TSTP Solution File: LAT090-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LAT090-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n011.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 06:04:34 EDT 2022
% Result : Unsatisfiable 5.58s 5.72s
% Output : Proof 5.58s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT090-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n011.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 30 10:50:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 5.58/5.72 % SZS status Unsatisfiable
% 5.58/5.72 % SZS output start Proof
% 5.58/5.72 The input problem is unsatisfiable because
% 5.58/5.72
% 5.58/5.72 [1] the following set of Horn clauses is unsatisfiable:
% 5.58/5.72
% 5.58/5.72 join(meet(A, B), meet(A, join(A, B))) = A
% 5.58/5.72 join(meet(A, A), meet(B, join(A, A))) = A
% 5.58/5.72 join(meet(A, B), meet(B, join(A, B))) = B
% 5.58/5.72 meet(meet(join(A, B), join(C, A)), A) = A
% 5.58/5.72 join(join(meet(A, B), meet(C, A)), A) = A
% 5.58/5.72 join(a, a) = a ==> \bottom
% 5.58/5.72
% 5.58/5.72 This holds because
% 5.58/5.72
% 5.58/5.72 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 5.58/5.72
% 5.58/5.72 E:
% 5.58/5.72 f1(a) = false__
% 5.58/5.72 f1(join(a, a)) = true__
% 5.58/5.72 join(join(meet(A, B), meet(C, A)), A) = A
% 5.58/5.72 join(meet(A, A), meet(B, join(A, A))) = A
% 5.58/5.72 join(meet(A, B), meet(A, join(A, B))) = A
% 5.58/5.72 join(meet(A, B), meet(B, join(A, B))) = B
% 5.58/5.72 meet(meet(join(A, B), join(C, A)), A) = A
% 5.58/5.72 G:
% 5.58/5.72 true__ = false__
% 5.58/5.72
% 5.58/5.72 This holds because
% 5.58/5.72
% 5.58/5.72 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 5.58/5.72
% 5.58/5.72
% 5.58/5.72 f1(a) -> false__
% 5.58/5.72 f1(join(a, a)) -> true__
% 5.58/5.72 join(Y0, meet(Y1, Y0)) -> Y0
% 5.58/5.72 join(Y0, meet(Y1, join(Y0, Y0))) -> Y0
% 5.58/5.72 join(Y1, Y1) -> Y1
% 5.58/5.72 join(Y1, meet(Y1, join(meet(Y1, join(X1, Y1)), Y1))) -> Y1
% 5.58/5.72 join(Y1, meet(Y1, join(meet(join(Y1, X1), Y1), Y1))) -> Y1
% 5.58/5.72 join(Y1, meet(Y1, join(meet(join(Y1, X1), join(X2, Y1)), Y1))) -> Y1
% 5.58/5.72 join(join(Y1, meet(Y1, join(X1, Y1))), meet(Y1, join(X1, Y1))) -> meet(Y1, join(X1, Y1))
% 5.58/5.72 join(join(Y1, meet(Y2, Y1)), Y1) -> Y1
% 5.58/5.72 join(join(Y1, meet(join(Y1, X1), Y1)), meet(join(Y1, X1), Y1)) -> meet(join(Y1, X1), Y1)
% 5.58/5.72 join(join(meet(A, B), meet(C, A)), A) -> A
% 5.58/5.72 join(join(meet(Y0, Y1), Y0), Y0) -> Y0
% 5.58/5.72 join(meet(A, B), meet(A, join(A, B))) -> A
% 5.58/5.72 join(meet(A, B), meet(B, join(A, B))) -> B
% 5.58/5.72 join(meet(Y0, meet(Y0, join(meet(join(Y0, X1), Y0), Y0))), meet(Y0, Y0)) -> Y0
% 5.58/5.72 join(meet(join(meet(Y0, Y1), Y0), Y0), Y0) -> Y0
% 5.58/5.72 join(meet(join(meet(Y1, X1), meet(X2, Y1)), Y1), meet(Y1, Y1)) -> Y1
% 5.58/5.72 join(meet(meet(X0, X0), meet(X1, join(X0, X0))), meet(meet(X0, X0), X0)) -> X0
% 5.58/5.72 join(meet(meet(X0, X1), meet(X0, join(X0, X1))), meet(meet(X0, X1), X0)) -> meet(X0, X1)
% 5.58/5.72 join(meet(meet(X0, X1), meet(X1, join(X0, X1))), meet(meet(X0, X1), X1)) -> meet(X0, X1)
% 5.58/5.72 meet(Y1, Y1) -> Y1
% 5.58/5.72 meet(join(meet(Y1, X1), Y1), Y1) -> join(meet(Y1, X1), Y1)
% 5.58/5.72 meet(meet(X0, join(Y2, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1)
% 5.58/5.72 meet(meet(X0, meet(X0, X1)), meet(X0, X1)) -> meet(X0, X1)
% 5.58/5.72 meet(meet(X1, join(Y2, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1)
% 5.58/5.72 meet(meet(X1, meet(X0, X1)), meet(X0, X1)) -> meet(X0, X1)
% 5.58/5.72 meet(meet(Y0, Y0), meet(Y0, join(X0, Y0))) -> meet(Y0, join(X0, Y0))
% 5.58/5.72 meet(meet(Y0, Y0), meet(Y0, join(Y0, X1))) -> meet(Y0, join(Y0, X1))
% 5.58/5.72 meet(meet(Y0, join(Y1, Y0)), Y0) -> Y0
% 5.58/5.72 meet(meet(Y1, join(Y1, meet(X1, Y1))), join(Y1, meet(X1, Y1))) -> join(Y1, meet(X1, Y1))
% 5.58/5.72 meet(meet(Y1, join(meet(Y1, X1), Y1)), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1)
% 5.58/5.72 meet(meet(join(A, B), join(C, A)), A) -> A
% 5.58/5.72 meet(meet(join(X0, X0), X0), meet(Y2, join(X0, X0))) -> meet(Y2, X0)
% 5.58/5.72 meet(meet(join(Y0, Y1), Y0), Y0) -> Y0
% 5.58/5.72 meet(meet(join(Y2, X1), Y2), meet(Y2, join(Y2, X1))) -> meet(Y2, join(Y2, X1))
% 5.58/5.72 meet(meet(meet(X0, X1), meet(X0, X1)), meet(meet(X0, X1), X0)) -> meet(meet(X0, X1), X0)
% 5.58/5.72 meet(meet(meet(X0, join(X0, X1)), X0), meet(X0, join(X0, X1))) -> meet(X0, join(X0, X1))
% 5.58/5.72 meet(meet(meet(X1, Y1), Y1), meet(X1, Y1)) -> meet(X1, Y1)
% 5.58/5.72 meet(meet(meet(join(Y2, X1), Y2), join(Y1, Y2)), Y2) -> Y2
% 5.58/5.72 true__ -> false__
% 5.58/5.72 with the LPO induced by
% 5.58/5.72 join > meet > a > f1 > true__ > false__
% 5.58/5.72
% 5.58/5.72 % SZS output end Proof
% 5.58/5.72
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