%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP181-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n050.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 00:22:33 EDT 2014

% Result   : Timeout 300.06s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP181-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n050.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 06:34:08 CDT 2014
% % CPUTime  : 300.06 
% Processing problem /tmp/CiME_8978_n050.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " least_upper_bound,greatest_lower_bound : AC; b,c,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);
% inverse(identity) = identity;
% inverse(inverse(X)) = X;
% inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X));
% a greatest_lower_bound c = b greatest_lower_bound c;
% a least_upper_bound c = b least_upper_bound c;
% ";
% 
% let s1 = status F "
% b lr_lex;
% c 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 > c > b";
% 
% let s2 = status F "
% b mul;
% c 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 = c = b";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " a = b;"
% ;
% (*
% 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),
% inverse(identity) = identity,
% inverse(inverse(X)) = X,
% inverse(multiply(X,Y)) =
% multiply(inverse(Y),inverse(X)),
% c greatest_lower_bound a =
% b greatest_lower_bound c,
% c least_upper_bound a = b least_upper_bound c }
% (16 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 = { a = b } (1 equation(s))
% time is now on
% 
% Initializing completion ...
% New rule produced : [1] inverse(identity) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 15
% Current number of rules: 1
% New rule produced : [2] inverse(inverse(X)) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 14
% Current number of rules: 2
% New rule produced : [3] X least_upper_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 13
% Current number of rules: 3
% New rule produced : [4] X greatest_lower_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 12
% Current number of rules: 4
% New rule produced : [5] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 5
% New rule produced : [6] c least_upper_bound a -> b least_upper_bound c
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 6
% New rule produced : [7] c greatest_lower_bound a -> b greatest_lower_bound c
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 7
% New rule produced : [8] multiply(inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 8
% New rule produced : [9] (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: 9
% New rule produced : [10] (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: 10
% New rule produced :
% [11] inverse(multiply(X,Y)) -> multiply(inverse(Y),inverse(X))
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 11
% New rule produced :
% [12] 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: 12
% New rule produced :
% [13]
% 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: 13
% New rule produced :
% [14]
% 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: 14
% New rule produced :
% [15]
% 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: 15
% New rule produced :
% [16]
% 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: 16
% New rule produced : [17] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] (b greatest_lower_bound c) least_upper_bound a -> a
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] (b least_upper_bound c) greatest_lower_bound a -> a
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] multiply(inverse(X),identity) -> inverse(X)
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [21] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22]
% (b greatest_lower_bound c greatest_lower_bound X) least_upper_bound a -> a
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [23] (b least_upper_bound c least_upper_bound X) greatest_lower_bound a -> a
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [24]
% (a greatest_lower_bound X) least_upper_bound b least_upper_bound c ->
% b least_upper_bound c
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [25]
% (a least_upper_bound X) greatest_lower_bound b greatest_lower_bound c ->
% b greatest_lower_bound c
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [26] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [27] multiply(X,identity) -> X
% Rule [20] multiply(inverse(X),identity) -> inverse(X) collapsed.
% Current number of equations to process: 110
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [28]
% (b greatest_lower_bound c greatest_lower_bound X) least_upper_bound (a greatest_lower_bound X)
% -> a greatest_lower_bound X
% Current number of equations to process: 206
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [29]
% (b greatest_lower_bound c) least_upper_bound (b greatest_lower_bound a) ->
% b greatest_lower_bound a
% Current number of equations to process: 249
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [30]
% (b least_upper_bound c least_upper_bound X) greatest_lower_bound (a least_upper_bound X)
% -> a least_upper_bound X
% Current number of equations to process: 269
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [31]
% (b least_upper_bound c) greatest_lower_bound (b least_upper_bound a) ->
% b least_upper_bound a
% Current number of equations to process: 312
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [32]
% multiply(X,c) least_upper_bound multiply(X,a) ->
% multiply(X,b) least_upper_bound multiply(X,c)
% Current number of equations to process: 333
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [33]
% identity least_upper_bound multiply(inverse(c),a) ->
% identity least_upper_bound multiply(inverse(c),b)
% Current number of equations to process: 350
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [34]
% multiply(X,c) greatest_lower_bound multiply(X,a) ->
% multiply(X,b) greatest_lower_bound multiply(X,c)
% Current number of equations to process: 374
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [35]
% identity greatest_lower_bound multiply(inverse(c),a) ->
% identity greatest_lower_bound multiply(inverse(c),b)
% Current number of equations to process: 391
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [36]
% multiply(c,X) least_upper_bound multiply(a,X) ->
% multiply(b,X) least_upper_bound multiply(c,X)
% Current number of equations to process: 415
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [37]
% identity least_upper_bound multiply(a,inverse(c)) ->
% identity least_upper_bound multiply(b,inverse(c))
% Current number of equations to process: 435
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [38]
% multiply(c,X) greatest_lower_bound multiply(a,X) ->
% multiply(b,X) greatest_lower_bound multiply(c,X)
% Current number of equations to process: 462
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [39]
% identity greatest_lower_bound multiply(a,inverse(c)) ->
% identity greatest_lower_bound multiply(b,inverse(c))
% Current number of equations to process: 482
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [40]
% (b greatest_lower_bound c greatest_lower_bound X) least_upper_bound (b greatest_lower_bound a)
% -> b greatest_lower_bound a
% Current number of equations to process: 509
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [41]
% ((b greatest_lower_bound a) least_upper_bound X) greatest_lower_bound b greatest_lower_bound c
% -> b greatest_lower_bound c
% Current number of equations to process: 522
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [42]
% ((b least_upper_bound a) greatest_lower_bound X) least_upper_bound b least_upper_bound c
% -> b least_upper_bound c
% Current number of equations to process: 561
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [43]
% (b least_upper_bound c least_upper_bound X) greatest_lower_bound (b least_upper_bound a)
% -> b least_upper_bound a
% Current number of equations to process: 602
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [44]
% ((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: 610
% Current number of ordered equations: 1
% Current number of rules: 43
% New rule produced :
% [45]
% ((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: 622
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [46]
% 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: 1524
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [47]
% inverse(identity least_upper_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X least_upper_bound Y),X)
% Current number of equations to process: 1524
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [48]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(inverse(identity least_upper_bound Y),inverse(X))
% Current number of equations to process: 1533
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [49]
% inverse(identity least_upper_bound multiply(X,Y)) <->
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X))
% Current number of equations to process: 1532
% Current number of ordered equations: 1
% Current number of rules: 48
% New rule produced :
% [50]
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X)) <->
% inverse(identity least_upper_bound multiply(X,Y))
% Current number of equations to process: 1532
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [51]
% inverse(identity least_upper_bound inverse(X)) ->
% multiply(inverse(identity least_upper_bound X),X)
% Current number of equations to process: 1538
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [52]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(inverse(identity least_upper_bound multiply(X,Y)),X)
% Rule
% [51]
% inverse(identity least_upper_bound inverse(X)) ->
% multiply(inverse(identity least_upper_bound X),X) collapsed.
% Current number of equations to process: 1545
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced :
% [53]
% multiply(inverse(identity least_upper_bound multiply(X,Y)),X) <->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 1545
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [54]
% 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: 1599
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [55]
% inverse(identity greatest_lower_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X greatest_lower_bound Y),X)
% Current number of equations to process: 1601
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [56]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(inverse(identity greatest_lower_bound Y),inverse(X))
% Current number of equations to process: 1610
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [57]
% inverse(identity greatest_lower_bound multiply(X,Y)) <->
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X))
% Current number of equations to process: 1609
% Current number of ordered equations: 1
% Current number of rules: 55
% New rule produced :
% [58]
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y))
% Current number of equations to process: 1609
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [59]
% inverse(identity greatest_lower_bound inverse(X)) ->
% multiply(inverse(identity greatest_lower_bound X),X)
% Current number of equations to process: 1620
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [60]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X)
% Rule
% [59]
% inverse(identity greatest_lower_bound inverse(X)) ->
% multiply(inverse(identity greatest_lower_bound X),X) collapsed.
% Current number of equations to process: 1637
% Current number of ordered equations: 1
% Current number of rules: 57
% New rule produced :
% [61]
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X) <->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 1637
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [62]
% 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: 1719
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [63]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),inverse(identity least_upper_bound X))
% Current number of equations to process: 1726
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [64]
% inverse(identity least_upper_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X least_upper_bound Y))
% Current number of equations to process: 1734
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [65]
% inverse(identity least_upper_bound multiply(X,Y)) <->
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X))
% Current number of equations to process: 1733
% Current number of ordered equations: 1
% Current number of rules: 62
% New rule produced :
% [66]
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X)) <->
% inverse(identity least_upper_bound multiply(X,Y))
% Current number of equations to process: 1733
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [67]
% multiply(inverse(identity least_upper_bound X),X) ->
% multiply(X,inverse(identity least_upper_bound X))
% Current number of equations to process: 1752
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [68]
% multiply(inverse(identity least_upper_bound X),inverse(X)) ->
% multiply(inverse(X),inverse(identity least_upper_bound X))
% Current number of equations to process: 1757
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [69]
% multiply(X,inverse(inverse(Y) least_upper_bound X)) <->
% multiply(inverse(inverse(X) least_upper_bound Y),Y)
% Current number of equations to process: 1778
% Current number of ordered equations: 1
% Current number of rules: 66
% New rule produced :
% [70]
% multiply(inverse(inverse(X) least_upper_bound Y),Y) <->
% multiply(X,inverse(inverse(Y) least_upper_bound X))
% Current number of equations to process: 1778
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [71]
% inverse(inverse(X) least_upper_bound inverse(Y)) ->
% multiply(X,multiply(inverse(X least_upper_bound Y),Y))
% Current number of equations to process: 1797
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [72]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(X,inverse(identity least_upper_bound multiply(Y,X)))
% Current number of equations to process: 1810
% Current number of ordered equations: 1
% Current number of rules: 69
% New rule produced :
% [73]
% multiply(X,inverse(identity least_upper_bound multiply(Y,X))) <->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 1810
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [74]
% 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: 2074
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [75]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),inverse(identity greatest_lower_bound X))
% Current number of equations to process: 2081
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [76]
% inverse(identity greatest_lower_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X greatest_lower_bound Y))
% Current number of equations to process: 2089
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [77]
% inverse(identity greatest_lower_bound multiply(X,Y)) <->
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X))
% Current number of equations to process: 2088
% Current number of ordered equations: 1
% Current number of rules: 74
% New rule produced :
% [78]
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y))
% Current number of equations to process: 2088
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [79]
% multiply(inverse(identity greatest_lower_bound X),X) ->
% multiply(X,inverse(identity greatest_lower_bound X))
% Current number of equations to process: 2121
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [80]
% multiply(inverse(identity greatest_lower_bound X),inverse(X)) ->
% multiply(inverse(X),inverse(identity greatest_lower_bound X))
% Current number of equations to process: 2128
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [81]
% multiply(X,inverse(inverse(Y) greatest_lower_bound X)) <->
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y)
% Current number of equations to process: 2166
% Current number of ordered equations: 1
% Current number of rules: 78
% New rule produced :
% [82]
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y) <->
% multiply(X,inverse(inverse(Y) greatest_lower_bound X))
% Current number of equations to process: 2166
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [83]
% inverse(inverse(X) greatest_lower_bound inverse(Y)) ->
% multiply(X,multiply(inverse(X greatest_lower_bound Y),Y))
% Current number of equations to process: 2193
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [84]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(X,inverse(identity greatest_lower_bound multiply(Y,X)))
% Current number of equations to process: 2215
% Current number of ordered equations: 1
% Current number of rules: 81
% New rule produced :
% [85]
% multiply(X,inverse(identity greatest_lower_bound multiply(Y,X))) <->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 2215
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [86]
% ((b greatest_lower_bound c) least_upper_bound X) greatest_lower_bound 
% (a least_upper_bound X) -> (b greatest_lower_bound c) least_upper_bound X
% Current number of equations to process: 2552
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [87]
% ((a greatest_lower_bound X) least_upper_bound b) greatest_lower_bound 
% (b least_upper_bound c) -> (a greatest_lower_bound X) least_upper_bound b
% Current number of equations to process: 2610
% Current number of ordered equations: 2
% Current number of rules: 84
% New rule produced :
% [88]
% ((a greatest_lower_bound X) least_upper_bound c) greatest_lower_bound 
% (b least_upper_bound c) -> (a greatest_lower_bound X) least_upper_bound c
% Current number of equations to process: 2610
% Current number of ordered equations: 1
% Current number of rules: 85
% New rule produced :
% [89]
% ((a least_upper_bound X) greatest_lower_bound c) least_upper_bound (b greatest_lower_bound c)
% -> (a least_upper_bound X) greatest_lower_bound c
% Current number of equations to process: 2688
% Current number of ordered equations: 2
% Current number of rules: 86
% New rule produced :
% [90]
% ((a least_upper_bound X) greatest_lower_bound b) least_upper_bound (b greatest_lower_bound c)
% -> (a least_upper_bound X) greatest_lower_bound b
% Current number of equations to process: 2688
% Current number of ordered equations: 1
% Current number of rules: 87
% New rule produced :
% [91]
% ((b least_upper_bound c) greatest_lower_bound X) least_upper_bound (a greatest_lower_bound X)
% -> (b least_upper_bound c) greatest_lower_bound X
% Current number of equations to process: 2769
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [92]
% ((c least_upper_bound X) greatest_lower_bound a) least_upper_bound (b greatest_lower_bound c)
% -> (c least_upper_bound X) greatest_lower_bound a
% Current number of equations to process: 2829
% Current number of ordered equations: 1
% Current number of rules: 89
% New rule produced :
% [93]
% ((b greatest_lower_bound X) least_upper_bound a) greatest_lower_bound 
% (b least_upper_bound c) -> (b greatest_lower_bound X) least_upper_bound a
% Current number of equations to process: 2867
% Current number of ordered equations: 2
% Current number of rules: 90
% New rule produced :
% [94]
% ((c greatest_lower_bound X) least_upper_bound a) greatest_lower_bound 
% (b least_upper_bound c) -> (c greatest_lower_bound X) least_upper_bound a
% Current number of equations to process: 2867
% Current number of ordered equations: 1
% Current number of rules: 91
% New rule produced :
% [95]
% ((b least_upper_bound X) greatest_lower_bound a) least_upper_bound (b greatest_lower_bound c)
% -> (b least_upper_bound X) greatest_lower_bound a
% Current number of equations to process: 2950
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [96]
% inverse(multiply(inverse(X),Y) least_upper_bound Z) <->
% multiply(inverse(multiply(X,Z) least_upper_bound Y),X)
% Rule
% [47]
% inverse(identity least_upper_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X least_upper_bound Y),X) collapsed.
% Current number of equations to process: 2987
% Current number of ordered equations: 1
% Current number of rules: 92
% New rule produced :
% [97]
% 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: 2987
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [98]
% inverse(multiply(inverse(X),Y) greatest_lower_bound Z) <->
% multiply(inverse(multiply(X,Z) greatest_lower_bound Y),X)
% Rule
% [55]
% inverse(identity greatest_lower_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X greatest_lower_bound Y),X) collapsed.
% Current number of equations to process: 3122
% Current number of ordered equations: 1
% Current number of rules: 93
% New rule produced :
% [99]
% multiply(inverse(multiply(X,Z) greatest_lower_bound Y),X) <->
% inverse(multiply(inverse(X),Y) greatest_lower_bound Z)
% Current number of equations to process: 3122
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [100]
% inverse(identity least_upper_bound X) least_upper_bound multiply(X,inverse(
% identity least_upper_bound X))
% -> identity
% Current number of equations to process: 3260
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [101]
% identity least_upper_bound inverse(identity least_upper_bound X) -> identity
% Current number of equations to process: 3265
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [102]
% identity greatest_lower_bound inverse(identity least_upper_bound X) ->
% inverse(identity least_upper_bound X)
% Current number of equations to process: 3292
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [103]
% identity least_upper_bound multiply(X,inverse(identity least_upper_bound X))
% -> identity
% Current number of equations to process: 3291
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [104]
% (inverse(identity least_upper_bound X) greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Current number of equations to process: 3290
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [105]
% (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: 3289
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [106]
% (multiply(X,inverse(identity least_upper_bound X)) greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Current number of equations to process: 3297
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [107]
% 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: 3299
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [108]
% multiply(X,inverse(identity least_upper_bound Y)) least_upper_bound X -> X
% Current number of equations to process: 3352
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [109]
% multiply(inverse(identity least_upper_bound Y),X) least_upper_bound X -> X
% Current number of equations to process: 3351
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [110]
% identity least_upper_bound multiply(inverse(b least_upper_bound c),c) ->
% identity
% Current number of equations to process: 3350
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [111]
% identity least_upper_bound multiply(c,inverse(b least_upper_bound c)) ->
% identity
% Current number of equations to process: 3349
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [112]
% identity least_upper_bound multiply(X,inverse(X least_upper_bound Y)) ->
% identity
% Rule
% [103]
% identity least_upper_bound multiply(X,inverse(identity least_upper_bound X))
% -> identity collapsed.
% Rule
% [111]
% identity least_upper_bound multiply(c,inverse(b least_upper_bound c)) ->
% identity collapsed.
% Current number of equations to process: 3371
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [113]
% identity least_upper_bound multiply(inverse(X least_upper_bound Y),X) ->
% identity
% Rule
% [110]
% identity least_upper_bound multiply(inverse(b least_upper_bound c),c) ->
% identity collapsed.
% Current number of equations to process: 3378
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [114]
% (multiply(inverse(b least_upper_bound c),c) greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 3486
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [115]
% (multiply(c,inverse(b least_upper_bound c)) greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 3485
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [116]
% (multiply(X,inverse(X least_upper_bound Y)) greatest_lower_bound Z) least_upper_bound identity
% -> identity
% Rule
% [106]
% (multiply(X,inverse(identity least_upper_bound X)) greatest_lower_bound Y) least_upper_bound identity
% -> identity collapsed.
% Rule
% [115]
% (multiply(c,inverse(b least_upper_bound c)) greatest_lower_bound X) least_upper_bound identity
% -> identity collapsed.
% Current number of equations to process: 3484
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [117]
% (multiply(inverse(X least_upper_bound Y),X) greatest_lower_bound Z) least_upper_bound identity
% -> identity
% Rule
% [114]
% (multiply(inverse(b least_upper_bound c),c) greatest_lower_bound X) least_upper_bound identity
% -> identity collapsed.
% Current number of equations to process: 3483
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [118]
% 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: 3537
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [119]
% 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: 3536
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [120]
% identity greatest_lower_bound multiply(inverse(b least_upper_bound c),c) ->
% multiply(inverse(b least_upper_bound c),c)
% Current number of equations to process: 3535
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [121]
% identity greatest_lower_bound multiply(c,inverse(b least_upper_bound c)) ->
% multiply(c,inverse(b least_upper_bound c))
% Current number of equations to process: 3534
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [122]
% identity greatest_lower_bound multiply(X,inverse(X least_upper_bound Y)) ->
% multiply(X,inverse(X least_upper_bound Y))
% Rule
% [107]
% identity greatest_lower_bound multiply(X,inverse(identity least_upper_bound X))
% -> multiply(X,inverse(identity least_upper_bound X)) collapsed.
% Rule
% [121]
% identity greatest_lower_bound multiply(c,inverse(b least_upper_bound c)) ->
% multiply(c,inverse(b least_upper_bound c)) collapsed.
% Current number of equations to process: 3533
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [123] inverse(inverse(X) least_upper_bound Y) least_upper_bound X -> X
% Current number of equations to process: 3619
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [124]
% inverse(identity least_upper_bound X) least_upper_bound X ->
% identity least_upper_bound X
% Current number of equations to process: 3634
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [125]
% identity least_upper_bound multiply(a,inverse(b least_upper_bound c)) ->
% identity
% Current number of equations to process: 3770
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [126]
% identity least_upper_bound multiply(inverse(b least_upper_bound c),a) ->
% identity
% Current number of equations to process: 3850
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [127]
% (multiply(X,inverse(identity least_upper_bound Y)) greatest_lower_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 3939
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [128]
% multiply(X,multiply(inverse(b least_upper_bound c),c)) least_upper_bound X ->
% X
% Current number of equations to process: 3938
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [129]
% multiply(X,multiply(c,inverse(b least_upper_bound c))) least_upper_bound X ->
% X
% Current number of equations to process: 3937
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [130]
% multiply(X,multiply(Y,inverse(identity least_upper_bound Y))) least_upper_bound X
% -> X
% Current number of equations to process: 3935
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [131]
% multiply(X,multiply(Y,inverse(Y least_upper_bound Z))) least_upper_bound X ->
% X
% Rule
% [129]
% multiply(X,multiply(c,inverse(b least_upper_bound c))) least_upper_bound X ->
% X collapsed.
% Rule
% [130]
% multiply(X,multiply(Y,inverse(identity least_upper_bound Y))) least_upper_bound X
% -> X collapsed.
% Current number of equations to process: 3934
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [132]
% multiply(X,multiply(inverse(Y least_upper_bound Z),Y)) least_upper_bound X ->
% X
% Rule
% [128]
% multiply(X,multiply(inverse(b least_upper_bound c),c)) least_upper_bound X ->
% X collapsed.
% Current number of equations to process: 3932
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [133]
% (multiply(inverse(identity least_upper_bound Y),X) greatest_lower_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 3930
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [134]
% multiply(inverse(b least_upper_bound c),multiply(c,X)) least_upper_bound X ->
% X
% Current number of equations to process: 3929
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [135]
% multiply(c,multiply(inverse(b least_upper_bound c),X)) least_upper_bound X ->
% X
% Current number of equations to process: 3928
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [136]
% multiply(X,multiply(inverse(identity least_upper_bound X),Y)) least_upper_bound Y
% -> Y
% Current number of equations to process: 3926
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [137]
% multiply(X,multiply(inverse(X least_upper_bound Y),Z)) least_upper_bound Z ->
% Z
% Rule
% [135]
% multiply(c,multiply(inverse(b least_upper_bound c),X)) least_upper_bound X ->
% X collapsed.
% Rule
% [136]
% multiply(X,multiply(inverse(identity least_upper_bound X),Y)) least_upper_bound Y
% -> Y collapsed.
% Current number of equations to process: 3925
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [138]
% multiply(inverse(X least_upper_bound Y),multiply(X,Z)) least_upper_bound Z ->
% Z
% Rule
% [134]
% multiply(inverse(b least_upper_bound c),multiply(c,X)) least_upper_bound X ->
% X collapsed.
% Current number of equations to process: 3924
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [139]
% identity least_upper_bound multiply(a,inverse(b least_upper_bound c least_upper_bound X))
% -> identity
% Current number of equations to process: 3923
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [140]
% identity least_upper_bound multiply(inverse(b least_upper_bound c least_upper_bound X),a)
% -> identity
% Current number of equations to process: 3920
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [141]
% (multiply(a,inverse(b least_upper_bound c)) greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 3974
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [142]
% (multiply(inverse(b least_upper_bound c),a) greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 4095
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [143]
% identity greatest_lower_bound multiply(inverse(X least_upper_bound Y),X) ->
% multiply(inverse(X least_upper_bound Y),X)
% Rule
% [120]
% identity greatest_lower_bound multiply(inverse(b least_upper_bound c),c) ->
% multiply(inverse(b least_upper_bound c),c) collapsed.
% Current number of equations to process: 4148
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [144]
% (b greatest_lower_bound multiply(c,inverse(identity least_upper_bound X))) least_upper_bound a
% -> a
% Current number of equations to process: 4194
% Current number of ordered equations: 1
% Current number of rules: 124
% New rule produced :
% [145]
% (c greatest_lower_bound multiply(b,inverse(identity least_upper_bound X))) least_upper_bound a
% -> a
% Current number of equations to process: 4194
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [146]
% (b greatest_lower_bound multiply(inverse(identity least_upper_bound X),c)) least_upper_bound a
% -> a
% Current number of equations to process: 4337
% Current number of ordered equations: 1
% Current number of rules: 126
% New rule produced :
% [147]
% (c greatest_lower_bound multiply(inverse(identity least_upper_bound X),b)) least_upper_bound a
% -> a
% Current number of equations to process: 4337
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [148]
% identity greatest_lower_bound multiply(a,inverse(b least_upper_bound c)) ->
% multiply(a,inverse(b least_upper_bound c))
% Current number of equations to process: 4536
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [149]
% inverse(X least_upper_bound Y) least_upper_bound inverse(X) -> inverse(X)
% Current number of equations to process: 4646
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [150]
% identity least_upper_bound inverse(X) least_upper_bound X ->
% inverse(X) least_upper_bound X
% Current number of equations to process: 2350
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [151]
% inverse(inverse(X greatest_lower_bound Y) least_upper_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 2350
% Current number of ordered equations: 1
% Current number of rules: 131
% New rule produced :
% [152]
% (inverse(inverse(X) least_upper_bound Y) greatest_lower_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 2350
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [153]
% inverse(inverse(X) least_upper_bound Y) greatest_lower_bound X ->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 2349
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [154]
% a least_upper_bound inverse(inverse(b greatest_lower_bound c) least_upper_bound X)
% -> a
% Current number of equations to process: 2348
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [155]
% 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: 2346
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [156]
% a least_upper_bound inverse((b greatest_lower_bound c) least_upper_bound identity)
% -> a least_upper_bound identity
% Current number of equations to process: 2345
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [157]
% b least_upper_bound c least_upper_bound inverse(inverse(a) least_upper_bound X)
% -> b least_upper_bound c
% Current number of equations to process: 2435
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [158]
% b least_upper_bound c least_upper_bound inverse(a least_upper_bound identity)
% -> b least_upper_bound c least_upper_bound identity
% Current number of equations to process: 2434
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [159]
% multiply(X,multiply(a,inverse(b least_upper_bound c))) least_upper_bound X ->
% X
% Current number of equations to process: 2433
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [160]
% multiply(a,multiply(inverse(b least_upper_bound c),X)) least_upper_bound X ->
% X
% Current number of equations to process: 2432
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [161]
% multiply(X,multiply(inverse(b least_upper_bound c),a)) least_upper_bound X ->
% X
% Current number of equations to process: 2431
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [162]
% multiply(inverse(b least_upper_bound c),multiply(a,X)) least_upper_bound X ->
% X
% Current number of equations to process: 2430
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [163]
% 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: 3701
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [164]
% identity greatest_lower_bound multiply(inverse(b least_upper_bound c),a) ->
% multiply(inverse(b least_upper_bound c),a)
% Current number of equations to process: 3699
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [165]
% (b greatest_lower_bound inverse(inverse(c) least_upper_bound X)) least_upper_bound a
% -> a
% Current number of equations to process: 3908
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [166]
% (c greatest_lower_bound inverse(inverse(b) least_upper_bound X)) least_upper_bound a
% -> a
% Current number of equations to process: 3981
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [167]
% inverse(b least_upper_bound c) least_upper_bound inverse(a) -> inverse(a)
% Current number of equations to process: 4264
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [168]
% inverse(X greatest_lower_bound Y) least_upper_bound inverse(X) ->
% inverse(X greatest_lower_bound Y)
% Current number of equations to process: 4309
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [169]
% inverse(X least_upper_bound Y) greatest_lower_bound inverse(X) ->
% inverse(X least_upper_bound Y)
% Current number of equations to process: 4308
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [170]
% inverse(b greatest_lower_bound c) least_upper_bound inverse(a) ->
% inverse(b greatest_lower_bound c)
% Current number of equations to process: 4307
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [171]
% (inverse(X) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 4805
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [172]
% (inverse(X) least_upper_bound X least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 4806
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [173]
% (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: 4904
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [174]
% identity least_upper_bound inverse(inverse(X) least_upper_bound X least_upper_bound Y)
% -> identity
% Current number of equations to process: 2413
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [175]
% inverse(b least_upper_bound c least_upper_bound X) least_upper_bound 
% inverse(a) -> inverse(a)
% Current number of equations to process: 2442
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [176]
% (inverse(X least_upper_bound Y) greatest_lower_bound Z) least_upper_bound 
% inverse(X) -> inverse(X)
% Current number of equations to process: 2441
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [177]
% (identity greatest_lower_bound Y) least_upper_bound inverse(X) least_upper_bound X
% -> inverse(X) least_upper_bound X
% Current number of equations to process: 2440
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [178]
% identity least_upper_bound multiply(X,inverse(identity least_upper_bound 
% multiply(X,X))) -> identity
% Current number of equations to process: 3070
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [179]
% a greatest_lower_bound inverse(inverse(c) least_upper_bound X) ->
% b greatest_lower_bound inverse(inverse(c) least_upper_bound X)
% Current number of equations to process: 3069
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [180]
% 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: 4085
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [181]
% (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: 4084
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [182]
% inverse(a least_upper_bound X) least_upper_bound inverse(b greatest_lower_bound c)
% -> inverse(b greatest_lower_bound c)
% Current number of equations to process: 4083
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [183]
% inverse(b least_upper_bound c) least_upper_bound inverse(a greatest_lower_bound X)
% -> inverse(a greatest_lower_bound X)
% Current number of equations to process: 4082
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [184]
% inverse(b greatest_lower_bound c) least_upper_bound inverse(b greatest_lower_bound a)
% -> inverse(b greatest_lower_bound c)
% Current number of equations to process: 4081
% Current number of ordered equations: 0
% Current number of rules: 164
% New rule produced :
% [185]
% (inverse(X) 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: 4080
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [186]
% b least_upper_bound c least_upper_bound identity least_upper_bound inverse(a)
% -> b least_upper_bound c least_upper_bound inverse(a)
% Current number of equations to process: 4079
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [187]
% (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: 4077
% Current number of ordered equations: 1
% Current number of rules: 167
% New rule produced :
% [188]
% 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: 4077
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced :
% [189]
% (identity least_upper_bound inverse(X)) greatest_lower_bound (inverse(X) least_upper_bound X)
% -> identity least_upper_bound inverse(X)
% Current number of equations to process: 4076
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced :
% [190]
% a least_upper_bound identity least_upper_bound inverse(b greatest_lower_bound c)
% -> a least_upper_bound inverse(b greatest_lower_bound c)
% Current number of equations to process: 4075
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced :
% [191]
% inverse(identity least_upper_bound Y) least_upper_bound inverse(X) least_upper_bound X
% -> inverse(X) least_upper_bound X
% Current number of equations to process: 4074
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [192]
% inverse(b least_upper_bound c) greatest_lower_bound inverse(a) ->
% inverse(b least_upper_bound c)
% Current number of equations to process: 4420
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [193]
% (inverse(b least_upper_bound c) greatest_lower_bound X) least_upper_bound 
% inverse(a) -> inverse(a)
% Current number of equations to process: 4537
% Current number of ordered equations: 0
% Current number of rules: 173
% Rule [187]
% (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 
% [187]
% (identity greatest_lower_bound X) least_upper_bound inverse(identity greatest_lower_bound X)
% -> inverse(identity greatest_lower_bound X)
% New rule produced :
% [194]
% identity least_upper_bound inverse(identity greatest_lower_bound X) ->
% inverse(identity greatest_lower_bound X)
% Current number of equations to process: 4586
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced :
% [195]
% inverse(X greatest_lower_bound Y) greatest_lower_bound inverse(X) ->
% inverse(X)
% Current number of equations to process: 4585
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced :
% [196]
% inverse(inverse(X) greatest_lower_bound Y) least_upper_bound X ->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 4618
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced :
% [197]
% (inverse(X greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound 
% inverse(X) -> inverse(X)
% Current number of equations to process: 4681
% Current number of ordered equations: 0
% Current number of rules: 177
% New rule produced :
% [198]
% inverse(b greatest_lower_bound c) greatest_lower_bound inverse(a) ->
% inverse(a)
% Current number of equations to process: 1444
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [199]
% inverse(b greatest_lower_bound c greatest_lower_bound X) greatest_lower_bound 
% inverse(a) -> inverse(a)
% Current number of equations to process: 1539
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [200]
% identity greatest_lower_bound inverse(inverse(identity least_upper_bound X) greatest_lower_bound Y)
% -> identity
% Current number of equations to process: 1694
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [201]
% (inverse(b greatest_lower_bound c) least_upper_bound X) greatest_lower_bound 
% inverse(a) -> inverse(a)
% Current number of equations to process: 1985
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [202]
% (b least_upper_bound c least_upper_bound inverse(a)) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 2103
% Current number of ordered equations: 0
% Current number of rules: 182
% New rule produced :
% [203]
% (inverse(X greatest_lower_bound Y) least_upper_bound X) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 2128
% Current number of ordered equations: 0
% Current number of rules: 183
% New rule produced :
% [204]
% (a least_upper_bound inverse(b greatest_lower_bound c)) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 2161
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [205]
% identity greatest_lower_bound inverse(identity greatest_lower_bound X) ->
% identity
% Current number of equations to process: 2657
% Current number of ordered equations: 0
% Current number of rules: 185
% New rule produced :
% [206]
% a least_upper_bound inverse(inverse(b) least_upper_bound inverse(c) least_upper_bound X)
% -> a
% Current number of equations to process: 3345
% Current number of ordered equations: 0
% Current number of rules: 186
% New rule produced :
% [207]
% (multiply(X,inverse(Y)) least_upper_bound multiply(X,Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 3344
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [208]
% (multiply(inverse(Y),X) least_upper_bound multiply(Y,X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 3343
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [209]
% (inverse(X greatest_lower_bound Y) least_upper_bound X least_upper_bound Z) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 3342
% Current number of ordered equations: 0
% Current number of rules: 189
% New rule produced :
% [210]
% (a least_upper_bound inverse(b greatest_lower_bound c) least_upper_bound X) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 3341
% Current number of ordered equations: 0
% Current number of rules: 190
% New rule produced :
% [211]
% (b least_upper_bound c least_upper_bound inverse(a) least_upper_bound X) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 3340
% Current number of ordered equations: 0
% Current number of rules: 191
% New rule produced :
% [212]
% (a least_upper_bound inverse(b greatest_lower_bound c greatest_lower_bound X)) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 3337
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced :
% [213]
% (b least_upper_bound c least_upper_bound inverse(a greatest_lower_bound X)) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 3336
% Current number of ordered equations: 0
% Current number of rules: 193
% New rule produced :
% [214]
% ((b greatest_lower_bound a) least_upper_bound inverse(b greatest_lower_bound c)) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 3335
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [215]
% inverse(inverse(X least_upper_bound Y) greatest_lower_bound Z) greatest_lower_bound X
% -> X
% Rule
% [200]
% identity greatest_lower_bound inverse(inverse(identity least_upper_bound X) greatest_lower_bound Y)
% -> identity collapsed.
% Current number of equations to process: 4116
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [216]
% (inverse(identity greatest_lower_bound X) least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 3107
% Current number of ordered equations: 0
% Current number of rules: 195
% New rule produced :
% [217]
% (inverse(a) least_upper_bound X) greatest_lower_bound inverse(b least_upper_bound c)
% -> inverse(b least_upper_bound c)
% Current number of equations to process: 3461
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [218]
% (inverse(X) greatest_lower_bound Z) least_upper_bound inverse(X greatest_lower_bound Y)
% -> inverse(X greatest_lower_bound Y)
% Current number of equations to process: 3459
% Current number of ordered equations: 0
% Current number of rules: 197
% New rule produced :
% [219]
% inverse(b least_upper_bound c) least_upper_bound inverse(b least_upper_bound a)
% -> inverse(b least_upper_bound a)
% Current number of equations to process: 3457
% Current number of ordered equations: 0
% Current number of rules: 198
% New rule produced :
% [220]
% inverse(X least_upper_bound Y) greatest_lower_bound inverse(X greatest_lower_bound Z)
% -> inverse(X least_upper_bound Y)
% Current number of equations to process: 3455
% Current number of ordered equations: 0
% Current number of rules: 199
% New rule produced :
% [221]
% inverse(a least_upper_bound X) greatest_lower_bound inverse(b greatest_lower_bound c)
% -> inverse(a least_upper_bound X)
% Current number of equations to process: 3453
% Current number of ordered equations: 0
% Current number of rules: 200
% New rule produced :
% [222]
% inverse(b least_upper_bound c) greatest_lower_bound inverse(a greatest_lower_bound X)
% -> inverse(b least_upper_bound c)
% Current number of equations to process: 3452
% Current number of ordered equations: 0
% Current number of rules: 201
% New rule produced :
% [223]
% inverse(b greatest_lower_bound c) greatest_lower_bound inverse(b greatest_lower_bound a)
% -> inverse(b greatest_lower_bound a)
% Current number of equations to process: 3451
% Current number of ordered equations: 0
% Current number of rules: 202
% New rule produced :
% [224]
% (inverse(a) greatest_lower_bound X) least_upper_bound inverse(b greatest_lower_bound c)
% -> inverse(b greatest_lower_bound c)
% Current number of equations to process: 3450
% Current number of ordered equations: 0
% Current number of rules: 203
% New rule produced :
% [225]
% (identity greatest_lower_bound Y) least_upper_bound inverse(identity greatest_lower_bound X)
% -> inverse(identity greatest_lower_bound X)
% Rule
% [187]
% (identity greatest_lower_bound X) least_upper_bound inverse(identity greatest_lower_bound X)
% -> inverse(identity greatest_lower_bound X) collapsed.
% Current number of equations to process: 3574
% Current number of ordered equations: 0
% Current number of rules: 203
% New rule produced :
% [226]
% a greatest_lower_bound inverse(inverse(b least_upper_bound c) greatest_lower_bound X)
% -> a
% Current number of equations to process: 4702
% Current number of ordered equations: 0
% Current number of rules: 204
% New rule produced :
% [227] inverse(inverse(X) greatest_lower_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 4968
% Current number of ordered equations: 0
% Current number of rules: 205
% New rule produced :
% [228]
% (inverse(inverse(X) greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 1858
% Current number of ordered equations: 0
% Current number of rules: 206
% New rule produced :
% [229]
% (b least_upper_bound inverse(inverse(c) greatest_lower_bound X)) greatest_lower_bound a
% -> a
% Current number of equations to process: 1856
% Current number of ordered equations: 1
% Current number of rules: 207
% New rule produced :
% [230]
% (c least_upper_bound inverse(inverse(b) greatest_lower_bound X)) greatest_lower_bound a
% -> a
% Current number of equations to process: 1856
% Current number of ordered equations: 0
% Current number of rules: 208
% New rule produced :
% [231]
% a least_upper_bound inverse(inverse(c) greatest_lower_bound X) ->
% b least_upper_bound inverse(inverse(c) greatest_lower_bound X)
% Current number of equations to process: 3113
% Current number of ordered equations: 0
% Current number of rules: 209
% New rule produced :
% [232]
% b greatest_lower_bound c greatest_lower_bound inverse(inverse(a) greatest_lower_bound X)
% -> b greatest_lower_bound c
% Current number of equations to process: 3112
% Current number of ordered equations: 0
% Current number of rules: 210
% New rule produced :
% [233]
% identity greatest_lower_bound inverse(inverse(X) greatest_lower_bound X greatest_lower_bound Y)
% -> identity
% Current number of equations to process: 4336
% Current number of ordered equations: 0
% Current number of rules: 211
% New rule produced :
% [234]
% multiply(X,inverse(identity greatest_lower_bound Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 4512
% Current number of ordered equations: 0
% Current number of rules: 212
% New rule produced :
% [235]
% multiply(inverse(identity greatest_lower_bound Y),X) greatest_lower_bound X
% -> X
% Current number of equations to process: 4511
% Current number of ordered equations: 0
% Current number of rules: 213
% New rule produced :
% [236]
% identity greatest_lower_bound multiply(inverse(b greatest_lower_bound c),c)
% -> identity
% Current number of equations to process: 4510
% Current number of ordered equations: 0
% Current number of rules: 214
% New rule produced :
% [237]
% identity greatest_lower_bound multiply(c,inverse(b greatest_lower_bound c))
% -> identity
% Current number of equations to process: 4509
% Current number of ordered equations: 0
% Current number of rules: 215
% New rule produced :
% [238]
% identity greatest_lower_bound multiply(X,inverse(identity greatest_lower_bound X))
% -> identity
% Current number of equations to process: 4535
% Current number of ordered equations: 0
% Current number of rules: 216
% New rule produced :
% [239]
% identity greatest_lower_bound multiply(X,inverse(X greatest_lower_bound Y))
% -> identity
% Rule
% [237]
% identity greatest_lower_bound multiply(c,inverse(b greatest_lower_bound c))
% -> identity collapsed.
% Rule
% [238]
% identity greatest_lower_bound multiply(X,inverse(identity greatest_lower_bound X))
% -> identity collapsed.
% Current number of equations to process: 4536
% Current number of ordered equations: 0
% Current number of rules: 215
% New rule produced :
% [240]
% identity greatest_lower_bound multiply(inverse(X greatest_lower_bound Y),X)
% -> identity
% Rule
% [236]
% identity greatest_lower_bound multiply(inverse(b greatest_lower_bound c),c)
% -> identity collapsed.
% Current number of equations to process: 4544
% Current number of ordered equations: 0
% Current number of rules: 215
% New rule produced :
% [241]
% (b least_upper_bound c least_upper_bound inverse(b least_upper_bound a)) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 4599
% Current number of ordered equations: 0
% Current number of rules: 216
% New rule produced :
% [242]
% a least_upper_bound multiply(b,multiply(inverse(b least_upper_bound c),c)) ->
% a
% Current number of equations to process: 4597
% Current number of ordered equations: 0
% Current number of rules: 217
% New rule produced :
% [243]
% (a least_upper_bound inverse(b) least_upper_bound inverse(c)) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 4756
% Current number of ordered equations: 0
% Current number of rules: 218
% New rule produced :
% [244] (identity least_upper_bound multiply(X,X)) greatest_lower_bound X -> X
% Current number of equations to process: 4882
% Current number of ordered equations: 0
% Current number of rules: 219
% New rule produced :
% [245]
% (multiply(inverse(b greatest_lower_bound c),c) least_upper_bound X) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 4671
% Current number of ordered equations: 0
% Current number of rules: 220
% New rule produced :
% [246]
% (multiply(c,inverse(b greatest_lower_bound c)) least_upper_bound X) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 4670
% Current number of ordered equations: 0
% Current number of rules: 221
% New rule produced :
% [247]
% (multiply(X,inverse(identity greatest_lower_bound X)) least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 4669
% Current number of ordered equations: 0
% Current number of rules: 222
% New rule produced :
% [248]
% (multiply(X,inverse(X greatest_lower_bound Y)) least_upper_bound Z) greatest_lower_bound identity
% -> identity
% Rule
% [246]
% (multiply(c,inverse(b greatest_lower_bound c)) least_upper_bound X) greatest_lower_bound identity
% -> identity collapsed.
% Rule
% [247]
% (multiply(X,inverse(identity greatest_lower_bound X)) least_upper_bound Y) greatest_lower_bound identity
% -> identity collapsed.
% Current number of equations to process: 4668
% Current number of ordered equations: 0
% Current number of rules: 221
% New rule produced :
% [249]
% (multiply(inverse(X greatest_lower_bound Y),X) least_upper_bound Z) greatest_lower_bound identity
% -> identity
% Rule
% [245]
% (multiply(inverse(b greatest_lower_bound c),c) least_upper_bound X) greatest_lower_bound identity
% -> identity collapsed.
% Current number of equations to process: 4667
% Current number of ordered equations: 0
% Current number of rules: 221
% New rule produced :
% [250]
% multiply(X,inverse(identity greatest_lower_bound Y)) least_upper_bound X ->
% multiply(X,inverse(identity greatest_lower_bound Y))
% Current number of equations to process: 4668
% Current number of ordered equations: 0
% Current number of rules: 222
% New rule produced :
% [251]
% multiply(inverse(identity greatest_lower_bound X),Y) least_upper_bound Y ->
% multiply(inverse(identity greatest_lower_bound X),Y)
% Current number of equations to process: 4667
% Current number of ordered equations: 0
% Current number of rules: 223
% New rule produced :
% [252]
% identity least_upper_bound multiply(inverse(b greatest_lower_bound c),c) ->
% multiply(inverse(b greatest_lower_bound c),c)
% Current number of equations to process: 4666
% Current number of ordered equations: 0
% Current number of rules: 224
% New rule produced :
% [253]
% identity least_upper_bound multiply(c,inverse(b greatest_lower_bound c)) ->
% multiply(c,inverse(b greatest_lower_bound c))
% Current number of equations to process: 4665
% Current number of ordered equations: 0
% Current number of rules: 225
% New rule produced :
% [254]
% identity least_upper_bound multiply(X,inverse(identity greatest_lower_bound X))
% -> multiply(X,inverse(identity greatest_lower_bound X))
% Current number of equations to process: 4664
% Current number of ordered equations: 0
% Current number of rules: 226
% New rule produced :
% [255]
% identity least_upper_bound multiply(X,inverse(X greatest_lower_bound Y)) ->
% multiply(X,inverse(X greatest_lower_bound Y))
% Rule
% [253]
% identity least_upper_bound multiply(c,inverse(b greatest_lower_bound c)) ->
% multiply(c,inverse(b greatest_lower_bound c)) collapsed.
% Rule
% [254]
% identity least_upper_bound multiply(X,inverse(identity greatest_lower_bound X))
% -> multiply(X,inverse(identity greatest_lower_bound X)) collapsed.
% Current number of equations to process: 4663
% Current number of ordered equations: 0
% Current number of rules: 225
% New rule produced :
% [256]
% identity least_upper_bound multiply(inverse(X greatest_lower_bound Y),X) ->
% multiply(inverse(X greatest_lower_bound Y),X)
% Rule
% [252]
% identity least_upper_bound multiply(inverse(b greatest_lower_bound c),c) ->
% multiply(inverse(b greatest_lower_bound c),c) collapsed.
% Current number of equations to process: 4662
% Current number of ordered equations: 0
% Current number of rules: 225
% New rule produced :
% [257]
% inverse(b least_upper_bound c) greatest_lower_bound inverse(b least_upper_bound a)
% -> inverse(b least_upper_bound c)
% Current number of equations to process: 4661
% Current number of ordered equations: 0
% Current number of rules: 226
% New rule produced :
% [258]
% multiply(X,multiply(inverse(X greatest_lower_bound Y),Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 3079
% Current number of ordered equations: 1
% Current number of rules: 227
% New rule produced :
% [259]
% multiply(X,multiply(inverse(X greatest_lower_bound Y),Y)) greatest_lower_bound Y
% -> Y
% Current number of equations to process: 3079
% Current number of ordered equations: 0
% Current number of rules: 228
% New rule produced :
% [260]
% (multiply(inverse(identity greatest_lower_bound X),Y) least_upper_bound Z) greatest_lower_bound Y
% -> Y
% Current number of equations to process: 3078
% Current number of ordered equations: 0
% Current number of rules: 229
% New rule produced :
% [261]
% (multiply(X,inverse(identity greatest_lower_bound Y)) least_upper_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 3077
% Current number of ordered equations: 0
% Current number of rules: 230
% New rule produced :
% [262]
% (b least_upper_bound multiply(inverse(identity greatest_lower_bound X),c)) greatest_lower_bound a
% -> a
% Current number of equations to process: 3076
% Current number of ordered equations: 0
% Current number of rules: 231
% New rule produced :
% [263]
% (b least_upper_bound multiply(c,inverse(identity greatest_lower_bound X))) greatest_lower_bound a
% -> a
% Current number of equations to process: 3075
% Current number of ordered equations: 0
% Current number of rules: 232
% New rule produced :
% [264]
% a greatest_lower_bound inverse(inverse(b) greatest_lower_bound inverse(c) greatest_lower_bound X)
% -> a
% Current number of equations to process: 3074
% Current number of ordered equations: 0
% Current number of rules: 233
% New rule produced :
% [265]
% (c least_upper_bound multiply(inverse(identity greatest_lower_bound X),b)) greatest_lower_bound a
% -> a
% Current number of equations to process: 3073
% Current number of ordered equations: 0
% Current number of rules: 234
% New rule produced :
% [266]
% (c least_upper_bound multiply(b,inverse(identity greatest_lower_bound X))) greatest_lower_bound a
% -> a
% Current number of equations to process: 3072
% Current number of ordered equations: 0
% Current number of rules: 235
% New rule produced :
% [267]
% identity greatest_lower_bound multiply(a,inverse(b greatest_lower_bound c))
% -> identity
% Current number of equations to process: 4910
% Current number of ordered equations: 0
% Current number of rules: 236
% New rule produced :
% [268]
% identity greatest_lower_bound multiply(inverse(b greatest_lower_bound c),a)
% -> identity
% Current number of equations to process: 2413
% Current number of ordered equations: 0
% Current number of rules: 237
% New rule produced :
% [269]
% identity greatest_lower_bound multiply(a,inverse(identity greatest_lower_bound 
% multiply(a,a))) -> identity
% Current number of equations to process: 2578
% Current number of ordered equations: 0
% Current number of rules: 238
% New rule produced :
% [270]
% identity greatest_lower_bound multiply(X,inverse(identity greatest_lower_bound 
% multiply(X,X))) -> identity
% Rule
% [269]
% identity greatest_lower_bound multiply(a,inverse(identity greatest_lower_bound 
% multiply(a,a))) -> identity
% collapsed.
% Current number of equations to process: 2577
% Current number of ordered equations: 0
% Current number of rules: 238
% New rule produced :
% [271]
% multiply(X,multiply(inverse(b greatest_lower_bound c),c)) greatest_lower_bound X
% -> X
% Current number of equations to process: 2571
% Current number of ordered equations: 0
% Current number of rules: 239
% New rule produced :
% [272]
% multiply(X,multiply(c,inverse(b greatest_lower_bound c))) greatest_lower_bound X
% -> X
% Current number of equations to process: 2570
% Current number of ordered equations: 0
% Current number of rules: 240
% New rule produced :
% [273]
% multiply(X,multiply(Y,inverse(identity greatest_lower_bound Y))) greatest_lower_bound X
% -> X
% Current number of equations to process: 2569
% Current number of ordered equations: 0
% Current number of rules: 241
% New rule produced :
% [274]
% multiply(X,multiply(Y,inverse(Y greatest_lower_bound Z))) greatest_lower_bound X
% -> X
% Rule
% [272]
% multiply(X,multiply(c,inverse(b greatest_lower_bound c))) greatest_lower_bound X
% -> X collapsed.
% Rule
% [273]
% multiply(X,multiply(Y,inverse(identity greatest_lower_bound Y))) greatest_lower_bound X
% -> X collapsed.
% Current number of equations to process: 2568
% Current number of ordered equations: 0
% Current number of rules: 240
% New rule produced :
% [275]
% multiply(X,multiply(inverse(Y greatest_lower_bound Z),Y)) greatest_lower_bound X
% -> X
% Rule
% [258]
% multiply(X,multiply(inverse(X greatest_lower_bound Y),Y)) greatest_lower_bound X
% -> X collapsed.
% Rule
% [271]
% multiply(X,multiply(inverse(b greatest_lower_bound c),c)) greatest_lower_bound X
% -> X collapsed.
% Current number of equations to process: 2567
% Current number of ordered equations: 0
% Current number of rules: 239
% New rule produced :
% [276]
% multiply(inverse(b greatest_lower_bound c),multiply(c,X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 2565
% Current number of ordered equations: 0
% Current number of rules: 240
% New rule produced :
% [277]
% multiply(c,multiply(inverse(b greatest_lower_bound c),X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 2564
% Current number of ordered equations: 0
% Current number of rules: 241
% New rule produced :
% [278]
% multiply(X,multiply(inverse(identity greatest_lower_bound X),Y)) greatest_lower_bound Y
% -> Y
% Current number of equations to process: 2563
% Current number of ordered equations: 0
% Current number of rules: 242
% New rule produced :
% [279]
% multiply(X,multiply(inverse(X greatest_lower_bound Y),Z)) greatest_lower_bound Z
% -> Z
% Rule
% [259]
% multiply(X,multiply(inverse(X greatest_lower_bound Y),Y)) greatest_lower_bound Y
% -> Y collapsed.
% Rule
% [277]
% multiply(c,multiply(inverse(b greatest_lower_bound c),X)) greatest_lower_bound X
% -> X collapsed.
% Rule
% [278]
% multiply(X,multiply(inverse(identity greatest_lower_bound X),Y)) greatest_lower_bound Y
% -> Y collapsed.
% Current number of equations to process: 2562
% Current number of ordered equations: 0
% Current number of rules: 240
% New rule produced :
% [280]
% multiply(inverse(X greatest_lower_bound Y),multiply(X,Z)) greatest_lower_bound Z
% -> Z
% Rule
% [276]
% multiply(inverse(b greatest_lower_bound c),multiply(c,X)) greatest_lower_bound X
% -> X collapsed.
% Current number of equations to process: 2561
% Current number of ordered equations: 0
% Current number of rules: 240
% New rule produced :
% [281]
% identity greatest_lower_bound multiply(inverse(b greatest_lower_bound c greatest_lower_bound X),a)
% -> identity
% Current number of equations to process: 2559
% Current number of ordered equations: 0
% Current number of rules: 241
% New rule produced :
% [282]
% identity greatest_lower_bound multiply(a,inverse(b greatest_lower_bound c greatest_lower_bound X))
% -> identity
% Current number of equations to process: 2558
% Current number of ordered equations: 0
% Current number of rules: 242
% New rule produced :
% [283]
% identity least_upper_bound multiply(X,X) least_upper_bound X ->
% identity least_upper_bound multiply(X,X)
% Current number of equations to process: 3127
% Current number of ordered equations: 0
% Current number of rules: 243
% New rule produced :
% [284]
% (identity least_upper_bound multiply(X,X) least_upper_bound Y) greatest_lower_bound X
% -> X
% Current number of equations to process: 3126
% Current number of ordered equations: 0
% Current number of rules: 244
% New rule produced :
% [285]
% inverse(identity least_upper_bound multiply(X,X)) least_upper_bound inverse(X)
% -> inverse(X)
% Current number of equations to process: 3125
% Current number of ordered equations: 0
% Current number of rules: 245
% New rule produced :
% [286]
% identity least_upper_bound inverse(a least_upper_bound inverse(b) least_upper_bound 
% inverse(c)) -> Cputime limit exceeded (core dumped)
% 
% EOF
%------------------------------------------------------------------------------