%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP205-1 : TPTP v6.0.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n124.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 00:22:40 EDT 2014

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

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP205-1 : TPTP v6.0.0. Released v2.3.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n124.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Fri Jun  6 07:36:08 CDT 2014
% % CPUTime  : 300.09 
% Processing problem /tmp/CiME_58046_n124.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " z,y,x,identity : constant;  left_inverse : 1;  right_inverse : 1;  right_division : 2;  left_division : 2;  multiply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% multiply(identity,X) = X;
% multiply(X,identity) = X;
% multiply(X,left_division(X,Y)) = Y;
% left_division(X,multiply(X,Y)) = Y;
% multiply(right_division(X,Y),Y) = X;
% right_division(multiply(X,Y),Y) = X;
% multiply(X,right_inverse(X)) = identity;
% multiply(left_inverse(X),X) = identity;
% multiply(multiply(multiply(X,Y),X),Z) = multiply(X,multiply(Y,multiply(X,Z)));
% ";
% 
% let s1 = status F "
% z lr_lex;
% y lr_lex;
% x lr_lex;
% left_inverse lr_lex;
% right_inverse lr_lex;
% right_division lr_lex;
% left_division lr_lex;
% multiply lr_lex;
% identity lr_lex;
% ";
% 
% let p1 = precedence F "
% right_inverse > left_inverse > multiply > left_division > right_division > identity > x > y > z";
% 
% let s2 = status F "
% z mul;
% y mul;
% x mul;
% left_inverse mul;
% right_inverse mul;
% right_division mul;
% left_division mul;
% multiply mul;
% identity mul;
% ";
% 
% let p2 = precedence F "
% right_inverse > left_inverse > multiply > left_division > right_division > identity = x = y = z";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " multiply(x,multiply(multiply(y,z),x)) = multiply(multiply(x,y),multiply(z,x));"
% ;
% (*
% 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 = { multiply(identity,X) = X,
% multiply(X,identity) = X,
% multiply(X,left_division(X,Y)) = Y,
% left_division(X,multiply(X,Y)) = Y,
% multiply(right_division(X,Y),Y) = X,
% right_division(multiply(X,Y),Y) = X,
% multiply(X,right_inverse(X)) = identity,
% multiply(left_inverse(X),X) = identity,
% multiply(multiply(multiply(X,Y),X),Z) =
% multiply(X,multiply(Y,multiply(X,Z))) }
% (9 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 = { multiply(x,multiply(multiply(y,z),x)) =
% multiply(multiply(x,y),multiply(z,x)) }
% (1 equation(s))
% time is now on
% 
% Initializing completion ...
% New rule produced : [1] multiply(X,identity) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 1
% New rule produced : [2] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 2
% New rule produced : [3] multiply(X,right_inverse(X)) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 3
% New rule produced : [4] multiply(left_inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 4
% New rule produced : [5] right_division(multiply(X,Y),Y) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 5
% New rule produced : [6] left_division(X,multiply(X,Y)) -> Y
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 6
% New rule produced : [7] multiply(X,left_division(X,Y)) -> Y
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 7
% New rule produced : [8] multiply(right_division(X,Y),Y) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [9]
% multiply(multiply(multiply(X,Y),X),Z) ->
% multiply(X,multiply(Y,multiply(X,Z)))
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [10] right_inverse(identity) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] left_inverse(identity) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] right_division(X,identity) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] right_division(X,X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [14] right_division(identity,right_inverse(X)) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] left_inverse(X) -> right_division(identity,X)
% Rule [4] multiply(left_inverse(X),X) -> identity collapsed.
% Rule [11] left_inverse(identity) -> identity collapsed.
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [16] left_division(X,X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [17] left_division(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [18] right_inverse(X) -> left_division(X,identity)
% Rule [3] multiply(X,right_inverse(X)) -> identity collapsed.
% Rule [10] right_inverse(identity) -> identity collapsed.
% Rule [14] right_division(identity,right_inverse(X)) -> X collapsed.
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [19] right_division(identity,left_division(X,identity)) -> X
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [20] right_division(X,left_division(Y,X)) -> Y
% Rule [19] right_division(identity,left_division(X,identity)) -> X collapsed.
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [21] left_division(right_division(X,Y),X) -> Y
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [22] multiply(multiply(X,Y),X) -> multiply(X,multiply(Y,X))
% Rule
% [9]
% multiply(multiply(multiply(X,Y),X),Z) ->
% multiply(X,multiply(Y,multiply(X,Z))) collapsed.
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [23]
% multiply(multiply(X,multiply(Y,X)),Z) ->
% multiply(X,multiply(Y,multiply(X,Z)))
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [24] right_division(multiply(X,multiply(Y,X)),X) -> multiply(X,Y)
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [25] multiply(Y,multiply(left_division(Y,X),Y)) -> multiply(X,Y)
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [26] left_division(multiply(X,Y),multiply(X,multiply(Y,X))) -> X
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [27] multiply(multiply(X,X),Y) -> multiply(X,multiply(X,Y))
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [28] multiply(X,right_division(Y,X)) -> right_division(multiply(X,Y),X)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [29] multiply(left_division(X,Y),X) -> left_division(X,multiply(Y,X))
% Rule [25] multiply(Y,multiply(left_division(Y,X),Y)) -> multiply(X,Y)
% collapsed.
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [30] right_division(multiply(X,multiply(X,Y)),Y) -> multiply(X,X)
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [31] left_division(X,right_division(multiply(X,Y),X)) -> right_division(Y,X)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [32] right_division(left_division(X,multiply(Y,X)),X) -> left_division(X,Y)
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [33] right_division(multiply(X,Y),left_division(X,Y)) <-> multiply(X,X)
% Current number of equations to process: 49
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [34] multiply(X,X) <-> right_division(multiply(X,Y),left_division(X,Y))
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 26
% Rule [18] right_inverse(X) -> left_division(X,identity) is composed into 
% [18] right_inverse(X) -> right_division(identity,X)
% New rule produced :
% [35] left_division(X,identity) -> right_division(identity,X)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [36]
% left_division(X,right_division(Y,X)) -> right_division(left_division(X,Y),X)
% Rule
% [31] left_division(X,right_division(multiply(X,Y),X)) -> right_division(Y,X)
% collapsed.
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [37] left_division(multiply(X,X),X) -> right_division(X,multiply(X,X))
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 28
% Rule [33] right_division(multiply(X,Y),left_division(X,Y)) <-> multiply(X,X) is composed into 
% [33]
% right_division(multiply(X,Y),left_division(X,Y)) ->
% right_division(X,right_division(identity,X))
% Rule [30] right_division(multiply(X,multiply(X,Y)),Y) -> multiply(X,X) is composed into 
% [30]
% right_division(multiply(X,multiply(X,Y)),Y) ->
% right_division(X,right_division(identity,X))
% New rule produced :
% [38] multiply(X,X) -> right_division(X,right_division(identity,X))
% Rule [27] multiply(multiply(X,X),Y) -> multiply(X,multiply(X,Y)) collapsed.
% Rule [34] multiply(X,X) <-> right_division(multiply(X,Y),left_division(X,Y))
% collapsed.
% Rule [37] left_division(multiply(X,X),X) -> right_division(X,multiply(X,X))
% collapsed.
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [39] right_division(identity,right_division(identity,X)) -> X
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [40] right_division(right_division(X,right_division(identity,X)),X) -> X
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [41] left_division(X,right_division(X,right_division(identity,X))) -> X
% Current number of equations to process: 79
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [42]
% left_division(right_division(identity,X),X) ->
% right_division(X,right_division(identity,X))
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [43]
% right_division(X,right_division(X,right_division(identity,X))) ->
% right_division(identity,X)
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [44]
% multiply(right_division(X,right_division(identity,X)),Y) ->
% multiply(X,multiply(X,Y))
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [45]
% left_division(right_division(X,right_division(identity,X)),multiply(X,
% multiply(X,Y))) ->
% Y
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [46]
% multiply(Y,multiply(Y,left_division(right_division(Y,right_division(identity,Y)),X)))
% -> X
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [47] right_division(right_division(multiply(X,Y),X),right_division(Y,X)) -> X
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [48] left_division(left_division(X,Y),left_division(X,multiply(Y,X))) -> X
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [49]
% right_division(X,left_division(Y,left_division(Y,X))) ->
% right_division(Y,right_division(identity,Y))
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [50]
% right_division(right_division(X,Y),right_division(left_division(Y,X),Y)) -> Y
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [51]
% right_division(right_division(identity,X),right_division(right_division(identity,X),X))
% -> X
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [52]
% left_division(right_division(X,right_division(identity,X)),Y) ->
% left_division(X,left_division(X,Y))
% Rule
% [45]
% left_division(right_division(X,right_division(identity,X)),multiply(X,
% multiply(X,Y))) ->
% Y collapsed.
% Rule
% [46]
% multiply(Y,multiply(Y,left_division(right_division(Y,right_division(identity,Y)),X)))
% -> X collapsed.
% Current number of equations to process: 141
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [53]
% right_division(identity,right_division(right_division(identity,X),X)) ->
% right_division(X,right_division(identity,X))
% Current number of equations to process: 152
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [54]
% right_division(right_division(identity,X),X) ->
% right_division(identity,right_division(X,right_division(identity,X)))
% Rule
% [51]
% right_division(right_division(identity,X),right_division(right_division(identity,X),X))
% -> X collapsed.
% Rule
% [53]
% right_division(identity,right_division(right_division(identity,X),X)) ->
% right_division(X,right_division(identity,X)) collapsed.
% Current number of equations to process: 175
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [55]
% multiply(X,multiply(multiply(Y,X),X)) ->
% multiply(X,multiply(Y,right_division(X,right_division(identity,X))))
% Current number of equations to process: 178
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [56]
% multiply(multiply(X,Y),Y) ->
% multiply(X,right_division(Y,right_division(identity,Y)))
% Rule
% [55]
% multiply(X,multiply(multiply(Y,X),X)) ->
% multiply(X,multiply(Y,right_division(X,right_division(identity,X))))
% collapsed.
% Current number of equations to process: 193
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [57]
% right_division(multiply(right_division(X,Y),X),Y) ->
% right_division(right_division(X,Y),right_division(identity,right_division(X,Y)))
% Current number of equations to process: 213
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [58]
% right_division(right_division(identity,right_division(X,right_division(identity,X))),
% right_division(identity,X)) -> right_division(identity,X)
% Current number of equations to process: 224
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [59]
% left_division(right_division(identity,X),right_division(identity,right_division(X,
% right_division(identity,X))))
% -> right_division(identity,X)
% Current number of equations to process: 228
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [60]
% left_division(right_division(identity,right_division(X,right_division(identity,X))),X)
% ->
% right_division(X,right_division(identity,right_division(X,right_division(identity,X))))
% Current number of equations to process: 227
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [61]
% multiply(right_division(identity,right_division(X,right_division(identity,X))),X)
% -> right_division(identity,X)
% Current number of equations to process: 234
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [62]
% multiply(X,right_division(identity,right_division(X,right_division(identity,X))))
% -> right_division(identity,X)
% Current number of equations to process: 242
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [63]
% multiply(right_division(X,Y),right_division(Y,right_division(identity,Y))) ->
% multiply(X,Y)
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [64]
% left_division(right_division(X,Y),multiply(X,Y)) ->
% right_division(Y,right_division(identity,Y))
% Current number of equations to process: 259
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [65]
% left_division(right_division(right_division(X,Y),Y),X) ->
% right_division(Y,right_division(identity,Y))
% Current number of equations to process: 276
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [66]
% right_division(right_division(X,Y),Y) ->
% right_division(X,right_division(Y,right_division(identity,Y)))
% Rule
% [54]
% right_division(right_division(identity,X),X) ->
% right_division(identity,right_division(X,right_division(identity,X)))
% collapsed.
% Rule
% [65]
% left_division(right_division(right_division(X,Y),Y),X) ->
% right_division(Y,right_division(identity,Y)) collapsed.
% Current number of equations to process: 297
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [67]
% right_division(multiply(X,right_division(Y,right_division(identity,Y))),Y) ->
% multiply(X,Y)
% Current number of equations to process: 313
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [68]
% right_division(multiply(X,Y),right_division(Y,right_division(identity,Y))) ->
% right_division(X,Y)
% Current number of equations to process: 325
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [69]
% multiply(multiply(right_division(X,Y),X),Y) ->
% multiply(right_division(X,Y),multiply(X,Y))
% Current number of equations to process: 337
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [70]
% multiply(right_division(X,right_division(Y,right_division(identity,Y))),Y) ->
% right_division(X,Y)
% Rule
% [61]
% multiply(right_division(identity,right_division(X,right_division(identity,X))),X)
% -> right_division(identity,X) collapsed.
% Current number of equations to process: 365
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [71]
% multiply(multiply(X,Y),left_division(X,Y)) ->
% multiply(X,multiply(Y,left_division(X,Y)))
% Current number of equations to process: 381
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [72]
% multiply(right_division(X,Y),right_division(multiply(Y,X),Y)) ->
% multiply(X,right_division(X,Y))
% Current number of equations to process: 412
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [73]
% multiply(multiply(X,Y),Z) ->
% multiply(X,multiply(right_division(Y,X),multiply(X,Z)))
% Rule [22] multiply(multiply(X,Y),X) -> multiply(X,multiply(Y,X)) collapsed.
% Rule
% [23]
% multiply(multiply(X,multiply(Y,X)),Z) ->
% multiply(X,multiply(Y,multiply(X,Z))) collapsed.
% Rule
% [56]
% multiply(multiply(X,Y),Y) ->
% multiply(X,right_division(Y,right_division(identity,Y))) collapsed.
% Rule
% [69]
% multiply(multiply(right_division(X,Y),X),Y) ->
% multiply(right_division(X,Y),multiply(X,Y)) collapsed.
% Rule
% [71]
% multiply(multiply(X,Y),left_division(X,Y)) ->
% multiply(X,multiply(Y,left_division(X,Y))) collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% multiply(x,multiply(y,multiply(right_division(z,y),multiply(y,x)))) = 
% multiply(x,multiply(right_division(y,x),multiply(x,multiply(z,x))))
% 
% Current number of equations to process: 451
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [74]
% multiply(X,multiply(right_division(identity,X),multiply(X,Y))) ->
% multiply(X,Y)
% Current number of equations to process: 474
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [75] multiply(right_division(identity,Y),multiply(Y,X)) -> X
% Rule
% [74]
% multiply(X,multiply(right_division(identity,X),multiply(X,Y))) ->
% multiply(X,Y) collapsed.
% Current number of equations to process: 488
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [76] multiply(right_division(identity,right_division(X,Y)),X) -> Y
% Current number of equations to process: 495
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [77] right_division(X,multiply(Y,X)) -> right_division(identity,Y)
% Current number of equations to process: 498
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [78] multiply(X,Y) -> left_division(right_division(identity,X),Y)
% Rule [1] multiply(X,identity) -> X collapsed.
% Rule [2] multiply(identity,X) -> X collapsed.
% Rule [5] right_division(multiply(X,Y),Y) -> X collapsed.
% Rule [6] left_division(X,multiply(X,Y)) -> Y collapsed.
% Rule [7] multiply(X,left_division(X,Y)) -> Y collapsed.
% Rule [8] multiply(right_division(X,Y),Y) -> X collapsed.
% Rule [24] right_division(multiply(X,multiply(Y,X)),X) -> multiply(X,Y)
% collapsed.
% Rule [26] left_division(multiply(X,Y),multiply(X,multiply(Y,X))) -> X
% collapsed.
% Rule [28] multiply(X,right_division(Y,X)) -> right_division(multiply(X,Y),X)
% collapsed.
% Rule [29] multiply(left_division(X,Y),X) -> left_division(X,multiply(Y,X))
% collapsed.
% Rule
% [30]
% right_division(multiply(X,multiply(X,Y)),Y) ->
% right_division(X,right_division(identity,X)) collapsed.
% Rule
% [32] right_division(left_division(X,multiply(Y,X)),X) -> left_division(X,Y)
% collapsed.
% Rule
% [33]
% right_division(multiply(X,Y),left_division(X,Y)) ->
% right_division(X,right_division(identity,X)) collapsed.
% Rule [38] multiply(X,X) -> right_division(X,right_division(identity,X))
% collapsed.
% Rule
% [44]
% multiply(right_division(X,right_division(identity,X)),Y) ->
% multiply(X,multiply(X,Y)) collapsed.
% Rule
% [47] right_division(right_division(multiply(X,Y),X),right_division(Y,X)) -> X
% collapsed.
% Rule
% [48] left_division(left_division(X,Y),left_division(X,multiply(Y,X))) -> X
% collapsed.
% Rule
% [57]
% right_division(multiply(right_division(X,Y),X),Y) ->
% right_division(right_division(X,Y),right_division(identity,right_division(X,Y)))
% collapsed.
% Rule
% [62]
% multiply(X,right_division(identity,right_division(X,right_division(identity,X))))
% -> right_division(identity,X) collapsed.
% Rule
% [63]
% multiply(right_division(X,Y),right_division(Y,right_division(identity,Y))) ->
% multiply(X,Y) collapsed.
% Rule
% [64]
% left_division(right_division(X,Y),multiply(X,Y)) ->
% right_division(Y,right_division(identity,Y)) collapsed.
% Rule
% [67]
% right_division(multiply(X,right_division(Y,right_division(identity,Y))),Y) ->
% multiply(X,Y) collapsed.
% Rule
% [68]
% right_division(multiply(X,Y),right_division(Y,right_division(identity,Y))) ->
% right_division(X,Y) collapsed.
% Rule
% [70]
% multiply(right_division(X,right_division(Y,right_division(identity,Y))),Y) ->
% right_division(X,Y) collapsed.
% Rule
% [72]
% multiply(right_division(X,Y),right_division(multiply(Y,X),Y)) ->
% multiply(X,right_division(X,Y)) collapsed.
% Rule
% [73]
% multiply(multiply(X,Y),Z) ->
% multiply(X,multiply(right_division(Y,X),multiply(X,Z))) collapsed.
% Rule [75] multiply(right_division(identity,Y),multiply(Y,X)) -> X collapsed.
% Rule [76] multiply(right_division(identity,right_division(X,Y)),X) -> Y
% collapsed.
% Rule [77] right_division(X,multiply(Y,X)) -> right_division(identity,Y)
% collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% left_division(right_division(identity,x),left_division(right_division(identity,y),
% left_division(right_division(identity,
% right_division(z,y)),
% left_division(right_division(identity,y),x)))) = 
% left_division(right_division(identity,x),left_division(right_division(identity,
% right_division(y,x)),
% left_division(right_division(identity,x),
% left_division(right_division(identity,z),x))))
% 
% Current number of equations to process: 520
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [79] left_division(X,left_division(right_division(identity,X),Y)) -> Y
% Current number of equations to process: 516
% Current number of ordered equations: 3
% Current number of rules: 24
% New rule produced :
% [80] left_division(right_division(identity,X),left_division(X,Y)) -> Y
% Current number of equations to process: 516
% Current number of ordered equations: 2
% Current number of rules: 25
% New rule produced :
% [81] left_division(right_division(identity,right_division(X,Y)),Y) -> X
% Current number of equations to process: 516
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [82] right_division(left_division(right_division(identity,X),Y),Y) -> X
% Current number of equations to process: 516
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [83] right_division(left_division(X,Y),Y) -> right_division(identity,X)
% Rule [82] right_division(left_division(right_division(identity,X),Y),Y) -> X
% collapsed.
% Current number of equations to process: 524
% Current number of ordered equations: 0
% Current number of rules: 27
% Rule [36]
% left_division(X,right_division(Y,X)) ->
% right_division(left_division(X,Y),X) is composed into [36]
% left_division(X,
% right_division(Y,X))
% ->
% right_division(identity,
% right_division(X,
% left_division(X,Y)))
% New rule produced :
% [84] right_division(X,Y) <-> right_division(identity,right_division(Y,X))
% Rule [40] right_division(right_division(X,right_division(identity,X)),X) -> X
% collapsed.
% Rule
% [50]
% right_division(right_division(X,Y),right_division(left_division(Y,X),Y)) -> Y
% collapsed.
% Rule
% [58]
% right_division(right_division(identity,right_division(X,right_division(identity,X))),
% right_division(identity,X)) -> right_division(identity,X) collapsed.
% Rule
% [66]
% right_division(right_division(X,Y),Y) ->
% right_division(X,right_division(Y,right_division(identity,Y))) collapsed.
% Rule [83] right_division(left_division(X,Y),Y) -> right_division(identity,X)
% collapsed.
% Current number of equations to process: 530
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [85] right_division(identity,right_division(Y,X)) <-> right_division(X,Y)
% The conjecture has been reduced. 
% Conjecture is now:
% left_division(right_division(identity,x),left_division(right_division(identity,y),
% left_division(right_division(y,z),
% left_division(right_division(identity,y),x)))) = 
% left_division(right_division(identity,x),left_division(right_division(x,y),
% left_division(right_division(identity,x),
% left_division(right_division(identity,z),x))))
% 
% Current number of equations to process: 530
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [86]
% left_division(right_division(X,Y),left_division(right_division(Y,X),Z)) -> Z
% Current number of equations to process: 540
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [87]
% left_division(right_division(X,Y),right_division(identity,right_division(Y,X)))
% -> identity
% Current number of equations to process: 545
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [88]
% left_division(right_division(identity,X),right_division(Y,X)) ->
% right_division(identity,right_division(X,left_division(right_division(identity,X),Y)))
% Current number of equations to process: 544
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [89]
% left_division(right_division(identity,left_division(X,Y)),X) ->
% left_division(X,left_division(right_division(identity,Y),X))
% Current number of equations to process: 543
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [90]
% right_division(identity,right_division(X,left_division(X,left_division(
% right_division(identity,Y),X))))
% -> left_division(X,Y)
% Current number of equations to process: 542
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [91]
% left_division(right_division(identity,right_division(X,Y)),right_division(Y,X))
% -> identity
% Current number of equations to process: 551
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [92]
% right_division(X,right_division(Y,right_division(identity,Y))) <->
% right_division(identity,right_division(Y,right_division(X,Y)))
% Current number of equations to process: 587
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [93]
% right_division(identity,right_division(Y,right_division(X,Y))) <->
% right_division(X,right_division(Y,right_division(identity,Y)))
% Current number of equations to process: 587
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [94]
% right_division(X,right_division(Y,X)) <->
% right_division(right_division(X,right_division(identity,X)),Y)
% Current number of equations to process: 595
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [95]
% right_division(right_division(X,right_division(identity,X)),Y) <->
% right_division(X,right_division(Y,X))
% Current number of equations to process: 595
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [96]
% left_division(right_division(identity,X),right_division(identity,right_division(X,
% left_division(X,Y))))
% -> right_division(Y,X)
% Current number of equations to process: 664
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [97]
% right_division(right_division(identity,right_division(X,Y)),right_division(Y,X))
% -> identity
% Current number of equations to process: 675
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [98]
% right_division(right_division(X,Y),right_division(identity,right_division(Y,X)))
% -> identity
% Current number of equations to process: 682
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [99]
% left_division(X,right_division(identity,right_division(X,Y))) ->
% right_division(identity,right_division(X,left_division(X,Y)))
% Current number of equations to process: 694
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [100]
% left_division(right_division(right_division(X,right_division(identity,X)),Y),X)
% -> right_division(Y,X)
% Current number of equations to process: 707
% Current number of ordered equations: 0
% Current number of rules: 39
% Rule [94]
% right_division(X,right_division(Y,X)) <->
% right_division(right_division(X,right_division(identity,X)),Y) is composed into 
% [94]
% right_division(X,right_division(Y,X)) <->
% right_division(X,right_division(identity,right_division(X,Y)))
% New rule produced :
% [101]
% right_division(right_division(X,right_division(identity,X)),Y) ->
% right_division(X,right_division(identity,right_division(X,Y)))
% Rule
% [95]
% right_division(right_division(X,right_division(identity,X)),Y) <->
% right_division(X,right_division(Y,X)) collapsed.
% Rule
% [100]
% left_division(right_division(right_division(X,right_division(identity,X)),Y),X)
% -> right_division(Y,X) collapsed.
% Current number of equations to process: 722
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [102]
% right_division(identity,right_division(Z,left_division(right_division(identity,X),
% left_division(right_division(identity,Y),
% left_division(right_division(identity,X),Z)))))
% ->
% left_division(right_division(identity,X),left_division(right_division(identity,Y),X))
% Current number of equations to process: 754
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [103]
% right_division(identity,right_division(left_division(X,Y),left_division(
% right_division(identity,
% left_division(X,Y)),Y)))
% -> left_division(X,left_division(right_division(identity,Y),X))
% Current number of equations to process: 800
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [104]
% right_division(identity,right_division(X,left_division(right_division(identity,X),
% left_division(right_division(identity,X),
% left_division(right_division(identity,Y),X)))))
% ->
% left_division(right_division(identity,X),left_division(right_division(identity,X),Y))
% Current number of equations to process: 836
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [105]
% left_division(right_division(identity,right_division(X,Y)),right_division(identity,
% right_division(Y,
% left_division(
% right_division(identity,Y),X))))
% -> left_division(right_division(identity,X),right_division(X,Y))
% Current number of equations to process: 883
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [106]
% right_division(identity,right_division(X,left_division(right_division(identity,X),
% left_division(right_division(identity,Y),
% left_division(right_division(identity,Y),X)))))
% ->
% left_division(right_division(identity,X),right_division(Y,right_division(identity,Y)))
% Current number of equations to process: 916
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [107]
% right_division(identity,right_division(right_division(Y,X),right_division(identity,
% right_division(X,
% left_division(
% right_division(identity,X),Y)))))
% -> X
% Current number of equations to process: 967
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [108]
% left_division(left_division(X,Y),left_division(X,left_division(right_division(identity,Y),X)))
% -> X
% Current number of equations to process: 1015
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [109]
% right_division(identity,right_division(X,left_division(right_division(identity,X),Y)))
% <->
% left_division(right_division(Y,X),left_division(right_division(identity,Y),
% right_division(Y,X)))
% Current number of equations to process: 1044
% Current number of ordered equations: 1
% Current number of rules: 46
% New rule produced :
% [110]
% left_division(right_division(Y,X),left_division(right_division(identity,Y),
% right_division(Y,X))) <->
% right_division(identity,right_division(X,left_division(right_division(identity,X),Y)))
% Current number of equations to process: 1044
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [111]
% left_division(right_division(identity,left_division(X,left_division(right_division(identity,Y),X))),
% left_division(X,Y)) ->
% left_division(right_division(identity,left_division(X,Y)),Y)
% Current number of equations to process: 1128
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [112]
% left_division(right_division(identity,Y),left_division(right_division(identity,
% left_division(Y,X)),
% left_division(right_division(identity,Y),Z)))
% <->
% left_division(right_division(identity,left_division(right_division(identity,X),Y)),Z)
% Current number of equations to process: 1172
% Current number of ordered equations: 1
% Current number of rules: 49
% New rule produced :
% [113]
% left_division(right_division(identity,left_division(right_division(identity,X),Y)),Z)
% <->
% left_division(right_division(identity,Y),left_division(right_division(identity,
% left_division(Y,X)),
% left_division(right_division(identity,Y),Z)))
% Current number of equations to process: 1172
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [114]
% right_division(identity,right_division(left_division(X,Y),left_division(
% right_division(identity,X),Y)))
% -> right_division(X,right_division(identity,X))
% Current number of equations to process: 1288
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [115]
% right_division(identity,right_division(X,left_division(X,left_division(
% right_division(identity,Y),
% left_division(
% right_division(identity,Y),X)))))
% -> left_division(X,right_division(Y,right_division(identity,Y)))
% Current number of equations to process: 1345
% Current number of ordered equations: 3
% Current number of rules: 52
% New rule produced :
% [116]
% right_division(identity,right_division(left_division(X,Y),left_division(
% left_division(X,Y),Y)))
% <-> left_division(left_division(X,Y),X)
% Current number of equations to process: 1410
% Current number of ordered equations: 2
% Current number of rules: 53
% New rule produced :
% [117]
% right_division(right_division(X,Y),right_division(identity,right_division(Y,
% left_division(Y,X))))
% -> Y
% Current number of equations to process: 1410
% Current number of ordered equations: 1
% Current number of rules: 54
% New rule produced :
% [118]
% left_division(left_division(X,Y),X) <->
% right_division(identity,right_division(left_division(X,Y),left_division(
% left_division(X,Y),Y)))
% Current number of equations to process: 1410
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [119]
% right_division(identity,right_division(X,left_division(X,left_division(X,
% left_division(
% right_division(identity,Y),X)))))
% -> left_division(X,left_division(X,Y))
% Current number of equations to process: 1509
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [120]
% right_division(identity,right_division(X,right_division(X,right_division(identity,
% right_division(X,
% right_division(identity,X))))))
% -> right_division(X,right_division(identity,X))
% Current number of equations to process: 1571
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [121]
% left_division(X,right_division(X,right_division(identity,right_division(X,
% right_division(identity,X)))))
% -> right_division(X,right_division(identity,X))
% Current number of equations to process: 1622
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [122]
% right_division(right_division(identity,X),right_division(identity,right_division(X,
% right_division(identity,X))))
% -> X
% Current number of equations to process: 1643
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [123]
% left_division(left_division(right_division(identity,X),Y),left_division(
% right_division(identity,X),
% right_division(Y,
% right_division(identity,Y))))
% -> Y
% Current number of equations to process: 1659
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [124]
% left_division(right_division(X,Y),left_division(right_division(identity,X),Y))
% -> right_division(Y,right_division(identity,Y))
% Current number of equations to process: 1711
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [125]
% left_division(right_division(X,right_division(Y,right_division(identity,Y))),
% right_division(X,Y)) -> Y
% Current number of equations to process: 1754
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [126]
% right_division(identity,right_division(Y,left_division(right_division(identity,
% right_division(X,Y)),
% left_division(right_division(identity,X),Y))))
% -> left_division(right_division(identity,right_division(X,Y)),X)
% Current number of equations to process: 1795
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [127]
% right_division(X,left_division(X,left_division(right_division(identity,Y),X)))
% -> right_division(identity,left_division(X,Y))
% Rule
% [90]
% right_division(identity,right_division(X,left_division(X,left_division(
% right_division(identity,Y),X))))
% -> left_division(X,Y) collapsed.
% Current number of equations to process: 1874
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [128]
% right_division(X,left_division(X,left_division(Y,X))) ->
% right_division(identity,left_division(X,right_division(identity,Y)))
% Rule
% [127]
% right_division(X,left_division(X,left_division(right_division(identity,Y),X)))
% -> right_division(identity,left_division(X,Y)) collapsed.
% Current number of equations to process: 1879
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [129]
% left_division(right_division(X,right_division(Y,X)),right_division(X,
% right_division(identity,X)))
% -> Y
% Current number of equations to process: 1906
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [130]
% left_division(right_division(identity,right_division(X,right_division(Y,X))),Y)
% -> right_division(X,right_division(identity,X))
% Current number of equations to process: 1944
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [131]
% right_division(identity,right_division(X,right_division(Y,right_division(identity,Y))))
% <-> right_division(Y,right_division(X,Y))
% Current number of equations to process: 1974
% Current number of ordered equations: 1
% Current number of rules: 66
% New rule produced :
% [132]
% right_division(Y,right_division(X,Y)) <->
% right_division(identity,right_division(X,right_division(Y,right_division(identity,Y))))
% Current number of equations to process: 1974
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [133]
% left_division(left_division(X,right_division(identity,Y)),left_division(X,
% left_division(Y,X)))
% -> X
% Current number of equations to process: 2058
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [134]
% left_division(right_division(identity,left_division(right_division(identity,X),Y)),
% right_division(identity,Y)) -> X
% Current number of equations to process: 2104
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [135]
% left_division(right_division(identity,X),right_division(identity,Y)) ->
% right_division(X,Y)
% Rule
% [59]
% left_division(right_division(identity,X),right_division(identity,right_division(X,
% right_division(identity,X))))
% -> right_division(identity,X) collapsed.
% Rule
% [96]
% left_division(right_division(identity,X),right_division(identity,right_division(X,
% left_division(X,Y))))
% -> right_division(Y,X) collapsed.
% Rule
% [105]
% left_division(right_division(identity,right_division(X,Y)),right_division(identity,
% right_division(Y,
% left_division(
% right_division(identity,Y),X))))
% -> left_division(right_division(identity,X),right_division(X,Y)) collapsed.
% Rule
% [134]
% left_division(right_division(identity,left_division(right_division(identity,X),Y)),
% right_division(identity,Y)) -> X collapsed.
% Current number of equations to process: 2112
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [136]
% right_division(X,right_division(X,left_division(X,Y))) -> right_division(Y,X)
% Current number of equations to process: 2111
% Current number of ordered equations: 0
% Current number of rules: 67
% Rule [128]
% right_division(X,left_division(X,left_division(Y,X))) ->
% right_division(identity,left_division(X,right_division(identity,Y))) is composed into 
% [128]
% right_division(X,left_division(X,left_division(Y,X))) ->
% right_division(identity,right_division(right_division(identity,X),Y))
% New rule produced :
% [137]
% left_division(X,right_division(identity,Y)) ->
% right_division(right_division(identity,X),Y)
% Rule
% [87]
% left_division(right_division(X,Y),right_division(identity,right_division(Y,X)))
% -> identity collapsed.
% Rule
% [99]
% left_division(X,right_division(identity,right_division(X,Y))) ->
% right_division(identity,right_division(X,left_division(X,Y))) collapsed.
% Rule
% [133]
% left_division(left_division(X,right_division(identity,Y)),left_division(X,
% left_division(Y,X)))
% -> X collapsed.
% Rule
% [135]
% left_division(right_division(identity,X),right_division(identity,Y)) ->
% right_division(X,Y) collapsed.
% Current number of equations to process: 2122
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [138]
% left_division(right_division(X,Y),Y) -> right_division(Y,left_division(Y,X))
% Rule
% [42]
% left_division(right_division(identity,X),X) ->
% right_division(X,right_division(identity,X)) collapsed.
% Current number of equations to process: 2126
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [139] left_division(X,right_division(X,Y)) -> right_division(identity,Y)
% Rule [41] left_division(X,right_division(X,right_division(identity,X))) -> X
% collapsed.
% Rule
% [121]
% left_division(X,right_division(X,right_division(identity,right_division(X,
% right_division(identity,X)))))
% -> right_division(X,right_division(identity,X)) collapsed.
% Current number of equations to process: 2167
% Current number of ordered equations: 0
% Current number of rules: 63
% Rule [78] multiply(X,Y) -> left_division(right_division(identity,X),Y) is composed into 
% [78]
% multiply(X,Y) ->
% right_division(right_division(identity,right_division(identity,X)),right_division(identity,Y))
% New rule produced :
% [140]
% left_division(X,Y) ->
% right_division(right_division(identity,X),right_division(identity,Y))
% Rule [16] left_division(X,X) -> identity collapsed.
% Rule [17] left_division(identity,X) -> X collapsed.
% Rule [20] right_division(X,left_division(Y,X)) -> Y collapsed.
% Rule [21] left_division(right_division(X,Y),X) -> Y collapsed.
% Rule [35] left_division(X,identity) -> right_division(identity,X) collapsed.
% Rule
% [36]
% left_division(X,right_division(Y,X)) ->
% right_division(identity,right_division(X,left_division(X,Y))) collapsed.
% Rule
% [49]
% right_division(X,left_division(Y,left_division(Y,X))) ->
% right_division(Y,right_division(identity,Y)) collapsed.
% Rule
% [52]
% left_division(right_division(X,right_division(identity,X)),Y) ->
% left_division(X,left_division(X,Y)) collapsed.
% Rule
% [60]
% left_division(right_division(identity,right_division(X,right_division(identity,X))),X)
% ->
% right_division(X,right_division(identity,right_division(X,right_division(identity,X))))
% collapsed.
% Rule [79] left_division(X,left_division(right_division(identity,X),Y)) -> Y
% collapsed.
% Rule [80] left_division(right_division(identity,X),left_division(X,Y)) -> Y
% collapsed.
% Rule [81] left_division(right_division(identity,right_division(X,Y)),Y) -> X
% collapsed.
% Rule
% [86]
% left_division(right_division(X,Y),left_division(right_division(Y,X),Z)) -> Z
% collapsed.
% Rule
% [88]
% left_division(right_division(identity,X),right_division(Y,X)) ->
% right_division(identity,right_division(X,left_division(right_division(identity,X),Y)))
% collapsed.
% Rule
% [89]
% left_division(right_division(identity,left_division(X,Y)),X) ->
% left_division(X,left_division(right_division(identity,Y),X)) collapsed.
% Rule
% [91]
% left_division(right_division(identity,right_division(X,Y)),right_division(Y,X))
% -> identity collapsed.
% Rule
% [102]
% right_division(identity,right_division(Z,left_division(right_division(identity,X),
% left_division(right_division(identity,Y),
% left_division(right_division(identity,X),Z)))))
% ->
% left_division(right_division(identity,X),left_division(right_division(identity,Y),X))
% collapsed.
% Rule
% [103]
% right_division(identity,right_division(left_division(X,Y),left_division(
% right_division(identity,
% left_division(X,Y)),Y)))
% -> left_division(X,left_division(right_division(identity,Y),X)) collapsed.
% Rule
% [104]
% right_division(identity,right_division(X,left_division(right_division(identity,X),
% left_division(right_division(identity,X),
% left_division(right_division(identity,Y),X)))))
% ->
% left_division(right_division(identity,X),left_division(right_division(identity,X),Y))
% collapsed.
% Rule
% [106]
% right_division(identity,right_division(X,left_division(right_division(identity,X),
% left_division(right_division(identity,Y),
% left_division(right_division(identity,Y),X)))))
% ->
% left_division(right_division(identity,X),right_division(Y,right_division(identity,Y)))
% collapsed.
% Rule
% [107]
% right_division(identity,right_division(right_division(Y,X),right_division(identity,
% right_division(X,
% left_division(
% right_division(identity,X),Y)))))
% -> X collapsed.
% Rule
% [108]
% left_division(left_division(X,Y),left_division(X,left_division(right_division(identity,Y),X)))
% -> X collapsed.
% Rule
% [109]
% right_division(identity,right_division(X,left_division(right_division(identity,X),Y)))
% <->
% left_division(right_division(Y,X),left_division(right_division(identity,Y),
% right_division(Y,X))) collapsed.
% Rule
% [110]
% left_division(right_division(Y,X),left_division(right_division(identity,Y),
% right_division(Y,X))) <->
% right_division(identity,right_division(X,left_division(right_division(identity,X),Y)))
% collapsed.
% Rule
% [111]
% left_division(right_division(identity,left_division(X,left_division(right_division(identity,Y),X))),
% left_division(X,Y)) ->
% left_division(right_division(identity,left_division(X,Y)),Y) collapsed.
% Rule
% [112]
% left_division(right_division(identity,Y),left_division(right_division(identity,
% left_division(Y,X)),
% left_division(right_division(identity,Y),Z)))
% <->
% left_division(right_division(identity,left_division(right_division(identity,X),Y)),Z)
% collapsed.
% Rule
% [113]
% left_division(right_division(identity,left_division(right_division(identity,X),Y)),Z)
% <->
% left_division(right_division(identity,Y),left_division(right_division(identity,
% left_division(Y,X)),
% left_division(right_division(identity,Y),Z)))
% collapsed.
% Rule
% [114]
% right_division(identity,right_division(left_division(X,Y),left_division(
% right_division(identity,X),Y)))
% -> right_division(X,right_division(identity,X)) collapsed.
% Rule
% [115]
% right_division(identity,right_division(X,left_division(X,left_division(
% right_division(identity,Y),
% left_division(
% right_division(identity,Y),X)))))
% -> left_division(X,right_division(Y,right_division(identity,Y))) collapsed.
% Rule
% [116]
% right_division(identity,right_division(left_division(X,Y),left_division(
% left_division(X,Y),Y)))
% <-> left_division(left_division(X,Y),X) collapsed.
% Rule
% [117]
% right_division(right_division(X,Y),right_division(identity,right_division(Y,
% left_division(Y,X))))
% -> Y collapsed.
% Rule
% [118]
% left_division(left_division(X,Y),X) <->
% right_division(identity,right_division(left_division(X,Y),left_division(
% left_division(X,Y),Y)))
% collapsed.
% Rule
% [119]
% right_division(identity,right_division(X,left_division(X,left_division(X,
% left_division(
% right_division(identity,Y),X)))))
% -> left_division(X,left_division(X,Y)) collapsed.
% Rule
% [123]
% left_division(left_division(right_division(identity,X),Y),left_division(
% right_division(identity,X),
% right_division(Y,
% right_division(identity,Y))))
% -> Y collapsed.
% Rule
% [124]
% left_division(right_division(X,Y),left_division(right_division(identity,X),Y))
% -> right_division(Y,right_division(identity,Y)) collapsed.
% Rule
% [125]
% left_division(right_division(X,right_division(Y,right_division(identity,Y))),
% right_division(X,Y)) -> Y collapsed.
% Rule
% [126]
% right_division(identity,right_division(Y,left_division(right_division(identity,
% right_division(X,Y)),
% left_division(right_division(identity,X),Y))))
% -> left_division(right_division(identity,right_division(X,Y)),X) collapsed.
% Rule
% [128]
% right_division(X,left_division(X,left_division(Y,X))) ->
% right_division(identity,right_division(right_division(identity,X),Y))
% collapsed.
% Rule
% [129]
% left_division(right_division(X,right_division(Y,X)),right_division(X,
% right_division(identity,X)))
% -> Y collapsed.
% Rule
% [130]
% left_division(right_division(identity,right_division(X,right_division(Y,X))),Y)
% -> right_division(X,right_division(identity,X)) collapsed.
% Rule
% [136]
% right_division(X,right_division(X,left_division(X,Y))) -> right_division(Y,X)
% collapsed.
% Rule
% [137]
% left_division(X,right_division(identity,Y)) ->
% right_division(right_division(identity,X),Y) collapsed.
% Rule
% [138]
% left_division(right_division(X,Y),Y) -> right_division(Y,left_division(Y,X))
% collapsed.
% Rule [139] left_division(X,right_division(X,Y)) -> right_division(identity,Y)
% collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% right_division(x,right_division(identity,right_division(y,right_division(identity,
% right_division(
% right_division(z,y),
% right_division(identity,
% right_division(y,
% right_division(identity,x)))))))) = 
% right_division(x,right_division(identity,right_division(right_division(y,x),
% right_division(identity,right_division(x,
% right_division(identity,
% right_division(z,
% right_division(identity,x))))))))
% 
% Current number of equations to process: 2202
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [141] right_division(right_division(X,Y),right_division(identity,Y)) -> X
% Current number of equations to process: 2199
% Current number of ordered equations: 2
% Current number of rules: 21
% New rule produced :
% [142]
% right_division(X,right_division(identity,right_division(right_division(identity,X),
% right_division(identity,Y)))) -> Y
% Current number of equations to process: 2199
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [143]
% right_division(right_division(identity,X),right_division(identity,right_division(X,
% right_division(identity,Y))))
% -> Y
% Rule
% [122]
% right_division(right_division(identity,X),right_division(identity,right_division(X,
% right_division(identity,X))))
% -> X collapsed.
% Current number of equations to process: 2199
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [144]
% right_division(X,right_division(right_division(identity,Y),right_division(identity,X)))
% -> Y
% Current number of equations to process: 2198
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [145]
% right_division(identity,right_division(right_division(identity,X),right_division(identity,
% right_division(X,Y))))
% -> Y
% Current number of equations to process: 2197
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [146]
% right_division(identity,right_division(Y,right_division(X,right_division(identity,Y))))
% -> X
% Current number of equations to process: 2196
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [147]
% right_division(right_division(identity,X),right_division(right_division(identity,Y),X))
% -> Y
% Current number of equations to process: 2195
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [148]
% right_division(identity,right_division(X,right_division(right_division(identity,X),
% right_division(identity,Y)))) <->
% right_division(right_division(identity,X),right_division(X,Y))
% Current number of equations to process: 2193
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [149]
% right_division(right_division(identity,X),right_division(X,Y)) <->
% right_division(identity,right_division(X,right_division(right_division(identity,X),
% right_division(identity,Y))))
% Current number of equations to process: 2193
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [150]
% right_division(X,right_division(identity,right_division(right_division(identity,X),Y)))
% -> right_division(identity,Y)
% Rule
% [142]
% right_division(X,right_division(identity,right_division(right_division(identity,X),
% right_division(identity,Y)))) -> Y
% collapsed.
% Current number of equations to process: 2192
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [151]
% right_division(right_division(identity,X),right_division(identity,right_division(X,Y)))
% -> right_division(identity,Y)
% Rule
% [143]
% right_division(right_division(identity,X),right_division(identity,right_division(X,
% right_division(identity,Y))))
% -> Y collapsed.
% Rule
% [145]
% right_division(identity,right_division(right_division(identity,X),right_division(identity,
% right_division(X,Y))))
% -> Y collapsed.
% Current number of equations to process: 2191
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [152]
% right_division(right_division(identity,Y),right_division(X,Y)) ->
% right_division(identity,X)
% Rule
% [147]
% right_division(right_division(identity,X),right_division(right_division(identity,Y),X))
% -> Y collapsed.
% Current number of equations to process: 2200
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [153]
% right_division(right_division(X,right_division(Y,Z)),right_division(Z,Y)) ->
% X
% Rule
% [97]
% right_division(right_division(identity,right_division(X,Y)),right_division(Y,X))
% -> identity collapsed.
% Current number of equations to process: 2199
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [154]
% right_division(X,right_division(Y,right_division(identity,X))) <->
% right_division(identity,Y)
% Rule
% [43]
% right_division(X,right_division(X,right_division(identity,X))) ->
% right_division(identity,X) collapsed.
% Rule
% [144]
% right_division(X,right_division(right_division(identity,Y),right_division(identity,X)))
% -> Y collapsed.
% Current number of equations to process: 2211
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [155]
% right_division(right_division(X,Y),right_division(Z,right_division(Y,X))) ->
% right_division(identity,Z)
% Rule
% [98]
% right_division(right_division(X,Y),right_division(identity,right_division(Y,X)))
% -> identity collapsed.
% Current number of equations to process: 2339
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [156]
% right_division(identity,right_division(Z,right_division(Y,X))) <->
% right_division(right_division(identity,right_division(X,Y)),Z)
% Current number of equations to process: 2337
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [157]
% right_division(right_division(identity,right_division(X,Y)),Z) <->
% right_division(identity,right_division(Z,right_division(Y,X)))
% Current number of equations to process: 2337
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [158]
% right_division(right_division(identity,right_division(right_division(identity,X),Y)),
% right_division(identity,right_division(right_division(identity,X),right_division(identity,
% right_division(
% right_division(identity,Y),
% right_division(identity,X))))))
% -> X
% Current number of equations to process: 2410
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [159]
% right_division(identity,right_division(X,right_division(right_division(identity,X),
% right_division(identity,right_division(
% right_division(identity,Y),
% right_division(identity,X))))))
% -> right_division(right_division(identity,X),Y)
% Current number of equations to process: 2450
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [160]
% right_division(right_division(identity,right_division(right_division(identity,X),
% right_division(identity,Y))),right_division(identity,
% right_division(
% right_division(identity,X),
% right_division(identity,
% right_division(Y,
% right_division(identity,Y))))))
% -> Y
% Current number of equations to process: 2490
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [161]
% right_division(right_division(X,right_division(Y,X)),right_division(identity,Y))
% -> right_division(X,right_division(identity,X))
% Current number of equations to process: 2530
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [162]
% right_division(right_division(identity,right_division(right_division(identity,X),Y)),
% right_division(identity,right_division(right_division(identity,X),right_division(identity,Y))))
% -> right_division(Y,right_division(identity,Y))
% Current number of equations to process: 2563
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [163]
% right_division(right_division(identity,right_division(X,Y)),right_division(identity,
% right_division(X,
% right_division(identity,X))))
% -> right_division(Y,right_division(identity,X))
% Current number of equations to process: 2604
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [164]
% right_division(right_division(X,Y),right_division(identity,right_division(Y,
% right_division(
% right_division(identity,Y),
% right_division(identity,X)))))
% -> Y
% Current number of equations to process: 2639
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [165]
% right_division(identity,right_division(X,right_division(X,right_division(identity,Y))))
% -> right_division(X,right_division(X,Y))
% Rule
% [120]
% right_division(identity,right_division(X,right_division(X,right_division(identity,
% right_division(X,
% right_division(identity,X))))))
% -> right_division(X,right_division(identity,X)) collapsed.
% Current number of equations to process: 2685
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [166]
% right_division(X,right_division(X,right_division(identity,Y))) <->
% right_division(identity,right_division(X,right_division(X,Y)))
% Current number of equations to process: 2692
% Current number of ordered equations: 1
% Current number of rules: 36
% New rule produced :
% [167]
% right_division(identity,right_division(X,right_division(X,Y))) <->
% right_division(X,right_division(X,right_division(identity,Y)))
% Current number of equations to process: 2692
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [168]
% right_division(identity,right_division(right_division(identity,X),right_division(
% right_division(identity,X),Y)))
% <->
% right_division(right_division(identity,X),right_division(identity,right_division(
% right_division(identity,Y),
% right_division(identity,X))))
% Current number of equations to process: 2806
% Current number of ordered equations: 1
% Current number of rules: 38
% New rule produced :
% [169]
% right_division(right_division(identity,X),right_division(identity,right_division(
% right_division(identity,Y),
% right_division(identity,X))))
% <->
% right_division(identity,right_division(right_division(identity,X),right_division(
% right_division(identity,X),Y)))
% Current number of equations to process: 2806
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [170]
% right_division(right_division(X,Y),right_division(Z,right_division(Y,
% right_division(identity,Z))))
% -> X
% Current number of equations to process: 2911
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [171]
% right_division(identity,right_division(right_division(identity,right_division(X,Y)),Z))
% <-> right_division(Z,right_division(Y,X))
% Current number of equations to process: 2939
% Current number of ordered equations: 1
% Current number of rules: 41
% New rule produced :
% [172]
% right_division(Z,right_division(Y,X)) <->
% right_division(identity,right_division(right_division(identity,right_division(X,Y)),Z))
% Current number of equations to process: 2939
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [173]
% right_division(right_division(identity,X),right_division(identity,right_division(
% right_division(X,Y),
% right_division(identity,
% right_division(Y,
% right_division(Y,X))))))
% -> right_division(X,Y)
% Current number of equations to process: 3103
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [174]
% right_division(right_division(identity,right_division(right_division(identity,X),
% right_division(identity,right_division(Y,
% right_division(identity,X))))),
% right_division(right_division(identity,Y),right_division(right_division(identity,X),
% right_division(identity,Y)))) ->
% right_division(right_division(identity,X),right_division(identity,Y))
% Current number of equations to process: 3148
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [175]
% right_division(right_division(X,right_division(X,right_division(X,right_division(identity,Y)))),
% right_division(Y,X)) -> right_division(X,right_division(identity,X))
% Current number of equations to process: 3230
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [176]
% right_division(right_division(X,Y),right_division(identity,right_division(X,Y)))
% ->
% right_division(identity,right_division(Y,right_division(right_division(X,Y),
% right_division(identity,X))))
% Current number of equations to process: 3287
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [177]
% right_division(identity,right_division(X,right_division(right_division(identity,X),
% right_division(identity,right_division(Y,
% right_division(identity,
% right_division(Y,
% right_division(identity,X))))))))
% ->
% right_division(right_division(identity,X),right_division(identity,right_division(Y,
% right_division(identity,Y))))
% Current number of equations to process: 3339
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [178]
% right_division(right_division(X,right_division(identity,right_division(X,
% right_division(identity,X)))),
% right_division(identity,Y)) ->
% right_division(X,right_division(identity,right_division(X,right_division(identity,
% right_division(X,
% right_division(identity,Y))))))
% Current number of equations to process: 3407
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [179]
% right_division(X,right_division(identity,right_division(Y,right_division(identity,Y))))
% <->
% right_division(X,right_division(X,right_division(Y,right_division(identity,
% right_division(Y,right_division(identity,X))))))
% Current number of equations to process: 3462
% Current number of ordered equations: 1
% Current number of rules: 49
% New rule produced :
% [180]
% right_division(X,right_division(X,right_division(Y,right_division(identity,
% right_division(Y,right_division(identity,X))))))
% <->
% right_division(X,right_division(identity,right_division(Y,right_division(identity,Y))))
% Current number of equations to process: 3462
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [181]
% right_division(right_division(identity,right_division(X,right_division(identity,X))),
% right_division(identity,Y)) ->
% right_division(right_division(identity,X),right_division(identity,right_division(
% right_division(identity,X),
% right_division(identity,Y))))
% Current number of equations to process: 3552
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [182]
% right_division(right_division(X,right_division(X,Y)),right_division(Y,
% right_division(X,Y))) ->
% right_division(X,Y)
% Current number of equations to process: 3604
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [183]
% right_division(identity,right_division(X,right_division(identity,right_division(
% right_division(
% right_division(identity,X),
% right_division(identity,Y)),
% right_division(identity,
% right_division(
% right_division(identity,Y),
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))))
% -> right_division(right_division(identity,X),right_division(identity,Y))
% Current number of equations to process: 3668
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [184]
% right_division(right_division(right_division(identity,X),right_division(identity,
% right_division(
% right_division(identity,X),
% right_division(identity,Y)))),
% right_division(right_division(identity,Y),right_division(identity,right_division(
% right_division(identity,X),
% right_division(identity,Y)))))
% -> right_division(right_division(identity,X),right_division(identity,Y))
% Current number of equations to process: 3767
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [185]
% right_division(right_division(identity,X),right_division(identity,right_division(
% right_division(identity,
% right_division(Y,X)),
% right_division(identity,
% right_division(Y,
% right_division(identity,
% right_division(Y,X)))))))
% -> right_division(Y,X)
% Current number of equations to process: 3870
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [186]
% right_division(X,right_division(identity,right_division(right_division(identity,Y),
% right_division(identity,right_division(X,Y)))))
% <->
% right_division(identity,right_division(Y,right_division(right_division(X,Y),
% right_division(identity,X))))
% Current number of equations to process: 3939
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [187]
% right_division(identity,right_division(Y,right_division(right_division(X,Y),
% right_division(identity,X)))) <->
% right_division(X,right_division(identity,right_division(right_division(identity,Y),
% right_division(identity,right_division(X,Y)))))
% Current number of equations to process: 3939
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [188]
% right_division(X,right_division(identity,right_division(right_division(
% right_division(identity,X),
% right_division(identity,Y)),
% right_division(identity,right_division(
% right_division(identity,Y),
% right_division(identity,
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))))
% -> right_division(right_division(identity,X),right_division(identity,Y))
% Current number of equations to process: 4103
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [189]
% right_division(X,right_division(identity,right_division(right_division(Y,X),
% right_division(identity,right_division(X,
% right_division(identity,Y))))))
% ->
% right_division(X,right_division(identity,right_division(Y,right_division(identity,Y))))
% Current number of equations to process: 4195
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [190]
% right_division(X,right_division(identity,right_division(X,right_division(identity,
% right_division(Y,
% right_division(identity,Y))))))
% <->
% right_division(identity,right_division(right_division(identity,Y),right_division(X,
% right_division(identity,
% right_division(X,
% right_division(identity,Y))))))
% Current number of equations to process: 4259
% Current number of ordered equations: 1
% Current number of rules: 60
% New rule produced :
% [191]
% right_division(identity,right_division(right_division(identity,Y),right_division(X,
% right_division(identity,
% right_division(X,
% right_division(identity,Y))))))
% <->
% right_division(X,right_division(identity,right_division(X,right_division(identity,
% right_division(Y,
% right_division(identity,Y))))))
% Current number of equations to process: 4259
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [192]
% right_division(identity,right_division(right_division(identity,Y),right_division(identity,
% right_division(X,
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))
% <->
% right_division(right_division(identity,X),right_division(identity,right_division(Y,
% right_division(identity,
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))
% Current number of equations to process: 4437
% Current number of ordered equations: 1
% Current number of rules: 62
% New rule produced :
% [193]
% right_division(right_division(identity,X),right_division(identity,right_division(Y,
% right_division(identity,
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))
% <->
% right_division(identity,right_division(right_division(identity,Y),right_division(identity,
% right_division(X,
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))
% Current number of equations to process: 4437
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [194]
% right_division(identity,right_division(right_division(identity,Y),right_division(X,
% right_division(Y,
% right_division(identity,Y)))))
% -> right_division(X,Y)
% Current number of equations to process: 4670
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [195]
% right_division(identity,right_division(right_division(right_division(identity,X),
% right_division(identity,Y)),right_division(X,
% right_division(identity,
% right_division(Y,
% right_division(identity,
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))))
% -> right_division(X,right_division(identity,Y))
% Current number of equations to process: 4742
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [196]
% right_division(right_division(identity,right_division(X,right_division(identity,Y))),
% right_division(identity,right_division(X,right_division(identity,right_division(Y,
% right_division(identity,
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))))
% -> right_division(right_division(identity,X),right_division(identity,Y))
% Current number of equations to process: 4876
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [197]
% right_division(right_division(X,right_division(identity,right_division(X,Y))),
% right_division(Y,right_division(Y,X))) -> right_division(X,Y)
% Current number of equations to process: 4971
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [198]
% right_division(X,right_division(right_division(right_division(identity,X),
% right_division(identity,Y)),right_division(identity,
% right_division(
% right_division(identity,Y),
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))
% -> right_division(Y,right_division(identity,X))
% Current number of equations to process: 1538
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [199]
% right_division(identity,right_division(Z,right_division(X,right_division(identity,
% right_division(
% right_division(Y,X),
% right_division(identity,
% right_division(X,
% right_division(identity,Z))))))))
% -> right_division(X,right_division(identity,Y))
% Current number of equations to process: 1636
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [200]
% right_division(Z,right_division(identity,right_division(right_division(identity,
% right_division(Z,
% right_division(
% right_division(identity,Z),
% right_division(identity,X)))),
% right_division(identity,right_division(Z,
% right_division(identity,Y))))))
% -> right_division(X,right_division(identity,Y))
% Current number of equations to process: 1793
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [201]
% right_division(X,right_division(Y,right_division(identity,right_division(Y,
% right_division(identity,X)))))
% <-> right_division(identity,right_division(Y,right_division(identity,Y)))
% Rule
% [180]
% right_division(X,right_division(X,right_division(Y,right_division(identity,
% right_division(Y,right_division(identity,X))))))
% <->
% right_division(X,right_division(identity,right_division(Y,right_division(identity,Y))))
% collapsed.
% Current number of equations to process: 1904
% Current number of ordered equations: 1
% Current number of rules: 70
% New rule produced :
% [202]
% right_division(identity,right_division(Y,right_division(identity,Y))) <->
% right_division(X,right_division(Y,right_division(identity,right_division(Y,
% right_division(identity,X)))))
% Rule
% [179]
% right_division(X,right_division(identity,right_division(Y,right_division(identity,Y))))
% <->
% right_division(X,right_division(X,right_division(Y,right_division(identity,
% right_division(Y,right_division(identity,X))))))
% collapsed.
% Current number of equations to process: 1904
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [203]
% right_division(right_division(X,Y),right_division(right_division(identity,X),Y))
% -> right_division(X,right_division(identity,X))
% Current number of equations to process: 1926
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [204]
% right_division(X,right_division(X,right_division(right_division(identity,X),
% right_division(identity,Y)))) <->
% right_division(Y,X)
% Current number of equations to process: 2097
% Current number of ordered equations: 1
% Current number of rules: 72
% New rule produced :
% [205]
% right_division(Y,X) <->
% right_division(X,right_division(X,right_division(right_division(identity,X),
% right_division(identity,Y))))
% Current number of equations to process: 2097
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [206]
% right_division(X,right_division(X,right_division(right_division(identity,X),Y)))
% <-> right_division(right_division(identity,Y),X)
% Current number of equations to process: 2109
% Current number of ordered equations: 1
% Current number of rules: 74
% New rule produced :
% [207]
% right_division(right_division(identity,Y),X) <->
% right_division(X,right_division(X,right_division(right_division(identity,X),Y)))
% Current number of equations to process: 2109
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [208]
% right_division(identity,right_division(X,right_division(right_division(Y,X),
% right_division(identity,Y)))) <->
% right_division(right_division(identity,right_division(X,Y)),right_division(identity,
% right_division(Y,X)))
% Current number of equations to process: 2555
% Current number of ordered equations: 1
% Current number of rules: 76
% New rule produced :
% [209]
% right_division(right_division(identity,right_division(X,Y)),right_division(identity,
% right_division(Y,X)))
% <->
% right_division(identity,right_division(X,right_division(right_division(Y,X),
% right_division(identity,Y))))
% Current number of equations to process: 2555
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [210]
% right_division(identity,right_division(X,right_division(identity,right_division(X,Y))))
% <-> right_division(Y,right_division(X,right_division(identity,X)))
% Current number of equations to process: 2768
% Current number of ordered equations: 1
% Current number of rules: 78
% New rule produced :
% [211]
% right_division(Y,right_division(X,right_division(identity,X))) <->
% right_division(identity,right_division(X,right_division(identity,right_division(X,Y))))
% Current number of equations to process: 2768
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [212]
% right_division(identity,right_division(Y,right_division(right_division(identity,X),
% right_division(identity,right_division(Y,
% right_division(identity,Y))))))
% -> right_division(right_division(identity,X),right_division(identity,Y))
% Current number of equations to process: 2967
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [213]
% right_division(identity,right_division(X,right_division(Y,right_division(identity,Y))))
% <-> right_division(Y,right_division(identity,right_division(Y,X)))
% Current number of equations to process: 3073
% Current number of ordered equations: 1
% Current number of rules: 81
% New rule produced :
% [214]
% right_division(Y,right_division(identity,right_division(Y,X))) <->
% right_division(identity,right_division(X,right_division(Y,right_division(identity,Y))))
% Current number of equations to process: 3073
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [215]
% right_division(right_division(right_division(identity,X),right_division(identity,Y)),
% right_division(identity,right_division(right_division(identity,Y),right_division(identity,
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))
% ->
% right_division(right_division(identity,X),right_division(identity,right_division(
% right_division(identity,X),
% right_division(identity,Y))))
% Rule
% [188]
% right_division(X,right_division(identity,right_division(right_division(
% right_division(identity,X),
% right_division(identity,Y)),
% right_division(identity,right_division(
% right_division(identity,Y),
% right_division(identity,
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))))
% -> right_division(right_division(identity,X),right_division(identity,Y))
% collapsed.
% Current number of equations to process: 3278
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [216]
% right_division(X,right_division(identity,right_division(right_division(identity,Y),X)))
% <-> right_division(identity,right_division(X,right_division(X,Y)))
% Rule
% [169]
% right_division(right_division(identity,X),right_division(identity,right_division(
% right_division(identity,Y),
% right_division(identity,X))))
% <->
% right_division(identity,right_division(right_division(identity,X),right_division(
% right_division(identity,X),Y)))
% collapsed.
% Current number of equations to process: 3408
% Current number of ordered equations: 1
% Current number of rules: 82
% New rule produced :
% [217]
% right_division(identity,right_division(X,right_division(X,Y))) <->
% right_division(X,right_division(identity,right_division(right_division(identity,Y),X)))
% Rule
% [168]
% right_division(identity,right_division(right_division(identity,X),right_division(
% right_division(identity,X),Y)))
% <->
% right_division(right_division(identity,X),right_division(identity,right_division(
% right_division(identity,Y),
% right_division(identity,X))))
% collapsed.
% Current number of equations to process: 3408
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [218]
% right_division(right_division(identity,Y),X) <->
% right_division(right_division(identity,X),right_division(X,right_division(X,Y)))
% Current number of equations to process: 3437
% Current number of ordered equations: 1
% Current number of rules: 83
% New rule produced :
% [219]
% right_division(right_division(identity,X),right_division(X,right_division(X,Y)))
% <-> right_division(right_division(identity,Y),X)
% Current number of equations to process: 3437
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [220]
% right_division(right_division(identity,right_division(X,right_division(identity,X))),Y)
% ->
% right_division(right_division(identity,X),right_division(identity,right_division(
% right_division(identity,X),Y)))
% Rule
% [181]
% right_division(right_division(identity,right_division(X,right_division(identity,X))),
% right_division(identity,Y)) ->
% right_division(right_division(identity,X),right_division(identity,right_division(
% right_division(identity,X),
% right_division(identity,Y))))
% collapsed.
% Current number of equations to process: 3895
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [221]
% right_division(right_division(identity,right_division(X,Y)),right_division(identity,
% right_division(
% right_division(identity,
% right_division(Y,X)),Z)))
% -> right_division(identity,Z)
% Current number of equations to process: 3980
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [222]
% right_division(X,right_division(right_division(identity,X),right_division(identity,Y)))
% <-> right_division(right_division(X,Y),right_division(identity,X))
% Current number of equations to process: 4084
% Current number of ordered equations: 1
% Current number of rules: 86
% New rule produced :
% [223]
% right_division(right_division(X,Y),right_division(identity,X)) <->
% right_division(X,right_division(right_division(identity,X),right_division(identity,Y)))
% Current number of equations to process: 4084
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [224]
% right_division(right_division(X,right_division(X,Y)),right_division(identity,X))
% -> right_division(X,right_division(identity,Y))
% Current number of equations to process: 4108
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [225]
% right_division(right_division(X,Y),right_division(identity,right_division(
% right_division(Y,X),Z)))
% -> right_division(identity,Z)
% Current number of equations to process: 4349
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [226]
% right_division(X,right_division(Y,right_division(right_division(identity,X),Y)))
% <-> right_division(identity,right_division(Y,right_division(identity,Y)))
% Current number of equations to process: 4439
% Current number of ordered equations: 1
% Current number of rules: 90
% New rule produced :
% [227]
% right_division(identity,right_division(Y,right_division(identity,Y))) <->
% right_division(X,right_division(Y,right_division(right_division(identity,X),Y)))
% Current number of equations to process: 4439
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [228]
% right_division(identity,right_division(Y,right_division(identity,Y))) <->
% right_division(right_division(identity,X),right_division(Y,right_division(X,Y)))
% Current number of equations to process: 4552
% Current number of ordered equations: 1
% Current number of rules: 92
% New rule produced :
% [229]
% right_division(right_division(identity,X),right_division(Y,right_division(X,Y)))
% <-> right_division(identity,right_division(Y,right_division(identity,Y)))
% Current number of equations to process: 4552
% Current number of ordered equations: 0
% Current number of rules: 93
% Rule [218]
% right_division(right_division(identity,Y),X) <->
% right_division(right_division(identity,X),right_division(X,right_division(X,Y))) is composed into 
% [218]
% right_division(right_division(identity,Y),X) <->
% right_division(identity,right_division(X,right_division(identity,Y)))
% New rule produced :
% [230]
% right_division(right_division(identity,X),right_division(X,right_division(X,Y)))
% -> right_division(identity,right_division(X,right_division(identity,Y)))
% Rule
% [219]
% right_division(right_division(identity,X),right_division(X,right_division(X,Y)))
% <-> right_division(right_division(identity,Y),X) collapsed.
% Current number of equations to process: 4692
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [231]
% right_division(X,right_division(Y,right_division(Z,right_division(X,right_division(identity,Z)))))
% <-> right_division(identity,Y)
% Current number of equations to process: 4764
% Current number of ordered equations: 1
% Current number of rules: 94
% New rule produced :
% [232]
% right_division(identity,Y) <->
% right_division(X,right_division(Y,right_division(Z,right_division(X,right_division(identity,Z)))))
% The conjecture has been reduced. 
% Conjecture is now:
% right_division(x,right_division(identity,right_division(y,right_division(identity,
% right_division(
% right_division(z,y),
% right_division(identity,
% right_division(y,
% right_division(z,
% right_division(x,
% right_division(identity,z)))))))))) = 
% right_division(x,right_division(identity,right_division(right_division(y,x),
% right_division(identity,right_division(x,
% right_division(z,
% right_division(z,
% right_division(identity,
% right_division(x,
% right_division(identity,z))))))))))
% 
% Current number of equations to process: 4764
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [233]
% right_division(right_division(X,right_division(Y,right_division(identity,X))),
% right_division(Z,Y)) -> right_division(identity,Z)
% Current number of equations to process: 4948
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [234]
% right_division(X,right_division(X,right_division(Z,Y))) <->
% right_division(identity,right_division(X,right_division(X,right_division(Y,Z))))
% Current number of equations to process: 4980
% Current number of ordered equations: 1
% Current number of rules: 97
% New rule produced :
% [235]
% right_division(identity,right_division(X,right_division(X,right_division(Y,Z))))
% <-> right_division(X,right_division(X,right_division(Z,Y)))
% Current number of equations to process: 4980
% Current number of ordered equations: 0
% Current number of rules: 98
% Rule [207]
% right_division(right_division(identity,Y),X) <->
% right_division(X,right_division(X,right_division(right_division(identity,X),Y))) is composed into 
% [207]
% right_division(right_division(identity,Y),X) <->
% right_division(identity,right_division(X,right_division(identity,Y)))
% Rule [205]
% right_division(Y,X) <->
% right_division(X,right_division(X,right_division(right_division(identity,X),
% right_division(identity,Y)))) is composed into 
% [205]
% right_division(Y,X) <->
% right_division(identity,right_division(X,right_division(identity,right_division(identity,Y))))
% New rule produced :
% [236]
% right_division(X,right_division(X,right_division(right_division(identity,X),Y)))
% -> right_division(identity,right_division(X,right_division(identity,Y)))
% Rule
% [204]
% right_division(X,right_division(X,right_division(right_division(identity,X),
% right_division(identity,Y)))) <->
% right_division(Y,X) collapsed.
% Rule
% [206]
% right_division(X,right_division(X,right_division(right_division(identity,X),Y)))
% <-> right_division(right_division(identity,Y),X) collapsed.
% Current number of equations to process: 1674
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [237]
% right_division(X,right_division(X,right_division(identity,Y))) <->
% right_division(identity,right_division(X,right_division(identity,right_division(Y,X))))
% Current number of equations to process: 1739
% Current number of ordered equations: 1
% Current number of rules: 98
% New rule produced :
% [238]
% right_division(identity,right_division(X,right_division(identity,right_division(Y,X))))
% <-> right_division(X,right_division(X,right_division(identity,Y)))
% Current number of equations to process: 1739
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [239]
% right_division(identity,right_division(right_division(identity,X),Y)) <->
% right_division(Y,right_division(Z,right_division(X,right_division(identity,Z))))
% Current number of equations to process: 2004
% Current number of ordered equations: 1
% Current number of rules: 100
% New rule produced :
% [240]
% right_division(Y,right_division(Z,right_division(X,right_division(identity,Z))))
% <-> right_division(identity,right_division(right_division(identity,X),Y))
% Current number of equations to process: 2004
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [241]
% right_division(identity,right_division(right_division(X,Y),Z)) <->
% right_division(Z,right_division(identity,right_division(Y,X)))
% Current number of equations to process: 2017
% Current number of ordered equations: 1
% Current number of rules: 102
% Rule [208]
% right_division(identity,right_division(X,right_division(right_division(Y,X),
% right_division(identity,Y))))
% <->
% right_division(right_division(identity,right_division(X,Y)),right_division(identity,
% right_division(Y,X))) is composed into 
% [208]
% right_division(identity,right_division(X,right_division(right_division(Y,X),
% right_division(identity,Y)))) <->
% right_division(identity,right_division(right_division(X,Y),right_division(identity,
% right_division(X,Y))))
% New rule produced :
% [242]
% right_division(Z,right_division(identity,right_division(Y,X))) <->
% right_division(identity,right_division(right_division(X,Y),Z))
% Rule
% [209]
% right_division(right_division(identity,right_division(X,Y)),right_division(identity,
% right_division(Y,X)))
% <->
% right_division(identity,right_division(X,right_division(right_division(Y,X),
% right_division(identity,Y))))
% collapsed.
% Current number of equations to process: 2018
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [243]
% right_division(identity,right_division(X,right_division(identity,right_division(Y,Z))))
% <-> right_division(right_division(Z,Y),X)
% Current number of equations to process: 2632
% Current number of ordered equations: 1
% Current number of rules: 103
% New rule produced :
% [244]
% right_division(right_division(Z,Y),X) <->
% right_division(identity,right_division(X,right_division(identity,right_division(Y,Z))))
% Current number of equations to process: 2632
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [245]
% right_division(X,right_division(right_division(Y,X),right_division(identity,Y)))
% <-> right_division(right_division(X,Y),right_division(Y,X))
% Current number of equations to process: 3022
% Current number of ordered equations: 1
% Current number of rules: 105
% New rule produced :
% [246]
% right_division(right_division(X,Y),right_division(Y,X)) <->
% right_division(X,right_division(right_division(Y,X),right_division(identity,Y)))
% Current number of equations to process: 3022
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [247]
% right_division(right_division(X,right_division(Y,X)),right_division(Y,
% right_division(Y,X))) ->
% right_division(X,Y)
% Current number of equations to process: 3186
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [248]
% right_division(right_division(identity,X),right_division(Y,right_division(X,
% right_division(identity,X))))
% -> right_division(X,Y)
% Rule
% [194]
% right_division(identity,right_division(right_division(identity,Y),right_division(X,
% right_division(Y,
% right_division(identity,Y)))))
% -> right_division(X,Y) collapsed.
% Current number of equations to process: 3290
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [249]
% right_division(X,right_division(right_division(identity,X),Y)) <->
% right_division(right_division(X,right_division(identity,Y)),right_division(identity,X))
% Current number of equations to process: 3330
% Current number of ordered equations: 1
% Current number of rules: 108
% New rule produced :
% [250]
% right_division(right_division(X,right_division(identity,Y)),right_division(identity,X))
% <-> right_division(X,right_division(right_division(identity,X),Y))
% Current number of equations to process: 3330
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [251]
% right_division(identity,right_division(X,right_division(identity,Y))) <->
% right_division(right_division(Z,right_division(Y,right_division(identity,Z))),X)
% Current number of equations to process: 3522
% Current number of ordered equations: 1
% Current number of rules: 110
% New rule produced :
% [252]
% right_division(right_division(Z,right_division(Y,right_division(identity,Z))),X)
% <-> right_division(identity,right_division(X,right_division(identity,Y)))
% Current number of equations to process: 3522
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [253]
% right_division(right_division(X,right_division(identity,Y)),right_division(identity,
% right_division(X,
% right_division(identity,
% right_division(X,
% right_division(identity,Y))))))
% ->
% right_division(X,right_division(identity,right_division(Y,right_division(identity,
% right_division(X,
% right_division(identity,
% right_division(X,
% right_division(identity,Y))))))))
% Current number of equations to process: 3820
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [254]
% right_division(right_division(identity,right_division(X,right_division(identity,
% right_division(Y,
% right_division(identity,X))))),
% right_division(identity,right_division(X,right_division(identity,right_division(Y,
% right_division(identity,
% right_division(X,
% right_division(identity,Z))))))))
% -> Z
% Current number of equations to process: 3957
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [255]
% right_division(Y,right_division(identity,right_division(Z,right_division(identity,
% right_division(Y,
% right_division(identity,
% right_division(
% right_division(identity,
% right_division(Y,
% right_division(identity,
% right_division(Z,
% right_division(identity,Y))))),
% right_division(identity,X))))))))
% -> X
% Current number of equations to process: 4159
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [256]
% right_division(right_division(X,right_division(identity,right_division(X,
% right_division(identity,
% right_division(Y,
% right_division(identity,X)))))),
% right_division(identity,Z)) ->
% right_division(X,right_division(identity,right_division(right_division(X,
% right_division(identity,Y)),
% right_division(identity,right_division(X,
% right_division(identity,Z))))))
% Current number of equations to process: 4337
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [257]
% right_division(right_division(identity,right_division(X,right_division(identity,
% right_division(X,
% right_division(identity,Y))))),
% right_division(identity,right_division(X,right_division(identity,right_division(X,
% right_division(identity,
% right_division(Y,
% right_division(identity,X))))))))
% -> X
% Current number of equations to process: 4539
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [258]
% right_division(identity,right_division(Y,right_division(X,right_division(identity,
% right_division(X,
% right_division(identity,Y))))))
% -> right_division(X,right_division(identity,X))
% Current number of equations to process: 4675
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [259]
% right_division(right_division(X,right_division(identity,right_division(X,
% right_division(identity,Y)))),
% right_division(identity,right_division(X,right_division(identity,X)))) ->
% right_division(X,right_division(identity,right_division(X,right_division(identity,
% right_division(Y,
% right_division(identity,
% right_division(X,
% right_division(identity,X))))))))
% Current number of equations to process: 4797
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [260]
% right_division(right_division(X,right_division(identity,right_division(Y,
% right_division(identity,
% right_division(Y,
% right_division(identity,X)))))),
% right_division(identity,Z)) ->
% right_division(X,right_division(identity,right_division(Y,right_division(identity,
% right_division(Y,
% right_division(identity,
% right_division(X,
% right_division(identity,Z))))))))
% Current number of equations to process: 4909
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [261]
% right_division(right_division(identity,right_division(X,right_division(identity,
% right_division(Y,
% right_division(identity,Y))))),
% right_division(identity,right_division(X,right_division(identity,right_division(Y,
% right_division(identity,
% right_division(Y,
% right_division(identity,X))))))))
% -> X
% Current number of equations to process: 1104
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [262]
% right_division(X,right_division(identity,right_division(X,right_division(identity,
% right_division(Y,
% right_division(X,
% right_division(identity,X)))))))
% <->
% right_division(identity,right_division(X,right_division(X,right_division(X,
% right_division(X,
% right_division(identity,Y))))))
% Current number of equations to process: 1211
% Current number of ordered equations: 1
% Current number of rules: 121
% New rule produced :
% [263]
% right_division(identity,right_division(X,right_division(X,right_division(X,
% right_division(X,
% right_division(identity,Y))))))
% <->
% right_division(X,right_division(identity,right_division(X,right_division(identity,
% right_division(Y,
% right_division(X,
% right_division(identity,X)))))))
% Current number of equations to process: 1211
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [264]
% right_division(right_division(X,right_division(X,Y)),right_division(identity,
% right_division(X,
% right_division(right_division(identity,X),
% right_division(identity,Y)))))
% -> right_division(X,right_division(identity,X))
% Current number of equations to process: 1487
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [265]
% right_division(identity,right_division(right_division(X,right_division(identity,Y)),
% right_division(X,right_division(X,right_division(X,
% right_division(identity,
% right_division(Y,
% right_division(identity,X))))))))
% -> X
% Current number of equations to process: 1639
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [266]
% right_division(right_division(identity,right_division(X,right_division(X,
% right_division(X,Y)))),
% right_division(identity,right_division(X,right_division(Y,X)))) -> X
% Current number of equations to process: 1796
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [267]
% right_division(right_division(identity,right_division(right_division(identity,Y),
% right_division(identity,X))),right_division(
% right_division(identity,
% right_division(
% right_division(identity,Y),
% right_division(identity,X))),
% right_division(
% right_division(identity,Y),
% right_division(identity,
% right_division(X,
% right_division(identity,Y))))))
% -> X
% Current number of equations to process: 1924
% Current number of ordered equations: 1
% Current number of rules: 126
% New rule produced :
% [268]
% right_division(right_division(identity,right_division(right_division(identity,X),
% right_division(identity,right_division(
% right_division(identity,X),
% right_division(identity,Y))))),
% right_division(identity,right_division(right_division(identity,X),right_division(identity,
% right_division(
% right_division(identity,X),
% right_division(identity,
% right_division(Y,
% right_division(identity,X))))))))
% -> X
% Current number of equations to process: 1924
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [269]
% right_division(right_division(X,Y),right_division(identity,right_division(Y,
% right_division(
% right_division(identity,Y),
% right_division(identity,
% right_division(
% right_division(identity,Y),
% right_division(identity,X)))))))
% -> right_division(Y,right_division(identity,Y))
% Current number of equations to process: 2363
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [270]
% right_division(right_division(identity,right_division(Y,right_division(X,Y))),
% right_division(identity,right_division(Y,right_division(identity,right_division(Y,
% right_division(
% right_division(identity,Y),
% right_division(identity,X)))))))
% -> Y
% Current number of equations to process: 2522
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [271]
% right_division(right_division(right_division(identity,X),right_division(identity,Y)),
% right_division(identity,right_division(X,right_division(right_division(identity,X),
% right_division(identity,right_division(
% right_division(identity,X),
% right_division(identity,
% right_division(Y,
% right_division(identity,X)))))))))
% -> X
% Current number of equations to process: 2689
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [272]
% right_division(X,right_division(identity,right_division(Y,right_division(identity,X))))
% <->
% right_division(X,right_division(X,right_division(Y,right_division(identity,
% right_division(X,right_division(identity,X))))))
% The conjecture has been reduced. 
% Conjecture is now:
% right_division(x,right_division(identity,right_division(y,right_division(identity,
% right_division(
% right_division(z,y),
% right_division(identity,
% right_division(y,
% right_division(z,
% right_division(x,
% right_division(identity,z)))))))))) = 
% right_division(x,right_division(identity,right_division(right_division(y,x),
% right_division(identity,right_division(x,
% right_division(z,
% right_division(z,
% right_division(z,
% right_division(x,
% right_division(identity,
% right_division(z,
% right_division(identity,z))))))))))))
% 
% Current number of equations to process: 2879
% Current number of ordered equations: 1
% Current number of rules: 131
% New rule produced :
% [273]
% right_division(X,right_division(X,right_division(Y,right_division(identity,
% right_division(X,right_division(identity,X))))))
% <->
% right_division(X,right_division(identity,right_division(Y,right_division(identity,X))))
% Current number of equations to process: 2879
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [274]
% right_division(X,right_division(identity,right_division(right_division(Y,X),
% right_division(identity,right_division(X,
% right_division(identity,X))))))
% ->
% right_division(X,right_division(identity,right_division(Y,right_division(identity,X))))
% Current number of equations to process: 3098
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [275]
% right_division(right_division(X,right_division(identity,Y)),right_division(identity,
% right_division(Y,
% right_division(identity,Y))))
% ->
% right_division(identity,right_division(right_division(identity,Y),right_division(X,
% right_division(identity,
% right_division(Y,
% right_division(identity,Y))))))
% Current number of equations to process: 3175
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [276]
% right_division(right_division(X,Y),right_division(identity,right_division(Y,
% right_division(identity,Y))))
% -> right_division(X,right_division(identity,Y))
% Rule
% [274]
% right_division(X,right_division(identity,right_division(right_division(Y,X),
% right_division(identity,right_division(X,
% right_division(identity,X))))))
% ->
% right_division(X,right_division(identity,right_division(Y,right_division(identity,X))))
% collapsed.
% Current number of equations to process: 3269
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [277]
% right_division(identity,right_division(Y,right_division(X,right_division(identity,
% right_division(Y,
% right_division(identity,Y))))))
% -> right_division(X,right_division(identity,Y))
% Rule
% [212]
% right_division(identity,right_division(Y,right_division(right_division(identity,X),
% right_division(identity,right_division(Y,
% right_division(identity,Y))))))
% -> right_division(right_division(identity,X),right_division(identity,Y))
% collapsed.
% Current number of equations to process: 3338
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [278]
% right_division(Y,right_division(right_division(identity,X),right_division(identity,
% right_division(Y,
% right_division(
% right_division(identity,Y),
% right_division(identity,X))))))
% ->
% right_division(X,right_division(identity,right_division(right_division(identity,Y),
% right_division(identity,X))))
% Current number of equations to process: 3468
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [279]
% right_division(right_division(X,right_division(identity,Y)),right_division(identity,
% right_division(X,
% right_division(identity,X))))
% ->
% right_division(X,right_division(identity,right_division(Y,right_division(identity,
% right_division(X,
% right_division(identity,X))))))
% Rule
% [259]
% right_division(right_division(X,right_division(identity,right_division(X,
% right_division(identity,Y)))),
% right_division(identity,right_division(X,right_division(identity,X)))) ->
% right_division(X,right_division(identity,right_division(X,right_division(identity,
% right_division(Y,
% right_division(identity,
% right_division(X,
% right_division(identity,X))))))))
% collapsed.
% Current number of equations to process: 3614
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [280]
% right_division(identity,right_division(right_division(identity,X),right_division(
% right_division(identity,X),
% right_division(
% right_division(identity,X),Y))))
% <->
% right_division(right_division(identity,X),right_division(identity,right_division(Y,
% right_division(identity,
% right_division(X,
% right_division(identity,X))))))
% Current number of equations to process: 3737
% Current number of ordered equations: 1
% Current number of rules: 136
% New rule produced :
% [281]
% right_division(right_division(identity,X),right_division(identity,right_division(Y,
% right_division(identity,
% right_division(X,
% right_division(identity,X))))))
% <->
% right_division(identity,right_division(right_division(identity,X),right_division(
% right_division(identity,X),
% right_division(
% right_division(identity,X),Y))))
% Current number of equations to process: 3737
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [282]
% right_division(identity,right_division(X,right_division(right_division(identity,X),
% right_division(identity,right_division(Y,
% right_division(identity,
% right_division(X,
% right_division(identity,X))))))))
% ->
% right_division(right_division(identity,X),right_division(identity,right_division(Y,
% right_division(identity,X))))
% Current number of equations to process: 4101
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [283]
% right_division(right_division(identity,X),right_division(identity,right_division(
% right_division(identity,X),
% right_division(
% right_division(identity,Y),
% right_division(X,
% right_division(identity,
% right_division(X,
% right_division(identity,Y))))))))
% -> right_division(Y,right_division(identity,Y))
% Current number of equations to process: 4245
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [284]
% right_division(right_division(identity,right_division(X,right_division(X,Y))),
% right_division(identity,right_division(X,right_division(identity,right_division(Y,
% right_division(identity,X))))))
% -> right_division(X,right_division(identity,X))
% Current number of equations to process: 4453
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [285]
% right_division(right_division(X,right_division(right_division(identity,X),
% right_division(identity,Y))),right_division(identity,
% right_division(
% right_division(identity,X),
% right_division(identity,
% right_division(Y,
% right_division(identity,X))))))
% -> right_division(X,right_division(identity,X))
% Current number of equations to process: 4617
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [286]
% right_division(right_division(identity,X),right_division(identity,right_division(Y,
% right_division(X,
% right_division(identity,X)))))
% ->
% right_division(identity,right_division(X,right_division(identity,right_division(X,
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))
% Current number of equations to process: 4790
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [287]
% right_division(identity,right_division(X,right_division(X,right_division(X,
% right_division(Y,
% right_division(identity,X))))))
% -> right_division(X,right_division(X,Y))
% Current number of equations to process: 4862
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [288]
% right_division(X,right_division(identity,right_division(Y,right_division(X,
% right_division(identity,X)))))
% <->
% right_division(identity,right_division(X,right_division(X,right_division(X,Y))))
% Current number of equations to process: 4981
% Current number of ordered equations: 1
% Current number of rules: 144
% New rule produced :
% [289]
% right_division(identity,right_division(X,right_division(X,right_division(X,Y))))
% <->
% right_division(X,right_division(identity,right_division(Y,right_division(X,
% right_division(identity,X)))))
% Current number of equations to process: 4981
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [290]
% right_division(identity,right_division(X,right_division(identity,right_division(X,
% right_division(
% right_division(identity,X),
% right_division(identity,
% right_division(Y,
% right_division(identity,X))))))))
% ->
% right_division(identity,right_division(X,right_division(right_division(identity,X),
% right_division(identity,Y))))
% Current number of equations to process: 1314
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [291]
% right_division(identity,right_division(Y,right_division(X,right_division(identity,
% right_division(X,
% right_division(identity,
% right_division(Y,
% right_division(identity,Y))))))))
% ->
% right_division(X,right_division(identity,right_division(X,right_division(identity,Y))))
% Current number of equations to process: 1516
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [292]
% right_division(right_division(identity,right_division(right_division(X,Y),
% right_division(identity,X))),right_division(identity,
% right_division(
% right_division(X,Y),
% right_division(identity,
% right_division(X,
% right_division(identity,Y))))))
% -> Y
% Current number of equations to process: 1668
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [293]
% right_division(right_division(right_division(identity,X),right_division(identity,Y)),
% right_division(X,right_division(right_division(identity,X),right_division(identity,Y))))
% ->
% right_division(identity,right_division(right_division(X,Y),right_division(identity,
% right_division(X,
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))
% Current number of equations to process: 1774
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [294]
% right_division(right_division(identity,right_division(X,right_division(identity,Y))),
% right_division(identity,right_division(X,right_division(identity,right_division(
% right_division(Y,X),
% right_division(identity,
% right_division(X,
% right_division(identity,Z))))))))
% -> Z
% Current number of equations to process: 1973
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [295]
% right_division(Y,right_division(identity,right_division(right_division(Z,Y),
% right_division(identity,right_division(Y,
% right_division(identity,
% right_division(
% right_division(identity,
% right_division(Y,
% right_division(identity,Z))),
% right_division(identity,X))))))))
% -> X
% Current number of equations to process: 2245
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [296]
% right_division(identity,right_division(right_division(identity,right_division(X,Y)),
% right_division(identity,right_division(X,right_division(Y,
% right_division(identity,Y))))))
% -> Y
% Current number of equations to process: 2488
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [297]
% right_division(right_division(identity,X),right_division(identity,right_division(
% right_division(X,
% right_division(identity,Y)),
% right_division(identity,X))))
% -> right_division(Y,right_division(identity,X))
% Current number of equations to process: 2689
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [298]
% right_division(right_division(identity,right_division(right_division(X,Y),
% right_division(Y,X))),right_division(identity,Z))
% ->
% right_division(right_division(identity,right_division(X,Y)),right_division(identity,
% right_division(
% right_division(identity,
% right_division(X,Y)),
% right_division(identity,Z))))
% Current number of equations to process: 2765
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [299]
% right_division(right_division(identity,right_division(X,right_division(identity,
% right_division(X,Y)))),
% right_division(identity,right_division(X,right_division(Y,X)))) -> identity
% Current number of equations to process: 2974
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [300]
% right_division(right_division(identity,right_division(X,right_division(Y,X))),
% right_division(identity,right_division(X,right_division(identity,right_division(X,Y)))))
% -> identity
% Current number of equations to process: 3099
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [301]
% right_division(right_division(X,Y),right_division(Z,right_division(X,Y))) <->
% right_division(right_division(right_division(X,Y),right_division(Y,X)),Z)
% Current number of equations to process: 3197
% Current number of ordered equations: 1
% Current number of rules: 157
% New rule produced :
% [302]
% right_division(right_division(right_division(X,Y),right_division(Y,X)),Z) <->
% right_division(right_division(X,Y),right_division(Z,right_division(X,Y)))
% Current number of equations to process: 3197
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [303]
% right_division(right_division(X,right_division(Y,X)),right_division(X,
% right_division(identity,
% right_division(X,Y))))
% -> identity
% Current number of equations to process: 3848
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [304]
% right_division(right_division(X,right_division(identity,right_division(X,Y))),
% right_division(X,right_division(Y,X))) -> identity
% Current number of equations to process: 3965
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [305]
% right_division(right_division(identity,right_division(X,Y)),right_division(identity,
% right_division(X,
% right_division(
% right_division(identity,X),
% right_division(identity,Y)))))
% -> X
% Current number of equations to process: 4050
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [306]
% right_division(identity,right_division(right_division(identity,Y),right_division(X,
% right_division(identity,
% right_division(X,Y)))))
% -> right_division(X,right_division(identity,X))
% Current number of equations to process: 4238
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [307]
% right_division(right_division(identity,right_division(right_division(identity,X),
% right_division(identity,right_division(Y,Z)))),
% right_division(identity,right_division(right_division(identity,X),right_division(identity,
% right_division(
% right_division(identity,
% right_division(Z,Y)),
% right_division(identity,X))))))
% -> X
% Current number of equations to process: 4479
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [308]
% right_division(X,right_division(identity,right_division(Y,right_division(identity,Y))))
% <->
% right_division(identity,right_division(right_division(identity,Y),right_division(X,
% right_division(identity,Y))))
% Rule
% [163]
% right_division(right_division(identity,right_division(X,Y)),right_division(identity,
% right_division(X,
% right_division(identity,X))))
% -> right_division(Y,right_division(identity,X)) collapsed.
% Rule
% [275]
% right_division(right_division(X,right_division(identity,Y)),right_division(identity,
% right_division(Y,
% right_division(identity,Y))))
% ->
% right_division(identity,right_division(right_division(identity,Y),right_division(X,
% right_division(identity,
% right_division(Y,
% right_division(identity,Y))))))
% collapsed.
% Current number of equations to process: 4698
% Current number of ordered equations: 1
% Current number of rules: 162
% New rule produced :
% [309]
% right_division(identity,right_division(right_division(identity,Y),right_division(X,
% right_division(identity,Y))))
% <->
% right_division(X,right_division(identity,right_division(Y,right_division(identity,Y))))
% Current number of equations to process: 4698
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [310]
% right_division(right_division(X,Y),right_division(identity,right_division(Y,
% right_division(identity,X))))
% -> right_division(X,right_division(identity,X))
% Rule
% [189]
% right_division(X,right_division(identity,right_division(right_division(Y,X),
% right_division(identity,right_division(X,
% right_division(identity,Y))))))
% ->
% right_division(X,right_division(identity,right_division(Y,right_division(identity,Y))))
% collapsed.
% Current number of equations to process: 1622
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [311]
% right_division(right_division(identity,right_division(right_division(X,Y),Z)),
% right_division(identity,right_division(right_division(identity,right_division(Y,X)),
% right_division(identity,Z)))) ->
% right_division(Z,right_division(identity,Z))
% Current number of equations to process: 1773
% Current number of ordered equations: 0
% Current number of rules: 164
% New rule produced :
% [312]
% right_division(X,right_division(right_division(identity,X),right_division(identity,
% right_division(Y,
% right_division(identity,Y)))))
% <->
% right_division(identity,right_division(right_division(identity,X),right_division(identity,
% right_division(Y,
% right_division(X,Y)))))
% Current number of equations to process: 2040
% Current number of ordered equations: 1
% Current number of rules: 165
% New rule produced :
% [313]
% right_division(identity,right_division(right_division(identity,X),right_division(identity,
% right_division(Y,
% right_division(X,Y)))))
% <->
% right_division(X,right_division(right_division(identity,X),right_division(identity,
% right_division(Y,
% right_division(identity,Y)))))
% Current number of equations to process: 2040
% Current number of ordered equations: 0
% Current number of rules: 166
% Rule [187]
% right_division(identity,right_division(Y,right_division(right_division(X,Y),
% right_division(identity,X))))
% <->
% right_division(X,right_division(identity,right_division(right_division(identity,Y),
% right_division(identity,
% right_division(X,Y))))) is composed into 
% [187]
% right_division(identity,right_division(Y,right_division(right_division(X,Y),
% right_division(identity,X)))) <->
% right_division(X,right_division(Y,right_division(right_division(identity,Y),
% right_division(identity,X))))
% New rule produced :
% [314]
% right_division(identity,right_division(right_division(identity,Y),right_division(identity,
% right_division(X,Y))))
% ->
% right_division(Y,right_division(right_division(identity,Y),right_division(identity,X)))
% Rule
% [186]
% right_division(X,right_division(identity,right_division(right_division(identity,Y),
% right_division(identity,right_division(X,Y)))))
% <->
% right_division(identity,right_division(Y,right_division(right_division(X,Y),
% right_division(identity,X))))
% collapsed.
% Current number of equations to process: 2458
% Current number of ordered equations: 1
% Current number of rules: 166
% New rule produced :
% [315]
% right_division(right_division(X,Y),right_division(identity,right_division(Y,
% right_division(X,Y))))
% -> right_division(X,right_division(X,Y))
% Rule
% [183]
% right_division(identity,right_division(X,right_division(identity,right_division(
% right_division(
% right_division(identity,X),
% right_division(identity,Y)),
% right_division(identity,
% right_division(
% right_division(identity,Y),
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))))
% -> right_division(right_division(identity,X),right_division(identity,Y))
% collapsed.
% Rule
% [198]
% right_division(X,right_division(right_division(right_division(identity,X),
% right_division(identity,Y)),right_division(identity,
% right_division(
% right_division(identity,Y),
% right_division(
% right_division(identity,X),
% right_division(identity,Y))))))
% -> right_division(Y,right_division(identity,X)) collapsed.
% Current number of equations to process: 2459
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [316]
% right_division(right_division(identity,X),right_division(right_division(identity,Y),
% right_division(identity,right_division(
% right_division(identity,Y),X))))
% -> right_division(Y,right_division(identity,Y))
% Current number of equations to process: 2881
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [317]
% right_division(identity,right_division(X,right_division(Y,right_division(Z,
% right_division(X,
% right_division(identity,Z))))))
% -> Y
% Current number of equations to process: 3037
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced :
% [318]
% right_division(X,right_division(right_division(identity,X),right_division(identity,Y)))
% <->
% right_division(identity,right_division(right_division(identity,X),right_division(X,Y)))
% Current number of equations to process: 3181
% Current number of ordered equations: 2
% Current number of rules: 168
% New rule produced :
% [319]
% right_division(identity,right_division(right_division(identity,X),right_division(X,Y)))
% <->
% right_division(X,right_division(right_division(identity,X),right_division(identity,Y)))
% Current number of equations to process: 3181
% Current number of ordered equations: 1
% Current number of rules: 169
% New rule produced :
% [320]
% right_division(right_division(identity,X),right_division(X,right_division(identity,Y)))
% ->
% right_division(identity,right_division(X,right_division(right_division(identity,X),Y)))
% Current number of equations to process: 3181
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced :
% [321]
% right_division(right_division(right_division(identity,right_division(X,Y)),Z),
% right_division(right_division(Y,X),Z)) -> identity
% Current number of equations to process: 3725
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [322]
% right_division(right_division(right_division(X,Y),Z),right_division(right_division(identity,
% right_division(Y,X)),Z))
% -> identity
% Current number of equations to process: 3927
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [323]
% right_division(identity,right_division(Y,right_division(Z,right_division(X,
% right_division(identity,Z)))))
% <-> right_division(right_division(identity,X),Y)
% Current number of equations to process: 4095
% Current number of ordered equations: 1
% Current number of rules: 173
% New rule produced :
% [324]
% right_division(right_division(identity,X),Y) <->
% right_division(identity,right_division(Y,right_division(Z,right_division(X,
% right_division(identity,Z)))))
% Current number of equations to process: 4095
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced :
% [325]
% right_division(identity,right_division(V_3,right_division(right_division(Y,X),Z)))
% <->
% right_division(right_division(right_division(identity,right_division(X,Y)),Z),V_3)
% Current number of equations to process: 4531
% Current number of ordered equations: 1
% Current number of rules: 175
% New rule produced :
% [326]
% right_division(right_division(right_division(identity,right_division(X,Y)),Z),V_3)
% <->
% right_division(identity,right_division(V_3,right_division(right_division(Y,X),Z)))
% Current number of equations to process: 4531
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced :
% [327]
% right_division(identity,right_division(X,right_division(Y,right_division(
% right_division(identity,X),Y))))
% -> right_division(Y,right_division(identity,Y))
% Current number of equations to process: 1710
% Current number of ordered equations: 0
% Current number of rules: 177
% New rule produced :
% [328]
% right_division(identity,right_division(right_division(identity,X),right_division(Y,
% right_division(X,Y))))
% <-> right_division(Y,right_division(identity,Y))
% Current number of equations to process: 1873
% Current number of ordered equations: 1
% Current number of rules: 178
% New rule produced :
% [329]
% right_division(Y,right_division(identity,Y)) <->
% right_division(identity,right_division(right_division(identity,X),right_division(Y,
% right_division(X,Y))))
% Current number of equations to process: 1873
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [330]
% right_division(X,right_division(X,Y)) <->
% right_division(identity,right_division(X,right_division(identity,right_division(
% right_division(identity,Y),X))))
% Current number of equations to process: 2273
% Current number of ordered equations: 1
% Current number of rules: 180
% New rule produced :
% [331]
% right_division(identity,right_division(X,right_division(identity,right_division(
% right_division(identity,Y),X))))
% <-> right_division(X,right_division(X,Y))
% Current number of equations to process: 2273
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [332]
% right_division(right_division(identity,right_division(X,right_division(X,Y))),
% right_division(right_division(identity,Y),X)) -> X
% Current number of equations to process: 2799
% Current number of ordered equations: 0
% Current number of rules: 182
% New rule produced :
% [333]
% right_division(identity,right_division(right_division(X,right_division(Y,Z)),V_3))
% <->
% right_division(V_3,right_division(X,right_division(identity,right_division(Z,Y))))
% Current number of equations to process: 2974
% Current number of ordered equations: 1
% Current number of rules: 183
% New rule produced :
% [334]
% right_division(V_3,right_division(X,right_division(identity,right_division(Z,Y))))
% <->
% right_division(identity,right_division(right_division(X,right_division(Y,Z)),V_3))
% Current number of equations to process: 2974
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [335]
% right_division(right_division(X,right_division(Y,Z)),right_division(X,
% right_division(identity,
% right_division(Z,Y))))
% -> identity
% Rule
% [303]
% right_division(right_division(X,right_division(Y,X)),right_division(X,
% right_division(identity,
% right_division(X,Y))))
% -> identity collapsed.
% Current number of equations to process: 4111
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [336]
% right_division(right_division(X,right_division(identity,right_division(Y,Z))),
% right_division(X,right_division(Z,Y))) -> identity
% Rule
% [304]
% right_division(right_division(X,right_division(identity,right_division(X,Y))),
% right_division(X,right_division(Y,X))) -> identity collapsed.
% Current number of equations to process: 4327
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [337]
% right_division(identity,right_division(right_division(X,Y),right_division(Y,X)))
% <->
% right_division(Y,right_division(right_division(X,Y),right_division(identity,X)))
% Current number of equations to process: 4488
% Current number of ordered equations: 1
% Current number of rules: 185
% New rule produced :
% [338]
% right_division(Y,right_division(right_division(X,Y),right_division(identity,X)))
% <->
% right_division(identity,right_division(right_division(X,Y),right_division(Y,X)))
% Current number of equations to process: 4488
% Current number of ordered equations: 0
% Current number of rules: 186
% New rule produced :
% [339]
% right_division(right_division(identity,right_division(X,Y)),right_division(
% right_division(identity,Y),X))
% -> right_division(Y,right_division(identity,Y))
% Current number of equations to process: 4810
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [340]
% right_division(X,right_division(X,right_division(identity,right_division(Y,
% right_division(identity,X)))))
% <-> right_division(right_division(identity,Y),X)
% Current number of equations to process: 4951
% Current number of ordered equations: 1
% Current number of rules: 188
% New rule produced :
% [341]
% right_division(right_division(identity,Y),X) <->
% right_division(X,right_division(X,right_division(identity,right_division(Y,
% right_division(identity,X)))))
% Current number of equations to process: 4951
% Current number of ordered equations: 0
% Current number of rules: 189
% New rule produced :
% [342]
% right_divisCputime limit exceeded (core dumped)
% 
% EOF
%------------------------------------------------------------------------------