%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP187-1 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n078.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 00:22:36 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP187-1 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n078.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 07:04:33 CDT 2014
% % CPUTime  : 300.10 
% Processing problem /tmp/CiME_47052_n078.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " least_upper_bound,greatest_lower_bound : AC; b,a,identity : constant;  inverse : 1;  multiply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z));
% multiply(identity,X) = X;
% multiply(inverse(X),X) = identity;
% X least_upper_bound X = X;
% X greatest_lower_bound X = X;
% X least_upper_bound (X greatest_lower_bound Y) = X;
% X greatest_lower_bound (X least_upper_bound Y) = X;
% multiply(X,Y least_upper_bound Z) = multiply(X,Y) least_upper_bound multiply(X,Z);
% multiply(X,Y greatest_lower_bound Z) = multiply(X,Y) greatest_lower_bound multiply(X,Z);
% multiply(Y least_upper_bound Z,X) = multiply(Y,X) least_upper_bound multiply(Z,X);
% multiply(Y greatest_lower_bound Z,X) = multiply(Y,X) greatest_lower_bound multiply(Z,X);
% (a least_upper_bound inverse(a)) greatest_lower_bound (b least_upper_bound inverse(b)) = identity;
% ";
% 
% let s1 = status F "
% b lr_lex;
% a lr_lex;
% inverse lr_lex;
% identity lr_lex;
% least_upper_bound mul;
% greatest_lower_bound mul;
% multiply mul;
% ";
% 
% let p1 = precedence F "
% multiply > inverse > greatest_lower_bound > least_upper_bound > identity > a > b";
% 
% let s2 = status F "
% b mul;
% a mul;
% least_upper_bound mul;
% greatest_lower_bound mul;
% inverse mul;
% multiply mul;
% identity mul;
% ";
% 
% let p2 = precedence F "
% multiply > inverse > greatest_lower_bound > least_upper_bound > identity = a = b";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " multiply(a,b) = multiply(b,a);"
% ;
% (*
% 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(multiply(X,Y),Z) =
% multiply(X,multiply(Y,Z)),
% multiply(identity,X) = X,
% multiply(inverse(X),X) = identity,
% X least_upper_bound X = X,
% X greatest_lower_bound X = X,
% (X greatest_lower_bound Y) least_upper_bound X =
% X,
% (X least_upper_bound Y) greatest_lower_bound X =
% X,
% multiply(X,Y least_upper_bound Z) =
% multiply(X,Y) least_upper_bound multiply(X,Z),
% multiply(X,Y greatest_lower_bound Z) =
% multiply(X,Y) greatest_lower_bound multiply(X,Z),
% multiply(Y least_upper_bound Z,X) =
% multiply(Y,X) least_upper_bound multiply(Z,X),
% multiply(Y greatest_lower_bound Z,X) =
% multiply(Y,X) greatest_lower_bound multiply(Z,X),
% (b least_upper_bound inverse(b)) greatest_lower_bound 
% (a least_upper_bound inverse(a)) = identity }
% (12 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { multiply(a,b) = multiply(b,a) }
% (1 equation(s))
% time is now on
% 
% Initializing completion ...
% New rule produced : [1] X least_upper_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 1
% New rule produced : [2] X greatest_lower_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 2
% New rule produced : [3] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 3
% New rule produced : [4] multiply(inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 4
% New rule produced : [5] (X greatest_lower_bound Y) least_upper_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 5
% New rule produced : [6] (X least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 6
% New rule produced :
% [7] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 7
% New rule produced :
% [8]
% (b least_upper_bound inverse(b)) greatest_lower_bound (a least_upper_bound 
% inverse(a)) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 8
% New rule produced :
% [9]
% multiply(X,Y least_upper_bound Z) ->
% multiply(X,Y) least_upper_bound multiply(X,Z)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 9
% New rule produced :
% [10]
% multiply(X,Y greatest_lower_bound Z) ->
% multiply(X,Y) greatest_lower_bound multiply(X,Z)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 10
% New rule produced :
% [11]
% multiply(Y least_upper_bound Z,X) ->
% multiply(Y,X) least_upper_bound multiply(Z,X)
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 11
% New rule produced :
% [12]
% multiply(Y greatest_lower_bound Z,X) ->
% multiply(Y,X) greatest_lower_bound multiply(Z,X)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14]
% (a least_upper_bound inverse(a)) greatest_lower_bound identity -> identity
% Current number of equations to process: 48
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [15]
% (b least_upper_bound inverse(b)) greatest_lower_bound identity -> identity
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16]
% (a least_upper_bound inverse(a)) greatest_lower_bound b ->
% b greatest_lower_bound identity
% Current number of equations to process: 78
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [17]
% (b least_upper_bound inverse(b)) greatest_lower_bound a ->
% a greatest_lower_bound identity
% Current number of equations to process: 78
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18]
% a least_upper_bound identity least_upper_bound inverse(a) ->
% a least_upper_bound inverse(a)
% Current number of equations to process: 76
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced :
% [19]
% b least_upper_bound identity least_upper_bound inverse(b) ->
% b least_upper_bound inverse(b)
% Current number of equations to process: 76
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20]
% (b least_upper_bound inverse(b) least_upper_bound X) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 74
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [21]
% (a least_upper_bound inverse(a) least_upper_bound X) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22]
% (a least_upper_bound inverse(a)) greatest_lower_bound inverse(b) ->
% identity greatest_lower_bound inverse(b)
% Current number of equations to process: 72
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [23]
% (b least_upper_bound inverse(b)) greatest_lower_bound inverse(a) ->
% identity greatest_lower_bound inverse(a)
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [24] multiply(inverse(identity),X) -> X
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [25] multiply(inverse(inverse(X)),identity) -> X
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [26] multiply(inverse(inverse(X)),Y) -> multiply(X,Y)
% Rule [25] multiply(inverse(inverse(X)),identity) -> X collapsed.
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [27] multiply(X,identity) -> X
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [28]
% b greatest_lower_bound a greatest_lower_bound identity ->
% b greatest_lower_bound a
% Current number of equations to process: 122
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [29]
% b greatest_lower_bound identity greatest_lower_bound inverse(a) ->
% b greatest_lower_bound inverse(a)
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [30]
% a greatest_lower_bound identity greatest_lower_bound inverse(b) ->
% a greatest_lower_bound inverse(b)
% Current number of equations to process: 138
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [31] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 282
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [32] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 282
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [33] inverse(identity) -> identity
% Rule [24] multiply(inverse(identity),X) -> X collapsed.
% Current number of equations to process: 282
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [34] inverse(inverse(X)) -> X
% Rule [26] multiply(inverse(inverse(X)),Y) -> multiply(X,Y) collapsed.
% Current number of equations to process: 282
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [35] (b greatest_lower_bound a) least_upper_bound identity -> identity
% Current number of equations to process: 305
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [36]
% (b greatest_lower_bound a greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 316
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [37]
% (b greatest_lower_bound inverse(a)) least_upper_bound identity -> identity
% Current number of equations to process: 345
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [38]
% (b greatest_lower_bound a) least_upper_bound (a greatest_lower_bound identity)
% -> a greatest_lower_bound identity
% Current number of equations to process: 354
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [39]
% (b greatest_lower_bound a) least_upper_bound (b greatest_lower_bound identity)
% -> b greatest_lower_bound identity
% Current number of equations to process: 354
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [40]
% (identity least_upper_bound X) greatest_lower_bound b greatest_lower_bound a
% -> b greatest_lower_bound a
% Current number of equations to process: 353
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [41]
% (b greatest_lower_bound inverse(a) greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 352
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [42]
% (a greatest_lower_bound inverse(b)) least_upper_bound identity -> identity
% Current number of equations to process: 381
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [43]
% (a greatest_lower_bound inverse(b) greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 392
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [44] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% Current number of equations to process: 441
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [45] multiply(Y,inverse(multiply(X,Y))) -> inverse(X)
% Rule [44] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% collapsed.
% Current number of equations to process: 555
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [46] multiply(inverse(multiply(X,Y)),X) -> inverse(Y)
% Current number of equations to process: 555
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [47] inverse(multiply(Y,X)) -> multiply(inverse(X),inverse(Y))
% Rule [45] multiply(Y,inverse(multiply(X,Y))) -> inverse(X) collapsed.
% Rule [46] multiply(inverse(multiply(X,Y)),X) -> inverse(Y) collapsed.
% Current number of equations to process: 562
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [48]
% (a least_upper_bound identity) greatest_lower_bound (a least_upper_bound 
% inverse(a)) ->
% a least_upper_bound identity
% Current number of equations to process: 562
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [49]
% (b least_upper_bound inverse(b)) greatest_lower_bound (a least_upper_bound identity)
% -> identity
% Current number of equations to process: 573
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [50]
% (a least_upper_bound identity) greatest_lower_bound b ->
% b greatest_lower_bound identity
% Current number of equations to process: 580
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [51]
% (a least_upper_bound identity) greatest_lower_bound inverse(b) ->
% identity greatest_lower_bound inverse(b)
% Current number of equations to process: 581
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [52]
% (b least_upper_bound identity) greatest_lower_bound (b least_upper_bound 
% inverse(b)) ->
% b least_upper_bound identity
% Current number of equations to process: 624
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [53]
% (b least_upper_bound identity) greatest_lower_bound inverse(a) ->
% identity greatest_lower_bound inverse(a)
% Current number of equations to process: 625
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [54]
% (b least_upper_bound identity) greatest_lower_bound (a least_upper_bound 
% inverse(a)) -> identity
% Current number of equations to process: 636
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [55]
% (b least_upper_bound identity) greatest_lower_bound a ->
% a greatest_lower_bound identity
% Current number of equations to process: 643
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [56]
% (b least_upper_bound identity) greatest_lower_bound (a least_upper_bound identity)
% -> identity
% Current number of equations to process: 644
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [57]
% identity greatest_lower_bound inverse(b) greatest_lower_bound inverse(a) ->
% inverse(b) greatest_lower_bound inverse(a)
% Current number of equations to process: 704
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [58]
% (inverse(b) greatest_lower_bound inverse(a)) least_upper_bound identity ->
% identity
% Current number of equations to process: 739
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [59]
% (b greatest_lower_bound identity) least_upper_bound (b greatest_lower_bound 
% inverse(a)) ->
% b greatest_lower_bound identity
% Current number of equations to process: 757
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [60]
% (a greatest_lower_bound identity) least_upper_bound (a greatest_lower_bound 
% inverse(b)) ->
% a greatest_lower_bound identity
% Current number of equations to process: 771
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [61]
% (multiply(X,b) greatest_lower_bound multiply(X,a)) least_upper_bound X -> X
% Current number of equations to process: 786
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [62]
% (multiply(b,X) greatest_lower_bound multiply(a,X)) least_upper_bound X -> X
% Current number of equations to process: 812
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [63]
% (inverse(b) greatest_lower_bound inverse(a) greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 836
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [64]
% (identity greatest_lower_bound X) least_upper_bound a least_upper_bound 
% inverse(a) -> a least_upper_bound inverse(a)
% Current number of equations to process: 848
% Current number of ordered equations: 1
% Current number of rules: 58
% New rule produced :
% [65]
% (identity greatest_lower_bound X) least_upper_bound b least_upper_bound 
% inverse(b) -> b least_upper_bound inverse(b)
% Current number of equations to process: 848
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [66]
% (identity least_upper_bound X) greatest_lower_bound b greatest_lower_bound 
% inverse(a) -> b greatest_lower_bound inverse(a)
% Current number of equations to process: 913
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [67]
% (identity least_upper_bound X) greatest_lower_bound a greatest_lower_bound 
% inverse(b) -> a greatest_lower_bound inverse(b)
% Current number of equations to process: 948
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [68]
% (identity greatest_lower_bound multiply(inverse(b),a)) least_upper_bound 
% inverse(b) -> inverse(b)
% Current number of equations to process: 976
% Current number of ordered equations: 1
% Current number of rules: 62
% New rule produced :
% [69]
% (identity greatest_lower_bound multiply(inverse(a),b)) least_upper_bound 
% inverse(a) -> inverse(a)
% Current number of equations to process: 976
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [70]
% (identity greatest_lower_bound multiply(a,inverse(b))) least_upper_bound 
% inverse(b) -> inverse(b)
% Current number of equations to process: 1010
% Current number of ordered equations: 1
% Current number of rules: 64
% New rule produced :
% [71]
% (identity greatest_lower_bound multiply(b,inverse(a))) least_upper_bound 
% inverse(a) -> inverse(a)
% Current number of equations to process: 1010
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [72]
% (multiply(X,a) least_upper_bound multiply(X,inverse(a))) greatest_lower_bound X
% -> X
% Current number of equations to process: 1042
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [73] (identity least_upper_bound multiply(a,a)) greatest_lower_bound a -> a
% Current number of equations to process: 1068
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [74]
% a least_upper_bound identity least_upper_bound multiply(a,a) ->
% identity least_upper_bound multiply(a,a)
% Current number of equations to process: 1085
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [75]
% (identity least_upper_bound multiply(a,a) least_upper_bound X) greatest_lower_bound a
% -> a
% Current number of equations to process: 1126
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [76]
% (multiply(a,X) least_upper_bound multiply(inverse(a),X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 1143
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [77]
% (multiply(X,b) least_upper_bound multiply(X,inverse(b))) greatest_lower_bound X
% -> X
% Current number of equations to process: 1166
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [78] (identity least_upper_bound multiply(b,b)) greatest_lower_bound b -> b
% Current number of equations to process: 1192
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [79]
% b least_upper_bound identity least_upper_bound multiply(b,b) ->
% identity least_upper_bound multiply(b,b)
% Current number of equations to process: 1209
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [80]
% (identity least_upper_bound multiply(b,b) least_upper_bound X) greatest_lower_bound b
% -> b
% Current number of equations to process: 1250
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [81]
% (multiply(b,X) least_upper_bound multiply(inverse(b),X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 1267
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [82]
% (b greatest_lower_bound a greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X)
% -> identity greatest_lower_bound X
% Current number of equations to process: 1287
% Current number of ordered equations: 2
% Current number of rules: 76
% New rule produced :
% [83]
% (b greatest_lower_bound a greatest_lower_bound X) least_upper_bound (a greatest_lower_bound identity)
% -> a greatest_lower_bound identity
% Current number of equations to process: 1287
% Current number of ordered equations: 1
% Current number of rules: 77
% New rule produced :
% [84]
% (b greatest_lower_bound a greatest_lower_bound X) least_upper_bound (b greatest_lower_bound identity)
% -> b greatest_lower_bound identity
% Current number of equations to process: 1287
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [85]
% ((b greatest_lower_bound identity) least_upper_bound X) greatest_lower_bound b greatest_lower_bound a
% -> b greatest_lower_bound a
% Current number of equations to process: 1387
% Current number of ordered equations: 1
% Current number of rules: 79
% New rule produced :
% [86]
% ((a greatest_lower_bound identity) least_upper_bound X) greatest_lower_bound b greatest_lower_bound a
% -> b greatest_lower_bound a
% Current number of equations to process: 1387
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [87]
% (multiply(X,b) greatest_lower_bound multiply(X,inverse(a))) least_upper_bound X
% -> X
% Current number of equations to process: 1465
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [88] (identity greatest_lower_bound multiply(a,b)) least_upper_bound a -> a
% Current number of equations to process: 1491
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [89]
% (identity greatest_lower_bound multiply(a,b) greatest_lower_bound X) least_upper_bound a
% -> a
% Current number of equations to process: 1508
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [90]
% a greatest_lower_bound identity greatest_lower_bound multiply(a,b) ->
% identity greatest_lower_bound multiply(a,b)
% Current number of equations to process: 1530
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [91]
% (multiply(b,X) greatest_lower_bound multiply(inverse(a),X)) least_upper_bound X
% -> X
% Current number of equations to process: 1583
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [92] (identity greatest_lower_bound multiply(b,a)) least_upper_bound a -> a
% Current number of equations to process: 1584
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [93]
% (identity greatest_lower_bound multiply(b,a) greatest_lower_bound X) least_upper_bound a
% -> a
% Current number of equations to process: 1626
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [94]
% a greatest_lower_bound identity greatest_lower_bound multiply(b,a) ->
% identity greatest_lower_bound multiply(b,a)
% Current number of equations to process: 1648
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [95]
% (multiply(X,a) greatest_lower_bound multiply(X,inverse(b))) least_upper_bound X
% -> X
% Current number of equations to process: 1697
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [96] (identity greatest_lower_bound multiply(b,a)) least_upper_bound b -> b
% Current number of equations to process: 1723
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [97]
% (identity greatest_lower_bound multiply(b,a) greatest_lower_bound X) least_upper_bound b
% -> b
% Current number of equations to process: 1740
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [98]
% b greatest_lower_bound identity greatest_lower_bound multiply(b,a) ->
% identity greatest_lower_bound multiply(b,a)
% Current number of equations to process: 1762
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [99]
% b greatest_lower_bound a greatest_lower_bound multiply(b,a) ->
% identity greatest_lower_bound multiply(b,a)
% Current number of equations to process: 1807
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [100]
% (multiply(a,X) greatest_lower_bound multiply(inverse(b),X)) least_upper_bound X
% -> X
% Current number of equations to process: 1891
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [101] (identity greatest_lower_bound multiply(a,b)) least_upper_bound b -> b
% Current number of equations to process: 1892
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [102]
% (identity greatest_lower_bound multiply(a,b) greatest_lower_bound X) least_upper_bound b
% -> b
% Current number of equations to process: 1934
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [103]
% b greatest_lower_bound identity greatest_lower_bound multiply(a,b) ->
% identity greatest_lower_bound multiply(a,b)
% Current number of equations to process: 1956
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [104]
% b greatest_lower_bound a greatest_lower_bound multiply(a,b) ->
% identity greatest_lower_bound multiply(a,b)
% Current number of equations to process: 2001
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [105]
% (a least_upper_bound identity) greatest_lower_bound (identity least_upper_bound 
% multiply(a,a)) ->
% a least_upper_bound identity
% Current number of equations to process: 2081
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [106]
% (b least_upper_bound inverse(b) least_upper_bound multiply(a,a)) greatest_lower_bound a
% -> a
% Current number of equations to process: 2096
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [107]
% (b least_upper_bound identity) greatest_lower_bound (identity least_upper_bound 
% multiply(b,b)) ->
% b least_upper_bound identity
% Current number of equations to process: 2112
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [108]
% (a least_upper_bound inverse(a) least_upper_bound multiply(b,b)) greatest_lower_bound b
% -> b
% Current number of equations to process: 2127
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [109]
% (b greatest_lower_bound inverse(a) greatest_lower_bound multiply(a,b)) least_upper_bound a
% -> a
% Current number of equations to process: 2143
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [110]
% (a greatest_lower_bound identity) least_upper_bound (identity greatest_lower_bound 
% multiply(a,b)) ->
% a greatest_lower_bound identity
% Current number of equations to process: 2158
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [111]
% (b greatest_lower_bound inverse(a) greatest_lower_bound multiply(b,a)) least_upper_bound a
% -> a
% Current number of equations to process: 2171
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [112]
% (a greatest_lower_bound identity) least_upper_bound (identity greatest_lower_bound 
% multiply(b,a)) ->
% a greatest_lower_bound identity
% Current number of equations to process: 2188
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [113]
% (a greatest_lower_bound inverse(b) greatest_lower_bound multiply(b,a)) least_upper_bound b
% -> b
% Current number of equations to process: 2201
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [114]
% (b greatest_lower_bound identity) least_upper_bound (identity greatest_lower_bound 
% multiply(b,a)) ->
% b greatest_lower_bound identity
% Current number of equations to process: 2218
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [115]
% (b greatest_lower_bound a) least_upper_bound (identity greatest_lower_bound 
% multiply(b,a)) ->
% b greatest_lower_bound a
% Current number of equations to process: 2231
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [116]
% (a greatest_lower_bound inverse(b) greatest_lower_bound multiply(a,b)) least_upper_bound b
% -> b
% Current number of equations to process: 2243
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [117]
% (b greatest_lower_bound identity) least_upper_bound (identity greatest_lower_bound 
% multiply(a,b)) ->
% b greatest_lower_bound identity
% Current number of equations to process: 2260
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [118]
% (b greatest_lower_bound a) least_upper_bound (identity greatest_lower_bound 
% multiply(a,b)) ->
% b greatest_lower_bound a
% Current number of equations to process: 2273
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [119]
% (a least_upper_bound inverse(a)) greatest_lower_bound (identity least_upper_bound 
% inverse(a)) ->
% identity least_upper_bound inverse(a)
% Current number of equations to process: 2282
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [120]
% (b least_upper_bound inverse(b)) greatest_lower_bound (identity least_upper_bound 
% inverse(a)) -> identity
% Current number of equations to process: 2293
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [121]
% (identity least_upper_bound inverse(a)) greatest_lower_bound b ->
% b greatest_lower_bound identity
% Current number of equations to process: 2300
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [122]
% (identity least_upper_bound inverse(a)) greatest_lower_bound inverse(b) ->
% identity greatest_lower_bound inverse(b)
% Current number of equations to process: 2301
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [123]
% (b least_upper_bound identity) greatest_lower_bound (identity least_upper_bound 
% inverse(a)) -> identity
% Current number of equations to process: 2302
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [124]
% (b least_upper_bound inverse(b)) greatest_lower_bound (identity least_upper_bound 
% inverse(b)) ->
% identity least_upper_bound inverse(b)
% Current number of equations to process: 2359
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [125]
% (identity least_upper_bound inverse(b)) greatest_lower_bound inverse(a) ->
% identity greatest_lower_bound inverse(a)
% Current number of equations to process: 2360
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [126]
% (a least_upper_bound inverse(a)) greatest_lower_bound (identity least_upper_bound 
% inverse(b)) -> identity
% Current number of equations to process: 2371
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [127]
% (identity least_upper_bound inverse(b)) greatest_lower_bound a ->
% a greatest_lower_bound identity
% Current number of equations to process: 2378
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [128]
% (a least_upper_bound identity) greatest_lower_bound (identity least_upper_bound 
% inverse(b)) -> identity
% Current number of equations to process: 2379
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [129]
% (identity least_upper_bound inverse(b)) greatest_lower_bound (identity least_upper_bound 
% inverse(a)) ->
% identity
% Current number of equations to process: 2379
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [130]
% (b greatest_lower_bound inverse(a)) least_upper_bound (identity greatest_lower_bound 
% inverse(a)) ->
% identity greatest_lower_bound inverse(a)
% Current number of equations to process: 2448
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [131]
% (a greatest_lower_bound inverse(b)) least_upper_bound (identity greatest_lower_bound 
% inverse(b)) ->
% identity greatest_lower_bound inverse(b)
% Current number of equations to process: 2463
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [132]
% (identity least_upper_bound multiply(inverse(a),inverse(a))) greatest_lower_bound 
% inverse(a) -> inverse(a)
% Current number of equations to process: 2475
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [133]
% (identity least_upper_bound multiply(inverse(b),inverse(b))) greatest_lower_bound 
% inverse(b) -> inverse(b)
% Current number of equations to process: 2492
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [134]
% (identity greatest_lower_bound multiply(inverse(b),inverse(a))) least_upper_bound 
% inverse(b) -> inverse(b)
% Current number of equations to process: 2509
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [135]
% (identity greatest_lower_bound multiply(inverse(a),inverse(b))) least_upper_bound 
% inverse(b) -> inverse(b)
% Current number of equations to process: 2528
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [136]
% (identity greatest_lower_bound multiply(inverse(a),inverse(b))) least_upper_bound 
% inverse(a) -> inverse(a)
% Current number of equations to process: 2547
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [137]
% (identity greatest_lower_bound multiply(inverse(b),inverse(a))) least_upper_bound 
% inverse(a) -> inverse(a)
% Current number of equations to process: 2566
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [138]
% ((X least_upper_bound Y) greatest_lower_bound Z) least_upper_bound (X greatest_lower_bound Z)
% -> (X least_upper_bound Y) greatest_lower_bound Z
% Current number of equations to process: 2584
% Current number of ordered equations: 1
% Current number of rules: 132
% New rule produced :
% [139]
% ((X greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound 
% (X least_upper_bound Z) -> (X greatest_lower_bound Y) least_upper_bound Z
% Current number of equations to process: 2614
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [140]
% ((a greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound b
% -> b greatest_lower_bound identity
% Current number of equations to process: 3179
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [141]
% ((a greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% inverse(b) -> identity greatest_lower_bound inverse(b)
% Current number of equations to process: 3190
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [142]
% ((b greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound a
% -> a greatest_lower_bound identity
% Current number of equations to process: 3247
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [143]
% ((b greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% (a least_upper_bound identity) -> identity
% Current number of equations to process: 3265
% Current number of ordered equations: 1
% Current number of rules: 137
% New rule produced :
% [144]
% ((a greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% (b least_upper_bound identity) -> identity
% Current number of equations to process: 3265
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [145]
% ((b greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% inverse(a) -> identity greatest_lower_bound inverse(a)
% Current number of equations to process: 3264
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [146]
% ((a greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% (b least_upper_bound inverse(b)) -> identity
% Current number of equations to process: 3375
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [147]
% ((b greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% (a least_upper_bound inverse(a)) -> identity
% Current number of equations to process: 3374
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [148]
% ((inverse(a) greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound b
% -> b greatest_lower_bound identity
% Current number of equations to process: 4388
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [149]
% ((b greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% (identity least_upper_bound inverse(a)) -> identity
% Current number of equations to process: 4418
% Current number of ordered equations: 1
% Current number of rules: 143
% New rule produced :
% [150]
% ((inverse(a) greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% (b least_upper_bound identity) -> identity
% Current number of equations to process: 4418
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [151]
% ((inverse(a) greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% inverse(b) -> identity greatest_lower_bound inverse(b)
% Current number of equations to process: 4417
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [152]
% ((inverse(b) greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound a
% -> a greatest_lower_bound identity
% Current number of equations to process: 4474
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [153]
% ((a greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% (identity least_upper_bound inverse(b)) -> identity
% Current number of equations to process: 4509
% Current number of ordered equations: 1
% Current number of rules: 147
% New rule produced :
% [154]
% ((inverse(b) greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% (a least_upper_bound identity) -> identity
% Current number of equations to process: 4509
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [155]
% ((inverse(b) greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% inverse(a) -> identity greatest_lower_bound inverse(a)
% Current number of equations to process: 4508
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [156]
% (a least_upper_bound inverse(a) least_upper_bound X) greatest_lower_bound 
% (identity least_upper_bound X) -> identity least_upper_bound X
% Current number of equations to process: 3093
% Current number of ordered equations: 1
% Current number of rules: 150
% New rule produced :
% [157]
% (a least_upper_bound identity) greatest_lower_bound (a least_upper_bound 
% inverse(a) least_upper_bound X)
% -> a least_upper_bound identity
% Current number of equations to process: 3093
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [158]
% (b least_upper_bound inverse(b) least_upper_bound X) greatest_lower_bound 
% (identity least_upper_bound X) -> identity least_upper_bound X
% Current number of equations to process: 3248
% Current number of ordered equations: 1
% Current number of rules: 152
% New rule produced :
% [159]
% (b least_upper_bound identity) greatest_lower_bound (b least_upper_bound 
% inverse(b) least_upper_bound X)
% -> b least_upper_bound identity
% Current number of equations to process: 3248
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [160]
% (b greatest_lower_bound identity) least_upper_bound (b greatest_lower_bound 
% inverse(a) greatest_lower_bound X)
% -> b greatest_lower_bound identity
% Current number of equations to process: 3398
% Current number of ordered equations: 1
% Current number of rules: 154
% New rule produced :
% [161]
% (b greatest_lower_bound inverse(a) greatest_lower_bound X) least_upper_bound 
% (identity greatest_lower_bound X) -> identity greatest_lower_bound X
% Current number of equations to process: 3398
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [162]
% (a greatest_lower_bound identity) least_upper_bound (a greatest_lower_bound 
% inverse(b) greatest_lower_bound X)
% -> a greatest_lower_bound identity
% Current number of equations to process: 3562
% Current number of ordered equations: 1
% Current number of rules: 156
% New rule produced :
% [163]
% (a greatest_lower_bound inverse(b) greatest_lower_bound X) least_upper_bound 
% (identity greatest_lower_bound X) -> identity greatest_lower_bound X
% Current number of equations to process: 3562
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [164]
% ((b greatest_lower_bound a) least_upper_bound X) greatest_lower_bound 
% (identity least_upper_bound X) ->
% (b greatest_lower_bound a) least_upper_bound X
% Current number of equations to process: 3732
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [165]
% ((identity least_upper_bound X) greatest_lower_bound b) least_upper_bound 
% (b greatest_lower_bound a) ->
% (identity least_upper_bound X) greatest_lower_bound b
% Current number of equations to process: 3880
% Current number of ordered equations: 1
% Current number of rules: 159
% New rule produced :
% [166]
% ((identity least_upper_bound X) greatest_lower_bound a) least_upper_bound 
% (b greatest_lower_bound a) ->
% (identity least_upper_bound X) greatest_lower_bound a
% Current number of equations to process: 3880
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [167]
% inverse(multiply(X,Y) least_upper_bound multiply(X,Z)) ->
% multiply(inverse(Y least_upper_bound Z),inverse(X))
% Current number of equations to process: 3971
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [168]
% inverse(identity least_upper_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X least_upper_bound Y),X)
% Current number of equations to process: 3972
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [169]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(inverse(identity least_upper_bound Y),inverse(X))
% Current number of equations to process: 3981
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [170]
% inverse(identity least_upper_bound multiply(X,Y)) <->
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X))
% Current number of equations to process: 3980
% Current number of ordered equations: 1
% Current number of rules: 164
% New rule produced :
% [171]
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X)) <->
% inverse(identity least_upper_bound multiply(X,Y))
% Current number of equations to process: 3980
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [172]
% inverse(identity least_upper_bound inverse(X)) ->
% multiply(inverse(identity least_upper_bound X),X)
% Current number of equations to process: 3983
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [173]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(inverse(identity least_upper_bound multiply(X,Y)),X)
% Rule
% [172]
% inverse(identity least_upper_bound inverse(X)) ->
% multiply(inverse(identity least_upper_bound X),X) collapsed.
% Current number of equations to process: 3994
% Current number of ordered equations: 1
% Current number of rules: 166
% New rule produced :
% [174]
% multiply(inverse(identity least_upper_bound multiply(X,Y)),X) <->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 3994
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced :
% [175]
% inverse(multiply(X,Y) greatest_lower_bound multiply(X,Z)) ->
% multiply(inverse(Y greatest_lower_bound Z),inverse(X))
% Current number of equations to process: 4102
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced :
% [176]
% inverse(identity greatest_lower_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X greatest_lower_bound Y),X)
% Current number of equations to process: 4105
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced :
% [177]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(inverse(identity greatest_lower_bound Y),inverse(X))
% Current number of equations to process: 4114
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced :
% [178]
% inverse(identity greatest_lower_bound multiply(X,Y)) <->
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X))
% Current number of equations to process: 4113
% Current number of ordered equations: 1
% Current number of rules: 171
% New rule produced :
% [179]
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y))
% Current number of equations to process: 4113
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [180]
% inverse(identity greatest_lower_bound inverse(X)) ->
% multiply(inverse(identity greatest_lower_bound X),X)
% Current number of equations to process: 4121
% Current number of ordered equations: 0
% Current number of rules: 173
% New rule produced :
% [181]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X)
% Rule
% [180]
% inverse(identity greatest_lower_bound inverse(X)) ->
% multiply(inverse(identity greatest_lower_bound X),X) collapsed.
% Current number of equations to process: 4142
% Current number of ordered equations: 1
% Current number of rules: 173
% New rule produced :
% [182]
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X) <->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 4142
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced :
% [183]
% inverse((b least_upper_bound multiply(b,a)) greatest_lower_bound identity) ->
% inverse(b greatest_lower_bound identity)
% Current number of equations to process: 4168
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced :
% [184]
% inverse((a least_upper_bound multiply(a,b)) greatest_lower_bound identity) ->
% inverse(a greatest_lower_bound identity)
% Current number of equations to process: 4169
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced :
% [185]
% inverse((b least_upper_bound multiply(b,inverse(a))) greatest_lower_bound identity)
% -> inverse(b greatest_lower_bound identity)
% Current number of equations to process: 4192
% Current number of ordered equations: 0
% Current number of rules: 177
% New rule produced :
% [186]
% inverse((a least_upper_bound multiply(a,inverse(b))) greatest_lower_bound identity)
% -> inverse(a greatest_lower_bound identity)
% Current number of equations to process: 4191
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [187]
% (b least_upper_bound multiply(b,a)) greatest_lower_bound identity ->
% b greatest_lower_bound identity
% Rule
% [183]
% inverse((b least_upper_bound multiply(b,a)) greatest_lower_bound identity) ->
% inverse(b greatest_lower_bound identity) collapsed.
% Current number of equations to process: 4304
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [188]
% (a least_upper_bound multiply(a,b)) greatest_lower_bound identity ->
% a greatest_lower_bound identity
% Rule
% [184]
% inverse((a least_upper_bound multiply(a,b)) greatest_lower_bound identity) ->
% inverse(a greatest_lower_bound identity) collapsed.
% Current number of equations to process: 4309
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [189]
% (b least_upper_bound multiply(b,inverse(a))) greatest_lower_bound identity ->
% b greatest_lower_bound identity
% Rule
% [185]
% inverse((b least_upper_bound multiply(b,inverse(a))) greatest_lower_bound identity)
% -> inverse(b greatest_lower_bound identity) collapsed.
% Current number of equations to process: 4314
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [190]
% (a least_upper_bound multiply(a,inverse(b))) greatest_lower_bound identity ->
% a greatest_lower_bound identity
% Rule
% [186]
% inverse((a least_upper_bound multiply(a,inverse(b))) greatest_lower_bound identity)
% -> inverse(a greatest_lower_bound identity) collapsed.
% Current number of equations to process: 4319
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [191]
% ((multiply(b,a) greatest_lower_bound X) least_upper_bound b) greatest_lower_bound identity
% -> b greatest_lower_bound identity
% Current number of equations to process: 4526
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [192]
% ((multiply(a,b) greatest_lower_bound X) least_upper_bound a) greatest_lower_bound identity
% -> a greatest_lower_bound identity
% Current number of equations to process: 4525
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [193]
% b greatest_lower_bound identity greatest_lower_bound multiply(b,inverse(a))
% -> identity greatest_lower_bound multiply(b,inverse(a))
% Current number of equations to process: 4624
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [194]
% (identity greatest_lower_bound multiply(b,inverse(a))) least_upper_bound b ->
% b
% Current number of equations to process: 4659
% Current number of ordered equations: 0
% Current number of rules: 182
% New rule produced :
% [195]
% (identity greatest_lower_bound multiply(b,inverse(a)) greatest_lower_bound X) least_upper_bound b
% -> b
% Current number of equations to process: 4672
% Current number of ordered equations: 0
% Current number of rules: 183
% New rule produced :
% [196]
% a greatest_lower_bound identity greatest_lower_bound multiply(a,inverse(b))
% -> identity greatest_lower_bound multiply(a,inverse(b))
% Current number of equations to process: 4679
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [197]
% (identity greatest_lower_bound multiply(a,inverse(b))) least_upper_bound a ->
% a
% Current number of equations to process: 4866
% Current number of ordered equations: 0
% Current number of rules: 185
% New rule produced :
% [198]
% (identity greatest_lower_bound multiply(a,inverse(b)) greatest_lower_bound X) least_upper_bound a
% -> a
% Current number of equations to process: 4879
% Current number of ordered equations: 0
% Current number of rules: 186
% New rule produced :
% [199]
% inverse(multiply(X,Y) least_upper_bound multiply(Z,Y)) ->
% multiply(inverse(Y),inverse(X least_upper_bound Z))
% Current number of equations to process: 1206
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [200]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),inverse(identity least_upper_bound X))
% Current number of equations to process: 1214
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [201]
% inverse(identity least_upper_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X least_upper_bound Y))
% Current number of equations to process: 1222
% Current number of ordered equations: 0
% Current number of rules: 189
% New rule produced :
% [202]
% inverse(identity least_upper_bound multiply(X,Y)) <->
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X))
% Current number of equations to process: 1221
% Current number of ordered equations: 1
% Current number of rules: 190
% New rule produced :
% [203]
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X)) <->
% inverse(identity least_upper_bound multiply(X,Y))
% Current number of equations to process: 1221
% Current number of ordered equations: 0
% Current number of rules: 191
% New rule produced :
% [204]
% multiply(inverse(identity least_upper_bound X),X) ->
% multiply(X,inverse(identity least_upper_bound X))
% Current number of equations to process: 1241
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced :
% [205]
% multiply(inverse(identity least_upper_bound X),inverse(X)) ->
% multiply(inverse(X),inverse(identity least_upper_bound X))
% Current number of equations to process: 1245
% Current number of ordered equations: 0
% Current number of rules: 193
% New rule produced :
% [206]
% multiply(X,inverse(inverse(Y) least_upper_bound X)) <->
% multiply(inverse(inverse(X) least_upper_bound Y),Y)
% Current number of equations to process: 1266
% Current number of ordered equations: 1
% Current number of rules: 194
% New rule produced :
% [207]
% multiply(inverse(inverse(X) least_upper_bound Y),Y) <->
% multiply(X,inverse(inverse(Y) least_upper_bound X))
% Current number of equations to process: 1266
% Current number of ordered equations: 0
% Current number of rules: 195
% New rule produced :
% [208]
% inverse(inverse(X) least_upper_bound inverse(Y)) ->
% multiply(X,multiply(inverse(X least_upper_bound Y),Y))
% Current number of equations to process: 1286
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [209]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(X,inverse(identity least_upper_bound multiply(Y,X)))
% Current number of equations to process: 1312
% Current number of ordered equations: 1
% Current number of rules: 197
% New rule produced :
% [210]
% multiply(X,inverse(identity least_upper_bound multiply(Y,X))) <->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 1312
% Current number of ordered equations: 0
% Current number of rules: 198
% New rule produced :
% [211]
% inverse(multiply(X,Y) greatest_lower_bound multiply(Z,Y)) ->
% multiply(inverse(Y),inverse(X greatest_lower_bound Z))
% Current number of equations to process: 1709
% Current number of ordered equations: 0
% Current number of rules: 199
% New rule produced :
% [212]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),inverse(identity greatest_lower_bound X))
% Current number of equations to process: 1717
% Current number of ordered equations: 0
% Current number of rules: 200
% New rule produced :
% [213]
% inverse(identity greatest_lower_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X greatest_lower_bound Y))
% Current number of equations to process: 1725
% Current number of ordered equations: 0
% Current number of rules: 201
% New rule produced :
% [214]
% inverse(identity greatest_lower_bound multiply(X,Y)) <->
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X))
% Current number of equations to process: 1724
% Current number of ordered equations: 1
% Current number of rules: 202
% New rule produced :
% [215]
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y))
% Current number of equations to process: 1724
% Current number of ordered equations: 0
% Current number of rules: 203
% New rule produced :
% [216]
% multiply(inverse(identity greatest_lower_bound X),X) ->
% multiply(X,inverse(identity greatest_lower_bound X))
% Current number of equations to process: 1759
% Current number of ordered equations: 0
% Current number of rules: 204
% New rule produced :
% [217]
% multiply(inverse(identity greatest_lower_bound X),inverse(X)) ->
% multiply(inverse(X),inverse(identity greatest_lower_bound X))
% Current number of equations to process: 1764
% Current number of ordered equations: 0
% Current number of rules: 205
% New rule produced :
% [218]
% multiply(X,inverse(inverse(Y) greatest_lower_bound X)) <->
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y)
% Current number of equations to process: 1802
% Current number of ordered equations: 1
% Current number of rules: 206
% New rule produced :
% [219]
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y) <->
% multiply(X,inverse(inverse(Y) greatest_lower_bound X))
% Current number of equations to process: 1802
% Current number of ordered equations: 0
% Current number of rules: 207
% New rule produced :
% [220]
% inverse(inverse(X) greatest_lower_bound inverse(Y)) ->
% multiply(X,multiply(inverse(X greatest_lower_bound Y),Y))
% Current number of equations to process: 1831
% Current number of ordered equations: 0
% Current number of rules: 208
% New rule produced :
% [221]
% inverse((b least_upper_bound multiply(a,b)) greatest_lower_bound identity) ->
% inverse(b greatest_lower_bound identity)
% Current number of equations to process: 1861
% Current number of ordered equations: 0
% Current number of rules: 209
% New rule produced :
% [222]
% inverse((a least_upper_bound multiply(b,a)) greatest_lower_bound identity) ->
% inverse(a greatest_lower_bound identity)
% Current number of equations to process: 1862
% Current number of ordered equations: 0
% Current number of rules: 210
% New rule produced :
% [223]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(X,inverse(identity greatest_lower_bound multiply(Y,X)))
% Current number of equations to process: 1869
% Current number of ordered equations: 1
% Current number of rules: 211
% New rule produced :
% [224]
% multiply(X,inverse(identity greatest_lower_bound multiply(Y,X))) <->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 1869
% Current number of ordered equations: 0
% Current number of rules: 212
% New rule produced :
% [225]
% inverse((b least_upper_bound multiply(inverse(a),b)) greatest_lower_bound identity)
% -> inverse(b greatest_lower_bound identity)
% Current number of equations to process: 1884
% Current number of ordered equations: 0
% Current number of rules: 213
% New rule produced :
% [226]
% inverse((a least_upper_bound multiply(inverse(b),a)) greatest_lower_bound identity)
% -> inverse(a greatest_lower_bound identity)
% Current number of equations to process: 1883
% Current number of ordered equations: 0
% Current number of rules: 214
% New rule produced :
% [227]
% (b least_upper_bound multiply(a,b)) greatest_lower_bound identity ->
% b greatest_lower_bound identity
% Rule
% [221]
% inverse((b least_upper_bound multiply(a,b)) greatest_lower_bound identity) ->
% inverse(b greatest_lower_bound identity) collapsed.
% Current number of equations to process: 2277
% Current number of ordered equations: 0
% Current number of rules: 214
% New rule produced :
% [228]
% (a least_upper_bound multiply(b,a)) greatest_lower_bound identity ->
% a greatest_lower_bound identity
% Rule
% [222]
% inverse((a least_upper_bound multiply(b,a)) greatest_lower_bound identity) ->
% inverse(a greatest_lower_bound identity) collapsed.
% Current number of equations to process: 2282
% Current number of ordered equations: 0
% Current number of rules: 214
% New rule produced :
% [229]
% (b least_upper_bound multiply(inverse(a),b)) greatest_lower_bound identity ->
% b greatest_lower_bound identity
% Rule
% [225]
% inverse((b least_upper_bound multiply(inverse(a),b)) greatest_lower_bound identity)
% -> inverse(b greatest_lower_bound identity) collapsed.
% Current number of equations to process: 2416
% Current number of ordered equations: 0
% Current number of rules: 214
% New rule produced :
% [230]
% (a least_upper_bound multiply(inverse(b),a)) greatest_lower_bound identity ->
% a greatest_lower_bound identity
% Rule
% [226]
% inverse((a least_upper_bound multiply(inverse(b),a)) greatest_lower_bound identity)
% -> inverse(a greatest_lower_bound identity) collapsed.
% Current number of equations to process: 2421
% Current number of ordered equations: 0
% Current number of rules: 214
% New rule produced :
% [231]
% ((multiply(a,b) greatest_lower_bound X) least_upper_bound b) greatest_lower_bound identity
% -> b greatest_lower_bound identity
% Current number of equations to process: 2642
% Current number of ordered equations: 0
% Current number of rules: 215
% New rule produced :
% [232]
% ((multiply(b,a) greatest_lower_bound X) least_upper_bound a) greatest_lower_bound identity
% -> a greatest_lower_bound identity
% Current number of equations to process: 2641
% Current number of ordered equations: 0
% Current number of rules: 216
% New rule produced :
% [233]
% b greatest_lower_bound identity greatest_lower_bound multiply(inverse(a),b)
% -> identity greatest_lower_bound multiply(inverse(a),b)
% Current number of equations to process: 2748
% Current number of ordered equations: 0
% Current number of rules: 217
% New rule produced :
% [234]
% (identity greatest_lower_bound multiply(inverse(a),b)) least_upper_bound b ->
% b
% Current number of equations to process: 2783
% Current number of ordered equations: 0
% Current number of rules: 218
% New rule produced :
% [235]
% (identity greatest_lower_bound multiply(inverse(a),b) greatest_lower_bound X) least_upper_bound b
% -> b
% Current number of equations to process: 2796
% Current number of ordered equations: 0
% Current number of rules: 219
% New rule produced :
% [236]
% a greatest_lower_bound identity greatest_lower_bound multiply(inverse(b),a)
% -> identity greatest_lower_bound multiply(inverse(b),a)
% Current number of equations to process: 2803
% Current number of ordered equations: 0
% Current number of rules: 220
% New rule produced :
% [237]
% (identity greatest_lower_bound multiply(inverse(b),a)) least_upper_bound a ->
% a
% Current number of equations to process: 2993
% Current number of ordered equations: 0
% Current number of rules: 221
% New rule produced :
% [238]
% (identity greatest_lower_bound multiply(inverse(b),a) greatest_lower_bound X) least_upper_bound a
% -> a
% Current number of equations to process: 3006
% Current number of ordered equations: 0
% Current number of rules: 222
% New rule produced :
% [239]
% (multiply(X,a) least_upper_bound X) greatest_lower_bound multiply(X,b) ->
% multiply(X,b) greatest_lower_bound X
% Current number of equations to process: 3165
% Current number of ordered equations: 0
% Current number of rules: 223
% New rule produced :
% [240]
% (inverse(b) least_upper_bound multiply(inverse(b),a)) greatest_lower_bound identity
% -> identity greatest_lower_bound inverse(b)
% Current number of equations to process: 3191
% Current number of ordered equations: 0
% Current number of rules: 224
% New rule produced :
% [241]
% (multiply(a,X) least_upper_bound X) greatest_lower_bound multiply(b,X) ->
% multiply(b,X) greatest_lower_bound X
% Current number of equations to process: 3291
% Current number of ordered equations: 0
% Current number of rules: 225
% New rule produced :
% [242]
% (inverse(b) least_upper_bound multiply(a,inverse(b))) greatest_lower_bound identity
% -> identity greatest_lower_bound inverse(b)
% Current number of equations to process: 3317
% Current number of ordered equations: 0
% Current number of rules: 226
% New rule produced :
% [243]
% (multiply(X,b) least_upper_bound X) greatest_lower_bound multiply(X,a) ->
% multiply(X,a) greatest_lower_bound X
% Current number of equations to process: 3406
% Current number of ordered equations: 0
% Current number of rules: 227
% New rule produced :
% [244]
% (inverse(a) least_upper_bound multiply(inverse(a),b)) greatest_lower_bound identity
% -> identity greatest_lower_bound inverse(a)
% Current number of equations to process: 3432
% Current number of ordered equations: 0
% Current number of rules: 228
% New rule produced :
% [245]
% (multiply(b,X) least_upper_bound X) greatest_lower_bound multiply(a,X) ->
% multiply(a,X) greatest_lower_bound X
% Current number of equations to process: 3532
% Current number of ordered equations: 0
% Current number of rules: 229
% New rule produced :
% [246]
% (inverse(a) least_upper_bound multiply(b,inverse(a))) greatest_lower_bound identity
% -> identity greatest_lower_bound inverse(a)
% Current number of equations to process: 3558
% Current number of ordered equations: 0
% Current number of rules: 230
% New rule produced :
% [247]
% (multiply(X,b) least_upper_bound X) greatest_lower_bound (multiply(X,a) least_upper_bound X)
% -> X
% Current number of equations to process: 3650
% Current number of ordered equations: 0
% Current number of rules: 231
% New rule produced :
% [248]
% (multiply(b,X) least_upper_bound X) greatest_lower_bound (multiply(a,X) least_upper_bound X)
% -> X
% Current number of equations to process: 3724
% Current number of ordered equations: 0
% Current number of rules: 232
% New rule produced :
% [249]
% (identity least_upper_bound X) greatest_lower_bound inverse(b) greatest_lower_bound 
% inverse(a) -> inverse(b) greatest_lower_bound inverse(a)
% Current number of equations to process: 3790
% Current number of ordered equations: 0
% Current number of rules: 233
% New rule produced :
% [250]
% (multiply(X,inverse(b)) greatest_lower_bound multiply(X,inverse(a))) least_upper_bound X
% -> X
% Current number of equations to process: 3917
% Current number of ordered equations: 0
% Current number of rules: 234
% New rule produced :
% [251]
% (multiply(inverse(b),X) greatest_lower_bound multiply(inverse(a),X)) least_upper_bound X
% -> X
% Current number of equations to process: 3994
% Current number of ordered equations: 0
% Current number of rules: 235
% New rule produced :
% [252]
% (multiply(X,b) greatest_lower_bound multiply(X,a) greatest_lower_bound Y) least_upper_bound X
% -> X
% Current number of equations to process: 4062
% Current number of ordered equations: 0
% Current number of rules: 236
% New rule produced :
% [253]
% (multiply(b,X) greatest_lower_bound multiply(a,X) greatest_lower_bound Y) least_upper_bound X
% -> X
% Current number of equations to process: 4137
% Current number of ordered equations: 0
% Current number of rules: 237
% New rule produced :
% [254]
% (a greatest_lower_bound X) least_upper_bound identity least_upper_bound 
% multiply(a,a) -> identity least_upper_bound multiply(a,a)
% Current number of equations to process: 4205
% Current number of ordered equations: 0
% Current number of rules: 238
% New rule produced :
% [255]
% (b greatest_lower_bound X) least_upper_bound identity least_upper_bound 
% multiply(b,b) -> identity least_upper_bound multiply(b,b)
% Current number of equations to process: 4322
% Current number of ordered equations: 0
% Current number of rules: 239
% New rule produced :
% [256]
% ((b least_upper_bound X) greatest_lower_bound identity) least_upper_bound 
% (b greatest_lower_bound a) ->
% (b least_upper_bound X) greatest_lower_bound identity
% Current number of equations to process: 4438
% Current number of ordered equations: 1
% Current number of rules: 240
% New rule produced :
% [257]
% ((a least_upper_bound X) greatest_lower_bound identity) least_upper_bound 
% (b greatest_lower_bound a) ->
% (a least_upper_bound X) greatest_lower_bound identity
% Current number of equations to process: 4438
% Current number of ordered equations: 0
% Current number of rules: 241
% New rule produced :
% [258]
% (a least_upper_bound X) greatest_lower_bound identity greatest_lower_bound 
% multiply(a,b) -> identity greatest_lower_bound multiply(a,b)
% Current number of equations to process: 4529
% Current number of ordered equations: 0
% Current number of rules: 242
% New rule produced :
% [259]
% (inverse(b) greatest_lower_bound inverse(a) greatest_lower_bound multiply(a,b)) least_upper_bound a
% -> a
% Current number of equations to process: 4646
% Current number of ordered equations: 0
% Current number of rules: 243
% New rule produced :
% [260]
% (a least_upper_bound X) greatest_lower_bound identity greatest_lower_bound 
% multiply(b,a) -> identity greatest_lower_bound multiply(b,a)
% Current number of equations to process: 4684
% Current number of ordered equations: 0
% Current number of rules: 244
% New rule produced :
% [261]
% (inverse(b) greatest_lower_bound inverse(a) greatest_lower_bound multiply(b,a)) least_upper_bound a
% -> a
% Current number of equations to process: 4799
% Current number of ordered equations: 0
% Current number of rules: 245
% New rule produced :
% [262]
% (inverse(b) greatest_lower_bound inverse(a) greatest_lower_bound multiply(b,a)) least_upper_bound b
% -> b
% Current number of equations to process: 4836
% Current number of ordered equations: 1
% Current number of rules: 246
% New rule produced :
% [263]
% (b least_upper_bound X) greatest_lower_bound identity greatest_lower_bound 
% multiply(b,a) -> identity greatest_lower_bound multiply(b,a)
% Current number of equations to process: 4876
% Current number of ordered equations: 0
% Current number of rules: 247
% New rule produced :
% [264]
% (b least_upper_bound X) greatest_lower_bound identity greatest_lower_bound 
% multiply(a,b) -> identity greatest_lower_bound multiply(a,b)
% Current number of equations to process: 4992
% Current number of ordered equations: 0
% Current number of rules: 248
% New rule produced :
% [265]
% (inverse(b) greatest_lower_bound inverse(a) greatest_lower_bound multiply(a,b)) least_upper_bound b
% -> b
% Current number of equations to process: 2521
% Current number of ordered equations: 0
% Current number of rules: 249
% New rule produced :
% [266]
% ((inverse(a) greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% (b least_upper_bound inverse(b)) -> identity
% Current number of equations to process: 2525
% Current number of ordered equations: 0
% Current number of rules: 250
% New rule produced :
% [267]
% ((inverse(b) greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% (a least_upper_bound inverse(a)) -> identity
% Current number of equations to process: 2577
% Current number of ordered equations: 0
% Current number of rules: 251
% New rule produced :
% [268]
% ((inverse(a) greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% (identity least_upper_bound inverse(b)) -> identity
% Current number of equations to process: 2629
% Current number of ordered equations: 1
% Current number of rules: 252
% New rule produced :
% [269]
% ((inverse(b) greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% (identity least_upper_bound inverse(a)) -> identity
% Current number of equations to process: 2629
% Current number of ordered equations: 0
% Current number of rules: 253
% New rule produced :
% [270]
% ((b greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound 
% ((a greatest_lower_bound Y) least_upper_bound identity) -> identity
% Current number of equations to process: 2732
% Current number of ordered equations: 0
% Current number of rules: 254
% New rule produced :
% [271]
% inverse(multiply(inverse(X),Y) least_upper_bound Z) <->
% multiply(inverse(multiply(X,Z) least_upper_bound Y),X)
% Rule
% [168]
% inverse(identity least_upper_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X least_upper_bound Y),X) collapsed.
% Current number of equations to process: 2777
% Current number of ordered equations: 1
% Current number of rules: 254
% New rule produced :
% [272]
% multiply(inverse(multiply(X,Z) least_upper_bound Y),X) <->
% inverse(multiply(inverse(X),Y) least_upper_bound Z)
% Current number of equations to process: 2777
% Current number of ordered equations: 0
% Current number of rules: 255
% New rule produced :
% [273]
% inverse(identity least_upper_bound X) least_upper_bound multiply(X,inverse(
% identity least_upper_bound X))
% -> identity
% Current number of equations to process: 2968
% Current number of ordered equations: 0
% Current number of rules: 256
% New rule produced :
% [274]
% identity least_upper_bound inverse(identity least_upper_bound X) -> identity
% Current number of equations to process: 2975
% Current number of ordered equations: 0
% Current number of rules: 257
% New rule produced :
% [275]
% identity greatest_lower_bound inverse(identity least_upper_bound X) ->
% inverse(identity least_upper_bound X)
% Current number of equations to process: 3002
% Current number of ordered equations: 0
% Current number of rules: 258
% New rule produced :
% [276]
% identity least_upper_bound multiply(X,inverse(identity least_upper_bound X))
% -> identity
% Current number of equations to process: 3001
% Current number of ordered equations: 0
% Current number of rules: 259
% New rule produced :
% [277]
% (inverse(identity least_upper_bound X) greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Current number of equations to process: 3000
% Current number of ordered equations: 0
% Current number of rules: 260
% New rule produced :
% [278]
% (identity least_upper_bound X) greatest_lower_bound inverse(identity least_upper_bound Y)
% -> inverse(identity least_upper_bound Y)
% Current number of equations to process: 2999
% Current number of ordered equations: 0
% Current number of rules: 261
% New rule produced :
% [279]
% (multiply(X,inverse(identity least_upper_bound X)) greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Current number of equations to process: 3012
% Current number of ordered equations: 0
% Current number of rules: 262
% New rule produced :
% [280]
% identity greatest_lower_bound multiply(X,inverse(identity least_upper_bound X))
% -> multiply(X,inverse(identity least_upper_bound X))
% Current number of equations to process: 3022
% Current number of ordered equations: 0
% Current number of rules: 263
% New rule produced :
% [281]
% multiply(X,inverse(identity least_upper_bound Y)) least_upper_bound X -> X
% Current number of equations to process: 3118
% Current number of ordered equations: 0
% Current number of rules: 264
% New rule produced :
% [282]
% multiply(inverse(identity least_upper_bound Y),X) least_upper_bound X -> X
% Current number of equations to process: 3117
% Current number of ordered equations: 0
% Current number of rules: 265
% New rule produced :
% [283]
% identity least_upper_bound multiply(X,inverse(X least_upper_bound Y)) ->
% identity
% Rule
% [276]
% identity least_upper_bound multiply(X,inverse(identity least_upper_bound X))
% -> identity collapsed.
% Current number of equations to process: 3149
% Current number of ordered equations: 0
% Current number of rules: 265
% New rule produced :
% [284]
% identity least_upper_bound multiply(inverse(X least_upper_bound Y),X) ->
% identity
% Current number of equations to process: 3164
% Current number of ordered equations: 0
% Current number of rules: 266
% New rule produced :
% [285]
% identity least_upper_bound inverse(a least_upper_bound inverse(a) least_upper_bound X)
% -> identity
% Current number of equations to process: 3164
% Current number of ordered equations: 0
% Current number of rules: 267
% New rule produced :
% [286]
% identity least_upper_bound inverse(b least_upper_bound inverse(b) least_upper_bound X)
% -> identity
% Current number of equations to process: 3163
% Current number of ordered equations: 0
% Current number of rules: 268
% New rule produced :
% [287]
% identity least_upper_bound multiply(a,inverse(identity least_upper_bound 
% multiply(a,a))) -> identity
% Current number of equations to process: 3395
% Current number of ordered equations: 0
% Current number of rules: 269
% New rule produced :
% [288]
% identity least_upper_bound multiply(b,inverse(identity least_upper_bound 
% multiply(b,b))) -> identity
% Current number of equations to process: 3394
% Current number of ordered equations: 0
% Current number of rules: 270
% New rule produced :
% [289]
% (inverse(identity least_upper_bound X) greatest_lower_bound multiply(a,b)) least_upper_bound a
% -> a
% Current number of equations to process: 3392
% Current number of ordered equations: 0
% Current number of rules: 271
% New rule produced :
% [290]
% (inverse(identity least_upper_bound X) greatest_lower_bound multiply(b,a)) least_upper_bound a
% -> a
% Current number of equations to process: 3391
% Current number of ordered equations: 0
% Current number of rules: 272
% New rule produced :
% [291]
% (inverse(identity least_upper_bound X) greatest_lower_bound multiply(b,a)) least_upper_bound b
% -> b
% Current number of equations to process: 3390
% Current number of ordered equations: 0
% Current number of rules: 273
% New rule produced :
% [292]
% (inverse(identity least_upper_bound X) greatest_lower_bound multiply(a,b)) least_upper_bound b
% -> b
% Current number of equations to process: 3389
% Current number of ordered equations: 0
% Current number of rules: 274
% New rule produced :
% [293]
% (multiply(X,inverse(X least_upper_bound Y)) greatest_lower_bound Z) least_upper_bound identity
% -> identity
% Rule
% [279]
% (multiply(X,inverse(identity least_upper_bound X)) greatest_lower_bound Y) least_upper_bound identity
% -> identity collapsed.
% Current number of equations to process: 3388
% Current number of ordered equations: 0
% Current number of rules: 274
% New rule produced :
% [294]
% (multiply(inverse(X least_upper_bound Y),X) greatest_lower_bound Z) least_upper_bound identity
% -> identity
% Current number of equations to process: 3387
% Current number of ordered equations: 0
% Current number of rules: 275
% New rule produced :
% [295]
% a least_upper_bound inverse(identity least_upper_bound X) least_upper_bound 
% inverse(a) -> a least_upper_bound inverse(a)
% Current number of equations to process: 3472
% Current number of ordered equations: 0
% Current number of rules: 276
% New rule produced :
% [296]
% b least_upper_bound inverse(identity least_upper_bound X) least_upper_bound 
% inverse(b) -> b least_upper_bound inverse(b)
% Current number of equations to process: 3471
% Current number of ordered equations: 0
% Current number of rules: 277
% New rule produced :
% [297]
% multiply(X,inverse(identity least_upper_bound Y)) greatest_lower_bound X ->
% multiply(X,inverse(identity least_upper_bound Y))
% Current number of equations to process: 3470
% Current number of ordered equations: 0
% Current number of rules: 278
% New rule produced :
% [298]
% multiply(inverse(identity least_upper_bound X),Y) greatest_lower_bound Y ->
% multiply(inverse(identity least_upper_bound X),Y)
% Current number of equations to process: 3469
% Current number of ordered equations: 0
% Current number of rules: 279
% New rule produced :
% [299]
% (a least_upper_bound inverse(a)) greatest_lower_bound inverse(identity least_upper_bound X)
% -> inverse(identity least_upper_bound X)
% Current number of equations to process: 3468
% Current number of ordered equations: 0
% Current number of rules: 280
% New rule produced :
% [300]
% (b least_upper_bound inverse(b)) greatest_lower_bound inverse(identity least_upper_bound X)
% -> inverse(identity least_upper_bound X)
% Current number of equations to process: 3467
% Current number of ordered equations: 0
% Current number of rules: 281
% New rule produced :
% [301]
% identity greatest_lower_bound multiply(X,inverse(X least_upper_bound Y)) ->
% multiply(X,inverse(X least_upper_bound Y))
% Rule
% [280]
% identity greatest_lower_bound multiply(X,inverse(identity least_upper_bound X))
% -> multiply(X,inverse(identity least_upper_bound X)) collapsed.
% Current number of equations to process: 3464
% Current number of ordered equations: 0
% Current number of rules: 281
% New rule produced :
% [302] inverse(inverse(X) least_upper_bound Y) least_upper_bound X -> X
% Current number of equations to process: 3563
% Current number of ordered equations: 0
% Current number of rules: 282
% New rule produced :
% [303]
% inverse(identity least_upper_bound X) least_upper_bound X ->
% identity least_upper_bound X
% Current number of equations to process: 3576
% Current number of ordered equations: 0
% Current number of rules: 283
% New rule produced :
% [304]
% (multiply(X,inverse(identity least_upper_bound Y)) greatest_lower_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 4106
% Current number of ordered equations: 0
% Current number of rules: 284
% New rule produced :
% [305]
% multiply(X,multiply(Y,inverse(identity least_upper_bound Y))) least_upper_bound X
% -> X
% Current number of equations to process: 4105
% Current number of ordered equations: 0
% Current number of rules: 285
% New rule produced :
% [306]
% multiply(X,multiply(Y,inverse(Y least_upper_bound Z))) least_upper_bound X ->
% X
% Rule
% [305]
% multiply(X,multiply(Y,inverse(identity least_upper_bound Y))) least_upper_bound X
% -> X collapsed.
% Current number of equations to process: 4104
% Current number of ordered equations: 0
% Current number of rules: 285
% New rule produced :
% [307]
% multiply(X,multiply(inverse(Y least_upper_bound Z),Y)) least_upper_bound X ->
% X
% Current number of equations to process: 4102
% Current number of ordered equations: 0
% Current number of rules: 286
% New rule produced :
% [308]
% (multiply(inverse(identity least_upper_bound Y),X) greatest_lower_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 4100
% Current number of ordered equations: 0
% Current number of rules: 287
% New rule produced :
% [309]
% multiply(X,multiply(inverse(identity least_upper_bound X),Y)) least_upper_bound Y
% -> Y
% Current number of equations to process: 4099
% Current number of ordered equations: 0
% Current number of rules: 288
% New rule produced :
% [310]
% multiply(X,multiply(inverse(X least_upper_bound Y),Z)) least_upper_bound Z ->
% Z
% Rule
% [309]
% multiply(X,multiply(inverse(identity least_upper_bound X),Y)) least_upper_bound Y
% -> Y collapsed.
% Current number of equations to process: 4098
% Current number of ordered equations: 0
% Current number of rules: 288
% New rule produced :
% [311]
% multiply(inverse(X least_upper_bound Y),multiply(X,Z)) least_upper_bound Z ->
% Z
% Current number of equations to process: 4097
% Current number of ordered equations: 0
% Current number of rules: 289
% New rule produced :
% [312]
% identity least_upper_bound multiply(inverse(identity least_upper_bound 
% multiply(a,a)),a) -> identity
% Current number of equations to process: 4092
% Current number of ordered equations: 0
% Current number of rules: 290
% New rule produced :
% [313]
% identity least_upper_bound multiply(inverse(identity least_upper_bound 
% multiply(b,b)),b) -> identity
% Current number of equations to process: 4091
% Current number of ordered equations: 0
% Current number of rules: 291
% New rule produced :
% [314]
% identity greatest_lower_bound multiply(inverse(X least_upper_bound Y),X) ->
% multiply(inverse(X least_upper_bound Y),X)
% Current number of equations to process: 4768
% Current number of ordered equations: 0
% Current number of rules: 292
% New rule produced :
% [315]
% (a greatest_lower_bound multiply(b,inverse(identity least_upper_bound X))) least_upper_bound identity
% -> identity
% Current number of equations to process: 2056
% Current number of ordered equations: 1
% Current number of rules: 293
% New rule produced :
% [316]
% (b greatest_lower_bound multiply(a,inverse(identity least_upper_bound X))) least_upper_bound identity
% -> identity
% Current number of equations to process: 2056
% Current number of ordered equations: 0
% Current number of rules: 294
% New rule produced :
% [317]
% (a greatest_lower_bound multiply(inverse(identity least_upper_bound X),b)) least_upper_bound identity
% -> identity
% Current number of equations to process: 2432
% Current number of ordered equations: 1
% Current number of rules: 295
% New rule produced :
% [318]
% (b greatest_lower_bound multiply(inverse(identity least_upper_bound X),a)) least_upper_bound identity
% -> identity
% Current number of equations to process: 2432
% Current number of ordered equations: 0
% Current number of rules: 296
% New rule produced :
% [319]
% inverse(X least_upper_bound Y) least_upper_bound inverse(X) -> inverse(X)
% Current number of equations to process: 3298
% Current number of ordered equations: 0
% Current number of rules: 297
% New rule produced :
% [320]
% identity least_upper_bound inverse(X) least_upper_bound X ->
% inverse(X) least_upper_bound X
% Rule
% [18]
% a least_upper_bound identity least_upper_bound inverse(a) ->
% a least_upper_bound inverse(a) collapsed.
% Rule
% [19]
% b least_upper_bound identity least_upper_bound inverse(b) ->
% b least_upper_bound inverse(b) collapsed.
% Current number of equations to process: 4060
% Current number of ordered equations: 0
% Current number of rules: 296
% New rule produced :
% [321]
% inverse(inverse(X greatest_lower_bound Y) least_upper_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 4058
% Current number of ordered equations: 1
% Current number of rules: 297
% New rule produced :
% [322]
% (inverse(inverse(X) least_upper_bound Y) greatest_lower_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 4058
% Current number of ordered equations: 0
% Current number of rules: 298
% New rule produced :
% [323]
% inverse(inverse(X) least_upper_bound Y) greatest_lower_bound X ->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 4057
% Current number of ordered equations: 0
% Current number of rules: 299
% New rule produced :
% [324]
% identity least_upper_bound inverse(inverse(b greatest_lower_bound a) least_upper_bound X)
% -> identity
% Current number of equations to process: 4056
% Current number of ordered equations: 0
% Current number of rules: 300
% New rule produced :
% [325]
% inverse((X greatest_lower_bound Y) least_upper_bound identity) least_upper_bound X
% -> identity least_upper_bound X
% Current number of equations to process: 4054
% Current number of ordered equations: 0
% Current number of rules: 301
% New rule produced :
% [326]
% inverse(X) least_upper_bound multiply(X,inverse(identity least_upper_bound X))
% -> identity least_upper_bound inverse(X)
% Current number of equations to process: 1909
% Current number of ordered equations: 0
% Current number of rules: 302
% New rule produced :
% [327]
% (a greatest_lower_bound inverse(inverse(b) least_upper_bound X)) least_upper_bound identity
% -> identity
% Current number of equations to process: 2247
% Current number of ordered equations: 0
% Current number of rules: 303
% New rule produced :
% [328]
% (b greatest_lower_bound inverse(inverse(a) least_upper_bound X)) least_upper_bound identity
% -> identity
% Current number of equations to process: 2315
% Current number of ordered equations: 0
% Current number of rules: 304
% New rule produced :
% [329]
% identity least_upper_bound inverse(b greatest_lower_bound a) ->
% inverse(b greatest_lower_bound a)
% Current number of equations to process: 2553
% Current number of ordered equations: 0
% Current number of rules: 305
% New rule produced :
% [330]
% inverse(X greatest_lower_bound Y) least_upper_bound inverse(X) ->
% inverse(X greatest_lower_bound Y)
% Current number of equations to process: 2722
% Current number of ordered equations: 0
% Current number of rules: 306
% New rule produced :
% [331]
% inverse(X least_upper_bound Y) greatest_lower_bound inverse(X) ->
% inverse(X least_upper_bound Y)
% Current number of equations to process: 2721
% Current number of ordered equations: 0
% Current number of rules: 307
% New rule produced :
% [332]
% (inverse(X) least_upper_bound X) greatest_lower_bound identity -> identity
% Rule
% [14]
% (a least_upper_bound inverse(a)) greatest_lower_bound identity -> identity
% collapsed.
% Rule
% [15]
% (b least_upper_bound inverse(b)) greatest_lower_bound identity -> identity
% collapsed.
% Current number of equations to process: 3703
% Current number of ordered equations: 0
% Current number of rules: 306
% New rule produced :
% [333]
% (inverse(X) least_upper_bound X least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Rule
% [20]
% (b least_upper_bound inverse(b) least_upper_bound X) greatest_lower_bound identity
% -> identity collapsed.
% Rule
% [21]
% (a least_upper_bound inverse(a) least_upper_bound X) greatest_lower_bound identity
% -> identity collapsed.
% Current number of equations to process: 3702
% Current number of ordered equations: 0
% Current number of rules: 305
% New rule produced :
% [334]
% (identity least_upper_bound X) greatest_lower_bound (inverse(X) least_upper_bound X)
% -> identity least_upper_bound X
% Rule
% [48]
% (a least_upper_bound identity) greatest_lower_bound (a least_upper_bound 
% inverse(a)) ->
% a least_upper_bound identity collapsed.
% Rule
% [52]
% (b least_upper_bound identity) greatest_lower_bound (b least_upper_bound 
% inverse(b)) ->
% b least_upper_bound identity collapsed.
% Current number of equations to process: 3914
% Current number of ordered equations: 0
% Current number of rules: 304
% New rule produced :
% [335]
% (inverse(X) least_upper_bound X) greatest_lower_bound b greatest_lower_bound a
% -> b greatest_lower_bound a
% Current number of equations to process: 3913
% Current number of ordered equations: 0
% Current number of rules: 305
% New rule produced :
% [336]
% identity least_upper_bound inverse(inverse(X) least_upper_bound X least_upper_bound Y)
% -> identity
% Rule
% [285]
% identity least_upper_bound inverse(a least_upper_bound inverse(a) least_upper_bound X)
% -> identity collapsed.
% Rule
% [286]
% identity least_upper_bound inverse(b least_upper_bound inverse(b) least_upper_bound X)
% -> identity collapsed.
% Current number of equations to process: 4520
% Current number of ordered equations: 0
% Current number of rules: 304
% New rule produced :
% [337]
% (inverse(X least_upper_bound Y) greatest_lower_bound Z) least_upper_bound 
% inverse(X) -> inverse(X)
% Current number of equations to process: 4530
% Current number of ordered equations: 0
% Current number of rules: 305
% New rule produced :
% [338]
% inverse(identity least_upper_bound multiply(a,a)) least_upper_bound inverse(a)
% -> inverse(a)
% Current number of equations to process: 4529
% Current number of ordered equations: 0
% Current number of rules: 306
% New rule produced :
% [339]
% inverse(identity least_upper_bound multiply(b,b)) least_upper_bound inverse(b)
% -> inverse(b)
% Current number of equations to process: 4528
% Current number of ordered equations: 0
% Current number of rules: 307
% New rule produced :
% [340]
% (identity greatest_lower_bound Y) least_upper_bound inverse(X) least_upper_bound X
% -> inverse(X) least_upper_bound X
% Rule
% [64]
% (identity greatest_lower_bound X) least_upper_bound a least_upper_bound 
% inverse(a) -> a least_upper_bound inverse(a) collapsed.
% Rule
% [65]
% (identity greatest_lower_bound X) least_upper_bound b least_upper_bound 
% inverse(b) -> b least_upper_bound inverse(b) collapsed.
% Current number of equations to process: 4526
% Current number of ordered equations: 0
% Current number of rules: 306
% New rule produced :
% [341]
% (b greatest_lower_bound a) least_upper_bound inverse(X) least_upper_bound X
% -> inverse(X) least_upper_bound X
% Current number of equations to process: 4524
% Current number of ordered equations: 1
% Current number of rules: 307
% New rule produced :
% [342]
% (b greatest_lower_bound a) least_upper_bound inverse(b greatest_lower_bound a)
% -> inverse(b greatest_lower_bound a)
% Current number of equations to process: 4524
% Current number of ordered equations: 0
% Current number of rules: 308
% New rule produced :
% [343]
% (inverse(X) least_upper_bound multiply(a,a) least_upper_bound X) greatest_lower_bound a
% -> a
% Rule
% [106]
% (b least_upper_bound inverse(b) least_upper_bound multiply(a,a)) greatest_lower_bound a
% -> a collapsed.
% Current number of equations to process: 4929
% Current number of ordered equations: 0
% Current number of rules: 308
% New rule produced :
% [344]
% (inverse(X) least_upper_bound multiply(b,b) least_upper_bound X) greatest_lower_bound b
% -> b
% Rule
% [108]
% (a least_upper_bound inverse(a) least_upper_bound multiply(b,b)) greatest_lower_bound b
% -> b collapsed.
% Current number of equations to process: 4928
% Current number of ordered equations: 0
% Current number of rules: 308
% New rule produced :
% [345]
% identity least_upper_bound multiply(X,inverse(identity least_upper_bound 
% multiply(X,X))) -> identity
% Rule
% [287]
% identity least_upper_bound multiply(a,inverse(identity least_upper_bound 
% multiply(a,a))) -> identity
% collapsed.
% Rule
% [288]
% identity least_upper_bound multiply(b,inverse(identity least_upper_bound 
% multiply(b,b))) -> identity
% collapsed.
% Current number of equations to process: 4927
% Current number of ordered equations: 0
% Current number of rules: 307
% New rule produced :
% [346]
% (inverse(inverse(a) least_upper_bound X) greatest_lower_bound inverse(b)) least_upper_bound identity
% -> identity
% Current number of equations to process: 4926
% Current number of ordered equations: 0
% Current number of rules: 308
% New rule produced :
% [347]
% (inverse(inverse(b) least_upper_bound X) greatest_lower_bound inverse(a)) least_upper_bound identity
% -> identity
% Current number of equations to process: 4925
% Current number of ordered equations: 0
% Current number of rules: 309
% New rule produced :
% [348]
% (identity least_upper_bound inverse(inverse(a) least_upper_bound X)) greatest_lower_bound b
% -> b greatest_lower_bound identity
% Current number of equations to process: 4924
% Current number of ordered equations: 0
% Current number of rules: 310
% New rule produced :
% [349]
% (identity least_upper_bound inverse(inverse(b) least_upper_bound X)) greatest_lower_bound a
% -> a greatest_lower_bound identity
% Current number of equations to process: 4923
% Current number of ordered equations: 0
% Current number of rules: 311
% New rule produced :
% [350]
% inverse(X least_upper_bound Y) least_upper_bound inverse(X greatest_lower_bound Z)
% -> inverse(X greatest_lower_bound Z)
% Current number of equations to process: 4967
% Current number of ordered equations: 0
% Current number of rules: 312
% New rule produced :
% [351]
% (inverse(X) least_upper_bound Y) greatest_lower_bound inverse(X least_upper_bound Z)
% -> inverse(X least_upper_bound Z)
% Current number of equations to process: 4966
% Current number of ordered equations: 0
% Current number of rules: 313
% New rule produced :
% [352]
% inverse(identity least_upper_bound X) least_upper_bound inverse(b greatest_lower_bound a)
% -> inverse(b greatest_lower_bound a)
% Current number of equations to process: 4964
% Current number of ordered equations: 0
% Current number of rules: 314
% New rule produced :
% [353]
% identity least_upper_bound inverse(b greatest_lower_bound a greatest_lower_bound X)
% -> inverse(b greatest_lower_bound a greatest_lower_bound X)
% Current number of equations to process: 4963
% Current number of ordered equations: 0
% Current number of rules: 315
% New rule produced :
% [354]
% inverse(b greatest_lower_bound a) least_upper_bound inverse(a greatest_lower_bound identity)
% -> inverse(b greatest_lower_bound a)
% Current number of equations to process: 4962
% Current number of ordered equations: 0
% Current number of rules: 316
% New rule produced :
% [355]
% inverse(b greatest_lower_bound a) least_upper_bound inverse(b greatest_lower_bound identity)
% -> inverse(b greatest_lower_bound a)
% Current number of equations to process: 4961
% Current number of ordered equations: 0
% Current number of rules: 317
% New rule produced :
% [356]
% b least_upper_bound multiply(inverse(b greatest_lower_bound a),b) ->
% multiply(inverse(b greatest_lower_bound a),b)
% Current number of equations to process: 4960
% Current number of ordered equations: 0
% Current number of rules: 318
% New rule produced :
% [357]
% a least_upper_bound multiply(inverse(b greatest_lower_bound a),a) ->
% multiply(inverse(b greatest_lower_bound a),a)
% Current number of equations to process: 4959
% Current number of ordered equations: 0
% Current number of rules: 319
% New rule produced :
% [358]
% b least_upper_bound multiply(b,inverse(b greatest_lower_bound a)) ->
% multiply(b,inverse(b greatest_lower_bound a))
% Current number of equations to process: 4958
% Current number of ordered equations: 0
% Current number of rules: 320
% New rule produced :
% [359]
% (inverse(X) least_upper_bound X) greatest_lower_bound inverse(identity least_upper_bound Y)
% -> inverse(identity least_upper_bound Y)
% Rule
% [299]
% (a least_upper_bound inverse(a)) greatest_lower_bound inverse(identity least_upper_bound X)
% -> inverse(identity least_upper_bound X) collapsed.
% Rule
% [300]
% (b least_upper_bound inverse(b)) greatest_lower_bound inverse(identity least_upper_bound X)
% -> inverse(identity least_upper_bound X) collapsed.
% Current number of equations to process: 4957
% Current number of ordered equations: 0
% Current number of rules: 319
% New rule produced :
% [360]
% (identity greatest_lower_bound X) least_upper_bound inverse(identity greatest_lower_bound X)
% -> identity least_upper_bound inverse(identity greatest_lower_bound X)
% Current number of equations to process: 4955
% Current number of ordered equations: 1
% Current number of rules: 320
% New rule produced :
% [361]
% identity least_upper_bound inverse(X greatest_lower_bound Y) least_upper_bound X
% -> inverse(X greatest_lower_bound Y) least_upper_bound X
% Current number of equations to process: 4955
% Current number of ordered equations: 0
% Current number of rules: 321
% New rule produced :
% [362]
% (identity least_upper_bound inverse(X)) greatest_lower_bound (inverse(X) least_upper_bound X)
% -> identity least_upper_bound inverse(X)
% Rule
% [119]
% (a least_upper_bound inverse(a)) greatest_lower_bound (identity least_upper_bound 
% inverse(a)) ->
% identity least_upper_bound inverse(a) collapsed.
% Rule
% [124]
% (b least_upper_bound inverse(b)) greatest_lower_bound (identity least_upper_bound 
% inverse(b)) ->
% identity least_upper_bound inverse(b) collapsed.
% Current number of equations to process: 4954
% Current number of ordered equations: 0
% Current number of rules: 320
% New rule produced :
% [363]
% (b greatest_lower_bound inverse(a)) least_upper_bound inverse(X) least_upper_bound X
% -> inverse(X) least_upper_bound X
% Current number of equations to process: 4953
% Current number of ordered equations: 0
% Current number of rules: 321
% New rule produced :
% [364]
% (a greatest_lower_bound inverse(b)) least_upper_bound inverse(X) least_upper_bound X
% -> inverse(X) least_upper_bound X
% Current number of equations to process: 4952
% Current number of ordered equations: 0
% Current number of rules: 322
% New rule produced :
% [365]
% (inverse(X) least_upper_bound X) greatest_lower_bound b greatest_lower_bound 
% inverse(a) -> b greatest_lower_bound inverse(a)
% Current number of equations to process: 4951
% Current number of ordered equations: 0
% Current number of rules: 323
% New rule produced :
% [366]
% (inverse(X) least_upper_bound X) greatest_lower_bound a greatest_lower_bound 
% inverse(b) -> a greatest_lower_bound inverse(b)
% Current number of equations to process: 4950
% Current number of ordered equations: 0
% Current number of rules: 324
% New rule produced :
% [367]
% inverse(identity least_upper_bound Y) least_upper_bound inverse(X) least_upper_bound X
% -> inverse(X) least_upper_bound X
% Rule
% [295]
% a least_upper_bound inverse(identity least_upper_bound X) least_upper_bound 
% inverse(a) -> a least_upper_bound inverse(a) collapsed.
% Rule
% [296]
% b least_upper_bound inverse(identity least_upper_bound X) least_upper_bound 
% inverse(b) -> b least_upper_bound inverse(b) collapsed.
% Current number of equations to process: 4949
% Current number of ordered equations: 0
% Current number of rules: 323
% New rule produced :
% [368]
% identity greatest_lower_bound inverse(b greatest_lower_bound a) -> identity
% Current number of equations to process: 1825
% Current number of ordered equations: 0
% Current number of rules: 324
% New rule produced :
% [369]
% (inverse(b greatest_lower_bound a) least_upper_bound X) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 1824
% Current number of ordered equations: 0
% Current number of rules: 325
% New rule produced :
% [370]
% b greatest_lower_bound a greatest_lower_bound inverse(b greatest_lower_bound a)
% -> b greatest_lower_bound a
% Current number of equations to process: 1864
% Current number of ordered equations: 0
% Current number of rules: 326
% New rule produced :
% [371]
% inverse(X greatest_lower_bound Y) greatest_lower_bound inverse(X) ->
% inverse(X)
% Current number of equations to process: 2026
% Current number of ordered equations: 0
% Current number of rules: 327
% Rule [360]
% (identity greatest_lower_bound X) least_upper_bound inverse(identity greatest_lower_bound X)
% -> identity least_upper_bound inverse(identity greatest_lower_bound X) is composed into 
% [360]
% (identity greatest_lower_bound X) least_upper_bound inverse(identity greatest_lower_bound X)
% -> inverse(identity greatest_lower_bound X)
% New rule produced :
% [372]
% identity least_upper_bound inverse(identity greatest_lower_bound X) ->
% inverse(identity greatest_lower_bound X)
% Current number of equations to process: 2167
% Current number of ordered equations: 0
% Current number of rules: 328
% New rule produced :
% [373]
% inverse(inverse(X) greatest_lower_bound Y) least_upper_bound X ->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 2324
% Current number of ordered equations: 0
% Current number of rules: 329
% New rule produced :
% [374]
% (identity greatest_lower_bound X) least_upper_bound inverse(b greatest_lower_bound a)
% -> inverse(b greatest_lower_bound a)
% Current number of equations to process: 2729
% Current number of ordered equations: 0
% Current number of rules: 330
% New rule produced :
% [375]
% (inverse(X greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound 
% inverse(X) -> inverse(X)
% Current number of equations to process: 2728
% Current number of ordered equations: 0
% Current number of rules: 331
% New rule produced :
% [376]
% (a greatest_lower_bound inverse(b least_upper_bound X)) least_upper_bound identity
% -> identity
% Current number of equations to process: 3461
% Current number of ordered equations: 0
% Current number of rules: 332
% New rule produced :
% [377]
% identity greatest_lower_bound inverse(a greatest_lower_bound inverse(b) greatest_lower_bound X)
% -> identity
% Current number of equations to process: 3460
% Current number of ordered equations: 0
% Current number of rules: 333
% New rule produced :
% [378]
% identity greatest_lower_bound inverse(b greatest_lower_bound a greatest_lower_bound X)
% -> identity
% Current number of equations to process: 3515
% Current number of ordered equations: 0
% Current number of rules: 334
% New rule produced :
% [379]
% (b greatest_lower_bound inverse(a least_upper_bound X)) least_upper_bound identity
% -> identity
% Current number of equations to process: 3552
% Current number of ordered equations: 0
% Current number of rules: 335
% New rule produced :
% [380]
% b greatest_lower_bound multiply(inverse(b greatest_lower_bound a),b) -> b
% Current number of equations to process: 3623
% Current number of ordered equations: 0
% Current number of rules: 336
% New rule produced :
% [381]
% a greatest_lower_bound multiply(inverse(b greatest_lower_bound a),a) -> a
% Current number of equations to process: 3630
% Current number of ordered equations: 0
% Current number of rules: 337
% New rule produced :
% [382]
% b greatest_lower_bound multiply(b,inverse(b greatest_lower_bound a)) -> b
% Current number of equations to process: 3637
% Current number of ordered equations: 0
% Current number of rules: 338
% New rule produced :
% [383]
% identity greatest_lower_bound inverse(b greatest_lower_bound inverse(a) greatest_lower_bound X)
% -> identity
% Current number of equations to process: 3644
% Current number of ordered equations: 0
% Current number of rules: 339
% New rule produced :
% [384]
% (inverse(a least_upper_bound X) greatest_lower_bound inverse(b)) least_upper_bound identity
% -> identity
% Current number of equations to process: 3642
% Current number of ordered equations: 1
% Current number of rules: 340
% New rule produced :
% [385]
% (inverse(b least_upper_bound X) greatest_lower_bound inverse(a)) least_upper_bound identity
% -> identity
% Current number of equations to process: 3642
% Current number of ordered equations: 0
% Current number of rules: 341
% New rule produced :
% [386]
% inverse(identity greatest_lower_bound multiply(a,b)) greatest_lower_bound 
% inverse(a) -> inverse(a)
% Current number of equations to process: 3957
% Current number of ordered equations: 0
% Current number of rules: 342
% New rule produced :
% [387]
% inverse(identity greatest_lower_bound multiply(b,a)) greatest_lower_bound 
% inverse(a) -> inverse(a)
% Current number of equations to process: 3956
% Current number of ordered equations: 0
% Current number of rules: 343
% New rule produced :
% [388]
% inverse(identity greatest_lower_bound multiply(b,a)) greatest_lower_bound 
% inverse(b) -> inverse(b)
% Current number of equations to process: 3955
% Current number of ordered equations: 0
% Current number of rules: 344
% New rule produced :
% [389]
% inverse(identity greatest_lower_bound multiply(a,b)) greatest_lower_bound 
% inverse(b) -> inverse(b)
% Current number of equations to process: 3954
% Current number of ordered equations: 0
% Current number of rules: 345
% New ruCputime limit exceeded (core dumped)
% 
% EOF
%------------------------------------------------------------------------------