TSTP Solution File: GRP183-4 by CiME---2.01
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP183-4 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n035.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 00:22:34 EDT 2014
% Result : Unsatisfiable 276.08s
% Output : Refutation 276.08s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP183-4 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command : tptp2X_and_run_cime %s
% % Computer : n035.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Fri Jun 6 06:47:18 CDT 2014
% % CPUTime : 276.08
% Processing problem /tmp/CiME_46160_n035.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " least_upper_bound,greatest_lower_bound : AC; a,identity : constant; inverse : 1; multiply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z));
% multiply(identity,X) = X;
% multiply(inverse(X),X) = identity;
% X least_upper_bound X = X;
% X greatest_lower_bound X = X;
% X least_upper_bound (X greatest_lower_bound Y) = X;
% X greatest_lower_bound (X least_upper_bound Y) = X;
% multiply(X,Y least_upper_bound Z) = multiply(X,Y) least_upper_bound multiply(X,Z);
% multiply(X,Y greatest_lower_bound Z) = multiply(X,Y) greatest_lower_bound multiply(X,Z);
% multiply(Y least_upper_bound Z,X) = multiply(Y,X) least_upper_bound multiply(Z,X);
% multiply(Y greatest_lower_bound Z,X) = multiply(Y,X) greatest_lower_bound multiply(Z,X);
% inverse(identity) = identity;
% inverse(inverse(X)) = X;
% inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X));
% ";
%
% let s1 = status F "
% a lr_lex;
% inverse lr_lex;
% identity lr_lex;
% least_upper_bound mul;
% greatest_lower_bound mul;
% multiply mul;
% ";
%
% let p1 = precedence F "
% multiply > inverse > greatest_lower_bound > least_upper_bound > identity > a";
%
% let s2 = status F "
% a mul;
% least_upper_bound mul;
% greatest_lower_bound mul;
% inverse mul;
% multiply mul;
% identity mul;
% ";
%
% let p2 = precedence F "
% multiply > inverse > greatest_lower_bound > least_upper_bound > identity = a";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " (a least_upper_bound identity) greatest_lower_bound (inverse(a) least_upper_bound identity) = identity;"
% ;
% (*
% 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)) }
% (14 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 least_upper_bound identity) greatest_lower_bound
% (identity least_upper_bound inverse(a)) =
% identity } (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: 13
% 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: 12
% 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: 11
% 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: 10
% 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: 9
% 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: 8
% 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: 7
% 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: 6
% Current number of rules: 8
% New rule produced :
% [9] inverse(multiply(X,Y)) -> multiply(inverse(Y),inverse(X))
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 9
% New rule produced :
% [10] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 10
% New rule produced :
% [11]
% 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: 11
% New rule produced :
% [12]
% 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: 12
% New rule produced :
% [13]
% 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: 13
% New rule produced :
% [14]
% 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: 14
% New rule produced : [15] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] multiply(inverse(X),identity) -> inverse(X)
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] multiply(X,identity) -> X
% Rule [16] multiply(inverse(X),identity) -> inverse(X) collapsed.
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [20]
% ((X least_upper_bound Y) greatest_lower_bound Z) least_upper_bound (X greatest_lower_bound Z)
% -> (X least_upper_bound Y) greatest_lower_bound Z
% Current number of equations to process: 58
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [21]
% ((X greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound
% (X least_upper_bound Z) -> (X greatest_lower_bound Y) least_upper_bound Z
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [22]
% inverse(multiply(X,Y) least_upper_bound multiply(X,Z)) ->
% multiply(inverse(Y least_upper_bound Z),inverse(X))
% Current number of equations to process: 218
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [23]
% inverse(identity least_upper_bound multiply(X,Y)) <->
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X))
% Current number of equations to process: 219
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [24]
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X)) <->
% inverse(identity least_upper_bound multiply(X,Y))
% Current number of equations to process: 219
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [25]
% inverse(identity least_upper_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X least_upper_bound Y),X)
% Current number of equations to process: 219
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [26]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(inverse(identity least_upper_bound Y),inverse(X))
% Current number of equations to process: 226
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [27]
% inverse(identity least_upper_bound inverse(identity least_upper_bound
% multiply(X,Y))) -> identity
% Current number of equations to process: 242
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [28]
% inverse(identity least_upper_bound inverse(X)) ->
% multiply(inverse(identity least_upper_bound X),X)
% Rule
% [27]
% inverse(identity least_upper_bound inverse(identity least_upper_bound
% multiply(X,Y))) -> identity
% collapsed.
% Current number of equations to process: 247
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [29]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(inverse(identity least_upper_bound multiply(X,Y)),X)
% Rule
% [28]
% inverse(identity least_upper_bound inverse(X)) ->
% multiply(inverse(identity least_upper_bound X),X) collapsed.
% Current number of equations to process: 256
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [30]
% multiply(inverse(identity least_upper_bound multiply(X,Y)),X) <->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 256
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [31]
% inverse(multiply(X,Y) greatest_lower_bound multiply(X,Z)) ->
% multiply(inverse(Y greatest_lower_bound Z),inverse(X))
% Current number of equations to process: 285
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [32]
% inverse(identity greatest_lower_bound multiply(X,Y)) <->
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X))
% Current number of equations to process: 286
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [33]
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y))
% Current number of equations to process: 286
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [34]
% inverse(identity greatest_lower_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X greatest_lower_bound Y),X)
% Current number of equations to process: 287
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [35]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(inverse(identity greatest_lower_bound Y),inverse(X))
% Current number of equations to process: 294
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [36]
% inverse(identity greatest_lower_bound inverse(X)) ->
% multiply(inverse(identity greatest_lower_bound X),X)
% Current number of equations to process: 337
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [37]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X)
% Rule
% [36]
% inverse(identity greatest_lower_bound inverse(X)) ->
% multiply(inverse(identity greatest_lower_bound X),X) collapsed.
% Current number of equations to process: 356
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [38]
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X) <->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 356
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [39]
% inverse(multiply(X,Y) least_upper_bound multiply(Z,Y)) ->
% multiply(inverse(Y),inverse(X least_upper_bound Z))
% Current number of equations to process: 405
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [40]
% inverse(identity least_upper_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X least_upper_bound Y))
% Current number of equations to process: 406
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [41]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),inverse(identity least_upper_bound X))
% Current number of equations to process: 409
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [42]
% inverse(identity least_upper_bound multiply(X,Y)) <->
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X))
% Current number of equations to process: 415
% Current number of ordered equations: 1
% Current number of rules: 38
% New rule produced :
% [43]
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X)) <->
% inverse(identity least_upper_bound multiply(X,Y))
% Current number of equations to process: 415
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [44]
% multiply(inverse(identity least_upper_bound X),X) ->
% multiply(X,inverse(identity least_upper_bound X))
% Current number of equations to process: 432
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [45]
% multiply(X,inverse(inverse(Y) least_upper_bound X)) <->
% multiply(inverse(inverse(X) least_upper_bound Y),Y)
% Current number of equations to process: 444
% Current number of ordered equations: 1
% Current number of rules: 41
% New rule produced :
% [46]
% multiply(inverse(inverse(X) least_upper_bound Y),Y) <->
% multiply(X,inverse(inverse(Y) least_upper_bound X))
% Current number of equations to process: 444
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [47]
% multiply(inverse(identity least_upper_bound X),inverse(X)) ->
% multiply(inverse(X),inverse(identity least_upper_bound X))
% Current number of equations to process: 460
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [48]
% inverse(inverse(X) least_upper_bound inverse(Y)) ->
% multiply(X,multiply(inverse(X least_upper_bound Y),Y))
% Current number of equations to process: 477
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [49]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(X,inverse(identity least_upper_bound multiply(Y,X)))
% Current number of equations to process: 497
% Current number of ordered equations: 1
% Current number of rules: 45
% New rule produced :
% [50]
% multiply(X,inverse(identity least_upper_bound multiply(Y,X))) <->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 497
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [51]
% inverse(multiply(X,Y) greatest_lower_bound multiply(Z,Y)) ->
% multiply(inverse(Y),inverse(X greatest_lower_bound Z))
% Current number of equations to process: 735
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [52]
% inverse(identity greatest_lower_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X greatest_lower_bound Y))
% Current number of equations to process: 736
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [53]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),inverse(identity greatest_lower_bound X))
% Current number of equations to process: 739
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [54]
% inverse(identity greatest_lower_bound multiply(X,Y)) <->
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X))
% Current number of equations to process: 745
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced :
% [55]
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y))
% Current number of equations to process: 745
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [56]
% multiply(inverse(identity greatest_lower_bound X),X) ->
% multiply(X,inverse(identity greatest_lower_bound X))
% Current number of equations to process: 776
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [57]
% multiply(X,inverse(inverse(Y) greatest_lower_bound X)) <->
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y)
% Current number of equations to process: 796
% Current number of ordered equations: 1
% Current number of rules: 53
% New rule produced :
% [58]
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y) <->
% multiply(X,inverse(inverse(Y) greatest_lower_bound X))
% Current number of equations to process: 796
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [59]
% multiply(inverse(identity greatest_lower_bound X),inverse(X)) ->
% multiply(inverse(X),inverse(identity greatest_lower_bound X))
% Current number of equations to process: 820
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [60]
% inverse(inverse(X) greatest_lower_bound inverse(Y)) ->
% multiply(X,multiply(inverse(X greatest_lower_bound Y),Y))
% Current number of equations to process: 848
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [61]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(X,inverse(identity greatest_lower_bound multiply(Y,X)))
% Current number of equations to process: 879
% Current number of ordered equations: 1
% Current number of rules: 57
% New rule produced :
% [62]
% multiply(X,inverse(identity greatest_lower_bound multiply(Y,X))) <->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 879
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [63]
% inverse(multiply(inverse(X),Y) least_upper_bound Z) <->
% multiply(inverse(multiply(X,Z) least_upper_bound Y),X)
% Rule
% [25]
% inverse(identity least_upper_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X least_upper_bound Y),X) collapsed.
% Current number of equations to process: 1192
% Current number of ordered equations: 1
% Current number of rules: 58
% New rule produced :
% [64]
% multiply(inverse(multiply(X,Z) least_upper_bound Y),X) <->
% inverse(multiply(inverse(X),Y) least_upper_bound Z)
% Current number of equations to process: 1192
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [65]
% inverse(multiply(inverse(X),Y) greatest_lower_bound Z) <->
% multiply(inverse(multiply(X,Z) greatest_lower_bound Y),X)
% Rule
% [34]
% inverse(identity greatest_lower_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X greatest_lower_bound Y),X) collapsed.
% Current number of equations to process: 1318
% Current number of ordered equations: 1
% Current number of rules: 59
% New rule produced :
% [66]
% multiply(inverse(multiply(X,Z) greatest_lower_bound Y),X) <->
% inverse(multiply(inverse(X),Y) greatest_lower_bound Z)
% Current number of equations to process: 1318
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [67]
% inverse(identity greatest_lower_bound X) greatest_lower_bound multiply(X,
% inverse(
% identity greatest_lower_bound X))
% -> identity
% Current number of equations to process: 1448
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [68]
% identity greatest_lower_bound inverse(identity greatest_lower_bound X) ->
% identity
% Current number of equations to process: 1453
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [69]
% identity least_upper_bound inverse(identity greatest_lower_bound X) ->
% inverse(identity greatest_lower_bound X)
% Current number of equations to process: 1468
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [70]
% identity greatest_lower_bound multiply(X,inverse(identity greatest_lower_bound X))
% -> identity
% Current number of equations to process: 1477
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [71]
% (inverse(identity greatest_lower_bound X) least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 1476
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [72]
% (identity greatest_lower_bound X) least_upper_bound inverse(identity greatest_lower_bound Y)
% -> inverse(identity greatest_lower_bound Y)
% Current number of equations to process: 1475
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [73]
% (multiply(X,inverse(identity greatest_lower_bound X)) least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 1484
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [74]
% identity least_upper_bound multiply(X,inverse(identity greatest_lower_bound X))
% -> multiply(X,inverse(identity greatest_lower_bound X))
% Current number of equations to process: 1482
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [75]
% multiply(X,inverse(identity greatest_lower_bound Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 1530
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [76]
% multiply(inverse(identity greatest_lower_bound Y),X) greatest_lower_bound X
% -> X
% Current number of equations to process: 1529
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [77]
% identity greatest_lower_bound multiply(X,inverse(X greatest_lower_bound Y))
% -> identity
% Rule
% [70]
% identity greatest_lower_bound multiply(X,inverse(identity greatest_lower_bound X))
% -> identity collapsed.
% Current number of equations to process: 1550
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [78]
% identity greatest_lower_bound multiply(inverse(X greatest_lower_bound Y),X)
% -> identity
% Current number of equations to process: 1557
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [79]
% (multiply(X,inverse(X greatest_lower_bound Y)) least_upper_bound Z) greatest_lower_bound identity
% -> identity
% Rule
% [73]
% (multiply(X,inverse(identity greatest_lower_bound X)) least_upper_bound Y) greatest_lower_bound identity
% -> identity collapsed.
% Current number of equations to process: 1664
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [80]
% (multiply(inverse(X greatest_lower_bound Y),X) least_upper_bound Z) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 1663
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [81]
% multiply(X,inverse(identity greatest_lower_bound Y)) least_upper_bound X ->
% multiply(X,inverse(identity greatest_lower_bound Y))
% Current number of equations to process: 1728
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [82]
% multiply(inverse(identity greatest_lower_bound X),Y) least_upper_bound Y ->
% multiply(inverse(identity greatest_lower_bound X),Y)
% Current number of equations to process: 1727
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [83]
% identity least_upper_bound multiply(X,inverse(X greatest_lower_bound Y)) ->
% multiply(X,inverse(X greatest_lower_bound Y))
% Rule
% [74]
% identity least_upper_bound multiply(X,inverse(identity greatest_lower_bound X))
% -> multiply(X,inverse(identity greatest_lower_bound X)) collapsed.
% Current number of equations to process: 1726
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [84] inverse(inverse(X) greatest_lower_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 1791
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [85]
% inverse(identity greatest_lower_bound X) greatest_lower_bound X ->
% identity greatest_lower_bound X
% Current number of equations to process: 1802
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [86]
% (multiply(X,inverse(identity greatest_lower_bound Y)) least_upper_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 2044
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [87]
% multiply(X,multiply(Y,inverse(identity greatest_lower_bound Y))) greatest_lower_bound X
% -> X
% Current number of equations to process: 2043
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [88]
% multiply(X,multiply(Y,inverse(Y greatest_lower_bound Z))) greatest_lower_bound X
% -> X
% Rule
% [87]
% multiply(X,multiply(Y,inverse(identity greatest_lower_bound Y))) greatest_lower_bound X
% -> X collapsed.
% Current number of equations to process: 2042
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [89]
% multiply(X,multiply(inverse(Y greatest_lower_bound Z),Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 2040
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [90]
% (multiply(inverse(identity greatest_lower_bound Y),X) least_upper_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 2038
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [91]
% multiply(X,multiply(inverse(identity greatest_lower_bound X),Y)) greatest_lower_bound Y
% -> Y
% Current number of equations to process: 2037
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [92]
% multiply(X,multiply(inverse(X greatest_lower_bound Y),Z)) greatest_lower_bound Z
% -> Z
% Rule
% [91]
% multiply(X,multiply(inverse(identity greatest_lower_bound X),Y)) greatest_lower_bound Y
% -> Y collapsed.
% Current number of equations to process: 2036
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [93]
% multiply(inverse(X greatest_lower_bound Y),multiply(X,Z)) greatest_lower_bound Z
% -> Z
% Current number of equations to process: 2035
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [94]
% identity least_upper_bound multiply(inverse(X greatest_lower_bound Y),X) ->
% multiply(inverse(X greatest_lower_bound Y),X)
% Current number of equations to process: 2256
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [95]
% inverse(X greatest_lower_bound Y) greatest_lower_bound inverse(X) ->
% inverse(X)
% Current number of equations to process: 2542
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [96]
% identity greatest_lower_bound inverse(X) greatest_lower_bound X ->
% inverse(X) greatest_lower_bound X
% Current number of equations to process: 2889
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [97]
% inverse(inverse(X) greatest_lower_bound Y) least_upper_bound X ->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 2888
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [98]
% inverse(inverse(X least_upper_bound Y) greatest_lower_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 2886
% Current number of ordered equations: 1
% Current number of rules: 87
% New rule produced :
% [99]
% (inverse(inverse(X) greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound X
% -> X
% Current number of equations to process: 2886
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [100]
% inverse((X least_upper_bound Y) greatest_lower_bound identity) greatest_lower_bound X
% -> identity greatest_lower_bound X
% Current number of equations to process: 2885
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [101]
% inverse(X) greatest_lower_bound multiply(X,inverse(identity greatest_lower_bound X))
% -> identity greatest_lower_bound inverse(X)
% Current number of equations to process: 3726
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [102]
% inverse(X greatest_lower_bound Y) least_upper_bound inverse(X) ->
% inverse(X greatest_lower_bound Y)
% Current number of equations to process: 3877
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [103]
% inverse(X least_upper_bound Y) greatest_lower_bound inverse(X) ->
% inverse(X least_upper_bound Y)
% Current number of equations to process: 3876
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [104]
% (inverse(X) greatest_lower_bound X) least_upper_bound identity -> identity
% Current number of equations to process: 4163
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [105]
% (inverse(X) greatest_lower_bound X greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Current number of equations to process: 4208
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [106]
% (identity greatest_lower_bound X) least_upper_bound (inverse(X) greatest_lower_bound X)
% -> identity greatest_lower_bound X
% Current number of equations to process: 4218
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [107]
% identity greatest_lower_bound inverse(inverse(X) greatest_lower_bound X greatest_lower_bound Y)
% -> identity
% Current number of equations to process: 4573
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [108]
% (inverse(X greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound
% inverse(X) -> inverse(X)
% Current number of equations to process: 4586
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [109]
% (identity least_upper_bound Y) greatest_lower_bound inverse(X) greatest_lower_bound X
% -> inverse(X) greatest_lower_bound X
% Current number of equations to process: 4585
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [110]
% identity greatest_lower_bound multiply(inverse(identity greatest_lower_bound
% multiply(X,X)),X) -> identity
% Current number of equations to process: 2447
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [111]
% (inverse(X) greatest_lower_bound Y) least_upper_bound inverse(X greatest_lower_bound Z)
% -> inverse(X greatest_lower_bound Z)
% Current number of equations to process: 2483
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [112]
% inverse(X least_upper_bound Y) greatest_lower_bound inverse(X greatest_lower_bound Z)
% -> inverse(X least_upper_bound Y)
% Current number of equations to process: 2482
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [113]
% (inverse(X) greatest_lower_bound X) least_upper_bound inverse(identity greatest_lower_bound Y)
% -> inverse(identity greatest_lower_bound Y)
% Current number of equations to process: 2481
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [114]
% (identity greatest_lower_bound inverse(X)) least_upper_bound (inverse(X) greatest_lower_bound X)
% -> identity greatest_lower_bound inverse(X)
% Current number of equations to process: 2480
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [115]
% (identity least_upper_bound X) greatest_lower_bound inverse(identity least_upper_bound X)
% -> identity greatest_lower_bound inverse(identity least_upper_bound X)
% Current number of equations to process: 2478
% Current number of ordered equations: 1
% Current number of rules: 104
% New rule produced :
% [116]
% identity greatest_lower_bound inverse(X least_upper_bound Y) greatest_lower_bound X
% -> inverse(X least_upper_bound Y) greatest_lower_bound X
% Current number of equations to process: 2478
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [117]
% inverse(identity greatest_lower_bound Y) greatest_lower_bound inverse(X) greatest_lower_bound X
% -> inverse(X) greatest_lower_bound X
% Current number of equations to process: 2477
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [118]
% inverse(X least_upper_bound Y) least_upper_bound inverse(X) -> inverse(X)
% Current number of equations to process: 2589
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [119]
% identity least_upper_bound inverse(inverse(identity greatest_lower_bound X) least_upper_bound Y)
% -> identity
% Current number of equations to process: 2718
% Current number of ordered equations: 0
% Current number of rules: 108
% Rule [115]
% (identity least_upper_bound X) greatest_lower_bound inverse(identity least_upper_bound X)
% -> identity greatest_lower_bound inverse(identity least_upper_bound X) is composed into
% [115]
% (identity least_upper_bound X) greatest_lower_bound inverse(identity least_upper_bound X)
% -> inverse(identity least_upper_bound X)
% New rule produced :
% [120]
% identity greatest_lower_bound inverse(identity least_upper_bound X) ->
% inverse(identity least_upper_bound X)
% Current number of equations to process: 2917
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [121]
% inverse(inverse(X) least_upper_bound Y) greatest_lower_bound X ->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 2922
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [122]
% (inverse(X least_upper_bound Y) greatest_lower_bound Z) least_upper_bound
% inverse(X) -> inverse(X)
% Current number of equations to process: 2921
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [123]
% (inverse(X least_upper_bound Y) greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 3159
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [124]
% identity least_upper_bound inverse(identity least_upper_bound X) -> identity
% Current number of equations to process: 3456
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [125]
% (multiply(X,inverse(Y)) greatest_lower_bound multiply(X,Y)) least_upper_bound X
% -> X
% Current number of equations to process: 3898
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [126]
% (multiply(inverse(Y),X) greatest_lower_bound multiply(Y,X)) least_upper_bound X
% -> X
% Current number of equations to process: 3897
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [127]
% (inverse(X least_upper_bound Y) greatest_lower_bound X greatest_lower_bound Z) least_upper_bound identity
% -> identity
% Current number of equations to process: 3896
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [128]
% inverse(inverse(X greatest_lower_bound Y) least_upper_bound Z) least_upper_bound X
% -> X
% Rule
% [119]
% identity least_upper_bound inverse(inverse(identity greatest_lower_bound X) least_upper_bound Y)
% -> identity collapsed.
% Current number of equations to process: 4202
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [129]
% (inverse(identity least_upper_bound X) greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Current number of equations to process: 4903
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [130]
% identity greatest_lower_bound multiply(X,inverse(identity greatest_lower_bound
% multiply(X,X))) -> identity
% Current number of equations to process: 2472
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [131]
% inverse(X least_upper_bound Y) least_upper_bound inverse(X greatest_lower_bound Z)
% -> inverse(X greatest_lower_bound Z)
% Current number of equations to process: 2570
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [132]
% (inverse(X) least_upper_bound Z) greatest_lower_bound inverse(X least_upper_bound Y)
% -> inverse(X least_upper_bound Y)
% Current number of equations to process: 2568
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [133]
% (identity least_upper_bound Y) greatest_lower_bound inverse(identity least_upper_bound X)
% -> inverse(identity least_upper_bound X)
% Rule
% [115]
% (identity least_upper_bound X) greatest_lower_bound inverse(identity least_upper_bound X)
% -> inverse(identity least_upper_bound X) collapsed.
% Current number of equations to process: 4001
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [134] inverse(inverse(X) least_upper_bound Y) least_upper_bound X -> X
% Current number of equations to process: 2559
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [135]
% (inverse(inverse(X) least_upper_bound Y) greatest_lower_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 2995
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [136]
% identity least_upper_bound inverse(inverse(X) least_upper_bound X least_upper_bound Y)
% -> identity
% Current number of equations to process: 4227
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [137]
% multiply(X,inverse(identity least_upper_bound Y)) least_upper_bound X -> X
% Current number of equations to process: 4291
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [138]
% multiply(inverse(identity least_upper_bound Y),X) least_upper_bound X -> X
% Current number of equations to process: 4290
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [139]
% identity least_upper_bound multiply(X,inverse(identity least_upper_bound X))
% -> identity
% Current number of equations to process: 4316
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [140]
% identity least_upper_bound multiply(X,inverse(X least_upper_bound Y)) ->
% identity
% Rule
% [139]
% identity least_upper_bound multiply(X,inverse(identity least_upper_bound X))
% -> identity collapsed.
% Current number of equations to process: 4317
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [141]
% identity least_upper_bound multiply(inverse(X least_upper_bound Y),X) ->
% identity
% Current number of equations to process: 4325
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [142] (identity greatest_lower_bound multiply(X,X)) least_upper_bound X -> X
% Current number of equations to process: 4365
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [143]
% (multiply(X,inverse(identity least_upper_bound X)) greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Current number of equations to process: 3316
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [144]
% (multiply(X,inverse(X least_upper_bound Y)) greatest_lower_bound Z) least_upper_bound identity
% -> identity
% Rule
% [143]
% (multiply(X,inverse(identity least_upper_bound X)) greatest_lower_bound Y) least_upper_bound identity
% -> identity collapsed.
% Current number of equations to process: 3315
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [145]
% (multiply(inverse(X least_upper_bound Y),X) greatest_lower_bound Z) least_upper_bound identity
% -> identity
% Current number of equations to process: 3314
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [146]
% multiply(X,inverse(identity least_upper_bound Y)) greatest_lower_bound X ->
% multiply(X,inverse(identity least_upper_bound Y))
% Current number of equations to process: 3517
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [147]
% multiply(inverse(identity least_upper_bound X),Y) greatest_lower_bound Y ->
% multiply(inverse(identity least_upper_bound X),Y)
% Current number of equations to process: 3516
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [148]
% identity greatest_lower_bound multiply(X,inverse(identity least_upper_bound X))
% -> multiply(X,inverse(identity least_upper_bound X))
% Current number of equations to process: 3515
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [149]
% identity greatest_lower_bound multiply(X,inverse(X least_upper_bound Y)) ->
% multiply(X,inverse(X least_upper_bound Y))
% Rule
% [148]
% identity greatest_lower_bound multiply(X,inverse(identity least_upper_bound X))
% -> multiply(X,inverse(identity least_upper_bound X)) collapsed.
% Current number of equations to process: 3514
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [150]
% identity greatest_lower_bound multiply(inverse(X least_upper_bound Y),X) ->
% multiply(inverse(X least_upper_bound Y),X)
% Current number of equations to process: 3513
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [151]
% (identity greatest_lower_bound multiply(X,X) greatest_lower_bound Y) least_upper_bound X
% -> X
% Current number of equations to process: 4019
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [152]
% identity greatest_lower_bound multiply(X,X) greatest_lower_bound X ->
% identity greatest_lower_bound multiply(X,X)
% Current number of equations to process: 4018
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [153]
% inverse(identity greatest_lower_bound multiply(X,X)) greatest_lower_bound
% inverse(X) -> inverse(X)
% Current number of equations to process: 4016
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [154]
% multiply(X,multiply(inverse(X least_upper_bound Y),Y)) least_upper_bound X ->
% X
% Current number of equations to process: 4041
% Current number of ordered equations: 1
% Current number of rules: 138
% New rule produced :
% [155]
% multiply(X,multiply(inverse(X least_upper_bound Y),Y)) least_upper_bound Y ->
% Y
% Current number of equations to process: 4041
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [156]
% (multiply(inverse(identity least_upper_bound X),Y) greatest_lower_bound Z) least_upper_bound Y
% -> Y
% Current number of equations to process: 4040
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [157]
% (multiply(X,inverse(identity least_upper_bound Y)) greatest_lower_bound Z) least_upper_bound X
% -> X
% Current number of equations to process: 4039
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [158]
% identity least_upper_bound multiply(X,inverse(identity least_upper_bound
% multiply(X,X))) -> identity
% Current number of equations to process: 4038
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [159]
% multiply(X,multiply(Y,inverse(identity least_upper_bound Y))) least_upper_bound X
% -> X
% Current number of equations to process: 4036
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [160]
% multiply(X,multiply(Y,inverse(Y least_upper_bound Z))) least_upper_bound X ->
% X
% Rule
% [159]
% multiply(X,multiply(Y,inverse(identity least_upper_bound Y))) least_upper_bound X
% -> X collapsed.
% Current number of equations to process: 4035
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [161]
% multiply(X,multiply(inverse(Y least_upper_bound Z),Y)) least_upper_bound X ->
% X
% Rule
% [154]
% multiply(X,multiply(inverse(X least_upper_bound Y),Y)) least_upper_bound X ->
% X collapsed.
% Current number of equations to process: 4034
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [162]
% multiply(X,multiply(inverse(identity least_upper_bound X),Y)) least_upper_bound Y
% -> Y
% Current number of equations to process: 4031
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [163]
% multiply(X,multiply(inverse(X least_upper_bound Y),Z)) least_upper_bound Z ->
% Z
% Rule
% [155]
% multiply(X,multiply(inverse(X least_upper_bound Y),Y)) least_upper_bound Y ->
% Y collapsed.
% Rule
% [162]
% multiply(X,multiply(inverse(identity least_upper_bound X),Y)) least_upper_bound Y
% -> Y collapsed.
% Current number of equations to process: 4030
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [164]
% multiply(inverse(X least_upper_bound Y),multiply(X,Z)) least_upper_bound Z ->
% Z
% Current number of equations to process: 4029
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [165]
% (inverse(X) greatest_lower_bound multiply(Y,Y) greatest_lower_bound X) least_upper_bound Y
% -> Y
% Current number of equations to process: 3876
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [166]
% (inverse(identity least_upper_bound X) greatest_lower_bound multiply(Y,Y)) least_upper_bound Y
% -> Y
% Current number of equations to process: 3875
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [167]
% (identity greatest_lower_bound multiply(X,X)) least_upper_bound (identity greatest_lower_bound X)
% -> identity greatest_lower_bound X
% Current number of equations to process: 3874
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [168]
% identity greatest_lower_bound inverse(X) greatest_lower_bound multiply(X,X)
% -> inverse(X) greatest_lower_bound multiply(X,X)
% Current number of equations to process: 3239
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [169]
% (inverse(X) greatest_lower_bound multiply(X,X)) least_upper_bound identity ->
% identity
% Current number of equations to process: 3305
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [170]
% (inverse(X) greatest_lower_bound multiply(X,X) greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Current number of equations to process: 3316
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [171]
% (inverse(X) greatest_lower_bound multiply(X,X)) least_upper_bound X -> X
% Current number of equations to process: 3662
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [172]
% (inverse(X) greatest_lower_bound multiply(X,X) greatest_lower_bound Y) least_upper_bound X
% -> X
% Current number of equations to process: 3667
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [173]
% (multiply(inverse(X),inverse(X)) greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 3698
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [174]
% (inverse(X least_upper_bound Y) greatest_lower_bound multiply(X,X)) least_upper_bound identity
% -> identity
% Current number of equations to process: 3862
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [175]
% (inverse(X least_upper_bound Y) greatest_lower_bound multiply(X,X)) least_upper_bound X
% -> X
% Current number of equations to process: 4146
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [176]
% inverse(X) greatest_lower_bound multiply(X,X) greatest_lower_bound X ->
% inverse(X) greatest_lower_bound multiply(X,X)
% Current number of equations to process: 4916
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [177]
% (multiply(inverse(X),inverse(X)) greatest_lower_bound X) least_upper_bound
% inverse(X) -> inverse(X)
% Current number of equations to process: 4974
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [178]
% inverse(identity least_upper_bound X) least_upper_bound multiply(X,inverse(
% identity least_upper_bound X))
% -> identity
% Current number of equations to process: 2788
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [179]
% inverse(X) least_upper_bound multiply(X,inverse(identity least_upper_bound X))
% -> identity least_upper_bound inverse(X)
% Current number of equations to process: 2839
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [180]
% inverse(identity least_upper_bound X) least_upper_bound X ->
% identity least_upper_bound X
% Current number of equations to process: 2980
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [181]
% identity least_upper_bound inverse(X) least_upper_bound X ->
% inverse(X) least_upper_bound X
% Current number of equations to process: 3012
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [182]
% (inverse(X) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 3693
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [183]
% (inverse(X) least_upper_bound X least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 3694
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [184]
% inverse((X greatest_lower_bound Y) least_upper_bound identity) least_upper_bound X
% -> identity least_upper_bound X
% Current number of equations to process: 3705
% Current number of ordered equations: 0
% Current number of rules: 164
% New rule produced :
% [185]
% (identity least_upper_bound X) greatest_lower_bound (inverse(X) least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 3703
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [186]
% (inverse(X greatest_lower_bound Y) least_upper_bound X) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 4614
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [187]
% (identity greatest_lower_bound Y) least_upper_bound inverse(X) least_upper_bound X
% -> inverse(X) least_upper_bound X
% Current number of equations to process: 1361
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced :
% [188]
% (multiply(X,inverse(Y)) least_upper_bound multiply(X,Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 2990
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced :
% [189]
% (multiply(inverse(Y),X) least_upper_bound multiply(Y,X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 2989
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced :
% [190]
% (inverse(X greatest_lower_bound Y) least_upper_bound X least_upper_bound Z) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 2988
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced :
% [191] (identity least_upper_bound multiply(X,X)) greatest_lower_bound X -> X
% Current number of equations to process: 3972
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [192]
% identity least_upper_bound multiply(X,X) least_upper_bound X ->
% identity least_upper_bound multiply(X,X)
% Current number of equations to process: 2342
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [193]
% (identity least_upper_bound multiply(X,X) least_upper_bound Y) greatest_lower_bound X
% -> X
% Current number of equations to process: 2341
% Current number of ordered equations: 0
% Current number of rules: 173
% New rule produced :
% [194]
% inverse(identity least_upper_bound multiply(X,X)) least_upper_bound inverse(X)
% -> inverse(X)
% Current number of equations to process: 2348
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced :
% [195]
% (identity least_upper_bound multiply(X,X)) greatest_lower_bound (identity least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 3051
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced :
% [196]
% identity least_upper_bound multiply(inverse(identity least_upper_bound
% multiply(X,X)),X) -> identity
% Current number of equations to process: 3050
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced :
% [197]
% (inverse(identity greatest_lower_bound X) least_upper_bound multiply(Y,Y)) greatest_lower_bound Y
% -> Y
% Current number of equations to process: 3049
% Current number of ordered equations: 0
% Current number of rules: 177
% New rule produced :
% [198]
% (inverse(X) least_upper_bound multiply(Y,Y) least_upper_bound X) greatest_lower_bound Y
% -> Y
% Current number of equations to process: 3048
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [199]
% identity least_upper_bound inverse(X greatest_lower_bound Y) least_upper_bound X
% -> inverse(X greatest_lower_bound Y) least_upper_bound X
% Current number of equations to process: 4068
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [200]
% (identity least_upper_bound inverse(X)) greatest_lower_bound (inverse(X) least_upper_bound X)
% -> identity least_upper_bound inverse(X)
% Current number of equations to process: 4270
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [201]
% (inverse(Y) greatest_lower_bound Y) least_upper_bound inverse(X) least_upper_bound X
% -> inverse(X) least_upper_bound X
% Current number of equations to process: 4268
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [202]
% (inverse(X) least_upper_bound X) greatest_lower_bound inverse(Y) greatest_lower_bound Y
% -> inverse(Y) greatest_lower_bound Y
% Current number of equations to process: 4267
% Current number of ordered equations: 0
% Current number of rules: 182
% New rule produced :
% [203]
% inverse(identity least_upper_bound Y) least_upper_bound inverse(X) least_upper_bound X
% -> inverse(X) least_upper_bound X
% Current number of equations to process: 4266
% Current number of ordered equations: 0
% Current number of rules: 183
% New rule produced :
% [204]
% (inverse(X) least_upper_bound X) greatest_lower_bound inverse(identity least_upper_bound Y)
% -> inverse(identity least_upper_bound Y)
% Current number of equations to process: 4265
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [205]
% identity least_upper_bound inverse(X) least_upper_bound multiply(X,X) ->
% inverse(X) least_upper_bound multiply(X,X)
% Current number of equations to process: 4252
% Current number of ordered equations: 0
% Current number of rules: 185
% New rule produced :
% [206]
% (inverse(X) least_upper_bound multiply(X,X)) greatest_lower_bound identity ->
% identity
% Current number of equations to process: 3649
% Current number of ordered equations: 0
% Current number of rules: 186
% New rule produced :
% [207]
% (inverse(X) least_upper_bound multiply(X,X) least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 3660
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [208]
% (inverse(X) least_upper_bound multiply(X,X)) greatest_lower_bound X -> X
% Current number of equations to process: 4091
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [209]
% (inverse(X) least_upper_bound multiply(X,X) least_upper_bound Y) greatest_lower_bound X
% -> X
% Current number of equations to process: 4090
% Current number of ordered equations: 0
% Current number of rules: 189
% New rule produced :
% [210]
% (multiply(inverse(X),inverse(X)) least_upper_bound X) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 4125
% Current number of ordered equations: 0
% Current number of rules: 190
% New rule produced :
% [211]
% (inverse(X greatest_lower_bound Y) least_upper_bound multiply(X,X)) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 4341
% Current number of ordered equations: 0
% Current number of rules: 191
% New rule produced :
% [212]
% (inverse(X greatest_lower_bound Y) least_upper_bound multiply(X,X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 4681
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced :
% [213]
% inverse(X) least_upper_bound multiply(X,X) least_upper_bound X ->
% inverse(X) least_upper_bound multiply(X,X)
% Current number of equations to process: 1222
% Current number of ordered equations: 0
% Current number of rules: 193
% New rule produced :
% [214]
% (multiply(inverse(X),inverse(X)) least_upper_bound X) greatest_lower_bound
% inverse(X) -> inverse(X)
% Current number of equations to process: 1298
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [215]
% (identity least_upper_bound X) greatest_lower_bound (inverse(identity greatest_lower_bound Y) least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 1970
% Current number of ordered equations: 0
% Current number of rules: 195
% New rule produced :
% [216]
% (identity least_upper_bound inverse(X)) greatest_lower_bound inverse(
% identity greatest_lower_bound X)
% -> identity least_upper_bound inverse(X)
% Current number of equations to process: 2147
% Current number of ordered equations: 0
% Current number of rules: 196
% Rule [44]
% multiply(inverse(identity least_upper_bound X),X) ->
% multiply(X,inverse(identity least_upper_bound X)) is composed into
% [44]
% multiply(inverse(identity least_upper_bound X),X) ->
% identity greatest_lower_bound X
% New rule produced :
% [217]
% multiply(X,inverse(identity least_upper_bound X)) ->
% identity greatest_lower_bound X
% Rule
% [178]
% inverse(identity least_upper_bound X) least_upper_bound multiply(X,inverse(
% identity least_upper_bound X))
% -> identity collapsed.
% Rule
% [179]
% inverse(X) least_upper_bound multiply(X,inverse(identity least_upper_bound X))
% -> identity least_upper_bound inverse(X) collapsed.
% Current number of equations to process: 2452
% Current number of ordered equations: 0
% Current number of rules: 195
% New rule produced :
% [218]
% (identity greatest_lower_bound X) least_upper_bound inverse(X) ->
% identity least_upper_bound inverse(X)
% Current number of equations to process: 2451
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [219]
% (identity greatest_lower_bound X) least_upper_bound inverse(identity least_upper_bound X)
% -> identity
% Current number of equations to process: 2450
% Current number of ordered equations: 0
% Current number of rules: 197
% New rule produced :
% [220]
% (identity least_upper_bound inverse(X)) greatest_lower_bound X ->
% identity greatest_lower_bound X
% Current number of equations to process: 2517
% Current number of ordered equations: 0
% Current number of rules: 198
% New rule produced :
% [221]
% (identity least_upper_bound inverse(X least_upper_bound Y)) greatest_lower_bound X
% -> identity greatest_lower_bound X
% Current number of equations to process: 2567
% Current number of ordered equations: 0
% Current number of rules: 199
% Rule [61]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(X,inverse(identity greatest_lower_bound multiply(Y,X))) is composed into
% [61]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(X,identity least_upper_bound inverse(multiply(Y,X)))
% Rule [55]
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y)) is composed into
% [55]
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X)) <->
% identity least_upper_bound inverse(multiply(X,Y))
% Rule [53]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),inverse(identity greatest_lower_bound X)) is composed into
% [53]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),identity least_upper_bound inverse(X))
% Rule [37]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X) is composed into
% [37]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(identity least_upper_bound inverse(multiply(X,Y)),X)
% Rule [35]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(inverse(identity greatest_lower_bound Y),inverse(X)) is composed into
% [35]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(identity least_upper_bound inverse(Y),inverse(X))
% Rule [33]
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y)) is composed into
% [33]
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X)) <->
% identity least_upper_bound inverse(multiply(X,Y))
% New rule produced :
% [222]
% inverse(identity greatest_lower_bound X) ->
% identity least_upper_bound inverse(X)
% Rule
% [32]
% inverse(identity greatest_lower_bound multiply(X,Y)) <->
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X)) collapsed.
% Rule
% [38]
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X) <->
% inverse(inverse(X) greatest_lower_bound Y) collapsed.
% Rule
% [52]
% inverse(identity greatest_lower_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X greatest_lower_bound Y)) collapsed.
% Rule
% [54]
% inverse(identity greatest_lower_bound multiply(X,Y)) <->
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X)) collapsed.
% Rule
% [56]
% multiply(inverse(identity greatest_lower_bound X),X) ->
% multiply(X,inverse(identity greatest_lower_bound X)) collapsed.
% Rule
% [59]
% multiply(inverse(identity greatest_lower_bound X),inverse(X)) ->
% multiply(inverse(X),inverse(identity greatest_lower_bound X)) collapsed.
% Rule
% [62]
% multiply(X,inverse(identity greatest_lower_bound multiply(Y,X))) <->
% inverse(inverse(X) greatest_lower_bound Y) collapsed.
% Rule
% [67]
% inverse(identity greatest_lower_bound X) greatest_lower_bound multiply(X,
% inverse(
% identity greatest_lower_bound X))
% -> identity collapsed.
% Rule
% [68]
% identity greatest_lower_bound inverse(identity greatest_lower_bound X) ->
% identity collapsed.
% Rule
% [69]
% identity least_upper_bound inverse(identity greatest_lower_bound X) ->
% inverse(identity greatest_lower_bound X) collapsed.
% Rule
% [71]
% (inverse(identity greatest_lower_bound X) least_upper_bound Y) greatest_lower_bound identity
% -> identity collapsed.
% Rule
% [72]
% (identity greatest_lower_bound X) least_upper_bound inverse(identity greatest_lower_bound Y)
% -> inverse(identity greatest_lower_bound Y) collapsed.
% Rule
% [75]
% multiply(X,inverse(identity greatest_lower_bound Y)) greatest_lower_bound X
% -> X collapsed.
% Rule
% [76]
% multiply(inverse(identity greatest_lower_bound Y),X) greatest_lower_bound X
% -> X collapsed.
% Rule
% [81]
% multiply(X,inverse(identity greatest_lower_bound Y)) least_upper_bound X ->
% multiply(X,inverse(identity greatest_lower_bound Y)) collapsed.
% Rule
% [82]
% multiply(inverse(identity greatest_lower_bound X),Y) least_upper_bound Y ->
% multiply(inverse(identity greatest_lower_bound X),Y) collapsed.
% Rule
% [85]
% inverse(identity greatest_lower_bound X) greatest_lower_bound X ->
% identity greatest_lower_bound X collapsed.
% Rule
% [86]
% (multiply(X,inverse(identity greatest_lower_bound Y)) least_upper_bound Z) greatest_lower_bound X
% -> X collapsed.
% Rule
% [90]
% (multiply(inverse(identity greatest_lower_bound Y),X) least_upper_bound Z) greatest_lower_bound X
% -> X collapsed.
% Rule
% [100]
% inverse((X least_upper_bound Y) greatest_lower_bound identity) greatest_lower_bound X
% -> identity greatest_lower_bound X collapsed.
% Rule
% [101]
% inverse(X) greatest_lower_bound multiply(X,inverse(identity greatest_lower_bound X))
% -> identity greatest_lower_bound inverse(X) collapsed.
% Rule
% [110]
% identity greatest_lower_bound multiply(inverse(identity greatest_lower_bound
% multiply(X,X)),X) -> identity
% collapsed.
% Rule
% [113]
% (inverse(X) greatest_lower_bound X) least_upper_bound inverse(identity greatest_lower_bound Y)
% -> inverse(identity greatest_lower_bound Y) collapsed.
% Rule
% [117]
% inverse(identity greatest_lower_bound Y) greatest_lower_bound inverse(X) greatest_lower_bound X
% -> inverse(X) greatest_lower_bound X collapsed.
% Rule
% [130]
% identity greatest_lower_bound multiply(X,inverse(identity greatest_lower_bound
% multiply(X,X))) -> identity
% collapsed.
% Rule
% [153]
% inverse(identity greatest_lower_bound multiply(X,X)) greatest_lower_bound
% inverse(X) -> inverse(X) collapsed.
% Rule
% [197]
% (inverse(identity greatest_lower_bound X) least_upper_bound multiply(Y,Y)) greatest_lower_bound Y
% -> Y collapsed.
% Rule
% [215]
% (identity least_upper_bound X) greatest_lower_bound (inverse(identity greatest_lower_bound Y) least_upper_bound X)
% -> identity least_upper_bound X collapsed.
% Rule
% [216]
% (identity least_upper_bound inverse(X)) greatest_lower_bound inverse(
% identity greatest_lower_bound X)
% -> identity least_upper_bound inverse(X) collapsed.
% Current number of equations to process: 2717
% Current number of ordered equations: 0
% Current number of rules: 171
% Rule [49]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(X,inverse(identity least_upper_bound multiply(Y,X))) is composed into
% [49]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(X,identity greatest_lower_bound inverse(multiply(Y,X)))
% Rule [43]
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X)) <->
% inverse(identity least_upper_bound multiply(X,Y)) is composed into
% [43]
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X)) <->
% identity greatest_lower_bound inverse(multiply(X,Y))
% Rule [41]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),inverse(identity least_upper_bound X)) is composed into
% [41]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),identity greatest_lower_bound inverse(X))
% Rule [29]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(inverse(identity least_upper_bound multiply(X,Y)),X) is composed into
% [29]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(identity greatest_lower_bound inverse(multiply(X,Y)),X)
% Rule [26]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(inverse(identity least_upper_bound Y),inverse(X)) is composed into
% [26]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(identity greatest_lower_bound inverse(Y),inverse(X))
% Rule [24]
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X)) <->
% inverse(identity least_upper_bound multiply(X,Y)) is composed into
% [24]
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X)) <->
% identity greatest_lower_bound inverse(multiply(X,Y))
% New rule produced :
% [223]
% inverse(identity least_upper_bound X) ->
% identity greatest_lower_bound inverse(X)
% Rule
% [23]
% inverse(identity least_upper_bound multiply(X,Y)) <->
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X)) collapsed.
% Rule
% [30]
% multiply(inverse(identity least_upper_bound multiply(X,Y)),X) <->
% inverse(inverse(X) least_upper_bound Y) collapsed.
% Rule
% [40]
% inverse(identity least_upper_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X least_upper_bound Y)) collapsed.
% Rule
% [42]
% inverse(identity least_upper_bound multiply(X,Y)) <->
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X)) collapsed.
% Rule
% [44]
% multiply(inverse(identity least_upper_bound X),X) ->
% identity greatest_lower_bound X collapsed.
% Rule
% [47]
% multiply(inverse(identity least_upper_bound X),inverse(X)) ->
% multiply(inverse(X),inverse(identity least_upper_bound X)) collapsed.
% Rule
% [50]
% multiply(X,inverse(identity least_upper_bound multiply(Y,X))) <->
% inverse(inverse(X) least_upper_bound Y) collapsed.
% Rule
% [120]
% identity greatest_lower_bound inverse(identity least_upper_bound X) ->
% inverse(identity least_upper_bound X) collapsed.
% Rule
% [124]
% identity least_upper_bound inverse(identity least_upper_bound X) -> identity
% collapsed.
% Rule
% [129]
% (inverse(identity least_upper_bound X) greatest_lower_bound Y) least_upper_bound identity
% -> identity collapsed.
% Rule
% [133]
% (identity least_upper_bound Y) greatest_lower_bound inverse(identity least_upper_bound X)
% -> inverse(identity least_upper_bound X) collapsed.
% Rule
% [137]
% multiply(X,inverse(identity least_upper_bound Y)) least_upper_bound X -> X
% collapsed.
% Rule
% [138]
% multiply(inverse(identity least_upper_bound Y),X) least_upper_bound X -> X
% collapsed.
% Rule
% [146]
% multiply(X,inverse(identity least_upper_bound Y)) greatest_lower_bound X ->
% multiply(X,inverse(identity least_upper_bound Y)) collapsed.
% Rule
% [147]
% multiply(inverse(identity least_upper_bound X),Y) greatest_lower_bound Y ->
% multiply(inverse(identity least_upper_bound X),Y) collapsed.
% Rule
% [156]
% (multiply(inverse(identity least_upper_bound X),Y) greatest_lower_bound Z) least_upper_bound Y
% -> Y collapsed.
% Rule
% [157]
% (multiply(X,inverse(identity least_upper_bound Y)) greatest_lower_bound Z) least_upper_bound X
% -> X collapsed.
% Rule
% [158]
% identity least_upper_bound multiply(X,inverse(identity least_upper_bound
% multiply(X,X))) -> identity
% collapsed.
% Rule
% [166]
% (inverse(identity least_upper_bound X) greatest_lower_bound multiply(Y,Y)) least_upper_bound Y
% -> Y collapsed.
% Rule
% [180]
% inverse(identity least_upper_bound X) least_upper_bound X ->
% identity least_upper_bound X collapsed.
% Rule
% [184]
% inverse((X greatest_lower_bound Y) least_upper_bound identity) least_upper_bound X
% -> identity least_upper_bound X collapsed.
% Rule
% [194]
% inverse(identity least_upper_bound multiply(X,X)) least_upper_bound inverse(X)
% -> inverse(X) collapsed.
% Rule
% [196]
% identity least_upper_bound multiply(inverse(identity least_upper_bound
% multiply(X,X)),X) -> identity
% collapsed.
% Rule
% [203]
% inverse(identity least_upper_bound Y) least_upper_bound inverse(X) least_upper_bound X
% -> inverse(X) least_upper_bound X collapsed.
% Rule
% [204]
% (inverse(X) least_upper_bound X) greatest_lower_bound inverse(identity least_upper_bound Y)
% -> inverse(identity least_upper_bound Y) collapsed.
% Rule
% [217]
% multiply(X,inverse(identity least_upper_bound X)) ->
% identity greatest_lower_bound X collapsed.
% Rule
% [219]
% (identity greatest_lower_bound X) least_upper_bound inverse(identity least_upper_bound X)
% -> identity collapsed.
% Current number of equations to process: 2728
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [224]
% (identity greatest_lower_bound inverse(X)) least_upper_bound X ->
% identity least_upper_bound X
% Current number of equations to process: 2727
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [225]
% (identity greatest_lower_bound inverse(X)) least_upper_bound (identity greatest_lower_bound X)
% -> identity
% Current number of equations to process: 2726
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [226]
% (identity greatest_lower_bound inverse(X greatest_lower_bound Y)) least_upper_bound X
% -> identity least_upper_bound X
% Current number of equations to process: 2753
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [227]
% (identity least_upper_bound X) greatest_lower_bound inverse(X) ->
% identity greatest_lower_bound inverse(X)
% Current number of equations to process: 2963
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [228]
% ((inverse(X) least_upper_bound Y) greatest_lower_bound identity) least_upper_bound X
% -> identity least_upper_bound X
% Current number of equations to process: 3319
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [229]
% ((inverse(X) greatest_lower_bound Y) least_upper_bound identity) greatest_lower_bound X
% -> identity greatest_lower_bound X
% Current number of equations to process: 3318
% Current number of ordered equations: 0
% Current number of rules: 151
% Rule [46]
% multiply(inverse(inverse(X) least_upper_bound Y),Y) <->
% multiply(X,inverse(inverse(Y) least_upper_bound X)) is composed into
% [46]
% multiply(inverse(inverse(X) least_upper_bound Y),Y) <->
% identity greatest_lower_bound multiply(X,inverse(inverse(Y)))
% New rule produced :
% [230]
% multiply(Y,inverse(X least_upper_bound Y)) ->
% identity greatest_lower_bound multiply(Y,inverse(X))
% Rule
% [43]
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X)) <->
% identity greatest_lower_bound inverse(multiply(X,Y)) collapsed.
% Rule
% [45]
% multiply(X,inverse(inverse(Y) least_upper_bound X)) <->
% multiply(inverse(inverse(X) least_upper_bound Y),Y) collapsed.
% Rule
% [140]
% identity least_upper_bound multiply(X,inverse(X least_upper_bound Y)) ->
% identity collapsed.
% Rule
% [144]
% (multiply(X,inverse(X least_upper_bound Y)) greatest_lower_bound Z) least_upper_bound identity
% -> identity collapsed.
% Rule
% [149]
% identity greatest_lower_bound multiply(X,inverse(X least_upper_bound Y)) ->
% multiply(X,inverse(X least_upper_bound Y)) collapsed.
% Rule
% [160]
% multiply(X,multiply(Y,inverse(Y least_upper_bound Z))) least_upper_bound X ->
% X collapsed.
% Current number of equations to process: 3318
% Current number of ordered equations: 0
% Current number of rules: 146
% Rule [58]
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y) <->
% multiply(X,inverse(inverse(Y) greatest_lower_bound X)) is composed into
% [58]
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y) <->
% identity least_upper_bound multiply(X,inverse(inverse(Y)))
% New rule produced :
% [231]
% multiply(Y,inverse(X greatest_lower_bound Y)) ->
% identity least_upper_bound multiply(Y,inverse(X))
% Rule
% [55]
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X)) <->
% identity least_upper_bound inverse(multiply(X,Y)) collapsed.
% Rule
% [57]
% multiply(X,inverse(inverse(Y) greatest_lower_bound X)) <->
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y) collapsed.
% Rule
% [77]
% identity greatest_lower_bound multiply(X,inverse(X greatest_lower_bound Y))
% -> identity collapsed.
% Rule
% [79]
% (multiply(X,inverse(X greatest_lower_bound Y)) least_upper_bound Z) greatest_lower_bound identity
% -> identity collapsed.
% Rule
% [83]
% identity least_upper_bound multiply(X,inverse(X greatest_lower_bound Y)) ->
% multiply(X,inverse(X greatest_lower_bound Y)) collapsed.
% Rule
% [88]
% multiply(X,multiply(Y,inverse(Y greatest_lower_bound Z))) greatest_lower_bound X
% -> X collapsed.
% Current number of equations to process: 3369
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [232]
% ((X least_upper_bound Y) greatest_lower_bound identity) least_upper_bound
% inverse(X) -> identity least_upper_bound inverse(X)
% Current number of equations to process: 3368
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [233]
% multiply(inverse(inverse(X) least_upper_bound Y),Y) ->
% identity greatest_lower_bound multiply(X,Y)
% Rule
% [46]
% multiply(inverse(inverse(X) least_upper_bound Y),Y) <->
% identity greatest_lower_bound multiply(X,inverse(inverse(Y))) collapsed.
% Current number of equations to process: 3367
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [234]
% inverse(inverse(X) least_upper_bound Y) -> inverse(Y) greatest_lower_bound X
% Rule
% [24]
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X)) <->
% identity greatest_lower_bound inverse(multiply(X,Y)) collapsed.
% Rule
% [29]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(identity greatest_lower_bound inverse(multiply(X,Y)),X) collapsed.
% Rule
% [48]
% inverse(inverse(X) least_upper_bound inverse(Y)) ->
% multiply(X,multiply(inverse(X least_upper_bound Y),Y)) collapsed.
% Rule
% [49]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(X,identity greatest_lower_bound inverse(multiply(Y,X))) collapsed.
% Rule
% [121]
% inverse(inverse(X) least_upper_bound Y) greatest_lower_bound X ->
% inverse(inverse(X) least_upper_bound Y) collapsed.
% Rule
% [128]
% inverse(inverse(X greatest_lower_bound Y) least_upper_bound Z) least_upper_bound X
% -> X collapsed.
% Rule [134] inverse(inverse(X) least_upper_bound Y) least_upper_bound X -> X
% collapsed.
% Rule
% [135]
% (inverse(inverse(X) least_upper_bound Y) greatest_lower_bound Z) least_upper_bound X
% -> X collapsed.
% Rule
% [136]
% identity least_upper_bound inverse(inverse(X) least_upper_bound X least_upper_bound Y)
% -> identity collapsed.
% Rule
% [233]
% multiply(inverse(inverse(X) least_upper_bound Y),Y) ->
% identity greatest_lower_bound multiply(X,Y) collapsed.
% Current number of equations to process: 3367
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [235]
% multiply(X,multiply(inverse(X least_upper_bound Y),Y)) ->
% X greatest_lower_bound Y
% Current number of equations to process: 3366
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [236]
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y) ->
% identity least_upper_bound multiply(X,Y)
% Rule
% [58]
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y) <->
% identity least_upper_bound multiply(X,inverse(inverse(Y))) collapsed.
% Current number of equations to process: 3365
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [237]
% inverse(inverse(X) greatest_lower_bound Y) -> inverse(Y) least_upper_bound X
% Rule
% [33]
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X)) <->
% identity least_upper_bound inverse(multiply(X,Y)) collapsed.
% Rule
% [37]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(identity least_upper_bound inverse(multiply(X,Y)),X) collapsed.
% Rule
% [60]
% inverse(inverse(X) greatest_lower_bound inverse(Y)) ->
% multiply(X,multiply(inverse(X greatest_lower_bound Y),Y)) collapsed.
% Rule
% [61]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(X,identity least_upper_bound inverse(multiply(Y,X))) collapsed.
% Rule
% [84] inverse(inverse(X) greatest_lower_bound Y) greatest_lower_bound X -> X
% collapsed.
% Rule
% [97]
% inverse(inverse(X) greatest_lower_bound Y) least_upper_bound X ->
% inverse(inverse(X) greatest_lower_bound Y) collapsed.
% Rule
% [98]
% inverse(inverse(X least_upper_bound Y) greatest_lower_bound Z) greatest_lower_bound X
% -> X collapsed.
% Rule
% [99]
% (inverse(inverse(X) greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound X
% -> X collapsed.
% Rule
% [107]
% identity greatest_lower_bound inverse(inverse(X) greatest_lower_bound X greatest_lower_bound Y)
% -> identity collapsed.
% Rule
% [236]
% multiply(inverse(inverse(X) greatest_lower_bound Y),Y) ->
% identity least_upper_bound multiply(X,Y) collapsed.
% Current number of equations to process: 3365
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [238]
% multiply(X,multiply(inverse(X greatest_lower_bound Y),Y)) ->
% X least_upper_bound Y
% Current number of equations to process: 3364
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [239]
% ((X greatest_lower_bound Y) least_upper_bound identity) greatest_lower_bound
% inverse(X) -> identity greatest_lower_bound inverse(X)
% Current number of equations to process: 3567
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [240]
% (identity least_upper_bound inverse(X)) greatest_lower_bound (identity least_upper_bound X)
% -> identity
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 3904
% Current number of ordered equations: 0
% Current number of rules: 128
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 33 rules have been used:
% [2]
% inverse(inverse(X)) -> X; trace = in the starting set
% [4] X greatest_lower_bound X -> X; trace = in the starting set
% [5] multiply(identity,X) -> X; trace = in the starting set
% [6] multiply(inverse(X),X) -> identity; trace = in the starting set
% [7] (X greatest_lower_bound Y) least_upper_bound X -> X; trace = in the starting set
% [8] (X least_upper_bound Y) greatest_lower_bound X -> X; trace = in the starting set
% [9] inverse(multiply(X,Y)) -> multiply(inverse(Y),inverse(X)); trace = in the starting set
% [10] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z)); trace = in the starting set
% [12] multiply(X,Y greatest_lower_bound Z) ->
% multiply(X,Y) greatest_lower_bound multiply(X,Z); trace = in the starting set
% [14] multiply(Y greatest_lower_bound Z,X) ->
% multiply(Y,X) greatest_lower_bound multiply(Z,X); trace = in the starting set
% [15] multiply(X,inverse(X)) -> identity; trace = Cp of 6 and 2
% [16] multiply(inverse(X),identity) -> inverse(X); trace = Cp of 9 and 5
% [17] multiply(inverse(Y),multiply(Y,X)) -> X; trace = Cp of 10 and 6
% [18] multiply(Y,multiply(inverse(Y),X)) -> X; trace = Cp of 15 and 10
% [19] multiply(X,identity) -> X; trace = Cp of 16 and 2
% [21] ((X greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound
% (X least_upper_bound Z) ->
% (X greatest_lower_bound Y) least_upper_bound Z; trace = Cp of 8 and 7
% [31] inverse(multiply(X,Y) greatest_lower_bound multiply(X,Z)) ->
% multiply(inverse(Y greatest_lower_bound Z),inverse(X)); trace = Cp of 12 and 9
% [35] inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(inverse(identity greatest_lower_bound Y),inverse(X)); trace = Cp of 31 and 19
% [37] inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X); trace = Cp of 35 and 17
% [51] inverse(multiply(X,Y) greatest_lower_bound multiply(Z,Y)) ->
% multiply(inverse(Y),inverse(X greatest_lower_bound Z)); trace = Cp of 14 and 9
% [55] multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y)); trace = Cp of 51 and 6
% [62] multiply(X,inverse(identity greatest_lower_bound multiply(Y,X))) <->
% inverse(inverse(X) greatest_lower_bound Y); trace = Cp of 55 and 18
% [67] inverse(identity greatest_lower_bound X) greatest_lower_bound multiply(X,
% inverse(
% identity greatest_lower_bound X))
% -> identity; trace = Cp of 35 and 6
% [68] identity greatest_lower_bound inverse(identity greatest_lower_bound X)
% -> identity; trace = Cp of 67 and 4
% [75] multiply(X,inverse(identity greatest_lower_bound Y)) greatest_lower_bound X
% -> X; trace = Cp of 68 and 12
% [84] inverse(inverse(X) greatest_lower_bound Y) greatest_lower_bound X -> X; trace = Cp of 75 and 62
% [95] inverse(X greatest_lower_bound Y) greatest_lower_bound inverse(X) ->
% inverse(X); trace = Cp of 84 and 2
% [102] inverse(X greatest_lower_bound Y) least_upper_bound inverse(X) ->
% inverse(X greatest_lower_bound Y); trace = Cp of 95 and 7
% [215] (identity least_upper_bound X) greatest_lower_bound (inverse(identity greatest_lower_bound Y) least_upper_bound X)
% -> identity least_upper_bound X; trace = Cp of 68 and 21
% [216] (identity least_upper_bound inverse(X)) greatest_lower_bound inverse(
% identity greatest_lower_bound X)
% -> identity least_upper_bound inverse(X); trace = Cp of 215 and 102
% [217] multiply(X,inverse(identity least_upper_bound X)) ->
% identity greatest_lower_bound X; trace = Cp of 216 and 37
% [222] inverse(identity greatest_lower_bound X) ->
% identity least_upper_bound inverse(X); trace = Cp of 217 and 9
% [240] (identity least_upper_bound inverse(X)) greatest_lower_bound (identity least_upper_bound X)
% -> identity; trace = Cp of 222 and 6
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 274.720000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------