TSTP Solution File: LDA001-1 by Moca---0.1
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% File : Moca---0.1
% Problem : LDA001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n027.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 16:45:01 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% 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 : LDA001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n027.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 : Mon May 30 02:22:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 The input problem is unsatisfiable because
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% 0.19/0.39 [1] the following set of Horn clauses is unsatisfiable:
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% 0.19/0.39 f(X, f(Y, Z)) = f(f(X, Y), f(X, Z))
% 0.19/0.39 n2 = f(n1, n1)
% 0.19/0.39 n3 = f(n2, n1)
% 0.19/0.39 u = f(n2, n2)
% 0.19/0.39 f(f(n3, n2), u) = f(f(u, u), u) ==> \bottom
% 0.19/0.39
% 0.19/0.39 This holds because
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% 0.19/0.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
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% 0.19/0.39 E:
% 0.19/0.39 f(X, f(Y, Z)) = f(f(X, Y), f(X, Z))
% 0.19/0.39 f1(f(f(n3, n2), u)) = true__
% 0.19/0.39 f1(f(f(u, u), u)) = false__
% 0.19/0.39 n2 = f(n1, n1)
% 0.19/0.39 n3 = f(n2, n1)
% 0.19/0.39 u = f(n2, n2)
% 0.19/0.39 G:
% 0.19/0.39 true__ = false__
% 0.19/0.39
% 0.19/0.39 This holds because
% 0.19/0.39
% 0.19/0.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
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% 0.19/0.39 f(f(Y1, f(X1, Y2)), f(f(f(Y1, X1), Y1), Y3)) = f(f(f(Y1, X1), Y1), f(f(f(Y1, X1), Y2), Y3))
% 0.19/0.39 f(f(X, Y), f(X, Z)) -> f(X, f(Y, Z))
% 0.19/0.39 f(f(X0, f(X1, X2)), f(f(X0, X1), Y2)) -> f(f(X0, X1), f(f(X0, X2), Y2))
% 0.19/0.39 f(f(Y0, f(X0, f(X1, X2))), f(f(Y0, f(X0, X1)), Y3)) -> f(f(Y0, f(X0, X1)), f(f(Y0, f(X0, X2)), Y3))
% 0.19/0.39 f(f(f(X0, X1), Y1), f(X0, f(X1, X2))) -> f(f(X0, X1), f(Y1, f(X0, X2)))
% 0.19/0.39 f(f(f(X0, X1), f(f(X0, X2), Y2)), f(f(X0, f(X1, X2)), Y3)) -> f(f(X0, f(X1, X2)), f(f(f(X0, X1), Y2), Y3))
% 0.19/0.39 f(f(f(X0, f(X1, X2)), Y1), f(f(X0, X1), f(f(X0, X2), X3))) -> f(f(X0, f(X1, X2)), f(Y1, f(f(X0, X1), X3)))
% 0.19/0.39 f(f(f(Y0, f(X0, X1)), Y2), f(Y0, f(X0, f(X1, X2)))) -> f(f(Y0, f(X0, X1)), f(Y2, f(Y0, f(X0, X2))))
% 0.19/0.39 f(f(f(f(Y1, X1), Y1), Y2), f(Y1, f(X1, Y3))) -> f(f(f(Y1, X1), Y1), f(Y2, f(f(Y1, X1), Y3)))
% 0.19/0.39 f1(f(f(f(f(n1, n1), n1), f(n1, n1)), f(n1, f(n1, n1)))) -> true__
% 0.19/0.39 f1(f(f(n3, n2), u)) -> true__
% 0.19/0.39 f1(f(f(u, u), u)) -> false__
% 0.19/0.39 f1(f(n1, f(n1, f(f(n1, n1), n1)))) -> false__
% 0.19/0.39 n2 -> f(n1, n1)
% 0.19/0.39 n3 -> f(n2, n1)
% 0.19/0.39 true__ -> false__
% 0.19/0.39 u -> f(n2, n2)
% 0.19/0.39 with the LPO induced by
% 0.19/0.39 f1 > n3 > u > n2 > n1 > f > true__ > false__
% 0.19/0.39
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
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