%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : SYN035-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : moca.sh %s

% Computer : n025.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 09:13:09 EDT 2022

% Result   : Unsatisfiable 0.18s 0.38s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SYN035-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : moca.sh %s
% 0.12/0.33  % Computer : n025.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 : Mon Jul 11 21:41:47 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.38  % SZS status Unsatisfiable
% 0.18/0.38  % SZS output start Proof
% 0.18/0.38  The input problem is unsatisfiable because
% 0.18/0.38  
% 0.18/0.38  [1] the following set of Horn clauses is unsatisfiable:
% 0.18/0.38  
% 0.18/0.38  	p(A, B)
% 0.18/0.38  	p(f(A, B), f(A, B)) & p(B, f(A, B)) ==> q(A, B)
% 0.18/0.38  	q(f(A, B), f(A, B)) & q(A, f(A, B)) & p(f(A, B), f(A, B)) & p(B, f(A, B)) ==> \bottom
% 0.18/0.38  
% 0.18/0.38  This holds because
% 0.18/0.38  
% 0.18/0.38  [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.18/0.38  
% 0.18/0.38  E:
% 0.18/0.38  	f1(true__, A, B) = q(A, B)
% 0.18/0.38  	f2(p(B, f(A, B)), A, B) = true__
% 0.18/0.38  	f2(true__, A, B) = f1(p(f(A, B), f(A, B)), A, B)
% 0.18/0.38  	f3(true__) = false__
% 0.18/0.38  	f4(true__, A, B) = f3(q(f(A, B), f(A, B)))
% 0.18/0.38  	f5(true__, A, B) = f4(q(A, f(A, B)), A, B)
% 0.18/0.38  	f6(p(B, f(A, B)), A, B) = true__
% 0.18/0.38  	f6(true__, A, B) = f5(p(f(A, B), f(A, B)), A, B)
% 0.18/0.38  	p(A, B) = true__
% 0.18/0.38  G:
% 0.18/0.38  	true__ = false__
% 0.18/0.38  
% 0.18/0.38  This holds because
% 0.18/0.38  
% 0.18/0.38  [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.18/0.38  
% 0.18/0.38  
% 0.18/0.38  	f1(true__, Y1, Y0) -> true__
% 0.18/0.38  	f2(p(B, f(A, B)), A, B) -> true__
% 0.18/0.38  	f2(true__, A, B) -> f1(p(f(A, B), f(A, B)), A, B)
% 0.18/0.38  	f3(true__) -> false__
% 0.18/0.38  	f4(f1(true__, Y1, f(Y1, Y0)), Y1, Y0) -> true__
% 0.18/0.38  	f4(true__, A, B) -> f3(q(f(A, B), f(A, B)))
% 0.18/0.38  	f5(true__, A, B) -> f4(q(A, f(A, B)), A, B)
% 0.18/0.38  	f6(p(B, f(A, B)), A, B) -> true__
% 0.18/0.38  	f6(true__, A, B) -> f5(p(f(A, B), f(A, B)), A, B)
% 0.18/0.38  	false__ -> true__
% 0.18/0.38  	p(A, B) -> true__
% 0.18/0.38  	q(A, B) -> f1(true__, A, B)
% 0.18/0.38  with the LPO induced by
% 0.18/0.38  	f6 > f5 > f4 > q > f3 > f2 > f > p > f1 > false__ > true__
% 0.18/0.38  
% 0.18/0.38  % SZS output end Proof
% 0.18/0.38  
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