TSTP Solution File: LAT033-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : LAT033-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n014.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 : Sun Jul 17 06:04:14 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% 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 : LAT033-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n014.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 : Wed Jun 29 09:06:27 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 The input problem is unsatisfiable because
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% 0.13/0.39 [1] the following set of Horn clauses is unsatisfiable:
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% 0.13/0.39 meet(X, join(X, Y)) = X
% 0.13/0.39 join(X, meet(X, Y)) = X
% 0.13/0.39 meet(X, Y) = meet(Y, X)
% 0.13/0.39 join(X, Y) = join(Y, X)
% 0.13/0.39 meet(meet(X, Y), Z) = meet(X, meet(Y, Z))
% 0.13/0.39 join(join(X, Y), Z) = join(X, join(Y, Z))
% 0.13/0.39 join(xx, xx) = xx ==> \bottom
% 0.13/0.39
% 0.13/0.39 This holds because
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% 0.13/0.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
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% 0.13/0.39 E:
% 0.13/0.39 f1(join(xx, xx)) = true__
% 0.13/0.39 f1(xx) = false__
% 0.13/0.39 join(X, Y) = join(Y, X)
% 0.13/0.39 join(X, meet(X, Y)) = X
% 0.13/0.39 join(join(X, Y), Z) = join(X, join(Y, Z))
% 0.13/0.39 meet(X, Y) = meet(Y, X)
% 0.13/0.39 meet(X, join(X, Y)) = X
% 0.13/0.39 meet(meet(X, Y), Z) = meet(X, meet(Y, Z))
% 0.13/0.39 G:
% 0.13/0.39 true__ = false__
% 0.13/0.39
% 0.13/0.39 This holds because
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% 0.13/0.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
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% 0.13/0.39 join(X, Y) = join(Y, X)
% 0.13/0.39 join(Y0, Y2) = join(Y2, join(Y2, Y0))
% 0.13/0.39 join(Y2, join(Y0, Y1)) = join(Y0, join(Y1, Y2))
% 0.13/0.39 meet(X, Y) = meet(Y, X)
% 0.13/0.39 meet(Y0, Y2) = meet(Y2, meet(Y2, Y0))
% 0.13/0.39 meet(Y1, meet(Y0, Y2)) = meet(Y0, meet(Y1, Y2))
% 0.13/0.39 meet(Y2, meet(Y0, Y1)) = meet(Y0, meet(Y1, Y2))
% 0.13/0.39 f1(join(xx, xx)) -> true__
% 0.13/0.39 f1(xx) -> false__
% 0.13/0.39 join(X, meet(X, Y)) -> X
% 0.13/0.39 join(Y0, Y0) -> Y0
% 0.13/0.39 join(Y0, meet(Y1, Y0)) -> Y0
% 0.13/0.39 join(Y1, join(Y2, join(Y1, Y2))) -> join(Y1, Y2)
% 0.13/0.39 join(join(X, Y), Z) -> join(X, join(Y, Z))
% 0.13/0.39 meet(X, join(X, Y)) -> X
% 0.13/0.39 meet(Y0, Y0) -> Y0
% 0.13/0.39 meet(Y0, join(Y1, Y0)) -> Y0
% 0.13/0.39 meet(Y1, meet(Y2, meet(Y1, Y2))) -> meet(Y1, Y2)
% 0.13/0.39 meet(Y2, meet(Y0, Y2)) -> meet(Y0, Y2)
% 0.13/0.39 meet(Y2, meet(Y1, meet(Y1, Y2))) -> meet(Y1, Y2)
% 0.13/0.39 meet(meet(X, Y), Z) -> meet(X, meet(Y, Z))
% 0.13/0.39 true__ -> false__
% 0.13/0.39 with the LPO induced by
% 0.13/0.39 xx > f1 > join > meet > true__ > false__
% 0.13/0.39
% 0.13/0.39 % SZS output end Proof
% 0.13/0.39
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