TSTP Solution File: ALG301-1 by CiME---2.01

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : ALG301-1 : TPTP v6.0.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n065.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.11.2.el6.x86_64
% CPULimit : 300s
% DateTime : Tue Jun 10 00:18:25 EDT 2014

% Result   : Timeout 300.03s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : ALG301-1 : TPTP v6.0.0. Released v4.1.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n065.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Fri Jun  6 08:04:38 CDT 2014
% % CPUTime  : 300.03 
% Processing problem /tmp/CiME_55430_n065.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " tptp0,tptp1 : constant;  product : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% product(A,product(A,product(A,product(B,product(C,A))))) = B;
% ";
% 
% let s1 = status F "
% tptp0 lr_lex;
% tptp1 lr_lex;
% product lr_lex;
% ";
% 
% let p1 = precedence F "
% product > tptp1 > tptp0";
% 
% let s2 = status F "
% tptp0 mul;
% tptp1 mul;
% product mul;
% ";
% 
% let p2 = precedence F "
% product > tptp1 = tptp0";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " tptp1 = tptp0;"
% ;
% (*
% let Red_Axioms = normalize_equations Defining_rules Axioms;
% 
% let Red_Conjectures =  normalize_equations Defining_rules Conjectures;
% *)
% #time on;
% 
% let res = prove_conj_by_ordered_completion o Axioms Conjectures;
% 
% #time off;
% 
% 
% let status = if res then "unsatisfiable" else "satisfiable";
% #quit;
% Verbose level is now 1
% 
% F : signature = <signature>
% X : variable_set = <variable set>
% 
% Axioms : (F,X) equations = { product(A,product(A,product(A,product(B,
% product(C,A))))) =
% B } (1 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { tptp1 = tptp0 } (1 equation(s))
% time is now on
% 
% Initializing completion ...
% New rule produced :
% [1] product(A,product(A,product(A,product(B,product(C,A))))) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 1
% New rule produced :
% [2]
% product(product(A,product(B,product(C,A))),product(product(A,product(B,
% product(C,A))),
% product(product(A,product(B,
% product(C,A))),B)))
% -> A
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3]
% product(product(A,product(A,product(B,product(C,A)))),product(product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)))) ->
% V_3
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [4]
% product(product(product(A,product(B,product(C,A))),B),product(product(
% product(A,
% product(B,
% product(C,A))),B),
% product(product(
% product(A,
% product(B,
% product(C,A))),B),A)))
% -> product(A,product(B,product(C,A)))
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [5]
% product(product(product(product(A,product(B,product(C,A))),B),A),product(
% product(
% product(
% product(A,
% product(B,
% product(C,A))),B),A),
% product(
% product(
% product(
% product(A,
% product(B,
% product(C,A))),B),A),
% product(A,
% product(B,
% product(C,A))))))
% -> product(product(A,product(B,product(C,A))),B)
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6]
% product(product(product(A,product(A,product(B,product(C,A)))),product(V_3,B)),
% product(product(product(A,product(A,product(B,product(C,A)))),product(V_3,B)),
% product(product(product(A,product(A,product(B,product(C,A)))),product(V_3,B)),V_3)))
% -> product(A,product(A,product(B,product(C,A))))
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7]
% product(product(A,product(A,product(product(B,product(B,product(C,product(V_3,B)))),
% product(V_4,A)))),product(product(A,product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),
% product(product(A,product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C)))
% -> B
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8]
% product(product(product(A,product(B,product(C,A))),product(product(A,
% product(B,
% product(C,A))),B)),
% product(product(product(A,product(B,product(C,A))),product(product(A,
% product(B,
% product(C,A))),B)),
% product(product(product(A,product(B,product(C,A))),product(product(A,
% product(B,
% product(C,A))),B)),
% product(V_3,A)))) -> V_3
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9]
% product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(V_3,B)),V_3),product(product(product(product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),V_3),
% product(product(product(product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),V_3),
% product(A,product(A,product(B,product(C,A)))))))
% -> product(product(A,product(A,product(B,product(C,A)))),product(V_3,B))
% Current number of equations to process: 119
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10]
% product(product(product(A,product(A,product(product(B,product(B,product(C,
% product(V_3,B)))),
% product(V_4,A)))),C),product(product(
% product(A,
% product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C),
% product(product(
% product(A,
% product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C),B)))
% ->
% product(A,product(A,product(product(B,product(B,product(C,product(V_3,B)))),
% product(V_4,A))))
% Current number of equations to process: 155
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11]
% product(product(product(product(product(A,product(B,product(C,A))),B),A),
% product(A,product(B,product(C,A)))),product(product(product(product(
% product(A,
% product(B,
% product(C,A))),B),A),
% product(A,product(B,
% product(C,A)))),
% product(product(product(product(
% product(A,
% product(B,
% product(C,A))),B),A),
% product(A,product(B,
% product(C,A)))),
% product(product(A,product(B,
% product(C,A))),B))))
% -> product(product(product(A,product(B,product(C,A))),B),A)
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12]
% product(product(product(product(A,product(B,product(C,A))),product(product(A,
% product(B,
% product(C,A))),B)),
% product(V_3,A)),product(product(product(product(A,product(B,product(C,A))),
% product(product(A,product(B,product(C,A))),B)),
% product(V_3,A)),product(product(product(
% product(A,
% product(B,
% product(C,A))),
% product(
% product(A,
% product(B,
% product(C,A))),B)),
% product(V_3,A)),V_3)))
% ->
% product(product(A,product(B,product(C,A))),product(product(A,product(B,
% product(C,A))),B))
% Current number of equations to process: 227
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13]
% product(product(product(A,product(A,product(B,product(C,A)))),product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B))),
% product(product(product(A,product(A,product(B,product(C,A)))),product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B))),
% product(product(product(A,product(A,product(B,product(C,A)))),product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B))),
% product(V_4,V_3)))) -> V_4
% Current number of equations to process: 274
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14]
% product(product(product(product(A,product(B,product(C,A))),B),product(
% product(
% product(A,
% product(B,
% product(C,A))),B),A)),
% product(product(product(product(A,product(B,product(C,A))),B),product(
% product(
% product(A,
% product(B,
% product(C,A))),B),A)),
% product(product(product(product(A,product(B,product(C,A))),B),product(
% product(
% product(A,
% product(B,
% product(C,A))),B),A)),
% product(V_3,product(A,product(B,product(C,A))))))) -> V_3
% Current number of equations to process: 338
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15]
% product(product(A,product(A,product(product(product(B,product(C,product(V_3,B))),
% product(product(B,product(C,product(V_3,B))),C)),
% product(V_4,A)))),product(product(A,product(A,
% product(
% product(
% product(B,
% product(C,
% product(V_3,B))),
% product(
% product(B,
% product(C,
% product(V_3,B))),C)),
% product(V_4,A)))),
% product(product(A,product(A,
% product(
% product(
% product(B,
% product(C,
% product(V_3,B))),
% product(
% product(B,
% product(C,
% product(V_3,B))),C)),
% product(V_4,A)))),B)))
% -> product(B,product(C,product(V_3,B)))
% Current number of equations to process: 386
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16]
% product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(V_3,B)),product(product(product(A,product(A,product(B,
% product(C,A)))),
% product(V_3,B)),V_3)),product(
% product(
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),
% product(
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),V_3)),
% product(
% product(
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),
% product(
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),V_3)),B)))
% -> A
% Current number of equations to process: 460
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17]
% product(product(product(product(A,product(A,product(product(B,product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C),B),product(
% product(
% product(
% product(A,
% product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C),B),
% product(
% product(
% product(
% product(A,
% product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C),B),
% product(A,
% product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))))))
% ->
% product(product(A,product(A,product(product(B,product(B,product(C,product(V_3,B)))),
% product(V_4,A)))),C)
% Current number of equations to process: 543
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18]
% product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(product(A,product(A,product(B,product(C,A)))),
% product(V_3,B))),product(V_4,V_3)),product(product(product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B))),
% product(V_4,V_3)),
% product(product(product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B))),
% product(V_4,V_3)),V_4)))
% ->
% product(product(A,product(A,product(B,product(C,A)))),product(product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)))
% Current number of equations to process: 623
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19]
% product(product(product(A,product(A,product(B,product(C,A)))),product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(
% product(V_3,
% product(V_3,
% product(V_4,
% product(V_5,V_3)))),B))),
% product(product(product(A,product(A,product(B,product(C,A)))),product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(
% product(V_3,
% product(V_3,
% product(V_4,
% product(V_5,V_3)))),B))),
% product(product(product(A,product(A,product(B,product(C,A)))),product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(
% product(V_3,
% product(V_3,
% product(V_4,
% product(V_5,V_3)))),B))),V_4)))
% -> V_3
% Current number of equations to process: 723
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20]
% product(product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(V_3,B)),V_3),product(A,product(A,product(B,
% product(C,A))))),
% product(product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(V_3,B)),V_3),product(A,product(A,product(B,
% product(C,A))))),
% product(product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(V_3,B)),V_3),product(A,product(A,product(B,
% product(C,A))))),
% product(product(A,product(A,product(B,product(C,A)))),product(V_3,B))))) ->
% product(product(product(A,product(A,product(B,product(C,A)))),product(V_3,B)),V_3)
% Current number of equations to process: 837
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21]
% product(product(product(product(product(A,product(B,product(C,A))),product(
% product(A,
% product(B,
% product(C,A))),B)),
% product(V_3,A)),V_3),product(product(product(product(
% product(A,
% product(B,
% product(C,A))),
% product(
% product(A,
% product(B,
% product(C,A))),B)),
% product(V_3,A)),V_3),
% product(product(product(product(
% product(A,
% product(B,
% product(C,A))),
% product(
% product(A,
% product(B,
% product(C,A))),B)),
% product(V_3,A)),V_3),
% product(product(A,product(B,product(C,A))),
% product(product(A,product(B,product(C,A))),B)))))
% ->
% product(product(product(A,product(B,product(C,A))),product(product(A,
% product(B,
% product(C,A))),B)),
% product(V_3,A))
% Current number of equations to process: 932
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22]
% product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(V_3,B)),product(product(product(A,product(A,product(B,
% product(C,A)))),
% product(V_3,B)),V_3)),product(
% product(
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),
% product(
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),V_3)),
% product(
% product(
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),
% product(
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),V_3)),
% product(V_4,
% product(A,
% product(A,
% product(B,
% product(C,A))))))))
% -> V_4
% Current number of equations to process: 1036
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [23]
% product(product(A,product(A,product(product(product(B,product(B,product(C,
% product(V_3,B)))),
% product(product(B,product(B,product(C,
% product(V_3,B)))),
% product(V_4,C))),product(V_5,A)))),
% product(product(A,product(A,product(product(product(B,product(B,product(C,
% product(V_3,B)))),
% product(product(B,product(B,product(C,
% product(V_3,B)))),
% product(V_4,C))),product(V_5,A)))),
% product(product(A,product(A,product(product(product(B,product(B,product(C,
% product(V_3,B)))),
% product(product(B,product(B,product(C,
% product(V_3,B)))),
% product(V_4,C))),product(V_5,A)))),V_4)))
% -> product(B,product(B,product(C,product(V_3,B))))
% Current number of equations to process: 1036
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [24]
% product(product(A,product(A,product(product(product(product(B,product(C,
% product(V_3,B))),C),
% product(product(product(B,product(C,
% product(V_3,B))),C),B)),
% product(V_4,A)))),product(product(A,product(A,
% product(
% product(
% product(
% product(B,
% product(C,
% product(V_3,B))),C),
% product(
% product(
% product(B,
% product(C,
% product(V_3,B))),C),B)),
% product(V_4,A)))),
% product(product(A,product(A,
% product(
% product(
% product(
% product(B,
% product(C,
% product(V_3,B))),C),
% product(
% product(
% product(B,
% product(C,
% product(V_3,B))),C),B)),
% product(V_4,A)))),
% product(B,product(C,product(V_3,B))))))
% -> product(product(B,product(C,product(V_3,B))),C)
% Current number of equations to process: 1293
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [25]
% product(product(product(A,product(A,product(product(product(B,product(C,
% product(V_3,B))),
% product(product(B,product(C,
% product(V_3,B))),C)),
% product(V_4,A)))),B),product(product(
% product(A,
% product(A,
% product(
% product(
% product(B,
% product(C,
% product(V_3,B))),
% product(
% product(B,
% product(C,
% product(V_3,B))),C)),
% product(V_4,A)))),B),
% product(product(
% product(A,
% product(A,
% product(
% product(
% product(B,
% product(C,
% product(V_3,B))),
% product(
% product(B,
% product(C,
% product(V_3,B))),C)),
% product(V_4,A)))),B),
% product(B,product(C,
% product(V_3,B))))))
% ->
% product(A,product(A,product(product(product(B,product(C,product(V_3,B))),
% product(product(B,product(C,product(V_3,B))),C)),
% product(V_4,A))))
% Current number of equations to process: 1420
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [26]
% product(product(product(product(product(A,product(B,product(C,A))),B),
% product(product(product(A,product(B,product(C,A))),B),A)),
% product(V_3,product(A,product(B,product(C,A))))),product(product(
% product(
% product(
% product(A,
% product(B,
% product(C,A))),B),
% product(
% product(
% product(A,
% product(B,
% product(C,A))),B),A)),
% product(V_3,
% product(A,
% product(B,
% product(C,A))))),
% product(product(
% product(
% product(
% product(A,
% product(B,
% product(C,A))),B),
% product(
% product(
% product(A,
% product(B,
% product(C,A))),B),A)),
% product(V_3,
% product(A,
% product(B,
% product(C,A))))),V_3)))
% ->
% product(product(product(A,product(B,product(C,A))),B),product(product(
% product(A,
% product(B,
% product(C,A))),B),A))
% Current number of equations to process: 1549
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [27]
% product(product(product(product(product(A,product(B,product(C,A))),B),A),
% product(product(product(product(A,product(B,product(C,A))),B),A),
% product(A,product(B,product(C,A))))),product(product(product(
% product(
% product(A,
% product(B,
% product(C,A))),B),A),
% product(product(
% product(
% product(A,
% product(B,
% product(C,A))),B),A),
% product(A,product(B,
% product(C,A))))),
% product(product(product(
% product(
% product(A,
% product(B,
% product(C,A))),B),A),
% product(product(
% product(
% product(A,
% product(B,
% product(C,A))),B),A),
% product(A,product(B,
% product(C,A))))),
% product(V_3,product(product(A,
% product(B,
% product(C,A))),B)))))
% -> V_3
% Current number of equations to process: 1655
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [28]
% product(product(product(product(product(product(A,product(B,product(C,A))),B),A),
% product(A,product(B,product(C,A)))),product(product(A,
% product(B,
% product(C,A))),B)),
% product(product(product(product(product(product(A,product(B,product(C,A))),B),A),
% product(A,product(B,product(C,A)))),product(product(A,
% product(B,
% product(C,A))),B)),
% product(product(product(product(product(product(A,product(B,product(C,A))),B),A),
% product(A,product(B,product(C,A)))),product(product(A,
% product(B,
% product(C,A))),B)),
% product(product(product(A,product(B,product(C,A))),B),A)))) ->
% product(product(product(product(A,product(B,product(C,A))),B),A),product(A,
% product(B,
% product(C,A))))
% Current number of equations to process: 1762
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [29]
% product(product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(V_3,B)),product(product(product(A,product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),V_3)),B),
% product(product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(V_3,B)),product(product(product(A,product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),V_3)),B),
% product(product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(V_3,B)),product(product(product(A,product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),V_3)),B),A)))
% ->
% product(product(product(A,product(A,product(B,product(C,A)))),product(V_3,B)),
% product(product(product(A,product(A,product(B,product(C,A)))),product(V_3,B)),V_3))
% Current number of equations to process: 1863
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [30]
% product(product(product(A,product(A,product(product(B,product(B,product(C,
% product(V_3,B)))),
% product(V_4,A)))),product(product(A,
% product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C)),
% product(product(product(A,product(A,product(product(B,product(B,product(C,
% product(V_3,B)))),
% product(V_4,A)))),product(product(A,
% product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C)),
% product(product(product(A,product(A,product(product(B,product(B,product(C,
% product(V_3,B)))),
% product(V_4,A)))),product(product(A,
% product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C)),
% product(V_5,B)))) -> V_5
% Current number of equations to process: 2009
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [31]
% product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(product(A,product(A,product(B,product(C,A)))),
% product(product(V_3,product(V_3,product(V_4,product(V_5,V_3)))),B))),V_4),
% product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(product(A,product(A,product(B,product(C,A)))),
% product(product(V_3,product(V_3,product(V_4,product(V_5,V_3)))),B))),V_4),
% product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(product(A,product(A,product(B,product(C,A)))),
% product(product(V_3,product(V_3,product(V_4,product(V_5,V_3)))),B))),V_4),V_3)))
% ->
% product(product(A,product(A,product(B,product(C,A)))),product(product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(product(V_3,
% product(V_3,
% product(V_4,
% product(V_5,V_3)))),B)))
% Current number of equations to process: 2205
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [32]
% product(product(product(product(A,product(B,product(C,A))),product(product(A,
% product(B,
% product(C,A))),B)),
% product(product(product(A,product(B,product(C,A))),product(product(A,
% product(B,
% product(C,A))),B)),
% product(V_3,A))),product(product(product(product(A,product(B,
% product(C,A))),
% product(product(A,product(B,
% product(C,A))),B)),
% product(product(product(A,product(B,
% product(C,A))),
% product(product(A,product(B,
% product(C,A))),B)),
% product(V_3,A))),product(product(product(
% product(A,
% product(B,
% product(C,A))),
% product(
% product(A,
% product(B,
% product(C,A))),B)),
% product(product(
% product(A,
% product(B,
% product(C,A))),
% product(
% product(A,
% product(B,
% product(C,A))),B)),
% product(V_3,A))),
% product(V_4,V_3)))) -> V_4
% Current number of equations to process: 2383
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [33]
% product(product(product(A,product(A,product(B,product(C,A)))),product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(
% product(
% product(V_3,
% product(V_4,
% product(V_5,V_3))),
% product(
% product(V_3,
% product(V_4,
% product(V_5,V_3))),V_4)),B))),
% product(product(product(A,product(A,product(B,product(C,A)))),product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(
% product(
% product(V_3,
% product(V_4,
% product(V_5,V_3))),
% product(
% product(V_3,
% product(V_4,
% product(V_5,V_3))),V_4)),B))),
% product(product(product(A,product(A,product(B,product(C,A)))),product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(
% product(
% product(V_3,
% product(V_4,
% product(V_5,V_3))),
% product(
% product(V_3,
% product(V_4,
% product(V_5,V_3))),V_4)),B))),V_3)))
% -> product(V_3,product(V_4,product(V_5,V_3)))
% Current number of equations to process: 2581
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [34]
% product(product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(product(A,product(A,product(B,product(C,A)))),
% product(V_3,B))),product(V_4,V_3)),V_4),product(
% product(
% product(
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B))),
% product(V_4,V_3)),V_4),
% product(
% product(
% product(
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B))),
% product(V_4,V_3)),V_4),
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B))))))
% ->
% product(product(product(A,product(A,product(B,product(C,A)))),product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B))),
% product(V_4,V_3))
% Current number of equations to process: 2787
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [35]
% product(product(product(A,product(A,product(product(product(B,product(B,
% product(C,
% product(V_3,B)))),
% product(product(B,product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,C))),product(V_5,A)))),V_4),
% product(product(product(A,product(A,product(product(product(B,product(B,
% product(C,
% product(V_3,B)))),
% product(product(B,product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,C))),product(V_5,A)))),V_4),
% product(product(product(A,product(A,product(product(product(B,product(B,
% product(C,
% product(V_3,B)))),
% product(product(B,product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,C))),product(V_5,A)))),V_4),
% product(B,product(B,product(C,product(V_3,B))))))) ->
% product(A,product(A,product(product(product(B,product(B,product(C,product(V_3,B)))),
% product(product(B,product(B,product(C,product(V_3,B)))),
% product(V_4,C))),product(V_5,A))))
% Current number of equations to process: 2996
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [36]
% product(product(A,product(A,product(product(product(product(B,product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,C)),product(product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,C)),V_4)),
% product(V_5,A)))),product(product(A,product(A,
% product(
% product(
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,C)),
% product(
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,C)),V_4)),
% product(V_5,A)))),
% product(product(A,product(A,
% product(
% product(
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,C)),
% product(
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,C)),V_4)),
% product(V_5,A)))),
% product(B,product(B,product(C,
% product(V_3,B)))))))
% -> product(product(B,product(B,product(C,product(V_3,B)))),product(V_4,C))
% Current number of equations to process: 3212
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [37]
% product(product(A,product(A,product(product(product(product(product(B,
% product(C,
% product(V_3,B))),C),B),
% product(product(product(product(B,
% product(C,
% product(V_3,B))),C),B),
% product(B,product(C,product(V_3,B))))),
% product(V_4,A)))),product(product(A,product(A,
% product(
% product(
% product(
% product(
% product(B,
% product(C,
% product(V_3,B))),C),B),
% product(
% product(
% product(
% product(B,
% product(C,
% product(V_3,B))),C),B),
% product(B,
% product(C,
% product(V_3,B))))),
% product(V_4,A)))),
% product(product(A,product(A,
% product(
% product(
% product(
% product(
% product(B,
% product(C,
% product(V_3,B))),C),B),
% product(
% product(
% product(
% product(B,
% product(C,
% product(V_3,B))),C),B),
% product(B,
% product(C,
% product(V_3,B))))),
% product(V_4,A)))),
% product(product(B,product(C,
% product(V_3,B))),C))))
% -> product(product(product(B,product(C,product(V_3,B))),C),B)
% Current number of equations to process: 3453
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [38]
% product(product(product(product(A,product(A,product(product(B,product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C),product(
% product(
% product(A,
% product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C),B)),
% product(product(product(product(A,product(A,product(product(B,product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C),product(
% product(
% product(A,
% product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C),B)),
% product(product(product(product(A,product(A,product(product(B,product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C),product(
% product(
% product(A,
% product(A,
% product(
% product(B,
% product(B,
% product(C,
% product(V_3,B)))),
% product(V_4,A)))),C),B)),
% product(B,product(B,product(C,product(V_3,B))))))) -> A
% Current number of equations to process: 3668
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [39]
% product(product(product(A,product(A,product(product(product(product(B,
% product(C,
% product(V_3,B))),C),
% product(product(product(B,
% product(C,
% product(V_3,B))),C),B)),
% product(V_4,A)))),product(B,product(C,
% product(V_3,B)))),
% product(product(product(A,product(A,product(product(product(product(B,
% product(C,
% product(V_3,B))),C),
% product(product(product(B,
% product(C,
% product(V_3,B))),C),B)),
% product(V_4,A)))),product(B,product(C,
% product(V_3,B)))),
% product(product(product(A,product(A,product(product(product(product(B,
% product(C,
% product(V_3,B))),C),
% product(product(product(B,
% product(C,
% product(V_3,B))),C),B)),
% product(V_4,A)))),product(B,product(C,
% product(V_3,B)))),
% product(product(B,product(C,product(V_3,B))),C)))) ->
% product(A,product(A,product(product(product(product(B,product(C,product(V_3,B))),C),
% product(product(product(B,product(C,product(V_3,B))),C),B)),
% product(V_4,A))))
% Current number of equations to process: 3893
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [40]
% product(product(product(product(product(product(A,product(B,product(C,A))),B),
% product(product(product(A,product(B,product(C,A))),B),A)),
% product(V_3,product(A,product(B,product(C,A))))),V_3),
% product(product(product(product(product(product(A,product(B,product(C,A))),B),
% product(product(product(A,product(B,product(C,A))),B),A)),
% product(V_3,product(A,product(B,product(C,A))))),V_3),
% product(product(product(product(product(product(A,product(B,product(C,A))),B),
% product(product(product(A,product(B,product(C,A))),B),A)),
% product(V_3,product(A,product(B,product(C,A))))),V_3),
% product(product(product(A,product(B,product(C,A))),B),product(product(
% product(A,
% product(B,
% product(C,A))),B),A)))))
% ->
% product(product(product(product(A,product(B,product(C,A))),B),product(
% product(
% product(A,
% product(B,
% product(C,A))),B),A)),
% product(V_3,product(A,product(B,product(C,A)))))
% Current number of equations to process: 4112
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [41]
% product(product(product(product(product(A,product(A,product(B,product(C,A)))),
% product(V_3,B)),product(product(product(A,product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),V_3)),
% product(V_4,product(A,product(A,product(B,product(C,A)))))),product(
% product(
% product(
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),
% product(
% product(
% product(A,
% product(A,
% product(B,
% product(C,A)))),
% product(V_3,B)),V_3)),
% product(V_4,
% product(A,
% product(A,
% product(B,
% product(C,A)))))),
% Cputime limit exceeded (core dumped)
% 
% EOF
%------------------------------------------------------------------------------