TSTP Solution File: GRP167-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP167-1 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n121.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 52.60s
% Output : Refutation 52.60s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP167-1 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command : tptp2X_and_run_cime %s
% % Computer : n121.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 05:46:48 CDT 2014
% % CPUTime : 52.60
% Processing problem /tmp/CiME_36392_n121.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);
% 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 "
% inverse > positive_part > negative_part > multiply > 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 "
% inverse > positive_part > negative_part > multiply > 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),
% 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) } (15 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] X least_upper_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 14
% Current number of rules: 1
% New rule produced : [2] X greatest_lower_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 13
% Current number of rules: 2
% New rule produced : [3] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 12
% Current number of rules: 3
% New rule produced : [4] identity least_upper_bound X -> positive_part(X)
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 4
% New rule produced : [5] identity greatest_lower_bound X -> negative_part(X)
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 5
% New rule produced : [6] multiply(inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 6
% New rule produced : [7] (X greatest_lower_bound Y) least_upper_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 7
% New rule produced : [8] (X least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 8
% New rule produced :
% [9] 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: 9
% New rule produced :
% [10]
% (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: 10
% New rule produced :
% [11]
% (Y greatest_lower_bound Z) least_upper_bound X ->
% (X least_upper_bound Y) greatest_lower_bound (X least_upper_bound Z)
% Rule [7] (X greatest_lower_bound Y) least_upper_bound X -> X collapsed.
% Rule
% [10]
% (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: 9
% New rule produced :
% [12]
% 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: 10
% New rule produced :
% [13]
% 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: 11
% New rule produced :
% [14]
% 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: 12
% New rule produced :
% [15]
% 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: 13
% New rule produced : [16] positive_part(identity) -> identity
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [17] negative_part(identity) -> identity
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [18] 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: 16
% New rule produced : [19] 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: 17
% New rule produced : [20] negative_part(positive_part(X)) -> identity
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [21] 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: 19
% New rule produced :
% [22] 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: 20
% New rule produced :
% [23] 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: 21
% New rule produced :
% [24] 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: 22
% New rule produced :
% [25]
% positive_part(X) least_upper_bound Y -> positive_part(X least_upper_bound Y)
% Rule [22] positive_part(X) least_upper_bound X -> positive_part(X) collapsed.
% Rule [24] 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: 21
% New rule produced :
% [26]
% negative_part(X) greatest_lower_bound Y ->
% negative_part(X greatest_lower_bound Y)
% Rule [23] 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: 21
% New rule produced :
% [27]
% 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: 22
% New rule produced : [28] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [29]
% positive_part(X) greatest_lower_bound positive_part(Y) ->
% positive_part(X greatest_lower_bound Y)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [30]
% 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: 25
% New rule produced :
% [31]
% multiply(X,positive_part(Y)) ->
% multiply(X,identity) least_upper_bound multiply(X,Y)
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [32]
% 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: 12
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [33] 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: 13
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [34] multiply(negative_part(X),Y) -> multiply(X,Y) greatest_lower_bound Y
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [35] positive_part(X least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [36] multiply(inverse(inverse(X)),identity) -> X
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [37] multiply(inverse(inverse(X)),Y) -> multiply(X,Y)
% Rule [36] multiply(inverse(inverse(X)),identity) -> X collapsed.
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 31
% Rule [32]
% multiply(X,negative_part(Y)) ->
% multiply(X,identity) greatest_lower_bound multiply(X,Y) is composed into
% [32] multiply(X,negative_part(Y)) -> multiply(X,Y) greatest_lower_bound X
% Rule [31]
% multiply(X,positive_part(Y)) ->
% multiply(X,identity) least_upper_bound multiply(X,Y) is composed into
% [31] multiply(X,positive_part(Y)) -> multiply(X,Y) least_upper_bound X
% New rule produced : [38] multiply(X,identity) -> X
% 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: 27
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [39] multiply(inverse(identity),X) -> X
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [40]
% positive_part(X greatest_lower_bound Y) greatest_lower_bound Y ->
% positive_part(X) greatest_lower_bound Y
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [41] positive_part(negative_part(X)) -> identity
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [42]
% positive_part(positive_part(X) greatest_lower_bound Y) ->
% positive_part(X greatest_lower_bound Y)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [43] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [44] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [45] inverse(identity) -> identity
% Rule [39] multiply(inverse(identity),X) -> X collapsed.
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [46] inverse(inverse(X)) -> X
% Rule [37] multiply(inverse(inverse(X)),Y) -> multiply(X,Y) collapsed.
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [47] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [48] multiply(Y,inverse(multiply(X,Y))) -> inverse(X)
% Rule [47] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% collapsed.
% Current number of equations to process: 76
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [49] multiply(inverse(multiply(X,Y)),X) -> inverse(Y)
% Current number of equations to process: 76
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [50] inverse(multiply(Y,X)) -> multiply(inverse(X),inverse(Y))
% Rule [48] multiply(Y,inverse(multiply(X,Y))) -> inverse(X) collapsed.
% Rule [49] multiply(inverse(multiply(X,Y)),X) -> inverse(Y) collapsed.
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [51]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(inverse(positive_part(Y)),inverse(X))
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [52]
% inverse(positive_part(inverse(X))) -> multiply(inverse(positive_part(X)),X)
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [53]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(inverse(negative_part(Y)),inverse(X))
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [54]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),inverse(positive_part(X)))
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [55]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),inverse(negative_part(X)))
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [56]
% inverse(positive_part(multiply(inverse(positive_part(X)),X))) -> identity
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [57]
% inverse(negative_part(inverse(X))) -> multiply(inverse(negative_part(X)),X)
% Current number of equations to process: 100
% Current number of ordered equations: 0
% Current number of rules: 46
% Rule [52]
% inverse(positive_part(inverse(X))) ->
% multiply(inverse(positive_part(X)),X) is composed into [52]
% inverse(positive_part(
% inverse(X)))
% ->
% multiply(X,
% inverse(positive_part(X)))
% New rule produced :
% [58]
% multiply(inverse(positive_part(X)),X) ->
% multiply(X,inverse(positive_part(X)))
% Rule
% [56]
% inverse(positive_part(multiply(inverse(positive_part(X)),X))) -> identity
% collapsed.
% Current number of equations to process: 120
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [59]
% inverse(positive_part(multiply(X,inverse(positive_part(X))))) -> identity
% Current number of equations to process: 119
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [60]
% multiply(inverse(positive_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(positive_part(X)))
% Current number of equations to process: 123
% Current number of ordered equations: 0
% Current number of rules: 48
% Rule [57]
% inverse(negative_part(inverse(X))) ->
% multiply(inverse(negative_part(X)),X) is composed into [57]
% inverse(negative_part(
% inverse(X)))
% ->
% multiply(X,
% inverse(negative_part(X)))
% New rule produced :
% [61]
% multiply(inverse(negative_part(X)),X) ->
% multiply(X,inverse(negative_part(X)))
% Current number of equations to process: 130
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [62] positive_part(multiply(X,inverse(positive_part(X)))) -> identity
% Rule
% [59]
% inverse(positive_part(multiply(X,inverse(positive_part(X))))) -> identity
% collapsed.
% Current number of equations to process: 147
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [63]
% inverse(negative_part(multiply(X,inverse(positive_part(X))))) ->
% positive_part(inverse(X))
% Current number of equations to process: 145
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced :
% [64]
% inverse(positive_part(multiply(X,inverse(negative_part(X))))) ->
% negative_part(inverse(X))
% Current number of equations to process: 145
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [65]
% multiply(inverse(negative_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(negative_part(X)))
% Current number of equations to process: 146
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced : [66] positive_part(inverse(positive_part(X))) -> identity
% Current number of equations to process: 169
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [67]
% negative_part(multiply(X,inverse(positive_part(X)))) ->
% multiply(X,inverse(positive_part(X)))
% Rule
% [63]
% inverse(negative_part(multiply(X,inverse(positive_part(X))))) ->
% positive_part(inverse(X)) collapsed.
% Current number of equations to process: 168
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [68]
% positive_part(multiply(X,inverse(positive_part(X))) greatest_lower_bound Y)
% -> identity
% Current number of equations to process: 167
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [69]
% positive_part(multiply(X,inverse(negative_part(X)))) ->
% multiply(X,inverse(negative_part(X)))
% Rule
% [64]
% inverse(positive_part(multiply(X,inverse(negative_part(X))))) ->
% negative_part(inverse(X)) collapsed.
% Current number of equations to process: 169
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [70]
% positive_part(multiply(Y,inverse(positive_part(Y))) least_upper_bound X) ->
% positive_part(X)
% Current number of equations to process: 170
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [71] negative_part(inverse(positive_part(X))) -> inverse(positive_part(X))
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [72]
% positive_part(inverse(positive_part(X)) greatest_lower_bound Y) -> identity
% Current number of equations to process: 180
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [73]
% positive_part(inverse(positive_part(Y)) least_upper_bound X) ->
% positive_part(X)
% Current number of equations to process: 182
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [74] multiply(X,inverse(positive_part(Y))) least_upper_bound X -> X
% Current number of equations to process: 181
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [75] multiply(inverse(positive_part(Y)),X) least_upper_bound X -> X
% Current number of equations to process: 180
% Current number of ordered equations: 0
% Current number of rules: 60
% 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: 180
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [77] negative_part(multiply(X,inverse(negative_part(X)))) -> identity
% Current number of equations to process: 203
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [78] positive_part(inverse(negative_part(X))) -> inverse(negative_part(X))
% Current number of equations to process: 210
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [79]
% negative_part(multiply(X,inverse(negative_part(X))) greatest_lower_bound Y)
% -> negative_part(Y)
% Current number of equations to process: 217
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [80]
% positive_part(Y) greatest_lower_bound inverse(positive_part(X)) ->
% inverse(positive_part(X))
% Current number of equations to process: 235
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [81]
% positive_part(multiply(inverse(positive_part(X)),inverse(positive_part(Y))))
% -> identity
% Current number of equations to process: 304
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced : [82] negative_part(inverse(negative_part(X))) -> identity
% Current number of equations to process: 312
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [83]
% negative_part(inverse(negative_part(X)) greatest_lower_bound Y) ->
% negative_part(Y)
% Current number of equations to process: 320
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [84]
% positive_part(inverse(negative_part(X)) least_upper_bound Y) ->
% inverse(negative_part(X)) least_upper_bound Y
% Current number of equations to process: 322
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [85]
% negative_part(multiply(X,inverse(negative_part(X))) least_upper_bound Y) ->
% identity
% Current number of equations to process: 325
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [86]
% 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: 324
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [87]
% inverse(negative_part(X)) greatest_lower_bound inverse(positive_part(Y)) ->
% inverse(positive_part(Y))
% Current number of equations to process: 353
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [88] multiply(X,inverse(negative_part(Y))) greatest_lower_bound X -> X
% Current number of equations to process: 366
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [89] multiply(inverse(negative_part(Y)),X) greatest_lower_bound X -> X
% Current number of equations to process: 365
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [90]
% negative_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y)) ->
% identity
% Current number of equations to process: 364
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [91] negative_part(inverse(negative_part(X)) least_upper_bound Y) -> identity
% Current number of equations to process: 365
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [92]
% positive_part(inverse(inverse(negative_part(X)) least_upper_bound Y)) ->
% identity
% Current number of equations to process: 378
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [93]
% inverse(negative_part(X)) least_upper_bound inverse(positive_part(Y)) ->
% inverse(negative_part(X))
% Current number of equations to process: 390
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [94]
% (inverse(negative_part(Y)) least_upper_bound X) greatest_lower_bound
% positive_part(X) -> positive_part(X)
% Current number of equations to process: 410
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [95]
% negative_part((inverse(negative_part(Y)) least_upper_bound Z) greatest_lower_bound X)
% -> negative_part(X)
% Current number of equations to process: 409
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [96]
% positive_part(multiply(X,inverse(negative_part(Y)))) greatest_lower_bound X
% -> X
% Current number of equations to process: 562
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [97]
% negative_part(multiply(inverse(negative_part(X)),inverse(negative_part(Y))))
% -> identity
% Current number of equations to process: 561
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [98]
% positive_part(multiply(inverse(negative_part(Y)),X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 560
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [99]
% inverse(negative_part(X)) greatest_lower_bound multiply(X,inverse(negative_part(X)))
% -> identity
% Current number of equations to process: 692
% Current number of ordered equations: 1
% Current number of rules: 84
% New rule produced :
% [100] inverse(negative_part(X)) greatest_lower_bound X -> negative_part(X)
% Current number of equations to process: 719
% Current number of ordered equations: 1
% Current number of rules: 85
% New rule produced :
% [101]
% inverse(negative_part(X least_upper_bound Y)) greatest_lower_bound X ->
% negative_part(X)
% Current number of equations to process: 775
% Current number of ordered equations: 1
% Current number of rules: 86
% New rule produced :
% [102]
% positive_part(inverse(negative_part(X)) greatest_lower_bound Y) greatest_lower_bound X
% -> negative_part(X)
% Current number of equations to process: 825
% Current number of ordered equations: 1
% Current number of rules: 87
% New rule produced :
% [103]
% inverse(positive_part(X)) least_upper_bound multiply(X,inverse(positive_part(X)))
% -> identity
% Current number of equations to process: 868
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [104] inverse(positive_part(X)) least_upper_bound X -> positive_part(X)
% Current number of equations to process: 895
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [105]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(inverse(positive_part(multiply(X,Y))),X)
% Current number of equations to process: 945
% Current number of ordered equations: 1
% Current number of rules: 90
% New rule produced :
% [106]
% multiply(inverse(positive_part(multiply(X,Y))),X) <->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 945
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [107] inverse(inverse(X) least_upper_bound Y) least_upper_bound X -> X
% Current number of equations to process: 993
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [108]
% inverse(X least_upper_bound Y) least_upper_bound inverse(X) -> inverse(X)
% Current number of equations to process: 1021
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [109] inverse(positive_part(X)) least_upper_bound inverse(X) -> inverse(X)
% Current number of equations to process: 1169
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [110]
% inverse(positive_part(inverse(X) least_upper_bound Y)) least_upper_bound X ->
% X
% Current number of equations to process: 1168
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [111]
% inverse(positive_part(X)) greatest_lower_bound inverse(X) ->
% inverse(positive_part(X))
% Current number of equations to process: 1296
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [112]
% positive_part(inverse(X) least_upper_bound X) ->
% inverse(X) least_upper_bound X
% Current number of equations to process: 1334
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [113] negative_part(inverse(X) least_upper_bound X) -> identity
% Current number of equations to process: 1508
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [114]
% negative_part((inverse(X) least_upper_bound X) greatest_lower_bound Y) ->
% negative_part(Y)
% Current number of equations to process: 1540
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [115]
% 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 :
% [116]
% positive_part(multiply(inverse(positive_part(multiply(X,X))),X)) -> identity
% Current number of equations to process: 1554
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [117]
% inverse(X least_upper_bound Y) greatest_lower_bound inverse(X) ->
% inverse(X least_upper_bound Y)
% Current number of equations to process: 1615
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [118]
% inverse(positive_part(X least_upper_bound Y)) least_upper_bound inverse(Y) ->
% inverse(Y)
% Current number of equations to process: 1624
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [119]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(inverse(negative_part(multiply(X,Y))),X)
% Current number of equations to process: 1888
% Current number of ordered equations: 1
% Current number of rules: 104
% New rule produced :
% [120]
% multiply(inverse(negative_part(multiply(X,Y))),X) <->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 1888
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [121] inverse(inverse(X) greatest_lower_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 1966
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [122]
% positive_part(inverse(inverse(X) greatest_lower_bound Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 1967
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [123]
% inverse(X greatest_lower_bound Y) greatest_lower_bound inverse(X) ->
% inverse(X)
% Current number of equations to process: 1989
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [124]
% inverse(inverse(positive_part(X)) greatest_lower_bound Y) greatest_lower_bound X
% -> X
% Current number of equations to process: 2200
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [125]
% inverse(negative_part(inverse(X) greatest_lower_bound Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 2199
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [126] inverse(negative_part(X)) greatest_lower_bound inverse(X) -> inverse(X)
% Current number of equations to process: 2352
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [127]
% negative_part(inverse(X) greatest_lower_bound X) ->
% inverse(X) greatest_lower_bound X
% Current number of equations to process: 2872
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [128] positive_part(inverse(X)) greatest_lower_bound X -> negative_part(X)
% Current number of equations to process: 2987
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [129]
% positive_part(inverse(X) greatest_lower_bound Y) greatest_lower_bound X ->
% negative_part(X)
% Current number of equations to process: 2986
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [130] positive_part(inverse(X) greatest_lower_bound X) -> identity
% Current number of equations to process: 3020
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [131]
% positive_part(X) greatest_lower_bound inverse(X) -> negative_part(inverse(X))
% Current number of equations to process: 3065
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [132]
% positive_part(inverse(X) greatest_lower_bound X greatest_lower_bound Y) ->
% identity
% Current number of equations to process: 3135
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [133]
% positive_part(inverse(X least_upper_bound Y)) greatest_lower_bound X ->
% negative_part(X)
% Current number of equations to process: 3202
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [134]
% negative_part(multiply(inverse(negative_part(multiply(X,X))),X)) -> identity
% Current number of equations to process: 3207
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [135]
% positive_part(X greatest_lower_bound Y) greatest_lower_bound inverse(X) ->
% negative_part(inverse(X))
% Current number of equations to process: 3206
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [136]
% positive_part(inverse(X least_upper_bound Y) greatest_lower_bound X) ->
% identity
% Current number of equations to process: 3416
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [137]
% negative_part(inverse(inverse(X) greatest_lower_bound X greatest_lower_bound Y))
% -> identity
% Current number of equations to process: 3489
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [138]
% positive_part(inverse(inverse(X) least_upper_bound X least_upper_bound Y)) ->
% identity
% Current number of equations to process: 3838
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [139]
% positive_part(inverse(X greatest_lower_bound Y)) greatest_lower_bound
% inverse(X) -> inverse(X)
% Current number of equations to process: 3940
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [140]
% inverse(negative_part(X greatest_lower_bound Y)) greatest_lower_bound
% inverse(Y) -> inverse(Y)
% Current number of equations to process: 3967
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [141]
% (inverse(negative_part(X)) least_upper_bound Y) greatest_lower_bound
% inverse(X) -> inverse(X)
% Current number of equations to process: 3964
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [142]
% positive_part(X) greatest_lower_bound inverse(Y) greatest_lower_bound Y ->
% inverse(Y) greatest_lower_bound Y
% Current number of equations to process: 3961
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [143]
% multiply(X,multiply(Y,inverse(positive_part(Y)))) least_upper_bound X -> X
% Current number of equations to process: 4991
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [144]
% multiply(Y,multiply(inverse(positive_part(Y)),X)) least_upper_bound X -> X
% Current number of equations to process: 2122
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [145]
% multiply(X,inverse(positive_part(Y))) greatest_lower_bound X ->
% multiply(X,inverse(positive_part(Y)))
% Current number of equations to process: 2226
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [146]
% multiply(inverse(positive_part(X)),Y) greatest_lower_bound Y ->
% multiply(inverse(positive_part(X)),Y)
% Current number of equations to process: 2406
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [147]
% multiply(X,multiply(Y,inverse(negative_part(Y)))) greatest_lower_bound X -> X
% Current number of equations to process: 2583
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [148]
% multiply(Y,multiply(inverse(negative_part(Y)),X)) greatest_lower_bound X -> X
% Current number of equations to process: 2701
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [149]
% multiply(X,inverse(negative_part(Y))) least_upper_bound X ->
% multiply(X,inverse(negative_part(Y)))
% Current number of equations to process: 2825
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [150]
% multiply(inverse(negative_part(X)),Y) least_upper_bound Y ->
% multiply(inverse(negative_part(X)),Y)
% Current number of equations to process: 2956
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [151]
% positive_part(inverse(inverse(negative_part(X)) least_upper_bound Y) greatest_lower_bound Z)
% -> identity
% Current number of equations to process: 3089
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [152]
% (multiply(X,inverse(negative_part(Y))) least_upper_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 3116
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [153]
% (multiply(inverse(negative_part(Y)),X) least_upper_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 3271
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [154]
% negative_part(inverse(multiply(X,inverse(positive_part(X))) greatest_lower_bound Y))
% -> identity
% Current number of equations to process: 3438
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [155]
% negative_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y) least_upper_bound Z)
% -> identity
% Current number of equations to process: 3451
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [156]
% positive_part(inverse(multiply(X,inverse(negative_part(X))) least_upper_bound Y))
% -> identity
% Current number of equations to process: 3473
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [157]
% inverse(X) greatest_lower_bound multiply(X,inverse(negative_part(X))) ->
% negative_part(inverse(X))
% Current number of equations to process: 3492
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [158]
% inverse(X) least_upper_bound multiply(X,inverse(positive_part(X))) ->
% positive_part(inverse(X))
% Current number of equations to process: 3547
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [159]
% inverse(inverse(X) least_upper_bound Y) greatest_lower_bound X ->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 3596
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [160]
% (inverse(X) least_upper_bound Y) greatest_lower_bound inverse(positive_part(X))
% -> inverse(positive_part(X))
% Current number of equations to process: 4212
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [161]
% (inverse(X) least_upper_bound X) greatest_lower_bound inverse(positive_part(Y))
% -> inverse(positive_part(Y))
% Current number of equations to process: 4301
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [162]
% inverse(positive_part(multiply(X,X) least_upper_bound X)) ->
% inverse(positive_part(multiply(X,X)))
% Current number of equations to process: 4354
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [163]
% positive_part(multiply(X,X) least_upper_bound X) ->
% positive_part(multiply(X,X))
% Rule
% [162]
% inverse(positive_part(multiply(X,X) least_upper_bound X)) ->
% inverse(positive_part(multiply(X,X))) collapsed.
% Current number of equations to process: 4356
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [164] positive_part(multiply(X,X)) greatest_lower_bound X -> X
% Current number of equations to process: 4360
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [165] positive_part(multiply(X,X) greatest_lower_bound X) -> positive_part(X)
% Current number of equations to process: 4398
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [166]
% inverse(positive_part(multiply(X,X))) least_upper_bound inverse(X) ->
% inverse(X)
% Current number of equations to process: 4484
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [167]
% (inverse(inverse(X) greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 4561
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [168]
% inverse(inverse(X least_upper_bound Y) greatest_lower_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 3438
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [169]
% positive_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 3826
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [170]
% inverse(X greatest_lower_bound Y) greatest_lower_bound inverse(positive_part(X))
% -> inverse(positive_part(X))
% Current number of equations to process: 4111
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [171]
% 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: 4425
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [172]
% positive_part(inverse(X least_upper_bound Y) greatest_lower_bound X greatest_lower_bound Z)
% -> identity
% Current number of equations to process: 4601
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [173]
% inverse(negative_part(multiply(X,X) greatest_lower_bound X)) ->
% inverse(negative_part(multiply(X,X)))
% Current number of equations to process: 4722
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [174]
% negative_part(multiply(X,X) greatest_lower_bound X) ->
% negative_part(multiply(X,X))
% Rule
% [173]
% inverse(negative_part(multiply(X,X) greatest_lower_bound X)) ->
% inverse(negative_part(multiply(X,X))) collapsed.
% Current number of equations to process: 4723
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [175]
% inverse(negative_part(multiply(X,X))) greatest_lower_bound inverse(X) ->
% inverse(X)
% Current number of equations to process: 4736
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [176]
% positive_part(inverse(X)) greatest_lower_bound multiply(X,X) ->
% negative_part(multiply(X,X))
% Current number of equations to process: 4780
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [177]
% positive_part(inverse(X) greatest_lower_bound multiply(X,X)) -> identity
% Current number of equations to process: 4883
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [178]
% positive_part(multiply(inverse(X),inverse(X)) greatest_lower_bound X) ->
% identity
% Current number of equations to process: 4923
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [179]
% positive_part(multiply(X,X)) greatest_lower_bound inverse(X) ->
% negative_part(inverse(X))
% Current number of equations to process: 4922
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [180]
% positive_part(multiply(inverse(X),inverse(X))) greatest_lower_bound X ->
% negative_part(X)
% Current number of equations to process: 1843
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [181]
% positive_part(multiply(inverse(positive_part(X)),inverse(Y)) greatest_lower_bound Y)
% -> identity
% Current number of equations to process: 2081
% Current number of ordered equations: 0
% Current number of rules: 164
% New rule produced :
% [182]
% positive_part(multiply(inverse(X),inverse(positive_part(Y))) greatest_lower_bound X)
% -> identity
% Current number of equations to process: 2125
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [183]
% positive_part(inverse(X) greatest_lower_bound multiply(X,inverse(positive_part(Y))))
% -> identity
% Current number of equations to process: 2166
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [184]
% positive_part(inverse(X) greatest_lower_bound multiply(inverse(positive_part(Y)),X))
% -> identity
% Current number of equations to process: 2196
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced :
% [185]
% negative_part(multiply(inverse(X),inverse(negative_part(Y))) least_upper_bound X)
% -> identity
% Current number of equations to process: 2225
% Current number of ordered equations: 1
% Current number of rules: 168
% New rule produced :
% [186]
% negative_part(inverse(X) least_upper_bound multiply(X,inverse(negative_part(Y))))
% -> identity
% Current number of equations to process: 2225
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced :
% [187]
% negative_part(inverse(X) least_upper_bound multiply(inverse(negative_part(Y)),X))
% -> identity
% Current number of equations to process: 2261
% Current number of ordered equations: 1
% Current number of rules: 170
% New rule produced :
% [188]
% negative_part(multiply(inverse(negative_part(X)),inverse(Y)) least_upper_bound Y)
% -> identity
% Current number of equations to process: 2261
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [189]
% negative_part(inverse(X greatest_lower_bound Y) least_upper_bound X) ->
% identity
% Current number of equations to process: 2296
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [190]
% positive_part(inverse(X)) greatest_lower_bound multiply(X,inverse(negative_part(X)))
% -> identity
% Current number of equations to process: 2339
% Current number of ordered equations: 0
% Current number of rules: 173
% New rule produced :
% [191]
% inverse(positive_part(multiply(inverse(X),inverse(X)))) least_upper_bound X
% -> X
% Current number of equations to process: 2404
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced :
% [192]
% (inverse(negative_part(Y)) least_upper_bound multiply(X,X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 2614
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced :
% [193]
% inverse(negative_part(multiply(inverse(X),inverse(X)))) greatest_lower_bound X
% -> X
% Current number of equations to process: 2752
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced :
% [194]
% positive_part(inverse(X) greatest_lower_bound multiply(X,X) greatest_lower_bound Y)
% -> identity
% Current number of equations to process: 3119
% Current number of ordered equations: 0
% Current number of rules: 177
% New rule produced :
% [195]
% negative_part(inverse(multiply(inverse(X),inverse(X)) greatest_lower_bound X))
% -> identity
% Current number of equations to process: 3164
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [196]
% negative_part(inverse(X greatest_lower_bound Y) least_upper_bound X least_upper_bound Z)
% -> identity
% Current number of equations to process: 3177
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [197]
% positive_part(inverse(X) least_upper_bound multiply(Y,Y)) greatest_lower_bound Y
% -> Y
% Current number of equations to process: 3287
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [198]
% positive_part(multiply(X,X) least_upper_bound Y) greatest_lower_bound X -> X
% Rule
% [197]
% positive_part(inverse(X) least_upper_bound multiply(Y,Y)) greatest_lower_bound Y
% -> Y collapsed.
% Current number of equations to process: 3288
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [199]
% positive_part((multiply(X,X) least_upper_bound Y) greatest_lower_bound X) ->
% positive_part(X)
% Current number of equations to process: 3410
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [200]
% positive_part(inverse(X least_upper_bound Y) greatest_lower_bound multiply(X,X))
% -> identity
% Current number of equations to process: 3437
% Current number of ordered equations: 0
% Current number of rules: 182
% New rule produced :
% [201]
% positive_part((X least_upper_bound Y) greatest_lower_bound Z) greatest_lower_bound X
% -> positive_part(Z) greatest_lower_bound X
% Current number of equations to process: 3478
% Current number of ordered equations: 0
% Current number of rules: 183
% New rule produced :
% [202]
% 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: 3820
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [203]
% positive_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y)) ->
% inverse(inverse(positive_part(X)) greatest_lower_bound Y)
% Rule
% [169]
% positive_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y)) greatest_lower_bound X
% -> X collapsed.
% Current number of equations to process: 3892
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [204]
% negative_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y) greatest_lower_bound Z)
% -> negative_part(Z)
% Current number of equations to process: 3918
% Current number of ordered equations: 0
% Current number of rules: 185
% New rule produced :
% [205]
% 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: 3962
% Current number of ordered equations: 0
% Current number of rules: 186
% New rule produced :
% [206]
% positive_part(inverse(inverse(negative_part(X)) least_upper_bound Y) least_upper_bound Z)
% -> positive_part(Z)
% Current number of equations to process: 3975
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [207]
% inverse(negative_part(multiply(X,inverse(negative_part(Y))))) greatest_lower_bound X
% -> negative_part(X)
% Current number of equations to process: 4022
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [208]
% inverse(negative_part(multiply(inverse(negative_part(X)),Y))) greatest_lower_bound Y
% -> negative_part(Y)
% Current number of equations to process: 4108
% Current number of ordered equations: 0
% Current number of rules: 189
% New rule produced :
% [209]
% inverse(positive_part(multiply(X,inverse(positive_part(Y))))) least_upper_bound X
% -> positive_part(X)
% Current number of equations to process: 4196
% Current number of ordered equations: 0
% Current number of rules: 190
% New rule produced :
% [210]
% inverse(positive_part(multiply(inverse(positive_part(X)),Y))) least_upper_bound Y
% -> positive_part(Y)
% Current number of equations to process: 4277
% Current number of ordered equations: 0
% Current number of rules: 191
% New rule produced :
% [211]
% positive_part(inverse(inverse(positive_part(X)) least_upper_bound Y) least_upper_bound X)
% -> positive_part(X)
% Current number of equations to process: 4366
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced :
% [212]
% negative_part(inverse(inverse(negative_part(X)) least_upper_bound Y) least_upper_bound X)
% -> negative_part(X)
% Current number of equations to process: 4400
% Current number of ordered equations: 0
% Current number of rules: 193
% New rule produced :
% [213]
% 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: 4429
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [214]
% 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: 4624
% Current number of ordered equations: 0
% Current number of rules: 195
% New rule produced :
% [215]
% (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: 4734
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [216]
% (inverse(X) least_upper_bound X) greatest_lower_bound positive_part(X) ->
% positive_part(X)
% Current number of equations to process: 4755
% Current number of ordered equations: 0
% Current number of rules: 197
% New rule produced :
% [217]
% (inverse(X) least_upper_bound X) greatest_lower_bound positive_part(inverse(X))
% -> positive_part(inverse(X))
% Current number of equations to process: 4754
% Current number of ordered equations: 0
% Current number of rules: 198
% New rule produced :
% [218]
% 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: 1626
% Current number of ordered equations: 0
% Current number of rules: 199
% New rule produced :
% [219]
% negative_part(inverse(inverse(negative_part(X)) greatest_lower_bound Y) greatest_lower_bound X)
% -> negative_part(X)
% Current number of equations to process: 1696
% Current number of ordered equations: 0
% Current number of rules: 200
% New rule produced :
% [220]
% inverse(positive_part(inverse(negative_part(X)) greatest_lower_bound Y)) greatest_lower_bound X
% -> negative_part(X)
% Current number of equations to process: 1718
% Current number of ordered equations: 0
% Current number of rules: 201
% New rule produced :
% [221]
% inverse(positive_part(X)) greatest_lower_bound Y ->
% negative_part(inverse(X) greatest_lower_bound Y)
% Rule
% [72]
% positive_part(inverse(positive_part(X)) greatest_lower_bound Y) -> identity
% collapsed.
% Rule
% [76]
% negative_part(inverse(positive_part(X)) greatest_lower_bound Y) ->
% inverse(positive_part(X)) greatest_lower_bound Y collapsed.
% Rule
% [80]
% positive_part(Y) greatest_lower_bound inverse(positive_part(X)) ->
% inverse(positive_part(X)) collapsed.
% Rule
% [87]
% inverse(negative_part(X)) greatest_lower_bound inverse(positive_part(Y)) ->
% inverse(positive_part(Y)) collapsed.
% Rule
% [90]
% negative_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y)) ->
% identity collapsed.
% Rule
% [111]
% inverse(positive_part(X)) greatest_lower_bound inverse(X) ->
% inverse(positive_part(X)) collapsed.
% Rule
% [124]
% inverse(inverse(positive_part(X)) greatest_lower_bound Y) greatest_lower_bound X
% -> X collapsed.
% Rule
% [155]
% negative_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y) least_upper_bound Z)
% -> identity collapsed.
% Rule
% [160]
% (inverse(X) least_upper_bound Y) greatest_lower_bound inverse(positive_part(X))
% -> inverse(positive_part(X)) collapsed.
% Rule
% [161]
% (inverse(X) least_upper_bound X) greatest_lower_bound inverse(positive_part(Y))
% -> inverse(positive_part(Y)) collapsed.
% Rule
% [170]
% inverse(X greatest_lower_bound Y) greatest_lower_bound inverse(positive_part(X))
% -> inverse(positive_part(X)) collapsed.
% Rule
% [203]
% positive_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y)) ->
% inverse(inverse(positive_part(X)) greatest_lower_bound Y) collapsed.
% Rule
% [204]
% negative_part(inverse(inverse(positive_part(X)) greatest_lower_bound Y) greatest_lower_bound Z)
% -> negative_part(Z) collapsed.
% Rule
% [220]
% 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: 1817
% Current number of ordered equations: 0
% Current number of rules: 188
% Rule [105]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(inverse(positive_part(multiply(X,Y))),X) is composed into
% [105]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(negative_part(inverse(multiply(X,Y))),X)
% Rule [54]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),inverse(positive_part(X))) is composed into
% [54]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),negative_part(inverse(X)))
% Rule [51]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(inverse(positive_part(Y)),inverse(X)) is composed into
% [51]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(negative_part(inverse(Y)),inverse(X))
% New rule produced :
% [222] inverse(positive_part(X)) -> negative_part(inverse(X))
% Rule
% [52]
% inverse(positive_part(inverse(X))) -> multiply(X,inverse(positive_part(X)))
% collapsed.
% Rule
% [58]
% multiply(inverse(positive_part(X)),X) ->
% multiply(X,inverse(positive_part(X))) collapsed.
% Rule
% [60]
% multiply(inverse(positive_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(positive_part(X))) collapsed.
% Rule [62] positive_part(multiply(X,inverse(positive_part(X)))) -> identity
% collapsed.
% Rule [66] positive_part(inverse(positive_part(X))) -> identity collapsed.
% Rule
% [67]
% negative_part(multiply(X,inverse(positive_part(X)))) ->
% multiply(X,inverse(positive_part(X))) collapsed.
% Rule
% [68]
% positive_part(multiply(X,inverse(positive_part(X))) greatest_lower_bound Y)
% -> identity collapsed.
% Rule
% [70]
% positive_part(multiply(Y,inverse(positive_part(Y))) least_upper_bound X) ->
% positive_part(X) collapsed.
% Rule
% [71] negative_part(inverse(positive_part(X))) -> inverse(positive_part(X))
% collapsed.
% Rule
% [73]
% positive_part(inverse(positive_part(Y)) least_upper_bound X) ->
% positive_part(X) collapsed.
% Rule [74] multiply(X,inverse(positive_part(Y))) least_upper_bound X -> X
% collapsed.
% Rule [75] multiply(inverse(positive_part(Y)),X) least_upper_bound X -> X
% collapsed.
% Rule
% [81]
% positive_part(multiply(inverse(positive_part(X)),inverse(positive_part(Y))))
% -> identity collapsed.
% Rule
% [93]
% inverse(negative_part(X)) least_upper_bound inverse(positive_part(Y)) ->
% inverse(negative_part(X)) collapsed.
% Rule
% [103]
% inverse(positive_part(X)) least_upper_bound multiply(X,inverse(positive_part(X)))
% -> identity collapsed.
% Rule [104] inverse(positive_part(X)) least_upper_bound X -> positive_part(X)
% collapsed.
% Rule
% [106]
% multiply(inverse(positive_part(multiply(X,Y))),X) <->
% inverse(inverse(X) least_upper_bound Y) collapsed.
% Rule
% [109] inverse(positive_part(X)) least_upper_bound inverse(X) -> inverse(X)
% collapsed.
% Rule
% [110]
% inverse(positive_part(inverse(X) least_upper_bound Y)) least_upper_bound X ->
% X collapsed.
% Rule
% [116]
% positive_part(multiply(inverse(positive_part(multiply(X,X))),X)) -> identity
% collapsed.
% Rule
% [118]
% inverse(positive_part(X least_upper_bound Y)) least_upper_bound inverse(Y) ->
% inverse(Y) collapsed.
% Rule
% [143]
% multiply(X,multiply(Y,inverse(positive_part(Y)))) least_upper_bound X -> X
% collapsed.
% Rule
% [144]
% multiply(Y,multiply(inverse(positive_part(Y)),X)) least_upper_bound X -> X
% collapsed.
% Rule
% [145]
% multiply(X,inverse(positive_part(Y))) greatest_lower_bound X ->
% multiply(X,inverse(positive_part(Y))) collapsed.
% Rule
% [146]
% multiply(inverse(positive_part(X)),Y) greatest_lower_bound Y ->
% multiply(inverse(positive_part(X)),Y) collapsed.
% Rule
% [154]
% negative_part(inverse(multiply(X,inverse(positive_part(X))) greatest_lower_bound Y))
% -> identity collapsed.
% Rule
% [158]
% inverse(X) least_upper_bound multiply(X,inverse(positive_part(X))) ->
% positive_part(inverse(X)) collapsed.
% Rule
% [166]
% inverse(positive_part(multiply(X,X))) least_upper_bound inverse(X) ->
% inverse(X) collapsed.
% Rule
% [181]
% positive_part(multiply(inverse(positive_part(X)),inverse(Y)) greatest_lower_bound Y)
% -> identity collapsed.
% Rule
% [182]
% positive_part(multiply(inverse(X),inverse(positive_part(Y))) greatest_lower_bound X)
% -> identity collapsed.
% Rule
% [183]
% positive_part(inverse(X) greatest_lower_bound multiply(X,inverse(positive_part(Y))))
% -> identity collapsed.
% Rule
% [184]
% positive_part(inverse(X) greatest_lower_bound multiply(inverse(positive_part(Y)),X))
% -> identity collapsed.
% Rule
% [191]
% inverse(positive_part(multiply(inverse(X),inverse(X)))) least_upper_bound X
% -> X collapsed.
% Rule
% [202]
% positive_part((inverse(positive_part(Z)) least_upper_bound Y) greatest_lower_bound X)
% -> positive_part(X greatest_lower_bound Y) collapsed.
% Rule
% [209]
% inverse(positive_part(multiply(X,inverse(positive_part(Y))))) least_upper_bound X
% -> positive_part(X) collapsed.
% Rule
% [210]
% inverse(positive_part(multiply(inverse(positive_part(X)),Y))) least_upper_bound Y
% -> positive_part(Y) collapsed.
% Rule
% [211]
% positive_part(inverse(inverse(positive_part(X)) least_upper_bound Y) least_upper_bound X)
% -> positive_part(X) collapsed.
% Rule
% [221]
% inverse(positive_part(X)) greatest_lower_bound Y ->
% negative_part(inverse(X) greatest_lower_bound Y) collapsed.
% Current number of equations to process: 1929
% Current number of ordered equations: 0
% Current number of rules: 151
% Rule [61]
% multiply(inverse(negative_part(X)),X) ->
% multiply(X,inverse(negative_part(X))) is composed into [61]
% multiply(
% inverse(negative_part(X)),X)
% ->
% positive_part(X)
% Rule [57]
% inverse(negative_part(inverse(X))) ->
% multiply(X,inverse(negative_part(X))) is composed into [57]
% inverse(negative_part(
% inverse(X)))
% ->
% positive_part(X)
% New rule produced :
% [223] multiply(X,inverse(negative_part(X))) -> positive_part(X)
% Rule
% [69]
% positive_part(multiply(X,inverse(negative_part(X)))) ->
% multiply(X,inverse(negative_part(X))) collapsed.
% Rule [77] negative_part(multiply(X,inverse(negative_part(X)))) -> identity
% collapsed.
% Rule
% [79]
% negative_part(multiply(X,inverse(negative_part(X))) greatest_lower_bound Y)
% -> negative_part(Y) collapsed.
% Rule
% [85]
% negative_part(multiply(X,inverse(negative_part(X))) least_upper_bound Y) ->
% identity collapsed.
% Rule
% [99]
% inverse(negative_part(X)) greatest_lower_bound multiply(X,inverse(negative_part(X)))
% -> identity collapsed.
% Rule
% [147]
% multiply(X,multiply(Y,inverse(negative_part(Y)))) greatest_lower_bound X -> X
% collapsed.
% Rule
% [156]
% positive_part(inverse(multiply(X,inverse(negative_part(X))) least_upper_bound Y))
% -> identity collapsed.
% Rule
% [157]
% inverse(X) greatest_lower_bound multiply(X,inverse(negative_part(X))) ->
% negative_part(inverse(X)) collapsed.
% Rule
% [190]
% positive_part(inverse(X)) greatest_lower_bound multiply(X,inverse(negative_part(X)))
% -> identity collapsed.
% Current number of equations to process: 1936
% Current number of ordered equations: 0
% Current number of rules: 143
% Rule [119]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(inverse(negative_part(multiply(X,Y))),X) is composed into
% [119]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(positive_part(inverse(multiply(X,Y))),X)
% Rule [55]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),inverse(negative_part(X))) is composed into
% [55]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),positive_part(inverse(X)))
% Rule [53]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(inverse(negative_part(Y)),inverse(X)) is composed into
% [53]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(positive_part(inverse(Y)),inverse(X))
% New rule produced :
% [224] inverse(negative_part(X)) -> positive_part(inverse(X))
% Rule [57] inverse(negative_part(inverse(X))) -> positive_part(X) collapsed.
% Rule [61] multiply(inverse(negative_part(X)),X) -> positive_part(X)
% collapsed.
% Rule
% [65]
% multiply(inverse(negative_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(negative_part(X))) collapsed.
% Rule
% [78] positive_part(inverse(negative_part(X))) -> inverse(negative_part(X))
% collapsed.
% Rule [82] negative_part(inverse(negative_part(X))) -> identity collapsed.
% Rule
% [83]
% negative_part(inverse(negative_part(X)) greatest_lower_bound Y) ->
% negative_part(Y) collapsed.
% Rule
% [84]
% positive_part(inverse(negative_part(X)) least_upper_bound Y) ->
% inverse(negative_part(X)) least_upper_bound Y collapsed.
% Rule
% [86]
% positive_part(X) greatest_lower_bound inverse(negative_part(Y)) ->
% positive_part(inverse(negative_part(Y)) greatest_lower_bound X) collapsed.
% Rule [88] multiply(X,inverse(negative_part(Y))) greatest_lower_bound X -> X
% collapsed.
% Rule [89] multiply(inverse(negative_part(Y)),X) greatest_lower_bound X -> X
% collapsed.
% Rule
% [91] negative_part(inverse(negative_part(X)) least_upper_bound Y) -> identity
% collapsed.
% Rule
% [92]
% positive_part(inverse(inverse(negative_part(X)) least_upper_bound Y)) ->
% identity collapsed.
% Rule
% [94]
% (inverse(negative_part(Y)) least_upper_bound X) greatest_lower_bound
% positive_part(X) -> positive_part(X) collapsed.
% Rule
% [95]
% negative_part((inverse(negative_part(Y)) least_upper_bound Z) greatest_lower_bound X)
% -> negative_part(X) collapsed.
% Rule
% [96]
% positive_part(multiply(X,inverse(negative_part(Y)))) greatest_lower_bound X
% -> X collapsed.
% Rule
% [97]
% negative_part(multiply(inverse(negative_part(X)),inverse(negative_part(Y))))
% -> identity collapsed.
% Rule
% [98]
% positive_part(multiply(inverse(negative_part(Y)),X)) greatest_lower_bound X
% -> X collapsed.
% Rule
% [100] inverse(negative_part(X)) greatest_lower_bound X -> negative_part(X)
% collapsed.
% Rule
% [101]
% inverse(negative_part(X least_upper_bound Y)) greatest_lower_bound X ->
% negative_part(X) collapsed.
% Rule
% [102]
% positive_part(inverse(negative_part(X)) greatest_lower_bound Y) greatest_lower_bound X
% -> negative_part(X) collapsed.
% Rule
% [120]
% multiply(inverse(negative_part(multiply(X,Y))),X) <->
% inverse(inverse(X) greatest_lower_bound Y) collapsed.
% Rule
% [125]
% inverse(negative_part(inverse(X) greatest_lower_bound Y)) greatest_lower_bound X
% -> X collapsed.
% Rule
% [126] inverse(negative_part(X)) greatest_lower_bound inverse(X) -> inverse(X)
% collapsed.
% Rule
% [134]
% negative_part(multiply(inverse(negative_part(multiply(X,X))),X)) -> identity
% collapsed.
% Rule
% [140]
% inverse(negative_part(X greatest_lower_bound Y)) greatest_lower_bound
% inverse(Y) -> inverse(Y) collapsed.
% Rule
% [141]
% (inverse(negative_part(X)) least_upper_bound Y) greatest_lower_bound
% inverse(X) -> inverse(X) collapsed.
% Rule
% [148]
% multiply(Y,multiply(inverse(negative_part(Y)),X)) greatest_lower_bound X -> X
% collapsed.
% Rule
% [149]
% multiply(X,inverse(negative_part(Y))) least_upper_bound X ->
% multiply(X,inverse(negative_part(Y))) collapsed.
% Rule
% [150]
% multiply(inverse(negative_part(X)),Y) least_upper_bound Y ->
% multiply(inverse(negative_part(X)),Y) collapsed.
% Rule
% [151]
% positive_part(inverse(inverse(negative_part(X)) least_upper_bound Y) greatest_lower_bound Z)
% -> identity collapsed.
% Rule
% [152]
% (multiply(X,inverse(negative_part(Y))) least_upper_bound Z) greatest_lower_bound X
% -> X collapsed.
% Rule
% [153]
% (multiply(inverse(negative_part(Y)),X) least_upper_bound Z) greatest_lower_bound X
% -> X collapsed.
% Rule
% [175]
% inverse(negative_part(multiply(X,X))) greatest_lower_bound inverse(X) ->
% inverse(X) collapsed.
% Rule
% [185]
% negative_part(multiply(inverse(X),inverse(negative_part(Y))) least_upper_bound X)
% -> identity collapsed.
% Rule
% [186]
% negative_part(inverse(X) least_upper_bound multiply(X,inverse(negative_part(Y))))
% -> identity collapsed.
% Rule
% [187]
% negative_part(inverse(X) least_upper_bound multiply(inverse(negative_part(Y)),X))
% -> identity collapsed.
% Rule
% [188]
% negative_part(multiply(inverse(negative_part(X)),inverse(Y)) least_upper_bound Y)
% -> identity collapsed.
% Rule
% [192]
% (inverse(negative_part(Y)) least_upper_bound multiply(X,X)) greatest_lower_bound X
% -> X collapsed.
% Rule
% [193]
% inverse(negative_part(multiply(inverse(X),inverse(X)))) greatest_lower_bound X
% -> X collapsed.
% Rule
% [205]
% negative_part(inverse(inverse(negative_part(X)) least_upper_bound Y)) ->
% inverse(inverse(negative_part(X)) least_upper_bound Y) collapsed.
% Rule
% [206]
% positive_part(inverse(inverse(negative_part(X)) least_upper_bound Y) least_upper_bound Z)
% -> positive_part(Z) collapsed.
% Rule
% [207]
% inverse(negative_part(multiply(X,inverse(negative_part(Y))))) greatest_lower_bound X
% -> negative_part(X) collapsed.
% Rule
% [208]
% inverse(negative_part(multiply(inverse(negative_part(X)),Y))) greatest_lower_bound Y
% -> negative_part(Y) collapsed.
% Rule
% [212]
% negative_part(inverse(inverse(negative_part(X)) least_upper_bound Y) least_upper_bound X)
% -> negative_part(X) collapsed.
% Rule
% [219]
% negative_part(inverse(inverse(negative_part(X)) greatest_lower_bound Y) greatest_lower_bound X)
% -> negative_part(X) collapsed.
% Rule [223] multiply(X,inverse(negative_part(X))) -> positive_part(X)
% collapsed.
% Current number of equations to process: 1960
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [225]
% positive_part(inverse(positive_part(Y) greatest_lower_bound X)) ->
% positive_part(inverse(X))
% Current number of equations to process: 1971
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [226]
% negative_part(inverse(X) least_upper_bound multiply(inverse(X),inverse(X)))
% -> negative_part(inverse(X))
% Current number of equations to process: 1970
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [227]
% negative_part(inverse(positive_part(X) greatest_lower_bound Y)) ->
% negative_part(inverse(X greatest_lower_bound Y))
% Current number of equations to process: 1969
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [228]
% (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: 1994
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [229] negative_part(multiply(X,X) least_upper_bound X) -> negative_part(X)
% Rule
% [226]
% negative_part(inverse(X) least_upper_bound multiply(inverse(X),inverse(X)))
% -> negative_part(inverse(X)) collapsed.
% Current number of equations to process: 2001
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [230]
% negative_part(inverse(inverse(Y) greatest_lower_bound X)) ->
% negative_part(inverse(X) least_upper_bound Y)
% Rule
% [137]
% negative_part(inverse(inverse(X) greatest_lower_bound X greatest_lower_bound Y))
% -> identity collapsed.
% Current number of equations to process: 2013
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [231]
% negative_part(multiply(inverse(X),inverse(X)) least_upper_bound X) ->
% identity
% Current number of equations to process: 2027
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [232]
% inverse(inverse(X) least_upper_bound Y) -> inverse(Y) greatest_lower_bound X
% Rule
% [105]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(negative_part(inverse(multiply(X,Y))),X) collapsed.
% Rule [107] inverse(inverse(X) least_upper_bound Y) least_upper_bound X -> X
% collapsed.
% Rule
% [138]
% positive_part(inverse(inverse(X) least_upper_bound X least_upper_bound Y)) ->
% identity collapsed.
% Rule
% [159]
% 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: 2030
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [233]
% inverse(inverse(X) greatest_lower_bound Y) -> inverse(Y) least_upper_bound X
% Rule
% [119]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(positive_part(inverse(multiply(X,Y))),X) collapsed.
% Rule
% [121] inverse(inverse(X) greatest_lower_bound Y) greatest_lower_bound X -> X
% collapsed.
% Rule
% [122]
% positive_part(inverse(inverse(X) greatest_lower_bound Y)) greatest_lower_bound X
% -> X collapsed.
% Rule
% [167]
% (inverse(inverse(X) greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound X
% -> X collapsed.
% Rule
% [168]
% inverse(inverse(X least_upper_bound Y) greatest_lower_bound Z) greatest_lower_bound X
% -> X collapsed.
% Rule
% [230]
% negative_part(inverse(inverse(Y) greatest_lower_bound X)) ->
% negative_part(inverse(X) least_upper_bound Y) collapsed.
% Current number of equations to process: 2029
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [234]
% (multiply(X,X) least_upper_bound X) greatest_lower_bound positive_part(X) ->
% X
% Rule
% [228]
% (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: 2049
% 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 39 rules have been used:
% [4]
% identity least_upper_bound X -> positive_part(X); trace = in the starting set
% [5] identity greatest_lower_bound X -> negative_part(X); trace = in the starting set
% [6] multiply(inverse(X),X) -> identity; trace = in the starting set
% [9] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z)); trace = in the starting set
% [12] multiply(X,Y least_upper_bound Z) ->
% multiply(X,Y) least_upper_bound multiply(X,Z); trace = in the starting set
% [13] multiply(X,Y greatest_lower_bound Z) ->
% multiply(X,Y) greatest_lower_bound multiply(X,Z); trace = in the starting set
% [14] multiply(Y least_upper_bound Z,X) ->
% multiply(Y,X) least_upper_bound multiply(Z,X); trace = in the starting set
% [25] positive_part(X) least_upper_bound Y ->
% positive_part(X least_upper_bound Y); trace = Self cp of 4
% [28] multiply(inverse(Y),multiply(Y,X)) -> X; trace = Cp of 9 and 6
% [31] multiply(X,positive_part(Y)) -> multiply(X,Y) least_upper_bound X; trace = Cp of 12 and 4
% [32] multiply(X,negative_part(Y)) ->
% multiply(X,identity) greatest_lower_bound multiply(X,Y); trace = Cp of 13 and 5
% [33] multiply(positive_part(X),Y) -> multiply(X,Y) least_upper_bound Y; trace = Cp of 14 and 4
% [37] multiply(inverse(inverse(X)),Y) -> multiply(X,Y); trace = Self cp of 28
% [38] multiply(X,identity) -> X; trace = Cp of 28 and 6
% [43] multiply(X,inverse(X)) -> identity; trace = Cp of 37 and 6
% [46] inverse(inverse(X)) -> X; trace = Cp of 38 and 37
% [47] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity; trace = Cp of 43 and 9
% [48] multiply(Y,inverse(multiply(X,Y))) -> inverse(X); trace = Cp of 47 and 28
% [50] inverse(multiply(Y,X)) -> multiply(inverse(X),inverse(Y)); trace = Cp of 48 and 28
% [51] inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(inverse(positive_part(Y)),inverse(X)); trace = Cp of 50 and 31
% [52] inverse(positive_part(inverse(X))) ->
% multiply(inverse(positive_part(X)),X); trace = Cp of 51 and 6
% [59] inverse(positive_part(multiply(X,inverse(positive_part(X))))) ->
% identity; trace = Self cp of 52
% [62] positive_part(multiply(X,inverse(positive_part(X)))) -> identity; trace = Cp of 59 and 46
% [66] positive_part(inverse(positive_part(X))) -> identity; trace = Cp of 62 and 52
% [74] multiply(X,inverse(positive_part(Y))) least_upper_bound X -> X; trace = Cp of 66 and 31
% [75] multiply(inverse(positive_part(Y)),X) least_upper_bound X -> X; trace = Cp of 66 and 33
% [103] inverse(positive_part(X)) least_upper_bound multiply(X,inverse(
% positive_part(X)))
% -> identity; trace = Cp of 43 and 33
% [104] inverse(positive_part(X)) least_upper_bound X -> positive_part(X); trace = Cp of 103 and 74
% [106] multiply(inverse(positive_part(multiply(X,Y))),X) <->
% inverse(inverse(X) least_upper_bound Y); trace = Cp of 51 and 28
% [107] inverse(inverse(X) least_upper_bound Y) least_upper_bound X -> X; trace = Cp of 106 and 75
% [108] inverse(X least_upper_bound Y) least_upper_bound inverse(X) ->
% inverse(X); trace = Cp of 107 and 46
% [109] inverse(positive_part(X)) least_upper_bound inverse(X) -> inverse(X); trace = Cp of 108 and 4
% [112] positive_part(inverse(X) least_upper_bound X) ->
% inverse(X) least_upper_bound X; trace = Cp of 109 and 104
% [116] positive_part(multiply(inverse(positive_part(multiply(X,X))),X)) ->
% identity; trace = Cp of 112 and 66
% [118] inverse(positive_part(X least_upper_bound Y)) least_upper_bound
% inverse(Y) -> inverse(Y); trace = Cp of 108 and 25
% [162] inverse(positive_part(multiply(X,X) least_upper_bound X)) ->
% inverse(positive_part(multiply(X,X))); trace = Cp of 116 and 106
% [163] positive_part(multiply(X,X) least_upper_bound X) ->
% positive_part(multiply(X,X)); trace = Cp of 162 and 46
% [228] (inverse(X) least_upper_bound multiply(inverse(X),inverse(X))) greatest_lower_bound
% positive_part(inverse(X)) -> inverse(X); trace = Cp of 163 and 118
% [234] (multiply(X,X) least_upper_bound X) greatest_lower_bound positive_part(X)
% -> X; trace = Cp of 228 and 46
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 51.370000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------