%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : SYN083-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : moca.sh %s

% Computer : n004.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 21 09:13:46 EDT 2022

% Result   : Unsatisfiable 0.13s 0.38s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYN083-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : moca.sh %s
% 0.13/0.33  % Computer : n004.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jul 11 14:09:52 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.38  % SZS status Unsatisfiable
% 0.13/0.38  % SZS output start Proof
% 0.13/0.38  The input problem is unsatisfiable because
% 0.13/0.38  
% 0.13/0.38  [1] the following set of Horn clauses is unsatisfiable:
% 0.13/0.38  
% 0.13/0.38  	f(X, f(Y, Z)) = f(f(X, Y), Z)
% 0.13/0.38  	f(a, f(b, f(c, d))) = f(f(f(a, b), c), d) ==> \bottom
% 0.13/0.38  
% 0.13/0.38  This holds because
% 0.13/0.38  
% 0.13/0.38  [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.13/0.38  
% 0.13/0.38  E:
% 0.13/0.38  	f(X, f(Y, Z)) = f(f(X, Y), Z)
% 0.13/0.38  	f1(f(a, f(b, f(c, d)))) = true__
% 0.13/0.38  	f1(f(f(f(a, b), c), d)) = false__
% 0.13/0.38  G:
% 0.13/0.38  	true__ = false__
% 0.13/0.38  
% 0.13/0.38  This holds because
% 0.13/0.38  
% 0.13/0.38  [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.13/0.38  
% 0.13/0.38  
% 0.13/0.38  	f(f(X, Y), Z) -> f(X, f(Y, Z))
% 0.13/0.38  	f1(f(a, f(b, f(c, d)))) -> true__
% 0.13/0.38  	f1(f(f(f(a, b), c), d)) -> false__
% 0.13/0.38  	true__ -> false__
% 0.13/0.38  with the LPO induced by
% 0.13/0.38  	d > c > b > a > f1 > f > true__ > false__
% 0.13/0.38  
% 0.13/0.38  % SZS output end Proof
% 0.13/0.38  
%------------------------------------------------------------------------------