TSTP Solution File: COL018-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : COL018-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n017.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 00:36:52 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n017.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 05:57:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 The input problem is unsatisfiable because
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% 0.20/0.40 [1] the following set of Horn clauses is unsatisfiable:
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% 0.20/0.40 apply(apply(l, X), Y) = apply(X, apply(Y, Y))
% 0.20/0.40 apply(apply(w, X), Y) = apply(apply(X, Y), Y)
% 0.20/0.40 apply(apply(apply(q, X), Y), Z) = apply(Y, apply(X, Z))
% 0.20/0.40 Y = apply(combinator, Y) ==> \bottom
% 0.20/0.40
% 0.20/0.40 This holds because
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% 0.20/0.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
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% 0.20/0.40 E:
% 0.20/0.40 apply(apply(apply(q, X), Y), Z) = apply(Y, apply(X, Z))
% 0.20/0.40 apply(apply(l, X), Y) = apply(X, apply(Y, Y))
% 0.20/0.40 apply(apply(w, X), Y) = apply(apply(X, Y), Y)
% 0.20/0.40 f1(Y, Y) = true__
% 0.20/0.40 f1(apply(combinator, Y), Y) = false__
% 0.20/0.40 G:
% 0.20/0.40 true__ = false__
% 0.20/0.40
% 0.20/0.40 This holds because
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% 0.20/0.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
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% 0.20/0.40 apply(X0, apply(apply(Y1, Y1), apply(Y1, Y1))) = apply(apply(l, apply(l, X0)), Y1)
% 0.20/0.40 apply(Y1, apply(Y1, Y1)) = apply(apply(w, l), Y1)
% 0.20/0.40 apply(apply(X0, apply(Y1, Y1)), Y1) = apply(apply(w, apply(l, X0)), Y1)
% 0.20/0.40 apply(apply(X0, apply(Y1, Y1)), apply(Y1, Y1)) = apply(apply(l, apply(w, X0)), Y1)
% 0.20/0.40 apply(apply(Y1, Y1), Y1) = apply(apply(w, w), Y1)
% 0.20/0.40 apply(apply(apply(X0, Y1), Y1), Y1) = apply(apply(w, apply(w, X0)), Y1)
% 0.20/0.40 apply(apply(apply(l, Y0), X1), apply(X1, X1)) = apply(apply(w, Y0), apply(X1, X1))
% 0.20/0.40 apply(apply(apply(l, l), X1), Y1) = apply(apply(X1, X1), apply(Y1, Y1))
% 0.20/0.40 apply(apply(apply(l, w), X1), Y1) = apply(apply(apply(X1, X1), Y1), Y1)
% 0.20/0.40 apply(apply(l, X), Y) = apply(X, apply(Y, Y))
% 0.20/0.40 apply(apply(l, apply(w, l)), X1) = apply(apply(X1, X1), apply(apply(X1, X1), apply(X1, X1)))
% 0.20/0.40 apply(apply(w, X), Y) = apply(apply(X, Y), Y)
% 0.20/0.40 apply(apply(w, apply(w, X0)), Y1) = apply(apply(w, apply(X0, Y1)), Y1)
% 0.20/0.40 apply(apply(apply(q, X), Y), Z) -> apply(Y, apply(X, Z))
% 0.20/0.40 apply(apply(apply(w, l), Y0), apply(Y0, Y0)) -> apply(apply(w, Y0), apply(Y0, Y0))
% 0.20/0.40 f1(Y, Y) -> true__
% 0.20/0.40 f1(apply(apply(l, combinator), X1), apply(X1, X1)) -> false__
% 0.20/0.40 f1(apply(combinator, Y), Y) -> false__
% 0.20/0.40 true__ -> false__
% 0.20/0.40 with the LPO induced by
% 0.20/0.40 w > combinator > l > q > apply > f1 > true__ > false__
% 0.20/0.40
% 0.20/0.40 % SZS output end Proof
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