%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP168-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n129.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 00:22:29 EDT 2014

% Result   : Timeout 300.02s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP168-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n129.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 05:55:18 CDT 2014
% % CPUTime  : 300.02 
% Processing problem /tmp/CiME_4055_n129.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " least_upper_bound,greatest_lower_bound : AC; c,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 greatest_lower_bound b = a;
% ";
% 
% let s1 = status F "
% c lr_lex;
% 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 "
% inverse > multiply > greatest_lower_bound > least_upper_bound > identity > a > b > c";
% 
% let s2 = status F "
% c mul;
% b mul;
% a mul;
% least_upper_bound mul;
% greatest_lower_bound mul;
% inverse mul;
% multiply mul;
% identity mul;
% ";
% 
% let p2 = precedence F "
% inverse > multiply > greatest_lower_bound > least_upper_bound > identity = a = b = c";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " multiply(inverse(c),multiply(a,c)) greatest_lower_bound multiply(inverse(c),multiply(b,c)) = multiply(inverse(c),multiply(a,c));"
% ;
% (*
% 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 greatest_lower_bound a = a } (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(inverse(c),multiply(b,c)) greatest_lower_bound 
% multiply(inverse(c),multiply(a,c)) =
% multiply(inverse(c),multiply(a,c)) }
% (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] b greatest_lower_bound a -> a
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 3
% New rule produced : [4] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 4
% New rule produced : [5] multiply(inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 5
% New rule produced : [6] (X greatest_lower_bound Y) least_upper_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] (X least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 7
% New rule produced :
% [8] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z))
% 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] b least_upper_bound a -> b
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [14] (a greatest_lower_bound X) least_upper_bound b -> b
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] (b least_upper_bound X) greatest_lower_bound a -> a
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17]
% (b greatest_lower_bound X) least_upper_bound (a greatest_lower_bound X) ->
% b greatest_lower_bound X
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18] multiply(X,b) greatest_lower_bound multiply(X,a) -> multiply(X,a)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19] multiply(b,X) greatest_lower_bound multiply(a,X) -> multiply(a,X)
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] multiply(inverse(identity),X) -> X
% Current number of equations to process: 96
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [21] multiply(inverse(inverse(X)),identity) -> X
% Current number of equations to process: 96
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [22] multiply(inverse(inverse(X)),Y) -> multiply(X,Y)
% Rule [21] multiply(inverse(inverse(X)),identity) -> X collapsed.
% Current number of equations to process: 96
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [23] multiply(X,identity) -> X
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [24]
% (b least_upper_bound X) greatest_lower_bound (a least_upper_bound X) ->
% a least_upper_bound X
% Current number of equations to process: 120
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [25] multiply(X,b) least_upper_bound multiply(X,a) -> multiply(X,b)
% Current number of equations to process: 119
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [26] multiply(b,X) least_upper_bound multiply(a,X) -> multiply(b,X)
% Current number of equations to process: 118
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [27] identity greatest_lower_bound multiply(inverse(a),b) -> identity
% Current number of equations to process: 127
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [28]
% identity greatest_lower_bound multiply(inverse(b),a) ->
% multiply(inverse(b),a)
% Current number of equations to process: 138
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [29] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [30] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [31] inverse(identity) -> identity
% Rule [20] multiply(inverse(identity),X) -> X collapsed.
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [32] inverse(inverse(X)) -> X
% Rule [22] multiply(inverse(inverse(X)),Y) -> multiply(X,Y) collapsed.
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [33] multiply(b,b) greatest_lower_bound multiply(a,a) -> multiply(a,a)
% Current number of equations to process: 185
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [34] identity least_upper_bound multiply(inverse(b),a) -> identity
% Current number of equations to process: 194
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [35]
% identity least_upper_bound multiply(inverse(a),b) -> multiply(inverse(a),b)
% Current number of equations to process: 204
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [36] multiply(b,b) least_upper_bound multiply(a,a) -> multiply(b,b)
% Current number of equations to process: 253
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [37]
% (multiply(inverse(a),b) least_upper_bound X) greatest_lower_bound identity ->
% identity
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [38] multiply(X,multiply(inverse(a),b)) greatest_lower_bound X -> X
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [39] multiply(inverse(a),multiply(b,X)) greatest_lower_bound X -> X
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [40]
% (multiply(inverse(b),a) greatest_lower_bound X) least_upper_bound identity ->
% identity
% Current number of equations to process: 249
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [41] identity greatest_lower_bound multiply(b,inverse(a)) -> identity
% Current number of equations to process: 267
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [42] identity least_upper_bound multiply(a,inverse(b)) -> identity
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [43]
% identity greatest_lower_bound multiply(a,inverse(b)) ->
% multiply(a,inverse(b))
% Current number of equations to process: 276
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [44]
% identity least_upper_bound multiply(b,inverse(a)) -> multiply(b,inverse(a))
% Current number of equations to process: 275
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [45] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% Current number of equations to process: 284
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [46] multiply(b,multiply(inverse(a),X)) greatest_lower_bound X -> X
% Current number of equations to process: 283
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [47] multiply(a,multiply(inverse(b),X)) least_upper_bound X -> X
% Current number of equations to process: 282
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [48] multiply(X,multiply(inverse(b),a)) least_upper_bound X -> X
% Current number of equations to process: 308
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [49] multiply(inverse(b),multiply(a,X)) least_upper_bound X -> X
% Current number of equations to process: 307
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [50] a greatest_lower_bound multiply(b,multiply(inverse(a),b)) -> a
% Current number of equations to process: 364
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [51] a greatest_lower_bound multiply(inverse(a),multiply(b,b)) -> a
% Current number of equations to process: 388
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [52] inverse(b) greatest_lower_bound inverse(a) -> inverse(b)
% Current number of equations to process: 402
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [53]
% (multiply(b,inverse(a)) least_upper_bound X) greatest_lower_bound identity ->
% identity
% Current number of equations to process: 464
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [54] multiply(X,multiply(b,inverse(a))) greatest_lower_bound X -> X
% Current number of equations to process: 463
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [55]
% (multiply(a,inverse(b)) greatest_lower_bound X) least_upper_bound identity ->
% identity
% Current number of equations to process: 462
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [56] multiply(X,multiply(a,inverse(b))) least_upper_bound X -> X
% Current number of equations to process: 461
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced : [57] multiply(Y,inverse(multiply(X,Y))) -> inverse(X)
% Rule [45] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% collapsed.
% Current number of equations to process: 502
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [58] b least_upper_bound multiply(a,multiply(inverse(b),a)) -> b
% Current number of equations to process: 585
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [59] inverse(b) least_upper_bound inverse(a) -> inverse(a)
% Current number of equations to process: 624
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [60] b least_upper_bound multiply(inverse(b),multiply(a,a)) -> b
% Current number of equations to process: 651
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [61]
% (inverse(b) greatest_lower_bound X) least_upper_bound inverse(a) ->
% inverse(a)
% Current number of equations to process: 704
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [62]
% (inverse(a) least_upper_bound X) greatest_lower_bound inverse(b) ->
% inverse(b)
% Current number of equations to process: 703
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [63] a greatest_lower_bound multiply(b,multiply(b,inverse(a))) -> a
% Current number of equations to process: 738
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced : [64] multiply(inverse(multiply(X,Y)),X) -> inverse(Y)
% Current number of equations to process: 812
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [65] inverse(multiply(Y,X)) -> multiply(inverse(X),inverse(Y))
% Rule [57] multiply(Y,inverse(multiply(X,Y))) -> inverse(X) collapsed.
% Rule [64] multiply(inverse(multiply(X,Y)),X) -> inverse(Y) collapsed.
% Current number of equations to process: 819
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [66] b least_upper_bound multiply(a,multiply(a,inverse(b))) -> b
% Current number of equations to process: 830
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [67]
% ((a least_upper_bound X) greatest_lower_bound b) least_upper_bound a ->
% (a least_upper_bound X) greatest_lower_bound b
% Current number of equations to process: 949
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [68]
% ((a least_upper_bound X) greatest_lower_bound b) least_upper_bound X ->
% a least_upper_bound X
% Current number of equations to process: 964
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [69]
% ((b greatest_lower_bound X) least_upper_bound a) greatest_lower_bound b ->
% (b greatest_lower_bound X) least_upper_bound a
% Current number of equations to process: 1074
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [70]
% ((b greatest_lower_bound X) least_upper_bound a) greatest_lower_bound X ->
% b greatest_lower_bound X
% Current number of equations to process: 1087
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [71]
% (((a least_upper_bound X) greatest_lower_bound b) least_upper_bound Y) greatest_lower_bound a
% -> a
% Current number of equations to process: 1195
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [72]
% (((b greatest_lower_bound X) least_upper_bound a) greatest_lower_bound Y) least_upper_bound b
% -> b
% Current number of equations to process: 1214
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [73]
% (identity greatest_lower_bound X) least_upper_bound multiply(inverse(a),b) ->
% multiply(inverse(a),b)
% Current number of equations to process: 1233
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [74]
% (identity least_upper_bound X) greatest_lower_bound multiply(inverse(b),a) ->
% multiply(inverse(b),a)
% Current number of equations to process: 1256
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [75]
% (identity greatest_lower_bound X) least_upper_bound multiply(b,inverse(a)) ->
% multiply(b,inverse(a))
% Current number of equations to process: 1278
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [76]
% (identity least_upper_bound X) greatest_lower_bound multiply(a,inverse(b)) ->
% multiply(a,inverse(b))
% Current number of equations to process: 1301
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [77]
% (b greatest_lower_bound X) least_upper_bound (a greatest_lower_bound X greatest_lower_bound Y)
% -> b greatest_lower_bound X
% Current number of equations to process: 1320
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [78]
% ((b greatest_lower_bound X) least_upper_bound Y) greatest_lower_bound a greatest_lower_bound X
% -> a greatest_lower_bound X
% Current number of equations to process: 1536
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [79]
% ((a least_upper_bound X) greatest_lower_bound Y) least_upper_bound b least_upper_bound X
% -> b least_upper_bound X
% Current number of equations to process: 1735
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [80]
% (b least_upper_bound X least_upper_bound Y) greatest_lower_bound (a least_upper_bound Y)
% -> a least_upper_bound Y
% Current number of equations to process: 1923
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [81]
% (multiply(X,b) least_upper_bound Y) greatest_lower_bound multiply(X,a) ->
% multiply(X,a)
% Current number of equations to process: 2153
% Current number of ordered equations: 1
% Current number of rules: 75
% New rule produced :
% [82]
% (multiply(a,X) greatest_lower_bound Y) least_upper_bound multiply(b,X) ->
% multiply(b,X)
% Current number of equations to process: 2194
% Current number of ordered equations: 1
% Current number of rules: 76
% New rule produced :
% [83]
% (multiply(b,X) least_upper_bound Y) greatest_lower_bound multiply(a,X) ->
% multiply(a,X)
% Current number of equations to process: 2239
% Current number of ordered equations: 1
% Current number of rules: 77
% New rule produced :
% [84]
% (multiply(X,a) greatest_lower_bound Y) least_upper_bound multiply(X,b) ->
% multiply(X,b)
% Current number of equations to process: 2277
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [85]
% (multiply(a,a) greatest_lower_bound X) least_upper_bound multiply(b,b) ->
% multiply(b,b)
% Current number of equations to process: 2308
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [86]
% (multiply(b,b) least_upper_bound X) greatest_lower_bound multiply(a,a) ->
% multiply(a,a)
% Current number of equations to process: 2340
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [87]
% (multiply(X,multiply(inverse(a),b)) least_upper_bound Y) greatest_lower_bound X
% -> X
% Current number of equations to process: 2365
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [88]
% (multiply(inverse(a),multiply(b,X)) least_upper_bound Y) greatest_lower_bound X
% -> X
% Current number of equations to process: 2417
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [89]
% (multiply(b,multiply(inverse(a),X)) least_upper_bound Y) greatest_lower_bound X
% -> X
% Current number of equations to process: 2500
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [90]
% (multiply(a,multiply(inverse(b),X)) greatest_lower_bound Y) least_upper_bound X
% -> X
% Current number of equations to process: 2570
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [91]
% (multiply(X,multiply(inverse(b),a)) greatest_lower_bound Y) least_upper_bound X
% -> X
% Current number of equations to process: 2641
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [92]
% (multiply(inverse(b),multiply(a,X)) greatest_lower_bound Y) least_upper_bound X
% -> X
% Current number of equations to process: 2687
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [93]
% (multiply(b,multiply(inverse(a),b)) least_upper_bound X) greatest_lower_bound a
% -> a
% Current number of equations to process: 2772
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [94]
% (multiply(inverse(a),multiply(b,b)) least_upper_bound X) greatest_lower_bound a
% -> a
% Current number of equations to process: 2787
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [95]
% (multiply(X,multiply(b,inverse(a))) least_upper_bound Y) greatest_lower_bound X
% -> X
% Current number of equations to process: 2802
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [96]
% (multiply(X,multiply(a,inverse(b))) greatest_lower_bound Y) least_upper_bound X
% -> X
% Current number of equations to process: 2866
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [97]
% (multiply(a,multiply(inverse(b),a)) greatest_lower_bound X) least_upper_bound b
% -> b
% Current number of equations to process: 2930
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [98]
% (multiply(inverse(b),multiply(a,a)) greatest_lower_bound X) least_upper_bound b
% -> b
% Current number of equations to process: 2945
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [99]
% (multiply(b,multiply(b,inverse(a))) least_upper_bound X) greatest_lower_bound a
% -> a
% Current number of equations to process: 2960
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [100]
% (multiply(a,multiply(a,inverse(b))) greatest_lower_bound X) least_upper_bound b
% -> b
% Current number of equations to process: 2975
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [101]
% (((X greatest_lower_bound Y) least_upper_bound a) greatest_lower_bound b) least_upper_bound X
% -> a least_upper_bound X
% Current number of equations to process: 2990
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [102]
% (((X least_upper_bound Y) greatest_lower_bound b) least_upper_bound a) greatest_lower_bound X
% -> b greatest_lower_bound X
% Current number of equations to process: 3399
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [103]
% multiply(X,multiply(inverse(b),a)) greatest_lower_bound X ->
% multiply(X,multiply(inverse(b),a))
% Current number of equations to process: 3820
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [104]
% multiply(inverse(b),multiply(a,X)) greatest_lower_bound X ->
% multiply(inverse(b),multiply(a,X))
% Current number of equations to process: 3922
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [105]
% multiply(inverse(b),a) greatest_lower_bound multiply(inverse(a),b) ->
% multiply(inverse(b),a)
% Current number of equations to process: 4102
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [106]
% multiply(a,multiply(inverse(b),X)) greatest_lower_bound X ->
% multiply(a,multiply(inverse(b),X))
% Current number of equations to process: 4155
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [107]
% multiply(b,multiply(inverse(a),X)) least_upper_bound X ->
% multiply(b,multiply(inverse(a),X))
% Current number of equations to process: 4326
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [108]
% multiply(X,multiply(inverse(a),b)) least_upper_bound X ->
% multiply(X,multiply(inverse(a),b))
% Current number of equations to process: 4494
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [109]
% multiply(inverse(a),multiply(b,X)) least_upper_bound X ->
% multiply(inverse(a),multiply(b,X))
% Current number of equations to process: 4591
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [110]
% multiply(inverse(b),a) least_upper_bound multiply(inverse(a),b) ->
% multiply(inverse(a),b)
% Current number of equations to process: 4775
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [111]
% multiply(inverse(b),X) greatest_lower_bound multiply(inverse(a),X) ->
% multiply(inverse(b),X)
% Current number of equations to process: 4828
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [112]
% multiply(b,inverse(a)) greatest_lower_bound multiply(inverse(b),a) ->
% multiply(inverse(b),a)
% Current number of equations to process: 4892
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [113]
% multiply(a,inverse(b)) least_upper_bound multiply(inverse(a),b) ->
% multiply(inverse(a),b)
% Current number of equations to process: 4949
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [114]
% multiply(X,multiply(a,inverse(b))) greatest_lower_bound X ->
% multiply(X,multiply(a,inverse(b)))
% Current number of equations to process: 2189
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [115]
% multiply(a,inverse(b)) greatest_lower_bound multiply(inverse(a),b) ->
% multiply(a,inverse(b))
% Current number of equations to process: 2300
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [116]
% multiply(b,inverse(a)) greatest_lower_bound multiply(a,inverse(b)) ->
% multiply(a,inverse(b))
% Current number of equations to process: 2355
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [117]
% multiply(X,multiply(b,inverse(a))) least_upper_bound X ->
% multiply(X,multiply(b,inverse(a)))
% Current number of equations to process: 2412
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [118]
% multiply(b,inverse(a)) least_upper_bound multiply(inverse(b),a) ->
% multiply(b,inverse(a))
% Current number of equations to process: 2523
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [119]
% multiply(b,inverse(a)) least_upper_bound multiply(a,inverse(b)) ->
% multiply(b,inverse(a))
% Current number of equations to process: 2578
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [120]
% multiply(inverse(b),X) least_upper_bound multiply(inverse(a),X) ->
% multiply(inverse(a),X)
% Current number of equations to process: 2629
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [121]
% a least_upper_bound multiply(b,multiply(inverse(a),b)) ->
% multiply(b,multiply(inverse(a),b))
% Current number of equations to process: 2691
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [122]
% a least_upper_bound multiply(inverse(a),multiply(b,b)) ->
% multiply(inverse(a),multiply(b,b))
% Current number of equations to process: 2722
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [123]
% (inverse(b) greatest_lower_bound X) least_upper_bound (inverse(a) greatest_lower_bound X)
% -> inverse(a) greatest_lower_bound X
% Current number of equations to process: 2752
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [124]
% multiply(X,inverse(b)) greatest_lower_bound multiply(X,inverse(a)) ->
% multiply(X,inverse(b))
% Current number of equations to process: 2916
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [125]
% inverse(b) greatest_lower_bound multiply(inverse(a),multiply(inverse(a),b))
% -> inverse(b)
% Current number of equations to process: 2977
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [126]
% inverse(b) greatest_lower_bound multiply(inverse(a),multiply(b,inverse(a)))
% -> inverse(b)
% Current number of equations to process: 3038
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [127]
% inverse(b) greatest_lower_bound multiply(b,multiply(inverse(a),inverse(a)))
% -> inverse(b)
% Current number of equations to process: 3099
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [128]
% b greatest_lower_bound multiply(a,multiply(inverse(b),a)) ->
% multiply(a,multiply(inverse(b),a))
% Current number of equations to process: 3156
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [129]
% (inverse(b) least_upper_bound X) greatest_lower_bound (inverse(a) least_upper_bound X)
% -> inverse(b) least_upper_bound X
% Current number of equations to process: 3191
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [130]
% multiply(X,inverse(b)) least_upper_bound multiply(X,inverse(a)) ->
% multiply(X,inverse(a))
% Current number of equations to process: 3352
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [131]
% inverse(a) least_upper_bound multiply(a,multiply(inverse(b),inverse(b))) ->
% inverse(a)
% Current number of equations to process: 3411
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [132]
% inverse(a) least_upper_bound multiply(inverse(b),multiply(inverse(b),a)) ->
% inverse(a)
% Current number of equations to process: 3470
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [133]
% inverse(a) least_upper_bound multiply(inverse(b),multiply(a,inverse(b))) ->
% inverse(a)
% Current number of equations to process: 3529
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [134]
% b greatest_lower_bound multiply(inverse(b),multiply(a,a)) ->
% multiply(inverse(b),multiply(a,a))
% Current number of equations to process: 3588
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [135]
% a least_upper_bound multiply(b,multiply(b,inverse(a))) ->
% multiply(b,multiply(b,inverse(a)))
% Current number of equations to process: 3623
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [136]
% b greatest_lower_bound multiply(a,multiply(a,inverse(b))) ->
% multiply(a,multiply(a,inverse(b)))
% Current number of equations to process: 3654
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [137]
% ((a least_upper_bound inverse(b)) greatest_lower_bound b) least_upper_bound 
% inverse(a) -> a least_upper_bound inverse(a)
% Current number of equations to process: 3688
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [138]
% ((b greatest_lower_bound inverse(a)) least_upper_bound a) greatest_lower_bound 
% inverse(b) -> b greatest_lower_bound inverse(b)
% Current number of equations to process: 3720
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [139]
% (b greatest_lower_bound inverse(a)) least_upper_bound (a greatest_lower_bound 
% inverse(b)) ->
% b greatest_lower_bound inverse(a)
% Current number of equations to process: 3746
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [140]
% (b least_upper_bound inverse(a)) greatest_lower_bound (a least_upper_bound 
% inverse(b)) ->
% a least_upper_bound inverse(b)
% Current number of equations to process: 3771
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [141]
% ((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: 3760
% Current number of ordered equations: 1
% Current number of rules: 135
% New rule produced :
% [142]
% ((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: 3760
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [143]
% ((b least_upper_bound Y) greatest_lower_bound (a least_upper_bound X)) least_upper_bound X
% -> a least_upper_bound X
% Current number of equations to process: 4326
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [144]
% ((b greatest_lower_bound X) least_upper_bound (a greatest_lower_bound Y)) greatest_lower_bound X
% -> b greatest_lower_bound X
% Current number of equations to process: 2051
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [145]
% ((a greatest_lower_bound X) least_upper_bound Y) greatest_lower_bound 
% (b least_upper_bound Y) -> (a greatest_lower_bound X) least_upper_bound Y
% Current number of equations to process: 3713
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [146]
% ((b least_upper_bound X) greatest_lower_bound Y) least_upper_bound (a greatest_lower_bound Y)
% -> (b least_upper_bound X) greatest_lower_bound Y
% Current number of equations to process: 3860
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [147]
% (identity greatest_lower_bound X) least_upper_bound (multiply(inverse(b),a) greatest_lower_bound X)
% -> identity greatest_lower_bound X
% Current number of equations to process: 4004
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [148]
% (identity least_upper_bound X) greatest_lower_bound (multiply(inverse(a),b) least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 4203
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [149]
% identity greatest_lower_bound multiply(inverse(a),multiply(b,multiply(
% inverse(a),b)))
% -> identity
% Current number of equations to process: 4403
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [150]
% identity greatest_lower_bound multiply(inverse(a),multiply(b,multiply(b,
% inverse(a)))) ->
% identity
% Current number of equations to process: 4488
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [151]
% (identity greatest_lower_bound X) least_upper_bound (multiply(a,inverse(b)) greatest_lower_bound X)
% -> identity greatest_lower_bound X
% Current number of equations to process: 4573
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [152]
% (identity least_upper_bound X) greatest_lower_bound (multiply(b,inverse(a)) least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 4778
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [153]
% identity greatest_lower_bound multiply(b,multiply(inverse(a),multiply(
% inverse(a),b)))
% -> identity
% Current number of equations to process: 4980
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [154]
% identity greatest_lower_bound multiply(b,multiply(inverse(a),multiply(b,
% inverse(a)))) ->
% identity
% Current number of equations to process: 1773
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [155]
% identity least_upper_bound multiply(a,multiply(inverse(b),multiply(inverse(b),a)))
% -> identity
% Current number of equations to process: 1861
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [156]
% identity least_upper_bound multiply(a,multiply(inverse(b),multiply(a,
% inverse(b)))) ->
% identity
% Current number of equations to process: 1949
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [157]
% identity least_upper_bound multiply(inverse(b),multiply(a,multiply(inverse(b),a)))
% -> identity
% Current number of equations to process: 2037
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [158]
% identity least_upper_bound multiply(inverse(b),multiply(a,multiply(a,
% inverse(b)))) ->
% identity
% Current number of equations to process: 2126
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [159]
% 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: 2213
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [160]
% inverse(identity least_upper_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X least_upper_bound Y),X)
% Current number of equations to process: 2214
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [161]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(inverse(identity least_upper_bound Y),inverse(X))
% Current number of equations to process: 2223
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [162]
% inverse(identity least_upper_bound multiply(X,Y)) <->
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X))
% Current number of equations to process: 2222
% Current number of ordered equations: 1
% Current number of rules: 156
% New rule produced :
% [163]
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X)) <->
% inverse(identity least_upper_bound multiply(X,Y))
% Current number of equations to process: 2222
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [164]
% inverse(identity least_upper_bound inverse(X)) ->
% multiply(inverse(identity least_upper_bound X),X)
% Current number of equations to process: 2225
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [165]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(inverse(identity least_upper_bound multiply(X,Y)),X)
% Rule
% [164]
% inverse(identity least_upper_bound inverse(X)) ->
% multiply(inverse(identity least_upper_bound X),X) collapsed.
% Current number of equations to process: 2236
% Current number of ordered equations: 1
% Current number of rules: 158
% New rule produced :
% [166]
% multiply(inverse(identity least_upper_bound multiply(X,Y)),X) <->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 2236
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [167]
% 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: 2368
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [168]
% inverse(identity greatest_lower_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X greatest_lower_bound Y),X)
% Current number of equations to process: 2371
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [169]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(inverse(identity greatest_lower_bound Y),inverse(X))
% Current number of equations to process: 2380
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [170]
% inverse(identity greatest_lower_bound multiply(X,Y)) <->
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X))
% Current number of equations to process: 2379
% Current number of ordered equations: 1
% Current number of rules: 163
% New rule produced :
% [171]
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y))
% Current number of equations to process: 2379
% Current number of ordered equations: 0
% Current number of rules: 164
% New rule produced :
% [172]
% inverse(identity greatest_lower_bound inverse(X)) ->
% multiply(inverse(identity greatest_lower_bound X),X)
% Current number of equations to process: 2387
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [173]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X)
% Rule
% [172]
% inverse(identity greatest_lower_bound inverse(X)) ->
% multiply(inverse(identity greatest_lower_bound X),X) collapsed.
% Current number of equations to process: 2408
% Current number of ordered equations: 1
% Current number of rules: 165
% New rule produced :
% [174]
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X) <->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 2408
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [175]
% 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: 2566
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced :
% [176]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),inverse(identity least_upper_bound X))
% Current number of equations to process: 2573
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced :
% [177]
% inverse(identity least_upper_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X least_upper_bound Y))
% Current number of equations to process: 2581
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced :
% [178]
% inverse(identity least_upper_bound multiply(X,Y)) <->
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X))
% Current number of equations to process: 2580
% Current number of ordered equations: 1
% Current number of rules: 170
% New rule produced :
% [179]
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X)) <->
% inverse(identity least_upper_bound multiply(X,Y))
% Current number of equations to process: 2580
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [180]
% multiply(inverse(identity least_upper_bound X),X) ->
% multiply(X,inverse(identity least_upper_bound X))
% Current number of equations to process: 2601
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [181]
% multiply(inverse(identity least_upper_bound X),inverse(X)) ->
% multiply(inverse(X),inverse(identity least_upper_bound X))
% Current number of equations to process: 2605
% Current number of ordered equations: 0
% Current number of rules: 173
% New rule produced :
% [182]
% multiply(inverse(inverse(X) least_upper_bound Y),Y) <->
% multiply(X,inverse(inverse(Y) least_upper_bound X))
% Current number of equations to process: 2626
% Current number of ordered equations: 1
% Current number of rules: 174
% New rule produced :
% [183]
% multiply(X,inverse(inverse(Y) least_upper_bound X)) <->
% multiply(inverse(inverse(X) least_upper_bound Y),Y)
% Current number of equations to process: 2626
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced :
% [184]
% inverse(inverse(X) least_upper_bound inverse(Y)) ->
% multiply(X,multiply(inverse(X least_upper_bound Y),Y))
% Current number of equations to process: 2646
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced :
% [185]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(X,inverse(identity least_upper_bound multiply(Y,X)))
% Current number of equations to process: 2671
% Current number of ordered equations: 1
% Current number of rules: 177
% New rule produced :
% [186]
% multiply(X,inverse(identity least_upper_bound multiply(Y,X))) <->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 2671
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [187]
% 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: 3183
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [188]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),inverse(identity greatest_lower_bound X))
% Current number of equations to process: 3190
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [189]
% inverse(identity greatest_lower_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X greatest_lower_bound Y))
% Current number of equations to process: 3198
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [190]
% inverse(identity greatest_lower_bound multiply(X,Y)) <->
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X))
% Current number of equations to process: 3197
% Current number of ordered equations: 1
% Current number of rules: 182
% New rule produced :
% [191]
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y))
% Current number of equations to process: 3197
% Current number of ordered equations: 0
% Current number of rules: 183
% New rule produced :
% [192]
% multiply(inverse(identity greatest_lower_bound X),X) ->
% multiply(X,inverse(identity greatest_lower_bound X))
% Current number of equations to process: 3232
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [193]
% multiply(inverse(identity greatest_lower_bound X),inverse(X)) ->
% multiply(inverse(X),inverse(identity greatest_lower_bound X))
% Current number of equations to process: 3238
% Current number of ordered equations: 0
% Current number of rules: 185
% New rule produced :
% [194]
% multiply(X,inverse(inverse(Y) greatest_lower_bound X)) <->
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y)
% Current number of equations to process: 3275
% Current number of ordered equations: 1
% Current number of rules: 186
% New rule produced :
% [195]
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y) <->
% multiply(X,inverse(inverse(Y) greatest_lower_bound X))
% Current number of equations to process: 3275
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [196]
% inverse(inverse(X) greatest_lower_bound inverse(Y)) ->
% multiply(X,multiply(inverse(X greatest_lower_bound Y),Y))
% Current number of equations to process: 3303
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [197]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(X,inverse(identity greatest_lower_bound multiply(Y,X)))
% Current number of equations to process: 3337
% Current number of ordered equations: 1
% Current number of rules: 189
% New rule produced :
% [198]
% multiply(X,inverse(identity greatest_lower_bound multiply(Y,X))) <->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 3337
% Current number of ordered equations: 0
% Current number of rules: 190
% New rule produced :
% [199]
% ((a least_upper_bound X) greatest_lower_bound b) least_upper_bound (a greatest_lower_bound Y)
% -> (a least_upper_bound X) greatest_lower_bound b
% Current number of equations to process: 3925
% Current number of ordered equations: 0
% Current number of rules: 191
% New rule produced :
% [200]
% ((a least_upper_bound multiply(inverse(b),a)) greatest_lower_bound b) least_upper_bound identity
% -> a least_upper_bound identity
% Current number of equations to process: 3992
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced :
% [201]
% ((a least_upper_bound multiply(a,inverse(b))) greatest_lower_bound b) least_upper_bound identity
% -> a least_upper_bound identity
% Current number of equations to process: 4063
% Current number of ordered equations: 0
% Current number of rules: 193
% New rule produced :
% [202]
% ((b greatest_lower_bound X) least_upper_bound a) greatest_lower_bound 
% (b least_upper_bound Y) -> (b greatest_lower_bound X) least_upper_bound a
% Current number of equations to process: 4133
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [203]
% ((b greatest_lower_bound multiply(inverse(a),b)) least_upper_bound a) greatest_lower_bound identity
% -> b greatest_lower_bound identity
% Current number of equations to process: 4198
% Current number of ordered equations: 0
% Current number of rules: 195
% New rule produced :
% [204]
% ((b greatest_lower_bound multiply(b,inverse(a))) least_upper_bound a) greatest_lower_bound identity
% -> b greatest_lower_bound identity
% Current number of equations to process: 4270
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [205]
% ((X least_upper_bound Y) greatest_lower_bound b) least_upper_bound (a greatest_lower_bound X)
% -> (X least_upper_bound Y) greatest_lower_bound b
% Current number of equations to process: 4341
% Current number of ordered equations: 0
% Current number of rules: 197
% New rule produced :
% [206]
% (b greatest_lower_bound identity) least_upper_bound (a greatest_lower_bound 
% multiply(inverse(b),a))
% -> b greatest_lower_bound identity
% Current number of equations to process: 4877
% Current number of ordered equations: 0
% Current number of rules: 198
% New rule produced :
% [207]
% (b greatest_lower_bound identity) least_upper_bound (a greatest_lower_bound 
% multiply(a,inverse(b)))
% -> b greatest_lower_bound identity
% Current number of equations to process: 4941
% Current number of ordered equations: 0
% Current number of rules: 199
% New rule produced :
% [208]
% (b least_upper_bound multiply(b,inverse(a))) greatest_lower_bound (a least_upper_bound identity)
% -> a least_upper_bound identity
% Current number of equations to process: 1209
% Current number of ordered equations: 0
% Current number of rules: 200
% New rule produced :
% [209]
% ((X greatest_lower_bound Y) least_upper_bound a) greatest_lower_bound 
% (b least_upper_bound X) -> (X greatest_lower_bound Y) least_upper_bound a
% Current number of equations to process: 1262
% Current number of ordered equations: 0
% Current number of rules: 201
% New rule produced :
% [210]
% (b least_upper_bound multiply(inverse(a),b)) greatest_lower_bound (a least_upper_bound identity)
% -> a least_upper_bound identity
% Current number of equations to process: 1800
% Current number of ordered equations: 0
% Current number of rules: 202
% New rule produced :
% [211]
% (((b least_upper_bound X) greatest_lower_bound (a least_upper_bound Y)) least_upper_bound Z) greatest_lower_bound a
% -> a
% Current number of equations to process: 1844
% Current number of ordered equations: 0
% Current number of rules: 203
% New rule produced :
% [212]
% (((b greatest_lower_bound X) least_upper_bound (a greatest_lower_bound Y)) greatest_lower_bound Z) least_upper_bound b
% -> b
% Current number of equations to process: 1941
% Current number of ordered equations: 0
% Current number of rules: 204
% New rule produced :
% [213]
% inverse(multiply(inverse(X),Y) least_upper_bound Z) <->
% multiply(inverse(multiply(X,Z) least_upper_bound Y),X)
% Rule
% [160]
% inverse(identity least_upper_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X least_upper_bound Y),X) collapsed.
% Current number of equations to process: 2040
% Current number of ordered equations: 1
% Current number of rules: 204
% New rule produced :
% [214]
% 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: 2040
% Current number of ordered equations: 0
% Current number of rules: 205
% New rule produced :
% [215]
% inverse(identity least_upper_bound X) least_upper_bound multiply(X,inverse(
% identity least_upper_bound X))
% -> identity
% Current number of equations to process: 2246
% Current number of ordered equations: 0
% Current number of rules: 206
% New rule produced :
% [216]
% identity least_upper_bound inverse(multiply(b,inverse(a)) least_upper_bound X)
% -> identity
% Current number of equations to process: 2248
% Current number of ordered equations: 0
% Current number of rules: 207
% New rule produced :
% [217]
% identity least_upper_bound inverse(identity least_upper_bound X) -> identity
% Current number of equations to process: 2254
% Current number of ordered equations: 0
% Current number of rules: 208
% New rule produced :
% [218]
% identity greatest_lower_bound inverse(identity least_upper_bound X) ->
% inverse(identity least_upper_bound X)
% Current number of equations to process: 2279
% Current number of ordered equations: 0
% Current number of rules: 209
% New rule produced :
% [219]
% identity least_upper_bound multiply(X,inverse(identity least_upper_bound X))
% -> identity
% Current number of equations to process: 2278
% Current number of ordered equations: 0
% Current number of rules: 210
% New rule produced :
% [220]
% (inverse(identity least_upper_bound X) greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Current number of equations to process: 2277
% Current number of ordered equations: 0
% Current number of rules: 211
% New rule produced :
% [221]
% (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: 2276
% Current number of ordered equations: 0
% Current number of rules: 212
% New rule produced :
% [222]
% identity least_upper_bound multiply(a,inverse(b least_upper_bound identity))
% -> identity
% Current number of equations to process: 2288
% Current number of ordered equations: 0
% Current number of rules: 213
% New rule produced :
% [223]
% (multiply(X,inverse(identity least_upper_bound X)) greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Current number of equations to process: 2305
% Current number of ordered equations: 0
% Current number of rules: 214
% New rule produced :
% [224]
% (multiply(a,inverse(b least_upper_bound identity)) greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 2330
% Current number of ordered equations: 0
% Current number of rules: 215
% New rule produced :
% [225]
% 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: 2368
% Current number of ordered equations: 0
% Current number of rules: 216
% New rule produced :
% [226]
% identity greatest_lower_bound multiply(a,inverse(b least_upper_bound identity))
% -> multiply(a,inverse(b least_upper_bound identity))
% Current number of equations to process: 2367
% Current number of ordered equations: 0
% Current number of rules: 217
% New rule produced :
% [227]
% identity least_upper_bound multiply(a,inverse(b least_upper_bound X)) ->
% identity
% Rule
% [222]
% identity least_upper_bound multiply(a,inverse(b least_upper_bound identity))
% -> identity collapsed.
% Current number of equations to process: 2558
% Current number of ordered equations: 0
% Current number of rules: 217
% New rule produced :
% [228]
% multiply(X,inverse(identity least_upper_bound Y)) least_upper_bound X -> X
% Current number of equations to process: 2644
% Current number of ordered equations: 0
% Current number of rules: 218
% New rule produced :
% [229]
% multiply(inverse(identity least_upper_bound Y),X) least_upper_bound X -> X
% Current number of equations to process: 2643
% Current number of ordered equations: 0
% Current number of rules: 219
% New rule produced :
% [230]
% identity least_upper_bound multiply(X,inverse(X least_upper_bound Y)) ->
% identity
% Rule
% [219]
% identity least_upper_bound multiply(X,inverse(identity least_upper_bound X))
% -> identity collapsed.
% Current number of equations to process: 2677
% Current number of ordered equations: 0
% Current number of rules: 219
% New rule produced :
% [231]
% identity least_upper_bound multiply(inverse(X least_upper_bound Y),X) ->
% identity
% Current number of equations to process: 2692
% Current number of ordered equations: 0
% Current number of rules: 220
% New rule produced :
% [232]
% identity least_upper_bound inverse(multiply(inverse(a),b) least_upper_bound X)
% -> identity
% Current number of equations to process: 2694
% Current number of ordered equations: 0
% Current number of rules: 221
% New rule produced :
% [233]
% identity least_upper_bound multiply(inverse(inverse(a) least_upper_bound X),
% inverse(b)) -> identity
% Current number of equations to process: 2944
% Current number of ordered equations: 0
% Current number of rules: 222
% New rule produced :
% [234]
% (multiply(X,inverse(X least_upper_bound Y)) greatest_lower_bound Z) least_upper_bound identity
% -> identity
% Rule
% [223]
% (multiply(X,inverse(identity least_upper_bound X)) greatest_lower_bound Y) least_upper_bound identity
% -> identity collapsed.
% Current number of equations to process: 2942
% Current number of ordered equations: 0
% Current number of rules: 222
% New rule produced :
% [235]
% (multiply(inverse(X least_upper_bound Y),X) greatest_lower_bound Z) least_upper_bound identity
% -> identity
% Current number of equations to process: 2941
% Current number of ordered equations: 0
% Current number of rules: 223
% New rule produced :
% [236]
% inverse(identity least_upper_bound X) least_upper_bound multiply(b,inverse(a))
% -> multiply(b,inverse(a))
% Current number of equations to process: 3148
% Current number of ordered equations: 0
% Current number of rules: 224
% New rule produced :
% [237]
% inverse(identity least_upper_bound X) least_upper_bound multiply(inverse(a),b)
% -> multiply(inverse(a),b)
% Current number of equations to process: 3147
% Current number of ordered equations: 0
% Current number of rules: 225
% New rule produced :
% [238]
% 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: 3146
% Current number of ordered equations: 0
% Current number of rules: 226
% New rule produced :
% [239]
% 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: 3145
% Current number of ordered equations: 0
% Current number of rules: 227
% New rule produced :
% [240]
% inverse(identity least_upper_bound X) greatest_lower_bound multiply(inverse(a),b)
% -> inverse(identity least_upper_bound X)
% Current number of equations to process: 3144
% Current number of ordered equations: 0
% Current number of rules: 228
% New rule produced :
% [241]
% inverse(identity least_upper_bound X) greatest_lower_bound multiply(b,
% inverse(a)) ->
% inverse(identity least_upper_bound X)
% Current number of equations to process: 3143
% Current number of ordered equations: 0
% Current number of rules: 229
% New rule produced :
% [242]
% identity greatest_lower_bound multiply(X,inverse(X least_upper_bound Y)) ->
% multiply(X,inverse(X least_upper_bound Y))
% Rule
% [225]
% 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: 3140
% Current number of ordered equations: 0
% Current number of rules: 229
% New rule produced :
% [243]
% 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: 3139
% Current number of ordered equations: 0
% Current number of rules: 230
% New rule produced :
% [244]
% b greatest_lower_bound multiply(a,inverse(b least_upper_bound identity)) ->
% multiply(a,inverse(b least_upper_bound identity))
% Current number of equations to process: 3203
% Current number of ordered equations: 0
% Current number of rules: 231
% New rule produced :
% [245]
% b least_upper_bound multiply(a,inverse(identity least_upper_bound X)) -> b
% Current number of equations to process: 3412
% Current number of ordered equations: 0
% Current number of rules: 232
% New rule produced :
% [246] inverse(inverse(X) least_upper_bound Y) least_upper_bound X -> X
% Current number of equations to process: 3533
% Current number of ordered equations: 0
% Current number of rules: 233
% New rule produced :
% [247]
% inverse(identity least_upper_bound X) least_upper_bound X ->
% identity least_upper_bound X
% Current number of equations to process: 3554
% Current number of ordered equations: 0
% Current number of rules: 234
% New rule produced :
% [248]
% b least_upper_bound multiply(inverse(identity least_upper_bound X),a) -> b
% Current number of equations to process: 3615
% Current number of ordered equations: 0
% Current number of rules: 235
% New rule produced :
% [249]
% identity least_upper_bound multiply(inverse(b least_upper_bound X),a) ->
% identity
% Current number of equations to process: 4054
% Current number of ordered equations: 0
% Current number of rules: 236
% New rule produced :
% [250]
% (multiply(a,inverse(b least_upper_bound X)) greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Rule
% [224]
% (multiply(a,inverse(b least_upper_bound identity)) greatest_lower_bound X) least_upper_bound identity
% -> identity collapsed.
% Current number of equations to process: 4382
% Current number of ordered equations: 0
% Current number of rules: 236
% New rule produced :
% [251]
% multiply(X,multiply(a,inverse(b least_upper_bound Y))) least_upper_bound X ->
% X
% Current number of equations to process: 4381
% Current number of ordered equations: 0
% Current number of rules: 237
% New rule produced :
% [252]
% multiply(a,multiply(inverse(b least_upper_bound Y),X)) least_upper_bound X ->
% X
% Current number of equations to process: 4380
% Current number of ordered equations: 0
% Current number of rules: 238
% New rule produced :
% [253]
% (multiply(X,inverse(identity least_upper_bound Y)) greatest_lower_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 4378
% Current number of ordered equations: 0
% Current number of rules: 239
% New rule produced :
% [254]
% (multiply(a,inverse(identity least_upper_bound X)) greatest_lower_bound Y) least_upper_bound b
% -> b
% Current number of equations to process: 4377
% Current number of ordered equations: 0
% Current number of rules: 240
% New rule produced :
% [255]
% multiply(X,multiply(Y,inverse(identity least_upper_bound Y))) least_upper_bound X
% -> X
% Current number of equations to process: 4375
% Current number of ordered equations: 0
% Current number of rules: 241
% New rule produced :
% [256]
% multiply(X,multiply(Y,inverse(Y least_upper_bound Z))) least_upper_bound X ->
% X
% Rule
% [255]
% multiply(X,multiply(Y,inverse(identity least_upper_bound Y))) least_upper_bound X
% -> X collapsed.
% Current number of equations to process: 4374
% Current number of ordered equations: 0
% Current number of rules: 241
% New rule produced :
% [257]
% multiply(X,multiply(inverse(Y least_upper_bound Z),Y)) least_upper_bound X ->
% X
% Current number of equations to process: 4372
% Current number of ordered equations: 0
% Current number of rules: 242
% New rule produced :
% [258]
% (multiply(inverse(identity least_upper_bound Y),X) greatest_lower_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 4370
% Current number of ordered equations: 0
% Current number of rules: 243
% New rule produced :
% [259]
% (multiply(inverse(identity least_upper_bound X),a) greatest_lower_bound Y) least_upper_bound b
% -> b
% Current number of equations to process: 4369
% Current number of ordered equations: 0
% Current number of rules: 244
% New rule produced :
% [260]
% multiply(X,multiply(inverse(identity least_upper_bound X),Y)) least_upper_bound Y
% -> Y
% Current number of equations to process: 4367
% Current number of ordered equations: 0
% Current number of rules: 245
% New rule produced :
% [261]
% multiply(X,multiply(inverse(X least_upper_bound Y),Z)) least_upper_bound Z ->
% Z
% Rule
% [260]
% multiply(X,multiply(inverse(identity least_upper_bound X),Y)) least_upper_bound Y
% -> Y collapsed.
% Current number of equations to process: 4366
% Current number of ordered equations: 0
% Current number of rules: 245
% New rule produced :
% [262]
% multiply(inverse(X least_upper_bound Y),multiply(X,Z)) least_upper_bound Z ->
% Z
% Current number of equations to process: 4365
% Current number of ordered equations: 0
% Current number of rules: 246
% New rule produced :
% [263]
% identity least_upper_bound multiply(a,inverse((a least_upper_bound X) greatest_lower_bound b))
% -> identity
% Current number of equations to process: 4361
% Current number of ordered equations: 1
% Current number of rules: 247
% New rule produced :
% [264]
% identity least_upper_bound multiply(inverse(b),inverse(inverse(a) least_upper_bound X))
% -> identity
% Current number of equations to process: 4360
% Current number of ordered equations: 0
% Current number of rules: 248
% New rule produced :
% [265]
% identity least_upper_bound multiply(inverse((a least_upper_bound X) greatest_lower_bound b),a)
% -> identity
% Current number of equations to process: 4357
% Current number of ordered equations: 0
% Current number of rules: 249
% New rule produced :
% [266]
% (multiply(inverse(b least_upper_bound X),a) greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Current number of equations to process: 4356
% Current number of ordered equations: 0
% Current number of rules: 250
% New rule produced :
% [267]
% identity greatest_lower_bound multiply(a,inverse(b least_upper_bound X)) ->
% multiply(a,inverse(b least_upper_bound X))
% Rule
% [226]
% identity greatest_lower_bound multiply(a,inverse(b least_upper_bound identity))
% -> multiply(a,inverse(b least_upper_bound identity)) collapsed.
% Current number of equations to process: 1188
% Current number of ordered equations: 0
% Current number of rules: 250
% New rule produced :
% [268]
% inverse(a) least_upper_bound multiply(inverse(b),inverse(identity least_upper_bound X))
% -> inverse(a)
% Current number of equations to process: 1187
% Current number of ordered equations: 0
% Current number of rules: 251
% New rule produced :
% [269]
% b greatest_lower_bound multiply(a,inverse(identity least_upper_bound X)) ->
% multiply(a,inverse(identity least_upper_bound X))
% Rule
% [244]
% b greatest_lower_bound multiply(a,inverse(b least_upper_bound identity)) ->
% multiply(a,inverse(b least_upper_bound identity)) collapsed.
% Current number of equations to process: 1186
% Current number of ordered equations: 0
% Current number of rules: 251
% New rule produced :
% [270]
% inverse(a) least_upper_bound multiply(inverse(identity least_upper_bound X),
% inverse(b)) -> inverse(a)
% Current number of equations to process: 1184
% Current number of ordered equations: 0
% Current number of rules: 252
% New rule produced :
% [271]
% b greatest_lower_bound multiply(inverse(identity least_upper_bound X),a) ->
% multiply(inverse(identity least_upper_bound X),a)
% Current number of equations to process: 1183
% Current number of ordered equations: 0
% Current number of rules: 253
% New rule produced :
% [272]
% identity greatest_lower_bound multiply(inverse(b least_upper_bound X),a) ->
% multiply(inverse(b least_upper_bound X),a)
% Current number of equations to process: 1180
% Current number of ordered equations: 0
% Current number of rules: 254
% New rule produced :
% [273] b least_upper_bound inverse(inverse(a) least_upper_bound X) -> b
% Current number of equations to process: 2870
% Current number of ordered equations: 0
% Current number of rules: 255
% New rule produced :
% [274]
% b least_upper_bound inverse(a least_upper_bound identity) ->
% b least_upper_bound identity
% Current number of equations to process: 2877
% Current number of ordered equations: 0
% Current number of rules: 256
% New rule produced :
% [275]
% inverse(X least_upper_bound Y) least_upper_bound inverse(X) -> inverse(X)
% Current number of equations to process: 3013
% Current number of ordered equations: 0
% Current number of rules: 257
% New rule produced :
% [276]
% identity least_upper_bound inverse(X) least_upper_bound X ->
% inverse(X) least_upper_bound X
% Current number of equations to process: 4222
% Current number of ordered equations: 0
% Current number of rules: 258
% New rule produced :
% [277]
% (inverse(inverse(X) least_upper_bound Y) greatest_lower_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 4220
% Current number of ordered equations: 1
% Current number of rules: 259
% New rule produced :
% [278]
% inverse(inverse(X greatest_lower_bound Y) least_upper_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 4220
% Current number of ordered equations: 0
% Current number of rules: 260
% New rule produced :
% [279]
% inverse(inverse(X) least_upper_bound Y) greatest_lower_bound X ->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 4219
% Current number of ordered equations: 0
% Current number of rules: 261
% New rule produced :
% [280]
% b least_upper_bound inverse(inverse(a greatest_lower_bound X) least_upper_bound Y)
% -> b
% Current number of equations to process: 4218
% Current number of ordered equations: 0
% Current number of rules: 262
% New rule produced :
% [281]
% 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: 4216
% Current number of ordered equations: 0
% Current number of rules: 263
% New rule produced :
% [282]
% b least_upper_bound inverse((a greatest_lower_bound X) least_upper_bound identity)
% -> b least_upper_bound identity
% Current number of equations to process: 4215
% Current number of ordered equations: 0
% Current number of rules: 264
% New rule produced :
% [283]
% b least_upper_bound multiply(a,multiply(X,inverse(identity least_upper_bound X)))
% -> b
% Current number of equations to process: 4428
% Current number of ordered equations: 0
% Current number of rules: 265
% New rule produced :
% [284]
% b least_upper_bound multiply(a,multiply(X,inverse(X least_upper_bound Y))) ->
% b
% Rule
% [283]
% b least_upper_bound multiply(a,multiply(X,inverse(identity least_upper_bound X)))
% -> b collapsed.
% Current number of equations to process: 4427
% Current number of ordered equations: 0
% Current number of rules: 265
% New rule produced :
% [285]
% b least_upper_bound multiply(a,multiply(inverse(X least_upper_bound Y),X)) ->
% b
% Current number of equations to process: 4425
% Current number of ordered equations: 0
% Current number of rules: 266
% New rule produced :
% [286]
% b least_upper_bound multiply(X,multiply(inverse(identity least_upper_bound X),a))
% -> b
% Current number of equations to process: 4423
% Current number of ordered equations: 0
% Current number of rules: 267
% New rule produced :
% [287]
% b least_upper_bound multiply(X,multiply(inverse(X least_upper_bound Y),a)) ->
% b
% Rule
% [286]
% b least_upper_bound multiply(X,multiply(inverse(identity least_upper_bound X),a))
% -> b collapsed.
% Current number of equations to process: 4422
% Current number of ordered equations: 0
% Current number of rules: 267
% New rule produced :
% [288]
% b least_upper_bound multiply(inverse(X least_upper_bound Y),multiply(X,a)) ->
% b
% Current number of equations to process: 4421
% Current number of ordered equations: 0
% Current number of rules: 268
% New rule produced :
% [289]
% multiply(X,multiply(inverse(b least_upper_bound Y),a)) least_upper_bound X ->
% X
% Current number of equations to process: 4420
% Current number of ordered equations: 0
% Current number of rules: 269
% New rule produced :
% [290]
% multiply(inverse(b least_upper_bound Y),multiply(a,X)) least_upper_bound X ->
% X
% Current number of equations to process: 4419
% Current number of ordered equations: 0
% Current number of rules: 270
% New rule produced :
% [291]
% inverse(b least_upper_bound X) least_upper_bound inverse(a) -> inverse(a)
% Current number of equations to process: 4572
% Current number of ordered equations: 0
% Current number of rules: 271
% New rule produced :
% [292]
% b least_upper_bound multiply(a,multiply(a,inverse(b least_upper_bound X))) ->
% b
% Current number of equations to process: 4630
% Current number of ordered equations: 0
% Current number of rules: 272
% New rule produced :
% [293]
% b least_upper_bound multiply(a,multiply(inverse(b least_upper_bound X),a)) ->
% b
% Current number of equations to process: 4838
% Current number of ordered equations: 0
% Current number of rules: 273
% New rule produced :
% [294]
% (inverse(inverse(a) least_upper_bound X) greatest_lower_bound Y) least_upper_bound b
% -> b
% Current number of equations to process: 2113
% Current number of ordered equations: 0
% Current number of rules: 274
% New rule produced :
% [295]
% inverse(b least_upper_bound X) greatest_lower_bound inverse(a) ->
% inverse(b least_upper_bound X)
% Current number of equations to process: 2235
% Current number of ordered equations: 0
% Current number of rules: 275
% New rule produced :
% [296]
% b greatest_lower_bound inverse(inverse(a) least_upper_bound X) ->
% inverse(inverse(a) least_upper_bound X)
% Current number of equations to process: 2238
% Current number of ordered equations: 0
% Current number of rules: 276
% New rule produced :
% [297]
% 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: 4527
% Current number of ordered equations: 0
% Current number of rules: 277
% New rule produced :
% [298]
% (inverse(a) least_upper_bound X) greatest_lower_bound inverse(b least_upper_bound Y)
% -> inverse(b least_upper_bound Y)
% Current number of equations to process: 4524
% Current number of ordered equations: 0
% Current number of rules: 278
% New rule produced :
% [299]
% inverse(X greatest_lower_bound Y) least_upper_bound inverse(X) ->
% inverse(X greatest_lower_bound Y)
% Current number of equations to process: 2677
% Current number of ordered equations: 0
% Current number of rules: 279
% New rule produced :
% [300]
% inverse(X least_upper_bound Y) greatest_lower_bound inverse(X) ->
% inverse(X least_upper_bound Y)
% Current number of equations to process: 2676
% Current number of ordered equations: 0
% Current number of rules: 280
% New rule produced :
% [301]
% inverse(a greatest_lower_bound X) least_upper_bound inverse(b) ->
% inverse(a greatest_lower_bound X)
% Current number of equations to process: 2675
% Current number of ordered equations: 0
% Current number of rules: 281
% New rule produced :
% [302]
% a least_upper_bound inverse(inverse(b) greatest_lower_bound X) ->
% inverse(inverse(b) greatest_lower_bound X)
% Current number of equations to process: 2966
% Current number of ordered equations: 0
% Current number of rules: 282
% New rule produced :
% [303]
% b least_upper_bound identity least_upper_bound inverse(a) ->
% b least_upper_bound inverse(a)
% Current number of equations to process: 3407
% Current number of ordered equations: 0
% Current number of rules: 283
% New rule produced :
% [304]
% (inverse(X) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 3529
% Current number of ordered equations: 0
% Current number of rules: 284
% New rule produced :
% [305]
% (inverse(X) least_upper_bound X least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 3528
% Current number of ordered equations: 0
% Current number of rules: 285
% New rule produced :
% [306]
% (identity least_upper_bound X) greatest_lower_bound (inverse(X) 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: 286
% New rule produced :
% [307]
% (b least_upper_bound inverse(b)) greatest_lower_bound (a least_upper_Cputime limit exceeded (core dumped)
% 
% EOF
%------------------------------------------------------------------------------