TSTP Solution File: GRP138-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP138-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n029.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 10:53:21 EDT 2022
% Result : Unsatisfiable 151.76s 151.11s
% Output : Proof 151.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP138-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.13 % Command : moca.sh %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 20:53:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 151.76/151.11 % SZS status Unsatisfiable
% 151.76/151.11 % SZS output start Proof
% 151.76/151.11 The input problem is unsatisfiable because
% 151.76/151.11
% 151.76/151.11 [1] the following set of Horn clauses is unsatisfiable:
% 151.76/151.11
% 151.76/151.11 multiply(identity, X) = X
% 151.76/151.11 multiply(inverse(X), X) = identity
% 151.76/151.11 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 151.76/151.11 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 151.76/151.11 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 151.76/151.11 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 151.76/151.11 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 151.76/151.11 least_upper_bound(X, X) = X
% 151.76/151.11 greatest_lower_bound(X, X) = X
% 151.76/151.11 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 151.76/151.11 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 151.76/151.11 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 151.76/151.11 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 151.76/151.11 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 151.76/151.11 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 151.76/151.11 least_upper_bound(a, c) = a
% 151.76/151.11 least_upper_bound(b, c) = b
% 151.76/151.11 least_upper_bound(greatest_lower_bound(a, b), c) = greatest_lower_bound(a, b) ==> \bottom
% 151.76/151.11
% 151.76/151.11 This holds because
% 151.76/151.11
% 151.76/151.11 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 151.76/151.11
% 151.76/151.11 E:
% 151.76/151.11 f1(greatest_lower_bound(a, b)) = false__
% 151.76/151.11 f1(least_upper_bound(greatest_lower_bound(a, b), c)) = true__
% 151.76/151.11 greatest_lower_bound(X, X) = X
% 151.76/151.11 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 151.76/151.11 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 151.76/151.11 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 151.76/151.11 least_upper_bound(X, X) = X
% 151.76/151.11 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 151.76/151.11 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 151.76/151.11 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 151.76/151.11 least_upper_bound(a, c) = a
% 151.76/151.11 least_upper_bound(b, c) = b
% 151.76/151.11 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 151.76/151.11 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 151.76/151.11 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 151.76/151.11 multiply(identity, X) = X
% 151.76/151.11 multiply(inverse(X), X) = identity
% 151.76/151.11 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 151.76/151.11 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 151.76/151.11 G:
% 151.76/151.11 true__ = false__
% 151.76/151.11
% 151.76/151.11 This holds because
% 151.76/151.11
% 151.76/151.11 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 151.76/151.11
% 151.76/151.11 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 151.76/151.11 greatest_lower_bound(Y0, c) = greatest_lower_bound(c, Y0)
% 151.76/151.11 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 151.76/151.11 least_upper_bound(Y0, a) = least_upper_bound(a, Y0)
% 151.76/151.11 f1(greatest_lower_bound(a, b)) -> false__
% 151.76/151.11 f1(greatest_lower_bound(b, a)) -> false__
% 151.76/151.11 f1(least_upper_bound(c, greatest_lower_bound(a, b))) -> true__
% 151.76/151.11 f1(least_upper_bound(c, greatest_lower_bound(b, a))) -> true__
% 151.76/151.11 f1(least_upper_bound(greatest_lower_bound(a, b), c)) -> true__
% 151.76/151.11 greatest_lower_bound(X, X) -> X
% 151.76/151.11 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X
% 151.76/151.11 greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y0)) -> greatest_lower_bound(Y0, Y1)
% 151.76/151.11 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0
% 151.76/151.11 greatest_lower_bound(Y1, greatest_lower_bound(X1, Y1)) -> greatest_lower_bound(X1, Y1)
% 151.76/151.11 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2)
% 151.76/151.11 greatest_lower_bound(a, c) -> c
% 151.76/151.11 greatest_lower_bound(a, greatest_lower_bound(Y0, c)) -> greatest_lower_bound(c, Y0)
% 151.76/151.11 greatest_lower_bound(a, greatest_lower_bound(c, Y2)) -> greatest_lower_bound(c, Y2)
% 151.76/151.11 greatest_lower_bound(a, least_upper_bound(c, greatest_lower_bound(X1, a))) -> least_upper_bound(c, greatest_lower_bound(X1, a))
% 151.76/151.11 greatest_lower_bound(a, least_upper_bound(c, greatest_lower_bound(a, X1))) -> least_upper_bound(c, greatest_lower_bound(a, X1))
% 151.76/151.11 greatest_lower_bound(b, c) -> c
% 151.76/151.11 greatest_lower_bound(b, greatest_lower_bound(Y0, c)) -> greatest_lower_bound(Y0, c)
% 151.76/151.11 greatest_lower_bound(b, greatest_lower_bound(c, Y0)) -> greatest_lower_bound(c, Y0)
% 151.76/151.11 greatest_lower_bound(b, least_upper_bound(greatest_lower_bound(X1, b), c)) -> least_upper_bound(greatest_lower_bound(X1, b), c)
% 151.76/151.11 greatest_lower_bound(b, least_upper_bound(greatest_lower_bound(b, X1), c)) -> least_upper_bound(greatest_lower_bound(b, X1), c)
% 151.76/151.11 greatest_lower_bound(c, a) -> c
% 151.76/151.11 greatest_lower_bound(c, b) -> c
% 151.76/151.11 greatest_lower_bound(c, greatest_lower_bound(X0, a)) -> greatest_lower_bound(c, X0)
% 151.76/151.11 greatest_lower_bound(c, greatest_lower_bound(Y0, b)) -> greatest_lower_bound(c, Y0)
% 151.76/151.11 greatest_lower_bound(c, greatest_lower_bound(a, Y0)) -> greatest_lower_bound(c, Y0)
% 151.76/151.11 greatest_lower_bound(c, greatest_lower_bound(b, Y2)) -> greatest_lower_bound(c, Y2)
% 151.76/151.11 greatest_lower_bound(c, least_upper_bound(X1, a)) -> c
% 151.76/151.11 greatest_lower_bound(c, least_upper_bound(Y0, b)) -> c
% 151.76/151.11 greatest_lower_bound(c, least_upper_bound(a, X1)) -> c
% 151.76/151.11 greatest_lower_bound(c, least_upper_bound(b, X0)) -> c
% 151.76/151.11 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 151.76/151.11 greatest_lower_bound(least_upper_bound(X0, a), least_upper_bound(a, X0)) -> least_upper_bound(X0, a)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(X0, b), least_upper_bound(b, X0)) -> least_upper_bound(X0, b)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(X0, c), least_upper_bound(a, X0)) -> least_upper_bound(X0, c)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(X0, c), least_upper_bound(b, X0)) -> least_upper_bound(X0, c)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(Y0, b), c) -> c
% 151.76/151.11 greatest_lower_bound(least_upper_bound(Y0, b), least_upper_bound(Y0, c)) -> least_upper_bound(Y0, c)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(Y0, b), least_upper_bound(c, Y0)) -> least_upper_bound(c, Y0)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(Y0, c), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, c)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(a, Y0), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(a, Y0), least_upper_bound(Y0, c)) -> least_upper_bound(Y0, c)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(b, X0), least_upper_bound(c, X0)) -> least_upper_bound(c, X0)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(b, Y0), c) -> c
% 151.76/151.11 greatest_lower_bound(least_upper_bound(b, Y0), least_upper_bound(Y0, b)) -> least_upper_bound(Y0, b)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(b, Y0), least_upper_bound(Y0, c)) -> least_upper_bound(Y0, c)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(c, X0), least_upper_bound(a, X0)) -> least_upper_bound(c, X0)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(c, Y0), least_upper_bound(Y0, a)) -> least_upper_bound(c, Y0)
% 151.76/151.11 greatest_lower_bound(least_upper_bound(c, Y0), least_upper_bound(a, Y0)) -> least_upper_bound(Y0, c)
% 151.76/151.11 inverse(identity) -> identity
% 151.76/151.11 inverse(inverse(Y1)) -> Y1
% 151.76/151.11 least_upper_bound(X, X) -> X
% 151.76/151.11 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X
% 151.76/151.11 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0
% 151.76/151.11 least_upper_bound(Y0, least_upper_bound(Y1, Y0)) -> least_upper_bound(Y0, Y1)
% 151.76/151.11 least_upper_bound(Y1, least_upper_bound(X1, Y1)) -> least_upper_bound(X1, Y1)
% 151.76/151.11 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2)
% 151.76/151.11 least_upper_bound(a, c) -> a
% 151.76/151.11 least_upper_bound(a, greatest_lower_bound(Y0, c)) -> a
% 151.76/151.11 least_upper_bound(a, greatest_lower_bound(c, X1)) -> a
% 151.76/151.11 least_upper_bound(a, least_upper_bound(Y0, c)) -> least_upper_bound(a, Y0)
% 151.76/151.11 least_upper_bound(a, least_upper_bound(c, Y2)) -> least_upper_bound(a, Y2)
% 151.76/151.11 least_upper_bound(b, c) -> b
% 151.76/151.11 least_upper_bound(b, greatest_lower_bound(Y0, c)) -> b
% 151.76/151.11 least_upper_bound(b, greatest_lower_bound(c, X1)) -> b
% 151.76/151.11 least_upper_bound(b, least_upper_bound(Y0, c)) -> least_upper_bound(b, Y0)
% 151.76/151.11 least_upper_bound(b, least_upper_bound(c, Y2)) -> least_upper_bound(b, Y2)
% 151.76/151.11 least_upper_bound(c, a) -> a
% 151.76/151.11 least_upper_bound(c, b) -> b
% 151.76/151.11 least_upper_bound(c, greatest_lower_bound(a, least_upper_bound(c, X1))) -> greatest_lower_bound(a, least_upper_bound(c, X1))
% 151.76/151.11 least_upper_bound(c, greatest_lower_bound(b, a)) -> greatest_lower_bound(b, a)
% 151.76/151.11 least_upper_bound(c, greatest_lower_bound(b, least_upper_bound(c, X1))) -> greatest_lower_bound(b, least_upper_bound(c, X1))
% 151.76/151.11 least_upper_bound(c, greatest_lower_bound(least_upper_bound(X1, c), a)) -> greatest_lower_bound(least_upper_bound(X1, c), a)
% 151.76/151.11 least_upper_bound(c, greatest_lower_bound(least_upper_bound(c, X1), a)) -> greatest_lower_bound(least_upper_bound(c, X1), a)
% 151.76/151.11 least_upper_bound(c, least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a)
% 151.76/151.11 least_upper_bound(c, least_upper_bound(Y0, b)) -> least_upper_bound(b, Y0)
% 151.76/151.11 least_upper_bound(c, least_upper_bound(a, Y0)) -> least_upper_bound(a, Y0)
% 151.76/151.11 least_upper_bound(c, least_upper_bound(b, Y2)) -> least_upper_bound(b, Y2)
% 151.76/151.11 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(c, X0)) -> greatest_lower_bound(X0, a)
% 151.76/151.11 least_upper_bound(greatest_lower_bound(X0, b), greatest_lower_bound(c, X0)) -> greatest_lower_bound(X0, b)
% 151.76/151.11 least_upper_bound(greatest_lower_bound(X0, c), greatest_lower_bound(c, X0)) -> greatest_lower_bound(X0, c)
% 151.76/151.11 least_upper_bound(greatest_lower_bound(Y0, b), greatest_lower_bound(Y0, c)) -> greatest_lower_bound(Y0, b)
% 151.76/151.11 least_upper_bound(greatest_lower_bound(Y0, c), a) -> a
% 151.76/151.11 least_upper_bound(greatest_lower_bound(Y0, c), greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, a)
% 151.76/151.11 least_upper_bound(greatest_lower_bound(a, X0), greatest_lower_bound(c, X0)) -> greatest_lower_bound(a, X0)
% 151.76/151.11 least_upper_bound(greatest_lower_bound(a, Y0), greatest_lower_bound(Y0, c)) -> greatest_lower_bound(a, Y0)
% 151.76/151.11 least_upper_bound(greatest_lower_bound(b, X0), greatest_lower_bound(c, X0)) -> greatest_lower_bound(b, X0)
% 151.76/151.11 least_upper_bound(greatest_lower_bound(c, Y0), a) -> a
% 151.76/151.11 least_upper_bound(greatest_lower_bound(c, Y0), greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, a)
% 151.76/151.11 least_upper_bound(greatest_lower_bound(c, Y0), greatest_lower_bound(Y0, b)) -> greatest_lower_bound(Y0, b)
% 151.76/151.11 least_upper_bound(greatest_lower_bound(c, Y0), greatest_lower_bound(Y0, c)) -> greatest_lower_bound(Y0, c)
% 151.76/151.11 least_upper_bound(greatest_lower_bound(c, Y0), greatest_lower_bound(a, Y0)) -> greatest_lower_bound(a, Y0)
% 151.76/151.11 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z))
% 151.76/151.11 least_upper_bound(multiply(Y0, a), multiply(Y0, c)) -> multiply(Y0, a)
% 151.76/151.11 least_upper_bound(multiply(Y0, b), multiply(Y0, c)) -> multiply(Y0, b)
% 151.76/151.11 least_upper_bound(multiply(Y0, c), multiply(Y0, b)) -> multiply(Y0, b)
% 151.76/151.11 least_upper_bound(multiply(a, Y2), multiply(c, Y2)) -> multiply(a, Y2)
% 151.76/151.11 multiply(X, greatest_lower_bound(Y, Z)) -> greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 151.76/151.11 multiply(X, least_upper_bound(Y, Z)) -> least_upper_bound(multiply(X, Y), multiply(X, Z))
% 151.76/151.11 multiply(X0, inverse(X0)) -> identity
% 151.76/151.11 multiply(X0, multiply(inverse(X0), Y1)) -> Y1
% 151.76/151.11 multiply(Y0, identity) -> Y0
% 151.76/151.11 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity
% 151.76/151.11 multiply(greatest_lower_bound(Y, Z), X) -> greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 151.76/151.11 multiply(greatest_lower_bound(Y0, identity), Y1) -> greatest_lower_bound(Y1, multiply(Y0, Y1))
% 151.76/151.11 multiply(identity, X) -> X
% 151.76/151.11 multiply(inverse(X), X) -> identity
% 151.76/151.11 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 151.76/151.11 multiply(least_upper_bound(Y, Z), X) -> least_upper_bound(multiply(Y, X), multiply(Z, X))
% 151.76/151.11 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 151.76/151.11 true__ -> false__
% 151.76/151.11 with the LPO induced by
% 151.76/151.11 f1 > a > c > b > multiply > greatest_lower_bound > least_upper_bound > identity > inverse > true__ > false__
% 151.76/151.11
% 151.76/151.11 % SZS output end Proof
% 151.76/151.11
%------------------------------------------------------------------------------