TSTP Solution File: COL051-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : COL051-1 : 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 00:37:11 EDT 2022
% Result : Unsatisfiable 0.15s 0.51s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : COL051-1 : TPTP v8.1.0. Released v1.0.0.
% 0.09/0.11 % Command : moca.sh %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Tue May 31 11:06:58 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.15/0.51 % SZS status Unsatisfiable
% 0.15/0.51 % SZS output start Proof
% 0.15/0.51 The input problem is unsatisfiable because
% 0.15/0.51
% 0.15/0.51 [1] the following set of Horn clauses is unsatisfiable:
% 0.15/0.51
% 0.15/0.51 response(mocking_bird, Y) = response(Y, Y)
% 0.15/0.51 response(compose(X, Y), W) = response(X, response(Y, W))
% 0.15/0.51 response(X, X) = X ==> \bottom
% 0.15/0.51
% 0.15/0.51 This holds because
% 0.15/0.51
% 0.15/0.51 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.15/0.51
% 0.15/0.51 E:
% 0.15/0.51 f1(X, X) = false__
% 0.15/0.51 f1(response(X, X), X) = true__
% 0.15/0.51 response(compose(X, Y), W) = response(X, response(Y, W))
% 0.15/0.51 response(mocking_bird, Y) = response(Y, Y)
% 0.15/0.51 G:
% 0.15/0.51 true__ = false__
% 0.15/0.51
% 0.15/0.51 This holds because
% 0.15/0.51
% 0.15/0.51 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.15/0.51
% 0.15/0.51 response(X0, response(X1, response(Y1, compose(compose(X0, X1), Y1)))) = response(mocking_bird, compose(compose(X0, X1), Y1))
% 0.15/0.51 response(X0, response(X1, response(Y1, response(Y2, compose(compose(compose(X0, X1), Y1), Y2))))) = response(mocking_bird, compose(compose(compose(X0, X1), Y1), Y2))
% 0.15/0.51 response(Y0, response(X0, response(X1, compose(Y0, compose(X0, X1))))) = response(mocking_bird, compose(Y0, compose(X0, X1)))
% 0.15/0.51 response(Y0, response(X0, response(X1, response(Y2, compose(Y0, compose(compose(X0, X1), Y2)))))) = response(mocking_bird, compose(Y0, compose(compose(X0, X1), Y2)))
% 0.15/0.51 response(Y0, response(X0, response(X1, response(Y2, compose(compose(Y0, compose(X0, X1)), Y2))))) = response(mocking_bird, compose(compose(Y0, compose(X0, X1)), Y2))
% 0.15/0.51 response(Y0, response(Y1, response(X0, response(X1, compose(compose(Y0, Y1), compose(X0, X1)))))) = response(mocking_bird, compose(compose(Y0, Y1), compose(X0, X1)))
% 0.15/0.51 response(mocking_bird, Y) = response(Y, Y)
% 0.15/0.51 response(mocking_bird, compose(Y0, Y1)) = response(Y0, response(Y1, compose(Y0, Y1)))
% 0.15/0.51 f1(X, X) -> false__
% 0.15/0.51 f1(response(X, X), X) -> true__
% 0.15/0.51 f1(response(X0, response(X1, compose(X0, X1))), compose(X0, X1)) -> true__
% 0.15/0.51 f1(response(X0, response(X1, response(Y1, compose(compose(X0, X1), Y1)))), compose(compose(X0, X1), Y1)) -> true__
% 0.15/0.51 f1(response(Y0, response(X0, response(X1, compose(Y0, compose(X0, X1))))), compose(Y0, compose(X0, X1))) -> true__
% 0.15/0.51 f1(response(mocking_bird, Y0), Y0) -> true__
% 0.15/0.51 f1(response(mocking_bird, compose(compose(mocking_bird, X1), X2)), response(X1, response(X2, compose(compose(mocking_bird, X1), X2)))) -> true__
% 0.15/0.51 f1(response(mocking_bird, compose(mocking_bird, X1)), response(X1, compose(mocking_bird, X1))) -> true__
% 0.15/0.51 f1(response(mocking_bird, compose(mocking_bird, compose(X0, X1))), response(X0, response(X1, compose(mocking_bird, compose(X0, X1))))) -> true__
% 0.15/0.51 false__ -> true__
% 0.15/0.51 response(compose(X, Y), W) -> response(X, response(Y, W))
% 0.15/0.51 with the LPO induced by
% 0.15/0.51 mocking_bird > f1 > response > compose > false__ > true__
% 0.15/0.51
% 0.15/0.51 % SZS output end Proof
% 0.15/0.51
%------------------------------------------------------------------------------