%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sat Jul 16 10:53:54 EDT 2022 % Result : Unsatisfiable 83.86s 83.62s % Output : Proof 83.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1. % 0.07/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n008.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon Jun 13 10:47:37 EDT 2022 % 0.12/0.33 % CPUTime : % 83.86/83.62 % SZS status Unsatisfiable % 83.86/83.62 % SZS output start Proof % 83.86/83.62 The input problem is unsatisfiable because % 83.86/83.62 % 83.86/83.62 [1] the following set of Horn clauses is unsatisfiable: % 83.86/83.62 % 83.86/83.62 multiply(identity, X) = X % 83.86/83.62 multiply(inverse(X), X) = identity % 83.86/83.62 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 83.86/83.62 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 83.86/83.62 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 83.86/83.62 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z) % 83.86/83.62 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z) % 83.86/83.62 least_upper_bound(X, X) = X % 83.86/83.62 greatest_lower_bound(X, X) = X % 83.86/83.62 least_upper_bound(X, greatest_lower_bound(X, Y)) = X % 83.86/83.62 greatest_lower_bound(X, least_upper_bound(X, Y)) = X % 83.86/83.62 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)) % 83.86/83.62 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 83.86/83.62 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X)) % 83.86/83.62 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 83.86/83.62 inverse(identity) = identity % 83.86/83.62 inverse(inverse(X)) = X % 83.86/83.62 inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)) % 83.86/83.62 inverse(greatest_lower_bound(X, Y)) = least_upper_bound(inverse(X), inverse(Y)) % 83.86/83.62 inverse(least_upper_bound(X, Y)) = greatest_lower_bound(inverse(X), inverse(Y)) % 83.86/83.62 multiply(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity))) = multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(a, identity)) ==> \bottom % 83.86/83.62 % 83.86/83.62 This holds because % 83.86/83.62 % 83.86/83.62 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 83.86/83.62 % 83.86/83.62 E: % 83.86/83.62 f1(multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(a, identity))) = false__ % 83.86/83.62 f1(multiply(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity)))) = true__ % 83.86/83.62 greatest_lower_bound(X, X) = X % 83.86/83.62 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 83.86/83.62 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z) % 83.86/83.62 greatest_lower_bound(X, least_upper_bound(X, Y)) = X % 83.86/83.62 inverse(greatest_lower_bound(X, Y)) = least_upper_bound(inverse(X), inverse(Y)) % 83.86/83.62 inverse(identity) = identity % 83.86/83.62 inverse(inverse(X)) = X % 83.86/83.62 inverse(least_upper_bound(X, Y)) = greatest_lower_bound(inverse(X), inverse(Y)) % 83.86/83.62 inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)) % 83.86/83.62 least_upper_bound(X, X) = X % 83.86/83.62 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 83.86/83.62 least_upper_bound(X, greatest_lower_bound(X, Y)) = X % 83.86/83.62 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z) % 83.86/83.62 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 83.86/83.62 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)) % 83.86/83.62 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 83.86/83.62 multiply(identity, X) = X % 83.86/83.62 multiply(inverse(X), X) = identity % 83.86/83.62 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X)) % 83.86/83.62 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 83.86/83.62 G: % 83.86/83.62 true__ = false__ % 83.86/83.62 % 83.86/83.62 This holds because % 83.86/83.62 % 83.86/83.62 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 83.86/83.62 % 83.86/83.62 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 83.86/83.62 greatest_lower_bound(X1, multiply(X0, X1)) = multiply(greatest_lower_bound(identity, inverse(X0)), multiply(X0, X1)) % 83.86/83.62 greatest_lower_bound(X1, multiply(inverse(Y1), X1)) = multiply(greatest_lower_bound(Y1, identity), multiply(inverse(Y1), X1)) % 83.86/83.62 greatest_lower_bound(X1, multiply(inverse(Y1), X1)) = multiply(greatest_lower_bound(identity, Y1), multiply(inverse(Y1), X1)) % 83.86/83.62 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(inverse(greatest_lower_bound(X1, inverse(Y1))), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(inverse(greatest_lower_bound(inverse(X1), inverse(Y1))), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(inverse(greatest_lower_bound(inverse(Y1), X1)), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(inverse(greatest_lower_bound(inverse(Y1), inverse(X1))), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(Y1, inverse(greatest_lower_bound(X1, identity))), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(Y1, inverse(greatest_lower_bound(Y1, identity))), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(Y1, inverse(greatest_lower_bound(identity, X1))), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(inverse(greatest_lower_bound(X1, identity)), Y1), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity, X1)), Y1), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, greatest_lower_bound(X0, identity)) = greatest_lower_bound(identity, greatest_lower_bound(X0, greatest_lower_bound(identity, Y0))) % 83.86/83.62 greatest_lower_bound(Y0, greatest_lower_bound(identity, Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(identity, greatest_lower_bound(Y1, Y0))) % 83.86/83.62 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(inverse(greatest_lower_bound(X0, identity)), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(inverse(greatest_lower_bound(identity, X0)), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(X0, inverse(greatest_lower_bound(X0, X1))), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(X0, inverse(greatest_lower_bound(X1, X0))), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(X0, inverse(greatest_lower_bound(identity, X0))), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(greatest_lower_bound(X0, X1)), X0), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(greatest_lower_bound(X0, X1)), X1), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, inverse(X0)) = greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(greatest_lower_bound(X0, X1)), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, inverse(X0)) = greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(greatest_lower_bound(X1, X0)), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, inverse(X0)) = greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(greatest_lower_bound(identity, X0)), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, multiply(X0, Y0)) = multiply(greatest_lower_bound(identity, greatest_lower_bound(X0, identity)), Y0) % 83.86/83.62 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1))) % 83.86/83.62 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0)) % 83.86/83.62 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1))) % 83.86/83.62 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0)) % 83.86/83.62 greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y2)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2)) % 83.86/83.62 greatest_lower_bound(Y1, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, identity), Y1) % 83.86/83.62 greatest_lower_bound(Y1, multiply(Y2, Y1)) = multiply(greatest_lower_bound(identity, Y2), Y1) % 83.86/83.62 greatest_lower_bound(Y2, greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2)) % 83.86/83.62 greatest_lower_bound(identity, X1) = multiply(greatest_lower_bound(Y0, multiply(inverse(X1), Y0)), multiply(inverse(Y0), X1)) % 83.86/83.62 greatest_lower_bound(identity, inverse(Y1)) = multiply(greatest_lower_bound(Y1, identity), inverse(Y1)) % 83.86/83.62 greatest_lower_bound(identity, multiply(X0, Y1)) = multiply(X0, greatest_lower_bound(Y1, inverse(X0))) % 83.86/83.63 greatest_lower_bound(identity, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1) % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(X1), inverse(X0))) = multiply(greatest_lower_bound(identity, multiply(X0, X1)), multiply(inverse(X1), inverse(X0))) % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), greatest_lower_bound(Y1, Y2)) % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), greatest_lower_bound(Y1, Y2)) % 83.86/83.63 inverse(greatest_lower_bound(X0, multiply(X0, inverse(Y1)))) = multiply(Y1, multiply(inverse(greatest_lower_bound(identity, Y1)), inverse(X0))) % 83.86/83.63 inverse(greatest_lower_bound(X0, multiply(X0, inverse(Y1)))) = multiply(inverse(greatest_lower_bound(identity, Y1)), multiply(Y1, inverse(X0))) % 83.86/83.63 inverse(greatest_lower_bound(X0, multiply(X0, inverse(Y1)))) = multiply(inverse(greatest_lower_bound(identity, inverse(Y1))), inverse(X0)) % 83.86/83.63 inverse(greatest_lower_bound(X0, multiply(greatest_lower_bound(identity, Y2), inverse(Y2)))) = inverse(greatest_lower_bound(identity, greatest_lower_bound(X0, inverse(Y2)))) % 83.86/83.63 inverse(greatest_lower_bound(Y1, identity)) = multiply(inverse(greatest_lower_bound(identity, inverse(Y1))), inverse(Y1)) % 83.86/83.63 inverse(greatest_lower_bound(Y1, multiply(X0, Y1))) = multiply(inverse(Y1), inverse(greatest_lower_bound(X0, identity))) % 83.86/83.63 inverse(greatest_lower_bound(Y1, multiply(X0, Y1))) = multiply(inverse(Y1), inverse(greatest_lower_bound(identity, X0))) % 83.86/83.63 inverse(greatest_lower_bound(identity, greatest_lower_bound(inverse(Y0), X0))) = inverse(greatest_lower_bound(X0, multiply(greatest_lower_bound(identity, Y0), inverse(Y0)))) % 83.86/83.63 inverse(greatest_lower_bound(identity, multiply(X0, inverse(Y0)))) = multiply(Y0, multiply(inverse(X0), inverse(greatest_lower_bound(identity, multiply(Y0, inverse(X0)))))) % 83.86/83.63 inverse(greatest_lower_bound(inverse(X1), multiply(inverse(X1), inverse(X0)))) = multiply(inverse(greatest_lower_bound(X0, identity)), multiply(X0, X1)) % 83.86/83.63 inverse(greatest_lower_bound(inverse(Y0), inverse(Y1))) = inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(inverse(greatest_lower_bound(X1, Y1)), inverse(Y0)))) % 83.86/83.63 inverse(greatest_lower_bound(inverse(Y0), inverse(Y1))) = inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(inverse(greatest_lower_bound(Y1, X1)), inverse(Y0)))) % 83.86/83.63 inverse(greatest_lower_bound(inverse(Y0), multiply(inverse(Y1), greatest_lower_bound(identity, inverse(X1))))) = inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(inverse(Y0), multiply(inverse(Y1), inverse(X1))))) % 83.86/83.63 inverse(greatest_lower_bound(inverse(Y0), multiply(inverse(Y1), greatest_lower_bound(identity, inverse(X1))))) = inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(multiply(inverse(Y1), inverse(X1)), inverse(Y0)))) % 83.86/83.63 inverse(greatest_lower_bound(inverse(Y0), multiply(inverse(Y1), multiply(greatest_lower_bound(identity, X1), inverse(X1))))) = inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(inverse(Y0), multiply(inverse(Y1), inverse(X1))))) % 83.86/83.63 inverse(greatest_lower_bound(inverse(Y0), multiply(inverse(Y1), multiply(greatest_lower_bound(identity, X1), inverse(X1))))) = inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(multiply(inverse(Y1), inverse(X1)), inverse(Y0)))) % 83.86/83.63 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 83.86/83.63 least_upper_bound(Y1, least_upper_bound(Y0, Y2)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2)) % 83.86/83.63 least_upper_bound(Y1, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, identity), Y1) % 83.86/83.63 least_upper_bound(Y1, multiply(Y2, Y1)) = multiply(least_upper_bound(identity, Y2), Y1) % 83.86/83.63 least_upper_bound(Y2, least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2)) % 83.86/83.63 least_upper_bound(identity, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1) % 83.86/83.63 least_upper_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), least_upper_bound(Y1, Y2)) % 83.86/83.63 least_upper_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), least_upper_bound(Y1, Y2)) % 83.86/83.63 least_upper_bound(inverse(Y0), greatest_lower_bound(inverse(X0), inverse(X1))) = inverse(greatest_lower_bound(Y0, least_upper_bound(X0, X1))) % 83.86/83.63 multiply(X0, multiply(inverse(greatest_lower_bound(identity, X0)), X1)) = multiply(inverse(greatest_lower_bound(X0, identity)), multiply(X0, X1)) % 83.86/83.63 multiply(greatest_lower_bound(X0, Y1), inverse(X0)) = greatest_lower_bound(identity, multiply(Y1, inverse(X0))) % 83.86/83.63 multiply(greatest_lower_bound(Y0, X0), inverse(X0)) = greatest_lower_bound(identity, multiply(Y0, inverse(X0))) % 83.86/83.63 multiply(inverse(X1), multiply(inverse(X0), inverse(greatest_lower_bound(identity, multiply(inverse(X1), inverse(X0)))))) = inverse(greatest_lower_bound(identity, multiply(X0, X1))) % 83.86/83.63 multiply(inverse(X1), multiply(inverse(X0), inverse(greatest_lower_bound(identity, multiply(inverse(X1), inverse(X0)))))) = multiply(X0, multiply(X1, multiply(inverse(greatest_lower_bound(identity, multiply(X0, X1))), multiply(inverse(X1), inverse(X0))))) % 83.86/83.63 multiply(inverse(greatest_lower_bound(X0, identity)), Y1) = inverse(greatest_lower_bound(inverse(Y1), multiply(inverse(Y1), X0))) % 83.86/83.63 multiply(inverse(greatest_lower_bound(X0, identity)), Y1) = multiply(X0, multiply(inverse(greatest_lower_bound(identity, X0)), multiply(inverse(X0), Y1))) % 83.86/83.63 f1(multiply(a, multiply(inverse(greatest_lower_bound(identity, a)), inverse(greatest_lower_bound(identity, a))))) -> false__ % 83.86/83.63 f1(multiply(a, multiply(inverse(greatest_lower_bound(identity, a)), multiply(a, multiply(inverse(greatest_lower_bound(identity, a)), inverse(a)))))) -> true__ % 83.86/83.63 f1(multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(a, identity))) -> false__ % 83.86/83.63 f1(multiply(inverse(greatest_lower_bound(identity, a)), inverse(greatest_lower_bound(identity, greatest_lower_bound(inverse(greatest_lower_bound(false__, identity)), inverse(a)))))) -> false__ % 83.86/83.63 f1(multiply(inverse(greatest_lower_bound(identity, a)), inverse(greatest_lower_bound(identity, inverse(a))))) -> false__ % 83.86/83.63 f1(multiply(inverse(greatest_lower_bound(identity, a)), least_upper_bound(identity, a))) -> false__ % 83.86/83.63 f1(multiply(inverse(greatest_lower_bound(identity, greatest_lower_bound(inverse(greatest_lower_bound(false__, identity)), inverse(a)))), inverse(greatest_lower_bound(identity, a)))) -> true__ % 83.86/83.63 f1(multiply(inverse(greatest_lower_bound(identity, inverse(a))), inverse(greatest_lower_bound(identity, a)))) -> true__ % 83.86/83.63 f1(multiply(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity)))) -> true__ % 83.86/83.63 f1(multiply(least_upper_bound(identity, a), inverse(greatest_lower_bound(identity, a)))) -> true__ % 83.86/83.63 greatest_lower_bound(X, X) -> X % 83.86/83.63 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X % 83.86/83.63 greatest_lower_bound(X0, greatest_lower_bound(identity, X0)) -> greatest_lower_bound(identity, X0) % 83.86/83.63 greatest_lower_bound(X0, greatest_lower_bound(identity, multiply(X0, inverse(greatest_lower_bound(Y1, identity))))) -> greatest_lower_bound(X0, identity) % 83.86/83.63 greatest_lower_bound(X0, greatest_lower_bound(identity, multiply(X0, inverse(greatest_lower_bound(identity, Y1))))) -> greatest_lower_bound(X0, identity) % 83.86/83.63 greatest_lower_bound(X0, inverse(greatest_lower_bound(inverse(X0), Y1))) -> X0 % 83.86/83.63 greatest_lower_bound(X1, greatest_lower_bound(X2, greatest_lower_bound(identity, greatest_lower_bound(X1, X2)))) -> greatest_lower_bound(identity, greatest_lower_bound(X1, X2)) % 83.86/83.63 greatest_lower_bound(X1, greatest_lower_bound(identity, greatest_lower_bound(X2, greatest_lower_bound(X1, X2)))) -> greatest_lower_bound(identity, greatest_lower_bound(X1, X2)) % 83.86/83.63 greatest_lower_bound(X2, greatest_lower_bound(X1, greatest_lower_bound(identity, greatest_lower_bound(X1, X2)))) -> greatest_lower_bound(identity, greatest_lower_bound(X1, X2)) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(Y1, inverse(greatest_lower_bound(X1, inverse(greatest_lower_bound(Y0, Y1)))))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(Y1, inverse(greatest_lower_bound(inverse(X1), inverse(greatest_lower_bound(Y0, Y1)))))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(Y1, inverse(greatest_lower_bound(inverse(greatest_lower_bound(Y0, Y1)), X1)))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(greatest_lower_bound(Y0, Y1), X1))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(Y1, multiply(greatest_lower_bound(Y0, Y1), inverse(greatest_lower_bound(X1, identity))))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(Y1, multiply(greatest_lower_bound(Y0, Y1), inverse(greatest_lower_bound(identity, X1))))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(Y2, inverse(greatest_lower_bound(inverse(Y0), inverse(Y1))))) -> greatest_lower_bound(Y0, Y2) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(identity, greatest_lower_bound(Y0, Y2))) -> greatest_lower_bound(identity, greatest_lower_bound(Y0, Y2)) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(inverse(greatest_lower_bound(X1, inverse(Y0))), Y2)) -> greatest_lower_bound(Y0, Y2) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(inverse(greatest_lower_bound(inverse(X1), inverse(Y0))), Y2)) -> greatest_lower_bound(Y0, Y2) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(inverse(greatest_lower_bound(inverse(Y0), X1)), Y2)) -> greatest_lower_bound(Y0, Y2) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(Y0, X1), Y2)) -> greatest_lower_bound(Y0, Y2) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(multiply(Y0, inverse(greatest_lower_bound(X1, identity))), Y2)) -> greatest_lower_bound(Y0, Y2) % 83.86/83.63 greatest_lower_bound(Y0, greatest_lower_bound(multiply(Y0, inverse(greatest_lower_bound(identity, X1))), Y2)) -> greatest_lower_bound(Y0, Y2) % 83.86/83.63 greatest_lower_bound(Y0, inverse(greatest_lower_bound(X0, inverse(Y0)))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, inverse(Y0))))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, inverse(greatest_lower_bound(X1, greatest_lower_bound(inverse(Y0), X2)))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, inverse(greatest_lower_bound(inverse(X1), greatest_lower_bound(inverse(X2), inverse(Y0))))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, inverse(greatest_lower_bound(inverse(X1), greatest_lower_bound(inverse(Y0), inverse(X2))))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, inverse(greatest_lower_bound(inverse(Y0), greatest_lower_bound(inverse(Y1), inverse(X1))))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, inverse(greatest_lower_bound(inverse(Y0), inverse(Y1)))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, inverse(greatest_lower_bound(inverse(Y1), inverse(Y0)))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, multiply(X0, multiply(inverse(greatest_lower_bound(X0, identity)), Y0))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, multiply(Y0, inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, identity))))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, multiply(Y0, inverse(greatest_lower_bound(X1, greatest_lower_bound(identity, X2))))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, multiply(Y0, inverse(greatest_lower_bound(X1, identity)))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, multiply(Y0, inverse(greatest_lower_bound(Y0, identity)))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, multiply(Y0, inverse(greatest_lower_bound(identity, X1)))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, multiply(Y0, multiply(X0, inverse(greatest_lower_bound(X0, identity))))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0)) % 83.86/83.63 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0)) % 83.86/83.63 greatest_lower_bound(Y0, multiply(inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, identity))), Y0)) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, multiply(inverse(greatest_lower_bound(X1, greatest_lower_bound(identity, X2))), Y0)) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, multiply(inverse(greatest_lower_bound(identity, X1)), multiply(X1, Y0))) -> Y0 % 83.86/83.63 greatest_lower_bound(Y0, multiply(inverse(greatest_lower_bound(identity, inverse(X1))), Y0)) -> Y0 % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(Y0, inverse(greatest_lower_bound(X1, inverse(Y1))))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(Y0, inverse(greatest_lower_bound(inverse(X1), inverse(Y1))))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(Y0, inverse(greatest_lower_bound(inverse(Y1), X1)))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(Y0, inverse(greatest_lower_bound(inverse(Y1), inverse(X1))))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(Y1, inverse(greatest_lower_bound(X1, identity))))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(Y1, inverse(greatest_lower_bound(Y1, identity))))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(Y1, inverse(greatest_lower_bound(identity, X1))))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(inverse(greatest_lower_bound(X1, identity)), Y1))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(inverse(greatest_lower_bound(identity, X1)), Y1))) -> greatest_lower_bound(Y0, Y1) % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2) % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(inverse(X1), Y1)) -> greatest_lower_bound(inverse(X1), Y1) % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(inverse(greatest_lower_bound(false__, inverse(Y1))), X1)) -> greatest_lower_bound(Y1, X1) % 83.86/83.63 greatest_lower_bound(Y1, greatest_lower_bound(inverse(greatest_lower_bound(false__, inverse(Y1))), inverse(X1))) -> greatest_lower_bound(Y1, inverse(X1)) % 83.86/83.63 greatest_lower_bound(Y1, multiply(X0, multiply(inverse(greatest_lower_bound(X0, X1)), Y1))) -> Y1 % 83.86/83.63 greatest_lower_bound(Y1, multiply(X0, multiply(inverse(greatest_lower_bound(X1, X0)), Y1))) -> Y1 % 83.86/83.63 greatest_lower_bound(Y1, multiply(X0, multiply(inverse(greatest_lower_bound(identity, X0)), Y1))) -> Y1 % 83.86/83.63 greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y1)) -> multiply(greatest_lower_bound(identity, X1), Y1) % 83.86/83.63 greatest_lower_bound(Y1, multiply(inverse(greatest_lower_bound(X0, X1)), multiply(X0, Y1))) -> Y1 % 83.86/83.63 greatest_lower_bound(Y1, multiply(inverse(greatest_lower_bound(X0, X1)), multiply(X1, Y1))) -> Y1 % 83.86/83.63 greatest_lower_bound(Y1, multiply(inverse(greatest_lower_bound(X0, identity)), Y1)) -> Y1 % 83.86/83.63 greatest_lower_bound(Y1, multiply(inverse(greatest_lower_bound(identity, X0)), Y1)) -> Y1 % 83.86/83.63 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z)) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(X0, greatest_lower_bound(X1, identity))) -> greatest_lower_bound(identity, greatest_lower_bound(X0, X1)) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(X0, greatest_lower_bound(identity, Y2))) -> greatest_lower_bound(X0, greatest_lower_bound(identity, Y2)) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(X0, identity)) -> greatest_lower_bound(X0, identity) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(X0, multiply(greatest_lower_bound(Y1, identity), inverse(greatest_lower_bound(Y1, inverse(greatest_lower_bound(identity, X0))))))) -> greatest_lower_bound(X0, identity) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(X0, multiply(greatest_lower_bound(identity, Y1), inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity, X0)), Y1))))) -> greatest_lower_bound(X0, identity) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(Y0, greatest_lower_bound(X0, identity))) -> greatest_lower_bound(Y0, greatest_lower_bound(X0, identity)) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(Y0, inverse(greatest_lower_bound(X0, identity)))) -> greatest_lower_bound(Y0, identity) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(Y0, inverse(greatest_lower_bound(identity, X0)))) -> greatest_lower_bound(Y0, identity) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(X0, inverse(greatest_lower_bound(X0, X1))))) -> greatest_lower_bound(Y0, identity) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(X0, inverse(greatest_lower_bound(X1, X0))))) -> greatest_lower_bound(Y0, identity) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(X0, inverse(greatest_lower_bound(identity, X0))))) -> greatest_lower_bound(Y0, identity) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(inverse(greatest_lower_bound(X0, X1)), X0))) -> greatest_lower_bound(Y0, identity) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(inverse(greatest_lower_bound(X0, X1)), X1))) -> greatest_lower_bound(Y0, identity) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(inverse(greatest_lower_bound(X0, identity)), Y2)) -> greatest_lower_bound(identity, Y2) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(inverse(greatest_lower_bound(false__, identity)), X1)) -> greatest_lower_bound(identity, X1) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(inverse(greatest_lower_bound(false__, identity)), inverse(X1))) -> multiply(greatest_lower_bound(identity, X1), inverse(X1)) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(inverse(greatest_lower_bound(identity, X0)), Y2)) -> greatest_lower_bound(identity, Y2) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(greatest_lower_bound(X0, X1)), X0), Y2)) -> greatest_lower_bound(identity, Y2) % 83.86/83.63 greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(greatest_lower_bound(X0, X1)), X1), Y2)) -> greatest_lower_bound(identity, Y2) % 83.86/83.63 greatest_lower_bound(identity, inverse(Y1)) -> multiply(greatest_lower_bound(identity, Y1), inverse(Y1)) % 83.86/83.63 greatest_lower_bound(identity, inverse(greatest_lower_bound(X0, identity))) -> identity % 83.86/83.63 greatest_lower_bound(identity, inverse(greatest_lower_bound(identity, Y1))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(X0, inverse(greatest_lower_bound(X0, X1)))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(X0, inverse(greatest_lower_bound(X1, X0)))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(X0, inverse(greatest_lower_bound(identity, X0)))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(Y1, multiply(inverse(greatest_lower_bound(X1, identity)), inverse(Y1)))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(Y1, multiply(inverse(greatest_lower_bound(Y1, identity)), inverse(Y1)))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(Y1, multiply(inverse(greatest_lower_bound(identity, X1)), inverse(Y1)))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, identity), inverse(X0))) -> multiply(greatest_lower_bound(identity, X0), inverse(X0)) % 83.86/83.63 greatest_lower_bound(identity, multiply(greatest_lower_bound(X1, X2), inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, Y1))))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(greatest_lower_bound(X1, X2), inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, identity))))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(greatest_lower_bound(X1, X2), inverse(greatest_lower_bound(X1, greatest_lower_bound(Y1, X2))))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(greatest_lower_bound(X1, X2), inverse(greatest_lower_bound(X1, greatest_lower_bound(identity, X2))))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(greatest_lower_bound(X1, X2), inverse(greatest_lower_bound(X2, greatest_lower_bound(Y1, X1))))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(greatest_lower_bound(identity, X0), inverse(X0))) -> multiply(greatest_lower_bound(identity, X0), inverse(X0)) % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(Y0), inverse(greatest_lower_bound(X1, inverse(Y0))))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(Y0), inverse(greatest_lower_bound(inverse(Y0), X1)))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(Y0), inverse(greatest_lower_bound(inverse(Y0), inverse(X1))))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(Y0), multiply(inverse(greatest_lower_bound(X1, identity)), Y0))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(Y0), multiply(inverse(greatest_lower_bound(X1, identity)), multiply(X1, Y0)))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(Y0), multiply(inverse(greatest_lower_bound(identity, X1)), Y0))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(Y0), multiply(inverse(greatest_lower_bound(identity, X1)), multiply(X1, Y0)))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(X1, Y0)), Y0)) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))), Y0)) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))), greatest_lower_bound(X1, X2))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))), Y0)) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))), greatest_lower_bound(X1, X2))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(X2, greatest_lower_bound(Y0, X1))), greatest_lower_bound(X1, X2))) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(Y0, X1)), Y0)) -> identity % 83.86/83.63 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(inverse(X0), X1)), X1)) -> identity % 83.86/83.63 greatest_lower_bound(inverse(X0), greatest_lower_bound(Y0, inverse(greatest_lower_bound(X0, X1)))) -> greatest_lower_bound(Y0, inverse(X0)) % 83.86/83.63 greatest_lower_bound(inverse(X0), greatest_lower_bound(Y0, inverse(greatest_lower_bound(X1, X0)))) -> greatest_lower_bound(Y0, inverse(X0)) % 83.86/83.63 greatest_lower_bound(inverse(X0), greatest_lower_bound(Y0, inverse(greatest_lower_bound(identity, X0)))) -> greatest_lower_bound(Y0, inverse(X0)) % 83.86/83.63 greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(X1), inverse(greatest_lower_bound(Y1, inverse(greatest_lower_bound(inverse(X0), inverse(X1))))))) -> greatest_lower_bound(inverse(X0), inverse(X1)) % 83.86/83.63 greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(X1), inverse(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X0), inverse(X1))), Y1)))) -> greatest_lower_bound(inverse(X0), inverse(X1)) % 83.86/83.63 greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(X1), multiply(greatest_lower_bound(inverse(X0), inverse(X1)), inverse(greatest_lower_bound(identity, greatest_lower_bound(inverse(X0), inverse(X1))))))) -> greatest_lower_bound(inverse(X0), inverse(X1)) % 83.86/83.63 greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(greatest_lower_bound(X0, X1)), Y2)) -> greatest_lower_bound(inverse(X0), Y2) % 83.86/83.63 greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(greatest_lower_bound(X0, inverse(Y1))), Y2)) -> greatest_lower_bound(inverse(X0), Y2) % 83.86/83.63 greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(greatest_lower_bound(X1, X0)), Y2)) -> greatest_lower_bound(inverse(X0), Y2) % 83.86/83.63 greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(greatest_lower_bound(X1, X0)), inverse(greatest_lower_bound(Y1, X0)))) -> inverse(X0) % 83.86/83.63 greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(greatest_lower_bound(X1, X0)), inverse(greatest_lower_bound(inverse(Y1), X0)))) -> inverse(X0) % 83.86/83.63 greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(greatest_lower_bound(identity, X0)), Y2)) -> greatest_lower_bound(inverse(X0), Y2) % 83.86/83.63 greatest_lower_bound(inverse(X0), inverse(greatest_lower_bound(identity, X0))) -> inverse(X0) % 83.86/83.63 greatest_lower_bound(inverse(X1), inverse(greatest_lower_bound(inverse(Y1), X1))) -> inverse(X1) % 83.86/83.63 greatest_lower_bound(inverse(Y0), greatest_lower_bound(inverse(greatest_lower_bound(Y0, X1)), inverse(X2))) -> greatest_lower_bound(inverse(Y0), inverse(X2)) % 83.86/83.63 greatest_lower_bound(inverse(Y0), inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, Y0)))) -> inverse(Y0) % 83.86/83.63 greatest_lower_bound(inverse(Y0), inverse(greatest_lower_bound(X1, greatest_lower_bound(Y0, X2)))) -> inverse(Y0) % 83.86/83.63 greatest_lower_bound(inverse(Y0), inverse(greatest_lower_bound(Y0, X1))) -> inverse(Y0) % 83.86/83.63 greatest_lower_bound(inverse(Y0), inverse(greatest_lower_bound(Y1, Y0))) -> inverse(Y0) % 83.86/83.63 greatest_lower_bound(inverse(Y0), multiply(inverse(Y0), inverse(X1))) -> multiply(inverse(Y0), greatest_lower_bound(identity, inverse(X1))) % 83.86/83.63 greatest_lower_bound(inverse(Y0), multiply(inverse(Y0), inverse(greatest_lower_bound(X1, identity)))) -> inverse(Y0) % 83.86/83.63 greatest_lower_bound(inverse(Y0), multiply(inverse(Y0), inverse(greatest_lower_bound(identity, X1)))) -> inverse(Y0) % 83.86/83.63 greatest_lower_bound(inverse(Y1), greatest_lower_bound(X1, inverse(Y1))) -> greatest_lower_bound(X1, inverse(Y1)) % 83.86/83.63 greatest_lower_bound(inverse(Y1), greatest_lower_bound(inverse(greatest_lower_bound(Y1, false__)), X1)) -> greatest_lower_bound(inverse(Y1), X1) % 83.86/83.63 greatest_lower_bound(inverse(Y1), greatest_lower_bound(inverse(greatest_lower_bound(Y1, false__)), inverse(X1))) -> greatest_lower_bound(inverse(Y1), inverse(X1)) % 83.86/83.63 greatest_lower_bound(inverse(Y1), greatest_lower_bound(inverse(greatest_lower_bound(false__, Y1)), X1)) -> greatest_lower_bound(inverse(Y1), X1) % 83.86/83.63 greatest_lower_bound(inverse(Y1), greatest_lower_bound(inverse(greatest_lower_bound(false__, Y1)), inverse(X1))) -> greatest_lower_bound(inverse(Y1), inverse(X1)) % 83.86/83.63 greatest_lower_bound(inverse(greatest_lower_bound(X1, X2)), inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)))) -> inverse(greatest_lower_bound(X1, X2)) % 83.86/83.63 greatest_lower_bound(inverse(greatest_lower_bound(X1, X2)), inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)))) -> inverse(greatest_lower_bound(X1, X2)) % 83.86/83.63 greatest_lower_bound(inverse(greatest_lower_bound(X1, X2)), inverse(greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)))) -> inverse(greatest_lower_bound(X1, X2)) % 83.86/83.63 greatest_lower_bound(inverse(greatest_lower_bound(X1, X2)), inverse(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)))) -> inverse(greatest_lower_bound(X1, X2)) % 83.86/83.63 greatest_lower_bound(inverse(greatest_lower_bound(inverse(X1), inverse(X2))), inverse(greatest_lower_bound(inverse(X1), greatest_lower_bound(inverse(Y1), inverse(X2))))) -> inverse(greatest_lower_bound(inverse(X1), inverse(X2))) % 83.86/83.63 greatest_lower_bound(inverse(greatest_lower_bound(inverse(X1), inverse(X2))), inverse(greatest_lower_bound(inverse(X2), greatest_lower_bound(inverse(Y1), inverse(X1))))) -> inverse(greatest_lower_bound(inverse(X1), inverse(X2))) % 83.86/83.63 greatest_lower_bound(inverse(greatest_lower_bound(inverse(Y1), inverse(X2))), inverse(greatest_lower_bound(inverse(greatest_lower_bound(Y1, X1)), inverse(X2)))) -> inverse(greatest_lower_bound(inverse(greatest_lower_bound(Y1, X1)), inverse(X2))) % 83.86/83.63 greatest_lower_bound(least_upper_bound(X0, X1), least_upper_bound(X0, least_upper_bound(X1, Y1))) -> least_upper_bound(X0, X1) % 83.86/83.63 greatest_lower_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, greatest_lower_bound(Y, Z)) % 83.86/83.63 greatest_lower_bound(multiply(X0, X1), inverse(greatest_lower_bound(Y1, multiply(inverse(X1), inverse(X0))))) -> multiply(X0, X1) % 83.86/83.63 greatest_lower_bound(multiply(X0, X1), inverse(greatest_lower_bound(inverse(Y1), multiply(inverse(X1), inverse(X0))))) -> multiply(X0, X1) % 83.86/83.63 greatest_lower_bound(multiply(X0, X1), inverse(greatest_lower_bound(multiply(inverse(X1), inverse(X0)), Y1))) -> multiply(X0, X1) % 83.86/83.63 greatest_lower_bound(multiply(X0, X1), inverse(greatest_lower_bound(multiply(inverse(X1), inverse(X0)), inverse(Y1)))) -> multiply(X0, X1) % 83.86/83.63 greatest_lower_bound(multiply(X0, greatest_lower_bound(X1, X2)), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X0, X2), Y2)) % 83.86/83.63 greatest_lower_bound(multiply(X0, inverse(greatest_lower_bound(identity, X0))), inverse(greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, multiply(X0, inverse(greatest_lower_bound(Y1, identity)))), multiply(greatest_lower_bound(Y1, identity), inverse(X0)))))) -> multiply(X0, inverse(greatest_lower_bound(identity, X0))) % 83.86/83.63 greatest_lower_bound(multiply(X0, inverse(greatest_lower_bound(identity, X0))), inverse(greatest_lower_bound(identity, greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, Y1), inverse(X0)))))) -> multiply(X0, inverse(greatest_lower_bound(identity, X0))) % 83.86/83.63 greatest_lower_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(greatest_lower_bound(multiply(X0, X1), Y2), Y1) % 83.86/83.63 greatest_lower_bound(multiply(Y, X), multiply(Z, X)) -> multiply(greatest_lower_bound(Y, Z), X) % 83.86/83.63 greatest_lower_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(greatest_lower_bound(Y0, multiply(X0, X1)), Y1) % 83.86/83.63 greatest_lower_bound(multiply(greatest_lower_bound(X0, X2), X1), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X2, X1), Y2)) % 83.86/83.63 greatest_lower_bound(multiply(inverse(X1), inverse(X0)), inverse(greatest_lower_bound(Y1, multiply(X0, X1)))) -> multiply(inverse(X1), inverse(X0)) % 83.86/83.63 greatest_lower_bound(multiply(inverse(X1), inverse(X0)), inverse(greatest_lower_bound(identity, multiply(X0, X1)))) -> multiply(inverse(X1), inverse(X0)) % 83.86/83.63 greatest_lower_bound(multiply(inverse(X1), inverse(X0)), inverse(greatest_lower_bound(multiply(X0, X1), Y1))) -> multiply(inverse(X1), inverse(X0)) % 83.86/83.63 inverse(greatest_lower_bound(X0, greatest_lower_bound(identity, X0))) -> inverse(greatest_lower_bound(identity, X0)) % 83.86/83.63 inverse(greatest_lower_bound(X0, multiply(X0, inverse(greatest_lower_bound(X0, identity))))) -> inverse(X0) % 83.86/83.63 inverse(greatest_lower_bound(Y0, inverse(greatest_lower_bound(X1, inverse(Y0))))) -> inverse(Y0) % 83.86/83.63 inverse(greatest_lower_bound(Y0, inverse(greatest_lower_bound(inverse(Y0), X1)))) -> inverse(Y0) % 83.86/83.63 inverse(greatest_lower_bound(identity, greatest_lower_bound(X0, identity))) -> inverse(greatest_lower_bound(identity, X0)) % 83.86/83.63 inverse(greatest_lower_bound(identity, multiply(inverse(X1), inverse(greatest_lower_bound(X0, inverse(X1)))))) -> identity % 83.86/83.64 inverse(greatest_lower_bound(inverse(X0), greatest_lower_bound(inverse(greatest_lower_bound(X1, X0)), Y1))) -> inverse(greatest_lower_bound(inverse(X0), Y1)) % 83.86/83.64 inverse(greatest_lower_bound(inverse(X1), multiply(inverse(X1), inverse(X0)))) -> multiply(inverse(greatest_lower_bound(identity, X0)), multiply(X0, X1)) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y0), greatest_lower_bound(inverse(Y1), inverse(greatest_lower_bound(X1, inverse(greatest_lower_bound(inverse(Y0), inverse(Y1)))))))) -> inverse(greatest_lower_bound(inverse(Y0), inverse(Y1))) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y0), greatest_lower_bound(inverse(Y2), inverse(greatest_lower_bound(Y0, Y1))))) -> inverse(greatest_lower_bound(inverse(Y0), inverse(Y2))) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y0), greatest_lower_bound(inverse(greatest_lower_bound(X1, Y0)), inverse(Y2)))) -> inverse(greatest_lower_bound(inverse(Y0), inverse(Y2))) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y0), greatest_lower_bound(inverse(greatest_lower_bound(Y0, Y1)), X1))) -> inverse(greatest_lower_bound(inverse(Y0), X1)) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y0), greatest_lower_bound(inverse(greatest_lower_bound(Y0, Y1)), inverse(Y2)))) -> inverse(greatest_lower_bound(inverse(Y0), inverse(Y2))) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y0), inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))))) -> Y0 % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y0), inverse(greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))))) -> Y0 % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y0), inverse(greatest_lower_bound(Y1, Y0)))) -> Y0 % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y0), multiply(inverse(Y0), greatest_lower_bound(identity, inverse(X1))))) -> inverse(greatest_lower_bound(inverse(Y0), multiply(inverse(Y0), inverse(X1)))) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y0), multiply(inverse(Y0), inverse(greatest_lower_bound(X1, identity))))) -> Y0 % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y0), multiply(inverse(Y0), inverse(greatest_lower_bound(identity, X1))))) -> Y0 % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(X1, greatest_lower_bound(X2, inverse(Y1))))) -> inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, inverse(Y1)))) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(X1, greatest_lower_bound(inverse(Y1), X2)))) -> inverse(greatest_lower_bound(X1, greatest_lower_bound(inverse(Y1), X2))) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(X1, inverse(Y1)))) -> inverse(greatest_lower_bound(X1, inverse(Y1))) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(inverse(Y0), inverse(greatest_lower_bound(X1, Y1))))) -> inverse(greatest_lower_bound(inverse(Y0), inverse(Y1))) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(inverse(Y0), inverse(greatest_lower_bound(Y1, X1))))) -> inverse(greatest_lower_bound(inverse(Y0), inverse(Y1))) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(inverse(greatest_lower_bound(Y1, false__)), X1))) -> inverse(greatest_lower_bound(inverse(Y1), X1)) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y1), greatest_lower_bound(inverse(greatest_lower_bound(Y1, false__)), inverse(X1)))) -> inverse(greatest_lower_bound(inverse(Y1), inverse(X1))) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y1), multiply(inverse(Y1), X0))) -> multiply(inverse(greatest_lower_bound(identity, X0)), Y1) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y1), multiply(inverse(Y1), greatest_lower_bound(identity, inverse(X1))))) -> multiply(inverse(greatest_lower_bound(identity, inverse(X1))), Y1) % 83.86/83.64 inverse(greatest_lower_bound(inverse(Y1), multiply(inverse(Y1), inverse(Y0)))) -> multiply(inverse(greatest_lower_bound(identity, inverse(Y0))), Y1) % 83.86/83.64 inverse(greatest_lower_bound(inverse(greatest_lower_bound(X1, X2)), inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, Y1))))) -> greatest_lower_bound(X1, X2) % 83.86/83.64 inverse(greatest_lower_bound(inverse(greatest_lower_bound(X1, X2)), inverse(greatest_lower_bound(X1, greatest_lower_bound(Y1, X2))))) -> greatest_lower_bound(X1, X2) % 83.86/83.64 inverse(greatest_lower_bound(inverse(greatest_lower_bound(X1, X2)), inverse(greatest_lower_bound(X2, greatest_lower_bound(Y1, X1))))) -> greatest_lower_bound(X1, X2) % 83.86/83.64 inverse(greatest_lower_bound(inverse(greatest_lower_bound(Y1, X2)), inverse(greatest_lower_bound(inverse(greatest_lower_bound(inverse(Y1), inverse(X1))), X2)))) -> greatest_lower_bound(inverse(greatest_lower_bound(inverse(Y1), inverse(X1))), X2) % 83.86/83.64 inverse(greatest_lower_bound(multiply(inverse(X1), inverse(X0)), inverse(greatest_lower_bound(Y1, multiply(X0, X1))))) -> multiply(X0, X1) % 83.86/83.64 inverse(identity) -> identity % 83.86/83.64 inverse(inverse(X)) -> X % 83.86/83.64 inverse(least_upper_bound(X, Y)) -> greatest_lower_bound(inverse(X), inverse(Y)) % 83.86/83.64 inverse(multiply(X, Y)) -> multiply(inverse(Y), inverse(X)) % 83.86/83.64 least_upper_bound(X, X) -> X % 83.86/83.64 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X % 83.86/83.64 least_upper_bound(X0, X1) -> inverse(greatest_lower_bound(inverse(X0), inverse(X1))) % 83.86/83.64 least_upper_bound(X0, inverse(Y1)) -> inverse(greatest_lower_bound(inverse(X0), Y1)) % 83.86/83.64 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0 % 83.86/83.64 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(least_upper_bound(Y0, Y1), X1))) -> least_upper_bound(Y0, Y1) % 83.86/83.64 least_upper_bound(Y0, least_upper_bound(Y1, least_upper_bound(Y0, Y1))) -> least_upper_bound(Y0, Y1) % 83.86/83.64 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y0, X1), Y2)) -> least_upper_bound(Y0, Y2) % 83.86/83.64 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2) % 83.86/83.64 least_upper_bound(greatest_lower_bound(X0, X1), greatest_lower_bound(X0, greatest_lower_bound(X1, Y1))) -> greatest_lower_bound(X0, X1) % 83.86/83.64 least_upper_bound(greatest_lower_bound(inverse(X0), inverse(X1)), inverse(Y1)) -> inverse(greatest_lower_bound(least_upper_bound(X0, X1), Y1)) % 83.86/83.64 least_upper_bound(identity, inverse(Y0)) -> inverse(greatest_lower_bound(Y0, identity)) % 83.86/83.64 least_upper_bound(identity, inverse(Y1)) -> inverse(greatest_lower_bound(identity, Y1)) % 83.86/83.64 least_upper_bound(inverse(X), inverse(Y)) -> inverse(greatest_lower_bound(X, Y)) % 83.86/83.64 least_upper_bound(inverse(Y0), X0) -> inverse(greatest_lower_bound(Y0, inverse(X0))) % 83.86/83.64 least_upper_bound(inverse(Y0), multiply(inverse(X1), inverse(X0))) -> inverse(greatest_lower_bound(Y0, multiply(X0, X1))) % 83.86/83.64 least_upper_bound(inverse(greatest_lower_bound(X0, X1)), Y2) -> least_upper_bound(inverse(X0), least_upper_bound(inverse(X1), Y2)) % 83.86/83.64 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z)) % 83.86/83.64 least_upper_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, least_upper_bound(Y, Z)) % 83.86/83.64 least_upper_bound(multiply(X0, least_upper_bound(X1, X2)), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X0, X2), Y2)) % 83.86/83.64 least_upper_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(least_upper_bound(multiply(X0, X1), Y2), Y1) % 83.86/83.64 least_upper_bound(multiply(Y, X), multiply(Z, X)) -> multiply(least_upper_bound(Y, Z), X) % 83.86/83.64 least_upper_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(least_upper_bound(Y0, multiply(X0, X1)), Y1) % 83.86/83.64 least_upper_bound(multiply(inverse(X1), inverse(X0)), inverse(Y1)) -> inverse(greatest_lower_bound(multiply(X0, X1), Y1)) % 83.86/83.64 least_upper_bound(multiply(least_upper_bound(X0, X2), X1), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X2, X1), Y2)) % 83.86/83.64 multiply(X0, identity) -> X0 % 83.86/83.64 multiply(X0, inverse(X0)) -> identity % 83.86/83.64 multiply(X0, inverse(greatest_lower_bound(inverse(Y1), X0))) -> inverse(greatest_lower_bound(identity, multiply(inverse(Y1), inverse(X0)))) % 83.86/83.64 multiply(X0, multiply(X1, multiply(inverse(X1), inverse(X0)))) -> identity % 83.86/83.64 multiply(X0, multiply(greatest_lower_bound(X1, inverse(X0)), inverse(greatest_lower_bound(identity, multiply(X0, greatest_lower_bound(X1, inverse(X0))))))) -> identity % 83.86/83.64 multiply(X0, multiply(inverse(X0), Y1)) -> Y1 % 83.86/83.64 multiply(Y0, greatest_lower_bound(inverse(Y0), Y1)) -> greatest_lower_bound(identity, multiply(Y0, Y1)) % 83.86/83.64 multiply(Y1, multiply(inverse(greatest_lower_bound(identity, Y1)), multiply(inverse(Y1), X1))) -> multiply(inverse(greatest_lower_bound(identity, Y1)), X1) % 83.86/83.64 multiply(greatest_lower_bound(X0, identity), multiply(inverse(X0), inverse(greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, identity), inverse(X0)))))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(X0, inverse(X1)), multiply(X1, inverse(greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, inverse(X1)), X1))))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), inverse(greatest_lower_bound(identity, greatest_lower_bound(X1, X2)))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), inverse(greatest_lower_bound(identity, greatest_lower_bound(X1, X2)))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(X1, identity), multiply(inverse(greatest_lower_bound(identity, X1)), Y0)) -> Y0 % 83.86/83.64 multiply(greatest_lower_bound(X2, greatest_lower_bound(identity, X1)), inverse(greatest_lower_bound(identity, greatest_lower_bound(X1, X2)))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(Y1, greatest_lower_bound(Y2, identity)), inverse(greatest_lower_bound(identity, greatest_lower_bound(Y1, greatest_lower_bound(Y2, identity))))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(Y1, greatest_lower_bound(identity, Y2)), inverse(greatest_lower_bound(identity, greatest_lower_bound(Y1, greatest_lower_bound(identity, Y2))))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(Y1, identity), inverse(greatest_lower_bound(identity, Y1))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(identity, X0), inverse(greatest_lower_bound(X0, identity))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(identity, X0), multiply(inverse(X0), inverse(greatest_lower_bound(identity, multiply(greatest_lower_bound(identity, X0), inverse(X0)))))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(identity, X0), multiply(inverse(X0), multiply(inverse(greatest_lower_bound(identity, X0)), multiply(X0, Y1)))) -> Y1 % 83.86/83.64 multiply(greatest_lower_bound(identity, X0), multiply(inverse(greatest_lower_bound(X0, identity)), Y2)) -> Y2 % 83.86/83.64 multiply(greatest_lower_bound(identity, X1), multiply(X1, multiply(inverse(greatest_lower_bound(identity, X1)), inverse(X1)))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(identity, greatest_lower_bound(X1, X2)), inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(identity, greatest_lower_bound(X1, X2)), inverse(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(identity, greatest_lower_bound(X1, X2)), inverse(greatest_lower_bound(X2, greatest_lower_bound(identity, X1)))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(identity, greatest_lower_bound(X1, greatest_lower_bound(X2, identity))), inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(identity, greatest_lower_bound(X1, greatest_lower_bound(identity, X2))), inverse(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(identity, greatest_lower_bound(Y1, identity)), inverse(greatest_lower_bound(Y1, identity))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(identity, inverse(X0)), identity) -> greatest_lower_bound(identity, inverse(X0)) % 83.86/83.64 multiply(greatest_lower_bound(identity, inverse(X0)), inverse(greatest_lower_bound(inverse(Y1), multiply(inverse(Y1), inverse(X0))))) -> Y1 % 83.86/83.64 multiply(greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, identity), inverse(X0))), multiply(X0, inverse(greatest_lower_bound(X0, identity)))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(identity, multiply(greatest_lower_bound(identity, X0), inverse(X0))), multiply(X0, inverse(greatest_lower_bound(identity, X0)))) -> identity % 83.86/83.64 multiply(greatest_lower_bound(inverse(X0), inverse(X1)), identity) -> greatest_lower_bound(inverse(X0), inverse(X1)) % 83.86/83.64 multiply(greatest_lower_bound(inverse(X0), inverse(X1)), least_upper_bound(X0, X1)) -> identity % 83.86/83.64 multiply(greatest_lower_bound(inverse(X0), inverse(X1)), multiply(inverse(greatest_lower_bound(inverse(X0), inverse(X1))), Y1)) -> Y1 % 83.86/83.64 multiply(greatest_lower_bound(inverse(Y1), Y2), Y1) -> greatest_lower_bound(identity, multiply(Y2, Y1)) % 83.86/83.64 multiply(identity, X) -> X % 83.86/83.64 multiply(inverse(X), X) -> identity % 83.86/83.64 multiply(inverse(X1), multiply(inverse(X0), multiply(X0, X1))) -> identity % 83.86/83.64 multiply(inverse(Y0), multiply(X0, multiply(inverse(X0), Y0))) -> identity % 83.86/83.64 multiply(inverse(Y0), multiply(greatest_lower_bound(identity, greatest_lower_bound(X1, identity)), inverse(greatest_lower_bound(X1, identity)))) -> inverse(Y0) % 83.86/83.64 multiply(inverse(Y1), identity) -> inverse(Y1) % 83.86/83.64 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2 % 83.86/83.64 multiply(inverse(greatest_lower_bound(X0, identity)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1 % 83.86/83.64 multiply(inverse(greatest_lower_bound(X0, identity)), multiply(greatest_lower_bound(identity, X0), inverse(X0))) -> inverse(X0) % 83.86/83.64 multiply(inverse(greatest_lower_bound(identity, X0)), X0) -> multiply(X0, inverse(greatest_lower_bound(identity, X0))) % 83.86/83.64 multiply(inverse(greatest_lower_bound(identity, X0)), greatest_lower_bound(X0, identity)) -> identity % 83.86/83.64 multiply(inverse(greatest_lower_bound(identity, X0)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1 % 83.86/83.64 multiply(inverse(greatest_lower_bound(identity, X1)), multiply(greatest_lower_bound(X1, identity), Y0)) -> Y0 % 83.86/83.64 multiply(inverse(greatest_lower_bound(identity, Y0)), multiply(Y0, Y1)) -> multiply(Y0, multiply(inverse(greatest_lower_bound(identity, Y0)), Y1)) % 83.86/83.64 multiply(inverse(greatest_lower_bound(identity, greatest_lower_bound(inverse(X0), inverse(X1)))), greatest_lower_bound(inverse(X0), inverse(X1))) -> multiply(greatest_lower_bound(inverse(X0), inverse(X1)), inverse(greatest_lower_bound(identity, greatest_lower_bound(inverse(X0), inverse(X1))))) % 83.86/83.64 multiply(inverse(greatest_lower_bound(identity, inverse(greatest_lower_bound(X0, identity)))), Y0) -> Y0 % 83.86/83.64 multiply(inverse(greatest_lower_bound(identity, multiply(greatest_lower_bound(identity, X1), inverse(X1)))), Y1) -> multiply(X1, multiply(inverse(greatest_lower_bound(identity, X1)), Y1)) % 83.86/83.64 multiply(inverse(greatest_lower_bound(inverse(X0), inverse(Y1))), inverse(X0)) -> inverse(greatest_lower_bound(identity, multiply(X0, inverse(Y1)))) % 83.86/83.64 multiply(inverse(greatest_lower_bound(inverse(X1), inverse(greatest_lower_bound(identity, X1)))), Y1) -> multiply(X1, Y1) % 83.86/83.64 multiply(inverse(greatest_lower_bound(inverse(Y0), inverse(X0))), inverse(X0)) -> inverse(greatest_lower_bound(identity, multiply(X0, inverse(Y0)))) % 83.86/83.64 multiply(inverse(greatest_lower_bound(inverse(Y1), Y0)), Y0) -> inverse(greatest_lower_bound(identity, multiply(inverse(Y0), inverse(Y1)))) % 83.86/83.64 multiply(least_upper_bound(inverse(Y1), Y2), Y1) -> least_upper_bound(identity, multiply(Y2, Y1)) % 83.86/83.64 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 83.86/83.64 true__ -> false__ % 83.86/83.64 with the LPO induced by % 83.86/83.64 a > f1 > least_upper_bound > greatest_lower_bound > inverse > multiply > identity > true__ > false__ % 83.86/83.64 % 83.86/83.64 % SZS output end Proof % 83.86/83.64 %------------------------------------------------------------------------------