TSTP Solution File: COL050-1 by Moca---0.1

View Problem - Process Solution

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% File     : Moca---0.1
% Problem  : COL050-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : moca.sh %s

% Computer : n029.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 0.46s 0.64s
% Output   : Proof 0.46s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : COL050-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : moca.sh %s
% 0.12/0.33  % Computer : n029.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue May 31 07:34:29 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.46/0.64  % SZS status Unsatisfiable
% 0.46/0.64  % SZS output start Proof
% 0.46/0.64  The input problem is unsatisfiable because
% 0.46/0.64  
% 0.46/0.64  [1] the following set of Horn clauses is unsatisfiable:
% 0.46/0.64  
% 0.46/0.64  	response(mocking_bird, Y) = response(Y, Y)
% 0.46/0.64  	response(compose(X, Y), W) = response(X, response(Y, W))
% 0.46/0.64  	response(a, Y) = Y ==> \bottom
% 0.46/0.64  
% 0.46/0.64  This holds because
% 0.46/0.64  
% 0.46/0.64  [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.46/0.64  
% 0.46/0.64  E:
% 0.46/0.64  	f1(Y, Y) = false__
% 0.46/0.64  	f1(response(a, Y), Y) = true__
% 0.46/0.64  	response(compose(X, Y), W) = response(X, response(Y, W))
% 0.46/0.64  	response(mocking_bird, Y) = response(Y, Y)
% 0.46/0.64  G:
% 0.46/0.64  	true__ = false__
% 0.46/0.64  
% 0.46/0.64  This holds because
% 0.46/0.64  
% 0.46/0.64  [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.46/0.64  
% 0.46/0.64  	response(X0, response(X1, response(Y1, compose(compose(X0, X1), Y1)))) = response(mocking_bird, compose(compose(X0, X1), Y1))
% 0.46/0.64  	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))
% 0.46/0.64  	response(Y0, response(X0, response(X1, compose(Y0, compose(X0, X1))))) = response(mocking_bird, compose(Y0, compose(X0, X1)))
% 0.46/0.64  	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)))
% 0.46/0.64  	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))
% 0.46/0.64  	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)))
% 0.46/0.64  	response(mocking_bird, Y) = response(Y, Y)
% 0.46/0.64  	response(mocking_bird, compose(Y0, Y1)) = response(Y0, response(Y1, compose(Y0, Y1)))
% 0.46/0.64  	f1(Y, Y) -> false__
% 0.46/0.64  	f1(response(a, Y), Y) -> true__
% 0.46/0.64  	f1(response(mocking_bird, compose(a, X1)), response(X1, compose(a, X1))) -> true__
% 0.46/0.64  	f1(response(mocking_bird, compose(a, compose(X0, X1))), response(X0, response(X1, compose(a, compose(X0, X1))))) -> true__
% 0.46/0.64  	f1(response(mocking_bird, compose(compose(a, X1), X2)), response(X1, response(X2, compose(compose(a, X1), X2)))) -> true__
% 0.46/0.64  	response(compose(X, Y), W) -> response(X, response(Y, W))
% 0.46/0.64  	true__ -> false__
% 0.46/0.64  with the LPO induced by
% 0.46/0.64  	mocking_bird > f1 > response > compose > a > true__ > false__
% 0.46/0.64  
% 0.46/0.64  % SZS output end Proof
% 0.46/0.64  
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