TSTP Solution File: COL016-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : COL016-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n020.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 00:36:51 EDT 2022
% Result : Unsatisfiable 0.60s 0.79s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : COL016-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n020.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 14:13:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.60/0.79 % SZS status Unsatisfiable
% 0.60/0.79 % SZS output start Proof
% 0.60/0.79 The input problem is unsatisfiable because
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% 0.60/0.79 [1] the following set of Horn clauses is unsatisfiable:
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% 0.60/0.79 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 0.60/0.79 apply(apply(l, X), Y) = apply(X, apply(Y, Y))
% 0.60/0.79 apply(m, X) = apply(X, X)
% 0.60/0.79 Y = apply(combinator, Y) ==> \bottom
% 0.60/0.79
% 0.60/0.79 This holds because
% 0.60/0.79
% 0.60/0.79 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
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% 0.60/0.79 E:
% 0.60/0.79 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 0.60/0.79 apply(apply(l, X), Y) = apply(X, apply(Y, Y))
% 0.60/0.79 apply(m, X) = apply(X, X)
% 0.60/0.79 f1(Y, Y) = true__
% 0.60/0.79 f1(apply(combinator, Y), Y) = false__
% 0.60/0.79 G:
% 0.60/0.79 true__ = false__
% 0.60/0.79
% 0.60/0.79 This holds because
% 0.60/0.79
% 0.60/0.79 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.60/0.79
% 0.60/0.79 apply(X0, apply(apply(Y1, Y1), apply(Y1, Y1))) = apply(X0, apply(m, apply(m, Y1)))
% 0.60/0.79 apply(apply(Y0, Y0), apply(m, Y0)) = apply(m, apply(m, Y0))
% 0.60/0.79 apply(apply(Y1, Y1), apply(Y1, Y1)) = apply(apply(l, m), Y1)
% 0.60/0.79 apply(apply(Y1, Y1), apply(Y1, Y1)) = apply(m, apply(m, Y1))
% 0.60/0.79 apply(apply(apply(X1, X1), apply(X1, X1)), apply(m, apply(m, X1))) = apply(m, apply(apply(X1, X1), apply(X1, X1)))
% 0.60/0.79 apply(apply(apply(X1, X1), apply(X1, X1)), apply(m, apply(m, X1))) = apply(m, apply(m, apply(X1, X1)))
% 0.60/0.79 apply(apply(l, X), Y) = apply(X, apply(Y, Y))
% 0.60/0.79 apply(apply(m, l), Y1) = apply(l, apply(Y1, Y1))
% 0.60/0.79 apply(m, X) = apply(X, X)
% 0.60/0.79 apply(m, apply(Y0, Y0)) = apply(apply(Y0, Y0), apply(m, Y0))
% 0.60/0.79 apply(m, apply(apply(b, Y0), Y1)) = apply(Y0, apply(Y1, apply(apply(b, Y0), Y1)))
% 0.60/0.79 apply(m, apply(m, apply(m, X1))) = apply(apply(apply(X1, X1), apply(X1, X1)), apply(apply(X1, X1), apply(X1, X1)))
% 0.60/0.79 apply(m, apply(m, apply(m, X1))) = apply(apply(apply(X1, X1), apply(X1, X1)), apply(m, apply(X1, X1)))
% 0.60/0.79 apply(Y0, apply(m, apply(l, Y0))) -> apply(m, apply(l, Y0))
% 0.60/0.79 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z))
% 0.60/0.79 apply(apply(apply(m, b), Y1), Y2) -> apply(b, apply(Y1, Y2))
% 0.60/0.79 apply(apply(l, Y0), Y1) -> apply(Y0, apply(m, Y1))
% 0.60/0.79 apply(apply(m, Y0), apply(Y0, Y0)) -> apply(m, apply(m, Y0))
% 0.60/0.79 apply(apply(m, apply(b, Y0)), Y2) -> apply(Y0, apply(apply(b, Y0), Y2))
% 0.60/0.79 apply(apply(m, apply(m, X0)), apply(apply(X0, X0), apply(X0, X0))) -> apply(m, apply(m, apply(X0, X0)))
% 0.60/0.79 apply(apply(m, apply(m, b)), Y1) -> apply(b, apply(apply(m, b), Y1))
% 0.60/0.79 apply(apply(m, apply(m, l)), apply(m, apply(m, apply(m, l)))) -> apply(m, apply(m, apply(m, l)))
% 0.60/0.79 apply(apply(m, l), Y0) -> apply(l, apply(m, Y0))
% 0.60/0.79 apply(b, apply(Y0, apply(apply(m, b), Y0))) -> apply(m, apply(apply(m, b), Y0))
% 0.60/0.79 apply(l, apply(l, apply(m, apply(m, l)))) -> apply(l, apply(m, apply(m, l)))
% 0.60/0.79 apply(l, apply(m, apply(m, l))) -> apply(m, apply(m, l))
% 0.60/0.79 f1(Y, Y) -> true__
% 0.60/0.79 f1(apply(combinator, Y), Y) -> false__
% 0.60/0.79 f1(apply(combinator, apply(m, X1)), apply(X1, X1)) -> false__
% 0.60/0.79 f1(apply(combinator, apply(m, apply(X0, X0))), apply(m, apply(m, X0))) -> false__
% 0.60/0.79 f1(apply(combinator, apply(m, apply(m, X1))), apply(apply(X1, X1), apply(X1, X1))) -> false__
% 0.60/0.79 f1(apply(m, combinator), combinator) -> false__
% 0.60/0.79 true__ -> false__
% 0.60/0.79 with the LPO induced by
% 0.60/0.79 l > combinator > b > m > apply > f1 > true__ > false__
% 0.60/0.79
% 0.60/0.79 % SZS output end Proof
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