TSTP Solution File: LAT014-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LAT014-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n024.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 06:04:07 EDT 2022
% Result : Unsatisfiable 0.48s 0.63s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : LAT014-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n024.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 : Wed Jun 29 15:40:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.48/0.63 % SZS status Unsatisfiable
% 0.48/0.63 % SZS output start Proof
% 0.48/0.63 The input problem is unsatisfiable because
% 0.48/0.63
% 0.48/0.63 [1] the following set of Horn clauses is unsatisfiable:
% 0.48/0.63
% 0.48/0.63 join(X, meet(Y, meet(X, Z))) = X
% 0.48/0.63 meet(X, join(Y, join(X, Z))) = X
% 0.48/0.63 join(join(meet(X, Y), meet(Y, Z)), Y) = Y
% 0.48/0.63 meet(meet(join(X, Y), join(Y, Z)), Y) = Y
% 0.48/0.63 meet(a, join(a, b)) = a ==> \bottom
% 0.48/0.63
% 0.48/0.63 This holds because
% 0.48/0.63
% 0.48/0.63 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.48/0.63
% 0.48/0.63 E:
% 0.48/0.63 f1(a) = false__
% 0.48/0.63 f1(meet(a, join(a, b))) = true__
% 0.48/0.63 join(X, meet(Y, meet(X, Z))) = X
% 0.48/0.63 join(join(meet(X, Y), meet(Y, Z)), Y) = Y
% 0.48/0.63 meet(X, join(Y, join(X, Z))) = X
% 0.48/0.63 meet(meet(join(X, Y), join(Y, Z)), Y) = Y
% 0.48/0.63 G:
% 0.48/0.63 true__ = false__
% 0.48/0.63
% 0.48/0.63 This holds because
% 0.48/0.63
% 0.48/0.63 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.48/0.63
% 0.48/0.63
% 0.48/0.63 f1(a) -> false__
% 0.48/0.63 f1(meet(a, join(a, b))) -> true__
% 0.48/0.63 join(X, meet(Y, meet(X, Z))) -> X
% 0.48/0.63 join(Y0, Y0) -> Y0
% 0.48/0.63 join(Y0, join(X1, Y0)) -> join(X1, Y0)
% 0.48/0.63 join(Y0, join(X1, join(Y0, X2))) -> join(X1, join(Y0, X2))
% 0.48/0.63 join(Y0, join(Y0, X1)) -> join(Y0, X1)
% 0.48/0.63 join(Y0, meet(Y0, Y2)) -> Y0
% 0.48/0.63 join(Y0, meet(Y1, Y0)) -> Y0
% 0.48/0.63 join(join(X1, Y1), Y1) -> join(X1, Y1)
% 0.48/0.63 join(join(X1, join(Y1, X2)), Y1) -> join(X1, join(Y1, X2))
% 0.48/0.63 join(join(Y0, join(X1, Y0)), join(X1, Y0)) -> join(X1, Y0)
% 0.48/0.63 join(join(Y0, meet(join(X1, join(Y0, X2)), Y2)), join(X1, join(Y0, X2))) -> join(X1, join(Y0, X2))
% 0.48/0.63 join(join(Y1, X1), Y1) -> join(Y1, X1)
% 0.48/0.63 join(join(Y1, meet(Y1, Y2)), Y1) -> Y1
% 0.48/0.63 join(join(meet(X, Y), meet(Y, Z)), Y) -> Y
% 0.48/0.63 join(join(meet(Y0, Y1), Y1), Y1) -> Y1
% 0.48/0.63 join(meet(Y0, Y1), Y1) -> Y1
% 0.48/0.63 meet(X, join(Y, join(X, Z))) -> X
% 0.48/0.63 meet(Y0, Y0) -> Y0
% 0.48/0.63 meet(Y0, join(Y0, Y2)) -> Y0
% 0.48/0.63 meet(Y0, join(Y1, Y0)) -> Y0
% 0.48/0.63 meet(Y0, meet(X1, Y0)) -> meet(X1, Y0)
% 0.48/0.63 meet(Y0, meet(X1, meet(Y0, X2))) -> meet(X1, meet(Y0, X2))
% 0.48/0.63 meet(Y0, meet(Y0, X1)) -> meet(Y0, X1)
% 0.48/0.63 meet(join(X0, Y1), Y1) -> Y1
% 0.48/0.63 meet(meet(X0, Y2), join(Y1, Y2)) -> meet(X0, Y2)
% 0.48/0.63 meet(meet(X1, Y1), Y1) -> meet(X1, Y1)
% 0.48/0.63 meet(meet(X1, meet(Y1, X2)), Y1) -> meet(X1, meet(Y1, X2))
% 0.48/0.63 meet(meet(Y0, join(meet(X1, meet(Y0, X2)), Y2)), meet(X1, meet(Y0, X2))) -> meet(X1, meet(Y0, X2))
% 0.48/0.63 meet(meet(Y1, X1), Y1) -> meet(Y1, X1)
% 0.48/0.63 meet(meet(join(X, Y), join(Y, Z)), Y) -> Y
% 0.48/0.63 meet(meet(join(Y0, Y1), Y1), Y1) -> Y1
% 0.48/0.63 true__ -> false__
% 0.48/0.63 with the LPO induced by
% 0.48/0.63 b > a > f1 > meet > join > true__ > false__
% 0.48/0.63
% 0.48/0.63 % SZS output end Proof
% 0.48/0.63
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