%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : SYN079-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : moca.sh %s

% Computer : n003.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 09:13:43 EDT 2022

% Result   : Unsatisfiable 0.71s 0.88s
% Output   : Proof 0.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN079-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : moca.sh %s
% 0.13/0.33  % Computer : n003.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 : Tue Jul 12 04:43:00 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.71/0.88  % SZS status Unsatisfiable
% 0.71/0.88  % SZS output start Proof
% 0.71/0.88  The input problem is unsatisfiable because
% 0.71/0.88  
% 0.71/0.88  [1] the following set of Horn clauses is unsatisfiable:
% 0.71/0.88  
% 0.71/0.88  	big_f(f(a, b), f(b, c))
% 0.71/0.88  	big_f(f(b, c), f(a, c))
% 0.71/0.88  	big_f(X, Y) & big_f(Y, Z) ==> big_f(X, Z)
% 0.71/0.88  	big_f(f(a, b), f(a, c)) ==> \bottom
% 0.71/0.88  
% 0.71/0.88  This holds because
% 0.71/0.88  
% 0.71/0.88  [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.71/0.88  
% 0.71/0.88  E:
% 0.71/0.88  	big_f(f(a, b), f(b, c)) = true__
% 0.71/0.88  	big_f(f(b, c), f(a, c)) = true__
% 0.71/0.88  	f1(true__, X, Z) = big_f(X, Z)
% 0.71/0.88  	f2(big_f(Y, Z), X, Y, Z) = true__
% 0.71/0.88  	f2(true__, X, Y, Z) = f1(big_f(X, Y), X, Z)
% 0.71/0.88  	f3(big_f(f(a, b), f(a, c))) = true__
% 0.71/0.88  	f3(true__) = false__
% 0.71/0.88  G:
% 0.71/0.88  	true__ = false__
% 0.71/0.88  
% 0.71/0.88  This holds because
% 0.71/0.88  
% 0.71/0.88  [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.71/0.88  
% 0.71/0.88  
% 0.71/0.88  	big_f(X, Z) -> f1(true__, X, Z)
% 0.71/0.88  	big_f(f(a, b), f(b, c)) -> true__
% 0.71/0.88  	big_f(f(b, c), f(a, c)) -> true__
% 0.71/0.88  	f1(f1(true__, Y2, f(a, b)), Y2, f(a, c)) -> true__
% 0.71/0.88  	f1(f1(true__, Y2, f(a, b)), Y2, f(b, c)) -> true__
% 0.71/0.88  	f1(f1(true__, Y2, f(b, c)), Y2, f(a, c)) -> true__
% 0.71/0.88  	f1(true__, f(a, b), f(a, c)) -> true__
% 0.71/0.88  	f1(true__, f(a, b), f(b, c)) -> true__
% 0.71/0.88  	f1(true__, f(b, c), f(a, c)) -> true__
% 0.71/0.88  	f2(big_f(Y, Z), X, Y, Z) -> true__
% 0.71/0.88  	f2(f1(true__, Y0, Y1), Y2, Y0, Y1) -> true__
% 0.71/0.88  	f2(true__, X, Y, Z) -> f1(big_f(X, Y), X, Z)
% 0.71/0.88  	f3(big_f(f(a, b), f(a, c))) -> true__
% 0.71/0.88  	f3(f1(true__, f(a, b), f(a, c))) -> true__
% 0.71/0.88  	f3(true__) -> false__
% 0.71/0.88  	false__ -> true__
% 0.71/0.88  with the LPO induced by
% 0.71/0.88  	f3 > f2 > big_f > f1 > c > b > a > f > false__ > true__
% 0.71/0.88  
% 0.71/0.88  % SZS output end Proof
% 0.71/0.88  
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