%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP114-1 : TPTP v6.0.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n102.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 00:22:17 EDT 2014

% Result   : Unsatisfiable 77.42s
% Output   : Refutation 77.42s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP114-1 : TPTP v6.0.0. Released v1.2.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n102.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 01:33:33 CDT 2014
% % CPUTime  : 77.42 
% Processing problem /tmp/CiME_38649_n102.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " union,intersection : 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;
% inverse(identity) = identity;
% inverse(inverse(X)) = X;
% inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X));
% X intersection X = X;
% X union X = X;
% (X intersection Y) union Y = Y;
% (X union Y) intersection Y = Y;
% multiply(X,Y union Z) = multiply(X,Y) union multiply(X,Z);
% multiply(X,Y intersection Z) = multiply(X,Y) intersection multiply(X,Z);
% multiply(Y union Z,X) = multiply(Y,X) union multiply(Z,X);
% multiply(Y intersection Z,X) = multiply(Y,X) intersection multiply(Z,X);
% positive_part(X) = X union identity;
% negative_part(X) = X intersection identity;
% ";
% 
% let s1 = status F "
% a lr_lex;
% negative_part lr_lex;
% positive_part lr_lex;
% inverse lr_lex;
% identity lr_lex;
% union mul;
% intersection mul;
% multiply mul;
% ";
% 
% let p1 = precedence F "
% positive_part > negative_part > multiply > inverse > intersection > union > identity > a";
% 
% let s2 = status F "
% a mul;
% negative_part mul;
% positive_part mul;
% union mul;
% intersection mul;
% inverse mul;
% multiply mul;
% identity mul;
% ";
% 
% let p2 = precedence F "
% positive_part > negative_part > multiply > inverse > intersection > union > identity = a";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " multiply(positive_part(a),negative_part(a)) = 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,
% inverse(identity) = identity,
% inverse(inverse(X)) = X,
% inverse(multiply(X,Y)) =
% multiply(inverse(Y),inverse(X)),
% X intersection X = X,
% X union X = X,
% (X intersection Y) union Y = Y,
% (X union Y) intersection Y = Y,
% multiply(X,Y union Z) =
% multiply(X,Y) union multiply(X,Z),
% multiply(X,Y intersection Z) =
% multiply(X,Y) intersection multiply(X,Z),
% multiply(Y union Z,X) =
% multiply(Y,X) union multiply(Z,X),
% multiply(Y intersection Z,X) =
% multiply(Y,X) intersection multiply(Z,X),
% positive_part(X) = identity union X,
% negative_part(X) = identity intersection X }
% (16 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { multiply(positive_part(a),negative_part(a))
% = a } (1 equation(s))
% time is now on
% 
% Initializing completion ...
% New rule produced : [1] inverse(identity) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 15
% Current number of rules: 1
% New rule produced : [2] inverse(inverse(X)) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 14
% Current number of rules: 2
% New rule produced : [3] X union X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 13
% Current number of rules: 3
% New rule produced : [4] X intersection X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 12
% Current number of rules: 4
% New rule produced : [5] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 5
% New rule produced : [6] identity union X -> positive_part(X)
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 6
% New rule produced : [7] identity intersection X -> negative_part(X)
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 7
% New rule produced : [8] multiply(inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 8
% New rule produced : [9] (X intersection Y) union Y -> Y
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 9
% New rule produced : [10] (X union Y) intersection Y -> Y
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 10
% New rule produced :
% [11] inverse(multiply(X,Y)) -> multiply(inverse(Y),inverse(X))
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 11
% New rule produced :
% [12] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 12
% New rule produced :
% [13] multiply(X,Y union Z) -> multiply(X,Y) union multiply(X,Z)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 13
% New rule produced :
% [14] multiply(X,Y intersection Z) -> multiply(X,Y) intersection multiply(X,Z)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 14
% New rule produced :
% [15] multiply(Y union Z,X) -> multiply(Y,X) union multiply(Z,X)
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 15
% New rule produced :
% [16] multiply(Y intersection Z,X) -> multiply(Y,X) intersection multiply(Z,X)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] positive_part(identity) -> identity
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] negative_part(identity) -> identity
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] positive_part(positive_part(X)) -> positive_part(X)
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] negative_part(negative_part(X)) -> negative_part(X)
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [21] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [22] positive_part(X) union X -> positive_part(X)
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [23] negative_part(X) intersection X -> negative_part(X)
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [24] positive_part(negative_part(X)) -> identity
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [25] negative_part(X) union X -> X
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [26] negative_part(positive_part(X)) -> identity
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [27] positive_part(X) intersection X -> X
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [28] positive_part(negative_part(X) intersection Y) -> identity
% Current number of equations to process: 78
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [29] negative_part(positive_part(X) union Y) -> identity
% Current number of equations to process: 77
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [30] positive_part(X) union Y -> positive_part(X union Y)
% Rule [22] positive_part(X) union X -> positive_part(X) collapsed.
% Rule [29] negative_part(positive_part(X) union Y) -> identity collapsed.
% Current number of equations to process: 75
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [31] negative_part(X) intersection Y -> negative_part(X intersection Y)
% Rule [23] negative_part(X) intersection X -> negative_part(X) collapsed.
% Rule [28] positive_part(negative_part(X) intersection Y) -> identity
% collapsed.
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [32] positive_part(negative_part(X) union Y) -> positive_part(Y)
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [33] negative_part(positive_part(X) intersection Y) -> negative_part(Y)
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [34] multiply(inverse(X),identity) -> inverse(X)
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [35] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [36] multiply(X,positive_part(Y)) -> multiply(X,identity) union multiply(X,Y)
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [37]
% multiply(X,negative_part(Y)) ->
% multiply(X,identity) intersection multiply(X,Y)
% The conjecture has been reduced. 
% Conjecture is now:
% multiply(positive_part(a),a) intersection multiply(positive_part(a),identity) = a
% 
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [38] multiply(positive_part(X),Y) -> multiply(X,Y) union Y
% The conjecture has been reduced. 
% Conjecture is now:
% (a union multiply(a,a)) intersection positive_part(multiply(a,identity)) = a
% 
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [39] multiply(negative_part(X),Y) -> multiply(X,Y) intersection Y
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [40] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [41] negative_part(X intersection Y) union Y -> Y
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [42] positive_part(X union Y) intersection Y -> Y
% Current number of equations to process: 127
% Current number of ordered equations: 0
% Current number of rules: 38
% Rule [37]
% multiply(X,negative_part(Y)) ->
% multiply(X,identity) intersection multiply(X,Y) is composed into 
% [37] multiply(X,negative_part(Y)) -> multiply(X,Y) intersection X
% Rule [36]
% multiply(X,positive_part(Y)) -> multiply(X,identity) union multiply(X,Y) is composed into 
% [36] multiply(X,positive_part(Y)) -> multiply(X,Y) union X
% New rule produced : [43] multiply(X,identity) -> X
% Rule [34] multiply(inverse(X),identity) -> inverse(X) collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% (a union multiply(a,a)) intersection positive_part(a) = a
% 
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [44]
% positive_part((positive_part(X) intersection Y) union X) -> positive_part(X)
% Current number of equations to process: 160
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [45]
% positive_part(X union Y) intersection positive_part(Y) -> positive_part(Y)
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [46]
% negative_part(X intersection Y) union negative_part(Y) -> negative_part(Y)
% Current number of equations to process: 158
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [47]
% negative_part((negative_part(X) union Y) intersection X) -> negative_part(X)
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [48]
% (negative_part(X) union Y) intersection positive_part(Y) ->
% negative_part(X) union Y
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [49]
% (positive_part(X) intersection Y) union negative_part(Y) ->
% positive_part(X) intersection Y
% Current number of equations to process: 155
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [50]
% inverse(multiply(X,Y) union X) ->
% multiply(inverse(positive_part(Y)),inverse(X))
% Current number of equations to process: 154
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [51]
% inverse(multiply(X,Y) intersection X) ->
% multiply(inverse(negative_part(Y)),inverse(X))
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [52]
% inverse(multiply(X,Y) union Y) ->
% multiply(inverse(Y),inverse(positive_part(X)))
% Current number of equations to process: 434
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [53]
% inverse(multiply(X,Y) intersection Y) ->
% multiply(inverse(Y),inverse(negative_part(X)))
% Current number of equations to process: 433
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [54]
% positive_part(X intersection Y) intersection positive_part(Y) ->
% positive_part(X intersection Y)
% Current number of equations to process: 432
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [55]
% negative_part(X union Y) union negative_part(Y) -> negative_part(X union Y)
% Current number of equations to process: 431
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [56]
% negative_part(negative_part(X) union negative_part(Y)) ->
% negative_part(X) union negative_part(Y)
% Current number of equations to process: 440
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [57]
% positive_part(positive_part(X) intersection positive_part(Y)) ->
% positive_part(X) intersection positive_part(Y)
% Current number of equations to process: 474
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [58]
% inverse(positive_part(inverse(X))) -> multiply(inverse(positive_part(X)),X)
% Current number of equations to process: 485
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [59]
% inverse(negative_part(inverse(X))) -> multiply(inverse(negative_part(X)),X)
% Current number of equations to process: 495
% Current number of ordered equations: 0
% Current number of rules: 54
% Rule [58]
% inverse(positive_part(inverse(X))) ->
% multiply(inverse(positive_part(X)),X) is composed into [58]
% inverse(positive_part(
% inverse(X)))
% ->
% multiply(X,
% inverse(positive_part(X)))
% New rule produced :
% [60]
% multiply(inverse(positive_part(X)),X) ->
% multiply(X,inverse(positive_part(X)))
% Current number of equations to process: 506
% Current number of ordered equations: 0
% Current number of rules: 55
% Rule [59]
% inverse(negative_part(inverse(X))) ->
% multiply(inverse(negative_part(X)),X) is composed into [59]
% 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: 517
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [62]
% multiply(inverse(positive_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(positive_part(X)))
% Current number of equations to process: 517
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [63]
% multiply(inverse(negative_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(negative_part(X)))
% Current number of equations to process: 567
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [64]
% inverse(negative_part(multiply(X,inverse(positive_part(X))))) ->
% positive_part(inverse(X))
% Current number of equations to process: 748
% Current number of ordered equations: 1
% Current number of rules: 59
% New rule produced :
% [65]
% inverse(positive_part(multiply(X,inverse(negative_part(X))))) ->
% negative_part(inverse(X))
% Current number of equations to process: 748
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [66]
% negative_part(multiply(X,inverse(positive_part(X)))) ->
% multiply(X,inverse(positive_part(X)))
% Rule
% [64]
% inverse(negative_part(multiply(X,inverse(positive_part(X))))) ->
% positive_part(inverse(X)) collapsed.
% Current number of equations to process: 769
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [67]
% positive_part(multiply(X,inverse(negative_part(X)))) ->
% multiply(X,inverse(negative_part(X)))
% Rule
% [65]
% inverse(positive_part(multiply(X,inverse(negative_part(X))))) ->
% negative_part(inverse(X)) collapsed.
% Current number of equations to process: 772
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [68] positive_part(multiply(X,inverse(positive_part(X)))) -> identity
% Current number of equations to process: 776
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [69] negative_part(inverse(positive_part(X))) -> inverse(positive_part(X))
% Current number of equations to process: 788
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [70] negative_part(multiply(X,inverse(negative_part(X)))) -> identity
% Current number of equations to process: 793
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [71] positive_part(inverse(negative_part(X))) -> inverse(negative_part(X))
% Current number of equations to process: 804
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced : [72] positive_part(inverse(positive_part(X))) -> identity
% Current number of equations to process: 817
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [73] positive_part(inverse(positive_part(X)) union Y) -> positive_part(Y)
% Current number of equations to process: 819
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [74]
% positive_part(Y) intersection inverse(positive_part(X)) ->
% inverse(positive_part(X))
% Current number of equations to process: 829
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced : [75] negative_part(inverse(negative_part(X))) -> identity
% Current number of equations to process: 841
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [76]
% negative_part(inverse(negative_part(X)) intersection Y) -> negative_part(Y)
% Current number of equations to process: 841
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [77] positive_part(inverse(positive_part(X)) intersection Y) -> identity
% Current number of equations to process: 859
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [78]
% negative_part(Y) union inverse(negative_part(X)) -> inverse(negative_part(X))
% Current number of equations to process: 862
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced : [79] multiply(X,inverse(positive_part(Y))) union X -> X
% Current number of equations to process: 861
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced : [80] multiply(inverse(positive_part(Y)),X) union X -> X
% Current number of equations to process: 860
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [81]
% positive_part(inverse(positive_part(X) intersection positive_part(Y))) ->
% identity
% Current number of equations to process: 859
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [82] negative_part(inverse(negative_part(X)) union Y) -> identity
% Current number of equations to process: 906
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [83] multiply(X,inverse(negative_part(Y))) intersection X -> X
% Current number of equations to process: 905
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [84] multiply(inverse(negative_part(Y)),X) intersection X -> X
% Current number of equations to process: 904
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [85]
% negative_part(inverse(negative_part(X) union negative_part(Y))) -> identity
% Current number of equations to process: 903
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [86]
% positive_part(multiply(X,inverse(positive_part(X))) intersection Y) ->
% identity
% Current number of equations to process: 1241
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [87]
% negative_part(inverse(positive_part(X)) intersection Y) ->
% inverse(positive_part(X)) intersection Y
% Current number of equations to process: 1242
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [88] negative_part(multiply(X,inverse(negative_part(X))) union Y) -> identity
% Current number of equations to process: 1241
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [89]
% positive_part(inverse(negative_part(X)) union Y) ->
% inverse(negative_part(X)) union Y
% Current number of equations to process: 1240
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [90]
% inverse(negative_part(X)) intersection inverse(positive_part(Y)) ->
% inverse(positive_part(Y))
% Current number of equations to process: 1238
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [91]
% inverse(negative_part(X)) union inverse(positive_part(Y)) ->
% inverse(negative_part(X))
% Current number of equations to process: 1231
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [92] negative_part(multiply(X,inverse(positive_part(Y)))) union X -> X
% Current number of equations to process: 1229
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [93]
% positive_part(multiply(inverse(positive_part(X)),inverse(positive_part(Y))))
% -> identity
% Current number of equations to process: 1228
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [94] negative_part(multiply(inverse(positive_part(Y)),X)) union X -> X
% Current number of equations to process: 1227
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [95]
% positive_part(inverse(positive_part(X) intersection inverse(negative_part(Y))))
% -> identity
% Current number of equations to process: 1225
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [96] positive_part(multiply(X,inverse(negative_part(Y)))) intersection X -> X
% Current number of equations to process: 1220
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [97]
% negative_part(multiply(inverse(negative_part(X)),inverse(negative_part(Y))))
% -> identity
% Current number of equations to process: 1219
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [98] positive_part(multiply(inverse(negative_part(Y)),X)) intersection X -> X
% Current number of equations to process: 1218
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [99]
% negative_part(inverse(negative_part(X) union inverse(positive_part(Y)))) ->
% identity
% Current number of equations to process: 1216
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [100]
% negative_part(inverse(inverse(positive_part(X)) intersection Y)) -> identity
% Current number of equations to process: 1240
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [101] positive_part(inverse(inverse(negative_part(X)) union Y)) -> identity
% Current number of equations to process: 1277
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [102]
% positive_part(multiply(X,inverse(positive_part(X))) union Y) ->
% positive_part(Y)
% Current number of equations to process: 1630
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [103]
% negative_part(multiply(X,inverse(negative_part(X))) intersection Y) ->
% negative_part(Y)
% Current number of equations to process: 1636
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [104]
% positive_part((inverse(positive_part(Y)) intersection Z) union X) ->
% positive_part(X)
% Current number of equations to process: 1632
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [105]
% negative_part((inverse(negative_part(Y)) union Z) intersection X) ->
% negative_part(X)
% Current number of equations to process: 1628
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [106]
% (inverse(positive_part(X)) intersection Y) union negative_part(Y) ->
% negative_part(Y)
% Current number of equations to process: 1622
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [107]
% (inverse(negative_part(X)) union Y) intersection positive_part(Y) ->
% positive_part(Y)
% Current number of equations to process: 1620
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [108]
% inverse(positive_part(X)) union multiply(X,inverse(positive_part(X))) ->
% identity
% Current number of equations to process: 1831
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [109] inverse(positive_part(X)) union X -> positive_part(X)
% Current number of equations to process: 1863
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [110] inverse(positive_part(X intersection Y)) union Y -> positive_part(Y)
% Current number of equations to process: 1929
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [111]
% inverse(negative_part(X)) intersection multiply(X,inverse(negative_part(X)))
% -> identity
% Current number of equations to process: 2084
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [112] inverse(negative_part(X)) intersection X -> negative_part(X)
% Current number of equations to process: 2116
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [113] inverse(negative_part(X union Y)) intersection Y -> negative_part(Y)
% Current number of equations to process: 2181
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [114]
% inverse(inverse(X) union Y) <->
% multiply(inverse(positive_part(multiply(X,Y))),X)
% Current number of equations to process: 2336
% Current number of ordered equations: 1
% Current number of rules: 107
% New rule produced :
% [115]
% multiply(inverse(positive_part(multiply(X,Y))),X) <->
% inverse(inverse(X) union Y)
% Current number of equations to process: 2336
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced : [116] inverse(inverse(X) union Y) union X -> X
% Current number of equations to process: 2396
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [117] negative_part(inverse(inverse(X) union Y)) union X -> X
% Current number of equations to process: 2401
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced : [118] inverse(X union Y) union inverse(X) -> inverse(X)
% Current number of equations to process: 2445
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [119] inverse(inverse(negative_part(X)) union Y) union X -> X
% Current number of equations to process: 2684
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [120] inverse(positive_part(inverse(X) union Y)) union X -> X
% Current number of equations to process: 2683
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [121] inverse(positive_part(X)) union inverse(X) -> inverse(X)
% Current number of equations to process: 2898
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [122] inverse(negative_part(X)) union inverse(X) -> inverse(negative_part(X))
% Current number of equations to process: 2933
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [123] positive_part(inverse(X) union X) -> inverse(X) union X
% Current number of equations to process: 3588
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [124]
% inverse(positive_part(X)) intersection inverse(X) ->
% inverse(positive_part(X))
% Current number of equations to process: 3664
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [125] inverse(negative_part(X)) intersection inverse(X) -> inverse(X)
% Current number of equations to process: 3760
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [126] negative_part((inverse(X) union X) intersection Y) -> negative_part(Y)
% Current number of equations to process: 3816
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced : [127] negative_part(inverse(X) union X) -> identity
% Current number of equations to process: 3816
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [128] (inverse(X) union X) intersection positive_part(X) -> positive_part(X)
% Current number of equations to process: 3875
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [129] negative_part(inverse(X) intersection X) -> inverse(X) intersection X
% Current number of equations to process: 4004
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [130] negative_part(inverse(X) union X union Y) -> identity
% Current number of equations to process: 4015
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [131]
% positive_part(inverse(X)) intersection inverse(negative_part(X)) ->
% positive_part(inverse(X))
% Current number of equations to process: 4014
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [132]
% positive_part(multiply(inverse(positive_part(multiply(X,X))),X)) -> identity
% Current number of equations to process: 4013
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [133]
% negative_part(inverse(X)) union inverse(positive_part(X)) ->
% negative_part(inverse(X))
% Current number of equations to process: 4012
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [134] positive_part(inverse(X) intersection X) -> identity
% Current number of equations to process: 4129
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [135] negative_part(inverse(inverse(X) intersection X)) -> identity
% Current number of equations to process: 4156
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [136] positive_part((inverse(X) intersection X) union Y) -> positive_part(Y)
% Current number of equations to process: 4187
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [137] (inverse(X) intersection X) union negative_part(X) -> negative_part(X)
% Current number of equations to process: 4186
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [138] negative_part(inverse(X intersection Y) union Y) -> identity
% Current number of equations to process: 4198
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [139]
% positive_part(inverse(inverse(X) intersection X)) ->
% inverse(inverse(X) intersection X)
% Current number of equations to process: 4273
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [140] negative_part(inverse(inverse(X) intersection X) union Y) -> identity
% Current number of equations to process: 4272
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [141] positive_part(inverse(inverse(X) union X union Y)) -> identity
% Current number of equations to process: 4271
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [142] positive_part(inverse(X)) intersection X -> negative_part(X)
% Current number of equations to process: 4345
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [143] positive_part(inverse(X union Y)) intersection X -> negative_part(X)
% Current number of equations to process: 4348
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [144] negative_part(inverse(X)) union X -> positive_part(X)
% Current number of equations to process: 4439
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [145] negative_part(inverse(X intersection Y)) union X -> positive_part(X)
% Current number of equations to process: 4442
% Current number of ordered equations: 0
% Current number of rules: 138
% 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 [59]
% inverse(negative_part(inverse(X))) ->
% multiply(X,inverse(negative_part(X))) is composed into [59]
% inverse(negative_part(
% inverse(X)))
% ->
% positive_part(X)
% New rule produced :
% [146] multiply(X,inverse(negative_part(X))) -> positive_part(X)
% Rule
% [67]
% positive_part(multiply(X,inverse(negative_part(X)))) ->
% multiply(X,inverse(negative_part(X))) collapsed.
% Rule [70] negative_part(multiply(X,inverse(negative_part(X)))) -> identity
% collapsed.
% Rule
% [88] negative_part(multiply(X,inverse(negative_part(X))) union Y) -> identity
% collapsed.
% Rule
% [103]
% negative_part(multiply(X,inverse(negative_part(X))) intersection Y) ->
% negative_part(Y) collapsed.
% Rule
% [111]
% inverse(negative_part(X)) intersection multiply(X,inverse(negative_part(X)))
% -> identity collapsed.
% Current number of equations to process: 4452
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [147] positive_part(X) intersection inverse(negative_part(X)) -> identity
% Current number of equations to process: 4451
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [148] positive_part(inverse(X) intersection X intersection Y) -> identity
% Current number of equations to process: 4481
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [149] positive_part(X) intersection inverse(X) -> negative_part(inverse(X))
% Current number of equations to process: 4857
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [150]
% positive_part(inverse(X) intersection Y) intersection X -> negative_part(X)
% Current number of equations to process: 4924
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [151] negative_part(X) union inverse(X) -> positive_part(inverse(X))
% Current number of equations to process: 2344
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [152] negative_part(inverse(X) union Y) union X -> positive_part(X)
% Current number of equations to process: 2477
% Current number of ordered equations: 0
% Current number of rules: 140
% Rule [114]
% inverse(inverse(X) union Y) <->
% multiply(inverse(positive_part(multiply(X,Y))),X) is composed into 
% [114]
% inverse(inverse(X) union Y) <->
% multiply(negative_part(inverse(multiply(X,Y))),X)
% Rule [52]
% inverse(multiply(X,Y) union Y) ->
% multiply(inverse(Y),inverse(positive_part(X))) is composed into 
% [52]
% inverse(multiply(X,Y) union Y) ->
% multiply(inverse(Y),negative_part(inverse(X)))
% Rule [50]
% inverse(multiply(X,Y) union X) ->
% multiply(inverse(positive_part(Y)),inverse(X)) is composed into 
% [50]
% inverse(multiply(X,Y) union X) ->
% multiply(negative_part(inverse(Y)),inverse(X))
% New rule produced :
% [153] inverse(positive_part(X)) -> negative_part(inverse(X))
% Rule
% [58]
% inverse(positive_part(inverse(X))) -> multiply(X,inverse(positive_part(X)))
% collapsed.
% Rule
% [60]
% multiply(inverse(positive_part(X)),X) ->
% multiply(X,inverse(positive_part(X))) collapsed.
% Rule
% [62]
% multiply(inverse(positive_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(positive_part(X))) collapsed.
% Rule
% [66]
% 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)))) -> identity
% collapsed.
% Rule
% [69] negative_part(inverse(positive_part(X))) -> inverse(positive_part(X))
% collapsed.
% Rule [72] positive_part(inverse(positive_part(X))) -> identity collapsed.
% Rule
% [73] positive_part(inverse(positive_part(X)) union Y) -> positive_part(Y)
% collapsed.
% Rule
% [74]
% positive_part(Y) intersection inverse(positive_part(X)) ->
% inverse(positive_part(X)) collapsed.
% Rule [77] positive_part(inverse(positive_part(X)) intersection Y) -> identity
% collapsed.
% Rule [79] multiply(X,inverse(positive_part(Y))) union X -> X collapsed.
% Rule [80] multiply(inverse(positive_part(Y)),X) union X -> X collapsed.
% Rule
% [86]
% positive_part(multiply(X,inverse(positive_part(X))) intersection Y) ->
% identity collapsed.
% Rule
% [87]
% negative_part(inverse(positive_part(X)) intersection Y) ->
% inverse(positive_part(X)) intersection Y collapsed.
% Rule
% [90]
% inverse(negative_part(X)) intersection inverse(positive_part(Y)) ->
% inverse(positive_part(Y)) collapsed.
% Rule
% [91]
% inverse(negative_part(X)) union inverse(positive_part(Y)) ->
% inverse(negative_part(X)) collapsed.
% Rule [92] negative_part(multiply(X,inverse(positive_part(Y)))) union X -> X
% collapsed.
% Rule
% [93]
% positive_part(multiply(inverse(positive_part(X)),inverse(positive_part(Y))))
% -> identity collapsed.
% Rule [94] negative_part(multiply(inverse(positive_part(Y)),X)) union X -> X
% collapsed.
% Rule
% [99]
% negative_part(inverse(negative_part(X) union inverse(positive_part(Y)))) ->
% identity collapsed.
% Rule
% [100]
% negative_part(inverse(inverse(positive_part(X)) intersection Y)) -> identity
% collapsed.
% Rule
% [102]
% positive_part(multiply(X,inverse(positive_part(X))) union Y) ->
% positive_part(Y) collapsed.
% Rule
% [104]
% positive_part((inverse(positive_part(Y)) intersection Z) union X) ->
% positive_part(X) collapsed.
% Rule
% [106]
% (inverse(positive_part(X)) intersection Y) union negative_part(Y) ->
% negative_part(Y) collapsed.
% Rule
% [108]
% inverse(positive_part(X)) union multiply(X,inverse(positive_part(X))) ->
% identity collapsed.
% Rule [109] inverse(positive_part(X)) union X -> positive_part(X) collapsed.
% Rule
% [110] inverse(positive_part(X intersection Y)) union Y -> positive_part(Y)
% collapsed.
% Rule
% [115]
% multiply(inverse(positive_part(multiply(X,Y))),X) <->
% inverse(inverse(X) union Y) collapsed.
% Rule [120] inverse(positive_part(inverse(X) union Y)) union X -> X collapsed.
% Rule [121] inverse(positive_part(X)) union inverse(X) -> inverse(X)
% collapsed.
% Rule
% [124]
% inverse(positive_part(X)) intersection inverse(X) ->
% inverse(positive_part(X)) collapsed.
% Rule
% [132]
% positive_part(multiply(inverse(positive_part(multiply(X,X))),X)) -> identity
% collapsed.
% Rule
% [133]
% negative_part(inverse(X)) union inverse(positive_part(X)) ->
% negative_part(inverse(X)) collapsed.
% Current number of equations to process: 2719
% Current number of ordered equations: 0
% Current number of rules: 108
% Rule [53]
% inverse(multiply(X,Y) intersection Y) ->
% multiply(inverse(Y),inverse(negative_part(X))) is composed into 
% [53]
% inverse(multiply(X,Y) intersection Y) ->
% multiply(inverse(Y),positive_part(inverse(X)))
% Rule [51]
% inverse(multiply(X,Y) intersection X) ->
% multiply(inverse(negative_part(Y)),inverse(X)) is composed into 
% [51]
% inverse(multiply(X,Y) intersection X) ->
% multiply(positive_part(inverse(Y)),inverse(X))
% New rule produced :
% [154] inverse(negative_part(X)) -> positive_part(inverse(X))
% Rule [59] inverse(negative_part(inverse(X))) -> positive_part(X) collapsed.
% Rule [61] multiply(inverse(negative_part(X)),X) -> positive_part(X)
% collapsed.
% Rule
% [63]
% multiply(inverse(negative_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(negative_part(X))) collapsed.
% Rule
% [71] positive_part(inverse(negative_part(X))) -> inverse(negative_part(X))
% collapsed.
% Rule [75] negative_part(inverse(negative_part(X))) -> identity collapsed.
% Rule
% [76]
% negative_part(inverse(negative_part(X)) intersection Y) -> negative_part(Y)
% collapsed.
% Rule
% [78]
% negative_part(Y) union inverse(negative_part(X)) -> inverse(negative_part(X))
% collapsed.
% Rule [82] negative_part(inverse(negative_part(X)) union Y) -> identity
% collapsed.
% Rule [83] multiply(X,inverse(negative_part(Y))) intersection X -> X
% collapsed.
% Rule [84] multiply(inverse(negative_part(Y)),X) intersection X -> X
% collapsed.
% Rule
% [89]
% positive_part(inverse(negative_part(X)) union Y) ->
% inverse(negative_part(X)) union Y collapsed.
% Rule
% [95]
% positive_part(inverse(positive_part(X) intersection inverse(negative_part(Y))))
% -> identity collapsed.
% Rule
% [96] positive_part(multiply(X,inverse(negative_part(Y)))) intersection 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)) intersection X -> X
% collapsed.
% Rule
% [101] positive_part(inverse(inverse(negative_part(X)) union Y)) -> identity
% collapsed.
% Rule
% [105]
% negative_part((inverse(negative_part(Y)) union Z) intersection X) ->
% negative_part(X) collapsed.
% Rule
% [107]
% (inverse(negative_part(X)) union Y) intersection positive_part(Y) ->
% positive_part(Y) collapsed.
% Rule [112] inverse(negative_part(X)) intersection X -> negative_part(X)
% collapsed.
% Rule
% [113] inverse(negative_part(X union Y)) intersection Y -> negative_part(Y)
% collapsed.
% Rule [119] inverse(inverse(negative_part(X)) union Y) union X -> X collapsed.
% Rule
% [122] inverse(negative_part(X)) union inverse(X) -> inverse(negative_part(X))
% collapsed.
% Rule [125] inverse(negative_part(X)) intersection inverse(X) -> inverse(X)
% collapsed.
% Rule
% [131]
% positive_part(inverse(X)) intersection inverse(negative_part(X)) ->
% positive_part(inverse(X)) collapsed.
% Rule [146] multiply(X,inverse(negative_part(X))) -> positive_part(X)
% collapsed.
% Rule
% [147] positive_part(X) intersection inverse(negative_part(X)) -> identity
% collapsed.
% Current number of equations to process: 2724
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [155] positive_part(inverse(X)) intersection positive_part(X) -> identity
% Current number of equations to process: 2731
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [156] positive_part(inverse(X union Y) intersection Y) -> identity
% Current number of equations to process: 2739
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [157]
% positive_part(X intersection Y) intersection inverse(Y) ->
% negative_part(inverse(Y))
% Current number of equations to process: 2845
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [158] negative_part(X union Y) union inverse(Y) -> positive_part(inverse(Y))
% Current number of equations to process: 2971
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [159] negative_part(inverse(X)) union negative_part(X) -> identity
% Current number of equations to process: 3067
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [160]
% negative_part(inverse(negative_part(Y) union X)) -> negative_part(inverse(X))
% Rule
% [85]
% negative_part(inverse(negative_part(X) union negative_part(Y))) -> identity
% collapsed.
% Current number of equations to process: 3085
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [161]
% positive_part(inverse(positive_part(Y) intersection X)) ->
% positive_part(inverse(X))
% Rule
% [81]
% positive_part(inverse(positive_part(X) intersection positive_part(Y))) ->
% identity collapsed.
% Current number of equations to process: 3084
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [162]
% negative_part(inverse(inverse(X) intersection X intersection Y)) -> identity
% Current number of equations to process: 3187
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [163]
% positive_part(inverse(X union Y)) intersection positive_part(Y) -> identity
% Current number of equations to process: 3186
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [164]
% positive_part(inverse(X) intersection Y) intersection positive_part(X) ->
% identity
% Current number of equations to process: 3184
% Current number of ordered equations: 1
% Current number of rules: 91
% New rule produced :
% [165]
% positive_part(X intersection Y) intersection positive_part(inverse(Y)) ->
% identity
% Current number of equations to process: 3184
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [166] negative_part(inverse(inverse(X union Y) intersection Y)) -> identity
% Current number of equations to process: 3183
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [167]
% negative_part(inverse(X intersection Y)) union negative_part(Y) -> identity
% Current number of equations to process: 3505
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [168] negative_part(inverse(X) union Y) union negative_part(X) -> identity
% Current number of equations to process: 3503
% Current number of ordered equations: 1
% Current number of rules: 95
% New rule produced :
% [169] negative_part(X union Y) union negative_part(inverse(Y)) -> identity
% Current number of equations to process: 3503
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [170] negative_part(inverse(X union Y)) union inverse(X) -> inverse(X)
% Current number of equations to process: 3944
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [171] inverse(X intersection Y) union inverse(Y) -> inverse(X intersection Y)
% Current number of equations to process: 3971
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [172] inverse(X union Y) intersection inverse(X) -> inverse(X union Y)
% Current number of equations to process: 3970
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [173] negative_part(Y) union inverse(X) union X -> inverse(X) union X
% Current number of equations to process: 3963
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [174]
% positive_part(Y) intersection inverse(X) intersection X ->
% inverse(X) intersection X
% Current number of equations to process: 3959
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [175]
% negative_part(inverse(inverse(X) intersection X) intersection Y) ->
% negative_part(Y)
% Current number of equations to process: 3958
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [176] inverse(X intersection Y) intersection inverse(Y) -> inverse(Y)
% Current number of equations to process: 4209
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [177]
% positive_part(inverse(X intersection Y)) intersection inverse(Y) ->
% inverse(Y)
% Current number of equations to process: 4451
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [178] inverse(inverse(Y) union X) -> inverse(X) intersection Y
% Rule
% [114]
% inverse(inverse(X) union Y) <->
% multiply(negative_part(inverse(multiply(X,Y))),X) collapsed.
% Rule [116] inverse(inverse(X) union Y) union X -> X collapsed.
% Rule [117] negative_part(inverse(inverse(X) union Y)) union X -> X collapsed.
% Rule [141] positive_part(inverse(inverse(X) union X union Y)) -> identity
% collapsed.
% Current number of equations to process: 4458
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [179]
% inverse(negative_part(X) union Y) intersection Y -> inverse(Y) intersection Y
% Current number of equations to process: 2194
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [180] inverse(inverse(X) intersection Y) intersection X -> X
% Current number of equations to process: 2419
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [181] positive_part(inverse(inverse(X) intersection Y)) intersection X -> X
% Current number of equations to process: 2719
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [182] inverse(X union Y) -> inverse(X) intersection inverse(Y)
% Rule
% [50]
% inverse(multiply(X,Y) union X) ->
% multiply(negative_part(inverse(Y)),inverse(X)) collapsed.
% Rule
% [52]
% inverse(multiply(X,Y) union Y) ->
% multiply(inverse(Y),negative_part(inverse(X))) collapsed.
% Rule [118] inverse(X union Y) union inverse(X) -> inverse(X) collapsed.
% Rule
% [143] positive_part(inverse(X union Y)) intersection X -> negative_part(X)
% collapsed.
% Rule [156] positive_part(inverse(X union Y) intersection Y) -> identity
% collapsed.
% Rule
% [160]
% negative_part(inverse(negative_part(Y) union X)) -> negative_part(inverse(X))
% collapsed.
% Rule
% [163]
% positive_part(inverse(X union Y)) intersection positive_part(Y) -> identity
% collapsed.
% Rule
% [166] negative_part(inverse(inverse(X union Y) intersection Y)) -> identity
% collapsed.
% Rule [170] negative_part(inverse(X union Y)) union inverse(X) -> inverse(X)
% collapsed.
% Rule [172] inverse(X union Y) intersection inverse(X) -> inverse(X union Y)
% collapsed.
% Rule [178] inverse(inverse(Y) union X) -> inverse(X) intersection Y
% collapsed.
% Rule
% [179]
% inverse(negative_part(X) union Y) intersection Y -> inverse(Y) intersection Y
% collapsed.
% Current number of equations to process: 2976
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [183] inverse(inverse(X) intersection inverse(Y)) -> X union Y
% Current number of equations to process: 3607
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [184] inverse(inverse(X) intersection Y) -> inverse(Y) union X
% Rule [135] negative_part(inverse(inverse(X) intersection X)) -> identity
% collapsed.
% Rule
% [139]
% positive_part(inverse(inverse(X) intersection X)) ->
% inverse(inverse(X) intersection X) collapsed.
% Rule
% [140] negative_part(inverse(inverse(X) intersection X) union Y) -> identity
% collapsed.
% Rule
% [162]
% negative_part(inverse(inverse(X) intersection X intersection Y)) -> identity
% collapsed.
% Rule
% [175]
% negative_part(inverse(inverse(X) intersection X) intersection Y) ->
% negative_part(Y) collapsed.
% Rule [180] inverse(inverse(X) intersection Y) intersection X -> X collapsed.
% Rule
% [181] positive_part(inverse(inverse(X) intersection Y)) intersection X -> X
% collapsed.
% Rule [183] inverse(inverse(X) intersection inverse(Y)) -> X union Y
% collapsed.
% Current number of equations to process: 3678
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [185] inverse(X intersection Y) -> inverse(X) union inverse(Y)
% Rule
% [51]
% inverse(multiply(X,Y) intersection X) ->
% multiply(positive_part(inverse(Y)),inverse(X)) collapsed.
% Rule
% [53]
% inverse(multiply(X,Y) intersection Y) ->
% multiply(inverse(Y),positive_part(inverse(X))) collapsed.
% Rule [138] negative_part(inverse(X intersection Y) union Y) -> identity
% collapsed.
% Rule
% [145] negative_part(inverse(X intersection Y)) union X -> positive_part(X)
% collapsed.
% Rule
% [161]
% positive_part(inverse(positive_part(Y) intersection X)) ->
% positive_part(inverse(X)) collapsed.
% Rule
% [167]
% negative_part(inverse(X intersection Y)) union negative_part(Y) -> identity
% collapsed.
% Rule
% [171] inverse(X intersection Y) union inverse(Y) -> inverse(X intersection Y)
% collapsed.
% Rule [176] inverse(X intersection Y) intersection inverse(Y) -> inverse(Y)
% collapsed.
% Rule
% [177]
% positive_part(inverse(X intersection Y)) intersection inverse(Y) ->
% inverse(Y) collapsed.
% Rule [184] inverse(inverse(X) intersection Y) -> inverse(Y) union X
% collapsed.
% Current number of equations to process: 3717
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [186]
% positive_part((negative_part(inverse(X)) union negative_part(inverse(Y))) intersection Z)
% -> identity
% Current number of equations to process: 3746
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [187]
% negative_part((positive_part(inverse(X)) intersection positive_part(inverse(Y))) union Z)
% -> identity
% Current number of equations to process: 3752
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [188]
% (inverse(X) union X) intersection positive_part(inverse(X)) ->
% positive_part(inverse(X))
% Current number of equations to process: 3733
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [189]
% (inverse(X) intersection X) union negative_part(inverse(X)) ->
% negative_part(inverse(X))
% Current number of equations to process: 3762
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [190] (multiply(X,inverse(Y)) union multiply(X,Y)) intersection X -> X
% Current number of equations to process: 3801
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced : [191] positive_part(multiply(X,X)) intersection X -> X
% Current number of equations to process: 3804
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [192] positive_part(multiply(X,X) union X) -> positive_part(multiply(X,X))
% Current number of equations to process: 3908
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [193] positive_part(multiply(X,X) union Y) intersection X -> X
% Current number of equations to process: 3910
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [194]
% positive_part(multiply(X,X)) intersection positive_part(X) ->
% positive_part(X)
% Current number of equations to process: 3917
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [195] (multiply(inverse(X),Y) union multiply(X,Y)) intersection Y -> Y
% Current number of equations to process: 4004
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [196]
% positive_part((negative_part(inverse(X)) union negative_part(Y)) intersection Z)
% -> identity
% Rule
% [186]
% positive_part((negative_part(inverse(X)) union negative_part(inverse(Y))) intersection Z)
% -> identity collapsed.
% Current number of equations to process: 4012
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [197]
% positive_part((negative_part(X) union negative_part(Y)) intersection Z) ->
% identity
% Rule
% [196]
% positive_part((negative_part(inverse(X)) union negative_part(Y)) intersection Z)
% -> identity collapsed.
% Current number of equations to process: 4018
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [198]
% negative_part((positive_part(X) intersection positive_part(Y)) union 
% inverse(Z)) -> identity
% Current number of equations to process: 4027
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [199]
% negative_part((positive_part(X) intersection positive_part(Y)) union Z) ->
% identity
% Rule
% [187]
% negative_part((positive_part(inverse(X)) intersection positive_part(inverse(Y))) union Z)
% -> identity collapsed.
% Rule
% [198]
% negative_part((positive_part(X) intersection positive_part(Y)) union 
% inverse(Z)) -> identity collapsed.
% Current number of equations to process: 4034
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [200]
% (negative_part(X) union Y) intersection (X union Y) ->
% negative_part(X) union Y
% Current number of equations to process: 4041
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [201]
% (positive_part(X) intersection Y) union (X intersection Y) ->
% positive_part(X) intersection Y
% Current number of equations to process: 4304
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [202]
% positive_part(((negative_part(Y) union X) intersection Z) union X) ->
% positive_part(X)
% Current number of equations to process: 4656
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [203]
% negative_part(((positive_part(Y) intersection X) union Z) intersection X) ->
% negative_part(X)
% Current number of equations to process: 4685
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [204]
% positive_part((positive_part(X intersection Y) intersection Z) union Y) ->
% positive_part(Y)
% Current number of equations to process: 4712
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [205]
% negative_part((negative_part(X union Y) union Z) intersection Y) ->
% negative_part(Y)
% Current number of equations to process: 4788
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [206] positive_part(inverse(X) union X union Y) -> inverse(X) union X union Y
% Current number of equations to process: 4812
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [207]
% negative_part(inverse(X) intersection X intersection Y) ->
% inverse(X) intersection X intersection Y
% Current number of equations to process: 4842
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [208]
% negative_part((inverse(Y) union Y union Z) intersection X) ->
% negative_part(X)
% Current number of equations to process: 4875
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [209]
% (inverse(X) union X union Y) intersection positive_part(X) ->
% positive_part(X)
% Current number of equations to process: 4893
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [210]
% positive_part((inverse(Y) intersection Y intersection Z) union X) ->
% positive_part(X)
% Current number of equations to process: 4935
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [211]
% (inverse(X) intersection X intersection Y) union negative_part(X) ->
% negative_part(X)
% Current number of equations to process: 4956
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [212]
% positive_part((X intersection Y) union multiply(X,X)) ->
% positive_part(multiply(X,X))
% Current number of equations to process: 1286
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [213]
% negative_part(multiply(inverse(X),inverse(X))) union inverse(X) -> inverse(X)
% Current number of equations to process: 1326
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced : [214] negative_part(multiply(X,X)) union X -> X
% Rule
% [213]
% negative_part(multiply(inverse(X),inverse(X))) union inverse(X) -> inverse(X)
% collapsed.
% Current number of equations to process: 1331
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [215]
% negative_part(multiply(X,X) intersection X) -> negative_part(multiply(X,X))
% Current number of equations to process: 1366
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [216] negative_part(multiply(X,X) intersection Y) union X -> X
% Current number of equations to process: 1379
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [217] negative_part(multiply(X,X)) union negative_part(X) -> negative_part(X)
% Current number of equations to process: 1391
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [218]
% positive_part(multiply(X,X) union Y) intersection positive_part(X) ->
% positive_part(X)
% Current number of equations to process: 1495
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [219]
% (inverse(X) union X union Y) intersection positive_part(Y) ->
% positive_part(Y)
% Current number of equations to process: 1557
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [220]
% (inverse(X) intersection X intersection Y) union negative_part(Y) ->
% negative_part(Y)
% Current number of equations to process: 1659
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [221]
% negative_part((X union Y) intersection multiply(X,X)) ->
% negative_part(multiply(X,X))
% Current number of equations to process: 1767
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [222]
% negative_part(multiply(X,X) intersection Y) union negative_part(X) ->
% negative_part(X)
% Current number of equations to process: 1810
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [223] negative_part(negative_part(X) union Y) union X union Y -> X union Y
% Current number of equations to process: 1863
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [224] negative_part((X intersection Y) union negative_part(Y)) union Y -> Y
% Current number of equations to process: 3184
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [225]
% negative_part((X intersection Y) union negative_part(X)) -> negative_part(X)
% Rule
% [224] negative_part((X intersection Y) union negative_part(Y)) union Y -> Y
% collapsed.
% Current number of equations to process: 3889
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [226]
% negative_part(negative_part(X union Y) union Y) -> negative_part(X union Y)
% Current number of equations to process: 3923
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [227]
% positive_part(positive_part(X) intersection Y) intersection X intersection Y
% -> X intersection Y
% Current number of equations to process: 4022
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [228]
% positive_part((X union Y) intersection positive_part(Y)) intersection Y -> Y
% Current number of equations to process: 1855
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [229]
% positive_part((X union Y) intersection positive_part(X)) -> positive_part(X)
% Rule
% [228]
% positive_part((X union Y) intersection positive_part(Y)) intersection Y -> Y
% collapsed.
% Current number of equations to process: 2578
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [230]
% positive_part(positive_part(X intersection Y) intersection Y) ->
% positive_part(X intersection Y)
% Current number of equations to process: 2603
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [231]
% positive_part(positive_part(X) intersection Y) intersection positive_part(X)
% -> positive_part(positive_part(X) intersection Y)
% Current number of equations to process: 2707
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [232]
% positive_part(positive_part(inverse(X)) intersection Y) intersection X ->
% negative_part(X)
% Current number of equations to process: 2737
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [233]
% positive_part(positive_part(inverse(X)) intersection Y) intersection 
% positive_part(X) -> identity
% Current number of equations to process: 2735
% Current number of ordered equations: 1
% Current number of rules: 119
% New rule produced :
% [234]
% positive_part(positive_part(X) intersection Y) intersection positive_part(
% inverse(X)) ->
% identity
% Current number of equations to process: 2735
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [235]
% positive_part(positive_part(X) intersection Y) intersection Y ->
% positive_part(X) intersection Y
% Rule
% [227]
% positive_part(positive_part(X) intersection Y) intersection X intersection Y
% -> X intersection Y collapsed.
% Current number of equations to process: 2738
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [236]
% positive_part(positive_part(X) intersection Y) intersection inverse(X) ->
% negative_part(inverse(X))
% Current number of equations to process: 2787
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [237]
% negative_part(negative_part(inverse(X)) union inverse(Y)) union X ->
% positive_part(X)
% Current number of equations to process: 3175
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [238]
% negative_part(negative_part(inverse(X)) union Y) union X -> positive_part(X)
% Rule
% [237]
% negative_part(negative_part(inverse(X)) union inverse(Y)) union X ->
% positive_part(X) collapsed.
% Current number of equations to process: 3198
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [239]
% negative_part(negative_part(X) union Y) union inverse(X) ->
% positive_part(inverse(X))
% Current number of equations to process: 3235
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [240]
% negative_part(negative_part(X) union Y) union negative_part(X) ->
% negative_part(negative_part(X) union Y)
% Current number of equations to process: 3278
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [241]
% negative_part(negative_part(inverse(X)) union Y) union negative_part(X) ->
% identity
% Current number of equations to process: 3312
% Current number of ordered equations: 1
% Current number of rules: 125
% New rule produced :
% [242]
% negative_part(negative_part(X) union Y) union negative_part(inverse(X)) ->
% identity
% Current number of equations to process: 3312
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [243]
% negative_part(negative_part(X) union Y) union Y -> negative_part(X) union Y
% Rule
% [223] negative_part(negative_part(X) union Y) union X union Y -> X union Y
% collapsed.
% Current number of equations to process: 3339
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [244]
% (negative_part(X) union negative_part(Y)) intersection positive_part(Z) ->
% negative_part(X) union negative_part(Y)
% Current number of equations to process: 3665
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [245]
% (positive_part(X) intersection positive_part(Y)) union negative_part(Z) ->
% positive_part(X) intersection positive_part(Y)
% Current number of equations to process: 3704
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [246]
% negative_part(multiply(inverse(X),inverse(Y)) union multiply(Y,X)) ->
% identity
% Current number of equations to process: 3616
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [247]
% positive_part(multiply(X,inverse(Y)) union multiply(X,Y)) intersection X -> X
% Current number of equations to process: 3634
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [248]
% positive_part(multiply(inverse(X),Y) union multiply(X,Y)) intersection Y -> Y
% Current number of equations to process: 3700
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [249]
% negative_part((positive_part(inverse(X)) intersection inverse(Y)) union X union Y)
% -> identity
% Current number of equations to process: 3769
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [250]
% positive_part(multiply(inverse(X),inverse(Y)) intersection multiply(Y,X)) ->
% identity
% Current number of equations to process: 3782
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [251] (multiply(X,inverse(Y)) intersection multiply(X,Y)) union X -> X
% Current number of equations to process: 3805
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [252] (multiply(inverse(Y),X) intersection multiply(Y,X)) union X -> X
% Current number of equations to process: 3907
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [253]
% negative_part((positive_part(X) intersection Y) union inverse(X) union 
% inverse(Y)) -> identity
% Current number of equations to process: 4009
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [254]
% positive_part((negative_part(inverse(X)) union inverse(Y)) intersection X intersection Y)
% -> identity
% Current number of equations to process: 4025
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [255]
% (negative_part(X) union Y) intersection positive_part(inverse(Y)) ->
% negative_part(negative_part(X) union Y)
% Current number of equations to process: 4045
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [256]
% positive_part((negative_part(X) union Y) intersection inverse(X) intersection 
% inverse(Y)) -> identity
% Current number of equations to process: 4100
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [257]
% (positive_part(X) intersection Y) union negative_part(inverse(Y)) ->
% positive_part(positive_part(X) intersection Y)
% Current number of equations to process: 4122
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [258]
% positive_part(inverse(Y) intersection inverse(Z)) intersection positive_part(
% X intersection Y)
% -> identity
% Current number of equations to process: 4169
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [259]
% positive_part(inverse(X) intersection Y) intersection positive_part(X intersection Z)
% -> identity
% Rule
% [258]
% positive_part(inverse(Y) intersection inverse(Z)) intersection positive_part(
% X intersection Y)
% -> identity collapsed.
% Current number of equations to process: 4230
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [260]
% negative_part(inverse(Y) union inverse(Z)) union negative_part(X union Y) ->
% identity
% Current number of equations to process: 4257
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [261]
% negative_part(inverse(X) union Y) union negative_part(X union Z) -> identity
% Rule
% [260]
% negative_part(inverse(Y) union inverse(Z)) union negative_part(X union Y) ->
% identity collapsed.
% Current number of equations to process: 4313
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [262]
% negative_part((inverse(Y) intersection X) union inverse(X) union Y) ->
% identity
% Current number of equations to process: 4344
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [263]
% positive_part((inverse(Y) union X) intersection inverse(X) intersection Y) ->
% identity
% Current number of equations to process: 4358
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [264]
% negative_part((inverse(X) intersection inverse(Y)) union X union Y) ->
% identity
% Current number of equations to process: 4357
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [265]
% positive_part((X union Y) intersection inverse(X) intersection inverse(Y)) ->
% identity
% Current number of equations to process: 4373
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [266]
% positive_part((inverse(X) union inverse(Y)) intersection X intersection Y) ->
% identity
% Current number of equations to process: 4388
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [267]
% negative_part((X intersection Y) union inverse(X) union inverse(Y)) ->
% identity
% Current number of equations to process: 4404
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [268]
% positive_part(((inverse(X) intersection X) union negative_part(Y)) intersection Z)
% -> identity
% Current number of equations to process: 4420
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [269]
% negative_part(((inverse(X) union X) intersection positive_part(Y)) union Z)
% -> identity
% Current number of equations to process: 4439
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [270] (inverse(X) union multiply(Y,Y) union X) intersection Y -> Y
% Current number of equations to process: 4452
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [271] (inverse(X) intersection multiply(Y,Y) intersection X) union Y -> Y
% Current number of equations to process: 4522
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [272]
% negative_part(multiply(inverse(X),Y) union multiply(inverse(Y),X)) ->
% identity
% Current number of equations to process: 4578
% Current number of ordered equations: 1
% Current number of rules: 153
% New rule produced :
% [273]
% negative_part(multiply(X,inverse(Y)) union multiply(Y,inverse(X))) ->
% identity
% Current number of equations to process: 4578
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [274]
% positive_part(multiply(inverse(X),Y) intersection multiply(inverse(Y),X)) ->
% identity
% Current number of equations to process: 4611
% Current number of ordered equations: 1
% Current number of rules: 155
% New rule produced :
% [275]
% positive_part(multiply(X,inverse(Y)) intersection multiply(Y,inverse(X))) ->
% identity
% Current number of equations to process: 4611
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [276]
% positive_part((positive_part(X) intersection Z) union X union Y) ->
% positive_part(X union Y)
% Current number of equations to process: 4634
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [277]
% negative_part((negative_part(X) union Z) intersection X intersection Y) ->
% negative_part(X intersection Y)
% Current number of equations to process: 4742
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [278]
% (positive_part(X) intersection Y) union negative_part(X intersection Y) ->
% positive_part(X) intersection Y
% Current number of equations to process: 4846
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [279]
% (positive_part(X) intersection Y) union negative_part(Y intersection Z) ->
% positive_part(X) intersection Y
% Rule
% [278]
% (positive_part(X) intersection Y) union negative_part(X intersection Y) ->
% positive_part(X) intersection Y collapsed.
% Current number of equations to process: 1642
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [280]
% (negative_part(X) union Y) intersection positive_part(X union Y) ->
% negative_part(X) union Y
% Current number of equations to process: 1973
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [281]
% (negative_part(X) union Y) intersection positive_part(Y union Z) ->
% negative_part(X) union Y
% Rule
% [280]
% (negative_part(X) union Y) intersection positive_part(X union Y) ->
% negative_part(X) union Y collapsed.
% Current number of equations to process: 2392
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [282]
% positive_part(X union Y) intersection positive_part(X intersection Z) ->
% positive_part(X intersection Z)
% Current number of equations to process: 2717
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [283]
% negative_part(X union Y) union negative_part(Y intersection Z) ->
% negative_part(X union Y)
% Current number of equations to process: 3175
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [284]
% (inverse(X) intersection multiply(inverse(X),inverse(X))) union negative_part(
% inverse(X))
% -> inverse(X)
% Current number of equations to process: 3647
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [285] (multiply(X,X) union X) intersection positive_part(X) -> X
% The conjecture has been reduced. 
% Conjecture is now:
% Trivial
% 
% Current number of equations to process: 3655
% Current number of ordered equations: 0
% Current number of rules: 164
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% 
% The following 41 rules have been used:
% [2] 
% inverse(inverse(X)) -> X; trace = in the starting set
% [5] multiply(identity,X) -> X; trace = in the starting set
% [6] identity union X -> positive_part(X); trace = in the starting set
% [7] identity intersection X -> negative_part(X); trace = in the starting set
% [8] multiply(inverse(X),X) -> identity; trace = in the starting set
% [9] (X intersection Y) union Y -> Y; trace = in the starting set
% [10] (X union Y) intersection Y -> Y; trace = in the starting set
% [11] inverse(multiply(X,Y)) -> multiply(inverse(Y),inverse(X)); trace = in the starting set
% [12] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z)); trace = in the starting set
% [13] multiply(X,Y union Z) -> multiply(X,Y) union multiply(X,Z); trace = in the starting set
% [14] multiply(X,Y intersection Z) -> multiply(X,Y) intersection multiply(X,Z); trace = in the starting set
% [15] multiply(Y union Z,X) -> multiply(Y,X) union multiply(Z,X); trace = in the starting set
% [21] multiply(X,inverse(X)) -> identity; trace = Cp of 8 and 2
% [24] positive_part(negative_part(X)) -> identity; trace = Cp of 9 and 7
% [34] multiply(inverse(X),identity) -> inverse(X); trace = Cp of 11 and 5
% [35] multiply(inverse(Y),multiply(Y,X)) -> X; trace = Cp of 12 and 8
% [36] multiply(X,positive_part(Y)) -> multiply(X,Y) union X; trace = Cp of 13 and 6
% [37] multiply(X,negative_part(Y)) -> multiply(X,Y) intersection X; trace = Cp of 14 and 7
% [38] multiply(positive_part(X),Y) -> multiply(X,Y) union Y; trace = Cp of 15 and 6
% [40] multiply(Y,multiply(inverse(Y),X)) -> X; trace = Cp of 21 and 12
% [43] multiply(X,identity) -> X; trace = Cp of 34 and 2
% [50] inverse(multiply(X,Y) union X) ->
% multiply(inverse(positive_part(Y)),inverse(X)); trace = Cp of 36 and 11
% [51] inverse(multiply(X,Y) intersection X) ->
% multiply(inverse(negative_part(Y)),inverse(X)); trace = Cp of 37 and 11
% [52] inverse(multiply(X,Y) union Y) ->
% multiply(inverse(Y),inverse(positive_part(X))); trace = Cp of 38 and 11
% [58] inverse(positive_part(inverse(X))) ->
% multiply(X,inverse(positive_part(X))); trace = Cp of 50 and 8
% [59] inverse(negative_part(inverse(X))) ->
% multiply(X,inverse(negative_part(X))); trace = Cp of 51 and 8
% [62] multiply(inverse(positive_part(X)),inverse(X)) ->
% multiply(inverse(X),inverse(positive_part(X))); trace = Cp of 52 and 50
% [64] inverse(negative_part(multiply(X,inverse(positive_part(X))))) ->
% positive_part(inverse(X)); trace = Cp of 59 and 58
% [66] negative_part(multiply(X,inverse(positive_part(X)))) ->
% multiply(X,inverse(positive_part(X))); trace = Cp of 64 and 2
% [68] positive_part(multiply(X,inverse(positive_part(X)))) -> identity; trace = Cp of 66 and 24
% [72] positive_part(inverse(positive_part(X))) -> identity; trace = Cp of 68 and 58
% [80] multiply(inverse(positive_part(Y)),X) union X -> X; trace = Cp of 72 and 38
% [114] inverse(inverse(X) union Y) <->
% multiply(negative_part(inverse(multiply(X,Y))),X); trace = Cp of 50 and 35
% [115] multiply(inverse(positive_part(multiply(X,Y))),X) <->
% inverse(inverse(X) union Y); trace = Cp of 50 and 35
% [116] inverse(inverse(X) union Y) union X -> X; trace = Cp of 115 and 80
% [118] inverse(X union Y) union inverse(X) -> inverse(X); trace = Cp of 116 and 2
% [172] inverse(X union Y) intersection inverse(X) -> inverse(X union Y); trace = Cp of 118 and 10
% [178] inverse(inverse(Y) union X) -> inverse(X) intersection Y; trace = Cp of 172 and 114
% [182] inverse(X union Y) -> inverse(X) intersection inverse(Y); trace = Cp of 178 and 2
% [284] (inverse(X) intersection multiply(inverse(X),inverse(X))) union 
% negative_part(inverse(X)) -> inverse(X); trace = Cp of 62 and 40
% [285] (multiply(X,X) union X) intersection positive_part(X) -> X; trace = Cp of 284 and 182
% % SZS output end Refutation
% All conjectures have been proven
% 
% Execution time: 76.140000 sec
% res : bool = true
% time is now off
% 
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
% 
% EOF
%------------------------------------------------------------------------------