TSTP Solution File: GRP146-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP146-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n021.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 10:53:25 EDT 2022
% Result : Unsatisfiable 3.79s 3.85s
% Output : Proof 3.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP146-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n021.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 20:46:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.79/3.85 % SZS status Unsatisfiable
% 3.79/3.85 % SZS output start Proof
% 3.79/3.85 The input problem is unsatisfiable because
% 3.79/3.85
% 3.79/3.85 [1] the following set of Horn clauses is unsatisfiable:
% 3.79/3.85
% 3.79/3.85 multiply(identity, X) = X
% 3.79/3.85 multiply(inverse(X), X) = identity
% 3.79/3.85 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 3.79/3.85 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 3.79/3.85 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 3.79/3.85 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 3.79/3.85 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 3.79/3.85 least_upper_bound(X, X) = X
% 3.79/3.85 greatest_lower_bound(X, X) = X
% 3.79/3.85 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 3.79/3.85 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 3.79/3.85 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 3.79/3.85 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 3.79/3.85 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 3.79/3.85 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 3.79/3.85 least_upper_bound(a, c) = c
% 3.79/3.85 least_upper_bound(b, c) = c
% 3.79/3.85 least_upper_bound(least_upper_bound(a, b), c) = c ==> \bottom
% 3.79/3.85
% 3.79/3.85 This holds because
% 3.79/3.85
% 3.79/3.85 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 3.79/3.85
% 3.79/3.85 E:
% 3.79/3.85 f1(c) = false__
% 3.79/3.85 f1(least_upper_bound(least_upper_bound(a, b), c)) = true__
% 3.79/3.85 greatest_lower_bound(X, X) = X
% 3.79/3.85 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 3.79/3.85 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 3.79/3.85 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 3.79/3.85 least_upper_bound(X, X) = X
% 3.79/3.85 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 3.79/3.85 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 3.79/3.85 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 3.79/3.85 least_upper_bound(a, c) = c
% 3.79/3.85 least_upper_bound(b, c) = c
% 3.79/3.85 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 3.79/3.85 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 3.79/3.85 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 3.79/3.85 multiply(identity, X) = X
% 3.79/3.85 multiply(inverse(X), X) = identity
% 3.79/3.85 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 3.79/3.85 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 3.79/3.85 G:
% 3.79/3.85 true__ = false__
% 3.79/3.85
% 3.79/3.85 This holds because
% 3.79/3.85
% 3.79/3.85 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 3.79/3.85
% 3.79/3.85 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 3.79/3.85 greatest_lower_bound(X1, multiply(X0, X1)) = multiply(greatest_lower_bound(identity, inverse(X0)), multiply(X0, X1))
% 3.79/3.85 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, Y1), Y0))
% 3.79/3.85 greatest_lower_bound(Y0, a) = greatest_lower_bound(a, greatest_lower_bound(c, Y0))
% 3.79/3.85 greatest_lower_bound(Y0, b) = greatest_lower_bound(c, greatest_lower_bound(b, Y0))
% 3.79/3.85 greatest_lower_bound(Y0, multiply(X0, Y0)) = multiply(greatest_lower_bound(identity, greatest_lower_bound(X0, identity)), Y0)
% 3.79/3.85 greatest_lower_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(greatest_lower_bound(identity, multiply(X0, X1)), Y0)
% 3.79/3.85 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1)))
% 3.79/3.85 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0))
% 3.79/3.85 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1)))
% 3.79/3.85 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0))
% 3.79/3.85 greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y2)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2))
% 3.79/3.85 greatest_lower_bound(Y1, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, identity), Y1)
% 3.79/3.85 greatest_lower_bound(Y1, multiply(Y2, Y1)) = multiply(greatest_lower_bound(identity, Y2), Y1)
% 3.79/3.85 greatest_lower_bound(Y2, greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2))
% 3.79/3.85 greatest_lower_bound(identity, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1)
% 3.79/3.85 greatest_lower_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), greatest_lower_bound(Y1, Y2))
% 3.79/3.85 greatest_lower_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), greatest_lower_bound(Y1, Y2))
% 3.79/3.85 greatest_lower_bound(multiply(Y0, Y1), identity) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1)
% 3.79/3.85 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 3.79/3.85 least_upper_bound(X1, multiply(X0, X1)) = multiply(least_upper_bound(identity, inverse(X0)), multiply(X0, X1))
% 3.79/3.85 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, Y1), Y0))
% 3.79/3.85 least_upper_bound(Y0, c) = least_upper_bound(c, least_upper_bound(b, Y0))
% 3.79/3.85 least_upper_bound(Y0, least_upper_bound(c, X0)) = least_upper_bound(c, least_upper_bound(X0, least_upper_bound(Y0, b)))
% 3.79/3.85 least_upper_bound(Y0, least_upper_bound(c, X0)) = least_upper_bound(c, least_upper_bound(b, least_upper_bound(X0, Y0)))
% 3.79/3.85 least_upper_bound(Y0, multiply(X0, Y0)) = multiply(least_upper_bound(identity, least_upper_bound(X0, identity)), Y0)
% 3.79/3.85 least_upper_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(least_upper_bound(identity, multiply(X0, X1)), Y0)
% 3.79/3.85 least_upper_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(least_upper_bound(multiply(X0, X1), identity), Y0)
% 3.79/3.85 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y1)) = least_upper_bound(Y1, least_upper_bound(Y0, multiply(X1, Y1)))
% 3.79/3.85 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y1)) = least_upper_bound(Y1, least_upper_bound(multiply(X1, Y1), Y0))
% 3.79/3.85 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y1)) = least_upper_bound(Y1, least_upper_bound(Y0, multiply(X1, Y1)))
% 3.79/3.85 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y1)) = least_upper_bound(Y1, least_upper_bound(multiply(X1, Y1), Y0))
% 3.79/3.85 least_upper_bound(Y1, least_upper_bound(Y0, Y2)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2))
% 3.79/3.85 least_upper_bound(Y1, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, identity), Y1)
% 3.79/3.85 least_upper_bound(Y1, multiply(Y2, Y1)) = multiply(least_upper_bound(identity, Y2), Y1)
% 3.79/3.85 least_upper_bound(Y2, least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2))
% 3.79/3.85 least_upper_bound(a, least_upper_bound(X1, least_upper_bound(X2, c))) = least_upper_bound(c, least_upper_bound(X1, X2))
% 3.79/3.85 least_upper_bound(a, least_upper_bound(X1, least_upper_bound(c, X2))) = least_upper_bound(c, least_upper_bound(X1, X2))
% 3.79/3.85 least_upper_bound(a, least_upper_bound(X2, least_upper_bound(c, X1))) = least_upper_bound(c, least_upper_bound(X1, X2))
% 3.79/3.85 least_upper_bound(a, least_upper_bound(Y0, c)) = least_upper_bound(c, Y0)
% 3.79/3.85 least_upper_bound(b, least_upper_bound(X2, least_upper_bound(c, X1))) = least_upper_bound(c, least_upper_bound(X1, X2))
% 3.79/3.85 least_upper_bound(identity, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1)
% 3.79/3.85 least_upper_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), least_upper_bound(Y1, Y2))
% 3.79/3.85 least_upper_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), least_upper_bound(Y1, Y2))
% 3.79/3.85 least_upper_bound(multiply(Y0, Y1), identity) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1)
% 3.79/3.85 multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1))
% 3.79/3.85 multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1))
% 3.79/3.85 multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1))
% 3.79/3.85 multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1))
% 3.79/3.85 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))))
% 3.79/3.85 f1(c) -> false__
% 3.79/3.85 f1(least_upper_bound(a, least_upper_bound(c, b))) -> true__
% 3.79/3.85 f1(least_upper_bound(c, least_upper_bound(a, b))) -> true__
% 3.79/3.85 f1(least_upper_bound(least_upper_bound(a, b), c)) -> true__
% 3.79/3.85 greatest_lower_bound(X, X) -> X
% 3.79/3.85 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X
% 3.79/3.85 greatest_lower_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y1)
% 3.79/3.85 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(X1, greatest_lower_bound(Y0, Y1)))) -> greatest_lower_bound(Y0, Y1)
% 3.79/3.85 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(greatest_lower_bound(Y0, Y1), X1))) -> greatest_lower_bound(Y0, Y1)
% 3.79/3.85 greatest_lower_bound(Y0, greatest_lower_bound(Y2, least_upper_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y2)
% 3.79/3.85 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(X1, Y0), Y2)) -> greatest_lower_bound(Y0, Y2)
% 3.79/3.85 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(Y0, X1), Y2)) -> greatest_lower_bound(Y0, Y2)
% 3.79/3.85 greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, Y0))) -> Y0
% 3.79/3.85 greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(Y0, X2))) -> Y0
% 3.79/3.85 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0
% 3.79/3.85 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0))
% 3.79/3.85 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0))
% 3.79/3.85 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, identity), Y0)) -> Y0
% 3.79/3.85 greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> Y0
% 3.79/3.85 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, Y1))) -> greatest_lower_bound(Y0, Y1)
% 3.79/3.85 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(Y1, X1))) -> greatest_lower_bound(Y0, Y1)
% 3.79/3.85 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2)
% 3.79/3.85 greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y1)) -> multiply(greatest_lower_bound(identity, X1), Y1)
% 3.79/3.85 greatest_lower_bound(a, c) -> a
% 3.79/3.85 greatest_lower_bound(a, greatest_lower_bound(Y0, c)) -> greatest_lower_bound(Y0, a)
% 3.79/3.85 greatest_lower_bound(a, greatest_lower_bound(c, Y2)) -> greatest_lower_bound(a, Y2)
% 3.79/3.85 greatest_lower_bound(a, least_upper_bound(c, X0)) -> a
% 3.79/3.85 greatest_lower_bound(b, least_upper_bound(c, X0)) -> b
% 3.79/3.85 greatest_lower_bound(c, b) -> b
% 3.79/3.85 greatest_lower_bound(c, greatest_lower_bound(Y0, b)) -> greatest_lower_bound(Y0, b)
% 3.79/3.85 greatest_lower_bound(c, greatest_lower_bound(b, Y2)) -> greatest_lower_bound(b, Y2)
% 3.79/3.85 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 3.79/3.85 greatest_lower_bound(identity, multiply(inverse(X0), least_upper_bound(X0, X1))) -> identity
% 3.79/3.85 greatest_lower_bound(identity, multiply(inverse(a), c)) -> identity
% 3.79/3.85 greatest_lower_bound(identity, multiply(inverse(c), b)) -> multiply(inverse(c), b)
% 3.79/3.85 greatest_lower_bound(identity, multiply(least_upper_bound(X0, inverse(X1)), X1)) -> identity
% 3.79/3.85 greatest_lower_bound(least_upper_bound(X0, X1), least_upper_bound(X0, least_upper_bound(X1, Y1))) -> least_upper_bound(X0, X1)
% 3.79/3.85 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(X1, least_upper_bound(Y1, X2))) -> least_upper_bound(X1, X2)
% 3.79/3.85 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(X2, least_upper_bound(Y1, X1))) -> least_upper_bound(X1, X2)
% 3.79/3.85 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)
% 3.79/3.85 greatest_lower_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, greatest_lower_bound(Y, Z))
% 3.79/3.85 greatest_lower_bound(multiply(X0, greatest_lower_bound(X1, X2)), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X0, X2), Y2))
% 3.79/3.85 greatest_lower_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(greatest_lower_bound(multiply(X0, X1), Y2), Y1)
% 3.79/3.85 greatest_lower_bound(multiply(Y, X), multiply(Z, X)) -> multiply(greatest_lower_bound(Y, Z), X)
% 3.79/3.85 greatest_lower_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(greatest_lower_bound(Y0, multiply(X0, X1)), Y1)
% 3.79/3.85 greatest_lower_bound(multiply(greatest_lower_bound(X0, X2), X1), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X2, X1), Y2))
% 3.79/3.85 least_upper_bound(X, X) -> X
% 3.79/3.85 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X
% 3.79/3.85 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))) -> Y0
% 3.79/3.85 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))) -> Y0
% 3.79/3.85 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0
% 3.79/3.85 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(X1, least_upper_bound(Y0, Y1)))) -> least_upper_bound(Y0, Y1)
% 3.79/3.85 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(least_upper_bound(Y0, Y1), X1))) -> least_upper_bound(Y0, Y1)
% 3.79/3.85 least_upper_bound(Y0, least_upper_bound(Y1, least_upper_bound(Y0, Y1))) -> least_upper_bound(Y0, Y1)
% 3.79/3.85 least_upper_bound(Y0, least_upper_bound(Y2, greatest_lower_bound(Y0, Y1))) -> least_upper_bound(Y0, Y2)
% 3.79/3.85 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y0, X1), Y2)) -> least_upper_bound(Y0, Y2)
% 3.79/3.85 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y1, Y0), Y2)) -> least_upper_bound(Y0, Y2)
% 3.79/3.85 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> Y0
% 3.79/3.85 least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> Y0
% 3.79/3.85 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0))
% 3.79/3.85 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0))
% 3.79/3.85 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, Y1))) -> least_upper_bound(Y0, Y1)
% 3.79/3.85 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(Y1, X1))) -> least_upper_bound(Y0, Y1)
% 3.79/3.85 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2)
% 3.79/3.85 least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y1)) -> multiply(least_upper_bound(identity, X1), Y1)
% 3.79/3.85 least_upper_bound(a, c) -> c
% 3.79/3.85 least_upper_bound(a, least_upper_bound(Y0, c)) -> least_upper_bound(Y0, c)
% 3.79/3.85 least_upper_bound(a, least_upper_bound(Y0, least_upper_bound(c, X0))) -> least_upper_bound(Y0, least_upper_bound(c, X0))
% 3.79/3.85 least_upper_bound(a, least_upper_bound(c, Y2)) -> least_upper_bound(c, Y2)
% 3.79/3.85 least_upper_bound(a, multiply(least_upper_bound(X1, identity), c)) -> multiply(least_upper_bound(identity, X1), c)
% 3.79/3.85 least_upper_bound(a, multiply(least_upper_bound(identity, X1), c)) -> multiply(least_upper_bound(identity, X1), c)
% 3.79/3.85 least_upper_bound(b, c) -> c
% 3.79/3.85 least_upper_bound(b, least_upper_bound(X1, least_upper_bound(X2, c))) -> least_upper_bound(c, least_upper_bound(X1, X2))
% 3.79/3.85 least_upper_bound(b, least_upper_bound(X1, least_upper_bound(c, X2))) -> least_upper_bound(c, least_upper_bound(X1, X2))
% 3.79/3.85 least_upper_bound(b, least_upper_bound(Y0, least_upper_bound(c, X0))) -> least_upper_bound(Y0, least_upper_bound(c, X0))
% 3.79/3.85 least_upper_bound(b, least_upper_bound(c, Y2)) -> least_upper_bound(c, Y2)
% 3.79/3.85 least_upper_bound(b, multiply(least_upper_bound(X1, identity), c)) -> multiply(least_upper_bound(identity, X1), c)
% 3.79/3.85 least_upper_bound(b, multiply(least_upper_bound(identity, X1), c)) -> multiply(least_upper_bound(identity, X1), c)
% 3.79/3.85 least_upper_bound(c, b) -> c
% 3.79/3.85 least_upper_bound(c, least_upper_bound(Y0, b)) -> least_upper_bound(Y0, c)
% 3.79/3.85 least_upper_bound(c, least_upper_bound(Y0, b)) -> least_upper_bound(c, Y0)
% 3.79/3.85 least_upper_bound(c, least_upper_bound(b, Y0)) -> least_upper_bound(c, Y0)
% 3.79/3.85 least_upper_bound(c, least_upper_bound(b, least_upper_bound(X0, Y2))) -> least_upper_bound(c, least_upper_bound(X0, Y2))
% 3.79/3.85 least_upper_bound(greatest_lower_bound(X0, X1), greatest_lower_bound(X0, greatest_lower_bound(X1, Y1))) -> greatest_lower_bound(X0, X1)
% 3.79/3.85 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X1, greatest_lower_bound(Y1, X2))) -> greatest_lower_bound(X1, X2)
% 3.79/3.85 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X2, greatest_lower_bound(Y1, X1))) -> greatest_lower_bound(X1, X2)
% 3.79/3.85 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)
% 3.79/3.85 least_upper_bound(identity, multiply(greatest_lower_bound(X0, inverse(X1)), X1)) -> identity
% 3.79/3.85 least_upper_bound(identity, multiply(inverse(a), c)) -> multiply(inverse(a), c)
% 3.79/3.85 least_upper_bound(identity, multiply(inverse(c), b)) -> identity
% 3.79/3.85 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z))
% 3.79/3.85 least_upper_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, least_upper_bound(Y, Z))
% 3.79/3.85 least_upper_bound(multiply(X0, least_upper_bound(X1, X2)), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X0, X2), Y2))
% 3.79/3.85 least_upper_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(least_upper_bound(multiply(X0, X1), Y2), Y1)
% 3.79/3.85 least_upper_bound(multiply(Y, X), multiply(Z, X)) -> multiply(least_upper_bound(Y, Z), X)
% 3.79/3.85 least_upper_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(least_upper_bound(Y0, multiply(X0, X1)), Y1)
% 3.79/3.85 least_upper_bound(multiply(least_upper_bound(X0, X2), X1), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X2, X1), Y2))
% 3.79/3.85 multiply(greatest_lower_bound(inverse(Y1), Y2), Y1) -> greatest_lower_bound(identity, multiply(Y2, Y1))
% 3.79/3.85 multiply(identity, X) -> X
% 3.79/3.85 multiply(inverse(X), X) -> identity
% 3.79/3.85 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 3.79/3.85 multiply(inverse(greatest_lower_bound(X0, identity)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1
% 3.79/3.85 multiply(inverse(greatest_lower_bound(identity, X0)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1
% 3.79/3.85 multiply(inverse(identity), Y1) -> Y1
% 3.79/3.85 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1)
% 3.79/3.85 multiply(inverse(inverse(Y1)), identity) -> Y1
% 3.79/3.85 multiply(inverse(least_upper_bound(X0, identity)), least_upper_bound(Y1, multiply(X0, Y1))) -> Y1
% 3.79/3.85 multiply(inverse(least_upper_bound(X0, inverse(Y1))), least_upper_bound(multiply(X0, Y1), identity)) -> Y1
% 3.79/3.85 multiply(inverse(least_upper_bound(identity, X0)), least_upper_bound(Y1, multiply(X0, Y1))) -> Y1
% 3.79/3.85 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1
% 3.79/3.85 multiply(least_upper_bound(inverse(Y1), Y2), Y1) -> least_upper_bound(identity, multiply(Y2, Y1))
% 3.79/3.85 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 3.79/3.85 true__ -> false__
% 3.79/3.85 with the LPO induced by
% 3.79/3.85 f1 > b > c > a > inverse > identity > least_upper_bound > greatest_lower_bound > multiply > true__ > false__
% 3.79/3.85
% 3.79/3.85 % SZS output end Proof
% 3.79/3.85
%------------------------------------------------------------------------------