%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP167-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n127.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   : Unsatisfiable 53.22s
% Output   : Refutation 53.22s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP167-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n127.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 05:48:18 CDT 2014
% % CPUTime  : 53.22 
% Processing problem /tmp/CiME_53874_n127.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " least_upper_bound,greatest_lower_bound : AC; a,identity : constant;  negative_part : 1;  positive_part : 1;  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));
% positive_part(X) = X least_upper_bound identity;
% negative_part(X) = X greatest_lower_bound identity;
% X least_upper_bound (Y greatest_lower_bound Z) = (X least_upper_bound Y) greatest_lower_bound (X least_upper_bound Z);
% X greatest_lower_bound (Y least_upper_bound Z) = (X greatest_lower_bound Y) least_upper_bound (X greatest_lower_bound Z);
% ";
% 
% let s1 = status F "
% a lr_lex;
% negative_part lr_lex;
% positive_part lr_lex;
% inverse lr_lex;
% identity lr_lex;
% least_upper_bound mul;
% greatest_lower_bound mul;
% multiply mul;
% ";
% 
% let p1 = precedence F "
% positive_part > negative_part > multiply > inverse > greatest_lower_bound > least_upper_bound > identity > a";
% 
% let s2 = status F "
% a mul;
% negative_part mul;
% positive_part mul;
% least_upper_bound mul;
% greatest_lower_bound mul;
% inverse mul;
% multiply mul;
% identity mul;
% ";
% 
% let p2 = precedence F "
% positive_part > negative_part > multiply > inverse > greatest_lower_bound > least_upper_bound > identity = a";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " a = multiply(positive_part(a),negative_part(a));"
% ;
% (*
% let Red_Axioms = normalize_equations Defining_rules Axioms;
% 
% let Red_Conjectures =  normalize_equations Defining_rules Conjectures;
% *)
% #time on;
% 
% let res = prove_conj_by_ordered_completion o Axioms Conjectures;
% 
% #time off;
% 
% 
% let status = if res then "unsatisfiable" else "satisfiable";
% #quit;
% Verbose level is now 1
% 
% F : signature = <signature>
% X : variable_set = <variable set>
% 
% Axioms : (F,X) equations = { multiply(multiply(X,Y),Z) =
% multiply(X,multiply(Y,Z)),
% multiply(identity,X) = X,
% multiply(inverse(X),X) = identity,
% X least_upper_bound X = X,
% X greatest_lower_bound X = X,
% (X greatest_lower_bound Y) least_upper_bound X =
% X,
% (X least_upper_bound Y) greatest_lower_bound X =
% X,
% multiply(X,Y least_upper_bound Z) =
% multiply(X,Y) least_upper_bound multiply(X,Z),
% multiply(X,Y greatest_lower_bound Z) =
% multiply(X,Y) greatest_lower_bound multiply(X,Z),
% multiply(Y least_upper_bound Z,X) =
% multiply(Y,X) least_upper_bound multiply(Z,X),
% multiply(Y greatest_lower_bound Z,X) =
% multiply(Y,X) greatest_lower_bound multiply(Z,X),
% inverse(identity) = identity,
% inverse(inverse(X)) = X,
% inverse(multiply(X,Y)) =
% multiply(inverse(Y),inverse(X)),
% positive_part(X) = identity least_upper_bound X,
% negative_part(X) =
% identity greatest_lower_bound X,
% (Y greatest_lower_bound Z) least_upper_bound X =
% (X least_upper_bound Y) greatest_lower_bound 
% (X least_upper_bound Z),
% (Y least_upper_bound Z) greatest_lower_bound X =
% (X greatest_lower_bound Y) least_upper_bound 
% (X greatest_lower_bound Z) } (18 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 =
% multiply(positive_part(a),negative_part(a)) }
% (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: 17
% 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: 16
% 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: 15
% 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: 14
% 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: 13
% Current number of rules: 5
% New rule produced : [6] identity least_upper_bound X -> positive_part(X)
% Current number of equations to process: 0
% Current number of ordered equations: 12
% Current number of rules: 6
% New rule produced : [7] identity greatest_lower_bound X -> negative_part(X)
% Current number of equations to process: 0
% Current number of ordered equations: 11
% 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: 10
% 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: 9
% 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: 8
% 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: 7
% 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: 6
% Current number of rules: 12
% New rule produced :
% [13]
% (X greatest_lower_bound Y) least_upper_bound (X greatest_lower_bound Z) ->
% (Y least_upper_bound Z) greatest_lower_bound X
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 13
% New rule produced :
% [14]
% (Y greatest_lower_bound Z) least_upper_bound X ->
% (X least_upper_bound Y) greatest_lower_bound (X least_upper_bound Z)
% Rule [9] (X greatest_lower_bound Y) least_upper_bound X -> X collapsed.
% Rule
% [13]
% (X greatest_lower_bound Y) least_upper_bound (X greatest_lower_bound Z) ->
% (Y least_upper_bound Z) greatest_lower_bound X collapsed.
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 12
% New rule produced :
% [15]
% 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 :
% [16]
% 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 :
% [17]
% 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 :
% [18]
% 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 : [19] positive_part(identity) -> identity
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [20] negative_part(identity) -> identity
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [21] positive_part(positive_part(X)) -> positive_part(X)
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [22] negative_part(negative_part(X)) -> negative_part(X)
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [23] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [24] negative_part(positive_part(X)) -> identity
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [25] positive_part(X) greatest_lower_bound X -> X
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [26] positive_part(X) least_upper_bound X -> positive_part(X)
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [27] negative_part(X) greatest_lower_bound X -> negative_part(X)
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [28] multiply(inverse(X),identity) -> inverse(X)
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [29] negative_part(positive_part(X) least_upper_bound Y) -> identity
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [30]
% positive_part(X) least_upper_bound Y -> positive_part(X least_upper_bound Y)
% Rule [26] positive_part(X) least_upper_bound X -> positive_part(X) collapsed.
% Rule [29] negative_part(positive_part(X) least_upper_bound Y) -> identity
% collapsed.
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [31]
% negative_part(X) greatest_lower_bound Y ->
% negative_part(X greatest_lower_bound Y)
% Rule [27] negative_part(X) greatest_lower_bound X -> negative_part(X)
% collapsed.
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [32]
% negative_part(positive_part(X) greatest_lower_bound Y) -> negative_part(Y)
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [33] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [34]
% positive_part(X) greatest_lower_bound positive_part(Y) ->
% positive_part(X greatest_lower_bound Y)
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [35]
% negative_part(X) least_upper_bound Y ->
% (X least_upper_bound Y) greatest_lower_bound positive_part(Y)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [36]
% multiply(X,positive_part(Y)) ->
% multiply(X,identity) least_upper_bound multiply(X,Y)
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [37]
% multiply(X,negative_part(Y)) ->
% multiply(X,identity) greatest_lower_bound multiply(X,Y)
% The conjecture has been reduced. 
% Conjecture is now:
% a = multiply(positive_part(a),a) greatest_lower_bound multiply(positive_part(a),identity)
% 
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [38] multiply(positive_part(X),Y) -> multiply(X,Y) least_upper_bound Y
% The conjecture has been reduced. 
% Conjecture is now:
% a = (a least_upper_bound multiply(a,a)) greatest_lower_bound positive_part(
% multiply(a,identity))
% 
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [39] multiply(negative_part(X),Y) -> multiply(X,Y) greatest_lower_bound Y
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [40] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [41] positive_part(X least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 36
% Rule [37]
% multiply(X,negative_part(Y)) ->
% multiply(X,identity) greatest_lower_bound multiply(X,Y) is composed into 
% [37] multiply(X,negative_part(Y)) -> multiply(X,Y) greatest_lower_bound X
% Rule [36]
% multiply(X,positive_part(Y)) ->
% multiply(X,identity) least_upper_bound multiply(X,Y) is composed into 
% [36] multiply(X,positive_part(Y)) -> multiply(X,Y) least_upper_bound X
% New rule produced : [42] multiply(X,identity) -> X
% Rule [28] multiply(inverse(X),identity) -> inverse(X) collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% a = (a least_upper_bound multiply(a,a)) greatest_lower_bound positive_part(a)
% 
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [43]
% positive_part(X greatest_lower_bound Y) greatest_lower_bound Y ->
% positive_part(X) greatest_lower_bound Y
% Current number of equations to process: 41
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [44] positive_part(negative_part(X)) -> identity
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [45]
% positive_part(positive_part(X) greatest_lower_bound Y) ->
% positive_part(X greatest_lower_bound Y)
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [46]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(inverse(positive_part(Y)),inverse(X))
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [47]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(inverse(negative_part(Y)),inverse(X))
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [48]
% inverse(positive_part(inverse(X))) -> multiply(inverse(positive_part(X)),X)
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [49]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),inverse(positive_part(X)))
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [50]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),inverse(negative_part(X)))
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [51]
% inverse(negative_part(inverse(X))) -> multiply(inverse(negative_part(X)),X)
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 45
% Rule [48]
% inverse(positive_part(inverse(X))) ->
% multiply(inverse(positive_part(X)),X) is composed into [48]
% inverse(positive_part(
% inverse(X)))
% ->
% multiply(X,
% inverse(positive_part(X)))
% New rule produced :
% [52]
% multiply(inverse(positive_part(X)),X) ->
% multiply(X,inverse(positive_part(X)))
% Current number of equations to process: 105
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [53]
% multiply(inverse(positive_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(positive_part(X)))
% Current number of equations to process: 110
% Current number of ordered equations: 0
% Current number of rules: 47
% Rule [51]
% inverse(negative_part(inverse(X))) ->
% multiply(inverse(negative_part(X)),X) is composed into [51]
% inverse(negative_part(
% inverse(X)))
% ->
% multiply(X,
% inverse(negative_part(X)))
% New rule produced :
% [54]
% multiply(inverse(negative_part(X)),X) ->
% multiply(X,inverse(negative_part(X)))
% Current number of equations to process: 115
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [55]
% inverse(negative_part(multiply(X,inverse(positive_part(X))))) ->
% positive_part(inverse(X))
% Current number of equations to process: 132
% Current number of ordered equations: 1
% Current number of rules: 49
% New rule produced :
% [56]
% inverse(positive_part(multiply(X,inverse(negative_part(X))))) ->
% negative_part(inverse(X))
% Current number of equations to process: 132
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [57]
% multiply(inverse(negative_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(negative_part(X)))
% Current number of equations to process: 133
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [58]
% negative_part(multiply(X,inverse(positive_part(X)))) ->
% multiply(X,inverse(positive_part(X)))
% Rule
% [55]
% inverse(negative_part(multiply(X,inverse(positive_part(X))))) ->
% positive_part(inverse(X)) collapsed.
% Current number of equations to process: 147
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [59]
% positive_part(multiply(X,inverse(negative_part(X)))) ->
% multiply(X,inverse(negative_part(X)))
% Rule
% [56]
% inverse(positive_part(multiply(X,inverse(negative_part(X))))) ->
% negative_part(inverse(X)) collapsed.
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [60] positive_part(multiply(X,inverse(positive_part(X)))) -> identity
% Current number of equations to process: 168
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [61] negative_part(inverse(positive_part(X))) -> inverse(positive_part(X))
% Current number of equations to process: 168
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [62] negative_part(multiply(X,inverse(negative_part(X)))) -> identity
% Current number of equations to process: 172
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [63] positive_part(inverse(negative_part(X))) -> inverse(negative_part(X))
% Current number of equations to process: 179
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced : [64] positive_part(inverse(positive_part(X))) -> identity
% Current number of equations to process: 190
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced : [65] negative_part(inverse(negative_part(X))) -> identity
% Current number of equations to process: 206
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [66]
% negative_part(inverse(negative_part(X)) greatest_lower_bound Y) ->
% negative_part(Y)
% Current number of equations to process: 210
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [67]
% positive_part(inverse(positive_part(X)) greatest_lower_bound Y) -> identity
% Current number of equations to process: 216
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [68]
% positive_part(inverse(positive_part(Y)) least_upper_bound X) ->
% positive_part(X)
% Current number of equations to process: 223
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [69] negative_part(inverse(negative_part(X)) least_upper_bound Y) -> identity
% Current number of equations to process: 225
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [70] multiply(X,inverse(positive_part(Y))) least_upper_bound X -> X
% Current number of equations to process: 224
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [71] multiply(inverse(positive_part(Y)),X) least_upper_bound X -> X
% Current number of equations to process: 223
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [72] multiply(X,inverse(negative_part(Y))) greatest_lower_bound X -> X
% Current number of equations to process: 222
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [73] multiply(inverse(negative_part(Y)),X) greatest_lower_bound X -> X
% Current number of equations to process: 221
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [74]
% positive_part(Y) greatest_lower_bound inverse(positive_part(X)) ->
% inverse(positive_part(X))
% Current number of equations to process: 230
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [75]
% positive_part(multiply(X,inverse(positive_part(X))) greatest_lower_bound Y)
% -> identity
% Current number of equations to process: 389
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [76]
% negative_part(inverse(positive_part(X)) greatest_lower_bound Y) ->
% inverse(positive_part(X)) greatest_lower_bound Y
% Current number of equations to process: 391
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [77]
% positive_part(inverse(negative_part(X)) least_upper_bound Y) ->
% inverse(negative_part(X)) least_upper_bound Y
% Current number of equations to process: 390
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [78]
% negative_part(multiply(X,inverse(negative_part(X))) least_upper_bound Y) ->
% identity
% Current number of equations to process: 387
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [79]
% positive_part(multiply(inverse(positive_part(X)),inverse(positive_part(Y))))
% -> identity
% Current number of equations to process: 386
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [80]
% positive_part(multiply(X,inverse(negative_part(Y)))) greatest_lower_bound X
% -> X
% Current number of equations to process: 385
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [81]
% negative_part(multiply(inverse(negative_part(X)),inverse(negative_part(Y))))
% -> identity
% Current number of equations to process: 384
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [82]
% positive_part(multiply(inverse(negative_part(Y)),X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 383
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [83]
% inverse(negative_part(X)) greatest_lower_bound inverse(positive_part(Y)) ->
% inverse(positive_part(Y))
% Current number of equations to process: 380
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [84]
% negative_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y)) ->
% identity
% Current number of equations to process: 395
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [85]
% positive_part(inverse(inverse(negative_part(X)) least_upper_bound Y)) ->
% identity
% Current number of equations to process: 410
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [86]
% inverse(negative_part(X)) least_upper_bound inverse(positive_part(Y)) ->
% inverse(negative_part(X))
% Current number of equations to process: 424
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [87]
% negative_part(multiply(X,inverse(negative_part(X))) greatest_lower_bound Y)
% -> negative_part(Y)
% Current number of equations to process: 585
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [88]
% positive_part(multiply(Y,inverse(positive_part(Y))) least_upper_bound X) ->
% positive_part(X)
% Current number of equations to process: 588
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [89]
% positive_part(X) greatest_lower_bound inverse(negative_part(Y)) ->
% positive_part(inverse(negative_part(Y)) greatest_lower_bound X)
% Current number of equations to process: 586
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [90]
% (inverse(negative_part(Y)) least_upper_bound X) greatest_lower_bound 
% positive_part(X) -> positive_part(X)
% Current number of equations to process: 584
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [91]
% negative_part((inverse(negative_part(Y)) least_upper_bound Z) greatest_lower_bound X)
% -> negative_part(X)
% Current number of equations to process: 583
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [92]
% inverse(positive_part(X)) least_upper_bound multiply(X,inverse(positive_part(X)))
% -> identity
% Current number of equations to process: 692
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [93] inverse(positive_part(X)) least_upper_bound X -> positive_part(X)
% Current number of equations to process: 716
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [94]
% inverse(negative_part(X)) greatest_lower_bound multiply(X,inverse(negative_part(X)))
% -> identity
% Current number of equations to process: 771
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [95] inverse(negative_part(X)) greatest_lower_bound X -> negative_part(X)
% Current number of equations to process: 795
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [96]
% inverse(negative_part(X least_upper_bound Y)) greatest_lower_bound X ->
% negative_part(X)
% Current number of equations to process: 856
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [97]
% positive_part(inverse(negative_part(X)) greatest_lower_bound Y) greatest_lower_bound X
% -> negative_part(X)
% Current number of equations to process: 906
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [98]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(inverse(positive_part(multiply(X,Y))),X)
% Current number of equations to process: 949
% Current number of ordered equations: 1
% Current number of rules: 90
% New rule produced :
% [99]
% multiply(inverse(positive_part(multiply(X,Y))),X) <->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 949
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [100] inverse(inverse(X) least_upper_bound Y) least_upper_bound X -> X
% Current number of equations to process: 998
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [101]
% inverse(X least_upper_bound Y) least_upper_bound inverse(X) -> inverse(X)
% Current number of equations to process: 1028
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [102] inverse(positive_part(X)) least_upper_bound inverse(X) -> inverse(X)
% Current number of equations to process: 1164
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [103]
% inverse(positive_part(inverse(X) least_upper_bound Y)) least_upper_bound X ->
% X
% Current number of equations to process: 1165
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [104]
% inverse(positive_part(X)) greatest_lower_bound inverse(X) ->
% inverse(positive_part(X))
% Current number of equations to process: 1295
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [105]
% positive_part(inverse(X) least_upper_bound X) ->
% inverse(X) least_upper_bound X
% Current number of equations to process: 1330
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [106] negative_part(inverse(X) least_upper_bound X) -> identity
% Current number of equations to process: 1509
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [107]
% negative_part((inverse(X) least_upper_bound X) greatest_lower_bound Y) ->
% negative_part(Y)
% Current number of equations to process: 1541
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [108]
% negative_part(inverse(X) least_upper_bound X least_upper_bound Y) -> identity
% Current number of equations to process: 1553
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [109]
% positive_part(multiply(inverse(positive_part(multiply(X,X))),X)) -> identity
% Current number of equations to process: 1555
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [110]
% inverse(X least_upper_bound Y) greatest_lower_bound inverse(X) ->
% inverse(X least_upper_bound Y)
% Current number of equations to process: 1613
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [111]
% inverse(positive_part(X least_upper_bound Y)) least_upper_bound inverse(Y) ->
% inverse(Y)
% Current number of equations to process: 1620
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [112]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(inverse(negative_part(multiply(X,Y))),X)
% Current number of equations to process: 1881
% Current number of ordered equations: 1
% Current number of rules: 104
% New rule produced :
% [113]
% multiply(inverse(negative_part(multiply(X,Y))),X) <->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 1881
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [114] inverse(inverse(X) greatest_lower_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 1954
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [115]
% positive_part(inverse(inverse(X) greatest_lower_bound Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 1955
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [116]
% inverse(X greatest_lower_bound Y) greatest_lower_bound inverse(X) ->
% inverse(X)
% Current number of equations to process: 1979
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [117]
% inverse(inverse(positive_part(X)) greatest_lower_bound Y) greatest_lower_bound X
% -> X
% Current number of equations to process: 2190
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [118]
% inverse(negative_part(inverse(X) greatest_lower_bound Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 2189
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [119] inverse(negative_part(X)) greatest_lower_bound inverse(X) -> inverse(X)
% Current number of equations to process: 2330
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [120]
% negative_part(inverse(X) greatest_lower_bound X) ->
% inverse(X) greatest_lower_bound X
% Current number of equations to process: 2864
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [121] positive_part(inverse(X)) greatest_lower_bound X -> negative_part(X)
% Current number of equations to process: 2979
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [122]
% positive_part(inverse(X) greatest_lower_bound Y) greatest_lower_bound X ->
% negative_part(X)
% Current number of equations to process: 2978
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [123] positive_part(inverse(X) greatest_lower_bound X) -> identity
% Current number of equations to process: 3012
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [124]
% positive_part(X) greatest_lower_bound inverse(X) -> negative_part(inverse(X))
% Current number of equations to process: 3062
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [125]
% positive_part(inverse(X) greatest_lower_bound X greatest_lower_bound Y) ->
% identity
% Current number of equations to process: 3127
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [126]
% positive_part(inverse(X least_upper_bound Y)) greatest_lower_bound X ->
% negative_part(X)
% Current number of equations to process: 3198
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [127]
% negative_part(multiply(inverse(negative_part(multiply(X,X))),X)) -> identity
% Current number of equations to process: 3197
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [128]
% positive_part(X greatest_lower_bound Y) greatest_lower_bound inverse(X) ->
% negative_part(inverse(X))
% Current number of equations to process: 3196
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [129]
% positive_part(inverse(X least_upper_bound Y) greatest_lower_bound X) ->
% identity
% Current number of equations to process: 3409
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [130]
% negative_part(inverse(inverse(X) greatest_lower_bound X greatest_lower_bound Y))
% -> identity
% Current number of equations to process: 3485
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [131]
% positive_part(inverse(inverse(X) least_upper_bound X least_upper_bound Y)) ->
% identity
% Current number of equations to process: 3841
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [132]
% positive_part(inverse(X greatest_lower_bound Y)) greatest_lower_bound 
% inverse(X) -> inverse(X)
% Current number of equations to process: 3939
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [133]
% inverse(negative_part(X greatest_lower_bound Y)) greatest_lower_bound 
% inverse(Y) -> inverse(Y)
% Current number of equations to process: 3960
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [134]
% (inverse(negative_part(X)) least_upper_bound Y) greatest_lower_bound 
% inverse(X) -> inverse(X)
% Current number of equations to process: 3957
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [135]
% positive_part(X) greatest_lower_bound inverse(Y) greatest_lower_bound Y ->
% inverse(Y) greatest_lower_bound Y
% Current number of equations to process: 3954
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [136]
% multiply(X,multiply(Y,inverse(positive_part(Y)))) least_upper_bound X -> X
% Current number of equations to process: 2053
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [137]
% multiply(Y,multiply(inverse(positive_part(Y)),X)) least_upper_bound X -> X
% Current number of equations to process: 2146
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [138]
% multiply(inverse(positive_part(X)),Y) greatest_lower_bound Y ->
% multiply(inverse(positive_part(X)),Y)
% Current number of equations to process: 2249
% Current number of ordered equations: 1
% Current number of rules: 130
% New rule produced :
% [139]
% multiply(X,multiply(Y,inverse(negative_part(Y)))) greatest_lower_bound X -> X
% Current number of equations to process: 2432
% Current number of ordered equations: 1
% Current number of rules: 131
% New rule produced :
% [140]
% multiply(Y,multiply(inverse(negative_part(Y)),X)) greatest_lower_bound X -> X
% Current number of equations to process: 2548
% Current number of ordered equations: 1
% Current number of rules: 132
% New rule produced :
% [141]
% multiply(X,inverse(negative_part(Y))) least_upper_bound X ->
% multiply(X,inverse(negative_part(Y)))
% Current number of equations to process: 2670
% Current number of ordered equations: 1
% Current number of rules: 133
% New rule produced :
% [142]
% multiply(inverse(negative_part(X)),Y) least_upper_bound Y ->
% multiply(inverse(negative_part(X)),Y)
% Current number of equations to process: 2801
% Current number of ordered equations: 1
% Current number of rules: 134
% New rule produced :
% [143]
% multiply(X,inverse(positive_part(Y))) greatest_lower_bound X ->
% multiply(X,inverse(positive_part(Y)))
% Current number of equations to process: 2934
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [144]
% (multiply(X,inverse(negative_part(Y))) least_upper_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 3117
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [145]
% (multiply(inverse(negative_part(Y)),X) least_upper_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 3273
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [146]
% negative_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y) least_upper_bound Z)
% -> identity
% Current number of equations to process: 3442
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [147]
% positive_part(inverse(inverse(negative_part(X)) least_upper_bound Y) greatest_lower_bound Z)
% -> identity
% Current number of equations to process: 3466
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [148]
% negative_part(inverse(multiply(X,inverse(positive_part(X))) greatest_lower_bound Y))
% -> identity
% Current number of equations to process: 3493
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [149]
% positive_part(inverse(multiply(X,inverse(negative_part(X))) least_upper_bound Y))
% -> identity
% Current number of equations to process: 3505
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [150]
% inverse(X) least_upper_bound multiply(X,inverse(positive_part(X))) ->
% positive_part(inverse(X))
% Current number of equations to process: 3523
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [151]
% inverse(X) greatest_lower_bound multiply(X,inverse(negative_part(X))) ->
% negative_part(inverse(X))
% Current number of equations to process: 3569
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [152]
% inverse(inverse(X) least_upper_bound Y) greatest_lower_bound X ->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 3623
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [153]
% (inverse(X) least_upper_bound Y) greatest_lower_bound inverse(positive_part(X))
% -> inverse(positive_part(X))
% Current number of equations to process: 4239
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [154]
% (inverse(X) least_upper_bound X) greatest_lower_bound inverse(positive_part(Y))
% -> inverse(positive_part(Y))
% Current number of equations to process: 4326
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [155]
% inverse(positive_part(multiply(X,X) least_upper_bound X)) ->
% inverse(positive_part(multiply(X,X)))
% Current number of equations to process: 4378
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [156]
% positive_part(multiply(X,X) least_upper_bound X) ->
% positive_part(multiply(X,X))
% Rule
% [155]
% inverse(positive_part(multiply(X,X) least_upper_bound X)) ->
% inverse(positive_part(multiply(X,X))) collapsed.
% Current number of equations to process: 4380
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [157] positive_part(multiply(X,X)) greatest_lower_bound X -> X
% Current number of equations to process: 4391
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [158] positive_part(multiply(X,X) greatest_lower_bound X) -> positive_part(X)
% Current number of equations to process: 4423
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [159]
% inverse(positive_part(multiply(X,X))) least_upper_bound inverse(X) ->
% inverse(X)
% Current number of equations to process: 4511
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [160]
% (inverse(inverse(X) greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 4586
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [161]
% inverse(inverse(X least_upper_bound Y) greatest_lower_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 3462
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [162]
% positive_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 3853
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [163]
% inverse(X greatest_lower_bound Y) greatest_lower_bound inverse(positive_part(X))
% -> inverse(positive_part(X))
% Current number of equations to process: 4140
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [164]
% positive_part(X) greatest_lower_bound inverse(X least_upper_bound Y) ->
% negative_part(inverse(X least_upper_bound Y))
% Current number of equations to process: 4458
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [165]
% positive_part(inverse(X least_upper_bound Y) greatest_lower_bound X greatest_lower_bound Z)
% -> identity
% Current number of equations to process: 4632
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [166]
% inverse(negative_part(multiply(X,X) greatest_lower_bound X)) ->
% inverse(negative_part(multiply(X,X)))
% Current number of equations to process: 4754
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [167]
% negative_part(multiply(X,X) greatest_lower_bound X) ->
% negative_part(multiply(X,X))
% Rule
% [166]
% inverse(negative_part(multiply(X,X) greatest_lower_bound X)) ->
% inverse(negative_part(multiply(X,X))) collapsed.
% Current number of equations to process: 4757
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [168]
% inverse(negative_part(multiply(X,X))) greatest_lower_bound inverse(X) ->
% inverse(X)
% Current number of equations to process: 4769
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [169]
% positive_part(inverse(X)) greatest_lower_bound multiply(X,X) ->
% negative_part(multiply(X,X))
% Current number of equations to process: 4809
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [170]
% positive_part(inverse(X) greatest_lower_bound multiply(X,X)) -> identity
% Current number of equations to process: 4910
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [171]
% positive_part(multiply(inverse(X),inverse(X)) greatest_lower_bound X) ->
% identity
% Current number of equations to process: 4949
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [172]
% positive_part(multiply(X,X)) greatest_lower_bound inverse(X) ->
% negative_part(inverse(X))
% Current number of equations to process: 4948
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [173]
% positive_part(multiply(inverse(X),inverse(X))) greatest_lower_bound X ->
% negative_part(X)
% Current number of equations to process: 2514
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [174]
% positive_part(multiply(inverse(positive_part(X)),inverse(Y)) greatest_lower_bound Y)
% -> identity
% Current number of equations to process: 2757
% Current number of ordered equations: 0
% Current number of rules: 164
% New rule produced :
% [175]
% positive_part(multiply(inverse(X),inverse(positive_part(Y))) greatest_lower_bound X)
% -> identity
% Current number of equations to process: 2801
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [176]
% positive_part(inverse(X) greatest_lower_bound multiply(inverse(positive_part(Y)),X))
% -> identity
% Current number of equations to process: 2841
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [177]
% negative_part(inverse(X) least_upper_bound multiply(X,inverse(negative_part(Y))))
% -> identity
% Current number of equations to process: 2869
% Current number of ordered equations: 1
% Current number of rules: 167
% New rule produced :
% [178]
% negative_part(multiply(inverse(X),inverse(negative_part(Y))) least_upper_bound X)
% -> identity
% Current number of equations to process: 2869
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced :
% [179]
% negative_part(inverse(X) least_upper_bound multiply(inverse(negative_part(Y)),X))
% -> identity
% Current number of equations to process: 2903
% Current number of ordered equations: 1
% Current number of rules: 169
% New rule produced :
% [180]
% negative_part(multiply(inverse(negative_part(X)),inverse(Y)) least_upper_bound Y)
% -> identity
% Current number of equations to process: 2903
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced :
% [181]
% negative_part(inverse(X greatest_lower_bound Y) least_upper_bound X) ->
% identity
% Current number of equations to process: 2936
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [182]
% positive_part(inverse(X) greatest_lower_bound multiply(X,inverse(positive_part(Y))))
% -> identity
% Current number of equations to process: 2979
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [183]
% positive_part(inverse(X)) greatest_lower_bound multiply(X,inverse(negative_part(X)))
% -> identity
% Current number of equations to process: 3009
% Current number of ordered equations: 0
% Current number of rules: 173
% New rule produced :
% [184]
% inverse(positive_part(multiply(inverse(X),inverse(X)))) least_upper_bound X
% -> X
% Current number of equations to process: 3072
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced :
% [185]
% (inverse(negative_part(Y)) least_upper_bound multiply(X,X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 3282
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced :
% [186]
% inverse(negative_part(multiply(inverse(X),inverse(X)))) greatest_lower_bound X
% -> X
% Current number of equations to process: 3420
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced :
% [187]
% positive_part(inverse(X) greatest_lower_bound multiply(X,X) greatest_lower_bound Y)
% -> identity
% Current number of equations to process: 3787
% Current number of ordered equations: 0
% Current number of rules: 177
% New rule produced :
% [188]
% negative_part(inverse(multiply(inverse(X),inverse(X)) greatest_lower_bound X))
% -> identity
% Current number of equations to process: 3830
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [189]
% negative_part(inverse(X greatest_lower_bound Y) least_upper_bound X least_upper_bound Z)
% -> identity
% Current number of equations to process: 3843
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [190]
% positive_part(inverse(X) least_upper_bound multiply(Y,Y)) greatest_lower_bound Y
% -> Y
% Current number of equations to process: 3952
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [191]
% positive_part(multiply(X,X) least_upper_bound Y) greatest_lower_bound X -> X
% Rule
% [190]
% positive_part(inverse(X) least_upper_bound multiply(Y,Y)) greatest_lower_bound Y
% -> Y collapsed.
% Current number of equations to process: 3957
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [192]
% positive_part((multiply(X,X) least_upper_bound Y) greatest_lower_bound X) ->
% positive_part(X)
% Current number of equations to process: 4080
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [193]
% positive_part(inverse(X least_upper_bound Y) greatest_lower_bound multiply(X,X))
% -> identity
% Current number of equations to process: 4107
% Current number of ordered equations: 0
% Current number of rules: 182
% New rule produced :
% [194]
% positive_part((Y least_upper_bound Z) greatest_lower_bound X) greatest_lower_bound Y
% -> positive_part(X) greatest_lower_bound Y
% Current number of equations to process: 4147
% Current number of ordered equations: 0
% Current number of rules: 183
% New rule produced :
% [195]
% positive_part((inverse(positive_part(Z)) least_upper_bound Y) greatest_lower_bound X)
% -> positive_part(X greatest_lower_bound Y)
% Current number of equations to process: 4511
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [196]
% positive_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y)) ->
% inverse(inverse(positive_part(X)) greatest_lower_bound Y)
% Rule
% [162]
% positive_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y)) greatest_lower_bound X
% -> X collapsed.
% Current number of equations to process: 4584
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [197]
% negative_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y) greatest_lower_bound Z)
% -> negative_part(Z)
% Current number of equations to process: 4610
% Current number of ordered equations: 0
% Current number of rules: 185
% New rule produced :
% [198]
% negative_part(inverse(inverse(negative_part(X)) least_upper_bound Y)) ->
% inverse(inverse(negative_part(X)) least_upper_bound Y)
% Current number of equations to process: 4653
% Current number of ordered equations: 0
% Current number of rules: 186
% New rule produced :
% [199]
% positive_part(inverse(inverse(negative_part(X)) least_upper_bound Y) least_upper_bound Z)
% -> positive_part(Z)
% Current number of equations to process: 4666
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [200]
% inverse(positive_part(multiply(X,inverse(positive_part(Y))))) least_upper_bound X
% -> positive_part(X)
% Current number of equations to process: 4712
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [201]
% inverse(positive_part(multiply(inverse(positive_part(X)),Y))) least_upper_bound Y
% -> positive_part(Y)
% Current number of equations to process: 4794
% Current number of ordered equations: 0
% Current number of rules: 189
% New rule produced :
% [202]
% inverse(negative_part(multiply(X,inverse(negative_part(Y))))) greatest_lower_bound X
% -> negative_part(X)
% Current number of equations to process: 4885
% Current number of ordered equations: 0
% Current number of rules: 190
% New rule produced :
% [203]
% inverse(negative_part(multiply(inverse(negative_part(X)),Y))) greatest_lower_bound Y
% -> negative_part(Y)
% Current number of equations to process: 4969
% Current number of ordered equations: 0
% Current number of rules: 191
% New rule produced :
% [204]
% positive_part(inverse(inverse(positive_part(X)) least_upper_bound Y) least_upper_bound X)
% -> positive_part(X)
% Current number of equations to process: 2230
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced :
% [205]
% negative_part(inverse(inverse(negative_part(X)) least_upper_bound Y) least_upper_bound X)
% -> negative_part(X)
% Current number of equations to process: 2264
% Current number of ordered equations: 0
% Current number of rules: 193
% New rule produced :
% [206]
% positive_part(inverse(X)) greatest_lower_bound inverse(X least_upper_bound Y)
% -> inverse(X least_upper_bound Y)
% Current number of equations to process: 2291
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [207]
% positive_part(inverse(X) least_upper_bound X least_upper_bound Y) ->
% inverse(X) least_upper_bound X least_upper_bound Y
% Current number of equations to process: 2488
% Current number of ordered equations: 0
% Current number of rules: 195
% New rule produced :
% [208]
% (inverse(Y) least_upper_bound X least_upper_bound Y) greatest_lower_bound 
% positive_part(X) -> positive_part(X)
% Current number of equations to process: 2599
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [209]
% (inverse(X) least_upper_bound X) greatest_lower_bound positive_part(X) ->
% positive_part(X)
% Current number of equations to process: 2617
% Current number of ordered equations: 0
% Current number of rules: 197
% New rule produced :
% [210]
% (inverse(X) least_upper_bound X) greatest_lower_bound positive_part(inverse(X))
% -> positive_part(inverse(X))
% Current number of equations to process: 2618
% Current number of ordered equations: 0
% Current number of rules: 198
% New rule produced :
% [211]
% negative_part((inverse(Y) least_upper_bound Y least_upper_bound Z) greatest_lower_bound X)
% -> negative_part(X)
% Current number of equations to process: 3175
% Current number of ordered equations: 0
% Current number of rules: 199
% New rule produced :
% [212]
% negative_part(inverse(inverse(negative_part(X)) greatest_lower_bound Y) greatest_lower_bound X)
% -> negative_part(X)
% Current number of equations to process: 3245
% Current number of ordered equations: 0
% Current number of rules: 200
% New rule produced :
% [213]
% inverse(positive_part(inverse(negative_part(X)) greatest_lower_bound Y)) greatest_lower_bound X
% -> negative_part(X)
% Current number of equations to process: 3265
% Current number of ordered equations: 0
% Current number of rules: 201
% New rule produced :
% [214]
% inverse(positive_part(X)) greatest_lower_bound Y ->
% negative_part(inverse(X) greatest_lower_bound Y)
% Rule
% [67]
% positive_part(inverse(positive_part(X)) greatest_lower_bound Y) -> identity
% collapsed.
% Rule
% [74]
% positive_part(Y) greatest_lower_bound inverse(positive_part(X)) ->
% inverse(positive_part(X)) collapsed.
% Rule
% [76]
% negative_part(inverse(positive_part(X)) greatest_lower_bound Y) ->
% inverse(positive_part(X)) greatest_lower_bound Y collapsed.
% Rule
% [83]
% inverse(negative_part(X)) greatest_lower_bound inverse(positive_part(Y)) ->
% inverse(positive_part(Y)) collapsed.
% Rule
% [84]
% negative_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y)) ->
% identity collapsed.
% Rule
% [104]
% inverse(positive_part(X)) greatest_lower_bound inverse(X) ->
% inverse(positive_part(X)) collapsed.
% Rule
% [117]
% inverse(inverse(positive_part(X)) greatest_lower_bound Y) greatest_lower_bound X
% -> X collapsed.
% Rule
% [146]
% negative_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y) least_upper_bound Z)
% -> identity collapsed.
% Rule
% [153]
% (inverse(X) least_upper_bound Y) greatest_lower_bound inverse(positive_part(X))
% -> inverse(positive_part(X)) collapsed.
% Rule
% [154]
% (inverse(X) least_upper_bound X) greatest_lower_bound inverse(positive_part(Y))
% -> inverse(positive_part(Y)) collapsed.
% Rule
% [163]
% inverse(X greatest_lower_bound Y) greatest_lower_bound inverse(positive_part(X))
% -> inverse(positive_part(X)) collapsed.
% Rule
% [196]
% positive_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y)) ->
% inverse(inverse(positive_part(X)) greatest_lower_bound Y) collapsed.
% Rule
% [197]
% negative_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y) greatest_lower_bound Z)
% -> negative_part(Z) collapsed.
% Rule
% [213]
% inverse(positive_part(inverse(negative_part(X)) greatest_lower_bound Y)) greatest_lower_bound X
% -> negative_part(X) collapsed.
% Current number of equations to process: 3363
% Current number of ordered equations: 0
% Current number of rules: 188
% Rule [98]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(inverse(positive_part(multiply(X,Y))),X) is composed into 
% [98]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(negative_part(inverse(multiply(X,Y))),X)
% Rule [49]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),inverse(positive_part(X))) is composed into 
% [49]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),negative_part(inverse(X)))
% Rule [46]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(inverse(positive_part(Y)),inverse(X)) is composed into 
% [46]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(negative_part(inverse(Y)),inverse(X))
% New rule produced :
% [215] inverse(positive_part(X)) -> negative_part(inverse(X))
% Rule
% [48]
% inverse(positive_part(inverse(X))) -> multiply(X,inverse(positive_part(X)))
% collapsed.
% Rule
% [52]
% multiply(inverse(positive_part(X)),X) ->
% multiply(X,inverse(positive_part(X))) collapsed.
% Rule
% [53]
% multiply(inverse(positive_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(positive_part(X))) collapsed.
% Rule
% [58]
% negative_part(multiply(X,inverse(positive_part(X)))) ->
% multiply(X,inverse(positive_part(X))) collapsed.
% Rule [60] positive_part(multiply(X,inverse(positive_part(X)))) -> identity
% collapsed.
% Rule
% [61] negative_part(inverse(positive_part(X))) -> inverse(positive_part(X))
% collapsed.
% Rule [64] positive_part(inverse(positive_part(X))) -> identity collapsed.
% Rule
% [68]
% positive_part(inverse(positive_part(Y)) least_upper_bound X) ->
% positive_part(X) collapsed.
% Rule [70] multiply(X,inverse(positive_part(Y))) least_upper_bound X -> X
% collapsed.
% Rule [71] multiply(inverse(positive_part(Y)),X) least_upper_bound X -> X
% collapsed.
% Rule
% [75]
% positive_part(multiply(X,inverse(positive_part(X))) greatest_lower_bound Y)
% -> identity collapsed.
% Rule
% [79]
% positive_part(multiply(inverse(positive_part(X)),inverse(positive_part(Y))))
% -> identity collapsed.
% Rule
% [86]
% inverse(negative_part(X)) least_upper_bound inverse(positive_part(Y)) ->
% inverse(negative_part(X)) collapsed.
% Rule
% [88]
% positive_part(multiply(Y,inverse(positive_part(Y))) least_upper_bound X) ->
% positive_part(X) collapsed.
% Rule
% [92]
% inverse(positive_part(X)) least_upper_bound multiply(X,inverse(positive_part(X)))
% -> identity collapsed.
% Rule [93] inverse(positive_part(X)) least_upper_bound X -> positive_part(X)
% collapsed.
% Rule
% [99]
% multiply(inverse(positive_part(multiply(X,Y))),X) <->
% inverse(inverse(X) least_upper_bound Y) collapsed.
% Rule
% [102] inverse(positive_part(X)) least_upper_bound inverse(X) -> inverse(X)
% collapsed.
% Rule
% [103]
% inverse(positive_part(inverse(X) least_upper_bound Y)) least_upper_bound X ->
% X collapsed.
% Rule
% [109]
% positive_part(multiply(inverse(positive_part(multiply(X,X))),X)) -> identity
% collapsed.
% Rule
% [111]
% inverse(positive_part(X least_upper_bound Y)) least_upper_bound inverse(Y) ->
% inverse(Y) collapsed.
% Rule
% [136]
% multiply(X,multiply(Y,inverse(positive_part(Y)))) least_upper_bound X -> X
% collapsed.
% Rule
% [137]
% multiply(Y,multiply(inverse(positive_part(Y)),X)) least_upper_bound X -> X
% collapsed.
% Rule
% [138]
% multiply(inverse(positive_part(X)),Y) greatest_lower_bound Y ->
% multiply(inverse(positive_part(X)),Y) collapsed.
% Rule
% [143]
% multiply(X,inverse(positive_part(Y))) greatest_lower_bound X ->
% multiply(X,inverse(positive_part(Y))) collapsed.
% Rule
% [148]
% negative_part(inverse(multiply(X,inverse(positive_part(X))) greatest_lower_bound Y))
% -> identity collapsed.
% Rule
% [150]
% inverse(X) least_upper_bound multiply(X,inverse(positive_part(X))) ->
% positive_part(inverse(X)) collapsed.
% Rule
% [159]
% inverse(positive_part(multiply(X,X))) least_upper_bound inverse(X) ->
% inverse(X) collapsed.
% Rule
% [174]
% positive_part(multiply(inverse(positive_part(X)),inverse(Y)) greatest_lower_bound Y)
% -> identity collapsed.
% Rule
% [175]
% positive_part(multiply(inverse(X),inverse(positive_part(Y))) greatest_lower_bound X)
% -> identity collapsed.
% Rule
% [176]
% positive_part(inverse(X) greatest_lower_bound multiply(inverse(positive_part(Y)),X))
% -> identity collapsed.
% Rule
% [182]
% positive_part(inverse(X) greatest_lower_bound multiply(X,inverse(positive_part(Y))))
% -> identity collapsed.
% Rule
% [184]
% inverse(positive_part(multiply(inverse(X),inverse(X)))) least_upper_bound X
% -> X collapsed.
% Rule
% [195]
% positive_part((inverse(positive_part(Z)) least_upper_bound Y) greatest_lower_bound X)
% -> positive_part(X greatest_lower_bound Y) collapsed.
% Rule
% [200]
% inverse(positive_part(multiply(X,inverse(positive_part(Y))))) least_upper_bound X
% -> positive_part(X) collapsed.
% Rule
% [201]
% inverse(positive_part(multiply(inverse(positive_part(X)),Y))) least_upper_bound Y
% -> positive_part(Y) collapsed.
% Rule
% [204]
% positive_part(inverse(inverse(positive_part(X)) least_upper_bound Y) least_upper_bound X)
% -> positive_part(X) collapsed.
% Rule
% [214]
% inverse(positive_part(X)) greatest_lower_bound Y ->
% negative_part(inverse(X) greatest_lower_bound Y) collapsed.
% Current number of equations to process: 3475
% Current number of ordered equations: 0
% Current number of rules: 151
% Rule [54]
% multiply(inverse(negative_part(X)),X) ->
% multiply(X,inverse(negative_part(X))) is composed into [54]
% multiply(
% inverse(negative_part(X)),X)
% ->
% positive_part(X)
% Rule [51]
% inverse(negative_part(inverse(X))) ->
% multiply(X,inverse(negative_part(X))) is composed into [51]
% inverse(negative_part(
% inverse(X)))
% ->
% positive_part(X)
% New rule produced :
% [216] multiply(X,inverse(negative_part(X))) -> positive_part(X)
% Rule
% [59]
% positive_part(multiply(X,inverse(negative_part(X)))) ->
% multiply(X,inverse(negative_part(X))) collapsed.
% Rule [62] negative_part(multiply(X,inverse(negative_part(X)))) -> identity
% collapsed.
% Rule
% [78]
% negative_part(multiply(X,inverse(negative_part(X))) least_upper_bound Y) ->
% identity collapsed.
% Rule
% [87]
% negative_part(multiply(X,inverse(negative_part(X))) greatest_lower_bound Y)
% -> negative_part(Y) collapsed.
% Rule
% [94]
% inverse(negative_part(X)) greatest_lower_bound multiply(X,inverse(negative_part(X)))
% -> identity collapsed.
% Rule
% [139]
% multiply(X,multiply(Y,inverse(negative_part(Y)))) greatest_lower_bound X -> X
% collapsed.
% Rule
% [149]
% positive_part(inverse(multiply(X,inverse(negative_part(X))) least_upper_bound Y))
% -> identity collapsed.
% Rule
% [151]
% inverse(X) greatest_lower_bound multiply(X,inverse(negative_part(X))) ->
% negative_part(inverse(X)) collapsed.
% Rule
% [183]
% positive_part(inverse(X)) greatest_lower_bound multiply(X,inverse(negative_part(X)))
% -> identity collapsed.
% Current number of equations to process: 3484
% Current number of ordered equations: 0
% Current number of rules: 143
% Rule [112]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(inverse(negative_part(multiply(X,Y))),X) is composed into 
% [112]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(positive_part(inverse(multiply(X,Y))),X)
% Rule [50]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),inverse(negative_part(X))) is composed into 
% [50]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),positive_part(inverse(X)))
% Rule [47]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(inverse(negative_part(Y)),inverse(X)) is composed into 
% [47]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(positive_part(inverse(Y)),inverse(X))
% New rule produced :
% [217] inverse(negative_part(X)) -> positive_part(inverse(X))
% Rule [51] inverse(negative_part(inverse(X))) -> positive_part(X) collapsed.
% Rule [54] multiply(inverse(negative_part(X)),X) -> positive_part(X)
% collapsed.
% Rule
% [57]
% multiply(inverse(negative_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(negative_part(X))) collapsed.
% Rule
% [63] positive_part(inverse(negative_part(X))) -> inverse(negative_part(X))
% collapsed.
% Rule [65] negative_part(inverse(negative_part(X))) -> identity collapsed.
% Rule
% [66]
% negative_part(inverse(negative_part(X)) greatest_lower_bound Y) ->
% negative_part(Y) collapsed.
% Rule
% [69] negative_part(inverse(negative_part(X)) least_upper_bound Y) -> identity
% collapsed.
% Rule [72] multiply(X,inverse(negative_part(Y))) greatest_lower_bound X -> X
% collapsed.
% Rule [73] multiply(inverse(negative_part(Y)),X) greatest_lower_bound X -> X
% collapsed.
% Rule
% [77]
% positive_part(inverse(negative_part(X)) least_upper_bound Y) ->
% inverse(negative_part(X)) least_upper_bound Y collapsed.
% Rule
% [80]
% positive_part(multiply(X,inverse(negative_part(Y)))) greatest_lower_bound X
% -> X collapsed.
% Rule
% [81]
% negative_part(multiply(inverse(negative_part(X)),inverse(negative_part(Y))))
% -> identity collapsed.
% Rule
% [82]
% positive_part(multiply(inverse(negative_part(Y)),X)) greatest_lower_bound X
% -> X collapsed.
% Rule
% [85]
% positive_part(inverse(inverse(negative_part(X)) least_upper_bound Y)) ->
% identity collapsed.
% Rule
% [89]
% positive_part(X) greatest_lower_bound inverse(negative_part(Y)) ->
% positive_part(inverse(negative_part(Y)) greatest_lower_bound X) collapsed.
% Rule
% [90]
% (inverse(negative_part(Y)) least_upper_bound X) greatest_lower_bound 
% positive_part(X) -> positive_part(X) collapsed.
% Rule
% [91]
% negative_part((inverse(negative_part(Y)) least_upper_bound Z) greatest_lower_bound X)
% -> negative_part(X) collapsed.
% Rule
% [95] inverse(negative_part(X)) greatest_lower_bound X -> negative_part(X)
% collapsed.
% Rule
% [96]
% inverse(negative_part(X least_upper_bound Y)) greatest_lower_bound X ->
% negative_part(X) collapsed.
% Rule
% [97]
% positive_part(inverse(negative_part(X)) greatest_lower_bound Y) greatest_lower_bound X
% -> negative_part(X) collapsed.
% Rule
% [113]
% multiply(inverse(negative_part(multiply(X,Y))),X) <->
% inverse(inverse(X) greatest_lower_bound Y) collapsed.
% Rule
% [118]
% inverse(negative_part(inverse(X) greatest_lower_bound Y)) greatest_lower_bound X
% -> X collapsed.
% Rule
% [119] inverse(negative_part(X)) greatest_lower_bound inverse(X) -> inverse(X)
% collapsed.
% Rule
% [127]
% negative_part(multiply(inverse(negative_part(multiply(X,X))),X)) -> identity
% collapsed.
% Rule
% [133]
% inverse(negative_part(X greatest_lower_bound Y)) greatest_lower_bound 
% inverse(Y) -> inverse(Y) collapsed.
% Rule
% [134]
% (inverse(negative_part(X)) least_upper_bound Y) greatest_lower_bound 
% inverse(X) -> inverse(X) collapsed.
% Rule
% [140]
% multiply(Y,multiply(inverse(negative_part(Y)),X)) greatest_lower_bound X -> X
% collapsed.
% Rule
% [141]
% multiply(X,inverse(negative_part(Y))) least_upper_bound X ->
% multiply(X,inverse(negative_part(Y))) collapsed.
% Rule
% [142]
% multiply(inverse(negative_part(X)),Y) least_upper_bound Y ->
% multiply(inverse(negative_part(X)),Y) collapsed.
% Rule
% [144]
% (multiply(X,inverse(negative_part(Y))) least_upper_bound Z) greatest_lower_bound X
% -> X collapsed.
% Rule
% [145]
% (multiply(inverse(negative_part(Y)),X) least_upper_bound Z) greatest_lower_bound X
% -> X collapsed.
% Rule
% [147]
% positive_part(inverse(inverse(negative_part(X)) least_upper_bound Y) greatest_lower_bound Z)
% -> identity collapsed.
% Rule
% [168]
% inverse(negative_part(multiply(X,X))) greatest_lower_bound inverse(X) ->
% inverse(X) collapsed.
% Rule
% [177]
% negative_part(inverse(X) least_upper_bound multiply(X,inverse(negative_part(Y))))
% -> identity collapsed.
% Rule
% [178]
% negative_part(multiply(inverse(X),inverse(negative_part(Y))) least_upper_bound X)
% -> identity collapsed.
% Rule
% [179]
% negative_part(inverse(X) least_upper_bound multiply(inverse(negative_part(Y)),X))
% -> identity collapsed.
% Rule
% [180]
% negative_part(multiply(inverse(negative_part(X)),inverse(Y)) least_upper_bound Y)
% -> identity collapsed.
% Rule
% [185]
% (inverse(negative_part(Y)) least_upper_bound multiply(X,X)) greatest_lower_bound X
% -> X collapsed.
% Rule
% [186]
% inverse(negative_part(multiply(inverse(X),inverse(X)))) greatest_lower_bound X
% -> X collapsed.
% Rule
% [198]
% negative_part(inverse(inverse(negative_part(X)) least_upper_bound Y)) ->
% inverse(inverse(negative_part(X)) least_upper_bound Y) collapsed.
% Rule
% [199]
% positive_part(inverse(inverse(negative_part(X)) least_upper_bound Y) least_upper_bound Z)
% -> positive_part(Z) collapsed.
% Rule
% [202]
% inverse(negative_part(multiply(X,inverse(negative_part(Y))))) greatest_lower_bound X
% -> negative_part(X) collapsed.
% Rule
% [203]
% inverse(negative_part(multiply(inverse(negative_part(X)),Y))) greatest_lower_bound Y
% -> negative_part(Y) collapsed.
% Rule
% [205]
% negative_part(inverse(inverse(negative_part(X)) least_upper_bound Y) least_upper_bound X)
% -> negative_part(X) collapsed.
% Rule
% [212]
% negative_part(inverse(inverse(negative_part(X)) greatest_lower_bound Y) greatest_lower_bound X)
% -> negative_part(X) collapsed.
% Rule [216] multiply(X,inverse(negative_part(X))) -> positive_part(X)
% collapsed.
% Current number of equations to process: 3508
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [218]
% positive_part(inverse(positive_part(Y) greatest_lower_bound X)) ->
% positive_part(inverse(X))
% Current number of equations to process: 3518
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [219]
% negative_part(inverse(X) least_upper_bound multiply(inverse(X),inverse(X)))
% -> negative_part(inverse(X))
% Current number of equations to process: 3517
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [220]
% negative_part(inverse(positive_part(X) greatest_lower_bound Y)) ->
% negative_part(inverse(X greatest_lower_bound Y))
% Current number of equations to process: 3516
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [221]
% (inverse(X) least_upper_bound multiply(inverse(X),inverse(X))) greatest_lower_bound 
% positive_part(inverse(X)) -> inverse(X)
% Current number of equations to process: 3541
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [222] negative_part(multiply(X,X) least_upper_bound X) -> negative_part(X)
% Rule
% [219]
% negative_part(inverse(X) least_upper_bound multiply(inverse(X),inverse(X)))
% -> negative_part(inverse(X)) collapsed.
% Current number of equations to process: 3548
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [223]
% negative_part(inverse(inverse(Y) greatest_lower_bound X)) ->
% negative_part(inverse(X) least_upper_bound Y)
% Rule
% [130]
% negative_part(inverse(inverse(X) greatest_lower_bound X greatest_lower_bound Y))
% -> identity collapsed.
% Current number of equations to process: 3560
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [224]
% negative_part(multiply(inverse(X),inverse(X)) least_upper_bound X) ->
% identity
% Current number of equations to process: 3574
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [225]
% inverse(inverse(X) least_upper_bound Y) -> inverse(Y) greatest_lower_bound X
% Rule
% [98]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(negative_part(inverse(multiply(X,Y))),X) collapsed.
% Rule [100] inverse(inverse(X) least_upper_bound Y) least_upper_bound X -> X
% collapsed.
% Rule
% [131]
% positive_part(inverse(inverse(X) least_upper_bound X least_upper_bound Y)) ->
% identity collapsed.
% Rule
% [152]
% inverse(inverse(X) least_upper_bound Y) greatest_lower_bound X ->
% inverse(inverse(X) least_upper_bound Y) collapsed.
% Current number of equations to process: 3577
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [226]
% inverse(inverse(X) greatest_lower_bound Y) -> inverse(Y) least_upper_bound X
% Rule
% [112]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(positive_part(inverse(multiply(X,Y))),X) collapsed.
% Rule
% [114] inverse(inverse(X) greatest_lower_bound Y) greatest_lower_bound X -> X
% collapsed.
% Rule
% [115]
% positive_part(inverse(inverse(X) greatest_lower_bound Y)) greatest_lower_bound X
% -> X collapsed.
% Rule
% [160]
% (inverse(inverse(X) greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound X
% -> X collapsed.
% Rule
% [161]
% inverse(inverse(X least_upper_bound Y) greatest_lower_bound Z) greatest_lower_bound X
% -> X collapsed.
% Rule
% [223]
% negative_part(inverse(inverse(Y) greatest_lower_bound X)) ->
% negative_part(inverse(X) least_upper_bound Y) collapsed.
% Current number of equations to process: 3576
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [227]
% (multiply(X,X) least_upper_bound X) greatest_lower_bound positive_part(X) ->
% X
% Rule
% [221]
% (inverse(X) least_upper_bound multiply(inverse(X),inverse(X))) greatest_lower_bound 
% positive_part(inverse(X)) -> inverse(X) collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% Trivial
% 
% Current number of equations to process: 3600
% Current number of ordered equations: 0
% Current number of rules: 95
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% 
% The following 45 rules have been used:
% [2] 
% inverse(inverse(X)) -> X; trace = in the starting set
% [3] X least_upper_bound X -> X; trace = in the starting set
% [5] multiply(identity,X) -> X; trace = in the starting set
% [6] identity least_upper_bound X -> positive_part(X); trace = in the starting set
% [7] identity greatest_lower_bound X -> negative_part(X); trace = in the starting set
% [8] multiply(inverse(X),X) -> identity; trace = in the starting set
% [11] inverse(multiply(X,Y)) -> multiply(inverse(Y),inverse(X)); trace = in the starting set
% [12] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z)); trace = in the starting set
% [14] (Y greatest_lower_bound Z) least_upper_bound X ->
% (X least_upper_bound Y) greatest_lower_bound (X least_upper_bound Z); trace = in the starting set
% [15] multiply(X,Y least_upper_bound Z) ->
% multiply(X,Y) least_upper_bound multiply(X,Z); trace = in the starting set
% [16] multiply(X,Y greatest_lower_bound Z) ->
% multiply(X,Y) greatest_lower_bound multiply(X,Z); trace = in the starting set
% [17] multiply(Y least_upper_bound Z,X) ->
% multiply(Y,X) least_upper_bound multiply(Z,X); trace = in the starting set
% [19] positive_part(identity) -> identity; trace = Cp of 6 and 3
% [28] multiply(inverse(X),identity) -> inverse(X); trace = Cp of 11 and 5
% [30] positive_part(X) least_upper_bound Y ->
% positive_part(X least_upper_bound Y); trace = Self cp of 6
% [33] multiply(inverse(Y),multiply(Y,X)) -> X; trace = Cp of 12 and 8
% [34] positive_part(X) greatest_lower_bound positive_part(Y) ->
% positive_part(X greatest_lower_bound Y); trace = Cp of 14 and 6
% [36] multiply(X,positive_part(Y)) -> multiply(X,Y) least_upper_bound X; trace = Cp of 15 and 6
% [37] multiply(X,negative_part(Y)) -> multiply(X,Y) greatest_lower_bound X; trace = Cp of 16 and 7
% [38] multiply(positive_part(X),Y) -> multiply(X,Y) least_upper_bound Y; trace = Cp of 17 and 6
% [42] multiply(X,identity) -> X; trace = Cp of 28 and 2
% [44] positive_part(negative_part(X)) -> identity; trace = Cp of 34 and 19
% [46] inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(inverse(positive_part(Y)),inverse(X)); trace = Cp of 36 and 11
% [47] inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(inverse(negative_part(Y)),inverse(X)); trace = Cp of 37 and 11
% [48] inverse(positive_part(inverse(X))) ->
% multiply(X,inverse(positive_part(X))); trace = Cp of 46 and 8
% [51] inverse(negative_part(inverse(X))) ->
% multiply(X,inverse(negative_part(X))); trace = Cp of 47 and 8
% [55] inverse(negative_part(multiply(X,inverse(positive_part(X))))) ->
% positive_part(inverse(X)); trace = Cp of 51 and 48
% [58] negative_part(multiply(X,inverse(positive_part(X)))) ->
% multiply(X,inverse(positive_part(X))); trace = Cp of 55 and 2
% [60] positive_part(multiply(X,inverse(positive_part(X)))) -> identity; trace = Cp of 58 and 44
% [64] positive_part(inverse(positive_part(X))) -> identity; trace = Cp of 60 and 48
% [70] multiply(X,inverse(positive_part(Y))) least_upper_bound X -> X; trace = Cp of 64 and 36
% [71] multiply(inverse(positive_part(Y)),X) least_upper_bound X -> X; trace = Cp of 64 and 38
% [92] inverse(positive_part(X)) least_upper_bound multiply(X,inverse(positive_part(X)))
% -> identity; trace = Cp of 36 and 8
% [93] inverse(positive_part(X)) least_upper_bound X -> positive_part(X); trace = Cp of 92 and 70
% [99] multiply(inverse(positive_part(multiply(X,Y))),X) <->
% inverse(inverse(X) least_upper_bound Y); trace = Cp of 46 and 33
% [100] inverse(inverse(X) least_upper_bound Y) least_upper_bound X -> X; trace = Cp of 99 and 71
% [101] inverse(X least_upper_bound Y) least_upper_bound inverse(X) ->
% inverse(X); trace = Cp of 100 and 2
% [102] inverse(positive_part(X)) least_upper_bound inverse(X) -> inverse(X); trace = Cp of 101 and 6
% [105] positive_part(inverse(X) least_upper_bound X) ->
% inverse(X) least_upper_bound X; trace = Cp of 102 and 93
% [109] positive_part(multiply(inverse(positive_part(multiply(X,X))),X)) ->
% identity; trace = Cp of 105 and 64
% [111] inverse(positive_part(X least_upper_bound Y)) least_upper_bound 
% inverse(Y) -> inverse(Y); trace = Cp of 101 and 30
% [155] inverse(positive_part(multiply(X,X) least_upper_bound X)) ->
% inverse(positive_part(multiply(X,X))); trace = Cp of 109 and 99
% [156] positive_part(multiply(X,X) least_upper_bound X) ->
% positive_part(multiply(X,X)); trace = Cp of 155 and 2
% [221] (inverse(X) least_upper_bound multiply(inverse(X),inverse(X))) greatest_lower_bound 
% positive_part(inverse(X)) -> inverse(X); trace = Cp of 156 and 111
% [227] (multiply(X,X) least_upper_bound X) greatest_lower_bound positive_part(X)
% -> X; trace = Cp of 221 and 2
% % SZS output end Refutation
% All conjectures have been proven
% 
% Execution time: 51.990000 sec
% res : bool = true
% time is now off
% 
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
% 
% EOF
%------------------------------------------------------------------------------