TSTP Solution File: COL031-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : COL031-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n019.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 00:36:57 EDT 2022
% Result : Unsatisfiable 2.37s 2.52s
% Output : Proof 2.37s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : COL031-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : moca.sh %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue May 31 11:18:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 2.37/2.52 % SZS status Unsatisfiable
% 2.37/2.52 % SZS output start Proof
% 2.37/2.52 The input problem is unsatisfiable because
% 2.37/2.52
% 2.37/2.52 [1] the following set of Horn clauses is unsatisfiable:
% 2.37/2.52
% 2.37/2.52 apply(apply(l, X), Y) = apply(X, apply(Y, Y))
% 2.37/2.52 apply(apply(o, X), Y) = apply(Y, apply(X, Y))
% 2.37/2.52 apply(Y, f(Y)) = apply(f(Y), apply(Y, f(Y))) ==> \bottom
% 2.37/2.52
% 2.37/2.52 This holds because
% 2.37/2.52
% 2.37/2.52 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.37/2.52
% 2.37/2.52 E:
% 2.37/2.52 apply(apply(l, X), Y) = apply(X, apply(Y, Y))
% 2.37/2.52 apply(apply(o, X), Y) = apply(Y, apply(X, Y))
% 2.37/2.52 f1(apply(Y, f(Y)), Y) = true__
% 2.37/2.52 f1(apply(f(Y), apply(Y, f(Y))), Y) = false__
% 2.37/2.52 G:
% 2.37/2.52 true__ = false__
% 2.37/2.52
% 2.37/2.52 This holds because
% 2.37/2.52
% 2.37/2.52 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.37/2.52
% 2.37/2.52 apply(X0, apply(apply(Y1, Y1), apply(Y1, Y1))) = apply(apply(l, apply(l, X0)), Y1)
% 2.37/2.52 apply(Y0, apply(X0, apply(Y0, Y0))) = apply(apply(o, apply(l, X0)), Y0)
% 2.37/2.52 apply(Y0, apply(Y0, apply(X0, Y0))) = apply(apply(o, apply(o, X0)), Y0)
% 2.37/2.52 apply(Y0, apply(Y0, apply(X0, apply(Y0, Y0)))) = apply(apply(o, apply(o, apply(l, X0))), Y0)
% 2.37/2.52 apply(Y0, apply(Y0, apply(Y0, apply(X0, Y0)))) = apply(apply(o, apply(o, apply(o, X0))), Y0)
% 2.37/2.52 apply(Y0, apply(Y0, apply(apply(X0, X0), Y0))) = apply(apply(o, apply(apply(l, o), X0)), Y0)
% 2.37/2.52 apply(Y0, apply(apply(X0, X0), apply(Y0, Y0))) = apply(apply(o, apply(apply(l, l), X0)), Y0)
% 2.37/2.52 apply(Y0, apply(apply(apply(l, l), X0), X0)) = apply(apply(l, Y0), apply(X0, X0))
% 2.37/2.52 apply(Y0, apply(apply(apply(l, l), X0), Y0)) = apply(apply(o, apply(l, apply(X0, X0))), Y0)
% 2.37/2.52 apply(Y0, apply(apply(apply(l, l), Y1), Y1)) = apply(apply(l, apply(l, Y0)), Y1)
% 2.37/2.52 apply(Y0, apply(apply(apply(l, o), X1), Y0)) = apply(apply(o, apply(o, apply(X1, X1))), Y0)
% 2.37/2.52 apply(apply(X1, X1), apply(apply(l, Y1), X1)) = apply(apply(o, Y1), apply(X1, X1))
% 2.37/2.52 apply(apply(X1, Y1), apply(apply(o, X1), Y1)) = apply(apply(o, Y1), apply(X1, Y1))
% 2.37/2.52 apply(apply(Y0, Y0), apply(apply(l, Y1), Y0)) = apply(apply(l, apply(o, Y1)), Y0)
% 2.37/2.52 apply(apply(Y1, Y1), apply(X0, apply(Y1, Y1))) = apply(apply(l, apply(o, X0)), Y1)
% 2.37/2.52 apply(apply(Y1, Y1), apply(o, apply(Y1, Y1))) = apply(apply(apply(l, l), o), Y1)
% 2.37/2.52 apply(apply(apply(apply(l, o), X1), l), Y1) = apply(apply(apply(X1, X1), l), apply(Y1, Y1))
% 2.37/2.52 apply(apply(apply(apply(l, o), X1), o), Y1) = apply(Y1, apply(apply(apply(X1, X1), o), Y1))
% 2.37/2.52 apply(apply(apply(l, l), X0), apply(Y1, Y1)) = apply(apply(l, apply(l, apply(X0, X0))), Y1)
% 2.37/2.52 apply(apply(apply(l, l), X1), Y1) = apply(apply(X1, X1), apply(Y1, Y1))
% 2.37/2.52 apply(apply(apply(l, l), o), Y1) = apply(apply(Y1, Y1), apply(apply(l, o), Y1))
% 2.37/2.52 apply(apply(apply(l, o), X1), Y1) = apply(Y1, apply(apply(X1, X1), Y1))
% 2.37/2.52 apply(apply(apply(o, X1), l), Y1) = apply(apply(X1, l), apply(Y1, Y1))
% 2.37/2.52 apply(apply(l, X), Y) = apply(X, apply(Y, Y))
% 2.37/2.52 apply(apply(o, X), Y) = apply(Y, apply(X, Y))
% 2.37/2.52 apply(apply(apply(l, o), X0), apply(X0, X0)) -> apply(apply(apply(l, l), X0), apply(X0, X0))
% 2.37/2.52 f1(apply(Y, f(Y)), Y) -> true__
% 2.37/2.52 f1(apply(apply(apply(l, o), X1), f(apply(X1, X1))), apply(X1, X1)) -> false__
% 2.37/2.52 f1(apply(apply(o, Y0), f(Y0)), Y0) -> false__
% 2.37/2.52 f1(apply(apply(o, apply(Y0, Y0)), f(apply(Y0, Y0))), apply(Y0, Y0)) -> false__
% 2.37/2.52 f1(apply(f(Y), apply(Y, f(Y))), Y) -> false__
% 2.37/2.52 false__ -> true__
% 2.37/2.52 with the LPO induced by
% 2.37/2.52 o > l > f > apply > f1 > false__ > true__
% 2.37/2.52
% 2.37/2.52 % SZS output end Proof
% 2.37/2.52
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