TSTP Solution File: GRP112-10 by CiME---2.01

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP112-10 : TPTP v7.3.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n184.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.5MB
% OS       : Linux 3.10.0-862.11.6.el7.x86_64
% CPULimit : 300s
% DateTime : Wed Feb 27 12:44:34 EST 2019

% Result   : Timeout 300.09s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : GRP112-10 : TPTP v7.3.0. Released v7.3.0.
% 0.03/0.04  % Command  : tptp2X_and_run_cime %s
% 0.03/0.25  % Computer : n184.star.cs.uiowa.edu
% 0.03/0.25  % Model    : x86_64 x86_64
% 0.03/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.25  % Memory   : 32218.5MB
% 0.03/0.25  % OS       : Linux 3.10.0-862.11.6.el7.x86_64
% 0.08/0.25  % CPULimit : 300
% 0.08/0.25  % DateTime : Wed Feb 20 20:12:13 CST 2019
% 0.08/0.25  % CPUTime  : 
% 1.14/1.43  Processing problem /tmp/CiME_44529_n184.star.cs.uiowa.edu
% 1.14/1.43  #verbose 1;
% 1.14/1.43                let F = signature " b4,b1,a4,a1,c3,b3,a3,a2,b2 : constant;  tuple : 4;  inverse : 1;  multiply : 2;";
% 1.14/1.43  let X = vars "X Y Z";
% 1.14/1.43  let Axioms = equations F X "
% 1.14/1.43   multiply(multiply(multiply(X,Y),Z),multiply(X,Z)) = Y;
% 1.14/1.43  ";
% 1.14/1.43  
% 1.14/1.43  let s1 = status F "
% 1.14/1.43   b4 lr_lex;
% 1.14/1.43   b1 lr_lex;
% 1.14/1.43   tuple lr_lex;
% 1.14/1.43   a4 lr_lex;
% 1.14/1.43   a1 lr_lex;
% 1.14/1.43   c3 lr_lex;
% 1.14/1.43   b3 lr_lex;
% 1.14/1.43   a3 lr_lex;
% 1.14/1.43   a2 lr_lex;
% 1.14/1.43   inverse lr_lex;
% 1.14/1.43   b2 lr_lex;
% 1.14/1.43   multiply lr_lex;
% 1.14/1.43  ";
% 1.14/1.43  
% 1.14/1.43  let p1 = precedence F "
% 1.14/1.43  tuple > multiply > inverse > b2 > a2 > a3 > b3 > c3 > a1 > a4 > b1 > b4";
% 1.14/1.43  
% 1.14/1.43  let s2 = status F "
% 1.14/1.43  b4 mul;
% 1.14/1.43  b1 mul;
% 1.14/1.43  tuple mul;
% 1.14/1.43  a4 mul;
% 1.14/1.43  a1 mul;
% 1.14/1.43  c3 mul;
% 1.14/1.43  b3 mul;
% 1.14/1.43  a3 mul;
% 1.14/1.43  a2 mul;
% 1.14/1.43  inverse mul;
% 1.14/1.43  b2 mul;
% 1.14/1.43  multiply mul;
% 1.14/1.43  ";
% 1.14/1.43  
% 1.14/1.43  let p2 = precedence F "
% 1.14/1.43  tuple > multiply > inverse > b2 = a2 = a3 = b3 = c3 = a1 = a4 = b1 = b4";
% 1.14/1.43  
% 1.14/1.43  let o_auto = AUTO Axioms;
% 1.14/1.43  
% 1.14/1.43  let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 1.14/1.43  
% 1.14/1.43  let Conjectures = equations F X " tuple(multiply(multiply(inverse(b2),b2),a2),multiply(multiply(a3,b3),c3),multiply(inverse(a1),a1),multiply(a4,a4)) = tuple(a2,multiply(a3,multiply(b3,c3)),multiply(inverse(b1),b1),multiply(b4,b4));"
% 1.14/1.43  ;
% 1.14/1.43  (*
% 1.14/1.43  let Red_Axioms = normalize_equations Defining_rules Axioms;
% 1.14/1.43  
% 1.14/1.43  let Red_Conjectures =  normalize_equations Defining_rules Conjectures;
% 1.14/1.43  *)
% 1.14/1.43  #time on;
% 1.14/1.43  
% 1.14/1.43  let res = prove_conj_by_ordered_completion o Axioms Conjectures;
% 1.14/1.43  
% 1.14/1.43  #time off;
% 1.14/1.43  
% 1.14/1.43  
% 1.14/1.43  let status = if res then "unsatisfiable" else "satisfiable";
% 1.14/1.43  #quit;
% 1.14/1.43  Verbose level is now 1
% 1.14/1.43  
% 1.14/1.43  F : signature = <signature>
% 1.14/1.43  X : variable_set = <variable set>
% 1.14/1.43  
% 1.14/1.43  Axioms : (F,X) equations = { multiply(multiply(multiply(X,Y),Z),multiply(X,Z))
% 1.14/1.43                               = Y } (1 equation(s))
% 1.14/1.43  s1 : F status = <status>
% 1.14/1.43  p1 : F precedence = <precedence>
% 1.14/1.43  s2 : F status = <status>
% 1.14/1.43  p2 : F precedence = <precedence>
% 1.14/1.43  o_auto : F term_ordering = <term ordering>
% 1.14/1.43  o : F term_ordering = <term ordering>
% 1.14/1.43  Conjectures : (F,X) equations = { tuple(multiply(multiply(inverse(b2),b2),a2),
% 1.14/1.43                                    multiply(multiply(a3,b3),c3),multiply(
% 1.14/1.43                                                                 inverse(a1),a1),
% 1.14/1.43                                    multiply(a4,a4)) =
% 1.14/1.43                                    tuple(a2,multiply(a3,multiply(b3,c3)),
% 1.14/1.43                                    multiply(inverse(b1),b1),multiply(b4,b4)) }
% 1.14/1.43                                    (1 equation(s))
% 1.14/1.43  time is now on
% 1.14/1.43  
% 1.14/1.43  Initializing completion ...
% 1.14/1.43  New rule produced :
% 1.14/1.43  [1] multiply(multiply(multiply(X,Y),Z),multiply(X,Z)) -> Y
% 1.14/1.43  Current number of equations to process: 0
% 1.14/1.43  Current number of ordered equations: 0
% 1.14/1.43  Current number of rules: 1
% 1.14/1.43  New rule produced :
% 1.14/1.43  [2] multiply(X,multiply(multiply(Y,X),multiply(Y,Z))) -> Z
% 1.14/1.43  Current number of equations to process: 2
% 1.14/1.43  Current number of ordered equations: 0
% 1.14/1.43  Current number of rules: 2
% 1.14/1.43  New rule produced :
% 1.14/1.43  [3]
% 1.14/1.43  multiply(X,multiply(multiply(Y,X),Z)) <->
% 1.14/1.43  multiply(multiply(V_3,Y),multiply(V_3,Z))
% 1.14/1.43  Current number of equations to process: 8
% 1.14/1.43  Current number of ordered equations: 1
% 1.14/1.43  Current number of rules: 3
% 1.14/1.43  New rule produced :
% 1.14/1.43  [4]
% 1.14/1.43  multiply(multiply(V_3,Y),multiply(V_3,Z)) <->
% 1.14/1.43  multiply(X,multiply(multiply(Y,X),Z))
% 1.14/1.43  Current number of equations to process: 8
% 1.14/1.43  Current number of ordered equations: 0
% 1.14/1.43  Current number of rules: 4
% 1.14/1.43  New rule produced :
% 1.14/1.43  [5] multiply(multiply(Y,Z),multiply(Y,multiply(Z,X))) -> X
% 1.14/1.43  Current number of equations to process: 19
% 1.14/1.43  Current number of ordered equations: 0
% 1.14/1.43  Current number of rules: 5
% 1.14/1.43  New rule produced :
% 1.14/1.43  [6] multiply(X,multiply(Y,multiply(multiply(X,Y),Z))) -> Z
% 1.14/1.43  Current number of equations to process: 30
% 1.14/1.43  Current number of ordered equations: 0
% 1.14/1.43  Current number of rules: 6
% 1.14/1.43  New rule produced :
% 1.14/1.43  [7] multiply(multiply(multiply(X,Y),X),Z) -> multiply(Y,Z)
% 1.14/1.43  Current number of equations to process: 34
% 1.14/1.43  Current number of ordered equations: 0
% 1.14/1.43  Current number of rules: 7
% 1.14/1.43  New rule produced :
% 1.14/1.43  [8] multiply(multiply(X,multiply(Y,X)),Z) -> multiply(Y,Z)
% 1.14/1.43  Current number of equations to process: 44
% 1.14/1.43  Current number of ordered equations: 0
% 1.14/1.43  Current number of rules: 8
% 1.14/1.43  New rule produced :
% 1.14/1.43  [9] multiply(X,multiply(Y,multiply(Y,multiply(Z,X)))) -> Z
% 1.14/1.43  Current number of equations to process: 42
% 1.14/1.43  Current number of ordered equations: 1
% 1.14/1.43  Current number of rules: 9
% 1.23/1.48  New rule produced :
% 1.23/1.48  [10] multiply(multiply(multiply(multiply(X,Y),Z),X),Y) -> Z
% 1.23/1.48  Current number of equations to process: 42
% 1.23/1.48  Current number of ordered equations: 0
% 1.23/1.48  Current number of rules: 10
% 1.23/1.48  New rule produced :
% 1.23/1.48  [11] multiply(multiply(X,Y),multiply(Z,Y)) -> multiply(X,Z)
% 1.23/1.48  Rule [1] multiply(multiply(multiply(X,Y),Z),multiply(X,Z)) -> Y collapsed.
% 1.23/1.48  Current number of equations to process: 54
% 1.23/1.48  Current number of ordered equations: 0
% 1.23/1.48  Current number of rules: 10
% 1.23/1.48  New rule produced : [12] multiply(multiply(X,Y),X) -> Y
% 1.23/1.48  Rule [7] multiply(multiply(multiply(X,Y),X),Z) -> multiply(Y,Z) collapsed.
% 1.23/1.48  Current number of equations to process: 53
% 1.23/1.48  Current number of ordered equations: 0
% 1.23/1.48  Current number of rules: 10
% 1.23/1.48  New rule produced :
% 1.23/1.48  [13] multiply(multiply(Z,multiply(Z,X)),Y) -> multiply(X,Y)
% 1.23/1.48  Current number of equations to process: 65
% 1.23/1.48  Current number of ordered equations: 0
% 1.23/1.48  Current number of rules: 11
% 1.23/1.48  New rule produced :
% 1.23/1.48  [14] multiply(X,Y) <-> multiply(Z,multiply(Y,multiply(Z,X)))
% 1.23/1.48  Rule [10] multiply(multiply(multiply(multiply(X,Y),Z),X),Y) -> Z collapsed.
% 1.23/1.48  Rule [12] multiply(multiply(X,Y),X) -> Y collapsed.
% 1.23/1.48  The conjecture has been reduced. 
% 1.23/1.48  Conjecture is now:
% 1.23/1.48  tuple(multiply(b4,multiply(a2,multiply(b4,multiply(b4,multiply(b2,multiply(b4,
% 1.23/1.48                                                                    inverse(b2))))))),
% 1.23/1.48  multiply(b4,multiply(c3,multiply(b4,multiply(b4,multiply(b3,multiply(b4,a3)))))),
% 1.23/1.48  multiply(b4,multiply(a1,multiply(b4,inverse(a1)))),multiply(a4,a4)) = 
% 1.23/1.48  tuple(a2,multiply(a3,multiply(b4,multiply(c3,multiply(b4,b3)))),multiply(b4,
% 1.23/1.48                                                                  multiply(b1,
% 1.23/1.48                                                                  multiply(b4,
% 1.23/1.48                                                                  inverse(b1)))),
% 1.23/1.48  multiply(b4,b4))
% 1.23/1.48  
% 1.23/1.48  Current number of equations to process: 82
% 1.23/1.48  Current number of ordered equations: 1
% 1.23/1.48  Current number of rules: 10
% 1.23/1.48  New rule produced :
% 1.23/1.48  [15] multiply(b4,multiply(X,multiply(b4,multiply(X,Y)))) -> Y
% 1.23/1.48  Current number of equations to process: 81
% 1.23/1.48  Current number of ordered equations: 1
% 1.23/1.48  Current number of rules: 11
% 1.23/1.48  New rule produced :
% 1.23/1.48  [16] multiply(Z,multiply(Y,multiply(Z,X))) <-> multiply(X,Y)
% 1.23/1.48  Current number of equations to process: 81
% 1.23/1.48  Current number of ordered equations: 0
% 1.23/1.48  Current number of rules: 12
% 1.23/1.48  New rule produced : [17] multiply(X,multiply(Y,X)) -> Y
% 1.23/1.48  Rule [8] multiply(multiply(X,multiply(Y,X)),Z) -> multiply(Y,Z) collapsed.
% 1.23/1.48  Current number of equations to process: 93
% 1.23/1.48  Current number of ordered equations: 0
% 1.23/1.48  Current number of rules: 12
% 1.23/1.48  New rule produced :
% 1.23/1.48  [18] multiply(Y,multiply(Z,X)) <-> multiply(multiply(X,Y),Z)
% 1.23/1.48  Current number of equations to process: 92
% 1.23/1.48  Current number of ordered equations: 1
% 1.23/1.48  Current number of rules: 13
% 1.23/1.48  New rule produced :
% 1.23/1.48  [19] multiply(multiply(X,Y),Z) <-> multiply(Y,multiply(Z,X))
% 1.23/1.48  Current number of equations to process: 92
% 1.23/1.48  Current number of ordered equations: 0
% 1.23/1.48  Current number of rules: 14
% 1.23/1.48  New rule produced : [20] multiply(Y,Y) <-> multiply(X,X)
% 1.23/1.48  The conjecture has been reduced. 
% 1.23/1.48  Conjecture is now:
% 1.23/1.48  tuple(multiply(b4,multiply(a2,multiply(b4,multiply(b4,multiply(b2,multiply(b4,
% 1.23/1.48                                                                    inverse(b2))))))),
% 1.23/1.48  multiply(b4,multiply(c3,multiply(b4,multiply(b4,multiply(b3,multiply(b4,a3)))))),
% 1.23/1.48  multiply(b4,multiply(a1,multiply(b4,inverse(a1)))),multiply(b4,b4)) = 
% 1.23/1.48  tuple(a2,multiply(a3,multiply(b4,multiply(c3,multiply(b4,b3)))),multiply(b4,
% 1.23/1.48                                                                  multiply(b1,
% 1.23/1.48                                                                  multiply(b4,
% 1.23/1.48                                                                  inverse(b1)))),
% 1.23/1.48  multiply(b4,b4))
% 1.23/1.48  
% 1.23/1.48  Current number of equations to process: 94
% 1.23/1.48  Current number of ordered equations: 0
% 1.23/1.48  Current number of rules: 15
% 1.23/1.48  New rule produced : [21] multiply(X,multiply(Y,Y)) -> X
% 1.23/1.48  Current number of equations to process: 100
% 1.23/1.48  Current number of ordered equations: 0
% 1.23/1.48  Current number of rules: 16
% 1.23/1.48  New rule produced :
% 1.23/1.48  [22] multiply(multiply(multiply(Z,Z),X),Y) -> multiply(X,Y)
% 1.23/1.48  Current number of equations to process: 122
% 1.23/1.48  Current number of ordered equations: 0
% 1.23/1.54  Current number of rules: 17
% 1.23/1.54  New rule produced : [23] multiply(Y,multiply(Y,X)) -> X
% 1.23/1.54  Rule [9] multiply(X,multiply(Y,multiply(Y,multiply(Z,X)))) -> Z collapsed.
% 1.23/1.54  Rule [13] multiply(multiply(Z,multiply(Z,X)),Y) -> multiply(X,Y) collapsed.
% 1.23/1.54  The conjecture has been reduced. 
% 1.23/1.54  Conjecture is now:
% 1.23/1.54  tuple(multiply(b4,multiply(a2,multiply(b2,multiply(b4,inverse(b2))))),
% 1.23/1.54  multiply(b4,multiply(c3,multiply(b3,multiply(b4,a3)))),multiply(b4,multiply(a1,
% 1.23/1.54                                                                     multiply(b4,
% 1.23/1.54                                                                     inverse(a1)))),
% 1.23/1.54  multiply(b4,b4)) = tuple(a2,multiply(a3,multiply(b4,multiply(c3,multiply(b4,b3)))),
% 1.23/1.54                     multiply(b4,multiply(b1,multiply(b4,inverse(b1)))),
% 1.23/1.54                     multiply(b4,b4))
% 1.23/1.54  
% 1.23/1.54  Current number of equations to process: 136
% 1.23/1.54  Current number of ordered equations: 0
% 1.23/1.54  Current number of rules: 16
% 1.23/1.54  New rule produced :
% 1.23/1.54  [24] multiply(multiply(X,Y),Z) <-> multiply(multiply(Y,X),Z)
% 1.23/1.54  Current number of equations to process: 135
% 1.23/1.54  Current number of ordered equations: 0
% 1.23/1.54  Current number of rules: 17
% 1.23/1.54  New rule produced :
% 1.23/1.54  [25] multiply(multiply(b4,X),Y) -> multiply(b4,multiply(X,Y))
% 1.23/1.54  Current number of equations to process: 153
% 1.23/1.54  Current number of ordered equations: 0
% 1.23/1.54  Current number of rules: 18
% 1.23/1.54  New rule produced :
% 1.23/1.54  [26] multiply(b4,multiply(multiply(X,b4),Y)) -> multiply(X,Y)
% 1.23/1.54  Current number of equations to process: 152
% 1.23/1.54  Current number of ordered equations: 0
% 1.23/1.54  Current number of rules: 19
% 1.23/1.54  New rule produced :
% 1.23/1.54  [27] multiply(multiply(X,multiply(Y,Z)),multiply(Z,Y)) -> X
% 1.23/1.54  Current number of equations to process: 156
% 1.23/1.54  Current number of ordered equations: 0
% 1.23/1.54  Current number of rules: 20
% 1.23/1.54  New rule produced :
% 1.23/1.54  [28] multiply(X,multiply(multiply(X,Y),multiply(Y,Z))) -> Z
% 1.23/1.54  Current number of equations to process: 155
% 1.23/1.54  Current number of ordered equations: 0
% 1.23/1.54  Current number of rules: 21
% 1.23/1.54  New rule produced :
% 1.23/1.54  [29] multiply(multiply(X,Y),multiply(Y,multiply(X,Z))) -> Z
% 1.23/1.54  Current number of equations to process: 154
% 1.23/1.54  Current number of ordered equations: 0
% 1.23/1.55  Current number of rules: 22
% 1.23/1.55  New rule produced :
% 1.23/1.55  [30] multiply(Y,multiply(Z,multiply(multiply(Z,Y),X))) -> X
% 1.23/1.55  Current number of equations to process: 153
% 1.23/1.55  Current number of ordered equations: 0
% 1.23/1.55  Current number of rules: 23
% 1.23/1.55  New rule produced :
% 1.23/1.55  [31] multiply(Y,multiply(b4,multiply(Y,X))) -> multiply(b4,X)
% 1.23/1.55  Rule [15] multiply(b4,multiply(X,multiply(b4,multiply(X,Y)))) -> Y collapsed.
% 1.23/1.55  Current number of equations to process: 163
% 1.23/1.55  Current number of ordered equations: 0
% 1.23/1.55  Current number of rules: 23
% 1.23/1.55  New rule produced :
% 1.23/1.55  [32] multiply(Z,multiply(multiply(Z,X),Y)) -> multiply(X,Y)
% 1.23/1.55  Rule [28] multiply(X,multiply(multiply(X,Y),multiply(Y,Z))) -> Z collapsed.
% 1.23/1.55  Rule [30] multiply(Y,multiply(Z,multiply(multiply(Z,Y),X))) -> X collapsed.
% 1.23/1.55  Current number of equations to process: 168
% 1.23/1.55  Current number of ordered equations: 0
% 1.23/1.55  Current number of rules: 22
% 1.23/1.55  New rule produced :
% 1.23/1.55  [33] multiply(multiply(X,Y),Z) <-> multiply(multiply(X,Z),Y)
% 1.23/1.55  Current number of equations to process: 171
% 1.23/1.55  Current number of ordered equations: 0
% 1.23/1.55  Current number of rules: 23
% 1.23/1.55  New rule produced :
% 1.23/1.55  [34] multiply(X,multiply(Y,Z)) <-> multiply(Z,multiply(X,Y))
% 1.23/1.55  Rule [11] multiply(multiply(X,Y),multiply(Z,Y)) -> multiply(X,Z) collapsed.
% 1.23/1.55  Rule [27] multiply(multiply(X,multiply(Y,Z)),multiply(Z,Y)) -> X collapsed.
% 1.23/1.55  Current number of equations to process: 194
% 1.23/1.55  Current number of ordered equations: 1
% 1.23/1.55  Current number of rules: 22
% 1.23/1.55  New rule produced :
% 1.23/1.55  [35] multiply(Z,multiply(X,Y)) <-> multiply(X,multiply(Y,Z))
% 1.23/1.55  Current number of equations to process: 194
% 1.23/1.55  Current number of ordered equations: 0
% 1.23/1.55  Current number of rules: 23
% 1.23/1.55  Rule [4]
% 1.23/1.55       multiply(multiply(V_3,Y),multiply(V_3,Z)) <->
% 1.23/1.55       multiply(X,multiply(multiply(Y,X),Z)) is composed into [4]
% 1.23/1.55                                                              multiply(
% 1.23/1.55                                                              multiply(V_3,Y),
% 1.23/1.55                                                              multiply(V_3,Z))
% 1.23/1.55                                                              -> multiply(Y,Z)
% 1.23/1.55  New rule produced :
% 1.23/1.55  [36] multiply(Y,multiply(multiply(X,Y),Z)) -> multiply(X,Z)
% 3.07/3.26  Rule [2] multiply(X,multiply(multiply(Y,X),multiply(Y,Z))) -> Z collapsed.
% 3.07/3.26  Rule
% 3.07/3.26  [3]
% 3.07/3.26  multiply(X,multiply(multiply(Y,X),Z)) <->
% 3.07/3.26  multiply(multiply(V_3,Y),multiply(V_3,Z)) collapsed.
% 3.07/3.26  Rule [6] multiply(X,multiply(Y,multiply(multiply(X,Y),Z))) -> Z collapsed.
% 3.07/3.26  Rule [26] multiply(b4,multiply(multiply(X,b4),Y)) -> multiply(X,Y) collapsed.
% 3.07/3.26  Current number of equations to process: 205
% 3.07/3.26  Current number of ordered equations: 0
% 3.07/3.26  Current number of rules: 20
% 3.07/3.26  multiply(Y,X) = multiply(X,Y) (birth = 130, lhs_size = 3, rhs_size = 7,trace = Cp of 16 and 5)
% 3.07/3.26  Initializing completion ...
% 3.07/3.26  New rule produced : [1] Y multiply Y <-> X multiply X
% 3.07/3.26  Current number of equations to process: 181
% 3.07/3.26  Current number of ordered equations: 30
% 3.07/3.26  Current number of rules: 1
% 3.07/3.26  New rule produced : [2] X <-> (X multiply Y) multiply Y
% 3.07/3.26  Current number of equations to process: 181
% 3.07/3.26  Current number of ordered equations: 28
% 3.07/3.26  Current number of rules: 2
% 3.07/3.26  New rule produced : [3] X <-> (Y multiply Y) multiply X
% 3.07/3.26  Current number of equations to process: 181
% 3.07/3.26  Current number of ordered equations: 26
% 3.07/3.26  Current number of rules: 3
% 3.07/3.26  New rule produced : [4] (X multiply Y) multiply Y <-> X
% 3.07/3.26  Current number of equations to process: 181
% 3.07/3.26  Current number of ordered equations: 24
% 3.07/3.26  Current number of rules: 4
% 3.07/3.26  New rule produced : [5] (Y multiply Y) multiply X <-> X
% 3.07/3.26  Current number of equations to process: 181
% 3.07/3.26  Current number of ordered equations: 22
% 3.07/3.26  Current number of rules: 5
% 3.07/3.26  (X multiply Y) multiply Z = (X multiply Z) multiply Y (birth = 0, lhs_size = 5, rhs_size = 5,trace = in the starting set)
% 3.07/3.26  Initializing completion ...
% 3.07/3.26  New rule produced : [1] Y multiply Y <-> X multiply X
% 3.07/3.26  Current number of equations to process: 78
% 3.07/3.26  Current number of ordered equations: 4
% 3.07/3.26  Current number of rules: 1
% 3.07/3.26  New rule produced : [2] X <-> X multiply Y multiply Y
% 3.07/3.26  Current number of equations to process: 82
% 3.07/3.26  Current number of ordered equations: 3
% 3.07/3.26  Current number of rules: 2
% 3.07/3.26  New rule produced : [3] X multiply Y multiply Y <-> X
% 3.07/3.26  Current number of equations to process: 82
% 3.07/3.26  Current number of ordered equations: 2
% 3.07/3.26  Current number of rules: 3
% 3.07/3.26  New rule produced : [4] Y <-> X multiply X multiply Y multiply Z multiply Z
% 3.07/3.26  Current number of equations to process: 75
% 3.07/3.26  Current number of ordered equations: 1
% 3.07/3.26  Current number of rules: 4
% 3.07/3.26  New rule produced : [5] X multiply X multiply Y multiply Z multiply Z <-> Y
% 3.07/3.26  Current number of equations to process: 75
% 3.07/3.26  Current number of ordered equations: 0
% 3.07/3.26  Current number of rules: 5
% 3.07/3.26  New rule produced :
% 3.07/3.26  [6]
% 3.07/3.26  Z multiply Z multiply V_3 multiply V_3 <-> X multiply X multiply Y multiply Y
% 3.07/3.26  Current number of equations to process: 79
% 3.07/3.26  Current number of ordered equations: 0
% 3.07/3.26  Current number of rules: 6
% 3.07/3.26  New rule produced :
% 3.07/3.26  [7]
% 3.07/3.26  Y multiply V_3 multiply V_3 <-> X multiply X multiply Y multiply Z multiply Z
% 3.07/3.26  Current number of equations to process: 100
% 3.07/3.26  Current number of ordered equations: 2
% 3.07/3.26  Current number of rules: 7
% 3.07/3.26  New rule produced :
% 3.07/3.26  [8]
% 3.07/3.26  X multiply X multiply Y multiply Y multiply Z <-> Z multiply V_3 multiply V_3
% 3.07/3.26  Current number of equations to process: 100
% 3.07/3.26  Current number of ordered equations: 0
% 3.07/3.26  Current number of rules: 8
% 3.07/3.26  New rule produced :
% 3.07/3.26  [9]
% 3.07/3.26  Z <-> b4 multiply b4 multiply X multiply X multiply Y multiply Y multiply Z
% 3.07/3.26  Current number of equations to process: 162
% 3.07/3.26  Current number of ordered equations: 5
% 3.07/3.26  Current number of rules: 9
% 3.07/3.26  New rule produced :
% 3.07/3.26  [10]
% 3.07/3.26  Z <-> X multiply X multiply Y multiply Y multiply Z multiply V_3 multiply V_3
% 3.07/3.26  Rule
% 3.07/3.26  [9]
% 3.07/3.26  Z <-> b4 multiply b4 multiply X multiply X multiply Y multiply Y multiply Z
% 3.07/3.26  collapsed.
% 3.07/3.26  Current number of equations to process: 162
% 3.07/3.26  Current number of ordered equations: 3
% 3.07/3.26  Current number of rules: 9
% 3.07/3.26  New rule produced :
% 3.07/3.26  [11]
% 3.07/3.26  b4 multiply b4 multiply X multiply X multiply Y multiply Y multiply Z <-> Z
% 3.07/3.26  Current number of equations to process: 162
% 3.07/3.26  Current number of ordered equations: 2
% 3.07/3.26  Current number of rules: 10
% 3.07/3.26  New rule produced :
% 3.07/3.26  [12]
% 3.07/3.26  X multiply X multiply Y multiply Y multiply Z multiply Z multiply V_3 <-> V_3
% 3.07/3.26  Rule
% 3.07/3.26  [11]
% 3.07/3.26  b4 multiply b4 multiply X multiply X multiply Y multiply Y multiply Z <-> Z
% 3.07/3.26  collapsed.
% 3.07/3.26  Current number of equations to process: 162
% 3.07/3.26  Current number of ordered equations: 0
% 3.07/3.26  Current numbe
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