TSTP Solution File: COL025-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : COL025-1 : 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 00:36:55 EDT 2022
% Result : Unsatisfiable 0.57s 0.83s
% Output : Proof 0.57s
% 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 : COL025-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % 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 14:35:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.57/0.83 % SZS status Unsatisfiable
% 0.57/0.83 % SZS output start Proof
% 0.57/0.83 The input problem is unsatisfiable because
% 0.57/0.83
% 0.57/0.83 [1] the following set of Horn clauses is unsatisfiable:
% 0.57/0.83
% 0.57/0.83 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 0.57/0.83 apply(apply(w, X), Y) = apply(apply(X, Y), Y)
% 0.57/0.83 Y = apply(combinator, Y) ==> \bottom
% 0.57/0.83
% 0.57/0.83 This holds because
% 0.57/0.83
% 0.57/0.83 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.57/0.83
% 0.57/0.83 E:
% 0.57/0.83 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 0.57/0.83 apply(apply(w, X), Y) = apply(apply(X, Y), Y)
% 0.57/0.83 f1(Y, Y) = true__
% 0.57/0.83 f1(apply(combinator, Y), Y) = false__
% 0.57/0.83 G:
% 0.57/0.83 true__ = false__
% 0.57/0.83
% 0.57/0.83 This holds because
% 0.57/0.83
% 0.57/0.83 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.57/0.83
% 0.57/0.83 apply(X0, apply(apply(Y1, Y1), apply(Y1, Y1))) = apply(apply(w, apply(b, apply(w, apply(b, X0)))), Y1)
% 0.57/0.83 apply(apply(X0, apply(X1, Y1)), Y1) = apply(apply(w, apply(apply(b, X0), X1)), Y1)
% 0.57/0.83 apply(apply(X0, apply(Y1, Y1)), Y1) = apply(apply(w, apply(w, apply(b, X0))), Y1)
% 0.57/0.83 apply(apply(X0, apply(Y1, Y1)), apply(Y1, Y1)) = apply(apply(w, apply(b, apply(w, X0))), Y1)
% 0.57/0.83 apply(apply(Y1, Y1), Y1) = apply(apply(w, w), Y1)
% 0.57/0.83 apply(apply(w, X), Y) = apply(apply(X, Y), Y)
% 0.57/0.83 apply(apply(w, apply(X0, Y1)), Y1) = apply(apply(w, apply(w, X0)), Y1)
% 0.57/0.83 apply(apply(w, apply(apply(w, apply(b, b)), X1)), Y1) = apply(apply(X1, X1), apply(Y1, Y1))
% 0.57/0.83 apply(apply(w, apply(b, Y0)), Y2) = apply(Y0, apply(Y2, Y2))
% 0.57/0.83 apply(apply(w, apply(w, b)), Y1) = apply(Y1, apply(Y1, Y1))
% 0.57/0.83 apply(apply(w, apply(w, w)), Y1) = apply(apply(w, apply(Y1, Y1)), Y1)
% 0.57/0.83 apply(Y0, apply(apply(b, Y0), apply(b, Y0))) -> apply(apply(w, w), apply(b, Y0))
% 0.57/0.83 apply(apply(X0, apply(X0, apply(apply(w, b), X0))), apply(apply(w, b), X0)) -> apply(apply(w, w), apply(apply(w, b), X0))
% 0.57/0.83 apply(apply(X0, apply(X1, apply(apply(b, X0), X1))), apply(apply(b, X0), X1)) -> apply(apply(w, w), apply(apply(b, X0), X1))
% 0.57/0.83 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z))
% 0.57/0.83 apply(apply(apply(w, apply(b, Y0)), X1), apply(X1, X1)) -> apply(apply(w, Y0), apply(X1, X1))
% 0.57/0.83 apply(apply(apply(w, b), Y1), Y2) -> apply(Y1, apply(Y1, Y2))
% 0.57/0.83 apply(apply(apply(w, w), b), Y2) -> apply(b, apply(b, Y2))
% 0.57/0.83 apply(apply(w, b), apply(apply(w, b), apply(w, b))) -> apply(apply(w, w), apply(w, b))
% 0.57/0.83 f1(Y, Y) -> true__
% 0.57/0.83 f1(apply(apply(w, apply(b, combinator)), X1), apply(X1, X1)) -> false__
% 0.57/0.83 f1(apply(combinator, Y), Y) -> false__
% 0.57/0.83 true__ -> false__
% 0.57/0.83 with the LPO induced by
% 0.57/0.83 b > f1 > apply > w > combinator > true__ > false__
% 0.57/0.83
% 0.57/0.83 % SZS output end Proof
% 0.57/0.83
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