TSTP Solution File: GRP169-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP169-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n025.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 10:53:38 EDT 2022
% Result : Unsatisfiable 36.00s 35.82s
% Output : Proof 36.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP169-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : moca.sh %s
% 0.11/0.31 % Computer : n025.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon Jun 13 15:40:39 EDT 2022
% 0.11/0.32 % CPUTime :
% 36.00/35.82 % SZS status Unsatisfiable
% 36.00/35.82 % SZS output start Proof
% 36.00/35.82 The input problem is unsatisfiable because
% 36.00/35.82
% 36.00/35.82 [1] the following set of Horn clauses is unsatisfiable:
% 36.00/35.82
% 36.00/35.82 multiply(identity, X) = X
% 36.00/35.82 multiply(inverse(X), X) = identity
% 36.00/35.82 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 36.00/35.82 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 36.00/35.82 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 36.00/35.82 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 36.00/35.82 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 36.00/35.82 least_upper_bound(X, X) = X
% 36.00/35.82 greatest_lower_bound(X, X) = X
% 36.00/35.82 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 36.00/35.82 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 36.00/35.82 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 36.00/35.82 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 36.00/35.82 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 36.00/35.82 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 36.00/35.82 least_upper_bound(inverse(a), inverse(b)) = inverse(b)
% 36.00/35.82 least_upper_bound(a, b) = a ==> \bottom
% 36.00/35.82
% 36.00/35.82 This holds because
% 36.00/35.82
% 36.00/35.82 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 36.00/35.82
% 36.00/35.82 E:
% 36.00/35.82 f1(a) = false__
% 36.00/35.82 f1(least_upper_bound(a, b)) = true__
% 36.00/35.82 greatest_lower_bound(X, X) = X
% 36.00/35.82 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 36.00/35.82 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 36.00/35.82 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 36.00/35.82 least_upper_bound(X, X) = X
% 36.00/35.82 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 36.00/35.82 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 36.00/35.82 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 36.00/35.82 least_upper_bound(inverse(a), inverse(b)) = inverse(b)
% 36.00/35.82 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 36.00/35.82 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 36.00/35.82 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 36.00/35.82 multiply(identity, X) = X
% 36.00/35.82 multiply(inverse(X), X) = identity
% 36.00/35.82 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 36.00/35.82 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 36.00/35.82 G:
% 36.00/35.82 true__ = false__
% 36.00/35.82
% 36.00/35.82 This holds because
% 36.00/35.82
% 36.00/35.82 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 36.00/35.82
% 36.00/35.82 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 36.00/35.82 greatest_lower_bound(X1, multiply(X0, X1)) = multiply(greatest_lower_bound(identity, inverse(X0)), multiply(X0, X1))
% 36.00/35.82 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, Y1), Y0))
% 36.00/35.82 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(X2, Y1)), Y0))
% 36.00/35.82 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(Y1, X2)), Y0))
% 36.00/35.82 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(X0), least_upper_bound(X0, X1)), Y0))
% 36.00/35.82 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(X0), least_upper_bound(X1, X0)), Y0))
% 36.00/35.82 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(b), a), Y0))
% 36.00/35.82 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(least_upper_bound(X0, inverse(X1)), X1), Y0))
% 36.00/35.82 greatest_lower_bound(Y0, inverse(a)) = greatest_lower_bound(inverse(a), greatest_lower_bound(Y0, least_upper_bound(inverse(b), X0)))
% 36.00/35.82 greatest_lower_bound(Y0, inverse(a)) = greatest_lower_bound(inverse(a), greatest_lower_bound(least_upper_bound(inverse(b), X0), Y0))
% 36.00/35.82 greatest_lower_bound(Y0, inverse(a)) = greatest_lower_bound(inverse(b), greatest_lower_bound(inverse(a), Y0))
% 36.00/35.82 greatest_lower_bound(Y0, multiply(X0, Y0)) = multiply(greatest_lower_bound(identity, greatest_lower_bound(X0, identity)), Y0)
% 36.00/35.82 greatest_lower_bound(Y0, multiply(X0, Y0)) = multiply(greatest_lower_bound(identity, inverse(inverse(X0))), Y0)
% 36.00/35.82 greatest_lower_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(greatest_lower_bound(identity, multiply(X0, X1)), Y0)
% 36.00/35.82 greatest_lower_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(greatest_lower_bound(multiply(X0, X1), identity), Y0)
% 36.00/35.82 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1)))
% 36.00/35.82 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0))
% 36.00/35.82 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1)))
% 36.00/35.82 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0))
% 36.00/35.82 greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y2)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2))
% 36.00/35.82 greatest_lower_bound(Y1, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, identity), Y1)
% 36.00/35.82 greatest_lower_bound(Y1, multiply(Y2, Y1)) = multiply(greatest_lower_bound(identity, Y2), Y1)
% 36.00/35.82 greatest_lower_bound(Y2, greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2))
% 36.00/35.82 greatest_lower_bound(identity, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1)
% 36.00/35.82 greatest_lower_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), greatest_lower_bound(Y1, Y2))
% 36.00/35.82 greatest_lower_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), greatest_lower_bound(Y1, Y2))
% 36.00/35.82 greatest_lower_bound(multiply(X0, X1), identity) = multiply(X0, greatest_lower_bound(X1, inverse(X0)))
% 36.00/35.82 greatest_lower_bound(multiply(X0, X1), identity) = multiply(X0, greatest_lower_bound(inverse(X0), X1))
% 36.00/35.82 greatest_lower_bound(multiply(Y0, Y1), identity) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1)
% 36.00/35.82 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 36.00/35.82 least_upper_bound(X1, multiply(X0, X1)) = multiply(least_upper_bound(identity, inverse(X0)), multiply(X0, X1))
% 36.00/35.82 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, Y1), Y0))
% 36.00/35.82 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)), Y0))
% 36.00/35.82 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)), Y0))
% 36.00/35.82 least_upper_bound(Y0, a) = least_upper_bound(b, least_upper_bound(a, Y0))
% 36.00/35.82 least_upper_bound(Y0, identity) = least_upper_bound(identity, least_upper_bound(multiply(greatest_lower_bound(X0, inverse(X1)), X1), Y0))
% 36.00/35.82 least_upper_bound(Y0, inverse(b)) = least_upper_bound(inverse(b), least_upper_bound(inverse(a), Y0))
% 36.00/35.82 least_upper_bound(Y0, multiply(X0, Y0)) = multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, inverse(inverse(X0)))), Y0))
% 36.00/35.82 least_upper_bound(Y0, multiply(X0, Y0)) = multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), inverse(inverse(X0))))), Y0))
% 36.00/35.82 least_upper_bound(Y0, multiply(X0, Y0)) = multiply(least_upper_bound(identity, least_upper_bound(X0, identity)), Y0)
% 36.00/35.82 least_upper_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(least_upper_bound(identity, multiply(X0, X1)), Y0)
% 36.00/35.82 least_upper_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(least_upper_bound(multiply(X0, X1), identity), Y0)
% 36.00/35.82 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y1)) = least_upper_bound(Y1, least_upper_bound(Y0, multiply(X1, Y1)))
% 36.00/35.82 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y1)) = least_upper_bound(Y1, least_upper_bound(multiply(X1, Y1), Y0))
% 36.00/35.82 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y1)) = least_upper_bound(Y1, least_upper_bound(Y0, multiply(X1, Y1)))
% 36.00/35.83 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y1)) = least_upper_bound(Y1, least_upper_bound(multiply(X1, Y1), Y0))
% 36.00/35.83 least_upper_bound(Y1, least_upper_bound(Y0, Y2)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2))
% 36.00/35.83 least_upper_bound(Y1, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, identity), Y1)
% 36.00/35.83 least_upper_bound(Y1, multiply(Y2, Y1)) = multiply(least_upper_bound(identity, Y2), Y1)
% 36.00/35.83 least_upper_bound(Y2, least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2))
% 36.00/35.83 least_upper_bound(identity, X1) = multiply(inverse(Y0), least_upper_bound(Y0, multiply(Y0, X1)))
% 36.00/35.83 least_upper_bound(identity, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1)
% 36.00/35.83 least_upper_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), least_upper_bound(Y1, Y2))
% 36.00/35.83 least_upper_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), least_upper_bound(Y1, Y2))
% 36.00/35.83 least_upper_bound(multiply(X0, X1), identity) = multiply(X0, least_upper_bound(X1, inverse(X0)))
% 36.00/35.83 least_upper_bound(multiply(X0, X1), identity) = multiply(X0, least_upper_bound(inverse(X0), X1))
% 36.00/35.83 least_upper_bound(multiply(Y0, Y1), identity) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1)
% 36.00/35.83 multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1))
% 36.00/35.83 multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1))
% 36.00/35.83 multiply(greatest_lower_bound(X1, identity), greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, multiply(X1, greatest_lower_bound(Y0, Y1))))
% 36.00/35.83 multiply(greatest_lower_bound(X2, greatest_lower_bound(identity, X1)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1))
% 36.00/35.83 multiply(greatest_lower_bound(identity, X1), greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, multiply(X1, greatest_lower_bound(Y0, Y1))))
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, least_upper_bound(multiply(inverse(b), a), Y2)))) = least_upper_bound(Y2, multiply(inverse(b), a))
% 36.00/35.83 multiply(least_upper_bound(X1, identity), least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, multiply(X1, least_upper_bound(Y0, Y1))))
% 36.00/35.83 multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1))
% 36.00/35.83 multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1))
% 36.00/35.83 multiply(least_upper_bound(X2, least_upper_bound(identity, X1)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1))
% 36.00/35.83 multiply(least_upper_bound(Y1, multiply(X0, Y1)), Y2) = multiply(least_upper_bound(identity, X0), multiply(Y1, Y2))
% 36.00/35.83 multiply(least_upper_bound(identity, X1), least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, multiply(X1, least_upper_bound(Y0, Y1))))
% 36.00/35.83 f1(a) -> false__
% 36.00/35.83 f1(least_upper_bound(a, b)) -> true__
% 36.00/35.83 f1(least_upper_bound(b, a)) -> true__
% 36.00/35.83 greatest_lower_bound(X, X) -> X
% 36.00/35.83 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X
% 36.00/35.83 greatest_lower_bound(X1, multiply(inverse(Y1), X1)) -> multiply(greatest_lower_bound(Y1, identity), multiply(inverse(Y1), X1))
% 36.00/35.83 greatest_lower_bound(X1, multiply(inverse(Y1), X1)) -> multiply(greatest_lower_bound(identity, Y1), multiply(inverse(Y1), X1))
% 36.00/35.83 greatest_lower_bound(X1, multiply(inverse(least_upper_bound(Y1, identity)), X1)) -> multiply(inverse(least_upper_bound(Y1, identity)), X1)
% 36.00/35.83 greatest_lower_bound(X1, multiply(inverse(least_upper_bound(identity, Y1)), X1)) -> multiply(inverse(least_upper_bound(identity, Y1)), X1)
% 36.00/35.83 greatest_lower_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y1)
% 36.00/35.83 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(X1, greatest_lower_bound(Y0, Y1)))) -> greatest_lower_bound(Y0, Y1)
% 36.00/35.83 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(greatest_lower_bound(Y0, Y1), X1))) -> greatest_lower_bound(Y0, Y1)
% 36.00/35.83 greatest_lower_bound(Y0, greatest_lower_bound(Y2, least_upper_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y2)
% 36.00/35.83 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(X1, Y0), Y2)) -> greatest_lower_bound(Y0, Y2)
% 36.00/35.83 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(Y0, X1), Y2)) -> greatest_lower_bound(Y0, Y2)
% 36.00/35.83 greatest_lower_bound(Y0, greatest_lower_bound(multiply(least_upper_bound(X1, identity), Y0), Y2)) -> greatest_lower_bound(Y0, Y2)
% 36.00/35.83 greatest_lower_bound(Y0, greatest_lower_bound(multiply(least_upper_bound(identity, X1), Y0), Y2)) -> greatest_lower_bound(Y0, Y2)
% 36.00/35.83 greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, Y0))) -> Y0
% 36.00/35.83 greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(Y0, X2))) -> Y0
% 36.00/35.83 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0
% 36.00/35.83 greatest_lower_bound(Y0, least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(X2, Y0)))) -> Y0
% 36.00/35.83 greatest_lower_bound(Y0, least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(Y0, X2)))) -> Y0
% 36.00/35.83 greatest_lower_bound(Y0, least_upper_bound(Y1, multiply(least_upper_bound(X1, identity), Y0))) -> Y0
% 36.00/35.83 greatest_lower_bound(Y0, least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y0))) -> Y0
% 36.00/35.83 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X1)), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0))
% 36.00/35.83 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0))
% 36.00/35.83 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0))
% 36.00/35.83 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), least_upper_bound(Y0, Y1))) -> greatest_lower_bound(Y0, multiply(X1, least_upper_bound(Y0, Y1)))
% 36.00/35.83 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, identity), Y0)) -> Y0
% 36.00/35.83 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y0)) -> Y0
% 36.00/35.83 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y0)) -> Y0
% 36.00/35.83 greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> Y0
% 36.00/35.83 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, Y1))) -> greatest_lower_bound(Y0, Y1)
% 36.00/35.83 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, Y1)))) -> greatest_lower_bound(Y0, Y1)
% 36.00/35.83 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(Y1, X2)))) -> greatest_lower_bound(Y0, Y1)
% 36.00/35.83 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(Y1, X1))) -> greatest_lower_bound(Y0, Y1)
% 36.00/35.83 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(least_upper_bound(X1, identity), Y1))) -> greatest_lower_bound(Y0, Y1)
% 36.00/35.83 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y1))) -> greatest_lower_bound(Y0, Y1)
% 36.00/35.83 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2)
% 36.00/35.83 greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(Y1, false__)), X1)) -> greatest_lower_bound(Y1, X1)
% 36.00/35.83 greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(Y1, false__)), greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)))) -> greatest_lower_bound(X1, greatest_lower_bound(X2, Y1))
% 36.00/35.83 greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(Y1, false__)), greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)))) -> greatest_lower_bound(X1, greatest_lower_bound(Y1, X2))
% 36.00/35.83 greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y1)) -> multiply(greatest_lower_bound(identity, X1), Y1)
% 36.00/35.83 greatest_lower_bound(Y1, multiply(inverse(b), multiply(a, Y1))) -> Y1
% 36.00/35.83 greatest_lower_bound(a, greatest_lower_bound(Y1, a)) -> greatest_lower_bound(Y1, a)
% 36.00/35.83 greatest_lower_bound(b, a) -> b
% 36.00/35.83 greatest_lower_bound(b, greatest_lower_bound(Y1, a)) -> greatest_lower_bound(Y1, b)
% 36.00/35.83 greatest_lower_bound(b, greatest_lower_bound(a, Y2)) -> greatest_lower_bound(b, Y2)
% 36.00/35.83 greatest_lower_bound(b, least_upper_bound(Y1, a)) -> b
% 36.00/35.83 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 36.00/35.83 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(inverse(X0), least_upper_bound(X0, X1)))) -> greatest_lower_bound(Y0, identity)
% 36.00/35.83 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(inverse(X0), least_upper_bound(X1, X0)))) -> greatest_lower_bound(Y0, identity)
% 36.00/35.83 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(inverse(b), a))) -> greatest_lower_bound(Y0, identity)
% 36.00/35.83 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(least_upper_bound(X0, inverse(X1)), X1))) -> greatest_lower_bound(Y0, identity)
% 36.00/35.83 greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(b), a), Y2)) -> greatest_lower_bound(identity, Y2)
% 36.00/35.83 greatest_lower_bound(identity, inverse(Y1)) -> multiply(greatest_lower_bound(Y1, identity), inverse(Y1))
% 36.00/35.83 greatest_lower_bound(identity, inverse(Y1)) -> multiply(greatest_lower_bound(identity, Y1), inverse(Y1))
% 36.00/35.83 greatest_lower_bound(identity, inverse(a)) -> multiply(greatest_lower_bound(identity, a), inverse(a))
% 36.00/35.83 greatest_lower_bound(identity, inverse(b)) -> multiply(greatest_lower_bound(identity, b), inverse(b))
% 36.00/35.83 greatest_lower_bound(identity, inverse(identity)) -> identity
% 36.00/35.83 greatest_lower_bound(identity, inverse(inverse(Y0))) -> greatest_lower_bound(identity, Y0)
% 36.00/35.83 greatest_lower_bound(identity, inverse(least_upper_bound(Y1, identity))) -> inverse(least_upper_bound(Y1, identity))
% 36.00/35.83 greatest_lower_bound(identity, inverse(least_upper_bound(Y1, least_upper_bound(Y2, identity)))) -> inverse(least_upper_bound(Y1, least_upper_bound(Y2, identity)))
% 36.00/35.83 greatest_lower_bound(identity, inverse(least_upper_bound(identity, Y1))) -> inverse(least_upper_bound(identity, Y1))
% 36.00/35.83 greatest_lower_bound(identity, inverse(multiply(X0, greatest_lower_bound(X1, inverse(X0))))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, inverse(multiply(X0, greatest_lower_bound(inverse(X0), X1)))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, least_upper_bound(Y0, inverse(identity))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, least_upper_bound(Y1, inverse(greatest_lower_bound(identity, inverse(identity))))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, least_upper_bound(Y1, inverse(inverse(identity)))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, least_upper_bound(inverse(greatest_lower_bound(identity, inverse(identity))), Y1)) -> identity
% 36.00/35.83 greatest_lower_bound(identity, least_upper_bound(inverse(identity), Y1)) -> identity
% 36.00/35.83 greatest_lower_bound(identity, least_upper_bound(inverse(inverse(identity)), Y1)) -> identity
% 36.00/35.83 greatest_lower_bound(identity, multiply(X0, greatest_lower_bound(X1, inverse(X0)))) -> multiply(X0, greatest_lower_bound(X1, inverse(X0)))
% 36.00/35.83 greatest_lower_bound(identity, multiply(X0, greatest_lower_bound(inverse(X0), X1))) -> multiply(X0, greatest_lower_bound(inverse(X0), X1))
% 36.00/35.83 greatest_lower_bound(identity, multiply(X0, least_upper_bound(Y1, inverse(X0)))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, multiply(X0, least_upper_bound(Y1, inverse(inverse(inverse(X0)))))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, multiply(X0, least_upper_bound(inverse(X0), Y1))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, multiply(X0, least_upper_bound(inverse(inverse(inverse(X0))), Y1))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, multiply(a, inverse(b))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, inverse(X1)), X1)) -> multiply(greatest_lower_bound(X0, inverse(X1)), X1)
% 36.00/35.83 greatest_lower_bound(identity, multiply(inverse(X0), greatest_lower_bound(X0, X1))) -> multiply(inverse(X0), greatest_lower_bound(X0, X1))
% 36.00/35.83 greatest_lower_bound(identity, multiply(inverse(X0), greatest_lower_bound(X1, X0))) -> multiply(inverse(X0), greatest_lower_bound(X1, X0))
% 36.00/35.83 greatest_lower_bound(identity, multiply(inverse(X0), least_upper_bound(X0, X1))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, multiply(inverse(X0), least_upper_bound(X1, X0))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, multiply(inverse(Y0), multiply(least_upper_bound(identity, X1), Y0))) -> identity
% 36.00/35.83 greatest_lower_bound(identity, multiply(inverse(b), a)) -> identity
% 36.00/35.83 greatest_lower_bound(identity, multiply(least_upper_bound(X0, inverse(X1)), X1)) -> identity
% 36.00/35.83 greatest_lower_bound(inverse(a), least_upper_bound(X1, least_upper_bound(X2, inverse(b)))) -> inverse(a)
% 36.00/35.83 greatest_lower_bound(inverse(a), least_upper_bound(Y0, inverse(b))) -> inverse(a)
% 36.00/35.83 greatest_lower_bound(inverse(a), least_upper_bound(inverse(b), X0)) -> inverse(a)
% 36.00/35.83 greatest_lower_bound(inverse(a), multiply(least_upper_bound(X1, identity), inverse(b))) -> inverse(a)
% 36.00/35.83 greatest_lower_bound(inverse(a), multiply(least_upper_bound(identity, X1), inverse(b))) -> inverse(a)
% 36.00/35.83 greatest_lower_bound(inverse(b), greatest_lower_bound(Y0, inverse(a))) -> greatest_lower_bound(Y0, inverse(a))
% 36.00/35.83 greatest_lower_bound(inverse(b), greatest_lower_bound(Y1, inverse(b))) -> greatest_lower_bound(Y1, inverse(b))
% 36.00/35.83 greatest_lower_bound(inverse(b), greatest_lower_bound(inverse(a), Y2)) -> greatest_lower_bound(inverse(a), Y2)
% 36.00/35.83 greatest_lower_bound(inverse(b), inverse(a)) -> inverse(a)
% 36.00/35.83 greatest_lower_bound(inverse(least_upper_bound(identity, Y2)), least_upper_bound(Y1, identity)) -> inverse(least_upper_bound(identity, Y2))
% 36.00/35.83 greatest_lower_bound(least_upper_bound(X0, X1), least_upper_bound(X0, least_upper_bound(X1, Y1))) -> least_upper_bound(X0, X1)
% 36.00/35.83 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(X1, least_upper_bound(Y1, X2))) -> least_upper_bound(X1, X2)
% 36.00/35.83 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(X2, least_upper_bound(Y1, X1))) -> least_upper_bound(X1, X2)
% 36.00/35.83 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(X2, Y2)))) -> least_upper_bound(X1, X2)
% 36.00/35.83 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(Y2, X2)))) -> least_upper_bound(X1, X2)
% 36.00/35.83 greatest_lower_bound(least_upper_bound(X1, Y1), least_upper_bound(X1, greatest_lower_bound(X2, Y1))) -> least_upper_bound(X1, greatest_lower_bound(X2, Y1))
% 36.00/35.83 greatest_lower_bound(least_upper_bound(X1, Y1), least_upper_bound(X1, greatest_lower_bound(Y1, X2))) -> least_upper_bound(X1, greatest_lower_bound(Y1, X2))
% 36.00/35.83 greatest_lower_bound(least_upper_bound(Y0, inverse(b)), inverse(a)) -> inverse(a)
% 36.00/35.83 greatest_lower_bound(least_upper_bound(Y1, X2), least_upper_bound(greatest_lower_bound(X1, Y1), X2)) -> least_upper_bound(greatest_lower_bound(X1, Y1), X2)
% 36.00/35.83 greatest_lower_bound(least_upper_bound(Y1, X2), least_upper_bound(greatest_lower_bound(Y1, X1), X2)) -> least_upper_bound(greatest_lower_bound(Y1, X1), X2)
% 36.00/35.83 greatest_lower_bound(least_upper_bound(false__, inverse(b)), inverse(a)) -> inverse(a)
% 36.00/35.83 greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1, Y1), X2), least_upper_bound(X2, Y1)) -> least_upper_bound(greatest_lower_bound(X1, Y1), X2)
% 36.00/35.83 greatest_lower_bound(least_upper_bound(inverse(b), Y0), inverse(a)) -> inverse(a)
% 36.00/35.83 greatest_lower_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, greatest_lower_bound(Y, Z))
% 36.00/35.83 greatest_lower_bound(multiply(X0, greatest_lower_bound(X1, X2)), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X0, X2), Y2))
% 36.00/35.83 greatest_lower_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(greatest_lower_bound(multiply(X0, X1), Y2), Y1)
% 36.00/35.83 greatest_lower_bound(multiply(X1, Y2), least_upper_bound(Y1, multiply(least_upper_bound(X1, identity), Y2))) -> multiply(X1, Y2)
% 36.00/35.83 greatest_lower_bound(multiply(X1, Y2), least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y2))) -> multiply(X1, Y2)
% 36.00/35.83 greatest_lower_bound(multiply(Y, X), multiply(Z, X)) -> multiply(greatest_lower_bound(Y, Z), X)
% 36.00/35.83 greatest_lower_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(greatest_lower_bound(Y0, multiply(X0, X1)), Y1)
% 36.00/35.83 greatest_lower_bound(multiply(greatest_lower_bound(X0, X2), X1), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X2, X1), Y2))
% 36.00/35.83 greatest_lower_bound(multiply(least_upper_bound(X1, identity), inverse(b)), inverse(a)) -> inverse(a)
% 36.00/35.83 greatest_lower_bound(multiply(least_upper_bound(identity, X1), inverse(b)), inverse(a)) -> inverse(a)
% 36.00/35.83 inverse(greatest_lower_bound(identity, inverse(identity))) -> identity
% 36.00/35.83 inverse(greatest_lower_bound(identity, least_upper_bound(X0, inverse(identity)))) -> identity
% 36.00/35.83 inverse(identity) -> identity
% 36.00/35.83 inverse(inverse(Y0)) -> Y0
% 36.00/35.83 inverse(inverse(identity)) -> identity
% 36.00/35.83 least_upper_bound(X, X) -> X
% 36.00/35.83 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X
% 36.00/35.83 least_upper_bound(X1, multiply(inverse(Y1), X1)) -> multiply(least_upper_bound(Y1, identity), multiply(inverse(Y1), X1))
% 36.00/35.83 least_upper_bound(X1, multiply(inverse(Y1), X1)) -> multiply(least_upper_bound(identity, Y1), multiply(inverse(Y1), X1))
% 36.00/35.83 least_upper_bound(X1, multiply(inverse(greatest_lower_bound(Y1, identity)), X1)) -> multiply(inverse(greatest_lower_bound(Y1, identity)), X1)
% 36.00/35.83 least_upper_bound(X1, multiply(inverse(greatest_lower_bound(identity, Y1)), X1)) -> multiply(inverse(greatest_lower_bound(identity, Y1)), X1)
% 36.00/35.83 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))) -> Y0
% 36.00/35.83 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))) -> Y0
% 36.00/35.83 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0
% 36.00/35.83 least_upper_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(X2, Y0)))) -> Y0
% 36.00/35.83 least_upper_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(Y0, X2)))) -> Y0
% 36.00/35.83 least_upper_bound(Y0, greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, identity), Y0))) -> Y0
% 36.00/35.83 least_upper_bound(Y0, greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y0))) -> Y0
% 36.00/35.83 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(X1, least_upper_bound(Y0, Y1)))) -> least_upper_bound(Y0, Y1)
% 36.00/35.83 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(least_upper_bound(Y0, Y1), X1))) -> least_upper_bound(Y0, Y1)
% 36.00/35.83 least_upper_bound(Y0, least_upper_bound(Y1, least_upper_bound(Y0, Y1))) -> least_upper_bound(Y0, Y1)
% 36.00/35.83 least_upper_bound(Y0, least_upper_bound(Y2, greatest_lower_bound(Y0, Y1))) -> least_upper_bound(Y0, Y2)
% 36.00/35.83 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y0, X1), Y2)) -> least_upper_bound(Y0, Y2)
% 36.00/35.83 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y1, Y0), Y2)) -> least_upper_bound(Y0, Y2)
% 36.00/35.83 least_upper_bound(Y0, least_upper_bound(multiply(greatest_lower_bound(X1, identity), Y0), Y2)) -> least_upper_bound(Y0, Y2)
% 36.00/35.83 least_upper_bound(Y0, least_upper_bound(multiply(greatest_lower_bound(identity, X1), Y0), Y2)) -> least_upper_bound(Y0, Y2)
% 36.00/35.83 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y0)) -> Y0
% 36.00/35.83 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y0)) -> Y0
% 36.00/35.83 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> Y0
% 36.00/35.83 least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> Y0
% 36.00/35.83 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0))
% 36.00/35.83 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), greatest_lower_bound(Y0, Y1))) -> least_upper_bound(Y0, multiply(X1, greatest_lower_bound(Y0, Y1)))
% 36.00/35.83 least_upper_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(identity, X1)), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0))
% 36.00/35.83 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0))
% 36.00/35.83 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), greatest_lower_bound(Y0, Y1))) -> least_upper_bound(Y0, multiply(X1, greatest_lower_bound(Y0, Y1)))
% 36.00/35.83 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, Y1))) -> least_upper_bound(Y0, Y1)
% 36.00/35.83 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)))) -> least_upper_bound(Y0, Y1)
% 36.00/35.83 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)))) -> least_upper_bound(Y0, Y1)
% 36.00/35.83 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(Y1, X1))) -> least_upper_bound(Y0, Y1)
% 36.00/35.83 least_upper_bound(Y1, least_upper_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1))) -> least_upper_bound(Y0, Y1)
% 36.00/35.83 least_upper_bound(Y1, least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1))) -> least_upper_bound(Y0, Y1)
% 36.00/35.83 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2)
% 36.00/35.83 least_upper_bound(Y1, multiply(inverse(b), multiply(a, Y1))) -> multiply(inverse(b), multiply(a, Y1))
% 36.00/35.83 least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y1)) -> multiply(least_upper_bound(identity, X1), Y1)
% 36.00/35.83 least_upper_bound(b, a) -> multiply(a, identity)
% 36.00/35.83 least_upper_bound(b, least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a)
% 36.00/35.83 least_upper_bound(b, least_upper_bound(a, Y2)) -> least_upper_bound(a, Y2)
% 36.00/35.83 least_upper_bound(greatest_lower_bound(X0, X1), greatest_lower_bound(X0, greatest_lower_bound(X1, Y1))) -> greatest_lower_bound(X0, X1)
% 36.00/35.83 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X1, greatest_lower_bound(Y1, X2))) -> greatest_lower_bound(X1, X2)
% 36.00/35.83 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X2, greatest_lower_bound(Y1, X1))) -> greatest_lower_bound(X1, X2)
% 36.00/35.83 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(X2, Y2)))) -> greatest_lower_bound(X1, X2)
% 36.00/35.83 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(Y2, X2)))) -> greatest_lower_bound(X1, X2)
% 36.00/35.83 least_upper_bound(greatest_lower_bound(X1, Y1), greatest_lower_bound(X1, least_upper_bound(X2, Y1))) -> greatest_lower_bound(X1, least_upper_bound(X2, Y1))
% 36.00/35.83 least_upper_bound(greatest_lower_bound(X1, Y1), greatest_lower_bound(X1, least_upper_bound(Y1, X2))) -> greatest_lower_bound(X1, least_upper_bound(Y1, X2))
% 36.00/35.83 least_upper_bound(greatest_lower_bound(X1, least_upper_bound(Y1, X2)), greatest_lower_bound(Y1, X1)) -> greatest_lower_bound(X1, least_upper_bound(Y1, X2))
% 36.00/35.83 least_upper_bound(greatest_lower_bound(Y1, X2), greatest_lower_bound(least_upper_bound(Y1, X1), X2)) -> greatest_lower_bound(least_upper_bound(Y1, X1), X2)
% 36.00/35.83 least_upper_bound(greatest_lower_bound(least_upper_bound(X1, Y1), X2), greatest_lower_bound(X2, Y1)) -> greatest_lower_bound(least_upper_bound(X1, Y1), X2)
% 36.00/35.83 least_upper_bound(identity, inverse(Y1)) -> multiply(least_upper_bound(Y1, identity), inverse(Y1))
% 36.00/35.83 least_upper_bound(identity, inverse(Y1)) -> multiply(least_upper_bound(identity, Y1), inverse(Y1))
% 36.00/35.83 least_upper_bound(identity, least_upper_bound(Y0, multiply(greatest_lower_bound(X0, inverse(X1)), X1))) -> least_upper_bound(Y0, identity)
% 36.00/35.83 least_upper_bound(identity, multiply(X0, greatest_lower_bound(Y1, inverse(X0)))) -> identity
% 36.00/35.83 least_upper_bound(identity, multiply(X0, greatest_lower_bound(inverse(X0), Y1))) -> identity
% 36.00/35.83 least_upper_bound(identity, multiply(X0, least_upper_bound(X1, inverse(X0)))) -> multiply(X0, least_upper_bound(X1, inverse(X0)))
% 36.00/35.83 least_upper_bound(identity, multiply(X0, least_upper_bound(inverse(X0), X1))) -> multiply(X0, least_upper_bound(inverse(X0), X1))
% 36.00/35.83 least_upper_bound(identity, multiply(greatest_lower_bound(X0, inverse(X1)), X1)) -> identity
% 36.00/35.83 least_upper_bound(identity, multiply(inverse(X0), greatest_lower_bound(X0, X1))) -> identity
% 36.00/35.83 least_upper_bound(identity, multiply(inverse(X0), greatest_lower_bound(X1, X0))) -> identity
% 36.00/35.83 least_upper_bound(identity, multiply(inverse(X0), least_upper_bound(X0, X1))) -> multiply(inverse(X0), least_upper_bound(X0, X1))
% 36.00/35.83 least_upper_bound(identity, multiply(inverse(X0), least_upper_bound(X1, X0))) -> multiply(inverse(X0), least_upper_bound(X1, X0))
% 36.00/35.83 least_upper_bound(identity, multiply(inverse(Y0), multiply(greatest_lower_bound(identity, X1), Y0))) -> identity
% 36.00/35.83 least_upper_bound(identity, multiply(inverse(b), a)) -> multiply(inverse(b), a)
% 36.00/35.83 least_upper_bound(identity, multiply(least_upper_bound(X0, inverse(X1)), X1)) -> multiply(least_upper_bound(X0, inverse(X1)), X1)
% 36.00/35.83 least_upper_bound(inverse(a), inverse(b)) -> inverse(b)
% 36.00/35.83 least_upper_bound(inverse(a), least_upper_bound(inverse(b), Y2)) -> least_upper_bound(inverse(b), Y2)
% 36.00/35.83 least_upper_bound(inverse(b), greatest_lower_bound(Y1, inverse(a))) -> inverse(b)
% 36.00/35.83 least_upper_bound(inverse(b), greatest_lower_bound(inverse(a), Y0)) -> inverse(b)
% 36.00/35.83 least_upper_bound(inverse(b), inverse(a)) -> inverse(b)
% 36.00/35.83 least_upper_bound(inverse(b), least_upper_bound(X0, greatest_lower_bound(Y1, inverse(a)))) -> least_upper_bound(inverse(b), X0)
% 36.00/35.83 least_upper_bound(inverse(b), least_upper_bound(Y0, inverse(a))) -> least_upper_bound(Y0, inverse(b))
% 36.00/35.83 least_upper_bound(inverse(b), least_upper_bound(Y0, inverse(a))) -> least_upper_bound(inverse(b), Y0)
% 36.00/35.83 least_upper_bound(inverse(b), least_upper_bound(inverse(a), Y2)) -> least_upper_bound(inverse(b), Y2)
% 36.00/35.83 least_upper_bound(inverse(greatest_lower_bound(identity, Y2)), greatest_lower_bound(Y1, identity)) -> inverse(greatest_lower_bound(identity, Y2))
% 36.00/35.83 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z))
% 36.00/35.83 least_upper_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, least_upper_bound(Y, Z))
% 36.00/35.83 least_upper_bound(multiply(X0, least_upper_bound(X1, X2)), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X0, X2), Y2))
% 36.00/35.83 least_upper_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(least_upper_bound(multiply(X0, X1), Y2), Y1)
% 36.00/35.83 least_upper_bound(multiply(X1, Y2), greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, identity), Y2))) -> multiply(X1, Y2)
% 36.00/35.83 least_upper_bound(multiply(X1, Y2), greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y2))) -> multiply(X1, Y2)
% 36.00/35.83 least_upper_bound(multiply(Y, X), multiply(Z, X)) -> multiply(least_upper_bound(Y, Z), X)
% 36.00/35.83 least_upper_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(least_upper_bound(Y0, multiply(X0, X1)), Y1)
% 36.00/35.83 least_upper_bound(multiply(inverse(b), a), greatest_lower_bound(Y1, identity)) -> multiply(inverse(b), a)
% 36.00/35.83 least_upper_bound(multiply(inverse(b), multiply(a, Y2)), greatest_lower_bound(Y1, Y2)) -> multiply(inverse(b), multiply(a, Y2))
% 36.00/35.83 least_upper_bound(multiply(least_upper_bound(X0, X2), X1), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X2, X1), Y2))
% 36.00/35.83 multiply(Y0, inverse(Y0)) -> identity
% 36.00/35.83 multiply(Y0, inverse(inverse(inverse(Y0)))) -> identity
% 36.00/35.83 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity
% 36.00/35.83 multiply(Y0, multiply(Y1, multiply(inverse(multiply(Y0, Y1)), X1))) -> X1
% 36.00/35.83 multiply(Y0, multiply(inverse(Y0), X1)) -> X1
% 36.00/35.83 multiply(Y1, identity) -> Y1
% 36.00/35.83 multiply(a, inverse(a)) -> identity
% 36.00/35.83 multiply(b, inverse(b)) -> identity
% 36.00/35.83 multiply(greatest_lower_bound(identity, inverse(a)), least_upper_bound(b, a)) -> greatest_lower_bound(identity, least_upper_bound(b, a))
% 36.00/35.83 multiply(greatest_lower_bound(identity, inverse(identity)), Y0) -> Y0
% 36.00/35.83 multiply(greatest_lower_bound(identity, inverse(inverse(X0))), identity) -> greatest_lower_bound(identity, X0)
% 36.00/35.83 multiply(greatest_lower_bound(identity, inverse(multiply(greatest_lower_bound(X0, inverse(X1)), X1))), identity) -> identity
% 36.00/35.83 multiply(greatest_lower_bound(identity, inverse(multiply(inverse(X0), greatest_lower_bound(X0, X1)))), identity) -> identity
% 36.00/35.83 multiply(greatest_lower_bound(identity, inverse(multiply(inverse(X0), greatest_lower_bound(X1, X0)))), identity) -> identity
% 36.00/35.83 multiply(greatest_lower_bound(identity, least_upper_bound(X0, inverse(identity))), identity) -> identity
% 36.00/35.83 multiply(greatest_lower_bound(inverse(Y1), Y2), Y1) -> greatest_lower_bound(identity, multiply(Y2, Y1))
% 36.00/35.83 multiply(identity, X) -> X
% 36.00/35.83 multiply(inverse(X), X) -> identity
% 36.00/35.83 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 36.00/35.83 multiply(inverse(a), least_upper_bound(b, a)) -> identity
% 36.00/35.83 multiply(inverse(a), multiply(least_upper_bound(b, a), Y2)) -> Y2
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, greatest_lower_bound(Y0, inverse(identity))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, greatest_lower_bound(Y1, inverse(greatest_lower_bound(identity, inverse(identity))))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, greatest_lower_bound(Y1, inverse(inverse(identity)))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, greatest_lower_bound(inverse(greatest_lower_bound(identity, inverse(identity))), Y1)))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, greatest_lower_bound(inverse(identity), Y1)))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, greatest_lower_bound(inverse(inverse(identity)), Y1)))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, inverse(inverse(X0))))) -> least_upper_bound(identity, X0)
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, inverse(multiply(X0, least_upper_bound(X1, inverse(X0))))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, inverse(multiply(X0, least_upper_bound(inverse(X0), X1)))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, inverse(multiply(inverse(X0), least_upper_bound(X0, X1)))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, inverse(multiply(inverse(X0), least_upper_bound(X1, X0)))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, inverse(multiply(inverse(b), a))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, inverse(multiply(least_upper_bound(X0, inverse(X1)), X1))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), a)))) -> multiply(inverse(false__), least_upper_bound(false__, multiply(false__, a)))
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), inverse(a))))) -> multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, a)), inverse(a)))
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), inverse(a))))) -> multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), a))), inverse(a)))
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), inverse(b))))) -> multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, b)), inverse(b)))
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), inverse(b))))) -> multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), b))), inverse(b)))
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), inverse(greatest_lower_bound(Y1, greatest_lower_bound(Y2, identity))))))) -> inverse(greatest_lower_bound(Y1, greatest_lower_bound(Y2, identity)))
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), inverse(greatest_lower_bound(Y1, identity)))))) -> inverse(greatest_lower_bound(Y1, identity))
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), inverse(greatest_lower_bound(identity, Y1)))))) -> inverse(greatest_lower_bound(identity, Y1))
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), multiply(inverse(b), a))))) -> multiply(inverse(b), a)
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, multiply(X0, greatest_lower_bound(Y1, inverse(inverse(inverse(X0)))))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, multiply(X0, greatest_lower_bound(inverse(inverse(inverse(X0))), Y1))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, multiply(b, inverse(a))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, multiply(inverse(least_upper_bound(X0, inverse(b))), inverse(a))))) -> identity
% 36.00/35.83 multiply(inverse(false__), least_upper_bound(false__, multiply(false__, multiply(inverse(least_upper_bound(inverse(b), X0)), inverse(a))))) -> identity
% 36.00/35.83 multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, greatest_lower_bound(X0, inverse(identity)))), identity)) -> identity
% 36.00/35.83 multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, inverse(a))), least_upper_bound(b, a))) -> multiply(inverse(false__), least_upper_bound(false__, multiply(false__, least_upper_bound(b, a))))
% 36.00/35.83 multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, inverse(identity))), Y0)) -> Y0
% 36.00/35.83 multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, inverse(inverse(X0)))), identity)) -> least_upper_bound(identity, X0)
% 36.00/35.83 multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, inverse(multiply(inverse(X0), least_upper_bound(X0, X1))))), identity)) -> identity
% 36.00/35.83 multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, inverse(multiply(inverse(X0), least_upper_bound(X1, X0))))), identity)) -> identity
% 36.00/35.83 multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, inverse(multiply(inverse(b), a)))), identity)) -> identity
% 36.00/35.83 multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, inverse(multiply(least_upper_bound(X0, inverse(X1)), X1)))), identity)) -> identity
% 36.00/35.83 multiply(inverse(false__), multiply(least_upper_bound(false__, multiply(false__, least_upper_bound(greatest_lower_bound(multiply(false__, false__), identity), inverse(identity)))), Y0)) -> Y0
% 36.00/35.83 multiply(inverse(greatest_lower_bound(X0, identity)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1
% 36.00/35.83 multiply(inverse(greatest_lower_bound(X0, inverse(Y1))), greatest_lower_bound(multiply(X0, Y1), identity)) -> Y1
% 36.00/35.83 multiply(inverse(greatest_lower_bound(identity, X0)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1
% 36.00/35.83 multiply(inverse(greatest_lower_bound(identity, inverse(identity))), Y1) -> Y1
% 36.00/35.83 multiply(inverse(greatest_lower_bound(inverse(Y1), X1)), greatest_lower_bound(identity, multiply(X1, Y1))) -> Y1
% 36.00/35.83 multiply(inverse(identity), Y1) -> Y1
% 36.00/35.83 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1)
% 36.00/35.83 multiply(inverse(inverse(Y1)), identity) -> Y1
% 36.00/35.83 multiply(inverse(least_upper_bound(X0, identity)), least_upper_bound(Y1, multiply(X0, Y1))) -> Y1
% 36.00/35.83 multiply(inverse(least_upper_bound(X0, inverse(Y1))), least_upper_bound(multiply(X0, Y1), identity)) -> Y1
% 36.00/35.83 multiply(inverse(least_upper_bound(identity, X0)), least_upper_bound(Y1, multiply(X0, Y1))) -> Y1
% 36.00/35.83 multiply(inverse(least_upper_bound(inverse(Y1), X1)), least_upper_bound(identity, multiply(X1, Y1))) -> Y1
% 36.00/35.83 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1
% 36.00/35.83 multiply(inverse(multiply(greatest_lower_bound(X1, identity), Y1)), greatest_lower_bound(Y1, multiply(X1, Y1))) -> identity
% 36.00/35.83 multiply(inverse(multiply(inverse(b), multiply(a, Y1))), least_upper_bound(Y1, multiply(inverse(b), multiply(a, Y1)))) -> identity
% 36.00/35.83 multiply(inverse(multiply(least_upper_bound(X1, identity), Y1)), least_upper_bound(Y1, multiply(X1, Y1))) -> identity
% 36.00/35.83 multiply(least_upper_bound(inverse(Y1), Y2), Y1) -> least_upper_bound(identity, multiply(Y2, Y1))
% 36.00/35.83 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 36.00/35.83 true__ -> false__
% 36.00/35.83 with the LPO induced by
% 36.00/35.83 a > f1 > b > inverse > identity > greatest_lower_bound > least_upper_bound > multiply > true__ > false__
% 36.00/35.83
% 36.00/35.83 % SZS output end Proof
% 36.00/35.83
%------------------------------------------------------------------------------