z \ y) = (z * x) \ y. [para(1026(a,1),939(a,1))]. given #988 (H,wt=19): 1051 L(T(T(x,y),y \ x),z,u) = L(x,T(x,y) \ z,u). [para(143(a,1),1023(a,1,1)),flip(a)]. given #989 (H,wt=19): 1070 (x \ ((y \ x) * z)) / y = x \ (y \ ((x * z) / y)). [para(876(a,1),1069(a,1,1))]. given #990 (H,wt=19): 1071 (x \ y) * (x * ((x \ z) * y)) = ((x \ y) * z) * y. [para(950(a,2),1062(a,1))]. given #991 (H,wt=19): 1075 L(T(T(x,y),y \ x),z,u) = L(x,K(y,x) * z,u). [para(1051(a,2),979(a,1))]. given #992 (H,wt=13): 1077 L(x,K(y,x) * z,u) = L(x,z,u). [para(143(a,1),1075(a,1,1)),flip(a)]. given #993 (H,wt=15): 1078 L(x,K(y,x) / z,u) = L(x,z \ 1,u). [para(345(a,1),1077(a,1,2))]. given #994 (H,wt=13): 1079 L(x,K(y,x) / z,u) = L(x,u,z). [para(1078(a,2),843(a,1))]. given #995 (H,wt=15): 1080 L(x,y,(K(z,x) / u) \ y) = L(x,y,u). [para(1079(a,1),845(a,2))]. given #996 (H,wt=15): 1081 L(x,y,(z / K(u,x)) * y) = L(x,y,z). [para(343(a,1),1080(a,1,3))]. given #997 (H,wt=15): 1082 L(x,y,(z * K(x,u)) * y) = L(x,y,z). [para(409(a,1),1081(a,1,3,1))]. given #998 (H,wt=13): 1083 L(x,y,z * K(x,u)) = L(x,y,z). [para(1082(a,1),835(a,1)),flip(a)]. given #999 (H,wt=20): 854 L(L((x \ y) * z,u,w),x,y) = L(x \ (y * z),u,w). [para(828(a,1),45(a,1,1)),flip(a)]. given #1000 (H,wt=20): 867 L(x \ y,z * z,x) = (x \ (z * z)) * (z \ (z \ y)). [para(170(a,1),852(a,2,2))]. given #1001 (H,wt=20): 980 L(L(L(x,y,z),u,w),z,y) = L(x,L(x,y,z) \ u,w). [para(966(a,1),832(a,1,1))]. given #1002 (H,wt=14): 1086 L(x,L(x,y,z) \ u,w) = L(x,u,w). [para(980(a,1),832(a,1))]. given #1003 (H,wt=14): 1087 L(x,L(x,y,z) * u,w) = L(x,u,w). [para(13(a,1),1086(a,1,2)),flip(a)]. given #1004 (H,wt=15): 1089 L(x,(y * x) \ z,u) = L(x,y \ z,u). [para(1074(a,1),1086(a,1,2))]. given #1005 (H,wt=20): 1007 x \ L(x * (y \ z),y \ z,z) = (y \ (z / x)) * x. [para(1005(a,2),952(a,1))]. given #1006 (H,wt=18): 1090 x \ L(x * (y \ z),z,y) = (y \ (z / x)) * x. [para(840(a,1),1007(a,1,2))]. given #1007 (H,wt=15): 1091 x \ ((x / y) * z) = (y \ (z / x)) * x. [para(954(a,1),1090(a,1,2))]. given #1008 (H,wt=20): 1085 L(x \ y,z * z,x) = ((x \ z) * z) * (z \ (z \ y)). [para(401(a,1),867(a,2,1))]. given #1009 (H,wt=20): 1092 L(x \ y,z * z,x) = z * ((z \ (x \ z)) * (z \ y)). [para(1085(a,2),261(a,1))]. given #1010 (H,wt=18): 1093 L(x \ y,z * z,x) = z * (T(x,z) \ (z \ y)). [para(376(a,1),1092(a,2,2))]. given #1011 (H,wt=18): 1094 x * (T(y,x) \ (x \ (y * z))) = L(z,x * x,y). [para(13(a,1),1093(a,1,1)),flip(a)]. given #1012 (H,wt=21): 879 L(x * ((y * x) \ z),y,x) != x * u | x \ (y \ z) = u. [para(863(a,2),19(a,1))]. given #1013 (H,wt=21): 1016 L(L(x / y,x,z) * u,z,u) = z * (((z \ x) / y) * u). [para(1012(a,2),943(a,1,1,1))]. given #1014 (H,wt=21): 1018 L(L(x / y,y,z) \ u,z,u) = ((z \ x) / y) \ (z \ u). [para(963(a,2),1013(a,1,1,1))]. given #1015 (H,wt=21): 1020 (x * L(x \ 1,y,z)) * u = x * (L(x \ 1,y,z) * u). [hyper(18,a,460,a,b,951,a)]. given #1016 (H,wt=19): 1097 x * (L(x \ 1,y,z) * u) = (L(x,y,z) \ x) * u. [para(991(a,1),1020(a,1,1)),flip(a)]. given #1017 (H,wt=17): 1098 (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). [para(992(a,1),1097(a,1,2)),flip(a)]. given #1018 (H,wt=17): 1099 L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u). [para(1098(a,1),1041(a,2))]. given #1019 (H,wt=17): 1100 x * (L(x,y,z) \ (x \ u)) = L(x,y,z) \ u. [para(14(a,1),1099(a,1,2)),flip(a)]. given #1020 (H,wt=17): 1101 L(x,y,z) \ (x \ u) = x \ (L(x,y,z) \ u). [hyper(56,a,1100,a),flip(a)]. given #1021 (H,wt=17): 1102 L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u. [para(1101(a,1),14(a,1,2))]. given #1022 (H,wt=17): 1103 x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u). [para(13(a,1),1102(a,1,2,2)),flip(a)]. given #1023 (H,wt=17): 1104 x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. [para(1103(a,1),14(a,1,2))]. given #1024 (H,wt=21): 1035 L(x,T(y,z),L(y,u,w)) = (x / L(y,u,w)) * L(y,u,w). [para(219(a,1),1033(a,1,2)),flip(a)]. given #1025 (H,wt=11): 1105 L(x,T(y,z),L(y,u,w)) = x. [para(1035(a,2),16(a,1))]. given #1026 (H,wt=11): 1106 L(x,T(L(y,z,u),w),y) = x. [para(305(a,1),1105(a,1,3))]. given #1027 (H,wt=11): 1107 L(x,L(T(y,z),u,w),y) = x. [para(40(a,2),1106(a,1,2))]. given #1028 (H,wt=21): 1042 (x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u). [hyper(17,a,863,a(flip),b,1040,a(flip))]. given #1029 (H,wt=19): 1109 (x * L(x \ 1,y,z)) \ u = L(x,y,z) * (x \ u). [para(1042(a,2),972(a,1))]. given #1030 (H,wt=17): 1110 (x / L(x,y,z)) \ u = L(x,y,z) * (x \ u). [para(993(a,1),1109(a,1,1))]. given #1031 (H,wt=21): 1045 x * (((y * x) * z) \ L((y * x) * z,x,y)) = L(x,y,z). [para(1037(a,2),1030(a,1))]. given #1032 (H,wt=18): 1111 L(x,y,z) = x * (((y * x) * z) \ (y * (x * z))). [para(869(a,1),1045(a,1,2,2)),flip(a)]. given #1033 (H,wt=13): 1112 L(x,y,z) = x * (a(y,x,z) \ 1). [para(339(a,1),1111(a,2,2))]. given #1034 (H,wt=11): 1114 L(x,y,z) = x / a(y,x,z). [para(1112(a,2),345(a,1))]. given #1035 (H,wt=11): 1115 L(x,y,z) * a(y,x,z) = x. [para(1114(a,2),16(a,1,1))]. given #1036 (H,wt=11): 1116 a(x,y,z) = L(y,x,z) \ y. [para(1114(a,2),54(a,1,1)),flip(a)]. given #1037 (H,wt=8): 1121 K(x,a(x,y,z)) = 1. [para(1116(a,2),1054(a,1,2))]. given #1038 (H,wt=8): 1122 T(x,a(x,y,z)) = x. [hyper(37,a,1121,a)]. given #1039 (H,wt=10): 1123 1 * K(a(x,y,z),x) = 1. [para(1121(a,1),405(a,1,1))]. given #1040 (H,wt=8): 1125 K(a(x,y,z),x) = 1. [hyper(55,a,1123,a),flip(a)]. given #1041 (H,wt=11): 1118 a(x,y,z) = L(z,y,x) \ z. [hyper(1047,a,1115,a),flip(a)]. given #1042 (H,wt=9): 1128 a(x,y,z) = a(z,x,y). [para(1118(a,2),1116(a,2))]. given #1043 (H,wt=8): 1130 K(a(x,y,z),z) = 1. [para(1128(a,2),1125(a,1,1))]. given #1044 (H,wt=11): 1119 a(x,y,z) * L(y,x,z) = y. [para(1116(a,2),267(a,1,1))]. given #1045 (H,wt=11): 1120 a(x,y,z) = y / L(y,x,z). [para(1116(a,2),268(a,2)),flip(a)]. given #1046 (H,wt=11): 1129 a(x,y,z) = L(x,z,y) \ x. [para(1128(a,2),1116(a,1))]. given #1047 (H,wt=11): 1131 T(a(x,y,z),z) = a(x,y,z). [hyper(37,a,1130,a)]. given #1048 (H,wt=11): 1133 a(x,y,z) = x / L(x,z,y). [para(1120(a,1),1128(a,2))]. given #1049 (H,wt=13): 1113 a(x,y,z) \ 1 = y \ L(y,x,z). [hyper(56,a,1112,a(flip)),flip(a)]. given #1050 (H,wt=13): 1124 a(x,y,z) * x = x * a(x,y,z). [para(1122(a,1),78(a,1,2))]. given #1051 (H,wt=13): 1134 a(x,y,z \ 1) = L(x,y,z) \ x. [para(843(a,1),1129(a,2,1))]. given #1052 (H,wt=11): 1138 a(x,y,z \ 1) = a(z,y,x). [para(1134(a,2),1118(a,2)),flip(a)]. given #1053 (H,wt=11): 1140 a(x,y \ 1,z) = a(y,x,z). [para(1138(a,1),1128(a,2))]. given #1054 (H,wt=13): 1139 a(K(x,y),z,u) = a(u,z,K(y,x)). [para(404(a,1),1138(a,1,3)),flip(a)]. given #1055 (H,wt=13): 1142 a(x,K(y,z),u) = a(x,u,K(z,y)). [para(1139(a,1),1128(a,1)),flip(a)]. given #1056 (H,wt=15): 1117 L(x,a(y,x,z),u) = L(x,u,L(x,y,z)). [para(1114(a,2),989(a,1,3)),flip(a)]. given #1057 (H,wt=9): 1143 L(x,a(y,x,z),u) = x. [para(1117(a,2),473(a,1))]. given #1058 (H,wt=9): 1144 L(x,a(x,y,z),u) = x. [para(1128(a,2),1143(a,1,2))]. given #1059 (H,wt=9): 1147 L(x,y,a(x,z,u)) = x. [para(1144(a,1),307(a,1,1))]. given #1060 (H,wt=11): 1149 L(x,y,a(y * x,z,u)) = x. [hyper(889,a,1147,a)]. given #1061 (H,wt=11): 1150 L(x,y / x,a(y,z,u)) = x. [para(16(a,1),1149(a,1,3,1))]. given #1062 (H,wt=9): 1151 L(x,y,a(y,z,u)) = x. [para(1150(a,1),968(a,1)),flip(a)]. given #1063 (H,wt=9): 1153 L(x,y,a(z,u,y)) = x. [para(1128(a,2),1151(a,1,3))]. given #1064 (H,wt=15): 1127 K(x,y \ L(y,z,u)) = K(a(u,z,y),x). [para(1118(a,2),562(a,1,1)),flip(a)]. given #1065 (H,wt=15): 1135 x * (L(x,y,z) \ u) = a(x,z,y) * u. [para(1129(a,2),1098(a,1,1)),flip(a)]. given #1066 (H,wt=15): 1137 L(x,y,z) * (x \ u) = a(x,z,y) \ u. [para(1133(a,2),1110(a,1,1)),flip(a)]. given #1067 (H,wt=15): 1141 a(x,T(y \ 1,z),u) = a(T(y,z),x,u). [para(375(a,1),1140(a,1,2))]. given #1068 (H,wt=15): 1145 L(L(x,y,z),a(x,u,w),v5) = L(x,y,z). [para(1144(a,1),45(a,1,1)),flip(a)]. given #1069 (H,wt=15): 1155 x \ (a(x,y,z) * u) = L(x,z,y) \ u. [hyper(56,a,1135,a)]. given #1070 (H,wt=13): 1158 L(x,y,z) \ L(z,x,y) = x \ z. [para(1119(a,1),1155(a,1,2)),flip(a)]. given #1071 (H,wt=14): 1159 L(x,L(y,x,z),u) = L(x,x \ y,u). [para(1158(a,1),1086(a,1,2)),flip(a)]. given #1072 (H,wt=12): 1160 L(x,L(y,x,z),u) = L(x,y,u). [para(1159(a,2),966(a,1))]. given #1073 (H,wt=12): 1161 L(x,L(y,z,x),u) = L(x,y,u). [para(305(a,1),1160(a,1,2)),flip(a)]. given #1074 (H,wt=14): 1162 L(x,y,L(z,x,u)) = L(x,z,y \ 1). [para(1160(a,1),844(a,1)),flip(a)]. given #1075 (H,wt=12): 1165 L(x,y,L(z,x,u)) = L(x,y,z). [para(1162(a,2),844(a,1))]. given #1076 (H,wt=15): 1157 a(x,T(y \ 1,z),u) = a(x,u,T(y,z)). [para(1141(a,2),1128(a,2)),flip(a)]. given #1077 (H,wt=15): 1166 a(x,y \ (z \ y),u) = a(x,u,T(z,y)). [para(320(a,1),1157(a,1,2))]. given #1078 (H,wt=16): 1154 L(a(x,y,z),u,z) = (a(x,y,z) / u) * u. [para(1153(a,1),1032(a,1,2)),flip(a)]. given #1079 (H,wt=12): 1167 L(a(x,y,z),u,z) = a(x,y,z). [para(1154(a,2),16(a,1))]. given #1080 (H,wt=17): 1146 (x * a(y,z,u)) * y = x * (a(y,z,u) * y). [para(1144(a,1),67(a,1,2))]. given #1081 (H,wt=17): 1148 (a(x,y,z) * u) * x = a(x,y,z) * (u * x). [para(1144(a,1),833(a,1,2,2)),flip(a)]. given #1082 (H,wt=12): 1168 L(a(x,y,z),u,x) = a(x,y,z). [hyper(1008,a,1148,a)]. given #1083 (H,wt=12): 1169 L(a(x,y,z),x,u) = a(x,y,z). [para(1168(a,1),304(a,1,1))]. given #1084 (H,wt=17): 1152 (x * y) * a(y,z,u) = x * (y * a(y,z,u)). [para(1151(a,1),959(a,1,1)),flip(a)]. given #1085 (H,wt=17): 1156 T(a(x,y,z) * u,x) = (L(x,z,y) \ u) * x. [para(1135(a,1),116(a,1,1))]. given #1086 (H,wt=17): 1164 L(x,(x * y) / z,u) = L(x,x * (y / z),u). [para(1011(a,1),1160(a,1,2))]. given #1087 (H,wt=15): 1170 L(x,(x * y) / z,u) = L(x,y / z,u). [para(1164(a,2),976(a,1))]. given #1088 (H,wt=18): 1163 L(x,L(y,z \ x,u),z) = z * L(z \ x,y,x). [para(1160(a,1),937(a,1,2)),flip(a)]. given #1089 (H,wt=14): 1171 L(x,L(y,z \ x,u),z) = L(x,y,z). [para(1163(a,2),937(a,1))]. given #1090 (H,wt=18): 1172 L(x,y,L(z,(x / y) \ x,u)) = L(x,z,x / y). [para(1171(a,1),989(a,1)),flip(a)]. given #1091 (H,wt=16): 1173 L(x,y,L(z,(x / y) \ x,u)) = L(x,y,z). [para(1172(a,2),989(a,1))]. given #1092 (H,wt=12): 1174 L(x,y,L(z,y,u)) = L(x,y,z). [para(54(a,1),1173(a,1,3,2))]. given #1093 (H,wt=14): 1175 L(x,L(y,z,u),z) = L(x,z,y \ z). [para(1174(a,1),1027(a,1)),flip(a)]. given #1094 (H,wt=12): 1176 L(x,L(y,z,u),z) = L(x,y,z). [para(1175(a,2),845(a,1))]. given #1095 (H,wt=12): 1178 L(x,L(y,z,u),u) = L(x,y,u). [para(305(a,1),1176(a,1,2)),flip(a)]. given #1096 (H,wt=16): 1179 L(x,L(y,z,u),u / z) = L(x,y,u / z). [para(836(a,1),1178(a,1,2))]. given #1097 (H,wt=19): 1136 T(a(x,y,z) * (z / u),u) = (u \ z) * a(x,y,z). [para(1131(a,1),1060(a,2,2))]. given #1098 (H,wt=21): 1050 x * ((y \ 1) * (z * (y \ 1))) = ((x / y) * z) * (y \ 1). [para(345(a,1),1021(a,1,1,1)),flip(a)]. given #1099 (H,wt=19): 1180 x * ((y \ 1) * (z * (y \ 1))) = ((x / y) * z) / y. [para(1050(a,2),345(a,1))]. given #1100 (H,wt=17): 1181 x * ((y \ 1) * (z / y)) = ((x / y) * z) / y. [para(345(a,1),1180(a,1,2,2))]. given #1101 (H,wt=15): 1182 ((x / y) * z) / y = x * (y \ (z / y)). [para(314(a,1),1181(a,1,2)),flip(a)]. given #1102 (H,wt=21): 1096 L(L(x / y,x,z) * u,z,u) = ((z \ y) / x) \ (z \ u). [para(1022(a,1),1018(a,1,1))]. given #1103 (H,wt=19): 1184 ((x \ y) / z) \ (x \ u) = x * (((x \ z) / y) * u). [para(1096(a,1),1016(a,1))]. given #1104 (H,wt=19): 1185 (x / (y \ z)) * (y \ u) = y * (((y \ x) / z) * u). [para(1184(a,1),343(a,1)),flip(a)]. given #1105 (H,wt=19): 1186 (x * (y \ z)) * (z \ u) = z * (((z \ x) / y) * u). [para(358(a,1),1185(a,1,1))]. given #1106 (H,wt=21): 1108 (x * y) / L(T(x,z),u,w) = x * (y / L(T(x,z),u,w)). [para(1107(a,1),962(a,1))]. given #1107 (H,wt=21): 1132 (x * y) / L(L(y,z,u),a(z,y,u),x) = x * a(z,y,u). [para(1119(a,1),87(a,1,1,2))]. given #1108 (H,wt=21): 1183 (((((x / y) \ y) * z) / y) * x) / y = T(z,y \ (x / y)). [para(1182(a,2),384(a,1))]. given #1109 (H,wt=21): 1188 (x * y) / L(L(y,z,u),a(y,u,z),x) = x * a(z,y,u). [para(1128(a,2),1132(a,1,2,2))]. given #1110 (H,wt=15): 1190 (x * y) / L(y,z,u) = x * a(z,y,u). [para(1145(a,1),1188(a,1,2))]. given #1111 (H,wt=15): 1191 (x * y) / L(y,z,u) = x * a(y,u,z). [para(1128(a,2),1190(a,2,2))]. given #1112 (H,wt=15): 1193 (x / y) * a(y,z,u) = x / L(y,u,z). [para(16(a,1),1191(a,1,1)),flip(a)]. given #1113 (H,wt=15): 1195 (x / y) * (y / L(x,z,u)) = a(x,u,z). [hyper(381,a,1193,a)]. given #1114 (H,wt=18): 1198 a(x,y,L(z,u,x)) = (x / w) * (w / L(x,z,y)). [para(1161(a,1),1195(a,1,2,2)),flip(a)]. given #1115 (H,wt=12): 1200 a(x,y,L(z,u,x)) = a(x,y,z). [para(1198(a,2),1195(a,1))]. given #1116 (H,wt=18): 1199 a(x,L(y,x,z),u) = (x / w) * (w / L(x,u,y)). [para(1165(a,1),1195(a,1,2,2)),flip(a)]. given #1117 (H,wt=12): 1201 a(x,L(y,x,z),u) = a(x,y,u). [para(1199(a,2),1195(a,1))]. given #1118 (H,wt=19): 1194 (x * y) / L(T(x,y),z,u) = y * a(T(x,y),u,z). [para(78(a,1),1191(a,1,1))]. given #1119 (H,wt=19): 1196 a(x,y * K(x,z),u) = (x / w) * (w / L(x,u,y)). [para(1083(a,1),1195(a,1,2,2)),flip(a)]. given #1120 (H,wt=13): 1203 a(x,y * K(x,z),u) = a(x,y,u). [para(1196(a,2),1195(a,1))]. given #1121 (H,wt=13): 1204 a(x,y / x,z) = a(x,x \ y,z). [para(429(a,1),1203(a,1,2)),flip(a)]. given #1122 (H,wt=19): 1202 x * (y / L(T(x,y),z,u)) = y * a(T(x,y),u,z). [para(1194(a,1),1108(a,1)),flip(a)]. given #1123 (H,wt=17): 1205 x * a(T(y,x),z,u) = y * (L(y,u,z) \ x). [para(235(a,1),1202(a,1,2)),flip(a)]. given #1124 (H,wt=15): 1206 x * a(T(y,x),z,u) = a(y,z,u) * x. [para(1205(a,2),1135(a,1))]. given #1125 (H,wt=15): 1207 x * a(y,T(z,x),u) = a(z,u,y) * x. [para(1128(a,1),1206(a,1,2))]. given #1126 (H,wt=13): 1208 a(x,T(y,z),u) = T(a(y,u,x),z). [hyper(94,a,1207,a),flip(a)]. given #1127 (H,wt=13): 1209 a(x,T(y,z),u) = T(a(x,y,u),z). [para(1128(a,1),1208(a,2,1))]. given #1128 (H,wt=11): 1211 a(x,T(y,z),z) = a(x,y,z). [para(1209(a,2),1131(a,1))]. given #1129 (H,wt=13): 1212 a(x,y / z,z) = a(x,z \ y,z). [para(80(a,1),1211(a,1,2)),flip(a)]. given #1130 (H,wt=17): 1210 T(a(x,y \ 1,z),u) = a(x,u \ (y \ u),z). [para(320(a,1),1209(a,1,2)),flip(a)]. given #1131 (H,wt=15): 1213 a(x,y \ (z \ y),u) = T(a(z,x,u),y). [para(1140(a,1),1210(a,1,1)),flip(a)]. given #1132 (H,wt=15): 1214 a(x,y \ (z \ y),u) = T(a(x,u,z),y). [para(1128(a,2),1213(a,2,1))]. given #1133 (H,wt=13): 1215 a(x,y,T(z,u)) = T(a(x,y,z),u). [para(1214(a,1),1166(a,1)),flip(a)]. given #1134 (H,wt=13): 1216 a(x,T(y,z),u) = a(x,y,T(u,z)). [para(1215(a,2),1209(a,2))]. given #1135 (H,wt=20): 1197 a(x,y,L(x,z,u) * w) = (x / v5) * (v5 / L(x,w,y)). [para(1087(a,1),1195(a,1,2,2)),flip(a)]. given #1136 (H,wt=14): 1217 a(x,y,L(x,z,u) * w) = a(x,y,w). [para(1197(a,2),1195(a,1))]. given #1137 (H,wt=11): 1218 a(x,y,x * z) = a(x,y,z). [para(110(a,1),1217(a,1,3,1))]. given #1138 (H,wt=21): 1189 ((((x * (y \ x)) * z) / x) * y) / x = T(z,x \ (y / x)). [para(380(a,1),1183(a,1,1,1,1,1))]. given #1139 (H,wt=21): 1219 ((x * ((y \ x) * (z / x))) * y) / x = T(z,x \ (y / x)). [para(1015(a,1),1189(a,1,1,1))]. given #1140 (H,wt=21): 1220 x * (((y \ x) * (z / x)) * (y / x)) = T(z,x \ (y / x)). [para(1219(a,1),1015(a,1)),flip(a)]. given #1141 (H,wt=22): 890 (x * L(y * z,y,x)) \ (x * (y * z)) = a(x,y,L(z,y,x)). [para(885(a,2),197(a,1,1,2))]. given #1142 (H,wt=22): 1063 x * (y * ((((x * y) \ z) * u) * z)) = L(z * (u * z),y,x). [para(1062(a,1),870(a,2,2,2)),flip(a)]. given #1143 (H,wt=22): 1221 L(x * (y * z),y,x) \ (x * (y * z)) = a(x,y,L(z,y,x)). [para(861(a,2),890(a,1,1))]. given #1144 (H,wt=19): 1222 a(x,y,z) = L(x * (y * z),y,x) \ (x * (y * z)). [para(1221(a,2),1200(a,1)),flip(a)]. given #1145 (H,wt=13): 1224 a(x,y,x * (y * z)) = a(x,y,z). [para(1222(a,2),1118(a,2))]. given #1146 (H,wt=11): 1226 a(x,y,y * z) = a(x,y,z). [para(1224(a,1),1218(a,1)),flip(a)]. given #1147 (H,wt=11): 1227 a(x,y,y \ z) = a(x,y,z). [para(14(a,1),1226(a,1,3)),flip(a)]. given #1148 (H,wt=16): 1223 T(x * (y * z),a(x,y,z)) = x * (y * z). [para(1222(a,2),264(a,1,2))]. given #1149 (H,wt=16): 1228 a(x,y,z) = (x * z) \ (y * ((y \ x) * z)). [para(1227(a,1),474(a,2)),flip(a)]. given #1150 (H,wt=16): 1229 a(x,y,z) = ((x * y) * z) / (x * (y * z)). [para(1223(a,1),296(a,1,2)),flip(a)]. given #1151 (H,wt=18): 1230 ((x * (y / z)) * z) / (x * y) = a(x,y / z,z). [para(16(a,1),1229(a,2,2,2)),flip(a)]. given #1152 (H,wt=18): 1231 ((x * (y / z)) * z) / (x * y) = a(x,z \ y,z). [para(1230(a,2),1212(a,1))]. given #1153 (H,wt=21): 1232 L((((x * (y / z)) * z) / y) / x,x,y) = a(x,z \ y,z). [para(1231(a,1),960(a,2))]. given #1154 (H,wt=18): 1233 L(L(x,y \ z,y) / x,x,z) = a(x,y \ z,y). [para(1056(a,1),1232(a,1,1,1))]. given #1155 (H,wt=18): 1234 L(x \ L(x,y \ z,y),x,z) = a(x,y \ z,y). [para(269(a,1),1233(a,1,1))]. given #1156 (H,wt=20): 1235 L(x \ L(x,y,z),x,z * y) = a(x,z \ (z * y),z). [para(13(a,1),1234(a,1,1,2,2))]. given #1157 (H,wt=16): 1236 a(x,y,z) = L(x \ L(x,y,z),x,z * y). [para(13(a,1),1235(a,2,2)),flip(a)]. given #1158 (H,wt=11): 1237 a(x,y,z) = x \ L(x,y,z). [para(1236(a,2),868(a,1))]. given #1159 (H,wt=11): 1238 L(x,y,z) = x * a(x,y,z). [para(1237(a,2),14(a,1,2)),flip(a)]. given #1160 (H,wt=11): 1241 L(x,y,z) = x * a(y,z,x). [para(1237(a,2),1034(a,1,2)),flip(a)]. given #1161 (H,wt=11): 1242 a(x,y,z) = y \ L(y,z,x). [para(1237(a,2),1038(a,2)),flip(a)]. given #1162 (H,wt=11): 1243 L(x,y,z) = a(x,y,z) * x. [para(1238(a,2),1124(a,2)),flip(a)]. given #1163 (H,wt=11): 1247 a(x,y,z) \ 1 = a(z,y,x). [para(1242(a,2),1113(a,2))]. given #1164 (H,wt=11): 1249 L(x,y,z) = a(z,x,y) * x. [para(1128(a,1),1243(a,2,1))]. given #1165 (H,wt=11): 1250 L(x,y,z) = a(y,z,x) * x. [para(1128(a,2),1243(a,2,1))]. given #1166 (H,wt=13): 1248 K(a(x,y,z),u) = K(u,a(x,z,y)). [para(1242(a,2),1127(a,1,2)),flip(a)]. given #1167 (H,wt=13): 1252 a(x,y,z) \ u = a(z,y,x) * u. [para(1247(a,1),314(a,1,1)),flip(a)]. given #1168 (H,wt=13): 1253 x / a(y,z,u) = x * a(u,z,y). [para(1247(a,1),334(a,1,2))]. given #1169 (H,wt=13): 1256 a(x,y,z) \ u = a(x,z,y) * u. [para(1128(a,1),1252(a,1,1))]. given #1170 (H,wt=13): 1257 x / a(y,z,u) = x * a(y,u,z). [para(1128(a,1),1253(a,1,2))]. given #1171 (H,wt=15): 1240 (x / y) * L(y,z,u) = x * a(y,z,u). [para(1237(a,2),855(a,2,2))]. given #1172 (H,wt=15): 1244 (x * y) * a(y,z,u) = x * L(y,z,u). [para(1238(a,2),1152(a,2,2))]. given #1173 (H,wt=15): 1245 x * a(x,y,T(z,u)) = L(x,T(y,u),z). [para(1216(a,1),1238(a,2,2)),flip(a)]. given #1174 (H,wt=13): 1265 L(x,T(y,z),u) = L(x,y,T(u,z)). [para(1245(a,1),1238(a,2)),flip(a)]. given #1175 (H,wt=15): 1251 (x * a(y,z,u)) * y = x * L(y,z,u). [para(1243(a,2),1146(a,2,2))]. given #1176 (H,wt=15): 1255 L(x,y,z * K(y,u)) = a(y,z,x) * x. [para(1203(a,1),1250(a,2,1))]. given #1177 (H,wt=13): 1268 L(x,y,z * K(y,u)) = L(x,y,z). [para(1255(a,2),1250(a,2)),flip(a)]. given #1178 (H,wt=15): 1259 a(x,x * y,z) * 1 = a(x * z,x,y). [para(1256(a,1),781(a,1))]. given #1179 (H,wt=13): 1270 a(x * y,x,z) = a(x,x * z,y). [hyper(57,a,1259,a),flip(a)]. given #1180 (H,wt=13): 1271 a(x,x * y,z) = a(x,y,x * z). [para(1270(a,1),1128(a,2)),flip(a)]. given #1181 (H,wt=11): 1272 a(x,x * y,z) = a(x,y,z). [para(1271(a,2),1218(a,1))]. given #1182 (H,wt=11): 1273 a(x,x \ y,z) = a(x,y,z). [para(14(a,1),1272(a,1,2)),flip(a)]. given #1183 (H,wt=11): 1274 a(x,y / x,z) = a(x,y,z). [para(1273(a,1),1204(a,2))]. given #1184 (H,wt=15): 1260 L(x,y,z) * (x \ u) = a(x,y,z) * u. [para(1256(a,1),1137(a,2))]. given #1185 (H,wt=15): 1269 L(x,y,z \ T(u,y)) = L(x,y,z \ u). [para(615(a,1),1268(a,1,3)),flip(a)]. given #1186 (H,wt=15): 1275 x \ (L(x,y,z) * u) = a(x,y,z) * u. [para(1260(a,1),1103(a,2))]. given #1187 (H,wt=15): 1276 x * (a(x,y,z) * u) = L(x,y,z) * u. [para(1260(a,1),1104(a,1,2))]. given #1188 (H,wt=17): 1246 K(x,y) * L(K(y,x),z,u) = a(z,u,K(y,x)). [hyper(413,a,1241,a(flip))]. given #1189 (H,wt=17): 1254 a(x,y,z) * L(y,x,u) = L(L(y,x,u),z,x). [para(1201(a,1),1249(a,2,1)),flip(a)]. given #1190 (H,wt=17): 1267 x \ (y * L(x,z,u)) = T(y * a(x,z,u),x). [para(1251(a,1),32(a,2,2)),flip(a)]. given #1191 (H,wt=17): 1277 x \ (y \ L(y * x,z,u)) = a(y * x,z,u). [hyper(1068,a,1275,a)]. given #1192 (H,wt=17): 1278 T(x * a(y,z,u),y) = (y \ x) * L(y,z,u). [para(1267(a,1),468(a,1))]. given #1193 (H,wt=17): 1279 x \ (y \ L(y * x,z,u)) = a(z,u,y * x). [para(1277(a,2),1128(a,2)),flip(a)]. given #1194 (H,wt=18): 1258 (a(x,y,z) * u) * a(x,z,y) = T(u,a(x,z,y)). [para(1256(a,1),120(a,2,1)),flip(a)]. given #1195 (H,wt=18): 1261 T(x * a(y,z,u),a(y,u,z)) = a(y,u,z) \ x. [para(1257(a,1),80(a,1,1))]. given #1196 (H,wt=18): 1281 T(x * a(y,z,u),a(y,u,z)) = a(y,z,u) * x. [para(1261(a,2),1256(a,1))]. given #1197 (H,wt=19): 1262 (x \ (y / x)) * L(x,z,u) = (x \ y) * a(x,z,u). [para(130(a,1),1240(a,1,1))]. given #1198 (H,wt=19): 1282 T((x / y) * a(y,z,u),y) = (y \ x) * a(y,z,u). [para(1262(a,1),1278(a,2))]. given #1199 (H,wt=17): 1283 T(x / L(y,z,u),y) = (y \ x) * a(y,u,z). [para(1193(a,1),1282(a,1,1))]. given #1200 (H,wt=19): 1284 T((x * y) / L(y,z,u),y) = T(x,y) * a(y,u,z). [para(32(a,2),1283(a,2,1))]. given #1201 (H,wt=17): 1285 T(x * a(y,z,u),y) = T(x,y) * a(y,z,u). [para(1191(a,1),1284(a,1,1))]. given #1202 (H,wt=20): 1264 ((L(x,y,z) \ u) * x) * a(x,y,z) = T(u,L(x,y,z)). [para(1244(a,2),120(a,2)),flip(a)]. given #1203 (H,wt=20): 1286 T(a(x,y,z) * u,x) * a(x,z,y) = T(u,L(x,z,y)). [para(1156(a,2),1264(a,1,1))]. given #1204 (H,wt=20): 1287 T((a(x,y,z) * u) * a(x,z,y),x) = T(u,L(x,z,y)). [para(1286(a,1),1285(a,2))]. given #1205 (H,wt=15): 1288 T(T(x,a(y,z,u)),y) = T(x,L(y,z,u)). [para(1258(a,1),1287(a,1,1))]. given #1206 (H,wt=15): 1289 T(T(x,y),a(y,z,u)) = T(x,L(y,z,u)). [para(1288(a,1),38(a,1)),flip(a)]. given #1207 (H,wt=19): 1290 T(x,L(y,z,u)) \ T(x,y) = K(a(y,z,u),T(x,y)). [para(1289(a,1),531(a,2,1)),flip(a)]. given #1208 (H,wt=19): 1291 K(x,y) * K(L(y,z,u),x) = K(a(y,z,u),T(x,y)). [para(1290(a,1),713(a,1)),flip(a)]. given #1209 (H,wt=23): 198 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(67(a,1),28(a,2,2,2)),flip(a)]. given #1210 (H,wt=16): 1292 L(L(x,y,z),z * y,z) = L(x,y,z * z). [para(198(a,1),771(a,1))]. given #1211 (H,wt=14): 1293 L(L(x,y,z),y,z) = L(x,y,z * z). [para(1292(a,1),827(a,1)),flip(a)]. given #1212 (H,wt=23): 614 ((x * y) * T(L(z,y,x),u)) \ (x * (y * z)) = K(u,L(z,y,x)). [para(67(a,1),609(a,1,2))]. given #1213 (H,wt=23): 629 ((x \ y) * (T(y,z) \ x)) \ K(z,y) = K(T(y,z) \ x,x \ y). [para(620(a,1),26(a,2,2)),flip(a)]. given #1214 (H,wt=19): 1295 K(T(x,y) \ z,z \ x) = K(y,T(x,z)) \ K(y,x). [para(731(a,1),629(a,1,1)),flip(a)]. given #1215 (H,wt=19): 1296 K(T(x,y) \ z,z \ x) = K(T(x,z),y) * K(y,x). [para(1295(a,2),406(a,1))]. given #1216 (H,wt=19): 1297 K(T(x,y) \ z,z \ x) = K(x,T(y,z)) * K(y,x). [para(721(a,1),1296(a,2,1))]. given #1217 (H,wt=15): 1298 K(T(x,y) \ z,z \ x) = K(z,K(y,x)). [para(1297(a,2),720(a,1))]. given #1218 (H,wt=13): 1299 K(K(x,y),z \ y) = K(z,K(x,y)). [para(1298(a,1),630(a,1)),flip(a)]. given #1219 (H,wt=13): 1300 K(x,K(y,z \ y)) = K(z,K(x,y)). [para(1299(a,1),747(a,1)),flip(a)]. given #1220 (H,wt=11): 1301 K(x,K(y,z)) = K(y,K(x,z)). [para(578(a,1),1300(a,1,2))]. given #1221 (H,wt=11): 1302 K(x,K(y,z)) = K(z,K(x,y)). [para(1301(a,1),746(a,1))]. given #1222 (H,wt=11): 1303 K(x,K(y,z)) = K(x,K(z,y)). [para(1302(a,1),746(a,1))]. given #1223 (H,wt=17): 1304 K(x,y) * K(x,K(y,z)) = K(x,T(y,z \ 1)). [para(1303(a,1),749(a,1,2))]. given #1224 (H,wt=13): 1305 K(x,T(y,z \ 1)) = K(x,T(y,z)). [para(1304(a,1),748(a,1))]. given #1225 (H,wt=13): 1306 K(x,T(y,z \ y)) = K(x,T(y,z)). [para(324(a,1),1305(a,1,2))]. given #1226 (H,wt=13): 1308 K(x,y \ K(y,z)) = K(y,T(x,z)). [para(1305(a,1),724(a,1)),flip(a)]. given #1227 (H,wt=17): 1307 K(x,T(y,z \ (u \ 1))) = K(x,T(y,u * z)). [para(341(a,1),1305(a,1,2,2))]. given #1228 (H,wt=17): 1310 K(a(x,y,z),T(u,x)) = K(u,a(x,y,z) \ 1). [para(1125(a,1),1308(a,1,2,2)),flip(a)]. given #1229 (H,wt=17): 1312 K(a(x,y,z),T(u,x)) = K(u,a(x,z,y) * 1). [para(1256(a,1),1310(a,2,2))]. given #1230 (H,wt=15): 1313 K(a(x,y,z),T(u,x)) = K(u,a(x,z,y)). [para(12(a,1),1312(a,2,2))]. given #1231 (H,wt=19): 1311 K(x,T(y,z \ (u / w))) = K(x,T(y,(w / u) * z)). [para(327(a,1),1307(a,1,2,2,2))]. given #1232 (H,wt=23): 690 K(x,y \ (x \ 1)) * ((x \ (y \ 1)) * z) = (y \ (x \ 1)) * z. [para(398(a,1),683(a,1,2,1))]. given #1233 (H,wt=21): 1314 K(x * y,x) * ((x \ (y \ 1)) * z) = (y \ (x \ 1)) * z. [para(563(a,1),690(a,1,1))]. given #1234 (H,wt=19): 1315 K(x,y) * ((y \ (x \ 1)) * z) = (x \ (y \ 1)) * z. [para(542(a,1),1314(a,1,1))]. given #1235 (H,wt=17): 1316 K(x,y) * ((x * y) \ z) = (x \ (y \ 1)) * z. [para(378(a,1),1315(a,1,2))]. given #1236 (H,wt=15): 1317 K(x,y) * ((x * y) \ z) = (y * x) \ z. [para(1316(a,2),378(a,1))]. given #1237 (H,wt=17): 1318 L(x,(y * x) \ z,u) = L(x,(x * y) \ z,u). [para(1317(a,1),1077(a,1,2)),flip(a)]. given #1238 (H,wt=15): 1319 L(x,(x * y) \ z,u) = L(x,y \ z,u). [para(1318(a,1),1089(a,1))]. given #1239 (H,wt=23): 708 ((x \ (y \ 1)) / z) * (z / (y \ (x \ 1))) = K(y,x \ (y \ 1)). [para(398(a,1),705(a,1,2,2))]. given #1240 (H,wt=23): 873 x \ (y * (z * (((x \ y) * z) \ u))) = L(L(u,z,x \ y),x,y). [para(870(a,2),828(a,1,1)),flip(a)]. given #1241 (H,wt=23): 1084 L(x \ (y * ((z * (x \ y)) \ u)),z,x \ y) = L(z \ u,x,y). [para(878(a,1),854(a,1,1)),flip(a)]. given #1242 (H,wt=23): 1187 x \ (y * (((y \ x) / z) * u)) = ((z \ y) / x) * (x * (y \ u)). [para(1186(a,1),812(a,1,2))]. given #1243 (H,wt=23): 1294 ((x * y) * L(T(z,u),y,x)) \ (x * (y * z)) = K(u,L(z,y,x)). [para(40(a,2),614(a,1,1,2))]. given #1244 (H,wt=20): 1324 (x * (y * T(z,u))) \ (x * (y * z)) = K(u,L(z,y,x)). [para(67(a,1),1294(a,1,1))]. given #1245 (H,wt=23): 1320 ((x * y) \ (z \ 1)) * (z / (x \ (y \ 1))) = K(x,y \ (x \ 1)). [para(399(a,1),708(a,1,1))]. given #1246 (H,wt=23): 1321 x \ (y * (z * ((z \ (y \ x)) * u))) = L(L(u,z,x \ y),x,y). [para(386(a,1),873(a,1,2,2,2))]. given #1247 (H,wt=23): 1322 L(x \ (y * (((y \ x) / z) * u)),z,x \ y) = L(z \ u,x,y). [para(392(a,1),1084(a,1,1,2,2))]. given #1248 (H,wt=23): 1325 ((x * y) \ (z \ 1)) * (z * ((y \ 1) \ x)) = K(x,y \ (x \ 1)). [para(358(a,1),1320(a,1,2))]. given #1249 (H,wt=21): 1327 ((x * y) \ (z \ 1)) * (z * (y * x)) = K(x,y \ (x \ 1)). [para(317(a,1),1325(a,1,2,2))]. given #1250 (H,wt=19): 1328 (x * (y * z)) \ (x * (z * y)) = K(y,z \ (y \ 1)). [para(1327(a,1),378(a,1)),flip(a)]. given #1251 (H,wt=16): 1329 L(K(x,y),y * x,z) = K(y,x \ (y \ 1)). [para(1328(a,1),107(a,1)),flip(a)]. given #1252 (H,wt=14): 1330 L(K(x,y),y * x,z) = K(y * x,y). [para(1329(a,2),563(a,1))]. given #1253 (H,wt=12): 1332 L(K(x,y),y * x,z) = K(x,y). [para(1330(a,2),542(a,1))]. given #1254 (H,wt=16): 1333 L(K(x,y),(x \ y) * y,z) = K(y,x \ y). [para(578(a,1),1332(a,1,1))]. given #1255 (H,wt=14): 1334 L(K(x,y),(x \ y) * y,z) = K(x,y). [para(1333(a,2),578(a,1))]. given #1256 (H,wt=23): 1326 L(((x \ y) / z) * (z * (y \ u)),x,z \ y) = L(x \ u,z,y). [para(1187(a,1),1322(a,1,1))]. given #1257 (H,wt=24): 180 T(x,(y * z) \ x) / (z * (x / (y * z))) = R(y,z,x / (y * z)). [para(177(a,2),30(a,2,1)),flip(a)]. given #1258 (H,wt=24): 612 L(K(x,y),z * T(y,x),u) = (u * (z * T(y,x))) \ (u * (z * y)). [para(607(a,1),28(a,2,2,2))]. given #1259 (H,wt=17): 1337 L(K(x,y),z * T(y,x),u) = K(x,L(y,z,u)). [para(612(a,2),1324(a,1))]. given #1260 (H,wt=15): 1338 L(K(x,y),z * y,u) = K(x,L(y,z,u)). [para(1337(a,1),986(a,1)),flip(a)]. given #1261 (H,wt=12): 1340 K(x,L(y,x \ y,z)) = K(x,y). [para(1338(a,1),1334(a,1))]. given #1262 (H,wt=10): 1341 K(x,L(y,z,x)) = K(x,y). [para(981(a,1),1340(a,1,2))]. given #1263 (H,wt=12): 1342 T(x,L(y,z,x)) = x * K(x,y). [para(1341(a,1),530(a,2,2))]. given #1264 (H,wt=10): 1343 T(x,L(y,z,x)) = T(x,y). [para(1342(a,2),530(a,2)),flip(a)]. given #1265 (H,wt=15): 1339 K(x,L(y,z / y,u)) = L(K(x,y),z,u). [para(16(a,1),1338(a,1,2)),flip(a)]. given #1266 (H,wt=13): 1345 L(K(x,y),z,u) = K(x,L(y,z,u)). [para(968(a,1),1339(a,1,2)),flip(a)]. given #1267 (H,wt=15): 1346 K(x,L(y \ 1,z,u)) = L(K(y,x),z,u). [para(559(a,1),1345(a,1,1)),flip(a)]. given #1268 (H,wt=13): 1349 L(K(x,y),z,u) = K(L(x,z,u),y). [para(1346(a,1),994(a,1))]. given #1269 (H,wt=13): 1350 K(L(x,y,z),u) = K(x,L(u,y,z)). [para(1349(a,1),1345(a,1))]. given #1270 (H,wt=17): 1347 K(x,L(y,z,u)) \ K(x,y) = a(u,z,K(x,y)). [para(1345(a,1),1118(a,2,1)),flip(a)]. given #1271 (H,wt=17): 1348 K(x,y) * K(y,L(x,z,u)) = a(z,u,K(y,x)). [para(1345(a,1),1246(a,1,2))]. given #1272 (H,wt=18): 1344 T((x * y) * z,L(x,y,z)) = T((x * y) * z,x). [para(990(a,1),1343(a,1,2))]. given #1273 (H,wt=15): 1353 T((x * y) * z,x) = z * (T(y,z) * x). [para(1344(a,1),1072(a,1))]. given #1274 (H,wt=17): 1354 T((x * (y / z)) * z,x) = z * ((z \ y) * x). [para(80(a,1),1353(a,2,2,1))]. given #1275 (H,wt=17): 1355 T((x / y) * (y * z),x) = y * ((y \ z) * x). [para(1055(a,1),1354(a,1,1))]. given #1276 (H,wt=19): 1351 K(x,y) * K(y,L(x,z,u)) = K(a(y,z,u),T(x,y)). [para(1350(a,1),1291(a,1,2))]. given #1277 (H,wt=15): 1356 K(a(x,y,z),T(u,x)) = a(y,z,K(x,u)). [para(1351(a,1),1348(a,1))]. given #1278 (H,wt=13): 1357 a(x,y,K(z,u)) = K(u,a(z,y,x)). [para(1356(a,1),1313(a,1))]. given #1279 (H,wt=13): 1358 a(x,y,K(z,u)) = K(u,a(x,z,y)). [para(1128(a,1),1357(a,2,2))]. given #1280 (H,wt=13): 1359 a(x,y,K(z,u)) = K(a(z,x,y),u). [para(1357(a,2),1248(a,2)),flip(a)]. given #1281 (H,wt=13): 1361 a(x,y,K(z,u)) = a(z,x,K(y,u)). [para(1358(a,2),1357(a,2))]. given #1282 (H,wt=13): 1362 a(x,K(y,z),u) = a(x,y,K(u,z)). [para(1361(a,2),1128(a,2))]. given #1283 (H,wt=13): 1364 a(x,y,K(z,u)) = a(x,u,K(y,z)). [para(1362(a,1),1142(a,1)),flip(a)]. given #1284 (H,wt=15): 1360 a(x,y,K(z,u)) * u = T(u,a(x,z,y)). [para(1358(a,2),544(a,2,1)),flip(a)]. given #1285 (H,wt=15): 1363 a(x,y,K(z,u)) * y = L(y,z,K(x,u)). [para(1361(a,1),1243(a,2,1)),flip(a)]. given #1286 (H,wt=13): 1366 L(x,K(y,z),u) = L(x,y,K(u,z)). [para(1363(a,1),1249(a,2))]. given #1287 (H,wt=13): 1367 L(x,y,K(z,u)) = L(x,u,K(y,z)). [para(1366(a,1),847(a,1)),flip(a)]. given #1288 (H,wt=15): 1365 a(x,y,K(z,u)) * u = L(u,K(y,z),x). [para(1364(a,2),1249(a,2,1)),flip(a)]. given #1289 (H,wt=13): 1370 L(x,K(y,z),u) = T(x,a(u,z,y)). [para(1365(a,1),1360(a,1))]. given #1290 (H,wt=13): 1371 L(x,y,K(z,u)) = T(x,a(z,u,y)). [para(1370(a,1),1366(a,1)),flip(a)]. given #1291 (H,wt=15): 1368 L(x,y \ z,K(u,z)) = L(x,u,K(y,z)). [para(578(a,1),1367(a,1,3)),flip(a)]. given #1292 (H,wt=15): 1369 L(x,y \ z,K(z,u)) = L(x,u,K(z,y)). [para(579(a,1),1367(a,2,3))]. given #1293 (H,wt=18): 1373 L(x * a(y,z,u),z,K(y,u)) = a(y,z,u) * x. [para(1371(a,2),1281(a,1))]. given #1294 (H,wt=21): 1375 L(x,y \ z,K((x * u) / w,z)) = L(x,u / w,K(y,z)). [para(1368(a,2),1170(a,1))]. given #1295 (H,wt=21): 1376 L(x,y \ z,K(z,u / (x * w))) = L(x,w / u,K(y,z)). [para(561(a,1),1375(a,1,3))]. given #1296 (H,wt=22): 1372 T(L(x,y,K(z,u)),K(a(z,u,y),w)) = T(x,T(a(z,u,y),w)). [para(1371(a,2),740(a,1,1))]. given #1297 (H,wt=22): 1377 T(L(x,y,K(z,u)),K(a(y,z,u),w)) = T(x,T(a(z,u,y),w)). [para(1128(a,1),1372(a,1,2,1))]. given #1298 (H,wt=22): 1378 T(L(x,y,K(z,u)),a(z,u,K(y,w))) = T(x,T(a(z,u,y),w)). [para(1359(a,2),1377(a,1,2))]. given #1299 (H,wt=22): 1379 L(L(x,y,K(z,u)),K(y,w),K(z,u)) = T(x,T(a(z,u,y),w)). [para(1378(a,1),1371(a,2))]. given #1300 (H,wt=22): 1380 L(L(x,y,K(z,u)),y,K(K(z,u),w)) = T(x,T(a(z,u,y),w)). [para(1379(a,1),1366(a,1)),flip(a)]. given #1301 (H,wt=22): 1381 L(L(x,y,K(z,u)),y,K(z,K(u,w))) = T(x,T(a(z,u,y),w)). [para(747(a,1),1380(a,1,3))]. given #1302 (H,wt=22): 1382 L(L(x,y,K(z,u)),y,K(z,K(u,w))) = T(x,T(a(y,z,u),w)). [para(1128(a,1),1381(a,2,2,1))]. given #1303 (H,wt=22): 1383 L(L(x,y,K(z,u)),y,K(z,K(u,w))) = T(x,a(y,z,T(u,w))). [para(1215(a,2),1382(a,2,2))]. given #1304 (H,wt=22): 1384 L(L(x,y,K(z,u)),y,K(z,K(u,w))) = L(x,T(u,w),K(y,z)). [para(1383(a,2),1371(a,2)),flip(a)]. given #1305 (H,wt=22): 1385 L(L(x,y,K(z,u)),y,K(z,K(u,w))) = L(x,u,T(K(y,z),w)). [para(1384(a,2),1265(a,1))]. given #1306 (H,wt=22): 1386 L(L(x,y,K(z,u)),y,K(z,K(u,w))) = L(x,u,K(y,T(z,w))). [para(717(a,2),1385(a,2,3))]. given #1307 (H,wt=23): 1352 K(x,K(y,L(z,u,w))) \ K(x,K(y,z)) = a(w,u,K(x,K(y,z))). [para(1345(a,1),1347(a,1,1,2))]. given #1308 (H,wt=23): 1374 L(x,(y / z) \ T(u,y),K(w,T(u,y))) = L(x,w,K(u,y \ z)). [para(725(a,1),1368(a,2,3))]. given #1309 (H,wt=23): 1387 L(x,(y / z) * T(u,z),K(w,T(u,z))) = L(x,w,K(u,z \ y)). [para(343(a,1),1374(a,1,2))]. given #1310 (H,wt=24): 777 x * L(y \ 1,z,u) != y * (w * L(y \ 1,z,u)) | y * w = x. [para(460(a,1),20(a,1)),flip(a)]. given #1311 (H,wt=24): 1263 (x * (y / z)) * L(L(z,u,w),y / z,x) = x * (y * a(z,u,w)). [para(1240(a,1),67(a,2,2))]. given #1312 (H,wt=22): 1388 (x * (y / z)) * L(L(z,y,x),u,w) = x * (y * a(z,u,w)). [para(983(a,1),1263(a,1,2))]. given #1313 (H,wt=24): 1336 T(x,(y * z) \ x) * (((y * z) / x) / z) = R(y,z,x / (y * z)). [para(180(a,1),390(a,1)),flip(a)]. given #1314 (H,wt=24): 1389 x * (K(y * z,x) * (((y * z) / x) / z)) = R(y,z,x / (y * z)). [para(1336(a,1),678(a,1)),flip(a)]. given #1315 (H,wt=18): 1390 R(x,y,z / (x * y)) = z * ((z \ (x * y)) / y). [para(766(a,1),1389(a,1,2)),flip(a)]. given #1316 (H,wt=13): 1391 R(x,y,z / (x * y)) = R(x,y,z). [para(1390(a,2),497(a,2)),flip(a)]. given #1317 (H,wt=15): 1392 R(x,x \ y,z / y) = R(x,x \ y,z). [para(14(a,1),1391(a,1,3,2))]. given #1318 (H,wt=13): 1393 R(x,x \ y,z) = R(x,y,z / y). [para(1392(a,1),967(a,1))]. given #1319 (H,wt=11): 1394 R(x,y,z / y) = R(x,y,z). [para(1393(a,1),967(a,1))]. given #1320 (H,wt=13): 1395 R(x,y,y \ z) = R(x,y,T(z,y)). [para(123(a,1),1394(a,1,3))]. given #1321 (H,wt=11): 1397 R(x,y,T(z,y)) = R(x,y,z). [para(1395(a,1),997(a,1))]. given #1322 (H,wt=13): 1396 R(x,y,z \ 1) = R(x,y,z \ y). [para(318(a,1),1394(a,1,3))]. given #1323 (H,wt=13): 1398 R(x,y,y / z) = R(x,y,z \ y). [para(232(a,1),1397(a,1,3)),flip(a)]. given #1324 (H,wt=16): 1399 R(x,y,z) * (z * y) = (x * y) * T(z,y). [para(1397(a,1),210(a,1,1))]. given #1325 (H,wt=16): 1401 L(x,y,z) * (z * y) = (x * y) * T(z,y). [para(958(a,1),1399(a,1,1))]. given #1326 (H,wt=17): 1402 T(x * y,x * z) = ((z \ y) * z) * T(x,z). [para(1401(a,1),206(a,1)),flip(a)]. given #1327 (H,wt=15): 1403 T(x * y,x * z) = T(y,z) * T(x,z). [para(120(a,2),1402(a,2,1))]. given #1328 (H,wt=17): 1404 T(x,y \ z) * T(y,y \ z) = T(y * x,z). [para(14(a,1),1403(a,1,2)),flip(a)]. given #1329 (H,wt=15): 1406 T(x,y \ z) * T(y,z) = T(y * x,z). [para(222(a,1),1404(a,1,2))]. given #1330 (H,wt=17): 1407 T(x,y \ z) \ T(y,z) = T(y * (x \ 1),z). [para(1406(a,1),400(a,1)),flip(a)]. given #1331 (H,wt=15): 1408 T(x,y \ z) \ T(y,z) = T(y / x,z). [para(345(a,1),1407(a,2,1))]. given #1332 (H,wt=19): 1400 R((x / y) \ z,x,z) = (x / y) \ R(z,x,y \ x). [para(1398(a,1),975(a,2,2))]. given #1333 (H,wt=19): 1405 T(x * y,x * a(x,z,u)) = T(y,a(x,z,u)) * x. [para(1122(a,1),1403(a,2,2))]. given #1334 (H,wt=17): 1411 T(x * y,L(x,z,u)) = T(y,a(x,z,u)) * x. [para(1238(a,2),1405(a,1,2))]. given #1335 (H,wt=17): 1412 T(x * y,L(x,z,u)) = T(y,a(z,u,x)) * x. [para(1128(a,2),1411(a,2,1,2))]. given #1336 (H,wt=17): 1413 T(x * y,L(x,z,u)) = L(y,x,K(z,u)) * x. [para(1371(a,2),1412(a,2,1))]. given #1337 (H,wt=17): 1414 L(x * y,y,K(z,u)) = T(y * x,L(y,z,u)). [para(1413(a,2),893(a,2))]. given #1338 (H,wt=19): 1409 L(x,y,T(z,u \ y) \ u) = L(x,y,T(u / z,y)). [para(1408(a,1),1269(a,1,3)),flip(a)]. given #1339 (H,wt=17): 1416 L(x,y,T(z,u \ y) \ u) = L(x,y,u / z). [para(1409(a,2),807(a,1))]. given #1340 (H,wt=19): 1410 R((x / y) * z,y,z) = (y / x) \ R(z,y,x \ y). [para(343(a,1),1400(a,1,1))]. given #1341 (H,wt=19): 1417 R((x / y) * z,y,z) = (x / y) * R(z,y,x \ y). [para(1410(a,2),343(a,1))]. given #1342 (H,wt=16): 1418 (x / y) * R(z,y,x \ y) = x * (y \ z). [para(1417(a,1),974(a,1))]. given #1343 (H,wt=13): 1419 R(x,y,z \ y) = L(x,y \ 1,z). [hyper(482,a,1418,a),flip(a)]. given #1344 (H,wt=13): 1420 R(x,y,z \ 1) = L(x,y \ 1,z). [para(1419(a,1),1396(a,2))]. given #1345 (H,wt=16): 1421 L(x,y \ 1,z) * (y / z) = (x * y) / z. [para(1420(a,1),491(a,1,1))]. given #1346 (H,wt=14): 1422 L(x,y,z) * (z / y) = (x * z) / y. [para(843(a,1),1421(a,1,1))]. given #1347 (H,wt=16): 1425 L(x,y,z) \ (z / y) = ((x \ 1) * z) / y. [para(1422(a,1),992(a,1)),flip(a)]. given #1348 (H,wt=14): 1427 L(x,y,z) \ (z / y) = (x \ z) / y. [para(314(a,1),1425(a,2,1))]. given #1349 (H,wt=18): 1424 (L(x \ y,z,y) * z) / x = (x \ y) * (z / x). [para(933(a,1),1422(a,1,1)),flip(a)]. given #1350 (H,wt=18): 1426 L(a(x,y,z),u,z) * (z / u) = L(z,x,y) / u. [para(1250(a,2),1422(a,2,1))]. given #1351 (H,wt=15): 1430 a(x,y,z) * (z / u) = L(z,x,y) / u. [para(1167(a,1),1426(a,1,1))]. given #1352 (H,wt=17): 1432 T(L(x,y,z) / u,u) = (u \ x) * a(y,z,x). [para(1430(a,1),1136(a,1,1))]. given #1353 (H,wt=15): 1433 (x \ y) * a(z,u,y) = x \ L(y,z,u). [para(1432(a,1),80(a,1))]. given #1354 (H,wt=18): 1429 L((x \ y) * z,z,y) / x = (x \ y) * (z / x). [para(893(a,2),1424(a,1,1))]. given #1355 (H,wt=15): 1435 (x \ (y * z)) / x = (x \ y) * (z / x). [para(1061(a,1),1429(a,1,1))]. given #1356 (H,wt=15): 1436 x \ ((y * z) / x) = (x \ y) * (z / x). [para(1435(a,1),130(a,1)),flip(a)]. given #1357 (H,wt=19): 1423 ((x \ (y * z)) * x) / y = ((x \ y) * z) * (x / y). [para(853(a,1),1422(a,1,1)),flip(a)]. given #1358 (H,wt=17): 1438 ((x \ y) * z) * (x / y) = T(y * z,x) / y. [para(120(a,2),1423(a,1,1)),flip(a)]. given #1359 (H,wt=19): 1437 (x \ ((y \ x) * z)) / y = x \ ((y \ x) * (z / y)). [para(1436(a,1),1070(a,2,2))]. given #1360 (H,wt=19): 1439 x * (T(x * (y / x),z) / x) = T(y,x \ (z / x)). [para(1438(a,1),1220(a,1,2))]. given #1361 (H,wt=19): 1440 T(x * ((x * (y / x)) / x),z) = T(y,x \ (z / x)). [para(1439(a,1),294(a,2))]. given #1362 (H,wt=19): 1441 T(x * (x * ((y / x) / x)),z) = T(y,x \ (z / x)). [para(137(a,1),1440(a,1,1,2))]. given #1363 (H,wt=19): 1442 T(x * (x * (y / (x * x))),z) = T(y,x \ (z / x)). [para(278(a,1),1441(a,1,1,2,2))]. given #1364 (H,wt=17): 1443 T(T(x,y \ (y \ x)),z) = T(x,y \ (z / y)). [para(1442(a,1),776(a,2))]. given #1365 (H,wt=23): 1415 T((x \ 1) * y,L(x \ 1,z,u)) = L(y / x,x \ 1,K(z,u)). [para(345(a,1),1414(a,1,1)),flip(a)]. given #1366 (H,wt=21): 1444 L(x / y,y \ 1,K(z,u)) = T(y \ x,L(y \ 1,z,u)). [para(314(a,1),1415(a,1,1)),flip(a)]. given #1367 (H,wt=19): 1445 T(x \ y,L(x \ 1,z,u)) = L(y / x,K(z,u),x). [para(1444(a,1),843(a,1))]. given #1368 (H,wt=19): 1446 T(x \ y,L(x \ 1,z,u)) = L(y / x,z,K(x,u)). [para(1445(a,2),1366(a,1))]. given #1369 (H,wt=25): 288 T(T(T(x,y \ x),z),T(x,z) / y) = y * (T(T(x,y \ x),z) / y). [para(192(a,1),177(a,1,2))]. given #1370 (H,wt=25): 433 (x \ y) * ((y \ x) \ (z \ (y \ x))) = T((y \ x) \ (z \ 1),y \ x). [para(331(a,2),353(a,1)),flip(a)]. given #1371 (H,wt=25): 1309 K(x,T(T(T(y,z \ y),u),z \ T(T(y,z \ y),u))) = K(x,T(y,u)). [para(185(a,1),1306(a,2,2))]. given #1372 (H,wt=21): 1449 K(x,T(T(T(y,z \ y),u),T(y,u) / z)) = K(x,T(y,u)). [para(192(a,1),1309(a,1,2,2))]. given #1373 (H,wt=25): 1434 T(K(x,a(y,z,u)) * u,a(y,z,u)) = T(a(y,z,u),x) \ L(u,y,z). [para(1433(a,1),694(a,2))]. given #1374 (H,wt=25): 1447 T(T(T(x,y \ x),z),T(x,z) / y) = T(y * (T(x,y \ x) / y),z). [para(288(a,2),294(a,2)),flip(a)]. given #1375 (H,wt=25): 1448 (x \ y) * ((y \ x) \ (z \ (y \ x))) = T((x \ y) * (z \ 1),y \ x). [para(353(a,1),433(a,2,1))]. given #1376 (H,wt=23): 1452 (x \ y) * ((y \ x) \ (z \ (y \ x))) = T((x \ y) / z,y \ x). [para(345(a,1),1448(a,2,1))]. given #1377 (H,wt=19): 1453 (x \ y) / T(z,y \ x) = T((x \ y) / z,y \ x). [para(1452(a,1),377(a,1)),flip(a)]. given #1378 (H,wt=25): 1450 T(K(x,a(y,z,u)) * u,a(y,z,u)) = a(y,z,T(u,x)) \ L(u,y,z). [para(1215(a,2),1434(a,2,1))]. given #1379 (H,wt=25): 1451 T(T(T(x,y \ x),z),T(x,z) / y) = T(y * (x * (y \ K(y,x))),z). [para(729(a,1),1447(a,2,1,2))]. given #1380 (H,wt=23): 1455 T(T(T(x,y \ x),z),T(x,z) / y) = T(T(x,y \ (y \ x)),z). [para(770(a,1),1451(a,2,1))]. given #1381 (H,wt=17): 1456 K(x,T(T(y,z \ (z \ y)),u)) = K(x,T(y,u)). [para(1455(a,1),1449(a,1,2))]. given #1382 (H,wt=15): 1457 K(x,T(y,z \ (u / z))) = K(x,T(y,u)). [para(1443(a,1),1456(a,1,2))]. given #1383 (H,wt=15): 1458 K(x,T(y,(z / u) * z)) = K(x,T(y,u)). [para(1457(a,1),1311(a,1)),flip(a)]. given #1384 (H,wt=15): 1459 K(x,T(y,z \ u)) = K(x,T(y,z * u)). [para(53(a,1),1458(a,1,2,2,1)),flip(a)]. given #1385 (H,wt=17): 1461 K(x,T(y,z * (u \ 1))) = K(x,T(y,u * z)). [para(1459(a,1),1307(a,1))]. given #1386 (H,wt=15): 1462 K(x,T(y,z / u)) = K(x,T(y,u * z)). [para(345(a,1),1461(a,1,2,2))]. given #1387 (H,wt=15): 1463 K(x,T(y,z * (u * z))) = K(x,T(y,u)). [para(15(a,1),1462(a,1,2,2)),flip(a)]. given #1388 (H,wt=19): 1466 K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (w * z))). [para(1066(a,1),1463(a,1,2,2)),flip(a)]. given #1389 (H,wt=22): 1464 K(x,T(y,(z * u) / ((w / u) / z))) = K(x,T(y,L(w,u,z))). [para(984(a,2),1462(a,2,2,2))]. given #1390 (H,wt=22): 1467 K(x,T(y,(z * u) * (z / (w / u)))) = K(x,T(y,L(w,u,z))). [para(357(a,1),1464(a,1,2,2))]. given #1391 (H,wt=22): 1468 K(x,T(y,(z * u) * (z * (u / w)))) = K(x,T(y,L(w,u,z))). [para(357(a,1),1467(a,1,2,2,2))]. given #1392 (H,wt=23): 1460 K(x,T(y,(z / u) \ (u * (w * u)))) = K(x,T(y,(z * w) * u)). [para(1048(a,1),1459(a,2,2,2))]. given #1393 (H,wt=23): 1465 K(x,T(y,(z \ u) * (z * ((z \ w) * u)))) = K(x,T(y,w * z)). [para(261(a,1),1463(a,1,2,2,2))]. given #1394 (H,wt=19): 1470 K(x,T(y,((z \ u) * w) * u)) = K(x,T(y,w * z)). [para(1071(a,1),1465(a,1,2,2))]. given #1395 (H,wt=23): 1469 K(x,T(y,(((z / u) \ u) * w) * u)) = K(x,T(y,(z * w) * u)). [para(1062(a,1),1460(a,1,2,2))]. given #1396 (H,wt=23): 1471 K(x,T(y,((z * (u \ z)) * w) * z)) = K(x,T(y,(u * w) * z)). [para(380(a,1),1469(a,1,2,2,1,1))]. given #1397 (H,wt=23): 1472 K(x,T(y,(z * (u \ (z * w))) * z)) = K(x,T(y,(u * w) * z)). [para(772(a,1),1471(a,1,2,2,1))]. given #1398 (H,wt=23): 1473 K(x,T(y,z * ((u \ (z * w)) * z))) = K(x,T(y,(u * w) * z)). [para(113(a,1),1472(a,1,2,2))]. given #1399 (H,wt=19): 1474 K(x,T(y,z \ (u * w))) = K(x,T(y,(z * w) * u)). [para(1473(a,1),1463(a,1)),flip(a)]. given #1400 (H,wt=19): 1475 K(x,T(y,(z * u) * w)) = K(x,T(y,z * (w * u))). [para(1474(a,1),1459(a,1))]. given #1401 (H,wt=19): 1478 K(x,T(y,(z \ u) * (u * w))) = K(x,T(y,w * z)). [para(1475(a,1),1470(a,1))]. given #1402 (H,wt=19): 1479 K(x,T(y,z * ((z * u) * w))) = K(x,T(y,u * w)). [para(1478(a,1),1466(a,1)),flip(a)]. given #1403 (H,wt=22): 1477 K(x,T(y,z * ((z * (u / w)) * u))) = K(x,T(y,L(w,u,z))). [para(1475(a,1),1468(a,1))]. given #1404 (H,wt=18): 1480 K(x,T(y,L(z,u,w))) = K(x,T(y,(u / z) * u)). [para(1477(a,1),1479(a,1))]. given #1405 (H,wt=14): 1481 K(x,T(y,L(z,u,w))) = K(x,T(y,z)). [para(1480(a,2),1458(a,1))]. given #1406 (H,wt=16): 1483 T(x,T(y,L(z,u,w))) = x * K(x,T(y,z)). [para(1481(a,1),530(a,2,2))]. given #1407 (H,wt=14): 1485 T(x,T(y,L(z,u,w))) = T(x,T(y,z)). [para(1483(a,2),530(a,2)),flip(a)]. given #1408 (H,wt=18): 1486 T(x,K(y,L(z,u,w))) = T(x,T(y,z)) * K(y,x). [para(1485(a,1),741(a,1,1)),flip(a)]. given #1409 (H,wt=14): 1487 T(x,K(y,L(z,u,w))) = T(x,K(y,z)). [para(1486(a,2),741(a,1))]. given #1410 (H,wt=16): 1488 K(K(x,L(y,z,u)),w) = T(w,K(x,y)) \ w. [para(1487(a,1),531(a,2,1))]. given #1411 (H,wt=14): 1489 K(K(x,L(y,z,u)),w) = K(K(x,y),w). [para(1488(a,2),531(a,2)),flip(a)]. given #1412 (H,wt=14): 1490 K(K(x,L(y,z,u)),w) = K(x,K(y,w)). [para(1489(a,2),747(a,1))]. given #1413 (H,wt=14): 1491 K(K(x,L(y,z,u)),w) = K(w,K(x,y)). [para(1490(a,2),1302(a,1))]. given #1414 (H,wt=14): 1492 K(x,K(L(y,z,u),w)) = K(w,K(x,y)). [para(1491(a,1),747(a,1)),flip(a)]. given #1415 (H,wt=14): 1493 K(x,K(y,L(z,u,w))) = K(z,K(x,y)). [para(1350(a,1),1492(a,1,2))]. given #1416 (H,wt=20): 1494 a(x,y,K(z,K(u,w))) = K(w,K(z,u)) \ K(z,K(u,w)). [para(1493(a,1),1352(a,1,1)),flip(a)]. given #1417 (H,wt=20): 1495 a(x,y,K(z,K(u,w))) = K(z,K(u,w)) \ K(z,K(u,w)). [para(1302(a,2),1494(a,2,1))]. given #1418 (H,wt=10): 1497 a(x,y,K(z,K(u,w))) = 1. [para(1495(a,2),50(a,1))]. given #1419 (H,wt=10): 1499 a(K(x,K(y,z)),u,w) = 1. [para(1497(a,1),1128(a,1)),flip(a)]. given #1420 (H,wt=10): 1500 L(x,y,K(z,K(u,w))) = x. [hyper(33,a,1499,a)]. given #1421 (H,wt=15): 1501 L(x,y,K(z,T(u,w))) = L(x,z,K(u,y)). [para(1500(a,1),1386(a,1)),flip(a)]. given #1422 (H,wt=21): 1502 L(x,y,K(z,(u / w) * T(z,w))) = L(x,y,K(z,w \ u)). [para(1501(a,1),1387(a,1))]. given #1423 (H,wt=17): 1503 L(x,y,K(z,u / w)) = L(x,y,K(z,w \ u)). [para(593(a,1),1502(a,1,3))]. given #1424 (H,wt=21): 1506 L(x,y \ z,K(z,(x * u) \ w)) = L(x,u / w,K(y,z)). [para(1503(a,1),1376(a,1))]. given #1425 (H,wt=19): 1507 L(x,(x * y) \ z,K(u,w)) = L(x,y / z,K(w,u)). [para(1506(a,1),1369(a,1)),flip(a)]. given #1426 (H,wt=17): 1508 L(x,y / z,K(u,w)) = L(x,y \ z,K(w,u)). [para(1507(a,1),1319(a,1))]. given #1427 (H,wt=25): 1454 T(K(x,a(y,z,u)) * u,a(y,z,u)) = a(y,T(u,x),z) * L(u,y,z). [para(1450(a,2),1256(a,1))]. given #1428 (H,wt=25): 1509 T(K(x,a(y,z,u)) * u,a(y,z,u)) = a(y,u,T(z,x)) * L(u,y,z). [para(1216(a,1),1454(a,2,1))]. given #1429 (H,wt=23): 1510 T(K(x,a(y,z,u)) * u,a(y,z,u)) = L(L(u,y,z),T(z,x),y). [para(1509(a,2),1254(a,1))]. given #1430 (H,wt=23): 1511 T(K(x,a(y,z,u)) * u,a(y,z,u)) = L(L(u,y,z),z,T(y,x)). [para(1510(a,2),1265(a,1))]. given #1431 (H,wt=23): 1512 T(a(x,y,K(z,u)) * x,a(z,y,x)) = L(L(x,z,y),y,T(z,u)). [para(1357(a,2),1511(a,1,1,1))]. given #1432 (H,wt=21): 1513 T(L(x,y,K(z,u)),a(z,y,x)) = L(L(x,z,y),y,T(z,u)). [para(1243(a,2),1512(a,1,1))]. given #1433 (H,wt=21): 1514 L(L(x,y,K(z,u)),x,K(z,y)) = L(L(x,z,y),y,T(z,u)). [para(1513(a,1),1371(a,2))]. given #1434 (H,wt=16): 1515 L(L(x,y,z),z,T(y,u)) = L(x,z,K(y,u)). [para(1514(a,1),276(a,1))]. given #1435 (H,wt=16): 1516 L(L(x,y,T(z,u)),z,y) = L(x,y,K(z,u)). [para(1515(a,1),45(a,1)),flip(a)]. given #1436 (H,wt=20): 1518 L(L(x,y,z),y / x,K(z,u)) = L(x,y / x,T(z,u)). [para(985(a,1),1515(a,1,1)),flip(a)]. given #1437 (H,wt=18): 1519 L(L(x,y,z),y / x,K(z,u)) = L(x,y,T(z,u)). [para(1518(a,2),968(a,1))]. given #1438 (H,wt=18): 1520 L(L(x,y,z),y \ x,K(u,z)) = L(x,y,T(z,u)). [para(1519(a,1),1508(a,1)),flip(a)]. given #1439 (H,wt=16): 1521 L(L(x,K(y,z),u),u,z) = L(x,u,T(z,y)). [para(1520(a,1),988(a,1)),flip(a)]. given #1440 (H,wt=16): 1522 L(L(x,y,K(z,u)),z,u) = L(x,z,T(u,y)). [para(1366(a,1),1521(a,1,1))]. given #1441 (H,wt=26): 1010 (x * y) * (((x * y) \ L(z,x,y)) * u) = ((z * x) * y) * ((x * y) \ u). [para(959(a,1),261(a,1,1)),flip(a)]. given #1442 (H,wt=23): 1524 ((x * y) * z) * ((y * z) \ u) = (y * z) * ((z \ (y \ x)) * u). [para(926(a,1),1010(a,1,2,1)),flip(a)]. given #1443 (H,wt=26): 1428 L(((x \ y) / z) * u,L(x,z,y),y / z) = L(x,z,y) \ ((y / z) * u). [para(1427(a,1),828(a,1,1,1))]. given #1444 (H,wt=23): 1525 L(((x \ y) / z) * u,x,y / z) = L(x,z,y) \ ((y / z) * u). [para(1428(a,1),1179(a,1)),flip(a)]. given #1445 (H,wt=26): 1523 L(L(x,y \ z,K(u,T(z,w))),u,T(z,w)) = L(x,u,T(T(z,w),y \ 1)). [para(395(a,2),1522(a,2,3))]. given #1446 (H,wt=24): 1526 L(L(x,y,K(z,u \ z)),y,T(z,w)) = L(x,y,T(T(z,w),u \ 1)). [para(1501(a,1),1523(a,1,1))]. given #1447 (H,wt=22): 1527 L(L(x,y,K(z,u)),y,T(u,w)) = L(x,y,T(T(u,w),z \ 1)). [para(578(a,1),1526(a,1,1,3))]. given #1448 (H,wt=28): 1095 (x \ 1) * (y \ ((x \ 1) \ (T(y,x) * z))) = L(z,(x \ 1) * (x \ 1),T(y,x)). [para(338(a,1),1094(a,1,2,1))]. given #1449 (H,wt=26): 1529 (x \ 1) * (y \ (x * (T(y,x) * z))) = L(z,(x \ 1) * (x \ 1),T(y,x)). [para(317(a,1),1095(a,1,2,2))]. given #1450 (H,wt=24): 1530 L(x,(y \ 1) * (y \ 1),T(z,y)) = y \ (z \ (y * (T(z,y) * x))). [para(1529(a,1),314(a,1))]. given #1451 (H,wt=22): 1531 x \ (y \ (x * (T(y,x) * z))) = L(z,x \ (x \ 1),T(y,x)). [para(314(a,1),1530(a,1,2)),flip(a)]. given #1452 (H,wt=20): 1532 x \ (y \ (x * (T(y,x) * z))) = L(z,T(y,x),x * x). [para(1531(a,2),846(a,1))]. given #1453 (H,wt=20): 1533 x \ (y \ (x * (T(y,x) * z))) = L(z,y,T(x * x,x)). [para(1532(a,2),1265(a,1))]. given #1454 (H,wt=18): 1534 x \ (y \ (x * (T(y,x) * z))) = L(z,y,x * x). [para(116(a,1),1533(a,2,3))]. given #1455 (H,wt=30): 1076 ((x * y) \ z) * ((x * y) * ((y \ (x \ u)) * z)) = (((x * y) \ z) * L(u,x,y)) * z. [para(926(a,1),1071(a,1,2,2,1))]. given #1456 (H,wt=30): 1280 (x * y) \ (((z / y) / x) \ L(L(z,y,x),u,w)) = a(u,w,((z / y) / x) * (x * y)). [para(984(a,2),1279(a,1,2,2,1))]. given #1457 (H,wt=30): 1535 (x * y) \ ((x / (z / y)) * L(L(z,y,x),u,w)) = a(u,w,((z / y) / x) * (x * y)). [para(343(a,1),1280(a,1,2))]. given #1458 (H,wt=30): 1536 (x * y) \ ((x * (y / z)) * L(L(z,y,x),u,w)) = a(u,w,((z / y) / x) * (x * y)). [para(357(a,1),1535(a,1,2,1))]. given #1459 (H,wt=25): 1537 a(x,y,((z / u) / w) * (w * u)) = (w * u) \ (w * (u * a(z,x,y))). [para(1388(a,1),1536(a,1,2)),flip(a)]. given #1460 (H,wt=20): 1538 a(x,y,((z / u) / w) * (w * u)) = L(a(z,x,y),u,w). [para(1537(a,2),28(a,2)),flip(a)]. given #1461 (H,wt=15): 1539 a(x,y,L(z,u,w)) = L(a(z,x,y),u,w). [para(984(a,2),1538(a,1,3))]. given #1462 (H,wt=15): 1540 a(x,y,L(z,u,w)) = L(a(y,z,x),u,w). [para(1128(a,1),1539(a,2,1))]. given #1463 (H,wt=15): 1541 a(x,y,L(z,u,w)) = L(a(x,y,z),u,w). [para(1128(a,2),1539(a,2,1))]. given #1464 (H,wt=15): 1542 a(x,y,L(z,u,w)) = a(z,x,L(y,u,w)). [para(1540(a,2),1539(a,2)),flip(a)]. given #1465 (H,wt=31): 813 ((x \ y) / T(z,y \ x)) * (T(z,y \ x) * u) = T(z,y \ x) \ (((x \ y) * z) * u). [para(396(a,1),812(a,1,2,1)),flip(a)]. given #1466 (H,wt=31): 1543 T((x \ y) / z,y \ x) * (T(z,y \ x) * u) = T(z,y \ x) \ (((x \ y) * z) * u). [para(1453(a,1),813(a,1,1))]. given #1467 (H,wt=37): 1323 ((x \ y) * z) \ (y * (((y \ ((x \ y) * z)) / x) * u)) = (z \ K(z,x \ y)) * (((x \ y) * z) * (y \ u)). [para(583(a,2),1187(a,2,1))]. given #1468 (H,wt=37): 1544 ((x \ y) * z) \ (y * ((y \ ((x \ y) * (z / x))) * u)) = (z \ K(z,x \ y)) * (((x \ y) * z) * (y \ u)). [para(1437(a,1),1323(a,1,2,2,1))]. given #1469 (H,wt=37): 1545 (x \ K(x,y \ z)) * (((y \ z) * x) * (z \ u)) = (x \ (z \ y)) * (z * ((z \ ((y \ z) * (x / y))) * u)). [para(1544(a,1),386(a,1))]. given #1470 (H,wt=37): 1547 K(x,y \ z) * (x \ (((y \ z) * x) * (z \ u))) = (x \ (z \ y)) * (z * ((z \ ((y \ z) * (x / y))) * u)). [para(1545(a,1),779(a,1)),flip(a)]. given #1471 (H,wt=37): 1548 K(x,y \ z) * ((x \ (y \ z)) * (x * (z \ u))) = (x \ (z \ y)) * (z * ((z \ ((y \ z) * (x / y))) * u)). [para(260(a,1),1547(a,1,2))]. given #1472 (H,wt=31): 1549 (x \ (y \ z)) * (y * ((y \ ((z \ y) * (x / z))) * u)) = ((z \ y) / x) * (x * (y \ u)). [para(1548(a,1),726(a,1))]. given #1473 (H,wt=38): 1073 x * ((y * ((x * y) \ z)) * ((u * x) * (y * ((x * y) \ z)))) = L(z,y,x) * (u * (x * (y * ((x * y) \ z)))). [para(870(a,2),1014(a,1,1)),flip(a)]. given #1474 (H,wt=33): 1550 x * ((y * ((x * y) \ z)) * ((u * x) * (y * ((x * y) \ z)))) = L(z,y,x) * (u * L(z,y,x)). [para(870(a,2),1073(a,2,2,2))]. given #1475 (H,wt=33): 1551 x * (y * (((x * y) \ z) * (((u * x) * y) * ((x * y) \ z)))) = L(z,y,x) * (u * L(z,y,x)). [para(1014(a,1),1550(a,1,2))]. given #1476 (H,wt=33): 1552 x * (y * (((x * y) \ z) * ((x * y) * ((y \ (x \ u)) * z)))) = L(z,y,x) * (u * L(z,y,x)). [para(1524(a,1),1551(a,1,2,2,2))]. given #1477 (H,wt=28): 1553 x * (y * ((((x * y) \ z) * L(u,x,y)) * z)) = L(z,y,x) * (u * L(z,y,x)). [para(1076(a,1),1552(a,1,2,2))]. given #1478 (H,wt=23): 1554 L(x * (L(y,z,u) * x),u,z) = L(x,u,z) * (y * L(x,u,z)). [para(1553(a,1),1063(a,1)),flip(a)]. given #1479 (H,wt=26): 1555 L(x * (L(y,z,u) * x),u,z) != L(x,u,z) * w | y * L(x,u,z) = w. [para(1554(a,2),19(a,1))]. given #1480 (H,wt=39): 1546 T(x \ 1,(y \ z) \ 1) * (((y \ z) * x) * (z \ u)) = (x \ (z \ y)) * (z * ((z \ ((y \ z) * (x / y))) * u)). [para(568(a,2),1545(a,1,1))]. given #1481 (H,wt=31): 1556 T(x \ 1,(y \ z) \ 1) * (((y \ z) * x) * (z \ u)) = ((y \ z) / x) * (x * (z \ u)). [para(1546(a,2),1549(a,1))]. given #1482 (H,wt=29): 1557 T(x \ 1,y \ z) * (((z \ y) * x) * (y \ u)) = ((z \ y) / x) * (x * (y \ u)). [para(333(a,1),1556(a,1,1,2))]. given #1483 (H,wt=27): 1558 T(x,y \ z) \ (((z \ y) * x) * (y \ u)) = ((z \ y) / x) * (x * (y \ u)). [para(1557(a,1),400(a,1)),flip(a)]. given #1484 (H,wt=47): 1335 L(T((x \ y) / z,(x \ y) \ 1) * (T(z,(x \ y) \ 1) * (y \ u)),x,T(z,(x \ y) \ 1) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). [para(397(a,1),1326(a,1,1,1))]. given #1485 (H,wt=45): 1559 L(T((x \ y) / z,y \ x) * (T(z,(x \ y) \ 1) * (y \ u)),x,T(z,(x \ y) \ 1) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). [para(333(a,1),1335(a,1,1,1,2))]. given #1486 (H,wt=43): 1560 L(T((x \ y) / z,y \ x) * (T(z,y \ x) * (y \ u)),x,T(z,(x \ y) \ 1) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). [para(333(a,1),1559(a,1,1,2,1,2))]. given #1487 (H,wt=39): 1561 L(T(x,y \ z) \ (((z \ y) * x) * (y \ u)),z,T(x,(z \ y) \ 1) \ y) = L(z \ u,T(x,(z \ y) \ 1),y). [para(1543(a,1),1560(a,1,1))]. given #1488 (H,wt=35): 1562 L(((x \ y) / z) * (z * (y \ u)),x,T(z,(x \ y) \ 1) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). [para(1558(a,1),1561(a,1,1))]. given #1489 (H,wt=33): 1563 L(((x \ y) / z) * (z * (y \ u)),x,T(z,y \ x) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). [para(333(a,1),1562(a,1,3,1,2))]. given #1490 (H,wt=29): 1564 L(((x \ y) / z) * (z * (y \ u)),x,y / z) = L(x \ u,T(z,(x \ y) \ 1),y). [para(1563(a,1),1416(a,1)),flip(a)]. given #1491 (H,wt=27): 1565 L(x \ y,T(z,(x \ u) \ 1),u) = L(x,z,u) \ ((u / z) * (z * (u \ y))). [para(1564(a,1),1525(a,1))]. given #1492 (H,wt=22): 1566 L(x \ y,T(z,(x \ u) \ 1),u) = L(x,z,u) \ L(y,z,u). [para(849(a,2),1565(a,2,2))]. given #1493 (H,wt=20): 1567 L(x \ y,T(z,u \ x),u) = L(x,z,u) \ L(y,z,u). [para(333(a,1),1566(a,1,2,2))]. given #1494 (H,wt=20): 1568 L(x \ y,z,T(u,u \ x)) = L(x,z,u) \ L(y,z,u). [para(1567(a,1),1265(a,1)),flip(a)]. given #1495 (H,wt=18): 1569 L(x \ y,z,T(u,x)) = L(x,z,u) \ L(y,z,u). [para(222(a,1),1568(a,1,3))]. given #1496 (H,wt=25): 1570 T(L(x \ y,z,T(u,x)),L(x,z,u) \ 1) = L(y,z,u) / L(x,z,u). [para(1569(a,2),347(a,1,1))]. given #1497 (H,wt=25): 1571 T(L(x \ y,z,T(u,x)),L(x \ 1,z,u)) = L(y,z,u) / L(x,z,u). [para(971(a,2),1570(a,1,2))]. given #1498 (H,wt=25): 1572 L(T(x \ y,L(x \ 1,z,u)),z,T(u,x)) = L(y,z,u) / L(x,z,u). [para(1571(a,1),40(a,2))]. given #1499 (H,wt=23): 1573 L(L(x / y,z,K(y,u)),z,T(u,y)) = L(x,z,u) / L(y,z,u). [para(1446(a,1),1572(a,1,1))]. given #1500 (H,wt=22): 1574 L(x / y,z,T(T(u,y),y \ 1)) = L(x,z,u) / L(y,z,u). [para(1573(a,1),1527(a,1)),flip(a)]. given #1501 (H,wt=16): 1575 L(x,y,z) / L(u,y,z) = L(x / u,y,z). [para(338(a,1),1574(a,1,3)),flip(a)]. given #1502 (H,wt=16): 1576 L(x * y,z,u) / L(y,z,u) = L(x,z,u). [para(15(a,1),1575(a,2,1))]. given #1503 (H,wt=16): 1578 L(x,y,z) * L(u,y,z) = L(x * u,y,z). [para(1576(a,1),16(a,1,1))]. given #1504 (H,wt=16): 1579 L(x,y,z) \ L(x * u,y,z) = L(u,y,z). [para(1576(a,1),54(a,1,1))]. given #1505 (H,wt=16): 1580 L(L(x,y,z) * u,z,y) = x * L(u,z,y). [hyper(17,a,1554,a(flip),b,1578,a)]. given #1506 (H,wt=16): 1582 L(x,y,z) \ L(u,y,z) = L(x \ u,y,z). [para(14(a,1),1579(a,1,2,1))]. given #1507 (H,wt=16): 1584 L(L(x,y,z) \ u,z,y) = x \ L(u,z,y). [para(829(a,1),1582(a,1,1)),flip(a)]. given #1508 (H,wt=21): 1581 T(L(x * y,z,u),L(x,z,u)) = L(y,z,u) * L(x,z,u). [para(1578(a,1),116(a,1,1))]. given #1509 (H,wt=21): 1586 L(T(x * y,L(x,z,u)),z,u) = L(y,z,u) * L(x,z,u). [para(1581(a,1),40(a,2))]. given #1510 (H,wt=21): 1587 L(L(x * y,y,K(z,u)),z,u) = L(x,z,u) * L(y,z,u). [para(1414(a,2),1586(a,1,1))]. given #1511 (H,wt=18): 1588 L(x * y,z,T(u,y)) = L(x,z,u) * L(y,z,u). [para(1587(a,1),1522(a,1)),flip(a)]. given #1512 (H,wt=15): 1589 L(x * y,z,T(u,y)) = L(x * y,z,u). [para(1588(a,2),1578(a,1))]. given #1513 (H,wt=15): 1590 L((x / y) * y,z,u) = L(x,z,T(u,y)). [para(16(a,1),1589(a,1,1)),flip(a)]. given #1514 (H,wt=11): 1591 L(x,y,T(z,u)) = L(x,y,z). [para(16(a,1),1590(a,1,1)),flip(a)]. given #1515 (H,wt=14): 1600 L(L(x,y,z),z,y) = L(x,y,K(z,u)). [para(1591(a,1),1516(a,1,1))]. given #1516 (H,wt=8): 1604 L(x,y,K(z,u)) = x. [para(1600(a,1),829(a,1))]. given #1517 (H,wt=8): 1611 T(x,a(y,z,u)) = x. [para(1604(a,1),1371(a,1)),flip(a)]. given #1518 (H,wt=11): 1618 T(a(x,y,z),u) = a(x,y,z). [hyper(35,a,1611,a)]. given #1519 (H,wt=13): 1612 a(x,y,z) * u = u * a(x,y,z). [para(1604(a,1),1373(a,1)),flip(a)]. given #1520 (H,wt=13): 1619 a(x,y,z) / u = u \ a(x,y,z). [para(1611(a,1),229(a,1,2))]. given #1521 (H,wt=15): 1628 x * (y * a(x,z,u)) = L(x,z,u) * y. [para(1612(a,1),1276(a,1,2))]. given #1522 (H,wt=21): 1630 T(a(x,y,z),u \ w) * T(u,w) = T(a(x,y,z) * u,w). [para(1612(a,2),1406(a,2,1))]. given #1523 (H,wt=17): 1633 T(a(x,y,z) * u,w) = a(x,y,z) * T(u,w). [para(1618(a,1),1630(a,1,1)),flip(a)]. given #1524 (H,wt=23): 1585 L(x / (L(y,z,u) \ w),u,z) = L(x,u,z) / (y \ L(w,u,z)). [para(1584(a,1),1575(a,1,2)),flip(a)]. given #1525 (H,wt=23): 1635 L(x / (L(y,z,u) \ w),u,z) = L(x,u,z) * (L(w,u,z) \ y). [para(1585(a,2),358(a,1))]. given #1526 (H,wt=23): 1636 L(x * (y \ L(z,u,w)),w,u) = L(x,w,u) * (L(y,w,u) \ z). [para(358(a,1),1635(a,1,1))]. given #1527 (H,wt=24): 1631 x \ (y \ (x * (a(z,u,w) * T(y,x)))) = L(a(z,u,w),y,x * x). [para(1612(a,2),1534(a,1,2,2,2))]. given #1528 (H,wt=24): 1637 x \ (y \ (x * T(a(z,u,w) * y,x))) = L(a(z,u,w),y,x * x). [para(1633(a,2),1631(a,1,2,2,2))]. given #1529 (H,wt=22): 1638 x \ (y \ ((a(z,u,w) * y) * x)) = L(a(z,u,w),y,x * x). [para(78(a,1),1637(a,1,2,2))]. given #1530 (H,wt=22): 1639 x \ ((y \ a(z,u,w)) * (y * x)) = L(a(z,u,w),y,x * x). [para(260(a,1),1638(a,1,2))]. given #1531 (H,wt=26): 1629 T((a(x,y,z) / u) * (u * w),a(x,y,z)) = u * (a(x,y,z) * (u \ w)). [para(1612(a,2),1355(a,2,2))]. given #1532 (H,wt=26): 1640 T((x \ a(y,z,u)) * (x * w),a(y,z,u)) = x * (a(y,z,u) * (x \ w)). [para(1619(a,1),1629(a,1,1,1))]. given #1533 (H,wt=21): 1641 (x \ a(y,z,u)) * (x * w) = x * (a(y,z,u) * (x \ w)). [para(1640(a,1),1611(a,1)),flip(a)]. given #1534 (H,wt=22): 1642 x \ (y * (a(z,u,w) * (y \ x))) = L(a(z,u,w),y,x * x). [para(1641(a,1),1639(a,1,2))]. given #1535 (H,wt=22): 1643 x \ (y * (a(z,u,w) * (y \ x))) = a(u,w,L(z,y,x * x)). [para(1642(a,2),1539(a,2)),flip(a)]. given #1536 (H,wt=27): 1632 x \ (y * (L(z,u,w) * (z \ (y \ x)))) = L(L(a(z,u,w),z,x \ y),x,y). [para(1628(a,1),1321(a,1,2,2))]. given #1537 (H,wt=25): 1644 L(L(a(x,y,z),x,u \ w),u,w) = u \ (w * (a(x,y,z) * (w \ u))). [para(1260(a,1),1632(a,1,2,2)),flip(a)]. given #1538 (H,wt=22): 1645 L(L(a(x,y,z),x,u \ w),u,w) = a(y,z,L(x,w,u * u)). [para(1644(a,2),1643(a,1))]. given #1539 (H,wt=17): 1646 a(x,y,L(z,u,w * w)) = L(a(z,x,y),w,u). [para(1169(a,1),1645(a,1,1)),flip(a)]. given #1540 (H,wt=17): 1648 a(x,y,L(z,u,w * w)) = a(x,y,L(z,w,u)). [para(1646(a,2),1539(a,2)),flip(a)]. given #1541 (H,wt=30): 1577 (L(x,y,z) \ (u / L(w,y,z))) * L(w,y,z) = L(w,y,z) \ (L(w / x,y,z) * u). [para(1575(a,1),1091(a,1,2,1)),flip(a)]. given #1542 (H,wt=46): 1649 ((x / L(y,z,u)) * L(y,z,u)) \ (L(w,z,u) * (L(y,z,u) \ (L(y / w,z,u) * x))) = a(x / L(y,z,u),L(w,z,u),L(y,z,u)). [para(1577(a,1),1228(a,2,2,2)),flip(a)]. given #1543 (H,wt=36): 1650 x \ (L(y,z,u) * (L(w,z,u) \ (L(w / y,z,u) * x))) = a(x / L(w,z,u),L(y,z,u),L(w,z,u)). [para(16(a,1),1649(a,1,1))]. given #1544 (H,wt=36): 1651 x \ L(y * (z \ L(L(z / y,u,w) * x,w,u)),u,w) = a(x / L(z,u,w),L(y,u,w),L(z,u,w)). [para(1636(a,2),1650(a,1,2))]. given #1545 (H,wt=33): 1652 a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = x \ L(w * (y \ ((y / w) * L(x,u,z))),z,u). [para(1580(a,1),1651(a,1,2,1,2,2)),flip(a)]. given #1546 (H,wt=33): 1653 a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = x \ L(w * ((w \ (L(x,u,z) / y)) * y),z,u). [para(1091(a,1),1652(a,2,2,1,2))]. given #1547 (H,wt=28): 1654 a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = x \ L(L(L(x,u,z),w,y),z,u). [para(948(a,2),1653(a,2,2,1))]. given #1548 (H,wt=22): 1655 a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = x \ L(x,w,y). [para(832(a,1),1654(a,2,2))]. given #1549 (H,wt=20): 1657 a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = a(x,w,y). [para(1655(a,2),1237(a,2)),flip(a)]. given #1550 (H,wt=20): 1658 a(L(x,y,z),u / L(x,y,z),L(w,y,z)) = a(u,w,x). [para(1657(a,1),1128(a,1)),flip(a)]. given #1551 (H,wt=15): 1659 a(L(x,y,z),u,L(w,y,z)) = a(u,w,x). [para(1658(a,1),1274(a,1)),flip(a)]. given #1552 (H,wt=15): 1660 a(x,y,L(L(z,u,w),u,w)) = a(x,y,z). [para(1659(a,1),1542(a,2))]. given #1553 (H,wt=14): 1661 a(x,y,L(z,u,w * w)) = a(x,y,z). [para(1293(a,1),1660(a,1,3))]. given #1554 (H,wt=12): 1662 a(x,y,L(z,u,w)) = a(x,y,z). [para(1661(a,1),1648(a,1)),flip(a)]. given #1555 (H,wt=12): 1665 L(a(x,y,z),u,w) = a(x,y,z). [para(1662(a,1),1541(a,1)),flip(a)]. given #1556 (H,wt=9): 1669 a(x,y,a(z,u,w)) = 1. [hyper(34,a,1665,a)]. -------- Proof 1 -------- "aa1". ============================== PROOF ================================= % Proof 1 at 28.04 (+ 1.20) seconds: "aa1". % Length of proof is 1560. % Level of proof is 188. % Maximum clause weight is 47.000. % Given clauses 1556 (8.277 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(a(x,y,z),u,w) = 1 # label("aa1") # 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)]. 45 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 47 ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang"). [assumption]. 48 a(a(c1,c2,c3),c4,c5) != 1 # label("aa1") # answer("aa1"). [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))]. 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 x * y != x | 1 = y. [para(12(a,1),19(a,1)),flip(a)]. 56 x * y != z | x \ z = y. [para(14(a,1),19(a,1)),flip(a)]. 57 x * 1 != y | x = y. [para(12(a,1),20(a,2))]. 58 x * y != z | z / y = x. [para(16(a,1),20(a,1)),flip(a)]. 59 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(24(a,2),14(a,1,2))]. 60 (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y). [para(14(a,1),24(a,2,1,2)),flip(a)]. 61 (x * y) * K(y,x) = y * x. [para(26(a,2),14(a,1,2))]. 62 x \ ((y \ x) * y) = K(y \ x,y). [para(14(a,1),26(a,2,1)),flip(a)]. 63 ((x \ y) * x) \ y = K(x,x \ y). [para(14(a,1),26(a,2,2)),flip(a)]. 64 (x * (y / x)) \ y = K(y / x,x). [para(16(a,1),26(a,2,2)),flip(a)]. 65 x \ (1 * (x * y)) = L(y,x,1). [para(11(a,1),28(a,2,1)),flip(a)]. 66 (x * 1) \ (x * y) = L(y,1,x). [para(11(a,1),28(a,2,2,2)),flip(a)]. 67 (x * y) * L(z,y,x) = x * (y * z). [para(28(a,2),14(a,1,2))]. 68 L(x \ y,x,z) = (z * x) \ (z * y). [para(14(a,1),28(a,2,2,2))]. 69 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(16(a,1),28(a,2,1)),flip(a)]. 70 L(x,y / x,z) = (z * (y / x)) \ (z * y). [para(16(a,1),28(a,2,2,2))]. 71 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(14(a,1),30(a,2,1,1))]. 72 R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)). [para(14(a,1),30(a,2,1))]. 73 R(x,y,z) * (y * z) = (x * y) * z. [para(30(a,2),16(a,1,1))]. 74 R(x / y,y,z) = (x * z) / (y * z). [para(16(a,1),30(a,2,1,1))]. 75 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(16(a,1),30(a,2,2)),flip(a)]. 76 T(1,x) = x \ x. [para(11(a,1),32(a,2,2))]. 77 T(x,x) = x. [para(32(a,2),13(a,1))]. 78 x * T(y,x) = y * x. [para(32(a,2),14(a,1,2))]. 79 T(x,x \ y) = (x \ y) \ y. [para(14(a,1),32(a,2,2))]. 80 T(x / y,y) = y \ x. [para(16(a,1),32(a,2,2))]. 81 x * (y * (x * 1)) = (x * y) * x. [hyper(18,a,12,a,b,47,a),flip(a)]. 82 ((x * 1) * x) * y = x * (x * y). [para(11(a,1),47(a,2,2))]. 83 x * ((x \ y) * (x * z)) = (y * x) * z. [para(14(a,1),47(a,1,1,1)),flip(a)]. 84 ((x * y) * (x * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [para(47(a,1),24(a,2,2)),flip(a)]. 86 T(T(x,y),x) = T(x,y). [para(77(a,1),38(a,1,1)),flip(a)]. 87 (x * (y * z)) / L(z,y,x) = x * y. [para(28(a,2),53(a,1,2))]. 88 (x * y) / T(x,y) = y. [para(32(a,2),53(a,1,2))]. 89 R(x,y,z) \ ((x * y) * z) = y * z. [para(30(a,2),54(a,1,1))]. 90 T(1,x) = 1. [para(76(a,2),50(a,1))]. 94 x * y != z * x | T(z,x) = y. [para(78(a,1),19(a,1)),flip(a)]. 95 T(x,y) \ (x * y) = T(y,T(x,y)). [para(78(a,1),32(a,2,2)),flip(a)]. 96 x * T(T(y,x),z) = T(y,z) * x. [para(38(a,1),78(a,1,2))]. 97 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(40(a,2),78(a,1,2))]. 98 T(T(x / y,z),y) = T(y \ x,z). [para(80(a,1),38(a,1,1)),flip(a)]. 99 K(T(x,y),x) = 1. [hyper(36,a,86,a)]. 100 T(x,T(x,y)) = x. [hyper(35,a,86,a)]. 101 K(x \ y,y / x) = 1. [para(80(a,1),99(a,1,1))]. 102 T(T(x,y),T(x,z)) = T(x,y). [para(100(a,1),38(a,1,1)),flip(a)]. 103 x / T(y,y \ x) = y \ x. [para(14(a,1),88(a,1,1))]. 104 (x * y) / T(y,T(x,y)) = T(x,y). [para(78(a,1),88(a,1,1))]. 105 T(x \ y,y / x) = x \ y. [hyper(37,a,101,a)]. 106 x * K(y,x / y) = y * (x / y). [para(16(a,1),61(a,1,1))]. 107 (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x). [para(61(a,1),28(a,2,2,2)),flip(a)]. 108 (x * y) / T(y * x,K(x,y)) = K(x,y). [para(61(a,1),88(a,1,1))]. 109 x \ (x * y) = L(y,x,1). [para(11(a,1),65(a,1,2))]. 110 L(x,y,1) = x. [para(109(a,1),13(a,1))]. 111 x \ (x * y) = L(y,1,x). [para(12(a,1),66(a,1,1))]. 112 L(x,1,y) = x. [para(111(a,1),13(a,1))]. 113 (x * y) * x = x * (y * x). [para(12(a,1),81(a,1,2,2)),flip(a)]. 114 (x * (y * x)) / x = x * y. [hyper(58,a,113,a)]. 115 (x * y) \ (x * (y * x)) = x. [hyper(56,a,113,a)]. 116 T(x * y,x) = y * x. [hyper(94,a,113,a(flip))]. 117 (x * y) * x != x * z | y * x = z. [para(113(a,2),19(a,1))]. 118 (x * (y * x)) * z = x * (y * (x * z)). [para(113(a,1),47(a,1,1))]. 119 T((x \ y) * x,x \ y) = y. [para(116(a,2),14(a,1))]. 120 T(x,y) = (y \ x) * y. [para(14(a,1),116(a,1,1))]. 121 T(x,x / y) = y * (x / y). [para(16(a,1),116(a,1,1))]. 122 T(x * y,y) = T(x,y) * y. [para(78(a,1),116(a,1,1))]. 123 T(x,y) / y = y \ x. [hyper(58,a,120,a(flip))]. 124 (x \ y) \ T(y,x) = x. [hyper(56,a,120,a(flip))]. 125 x \ T(y,x) = T(x \ y,x). [para(120(a,2),32(a,2,2)),flip(a)]. 126 (x \ T(x,y)) * x = T(x,y). [para(120(a,1),86(a,1))]. 127 K(x \ y,x) = y \ T(y,x). [para(120(a,2),62(a,1,2)),flip(a)]. 128 K(x,x \ y) = T(y,x) \ y. [para(120(a,2),63(a,1,1)),flip(a)]. 129 1 / x = x \ 1. [para(90(a,1),123(a,1,1))]. 130 (x \ y) / x = x \ (y / x). [para(80(a,1),123(a,1,1))]. 131 T(x,y) / x = x \ T(x,y). [para(86(a,1),123(a,1,1))]. 132 x / T(x,y) = T(x,y) \ x. [para(100(a,1),123(a,1,1))]. 133 T(x,y) / T(x,z) = T(x,z) \ T(x,y). [para(102(a,1),123(a,1,1))]. 134 (x \ y) / (y / x) = (y / x) \ (x \ y). [para(105(a,1),123(a,1,1))]. 135 (x \ 1) \ 1 = x. [para(129(a,1),53(a,1))]. 136 (x \ T(x,y)) \ T(x,y) = x. [para(86(a,1),124(a,1,2))]. 137 (x * y) / x = x * (y / x). [para(16(a,1),114(a,1,1,2))]. 138 (x * (y / x)) \ (x * y) = x. [para(16(a,1),115(a,1,2,2))]. 139 L(x,y,x) = x. [para(115(a,1),28(a,2))]. 140 L(T(x,y),z,x) = T(x,y). [para(139(a,1),40(a,2,1))]. 141 L(L(x,y,z),u,x) = L(x,y,z). [para(139(a,1),45(a,1,1)),flip(a)]. 142 L(T(T(x,y),z),u,x) = T(T(x,y),z). [para(140(a,1),40(a,2,1))]. 143 T(T(x,y),y \ x) = x. [para(120(a,2),119(a,1,1))]. 144 T(T(T(x,y),z),y \ x) = T(x,z). [para(143(a,1),38(a,1,1)),flip(a)]. 145 T(T(x,x / y),y) = x. [para(54(a,1),143(a,1,2))]. 146 T(x,T(x,y) \ x) = x. [para(100(a,1),143(a,1,1))]. 147 T(T(x,y),y \ x) = L(x,z,T(x,y)). [para(143(a,1),140(a,1,1)),flip(a)]. 148 T(T(x,y),x / y) = x. [para(145(a,1),38(a,1)),flip(a)]. 149 T(x,x / y) * y = y * x. [para(145(a,1),78(a,1,2)),flip(a)]. 150 K(x,T(x,y) \ x) = 1. [hyper(36,a,146,a)]. 151 T(T(T(x,y),z),x / y) = T(x,z). [para(148(a,1),38(a,1,1)),flip(a)]. 152 T(x,(y * (x / y)) \ x) = x. [para(121(a,1),146(a,1,2,1))]. 153 T(x \ (y / x),x) = x \ (x \ y). [para(80(a,1),125(a,1,2)),flip(a)]. 154 T(x,y) = x * K(y \ x,y). [para(127(a,2),14(a,1,2)),flip(a)]. 155 T(x,y) = K(y \ x,y) * x. [para(127(a,2),126(a,1,1)),flip(a)]. 156 T(x,y) * K(y,y \ x) = x. [para(128(a,2),14(a,1,2))]. 157 T(x,x \ T(x,y)) = x. [para(136(a,1),79(a,2))]. 158 T(x,K(y \ x,y)) = x. [para(127(a,2),157(a,1,2))]. 159 T(x * y,K(y,x)) = x * y. [para(13(a,1),158(a,1,2,1))]. 161 T(x,K(x / y,y)) = x. [para(64(a,1),152(a,1,2))]. 162 T(K(x / y,y),x) = K(x / y,y). [hyper(35,a,161,a)]. 163 T(x,y) != x * z | K(y \ x,y) = z. [para(154(a,2),19(a,1))]. 164 T(x,y) * K(T(y \ x,y),y) = T(T(x,y),y). [para(125(a,1),154(a,2,2,1)),flip(a)]. 165 (x * x) * y = x * (x * y). [para(12(a,1),82(a,1,1,1))]. 166 (x * (x * y)) / y = x * x. [hyper(58,a,165,a)]. 167 (x * (x * y)) \ ((x * x) * (y * z)) = L(z,y,x * x). [para(165(a,1),28(a,2,1)),flip(a)]. 168 (x * y) / (x \ y) = x * x. [para(14(a,1),166(a,1,1,2))]. 169 x / (y \ (y \ x)) = y * y. [para(14(a,1),168(a,1,1))]. 170 (x * x) \ y = x \ (x \ y). [para(169(a,1),54(a,1,1))]. 171 (x \ (x \ y)) * (x * x) = T(y,x * x). [para(170(a,1),120(a,2,1)),flip(a)]. 172 (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y). [para(79(a,1),96(a,1,2,1))]. 173 T(x,y \ x) * y = y * x. [para(143(a,1),96(a,1,2)),flip(a)]. 174 T(x,x / y) = T(x,y \ x). [hyper(18,a,149,a,b,173,a),flip(a)]. 175 x * y != z * x | T(y,x \ y) = z. [para(173(a,1),20(a,1))]. 176 T(x,(y \ x) \ x) = T(x,y). [para(53(a,1),174(a,1,2)),flip(a)]. 177 T(x,y \ x) = y * (x / y). [para(174(a,1),121(a,1))]. 178 T(x,T(y,y \ x)) = T(x,y). [para(79(a,2),176(a,1,2))]. 179 T(x * y,y) = x * ((x * y) / x). [para(13(a,1),177(a,1,2))]. 180 T(x,(y * z) \ x) / (z * (x / (y * z))) = R(y,z,x / (y * z)). [para(177(a,2),30(a,2,1)),flip(a)]. 181 T(T(x,y),z \ x) = T(z * (x / z),y). [para(177(a,1),38(a,1,1)),flip(a)]. 182 T(x * y,T(x,y)) = T(x * y,x). [para(13(a,1),178(a,1,2,2))]. 183 x * K(y,x / y) = T(x,y \ x). [para(106(a,2),177(a,2)),flip(a)]. 184 T(T(T(x,y),z),z \ x) = T(x,y). [para(38(a,1),144(a,1,1))]. 185 T(T(T(x,y \ x),z),y) = T(x,z). [para(53(a,1),151(a,1,2))]. 186 T(T(T(T(x,y),z),y \ x),T(x,y) / z) = x. [para(151(a,2),143(a,1))]. 187 K(x / y,y) / x = x \ K(x / y,y). [para(162(a,1),123(a,1,1))]. 188 T(x * y,y) = x * (x * (y / x)). [para(137(a,1),179(a,2,2))]. 189 T(x * y,T(x,y)) = y * x. [para(182(a,2),116(a,1))]. 190 K(T(x,y) \ (x * y),T(x,y)) = (x * y) \ (y * x). [para(189(a,1),127(a,2,2))]. 191 T(T(x,y),z \ x) * z = z * T(x,y). [para(184(a,1),96(a,1,2)),flip(a)]. 192 x \ T(T(y,x \ y),z) = T(y,z) / x. [para(185(a,1),123(a,1,1)),flip(a)]. 193 x * T(y,x \ y) = T(x * y,y). [para(177(a,2),188(a,2,2)),flip(a)]. 194 x * L(y,z,x / z) = (x / z) * (z * y). [para(16(a,1),67(a,1,1))]. 195 (x * y) * z != x * (y * u) | L(u,y,x) = z. [para(67(a,1),19(a,1)),flip(a)]. 197 (x * (y * L(z,y,x))) \ (x * (y * z)) = a(x,y,L(z,y,x)). [para(67(a,1),24(a,2,2)),flip(a)]. 198 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(67(a,1),28(a,2,2,2)),flip(a)]. 199 (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z). [para(78(a,1),67(a,1,1))]. 200 (x * y) * L(x,z,u) = x * (y * L(x,z,u)). [para(141(a,1),67(a,1,2))]. 201 L(x \ 1,x,y) = (y * x) \ y. [para(12(a,1),68(a,2,2))]. 202 L((x \ y) \ z,x \ y,x) = y \ (x * z). [para(14(a,1),68(a,2,1))]. 203 L(x \ (y \ z),x,y) = (y * x) \ z. [para(14(a,1),68(a,2,2))]. 204 L(x \ (y * x),x,y) = T(y,y * x). [para(68(a,2),32(a,2)),flip(a)]. 205 L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z). [para(78(a,1),68(a,2,1))]. 206 L(x \ y,x,z) * (z * x) = T(z * y,z * x). [para(68(a,2),120(a,2,1)),flip(a)]. 207 x / L(y \ 1,y,x) = x * y. [para(201(a,2),53(a,1,2))]. 208 x / L(y,y \ 1,x) = x * (y \ 1). [para(135(a,1),207(a,1,2,1))]. 210 R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y). [para(78(a,1),73(a,1,2))]. 211 R(1 / x,x,y) = y / (x * y). [para(11(a,1),74(a,2,1))]. 212 R((x / y) / z,z,y) = x / (z * y). [para(16(a,1),74(a,2,1))]. 213 R((x * y) / z,z,x) = (x * (y * x)) / (z * x). [para(113(a,1),74(a,2,1))]. 214 R(x \ 1,x,y) = y / (x * y). [para(129(a,1),211(a,1,1))]. 215 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(14(a,1),89(a,1,2,1))]. 216 R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z). [para(14(a,1),89(a,1,2))]. 217 (x * y) * T(T(x,z),u) = x * (y * T(T(x,z),u)). [para(142(a,1),67(a,1,2))]. 218 L(x,y,T(x,z)) = x. [para(147(a,1),143(a,1))]. 219 L(L(x,y,z),u,T(x,w)) = L(x,y,z). [para(218(a,1),45(a,1,1)),flip(a)]. 220 L(T(x,y),y,x) = T(x,x * y). [para(32(a,2),204(a,1,1))]. 221 T(x,x * y) = T(x,y). [para(220(a,1),140(a,1))]. 222 T(x,x \ y) = T(x,y). [para(14(a,1),221(a,1,2)),flip(a)]. 223 T(x,T(y,x)) = T(x,y * x). [para(78(a,1),221(a,1,2)),flip(a)]. 225 T(T(x,y),(x * y) \ x) = x. [para(221(a,1),143(a,1,1))]. 226 (x * y) * T(T(x,y),z) = T(x,z) * (x * y). [para(221(a,1),96(a,1,2,1))]. 227 T(T(T(x,y),z),y \ x) = T(x,T(x,y) * z). [para(221(a,1),144(a,1,1))]. 228 T(x,y) = (x \ y) \ y. [para(222(a,1),79(a,1))]. 229 x / T(y,x) = y \ x. [para(222(a,1),103(a,1,2))]. 230 T(x,T(y,x)) = T(x,y). [para(222(a,1),178(a,1,2))]. 231 (x \ y) * T(x,y) = y. [para(228(a,2),14(a,1,2))]. 232 T(x / y,x) = y \ x. [para(54(a,1),228(a,2,1))]. 233 T(x,y) \ y = T(x \ y,y). [para(228(a,2),228(a,2,1)),flip(a)]. 234 x / T(T(y,x),z) = T(y,z) \ x. [para(38(a,1),229(a,1,2))]. 235 x / L(T(y,x),z,u) = L(y,z,u) \ x. [para(40(a,2),229(a,1,2))]. 236 (x * y) / T(y,x) = T(x,y). [para(230(a,1),104(a,1,2))]. 237 ((x * y) \ x) * (y * x) = x. [para(116(a,1),231(a,1,2))]. 238 (x / y) * x = x * (y \ x). [para(232(a,1),78(a,1,2)),flip(a)]. 239 (x \ y) / y = y \ (y / x). [para(232(a,1),123(a,1,1))]. 240 T(x \ y,y \ (y / x)) = y / x. [para(232(a,1),143(a,1,1))]. 241 K(x \ (x / y),x) = (x / y) \ (y \ x). [para(232(a,1),127(a,2,2))]. 242 K(x,x \ (x / y)) = (y \ x) \ (x / y). [para(232(a,1),128(a,2,1))]. 243 (x \ y) * K(y,y \ (y / x)) = y / x. [para(232(a,1),156(a,1,1))]. 244 T(x \ y,y) = T(x \ y,x). [para(232(a,1),98(a,1,1)),flip(a)]. 245 T(x,y * x) = T(x,y). [para(223(a,1),230(a,1))]. 246 T(x,y / x) = T(x,y). [para(16(a,1),245(a,1,2)),flip(a)]. 247 (x / y) * T(y,x) = y * (x / y). [para(246(a,1),78(a,1,2))]. 248 T(x * (y / x),y / x) = T(x,y) * (y / x). [para(246(a,1),122(a,2,1))]. 249 T((x * y) \ x,x) = (y * x) \ x. [para(116(a,1),233(a,1,1)),flip(a)]. 250 T(x,y) * T(y,x) = x * y. [para(236(a,1),16(a,1,1))]. 251 x * (y * z) != z | (z * y) \ z = x. [para(237(a,1),20(a,1)),flip(a)]. 252 T(x \ y,x) = ((x \ y) \ y) \ y. [para(244(a,1),228(a,1))]. 253 (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). [para(250(a,1),28(a,2,1)),flip(a)]. 254 T(L(x \ 1,x,y),y) = (x * y) \ y. [para(201(a,2),249(a,1,1))]. 255 x * (((x \ y) \ y) \ y) = (x \ y) * x. [para(252(a,1),78(a,1,2))]. 256 x * (L(x,y,z) \ 1) = x / L(x,y,z). [para(141(a,1),208(a,1,2)),flip(a)]. 257 L(T(x \ 1,y),x,y) = (x * y) \ y. [para(254(a,1),40(a,2))]. 258 (x * y) * ((y * x) \ x) = x * (y * T(y \ 1,x)). [para(257(a,1),67(a,1,2))]. 259 (x \ y) * (x * x) = T(y * x,x). [hyper(94,a,83,a),flip(a)]. 260 x \ ((y * x) * z) = (x \ y) * (x * z). [hyper(56,a,83,a)]. 261 (x * y) * (y \ z) = y * ((y \ x) * z). [para(14(a,1),83(a,1,2,2)),flip(a)]. 262 L(x,y,z) * x = x * L(x,y,z). [para(77(a,1),97(a,1,2,1)),flip(a)]. 263 L(x / y,z,u) * y = y * L(y \ x,z,u). [para(80(a,1),97(a,1,2,1)),flip(a)]. 264 T(x,L(x,y,z) \ x) = x. [hyper(175,a,262,a)]. 265 T(x,L(x,y,z)) = x. [hyper(94,a,262,a)]. 266 K(x,L(x,y,z)) = 1. [hyper(36,a,265,a)]. 267 (L(x,y,z) \ x) * L(x,y,z) = x. [para(265(a,1),120(a,1)),flip(a)]. 268 x / L(x,y,z) = L(x,y,z) \ x. [para(265(a,1),123(a,1,1))]. 269 L(x,y,z) / x = x \ L(x,y,z). [para(265(a,1),229(a,1,2))]. 270 K(x,y) = (x * y) / (y * x). [para(159(a,1),108(a,1,2)),flip(a)]. 271 (x * T(y,x \ y)) / (x * y) = K(x,T(y,x \ y)). [para(173(a,1),270(a,2,2)),flip(a)]. 272 (x * y) * y = x * (y * y). [hyper(117,a,118,a)]. 273 x * (y * L(z,x * y,y)) = (x * y) * z. [hyper(17,a,67,a(flip),b,118,a(flip))]. 274 L(x,x,y) = x. [hyper(17,a,67,a,b,272,a),flip(a)]. 275 R(x,y,y) = x. [hyper(18,a,73,a,b,272,a(flip)),flip(a)]. 276 L(L(x,y,z),x,u) = L(x,y,z). [para(274(a,1),45(a,1,1)),flip(a)]. 277 (x * y) / (y * y) = x / y. [para(275(a,1),74(a,1)),flip(a)]. 278 (x / y) / y = x / (y * y). [para(275(a,1),212(a,1))]. 279 T(x / (y * y),y) = y \ (x / y). [para(278(a,1),80(a,1,1))]. 280 T(x,y / (x * x)) = T(x,y / x). [para(278(a,1),246(a,1,2))]. 281 T(x,y / (x * x)) = T(x,y). [para(280(a,2),246(a,1))]. 282 T((x \ y) * x,x) = T(y,x * x). [para(171(a,1),259(a,1)),flip(a)]. 283 T(x * (y / x),y / x) = T(y,(y / x) * (y / x)). [para(54(a,1),282(a,1,1,1))]. 284 T(T(x,y),y) = T(x,y * y). [para(120(a,2),282(a,1,1))]. 285 T(T(x,y \ x),z) = T(y * (x / y),z). [para(181(a,1),38(a,1)),flip(a)]. 287 T(T(x,y \ x),z) = y * (T(x,z) / y). [para(192(a,1),14(a,1,2)),flip(a)]. 288 T(T(T(x,y \ x),z),T(x,z) / y) = y * (T(T(x,y \ x),z) / y). [para(192(a,1),177(a,1,2))]. 289 T(x,y) = y * (((y \ x) \ x) \ x). [para(255(a,2),120(a,2))]. 290 x * (T(x,y) \ y) = T(y,x). [para(228(a,2),289(a,2,2,1)),flip(a)]. 291 (x * y) * ((y * x) \ x) = T(x,x * y). [para(116(a,1),290(a,1,2,1))]. 292 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(256(a,2),268(a,1))]. 293 T(T(x,(y * y) \ x),z) = T(y * (y * (x / (y * y))),z). [para(165(a,1),285(a,2,1))]. 294 T(x * (y / x),z) = x * (T(y,z) / x). [para(177(a,1),287(a,1,1))]. 295 T(x,y) = (x * y) * ((y * x) \ x). [para(291(a,2),221(a,1)),flip(a)]. 296 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(59(a,1),88(a,1,1))]. 297 (1 / x) * (x * y) = L(y,x,1 / x). [para(69(a,1),49(a,1)),flip(a)]. 298 L(x,y,1 / y) / (y * x) = 1 / y. [hyper(58,a,297,a)]. 299 (1 / x) \ L(y,x,1 / x) = x * y. [hyper(56,a,297,a)]. 300 L(x \ y,x,1 / x) = (1 / x) * y. [para(14(a,1),297(a,1,2)),flip(a)]. 301 L(x \ y,x,x \ 1) = (1 / x) * y. [para(129(a,1),300(a,1,3))]. 302 L(x \ y,x,x \ 1) = (x \ 1) * y. [para(129(a,1),301(a,2,1))]. 303 (x \ 1) * (x * y) = L(y,x,x \ 1). [para(13(a,1),302(a,1,1)),flip(a)]. 304 L(L(x,y * z,z),z,y) = x. [hyper(17,a,67,a,b,273,a(flip)),flip(a)]. 305 L(L(x,y,z),z,y / z) = x. [para(16(a,1),304(a,1,1,2))]. 306 L(L(x,y,z),z * y,y) = x. [para(304(a,1),45(a,1)),flip(a)]. 307 L(L(x,y,z / y),z,y) = x. [para(305(a,1),45(a,1)),flip(a)]. 308 L(x,y,1 / y) = x. [para(112(a,1),305(a,1,1))]. 309 K(L(x,y,z),x) = 1. [para(305(a,1),266(a,1,2))]. 310 L(x,y * z,z) = L(x,y,z / y). [para(304(a,1),305(a,1,1)),flip(a)]. 311 L(x,y,y \ 1) = x. [para(129(a,1),308(a,1,3))]. 312 x / (y * x) = 1 / y. [para(308(a,1),298(a,1,1))]. 313 (1 / x) \ y = x * y. [para(308(a,1),299(a,1,2))]. 314 (x \ 1) * y = x \ y. [para(311(a,1),302(a,1)),flip(a)]. 315 (x \ 1) * (x * y) = y. [para(311(a,1),303(a,2))]. 316 x / (y * x) = y \ 1. [para(312(a,2),129(a,1))]. 317 (x \ 1) \ y = x * y. [para(129(a,1),313(a,1,1))]. 318 (x \ y) / y = x \ 1. [hyper(58,a,314,a)]. 319 (x * (y \ 1)) \ (x * (y \ z)) = L(z,y \ 1,x). [para(314(a,1),28(a,2,2,2)),flip(a)]. 320 T(x \ 1,y) = y \ (x \ y). [para(314(a,1),32(a,2,2))]. 321 ((x * (y / x)) \ 1) * y = K(y / x,x). [para(314(a,2),64(a,1))]. 322 (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). [para(314(a,1),67(a,1,1))]. 323 L(x \ y,x,z \ 1) = (z \ x) \ ((z \ 1) * y). [para(314(a,1),68(a,2,1))]. 324 T(x,y \ 1) = T(x,y \ x). [para(314(a,1),245(a,1,2)),flip(a)]. 325 (x * y) \ x = y \ 1. [hyper(251,a,315,a)]. 326 R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). [para(315(a,1),30(a,2,1,1))]. 327 (x / y) \ 1 = y / x. [para(16(a,1),316(a,1,2)),flip(a)]. 328 (x * y) / ((z * x) * y) = R(z,x,y) \ 1. [para(73(a,1),316(a,1,2))]. 329 T(x \ 1,y) = (x * y) \ y. [para(316(a,1),232(a,1,1))]. 330 (x * (y / x)) \ 1 = x / (x * y). [para(138(a,1),318(a,1,1)),flip(a)]. 331 T(x \ (y \ 1),x) = x \ (x \ (y \ x)). [para(318(a,1),153(a,1,1,2))]. 332 x \ (x / y) = y \ 1. [para(318(a,1),239(a,1)),flip(a)]. 333 (x \ y) \ 1 = y \ x. [para(14(a,1),325(a,1,1)),flip(a)]. 334 x / (y \ 1) = x * y. [para(325(a,1),53(a,1,2))]. 335 T(x,y) \ 1 = (x * y) \ y. [para(78(a,1),325(a,1,1)),flip(a)]. 336 (x * y) \ (y * x) = K(x,y) \ 1. [para(61(a,1),325(a,1,1))]. 337 T(x,y) \ 1 = y \ (x \ y). [para(231(a,1),325(a,1,1)),flip(a)]. 338 T(T(x,y),y \ 1) = x. [para(325(a,1),225(a,1,2))]. 339 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(59(a,1),325(a,1,1))]. 341 (x * y) \ 1 = y \ (x \ 1). [para(315(a,1),325(a,1,1)),flip(a)]. 342 L(x / y,y / x,z) = (z * (y / x)) \ z. [para(327(a,1),201(a,1,1))]. 343 (x / y) \ z = (y / x) * z. [para(327(a,1),314(a,1,1)),flip(a)]. 344 (x / y) * ((y / x) * z) = z. [para(327(a,1),315(a,1,1))]. 345 x * (y \ 1) = x / y. [para(332(a,1),14(a,1,2))]. 346 x \ (T(x,y) \ x) = T(x,y) \ 1. [para(132(a,1),332(a,1,2))]. 347 T(x \ y,x \ 1) = y / x. [para(332(a,1),240(a,1,2))]. 348 (x / y) \ (y \ x) = K(y \ 1,x). [para(332(a,1),241(a,1,1)),flip(a)]. 349 (x \ y) \ (y / x) = K(y,x \ 1). [para(332(a,1),242(a,1,2)),flip(a)]. 350 (x \ y) * K(y,x \ 1) = y / x. [para(332(a,1),243(a,1,2,2))]. 352 R(x \ y,y \ x,z) = z / ((y \ x) * z). [para(333(a,1),214(a,1,1))]. 353 (x \ y) \ z = (y \ x) * z. [para(333(a,1),314(a,1,1)),flip(a)]. 354 (x \ y) * ((y \ x) * z) = z. [para(333(a,1),315(a,1,1))]. 355 (x * (y \ z)) \ x = z \ y. [para(333(a,1),325(a,2))]. 356 x \ (x / (y \ z)) = z \ y. [para(333(a,1),332(a,2))]. 357 x / (y / z) = x * (z / y). [para(327(a,1),334(a,1,2))]. 358 x / (y \ z) = x * (z \ y). [para(333(a,1),334(a,1,2))]. 359 T(x * y,y \ 1) = y * x. [para(116(a,1),338(a,1,1))]. 360 T(x,y \ 1) * y = y * x. [para(338(a,1),96(a,1,2)),flip(a)]. 361 T(x \ y,y \ 1) = y / x. [para(232(a,1),338(a,1,1))]. 362 T(x,y \ 1) \ y = y / x. [para(338(a,1),234(a,1,2)),flip(a)]. 364 x * (T(x,y) \ 1) = T(x,y) \ x. [para(345(a,2),132(a,1))]. 365 R(x,y,z \ 1) * (y / z) = (x * y) * (z \ 1). [para(345(a,1),73(a,1,2))]. 366 x * (y * (x * (z \ 1))) = (x * (y * x)) / z. [para(345(a,1),118(a,1)),flip(a)]. 367 (x \ 1) / y = x \ (y \ 1). [para(345(a,1),314(a,1))]. 368 L(L(x,y,y \ z),T(z,y),y) = x. [para(120(a,2),306(a,1,2))]. 369 L(L(x,y,z),z * y,y) = L(x,u,L(x,y,z)). [para(306(a,1),141(a,1,1)),flip(a)]. 370 L((x * y) \ z,x * y,y) = y \ (x \ z). [para(203(a,1),306(a,1,1))]. 371 L(L(x,y,z \ 1),z \ y,y) = x. [para(314(a,1),306(a,1,2))]. 372 T(x,y \ 1) = y * (x / y). [para(324(a,2),177(a,1))]. 374 (x * y) \ y = y \ (x \ y). [para(329(a,1),320(a,1))]. 375 T(x,y) \ 1 = T(x \ 1,y). [para(335(a,2),329(a,2)),flip(a)]. 376 (x \ (y \ x)) * z = T(y,x) \ z. [para(337(a,1),314(a,1,1))]. 377 x * (y \ (z \ y)) = x / T(z,y). [para(337(a,1),345(a,1,2))]. 378 (x \ (y \ 1)) * z = (y * x) \ z. [para(341(a,1),314(a,1,1))]. 379 x * (y \ (z \ 1)) = x / (z * y). [para(341(a,1),345(a,1,2))]. 380 (x / y) \ y = y * (x \ y). [para(343(a,2),238(a,1))]. 381 (x / y) * z != u | (y / x) * u = z. [para(344(a,1),19(a,1)),flip(a)]. 382 T(x,y \ 1) = (y * x) / y. [para(13(a,1),347(a,1,1))]. 384 ((x \ y) * z) * (y \ x) = T(z,y \ x). [para(353(a,1),120(a,2,1)),flip(a)]. 385 L((x \ y) * z,y \ x,y) = x \ (y * z). [para(353(a,1),202(a,1,1))]. 386 ((x \ y) * z) \ u = (z \ (y \ x)) * u. [para(353(a,1),353(a,1,1))]. 387 (x \ y) * z != u | (y \ x) * u = z. [para(354(a,1),19(a,1)),flip(a)]. 388 (x \ y) \ x = y \ (x * x). [para(169(a,1),356(a,1,2)),flip(a)]. 389 (x * (y / z)) \ u = ((z / y) / x) * u. [para(357(a,1),343(a,1,1))]. 390 x / (y * (z / u)) = x * ((u / z) / y). [para(357(a,1),357(a,1,2))]. 391 (x * y) * (y \ x) = x * x. [para(358(a,1),168(a,1))]. 392 (x * (y \ z)) \ u = ((z \ y) / x) * u. [para(358(a,1),343(a,1,1))]. 393 x / ((y \ z) * u) = x * (u \ (z \ y)). [para(353(a,1),358(a,1,2))]. 394 x / (y * (z \ u)) = x * ((u \ z) / y). [para(358(a,1),357(a,1,2))]. 395 T(T(x,y),z \ 1) = T(T(x,y),z \ x). [hyper(18,a,191,a,b,360,a)]. 396 T(x,y \ z) * (z \ y) = (z \ y) * x. [para(333(a,1),360(a,1,1,2))]. 397 x / T(y,x \ 1) = T(x / y,x \ 1). [para(362(a,1),361(a,1,1)),flip(a)]. 398 T(x \ (y \ 1),y) = y \ (x \ 1). [para(367(a,1),80(a,1,1))]. 399 (x \ (y \ 1)) / z = (y * x) \ (z \ 1). [para(341(a,1),367(a,1,1))]. 400 T(x \ 1,y) * z = T(x,y) \ z. [para(375(a,1),314(a,1,1))]. 401 x \ (y * y) = (x \ y) * y. [para(388(a,1),353(a,1))]. 402 (x / y) * (x / y) = x * (y \ (x / y)). [para(16(a,1),391(a,1,1)),flip(a)]. 403 L(x,y \ z,y) = L(x,(y \ z) * z,z). [para(53(a,1),310(a,2,3)),flip(a)]. 404 K(x,y) \ 1 = K(y,x). [para(336(a,1),26(a,2)),flip(a)]. 405 K(x,y) * K(y,x) = 1. [para(404(a,1),14(a,1,2))]. 406 K(x,y) \ z = K(y,x) * z. [para(404(a,1),314(a,1,1)),flip(a)]. 407 K(x,y) * (K(y,x) * z) = z. [para(404(a,1),315(a,1,1))]. 408 (x * K(y,z)) \ x = K(z,y). [para(404(a,1),325(a,2))]. 409 x / K(y,z) = x * K(z,y). [para(404(a,1),334(a,1,2))]. 410 (K(x,y) * z) / K(x,y) = T(z,K(y,x)). [para(404(a,1),382(a,1,2)),flip(a)]. 411 K(x,y) * (z * K(y,x)) = T(z,K(y,x)). [para(406(a,1),32(a,2)),flip(a)]. 412 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(406(a,1),353(a,1,1))]. 413 K(x,y) * z != u | K(y,x) * u = z. [para(407(a,1),19(a,1)),flip(a)]. 414 (x * K(y,z)) * K(z,y) = x. [para(408(a,1),14(a,1,2))]. 415 x * K(y,z) != u | u * K(z,y) = x. [para(414(a,1),20(a,1)),flip(a)]. 416 x \ (T(x,y) \ x) = T(x \ 1,y). [para(346(a,2),375(a,1))]. 417 (x / y) * K(y \ 1,x) = y \ x. [para(348(a,1),14(a,1,2))]. 418 (x \ y) / (y / x) = K(x \ 1,y). [para(348(a,1),134(a,2))]. 421 (x \ y) * (x / y) = K(x,y \ 1). [para(349(a,1),353(a,1)),flip(a)]. 423 x * T(x \ 1,y) = T(x,y) \ x. [para(375(a,1),364(a,1,2))]. 424 x * ((y \ x) * L(z,x,y \ 1)) = (x * (y \ x)) * z. [para(371(a,1),67(a,1,2)),flip(a)]. 425 (x \ 1) * (T(x,y) \ x) = T(x \ 1,y). [para(416(a,1),314(a,2))]. 426 (x \ y) * (x / y) = K(x \ 1,y). [para(418(a,1),357(a,1)),flip(a)]. 427 K(x \ 1,y) = K(x,y \ 1). [para(426(a,1),421(a,1))]. 428 K(x \ 1,y \ z) = K(x,z \ y). [para(333(a,1),427(a,2,2))]. 429 (x / y) * K(y,x \ 1) = y \ x. [para(427(a,1),417(a,1,2))]. 430 (x / (x * y)) * y = K(y / x,x). [para(330(a,1),321(a,1,1))]. 431 K(x / y,y) / x = y / (y * x). [hyper(58,a,430,a)]. 432 x \ K(x / y,y) = y / (y * x). [para(431(a,1),187(a,1)),flip(a)]. 433 (x \ y) * ((y \ x) \ (z \ (y \ x))) = T((y \ x) \ (z \ 1),y \ x). [para(331(a,2),353(a,1)),flip(a)]. 434 L(x,y / x,z) = ((x / y) / z) * (z * y). [para(389(a,1),70(a,2))]. 435 R(x,x \ y,z) = (y * z) * (z \ (y \ x)). [para(393(a,1),71(a,2))]. 436 T(x \ 1,y) \ (x \ 1) = x \ T(x,y). [para(425(a,1),355(a,1,1))]. 437 L(x / y,y / x,z) = (y / x) \ 1. [para(342(a,2),325(a,1))]. 439 L(x / y,y / x,z) = x / y. [para(437(a,2),327(a,1))]. 440 L(x,y / (x * y),z) = (x * y) / y. [para(15(a,1),439(a,1,1))]. 441 L(x,x \ 1,y) = (x * z) / z. [para(316(a,1),440(a,1,2))]. 442 L(x,x \ 1,y) = x. [para(441(a,2),15(a,1))]. 444 L(T(x,y),x \ 1,z) = T(x,y). [para(442(a,1),40(a,2,1))]. 445 L(x,y,x \ 1) = x. [para(442(a,1),307(a,1,1))]. 446 L(x \ 1,y,x) = x \ 1. [para(135(a,1),445(a,1,3))]. 447 L(L(x \ 1,y,z),u,x) = L(x \ 1,y,z). [para(446(a,1),45(a,1,1)),flip(a)]. 448 R(x \ y,y \ x,z) = (y \ x) \ 1. [para(352(a,2),316(a,1))]. 450 R(x \ y,y \ x,z) = x \ y. [para(448(a,2),333(a,1))]. 451 R(x,(y * x) \ y,z) = y \ (y * x). [para(13(a,1),450(a,1,1))]. 452 R(x,x \ 1,y) = z \ (z * x). [para(325(a,1),451(a,1,2))]. 453 R(x,x \ 1,y) = x. [para(452(a,2),13(a,1))]. 455 R(T(x,y),x \ 1,z) = T(x,y). [para(453(a,1),42(a,2,1))]. 456 (T(x,y) * (x \ 1)) * z = T(x,y) * ((x \ 1) * z). [para(455(a,1),73(a,1,1)),flip(a)]. 457 x \ (y \ ((y * x) * z)) = L(z,y * x,x). [para(13(a,1),370(a,1,1)),flip(a)]. 458 (x * (y * x)) \ z = x \ (y \ (x \ z)). [para(370(a,1),203(a,1)),flip(a)]. 459 R(x,x \ y,z) = z * ((z \ y) * (y \ x)). [para(435(a,2),261(a,1))]. 460 (x * y) * L(x \ 1,z,u) = x * (y * L(x \ 1,z,u)). [para(447(a,1),67(a,1,2))]. 461 T(x,y) * K(T(y \ x,y),y) = T(x,y * y). [para(164(a,2),284(a,1))]. 462 T(T(x,y),T(x,z) / y) = x. [para(144(a,1),186(a,1,1))]. 464 T(x,(T(x,y) / z) \ x) = T(x,z). [para(462(a,1),184(a,1,1))]. 465 T(x,(y / T(x,z)) * x) = T(x,y). [para(343(a,1),464(a,1,2))]. 466 T(x,y / T(x,z)) = T(x,y). [para(465(a,1),245(a,1)),flip(a)]. 467 R(x,y,L(x,z,u)) = x. [hyper(18,a,73,a,b,200,a(flip)),flip(a)]. 468 x \ (y * L(x,z,u)) = (x \ y) * L(x,z,u). [para(467(a,1),215(a,1,1))]. 469 T(x,T(x,y) * z) = T(x,z). [para(227(a,1),144(a,1))]. 471 (x * L(x \ y,z,u)) / x = L(y / x,z,u). [hyper(58,a,263,a)]. 472 (x * (y * x)) / z = x * (y * (x / z)). [para(345(a,1),366(a,1,2,2)),flip(a)]. 473 L(x,y,L(x,z,u)) = x. [para(369(a,1),306(a,1))]. 474 (x * y) \ (z * ((z \ x) * y)) = a(x,z,z \ y). [para(261(a,1),60(a,1,2))]. 475 R(x,y,(x * y) \ z) = z * ((z \ (x * y)) / y). [para(72(a,2),394(a,1))]. 476 R((x * y) / z,z,x) = x * (y * (x / (z * x))). [para(213(a,2),472(a,1))]. 477 (x / y) \ (x * (y \ z)) = L(z,y \ 1,x). [para(345(a,1),319(a,1,1))]. 478 L(x * y,x \ 1,z) = (z / x) \ (z * y). [para(13(a,1),477(a,1,2,2)),flip(a)]. 479 (x / y) * L(z,y \ 1,x) = x * (y \ z). [para(477(a,1),14(a,1,2))]. 480 (x / y) * (y * (x \ z)) = L(z,x \ 1,y). [para(477(a,1),343(a,1)),flip(a)]. 481 L(x * y,x \ 1,z) = (x / z) * (z * y). [para(478(a,2),343(a,1))]. 482 (x / y) * z != x * (y \ u) | L(u,y \ 1,x) = z. [para(479(a,1),19(a,1)),flip(a)]. 483 (x / y) * T(y,z) = x * (y \ T(y,z)). [para(444(a,1),479(a,1,2))]. 484 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(322(a,2),314(a,1))]. 485 x * L(y,z * x,z \ 1) = z \ ((z * x) * y). [para(13(a,1),484(a,1,1))]. 486 L(x \ y,x,z \ 1) = (z \ x) \ (z \ y). [para(314(a,1),323(a,2,2))]. 487 L(x \ (y * z),x,y \ 1) = (y \ x) \ z. [para(315(a,1),323(a,2,2))]. 488 L(x \ y,x,z \ 1) = (x \ z) * (z \ y). [para(486(a,2),353(a,1))]. 489 L(x \ (y * z),x,y \ 1) = (x \ y) * z. [para(487(a,2),353(a,1))]. 490 R(x \ 1,x * y,z) = R(x,y,z) \ 1. [para(326(a,2),328(a,1))]. 491 R(x,y,z \ 1) * (y / z) = (x * y) / z. [para(365(a,2),345(a,1))]. 492 R((x * y) / z,z,x) = x * (y * (z \ 1)). [para(316(a,1),476(a,2,2,2))]. 494 R((x * y) / z,z,x) = x * (y / z). [para(345(a,1),492(a,2,2))]. 495 R(x / y,y,z) = z * ((z \ x) / y). [para(14(a,1),494(a,1,1,1))]. 496 x \ R(y / z,z,x) = (x \ y) / z. [hyper(56,a,495,a(flip))]. 497 R(x,y,z) = z * ((z \ (x * y)) / y). [para(15(a,1),495(a,1,1))]. 498 x * ((x \ T(y,z \ y)) / (y / z)) = R(z,y / z,x). [para(177(a,2),497(a,2,2,1,2)),flip(a)]. 499 R(x,y,(x * y) \ z) = R(x,y,z). [para(497(a,2),475(a,2))]. 500 R(x,y,(x * y) * z) = R(x,y,z). [para(13(a,1),499(a,1,3)),flip(a)]. 501 R(x,x \ y,y \ z) = R(x,x \ y,z). [para(14(a,1),499(a,1,3,1))]. 502 R(x,y,z) \ z = y * ((x * y) \ z). [para(499(a,1),216(a,1,1))]. 503 R(x * y,x,z) \ z = x * ((x * (y * x)) \ z). [para(113(a,1),502(a,2,2,1))]. 504 x \ (y \ ((y * x) * z)) = L(z,y * x,y \ 1). [hyper(56,a,485,a)]. 505 R(x * y,x,z) \ z = x * (x \ (y \ (x \ z))). [para(458(a,1),503(a,2,2))]. 506 L(x,y * z,y \ 1) = L(x,y * z,z). [para(504(a,1),457(a,1))]. 507 R(x * y,x,z) \ z = y \ (x \ z). [para(505(a,2),14(a,1))]. 508 K(T(x,T(y,x)),T(y,x)) = (y * x) \ (x * y). [para(95(a,1),190(a,1,1))]. 509 K(T(x,T(y,x)),T(y,x)) = K(x,y). [para(508(a,2),26(a,2)),flip(a)]. 510 K(T(x,y),T(y,x)) = K(x,y). [para(230(a,1),509(a,1,1))]. 511 K(T(x,y),T(y,T(x,y))) = K(x,y). [para(230(a,2),510(a,1,2))]. 512 K(T(x,y),T(y / (x * x),x)) = K(x,y / (x * x)). [para(281(a,1),510(a,1,1))]. 513 x * (y * T(T(x,y),z)) = T(x,z) * (x * y). [para(217(a,1),226(a,1))]. 514 T(x,y) * (x * z) = x * (T(x,y) * z). [para(96(a,1),513(a,1,2)),flip(a)]. 515 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(14(a,1),514(a,1,2)),flip(a)]. 518 x * (y * T(y \ 1,x)) = T(x,y). [para(258(a,1),295(a,2)),flip(a)]. 520 x * (T(y,x) \ y) = T(x,y). [para(423(a,1),518(a,1,2))]. 521 K(x \ y,x) = T(x,y) \ x. [hyper(17,a,154,a(flip),b,520,a),flip(a)]. 522 T(x,y) != x * z | T(y,x) \ y = z. [para(520(a,1),19(a,1))]. 523 x * ((y * x) \ (x * y)) = T(x,x * y). [para(116(a,1),520(a,1,2,1))]. 524 K(x,K(x \ y,x)) = 1. [para(521(a,2),150(a,1,2))]. 525 K(x,K(y,x)) = 1. [para(13(a,1),524(a,1,2,1))]. 526 T(x,K(y,x)) = x. [hyper(37,a,525,a)]. 528 K(x,y) / y = y \ K(x,y). [para(526(a,1),229(a,1,2))]. 529 T(x,x * y) = x * K(x,y). [para(26(a,2),523(a,1,2)),flip(a)]. 530 T(x,y) = x * K(x,y). [para(529(a,1),221(a,1)),flip(a)]. 531 K(x,y) = T(y,x) \ y. [hyper(522,a,530,a),flip(a)]. 532 K(x \ y,x) = K(y,x). [hyper(163,a,530,a)]. 533 T(x,y) * K(y,x) = x. [hyper(415,a,530,a(flip))]. 534 K(x,y) = x \ T(x,y). [hyper(56,a,530,a(flip)),flip(a)]. 535 K(x,y) = y * T(y \ 1,x). [hyper(17,a,518,a,b,530,a(flip))]. 536 T(x,y) * L(z,K(x,y),x) = x * (K(x,y) * z). [para(530(a,2),67(a,1,1))]. 537 T(x,y) = x / K(y,x). [para(530(a,2),409(a,2)),flip(a)]. 538 K(x,x \ y) = K(x,y). [para(531(a,2),128(a,2))]. 539 K(x,y) = y / T(y,x). [para(531(a,2),132(a,2)),flip(a)]. 540 T(x \ 1,y) = x \ K(y,x). [para(531(a,2),416(a,1,2)),flip(a)]. 541 K(x,y \ 1) = y \ T(y,x). [para(531(a,2),436(a,1))]. 542 K(x * y,x) = K(y,x). [para(13(a,1),532(a,1,1)),flip(a)]. 543 T(x,K(x,y)) = x. [para(532(a,1),158(a,1,2))]. 544 T(x,y) = K(x,y) * x. [para(532(a,1),155(a,2,1))]. 545 T(K(x,y),x) = K(x,y). [hyper(35,a,543,a)]. 546 K(x,y * x) = x \ T(x,y). [para(245(a,1),534(a,2,2))]. 547 K(x,y / T(x,z)) = x \ T(x,y). [para(466(a,1),534(a,2,2))]. 548 K(x,T(x,y) * z) = x \ T(x,z). [para(469(a,1),534(a,2,2))]. 549 (x / y) * T(y,z) = x * K(y,z). [para(534(a,2),483(a,2,2))]. 550 (K(x,y) / y) * z = T(y,x) \ z. [para(537(a,2),343(a,1,1)),flip(a)]. 551 T(x,y) = K(y,x) \ x. [para(539(a,2),54(a,1,1)),flip(a)]. 552 T(K(x,y),z) * K(y,x) = K(K(x,y),z). [hyper(415,a,544,a(flip))]. 553 T(x,y) = K(x,y / x) * x. [para(544(a,1),246(a,1)),flip(a)]. 554 x * (y \ K(z,y)) = x / T(y,z). [para(551(a,2),358(a,1,2)),flip(a)]. 555 K(x,y) * T(K(y,x),z) = K(z,K(x,y)). [para(404(a,1),535(a,2,2,1)),flip(a)]. 556 T(x \ 1,y) = K(y,x) / x. [para(540(a,2),528(a,2)),flip(a)]. 557 T(x,y) = x * K(y,x \ 1). [para(541(a,2),14(a,1,2)),flip(a)]. 558 T(x,y) = K(y,x \ 1) * x. [para(541(a,2),126(a,1,1)),flip(a)]. 559 K(x,y \ 1) = K(y,x). [para(541(a,2),534(a,2)),flip(a)]. 560 K(x \ 1,y) = K(y,x). [para(135(a,1),559(a,1,2)),flip(a)]. 561 K(x / y,z) = K(z,y / x). [para(327(a,1),559(a,1,2)),flip(a)]. 562 K(x \ y,z) = K(z,y \ x). [para(333(a,1),559(a,1,2)),flip(a)]. 563 K(x,y \ (z \ 1)) = K(z * y,x). [para(341(a,1),559(a,1,2))]. 564 K(x,T(y \ 1,z)) = K(T(y,z),x). [para(375(a,1),559(a,1,2))]. 565 K(K(x,y),z) = K(z,K(y,x)). [para(404(a,1),559(a,1,2)),flip(a)]. 566 (x \ y) * K(x,y) = y / x. [para(559(a,1),350(a,1,2))]. 567 K(x * y,x) = K(x,y \ 1). [para(559(a,2),542(a,2))]. 568 T(x \ 1,y \ 1) = x \ K(x,y). [para(560(a,1),540(a,2,2))]. 569 K(x,y * x) = K(x,y). [para(546(a,2),534(a,2)),flip(a)]. 570 K(x,y / x) = K(x,y). [para(16(a,1),569(a,1,2)),flip(a)]. 571 K(x,x \ y) = K(x,T(y,x)). [para(120(a,2),569(a,1,2)),flip(a)]. 572 x * K(y,x) = y * (x / y). [para(570(a,1),106(a,1,2))]. 573 T(x,y \ x) = x * K(y,x). [para(570(a,1),183(a,1,2)),flip(a)]. 575 L(L(x,y,T(y \ 1,z)),K(z,y),y) = x. [para(556(a,2),307(a,1,1,3))]. 576 K(x,y) * K(z,K(y,x)) = T(K(x,y),z). [para(404(a,1),557(a,2,2,2)),flip(a)]. 577 T(x,y) = K(x * y,x \ 1) * x. [para(558(a,1),221(a,1)),flip(a)]. 578 K(x,y \ x) = K(y,x). [para(562(a,1),532(a,1))]. 579 K(x \ y,y) = K(y,x). [para(562(a,2),538(a,1))]. 580 K(x,x / y) = K(y,x). [para(54(a,1),579(a,1,1)),flip(a)]. 581 K(x / y,y) = K(x,y). [para(580(a,1),561(a,2))]. 582 K(x * y,y) = K(x,y). [para(15(a,1),581(a,1,1)),flip(a)]. 583 x \ K(x,y) = y / (y * x). [para(581(a,1),432(a,1,2))]. 584 K(x,x / (x * y)) = K(x,y \ 1). [para(567(a,1),580(a,2))]. 585 K(x,T(y,x)) = K(x,y). [para(571(a,1),538(a,1))]. 586 K(T(x,y),y) = K(x,y). [para(585(a,1),511(a,1))]. 587 T(x,y) * K(y \ x,y) = T(x,y * y). [para(586(a,1),461(a,1,2))]. 588 (x * (y / x)) * K(y,x) = y. [hyper(415,a,572,a)]. 589 (x / y) \ K(x / y,y) = y / T(x,y \ x). [para(177(a,2),583(a,2,2))]. 590 T(x \ K(x,y),y) = (y * x) \ y. [para(583(a,2),232(a,1,1))]. 591 (x * (y / x)) / K(y,x) = y / (K(y,x) * K(y,x)). [para(588(a,1),277(a,1,1)),flip(a)]. 592 K(x,y / T(x,z)) = K(x,y). [para(547(a,2),534(a,2)),flip(a)]. 593 K(x,y * T(x,z)) = K(x,y). [para(15(a,1),592(a,1,2)),flip(a)]. 594 K(x,(y / x) * T(x,z)) = K(x,y). [para(593(a,2),570(a,1))]. 595 K(x,T(x,y) * z) = K(x,z). [para(548(a,2),534(a,2)),flip(a)]. 596 K(x,T(x,y) \ z) = K(x,z). [para(14(a,1),595(a,1,2)),flip(a)]. 597 K(T(x,y),x \ z) = K(T(x,y),z). [para(143(a,1),596(a,1,2,1))]. 598 (x * y) * K(y,z) = x * T(y,z). [para(15(a,1),549(a,1,1)),flip(a)]. 599 (x / y) \ T(x,z) = y * K(x,z). [para(549(a,1),343(a,2))]. 600 T(x,y) \ T(x,z) = K(y,x) * K(x,z). [para(550(a,1),549(a,1))]. 601 x / T(y,z \ y) = x * (y \ K(y,z)). [para(579(a,1),554(a,1,2,2)),flip(a)]. 602 K(T(x,y \ 1),z) = K(z,x \ K(x,y)). [para(568(a,1),564(a,1,2)),flip(a)]. 603 K(x * y,x \ 1) = K(x,y / x). [hyper(18,a,553,a(flip),b,577,a(flip))]. 604 T(x \ K(x,y),y) = x \ 1. [para(590(a,2),325(a,1))]. 606 K(x,y * K(x,z)) = K(x,y). [para(549(a,1),594(a,1,2))]. 607 (x * T(y,z)) * K(z,y) = x * y. [hyper(415,a,598,a)]. 608 (x * y) \ (x * T(y,z)) = K(y,z). [hyper(56,a,598,a)]. 609 (x * T(y,z)) \ (x * y) = K(z,y). [para(598(a,1),408(a,1,1))]. 610 (x \ y) * K(y,z) = x \ T(y,z). [para(53(a,1),599(a,1,1)),flip(a)]. 611 (x / T(y,z)) * y = x * K(z,y). [para(16(a,1),607(a,1,1)),flip(a)]. 612 L(K(x,y),z * T(y,x),u) = (u * (z * T(y,x))) \ (u * (z * y)). [para(607(a,1),28(a,2,2,2))]. 613 x \ (y * T(y \ x,z)) = K(y \ x,z). [para(14(a,1),608(a,1,1))]. 614 ((x * y) * T(L(z,y,x),u)) \ (x * (y * z)) = K(u,L(z,y,x)). [para(67(a,1),609(a,1,2))]. 615 (x \ T(y,z)) * K(z,y) = x \ y. [hyper(415,a,610,a)]. 616 x \ T(y,z \ y) = (x \ y) * K(z,y). [para(578(a,1),610(a,1,2)),flip(a)]. 617 (x * K(y,z)) / z = x / T(z,y). [hyper(58,a,611,a)]. 618 T(x,y * K(z,x)) = T(x,y). [para(611(a,1),465(a,1,2))]. 619 K(x * K(y,z),z) = T(z,x) \ z. [para(618(a,1),531(a,2,1))]. 620 (T(x,y) \ z) * (z \ x) = K(y,x). [hyper(387,a,615,a)]. 621 (x * K(y,z / y)) / (z / y) = x / (y \ z). [para(80(a,1),617(a,2,2))]. 622 K(x * K(y,z),z) = K(x,z). [para(619(a,2),531(a,2)),flip(a)]. 623 K(x / K(y,z),z) = K(x,z). [para(16(a,1),622(a,1,1)),flip(a)]. 624 K(T(x,K(y,z)),y) = K(K(z,y) * x,y). [para(410(a,1),623(a,1,1))]. 625 K(x,K(y,x) / z) = K(z,x). [para(623(a,1),561(a,1)),flip(a)]. 626 K(x,K(x,y) / z) = K(z,x). [para(560(a,1),625(a,1,2,1))]. 627 K(T(x,K(y,z)),y) = K(y,x \ K(y,z)). [para(229(a,1),626(a,1,2)),flip(a)]. 628 K(x,K(x,y) * z) = K(z \ 1,x). [para(334(a,1),626(a,1,2))]. 629 ((x \ y) * (T(y,z) \ x)) \ K(z,y) = K(T(y,z) \ x,x \ y). [para(620(a,1),26(a,2,2)),flip(a)]. 630 K(T(x,y) \ z,z \ x) = K(K(y,x),z \ x). [para(620(a,1),582(a,1,1)),flip(a)]. 631 K(x,K(x,y) * z) = K(x,z). [para(628(a,2),560(a,1))]. 632 K(x,T(y,K(x,z))) = K(x,y * K(x,z)). [para(78(a,1),631(a,1,2)),flip(a)]. 633 T(x,K(x,y) * z) = x * K(x,z). [para(631(a,1),530(a,2,2))]. 634 T(x,K(x,y) * z) = T(x,z). [para(633(a,2),530(a,2)),flip(a)]. 635 T(x,K(y,x) * z) = T(x,z). [para(407(a,1),634(a,1,2)),flip(a)]. 636 K(K(x,y) * z,y) = T(y,z) \ y. [para(635(a,1),531(a,2,1))]. 637 K(K(x,y) * z,y) = K(z,y). [para(636(a,2),531(a,2)),flip(a)]. 638 (K(x,y) * z) * K(z,y) = T(K(x,y) * z,y). [para(637(a,1),530(a,2,2)),flip(a)]. 639 T(K(x,y),z) * K(y,x) = K(z,K(y,x)). [para(552(a,2),565(a,1))]. 640 T(x,y) * K(x,y) = T(x,y * y). [para(532(a,1),587(a,1,2))]. 641 x \ (T(y,z) * (y \ x)) = K((y \ x) \ x,z). [para(172(a,1),613(a,1,2))]. 642 K(T(x,K(y,z)),y) = K(x,y). [para(624(a,2),637(a,1))]. 644 K(x,y \ K(x,z)) = K(y,x). [para(627(a,1),642(a,1))]. 645 K(x,y \ K(z,x)) = K(y,x). [para(559(a,1),644(a,1,2,2))]. 647 K(x,T(y,K(x,z))) = K(x,y). [para(632(a,2),606(a,1))]. 648 T(T(x,K(y,z)),y) * K(y,x) = T(x,K(y,z)). [para(647(a,1),533(a,1,2))]. 650 x / T(y,x \ y) = (y / x) \ K(y,x). [para(581(a,1),589(a,1,2)),flip(a)]. 651 x / T(y,x \ y) = (x / y) * K(y,x). [para(650(a,2),343(a,1))]. 652 (x / y) * K(y,x) = x * (y \ K(y,x)). [para(651(a,1),601(a,1))]. 653 (x * K(y,z)) / (z / y) = x / (y \ z). [para(570(a,1),621(a,1,1,2))]. 654 (x * K(y,z)) * (y / z) = x / (y \ z). [para(653(a,1),357(a,1)),flip(a)]. 655 (x * K(y,z)) * (y / z) = x * (z \ y). [para(654(a,2),358(a,1))]. 656 T(K(x,y) * z,y) = K(x,y) * T(z,y). [para(638(a,1),598(a,1))]. 657 x \ (T(y,z) * (y \ x)) = K(T(y,x),z). [para(228(a,2),641(a,2,1))]. 658 T(x,y) * (x \ z) = z * K(T(x,z),y). [para(657(a,1),14(a,1,2)),flip(a)]. 659 T(x * y,y) / (x * y) = K(x,T(y,x \ y)). [para(193(a,1),271(a,1,1))]. 660 (x * y) \ T(x * y,y) = K(x,T(y,x \ y)). [para(659(a,1),131(a,1)),flip(a)]. 661 K(x \ (y * x),x) = K(y,T(x,y \ x)). [para(660(a,1),127(a,2))]. 662 K(x,T(y,x \ y)) = K(T(x,y),y). [para(32(a,2),661(a,1,1)),flip(a)]. 663 K(T(x,y),y) = K(x,x * (y / x)). [para(177(a,1),662(a,1,2)),flip(a)]. 664 K(x * (y / x),x \ 1) = K(y,y * ((x \ 1) / y)). [para(372(a,1),663(a,1,1))]. 665 T(x,(x / y) * (x / y)) = T(y,x) * (x / y). [para(283(a,1),248(a,1))]. 666 T(x,x * (y \ (x / y))) = T(y,x) * (x / y). [para(402(a,1),665(a,1,2))]. 667 T(x,y \ (x / y)) = T(y,x) * (x / y). [para(666(a,1),221(a,1)),flip(a)]. 668 L(x,y \ 1,T(y,z)) = x. [hyper(195,a,456,a)]. 669 L(x,y,T(y \ 1,z)) = x. [para(135(a,1),668(a,1,2))]. 670 L(x,K(y,z),z) = x. [para(669(a,1),575(a,1,1))]. 671 L(x,K(y,z),y) = x. [para(560(a,1),670(a,1,2))]. 673 x * (K(x,y) * z) = T(x,y) * z. [para(671(a,1),536(a,1,2)),flip(a)]. 674 x \ (T(x,y) * z) = K(x,y) * z. [hyper(56,a,673,a)]. 675 T(x,y) * (x \ z) = K(x,y) * z. [hyper(17,a,515,a,b,673,a),flip(a)]. 676 K(x,y) * (x * z) = T(x,y) * z. [hyper(17,a,514,a(flip),b,673,a)]. 677 T(x,y) * (K(y,x) * z) = x * z. [para(407(a,1),673(a,1,2)),flip(a)]. 678 T(x,y \ x) * z = x * (K(y,x) * z). [para(578(a,1),673(a,1,2,1)),flip(a)]. 679 K(x,y) * (T(x,y) \ z) = x \ z. [para(14(a,1),674(a,1,2)),flip(a)]. 680 x \ T(x,y * y) = K(x,y) * K(x,y). [para(640(a,1),674(a,1,2))]. 681 T(x,y) / T(x,z) = K(x,y) * K(z,x). [para(675(a,1),554(a,1)),flip(a)]. 682 x * K(T(y,x),z) = K(y,z) * x. [para(675(a,1),658(a,1)),flip(a)]. 683 K(x,y) * (T(y,x) * z) = y * z. [hyper(413,a,676,a)]. 684 T(x,y) * (T(y,x) * z) = x * (y * z). [para(676(a,1),677(a,1,2))]. 685 K(x,y) * (y \ z) = T(y,x) \ z. [hyper(413,a,679,a)]. 686 K(T(x,y),z) = T(K(x,z),y). [hyper(94,a,682,a),flip(a)]. 687 K(T(x,y),z) \ 1 = y \ (K(x,z) \ y). [para(686(a,2),337(a,1,1))]. 688 x * (T(x,y) \ z) = K(y,x) * z. [para(14(a,1),683(a,1,2)),flip(a)]. 689 K(x,y / x) * ((x \ y) * z) = (y / x) * z. [para(80(a,1),683(a,1,2,1))]. 690 K(x,y \ (x \ 1)) * ((x \ (y \ 1)) * z) = (y \ (x \ 1)) * z. [para(398(a,1),683(a,1,2,1))]. 691 K(x,y \ K(y,x)) * ((y \ 1) * z) = (y \ K(y,x)) * z. [para(604(a,1),683(a,1,2,1))]. 692 K(x,y) * (y \ (z * T(y,x))) = T(z,T(y,x)). [para(685(a,2),32(a,2)),flip(a)]. 693 x \ (K(y,x) * z) = T(x,y) \ z. [hyper(56,a,688,a)]. 694 T(K(x,y) * z,y) = (T(y,x) \ z) * y. [para(688(a,1),116(a,1,1))]. 695 (K(x,y) * z) \ y = z \ T(y,x). [para(688(a,1),355(a,1,1))]. 696 x / (y \ T(x,z)) = K(z,x) * y. [para(688(a,1),358(a,2))]. 697 (x \ K(y,z)) * y = x \ T(y,z). [para(695(a,1),412(a,1)),flip(a)]. 698 K(x,y) * (T(y,x) / z) = y / z. [para(54(a,1),696(a,1,2)),flip(a)]. 699 (x \ T(y,z)) / y = x \ K(y,z). [hyper(58,a,697,a)]. 700 K(x,y) * (x / z) = T(x,y) / z. [hyper(413,a,698,a)]. 701 (x / y) / (T(x,z) / y) = K(z,x). [hyper(58,a,698,a)]. 702 K(x \ 1,x \ y) * ((y / x) / z) = (x \ y) / z. [para(347(a,1),698(a,1,2,1))]. 703 (T(x,y) / z) \ K(x,y) = z / x. [para(54(a,1),699(a,1,1)),flip(a)]. 704 T(x,y \ x) / z = K(y,x) * (x / z). [para(578(a,1),700(a,1,1)),flip(a)]. 705 (x / y) * (y / T(x,z)) = K(z,x). [para(701(a,1),357(a,1)),flip(a)]. 706 (x / T(y,z)) * K(y,z) = x / y. [para(703(a,1),343(a,1)),flip(a)]. 707 (x \ y) * (x / T(T(y,x),z)) = K(z,T(y,x)). [para(123(a,1),705(a,1,1))]. 708 ((x \ (y \ 1)) / z) * (z / (y \ (x \ 1))) = K(y,x \ (y \ 1)). [para(398(a,1),705(a,1,2,2))]. 709 (x * T(y,z)) / y = x * K(y,z). [para(15(a,1),706(a,1,1)),flip(a)]. 710 (x / (y \ z)) * K(z / y,y) = x / (z / y). [para(80(a,1),706(a,1,1,2))]. 711 x \ (y * T(x,z)) = T(y * K(x,z),x). [para(709(a,1),80(a,1,1)),flip(a)]. 712 K(x,y) * K(x,y) = K(x,y * y). [para(680(a,1),534(a,2)),flip(a)]. 713 T(x,y) \ T(x,z) = K(x,z) * K(y,x). [para(681(a,1),133(a,1)),flip(a)]. 714 K(T(x,y),z) \ 1 = y \ (K(z,x) * y). [para(406(a,1),687(a,2,2))]. 715 x * (T(y,x \ y) / z) = T(x,y) * (y / z). [para(704(a,2),673(a,1,2))]. 716 K(T(x,y),z) \ 1 = T(K(z,x),y). [para(714(a,2),32(a,2)),flip(a)]. 717 K(x,T(y,z)) = T(K(x,y),z). [para(716(a,1),404(a,1)),flip(a)]. 718 K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). [para(717(a,2),555(a,1,2))]. 719 K(x,y) * K(z,K(y,x)) = K(x,T(y,z)). [para(717(a,2),576(a,2))]. 720 K(x,T(y,z)) * K(y,x) = K(z,K(y,x)). [para(717(a,2),639(a,1,1))]. 721 K(T(x,y),z) = K(x,T(z,y)). [para(717(a,2),686(a,2))]. 723 K(x / y,T(z,x)) = K(y \ x,z). [para(232(a,1),721(a,1,1)),flip(a)]. 724 K(x,T(y,z \ 1)) = K(y,x \ K(x,z)). [para(721(a,1),602(a,1))]. 725 K(x / y,T(z,x)) = K(z,x \ y). [para(723(a,2),562(a,1))]. 726 K(x,y) * ((x \ y) * z) = (y / x) * z. [para(570(a,1),689(a,1,1))]. 727 K(x,y) * (y / x) = (y / x) * K(x,y). [para(566(a,1),726(a,1,2))]. 728 K(x,y) * (y / x) = y * (x \ K(x,y)). [para(727(a,2),652(a,1))]. 729 T(x,y \ x) / y = x * (y \ K(y,x)). [para(728(a,1),704(a,2))]. 730 K(x,y) * T(z * K(y,x),y) = T(z,T(y,x)). [para(711(a,1),692(a,1,2))]. 731 (x \ y) * (T(y,z) \ x) = K(z,T(y,x)). [para(234(a,1),707(a,1,2))]. 732 (x * (y \ z)) * K(y / z,z) = x / (y / z). [para(358(a,1),710(a,1,1))]. 733 x * (T(y,x \ y) / x) = T(y,x \ (y / x)). [para(715(a,2),667(a,2)),flip(a)]. 734 T(K(x,y) * (z * K(y,x)),y) = T(z,T(y,x)). [para(730(a,1),656(a,2))]. 735 (x * (y \ z)) * K(y,z) = x / (y / z). [para(581(a,1),732(a,1,2))]. 736 (x * (y \ z)) * K(y,z) = x * (z / y). [para(735(a,2),357(a,1))]. 737 x \ ((y * (x \ z)) * T(x,z)) = T(y * (z / x),x). [para(736(a,1),711(a,2,1))]. 738 x * (y * (x \ K(x,y))) = T(y,x \ (y / x)). [para(729(a,1),733(a,1,2))]. 739 T(T(x,K(y,z)),y) = T(x,T(y,z)). [para(411(a,1),734(a,1,1))]. 740 T(T(x,y),K(y,z)) = T(x,T(y,z)). [para(739(a,1),38(a,1)),flip(a)]. 741 T(x,T(y,z)) * K(y,x) = T(x,K(y,z)). [para(739(a,1),648(a,1,1))]. 742 T(x,y) \ T(x,T(y,z)) = K(T(x,y),K(y,z)). [para(740(a,1),534(a,2,2)),flip(a)]. 743 K(x,y) * K(y,T(x,z)) = K(T(y,x),K(x,z)). [para(742(a,1),600(a,1)),flip(a)]. 744 K(T(x,y),K(y,z)) = K(z,K(y,x)). [para(743(a,1),718(a,1))]. 745 K(x,T(K(y,z),y)) = K(z,K(y,x)). [para(744(a,1),721(a,1)),flip(a)]. 746 K(x,K(y,z)) = K(z,K(y,x)). [para(545(a,1),745(a,1,2))]. 747 K(K(x,y),z) = K(x,K(y,z)). [para(746(a,1),565(a,2))]. 748 K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). [para(746(a,1),719(a,1,2))]. 749 K(x,y) * K(x,K(z,y)) = K(x,T(y,z \ 1)). [para(559(a,1),748(a,1,2,2))]. 750 K(T(x,y),x \ (y / x)) = K(x,y / (x * x)). [para(279(a,1),512(a,1,2))]. 751 (x * (y / x)) / K(y,x) = y / K(y,x * x). [para(712(a,1),591(a,2,2))]. 752 (x * (y / x)) / K(y,x) = y * K(x * x,y). [para(751(a,2),409(a,1))]. 753 (x * (y / x)) / K(y,x) = T(y,(x * x) \ y). [para(752(a,2),573(a,2)),flip(a)]. 754 (x * (y / x)) / K(y,x) = T(y,x \ (x \ y)). [para(170(a,1),753(a,2,2))]. 755 (x * (y / x)) * K(x,y) = T(y,x \ (x \ y)). [para(754(a,1),409(a,1)),flip(a)]. 756 K(x,(y / x) / x) = K(y,y * ((x \ 1) / y)). [para(664(a,1),603(a,1)),flip(a)]. 757 K(x,y / (x * x)) = K(y,y * ((x \ 1) / y)). [para(278(a,1),756(a,1,2))]. 758 K(x,y / (x * x)) = K(y,y * (x \ (y \ 1))). [para(367(a,1),757(a,2,2,2))]. 759 K(x,y / (x * x)) = K(y,y / (y * x)). [para(379(a,1),758(a,2,2))]. 760 K(x,y / (x * x)) = K(y,x \ 1). [para(759(a,2),584(a,1))]. 761 K(T(x,y),x \ (y / x)) = K(y,x \ 1). [para(760(a,1),750(a,2))]. 762 K(T(x,y),y / x) = K(y,x \ 1). [para(761(a,1),597(a,1)),flip(a)]. 763 K(T(x,y),y / x) = K(x,y). [para(762(a,2),559(a,1))]. 764 ((x / y) * T(y,x)) * K(y,x) = T(y,x) * (x / y). [para(763(a,1),61(a,1,2))]. 765 K(x,y \ x) * ((y / x) / z) = (x \ y) / z. [para(428(a,1),702(a,1,1))]. 766 K(x,y) * ((x / y) / z) = (y \ x) / z. [para(578(a,1),765(a,1,1))]. 767 (x * (y / x)) * K(x,y) = T(x,y) * (y / x). [para(247(a,1),764(a,1,1))]. 768 (x * (y / x)) * K(x,y) = T(y,x \ (y / x)). [para(767(a,2),667(a,2)),flip(a)]. 769 T(x,y \ (x / y)) = T(x,y \ (y \ x)). [para(768(a,1),755(a,1))]. 770 x * (y * (x \ K(x,y))) = T(y,x \ (x \ y)). [para(769(a,1),738(a,2))]. 771 (x * (x * y)) \ (x * (x * (y * z))) = L(z,y,x * x). [para(165(a,1),167(a,1,2))]. 772 (x * (y \ x)) * z = x * (y \ (x * z)). [para(484(a,1),424(a,1,2)),flip(a)]. 773 x * (((x \ y) * K(z,y)) / (y / z)) = R(z,y / z,x). [para(616(a,1),498(a,1,2,1))]. 774 x * (((x \ y) * K(z,y)) * (z / y)) = R(z,y / z,x). [para(357(a,1),773(a,1,2))]. 775 R(x,y / x,z) = z * ((z \ y) * (y \ x)). [para(655(a,1),774(a,1,2)),flip(a)]. 776 T(T(x,y \ (y \ x)),z) = T(y * (y * (x / (y * y))),z). [para(170(a,1),293(a,1,1,2))]. 778 K(x,y) * ((x \ 1) * z) = (x \ K(x,y)) * z. [para(645(a,1),691(a,1,1))]. 779 (x \ K(x,y)) * z = K(x,y) * (x \ z). [para(314(a,1),778(a,1,2)),flip(a)]. 781 a(x,y,x * z) \ 1 = a(x * y,x,z). [para(84(a,1),339(a,1)),flip(a)]. 782 (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). [para(684(a,1),253(a,1,2))]. 783 L(x,T(y,z),T(z,y)) = L(x,y,z). [para(782(a,1),28(a,2)),flip(a)]. 784 L(x,y * z,T(z,z * y)) = L(x,z * y,z). [para(116(a,1),783(a,1,2))]. 785 L(L(x,T(y,z) * T(z,y),T(z,y)),z,y) = x. [para(783(a,1),304(a,1))]. 786 L(x,y * z,T(z,y)) = L(x,z * y,z). [para(221(a,1),784(a,1,3))]. 787 L(L(x,y * z,T(z,y)),z,y) = x. [para(250(a,1),785(a,1,1,2))]. 788 L(L(x,y * z,y),y,z) = x. [para(786(a,1),787(a,1,1))]. 789 L(L(x,y,z),z,z \ y) = x. [para(14(a,1),788(a,1,1,2))]. 790 L(x,y * z,z) = L(x,z * y,z). [para(788(a,1),306(a,1,1))]. 791 L(L(x,y,y \ z),z,y) = x. [para(789(a,1),45(a,1)),flip(a)]. 792 L(x,y * z,z) = L(x,y,y \ z). [para(304(a,1),789(a,1,1)),flip(a)]. 793 L(x,(y \ z) * y,y) = L(x,z,y). [para(789(a,1),306(a,1,1))]. 794 L(x,y,y \ (z * y)) = L(x,y,z). [para(306(a,1),789(a,1,1))]. 795 L(x,y,z / y) = L(x,y,y \ z). [para(307(a,1),789(a,1,1)),flip(a)]. 796 L(x,T(y,z),z) = L(x,y,z). [para(789(a,1),368(a,1,1))]. 797 L(x,y,y \ (z \ y)) = L(x,y,z \ 1). [para(371(a,1),789(a,1,1))]. 798 L(x,y * z,y) = L(x,z,z \ y). [para(788(a,1),789(a,1,1)),flip(a)]. 799 L(((x \ y) * x) \ z,y,x) = x \ ((x \ y) \ z). [para(203(a,1),791(a,1,1))]. 800 L(x,y / z,z) = L(x,z \ y,z). [para(80(a,1),796(a,1,2)),flip(a)]. 801 L(x,y * (z / y),z / y) = L(x,z,z / y). [para(121(a,1),796(a,1,2))]. 802 L(x,y / z,y) = L(x,z \ y,y). [para(232(a,1),796(a,1,2)),flip(a)]. 803 L(x,y * (z / y),y \ 1) = L(x,z,y \ 1). [para(372(a,1),796(a,1,2))]. 804 (x * y) * L(z,x,y) = y * (T(x,y) * z). [para(796(a,1),199(a,1,2))]. 805 L(T(x,y) \ z,x,y) = (x * y) \ (y * z). [para(796(a,1),205(a,1))]. 806 L(x,y * z,y \ 1) = L(x,y,y \ z). [para(792(a,1),506(a,2))]. 807 L(x,y,T(z,y)) = L(x,y,z). [para(32(a,2),794(a,1,3))]. 808 L(x,y,y / z) = L(x,y,z \ y). [para(232(a,1),807(a,1,3)),flip(a)]. 809 x \ ((x / y) * (y * z)) = L(z,y,y \ x). [para(795(a,1),69(a,2))]. 810 x * L(y,z,z \ x) = (x / z) * (z * y). [para(795(a,1),194(a,1,2))]. 811 x * L(y,z,z \ x) = z \ ((z * x) * y). [para(806(a,1),485(a,1,2))]. 812 x \ ((x * y) * z) = (y / x) * (x * z). [para(811(a,1),810(a,1))]. 813 ((x \ y) / T(z,y \ x)) * (T(z,y \ x) * u) = T(z,y \ x) \ (((x \ y) * z) * u). [para(396(a,1),812(a,1,2,1)),flip(a)]. 814 L(x,y * (z / y),z / y) = L(x,z,y \ z). [para(801(a,2),808(a,1))]. 815 L(x,y * (z / y),z / y) = L(x,z,y \ 1). [para(803(a,1),506(a,1)),flip(a)]. 816 L(x,y,z \ 1) = L(x,y,z \ y). [para(815(a,1),814(a,1))]. 817 L(x,y,(z * y) \ 1) = L(x,y,y \ (z \ y)). [para(374(a,1),816(a,2,3))]. 818 L(x,y,y \ (z \ 1)) = L(x,y,y \ (z \ y)). [para(341(a,1),817(a,1,3))]. 819 L(x,y,y \ (z \ 1)) = L(x,y,z \ 1). [para(818(a,2),797(a,1))]. 820 L(L(x,y \ 1,z),z,y \ 1) = x. [para(819(a,1),789(a,1))]. 821 L(x,y \ 1,z) = L(x,y \ z,z). [para(820(a,1),371(a,1,1)),flip(a)]. 822 L(x,(y \ z) \ u,u) = L(x,z \ y,u). [para(333(a,1),821(a,1,2)),flip(a)]. 823 L(x,(y \ z) * u,u) = L(x,y \ z,u). [para(353(a,1),822(a,1,2))]. 825 L(x,y \ z,z) = L(x,y \ z,y). [para(823(a,1),403(a,2)),flip(a)]. 826 L(x,y \ z,y) = L(x,z,y). [para(823(a,1),793(a,1))]. 827 L(x,y * z,y) = L(x,z,y). [para(13(a,1),826(a,1,2)),flip(a)]. 828 L((x \ y) * z,x,y) = x \ (y * z). [para(826(a,1),385(a,1))]. 829 L(L(x,y,z),z,y) = x. [para(827(a,1),788(a,1,1))]. 830 L(x,y * z,z) = L(x,y,z). [para(827(a,1),790(a,2))]. 831 L(x,y,y \ z) = L(x,y,z). [para(827(a,1),798(a,1)),flip(a)]. 832 L(L(L(x,y,z),u,w),z,y) = L(x,u,w). [para(829(a,1),45(a,1,1)),flip(a)]. 833 x * (y * L(z,x,y)) = (x * y) * z. [para(829(a,1),67(a,1,2)),flip(a)]. 834 L((x * y) \ z,x,y) = y \ (x \ z). [para(203(a,1),829(a,1,1))]. 835 L(x,y,z * y) = L(x,y,z). [para(829(a,1),304(a,1,1)),flip(a)]. 836 L(x,y,z / y) = L(x,y,z). [para(829(a,1),305(a,1,1))]. 837 L(x,y,y * z) = L(x,y,z). [para(829(a,1),788(a,1,1)),flip(a)]. 838 L(x,y,z) = z \ ((z / y) * (y * x)). [para(831(a,1),809(a,2)),flip(a)]. 839 ((x * y) * x) \ ((x * y) * z) = L(x \ z,x,y). [para(837(a,1),68(a,1)),flip(a)]. 840 L(x,y \ z,z) = L(x,z,y). [para(825(a,2),826(a,1))]. 841 L(L(x,y,z \ 1),y,z) = x. [para(840(a,1),371(a,1))]. 842 L(x,y / z,y) = L(x,y,z). [para(840(a,1),802(a,2))]. 843 L(x,y \ 1,z) = L(x,z,y). [para(840(a,1),821(a,2))]. 844 L(x,y,z \ 1) = L(x,z,y). [para(841(a,1),829(a,1,1)),flip(a)]. 845 L(x,y,z \ y) = L(x,z,y). [para(53(a,1),842(a,1,2)),flip(a)]. 846 L(x,y \ (z \ 1),u) = L(x,u,z * y). [para(341(a,1),843(a,1,2))]. 847 L(x,K(y,z),u) = L(x,u,K(z,y)). [para(404(a,1),843(a,1,2))]. 848 (x / y) * L(z,x,y) = x * (y \ z). [para(843(a,1),479(a,1,2))]. 849 L(x,y,z) = (z / y) * (y * (z \ x)). [para(843(a,1),480(a,2)),flip(a)]. 850 L(x * y,z,x) = (x / z) * (z * y). [para(843(a,1),481(a,1))]. 851 (x \ y) * L(z,x,y) = x \ (y * z). [para(844(a,1),484(a,1,2))]. 852 L(x \ y,z,x) = (x \ z) * (z \ y). [para(844(a,1),488(a,1))]. 853 L(x \ (y * z),y,x) = (x \ y) * z. [para(844(a,1),489(a,1))]. 854 L(L((x \ y) * z,u,w),x,y) = L(x \ (y * z),u,w). [para(828(a,1),45(a,1,1)),flip(a)]. 855 (x / y) * L(y,z,u) = x * (y \ L(y,z,u)). [para(141(a,1),848(a,1,2))]. 856 R(x,y,z) \ z = (y / (x * y)) * L(z,y,x * y). [para(848(a,2),502(a,2))]. 857 L(x \ y,z,x) = x \ L(y,z,x). [para(849(a,2),838(a,2,2))]. 858 x \ L(x * y,z,x) = L(y,z,x). [para(13(a,1),857(a,1,1)),flip(a)]. 859 L(x \ L(x,y,z),u,x) = x \ L(x,y,z). [para(141(a,1),857(a,2,2))]. 860 L((x * y) \ z,x,x * y) = (x * y) \ L(z,x,y). [para(837(a,1),857(a,2,2))]. 861 L(x * y,z,x) = x * L(y,z,x). [para(858(a,1),14(a,1,2)),flip(a)]. 862 x * L(y * z,x,y) = (x * y) * z. [para(861(a,2),833(a,1,2))]. 863 L(x * ((y * x) \ z),y,x) = x * (x \ (y \ z)). [para(834(a,1),861(a,2,2))]. 864 L((x * y) * z,y,x * y) = x * (y * z). [para(15(a,1),850(a,2,1))]. 865 L(x * y,y \ z,x) = (x / (y \ z)) * T(z,y). [para(120(a,2),850(a,2,2))]. 866 L(x \ (y * z),z,x) = (x \ z) * T(y,z). [para(32(a,2),852(a,2,2))]. 867 L(x \ y,z * z,x) = (x \ (z * z)) * (z \ (z \ y)). [para(170(a,1),852(a,2,2))]. 868 L(x \ L(x,y,z),x,u) = x \ L(x,y,z). [para(859(a,1),304(a,1,1))]. 869 L((x * y) * z,y,x) = x * (y * z). [para(864(a,1),835(a,1)),flip(a)]. 870 L(x,y,z) = z * (y * ((z * y) \ x)). [para(14(a,1),869(a,1,1))]. 871 L((x * y) * z,x * y,x) = x * (y * z). [para(869(a,1),827(a,2))]. 872 L(x * (y * z),x,y) = (x * y) * z. [para(869(a,1),829(a,1,1))]. 873 x \ (y * (z * (((x \ y) * z) \ u))) = L(L(u,z,x \ y),x,y). [para(870(a,2),828(a,1,1)),flip(a)]. 874 L(T(x,y) \ z,x,y) = y \ ((y \ x) \ z). [para(120(a,2),799(a,1,1,1))]. 875 (x * y) \ (y * z) = y \ ((y \ x) \ z). [para(874(a,1),805(a,1)),flip(a)]. 876 (x * y) \ (y * z) = y \ ((x \ y) * z). [para(353(a,1),875(a,2,2))]. 877 (x * (y * x)) \ ((x * y) * z) = L(x \ z,x,y). [para(113(a,1),839(a,1,1))]. 878 L(x * ((y * x) \ z),y,x) = y \ z. [para(863(a,2),14(a,1))]. 880 x \ (y \ (x \ ((x * y) * z))) = L(x \ z,x,y). [para(877(a,1),458(a,1)),flip(a)]. 881 x \ (y \ ((y / x) * (x * z))) = L(x \ z,x,y). [para(812(a,1),880(a,1,2,2))]. 882 L(x \ y,x,z) = x \ L(y,x,z). [para(838(a,2),881(a,1,2)),flip(a)]. 883 x \ L(x * y,x,z) = L(y,x,z). [para(13(a,1),882(a,1,1)),flip(a)]. 884 x * L(x \ y,x,z) = L(y,x,z). [para(882(a,2),14(a,1,2))]. 885 L(x * y,x,z) = x * L(y,x,z). [para(883(a,1),14(a,1,2)),flip(a)]. 886 T(L(x * y,x,z),x) = L(y,x,z) * x. [para(883(a,1),120(a,2,1))]. 887 (x * y) * (y \ (x \ z)) = L(z,x * y,y). [para(370(a,1),884(a,1,2))]. 888 L(x / y,y,z) = L(x,y,z) / y. [para(884(a,1),471(a,1,1)),flip(a)]. 889 L(x * y,x,z) != x * u | L(y,x,z) = u. [para(885(a,2),19(a,1))]. 890 (x * L(y * z,y,x)) \ (x * (y * z)) = a(x,y,L(z,y,x)). [para(885(a,2),197(a,1,1,2))]. 891 L(x / (y \ 1),y \ 1,z) = L(x,z,y) / (y \ 1). [para(843(a,1),888(a,2,1))]. 892 L(T(x * y,x),x,z) = L(y,x,z) * x. [para(886(a,1),40(a,2))]. 893 L(x * y,y,z) = L(x,y,z) * y. [para(116(a,1),892(a,1,1))]. 894 x * ((x \ y) * (y \ z)) = L(z,y * x,x). [para(887(a,1),261(a,1)),flip(a)]. 895 L(x,y,z) = z * ((z \ y) * (y \ x)). [para(894(a,2),830(a,1)),flip(a)]. 896 L(x,y,z) = R(x,x \ y,z). [para(895(a,2),459(a,2)),flip(a)]. 897 L(x,y,z) = R(x,y / x,z). [para(895(a,2),775(a,2)),flip(a)]. 898 R(x,T(y,x),z) = L(x,y * x,z). [para(32(a,2),896(a,2,2)),flip(a)]. 900 R(x,y,z) = L(x,y * x,z). [para(15(a,1),897(a,2,2)),flip(a)]. 901 R(x \ y,x,z) = L(x \ y,y,z). [para(53(a,1),897(a,2,2)),flip(a)]. 902 R(x,y \ (z \ 1),u) = L(x,(z * y) \ x,u). [para(378(a,1),900(a,2,2))]. 903 R(x,T(y,x),z) = R(x,y,z). [para(898(a,2),900(a,2)),flip(a)]. 904 R(x \ 1,y * x,z) = R(x \ 1,x * y,z). [para(359(a,1),903(a,1,2)),flip(a)]. 905 R(x \ 1,y * x,z) = L((y * x) \ y,y,z). [para(325(a,1),901(a,1,1))]. 906 R(x,x \ (y \ 1),z) = L(x,x \ (y \ x),z). [para(374(a,1),902(a,2,2))]. 907 R(x \ 1,y * x,z) = R(x,y,z) \ 1. [para(904(a,2),490(a,1))]. 908 R(x,y / x,z) \ 1 = R(x \ 1,y,z). [para(16(a,1),907(a,1,2)),flip(a)]. 909 R(x \ 1,y,z) = L(x,y,z) \ 1. [para(897(a,2),908(a,1,1)),flip(a)]. 910 R(x \ 1,y,z) \ u = L(x,y,z) * u. [para(909(a,2),317(a,1,1))]. 911 L((x * y) \ x,x,z) = R(y,x,z) \ 1. [para(905(a,1),907(a,1))]. 912 L(x \ 1,y,z) = R(x,y,z) \ 1. [para(325(a,1),911(a,1,1))]. 914 L(x,x \ (y \ x),z) = L(x,y \ 1,z). [para(906(a,1),896(a,2)),flip(a)]. 915 L(x,x \ (y \ x),z) = L(x,z,y). [para(914(a,2),843(a,1))]. 916 R(x,y,z) \ z = (x \ 1) * L(z,y,x * y). [para(316(a,1),856(a,2,1))]. 918 R(x,y,z) \ z = (x \ 1) * L(z,y,x). [para(835(a,1),916(a,2,2))]. 919 R(x,y,z) \ z = x \ L(z,y,x). [para(918(a,2),314(a,1))]. 920 L(x \ y,z,x) = R(x,z,y) \ y. [para(919(a,2),857(a,2))]. 921 L(x \ y,z,x) = (R(x,z,y) \ 1) * y. [para(920(a,2),314(a,2)),flip(a)]. 922 L((x \ 1) \ y,x,z) = R(x \ 1,z,y) \ y. [para(920(a,1),844(a,1)),flip(a)]. 923 L(x \ y,z,x) = L(x \ 1,z,y) * y. [para(912(a,2),921(a,2,1))]. 924 L((x \ 1) \ y,x,z) = L(x,z,y) * y. [para(922(a,2),910(a,1))]. 925 L((x * y) \ z,x,y) = (x * y) \ L(z,x,y). [para(860(a,1),837(a,1)),flip(a)]. 926 (x * y) \ L(z,x,y) = y \ (x \ z). [para(925(a,1),834(a,1))]. 927 L(x / (y \ 1),y \ 1,z) = L(x,z,y) * y. [para(891(a,2),334(a,1))]. 928 L(x * y,y \ 1,z) = L(x,z,y) * y. [para(334(a,1),927(a,1,1))]. 929 L(x * y,z,y) = L(x,z,y) * y. [para(928(a,1),843(a,1)),flip(a)]. 930 L(x \ y,z,x) = L((x \ 1) * y,z,y). [para(929(a,2),923(a,2))]. 931 L((x \ 1) \ y,x,z) = L(x * y,z,y). [para(929(a,2),924(a,2))]. 932 L(x \ y,z,y) = L(x \ y,z,x). [para(314(a,1),930(a,2,1)),flip(a)]. 933 L(L(x \ y,z,y),x,z) = x \ y. [para(932(a,2),829(a,1,1))]. 934 L(x \ y,z \ y,x) = L(x \ y,y,z). [para(932(a,1),840(a,1))]. 935 L(x \ y,z,y) = x \ L(y,z,x). [para(932(a,2),857(a,1))]. 936 L(x \ y,y,z) = L(x \ y,x,z). [para(933(a,1),832(a,1,1))]. 937 x * L(x \ y,z,y) = L(y,z,x). [para(935(a,2),14(a,1,2))]. 938 L(x \ y,z * y,y) = x \ R(y,z,x). [para(900(a,2),935(a,2,2))]. 939 L(x \ (y \ z),y \ z,y) = (y * x) \ z. [para(936(a,2),203(a,1))]. 940 x * L(x \ y,y,z) = L(y,x,z). [para(936(a,2),884(a,1,2))]. 942 L(x * y,z,y) = L(x * y,x,z). [para(317(a,1),931(a,1,1)),flip(a)]. 943 L((x * y) * z,x,z) = x * (y * z). [para(942(a,2),871(a,1))]. 944 x \ L(x * y,z,y) = L(y,x,z). [para(942(a,2),883(a,1,2))]. 945 (x / y) \ L(x,z,y) = L(y,x / y,z). [para(16(a,1),944(a,1,2,1))]. 946 L(x * y,z,y) = z * ((z \ x) * y). [para(14(a,1),943(a,1,1,1))]. 947 L(x * y,x,z) * z = x * (y * z). [para(943(a,1),929(a,1)),flip(a)]. 948 L(x,y,z) = y * ((y \ (x / z)) * z). [para(16(a,1),946(a,1,1))]. 949 L(x * y,z,y) = (x * z) * (z \ y). [para(946(a,2),261(a,2)),flip(a)]. 950 (x \ y) * (x * ((x \ z) * y)) = x \ (y * (z * y)). [para(946(a,1),851(a,1,2))]. 951 ((x * y) * z) * y = x * ((y * z) * y). [para(872(a,1),947(a,1,1))]. 952 L(x \ y,y,z) = (x \ (y / z)) * z. [hyper(17,a,940,a,b,948,a(flip)),flip(a)]. 953 L((x / y) * z,y,z) = x * (y \ z). [para(16(a,1),949(a,2,1))]. 954 L(x * (y \ z),z,y) = (x / y) * z. [para(953(a,1),829(a,1,1))]. 956 L(x \ y,z,y) = x \ R(y,z,x). [para(938(a,1),830(a,1)),flip(a)]. 957 R(x,y,z) = z * L(z \ x,y,x). [para(956(a,2),14(a,1,2)),flip(a)]. 958 R(x,y,z) = L(x,y,z). [para(957(a,2),937(a,1))]. 959 L(x,y,z) * (y * z) = (x * y) * z. [para(958(a,1),73(a,1,1))]. 960 L((x / y) / z,z,y) = x / (z * y). [para(958(a,1),212(a,1))]. 961 ((x * (y / z)) * z) / y = L(x,y / z,z). [para(958(a,1),75(a,2))]. 962 L((x * y) / z,z,x) = x * (y / z). [para(958(a,1),494(a,1))]. 963 L(x / y,y,z) = z * ((z \ x) / y). [para(958(a,1),495(a,1))]. 964 R(x,y,z) = L(x,y,(x * y) * z). [para(958(a,1),500(a,1)),flip(a)]. 965 L(x * y,x,z) \ z = y \ (x \ z). [para(958(a,1),507(a,1,1))]. 966 L(x,x \ y,z) = L(x,y,z). [para(958(a,1),896(a,2)),flip(a)]. 967 R(x,x \ y,z) = R(x,y,z). [para(958(a,2),896(a,1)),flip(a)]. 968 L(x,y / x,z) = L(x,y,z). [para(958(a,1),897(a,2)),flip(a)]. 969 L(x,y * x,z) = L(x,y,z). [para(958(a,1),900(a,1)),flip(a)]. 970 R(x,y * x,z) = R(x,y,z). [para(958(a,2),900(a,2)),flip(a)]. 971 L(x \ 1,y,z) = L(x,y,z) \ 1. [para(958(a,1),909(a,1))]. 972 L(x \ 1,y,z) \ u = L(x,y,z) * u. [para(958(a,1),910(a,1,1))]. 973 L(x \ y,z,x) = L(x,z,y) \ y. [para(958(a,1),920(a,2,1))]. 974 R((x / y) * z,y,z) = x * (y \ z). [para(958(a,2),953(a,1))]. 975 R(x \ y,z,y) = x \ R(y,z,x). [para(958(a,2),956(a,1))]. 976 L(x,x * y,z) = L(x,y,z). [para(13(a,1),966(a,1,2)),flip(a)]. 977 L(T(x,y),x \ z,u) = T(L(x,z,u),y). [para(966(a,1),40(a,2,1))]. 978 L(x / y,y,z) = L(x / y,x,z). [para(54(a,1),966(a,1,2))]. 979 L(x,T(x,y) \ z,u) = L(x,K(y,x) * z,u). [para(693(a,1),966(a,1,2))]. 980 L(L(L(x,y,z),u,w),z,y) = L(x,L(x,y,z) \ u,w). [para(966(a,1),832(a,1,1))]. 981 L(x,y \ x,z) = L(x,z,y). [para(966(a,1),915(a,1))]. 982 R(x,x \ y,z) = R(x,y,y \ z). [para(967(a,1),501(a,1)),flip(a)]. 983 L(L(x,y,z),u / x,w) = L(L(x,u,w),y,z). [para(968(a,1),45(a,1,1)),flip(a)]. 984 L(x,y,z) = ((x / y) / z) * (z * y). [para(968(a,1),434(a,1))]. 985 L(L(x,y,z),z,y / x) = x. [para(968(a,1),829(a,1,1))]. 986 L(K(x,y),z * T(y,x),u) = L(K(x,y),z * y,u). [para(607(a,1),969(a,1,2)),flip(a)]. 987 L(x * y,z,x) = L(x * y,y,z). [para(13(a,1),981(a,1,2)),flip(a)]. 988 L(L(x,y,z),u \ x,w) = L(L(x,w,u),y,z). [para(981(a,1),45(a,1,1)),flip(a)]. 989 L(x,y,x / z) = L(x,z,y). [para(54(a,1),981(a,1,2)),flip(a)]. 990 L(x,y,(x * y) * z) = L(x,y,z). [para(964(a,1),958(a,1))]. 991 x * L(x \ 1,y,z) = L(x,y,z) \ x. [para(971(a,2),292(a,1,2))]. 992 L(x \ 1,y,z) * u = L(x,y,z) \ u. [para(971(a,2),314(a,1,1))]. 993 x * L(y \ 1,z,u) = x / L(y,z,u). [para(971(a,2),345(a,1,2))]. 994 K(x,L(y \ 1,z,u)) = K(L(y,z,u),x). [para(971(a,2),559(a,1,2))]. 995 L(x \ y,z \ y,x) = L(x,y,z) \ y. [para(840(a,1),973(a,2,1))]. 996 L(x \ y,z,y) = L(x,z,y) \ y. [para(973(a,1),932(a,2))]. 997 R(x,y,y \ z) = R(x,y,z). [para(982(a,1),967(a,1))]. 998 R(x,y,y * z) = R(x,y,z). [para(13(a,1),997(a,1,3)),flip(a)]. 999 (x * y) \ R(z / x,x,y) = ((x * y) \ z) / x. [para(998(a,1),496(a,1,2))]. 1000 R(x,y,(y * x) * z) = R(x,y * x,z). [para(998(a,1),970(a,1)),flip(a)]. 1001 L(L(x * y,z,x),z,y) = x * y. [para(987(a,2),829(a,1,1))]. 1002 L(x * y,y \ z,x) = L(x * y,y,z). [para(987(a,2),831(a,1))]. 1003 L((x \ y) * z,z,y) = L((x \ y) * z,x,y). [para(987(a,1),845(a,1))]. 1004 x * (y * L(z * x,y,z)) = (x * y) * (z * x). [para(987(a,2),833(a,1,2,2))]. 1005 x \ L(x * y,y,z) = L(y,z,x). [para(987(a,1),858(a,1,2))]. 1006 L(x * (y * z),y,z) = (x * y) * z. [para(864(a,1),1001(a,1,1))]. 1007 x \ L(x * (y \ z),y \ z,z) = (y \ (z / x)) * x. [para(1005(a,2),952(a,1))]. 1008 (x * y) * z != u * (y * z) | L(x,y,z) = u. [para(959(a,1),20(a,1))]. 1009 T((x * y) * z,L(x,y,z)) = (y * z) * L(x,y,z). [para(959(a,1),116(a,1,1))]. 1010 (x * y) * (((x * y) \ L(z,x,y)) * u) = ((z * x) * y) * ((x * y) \ u). [para(959(a,1),261(a,1,1)),flip(a)]. 1011 L(x * (y / z),x,z) = (x * y) / z. [para(962(a,1),829(a,1,1))]. 1012 L(x / y,x,z) = z * ((z \ x) / y). [para(963(a,1),978(a,1)),flip(a)]. 1013 L((x * y) \ z,x,z) = y \ (x \ z). [para(965(a,1),996(a,2))]. 1014 (x * y) * (z * (x * y)) = x * (y * ((z * x) * y)). [para(1006(a,1),833(a,1,2,2)),flip(a)]. 1015 ((x * y) * z) / x = x * (y * (z / x)). [para(1011(a,1),871(a,1))]. 1016 L(L(x / y,x,z) * u,z,u) = z * (((z \ x) / y) * u). [para(1012(a,2),943(a,1,1,1))]. 1017 L(((x * y) \ z) * x,x,z) = (y \ (x \ z)) * x. [para(1013(a,1),893(a,2,1))]. 1018 L(L(x / y,y,z) \ u,z,u) = ((z \ x) / y) \ (z \ u). [para(963(a,2),1013(a,1,1,1))]. 1019 (x / y) * L(y,z,x) = L(x,y / x,z). [para(945(a,1),343(a,1)),flip(a)]. 1020 (x * L(x \ 1,y,z)) * u = x * (L(x \ 1,y,z) * u). [hyper(18,a,460,a,b,951,a)]. 1021 ((x * y) * z) * y = x * (y * (z * y)). [para(113(a,1),951(a,2,2))]. 1022 L(x / y,z,u) \ w = L(y / x,z,u) * w. [para(327(a,1),972(a,1,1,1))]. 1023 L(T(x,y),x \ z,u) = L(T(x,y),z,u). [para(977(a,2),40(a,2)),flip(a)]. 1025 L(x \ y,y,z) = L(x,y,z) \ y. [para(995(a,1),934(a,1)),flip(a)]. 1026 L(x \ (y \ z),y \ z,y) = L(x,z,y) \ (y \ z). [para(826(a,1),1025(a,2,1))]. 1027 L(x,y,L(z \ y,y,u)) = L(x,L(z,y,u),y). [para(1025(a,2),845(a,1,3))]. 1028 R(x,y,(y * x) * z) = R(x,y,z). [para(1000(a,2),970(a,1))]. 1029 R(x,y,z) = L(x,y,(y * x) * z). [para(1028(a,1),958(a,1))]. 1030 L(x,y,(y * x) * z) = L(x,y,z). [para(1029(a,1),958(a,1))]. 1031 (x / (y \ z)) * T(z,y) = L(x * y,y,z). [para(1002(a,1),865(a,1)),flip(a)]. 1032 (x / y) * L(y,z,x) = L(x,y,z). [para(1019(a,2),968(a,1))]. 1033 (x / y) * L(y,x,z) = L(x,z,y). [hyper(381,a,1032,a)]. 1034 x * (y \ L(y,z,x)) = L(x,y,z). [para(1032(a,1),855(a,1)),flip(a)]. 1035 L(x,T(y,z),L(y,u,w)) = (x / L(y,u,w)) * L(y,u,w). [para(219(a,1),1033(a,1,2)),flip(a)]. 1036 L(x,L(y,z,u),y) = (x / y) * y. [para(473(a,1),1033(a,1,2)),flip(a)]. 1037 x * (y \ L(y,x,z)) = L(x,z,y). [para(1033(a,1),855(a,1)),flip(a)]. 1038 x \ L(x,y,z) = z \ L(z,x,y). [hyper(56,a,1034,a),flip(a)]. 1039 L(x,L(y,z,u),y) = x. [para(1036(a,2),16(a,1))]. 1040 L(x,y,L(y \ 1,z,u)) = x. [para(1039(a,1),844(a,1)),flip(a)]. 1041 L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. [para(1039(a,1),828(a,1)),flip(a)]. 1042 (x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u). [hyper(17,a,863,a(flip),b,1040,a(flip))]. 1043 L(x,y,z) / (z \ L(z,x,y)) = x. [hyper(58,a,1037,a)]. 1044 K(x \ L(x,y,z),y) = K(L(y,z,x),y). [para(1037(a,1),542(a,1,1)),flip(a)]. 1045 x * (((y * x) * z) \ L((y * x) * z,x,y)) = L(x,y,z). [para(1037(a,2),1030(a,1))]. 1046 L(x,y,z) * (L(z,x,y) \ z) = x. [para(1043(a,1),358(a,1)),flip(a)]. 1047 L(x,y,z) * u != x | L(z,x,y) \ z = u. [para(1046(a,1),19(a,1)),flip(a)]. 1048 (x / y) * (y * (z * y)) = (x * z) * y. [para(16(a,1),1021(a,1,1,1)),flip(a)]. 1049 (x \ 1) * (y * (z * y)) = ((x \ y) * z) * y. [para(314(a,1),1021(a,1,1,1)),flip(a)]. 1050 x * ((y \ 1) * (z * (y \ 1))) = ((x / y) * z) * (y \ 1). [para(345(a,1),1021(a,1,1,1)),flip(a)]. 1051 L(T(T(x,y),y \ x),z,u) = L(x,T(x,y) \ z,u). [para(143(a,1),1023(a,1,1)),flip(a)]. 1052 K(x \ L(x,y,z),y) = 1. [para(1044(a,2),309(a,1))]. 1054 K(x,L(y,x,z) \ y) = 1. [para(1052(a,1),562(a,1)),flip(a)]. 1055 (x * (y / z)) * z = (x / z) * (z * y). [para(16(a,1),1048(a,1,2,2)),flip(a)]. 1056 ((x * (y / z)) * z) / y = L(x,z \ y,z). [para(961(a,2),800(a,1))]. 1057 (x * (y \ z)) * T(y,z) = L(x * z,z,y). [para(358(a,1),1031(a,1,1))]. 1058 x \ L(y * z,z,x) = T(y * (z / x),x). [para(1057(a,1),737(a,1,2))]. 1059 L(x \ (y * z),z,x) = T(y * (z / x),x). [para(1058(a,1),857(a,2))]. 1060 T(x * (y / z),z) = (z \ y) * T(x,y). [para(1059(a,1),866(a,1))]. 1061 L((x \ y) * z,z,y) = x \ (y * z). [para(1003(a,2),828(a,1))]. 1062 x \ (y * (z * y)) = ((x \ y) * z) * y. [para(1049(a,1),314(a,1)),flip(a)]. 1063 x * (y * ((((x * y) \ z) * u) * z)) = L(z * (u * z),y,x). [para(1062(a,1),870(a,2,2,2)),flip(a)]. 1064 (x * y) \ L(z / x,x,y) = ((x * y) \ z) / x. [para(958(a,1),999(a,1,2))]. 1065 (x * y) * (z * x) = x * ((y * z) * x). [para(862(a,1),1004(a,1,2)),flip(a)]. 1066 x * (((x \ y) * z) * x) = y * (z * x). [para(14(a,1),1065(a,1,1)),flip(a)]. 1067 (x * y) \ (z * x) = (y \ (x \ z)) * x. [para(1017(a,1),1061(a,1)),flip(a)]. 1068 (x * y) \ (z * x) != u * x | y \ (x \ z) = u. [para(1067(a,2),20(a,1))]. 1069 ((x * y) \ z) / x = y \ (x \ (z / x)). [para(1064(a,1),926(a,1))]. 1070 (x \ ((y \ x) * z)) / y = x \ (y \ ((x * z) / y)). [para(876(a,1),1069(a,1,1))]. 1071 (x \ y) * (x * ((x \ z) * y)) = ((x \ y) * z) * y. [para(950(a,2),1062(a,1))]. 1072 T((x * y) * z,L(x,y,z)) = z * (T(y,z) * x). [para(1009(a,2),804(a,1))]. 1073 x * ((y * ((x * y) \ z)) * ((u * x) * (y * ((x * y) \ z)))) = L(z,y,x) * (u * (x * (y * ((x * y) \ z)))). [para(870(a,2),1014(a,1,1)),flip(a)]. 1074 L(x,y,z) \ (z \ y) = (z * x) \ y. [para(1026(a,1),939(a,1))]. 1075 L(T(T(x,y),y \ x),z,u) = L(x,K(y,x) * z,u). [para(1051(a,2),979(a,1))]. 1076 ((x * y) \ z) * ((x * y) * ((y \ (x \ u)) * z)) = (((x * y) \ z) * L(u,x,y)) * z. [para(926(a,1),1071(a,1,2,2,1))]. 1077 L(x,K(y,x) * z,u) = L(x,z,u). [para(143(a,1),1075(a,1,1)),flip(a)]. 1078 L(x,K(y,x) / z,u) = L(x,z \ 1,u). [para(345(a,1),1077(a,1,2))]. 1079 L(x,K(y,x) / z,u) = L(x,u,z). [para(1078(a,2),843(a,1))]. 1080 L(x,y,(K(z,x) / u) \ y) = L(x,y,u). [para(1079(a,1),845(a,2))]. 1081 L(x,y,(z / K(u,x)) * y) = L(x,y,z). [para(343(a,1),1080(a,1,3))]. 1082 L(x,y,(z * K(x,u)) * y) = L(x,y,z). [para(409(a,1),1081(a,1,3,1))]. 1083 L(x,y,z * K(x,u)) = L(x,y,z). [para(1082(a,1),835(a,1)),flip(a)]. 1084 L(x \ (y * ((z * (x \ y)) \ u)),z,x \ y) = L(z \ u,x,y). [para(878(a,1),854(a,1,1)),flip(a)]. 1085 L(x \ y,z * z,x) = ((x \ z) * z) * (z \ (z \ y)). [para(401(a,1),867(a,2,1))]. 1086 L(x,L(x,y,z) \ u,w) = L(x,u,w). [para(980(a,1),832(a,1))]. 1087 L(x,L(x,y,z) * u,w) = L(x,u,w). [para(13(a,1),1086(a,1,2)),flip(a)]. 1089 L(x,(y * x) \ z,u) = L(x,y \ z,u). [para(1074(a,1),1086(a,1,2))]. 1090 x \ L(x * (y \ z),z,y) = (y \ (z / x)) * x. [para(840(a,1),1007(a,1,2))]. 1091 x \ ((x / y) * z) = (y \ (z / x)) * x. [para(954(a,1),1090(a,1,2))]. 1092 L(x \ y,z * z,x) = z * ((z \ (x \ z)) * (z \ y)). [para(1085(a,2),261(a,1))]. 1093 L(x \ y,z * z,x) = z * (T(x,z) \ (z \ y)). [para(376(a,1),1092(a,2,2))]. 1094 x * (T(y,x) \ (x \ (y * z))) = L(z,x * x,y). [para(13(a,1),1093(a,1,1)),flip(a)]. 1095 (x \ 1) * (y \ ((x \ 1) \ (T(y,x) * z))) = L(z,(x \ 1) * (x \ 1),T(y,x)). [para(338(a,1),1094(a,1,2,1))]. 1096 L(L(x / y,x,z) * u,z,u) = ((z \ y) / x) \ (z \ u). [para(1022(a,1),1018(a,1,1))]. 1097 x * (L(x \ 1,y,z) * u) = (L(x,y,z) \ x) * u. [para(991(a,1),1020(a,1,1)),flip(a)]. 1098 (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). [para(992(a,1),1097(a,1,2)),flip(a)]. 1099 L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u). [para(1098(a,1),1041(a,2))]. 1100 x * (L(x,y,z) \ (x \ u)) = L(x,y,z) \ u. [para(14(a,1),1099(a,1,2)),flip(a)]. 1101 L(x,y,z) \ (x \ u) = x \ (L(x,y,z) \ u). [hyper(56,a,1100,a),flip(a)]. 1102 L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u. [para(1101(a,1),14(a,1,2))]. 1103 x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u). [para(13(a,1),1102(a,1,2,2)),flip(a)]. 1104 x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. [para(1103(a,1),14(a,1,2))]. 1105 L(x,T(y,z),L(y,u,w)) = x. [para(1035(a,2),16(a,1))]. 1106 L(x,T(L(y,z,u),w),y) = x. [para(305(a,1),1105(a,1,3))]. 1107 L(x,L(T(y,z),u,w),y) = x. [para(40(a,2),1106(a,1,2))]. 1108 (x * y) / L(T(x,z),u,w) = x * (y / L(T(x,z),u,w)). [para(1107(a,1),962(a,1))]. 1109 (x * L(x \ 1,y,z)) \ u = L(x,y,z) * (x \ u). [para(1042(a,2),972(a,1))]. 1110 (x / L(x,y,z)) \ u = L(x,y,z) * (x \ u). [para(993(a,1),1109(a,1,1))]. 1111 L(x,y,z) = x * (((y * x) * z) \ (y * (x * z))). [para(869(a,1),1045(a,1,2,2)),flip(a)]. 1112 L(x,y,z) = x * (a(y,x,z) \ 1). [para(339(a,1),1111(a,2,2))]. 1113 a(x,y,z) \ 1 = y \ L(y,x,z). [hyper(56,a,1112,a(flip)),flip(a)]. 1114 L(x,y,z) = x / a(y,x,z). [para(1112(a,2),345(a,1))]. 1115 L(x,y,z) * a(y,x,z) = x. [para(1114(a,2),16(a,1,1))]. 1116 a(x,y,z) = L(y,x,z) \ y. [para(1114(a,2),54(a,1,1)),flip(a)]. 1117 L(x,a(y,x,z),u) = L(x,u,L(x,y,z)). [para(1114(a,2),989(a,1,3)),flip(a)]. 1118 a(x,y,z) = L(z,y,x) \ z. [hyper(1047,a,1115,a),flip(a)]. 1119 a(x,y,z) * L(y,x,z) = y. [para(1116(a,2),267(a,1,1))]. 1120 a(x,y,z) = y / L(y,x,z). [para(1116(a,2),268(a,2)),flip(a)]. 1121 K(x,a(x,y,z)) = 1. [para(1116(a,2),1054(a,1,2))]. 1122 T(x,a(x,y,z)) = x. [hyper(37,a,1121,a)]. 1123 1 * K(a(x,y,z),x) = 1. [para(1121(a,1),405(a,1,1))]. 1124 a(x,y,z) * x = x * a(x,y,z). [para(1122(a,1),78(a,1,2))]. 1125 K(a(x,y,z),x) = 1. [hyper(55,a,1123,a),flip(a)]. 1127 K(x,y \ L(y,z,u)) = K(a(u,z,y),x). [para(1118(a,2),562(a,1,1)),flip(a)]. 1128 a(x,y,z) = a(z,x,y). [para(1118(a,2),1116(a,2))]. 1129 a(x,y,z) = L(x,z,y) \ x. [para(1128(a,2),1116(a,1))]. 1130 K(a(x,y,z),z) = 1. [para(1128(a,2),1125(a,1,1))]. 1131 T(a(x,y,z),z) = a(x,y,z). [hyper(37,a,1130,a)]. 1132 (x * y) / L(L(y,z,u),a(z,y,u),x) = x * a(z,y,u). [para(1119(a,1),87(a,1,1,2))]. 1133 a(x,y,z) = x / L(x,z,y). [para(1120(a,1),1128(a,2))]. 1134 a(x,y,z \ 1) = L(x,y,z) \ x. [para(843(a,1),1129(a,2,1))]. 1135 x * (L(x,y,z) \ u) = a(x,z,y) * u. [para(1129(a,2),1098(a,1,1)),flip(a)]. 1136 T(a(x,y,z) * (z / u),u) = (u \ z) * a(x,y,z). [para(1131(a,1),1060(a,2,2))]. 1137 L(x,y,z) * (x \ u) = a(x,z,y) \ u. [para(1133(a,2),1110(a,1,1)),flip(a)]. 1138 a(x,y,z \ 1) = a(z,y,x). [para(1134(a,2),1118(a,2)),flip(a)]. 1139 a(K(x,y),z,u) = a(u,z,K(y,x)). [para(404(a,1),1138(a,1,3)),flip(a)]. 1140 a(x,y \ 1,z) = a(y,x,z). [para(1138(a,1),1128(a,2))]. 1141 a(x,T(y \ 1,z),u) = a(T(y,z),x,u). [para(375(a,1),1140(a,1,2))]. 1142 a(x,K(y,z),u) = a(x,u,K(z,y)). [para(1139(a,1),1128(a,1)),flip(a)]. 1143 L(x,a(y,x,z),u) = x. [para(1117(a,2),473(a,1))]. 1144 L(x,a(x,y,z),u) = x. [para(1128(a,2),1143(a,1,2))]. 1145 L(L(x,y,z),a(x,u,w),v5) = L(x,y,z). [para(1144(a,1),45(a,1,1)),flip(a)]. 1146 (x * a(y,z,u)) * y = x * (a(y,z,u) * y). [para(1144(a,1),67(a,1,2))]. 1147 L(x,y,a(x,z,u)) = x. [para(1144(a,1),307(a,1,1))]. 1148 (a(x,y,z) * u) * x = a(x,y,z) * (u * x). [para(1144(a,1),833(a,1,2,2)),flip(a)]. 1149 L(x,y,a(y * x,z,u)) = x. [hyper(889,a,1147,a)]. 1150 L(x,y / x,a(y,z,u)) = x. [para(16(a,1),1149(a,1,3,1))]. 1151 L(x,y,a(y,z,u)) = x. [para(1150(a,1),968(a,1)),flip(a)]. 1152 (x * y) * a(y,z,u) = x * (y * a(y,z,u)). [para(1151(a,1),959(a,1,1)),flip(a)]. 1153 L(x,y,a(z,u,y)) = x. [para(1128(a,2),1151(a,1,3))]. 1154 L(a(x,y,z),u,z) = (a(x,y,z) / u) * u. [para(1153(a,1),1032(a,1,2)),flip(a)]. 1155 x \ (a(x,y,z) * u) = L(x,z,y) \ u. [hyper(56,a,1135,a)]. 1156 T(a(x,y,z) * u,x) = (L(x,z,y) \ u) * x. [para(1135(a,1),116(a,1,1))]. 1157 a(x,T(y \ 1,z),u) = a(x,u,T(y,z)). [para(1141(a,2),1128(a,2)),flip(a)]. 1158 L(x,y,z) \ L(z,x,y) = x \ z. [para(1119(a,1),1155(a,1,2)),flip(a)]. 1159 L(x,L(y,x,z),u) = L(x,x \ y,u). [para(1158(a,1),1086(a,1,2)),flip(a)]. 1160 L(x,L(y,x,z),u) = L(x,y,u). [para(1159(a,2),966(a,1))]. 1161 L(x,L(y,z,x),u) = L(x,y,u). [para(305(a,1),1160(a,1,2)),flip(a)]. 1162 L(x,y,L(z,x,u)) = L(x,z,y \ 1). [para(1160(a,1),844(a,1)),flip(a)]. 1163 L(x,L(y,z \ x,u),z) = z * L(z \ x,y,x). [para(1160(a,1),937(a,1,2)),flip(a)]. 1164 L(x,(x * y) / z,u) = L(x,x * (y / z),u). [para(1011(a,1),1160(a,1,2))]. 1165 L(x,y,L(z,x,u)) = L(x,y,z). [para(1162(a,2),844(a,1))]. 1166 a(x,y \ (z \ y),u) = a(x,u,T(z,y)). [para(320(a,1),1157(a,1,2))]. 1167 L(a(x,y,z),u,z) = a(x,y,z). [para(1154(a,2),16(a,1))]. 1168 L(a(x,y,z),u,x) = a(x,y,z). [hyper(1008,a,1148,a)]. 1169 L(a(x,y,z),x,u) = a(x,y,z). [para(1168(a,1),304(a,1,1))]. 1170 L(x,(x * y) / z,u) = L(x,y / z,u). [para(1164(a,2),976(a,1))]. 1171 L(x,L(y,z \ x,u),z) = L(x,y,z). [para(1163(a,2),937(a,1))]. 1172 L(x,y,L(z,(x / y) \ x,u)) = L(x,z,x / y). [para(1171(a,1),989(a,1)),flip(a)]. 1173 L(x,y,L(z,(x / y) \ x,u)) = L(x,y,z). [para(1172(a,2),989(a,1))]. 1174 L(x,y,L(z,y,u)) = L(x,y,z). [para(54(a,1),1173(a,1,3,2))]. 1175 L(x,L(y,z,u),z) = L(x,z,y \ z). [para(1174(a,1),1027(a,1)),flip(a)]. 1176 L(x,L(y,z,u),z) = L(x,y,z). [para(1175(a,2),845(a,1))]. 1178 L(x,L(y,z,u),u) = L(x,y,u). [para(305(a,1),1176(a,1,2)),flip(a)]. 1179 L(x,L(y,z,u),u / z) = L(x,y,u / z). [para(836(a,1),1178(a,1,2))]. 1180 x * ((y \ 1) * (z * (y \ 1))) = ((x / y) * z) / y. [para(1050(a,2),345(a,1))]. 1181 x * ((y \ 1) * (z / y)) = ((x / y) * z) / y. [para(345(a,1),1180(a,1,2,2))]. 1182 ((x / y) * z) / y = x * (y \ (z / y)). [para(314(a,1),1181(a,1,2)),flip(a)]. 1183 (((((x / y) \ y) * z) / y) * x) / y = T(z,y \ (x / y)). [para(1182(a,2),384(a,1))]. 1184 ((x \ y) / z) \ (x \ u) = x * (((x \ z) / y) * u). [para(1096(a,1),1016(a,1))]. 1185 (x / (y \ z)) * (y \ u) = y * (((y \ x) / z) * u). [para(1184(a,1),343(a,1)),flip(a)]. 1186 (x * (y \ z)) * (z \ u) = z * (((z \ x) / y) * u). [para(358(a,1),1185(a,1,1))]. 1187 x \ (y * (((y \ x) / z) * u)) = ((z \ y) / x) * (x * (y \ u)). [para(1186(a,1),812(a,1,2))]. 1188 (x * y) / L(L(y,z,u),a(y,u,z),x) = x * a(z,y,u). [para(1128(a,2),1132(a,1,2,2))]. 1189 ((((x * (y \ x)) * z) / x) * y) / x = T(z,x \ (y / x)). [para(380(a,1),1183(a,1,1,1,1,1))]. 1190 (x * y) / L(y,z,u) = x * a(z,y,u). [para(1145(a,1),1188(a,1,2))]. 1191 (x * y) / L(y,z,u) = x * a(y,u,z). [para(1128(a,2),1190(a,2,2))]. 1193 (x / y) * a(y,z,u) = x / L(y,u,z). [para(16(a,1),1191(a,1,1)),flip(a)]. 1194 (x * y) / L(T(x,y),z,u) = y * a(T(x,y),u,z). [para(78(a,1),1191(a,1,1))]. 1195 (x / y) * (y / L(x,z,u)) = a(x,u,z). [hyper(381,a,1193,a)]. 1196 a(x,y * K(x,z),u) = (x / w) * (w / L(x,u,y)). [para(1083(a,1),1195(a,1,2,2)),flip(a)]. 1197 a(x,y,L(x,z,u) * w) = (x / v5) * (v5 / L(x,w,y)). [para(1087(a,1),1195(a,1,2,2)),flip(a)]. 1198 a(x,y,L(z,u,x)) = (x / w) * (w / L(x,z,y)). [para(1161(a,1),1195(a,1,2,2)),flip(a)]. 1199 a(x,L(y,x,z),u) = (x / w) * (w / L(x,u,y)). [para(1165(a,1),1195(a,1,2,2)),flip(a)]. 1200 a(x,y,L(z,u,x)) = a(x,y,z). [para(1198(a,2),1195(a,1))]. 1201 a(x,L(y,x,z),u) = a(x,y,u). [para(1199(a,2),1195(a,1))]. 1202 x * (y / L(T(x,y),z,u)) = y * a(T(x,y),u,z). [para(1194(a,1),1108(a,1)),flip(a)]. 1203 a(x,y * K(x,z),u) = a(x,y,u). [para(1196(a,2),1195(a,1))]. 1204 a(x,y / x,z) = a(x,x \ y,z). [para(429(a,1),1203(a,1,2)),flip(a)]. 1205 x * a(T(y,x),z,u) = y * (L(y,u,z) \ x). [para(235(a,1),1202(a,1,2)),flip(a)]. 1206 x * a(T(y,x),z,u) = a(y,z,u) * x. [para(1205(a,2),1135(a,1))]. 1207 x * a(y,T(z,x),u) = a(z,u,y) * x. [para(1128(a,1),1206(a,1,2))]. 1208 a(x,T(y,z),u) = T(a(y,u,x),z). [hyper(94,a,1207,a),flip(a)]. 1209 a(x,T(y,z),u) = T(a(x,y,u),z). [para(1128(a,1),1208(a,2,1))]. 1210 T(a(x,y \ 1,z),u) = a(x,u \ (y \ u),z). [para(320(a,1),1209(a,1,2)),flip(a)]. 1211 a(x,T(y,z),z) = a(x,y,z). [para(1209(a,2),1131(a,1))]. 1212 a(x,y / z,z) = a(x,z \ y,z). [para(80(a,1),1211(a,1,2)),flip(a)]. 1213 a(x,y \ (z \ y),u) = T(a(z,x,u),y). [para(1140(a,1),1210(a,1,1)),flip(a)]. 1214 a(x,y \ (z \ y),u) = T(a(x,u,z),y). [para(1128(a,2),1213(a,2,1))]. 1215 a(x,y,T(z,u)) = T(a(x,y,z),u). [para(1214(a,1),1166(a,1)),flip(a)]. 1216 a(x,T(y,z),u) = a(x,y,T(u,z)). [para(1215(a,2),1209(a,2))]. 1217 a(x,y,L(x,z,u) * w) = a(x,y,w). [para(1197(a,2),1195(a,1))]. 1218 a(x,y,x * z) = a(x,y,z). [para(110(a,1),1217(a,1,3,1))]. 1219 ((x * ((y \ x) * (z / x))) * y) / x = T(z,x \ (y / x)). [para(1015(a,1),1189(a,1,1,1))]. 1220 x * (((y \ x) * (z / x)) * (y / x)) = T(z,x \ (y / x)). [para(1219(a,1),1015(a,1)),flip(a)]. 1221 L(x * (y * z),y,x) \ (x * (y * z)) = a(x,y,L(z,y,x)). [para(861(a,2),890(a,1,1))]. 1222 a(x,y,z) = L(x * (y * z),y,x) \ (x * (y * z)). [para(1221(a,2),1200(a,1)),flip(a)]. 1223 T(x * (y * z),a(x,y,z)) = x * (y * z). [para(1222(a,2),264(a,1,2))]. 1224 a(x,y,x * (y * z)) = a(x,y,z). [para(1222(a,2),1118(a,2))]. 1226 a(x,y,y * z) = a(x,y,z). [para(1224(a,1),1218(a,1)),flip(a)]. 1227 a(x,y,y \ z) = a(x,y,z). [para(14(a,1),1226(a,1,3)),flip(a)]. 1228 a(x,y,z) = (x * z) \ (y * ((y \ x) * z)). [para(1227(a,1),474(a,2)),flip(a)]. 1229 a(x,y,z) = ((x * y) * z) / (x * (y * z)). [para(1223(a,1),296(a,1,2)),flip(a)]. 1230 ((x * (y / z)) * z) / (x * y) = a(x,y / z,z). [para(16(a,1),1229(a,2,2,2)),flip(a)]. 1231 ((x * (y / z)) * z) / (x * y) = a(x,z \ y,z). [para(1230(a,2),1212(a,1))]. 1232 L((((x * (y / z)) * z) / y) / x,x,y) = a(x,z \ y,z). [para(1231(a,1),960(a,2))]. 1233 L(L(x,y \ z,y) / x,x,z) = a(x,y \ z,y). [para(1056(a,1),1232(a,1,1,1))]. 1234 L(x \ L(x,y \ z,y),x,z) = a(x,y \ z,y). [para(269(a,1),1233(a,1,1))]. 1235 L(x \ L(x,y,z),x,z * y) = a(x,z \ (z * y),z). [para(13(a,1),1234(a,1,1,2,2))]. 1236 a(x,y,z) = L(x \ L(x,y,z),x,z * y). [para(13(a,1),1235(a,2,2)),flip(a)]. 1237 a(x,y,z) = x \ L(x,y,z). [para(1236(a,2),868(a,1))]. 1238 L(x,y,z) = x * a(x,y,z). [para(1237(a,2),14(a,1,2)),flip(a)]. 1240 (x / y) * L(y,z,u) = x * a(y,z,u). [para(1237(a,2),855(a,2,2))]. 1241 L(x,y,z) = x * a(y,z,x). [para(1237(a,2),1034(a,1,2)),flip(a)]. 1242 a(x,y,z) = y \ L(y,z,x). [para(1237(a,2),1038(a,2)),flip(a)]. 1243 L(x,y,z) = a(x,y,z) * x. [para(1238(a,2),1124(a,2)),flip(a)]. 1244 (x * y) * a(y,z,u) = x * L(y,z,u). [para(1238(a,2),1152(a,2,2))]. 1245 x * a(x,y,T(z,u)) = L(x,T(y,u),z). [para(1216(a,1),1238(a,2,2)),flip(a)]. 1246 K(x,y) * L(K(y,x),z,u) = a(z,u,K(y,x)). [hyper(413,a,1241,a(flip))]. 1247 a(x,y,z) \ 1 = a(z,y,x). [para(1242(a,2),1113(a,2))]. 1248 K(a(x,y,z),u) = K(u,a(x,z,y)). [para(1242(a,2),1127(a,1,2)),flip(a)]. 1249 L(x,y,z) = a(z,x,y) * x. [para(1128(a,1),1243(a,2,1))]. 1250 L(x,y,z) = a(y,z,x) * x. [para(1128(a,2),1243(a,2,1))]. 1251 (x * a(y,z,u)) * y = x * L(y,z,u). [para(1243(a,2),1146(a,2,2))]. 1252 a(x,y,z) \ u = a(z,y,x) * u. [para(1247(a,1),314(a,1,1)),flip(a)]. 1253 x / a(y,z,u) = x * a(u,z,y). [para(1247(a,1),334(a,1,2))]. 1254 a(x,y,z) * L(y,x,u) = L(L(y,x,u),z,x). [para(1201(a,1),1249(a,2,1)),flip(a)]. 1255 L(x,y,z * K(y,u)) = a(y,z,x) * x. [para(1203(a,1),1250(a,2,1))]. 1256 a(x,y,z) \ u = a(x,z,y) * u. [para(1128(a,1),1252(a,1,1))]. 1257 x / a(y,z,u) = x * a(y,u,z). [para(1128(a,1),1253(a,1,2))]. 1258 (a(x,y,z) * u) * a(x,z,y) = T(u,a(x,z,y)). [para(1256(a,1),120(a,2,1)),flip(a)]. 1259 a(x,x * y,z) * 1 = a(x * z,x,y). [para(1256(a,1),781(a,1))]. 1260 L(x,y,z) * (x \ u) = a(x,y,z) * u. [para(1256(a,1),1137(a,2))]. 1261 T(x * a(y,z,u),a(y,u,z)) = a(y,u,z) \ x. [para(1257(a,1),80(a,1,1))]. 1262 (x \ (y / x)) * L(x,z,u) = (x \ y) * a(x,z,u). [para(130(a,1),1240(a,1,1))]. 1263 (x * (y / z)) * L(L(z,u,w),y / z,x) = x * (y * a(z,u,w)). [para(1240(a,1),67(a,2,2))]. 1264 ((L(x,y,z) \ u) * x) * a(x,y,z) = T(u,L(x,y,z)). [para(1244(a,2),120(a,2)),flip(a)]. 1265 L(x,T(y,z),u) = L(x,y,T(u,z)). [para(1245(a,1),1238(a,2)),flip(a)]. 1267 x \ (y * L(x,z,u)) = T(y * a(x,z,u),x). [para(1251(a,1),32(a,2,2)),flip(a)]. 1268 L(x,y,z * K(y,u)) = L(x,y,z). [para(1255(a,2),1250(a,2)),flip(a)]. 1269 L(x,y,z \ T(u,y)) = L(x,y,z \ u). [para(615(a,1),1268(a,1,3)),flip(a)]. 1270 a(x * y,x,z) = a(x,x * z,y). [hyper(57,a,1259,a),flip(a)]. 1271 a(x,x * y,z) = a(x,y,x * z). [para(1270(a,1),1128(a,2)),flip(a)]. 1272 a(x,x * y,z) = a(x,y,z). [para(1271(a,2),1218(a,1))]. 1273 a(x,x \ y,z) = a(x,y,z). [para(14(a,1),1272(a,1,2)),flip(a)]. 1274 a(x,y / x,z) = a(x,y,z). [para(1273(a,1),1204(a,2))]. 1275 x \ (L(x,y,z) * u) = a(x,y,z) * u. [para(1260(a,1),1103(a,2))]. 1276 x * (a(x,y,z) * u) = L(x,y,z) * u. [para(1260(a,1),1104(a,1,2))]. 1277 x \ (y \ L(y * x,z,u)) = a(y * x,z,u). [hyper(1068,a,1275,a)]. 1278 T(x * a(y,z,u),y) = (y \ x) * L(y,z,u). [para(1267(a,1),468(a,1))]. 1279 x \ (y \ L(y * x,z,u)) = a(z,u,y * x). [para(1277(a,2),1128(a,2)),flip(a)]. 1280 (x * y) \ (((z / y) / x) \ L(L(z,y,x),u,w)) = a(u,w,((z / y) / x) * (x * y)). [para(984(a,2),1279(a,1,2,2,1))]. 1281 T(x * a(y,z,u),a(y,u,z)) = a(y,z,u) * x. [para(1261(a,2),1256(a,1))]. 1282 T((x / y) * a(y,z,u),y) = (y \ x) * a(y,z,u). [para(1262(a,1),1278(a,2))]. 1283 T(x / L(y,z,u),y) = (y \ x) * a(y,u,z). [para(1193(a,1),1282(a,1,1))]. 1284 T((x * y) / L(y,z,u),y) = T(x,y) * a(y,u,z). [para(32(a,2),1283(a,2,1))]. 1285 T(x * a(y,z,u),y) = T(x,y) * a(y,z,u). [para(1191(a,1),1284(a,1,1))]. 1286 T(a(x,y,z) * u,x) * a(x,z,y) = T(u,L(x,z,y)). [para(1156(a,2),1264(a,1,1))]. 1287 T((a(x,y,z) * u) * a(x,z,y),x) = T(u,L(x,z,y)). [para(1286(a,1),1285(a,2))]. 1288 T(T(x,a(y,z,u)),y) = T(x,L(y,z,u)). [para(1258(a,1),1287(a,1,1))]. 1289 T(T(x,y),a(y,z,u)) = T(x,L(y,z,u)). [para(1288(a,1),38(a,1)),flip(a)]. 1290 T(x,L(y,z,u)) \ T(x,y) = K(a(y,z,u),T(x,y)). [para(1289(a,1),531(a,2,1)),flip(a)]. 1291 K(x,y) * K(L(y,z,u),x) = K(a(y,z,u),T(x,y)). [para(1290(a,1),713(a,1)),flip(a)]. 1292 L(L(x,y,z),z * y,z) = L(x,y,z * z). [para(198(a,1),771(a,1))]. 1293 L(L(x,y,z),y,z) = L(x,y,z * z). [para(1292(a,1),827(a,1)),flip(a)]. 1294 ((x * y) * L(T(z,u),y,x)) \ (x * (y * z)) = K(u,L(z,y,x)). [para(40(a,2),614(a,1,1,2))]. 1295 K(T(x,y) \ z,z \ x) = K(y,T(x,z)) \ K(y,x). [para(731(a,1),629(a,1,1)),flip(a)]. 1296 K(T(x,y) \ z,z \ x) = K(T(x,z),y) * K(y,x). [para(1295(a,2),406(a,1))]. 1297 K(T(x,y) \ z,z \ x) = K(x,T(y,z)) * K(y,x). [para(721(a,1),1296(a,2,1))]. 1298 K(T(x,y) \ z,z \ x) = K(z,K(y,x)). [para(1297(a,2),720(a,1))]. 1299 K(K(x,y),z \ y) = K(z,K(x,y)). [para(1298(a,1),630(a,1)),flip(a)]. 1300 K(x,K(y,z \ y)) = K(z,K(x,y)). [para(1299(a,1),747(a,1)),flip(a)]. 1301 K(x,K(y,z)) = K(y,K(x,z)). [para(578(a,1),1300(a,1,2))]. 1302 K(x,K(y,z)) = K(z,K(x,y)). [para(1301(a,1),746(a,1))]. 1303 K(x,K(y,z)) = K(x,K(z,y)). [para(1302(a,1),746(a,1))]. 1304 K(x,y) * K(x,K(y,z)) = K(x,T(y,z \ 1)). [para(1303(a,1),749(a,1,2))]. 1305 K(x,T(y,z \ 1)) = K(x,T(y,z)). [para(1304(a,1),748(a,1))]. 1306 K(x,T(y,z \ y)) = K(x,T(y,z)). [para(324(a,1),1305(a,1,2))]. 1307 K(x,T(y,z \ (u \ 1))) = K(x,T(y,u * z)). [para(341(a,1),1305(a,1,2,2))]. 1308 K(x,y \ K(y,z)) = K(y,T(x,z)). [para(1305(a,1),724(a,1)),flip(a)]. 1309 K(x,T(T(T(y,z \ y),u),z \ T(T(y,z \ y),u))) = K(x,T(y,u)). [para(185(a,1),1306(a,2,2))]. 1310 K(a(x,y,z),T(u,x)) = K(u,a(x,y,z) \ 1). [para(1125(a,1),1308(a,1,2,2)),flip(a)]. 1311 K(x,T(y,z \ (u / w))) = K(x,T(y,(w / u) * z)). [para(327(a,1),1307(a,1,2,2,2))]. 1312 K(a(x,y,z),T(u,x)) = K(u,a(x,z,y) * 1). [para(1256(a,1),1310(a,2,2))]. 1313 K(a(x,y,z),T(u,x)) = K(u,a(x,z,y)). [para(12(a,1),1312(a,2,2))]. 1314 K(x * y,x) * ((x \ (y \ 1)) * z) = (y \ (x \ 1)) * z. [para(563(a,1),690(a,1,1))]. 1315 K(x,y) * ((y \ (x \ 1)) * z) = (x \ (y \ 1)) * z. [para(542(a,1),1314(a,1,1))]. 1316 K(x,y) * ((x * y) \ z) = (x \ (y \ 1)) * z. [para(378(a,1),1315(a,1,2))]. 1317 K(x,y) * ((x * y) \ z) = (y * x) \ z. [para(1316(a,2),378(a,1))]. 1318 L(x,(y * x) \ z,u) = L(x,(x * y) \ z,u). [para(1317(a,1),1077(a,1,2)),flip(a)]. 1319 L(x,(x * y) \ z,u) = L(x,y \ z,u). [para(1318(a,1),1089(a,1))]. 1320 ((x * y) \ (z \ 1)) * (z / (x \ (y \ 1))) = K(x,y \ (x \ 1)). [para(399(a,1),708(a,1,1))]. 1321 x \ (y * (z * ((z \ (y \ x)) * u))) = L(L(u,z,x \ y),x,y). [para(386(a,1),873(a,1,2,2,2))]. 1322 L(x \ (y * (((y \ x) / z) * u)),z,x \ y) = L(z \ u,x,y). [para(392(a,1),1084(a,1,1,2,2))]. 1323 ((x \ y) * z) \ (y * (((y \ ((x \ y) * z)) / x) * u)) = (z \ K(z,x \ y)) * (((x \ y) * z) * (y \ u)). [para(583(a,2),1187(a,2,1))]. 1324 (x * (y * T(z,u))) \ (x * (y * z)) = K(u,L(z,y,x)). [para(67(a,1),1294(a,1,1))]. 1325 ((x * y) \ (z \ 1)) * (z * ((y \ 1) \ x)) = K(x,y \ (x \ 1)). [para(358(a,1),1320(a,1,2))]. 1326 L(((x \ y) / z) * (z * (y \ u)),x,z \ y) = L(x \ u,z,y). [para(1187(a,1),1322(a,1,1))]. 1327 ((x * y) \ (z \ 1)) * (z * (y * x)) = K(x,y \ (x \ 1)). [para(317(a,1),1325(a,1,2,2))]. 1328 (x * (y * z)) \ (x * (z * y)) = K(y,z \ (y \ 1)). [para(1327(a,1),378(a,1)),flip(a)]. 1329 L(K(x,y),y * x,z) = K(y,x \ (y \ 1)). [para(1328(a,1),107(a,1)),flip(a)]. 1330 L(K(x,y),y * x,z) = K(y * x,y). [para(1329(a,2),563(a,1))]. 1332 L(K(x,y),y * x,z) = K(x,y). [para(1330(a,2),542(a,1))]. 1333 L(K(x,y),(x \ y) * y,z) = K(y,x \ y). [para(578(a,1),1332(a,1,1))]. 1334 L(K(x,y),(x \ y) * y,z) = K(x,y). [para(1333(a,2),578(a,1))]. 1335 L(T((x \ y) / z,(x \ y) \ 1) * (T(z,(x \ y) \ 1) * (y \ u)),x,T(z,(x \ y) \ 1) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). [para(397(a,1),1326(a,1,1,1))]. 1336 T(x,(y * z) \ x) * (((y * z) / x) / z) = R(y,z,x / (y * z)). [para(180(a,1),390(a,1)),flip(a)]. 1337 L(K(x,y),z * T(y,x),u) = K(x,L(y,z,u)). [para(612(a,2),1324(a,1))]. 1338 L(K(x,y),z * y,u) = K(x,L(y,z,u)). [para(1337(a,1),986(a,1)),flip(a)]. 1339 K(x,L(y,z / y,u)) = L(K(x,y),z,u). [para(16(a,1),1338(a,1,2)),flip(a)]. 1340 K(x,L(y,x \ y,z)) = K(x,y). [para(1338(a,1),1334(a,1))]. 1341 K(x,L(y,z,x)) = K(x,y). [para(981(a,1),1340(a,1,2))]. 1342 T(x,L(y,z,x)) = x * K(x,y). [para(1341(a,1),530(a,2,2))]. 1343 T(x,L(y,z,x)) = T(x,y). [para(1342(a,2),530(a,2)),flip(a)]. 1344 T((x * y) * z,L(x,y,z)) = T((x * y) * z,x). [para(990(a,1),1343(a,1,2))]. 1345 L(K(x,y),z,u) = K(x,L(y,z,u)). [para(968(a,1),1339(a,1,2)),flip(a)]. 1346 K(x,L(y \ 1,z,u)) = L(K(y,x),z,u). [para(559(a,1),1345(a,1,1)),flip(a)]. 1347 K(x,L(y,z,u)) \ K(x,y) = a(u,z,K(x,y)). [para(1345(a,1),1118(a,2,1)),flip(a)]. 1348 K(x,y) * K(y,L(x,z,u)) = a(z,u,K(y,x)). [para(1345(a,1),1246(a,1,2))]. 1349 L(K(x,y),z,u) = K(L(x,z,u),y). [para(1346(a,1),994(a,1))]. 1350 K(L(x,y,z),u) = K(x,L(u,y,z)). [para(1349(a,1),1345(a,1))]. 1351 K(x,y) * K(y,L(x,z,u)) = K(a(y,z,u),T(x,y)). [para(1350(a,1),1291(a,1,2))]. 1352 K(x,K(y,L(z,u,w))) \ K(x,K(y,z)) = a(w,u,K(x,K(y,z))). [para(1345(a,1),1347(a,1,1,2))]. 1353 T((x * y) * z,x) = z * (T(y,z) * x). [para(1344(a,1),1072(a,1))]. 1354 T((x * (y / z)) * z,x) = z * ((z \ y) * x). [para(80(a,1),1353(a,2,2,1))]. 1355 T((x / y) * (y * z),x) = y * ((y \ z) * x). [para(1055(a,1),1354(a,1,1))]. 1356 K(a(x,y,z),T(u,x)) = a(y,z,K(x,u)). [para(1351(a,1),1348(a,1))]. 1357 a(x,y,K(z,u)) = K(u,a(z,y,x)). [para(1356(a,1),1313(a,1))]. 1358 a(x,y,K(z,u)) = K(u,a(x,z,y)). [para(1128(a,1),1357(a,2,2))]. 1359 a(x,y,K(z,u)) = K(a(z,x,y),u). [para(1357(a,2),1248(a,2)),flip(a)]. 1360 a(x,y,K(z,u)) * u = T(u,a(x,z,y)). [para(1358(a,2),544(a,2,1)),flip(a)]. 1361 a(x,y,K(z,u)) = a(z,x,K(y,u)). [para(1358(a,2),1357(a,2))]. 1362 a(x,K(y,z),u) = a(x,y,K(u,z)). [para(1361(a,2),1128(a,2))]. 1363 a(x,y,K(z,u)) * y = L(y,z,K(x,u)). [para(1361(a,1),1243(a,2,1)),flip(a)]. 1364 a(x,y,K(z,u)) = a(x,u,K(y,z)). [para(1362(a,1),1142(a,1)),flip(a)]. 1365 a(x,y,K(z,u)) * u = L(u,K(y,z),x). [para(1364(a,2),1249(a,2,1)),flip(a)]. 1366 L(x,K(y,z),u) = L(x,y,K(u,z)). [para(1363(a,1),1249(a,2))]. 1367 L(x,y,K(z,u)) = L(x,u,K(y,z)). [para(1366(a,1),847(a,1)),flip(a)]. 1368 L(x,y \ z,K(u,z)) = L(x,u,K(y,z)). [para(578(a,1),1367(a,1,3)),flip(a)]. 1369 L(x,y \ z,K(z,u)) = L(x,u,K(z,y)). [para(579(a,1),1367(a,2,3))]. 1370 L(x,K(y,z),u) = T(x,a(u,z,y)). [para(1365(a,1),1360(a,1))]. 1371 L(x,y,K(z,u)) = T(x,a(z,u,y)). [para(1370(a,1),1366(a,1)),flip(a)]. 1372 T(L(x,y,K(z,u)),K(a(z,u,y),w)) = T(x,T(a(z,u,y),w)). [para(1371(a,2),740(a,1,1))]. 1373 L(x * a(y,z,u),z,K(y,u)) = a(y,z,u) * x. [para(1371(a,2),1281(a,1))]. 1374 L(x,(y / z) \ T(u,y),K(w,T(u,y))) = L(x,w,K(u,y \ z)). [para(725(a,1),1368(a,2,3))]. 1375 L(x,y \ z,K((x * u) / w,z)) = L(x,u / w,K(y,z)). [para(1368(a,2),1170(a,1))]. 1376 L(x,y \ z,K(z,u / (x * w))) = L(x,w / u,K(y,z)). [para(561(a,1),1375(a,1,3))]. 1377 T(L(x,y,K(z,u)),K(a(y,z,u),w)) = T(x,T(a(z,u,y),w)). [para(1128(a,1),1372(a,1,2,1))]. 1378 T(L(x,y,K(z,u)),a(z,u,K(y,w))) = T(x,T(a(z,u,y),w)). [para(1359(a,2),1377(a,1,2))]. 1379 L(L(x,y,K(z,u)),K(y,w),K(z,u)) = T(x,T(a(z,u,y),w)). [para(1378(a,1),1371(a,2))]. 1380 L(L(x,y,K(z,u)),y,K(K(z,u),w)) = T(x,T(a(z,u,y),w)). [para(1379(a,1),1366(a,1)),flip(a)]. 1381 L(L(x,y,K(z,u)),y,K(z,K(u,w))) = T(x,T(a(z,u,y),w)). [para(747(a,1),1380(a,1,3))]. 1382 L(L(x,y,K(z,u)),y,K(z,K(u,w))) = T(x,T(a(y,z,u),w)). [para(1128(a,1),1381(a,2,2,1))]. 1383 L(L(x,y,K(z,u)),y,K(z,K(u,w))) = T(x,a(y,z,T(u,w))). [para(1215(a,2),1382(a,2,2))]. 1384 L(L(x,y,K(z,u)),y,K(z,K(u,w))) = L(x,T(u,w),K(y,z)). [para(1383(a,2),1371(a,2)),flip(a)]. 1385 L(L(x,y,K(z,u)),y,K(z,K(u,w))) = L(x,u,T(K(y,z),w)). [para(1384(a,2),1265(a,1))]. 1386 L(L(x,y,K(z,u)),y,K(z,K(u,w))) = L(x,u,K(y,T(z,w))). [para(717(a,2),1385(a,2,3))]. 1387 L(x,(y / z) * T(u,z),K(w,T(u,z))) = L(x,w,K(u,z \ y)). [para(343(a,1),1374(a,1,2))]. 1388 (x * (y / z)) * L(L(z,y,x),u,w) = x * (y * a(z,u,w)). [para(983(a,1),1263(a,1,2))]. 1389 x * (K(y * z,x) * (((y * z) / x) / z)) = R(y,z,x / (y * z)). [para(1336(a,1),678(a,1)),flip(a)]. 1390 R(x,y,z / (x * y)) = z * ((z \ (x * y)) / y). [para(766(a,1),1389(a,1,2)),flip(a)]. 1391 R(x,y,z / (x * y)) = R(x,y,z). [para(1390(a,2),497(a,2)),flip(a)]. 1392 R(x,x \ y,z / y) = R(x,x \ y,z). [para(14(a,1),1391(a,1,3,2))]. 1393 R(x,x \ y,z) = R(x,y,z / y). [para(1392(a,1),967(a,1))]. 1394 R(x,y,z / y) = R(x,y,z). [para(1393(a,1),967(a,1))]. 1395 R(x,y,y \ z) = R(x,y,T(z,y)). [para(123(a,1),1394(a,1,3))]. 1396 R(x,y,z \ 1) = R(x,y,z \ y). [para(318(a,1),1394(a,1,3))]. 1397 R(x,y,T(z,y)) = R(x,y,z). [para(1395(a,1),997(a,1))]. 1398 R(x,y,y / z) = R(x,y,z \ y). [para(232(a,1),1397(a,1,3)),flip(a)]. 1399 R(x,y,z) * (z * y) = (x * y) * T(z,y). [para(1397(a,1),210(a,1,1))]. 1400 R((x / y) \ z,x,z) = (x / y) \ R(z,x,y \ x). [para(1398(a,1),975(a,2,2))]. 1401 L(x,y,z) * (z * y) = (x * y) * T(z,y). [para(958(a,1),1399(a,1,1))]. 1402 T(x * y,x * z) = ((z \ y) * z) * T(x,z). [para(1401(a,1),206(a,1)),flip(a)]. 1403 T(x * y,x * z) = T(y,z) * T(x,z). [para(120(a,2),1402(a,2,1))]. 1404 T(x,y \ z) * T(y,y \ z) = T(y * x,z). [para(14(a,1),1403(a,1,2)),flip(a)]. 1405 T(x * y,x * a(x,z,u)) = T(y,a(x,z,u)) * x. [para(1122(a,1),1403(a,2,2))]. 1406 T(x,y \ z) * T(y,z) = T(y * x,z). [para(222(a,1),1404(a,1,2))]. 1407 T(x,y \ z) \ T(y,z) = T(y * (x \ 1),z). [para(1406(a,1),400(a,1)),flip(a)]. 1408 T(x,y \ z) \ T(y,z) = T(y / x,z). [para(345(a,1),1407(a,2,1))]. 1409 L(x,y,T(z,u \ y) \ u) = L(x,y,T(u / z,y)). [para(1408(a,1),1269(a,1,3)),flip(a)]. 1410 R((x / y) * z,y,z) = (y / x) \ R(z,y,x \ y). [para(343(a,1),1400(a,1,1))]. 1411 T(x * y,L(x,z,u)) = T(y,a(x,z,u)) * x. [para(1238(a,2),1405(a,1,2))]. 1412 T(x * y,L(x,z,u)) = T(y,a(z,u,x)) * x. [para(1128(a,2),1411(a,2,1,2))]. 1413 T(x * y,L(x,z,u)) = L(y,x,K(z,u)) * x. [para(1371(a,2),1412(a,2,1))]. 1414 L(x * y,y,K(z,u)) = T(y * x,L(y,z,u)). [para(1413(a,2),893(a,2))]. 1415 T((x \ 1) * y,L(x \ 1,z,u)) = L(y / x,x \ 1,K(z,u)). [para(345(a,1),1414(a,1,1)),flip(a)]. 1416 L(x,y,T(z,u \ y) \ u) = L(x,y,u / z). [para(1409(a,2),807(a,1))]. 1417 R((x / y) * z,y,z) = (x / y) * R(z,y,x \ y). [para(1410(a,2),343(a,1))]. 1418 (x / y) * R(z,y,x \ y) = x * (y \ z). [para(1417(a,1),974(a,1))]. 1419 R(x,y,z \ y) = L(x,y \ 1,z). [hyper(482,a,1418,a),flip(a)]. 1420 R(x,y,z \ 1) = L(x,y \ 1,z). [para(1419(a,1),1396(a,2))]. 1421 L(x,y \ 1,z) * (y / z) = (x * y) / z. [para(1420(a,1),491(a,1,1))]. 1422 L(x,y,z) * (z / y) = (x * z) / y. [para(843(a,1),1421(a,1,1))]. 1423 ((x \ (y * z)) * x) / y = ((x \ y) * z) * (x / y). [para(853(a,1),1422(a,1,1)),flip(a)]. 1424 (L(x \ y,z,y) * z) / x = (x \ y) * (z / x). [para(933(a,1),1422(a,1,1)),flip(a)]. 1425 L(x,y,z) \ (z / y) = ((x \ 1) * z) / y. [para(1422(a,1),992(a,1)),flip(a)]. 1426 L(a(x,y,z),u,z) * (z / u) = L(z,x,y) / u. [para(1250(a,2),1422(a,2,1))]. 1427 L(x,y,z) \ (z / y) = (x \ z) / y. [para(314(a,1),1425(a,2,1))]. 1428 L(((x \ y) / z) * u,L(x,z,y),y / z) = L(x,z,y) \ ((y / z) * u). [para(1427(a,1),828(a,1,1,1))]. 1429 L((x \ y) * z,z,y) / x = (x \ y) * (z / x). [para(893(a,2),1424(a,1,1))]. 1430 a(x,y,z) * (z / u) = L(z,x,y) / u. [para(1167(a,1),1426(a,1,1))]. 1432 T(L(x,y,z) / u,u) = (u \ x) * a(y,z,x). [para(1430(a,1),1136(a,1,1))]. 1433 (x \ y) * a(z,u,y) = x \ L(y,z,u). [para(1432(a,1),80(a,1))]. 1434 T(K(x,a(y,z,u)) * u,a(y,z,u)) = T(a(y,z,u),x) \ L(u,y,z). [para(1433(a,1),694(a,2))]. 1435 (x \ (y * z)) / x = (x \ y) * (z / x). [para(1061(a,1),1429(a,1,1))]. 1436 x \ ((y * z) / x) = (x \ y) * (z / x). [para(1435(a,1),130(a,1)),flip(a)]. 1437 (x \ ((y \ x) * z)) / y = x \ ((y \ x) * (z / y)). [para(1436(a,1),1070(a,2,2))]. 1438 ((x \ y) * z) * (x / y) = T(y * z,x) / y. [para(120(a,2),1423(a,1,1)),flip(a)]. 1439 x * (T(x * (y / x),z) / x) = T(y,x \ (z / x)). [para(1438(a,1),1220(a,1,2))]. 1440 T(x * ((x * (y / x)) / x),z) = T(y,x \ (z / x)). [para(1439(a,1),294(a,2))]. 1441 T(x * (x * ((y / x) / x)),z) = T(y,x \ (z / x)). [para(137(a,1),1440(a,1,1,2))]. 1442 T(x * (x * (y / (x * x))),z) = T(y,x \ (z / x)). [para(278(a,1),1441(a,1,1,2,2))]. 1443 T(T(x,y \ (y \ x)),z) = T(x,y \ (z / y)). [para(1442(a,1),776(a,2))]. 1444 L(x / y,y \ 1,K(z,u)) = T(y \ x,L(y \ 1,z,u)). [para(314(a,1),1415(a,1,1)),flip(a)]. 1445 T(x \ y,L(x \ 1,z,u)) = L(y / x,K(z,u),x). [para(1444(a,1),843(a,1))]. 1446 T(x \ y,L(x \ 1,z,u)) = L(y / x,z,K(x,u)). [para(1445(a,2),1366(a,1))]. 1447 T(T(T(x,y \ x),z),T(x,z) / y) = T(y * (T(x,y \ x) / y),z). [para(288(a,2),294(a,2)),flip(a)]. 1448 (x \ y) * ((y \ x) \ (z \ (y \ x))) = T((x \ y) * (z \ 1),y \ x). [para(353(a,1),433(a,2,1))]. 1449 K(x,T(T(T(y,z \ y),u),T(y,u) / z)) = K(x,T(y,u)). [para(192(a,1),1309(a,1,2,2))]. 1450 T(K(x,a(y,z,u)) * u,a(y,z,u)) = a(y,z,T(u,x)) \ L(u,y,z). [para(1215(a,2),1434(a,2,1))]. 1451 T(T(T(x,y \ x),z),T(x,z) / y) = T(y * (x * (y \ K(y,x))),z). [para(729(a,1),1447(a,2,1,2))]. 1452 (x \ y) * ((y \ x) \ (z \ (y \ x))) = T((x \ y) / z,y \ x). [para(345(a,1),1448(a,2,1))]. 1453 (x \ y) / T(z,y \ x) = T((x \ y) / z,y \ x). [para(1452(a,1),377(a,1)),flip(a)]. 1454 T(K(x,a(y,z,u)) * u,a(y,z,u)) = a(y,T(u,x),z) * L(u,y,z). [para(1450(a,2),1256(a,1))]. 1455 T(T(T(x,y \ x),z),T(x,z) / y) = T(T(x,y \ (y \ x)),z). [para(770(a,1),1451(a,2,1))]. 1456 K(x,T(T(y,z \ (z \ y)),u)) = K(x,T(y,u)). [para(1455(a,1),1449(a,1,2))]. 1457 K(x,T(y,z \ (u / z))) = K(x,T(y,u)). [para(1443(a,1),1456(a,1,2))]. 1458 K(x,T(y,(z / u) * z)) = K(x,T(y,u)). [para(1457(a,1),1311(a,1)),flip(a)]. 1459 K(x,T(y,z \ u)) = K(x,T(y,z * u)). [para(53(a,1),1458(a,1,2,2,1)),flip(a)]. 1460 K(x,T(y,(z / u) \ (u * (w * u)))) = K(x,T(y,(z * w) * u)). [para(1048(a,1),1459(a,2,2,2))]. 1461 K(x,T(y,z * (u \ 1))) = K(x,T(y,u * z)). [para(1459(a,1),1307(a,1))]. 1462 K(x,T(y,z / u)) = K(x,T(y,u * z)). [para(345(a,1),1461(a,1,2,2))]. 1463 K(x,T(y,z * (u * z))) = K(x,T(y,u)). [para(15(a,1),1462(a,1,2,2)),flip(a)]. 1464 K(x,T(y,(z * u) / ((w / u) / z))) = K(x,T(y,L(w,u,z))). [para(984(a,2),1462(a,2,2,2))]. 1465 K(x,T(y,(z \ u) * (z * ((z \ w) * u)))) = K(x,T(y,w * z)). [para(261(a,1),1463(a,1,2,2,2))]. 1466 K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (w * z))). [para(1066(a,1),1463(a,1,2,2)),flip(a)]. 1467 K(x,T(y,(z * u) * (z / (w / u)))) = K(x,T(y,L(w,u,z))). [para(357(a,1),1464(a,1,2,2))]. 1468 K(x,T(y,(z * u) * (z * (u / w)))) = K(x,T(y,L(w,u,z))). [para(357(a,1),1467(a,1,2,2,2))]. 1469 K(x,T(y,(((z / u) \ u) * w) * u)) = K(x,T(y,(z * w) * u)). [para(1062(a,1),1460(a,1,2,2))]. 1470 K(x,T(y,((z \ u) * w) * u)) = K(x,T(y,w * z)). [para(1071(a,1),1465(a,1,2,2))]. 1471 K(x,T(y,((z * (u \ z)) * w) * z)) = K(x,T(y,(u * w) * z)). [para(380(a,1),1469(a,1,2,2,1,1))]. 1472 K(x,T(y,(z * (u \ (z * w))) * z)) = K(x,T(y,(u * w) * z)). [para(772(a,1),1471(a,1,2,2,1))]. 1473 K(x,T(y,z * ((u \ (z * w)) * z))) = K(x,T(y,(u * w) * z)). [para(113(a,1),1472(a,1,2,2))]. 1474 K(x,T(y,z \ (u * w))) = K(x,T(y,(z * w) * u)). [para(1473(a,1),1463(a,1)),flip(a)]. 1475 K(x,T(y,(z * u) * w)) = K(x,T(y,z * (w * u))). [para(1474(a,1),1459(a,1))]. 1477 K(x,T(y,z * ((z * (u / w)) * u))) = K(x,T(y,L(w,u,z))). [para(1475(a,1),1468(a,1))]. 1478 K(x,T(y,(z \ u) * (u * w))) = K(x,T(y,w * z)). [para(1475(a,1),1470(a,1))]. 1479 K(x,T(y,z * ((z * u) * w))) = K(x,T(y,u * w)). [para(1478(a,1),1466(a,1)),flip(a)]. 1480 K(x,T(y,L(z,u,w))) = K(x,T(y,(u / z) * u)). [para(1477(a,1),1479(a,1))]. 1481 K(x,T(y,L(z,u,w))) = K(x,T(y,z)). [para(1480(a,2),1458(a,1))]. 1483 T(x,T(y,L(z,u,w))) = x * K(x,T(y,z)). [para(1481(a,1),530(a,2,2))]. 1485 T(x,T(y,L(z,u,w))) = T(x,T(y,z)). [para(1483(a,2),530(a,2)),flip(a)]. 1486 T(x,K(y,L(z,u,w))) = T(x,T(y,z)) * K(y,x). [para(1485(a,1),741(a,1,1)),flip(a)]. 1487 T(x,K(y,L(z,u,w))) = T(x,K(y,z)). [para(1486(a,2),741(a,1))]. 1488 K(K(x,L(y,z,u)),w) = T(w,K(x,y)) \ w. [para(1487(a,1),531(a,2,1))]. 1489 K(K(x,L(y,z,u)),w) = K(K(x,y),w). [para(1488(a,2),531(a,2)),flip(a)]. 1490 K(K(x,L(y,z,u)),w) = K(x,K(y,w)). [para(1489(a,2),747(a,1))]. 1491 K(K(x,L(y,z,u)),w) = K(w,K(x,y)). [para(1490(a,2),1302(a,1))]. 1492 K(x,K(L(y,z,u),w)) = K(w,K(x,y)). [para(1491(a,1),747(a,1)),flip(a)]. 1493 K(x,K(y,L(z,u,w))) = K(z,K(x,y)). [para(1350(a,1),1492(a,1,2))]. 1494 a(x,y,K(z,K(u,w))) = K(w,K(z,u)) \ K(z,K(u,w)). [para(1493(a,1),1352(a,1,1)),flip(a)]. 1495 a(x,y,K(z,K(u,w))) = K(z,K(u,w)) \ K(z,K(u,w)). [para(1302(a,2),1494(a,2,1))]. 1497 a(x,y,K(z,K(u,w))) = 1. [para(1495(a,2),50(a,1))]. 1499 a(K(x,K(y,z)),u,w) = 1. [para(1497(a,1),1128(a,1)),flip(a)]. 1500 L(x,y,K(z,K(u,w))) = x. [hyper(33,a,1499,a)]. 1501 L(x,y,K(z,T(u,w))) = L(x,z,K(u,y)). [para(1500(a,1),1386(a,1)),flip(a)]. 1502 L(x,y,K(z,(u / w) * T(z,w))) = L(x,y,K(z,w \ u)). [para(1501(a,1),1387(a,1))]. 1503 L(x,y,K(z,u / w)) = L(x,y,K(z,w \ u)). [para(593(a,1),1502(a,1,3))]. 1506 L(x,y \ z,K(z,(x * u) \ w)) = L(x,u / w,K(y,z)). [para(1503(a,1),1376(a,1))]. 1507 L(x,(x * y) \ z,K(u,w)) = L(x,y / z,K(w,u)). [para(1506(a,1),1369(a,1)),flip(a)]. 1508 L(x,y / z,K(u,w)) = L(x,y \ z,K(w,u)). [para(1507(a,1),1319(a,1))]. 1509 T(K(x,a(y,z,u)) * u,a(y,z,u)) = a(y,u,T(z,x)) * L(u,y,z). [para(1216(a,1),1454(a,2,1))]. 1510 T(K(x,a(y,z,u)) * u,a(y,z,u)) = L(L(u,y,z),T(z,x),y). [para(1509(a,2),1254(a,1))]. 1511 T(K(x,a(y,z,u)) * u,a(y,z,u)) = L(L(u,y,z),z,T(y,x)). [para(1510(a,2),1265(a,1))]. 1512 T(a(x,y,K(z,u)) * x,a(z,y,x)) = L(L(x,z,y),y,T(z,u)). [para(1357(a,2),1511(a,1,1,1))]. 1513 T(L(x,y,K(z,u)),a(z,y,x)) = L(L(x,z,y),y,T(z,u)). [para(1243(a,2),1512(a,1,1))]. 1514 L(L(x,y,K(z,u)),x,K(z,y)) = L(L(x,z,y),y,T(z,u)). [para(1513(a,1),1371(a,2))]. 1515 L(L(x,y,z),z,T(y,u)) = L(x,z,K(y,u)). [para(1514(a,1),276(a,1))]. 1516 L(L(x,y,T(z,u)),z,y) = L(x,y,K(z,u)). [para(1515(a,1),45(a,1)),flip(a)]. 1518 L(L(x,y,z),y / x,K(z,u)) = L(x,y / x,T(z,u)). [para(985(a,1),1515(a,1,1)),flip(a)]. 1519 L(L(x,y,z),y / x,K(z,u)) = L(x,y,T(z,u)). [para(1518(a,2),968(a,1))]. 1520 L(L(x,y,z),y \ x,K(u,z)) = L(x,y,T(z,u)). [para(1519(a,1),1508(a,1)),flip(a)]. 1521 L(L(x,K(y,z),u),u,z) = L(x,u,T(z,y)). [para(1520(a,1),988(a,1)),flip(a)]. 1522 L(L(x,y,K(z,u)),z,u) = L(x,z,T(u,y)). [para(1366(a,1),1521(a,1,1))]. 1523 L(L(x,y \ z,K(u,T(z,w))),u,T(z,w)) = L(x,u,T(T(z,w),y \ 1)). [para(395(a,2),1522(a,2,3))]. 1524 ((x * y) * z) * ((y * z) \ u) = (y * z) * ((z \ (y \ x)) * u). [para(926(a,1),1010(a,1,2,1)),flip(a)]. 1525 L(((x \ y) / z) * u,x,y / z) = L(x,z,y) \ ((y / z) * u). [para(1428(a,1),1179(a,1)),flip(a)]. 1526 L(L(x,y,K(z,u \ z)),y,T(z,w)) = L(x,y,T(T(z,w),u \ 1)). [para(1501(a,1),1523(a,1,1))]. 1527 L(L(x,y,K(z,u)),y,T(u,w)) = L(x,y,T(T(u,w),z \ 1)). [para(578(a,1),1526(a,1,1,3))]. 1529 (x \ 1) * (y \ (x * (T(y,x) * z))) = L(z,(x \ 1) * (x \ 1),T(y,x)). [para(317(a,1),1095(a,1,2,2))]. 1530 L(x,(y \ 1) * (y \ 1),T(z,y)) = y \ (z \ (y * (T(z,y) * x))). [para(1529(a,1),314(a,1))]. 1531 x \ (y \ (x * (T(y,x) * z))) = L(z,x \ (x \ 1),T(y,x)). [para(314(a,1),1530(a,1,2)),flip(a)]. 1532 x \ (y \ (x * (T(y,x) * z))) = L(z,T(y,x),x * x). [para(1531(a,2),846(a,1))]. 1533 x \ (y \ (x * (T(y,x) * z))) = L(z,y,T(x * x,x)). [para(1532(a,2),1265(a,1))]. 1534 x \ (y \ (x * (T(y,x) * z))) = L(z,y,x * x). [para(116(a,1),1533(a,2,3))]. 1535 (x * y) \ ((x / (z / y)) * L(L(z,y,x),u,w)) = a(u,w,((z / y) / x) * (x * y)). [para(343(a,1),1280(a,1,2))]. 1536 (x * y) \ ((x * (y / z)) * L(L(z,y,x),u,w)) = a(u,w,((z / y) / x) * (x * y)). [para(357(a,1),1535(a,1,2,1))]. 1537 a(x,y,((z / u) / w) * (w * u)) = (w * u) \ (w * (u * a(z,x,y))). [para(1388(a,1),1536(a,1,2)),flip(a)]. 1538 a(x,y,((z / u) / w) * (w * u)) = L(a(z,x,y),u,w). [para(1537(a,2),28(a,2)),flip(a)]. 1539 a(x,y,L(z,u,w)) = L(a(z,x,y),u,w). [para(984(a,2),1538(a,1,3))]. 1540 a(x,y,L(z,u,w)) = L(a(y,z,x),u,w). [para(1128(a,1),1539(a,2,1))]. 1541 a(x,y,L(z,u,w)) = L(a(x,y,z),u,w). [para(1128(a,2),1539(a,2,1))]. 1542 a(x,y,L(z,u,w)) = a(z,x,L(y,u,w)). [para(1540(a,2),1539(a,2)),flip(a)]. 1543 T((x \ y) / z,y \ x) * (T(z,y \ x) * u) = T(z,y \ x) \ (((x \ y) * z) * u). [para(1453(a,1),813(a,1,1))]. 1544 ((x \ y) * z) \ (y * ((y \ ((x \ y) * (z / x))) * u)) = (z \ K(z,x \ y)) * (((x \ y) * z) * (y \ u)). [para(1437(a,1),1323(a,1,2,2,1))]. 1545 (x \ K(x,y \ z)) * (((y \ z) * x) * (z \ u)) = (x \ (z \ y)) * (z * ((z \ ((y \ z) * (x / y))) * u)). [para(1544(a,1),386(a,1))]. 1546 T(x \ 1,(y \ z) \ 1) * (((y \ z) * x) * (z \ u)) = (x \ (z \ y)) * (z * ((z \ ((y \ z) * (x / y))) * u)). [para(568(a,2),1545(a,1,1))]. 1547 K(x,y \ z) * (x \ (((y \ z) * x) * (z \ u))) = (x \ (z \ y)) * (z * ((z \ ((y \ z) * (x / y))) * u)). [para(1545(a,1),779(a,1)),flip(a)]. 1548 K(x,y \ z) * ((x \ (y \ z)) * (x * (z \ u))) = (x \ (z \ y)) * (z * ((z \ ((y \ z) * (x / y))) * u)). [para(260(a,1),1547(a,1,2))]. 1549 (x \ (y \ z)) * (y * ((y \ ((z \ y) * (x / z))) * u)) = ((z \ y) / x) * (x * (y \ u)). [para(1548(a,1),726(a,1))]. 1550 x * ((y * ((x * y) \ z)) * ((u * x) * (y * ((x * y) \ z)))) = L(z,y,x) * (u * L(z,y,x)). [para(870(a,2),1073(a,2,2,2))]. 1551 x * (y * (((x * y) \ z) * (((u * x) * y) * ((x * y) \ z)))) = L(z,y,x) * (u * L(z,y,x)). [para(1014(a,1),1550(a,1,2))]. 1552 x * (y * (((x * y) \ z) * ((x * y) * ((y \ (x \ u)) * z)))) = L(z,y,x) * (u * L(z,y,x)). [para(1524(a,1),1551(a,1,2,2,2))]. 1553 x * (y * ((((x * y) \ z) * L(u,x,y)) * z)) = L(z,y,x) * (u * L(z,y,x)). [para(1076(a,1),1552(a,1,2,2))]. 1554 L(x * (L(y,z,u) * x),u,z) = L(x,u,z) * (y * L(x,u,z)). [para(1553(a,1),1063(a,1)),flip(a)]. 1556 T(x \ 1,(y \ z) \ 1) * (((y \ z) * x) * (z \ u)) = ((y \ z) / x) * (x * (z \ u)). [para(1546(a,2),1549(a,1))]. 1557 T(x \ 1,y \ z) * (((z \ y) * x) * (y \ u)) = ((z \ y) / x) * (x * (y \ u)). [para(333(a,1),1556(a,1,1,2))]. 1558 T(x,y \ z) \ (((z \ y) * x) * (y \ u)) = ((z \ y) / x) * (x * (y \ u)). [para(1557(a,1),400(a,1)),flip(a)]. 1559 L(T((x \ y) / z,y \ x) * (T(z,(x \ y) \ 1) * (y \ u)),x,T(z,(x \ y) \ 1) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). [para(333(a,1),1335(a,1,1,1,2))]. 1560 L(T((x \ y) / z,y \ x) * (T(z,y \ x) * (y \ u)),x,T(z,(x \ y) \ 1) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). [para(333(a,1),1559(a,1,1,2,1,2))]. 1561 L(T(x,y \ z) \ (((z \ y) * x) * (y \ u)),z,T(x,(z \ y) \ 1) \ y) = L(z \ u,T(x,(z \ y) \ 1),y). [para(1543(a,1),1560(a,1,1))]. 1562 L(((x \ y) / z) * (z * (y \ u)),x,T(z,(x \ y) \ 1) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). [para(1558(a,1),1561(a,1,1))]. 1563 L(((x \ y) / z) * (z * (y \ u)),x,T(z,y \ x) \ y) = L(x \ u,T(z,(x \ y) \ 1),y). [para(333(a,1),1562(a,1,3,1,2))]. 1564 L(((x \ y) / z) * (z * (y \ u)),x,y / z) = L(x \ u,T(z,(x \ y) \ 1),y). [para(1563(a,1),1416(a,1)),flip(a)]. 1565 L(x \ y,T(z,(x \ u) \ 1),u) = L(x,z,u) \ ((u / z) * (z * (u \ y))). [para(1564(a,1),1525(a,1))]. 1566 L(x \ y,T(z,(x \ u) \ 1),u) = L(x,z,u) \ L(y,z,u). [para(849(a,2),1565(a,2,2))]. 1567 L(x \ y,T(z,u \ x),u) = L(x,z,u) \ L(y,z,u). [para(333(a,1),1566(a,1,2,2))]. 1568 L(x \ y,z,T(u,u \ x)) = L(x,z,u) \ L(y,z,u). [para(1567(a,1),1265(a,1)),flip(a)]. 1569 L(x \ y,z,T(u,x)) = L(x,z,u) \ L(y,z,u). [para(222(a,1),1568(a,1,3))]. 1570 T(L(x \ y,z,T(u,x)),L(x,z,u) \ 1) = L(y,z,u) / L(x,z,u). [para(1569(a,2),347(a,1,1))]. 1571 T(L(x \ y,z,T(u,x)),L(x \ 1,z,u)) = L(y,z,u) / L(x,z,u). [para(971(a,2),1570(a,1,2))]. 1572 L(T(x \ y,L(x \ 1,z,u)),z,T(u,x)) = L(y,z,u) / L(x,z,u). [para(1571(a,1),40(a,2))]. 1573 L(L(x / y,z,K(y,u)),z,T(u,y)) = L(x,z,u) / L(y,z,u). [para(1446(a,1),1572(a,1,1))]. 1574 L(x / y,z,T(T(u,y),y \ 1)) = L(x,z,u) / L(y,z,u). [para(1573(a,1),1527(a,1)),flip(a)]. 1575 L(x,y,z) / L(u,y,z) = L(x / u,y,z). [para(338(a,1),1574(a,1,3)),flip(a)]. 1576 L(x * y,z,u) / L(y,z,u) = L(x,z,u). [para(15(a,1),1575(a,2,1))]. 1577 (L(x,y,z) \ (u / L(w,y,z))) * L(w,y,z) = L(w,y,z) \ (L(w / x,y,z) * u). [para(1575(a,1),1091(a,1,2,1)),flip(a)]. 1578 L(x,y,z) * L(u,y,z) = L(x * u,y,z). [para(1576(a,1),16(a,1,1))]. 1579 L(x,y,z) \ L(x * u,y,z) = L(u,y,z). [para(1576(a,1),54(a,1,1))]. 1580 L(L(x,y,z) * u,z,y) = x * L(u,z,y). [hyper(17,a,1554,a(flip),b,1578,a)]. 1581 T(L(x * y,z,u),L(x,z,u)) = L(y,z,u) * L(x,z,u). [para(1578(a,1),116(a,1,1))]. 1582 L(x,y,z) \ L(u,y,z) = L(x \ u,y,z). [para(14(a,1),1579(a,1,2,1))]. 1584 L(L(x,y,z) \ u,z,y) = x \ L(u,z,y). [para(829(a,1),1582(a,1,1)),flip(a)]. 1585 L(x / (L(y,z,u) \ w),u,z) = L(x,u,z) / (y \ L(w,u,z)). [para(1584(a,1),1575(a,1,2)),flip(a)]. 1586 L(T(x * y,L(x,z,u)),z,u) = L(y,z,u) * L(x,z,u). [para(1581(a,1),40(a,2))]. 1587 L(L(x * y,y,K(z,u)),z,u) = L(x,z,u) * L(y,z,u). [para(1414(a,2),1586(a,1,1))]. 1588 L(x * y,z,T(u,y)) = L(x,z,u) * L(y,z,u). [para(1587(a,1),1522(a,1)),flip(a)]. 1589 L(x * y,z,T(u,y)) = L(x * y,z,u). [para(1588(a,2),1578(a,1))]. 1590 L((x / y) * y,z,u) = L(x,z,T(u,y)). [para(16(a,1),1589(a,1,1)),flip(a)]. 1591 L(x,y,T(z,u)) = L(x,y,z). [para(16(a,1),1590(a,1,1)),flip(a)]. 1600 L(L(x,y,z),z,y) = L(x,y,K(z,u)). [para(1591(a,1),1516(a,1,1))]. 1604 L(x,y,K(z,u)) = x. [para(1600(a,1),829(a,1))]. 1611 T(x,a(y,z,u)) = x. [para(1604(a,1),1371(a,1)),flip(a)]. 1612 a(x,y,z) * u = u * a(x,y,z). [para(1604(a,1),1373(a,1)),flip(a)]. 1618 T(a(x,y,z),u) = a(x,y,z). [hyper(35,a,1611,a)]. 1619 a(x,y,z) / u = u \ a(x,y,z). [para(1611(a,1),229(a,1,2))]. 1628 x * (y * a(x,z,u)) = L(x,z,u) * y. [para(1612(a,1),1276(a,1,2))]. 1629 T((a(x,y,z) / u) * (u * w),a(x,y,z)) = u * (a(x,y,z) * (u \ w)). [para(1612(a,2),1355(a,2,2))]. 1630 T(a(x,y,z),u \ w) * T(u,w) = T(a(x,y,z) * u,w). [para(1612(a,2),1406(a,2,1))]. 1631 x \ (y \ (x * (a(z,u,w) * T(y,x)))) = L(a(z,u,w),y,x * x). [para(1612(a,2),1534(a,1,2,2,2))]. 1632 x \ (y * (L(z,u,w) * (z \ (y \ x)))) = L(L(a(z,u,w),z,x \ y),x,y). [para(1628(a,1),1321(a,1,2,2))]. 1633 T(a(x,y,z) * u,w) = a(x,y,z) * T(u,w). [para(1618(a,1),1630(a,1,1)),flip(a)]. 1635 L(x / (L(y,z,u) \ w),u,z) = L(x,u,z) * (L(w,u,z) \ y). [para(1585(a,2),358(a,1))]. 1636 L(x * (y \ L(z,u,w)),w,u) = L(x,w,u) * (L(y,w,u) \ z). [para(358(a,1),1635(a,1,1))]. 1637 x \ (y \ (x * T(a(z,u,w) * y,x))) = L(a(z,u,w),y,x * x). [para(1633(a,2),1631(a,1,2,2,2))]. 1638 x \ (y \ ((a(z,u,w) * y) * x)) = L(a(z,u,w),y,x * x). [para(78(a,1),1637(a,1,2,2))]. 1639 x \ ((y \ a(z,u,w)) * (y * x)) = L(a(z,u,w),y,x * x). [para(260(a,1),1638(a,1,2))]. 1640 T((x \ a(y,z,u)) * (x * w),a(y,z,u)) = x * (a(y,z,u) * (x \ w)). [para(1619(a,1),1629(a,1,1,1))]. 1641 (x \ a(y,z,u)) * (x * w) = x * (a(y,z,u) * (x \ w)). [para(1640(a,1),1611(a,1)),flip(a)]. 1642 x \ (y * (a(z,u,w) * (y \ x))) = L(a(z,u,w),y,x * x). [para(1641(a,1),1639(a,1,2))]. 1643 x \ (y * (a(z,u,w) * (y \ x))) = a(u,w,L(z,y,x * x)). [para(1642(a,2),1539(a,2)),flip(a)]. 1644 L(L(a(x,y,z),x,u \ w),u,w) = u \ (w * (a(x,y,z) * (w \ u))). [para(1260(a,1),1632(a,1,2,2)),flip(a)]. 1645 L(L(a(x,y,z),x,u \ w),u,w) = a(y,z,L(x,w,u * u)). [para(1644(a,2),1643(a,1))]. 1646 a(x,y,L(z,u,w * w)) = L(a(z,x,y),w,u). [para(1169(a,1),1645(a,1,1)),flip(a)]. 1648 a(x,y,L(z,u,w * w)) = a(x,y,L(z,w,u)). [para(1646(a,2),1539(a,2)),flip(a)]. 1649 ((x / L(y,z,u)) * L(y,z,u)) \ (L(w,z,u) * (L(y,z,u) \ (L(y / w,z,u) * x))) = a(x / L(y,z,u),L(w,z,u),L(y,z,u)). [para(1577(a,1),1228(a,2,2,2)),flip(a)]. 1650 x \ (L(y,z,u) * (L(w,z,u) \ (L(w / y,z,u) * x))) = a(x / L(w,z,u),L(y,z,u),L(w,z,u)). [para(16(a,1),1649(a,1,1))]. 1651 x \ L(y * (z \ L(L(z / y,u,w) * x,w,u)),u,w) = a(x / L(z,u,w),L(y,u,w),L(z,u,w)). [para(1636(a,2),1650(a,1,2))]. 1652 a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = x \ L(w * (y \ ((y / w) * L(x,u,z))),z,u). [para(1580(a,1),1651(a,1,2,1,2,2)),flip(a)]. 1653 a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = x \ L(w * ((w \ (L(x,u,z) / y)) * y),z,u). [para(1091(a,1),1652(a,2,2,1,2))]. 1654 a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = x \ L(L(L(x,u,z),w,y),z,u). [para(948(a,2),1653(a,2,2,1))]. 1655 a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = x \ L(x,w,y). [para(832(a,1),1654(a,2,2))]. 1657 a(x / L(y,z,u),L(w,z,u),L(y,z,u)) = a(x,w,y). [para(1655(a,2),1237(a,2)),flip(a)]. 1658 a(L(x,y,z),u / L(x,y,z),L(w,y,z)) = a(u,w,x). [para(1657(a,1),1128(a,1)),flip(a)]. 1659 a(L(x,y,z),u,L(w,y,z)) = a(u,w,x). [para(1658(a,1),1274(a,1)),flip(a)]. 1660 a(x,y,L(L(z,u,w),u,w)) = a(x,y,z). [para(1659(a,1),1542(a,2))]. 1661 a(x,y,L(z,u,w * w)) = a(x,y,z). [para(1293(a,1),1660(a,1,3))]. 1662 a(x,y,L(z,u,w)) = a(x,y,z). [para(1661(a,1),1648(a,1)),flip(a)]. 1665 L(a(x,y,z),u,w) = a(x,y,z). [para(1662(a,1),1541(a,1)),flip(a)]. 1669 a(x,y,a(z,u,w)) = 1. [hyper(34,a,1665,a)]. 1676 a(a(x,y,z),u,w) = 1. [para(1669(a,1),1128(a,1)),flip(a)]. 1677 $F # answer("aa1"). [resolve(1676,a,48,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=1556. Generated=2772641. Kept=1658. proofs=1. Usable=1539. Sos=100. Demods=0. Limbo=0, Disabled=48. Hints=2076. Kept_by_rule=0, Deleted_by_rule=2752251. Forward_subsumed=18732. Back_subsumed=18. 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=195. Nonunit_bsub_feature_tests=56. Megabytes=5.52. User_CPU=28.08, System_CPU=1.20, Wall_clock=30. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED THEOREM PROVED Exiting with 1 proof. ------ process 28884 exit (max_proofs) ------  Process 28884 exit (max_proofs) Wed Jan 29 20:28:32 2020