TSTP Solution File: COL029-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : COL029-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n018.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 : Fri Jul 15 00:36:56 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% 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
% 0.12/0.12 % Problem : COL029-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n018.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue May 31 15:28:58 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 The input problem is unsatisfiable because
% 0.19/0.43
% 0.19/0.43 [1] the following set of Horn clauses is unsatisfiable:
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% 0.19/0.43 apply(apply(u, X), Y) = apply(Y, apply(apply(X, X), Y))
% 0.19/0.43 apply(Y, f(Y)) = apply(f(Y), apply(Y, f(Y))) ==> \bottom
% 0.19/0.43
% 0.19/0.43 This holds because
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% 0.19/0.43 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
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% 0.19/0.43 E:
% 0.19/0.43 apply(apply(u, X), Y) = apply(Y, apply(apply(X, X), Y))
% 0.19/0.43 f1(apply(Y, f(Y)), Y) = true__
% 0.19/0.43 f1(apply(f(Y), apply(Y, f(Y))), Y) = false__
% 0.19/0.43 G:
% 0.19/0.43 true__ = false__
% 0.19/0.43
% 0.19/0.43 This holds because
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% 0.19/0.43 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
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% 0.19/0.43 apply(apply(apply(X1, X1), apply(Y1, Y1)), apply(apply(u, X1), apply(Y1, Y1))) = apply(apply(u, Y1), apply(apply(X1, X1), apply(Y1, Y1)))
% 0.19/0.43 apply(apply(u, X), Y) = apply(Y, apply(apply(X, X), Y))
% 0.19/0.43 apply(Y0, apply(apply(apply(u, X1), apply(apply(u, u), apply(X1, X1))), Y0)) -> apply(apply(u, apply(apply(u, u), apply(X1, X1))), Y0)
% 0.19/0.43 apply(apply(apply(apply(apply(X1, X1), u), apply(apply(X1, X1), u)), apply(Y1, Y1)), apply(apply(apply(u, X1), u), apply(Y1, Y1))) -> apply(apply(u, Y1), apply(apply(apply(apply(X1, X1), u), apply(apply(X1, X1), u)), apply(Y1, Y1)))
% 0.19/0.43 apply(apply(apply(u, X0), apply(X0, X0)), apply(apply(u, X0), apply(apply(X0, X0), apply(X0, X0)))) -> apply(apply(u, apply(X0, X0)), apply(apply(u, X0), apply(X0, X0)))
% 0.19/0.43 apply(apply(apply(u, X1), apply(X1, X1)), apply(apply(u, X1), apply(apply(X1, X1), apply(X1, X1)))) -> apply(apply(u, apply(X1, X1)), apply(apply(X1, X1), apply(apply(X1, X1), apply(X1, X1))))
% 0.19/0.43 apply(apply(u, apply(u, u)), apply(apply(u, u), apply(u, u))) -> apply(apply(u, u), apply(u, u))
% 0.19/0.43 f1(apply(Y, f(Y)), Y) -> true__
% 0.19/0.43 f1(apply(apply(apply(u, X1), u), f(apply(apply(apply(X1, X1), u), apply(apply(X1, X1), u)))), apply(apply(apply(X1, X1), u), apply(apply(X1, X1), u))) -> false__
% 0.19/0.43 f1(apply(apply(u, X1), f(apply(X1, X1))), apply(X1, X1)) -> false__
% 0.19/0.43 f1(apply(f(Y), apply(Y, f(Y))), Y) -> false__
% 0.19/0.43 false__ -> true__
% 0.19/0.43 with the LPO induced by
% 0.19/0.43 u > f > apply > f1 > false__ > true__
% 0.19/0.43
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43
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