TSTP Solution File: GRP189-2 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP189-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n032.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 10:53:58 EDT 2022
% Result : Unsatisfiable 0.12s 0.33s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GRP189-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.09 % Command : moca.sh %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 600
% 0.08/0.27 % DateTime : Tue Jun 14 06:11:57 EDT 2022
% 0.08/0.27 % CPUTime :
% 0.12/0.33 % SZS status Unsatisfiable
% 0.12/0.33 % SZS output start Proof
% 0.12/0.33 The input problem is unsatisfiable because
% 0.12/0.33
% 0.12/0.33 [1] the following set of Horn clauses is unsatisfiable:
% 0.12/0.33
% 0.12/0.33 multiply(identity, X) = X
% 0.12/0.33 multiply(inverse(X), X) = identity
% 0.12/0.33 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.12/0.33 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.12/0.33 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.12/0.33 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.12/0.33 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.12/0.33 least_upper_bound(X, X) = X
% 0.12/0.33 greatest_lower_bound(X, X) = X
% 0.12/0.33 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.12/0.33 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.12/0.33 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.12/0.33 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.12/0.33 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.12/0.33 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.12/0.33 inverse(identity) = identity
% 0.12/0.33 inverse(inverse(X)) = X
% 0.12/0.33 inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X))
% 0.12/0.33 greatest_lower_bound(b, least_upper_bound(a, b)) = b ==> \bottom
% 0.12/0.33
% 0.12/0.33 This holds because
% 0.12/0.33
% 0.12/0.33 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.12/0.33
% 0.12/0.33 E:
% 0.12/0.33 f1(b) = false__
% 0.12/0.33 f1(greatest_lower_bound(b, least_upper_bound(a, b))) = true__
% 0.12/0.33 greatest_lower_bound(X, X) = X
% 0.12/0.33 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.12/0.33 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.12/0.33 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.12/0.33 inverse(identity) = identity
% 0.12/0.33 inverse(inverse(X)) = X
% 0.12/0.33 inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X))
% 0.12/0.33 least_upper_bound(X, X) = X
% 0.12/0.33 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.12/0.33 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.12/0.33 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.12/0.33 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.12/0.33 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.12/0.33 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.12/0.33 multiply(identity, X) = X
% 0.12/0.33 multiply(inverse(X), X) = identity
% 0.12/0.33 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.12/0.33 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.12/0.33 G:
% 0.12/0.33 true__ = false__
% 0.12/0.33
% 0.12/0.33 This holds because
% 0.12/0.33
% 0.12/0.33 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.12/0.33
% 0.12/0.33 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.12/0.33 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.12/0.33 f1(b) -> false__
% 0.12/0.33 f1(greatest_lower_bound(b, least_upper_bound(a, b))) -> true__
% 0.12/0.33 greatest_lower_bound(X, X) -> X
% 0.12/0.33 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X
% 0.12/0.33 greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y0)) -> greatest_lower_bound(Y0, Y1)
% 0.12/0.33 greatest_lower_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y1)
% 0.12/0.33 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0
% 0.12/0.33 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2)
% 0.12/0.33 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 0.12/0.33 greatest_lower_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, greatest_lower_bound(Y, Z))
% 0.12/0.33 greatest_lower_bound(multiply(Y, X), multiply(Z, X)) -> multiply(greatest_lower_bound(Y, Z), X)
% 0.12/0.33 inverse(identity) -> identity
% 0.12/0.33 inverse(inverse(X)) -> X
% 0.12/0.33 inverse(multiply(X, Y)) -> multiply(inverse(Y), inverse(X))
% 0.12/0.33 least_upper_bound(X, X) -> X
% 0.12/0.33 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X
% 0.12/0.33 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0
% 0.12/0.33 least_upper_bound(Y0, least_upper_bound(Y1, Y0)) -> least_upper_bound(Y0, Y1)
% 0.12/0.33 least_upper_bound(Y0, least_upper_bound(Y1, least_upper_bound(Y0, Y1))) -> least_upper_bound(Y0, Y1)
% 0.12/0.33 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2)
% 0.12/0.33 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z))
% 0.12/0.33 least_upper_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, least_upper_bound(Y, Z))
% 0.12/0.33 least_upper_bound(multiply(Y, X), multiply(Z, X)) -> multiply(least_upper_bound(Y, Z), X)
% 0.12/0.33 multiply(X0, identity) -> X0
% 0.12/0.33 multiply(X0, inverse(X0)) -> identity
% 0.12/0.33 multiply(identity, X) -> X
% 0.12/0.33 multiply(inverse(X), X) -> identity
% 0.12/0.33 multiply(inverse(X1), multiply(inverse(X0), multiply(X0, X1))) -> identity
% 0.12/0.33 multiply(inverse(Y1), identity) -> inverse(Y1)
% 0.12/0.33 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 0.12/0.33 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 0.12/0.33 true__ -> false__
% 0.12/0.33 with the LPO induced by
% 0.12/0.33 a > b > f1 > inverse > identity > greatest_lower_bound > least_upper_bound > multiply > true__ > false__
% 0.12/0.33
% 0.12/0.33 % SZS output end Proof
% 0.12/0.33
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