%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : BOO027-1 : TPTP v8.1.0. Released v2.2.0.
% 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 : Thu Jul 14 23:46:34 EDT 2022

% Result   : Unknown 0.19s 0.44s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : BOO027-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12  % 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
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jun  1 17:55:45 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.43  % SZS status Satisfiable
% 0.19/0.43  % SZS output start Proof
% 0.19/0.43  The input problem is satisfiable because
% 0.19/0.43  
% 0.19/0.43  [1] the following set of Horn clauses is satisfiable:
% 0.19/0.43  
% 0.19/0.43  	multiply(X, add(Y, Z)) = add(multiply(Y, X), multiply(Z, X))
% 0.19/0.43  	add(X, inverse(X)) = one
% 0.19/0.43  	add(multiply(X, inverse(X)), add(multiply(X, Y), multiply(inverse(X), Y))) = Y
% 0.19/0.43  	add(multiply(X, inverse(Y)), add(multiply(X, Y), multiply(inverse(Y), Y))) = X
% 0.19/0.43  	add(multiply(X, inverse(Y)), add(multiply(X, X), multiply(inverse(Y), X))) = X
% 0.19/0.43  	add(a, a) = a ==> \bottom
% 0.19/0.43  
% 0.19/0.43  This holds because
% 0.19/0.43  
% 0.19/0.43  [2] the following E does not entail the following G (Claessen-Smallbone's transformation (2018)):
% 0.19/0.43  
% 0.19/0.43  E:
% 0.19/0.43  	add(X, inverse(X)) = one
% 0.19/0.43  	add(multiply(X, inverse(X)), add(multiply(X, Y), multiply(inverse(X), Y))) = Y
% 0.19/0.43  	add(multiply(X, inverse(Y)), add(multiply(X, X), multiply(inverse(Y), X))) = X
% 0.19/0.43  	add(multiply(X, inverse(Y)), add(multiply(X, Y), multiply(inverse(Y), Y))) = X
% 0.19/0.43  	f1(a) = true__
% 0.19/0.43  	f1(add(a, a)) = false__
% 0.19/0.43  	multiply(X, add(Y, Z)) = add(multiply(Y, X), multiply(Z, X))
% 0.19/0.43  G:
% 0.19/0.43  	true__ = false__
% 0.19/0.43  
% 0.19/0.43  This holds because
% 0.19/0.43  
% 0.19/0.43  [3] the following ground-complete ordered TRS entails E but does not entail G:
% 0.19/0.43  
% 0.19/0.43  
% 0.19/0.43  	add(X, inverse(X)) -> one
% 0.19/0.43  	add(multiply(Y, X), multiply(Z, X)) -> multiply(X, add(Y, Z))
% 0.19/0.43  	add(multiply(Y0, inverse(Y0)), multiply(Y1, one)) -> Y1
% 0.19/0.43  	add(multiply(Y0, inverse(Y1)), multiply(Y0, add(Y0, inverse(Y1)))) -> Y0
% 0.19/0.43  	add(multiply(Y0, inverse(Y1)), multiply(Y1, add(Y0, inverse(Y1)))) -> Y0
% 0.19/0.43  	f1(a) -> true__
% 0.19/0.43  	f1(add(a, a)) -> false__
% 0.19/0.43  with the LPO induced by
% 0.19/0.43  	inverse > one > add > multiply > a > f1 > false__ > true__
% 0.19/0.43  
% 0.19/0.43  % SZS output end Proof
% 0.19/0.43  
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