%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : SYN303-10 : TPTP v8.1.0. Released v7.5.0.
% 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 09:15:08 EDT 2022

% Result   : Unknown 0.18s 0.40s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SYN303-10 : TPTP v8.1.0. Released v7.5.0.
% 0.11/0.12  % Command  : moca.sh %s
% 0.12/0.33  % Computer : n004.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 : Tue Jul 12 08:56:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.40  % SZS status Satisfiable
% 0.18/0.40  % SZS output start Proof
% 0.18/0.40  The input problem is satisfiable because
% 0.18/0.40  
% 0.18/0.40  [1] the following set of Horn clauses is satisfiable:
% 0.18/0.40  
% 0.18/0.40  	ifeq(A, A, B, C) = B
% 0.18/0.40  	p(X, X) = true
% 0.18/0.40  	ifeq(p(X, Y), true, p(Y, X), true) = true
% 0.18/0.40  	ifeq(p(f(X), f(Y)), true, p(X, Y), true) = true
% 0.18/0.40  	ifeq(p(X, Y), true, p(f(X), f(Y)), true) = true
% 0.18/0.40  	p(a, f(X)) = true ==> \bottom
% 0.18/0.40  
% 0.18/0.40  This holds because
% 0.18/0.40  
% 0.18/0.40  [2] the following E does not entail the following G (Claessen-Smallbone's transformation (2018)):
% 0.18/0.40  
% 0.18/0.40  E:
% 0.18/0.40  	f1(p(a, f(X))) = false__
% 0.18/0.40  	f1(true) = true__
% 0.18/0.40  	ifeq(A, A, B, C) = B
% 0.18/0.40  	ifeq(p(X, Y), true, p(Y, X), true) = true
% 0.18/0.40  	ifeq(p(X, Y), true, p(f(X), f(Y)), true) = true
% 0.18/0.40  	ifeq(p(f(X), f(Y)), true, p(X, Y), true) = true
% 0.18/0.40  	p(X, X) = true
% 0.18/0.40  G:
% 0.18/0.40  	true__ = false__
% 0.18/0.40  
% 0.18/0.40  This holds because
% 0.18/0.40  
% 0.18/0.40  [3] the following ground-complete ordered TRS entails E but does not entail G:
% 0.18/0.40  
% 0.18/0.40  
% 0.18/0.40  	f1(p(a, f(X))) -> false__
% 0.18/0.40  	f1(true) -> true__
% 0.18/0.40  	ifeq(A, A, B, C) -> B
% 0.18/0.40  	ifeq(p(X, Y), true, p(Y, X), true) -> true
% 0.18/0.40  	ifeq(p(X, Y), true, p(f(X), f(Y)), true) -> true
% 0.18/0.40  	ifeq(p(f(X), f(Y)), true, p(X, Y), true) -> true
% 0.18/0.40  	p(X, X) -> true
% 0.18/0.40  with the LPO induced by
% 0.18/0.40  	a > f1 > f > p > true > ifeq > true__ > false__
% 0.18/0.40  
% 0.18/0.40  % SZS output end Proof
% 0.18/0.40  
%------------------------------------------------------------------------------