TSTP Solution File: COL027-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : COL027-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n025.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 20.23s 20.37s
% Output : Proof 20.23s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : COL027-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 15:53:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 20.23/20.37 % SZS status Unsatisfiable
% 20.23/20.37 % SZS output start Proof
% 20.23/20.37 The input problem is unsatisfiable because
% 20.23/20.37
% 20.23/20.37 [1] the following set of Horn clauses is unsatisfiable:
% 20.23/20.37
% 20.23/20.37 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 20.23/20.37 apply(apply(apply(h, X), Y), Z) = apply(apply(apply(X, Y), Z), Y)
% 20.23/20.37 Y = apply(combinator, Y) ==> \bottom
% 20.23/20.37
% 20.23/20.37 This holds because
% 20.23/20.37
% 20.23/20.37 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 20.23/20.37
% 20.23/20.37 E:
% 20.23/20.37 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 20.23/20.37 apply(apply(apply(h, X), Y), Z) = apply(apply(apply(X, Y), Z), Y)
% 20.23/20.37 f1(Y, Y) = true__
% 20.23/20.37 f1(apply(combinator, Y), Y) = false__
% 20.23/20.37 G:
% 20.23/20.37 true__ = false__
% 20.23/20.37
% 20.23/20.37 This holds because
% 20.23/20.37
% 20.23/20.37 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 20.23/20.37
% 20.23/20.37 apply(X0, apply(apply(Y1, Y2), Y1)) = apply(apply(apply(h, apply(b, apply(b, X0))), Y1), Y2)
% 20.23/20.37 apply(Y0, apply(X0, apply(X1, Y0))) = apply(apply(apply(h, b), Y0), apply(apply(b, X0), X1))
% 20.23/20.37 apply(Y0, apply(X0, apply(Y0, X0))) = apply(apply(apply(h, b), Y0), apply(apply(h, b), X0))
% 20.23/20.37 apply(Y1, apply(Y2, Y1)) = apply(apply(apply(h, b), Y1), Y2)
% 20.23/20.37 apply(Y2, apply(b, Y2)) = apply(apply(apply(h, h), b), Y2)
% 20.23/20.37 apply(apply(X0, apply(Y1, Y2)), Y1) = apply(apply(apply(h, apply(b, X0)), Y1), Y2)
% 20.23/20.37 apply(apply(X0, apply(Y1, apply(b, X0))), Y1) = apply(apply(apply(h, h), apply(b, X0)), Y1)
% 20.23/20.37 apply(apply(Y1, apply(Y2, Y1)), Y1) = apply(apply(apply(h, apply(h, b)), Y1), Y2)
% 20.23/20.37 apply(apply(apply(Y1, Y2), Y1), Y2) = apply(apply(apply(h, h), Y1), Y2)
% 20.23/20.37 apply(apply(apply(Y1, h), Y1), h) = apply(apply(apply(h, h), h), Y1)
% 20.23/20.37 apply(apply(apply(apply(apply(h, h), h), b), Y1), Y2) = apply(apply(h, apply(Y1, Y2)), Y1)
% 20.23/20.37 apply(apply(apply(apply(h, apply(h, b)), b), X1), Y2) = apply(apply(X1, b), apply(b, Y2))
% 20.23/20.37 apply(apply(apply(apply(h, apply(h, h)), b), h), Y2) = apply(apply(h, apply(b, Y2)), b)
% 20.23/20.37 apply(apply(apply(apply(h, apply(h, h)), h), b), Y1) = apply(apply(h, apply(h, Y1)), h)
% 20.23/20.37 apply(apply(apply(apply(h, h), apply(b, h)), b), Y2) = apply(h, apply(apply(b, Y2), b))
% 20.23/20.37 apply(apply(apply(h, X), Y), Z) = apply(apply(apply(X, Y), Z), Y)
% 20.23/20.37 apply(apply(apply(h, apply(apply(h, h), h)), b), Y0) = apply(apply(h, apply(Y0, b)), Y0)
% 20.23/20.37 apply(apply(apply(h, apply(h, apply(h, b))), b), Y0) = apply(apply(Y0, b), apply(b, b))
% 20.23/20.37 apply(apply(apply(h, apply(h, h)), Y1), Y2) = apply(apply(apply(h, apply(Y1, Y2)), Y1), Y2)
% 20.23/20.37 apply(apply(apply(h, apply(h, h)), Y1), h) = apply(apply(apply(h, apply(Y1, h)), Y1), h)
% 20.23/20.37 apply(apply(X0, apply(h, apply(b, X0))), h) -> apply(apply(apply(h, h), h), apply(b, X0))
% 20.23/20.37 apply(apply(Y1, apply(apply(h, b), Y1)), Y1) -> apply(apply(apply(h, h), apply(h, b)), Y1)
% 20.23/20.37 apply(apply(Y2, apply(b, Y2)), b) -> apply(apply(apply(h, apply(h, h)), b), Y2)
% 20.23/20.37 apply(apply(apply(apply(X0, Y1), Y2), Y1), Y1) -> apply(apply(apply(h, apply(h, X0)), Y1), Y2)
% 20.23/20.37 apply(apply(apply(apply(apply(h, b), b), X1), Y1), Y2) -> apply(apply(X1, b), apply(Y1, Y2))
% 20.23/20.37 apply(apply(apply(apply(h, X0), Y2), Y1), Y1) -> apply(apply(apply(h, apply(X0, Y2)), Y1), Y2)
% 20.23/20.37 apply(apply(apply(apply(h, apply(b, b)), Y1), X2), Y2) -> apply(apply(Y1, X2), apply(Y1, Y2))
% 20.23/20.37 apply(apply(apply(apply(h, apply(h, h)), b), b), Y2) -> apply(apply(b, b), apply(b, Y2))
% 20.23/20.37 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z))
% 20.23/20.37 apply(h, apply(b, h)) -> apply(apply(apply(h, h), h), b)
% 20.23/20.37 f1(Y, Y) -> true__
% 20.23/20.37 f1(apply(apply(apply(h, apply(b, apply(b, combinator))), X1), X2), apply(apply(X1, X2), X1)) -> false__
% 20.23/20.37 f1(apply(apply(apply(h, b), combinator), X1), apply(X1, combinator)) -> false__
% 20.23/20.37 f1(apply(apply(apply(h, b), combinator), apply(apply(b, X0), X1)), apply(X0, apply(X1, combinator))) -> false__
% 20.23/20.37 f1(apply(apply(apply(h, b), combinator), apply(apply(h, b), X0)), apply(X0, apply(combinator, X0))) -> false__
% 20.23/20.37 f1(apply(combinator, Y), Y) -> false__
% 20.23/20.37 false__ -> true__
% 20.23/20.37 with the LPO induced by
% 20.23/20.37 b > apply > h > combinator > f1 > false__ > true__
% 20.23/20.37
% 20.23/20.37 % SZS output end Proof
% 20.23/20.37
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