%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : GRP023-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : moca.sh %s

% Computer : n022.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 10:51:54 EDT 2022

% Result   : Unsatisfiable 0.21s 0.41s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : GRP023-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14  % Command  : moca.sh %s
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jun 13 18:00:18 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.21/0.41  % SZS status Unsatisfiable
% 0.21/0.41  % SZS output start Proof
% 0.21/0.41  The input problem is unsatisfiable because
% 0.21/0.41  
% 0.21/0.41  [1] the following set of Horn clauses is unsatisfiable:
% 0.21/0.41  
% 0.21/0.41  	multiply(identity, X) = X
% 0.21/0.41  	multiply(inverse(X), X) = identity
% 0.21/0.41  	multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.21/0.41  	multiply(X, identity) = X
% 0.21/0.41  	multiply(X, inverse(X)) = identity
% 0.21/0.41  	inverse(identity) = identity ==> \bottom
% 0.21/0.41  
% 0.21/0.41  This holds because
% 0.21/0.41  
% 0.21/0.41  [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.21/0.41  
% 0.21/0.41  E:
% 0.21/0.41  	f1(identity) = false__
% 0.21/0.41  	f1(inverse(identity)) = true__
% 0.21/0.41  	multiply(X, identity) = X
% 0.21/0.41  	multiply(X, inverse(X)) = identity
% 0.21/0.41  	multiply(identity, X) = X
% 0.21/0.41  	multiply(inverse(X), X) = identity
% 0.21/0.41  	multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.21/0.41  G:
% 0.21/0.41  	true__ = false__
% 0.21/0.41  
% 0.21/0.41  This holds because
% 0.21/0.41  
% 0.21/0.41  [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.21/0.41  
% 0.21/0.41  
% 0.21/0.41  	f1(identity) -> false__
% 0.21/0.41  	f1(inverse(identity)) -> true__
% 0.21/0.41  	inverse(identity) -> identity
% 0.21/0.41  	inverse(inverse(Y1)) -> Y1
% 0.21/0.41  	multiply(X, identity) -> X
% 0.21/0.41  	multiply(X, inverse(X)) -> identity
% 0.21/0.41  	multiply(X1, inverse(multiply(Y0, X1))) -> inverse(Y0)
% 0.21/0.41  	multiply(X1, inverse(multiply(inverse(Y0), X1))) -> Y0
% 0.21/0.41  	multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity
% 0.21/0.41  	multiply(Y0, multiply(Y1, multiply(inverse(multiply(Y0, Y1)), X1))) -> X1
% 0.21/0.41  	multiply(Y0, multiply(inverse(Y0), Y2)) -> Y2
% 0.21/0.41  	multiply(identity, X) -> X
% 0.21/0.41  	multiply(inverse(X), X) -> identity
% 0.21/0.41  	multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 0.21/0.41  	multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1)
% 0.21/0.41  	multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1
% 0.21/0.41  	multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 0.21/0.41  	true__ -> false__
% 0.21/0.41  with the LPO induced by
% 0.21/0.41  	f1 > inverse > identity > multiply > true__ > false__
% 0.21/0.41  
% 0.21/0.41  % SZS output end Proof
% 0.21/0.41  
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