TSTP Solution File: GRP171-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP171-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n009.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 10:53:41 EDT 2022
% Result : Unsatisfiable 15.36s 15.17s
% Output : Proof 15.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP171-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 22:28:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 15.36/15.17 % SZS status Unsatisfiable
% 15.36/15.17 % SZS output start Proof
% 15.36/15.17 The input problem is unsatisfiable because
% 15.36/15.17
% 15.36/15.17 [1] the following set of Horn clauses is unsatisfiable:
% 15.36/15.17
% 15.36/15.17 multiply(identity, X) = X
% 15.36/15.17 multiply(inverse(X), X) = identity
% 15.36/15.17 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 15.36/15.17 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 15.36/15.17 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 15.36/15.17 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 15.36/15.17 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 15.36/15.17 least_upper_bound(X, X) = X
% 15.36/15.17 greatest_lower_bound(X, X) = X
% 15.36/15.17 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 15.36/15.17 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 15.36/15.17 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 15.36/15.17 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 15.36/15.17 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 15.36/15.17 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 15.36/15.17 least_upper_bound(identity, a) = a
% 15.36/15.17 least_upper_bound(identity, b) = b
% 15.36/15.17 least_upper_bound(identity, multiply(a, b)) = multiply(a, b) ==> \bottom
% 15.36/15.17
% 15.36/15.17 This holds because
% 15.36/15.17
% 15.36/15.17 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 15.36/15.17
% 15.36/15.17 E:
% 15.36/15.17 f1(least_upper_bound(identity, multiply(a, b))) = true__
% 15.36/15.17 f1(multiply(a, b)) = false__
% 15.36/15.17 greatest_lower_bound(X, X) = X
% 15.36/15.17 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 15.36/15.17 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 15.36/15.17 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 15.36/15.17 least_upper_bound(X, X) = X
% 15.36/15.17 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 15.36/15.17 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 15.36/15.17 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 15.36/15.17 least_upper_bound(identity, a) = a
% 15.36/15.17 least_upper_bound(identity, b) = b
% 15.36/15.17 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 15.36/15.17 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 15.36/15.17 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 15.36/15.17 multiply(identity, X) = X
% 15.36/15.17 multiply(inverse(X), X) = identity
% 15.36/15.17 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 15.36/15.17 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 15.36/15.17 G:
% 15.36/15.17 true__ = false__
% 15.36/15.17
% 15.36/15.17 This holds because
% 15.36/15.17
% 15.36/15.17 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 15.36/15.17
% 15.36/15.17 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 15.36/15.17 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, Y1), Y0))
% 15.36/15.17 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(Y1, X1), Y0))
% 15.36/15.17 greatest_lower_bound(Y0, greatest_lower_bound(Y2, Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y2, Y0))
% 15.36/15.17 greatest_lower_bound(Y0, greatest_lower_bound(Y2, Y1)) = greatest_lower_bound(Y2, greatest_lower_bound(Y0, Y1))
% 15.36/15.17 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(X0, a), Y0))
% 15.36/15.17 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(a, X0), Y0))
% 15.36/15.17 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(b, X0), Y0))
% 15.36/15.17 greatest_lower_bound(Y2, greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(inverse(b), Y2)) = greatest_lower_bound(Y2, inverse(b))
% 15.36/15.17 greatest_lower_bound(inverse(b), greatest_lower_bound(a, Y2)) = greatest_lower_bound(Y2, inverse(b))
% 15.36/15.17 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 15.36/15.17 least_upper_bound(Y1, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, identity), Y1)
% 15.36/15.17 least_upper_bound(Y1, multiply(Y2, Y1)) = multiply(least_upper_bound(identity, Y2), Y1)
% 15.36/15.17 least_upper_bound(identity, least_upper_bound(Y0, a)) = least_upper_bound(a, Y0)
% 15.36/15.17 least_upper_bound(identity, least_upper_bound(Y0, b)) = least_upper_bound(b, Y0)
% 15.36/15.17 f1(least_upper_bound(identity, multiply(a, b))) -> true__
% 15.36/15.17 f1(multiply(a, b)) -> false__
% 15.36/15.17 greatest_lower_bound(X, X) -> X
% 15.36/15.17 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X
% 15.36/15.17 greatest_lower_bound(X1, multiply(inverse(a), X1)) -> multiply(inverse(a), X1)
% 15.36/15.17 greatest_lower_bound(X1, multiply(inverse(b), X1)) -> multiply(inverse(b), X1)
% 15.36/15.17 greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y0)) -> greatest_lower_bound(Y0, Y1)
% 15.36/15.17 greatest_lower_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y1)
% 15.36/15.17 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0
% 15.36/15.17 greatest_lower_bound(Y0, least_upper_bound(identity, least_upper_bound(Y0, a))) -> Y0
% 15.36/15.17 greatest_lower_bound(Y0, least_upper_bound(identity, least_upper_bound(Y0, b))) -> Y0
% 15.36/15.17 greatest_lower_bound(Y0, multiply(a, Y0)) -> Y0
% 15.36/15.17 greatest_lower_bound(Y0, multiply(b, Y0)) -> Y0
% 15.36/15.17 greatest_lower_bound(Y0, multiply(least_upper_bound(Y1, identity), Y0)) -> Y0
% 15.36/15.17 greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> Y0
% 15.36/15.17 greatest_lower_bound(Y1, greatest_lower_bound(X1, Y1)) -> greatest_lower_bound(X1, Y1)
% 15.36/15.17 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, Y1))) -> greatest_lower_bound(Y0, Y1)
% 15.36/15.17 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(Y1, X1))) -> greatest_lower_bound(Y0, Y1)
% 15.36/15.17 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2)
% 15.36/15.17 greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(Y1, Y2), Y0)) -> greatest_lower_bound(Y1, Y0)
% 15.36/15.17 greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(Y2, Y1), Y0)) -> greatest_lower_bound(Y1, Y0)
% 15.36/15.17 greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, identity), Y1)) -> multiply(greatest_lower_bound(X1, identity), Y1)
% 15.36/15.17 greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y1)) -> multiply(greatest_lower_bound(identity, X1), Y1)
% 15.36/15.17 greatest_lower_bound(a, greatest_lower_bound(least_upper_bound(false__, a), inverse(a))) -> inverse(a)
% 15.36/15.17 greatest_lower_bound(a, inverse(a)) -> inverse(a)
% 15.36/15.17 greatest_lower_bound(a, least_upper_bound(identity, least_upper_bound(Y1, a))) -> a
% 15.36/15.17 greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(false__, b), inverse(a))) -> inverse(a)
% 15.36/15.17 greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(false__, b), inverse(b))) -> inverse(b)
% 15.36/15.17 greatest_lower_bound(b, inverse(a)) -> inverse(a)
% 15.36/15.17 greatest_lower_bound(b, inverse(b)) -> inverse(b)
% 15.36/15.17 greatest_lower_bound(b, least_upper_bound(identity, least_upper_bound(Y1, b))) -> b
% 15.36/15.17 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 15.36/15.17 greatest_lower_bound(identity, a) -> identity
% 15.36/15.17 greatest_lower_bound(identity, b) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(X0, inverse(a))) -> greatest_lower_bound(X0, inverse(a))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(Y0, a)) -> greatest_lower_bound(identity, Y0)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(Y0, b)) -> greatest_lower_bound(identity, Y0)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(Y0, inverse(b))) -> greatest_lower_bound(Y0, inverse(b))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(Y0, least_upper_bound(a, X0))) -> greatest_lower_bound(Y0, identity)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(a, Y2)) -> greatest_lower_bound(identity, Y2)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(b, Y2)) -> greatest_lower_bound(identity, Y2)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(inverse(a), X0)) -> greatest_lower_bound(inverse(a), X0)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(Y1, a), Y0)) -> greatest_lower_bound(identity, Y0)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(a, Y1), Y0)) -> greatest_lower_bound(identity, Y0)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, a), greatest_lower_bound(X0, inverse(a)))) -> greatest_lower_bound(X0, inverse(a))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, a), greatest_lower_bound(inverse(a), X0))) -> greatest_lower_bound(inverse(a), X0)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, a), least_upper_bound(a, X0))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, a), multiply(X1, inverse(multiply(a, X1))))) -> multiply(X1, inverse(multiply(a, X1)))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, b), greatest_lower_bound(X0, inverse(a)))) -> greatest_lower_bound(X0, inverse(a))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, b), greatest_lower_bound(X0, inverse(b)))) -> greatest_lower_bound(X0, inverse(b))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, b), greatest_lower_bound(inverse(a), X0))) -> greatest_lower_bound(inverse(a), X0)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, b), greatest_lower_bound(inverse(b), X0))) -> greatest_lower_bound(inverse(b), X0)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, b), least_upper_bound(X0, a))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, b), multiply(X1, inverse(multiply(a, X1))))) -> multiply(X1, inverse(multiply(a, X1)))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, b), multiply(X1, inverse(multiply(b, X1))))) -> multiply(X1, inverse(multiply(b, X1)))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, b), multiply(a, a))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, b), multiply(a, b))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, b), multiply(b, a))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), greatest_lower_bound(X0, inverse(a)))) -> greatest_lower_bound(X0, inverse(a))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), greatest_lower_bound(inverse(a), X0))) -> greatest_lower_bound(inverse(a), X0)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), inverse(a))) -> inverse(a)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), inverse(b))) -> inverse(b)
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), inverse(least_upper_bound(Y1, identity)))) -> inverse(least_upper_bound(Y1, identity))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), inverse(least_upper_bound(identity, Y1)))) -> inverse(least_upper_bound(identity, Y1))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), least_upper_bound(X0, a))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), least_upper_bound(X0, b))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), least_upper_bound(a, X0))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), least_upper_bound(b, X0))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), multiply(X1, inverse(multiply(a, X1))))) -> multiply(X1, inverse(multiply(a, X1)))
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), multiply(a, a))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), multiply(a, b))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), multiply(b, a))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(false__, identity), multiply(b, b))) -> identity
% 15.36/15.17 greatest_lower_bound(identity, inverse(a)) -> inverse(a)
% 15.36/15.17 greatest_lower_bound(identity, inverse(b)) -> inverse(b)
% 15.36/15.17 greatest_lower_bound(identity, inverse(least_upper_bound(Y1, identity))) -> inverse(least_upper_bound(Y1, identity))
% 15.36/15.17 greatest_lower_bound(identity, inverse(least_upper_bound(identity, Y1))) -> inverse(least_upper_bound(identity, Y1))
% 15.36/15.17 greatest_lower_bound(identity, least_upper_bound(Y0, a)) -> identity
% 15.36/15.17 greatest_lower_bound(identity, least_upper_bound(Y0, b)) -> identity
% 15.36/15.17 greatest_lower_bound(identity, least_upper_bound(a, X0)) -> identity
% 15.36/15.17 greatest_lower_bound(identity, least_upper_bound(b, X0)) -> identity
% 15.36/15.17 greatest_lower_bound(identity, multiply(X1, inverse(multiply(a, X1)))) -> multiply(X1, inverse(multiply(a, X1)))
% 15.36/15.17 greatest_lower_bound(identity, multiply(X1, inverse(multiply(b, X1)))) -> multiply(X1, inverse(multiply(b, X1)))
% 15.36/15.17 greatest_lower_bound(identity, multiply(a, a)) -> identity
% 15.36/15.17 greatest_lower_bound(identity, multiply(a, b)) -> identity
% 15.36/15.17 greatest_lower_bound(identity, multiply(b, a)) -> identity
% 15.36/15.17 greatest_lower_bound(identity, multiply(b, b)) -> identity
% 15.36/15.17 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, identity), a)) -> identity
% 15.36/15.17 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, identity), b)) -> identity
% 15.36/15.17 greatest_lower_bound(identity, multiply(least_upper_bound(identity, X1), a)) -> identity
% 15.36/15.17 greatest_lower_bound(identity, multiply(least_upper_bound(identity, X1), b)) -> identity
% 15.36/15.17 greatest_lower_bound(inverse(b), a) -> inverse(b)
% 15.36/15.17 greatest_lower_bound(inverse(b), greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, inverse(b))
% 15.36/15.17 greatest_lower_bound(inverse(b), greatest_lower_bound(least_upper_bound(false__, inverse(b)), a)) -> inverse(b)
% 15.36/15.17 greatest_lower_bound(least_upper_bound(X0, a), least_upper_bound(a, X0)) -> least_upper_bound(X0, a)
% 15.36/15.17 greatest_lower_bound(least_upper_bound(X0, b), least_upper_bound(b, X0)) -> least_upper_bound(X0, b)
% 15.36/15.17 greatest_lower_bound(least_upper_bound(X0, inverse(a)), least_upper_bound(identity, X0)) -> least_upper_bound(X0, inverse(a))
% 15.36/15.17 greatest_lower_bound(least_upper_bound(false__, a), inverse(a)) -> inverse(a)
% 15.36/15.17 greatest_lower_bound(least_upper_bound(false__, b), inverse(a)) -> inverse(a)
% 15.36/15.17 greatest_lower_bound(least_upper_bound(false__, b), inverse(b)) -> inverse(b)
% 15.36/15.17 greatest_lower_bound(least_upper_bound(false__, identity), inverse(a)) -> inverse(a)
% 15.36/15.17 greatest_lower_bound(least_upper_bound(false__, identity), inverse(b)) -> inverse(b)
% 15.36/15.17 greatest_lower_bound(least_upper_bound(identity, X0), greatest_lower_bound(least_upper_bound(false__, least_upper_bound(identity, X0)), least_upper_bound(inverse(a), X0))) -> least_upper_bound(inverse(a), X0)
% 15.36/15.17 greatest_lower_bound(least_upper_bound(identity, X0), least_upper_bound(inverse(a), X0)) -> least_upper_bound(inverse(a), X0)
% 15.36/15.17 greatest_lower_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, greatest_lower_bound(Y, Z))
% 15.36/15.17 greatest_lower_bound(multiply(Y, X), multiply(Z, X)) -> multiply(greatest_lower_bound(Y, Z), X)
% 15.36/15.17 inverse(identity) -> identity
% 15.36/15.17 inverse(inverse(Y0)) -> Y0
% 15.36/15.17 inverse(inverse(identity)) -> identity
% 15.36/15.17 inverse(least_upper_bound(identity, inverse(identity))) -> identity
% 15.36/15.17 least_upper_bound(X, X) -> X
% 15.36/15.17 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X
% 15.36/15.17 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))) -> Y0
% 15.36/15.17 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0
% 15.36/15.17 least_upper_bound(Y0, greatest_lower_bound(Y2, greatest_lower_bound(Y0, Y1))) -> Y0
% 15.36/15.17 least_upper_bound(Y0, least_upper_bound(Y1, Y0)) -> least_upper_bound(Y0, Y1)
% 15.36/15.17 least_upper_bound(Y0, least_upper_bound(Y1, least_upper_bound(Y0, Y1))) -> least_upper_bound(Y0, Y1)
% 15.36/15.17 least_upper_bound(Y0, multiply(greatest_lower_bound(Y1, identity), Y0)) -> Y0
% 15.36/15.17 least_upper_bound(Y1, least_upper_bound(X1, Y1)) -> least_upper_bound(X1, Y1)
% 15.36/15.17 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2)
% 15.36/15.17 least_upper_bound(Y1, multiply(a, Y1)) -> multiply(a, Y1)
% 15.36/15.17 least_upper_bound(Y1, multiply(b, Y1)) -> multiply(b, Y1)
% 15.36/15.17 least_upper_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y1)) -> Y1
% 15.36/15.17 least_upper_bound(Y1, multiply(inverse(a), Y1)) -> Y1
% 15.36/15.17 least_upper_bound(Y1, multiply(inverse(b), Y1)) -> Y1
% 15.36/15.17 least_upper_bound(Y1, multiply(least_upper_bound(X1, identity), Y1)) -> multiply(least_upper_bound(X1, identity), Y1)
% 15.36/15.17 least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y1)) -> multiply(least_upper_bound(identity, X1), Y1)
% 15.36/15.17 least_upper_bound(Y2, least_upper_bound(X1, greatest_lower_bound(Y1, Y2))) -> least_upper_bound(Y2, X1)
% 15.36/15.17 least_upper_bound(a, greatest_lower_bound(Y1, identity)) -> a
% 15.36/15.17 least_upper_bound(a, greatest_lower_bound(identity, Y0)) -> a
% 15.36/15.17 least_upper_bound(a, inverse(a)) -> a
% 15.36/15.17 least_upper_bound(a, least_upper_bound(X0, greatest_lower_bound(Y1, identity))) -> least_upper_bound(a, X0)
% 15.36/15.17 least_upper_bound(b, greatest_lower_bound(Y1, identity)) -> b
% 15.36/15.17 least_upper_bound(b, greatest_lower_bound(identity, Y0)) -> b
% 15.36/15.17 least_upper_bound(b, inverse(a)) -> b
% 15.36/15.17 least_upper_bound(b, inverse(b)) -> b
% 15.36/15.17 least_upper_bound(b, least_upper_bound(X0, greatest_lower_bound(Y1, identity))) -> least_upper_bound(b, X0)
% 15.36/15.17 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(identity, X0)) -> greatest_lower_bound(X0, a)
% 15.36/15.17 least_upper_bound(greatest_lower_bound(X0, b), greatest_lower_bound(identity, X0)) -> greatest_lower_bound(X0, b)
% 15.36/15.17 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X1, greatest_lower_bound(X2, Y1))) -> greatest_lower_bound(X1, X2)
% 15.36/15.17 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X1, greatest_lower_bound(Y1, X2))) -> greatest_lower_bound(X1, X2)
% 15.36/15.17 least_upper_bound(greatest_lower_bound(Y0, identity), a) -> a
% 15.36/15.17 least_upper_bound(greatest_lower_bound(Y0, identity), b) -> b
% 15.36/15.17 least_upper_bound(greatest_lower_bound(a, X0), greatest_lower_bound(X0, inverse(b))) -> greatest_lower_bound(a, X0)
% 15.36/15.17 least_upper_bound(greatest_lower_bound(identity, X0), greatest_lower_bound(a, X0)) -> greatest_lower_bound(a, X0)
% 15.36/15.17 least_upper_bound(greatest_lower_bound(identity, X0), greatest_lower_bound(b, X0)) -> greatest_lower_bound(b, X0)
% 15.36/15.17 least_upper_bound(greatest_lower_bound(identity, Y0), a) -> a
% 15.36/15.17 least_upper_bound(greatest_lower_bound(identity, Y0), b) -> b
% 15.36/15.17 least_upper_bound(identity, a) -> a
% 15.36/15.17 least_upper_bound(identity, b) -> b
% 15.36/15.17 least_upper_bound(identity, greatest_lower_bound(X1, inverse(a))) -> identity
% 15.36/15.17 least_upper_bound(identity, greatest_lower_bound(Y1, inverse(b))) -> identity
% 15.36/15.17 least_upper_bound(identity, greatest_lower_bound(b, a)) -> greatest_lower_bound(b, a)
% 15.36/15.17 least_upper_bound(identity, greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(false__, b), a))) -> greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(false__, b), a))
% 15.36/15.17 least_upper_bound(identity, greatest_lower_bound(inverse(a), X1)) -> identity
% 15.36/15.17 least_upper_bound(identity, greatest_lower_bound(inverse(b), Y0)) -> identity
% 15.36/15.17 least_upper_bound(identity, inverse(X0)) -> multiply(least_upper_bound(identity, X0), inverse(X0))
% 15.36/15.17 least_upper_bound(identity, inverse(a)) -> identity
% 15.36/15.17 least_upper_bound(identity, inverse(b)) -> identity
% 15.36/15.17 least_upper_bound(identity, inverse(greatest_lower_bound(identity, Y1))) -> inverse(greatest_lower_bound(identity, Y1))
% 15.36/15.17 least_upper_bound(identity, inverse(identity)) -> identity
% 15.36/15.17 least_upper_bound(identity, least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a)
% 15.36/15.17 least_upper_bound(identity, least_upper_bound(Y0, b)) -> least_upper_bound(Y0, b)
% 15.36/15.17 least_upper_bound(identity, least_upper_bound(Y0, inverse(a))) -> least_upper_bound(identity, Y0)
% 15.36/15.17 least_upper_bound(identity, least_upper_bound(a, Y2)) -> least_upper_bound(a, Y2)
% 15.36/15.17 least_upper_bound(identity, least_upper_bound(b, Y2)) -> least_upper_bound(b, Y2)
% 15.36/15.17 least_upper_bound(identity, least_upper_bound(inverse(a), Y2)) -> least_upper_bound(identity, Y2)
% 15.36/15.17 least_upper_bound(identity, multiply(a, a)) -> multiply(a, a)
% 15.36/15.17 least_upper_bound(identity, multiply(a, b)) -> multiply(a, b)
% 15.36/15.17 least_upper_bound(identity, multiply(b, a)) -> multiply(b, a)
% 15.36/15.17 least_upper_bound(identity, multiply(b, b)) -> multiply(b, b)
% 15.36/15.17 least_upper_bound(identity, multiply(least_upper_bound(X0, identity), a)) -> multiply(least_upper_bound(X0, identity), a)
% 15.36/15.17 least_upper_bound(identity, multiply(least_upper_bound(X0, identity), b)) -> multiply(least_upper_bound(X0, identity), b)
% 15.36/15.17 least_upper_bound(identity, multiply(least_upper_bound(identity, X0), a)) -> multiply(least_upper_bound(identity, X0), a)
% 15.36/15.17 least_upper_bound(identity, multiply(least_upper_bound(identity, X0), b)) -> multiply(least_upper_bound(identity, X0), b)
% 15.36/15.17 least_upper_bound(inverse(b), a) -> a
% 15.36/15.17 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z))
% 15.36/15.17 least_upper_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, least_upper_bound(Y, Z))
% 15.36/15.17 least_upper_bound(multiply(Y, X), multiply(Z, X)) -> multiply(least_upper_bound(Y, Z), X)
% 15.36/15.17 least_upper_bound(multiply(a, Y2), greatest_lower_bound(Y1, Y2)) -> multiply(a, Y2)
% 15.36/15.17 least_upper_bound(multiply(a, a), greatest_lower_bound(Y1, identity)) -> multiply(a, a)
% 15.36/15.17 least_upper_bound(multiply(a, b), greatest_lower_bound(Y1, identity)) -> multiply(a, b)
% 15.36/15.17 least_upper_bound(multiply(b, Y2), greatest_lower_bound(Y1, Y2)) -> multiply(b, Y2)
% 15.36/15.17 least_upper_bound(multiply(b, a), greatest_lower_bound(Y1, identity)) -> multiply(b, a)
% 15.36/15.17 least_upper_bound(multiply(b, b), greatest_lower_bound(Y1, identity)) -> multiply(b, b)
% 15.36/15.17 multiply(X0, multiply(inverse(X0), Y1)) -> Y1
% 15.36/15.17 multiply(Y0, inverse(Y0)) -> identity
% 15.36/15.17 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity
% 15.36/15.17 multiply(Y1, identity) -> Y1
% 15.36/15.17 multiply(identity, X) -> X
% 15.36/15.17 multiply(inverse(X), X) -> identity
% 15.36/15.17 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 15.36/15.17 multiply(inverse(identity), Y1) -> Y1
% 15.36/15.17 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1)
% 15.36/15.17 multiply(inverse(inverse(Y1)), identity) -> Y1
% 15.36/15.17 multiply(least_upper_bound(identity, inverse(Y0)), Y0) -> least_upper_bound(Y0, identity)
% 15.36/15.17 multiply(least_upper_bound(identity, inverse(identity)), Y0) -> Y0
% 15.36/15.17 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 15.36/15.17 true__ -> false__
% 15.36/15.17 with the LPO induced by
% 15.36/15.17 a > f1 > b > inverse > identity > least_upper_bound > greatest_lower_bound > multiply > true__ > false__
% 15.36/15.17
% 15.36/15.17 % SZS output end Proof
% 15.36/15.17
%------------------------------------------------------------------------------