TSTP Solution File: COL030-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : COL030-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n026.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 28.14s 28.30s
% Output : Proof 28.14s
% 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 : COL030-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue May 31 09:18:26 EDT 2022
% 0.14/0.35 % CPUTime :
% 28.14/28.30 % SZS status Unsatisfiable
% 28.14/28.30 % SZS output start Proof
% 28.14/28.30 The input problem is unsatisfiable because
% 28.14/28.30
% 28.14/28.30 [1] the following set of Horn clauses is unsatisfiable:
% 28.14/28.30
% 28.14/28.30 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z))
% 28.14/28.30 apply(apply(l, X), Y) = apply(X, apply(Y, Y))
% 28.14/28.30 apply(Y, f(Y)) = apply(f(Y), apply(Y, f(Y))) ==> \bottom
% 28.14/28.30
% 28.14/28.30 This holds because
% 28.14/28.30
% 28.14/28.30 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 28.14/28.30
% 28.14/28.30 E:
% 28.14/28.30 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z))
% 28.14/28.30 apply(apply(l, X), Y) = apply(X, apply(Y, Y))
% 28.14/28.30 f1(apply(Y, f(Y)), Y) = true__
% 28.14/28.30 f1(apply(f(Y), apply(Y, f(Y))), Y) = false__
% 28.14/28.30 G:
% 28.14/28.30 true__ = false__
% 28.14/28.30
% 28.14/28.30 This holds because
% 28.14/28.30
% 28.14/28.30 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 28.14/28.30
% 28.14/28.30 apply(X0, apply(apply(Y1, Y1), apply(Y1, Y1))) = apply(apply(l, apply(l, X0)), Y1)
% 28.14/28.30 apply(Y0, apply(apply(apply(l, l), X0), X0)) = apply(apply(l, Y0), apply(X0, X0))
% 28.14/28.30 apply(Y0, apply(apply(apply(l, l), Y1), Y1)) = apply(apply(l, apply(l, Y0)), Y1)
% 28.14/28.30 apply(Y0, apply(apply(apply(s, X0), X0), X1)) = apply(apply(l, Y0), apply(X0, X1))
% 28.14/28.30 apply(Y0, apply(apply(apply(s, Y1), Y1), Y0)) = apply(apply(apply(s, l), Y1), Y0)
% 28.14/28.30 apply(Y1, apply(apply(Y2, Y1), apply(Y2, Y1))) = apply(apply(apply(s, l), Y2), Y1)
% 28.14/28.30 apply(apply(X0, apply(Y1, Y1)), apply(Y2, Y1)) = apply(apply(apply(s, apply(l, X0)), Y2), Y1)
% 28.14/28.30 apply(apply(Y0, Y1), apply(X0, apply(Y1, Y1))) = apply(apply(apply(s, Y0), apply(l, X0)), Y1)
% 28.14/28.30 apply(apply(Y0, Y1), apply(Y0, apply(Y1, Y1))) = apply(apply(apply(apply(s, s), l), Y0), Y1)
% 28.14/28.30 apply(apply(apply(apply(l, s), X1), Y1), Y2) = apply(apply(apply(X1, X1), Y2), apply(Y1, Y2))
% 28.14/28.30 apply(apply(apply(apply(s, s), X2), Y0), Y2) = apply(apply(Y0, Y2), apply(apply(X2, Y0), Y2))
% 28.14/28.30 apply(apply(apply(l, apply(s, Y0)), X1), Y2) = apply(apply(Y0, Y2), apply(apply(X1, X1), Y2))
% 28.14/28.30 apply(apply(apply(l, l), X0), apply(Y1, Y1)) = apply(apply(l, apply(l, apply(X0, X0))), Y1)
% 28.14/28.30 apply(apply(apply(l, l), X1), Y1) = apply(apply(X1, X1), apply(Y1, Y1))
% 28.14/28.30 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z))
% 28.14/28.30 apply(apply(l, X), Y) = apply(X, apply(Y, Y))
% 28.14/28.30 apply(Y0, apply(apply(apply(l, l), Y0), Y0)) -> apply(apply(l, Y0), apply(Y0, Y0))
% 28.14/28.30 f1(apply(Y, f(Y)), Y) -> true__
% 28.14/28.30 f1(apply(apply(apply(s, l), X1), f(apply(apply(s, X1), X1))), apply(apply(s, X1), X1)) -> false__
% 28.14/28.30 f1(apply(f(Y), apply(Y, f(Y))), Y) -> false__
% 28.14/28.30 true__ -> false__
% 28.14/28.30 with the LPO induced by
% 28.14/28.30 apply > f1 > f > s > l > true__ > false__
% 28.14/28.30
% 28.14/28.30 % SZS output end Proof
% 28.14/28.30
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