%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : GRP518-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : moca.sh %s

% Computer : n009.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 : Sat Jul 16 10:55:58 EDT 2022

% Result   : Unsatisfiable 2.93s 3.14s
% Output   : Proof 2.93s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP518-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12  % Command  : moca.sh %s
% 0.12/0.33  % Computer : n009.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
% 0.12/0.34  % DateTime : Tue Jun 14 12:43:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 2.93/3.14  % SZS status Unsatisfiable
% 2.93/3.14  % SZS output start Proof
% 2.93/3.14  The input problem is unsatisfiable because
% 2.93/3.14  
% 2.93/3.14  [1] the following set of Horn clauses is unsatisfiable:
% 2.93/3.14  
% 2.93/3.14  	multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) = C
% 2.93/3.14  	multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom
% 2.93/3.14  
% 2.93/3.14  This holds because
% 2.93/3.14  
% 2.93/3.14  [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.93/3.14  
% 2.93/3.14  E:
% 2.93/3.14  	f1(a2) = false__
% 2.93/3.14  	f1(multiply(multiply(inverse(b2), b2), a2)) = true__
% 2.93/3.14  	multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) = C
% 2.93/3.14  G:
% 2.93/3.14  	true__ = false__
% 2.93/3.14  
% 2.93/3.14  This holds because
% 2.93/3.14  
% 2.93/3.14  [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.93/3.14  
% 2.93/3.14  	multiply(Y0, X1) = multiply(multiply(inverse(Y3), multiply(inverse(Y2), X1)), multiply(Y0, multiply(Y3, Y2)))
% 2.93/3.14  	multiply(Y0, multiply(X2, Y1)) = multiply(multiply(inverse(X1), X2), multiply(Y0, multiply(X1, Y1)))
% 2.93/3.14  	f1(a2) -> false__
% 2.93/3.14  	f1(multiply(multiply(inverse(b2), b2), a2)) -> true__
% 2.93/3.14  	multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) -> C
% 2.93/3.14  	multiply(Y0, multiply(multiply(inverse(X2), Y2), multiply(multiply(inverse(multiply(Y0, X1)), X2), X1))) -> Y2
% 2.93/3.14  	multiply(multiply(inverse(Y0), Y0), Y2) -> Y2
% 2.93/3.14  	multiply(multiply(inverse(Y1), X1), multiply(multiply(inverse(X1), Y2), Y1)) -> Y2
% 2.93/3.14  	multiply(multiply(inverse(Y1), Y2), Y1) -> Y2
% 2.93/3.14  	multiply(multiply(inverse(Y3), Y1), multiply(multiply(inverse(multiply(Y1, Y2)), X1), multiply(Y3, Y2))) -> X1
% 2.93/3.14  	multiply(multiply(inverse(multiply(inverse(Y0), X1)), X2), X1) -> multiply(X2, Y0)
% 2.93/3.14  	multiply(multiply(inverse(multiply(inverse(multiply(Y0, Y1)), X1)), X2), X1) -> multiply(Y0, multiply(X2, Y1))
% 2.93/3.14  	true__ -> false__
% 2.93/3.14  with the LPO induced by
% 2.93/3.14  	b2 > inverse > multiply > a2 > f1 > true__ > false__
% 2.93/3.14  
% 2.93/3.14  % SZS output end Proof
% 2.93/3.14  
%------------------------------------------------------------------------------