TSTP Solution File: COL008-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : COL008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n032.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 00:36:47 EDT 2022
% Result : Unsatisfiable 0.53s 0.77s
% Output : Proof 0.53s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : COL008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.11 % Command : moca.sh %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Tue May 31 12:23:58 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.53/0.77 % SZS status Unsatisfiable
% 0.53/0.77 % SZS output start Proof
% 0.53/0.77 The input problem is unsatisfiable because
% 0.53/0.77
% 0.53/0.77 [1] the following set of Horn clauses is unsatisfiable:
% 0.53/0.77
% 0.53/0.77 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 0.53/0.77 apply(m, X) = apply(X, X)
% 0.53/0.77 Y = apply(combinator, Y) ==> \bottom
% 0.53/0.77
% 0.53/0.77 This holds because
% 0.53/0.77
% 0.53/0.77 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.53/0.77
% 0.53/0.77 E:
% 0.53/0.77 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 0.53/0.77 apply(m, X) = apply(X, X)
% 0.53/0.77 f1(Y, Y) = true__
% 0.53/0.77 f1(apply(combinator, Y), Y) = false__
% 0.53/0.77 G:
% 0.53/0.77 true__ = false__
% 0.53/0.77
% 0.53/0.77 This holds because
% 0.53/0.77
% 0.53/0.77 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.53/0.77
% 0.53/0.77 apply(X0, apply(X1, apply(Y1, apply(apply(b, apply(apply(b, X0), X1)), Y1)))) = apply(m, apply(apply(b, apply(apply(b, X0), X1)), Y1))
% 0.53/0.77 apply(Y0, apply(X0, apply(X1, apply(apply(b, Y0), apply(apply(b, X0), X1))))) = apply(m, apply(apply(b, Y0), apply(apply(b, X0), X1)))
% 0.53/0.77 apply(apply(m, apply(apply(b, apply(b, Y0)), X1)), Y2) = apply(Y0, apply(apply(X1, apply(apply(b, apply(b, Y0)), X1)), Y2))
% 0.53/0.77 apply(m, X) = apply(X, X)
% 0.53/0.77 apply(m, apply(apply(b, Y0), Y1)) = apply(Y0, apply(Y1, apply(apply(b, Y0), Y1)))
% 0.53/0.77 apply(Y0, apply(apply(b, Y0), apply(m, apply(b, Y0)))) -> apply(m, apply(m, apply(b, Y0)))
% 0.53/0.77 apply(Y0, apply(b, apply(X0, apply(apply(b, Y0), apply(apply(m, b), X0))))) -> apply(m, apply(apply(b, Y0), apply(apply(m, b), X0)))
% 0.53/0.77 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z))
% 0.53/0.77 apply(apply(apply(m, apply(apply(m, b), X1)), Y1), Y2) -> apply(apply(X1, apply(apply(m, b), X1)), apply(Y1, Y2))
% 0.53/0.77 apply(apply(apply(m, b), Y1), Y2) -> apply(b, apply(Y1, Y2))
% 0.53/0.77 apply(apply(m, apply(b, Y0)), Y2) -> apply(Y0, apply(apply(b, Y0), Y2))
% 0.53/0.77 apply(apply(m, apply(m, b)), Y1) -> apply(b, apply(apply(m, b), Y1))
% 0.53/0.77 apply(b, apply(X0, apply(X1, apply(apply(m, b), apply(apply(b, X0), X1))))) -> apply(m, apply(apply(m, b), apply(apply(b, X0), X1)))
% 0.53/0.77 apply(b, apply(X0, apply(Y1, apply(apply(b, apply(apply(m, b), X0)), Y1)))) -> apply(m, apply(apply(b, apply(apply(m, b), X0)), Y1))
% 0.53/0.77 apply(b, apply(Y0, apply(apply(m, b), Y0))) -> apply(m, apply(apply(m, b), Y0))
% 0.53/0.77 apply(b, apply(apply(m, b), apply(m, apply(m, b)))) -> apply(m, apply(m, apply(m, b)))
% 0.53/0.77 f1(Y, Y) -> true__
% 0.53/0.77 f1(apply(combinator, Y), Y) -> false__
% 0.53/0.77 f1(apply(m, apply(apply(b, combinator), X1)), apply(X1, apply(apply(b, combinator), X1))) -> false__
% 0.53/0.77 f1(apply(m, apply(m, apply(b, combinator))), apply(apply(b, combinator), apply(m, apply(b, combinator)))) -> false__
% 0.53/0.77 true__ -> false__
% 0.53/0.77 with the LPO induced by
% 0.53/0.77 b > f1 > apply > m > combinator > true__ > false__
% 0.53/0.77
% 0.53/0.77 % SZS output end Proof
% 0.53/0.77
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