%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : BOO037-2 : TPTP v6.0.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n081.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 00:19:15 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  : BOO037-2 : TPTP v6.0.0. Released v2.5.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n081.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 : Thu Jun  5 18:39:08 CDT 2014
% % CPUTime  : 300.03 
% Processing problem /tmp/CiME_8402_n081.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " multiply,add : infix commutative; additive_identity,multiplicative_identity : constant;  inverse : 1;add_multiply_inverse_multiplicative_identity_additive_identity__1, add_multiply_inverse_multiplicative_identity_additive_identity__2 : 0;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% (X multiply Y) add Z = (X add Z) multiply (Y add Z);
% X add (Y multiply Z) = (X add Y) multiply (X add Z);
% (X add Y) multiply Z = (X multiply Z) add (Y multiply Z);
% X multiply (Y add Z) = (X multiply Y) add (X multiply Z);
% X add inverse(X) = multiplicative_identity;
% inverse(X) add X = multiplicative_identity;
% X multiply inverse(X) = additive_identity;
% inverse(X) multiply X = additive_identity;
% X multiply multiplicative_identity = X;
% multiplicative_identity multiply X = X;
% X add additive_identity = X;
% additive_identity add X = X;
% ";
% 
% let s1 = status F "
% additive_identity lr_lex;
% multiplicative_identity lr_lex;
% inverse lr_lex;
% multiply mul;
% add mul;
% ";
% 
% let p1 = precedence F "
% add > multiply > inverse > multiplicative_identity > additive_identity > add_multiply_inverse_multiplicative_identity_additive_identity__1 > add_multiply_inverse_multiplicative_identity_additive_identity__2";
% 
% let s2 = status F "
% additive_identity mul;
% multiplicative_identity mul;
% inverse mul;
% multiply mul;
% add mul;
% ";
% 
% let p2 = precedence F "
% add > multiply > inverse > multiplicative_identity = additive_identity > add_multiply_inverse_multiplicative_identity_additive_identity__1 > add_multiply_inverse_multiplicative_identity_additive_identity__2";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X "add_multiply_inverse_multiplicative_identity_additive_identity__1 = add_multiply_inverse_multiplicative_identity_additive_identity__2"
% ;
% (*
% 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 = { (X multiply Y) add Z =
% (X add Z) multiply (Y add Z),
% (Y multiply Z) add X =
% (X add Y) multiply (X add Z),
% (X add Y) multiply Z =
% (X multiply Z) add (Y multiply Z),
% (Y add Z) multiply X =
% (X multiply Y) add (X multiply Z),
% inverse(X) add X = multiplicative_identity,
% inverse(X) add X = multiplicative_identity,
% inverse(X) multiply X = additive_identity,
% inverse(X) multiply X = additive_identity,
% multiplicative_identity multiply X = X,
% multiplicative_identity multiply X = X,
% additive_identity add X = X,
% additive_identity add X = X } (12 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 = { add_multiply_inverse_multiplicative_identity_additive_identity__1
% =
% add_multiply_inverse_multiplicative_identity_additive_identity__2 }
% (1 equation(s))
% time is now on
% 
% Initializing completion ...
% New rule produced : [1] multiplicative_identity multiply X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 1
% New rule produced : [2] additive_identity add X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 2
% New rule produced : [3] inverse(X) multiply X -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 3
% New rule produced : [4] inverse(X) add X -> multiplicative_identity
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 4
% New rule produced : [5] (X add Z) multiply (Y add Z) -> (X multiply Y) add Z
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 5
% New rule produced :
% [6] (Y add Z) multiply X -> (X multiply Y) add (X multiply Z)
% Rule [5] (X add Z) multiply (Y add Z) -> (X multiply Y) add Z collapsed.
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [7]
% ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add (Z multiply Z))
% -> (X multiply Y) add Z
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [8] inverse(multiplicative_identity) -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [9] inverse(additive_identity) -> multiplicative_identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [10] (inverse(Y) multiply X) add (X multiply Y) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [11] (additive_identity multiply Y) add (X multiply Y) -> X multiply Y
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [12]
% (inverse(X add Y) multiply X) add (inverse(X add Y) multiply Y) ->
% additive_identity
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [13] (X multiply X) add Y <-> (Y multiply Y) add X
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [14] (inverse(X) multiply Y) add X -> (X multiply X) add Y
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [15] (X multiply Y) add inverse(X) <-> (inverse(X) multiply inverse(X)) add Y
% Current number of equations to process: 11
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [16] (inverse(X) multiply inverse(X)) add Y <-> (X multiply Y) add inverse(X)
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [17]
% ((X multiply Y) add Y) add (multiplicative_identity add X) ->
% (X multiply Y) add multiplicative_identity
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [18] ((X multiply X) add X) add ((X multiply Y) add Y) -> X add Y
% Current number of equations to process: 5
% Current number of ordered equations: 2
% Current number of rules: 17
% New rule produced :
% [19] ((X multiply X) add (X multiply Y)) add (X add Y) -> X add Y
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [20] (X multiply Y) add ((inverse(X) multiply Y) add (Y multiply Y)) -> Y
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [21] (inverse(X) multiply Y) add ((X multiply Y) add (Y multiply Y)) -> Y
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [22] (additive_identity multiply X) add X -> X
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 21
% Rule [15]
% (X multiply Y) add inverse(X) <-> (inverse(X) multiply inverse(X)) add Y is composed into 
% [15] (X multiply Y) add inverse(X) -> inverse(X) add Y
% Rule [14] (inverse(X) multiply Y) add X -> (X multiply X) add Y is composed into 
% [14] (inverse(X) multiply Y) add X -> X add Y
% New rule produced : [23] X multiply X -> X
% Rule
% [7]
% ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add (Z multiply Z))
% -> (X multiply Y) add Z collapsed.
% Rule [13] (X multiply X) add Y <-> (Y multiply Y) add X collapsed.
% Rule
% [16] (inverse(X) multiply inverse(X)) add Y <-> (X multiply Y) add inverse(X)
% collapsed.
% Rule [18] ((X multiply X) add X) add ((X multiply Y) add Y) -> X add Y
% collapsed.
% Rule [19] ((X multiply X) add (X multiply Y)) add (X add Y) -> X add Y
% collapsed.
% Rule
% [20] (X multiply Y) add ((inverse(X) multiply Y) add (Y multiply Y)) -> Y
% collapsed.
% Rule
% [21] (inverse(X) multiply Y) add ((X multiply Y) add (Y multiply Y)) -> Y
% collapsed.
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [24]
% ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add Z) ->
% (X multiply Y) add Z
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [25] inverse(inverse(X)) multiply X -> X
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [26] inverse(inverse(X)) -> X
% Rule [25] inverse(inverse(X)) multiply X -> X collapsed.
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [27] additive_identity multiply X -> additive_identity
% Rule [11] (additive_identity multiply Y) add (X multiply Y) -> X multiply Y
% collapsed.
% Rule [22] (additive_identity multiply X) add X -> X collapsed.
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [28] ((X multiply Y) add Y) add (X add X) -> X add Y
% Current number of equations to process: 16
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced : [29] ((X multiply Y) add X) add (X add Y) -> X add Y
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [30] (X multiply Y) add ((inverse(X) multiply Y) add Y) -> Y
% Current number of equations to process: 14
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [31] (inverse(X) multiply Y) add ((X multiply Y) add Y) -> Y
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [32]
% (inverse(multiplicative_identity add X) multiply X) add inverse(multiplicative_identity add X)
% -> additive_identity
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [33] multiplicative_identity add X -> multiplicative_identity
% Rule
% [17]
% ((X multiply Y) add Y) add (multiplicative_identity add X) ->
% (X multiply Y) add multiplicative_identity collapsed.
% Rule
% [32]
% (inverse(multiplicative_identity add X) multiply X) add inverse(multiplicative_identity add X)
% -> additive_identity collapsed.
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [34] X add X -> X
% Rule [28] ((X multiply Y) add Y) add (X add X) -> X add Y collapsed.
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [35] ((X multiply Y) add Y) add X -> X add Y
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [36] ((X multiply Y) add X) add ((X multiply Y) add Y) -> X add Y
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [37] (inverse(X) multiply Y) add ((X multiply Y) add X) -> X add Y
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [38]
% ((X multiply Y) add (X multiply Z)) add inverse(X) ->
% (Y add Z) add inverse(X)
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [39]
% (X multiply Y) add ((inverse(X) multiply Y) add inverse(X)) ->
% inverse(X) add Y
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [40]
% ((inverse(Z) multiply Y) multiply X) add ((Y multiply Z) multiply X) ->
% X multiply Y
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [41]
% ((inverse(X) multiply Y) add (inverse(X) multiply Z)) add X ->
% (Y add Z) add X
% Current number of equations to process: 26
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [42]
% ((inverse(X) multiply Z) multiply Y) add (X multiply Y) ->
% (X multiply Y) add (Y multiply Z)
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [43]
% ((X multiply Z) multiply Y) add (inverse(X) multiply Y) ->
% (inverse(X) multiply Y) add (Y multiply Z)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [44] (inverse(X add Y) multiply X) add Y -> (X multiply Y) add Y
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [45]
% (inverse(X add Y) multiply Z) add ((X multiply Z) add (Y multiply Z)) -> Z
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [46]
% ((X multiply Y) add (X multiply Z)) add inverse(Y add Z) ->
% inverse(Y add Z) add X
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 32
% Rule [44] (inverse(X add Y) multiply X) add Y -> (X multiply Y) add Y is composed into 
% [44] (inverse(X add Y) multiply X) add Y -> Y
% New rule produced : [47] (X multiply Y) add X -> X
% Rule
% [24]
% ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add Z) ->
% (X multiply Y) add Z collapsed.
% Rule [29] ((X multiply Y) add X) add (X add Y) -> X add Y collapsed.
% Rule [30] (X multiply Y) add ((inverse(X) multiply Y) add Y) -> Y collapsed.
% Rule [31] (inverse(X) multiply Y) add ((X multiply Y) add Y) -> Y collapsed.
% Rule [35] ((X multiply Y) add Y) add X -> X add Y collapsed.
% Rule [36] ((X multiply Y) add X) add ((X multiply Y) add Y) -> X add Y
% collapsed.
% Rule [37] (inverse(X) multiply Y) add ((X multiply Y) add X) -> X add Y
% collapsed.
% Rule
% [39]
% (X multiply Y) add ((inverse(X) multiply Y) add inverse(X)) ->
% inverse(X) add Y collapsed.
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [48] ((X multiply Y) add (X multiply Z)) add Z -> (X multiply Y) add Z
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [49] (X add Y) add X -> X add Y
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [50] (X add Y) add inverse(X) -> multiplicative_identity
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [51] (inverse(X multiply Y) add Y) add inverse(X) -> multiplicative_identity
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [52] (X multiply Y) multiply Y -> X multiply Y
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [53]
% (inverse(X) multiply Y) multiply inverse(X multiply Y) ->
% inverse(X multiply Y) multiply Y
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [54]
% (X multiply Y) multiply inverse(inverse(Y) multiply X) ->
% inverse(inverse(Y) multiply X) multiply X
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [55] (inverse(X) add Y) add X -> multiplicative_identity
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [56] (inverse(inverse(X) multiply Y) add Y) add X -> multiplicative_identity
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [57] inverse(X add Y) multiply X -> additive_identity
% Rule
% [12]
% (inverse(X add Y) multiply X) add (inverse(X add Y) multiply Y) ->
% additive_identity collapsed.
% Rule [44] (inverse(X add Y) multiply X) add Y -> Y collapsed.
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [58] (inverse(inverse(X) add Y) multiply X) add (X multiply Y) -> X
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [59]
% ((inverse(X) multiply Y) multiply inverse(Y)) add (X multiply Y) ->
% X multiply Y
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [60]
% ((X multiply Y) multiply inverse(inverse(X) add Y)) add inverse(X) ->
% inverse(X)
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [61]
% ((X multiply Y) multiply inverse(X)) add (inverse(Y) multiply X) ->
% inverse(Y) multiply X
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [62]
% (inverse(X add Y) multiply inverse(X)) add (inverse(X) multiply Y) ->
% inverse(X)
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [63]
% (X multiply Y) add inverse(inverse(X) add Y) ->
% inverse(inverse(X) add Y) add X
% Current number of equations to process: 53
% Current number of ordered equations: 1
% Current number of rules: 39
% New rule produced :
% [64]
% (inverse(X) multiply Y) add inverse(X add Y) ->
% inverse(X add Y) add inverse(X)
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [65] ((X multiply Y) add (X multiply Z)) add X -> X
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [66] ((Y multiply Z) multiply X) add (X multiply Y) -> X multiply Y
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [67] inverse(X multiply Y) add X -> multiplicative_identity
% Rule
% [51] (inverse(X multiply Y) add Y) add inverse(X) -> multiplicative_identity
% collapsed.
% Rule
% [56] (inverse(inverse(X) multiply Y) add Y) add X -> multiplicative_identity
% collapsed.
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [68] (inverse(X multiply Y) multiply X) add Y -> X add Y
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [69] ((inverse(Z) multiply Y) multiply X) add Z -> (X multiply Y) add Z
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [70] ((X multiply Y) add (X multiply Z)) add (Y add Z) -> Y add Z
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [71]
% ((Y multiply Z) multiply X) add inverse(Z) -> (X multiply Y) add inverse(Z)
% Rule
% [60]
% ((X multiply Y) multiply inverse(inverse(X) add Y)) add inverse(X) ->
% inverse(X) collapsed.
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced : [72] (inverse(X) multiply Y) add (X add Y) -> X add Y
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [73] (X multiply Y) add (inverse(X) add Y) -> inverse(X) add Y
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [74] (inverse(X) add Y) add inverse(X multiply Y) -> multiplicative_identity
% Current number of equations to process: 77
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [75] (X add Y) add inverse(inverse(X) multiply Y) -> multiplicative_identity
% Current number of equations to process: 76
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [76]
% (X multiply Y) add inverse((Y multiply Z) multiply X) ->
% multiplicative_identity
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [77]
% inverse((X multiply Y) add (Y multiply Z)) add Y -> multiplicative_identity
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [78] (X add Y) add inverse(X multiply Z) -> multiplicative_identity
% Rule
% [74] (inverse(X) add Y) add inverse(X multiply Y) -> multiplicative_identity
% collapsed.
% Rule
% [75] (X add Y) add inverse(inverse(X) multiply Y) -> multiplicative_identity
% collapsed.
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [79] ((X multiply Y) multiply Z) multiply X -> (X multiply Y) multiply Z
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [80] ((inverse(Z) multiply X) add Y) add Z -> (X add Y) add Z
% Rule
% [41]
% ((inverse(X) multiply Y) add (inverse(X) multiply Z)) add X ->
% (Y add Z) add X collapsed.
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [81] (inverse(Y multiply Z) multiply X) add (X multiply Z) -> X
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced : [82] ((X multiply Y) multiply Z) add X -> X
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [83] ((X multiply Z) add Y) add inverse(Z) -> (X add Y) add inverse(Z)
% Rule
% [38]
% ((X multiply Y) add (X multiply Z)) add inverse(X) ->
% (Y add Z) add inverse(X) collapsed.
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [84] (inverse(Y) multiply X) add ((X multiply Y) add (X multiply Z)) -> X
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [85]
% ((X multiply Y) multiply inverse(Y)) multiply inverse(X multiply Y) ->
% additive_identity
% Current number of equations to process: 104
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [86]
% (inverse(X multiply Y) multiply Y) add (inverse(X) multiply Y) ->
% inverse(X) multiply Y
% Current number of equations to process: 117
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [87]
% ((inverse(Z) multiply Y) multiply X) add (Y multiply Z) ->
% (X multiply Y) add (Y multiply Z)
% Rule
% [59]
% ((inverse(X) multiply Y) multiply inverse(Y)) add (X multiply Y) ->
% X multiply Y collapsed.
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [88] (X multiply Y) multiply inverse(X) -> additive_identity
% Rule
% [61]
% ((X multiply Y) multiply inverse(X)) add (inverse(Y) multiply X) ->
% inverse(Y) multiply X collapsed.
% Rule
% [85]
% ((X multiply Y) multiply inverse(Y)) multiply inverse(X multiply Y) ->
% additive_identity collapsed.
% Current number of equations to process: 143
% Current number of ordered equations: 0
% Current number of rules: 54
% Rule [63]
% (X multiply Y) add inverse(inverse(X) add Y) ->
% inverse(inverse(X) add Y) add X is composed into [63]
% (X multiply Y) add 
% inverse(inverse(X) add Y)
% -> X
% New rule produced : [89] inverse(inverse(X) add Y) add X -> X
% Current number of equations to process: 143
% Current number of ordered equations: 0
% Current number of rules: 55
% Rule [64]
% (inverse(X) multiply Y) add inverse(X add Y) ->
% inverse(X add Y) add inverse(X) is composed into [64]
% (inverse(X) multiply Y) add 
% inverse(X add Y) ->
% inverse(X)
% New rule produced : [90] inverse(X add Y) add inverse(X) -> inverse(X)
% Current number of equations to process: 142
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [91] inverse(X add Y) multiply inverse(X) -> inverse(X add Y)
% Rule
% [62]
% (inverse(X add Y) multiply inverse(X)) add (inverse(X) multiply Y) ->
% inverse(X) collapsed.
% Current number of equations to process: 141
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [92] (X multiply Y) multiply inverse(inverse(X) add Y) -> additive_identity
% Current number of equations to process: 140
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [93] inverse(inverse(X) add Y) multiply X -> inverse(inverse(X) add Y)
% Rule [58] (inverse(inverse(X) add Y) multiply X) add (X multiply Y) -> X
% collapsed.
% Current number of equations to process: 139
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [94] (inverse(X) multiply Y) multiply inverse(X add Y) -> additive_identity
% Current number of equations to process: 138
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [95]
% ((X multiply Y) multiply Z) multiply inverse(X multiply Z) ->
% additive_identity
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [96]
% (X multiply Y) multiply inverse((X multiply Z) add Y) -> additive_identity
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [97]
% (inverse(X) multiply Y) multiply inverse(X add Z) ->
% inverse(X add Z) multiply Y
% Rule
% [94] (inverse(X) multiply Y) multiply inverse(X add Y) -> additive_identity
% collapsed.
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [98]
% (inverse(inverse(X) multiply Y) multiply Y) add (X multiply Y) ->
% X multiply Y
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [99] (X multiply Y) add ((inverse(Y) multiply X) add (X multiply Z)) -> X
% Current number of equations to process: 154
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [100]
% (inverse(inverse(Y) add Z) multiply X) add (X multiply Y) -> X multiply Y
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [101]
% (X multiply Y) multiply inverse(inverse(X) add Z) ->
% inverse(inverse(X) add Z) multiply Y
% Rule
% [92] (X multiply Y) multiply inverse(inverse(X) add Y) -> additive_identity
% collapsed.
% Current number of equations to process: 152
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [102]
% (inverse(X add Z) multiply Y) add (inverse(X) multiply Y) ->
% inverse(X) multiply Y
% Current number of equations to process: 151
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [103] (inverse(inverse(X add Y) add Z) multiply X) add (X multiply Z) -> X
% Current number of equations to process: 151
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [104] inverse(X multiply Y) add inverse(Y) -> inverse(X multiply Y)
% Current number of equations to process: 158
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [105] (inverse(X) multiply Y) multiply X -> additive_identity
% Current number of equations to process: 169
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [106] (X multiply Y) multiply inverse(X add Z) -> additive_identity
% Rule
% [96]
% (X multiply Y) multiply inverse((X multiply Z) add Y) -> additive_identity
% collapsed.
% Current number of equations to process: 190
% Current number of ordered equations: 1
% Current number of rules: 67
% New rule produced :
% [107] (inverse(X add Y) multiply Z) multiply X -> additive_identity
% Current number of equations to process: 190
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced : [108] inverse(inverse(X) multiply Y) multiply X -> X
% Current number of equations to process: 194
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [109] inverse(X multiply Y) multiply inverse(X) -> inverse(X)
% Current number of equations to process: 194
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [110] (inverse(inverse(X) multiply Y) multiply Y) add X -> X
% Current number of equations to process: 212
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [111] (inverse(X multiply Y) multiply X) add (X add Y) -> X add Y
% Current number of equations to process: 211
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [112]
% (X add Y) add inverse((X multiply Z) add (Y multiply Z)) ->
% multiplicative_identity
% Current number of equations to process: 213
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [113]
% (inverse(X) multiply Y) add inverse(inverse(X multiply Y) multiply Y) ->
% multiplicative_identity
% Current number of equations to process: 212
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [114]
% (X multiply Y) add inverse(inverse(inverse(Y) multiply X) multiply X) ->
% multiplicative_identity
% Current number of equations to process: 211
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [115] inverse(inverse(X) multiply Y) add X -> inverse(Y) add X
% Current number of equations to process: 217
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced : [116] (X multiply Z) add (X add Y) -> X add Y
% Rule [72] (inverse(X) multiply Y) add (X add Y) -> X add Y collapsed.
% Rule [73] (X multiply Y) add (inverse(X) add Y) -> inverse(X) add Y
% collapsed.
% Rule [111] (inverse(X multiply Y) multiply X) add (X add Y) -> X add Y
% collapsed.
% Current number of equations to process: 221
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced : [117] (inverse(inverse(X) add Y) multiply Z) add X -> X
% Current number of equations to process: 220
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [118] (inverse((inverse(X) multiply Y) add Z) multiply Y) add X -> X
% Current number of equations to process: 224
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [119]
% ((inverse(X multiply Z) multiply Y) multiply X) add Z -> (X multiply Y) add Z
% Current number of equations to process: 223
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [120] ((X multiply Y) add ((X multiply Z) add (X multiply V_3))) add X -> X
% Current number of equations to process: 225
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [121]
% ((X multiply Y) add Z) add inverse((inverse(Z) multiply Y) multiply X) ->
% multiplicative_identity
% Current number of equations to process: 224
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [122]
% ((inverse(X) multiply Y) multiply Z) multiply inverse((Y multiply Z) add X)
% -> additive_identity
% Current number of equations to process: 223
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [123] (inverse(X multiply Y) multiply Y) add inverse(X) -> inverse(X)
% Current number of equations to process: 240
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [124]
% (((X multiply Y) multiply Z) multiply V_3) add (X multiply Z) -> X multiply Z
% Current number of equations to process: 239
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [125] (Y multiply Z) add inverse(X multiply Y) -> inverse(X multiply Y) add Z
% Rule
% [76]
% (X multiply Y) add inverse((Y multiply Z) multiply X) ->
% multiplicative_identity collapsed.
% Rule
% [113]
% (inverse(X) multiply Y) add inverse(inverse(X multiply Y) multiply Y) ->
% multiplicative_identity collapsed.
% Rule
% [114]
% (X multiply Y) add inverse(inverse(inverse(Y) multiply X) multiply X) ->
% multiplicative_identity collapsed.
% Current number of equations to process: 245
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [126] inverse((Y multiply Z) multiply X) add Y -> multiplicative_identity
% Current number of equations to process: 244
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [127]
% inverse(inverse(X multiply Y) multiply Y) add inverse(X) ->
% multiplicative_identity
% Current number of equations to process: 243
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [128]
% inverse(inverse(inverse(Y) multiply X) multiply X) add Y ->
% multiplicative_identity
% Current number of equations to process: 242
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced : [129] inverse(X multiply Y) -> inverse(X) add inverse(Y)
% Rule
% [53]
% (inverse(X) multiply Y) multiply inverse(X multiply Y) ->
% inverse(X multiply Y) multiply Y collapsed.
% Rule
% [54]
% (X multiply Y) multiply inverse(inverse(Y) multiply X) ->
% inverse(inverse(Y) multiply X) multiply X collapsed.
% Rule [67] inverse(X multiply Y) add X -> multiplicative_identity collapsed.
% Rule [68] (inverse(X multiply Y) multiply X) add Y -> X add Y collapsed.
% Rule [78] (X add Y) add inverse(X multiply Z) -> multiplicative_identity
% collapsed.
% Rule [81] (inverse(Y multiply Z) multiply X) add (X multiply Z) -> X
% collapsed.
% Rule
% [86]
% (inverse(X multiply Y) multiply Y) add (inverse(X) multiply Y) ->
% inverse(X) multiply Y collapsed.
% Rule
% [95]
% ((X multiply Y) multiply Z) multiply inverse(X multiply Z) ->
% additive_identity collapsed.
% Rule
% [98]
% (inverse(inverse(X) multiply Y) multiply Y) add (X multiply Y) ->
% X multiply Y collapsed.
% Rule [104] inverse(X multiply Y) add inverse(Y) -> inverse(X multiply Y)
% collapsed.
% Rule [108] inverse(inverse(X) multiply Y) multiply X -> X collapsed.
% Rule [109] inverse(X multiply Y) multiply inverse(X) -> inverse(X) collapsed.
% Rule [110] (inverse(inverse(X) multiply Y) multiply Y) add X -> X collapsed.
% Rule [115] inverse(inverse(X) multiply Y) add X -> inverse(Y) add X
% collapsed.
% Rule
% [119]
% ((inverse(X multiply Z) multiply Y) multiply X) add Z -> (X multiply Y) add Z
% collapsed.
% Rule
% [121]
% ((X multiply Y) add Z) add inverse((inverse(Z) multiply Y) multiply X) ->
% multiplicative_identity collapsed.
% Rule [123] (inverse(X multiply Y) multiply Y) add inverse(X) -> inverse(X)
% collapsed.
% Rule
% [125] (Y multiply Z) add inverse(X multiply Y) -> inverse(X multiply Y) add Z
% collapsed.
% Rule
% [126] inverse((Y multiply Z) multiply X) add Y -> multiplicative_identity
% collapsed.
% Rule
% [127]
% inverse(inverse(X multiply Y) multiply Y) add inverse(X) ->
% multiplicative_identity collapsed.
% Rule
% [128]
% inverse(inverse(inverse(Y) multiply X) multiply X) add Y ->
% multiplicative_identity collapsed.
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [130] (inverse(X) add inverse(Z)) add (X add Y) -> multiplicative_identity
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [131] (inverse(X add Y) multiply Z) add inverse(X) -> inverse(X)
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [132]
% ((inverse(Y) add inverse(Z)) add inverse(X)) add Y -> multiplicative_identity
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [133] ((X multiply Y) multiply Z) multiply inverse(X) -> additive_identity
% Current number of equations to process: 249
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [134] (inverse((X multiply Y) add Z) multiply Y) add inverse(X) -> inverse(X)
% Current number of equations to process: 254
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [135]
% (inverse(inverse(X) add inverse(Y)) add inverse(Y)) add inverse(X) ->
% multiplicative_identity
% Current number of equations to process: 255
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [136]
% (inverse(inverse(X) add Y) add inverse(X)) add Y -> multiplicative_identity
% Rule
% [135]
% (inverse(inverse(X) add inverse(Y)) add inverse(Y)) add inverse(X) ->
% multiplicative_identity collapsed.
% Current number of equations to process: 254
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [137]
% (Y multiply Z) add (inverse(X) add inverse(Y)) ->
% (inverse(X) add inverse(Y)) add Z
% Current number of equations to process: 253
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [138]
% inverse((X multiply Y) add (X multiply Z)) multiply inverse(X) -> inverse(X)
% Current number of equations to process: 269
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [139] (((X multiply Y) multiply Z) multiply V_3) add X -> X
% Current number of equations to process: 271
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [140] ((X multiply Y) multiply Z) add (X add V_3) -> X add V_3
% Current number of equations to process: 282
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [141] (((X multiply Y) multiply Z) add (X multiply V_3)) add X -> X
% Current number of equations to process: 281
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [142]
% inverse((inverse(X) multiply Y) add (inverse(X) multiply Z)) multiply X -> X
% Current number of equations to process: 282
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [143]
% (((X multiply Y) multiply Z) multiply V_3) multiply X ->
% ((X multiply Y) multiply Z) multiply V_3
% Current number of equations to process: 280
% Current number of ordered equations: 1
% Current number of rules: 76
% New rule produced :
% [144]
% (((X multiply Y) multiply Z) multiply V_3) add (X multiply V_3) ->
% X multiply V_3
% Current number of equations to process: 280
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [145]
% inverse(((X multiply Y) multiply Z) add (X multiply V_3)) add X ->
% multiplicative_identity
% Current number of equations to process: 279
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced : [146] (X add Y) add (X add Z) -> (X add Y) add Z
% Current number of equations to process: 283
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced : [147] (inverse(inverse(Y) add Z) add X) add Y -> X add Y
% Current number of equations to process: 282
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [148] (inverse(X add Y) add Y) add X -> multiplicative_identity
% Rule
% [136]
% (inverse(inverse(X) add Y) add inverse(X)) add Y -> multiplicative_identity
% collapsed.
% Current number of equations to process: 283
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [149]
% (inverse(X) add inverse(Y)) add inverse(Z) <->
% (inverse(X) add inverse(Z)) add inverse(Y)
% Current number of equations to process: 289
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [150] (X multiply Y) add (inverse(Y) add Z) -> (inverse(Y) add Z) add X
% Rule
% [137]
% (Y multiply Z) add (inverse(X) add inverse(Y)) ->
% (inverse(X) add inverse(Y)) add Z collapsed.
% Current number of equations to process: 289
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [151] (((inverse(Z) multiply X) add Y) add X) add Z -> (X add Y) add Z
% Current number of equations to process: 293
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [152] (inverse(X add Z) add Y) add inverse(X) -> inverse(X) add Y
% Current number of equations to process: 298
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [153]
% ((X multiply Y) add Z) add (inverse(X) add inverse(Y)) ->
% multiplicative_identity
% Current number of equations to process: 297
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [154] (inverse(Z) add Y) add X <-> (X add Y) add inverse(Z)
% Rule [55] (inverse(X) add Y) add X -> multiplicative_identity collapsed.
% Rule [147] (inverse(inverse(Y) add Z) add X) add Y -> X add Y collapsed.
% Rule [148] (inverse(X add Y) add Y) add X -> multiplicative_identity
% collapsed.
% Rule [152] (inverse(X add Z) add Y) add inverse(X) -> inverse(X) add Y
% collapsed.
% Current number of equations to process: 301
% Current number of ordered equations: 1
% Current number of rules: 81
% New rule produced :
% [155] (X add Y) add inverse(Z) <-> (inverse(Z) add Y) add X
% Current number of equations to process: 301
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced : [156] (X add Y) add inverse(inverse(Y) add Z) -> X add Y
% Current number of equations to process: 300
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [157] (inverse(X) add Y) add inverse(X add Z) -> inverse(X) add Y
% Current number of equations to process: 299
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [158] (inverse(X) add Y) add inverse(Z) <-> (inverse(X) add inverse(Z)) add Y
% Rule
% [149]
% (inverse(X) add inverse(Y)) add inverse(Z) <->
% (inverse(X) add inverse(Z)) add inverse(Y) collapsed.
% Current number of equations to process: 299
% Current number of ordered equations: 1
% Current number of rules: 84
% New rule produced :
% [159] (inverse(X) add inverse(Z)) add Y <-> (inverse(X) add Y) add inverse(Z)
% Current number of equations to process: 299
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [160]
% (((X multiply Z) add Y) add X) add inverse(Z) -> (X add Y) add inverse(Z)
% Current number of equations to process: 300
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [161]
% ((X multiply Y) add inverse(Z)) add ((inverse(Y) add inverse(Z)) add 
% inverse(X)) -> multiplicative_identity
% Current number of equations to process: 303
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [162]
% ((X multiply Y) multiply Z) multiply inverse((X multiply Z) add inverse(Y))
% -> additive_identity
% Current number of equations to process: 302
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [163]
% ((X multiply Y) multiply Z) add inverse((Y multiply Z) add inverse(X)) -> X
% Current number of equations to process: 301
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [164]
% ((inverse(X) multiply Y) multiply Z) add ((X multiply Z) multiply Y) ->
% Y multiply Z
% Current number of equations to process: 300
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [165]
% ((X multiply Y) multiply inverse(Z)) add (X multiply Z) ->
% (X multiply Y) add (X multiply Z)
% Current number of equations to process: 299
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [166]
% ((X add Y) add Z) add inverse((inverse(Z) multiply X) add Y) ->
% multiplicative_identity
% Current number of equations to process: 298
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [167]
% (((X multiply Y) multiply Z) add ((X multiply V_3) multiply Z)) add X -> X
% Current number of equations to process: 296
% Current number of ordered equations: 1
% Current number of rules: 93
% New rule produced :
% [168]
% (((X multiply Y) multiply Z) add ((X multiply Y) multiply V_3)) add X -> X
% Current number of equations to process: 296
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [169]
% ((X add Y) add inverse(Z)) add inverse((X multiply Z) add Y) ->
% multiplicative_identity
% Current number of equations to process: 295
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [170]
% ((X multiply Y) multiply Z) add (inverse(X) multiply Y) ->
% (inverse(X) multiply Y) add (Y multiply Z)
% Current number of equations to process: 303
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [171]
% ((inverse(X) multiply Y) multiply Z) add inverse((Y multiply Z) add X) ->
% inverse(X)
% Current number of equations to process: 299
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [172]
% inverse((X multiply Y) add inverse(Z)) add inverse(Z) ->
% (inverse(X) add inverse(Z)) add inverse(Y)
% Current number of equations to process: 298
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [173]
% ((X multiply Y) multiply Z) add (inverse(Z) multiply X) ->
% (inverse(Z) multiply X) add (X multiply Y)
% Current number of equations to process: 295
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [174] (X multiply Y) multiply (X multiply Z) -> (X multiply Y) multiply Z
% Current number of equations to process: 303
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced : [175] inverse(inverse(X) add inverse(Y)) -> X multiply Y
% Current number of equations to process: 307
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [176] (inverse(X) multiply Y) multiply (X multiply Z) -> additive_identity
% Current number of equations to process: 307
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced : [177] ((Y multiply Z) add X) add Y -> X add Y
% Rule [48] ((X multiply Y) add (X multiply Z)) add Z -> (X multiply Y) add Z
% collapsed.
% Rule [65] ((X multiply Y) add (X multiply Z)) add X -> X collapsed.
% Rule
% [120] ((X multiply Y) add ((X multiply Z) add (X multiply V_3))) add X -> X
% collapsed.
% Rule [141] (((X multiply Y) multiply Z) add (X multiply V_3)) add X -> X
% collapsed.
% Rule [151] (((inverse(Z) multiply X) add Y) add X) add Z -> (X add Y) add Z
% collapsed.
% Rule
% [160]
% (((X multiply Z) add Y) add X) add inverse(Z) -> (X add Y) add inverse(Z)
% collapsed.
% Current number of equations to process: 308
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [178] (inverse(X) multiply Z) add (X add Y) -> (X add Y) add Z
% Current number of equations to process: 330
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [179] (inverse(X) add Y) add (X add Z) -> multiplicative_identity
% Rule
% [130] (inverse(X) add inverse(Z)) add (X add Y) -> multiplicative_identity
% collapsed.
% Current number of equations to process: 335
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [180]
% (inverse(X add Y) multiply Z) multiply inverse(X) ->
% inverse(X add Y) multiply Z
% Current number of equations to process: 339
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [181] inverse((X add Y) add Z) multiply X -> additive_identity
% Current number of equations to process: 345
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [182]
% inverse(inverse(X) add Y) multiply inverse(X add Z) -> additive_identity
% Current number of equations to process: 344
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [183]
% (X multiply Y) add ((inverse(X) add inverse(Y)) add inverse(Z)) ->
% multiplicative_identity
% Current number of equations to process: 343
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [184]
% inverse((X multiply Y) add inverse(inverse(X) add Z)) add X ->
% multiplicative_identity
% Current number of equations to process: 341
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [185]
% (inverse(inverse(X) add Y) multiply Z) multiply X ->
% inverse(inverse(X) add Y) multiply Z
% Current number of equations to process: 340
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [186] inverse(inverse(X add Y) add X) add inverse(X add Y) -> inverse(X)
% Current number of equations to process: 346
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [187]
% inverse((X add Y) add Z) multiply inverse(X) -> inverse((X add Y) add Z)
% Current number of equations to process: 380
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [188]
% inverse((inverse(X) add Y) add Z) multiply X ->
% inverse((inverse(X) add Y) add Z)
% Current number of equations to process: 379
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [189]
% inverse((inverse(X) multiply Y) add inverse(X add Z)) add inverse(X) ->
% multiplicative_identity
% Current number of equations to process: 382
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [190]
% ((inverse(Z) multiply X) multiply Y) add (Z add V_3) ->
% (X multiply Y) add (Z add V_3)
% Current number of equations to process: 381
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [191]
% ((inverse(X) multiply Z) add V_3) add (X add Y) -> (X add Y) add (Z add V_3)
% Current number of equations to process: 380
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [192] ((inverse(X) add Y) add inverse(Z)) add X -> multiplicative_identity
% Rule
% [132]
% ((inverse(Y) add inverse(Z)) add inverse(X)) add Y -> multiplicative_identity
% collapsed.
% Current number of equations to process: 394
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [193]
% (inverse(X) multiply Y) add inverse(inverse(Y) add X) ->
% inverse(X) multiply Y
% Current number of equations to process: 398
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [194]
% (X multiply Y) add inverse((inverse(X) add inverse(Y)) add Z) -> X multiply Y
% Current number of equations to process: 403
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [195] ((X add Y) add inverse(Z)) add inverse(X) -> multiplicative_identity
% Current number of equations to process: 440
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [196] (Y add Z) add inverse(X) <-> (inverse(X) add Y) add Z
% Current number of equations to process: 440
% Current number of ordered equations: 1
% Current number of rules: 114
% New rule produced :
% [197] (inverse(X) add Y) add Z <-> (Y add Z) add inverse(X)
% Current number of equations to process: 440
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [198] ((X add Y) add inverse(Z)) add X -> (X add Y) add inverse(Z)
% Current number of equations to process: 452
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [199]
% (inverse(X) multiply inverse(Y)) add inverse(X add Y) ->
% inverse(X) multiply inverse(Y)
% Current number of equations to process: 454
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [200]
% ((X multiply Z) multiply Y) add (inverse(Z) add V_3) ->
% (X multiply Y) add (inverse(Z) add V_3)
% Current number of equations to process: 471
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [201]
% ((X multiply Z) add V_3) add (inverse(X) add Y) ->
% (inverse(X) add Y) add (Z add V_3)
% Rule
% [153]
% ((X multiply Y) add Z) add (inverse(X) add inverse(Y)) ->
% multiplicative_identity collapsed.
% Rule
% [161]
% ((X multiply Y) add inverse(Z)) add ((inverse(Y) add inverse(Z)) add 
% inverse(X)) -> multiplicative_identity
% collapsed.
% Current number of equations to process: 471
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [202]
% ((inverse(Y) add inverse(Z)) add inverse(X)) add (inverse(Z) add Y) ->
% multiplicative_identity
% Current number of equations to process: 470
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [203]
% inverse(inverse(X add Y) add Z) add inverse(X) -> inverse(X) add inverse(Z)
% Rule
% [189]
% inverse((inverse(X) multiply Y) add inverse(X add Z)) add inverse(X) ->
% multiplicative_identity collapsed.
% Current number of equations to process: 477
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [204]
% (X add Y) add inverse(inverse(inverse(X) add Z) add Y) ->
% multiplicative_identity
% Current number of equations to process: 483
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [205]
% (inverse(X) add Y) add inverse(inverse(X add Z) add Y) ->
% multiplicative_identity
% Current number of equations to process: 482
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced : [206] inverse(inverse(X) add Y) -> inverse(Y) multiply X
% Rule [63] (X multiply Y) add inverse(inverse(X) add Y) -> X collapsed.
% Rule [89] inverse(inverse(X) add Y) add X -> X collapsed.
% Rule [93] inverse(inverse(X) add Y) multiply X -> inverse(inverse(X) add Y)
% collapsed.
% Rule
% [100]
% (inverse(inverse(Y) add Z) multiply X) add (X multiply Y) -> X multiply Y
% collapsed.
% Rule
% [101]
% (X multiply Y) multiply inverse(inverse(X) add Z) ->
% inverse(inverse(X) add Z) multiply Y collapsed.
% Rule
% [103] (inverse(inverse(X add Y) add Z) multiply X) add (X multiply Z) -> X
% collapsed.
% Rule [117] (inverse(inverse(X) add Y) multiply Z) add X -> X collapsed.
% Rule [156] (X add Y) add inverse(inverse(Y) add Z) -> X add Y collapsed.
% Rule
% [162]
% ((X multiply Y) multiply Z) multiply inverse((X multiply Z) add inverse(Y))
% -> additive_identity collapsed.
% Rule
% [163]
% ((X multiply Y) multiply Z) add inverse((Y multiply Z) add inverse(X)) -> X
% collapsed.
% Rule
% [172]
% inverse((X multiply Y) add inverse(Z)) add inverse(Z) ->
% (inverse(X) add inverse(Z)) add inverse(Y) collapsed.
% Rule [175] inverse(inverse(X) add inverse(Y)) -> X multiply Y collapsed.
% Rule
% [182]
% inverse(inverse(X) add Y) multiply inverse(X add Z) -> additive_identity
% collapsed.
% Rule
% [184]
% inverse((X multiply Y) add inverse(inverse(X) add Z)) add X ->
% multiplicative_identity collapsed.
% Rule
% [185]
% (inverse(inverse(X) add Y) multiply Z) multiply X ->
% inverse(inverse(X) add Y) multiply Z collapsed.
% Rule [186] inverse(inverse(X add Y) add X) add inverse(X add Y) -> inverse(X)
% collapsed.
% Rule
% [193]
% (inverse(X) multiply Y) add inverse(inverse(Y) add X) ->
% inverse(X) multiply Y collapsed.
% Rule
% [203]
% inverse(inverse(X add Y) add Z) add inverse(X) -> inverse(X) add inverse(Z)
% collapsed.
% Rule
% [204]
% (X add Y) add inverse(inverse(inverse(X) add Z) add Y) ->
% multiplicative_identity collapsed.
% Rule
% [205]
% (inverse(X) add Y) add inverse(inverse(X add Z) add Y) ->
% multiplicative_identity collapsed.
% Current number of equations to process: 499
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [207] ((inverse(X) multiply Y) multiply Z) multiply X -> additive_identity
% Current number of equations to process: 499
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [208]
% (((X multiply Y) multiply Z) multiply V_3) multiply inverse(X) ->
% additive_identity
% Current number of equations to process: 501
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [209]
% ((X multiply Y) multiply Z) multiply (inverse(Y) multiply X) ->
% additive_identity
% Current number of equations to process: 505
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [210]
% (X add Y) add inverse((inverse(Z) multiply X) add Y) ->
% multiplicative_identity
% Current number of equations to process: 507
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [211]
% ((inverse(X) multiply Y) multiply Z) multiply inverse(X add Y) ->
% additive_identity
% Current number of equations to process: 505
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [212]
% ((X multiply Y) multiply Z) multiply inverse(X add V_3) -> additive_identity
% Rule
% [211]
% ((inverse(X) multiply Y) multiply Z) multiply inverse(X add Y) ->
% additive_identity collapsed.
% Current number of equations to process: 514
% Current number of ordered equations: 1
% Current number of rules: 106
% New rule produced :
% [213]
% (inverse(X add Y) multiply Z) multiply (X multiply V_3) -> additive_identity
% Current number of equations to process: 514
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [214] (X multiply Y) multiply inverse((X add Z) add V_3) -> additive_identity
% Current number of equations to process: 515
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [215]
% ((inverse(X add Y) multiply Z) multiply V_3) multiply X -> additive_identity
% Current number of equations to process: 515
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [216]
% ((X multiply Y) multiply Z) multiply (inverse(X) multiply V_3) ->
% additive_identity
% Rule
% [209]
% ((X multiply Y) multiply Z) multiply (inverse(Y) multiply X) ->
% additive_identity collapsed.
% Current number of equations to process: 518
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [217]
% ((inverse(X) multiply Y) multiply Z) multiply (X multiply Y) ->
% additive_identity
% Current number of equations to process: 523
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [218] ((X multiply V_3) add Z) add (X add Y) -> (X add Y) add Z
% Rule [70] ((X multiply Y) add (X multiply Z)) add (Y add Z) -> Y add Z
% collapsed.
% Current number of equations to process: 527
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [219]
% ((inverse(X add Y) multiply Z) multiply V_3) add inverse(X) -> inverse(X)
% Current number of equations to process: 541
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [220]
% ((X multiply Y) multiply Z) add ((inverse(Y) multiply X) add (inverse(Z) multiply X))
% -> X
% Current number of equations to process: 539
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [221]
% (inverse(X) multiply Y) add ((inverse(Y) add X) add inverse(Z)) ->
% multiplicative_identity
% Current number of equations to process: 538
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [222]
% ((inverse(X add Y) multiply Z) multiply V_3) multiply (X multiply Z) ->
% additive_identity
% Current number of equations to process: 537
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [223]
% (X multiply V_3) add ((X add Y) add inverse(Z)) -> (X add Y) add inverse(Z)
% Current number of equations to process: 537
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [224]
% (inverse(X add Z) multiply V_3) add (inverse(X) add Y) -> inverse(X) add Y
% Current number of equations to process: 536
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [225]
% (inverse((inverse(X) multiply Y) add Z) multiply X) add (X multiply Z) -> X
% Current number of equations to process: 540
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [226]
% ((inverse((inverse(X) multiply Y) add Z) multiply V_3) multiply Y) add X -> X
% Current number of equations to process: 539
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [227]
% ((inverse(X) add inverse(Y)) add inverse(Z)) add (X add V_3) ->
% multiplicative_identity
% Rule
% [202]
% ((inverse(Y) add inverse(Z)) add inverse(X)) add (inverse(Z) add Y) ->
% multiplicative_identity collapsed.
% Current number of equations to process: 546
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [228] ((inverse(X) add Y) add Z) add X -> multiplicative_identity
% Rule
% [192] ((inverse(X) add Y) add inverse(Z)) add X -> multiplicative_identity
% collapsed.
% Current number of equations to process: 556
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [229] ((X add Y) add Z) add inverse(X) -> multiplicative_identity
% Rule
% [195] ((X add Y) add inverse(Z)) add inverse(X) -> multiplicative_identity
% collapsed.
% Current number of equations to process: 556
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [230]
% (inverse((inverse(X) multiply Y) add Z) multiply Y) multiply inverse(X) ->
% additive_identity
% Current number of equations to process: 564
% Current number of ordered equations: 0
% Current number of rules: 119
% (X add Z) add Y = (X add Y) add Z (birth = 2347, lhs_size = 5, rhs_size = 5,trace = Cp of 118 and 80)
% Initializing completion ...
% New rule produced : [1] inverse(multiplicative_identity) -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 112
% Current number of rules: 1
% New rule produced : [2] inverse(additive_identity) -> multiplicative_identity
% Current number of equations to process: 529
% Current number of ordered equations: 111
% Current number of rules: 2
% New rule produced : [3] inverse(inverse(X)) -> X
% Current number of equations to process: 529
% Current number of ordered equations: 110
% Current number of rules: 3
% New rule produced : [4] X multiply X -> X
% Current number of equations to process: 529
% Current number of ordered equations: 109
% Current number of rules: 4
% New rule produced : [5] multiplicative_identity multiply X -> X
% Current number of equations to process: 529
% Current number of ordered equations: 108
% Current number of rules: 5
% New rule produced : [6] additive_identity multiply X -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 107
% Current number of rules: 6
% New rule produced : [7] X add X -> X
% Current number of equations to process: 529
% Current number of ordered equations: 103
% Current number of rules: 7
% New rule produced :
% [8] multiplicative_identity add X -> multiplicative_identity
% Current number of equations to process: 529
% Current number of ordered equations: 102
% Current number of rules: 8
% New rule produced : [9] additive_identity add X -> X
% Current number of equations to process: 529
% Current number of ordered equations: 101
% Current number of rules: 9
% New rule produced : [10] inverse(X) multiply X -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 100
% Current number of rules: 10
% New rule produced : [11] inverse(X) add X -> multiplicative_identity
% Current number of equations to process: 529
% Current number of ordered equations: 96
% Current number of rules: 11
% New rule produced : [12] (X multiply Y) add X -> X
% Current number of equations to process: 529
% Current number of ordered equations: 91
% Current number of rules: 12
% New rule produced : [13] (X multiply Y) multiply Y -> X multiply Y
% Current number of equations to process: 529
% Current number of ordered equations: 90
% Current number of rules: 13
% New rule produced :
% [14] (X multiply Y) multiply inverse(X) -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 89
% Current number of rules: 14
% New rule produced :
% [15] (inverse(X) multiply Y) multiply X -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 88
% Current number of rules: 15
% New rule produced : [16] inverse(X add Y) multiply X -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 86
% Current number of rules: 16
% New rule produced : [17] inverse(X multiply Y) -> inverse(X) add inverse(Y)
% Current number of equations to process: 529
% Current number of ordered equations: 85
% Current number of rules: 17
% New rule produced : [18] inverse(inverse(X) add Y) -> inverse(Y) multiply X
% Current number of equations to process: 530
% Current number of ordered equations: 82
% Current number of rules: 18
% New rule produced : [19] (inverse(X) multiply Y) add X -> X add Y
% Current number of equations to process: 529
% Current number of ordered equations: 78
% Current number of rules: 19
% New rule produced : [20] ((X multiply Y) multiply Z) add X -> X
% Current number of equations to process: 529
% Current number of ordered equations: 74
% Current number of rules: 20
% New rule produced : [21] (X multiply Y) add inverse(X) -> inverse(X) add Y
% Current number of equations to process: 529
% Current number of ordered equations: 69
% Current number of rules: 21
% New rule produced : [22] inverse(X add Y) add inverse(X) -> inverse(X)
% Current number of equations to process: 529
% Current number of ordered equations: 67
% Current number of rules: 22
% New rule produced :
% [23] (X multiply Y) multiply inverse(X add Z) -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 65
% Current number of rules: 23
% New rule produced :
% [24] (inverse(X) multiply Y) multiply (X multiply Z) -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 64
% Current number of rules: 24
% New rule produced : [25] (inverse(Y) multiply X) add (X multiply Y) -> X
% Current number of equations to process: 529
% Current number of ordered equations: 62
% Current number of rules: 25
% New rule produced :
% [26] ((X multiply Y) multiply Z) multiply inverse(X) -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 61
% Current number of rules: 26
% New rule produced :
% [27] (inverse(X add Y) multiply Z) multiply X -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 60
% Current number of rules: 27
% New rule produced :
% [28] ((inverse(X) multiply Y) multiply Z) multiply X -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 59
% Current number of rules: 28
% New rule produced :
% [29] inverse(X add Y) multiply inverse(X) -> inverse(X add Y)
% Current number of equations to process: 529
% Current number of ordered equations: 57
% Current number of rules: 29
% New rule produced : [30] (X add Z) multiply (Y add Z) -> (X multiply Y) add Z
% Current number of equations to process: 529
% Current number of ordered equations: 55
% Current number of rules: 30
% New rule produced :
% [31] (Y add Z) multiply X -> (X multiply Y) add (X multiply Z)
% Rule [30] (X add Z) multiply (Y add Z) -> (X multiply Y) add Z collapsed.
% Current number of equations to process: 529
% Current number of ordered equations: 53
% Current number of rules: 30
% New rule produced :
% [32] (X multiply Y) multiply (X multiply Z) -> (X multiply Y) multiply Z
% Current number of equations to process: 529
% Current number of ordered equations: 52
% Current number of rules: 31
% New rule produced :
% [33] ((X multiply Y) multiply Z) multiply X -> (X multiply Y) multiply Z
% Current number of equations to process: 529
% Current number of ordered equations: 51
% Current number of rules: 32
% New rule produced :
% [34] (((X multiply Y) multiply Z) multiply V_3) add X -> X
% Current number of equations to process: 529
% Current number of ordered equations: 50
% Current number of rules: 33
% New rule produced :
% [35] (inverse(X) multiply Y) add inverse(X add Y) -> inverse(X)
% Current number of equations to process: 529
% Current number of ordered equations: 49
% Current number of rules: 34
% New rule produced :
% [36] (inverse(X add Y) multiply Z) add inverse(X) -> inverse(X)
% Current number of equations to process: 529
% Current number of ordered equations: 47
% Current number of rules: 35
% New rule produced :
% [37]
% ((X multiply Y) multiply Z) multiply (inverse(X) multiply V_3) ->
% additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 46
% Current number of rules: 36
% New rule produced :
% [38]
% ((X multiply Y) multiply Z) multiply inverse(X add V_3) -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 45
% Current number of rules: 37
% New rule produced :
% [39]
% (inverse(X add Y) multiply Z) multiply (X multiply V_3) -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 44
% Current number of rules: 38
% New rule produced :
% [40] ((inverse(Z) multiply Y) multiply X) add Z -> (X multiply Y) add Z
% Current number of equations to process: 529
% Current number of ordered equations: 42
% Current number of rules: 39
% New rule produced :
% [41] ((Y multiply Z) multiply X) add (X multiply Y) -> X multiply Y
% Current number of equations to process: 529
% Current number of ordered equations: 40
% Current number of rules: 40
% New rule produced :
% [42]
% ((inverse(X) multiply Y) multiply Z) multiply (X multiply Y) ->
% additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 39
% Current number of rules: 41
% New rule produced :
% [43]
% ((inverse(X add Y) multiply Z) multiply V_3) multiply X -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 38
% Current number of rules: 42
% New rule produced :
% [44]
% inverse((X multiply Y) add (Y multiply Z)) add Y -> multiplicative_identity
% Current number of equations to process: 529
% Current number of ordered equations: 37
% Current number of rules: 43
% New rule produced :
% [45]
% (((X multiply Y) multiply Z) multiply V_3) multiply inverse(X) ->
% additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 36
% Current number of rules: 44
% New rule produced :
% [46]
% ((Y multiply Z) multiply X) add inverse(Z) -> (X multiply Y) add inverse(Z)
% Current number of equations to process: 529
% Current number of ordered equations: 34
% Current number of rules: 45
% New rule produced :
% [47]
% inverse((inverse(Z) multiply X) add Y) add X add Y -> multiplicative_identity
% Current number of equations to process: 529
% Current number of ordered equations: 32
% Current number of rules: 46
% New rule produced :
% [48] (inverse((inverse(X) multiply Y) add Z) multiply Y) add X -> X
% Current number of equations to process: 529
% Current number of ordered equations: 31
% Current number of rules: 47
% New rule produced :
% [49]
% (inverse(X) multiply Y) multiply inverse(X add Z) ->
% inverse(X add Z) multiply Y
% Current number of equations to process: 529
% Current number of ordered equations: 30
% Current number of rules: 48
% New rule produced :
% [50]
% (inverse(X add Y) multiply Z) multiply inverse(X) ->
% inverse(X add Y) multiply Z
% Current number of equations to process: 529
% Current number of ordered equations: 29
% Current number of rules: 49
% New rule produced :
% [51]
% ((inverse(X add Y) multiply Z) multiply V_3) add inverse(X) -> inverse(X)
% Current number of equations to process: 529
% Current number of ordered equations: 28
% Current number of rules: 50
% New rule produced :
% [52]
% inverse((X multiply Y) add (X multiply Z)) multiply inverse(X) -> inverse(X)
% Current number of equations to process: 529
% Current number of ordered equations: 27
% Current number of rules: 51
% New rule produced :
% [53] (inverse((X multiply Y) add Z) multiply Y) add inverse(X) -> inverse(X)
% Current number of equations to process: 529
% Current number of ordered equations: 26
% Current number of rules: 52
% New rule produced :
% [54]
% inverse(((X multiply Y) multiply Z) add (X multiply V_3)) add X ->
% multiplicative_identity
% Current number of equations to process: 529
% Current number of ordered equations: 25
% Current number of rules: 53
% New rule produced :
% [55]
% ((inverse(X add Y) multiply Z) multiply V_3) multiply (X multiply Z) ->
% additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 24
% Current number of rules: 54
% New rule produced :
% [56]
% (inverse(X) multiply inverse(Y)) add inverse(X add Y) ->
% inverse(X) multiply inverse(Y)
% Current number of equations to process: 529
% Current number of ordered equations: 23
% Current number of rules: 55
% New rule produced :
% [57]
% (((X multiply Y) multiply Z) multiply V_3) multiply X ->
% ((X multiply Y) multiply Z) multiply V_3
% Current number of equations to process: 529
% Current number of ordered equations: 22
% Current number of rules: 56
% New rule produced :
% [58]
% (((X multiply Y) multiply Z) multiply V_3) add (X multiply Z) -> X multiply Z
% Current number of equations to process: 529
% Current number of ordered equations: 21
% Current number of rules: 57
% New rule produced :
% [59]
% (((X multiply Y) multiply Z) multiply V_3) add (X multiply V_3) ->
% X multiply V_3
% Current number of equations to process: 529
% Current number of ordered equations: 20
% Current number of rules: 58
% New rule produced :
% [60]
% inverse((inverse(X) multiply Y) add (inverse(X) multiply Z)) multiply X -> X
% Current number of equations to process: 529
% Current number of ordered equations: 19
% Current number of rules: 59
% New rule produced :
% [61]
% (inverse((inverse(X) multiply Y) add Z) multiply Y) multiply inverse(X) ->
% additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 18
% Current number of rules: 60
% New rule produced :
% [62]
% inverse((X multiply Z) add (Y multiply Z)) add X add Y ->
% multiplicative_identity
% Current number of equations to process: 529
% Current number of ordered equations: 17
% Current number of rules: 61
% New rule produced :
% [63]
% (inverse(X add Z) multiply Y) add (inverse(X) multiply Y) ->
% inverse(X) multiply Y
% Current number of equations to process: 529
% Current number of ordered equations: 16
% Current number of rules: 62
% New rule produced :
% [64]
% ((inverse(Z) multiply Y) multiply X) add (Y multiply Z) ->
% (X multiply Y) add (Y multiply Z)
% Current number of equations to process: 529
% Current number of ordered equations: 15
% Current number of rules: 63
% New rule produced :
% [65]
% ((inverse(Z) multiply Y) multiply X) add ((Y multiply Z) multiply X) ->
% X multiply Y
% Current number of equations to process: 529
% Current number of ordered equations: 14
% Current number of rules: 64
% New rule produced :
% [66]
% ((inverse(X) multiply Y) multiply Z) multiply inverse((Y multiply Z) add X)
% -> additive_identity
% Current number of equations to process: 529
% Current number of ordered equations: 13
% Current number of rules: 65
% New rule produced :
% [67]
% ((inverse(X) multiply Y) multiply Z) add ((X multiply Z) multiply Y) ->
% Y multiply Z
% Current number of equations to process: 529
% Current number of ordered equations: 12
% Current number of rules: 66
% New rule produced :
% [68]
% ((inverse(X) multiply Z) multiply Y) add (X multiply Y) ->
% (X multiply Y) add (Y multiply Z)
% Current number of equations to process: 529
% Current number of ordered equations: 11
% Current number of rules: 67
% New rule produced :
% [69]
% inverse((X multiply Z) add Y) add inverse(Z) add X add Y ->
% multiplicative_identity
% Current number of equations to process: 529
% Current number of ordered equations: 10
% Current number of rules: 68
% New rule produced :
% [70]
% (inverse((inverse(X) multiply Y) add Z) multiply X) add (X multiply Z) -> X
% Current number of equations to process: 529
% Current number of ordered equations: 9
% Current number of rules: 69
% New rule produced :
% [71]
% ((inverse((inverse(X) multiply Y) add Z) multiply V_3) multiply Y) add X -> X
% Current number of equations to process: 529
% Current number of ordered equations: 8
% Current number of rules: 70
% New rule produced :
% [72]
% ((X multiply Y) multiply inverse(Z)) add (X multiply Z) ->
% (X multiply Y) add (X multiply Z)
% Current number of equations to process: 529
% Current number of ordered equations: 7
% Current number of rules: 71
% New rule produced :
% [73]
% ((X multiply Y) multiply Z) add (inverse(X) multiply Y) ->
% (inverse(X) multiply Y) add (Y multiply Z)
% Current number of equations to process: 529
% Current number of ordered equations: 5
% Current number of rules: 72
% New rule produced :
% [74]
% ((X multiply Y) multiply Z) add (inverse(Z) multiply X) ->
% (inverse(Z) multiply X) add (X multiply Y)
% Current number of equations to process: 529
% Current number of ordered equations: 4
% Current number of rules: 73
% New rule produced :
% [75]
% ((inverse(X) multiply Y) multiply Z) add inverse((Y multiply Z) add X) ->
% inverse(X)
% Current number of equations to process: 529
% Current number of ordered equations: 3
% Current number of rules: 74
% New rule produced :
% [76]
% ((X multiply Z) multiply Y) add (inverse(X) multiply Y) ->
% (inverse(X) multiply Y) add (Y multiply Z)
% Current number of equations to process: 529
% Current number of ordered equations: 2
% Current number of rules: 75
% New rule produced :
% [77] (inverse(X add Y) multiply Z) add (X multiply Z) add (Y multiply Z) -> Z
% Current number of equations to process: 529
% Current number of ordered equations: 1
% Current number of rules: 76
% New rule produced :
% [78]
% (X multiply Y) add (X multiply Z) add inverse(Y add Z) ->
% inverse(Y add Z) add X
% Current number of equations to process: 529
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced : [79] inverse(X add Y) -> inverse(X) multiply inverse(Y)
% Rule [16] inverse(X add Y) multiply X -> additive_identity collapsed.
% Rule [18] inverse(inverse(X) add Y) -> inverse(Y) multiply X collapsed.
% Rule [22] inverse(X add Y) add inverse(X) -> inverse(X) collapsed.
% Rule [23] (X multiply Y) multiply inverse(X add Z) -> additive_identity
% collapsed.
% Rule [27] (inverse(X add Y) multiply Z) multiply X -> additive_identity
% collapsed.
% Rule [29] inverse(X add Y) multiply inverse(X) -> inverse(X add Y) collapsed.
% Rule [35] (inverse(X) multiply Y) add inverse(X add Y) -> inverse(X)
% collapsed.
% Rule [36] (inverse(X add Y) multiply Z) add inverse(X) -> inverse(X)
% collapsed.
% Rule
% [38]
% ((X multiply Y) multiply Z) multiply inverse(X add V_3) -> additive_identity
% collapsed.
% Rule
% [39]
% (inverse(X add Y) multiply Z) multiply (X multiply V_3) -> additive_identity
% collapsed.
% Rule
% [43]
% ((inverse(X add Y) multiply Z) multiply V_3) multiply X -> additive_identity
% collapsed.
% Rule
% [44]
% inverse((X multiply Y) add (Y multiply Z)) add Y -> multiplicative_identity
% collapsed.
% Rule
% [47]
% inverse((inverse(Z) multiply X) add Y) add X add Y -> multiplicative_identity
% collapsed.
% Rule [48] (inverse((inverse(X) multiply Y) add Z) multiply Y) add X -> X
% collapsed.
% Rule
% [49]
% (inverse(X) multiply Y) multiply inverse(X add Z) ->
% inverse(X add Z) multiply Y collapsed.
% Rule
% [50]
% (inverse(X add Y) multiply Z) multiply inverse(X) ->
% inverse(X add Y) multiply Z collapsed.
% Rule
% [51]
% ((inverse(X add Y) multiply Z) multiply V_3) add inverse(X) -> inverse(X)
% collapsed.
% Rule
% [52]
% inverse((X multiply Y) add (X multiply Z)) multiply inverse(X) -> inverse(X)
% collapsed.
% Rule
% [53] (inverse((X multiply Y) add Z) multiply Y) add inverse(X) -> inverse(X)
% collapsed.
% Rule
% [54]
% inverse(((X multiply Y) multiply Z) add (X multiply V_3)) add X ->
% multiplicative_identity collapsed.
% Rule
% [55]
% ((inverse(X add Y) multiply Z) multiply V_3) multiply (X multiply Z) ->
% additive_identity collapsed.
% Rule
% [56]
% (inverse(X) multiply inverse(Y)) add inverse(X add Y) ->
% inverse(X) multiply inverse(Y) collapsed.
% Rule
% [60]
% inverse((inverse(X) multiply Y) add (inverse(X) multiply Z)) multiply X -> X
% collapsed.
% Rule
% [61]
% (inverse((inverse(X) multiply Y) add Z) multiply Y) multiply inverse(X) ->
% additive_identity collapsed.
% Rule
% [62]
% inverse((X multiply Z) add (Y multiply Z)) add X add Y ->
% multiplicative_identity collapsed.
% Rule
% [63]
% (inverse(X add Z) multiply Y) add (inverse(X) multiply Y) ->
% inverse(X) multiply Y collapsed.
% Rule
% [66]
% ((inverse(X) multiply Y) multiply Z) multiply inverse((Y multiply Z) add X)
% -> additive_identity collapsed.
% Rule
% [69]
% inverse((X multiply Z) add Y) add inverse(Z) add X add Y ->
% multiplicative_identity collapsed.
% Rule
% [70]
% (inverse((inverse(X) multiply Y) add Z) multiply X) add (X multiply Z) -> X
% collapsed.
% Rule
% [71]
% ((inverse((inverse(X) multiply Y) add Z) multiply V_3) multiply Y) add X -> X
% collapsed.
% Rule
% [75]
% ((inverse(X) multiply Y) multiply Z) add inverse((Y multiply Z) add X) ->
% inverse(X) collapsed.
% Rule
% [77] (inverse(X add Y) multiply Z) add (X multiply Z) add (Y multiply Z) -> Z
% collapsed.
% Rule
% [78]
% (X multiply Y) add (X multiply Z) add inverse(Y add Z) ->
% inverse(Y add Z) add X collapsed.
% Current number of equations to process: 539
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [80]
% ((inverse(X) multiply inverse(Y)) multiply Z) multiply (X multiply V_3) ->
% additive_identity
% Current number of equations to process: 535
% Current number of ordered equations: 3
% Current number of rules: 46
% New rule produced :
% [81]
% (((inverse(X) multiply inverse(Y)) multiply Z) multiply V_3) multiply X ->
% additive_identity
% Current number of equations to process: 535
% Current number of ordered equations: 2
% Current number of rules: 47
% New rule produced :
% [82]
% (((inverse(X) multiply inverse(Y)) multiply Z) multiply V_3) multiply 
% (X multiply Z) -> additive_identity
% Current number of equations to process: 535
% Current number of ordered equations: 1
% Current number of rules: 48
% New rule produced :
% [83]
% (inverse(Y) multiply inverse(Z)) add (X multiply Y) add (X multiply Z) ->
% (inverse(Y) multiply inverse(Z)) add X
% Current number of equations to process: 535
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [84]
% (inverse(X) multiply Y) multiply Z <-> (inverse(X) multiply Z) multiply Y
% Current number of equations to process: 540
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [85]
% (Y multiply Z) multiply inverse(X) <-> (inverse(X) multiply Y) multiply Z
% Current number of equations to process: 539
% Current number of ordered equations: 1
% Current number of rules: 51
% New rule produced :
% [86]
% (inverse(X) multiply Y) multiply Z <-> (Y multiply Z) multiply inverse(X)
% Rule [15] (inverse(X) multiply Y) multiply X -> additive_identity collapsed.
% Current number of equations to process: 539
% Current number of ordered equations: 0
% Current number of rules: 51
% (X multiply Y) multiply Z = (X multiply Z) multiply Y (birth = 541, lhs_size = 5, rhs_size = 5,trace = Self cp of 32)
% Initializing completion ...
% New rule produced : [1] inverse(multiplicative_identity) -> additive_identity
% Current number of equations to process: 534
% Current number of ordered equations: 44
% Current number of rules: 1
% New rule produced : [2] inverse(additive_identity) -> multiplicative_identity
% Current number of equations to process: 534
% Current number of ordered equations: 43
% Current number of rules: 2
% New rule produced : [3] inverse(inverse(X)) -> X
% Current number of equations to process: 534
% Current number of ordered equations: 42
% Current number of rules: 3
% New rule produced : [4] X multiply X -> X
% Current number of equations to process: 536
% Current number of ordered equations: 36
% Current number of rules: 4
% New rule produced : [5] multiplicative_identity multiply X -> X
% Current number of equations to process: 534
% Current number of ordered equations: 37
% Current number of rules: 5
% New rule produced : [6] additive_identity multiply X -> additive_identity
% Current number of equations to process: 534
% Current number of ordered equations: 36
% Current number of rules: 6
% New rule produced : [7] X add X -> X
% Current number of equations to process: 534
% Current number of ordered equations: 35
% Current number of rules: 7
% New rule produced :
% [8] multiplicative_identity add X -> multiplicative_identity
% Current number of equations to process: 534
% Current number of ordered equations: 34
% Current number of rules: 8
% New rule produced : [9] additive_identity add X -> X
% Current number of equations to process: 534
% Current number of ordered equations: 33
% Current number of rules: 9
% New rule produced : [10] inverse(X) multiply X -> additive_identity
% Current number of equations to process: 534
% Current number of ordered equations: 26
% Current number of rules: 10
% New rule produced : [11] inverse(X) add X -> multiplicative_identity
% Current number of equations to process: 534
% Current number of ordered equations: 25
% Current number of rules: 11
% New rule produced : [12] (X multiply Y) add X -> X
% Current number of equations to process: 534
% Current number of ordered equations: 19
% Current number of rules: 12
% New rule produced : [13] inverse(X multiply Y) -> inverse(X) add inverse(Y)
% Current number of equations to process: 534
% Current number of ordered equations: 18
% Current number of rules: 13
% New rule produced : [14] inverse(X add Y) -> inverse(X) multiply inverse(Y)
% Current number of equations to process: 534
% Current number of ordered equations: 17
% Current number of rules: 14
% New rule produced : [15] (inverse(X) multiply Y) add X -> X add Y
% Current number of equations to process: 534
% Current number of ordered equations: 15
% Current number of rules: 15
% New rule produced : [16] (X multiply Y) add inverse(X) -> inverse(X) add Y
% Current number of equations to process: 534
% Current number of ordered equations: 13
% Current number of rules: 16
% New rule produced : [17] (inverse(Y) multiply X) add (X multiply Y) -> X
% Current number of equations to process: 534
% Current number of ordered equations: 10
% Current number of rules: 17
% New rule produced : [18] (X add Z) multiply (Y add Z) -> (X multiply Y) add Z
% Current number of equations to process: 534
% Current number of ordered equations: 8
% Current number of rules: 18
% New rule produced :
% [19] (Y add Z) multiply X -> (X multiply Y) add (X multiply Z)
% Rule [18] (X add Z) multiply (Y add Z) -> (X multiply Y) add Z collapsed.
% Current number of equations to process: 534
% Current number of ordered equations: 6
% Current number of rules: 18
% New rule produced :
% [20]
% (inverse(X) multiply Y multiply Z) add (X multiply Y) ->
% (X multiply Y) add (Y multiply Z)
% Current number of equations to process: 534
% Current number of ordered equations: 3
% Current number of rules: 19
% New rule produced :
% [21]
% (inverse(X) multiply Y) add (X multiply Y multiply Z) ->
% (inverse(X) multiply Y) add (Y multiply Z)
% Current number of equations to process: 534
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [22]
% (inverse(Y) multiply inverse(Z)) add (X multiply Y) add (X multiply Z) ->
% (inverse(Y) multiply inverse(Z)) add X
% Current number of equations to process: 534
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [23]
% (inverse(X) multiply Y) add (inverse(Z) multiply Y) add (X multiply Z) ->
% (X multiply Z) add Y
% Current number of equations to process: 620
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [24]
% (inverse(X) multiply Z) add (X multiply Y) add (Y multiply Z) ->
% (inverse(X) multiply Z) add (X multiply Y)
% Current number of equations to process: 610
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [25]
% (inverse(X) multiply Y) add (inverse(Y) multiply Z) add (X multiply Z) ->
% (inverse(X) multiply Y) add Z
% Current number of equations to process: 608
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [26]
% (inverse(X) multiply Y) add (X multiply Z) add (Y multiply Z multiply V_3) ->
% (inverse(X) multiply Y) add (X multiply Z)
% Current number of equations to process: 821
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [27]
% (inverse(X) multiply Y) add (inverse(Y) multiply X) add (Y multiply Z) <->
% (inverse(X) multiply Y) add (inverse(Y) multiply X) add (X multiply Z)
% Current number of equations to process: 1140
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [28]
% (inverse(X) multiply inverse(Y)) add (X multiply Y) add (X multiply Z) <->
% (inverse(X) multiply inverse(Y)) add (inverse(Y) multiply Z) add (X multiply Y)
% Current number of equations to process: 1245
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [29]
% (inverse(X) multiply inverse(Y)) add (inverse(Y) multiply Z) add (X multiply Y)
% <-> (inverse(X) multiply inverse(Y)) add (X multiply Y) add (X multiply Z)
% Current number of equations to process: 1249
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [30]
% (inverse(X) multiply Y) add (inverse(Y) mulCputime limit exceeded (core dumped)
% 
% EOF
%------------------------------------------------------------------------------