%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : SYN721-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Thu Jul 21 09:18:30 EDT 2022

% Result   : Unsatisfiable 0.61s 0.83s
% Output   : Proof 0.61s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN721-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13  % Command  : moca.sh %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 15:50:10 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.61/0.83  % SZS status Unsatisfiable
% 0.61/0.83  % SZS output start Proof
% 0.61/0.83  The input problem is unsatisfiable because
% 0.61/0.83  
% 0.61/0.83  [1] the following set of Horn clauses is unsatisfiable:
% 0.61/0.83  
% 0.61/0.83  	r(a, b)
% 0.61/0.83  	r(A, B) ==> q(A, A)
% 0.61/0.83  	q(A, B) ==> r(C, B)
% 0.61/0.83  	q(A, a) & r(b, A) ==> \bottom
% 0.61/0.83  
% 0.61/0.83  This holds because
% 0.61/0.83  
% 0.61/0.83  [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.61/0.83  
% 0.61/0.83  E:
% 0.61/0.83  	f1(r(A, B), A) = true__
% 0.61/0.83  	f1(true__, A) = q(A, A)
% 0.61/0.83  	f2(q(A, B), C, B) = true__
% 0.61/0.83  	f2(true__, C, B) = r(C, B)
% 0.61/0.83  	f3(true__) = false__
% 0.61/0.83  	f4(r(b, A), A) = true__
% 0.61/0.83  	f4(true__, A) = f3(q(A, a))
% 0.61/0.83  	r(a, b) = true__
% 0.61/0.83  G:
% 0.61/0.83  	true__ = false__
% 0.61/0.83  
% 0.61/0.83  This holds because
% 0.61/0.83  
% 0.61/0.83  [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.61/0.83  
% 0.61/0.83  
% 0.61/0.83  	f1(f2(true__, Y0, Y1), Y0) -> true__
% 0.61/0.83  	f1(r(A, B), A) -> true__
% 0.61/0.83  	f1(true__, Y0) -> true__
% 0.61/0.83  	f1(true__, a) -> true__
% 0.61/0.83  	f2(f1(true__, Y1), Y2, Y1) -> true__
% 0.61/0.83  	f2(q(A, B), C, B) -> true__
% 0.61/0.83  	f2(true__, Y1, a) -> true__
% 0.61/0.83  	f2(true__, a, b) -> true__
% 0.61/0.83  	f3(f1(true__, a)) -> f4(true__, a)
% 0.61/0.83  	f3(q(A, a)) -> f4(true__, A)
% 0.61/0.83  	f3(true__) -> false__
% 0.61/0.83  	f4(f2(true__, b, Y0), Y0) -> true__
% 0.61/0.83  	f4(r(b, A), A) -> true__
% 0.61/0.83  	f4(true__, a) -> false__
% 0.61/0.83  	false__ -> true__
% 0.61/0.83  	q(A, A) -> f1(true__, A)
% 0.61/0.83  	r(C, B) -> f2(true__, C, B)
% 0.61/0.83  	r(a, b) -> true__
% 0.61/0.83  with the LPO induced by
% 0.61/0.83  	f3 > f4 > q > f1 > a > b > r > f2 > false__ > true__
% 0.61/0.83  
% 0.61/0.83  % SZS output end Proof
% 0.61/0.83  
%------------------------------------------------------------------------------