TSTP Solution File: GRP182-1 by Moca---0.1
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% File : Moca---0.1
% Problem : GRP182-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n028.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 10:53:50 EDT 2022
% Result : Unsatisfiable 0.13s 0.41s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP182-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 03:25:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.41 % SZS status Unsatisfiable
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 The input problem is unsatisfiable because
% 0.13/0.41
% 0.13/0.41 [1] the following set of Horn clauses is unsatisfiable:
% 0.13/0.41
% 0.13/0.41 multiply(identity, X) = X
% 0.13/0.41 multiply(inverse(X), X) = identity
% 0.13/0.41 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.13/0.41 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.13/0.41 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.13/0.41 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.13/0.41 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.13/0.41 least_upper_bound(X, X) = X
% 0.13/0.41 greatest_lower_bound(X, X) = X
% 0.13/0.41 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.13/0.41 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.13/0.41 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.13/0.41 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.13/0.41 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.13/0.41 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.13/0.41 least_upper_bound(identity, greatest_lower_bound(a, identity)) = identity ==> \bottom
% 0.13/0.41
% 0.13/0.41 This holds because
% 0.13/0.41
% 0.13/0.41 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.13/0.41
% 0.13/0.41 E:
% 0.13/0.41 f1(identity) = false__
% 0.13/0.41 f1(least_upper_bound(identity, greatest_lower_bound(a, identity))) = true__
% 0.13/0.41 greatest_lower_bound(X, X) = X
% 0.13/0.41 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.13/0.41 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.13/0.41 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.13/0.41 least_upper_bound(X, X) = X
% 0.13/0.41 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.13/0.41 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.13/0.41 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.13/0.41 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.13/0.41 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.13/0.41 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.13/0.41 multiply(identity, X) = X
% 0.13/0.41 multiply(inverse(X), X) = identity
% 0.13/0.41 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.13/0.41 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.13/0.41 G:
% 0.13/0.41 true__ = false__
% 0.13/0.41
% 0.13/0.41 This holds because
% 0.13/0.41
% 0.13/0.41 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.13/0.41
% 0.13/0.41 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.13/0.41 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.13/0.41 f1(identity) -> false__
% 0.13/0.41 f1(least_upper_bound(identity, greatest_lower_bound(a, identity))) -> true__
% 0.13/0.41 greatest_lower_bound(X, X) -> X
% 0.13/0.41 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X
% 0.13/0.41 greatest_lower_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y1)
% 0.13/0.41 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2)
% 0.13/0.41 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 0.13/0.41 greatest_lower_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, greatest_lower_bound(Y, Z))
% 0.13/0.41 greatest_lower_bound(multiply(Y, X), multiply(Z, X)) -> multiply(greatest_lower_bound(Y, Z), X)
% 0.13/0.41 least_upper_bound(X, X) -> X
% 0.13/0.41 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X
% 0.13/0.41 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0
% 0.13/0.41 least_upper_bound(Y0, least_upper_bound(Y1, least_upper_bound(Y0, Y1))) -> least_upper_bound(Y0, Y1)
% 0.13/0.41 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2)
% 0.13/0.41 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z))
% 0.13/0.41 least_upper_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, least_upper_bound(Y, Z))
% 0.13/0.41 least_upper_bound(multiply(Y, X), multiply(Z, X)) -> multiply(least_upper_bound(Y, Z), X)
% 0.13/0.41 multiply(identity, X) -> X
% 0.13/0.41 multiply(inverse(X), X) -> identity
% 0.13/0.41 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 0.13/0.41 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 0.13/0.41 true__ -> false__
% 0.13/0.41 with the LPO induced by
% 0.13/0.41 a > f1 > inverse > identity > greatest_lower_bound > least_upper_bound > multiply > true__ > false__
% 0.13/0.41
% 0.13/0.41 % SZS output end Proof
% 0.13/0.41
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