TSTP Solution File: COL070-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : COL070-1 : TPTP v8.1.0. Released v1.2.0.
% 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 00:37:28 EDT 2022
% Result : Unsatisfiable 37.24s 37.48s
% Output : Proof 37.24s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL070-1 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n020.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 12:45:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 37.24/37.48 % SZS status Unsatisfiable
% 37.24/37.48 % SZS output start Proof
% 37.24/37.48 The input problem is unsatisfiable because
% 37.24/37.48
% 37.24/37.48 [1] the following set of Horn clauses is unsatisfiable:
% 37.24/37.48
% 37.24/37.48 apply(apply(apply(n1, X), Y), Z) = apply(apply(apply(X, Y), Y), Z)
% 37.24/37.48 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 37.24/37.48 Y = apply(combinator, Y) ==> \bottom
% 37.24/37.48
% 37.24/37.48 This holds because
% 37.24/37.48
% 37.24/37.48 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 37.24/37.48
% 37.24/37.48 E:
% 37.24/37.48 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z))
% 37.24/37.48 apply(apply(apply(n1, X), Y), Z) = apply(apply(apply(X, Y), Y), Z)
% 37.24/37.48 f1(Y, Y) = true__
% 37.24/37.48 f1(apply(combinator, Y), Y) = false__
% 37.24/37.48 G:
% 37.24/37.48 true__ = false__
% 37.24/37.48
% 37.24/37.48 This holds because
% 37.24/37.48
% 37.24/37.48 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 37.24/37.48
% 37.24/37.48 apply(X0, apply(apply(Y1, Y1), Y2)) = apply(apply(apply(n1, apply(b, apply(b, X0))), Y1), Y2)
% 37.24/37.48 apply(apply(X0, apply(Y1, Y1)), Y2) = apply(apply(apply(n1, apply(b, X0)), Y1), Y2)
% 37.24/37.48 apply(apply(Y1, apply(Y1, Y1)), Y2) = apply(apply(apply(n1, apply(n1, b)), Y1), Y2)
% 37.24/37.48 apply(apply(apply(Y1, Y1), Y1), Y2) = apply(apply(apply(n1, n1), Y1), Y2)
% 37.24/37.48 apply(apply(apply(n1, X), Y), Z) = apply(apply(apply(X, Y), Y), Z)
% 37.24/37.48 apply(apply(apply(n1, apply(n1, X0)), Y1), Y2) = apply(apply(apply(n1, apply(X0, Y1)), Y1), Y2)
% 37.24/37.48 apply(apply(apply(n1, apply(n1, apply(b, b))), Y1), Y2) = apply(apply(Y1, Y1), apply(Y1, Y2))
% 37.24/37.48 apply(apply(apply(n1, apply(n1, n1)), Y1), Y2) = apply(apply(apply(n1, apply(Y1, Y1)), Y1), Y2)
% 37.24/37.48 apply(apply(apply(apply(X0, Y1), Y1), Y1), Y2) -> apply(apply(apply(n1, apply(n1, X0)), Y1), Y2)
% 37.24/37.48 apply(apply(apply(apply(n1, apply(b, b)), X1), Y1), Y2) -> apply(apply(X1, X1), apply(Y1, Y2))
% 37.24/37.48 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z))
% 37.24/37.48 apply(apply(apply(n1, b), Y1), Y2) -> apply(Y1, apply(Y1, Y2))
% 37.24/37.48 f1(Y, Y) -> true__
% 37.24/37.48 f1(apply(apply(apply(n1, apply(b, apply(b, combinator))), X1), X2), apply(apply(X1, X1), X2)) -> false__
% 37.24/37.48 f1(apply(combinator, Y), Y) -> false__
% 37.24/37.48 false__ -> true__
% 37.24/37.48 with the LPO induced by
% 37.24/37.48 apply > n1 > b > combinator > f1 > false__ > true__
% 37.24/37.48
% 37.24/37.48 % SZS output end Proof
% 37.24/37.48
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