TSTP Solution File: SYN333-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : SYN333-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n023.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 : Thu Jul 21 09:15:24 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
% 0.07/0.12 % Problem : SYN333-1 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Tue Jul 12 05:11:24 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
% 0.19/0.39
% 0.19/0.39 [1] the following set of Horn clauses is unsatisfiable:
% 0.19/0.39
% 0.19/0.39 f(X, Y)
% 0.19/0.39 f(Y, z(X, Y)) & f(z(X, Y), z(X, Y)) ==> g(X, Y)
% 0.19/0.39 f(Y, z(X, Y)) & f(z(X, Y), z(X, Y)) & g(X, z(X, Y)) & g(z(X, Y), z(X, Y)) ==> \bottom
% 0.19/0.39
% 0.19/0.39 This holds because
% 0.19/0.39
% 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, Y) = true__
% 0.19/0.39 f1(true__, X, Y) = g(X, Y)
% 0.19/0.39 f2(f(z(X, Y), z(X, Y)), Y, X) = true__
% 0.19/0.39 f2(true__, Y, X) = f1(f(Y, z(X, Y)), X, Y)
% 0.19/0.39 f3(true__) = false__
% 0.19/0.39 f4(true__, Y, X) = f3(f(Y, z(X, Y)))
% 0.19/0.39 f5(true__, X, Y) = f4(f(z(X, Y), z(X, Y)), Y, X)
% 0.19/0.39 f6(g(z(X, Y), z(X, Y)), X, Y) = true__
% 0.19/0.39 f6(true__, X, Y) = f5(g(X, z(X, Y)), X, Y)
% 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:
% 0.19/0.39
% 0.19/0.39
% 0.19/0.39 f(X, Y) -> true__
% 0.19/0.39 f1(true__, Y0, Y1) -> true__
% 0.19/0.39 f2(f(z(X, Y), z(X, Y)), Y, X) -> true__
% 0.19/0.39 f2(true__, Y, X) -> f1(f(Y, z(X, Y)), X, Y)
% 0.19/0.39 f3(true__) -> false__
% 0.19/0.39 f4(true__, Y, X) -> f3(f(Y, z(X, Y)))
% 0.19/0.39 f5(true__, X, Y) -> f4(f(z(X, Y), z(X, Y)), Y, X)
% 0.19/0.39 f6(f1(true__, z(Y0, Y1), z(Y0, Y1)), Y0, Y1) -> true__
% 0.19/0.39 f6(g(z(X, Y), z(X, Y)), X, Y) -> true__
% 0.19/0.39 f6(true__, X, Y) -> f5(g(X, z(X, Y)), X, Y)
% 0.19/0.39 false__ -> true__
% 0.19/0.39 g(X, Y) -> f1(true__, X, Y)
% 0.19/0.39 with the LPO induced by
% 0.19/0.39 f2 > f6 > f5 > f4 > f > f3 > g > z > f1 > false__ > true__
% 0.19/0.39
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
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