TSTP Solution File: COL048-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : COL048-1 : 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 00:37:10 EDT 2022
% Result : Unsatisfiable 9.46s 9.58s
% Output : Proof 9.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL048-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n017.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 03:57:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 9.46/9.58 % SZS status Unsatisfiable
% 9.46/9.58 % SZS output start Proof
% 9.46/9.58 The input problem is unsatisfiable because
% 9.46/9.58
% 9.46/9.58 [1] the following set of Horn clauses is unsatisfiable:
% 9.46/9.58
% 9.46/9.58 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 9.46/9.58 apply(apply(w, X), Y) = apply(apply(X, Y), Y)
% 9.46/9.58 apply(m, X) = apply(X, X)
% 9.46/9.58 Y = apply(combinator, Y) ==> \bottom
% 9.46/9.58
% 9.46/9.58 This holds because
% 9.46/9.58
% 9.46/9.58 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 9.46/9.58
% 9.46/9.58 E:
% 9.46/9.58 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 9.46/9.58 apply(apply(w, X), Y) = apply(apply(X, Y), Y)
% 9.46/9.58 apply(m, X) = apply(X, X)
% 9.46/9.58 f1(Y, Y) = true__
% 9.46/9.58 f1(apply(combinator, Y), Y) = false__
% 9.46/9.58 G:
% 9.46/9.58 true__ = false__
% 9.46/9.58
% 9.46/9.58 This holds because
% 9.46/9.58
% 9.46/9.58 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 9.46/9.58
% 9.46/9.58 apply(apply(X0, apply(X1, Y1)), Y1) = apply(apply(w, apply(apply(b, X0), X1)), Y1)
% 9.46/9.58 apply(apply(X0, apply(X1, apply(apply(b, X0), X1))), apply(apply(b, X0), X1)) = apply(apply(m, w), apply(apply(b, X0), X1))
% 9.46/9.58 apply(apply(X0, apply(Y1, Y1)), Y1) = apply(apply(w, apply(w, apply(b, X0))), Y1)
% 9.46/9.58 apply(apply(X0, apply(Y1, Y1)), apply(Y1, Y1)) = apply(apply(w, X0), apply(m, Y1))
% 9.46/9.58 apply(apply(X0, apply(Y1, Y1)), apply(Y1, Y1)) = apply(apply(w, apply(b, apply(w, X0))), Y1)
% 9.46/9.58 apply(apply(Y1, Y1), Y1) = apply(apply(m, w), Y1)
% 9.46/9.58 apply(apply(Y1, Y1), Y1) = apply(apply(w, m), Y1)
% 9.46/9.58 apply(apply(Y1, Y1), apply(Y1, Y1)) = apply(apply(w, apply(b, m)), Y1)
% 9.46/9.58 apply(apply(Y1, Y1), apply(Y1, Y1)) = apply(m, apply(m, Y1))
% 9.46/9.58 apply(apply(apply(X0, Y1), Y1), Y1) = apply(apply(w, apply(w, X0)), Y1)
% 9.46/9.58 apply(apply(apply(Y1, Y1), Y1), Y1) = apply(apply(w, apply(m, w)), Y1)
% 9.46/9.58 apply(apply(apply(Y1, Y1), Y1), Y1) = apply(apply(w, apply(w, m)), Y1)
% 9.46/9.58 apply(apply(apply(apply(X0, Y1), Y1), Y1), Y1) = apply(apply(w, apply(w, apply(w, X0))), Y1)
% 9.46/9.58 apply(apply(apply(apply(m, Y1), Y1), Y1), Y1) = apply(apply(w, apply(w, apply(m, w))), Y1)
% 9.46/9.58 apply(apply(apply(m, Y1), Y1), Y1) = apply(apply(w, apply(m, w)), Y1)
% 9.46/9.58 apply(apply(apply(m, Y1), Y1), Y1) = apply(apply(w, apply(w, Y1)), Y1)
% 9.46/9.58 apply(apply(apply(w, apply(b, w)), X1), Y1) = apply(apply(apply(X1, X1), Y1), Y1)
% 9.46/9.58 apply(apply(b, apply(X0, Y1)), Y1) = apply(apply(w, apply(apply(m, b), X0)), Y1)
% 9.46/9.58 apply(apply(m, apply(Y1, Y1)), apply(Y1, Y1)) = apply(apply(m, w), apply(m, Y1))
% 9.46/9.58 apply(apply(m, w), Y1) = apply(apply(m, Y1), Y1)
% 9.46/9.58 apply(apply(m, w), apply(b, Y0)) = apply(Y0, apply(m, apply(b, Y0)))
% 9.46/9.58 apply(apply(w, X), Y) = apply(apply(X, Y), Y)
% 9.46/9.58 apply(apply(w, apply(b, Y0)), Y2) = apply(Y0, apply(Y2, Y2))
% 9.46/9.58 apply(apply(w, apply(m, X1)), Y1) = apply(apply(apply(X1, X1), Y1), Y1)
% 9.46/9.58 apply(apply(w, apply(m, b)), Y1) = apply(b, apply(Y1, Y1))
% 9.46/9.58 apply(apply(w, apply(m, w)), Y1) = apply(apply(w, apply(Y1, Y1)), Y1)
% 9.46/9.58 apply(apply(w, apply(m, w)), Y1) = apply(apply(w, apply(m, Y1)), Y1)
% 9.46/9.58 apply(apply(w, apply(w, X0)), Y1) = apply(apply(w, apply(X0, Y1)), Y1)
% 9.46/9.58 apply(apply(w, apply(w, apply(w, m))), Y1) = apply(apply(w, apply(w, apply(Y1, Y1))), Y1)
% 9.46/9.58 apply(apply(w, apply(w, m)), Y1) = apply(apply(w, apply(Y1, Y1)), Y1)
% 9.46/9.58 apply(m, X) = apply(X, X)
% 9.46/9.58 apply(m, apply(apply(b, Y0), Y1)) = apply(Y0, apply(Y1, apply(apply(b, Y0), Y1)))
% 9.46/9.58 apply(m, apply(apply(w, b), Y0)) = apply(Y0, apply(Y0, apply(apply(w, b), Y0)))
% 9.46/9.58 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z))
% 9.46/9.58 apply(apply(apply(m, b), Y1), Y2) -> apply(b, apply(Y1, Y2))
% 9.46/9.58 apply(apply(apply(w, b), Y1), Y2) -> apply(Y1, apply(Y1, Y2))
% 9.46/9.58 apply(apply(m, apply(b, Y0)), Y2) -> apply(Y0, apply(apply(b, Y0), Y2))
% 9.46/9.58 apply(apply(m, apply(m, b)), Y1) -> apply(b, apply(apply(m, b), Y1))
% 9.46/9.58 apply(apply(m, apply(w, b)), Y1) -> apply(apply(w, b), apply(apply(w, b), Y1))
% 9.46/9.58 apply(apply(m, w), apply(w, m)) -> apply(m, apply(w, m))
% 9.46/9.58 apply(apply(w, Y1), Y1) -> apply(apply(m, Y1), Y1)
% 9.46/9.58 apply(apply(w, Y1), Y1) -> apply(apply(m, w), Y1)
% 9.46/9.58 apply(apply(w, apply(b, Y0)), Y1) -> apply(Y0, apply(m, Y1))
% 9.46/9.58 apply(apply(w, apply(m, b)), Y0) -> apply(b, apply(m, Y0))
% 9.46/9.58 apply(apply(w, apply(m, w)), apply(w, m)) -> apply(apply(m, w), apply(w, m))
% 9.46/9.58 apply(apply(w, apply(w, Y1)), Y1) -> apply(apply(w, apply(m, w)), Y1)
% 9.46/9.58 apply(apply(w, apply(w, m)), Y1) -> apply(apply(w, apply(m, w)), Y1)
% 9.46/9.58 apply(apply(w, m), Y0) -> apply(apply(m, w), Y0)
% 9.46/9.58 apply(b, apply(Y0, apply(apply(m, b), Y0))) -> apply(m, apply(apply(m, b), Y0))
% 9.46/9.58 f1(Y, Y) -> true__
% 9.46/9.58 f1(apply(apply(w, apply(b, combinator)), X1), apply(X1, X1)) -> false__
% 9.46/9.58 f1(apply(combinator, Y), Y) -> false__
% 9.46/9.58 f1(apply(m, combinator), combinator) -> false__
% 9.46/9.58 true__ -> false__
% 9.46/9.58 with the LPO induced by
% 9.46/9.58 w > combinator > b > m > apply > f1 > true__ > false__
% 9.46/9.58
% 9.46/9.58 % SZS output end Proof
% 9.46/9.58
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