TSTP Solution File: COL022-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : COL022-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n024.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 00:36:53 EDT 2022
% Result : Unsatisfiable 15.30s 15.44s
% Output : Proof 15.30s
% 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 : COL022-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue May 31 12:11:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 15.30/15.44 % SZS status Unsatisfiable
% 15.30/15.44 % SZS output start Proof
% 15.30/15.44 The input problem is unsatisfiable because
% 15.30/15.44
% 15.30/15.44 [1] the following set of Horn clauses is unsatisfiable:
% 15.30/15.44
% 15.30/15.44 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 15.30/15.44 apply(m, X) = apply(X, X)
% 15.30/15.44 apply(apply(o, X), Y) = apply(Y, apply(X, Y))
% 15.30/15.44 Y = apply(combinator, Y) ==> \bottom
% 15.30/15.44
% 15.30/15.44 This holds because
% 15.30/15.44
% 15.30/15.44 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 15.30/15.44
% 15.30/15.44 E:
% 15.30/15.44 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 15.30/15.44 apply(apply(o, X), Y) = apply(Y, apply(X, Y))
% 15.30/15.44 apply(m, X) = apply(X, X)
% 15.30/15.44 f1(Y, Y) = true__
% 15.30/15.44 f1(apply(combinator, Y), Y) = false__
% 15.30/15.44 G:
% 15.30/15.44 true__ = false__
% 15.30/15.44
% 15.30/15.44 This holds because
% 15.30/15.44
% 15.30/15.44 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 15.30/15.44
% 15.30/15.44 apply(Y0, apply(X0, apply(X1, Y0))) = apply(apply(o, apply(apply(b, X0), X1)), Y0)
% 15.30/15.44 apply(Y0, apply(X0, apply(apply(b, X0), Y0))) = apply(apply(o, apply(m, apply(b, X0))), Y0)
% 15.30/15.44 apply(Y0, apply(Y0, Y0)) = apply(apply(o, m), Y0)
% 15.30/15.44 apply(Y0, apply(Y0, apply(X0, Y0))) = apply(apply(o, apply(o, X0)), Y0)
% 15.30/15.44 apply(Y0, apply(Y0, apply(Y0, Y0))) = apply(apply(o, apply(o, m)), Y0)
% 15.30/15.44 apply(Y0, apply(Y0, apply(Y0, apply(X0, Y0)))) = apply(apply(o, apply(o, apply(o, X0))), Y0)
% 15.30/15.44 apply(Y0, apply(Y0, apply(Y0, apply(Y0, Y0)))) = apply(apply(o, apply(o, apply(o, m))), Y0)
% 15.30/15.44 apply(Y0, apply(Y0, apply(Y0, apply(o, Y0)))) = apply(apply(o, apply(o, apply(m, o))), Y0)
% 15.30/15.44 apply(Y0, apply(Y1, apply(Y0, Y0))) = apply(apply(o, apply(apply(b, Y1), m)), Y0)
% 15.30/15.44 apply(Y0, apply(apply(Y0, Y0), apply(m, Y0))) = apply(apply(o, apply(apply(b, m), m)), Y0)
% 15.30/15.44 apply(Y0, apply(apply(Y2, Y0), apply(Y2, Y0))) = apply(apply(o, apply(apply(b, m), Y2)), Y0)
% 15.30/15.44 apply(Y0, apply(b, apply(X0, Y0))) = apply(apply(o, apply(apply(m, b), X0)), Y0)
% 15.30/15.44 apply(Y0, apply(b, apply(Y0, Y0))) = apply(apply(o, apply(apply(m, b), m)), Y0)
% 15.30/15.44 apply(Y0, apply(b, apply(apply(m, b), Y0))) = apply(apply(o, apply(m, apply(m, b))), Y0)
% 15.30/15.44 apply(Y0, apply(m, apply(o, apply(b, Y0)))) = apply(m, apply(apply(m, o), apply(b, Y0)))
% 15.30/15.44 apply(apply(X1, Y1), apply(apply(o, X1), Y1)) = apply(apply(o, Y1), apply(X1, Y1))
% 15.30/15.44 apply(apply(Y1, Y1), apply(apply(o, m), Y1)) = apply(apply(m, Y1), apply(Y1, apply(Y1, Y1)))
% 15.30/15.44 apply(apply(Y1, Y1), apply(apply(o, m), Y1)) = apply(apply(o, Y1), apply(m, Y1))
% 15.30/15.44 apply(apply(m, o), Y1) = apply(Y1, apply(o, Y1))
% 15.30/15.44 apply(apply(o, X), Y) = apply(Y, apply(X, Y))
% 15.30/15.44 apply(apply(o, apply(m, o)), Y1) = apply(Y1, apply(Y1, apply(o, Y1)))
% 15.30/15.44 apply(m, X) = apply(X, X)
% 15.30/15.44 apply(m, apply(apply(b, Y0), Y1)) = apply(Y0, apply(Y1, apply(apply(b, Y0), Y1)))
% 15.30/15.44 apply(Y0, apply(apply(o, apply(b, Y0)), Y1)) -> apply(m, apply(apply(b, Y0), Y1))
% 15.30/15.44 apply(Y0, apply(apply(o, m), apply(b, Y0))) -> apply(m, apply(m, apply(b, Y0)))
% 15.30/15.44 apply(apply(Y1, apply(o, Y1)), apply(apply(o, apply(m, o)), Y1)) -> apply(m, apply(o, Y1))
% 15.30/15.44 apply(apply(apply(apply(m, o), b), Y1), Y2) -> apply(apply(o, b), apply(Y1, Y2))
% 15.30/15.44 apply(apply(apply(apply(o, X1), b), Y1), Y2) -> apply(apply(X1, b), apply(Y1, Y2))
% 15.30/15.44 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z))
% 15.30/15.44 apply(apply(apply(m, b), Y1), Y2) -> apply(b, apply(Y1, Y2))
% 15.30/15.44 apply(apply(apply(m, o), Y1), apply(Y1, apply(Y1, apply(o, Y1)))) -> apply(m, apply(o, Y1))
% 15.30/15.44 apply(apply(apply(m, o), apply(b, Y0)), Y2) -> apply(Y0, apply(apply(o, apply(b, Y0)), Y2))
% 15.30/15.44 apply(apply(apply(m, o), apply(m, b)), Y1) -> apply(b, apply(apply(o, apply(m, b)), Y1))
% 15.30/15.44 apply(apply(apply(o, X1), apply(b, Y0)), Y2) -> apply(Y0, apply(apply(X1, apply(b, Y0)), Y2))
% 15.30/15.44 apply(apply(apply(o, X1), apply(m, b)), Y1) -> apply(b, apply(apply(X1, apply(m, b)), Y1))
% 15.30/15.44 apply(apply(m, apply(b, Y0)), Y2) -> apply(Y0, apply(apply(b, Y0), Y2))
% 15.30/15.44 apply(apply(m, apply(m, b)), Y1) -> apply(b, apply(apply(m, b), Y1))
% 15.30/15.44 apply(apply(o, Y1), apply(Y1, Y1)) -> apply(apply(m, Y1), apply(Y1, apply(Y1, Y1)))
% 15.30/15.44 apply(apply(o, Y1), apply(apply(m, o), Y1)) -> apply(m, apply(o, Y1))
% 15.30/15.44 apply(apply(o, apply(o, o)), m) -> apply(apply(o, apply(o, m)), apply(apply(o, o), m))
% 15.30/15.44 apply(b, apply(Y0, apply(apply(m, b), Y0))) -> apply(m, apply(apply(m, b), Y0))
% 15.30/15.44 apply(b, apply(apply(o, m), apply(m, b))) -> apply(m, apply(m, apply(m, b)))
% 15.30/15.44 f1(Y, Y) -> true__
% 15.30/15.44 f1(apply(apply(m, o), combinator), apply(o, combinator)) -> false__
% 15.30/15.44 f1(apply(apply(o, X1), combinator), apply(X1, combinator)) -> false__
% 15.30/15.44 f1(apply(combinator, Y), Y) -> false__
% 15.30/15.44 f1(apply(m, apply(apply(b, combinator), X1)), apply(X1, apply(apply(b, combinator), X1))) -> false__
% 15.30/15.44 f1(apply(m, apply(apply(b, combinator), Y0)), apply(apply(o, apply(b, combinator)), Y0)) -> false__
% 15.30/15.44 f1(apply(m, apply(m, apply(b, combinator))), apply(apply(o, m), apply(b, combinator))) -> false__
% 15.30/15.44 f1(apply(m, combinator), combinator) -> false__
% 15.30/15.44 false__ -> true__
% 15.30/15.44 with the LPO induced by
% 15.30/15.44 b > apply > o > m > combinator > f1 > false__ > true__
% 15.30/15.44
% 15.30/15.44 % SZS output end Proof
% 15.30/15.44
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