%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : SWV021-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : moca.sh %s

% Computer : n026.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 : Wed Jul 20 20:40:59 EDT 2022

% Result   : Unknown 3.29s 3.50s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV021-10 : TPTP v8.1.0. Released v7.5.0.
% 0.12/0.13  % Command  : moca.sh %s
% 0.13/0.34  % Computer : n026.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 : Wed Jun 15 12:46:52 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 3.29/3.50  % SZS status Satisfiable
% 3.29/3.50  % SZS output start Proof
% 3.29/3.50  The input problem is satisfiable because
% 3.29/3.50  
% 3.29/3.50  [1] the following set of Horn clauses is satisfiable:
% 3.29/3.50  
% 3.29/3.50  	ifeq(A, A, B, C) = B
% 3.29/3.50  	n0 = s(X) ==> \bottom
% 3.29/3.50  	ifeq(s(X), s(Y), X, Y) = Y
% 3.29/3.50  	add(n0, Y) = Y
% 3.29/3.50  	add(s(X), Y) = s(add(X, Y))
% 3.29/3.50  	add(X, Y) = add(Y, X)
% 3.29/3.50  
% 3.29/3.50  This holds because
% 3.29/3.50  
% 3.29/3.50  [2] the following E does not entail the following G (Claessen-Smallbone's transformation (2018)):
% 3.29/3.50  
% 3.29/3.50  E:
% 3.29/3.50  	add(X, Y) = add(Y, X)
% 3.29/3.50  	add(n0, Y) = Y
% 3.29/3.50  	add(s(X), Y) = s(add(X, Y))
% 3.29/3.50  	f1(n0) = false__
% 3.29/3.50  	f1(s(X)) = true__
% 3.29/3.50  	ifeq(A, A, B, C) = B
% 3.29/3.50  	ifeq(s(X), s(Y), X, Y) = Y
% 3.29/3.50  G:
% 3.29/3.50  	true__ = false__
% 3.29/3.50  
% 3.29/3.50  This holds because
% 3.29/3.50  
% 3.29/3.50  [3] the following ground-complete ordered TRS entails E but does not entail G:
% 3.29/3.50  
% 3.29/3.50  	add(X, Y) = add(Y, X)
% 3.29/3.50  	s(add(Y1, Y0)) = s(add(Y0, Y1))
% 3.29/3.50  	add(Y1, n0) -> Y1
% 3.29/3.50  	add(Y1, s(Y0)) -> s(add(Y1, Y0))
% 3.29/3.50  	add(n0, Y) -> Y
% 3.29/3.50  	add(s(X), Y) -> s(add(X, Y))
% 3.29/3.50  	f1(n0) -> false__
% 3.29/3.50  	f1(s(X)) -> true__
% 3.29/3.50  	ifeq(A, A, B, C) -> B
% 3.29/3.50  	ifeq(s(X), s(Y), X, Y) -> Y
% 3.29/3.50  with the LPO induced by
% 3.29/3.50  	ifeq > add > s > n0 > f1 > true__ > false__
% 3.29/3.50  
% 3.29/3.50  % SZS output end Proof
% 3.29/3.50  
%------------------------------------------------------------------------------