%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP002-3 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n103.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 00:22:08 EDT 2014
% Result : Unsatisfiable 142.93s
% Output : Refutation 142.93s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP002-3 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n103.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 : Thu Jun 5 15:40:13 CDT 2014
% % CPUTime : 142.93
% Processing problem /tmp/CiME_33056_n103.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b,a,identity : constant; commutator : 2; 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;
% commutator(X,Y) = multiply(X,multiply(Y,multiply(inverse(X),inverse(Y))));
% multiply(X,multiply(X,X)) = identity;
% ";
%
% let s1 = status F "
% b lr_lex;
% a lr_lex;
% commutator lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% identity lr_lex;
% ";
%
% let p1 = precedence F "
% commutator > multiply > inverse > identity > a > b";
%
% let s2 = status F "
% b mul;
% a mul;
% commutator mul;
% inverse mul;
% multiply mul;
% identity mul;
% ";
%
% let p2 = precedence F "
% commutator > multiply > inverse > identity = a = b";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " commutator(commutator(a,b),b) = 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,
% commutator(X,Y) =
% multiply(X,multiply(Y,multiply(inverse(X),
% inverse(Y)))),
% multiply(X,multiply(X,X)) = identity }
% (5 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 = { commutator(commutator(a,b),b) = identity }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 1
% New rule produced : [2] multiply(inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 2
% New rule produced : [3] multiply(X,multiply(X,X)) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 3
% New rule produced :
% [4] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 4
% New rule produced :
% [5]
% multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) -> commutator(X,Y)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [6] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] multiply(Y,multiply(Y,multiply(Y,X))) -> X
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [8] commutator(inverse(X),X) -> identity
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9]
% multiply(X,multiply(inverse(X),inverse(identity))) -> commutator(X,identity)
% Current number of equations to process: 1
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced :
% [10]
% multiply(X,multiply(inverse(identity),inverse(X))) -> commutator(identity,X)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] multiply(inverse(identity),X) -> X
% Rule
% [10]
% multiply(X,multiply(inverse(identity),inverse(X))) -> commutator(identity,X)
% collapsed.
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [12] multiply(X,inverse(X)) -> commutator(identity,X)
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [13] multiply(inverse(inverse(X)),identity) -> X
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [14] multiply(inverse(X),identity) -> multiply(X,X)
% Rule [13] multiply(inverse(inverse(X)),identity) -> X collapsed.
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [15] multiply(inverse(X),inverse(X)) -> X
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [16] multiply(inverse(inverse(X)),Y) -> multiply(X,Y)
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [17] multiply(X,identity) -> X
% Rule [14] multiply(inverse(X),identity) -> multiply(X,X) collapsed.
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [18] inverse(X) -> multiply(X,X)
% Rule [2] multiply(inverse(X),X) -> identity collapsed.
% Rule
% [5]
% multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) -> commutator(X,Y)
% collapsed.
% Rule [6] multiply(inverse(Y),multiply(Y,X)) -> X collapsed.
% Rule [8] commutator(inverse(X),X) -> identity collapsed.
% Rule
% [9]
% multiply(X,multiply(inverse(X),inverse(identity))) -> commutator(X,identity)
% collapsed.
% Rule [11] multiply(inverse(identity),X) -> X collapsed.
% Rule [12] multiply(X,inverse(X)) -> commutator(identity,X) collapsed.
% Rule [15] multiply(inverse(X),inverse(X)) -> X collapsed.
% Rule [16] multiply(inverse(inverse(X)),Y) -> multiply(X,Y) collapsed.
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [19]
% multiply(X,multiply(Y,multiply(X,multiply(X,multiply(Y,Y))))) ->
% commutator(X,Y)
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [20] commutator(multiply(X,X),X) -> identity
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [21] commutator(identity,X) -> identity
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [22] commutator(X,X) -> identity
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [23]
% multiply(X,multiply(X,commutator(X,Y))) <->
% multiply(Y,multiply(X,multiply(X,multiply(Y,Y))))
% Current number of equations to process: 7
% Current number of ordered equations: 1
% Current number of rules: 11
% New rule produced :
% [24]
% multiply(Y,multiply(X,multiply(X,multiply(Y,Y)))) <->
% multiply(X,multiply(X,commutator(X,Y)))
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [25] commutator(X,identity) -> identity
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [26]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,multiply(Y,Z)))))) ->
% Z
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [27]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,Y))))) -> identity
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [28] multiply(X,multiply(Y,multiply(X,multiply(Y,X)))) -> multiply(Y,Y)
% Rule
% [27]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,Y))))) -> identity
% collapsed.
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [29]
% multiply(X,multiply(X,multiply(Y,Y))) <->
% multiply(Y,multiply(X,multiply(Y,X)))
% Current number of equations to process: 26
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [30]
% multiply(Y,multiply(X,multiply(Y,X))) <->
% multiply(X,multiply(X,multiply(Y,Y)))
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [31]
% commutator(multiply(X,multiply(Y,multiply(X,Y))),multiply(X,Y)) -> identity
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [32]
% multiply(X,multiply(Y,multiply(X,commutator(Y,X)))) ->
% multiply(Y,multiply(X,X))
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [33]
% commutator(multiply(X,multiply(X,multiply(Y,Y))),multiply(Y,X)) -> identity
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [34]
% multiply(X,multiply(Y,multiply(Y,multiply(X,multiply(Y,X))))) ->
% commutator(X,Y)
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [35]
% multiply(X,multiply(X,multiply(Y,multiply(X,Y)))) <->
% multiply(Y,multiply(Y,commutator(Y,X)))
% Current number of equations to process: 48
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [36]
% multiply(Y,multiply(Y,commutator(Y,X))) <->
% multiply(X,multiply(X,multiply(Y,multiply(X,Y))))
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [37]
% multiply(X,multiply(Y,multiply(Y,commutator(Y,X)))) <->
% multiply(Y,multiply(X,Y))
% Current number of equations to process: 53
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [38]
% multiply(Y,multiply(X,Y)) <->
% multiply(X,multiply(Y,multiply(Y,commutator(Y,X))))
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [39]
% multiply(X,multiply(X,multiply(Y,multiply(X,X)))) <->
% multiply(Y,multiply(X,commutator(Y,X)))
% Current number of equations to process: 82
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [40]
% multiply(Y,multiply(X,commutator(Y,X))) <->
% multiply(X,multiply(X,multiply(Y,multiply(X,X))))
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [41]
% multiply(commutator(X,Y),Z) ->
% multiply(X,multiply(Y,multiply(X,multiply(X,multiply(Y,multiply(Y,Z))))))
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [42]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,Z))))) ->
% multiply(Y,multiply(Y,Z))
% Rule
% [26]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,multiply(Y,Z)))))) ->
% Z collapsed.
% Current number of equations to process: 120
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [43]
% multiply(X,multiply(Y,multiply(X,multiply(Y,Z)))) <->
% multiply(Y,multiply(Y,multiply(X,multiply(X,Z))))
% Current number of equations to process: 141
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [44]
% multiply(Y,multiply(Y,multiply(X,multiply(X,Z)))) <->
% multiply(X,multiply(Y,multiply(X,multiply(Y,Z))))
% Current number of equations to process: 141
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [45]
% multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(X,X))))) <->
% multiply(Y,multiply(X,Y))
% Current number of equations to process: 193
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [46]
% multiply(Y,multiply(X,Y)) <->
% multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(X,X)))))
% Current number of equations to process: 193
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [47] multiply(X,multiply(X,multiply(Y,X))) <-> multiply(Y,commutator(Y,X))
% Current number of equations to process: 211
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [48] multiply(Y,commutator(Y,X)) <-> multiply(X,multiply(X,multiply(Y,X)))
% Current number of equations to process: 211
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [49] multiply(X,multiply(Y,commutator(Y,X))) -> multiply(Y,X)
% Current number of equations to process: 214
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [50]
% multiply(X,multiply(Y,multiply(Y,X))) <->
% multiply(Y,multiply(X,multiply(X,Y)))
% Current number of equations to process: 240
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [51] multiply(X,commutator(Y,X)) <-> multiply(Y,multiply(X,multiply(Y,Y)))
% Current number of equations to process: 270
% Current number of ordered equations: 1
% Current number of rules: 37
% New rule produced :
% [52] multiply(Y,multiply(X,multiply(Y,Y))) <-> multiply(X,commutator(Y,X))
% Current number of equations to process: 270
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [53]
% multiply(X,multiply(Y,commutator(X,Y))) <->
% multiply(Y,multiply(X,commutator(Y,X)))
% Current number of equations to process: 270
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [54] commutator(X,multiply(X,X)) -> identity
% Current number of equations to process: 320
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [55]
% multiply(X,multiply(X,multiply(Y,commutator(X,Y)))) <->
% multiply(Y,multiply(X,X))
% Current number of equations to process: 321
% Current number of ordered equations: 1
% Current number of rules: 41
% New rule produced :
% [56]
% multiply(Y,multiply(X,X)) <->
% multiply(X,multiply(X,multiply(Y,commutator(X,Y))))
% Current number of equations to process: 321
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [57]
% multiply(X,multiply(Y,multiply(Y,commutator(X,Y)))) ->
% multiply(Y,multiply(Y,X))
% Current number of equations to process: 320
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [58]
% commutator(multiply(X,Y),multiply(X,multiply(Y,multiply(X,Y)))) -> identity
% Current number of equations to process: 330
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [59] multiply(Y,multiply(X,commutator(multiply(Y,Y),X))) -> multiply(X,Y)
% Current number of equations to process: 340
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [60]
% commutator(multiply(X,Y),multiply(Y,multiply(Y,multiply(X,X)))) -> identity
% Current number of equations to process: 366
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [61]
% multiply(X,multiply(X,multiply(Y,X))) <->
% multiply(Y,commutator(multiply(X,X),Y))
% Current number of equations to process: 372
% Current number of ordered equations: 1
% Current number of rules: 47
% New rule produced :
% [62]
% multiply(Y,commutator(multiply(X,X),Y)) <->
% multiply(X,multiply(X,multiply(Y,X)))
% Current number of equations to process: 372
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [63]
% multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(X,Y))))) ->
% commutator(X,Y)
% Current number of equations to process: 385
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [64] multiply(X,commutator(X,Y)) <-> multiply(X,commutator(multiply(Y,Y),X))
% Current number of equations to process: 399
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced :
% [65] multiply(X,commutator(multiply(Y,Y),X)) <-> multiply(X,commutator(X,Y))
% Current number of equations to process: 399
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced : [66] commutator(X,Y) <-> commutator(multiply(Y,Y),X)
% Rule
% [64] multiply(X,commutator(X,Y)) <-> multiply(X,commutator(multiply(Y,Y),X))
% collapsed.
% Current number of equations to process: 402
% Current number of ordered equations: 1
% Current number of rules: 51
% New rule produced : [67] commutator(multiply(Y,Y),X) <-> commutator(X,Y)
% Rule [20] commutator(multiply(X,X),X) -> identity collapsed.
% Rule
% [65] multiply(X,commutator(multiply(Y,Y),X)) <-> multiply(X,commutator(X,Y))
% collapsed.
% Current number of equations to process: 402
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [68]
% commutator(X,multiply(X,multiply(Y,multiply(Y,multiply(X,Y))))) -> identity
% Current number of equations to process: 414
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [69]
% multiply(X,multiply(Y,multiply(X,multiply(X,Y)))) <->
% multiply(Y,multiply(Y,commutator(X,Y)))
% Current number of equations to process: 415
% Current number of ordered equations: 1
% Current number of rules: 52
% New rule produced :
% [70]
% multiply(Y,multiply(Y,commutator(X,Y))) <->
% multiply(X,multiply(Y,multiply(X,multiply(X,Y))))
% Current number of equations to process: 415
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [71]
% multiply(Y,multiply(X,multiply(Y,multiply(X,multiply(X,Y))))) ->
% commutator(X,Y)
% Current number of equations to process: 414
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [72]
% multiply(X,multiply(X,multiply(Y,multiply(X,multiply(Y,Y))))) ->
% commutator(Y,X)
% Current number of equations to process: 413
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [73]
% multiply(X,multiply(X,commutator(Y,X))) <->
% multiply(Y,multiply(Y,multiply(X,multiply(X,Y))))
% Current number of equations to process: 412
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [74]
% multiply(Y,multiply(Y,multiply(X,multiply(X,Y)))) <->
% multiply(X,multiply(X,commutator(Y,X)))
% Current number of equations to process: 412
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [75]
% multiply(X,multiply(Y,commutator(X,Y))) <->
% multiply(Y,multiply(X,commutator(multiply(X,X),Y)))
% Current number of equations to process: 410
% Current number of ordered equations: 1
% Current number of rules: 58
% New rule produced :
% [76]
% multiply(Y,multiply(X,commutator(multiply(X,X),Y))) <->
% multiply(X,multiply(Y,commutator(X,Y)))
% Current number of equations to process: 410
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [77] commutator(Z,commutator(Y,X)) <-> commutator(commutator(X,Y),Z)
% Current number of equations to process: 429
% Current number of ordered equations: 1
% Current number of rules: 60
% New rule produced :
% [78] commutator(commutator(X,Y),Z) <-> commutator(Z,commutator(Y,X))
% The conjecture has been reduced.
% Conjecture is now:
% commutator(b,commutator(b,a)) = identity
%
% Current number of equations to process: 429
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [79] commutator(multiply(X,X),multiply(Y,Y)) -> commutator(X,Y)
% Current number of equations to process: 431
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [80]
% multiply(X,commutator(multiply(X,X),Y)) <->
% multiply(Y,multiply(X,multiply(Y,Y)))
% Current number of equations to process: 430
% Current number of ordered equations: 1
% Current number of rules: 63
% New rule produced :
% [81]
% multiply(Y,multiply(X,multiply(Y,Y))) <->
% multiply(X,commutator(multiply(X,X),Y))
% Current number of equations to process: 430
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [82]
% commutator(Z,multiply(X,Y)) <->
% commutator(multiply(X,multiply(Y,multiply(X,Y))),Z)
% Current number of equations to process: 429
% Current number of ordered equations: 1
% Current number of rules: 65
% New rule produced :
% [83]
% commutator(multiply(X,multiply(Y,multiply(X,Y))),Z) <->
% commutator(Z,multiply(X,Y))
% Rule
% [31]
% commutator(multiply(X,multiply(Y,multiply(X,Y))),multiply(X,Y)) -> identity
% collapsed.
% Current number of equations to process: 429
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [84] commutator(X,multiply(X,multiply(X,commutator(X,Y)))) -> identity
% Current number of equations to process: 437
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [85]
% commutator(X,multiply(X,multiply(X,commutator(multiply(Y,Y),X)))) -> identity
% Current number of equations to process: 437
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [86] commutator(multiply(X,X),multiply(X,commutator(Y,X))) -> identity
% Current number of equations to process: 437
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [87]
% multiply(X,multiply(Y,multiply(Y,multiply(X,multiply(X,Y))))) ->
% commutator(Y,X)
% Current number of equations to process: 477
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [88] commutator(commutator(X,Y),commutator(Y,X)) -> identity
% Current number of equations to process: 533
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [89]
% commutator(X,commutator(multiply(Y,Y),Z)) <-> commutator(commutator(Y,Z),X)
% Current number of equations to process: 544
% Current number of ordered equations: 1
% Current number of rules: 71
% New rule produced :
% [90]
% commutator(commutator(Y,Z),X) <-> commutator(X,commutator(multiply(Y,Y),Z))
% Current number of equations to process: 544
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [91]
% commutator(X,commutator(Y,Z)) <-> commutator(commutator(Y,multiply(Z,Z)),X)
% Current number of equations to process: 542
% Current number of ordered equations: 3
% Current number of rules: 73
% New rule produced :
% [92]
% commutator(commutator(X,Y),Z) <-> commutator(commutator(Y,X),multiply(Z,Z))
% Current number of equations to process: 542
% Current number of ordered equations: 2
% Current number of rules: 74
% New rule produced :
% [93]
% commutator(commutator(Y,X),multiply(Z,Z)) <-> commutator(commutator(X,Y),Z)
% Current number of equations to process: 542
% Current number of ordered equations: 1
% Current number of rules: 75
% New rule produced :
% [94]
% commutator(commutator(Y,multiply(Z,Z)),X) <-> commutator(X,commutator(Y,Z))
% Current number of equations to process: 542
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [95]
% commutator(X,commutator(Z,Y)) <-> commutator(multiply(X,X),commutator(Y,Z))
% Current number of equations to process: 552
% Current number of ordered equations: 3
% Current number of rules: 77
% New rule produced :
% [96]
% commutator(Z,commutator(X,Y)) <-> commutator(commutator(multiply(X,X),Y),Z)
% Current number of equations to process: 552
% Current number of ordered equations: 2
% Current number of rules: 78
% New rule produced :
% [97]
% commutator(multiply(X,X),commutator(Y,Z)) <-> commutator(X,commutator(Z,Y))
% Current number of equations to process: 552
% Current number of ordered equations: 1
% Current number of rules: 79
% New rule produced :
% [98]
% commutator(commutator(multiply(X,X),Y),Z) <-> commutator(Z,commutator(X,Y))
% Current number of equations to process: 552
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [99]
% commutator(Z,commutator(X,multiply(Y,Y))) <-> commutator(commutator(X,Y),Z)
% Current number of equations to process: 551
% Current number of ordered equations: 1
% Current number of rules: 81
% New rule produced :
% [100]
% commutator(commutator(X,Y),Z) <-> commutator(Z,commutator(X,multiply(Y,Y)))
% Current number of equations to process: 551
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [101]
% commutator(X,commutator(commutator(Y,Z),V_3)) <->
% commutator(commutator(commutator(Z,Y),V_3),X)
% Current number of equations to process: 558
% Current number of ordered equations: 1
% Current number of rules: 83
% New rule produced :
% [102]
% commutator(commutator(commutator(Z,Y),V_3),X) <->
% commutator(X,commutator(commutator(Y,Z),V_3))
% Current number of equations to process: 558
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [103]
% commutator(V_3,commutator(X,commutator(Z,Y))) <->
% commutator(commutator(X,commutator(Y,Z)),V_3)
% Current number of equations to process: 557
% Current number of ordered equations: 1
% Current number of rules: 85
% New rule produced :
% [104]
% commutator(commutator(X,commutator(Y,Z)),V_3) <->
% commutator(V_3,commutator(X,commutator(Z,Y)))
% Current number of equations to process: 557
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [105]
% commutator(commutator(X,Y),commutator(Z,V_3)) <->
% commutator(commutator(Y,X),commutator(V_3,Z))
% Current number of equations to process: 554
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced : [106] commutator(X,multiply(Y,Y)) <-> commutator(Y,X)
% Rule [54] commutator(X,multiply(X,X)) -> identity collapsed.
% Current number of equations to process: 555
% Current number of ordered equations: 1
% Current number of rules: 87
% New rule produced : [107] commutator(Y,X) <-> commutator(X,multiply(Y,Y))
% Current number of equations to process: 555
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [108]
% commutator(X,multiply(Y,multiply(Y,multiply(Z,Z)))) <->
% commutator(multiply(Z,Y),X)
% Current number of equations to process: 584
% Current number of ordered equations: 1
% Current number of rules: 89
% New rule produced :
% [109]
% commutator(multiply(Z,Y),X) <->
% commutator(X,multiply(Y,multiply(Y,multiply(Z,Z))))
% Current number of equations to process: 584
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [110]
% commutator(X,multiply(Y,multiply(Z,Y))) <->
% commutator(multiply(Z,multiply(Y,Z)),X)
% Current number of equations to process: 587
% Current number of ordered equations: 1
% Current number of rules: 91
% New rule produced :
% [111]
% commutator(multiply(Z,multiply(Y,Z)),X) <->
% commutator(X,multiply(Y,multiply(Z,Y)))
% Current number of equations to process: 587
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [112]
% commutator(Z,multiply(Y,X)) <->
% commutator(multiply(X,multiply(X,multiply(Y,Y))),Z)
% Current number of equations to process: 630
% Current number of ordered equations: 3
% Current number of rules: 93
% New rule produced :
% [113]
% commutator(Z,multiply(X,multiply(Y,multiply(X,Y)))) <->
% commutator(multiply(X,Y),Z)
% Rule
% [58]
% commutator(multiply(X,Y),multiply(X,multiply(Y,multiply(X,Y)))) -> identity
% collapsed.
% Current number of equations to process: 630
% Current number of ordered equations: 2
% Current number of rules: 93
% New rule produced :
% [114]
% commutator(multiply(X,Y),Z) <->
% commutator(Z,multiply(X,multiply(Y,multiply(X,Y))))
% Current number of equations to process: 630
% Current number of ordered equations: 1
% Current number of rules: 94
% New rule produced :
% [115]
% commutator(multiply(X,multiply(X,multiply(Y,Y))),Z) <->
% commutator(Z,multiply(Y,X))
% Current number of equations to process: 630
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [116]
% commutator(X,multiply(Y,multiply(X,multiply(X,multiply(Y,Y))))) -> identity
% Current number of equations to process: 662
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [117]
% commutator(X,multiply(Y,multiply(Y,multiply(X,multiply(Y,X))))) -> identity
% Current number of equations to process: 661
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [118]
% commutator(X,multiply(X,multiply(X,commutator(commutator(Y,Z),X)))) ->
% identity
% Current number of equations to process: 660
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [119] commutator(multiply(X,X),multiply(X,commutator(X,Y))) -> identity
% Current number of equations to process: 673
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [120] commutator(commutator(X,multiply(X,commutator(Y,X))),Z) -> identity
% Current number of equations to process: 675
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [121] commutator(X,commutator(Y,multiply(Y,commutator(Z,Y)))) -> identity
% Current number of equations to process: 674
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [122]
% commutator(multiply(X,X),multiply(Y,multiply(X,multiply(Y,Y)))) -> identity
% Current number of equations to process: 673
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [123]
% commutator(multiply(X,X),multiply(Y,multiply(Y,multiply(X,Y)))) -> identity
% Current number of equations to process: 672
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [124]
% commutator(multiply(X,X),multiply(X,commutator(multiply(X,X),Y))) -> identity
% Current number of equations to process: 671
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [125] commutator(commutator(X,Y),commutator(multiply(Y,Y),X)) -> identity
% Current number of equations to process: 686
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [126]
% commutator(commutator(X,Y),multiply(Z,Z)) <->
% commutator(commutator(multiply(X,X),Y),Z)
% Current number of equations to process: 703
% Current number of ordered equations: 1
% Current number of rules: 106
% New rule produced :
% [127]
% commutator(commutator(multiply(X,X),Y),Z) <->
% commutator(commutator(X,Y),multiply(Z,Z))
% Current number of equations to process: 703
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [128] commutator(commutator(X,Y),commutator(Y,multiply(X,X))) -> identity
% Current number of equations to process: 714
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [129]
% commutator(X,commutator(multiply(Y,Y),Z)) <->
% commutator(multiply(X,X),commutator(Y,Z))
% Current number of equations to process: 722
% Current number of ordered equations: 3
% Current number of rules: 109
% New rule produced :
% [130]
% commutator(Z,commutator(multiply(Y,Y),X)) <->
% commutator(commutator(multiply(X,X),Y),Z)
% Current number of equations to process: 722
% Current number of ordered equations: 2
% Current number of rules: 110
% New rule produced :
% [131]
% commutator(multiply(X,X),commutator(Y,Z)) <->
% commutator(X,commutator(multiply(Y,Y),Z))
% Current number of equations to process: 722
% Current number of ordered equations: 1
% Current number of rules: 111
% New rule produced :
% [132]
% commutator(commutator(multiply(X,X),Y),Z) <->
% commutator(Z,commutator(multiply(Y,Y),X))
% Current number of equations to process: 722
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [133]
% commutator(X,commutator(multiply(Y,Y),Z)) <->
% commutator(commutator(Z,Y),multiply(X,X))
% Current number of equations to process: 794
% Current number of ordered equations: 1
% Current number of rules: 113
% New rule produced :
% [134]
% commutator(commutator(Z,Y),multiply(X,X)) <->
% commutator(X,commutator(multiply(Y,Y),Z))
% Current number of equations to process: 794
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [135]
% commutator(commutator(X,Y),multiply(Z,Z)) <->
% commutator(commutator(X,multiply(Y,Y)),Z)
% Current number of equations to process: 800
% Current number of ordered equations: 1
% Current number of rules: 115
% New rule produced :
% [136]
% commutator(commutator(X,multiply(Y,Y)),Z) <->
% commutator(commutator(X,Y),multiply(Z,Z))
% Current number of equations to process: 800
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [137]
% commutator(multiply(Z,Z),commutator(Y,X)) <->
% commutator(commutator(multiply(X,X),Y),Z)
% Current number of equations to process: 845
% Current number of ordered equations: 1
% Current number of rules: 117
% New rule produced :
% [138]
% commutator(commutator(multiply(X,X),Y),Z) <->
% commutator(multiply(Z,Z),commutator(Y,X))
% Current number of equations to process: 845
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [139]
% commutator(multiply(Z,Z),commutator(Y,X)) <->
% commutator(commutator(X,multiply(Y,Y)),Z)
% Current number of equations to process: 880
% Current number of ordered equations: 1
% Current number of rules: 119
% New rule produced :
% [140]
% commutator(commutator(X,multiply(Y,Y)),Z) <->
% commutator(multiply(Z,Z),commutator(Y,X))
% Current number of equations to process: 880
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [141]
% commutator(commutator(X,multiply(Y,Y)),Z) <->
% commutator(commutator(multiply(X,X),Y),Z)
% Current number of equations to process: 917
% Current number of ordered equations: 1
% Current number of rules: 121
% New rule produced :
% [142]
% commutator(commutator(multiply(X,X),Y),Z) <->
% commutator(commutator(X,multiply(Y,Y)),Z)
% Current number of equations to process: 917
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [143]
% commutator(X,commutator(Y,multiply(Z,Z))) <->
% commutator(multiply(X,X),commutator(Y,Z))
% Current number of equations to process: 923
% Current number of ordered equations: 1
% Current number of rules: 123
% New rule produced :
% [144]
% commutator(multiply(X,X),commutator(Y,Z)) <->
% commutator(X,commutator(Y,multiply(Z,Z)))
% Current number of equations to process: 923
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [145]
% commutator(Z,commutator(Y,multiply(X,X))) <->
% commutator(commutator(X,Y),multiply(Z,Z))
% Current number of equations to process: 946
% Current number of ordered equations: 1
% Current number of rules: 125
% New rule produced :
% [146]
% commutator(commutator(X,Y),multiply(Z,Z)) <->
% commutator(Z,commutator(Y,multiply(X,X)))
% Current number of equations to process: 946
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [147]
% commutator(X,commutator(multiply(Y,Y),Z)) <->
% commutator(X,commutator(Y,multiply(Z,Z)))
% Current number of equations to process: 1064
% Current number of ordered equations: 1
% Current number of rules: 127
% New rule produced :
% [148]
% commutator(X,commutator(Y,multiply(Z,Z))) <->
% commutator(X,commutator(multiply(Y,Y),Z))
% Current number of equations to process: 1064
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [149]
% commutator(commutator(commutator(X,Y),Z),commutator(commutator(Y,X),Z)) ->
% identity
% Current number of equations to process: 1067
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [150]
% commutator(commutator(X,commutator(Y,Z)),commutator(X,commutator(Z,Y))) ->
% identity
% Current number of equations to process: 1066
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [151]
% commutator(commutator(X,multiply(Y,Y)),multiply(Z,Z)) ->
% commutator(commutator(X,Y),Z)
% Current number of equations to process: 1065
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [152]
% commutator(commutator(multiply(X,X),Y),multiply(Z,Z)) ->
% commutator(commutator(X,Y),Z)
% Current number of equations to process: 1064
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [153]
% commutator(multiply(X,X),commutator(multiply(Y,Y),Z)) <->
% commutator(commutator(Z,Y),X)
% Current number of equations to process: 1063
% Current number of ordered equations: 1
% Current number of rules: 133
% New rule produced :
% [154]
% commutator(commutator(Z,Y),X) <->
% commutator(multiply(X,X),commutator(multiply(Y,Y),Z))
% Current number of equations to process: 1063
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [155]
% commutator(multiply(X,X),commutator(Y,multiply(Z,Z))) ->
% commutator(X,commutator(Y,Z))
% Current number of equations to process: 1062
% Current number of ordered equations: 0
% Current number of rules: 135
% Rule [154]
% commutator(commutator(Z,Y),X) <->
% commutator(multiply(X,X),commutator(multiply(Y,Y),Z)) is composed into
% [154] commutator(commutator(Z,Y),X) <-> commutator(X,commutator(Y,Z))
% New rule produced :
% [156]
% commutator(multiply(X,X),commutator(multiply(Y,Y),Z)) ->
% commutator(X,commutator(Y,Z))
% Rule
% [153]
% commutator(multiply(X,X),commutator(multiply(Y,Y),Z)) <->
% commutator(commutator(Z,Y),X) collapsed.
% Current number of equations to process: 1057
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [157]
% commutator(commutator(commutator(X,Y),Z),commutator(Z,commutator(Y,X))) ->
% identity
% Current number of equations to process: 1115
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [158]
% commutator(commutator(X,commutator(Y,Z)),commutator(commutator(Z,Y),X)) ->
% identity
% Current number of equations to process: 1188
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [159] commutator(X,multiply(Y,Y)) <-> commutator(multiply(X,X),Y)
% Rule
% [141]
% commutator(commutator(X,multiply(Y,Y)),Z) <->
% commutator(commutator(multiply(X,X),Y),Z) collapsed.
% Rule
% [148]
% commutator(X,commutator(Y,multiply(Z,Z))) <->
% commutator(X,commutator(multiply(Y,Y),Z)) collapsed.
% Current number of equations to process: 1417
% Current number of ordered equations: 1
% Current number of rules: 136
% New rule produced :
% [160] commutator(multiply(X,X),Y) <-> commutator(X,multiply(Y,Y))
% Rule
% [142]
% commutator(commutator(multiply(X,X),Y),Z) <->
% commutator(commutator(X,multiply(Y,Y)),Z) collapsed.
% Rule
% [147]
% commutator(X,commutator(multiply(Y,Y),Z)) <->
% commutator(X,commutator(Y,multiply(Z,Z))) collapsed.
% Current number of equations to process: 1417
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [161] commutator(X,multiply(X,multiply(X,commutator(Y,X)))) -> identity
% Rule
% [85]
% commutator(X,multiply(X,multiply(X,commutator(multiply(Y,Y),X)))) -> identity
% collapsed.
% Rule
% [118]
% commutator(X,multiply(X,multiply(X,commutator(commutator(Y,Z),X)))) ->
% identity collapsed.
% Current number of equations to process: 1434
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [162]
% multiply(X,commutator(Y,multiply(X,X))) <->
% multiply(Y,multiply(Y,multiply(X,Y)))
% Current number of equations to process: 1461
% Current number of ordered equations: 1
% Current number of rules: 135
% New rule produced :
% [163]
% multiply(Y,multiply(Y,multiply(X,Y))) <->
% multiply(X,commutator(Y,multiply(X,X)))
% Current number of equations to process: 1461
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [164] multiply(X,multiply(Y,commutator(X,multiply(Y,Y)))) -> multiply(Y,X)
% Current number of equations to process: 1460
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [165]
% multiply(X,commutator(X,multiply(Y,Y))) <->
% multiply(Y,multiply(X,multiply(Y,Y)))
% Current number of equations to process: 1459
% Current number of ordered equations: 1
% Current number of rules: 138
% New rule produced :
% [166]
% multiply(Y,multiply(X,multiply(Y,Y))) <->
% multiply(X,commutator(X,multiply(Y,Y)))
% Current number of equations to process: 1459
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [167]
% commutator(X,commutator(Y,multiply(Z,Z))) <->
% commutator(commutator(Z,multiply(Y,Y)),X)
% Current number of equations to process: 1458
% Current number of ordered equations: 1
% Current number of rules: 140
% New rule produced :
% [168]
% commutator(commutator(Z,multiply(Y,Y)),X) <->
% commutator(X,commutator(Y,multiply(Z,Z)))
% Current number of equations to process: 1458
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [169]
% commutator(X,multiply(X,multiply(X,commutator(Y,multiply(X,X))))) -> identity
% Current number of equations to process: 1458
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [170]
% commutator(Z,multiply(Y,multiply(X,X))) <->
% commutator(multiply(X,multiply(Y,Y)),Z)
% Current number of equations to process: 1511
% Current number of ordered equations: 1
% Current number of rules: 143
% New rule produced :
% [171]
% commutator(multiply(X,multiply(Y,Y)),Z) <->
% commutator(Z,multiply(Y,multiply(X,X)))
% Current number of equations to process: 1511
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [172]
% commutator(X,multiply(Y,multiply(Y,Z))) <->
% commutator(multiply(Z,multiply(Z,Y)),X)
% Current number of equations to process: 1583
% Current number of ordered equations: 1
% Current number of rules: 145
% New rule produced :
% [173]
% commutator(multiply(Z,multiply(Z,Y)),X) <->
% commutator(X,multiply(Y,multiply(Y,Z)))
% Current number of equations to process: 1583
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [174]
% commutator(multiply(X,multiply(Y,X)),multiply(Y,multiply(X,Y))) -> identity
% Current number of equations to process: 1587
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [175] commutator(multiply(X,multiply(Y,multiply(X,X))),Y) -> identity
% Current number of equations to process: 1715
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [176]
% commutator(commutator(X,multiply(Y,multiply(X,multiply(Y,Y)))),Z) -> identity
% Current number of equations to process: 1965
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [177]
% commutator(X,commutator(Y,multiply(Z,multiply(Y,multiply(Z,Z))))) -> identity
% Current number of equations to process: 1964
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [178]
% commutator(multiply(X,multiply(Y,X)),multiply(Y,multiply(Y,X))) -> identity
% Current number of equations to process: 1965
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [179] commutator(commutator(X,multiply(X,commutator(X,Y))),Z) -> identity
% Current number of equations to process: 1988
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [180] commutator(X,commutator(Y,multiply(Y,commutator(Y,Z)))) -> identity
% Current number of equations to process: 1987
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [181]
% commutator(multiply(X,X),multiply(X,commutator(Y,multiply(X,X)))) -> identity
% Current number of equations to process: 2031
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [182]
% commutator(commutator(X,multiply(Y,multiply(Y,multiply(X,Y)))),Z) -> identity
% Current number of equations to process: 2030
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [183]
% commutator(commutator(X,multiply(X,commutator(multiply(X,X),Y))),Z) ->
% identity
% Current number of equations to process: 2029
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [184]
% commutator(X,commutator(Y,multiply(Z,multiply(Z,multiply(Y,Z))))) -> identity
% Current number of equations to process: 2028
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [185]
% commutator(X,commutator(Y,multiply(Y,commutator(multiply(Y,Y),Z)))) ->
% identity
% Current number of equations to process: 2027
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [186] commutator(multiply(X,multiply(X,multiply(Y,X))),Y) -> identity
% Current number of equations to process: 2044
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [187]
% commutator(X,multiply(Y,multiply(Y,multiply(X,multiply(X,Y))))) -> identity
% Current number of equations to process: 2043
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [188]
% commutator(X,multiply(Y,multiply(X,multiply(Y,multiply(Y,X))))) -> identity
% Current number of equations to process: 2046
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [189]
% commutator(commutator(multiply(X,X),Y),commutator(multiply(Y,Y),X)) ->
% identity
% Current number of equations to process: 2084
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [190]
% commutator(commutator(X,multiply(Y,Y)),commutator(Y,multiply(X,X))) ->
% identity
% Current number of equations to process: 2220
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [191]
% commutator(X,multiply(X,multiply(X,commutator(multiply(X,X),Y)))) -> identity
% Current number of equations to process: 4354
% Current number of ordered equations: 0
% Current number of rules: 164
% New rule produced :
% [192]
% commutator(commutator(X,multiply(X,commutator(Y,multiply(X,X)))),Z) ->
% identity
% Current number of equations to process: 4353
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [193]
% commutator(X,commutator(Y,multiply(Y,commutator(Z,multiply(Y,Y))))) ->
% identity
% Current number of equations to process: 4352
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [194]
% commutator(X,multiply(X,multiply(Y,multiply(X,multiply(Y,Y))))) -> identity
% Current number of equations to process: 4351
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced :
% [195]
% multiply(X,commutator(X,multiply(X,multiply(Y,X)))) ->
% multiply(X,commutator(X,Y))
% Current number of equations to process: 4383
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced :
% [196]
% commutator(multiply(X,multiply(Y,Y)),multiply(Y,multiply(X,X))) -> identity
% Current number of equations to process: 4677
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced :
% [197]
% commutator(multiply(X,multiply(X,Y)),multiply(Y,multiply(Y,X))) -> identity
% Current number of equations to process: 4859
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced :
% [198]
% commutator(multiply(X,multiply(X,Y)),multiply(X,multiply(Y,Y))) -> identity
% Current number of equations to process: 1191
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [199]
% commutator(multiply(X,multiply(X,Y)),multiply(X,multiply(Y,X))) -> identity
% Current number of equations to process: 1280
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [200]
% commutator(X,commutator(commutator(Y,Z),V_3)) <->
% commutator(commutator(commutator(multiply(Y,Y),Z),V_3),X)
% Current number of equations to process: 1305
% Current number of ordered equations: 3
% Current number of rules: 173
% New rule produced :
% [201]
% commutator(X,commutator(commutator(Y,Z),multiply(V_3,V_3))) <->
% commutator(commutator(V_3,commutator(Z,Y)),X)
% Current number of equations to process: 1305
% Current number of ordered equations: 2
% Current number of rules: 174
% New rule produced :
% [202]
% commutator(commutator(commutator(multiply(Y,Y),Z),V_3),X) <->
% commutator(X,commutator(commutator(Y,Z),V_3))
% Current number of equations to process: 1305
% Current number of ordered equations: 1
% Current number of rules: 175
% New rule produced :
% [203]
% commutator(commutator(V_3,commutator(Z,Y)),X) <->
% commutator(X,commutator(commutator(Y,Z),multiply(V_3,V_3)))
% Current number of equations to process: 1305
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced :
% [204]
% commutator(commutator(X,Y),commutator(V_3,Z)) <->
% commutator(commutator(multiply(X,X),Y),commutator(Z,V_3))
% Current number of equations to process: 1303
% Current number of ordered equations: 3
% Current number of rules: 177
% New rule produced :
% [205]
% commutator(V_3,commutator(commutator(multiply(X,X),Y),Z)) <->
% commutator(commutator(commutator(X,Y),Z),V_3)
% Current number of equations to process: 1303
% Current number of ordered equations: 2
% Current number of rules: 178
% New rule produced :
% [206]
% commutator(commutator(commutator(X,Y),Z),V_3) <->
% commutator(V_3,commutator(commutator(multiply(X,X),Y),Z))
% Current number of equations to process: 1303
% Current number of ordered equations: 1
% Current number of rules: 179
% New rule produced :
% [207]
% commutator(commutator(multiply(X,X),Y),commutator(Z,V_3)) <->
% commutator(commutator(X,Y),commutator(V_3,Z))
% Rule
% [189]
% commutator(commutator(multiply(X,X),Y),commutator(multiply(Y,Y),X)) ->
% identity collapsed.
% Current number of equations to process: 1303
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [208]
% commutator(V_3,commutator(commutator(Z,Y),X)) <->
% commutator(commutator(X,commutator(multiply(Y,Y),Z)),V_3)
% Current number of equations to process: 1302
% Current number of ordered equations: 1
% Current number of rules: 180
% New rule produced :
% [209]
% commutator(commutator(X,commutator(multiply(Y,Y),Z)),V_3) <->
% commutator(V_3,commutator(commutator(Z,Y),X))
% Current number of equations to process: 1302
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [210]
% commutator(X,commutator(Y,commutator(multiply(Z,Z),V_3))) <->
% commutator(commutator(Y,commutator(Z,V_3)),X)
% Current number of equations to process: 1396
% Current number of ordered equations: 5
% Current number of rules: 182
% New rule produced :
% [211]
% commutator(commutator(X,Y),commutator(Z,V_3)) <->
% commutator(commutator(Y,X),commutator(multiply(Z,Z),V_3))
% Current number of equations to process: 1396
% Current number of ordered equations: 4
% Current number of rules: 183
% New rule produced :
% [212]
% commutator(V_3,commutator(multiply(Z,Z),commutator(Y,X))) <->
% commutator(commutator(commutator(X,Y),Z),V_3)
% Current number of equations to process: 1396
% Current number of ordered equations: 3
% Current number of rules: 184
% New rule produced :
% [213]
% commutator(commutator(Y,X),commutator(multiply(Z,Z),V_3)) <->
% commutator(commutator(X,Y),commutator(Z,V_3))
% Current number of equations to process: 1396
% Current number of ordered equations: 2
% Current number of rules: 185
% New rule produced :
% [214]
% commutator(commutator(commutator(X,Y),Z),V_3) <->
% commutator(V_3,commutator(multiply(Z,Z),commutator(Y,X)))
% Current number of equations to process: 1396
% Current number of ordered equations: 1
% Current number of rules: 186
% New rule produced :
% [215]
% commutator(commutator(Y,commutator(Z,V_3)),X) <->
% commutator(X,commutator(Y,commutator(multiply(Z,Z),V_3)))
% Current number of equations to process: 1396
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [216]
% commutator(V_3,commutator(X,commutator(Y,Z))) <->
% commutator(commutator(X,commutator(multiply(Y,Y),Z)),V_3)
% Current number of equations to process: 1440
% Current number of ordered equations: 1
% Current number of rules: 188
% New rule produced :
% [217]
% commutator(commutator(X,commutator(multiply(Y,Y),Z)),V_3) <->
% commutator(V_3,commutator(X,commutator(Y,Z)))
% Current number of equations to process: 1440
% Current number of ordered equations: 0
% Current number of rules: 189
% New rule produced :
% [218]
% commutator(X,commutator(commutator(Y,multiply(Z,Z)),V_3)) <->
% commutator(commutator(V_3,commutator(Z,Y)),X)
% Current number of equations to process: 1439
% Current number of ordered equations: 1
% Current number of rules: 190
% New rule produced :
% [219]
% commutator(commutator(V_3,commutator(Z,Y)),X) <->
% commutator(X,commutator(commutator(Y,multiply(Z,Z)),V_3))
% Current number of equations to process: 1439
% Current number of ordered equations: 0
% Current number of rules: 191
% New rule produced :
% [220]
% commutator(X,commutator(commutator(Y,multiply(Z,Z)),V_3)) <->
% commutator(commutator(commutator(Y,Z),V_3),X)
% Current number of equations to process: 1438
% Current number of ordered equations: 1
% Current number of rules: 192
% New rule produced :
% [221]
% commutator(commutator(commutator(Y,Z),V_3),X) <->
% commutator(X,commutator(commutator(Y,multiply(Z,Z)),V_3))
% Current number of equations to process: 1438
% Current number of ordered equations: 0
% Current number of rules: 193
% New rule produced :
% [222]
% commutator(X,commutator(Y,commutator(Z,V_3))) <->
% commutator(commutator(commutator(V_3,Z),multiply(Y,Y)),X)
% Current number of equations to process: 1435
% Current number of ordered equations: 5
% Current number of rules: 194
% New rule produced :
% [223]
% commutator(commutator(X,Y),commutator(Z,V_3)) <->
% commutator(commutator(X,multiply(Y,Y)),commutator(V_3,Z))
% Current number of equations to process: 1435
% Current number of ordered equations: 4
% Current number of rules: 195
% New rule produced :
% [224]
% commutator(V_3,commutator(commutator(X,Y),Z)) <->
% commutator(commutator(commutator(X,multiply(Y,Y)),Z),V_3)
% Current number of equations to process: 1435
% Current number of ordered equations: 3
% Current number of rules: 196
% New rule produced :
% [225]
% commutator(commutator(commutator(V_3,Z),multiply(Y,Y)),X) <->
% commutator(X,commutator(Y,commutator(Z,V_3)))
% Current number of equations to process: 1435
% Current number of ordered equations: 2
% Current number of rules: 197
% New rule produced :
% [226]
% commutator(commutator(X,multiply(Y,Y)),commutator(V_3,Z)) <->
% commutator(commutator(X,Y),commutator(Z,V_3))
% Current number of equations to process: 1435
% Current number of ordered equations: 1
% Current number of rules: 198
% New rule produced :
% [227]
% commutator(commutator(commutator(X,multiply(Y,Y)),Z),V_3) <->
% commutator(V_3,commutator(commutator(X,Y),Z))
% Current number of equations to process: 1435
% Current number of ordered equations: 0
% Current number of rules: 199
% New rule produced :
% [228] commutator(X,multiply(X,commutator(Y,X))) -> identity
% Rule
% [120] commutator(commutator(X,multiply(X,commutator(Y,X))),Z) -> identity
% collapsed.
% Rule
% [121] commutator(X,commutator(Y,multiply(Y,commutator(Z,Y)))) -> identity
% collapsed.
% Current number of equations to process: 1449
% Current number of ordered equations: 0
% Current number of rules: 198
% New rule produced :
% [229]
% commutator(multiply(X,multiply(Y,X)),multiply(X,multiply(Y,Y))) -> identity
% Current number of equations to process: 1451
% Current number of ordered equations: 0
% Current number of rules: 199
% New rule produced :
% [230]
% commutator(commutator(commutator(X,Y),Z),V_3) <->
% commutator(commutator(commutator(Y,X),Z),multiply(V_3,V_3))
% Current number of equations to process: 1483
% Current number of ordered equations: 1
% Current number of rules: 200
% New rule produced :
% [231]
% commutator(commutator(commutator(Y,X),Z),multiply(V_3,V_3)) <->
% commutator(commutator(commutator(X,Y),Z),V_3)
% Current number of equations to process: 1483
% Current number of ordered equations: 0
% Current number of rules: 201
% New rule produced :
% [232]
% commutator(commutator(X,commutator(Y,Z)),V_3) <->
% commutator(commutator(X,commutator(Z,Y)),multiply(V_3,V_3))
% Current number of equations to process: 1481
% Current number of ordered equations: 1
% Current number of rules: 202
% New rule produced :
% [233]
% commutator(commutator(X,commutator(Z,Y)),multiply(V_3,V_3)) <->
% commutator(commutator(X,commutator(Y,Z)),V_3)
% Current number of equations to process: 1481
% Current number of ordered equations: 0
% Current number of rules: 203
% New rule produced :
% [234]
% commutator(commutator(X,multiply(Y,Y)),commutator(Z,V_3)) <->
% commutator(commutator(V_3,Z),commutator(Y,X))
% Current number of equations to process: 1480
% Current number of ordered equations: 1
% Current number of rules: 204
% New rule produced :
% [235]
% commutator(commutator(V_3,Z),commutator(Y,X)) <->
% commutator(commutator(X,multiply(Y,Y)),commutator(Z,V_3))
% Current number of equations to process: 1480
% Current number of ordered equations: 0
% Current number of rules: 205
% New rule produced :
% [236]
% commutator(X,commutator(commutator(Y,Z),V_3)) <->
% commutator(commutator(multiply(V_3,V_3),commutator(Z,Y)),X)
% Current number of equations to process: 1480
% Current number of ordered equations: 1
% Current number of rules: 206
% New rule produced :
% [237]
% commutator(commutator(multiply(V_3,V_3),commutator(Z,Y)),X) <->
% commutator(X,commutator(commutator(Y,Z),V_3))
% Current number of equations to process: 1480
% Current number of ordered equations: 0
% Current number of rules: 207
% New rule produced :
% [238]
% commutator(X,commutator(Y,commutator(Z,V_3))) <->
% commutator(commutator(Y,commutator(Z,multiply(V_3,V_3))),X)
% Current number of equations to process: 1476
% Current number of ordered equations: 3
% Current number of rules: 208
% New rule produced :
% [239]
% commutator(commutator(X,Y),commutator(Z,multiply(V_3,V_3))) <->
% commutator(commutator(Y,X),commutator(Z,V_3))
% Current number of equations to process: 1476
% Current number of ordered equations: 2
% Current number of rules: 209
% New rule produced :
% [240]
% commutator(commutator(Y,X),commutator(Z,V_3)) <->
% commutator(commutator(X,Y),commutator(Z,multiply(V_3,V_3)))
% Current number of equations to process: 1476
% Current number of ordered equations: 1
% Current number of rules: 210
% New rule produced :
% [241]
% commutator(commutator(Y,commutator(Z,multiply(V_3,V_3))),X) <->
% commutator(X,commutator(Y,commutator(Z,V_3)))
% Current number of equations to process: 1476
% Current number of ordered equations: 0
% Current number of rules: 211
% New rule produced :
% [242]
% commutator(V_3,commutator(X,commutator(Y,multiply(Z,Z)))) <->
% commutator(commutator(X,commutator(Y,Z)),V_3)
% Current number of equations to process: 1474
% Current number of ordered equations: 1
% Current number of rules: 212
% New rule produced :
% [243]
% commutator(commutator(X,commutator(Y,Z)),V_3) <->
% commutator(V_3,commutator(X,commutator(Y,multiply(Z,Z))))
% Current number of equations to process: 1474
% Current number of ordered equations: 0
% Current number of rules: 213
% New rule produced :
% [244]
% commutator(X,commutator(commutator(Y,Z),V_3)) <->
% commutator(multiply(X,X),commutator(commutator(Z,Y),V_3))
% Current number of equations to process: 1472
% Current number of ordered equations: 1
% Current number of rules: 214
% New rule produced :
% [245]
% commutator(multiply(X,X),commutator(commutator(Z,Y),V_3)) <->
% commutator(X,commutator(commutator(Y,Z),V_3))
% Current number of equations to process: 1472
% Current number of ordered equations: 0
% Current number of rules: 215
% New rule produced :
% [246]
% commutator(X,commutator(Y,commutator(Z,V_3))) <->
% commutator(multiply(X,X),commutator(Y,commutator(V_3,Z)))
% Current number of equations to process: 1470
% Current number of ordered equations: 1
% Current number of rules: 216
% New rule produced :
% [247]
% commutator(multiply(X,X),commutator(Y,commutator(V_3,Z))) <->
% commutator(X,commutator(Y,commutator(Z,V_3)))
% Current number of equations to process: 1470
% Current number of ordered equations: 0
% Current number of rules: 217
% New rule produced :
% [248]
% commutator(commutator(X,Y),commutator(multiply(Z,Z),V_3)) <->
% commutator(commutator(V_3,Z),commutator(Y,X))
% Rule
% [125] commutator(commutator(X,Y),commutator(multiply(Y,Y),X)) -> identity
% collapsed.
% Current number of equations to process: 1469
% Current number of ordered equations: 1
% Current number of rules: 217
% New rule produced :
% [249]
% commutator(commutator(V_3,Z),commutator(Y,X)) <->
% commutator(commutator(X,Y),commutator(multiply(Z,Z),V_3))
% Current number of equations to process: 1469
% Current number of ordered equations: 0
% Current number of rules: 218
% New rule produced :
% [250]
% commutator(X,commutator(Y,commutator(multiply(Z,Z),V_3))) <->
% commutator(commutator(commutator(V_3,Z),Y),X)
% Current number of equations to process: 1467
% Current number of ordered equations: 1
% Current number of rules: 219
% New rule produced :
% [251]
% commutator(commutator(commutator(V_3,Z),Y),X) <->
% commutator(X,commutator(Y,commutator(multiply(Z,Z),V_3)))
% Current number of equations to process: 1467
% Current number of ordered equations: 0
% Current number of rules: 220
% New rule produced :
% [252]
% commutator(X,commutator(commutator(multiply(Y,Y),Z),V_3)) <->
% commutator(commutator(V_3,commutator(Z,Y)),X)
% Current number of equations to process: 1466
% Current number of ordered equations: 1
% Current number of rules: 221
% New rule produced :
% [253]
% commutator(commutator(V_3,commutator(Z,Y)),X) <->
% commutator(X,commutator(commutator(multiply(Y,Y),Z),V_3))
% Current number of equations to process: 1466
% Current number of ordered equations: 0
% Current number of rules: 222
% New rule produced :
% [254]
% commutator(commutator(X,Y),commutator(Z,V_3)) <->
% commutator(commutator(multiply(V_3,V_3),Z),commutator(Y,X))
% Current number of equations to process: 1465
% Current number of ordered equations: 1
% Current number of rules: 223
% New rule produced :
% [255]
% commutator(commutator(multiply(V_3,V_3),Z),commutator(Y,X)) <->
% commutator(commutator(X,Y),commutator(Z,V_3))
% Current number of equations to process: 1465
% Current number of ordered equations: 0
% Current number of rules: 224
% New rule produced :
% [256]
% commutator(V_3,commutator(commutator(Z,Y),X)) <->
% commutator(commutator(X,commutator(Y,multiply(Z,Z))),V_3)
% Current number of equations to process: 1448
% Current number of ordered equations: 1
% Current number of rules: 225
% New rule produced :
% [257]
% commutator(commutator(X,commutator(Y,multiply(Z,Z))),V_3) <->
% commutator(V_3,commutator(commutator(Z,Y),X))
% Current number of equations to process: 1448
% Current number of ordered equations: 0
% Current number of rules: 226
% New rule produced :
% [258]
% commutator(V_3,commutator(Z,commutator(Y,X))) <->
% commutator(commutator(commutator(X,multiply(Y,Y)),Z),V_3)
% Current number of equations to process: 1447
% Current number of ordered equations: 1
% Current number of rules: 227
% New rule produced :
% [259]
% commutator(commutator(commutator(X,multiply(Y,Y)),Z),V_3) <->
% commutator(V_3,commutator(Z,commutator(Y,X)))
% Current number of equations to process: 1447
% Current number of ordered equations: 0
% Current number of rules: 228
% New rule produced :
% [260]
% commutator(commutator(X,Y),commutator(Z,V_3)) <->
% commutator(commutator(V_3,Z),commutator(Y,multiply(X,X)))
% Current number of equations to process: 1446
% Current number of ordered equations: 1
% Current number of rules: 229
% New rule produced :
% [261]
% commutator(commutator(V_3,Z),commutator(Y,multiply(X,X))) <->
% commutator(commutator(X,Y),commutator(Z,V_3))
% Rule
% [128] commutator(commutator(X,Y),commutator(Y,multiply(X,X))) -> identity
% collapsed.
% Rule
% [190]
% commutator(commutator(X,multiply(Y,Y)),commutator(Y,multiply(X,X))) ->
% identity collapsed.
% Current number of equations to process: 1446
% Current number of ordered equations: 0
% Current number of rules: 228
% New rule produced :
% [262]
% commutator(X,commutator(Y,commutator(Z,multiply(V_3,V_3)))) <->
% commutator(commutator(commutator(V_3,Z),Y),X)
% Current number of equations to process: 1444
% Current number of ordered equations: 3
% Current number of rules: 229
% New rule produced :
% [263]
% commutator(V_3,commutator(Z,commutator(Y,X))) <->
% commutator(commutator(commutator(multiply(X,X),Y),Z),V_3)
% Current number of equations to process: 1444
% Current number of ordered equations: 2
% Current number of rules: 230
% New rule produced :
% [264]
% commutator(commutator(commutator(multiply(X,X),Y),Z),V_3) <->
% commutator(V_3,commutator(Z,commutator(Y,X)))
% Current number of equations to process: 1444
% Current number of ordered equations: 1
% Current number of rules: 231
% New rule produced :
% [265]
% commutator(commutator(commutator(V_3,Z),Y),X) <->
% commutator(X,commutator(Y,commutator(Z,multiply(V_3,V_3))))
% Current number of equations to process: 1444
% Current number of ordered equations: 0
% Current number of rules: 232
% New rule produced :
% [266]
% commutator(multiply(X,X),commutator(Y,commutator(Z,V_3))) <->
% commutator(commutator(commutator(V_3,Z),Y),X)
% Current number of equations to process: 1437
% Current number of ordered equations: 1
% Current number of rules: 233
% New rule produced :
% [267]
% commutator(commutator(commutator(V_3,Z),Y),X) <->
% commutator(multiply(X,X),commutator(Y,commutator(Z,V_3)))
% Current number of equations to process: 1437
% Current number of ordered equations: 0
% Current number of rules: 234
% New rule produced :
% [268]
% commutator(X,commutator(Y,commutator(Z,V_3))) <->
% commutator(commutator(commutator(V_3,Z),Y),multiply(X,X))
% Current number of equations to process: 1436
% Current number of ordered equations: 1
% Current number of rules: 235
% New rule produced :
% [269]
% commutator(commutator(commutator(V_3,Z),Y),multiply(X,X)) <->
% commutator(X,commutator(Y,commutator(Z,V_3)))
% Current number of equations to process: 1436
% Current number of ordered equations: 0
% Current number of rules: 236
% New rule produced :
% [270]
% commutator(V_3,commutator(commutator(Z,Y),X)) <->
% commutator(commutator(X,commutator(Y,Z)),multiply(V_3,V_3))
% Current number of equations to process: 1428
% Current number of ordered equations: 1
% Current number of rules: 237
% New rule produced :
% [271]
% commutator(commutator(X,commutator(Y,Z)),multiply(V_3,V_3)) <->
% commutator(V_3,commutator(commutator(Z,Y),X))
% Current number of equations to process: 1428
% Current number of ordered equations: 0
% Current number of rules: 238
% New rule produced :
% [272]
% commutator(multiply(V_3,V_3),commutator(commutator(Z,Y),X)) <->
% commutator(commutator(X,commutator(Y,Z)),V_3)
% Current number of equations to process: 1427
% Current number of ordered equations: 1
% Current number of rules: 239
% New rule produced :
% [273]
% commutator(commutator(X,commutator(Y,Z)),V_3) <->
% commutator(multiply(V_3,V_3),commutator(commutator(Z,Y),X))
% Current number of equations to process: 1427
% Current number of ordered equations: 0
% Current number of rules: 240
% New rule produced :
% [274]
% commutator(X,multiply(Y,multiply(Z,multiply(Y,Z)))) <->
% commutator(multiply(X,X),multiply(Y,Z))
% Current number of equations to process: 1391
% Current number of ordered equations: 1
% Current number of rules: 241
% New rule produced :
% [275]
% commutator(multiply(X,X),multiply(Y,Z)) <->
% commutator(X,multiply(Y,multiply(Z,multiply(Y,Z))))
% Current number of equations to process: 1391
% Current number of ordered equations: 0
% Current number of rules: 242
% New rule produced :
% [276]
% multiply(X,multiply(Y,commutator(Y,multiply(X,X)))) <->
% multiply(Y,multiply(X,commutator(Y,X)))
% Current number of equations to process: 1381
% Current number of ordered equations: 1
% Current number of rules: 243
% New rule produced :
% [277]
% multiply(Y,multiply(X,commutator(Y,X))) <->
% multiply(X,multiply(Y,commutator(Y,multiply(X,X))))
% Current number of equations to process: 1381
% Current number of ordered equations: 0
% Current number of rules: 244
% New rule produced :
% [278]
% commutator(multiply(X,Y),multiply(Z,Z)) <->
% commutator(multiply(X,multiply(Y,multiply(X,Y))),Z)
% Current number of equations to process: 1380
% Current number of ordered equations: 1
% Current number of rules: 245
% New rule produced :
% [279]
% commutator(multiply(X,multiply(Y,multiply(X,Y))),Z) <->
% commutator(multiply(X,Y),multiply(Z,Z))
% Current number of equations to process: 1380
% Current number of ordered equations: 0
% Current number of rules: 246
% New rule produced :
% [280]
% commutator(multiply(Y,X),multiply(Z,Z)) <->
% commutator(multiply(X,multiply(X,multiply(Y,Y))),Z)
% Current number of equations to process: 1369
% Current number of ordered equations: 1
% Current number of rules: 247
% New rule produced :
% [281]
% commutator(multiply(X,multiply(X,multiply(Y,Y))),Z) <->
% commutator(multiply(Y,X),multiply(Z,Z))
% Current number of equations to process: 1369
% Current number of ordered equations: 0
% Current number of rules: 248
% New rule produced :
% [282]
% commutator(Z,multiply(X,commutator(Y,X))) <->
% commutator(multiply(X,multiply(X,commutator(X,Y))),Z)
% Current number of equations to process: 1368
% Current number of ordered equations: 1
% Current number of rules: 249
% New rule produced :
% [283]
% commutator(multiply(X,multiply(X,commutator(X,Y))),Z) <->
% commutator(Z,multiply(X,commutator(Y,X)))
% Current number of equations to process: 1368
% Current number of ordered equations: 0
% Current number of rules: 250
% New rule produced :
% [284]
% commutator(X,multiply(Z,multiply(Z,multiply(Y,Y)))) <->
% commutator(multiply(X,X),multiply(Y,Z))
% Current number of equations to process: 1367
% Current number of ordered equations: 1
% Current number of rules: 251
% New rule produced :
% [285]
% commutator(multiply(X,X),multiply(Y,Z)) <->
% commutator(X,multiply(Z,multiply(Z,multiply(Y,Y))))
% Current number of equations to process: 1367
% Current number of ordered equations: 0
% Current number of rules: 252
% New rule produced :
% [286]
% commutator(multiply(Y,multiply(X,Y)),multiply(Z,Z)) <->
% commutator(multiply(X,multiply(Y,X)),Z)
% Current number of equations to process: 1366
% Current number of ordered equations: 1
% Current number of rules: 253
% New rule produced :
% [287]
% commutator(multiply(X,multiply(Y,X)),Z) <->
% commutator(multiply(Y,multiply(X,Y)),multiply(Z,Z))
% Current number of equations to process: 1366
% Current number of ordered equations: 0
% Current number of rules: 254
% New rule produced :
% [288]
% commutator(X,multiply(Z,multiply(Y,Z))) <->
% commutator(multiply(X,X),multiply(Y,multiply(Z,Y)))
% Current number of equations to process: 1364
% Current number of ordered equations: 1
% Current number of rules: 255
% New rule produced :
% [289]
% commutator(multiply(X,X),multiply(Y,multiply(Z,Y))) <->
% commutator(X,multiply(Z,multiply(Y,Z)))
% Current number of equations to process: 1364
% Current number of ordered equations: 0
% Current number of rules: 256
% New rule produced :
% [290]
% commutator(X,multiply(Y,multiply(Y,commutator(Y,Z)))) <->
% commutator(multiply(Y,commutator(Z,Y)),X)
% Rule [84] commutator(X,multiply(X,multiply(X,commutator(X,Y)))) -> identity
% collapsed.
% Current number of equations to process: 1364
% Current number of ordered equations: 1
% Current number of rules: 256
% New rule produced :
% [291]
% commutator(multiply(Y,commutator(Z,Y)),X) <->
% commutator(X,multiply(Y,multiply(Y,commutator(Y,Z))))
% Current number of equations to process: 1364
% Current number of ordered equations: 0
% Current number of rules: 257
% New rule produced :
% [292] commutator(X,multiply(X,multiply(Y,X))) -> commutator(X,Y)
% Rule
% [195]
% multiply(X,commutator(X,multiply(X,multiply(Y,X)))) ->
% multiply(X,commutator(X,Y)) collapsed.
% Current number of equations to process: 1458
% Current number of ordered equations: 0
% Current number of rules: 257
% New rule produced :
% [293]
% commutator(multiply(X,multiply(Y,Y)),multiply(X,multiply(Y,X))) -> identity
% Current number of equations to process: 1506
% Current number of ordered equations: 0
% Current number of rules: 258
% New rule produced :
% [294]
% commutator(multiply(X,multiply(Y,Y)),multiply(Y,multiply(Y,X))) -> identity
% Current number of equations to process: 1531
% Current number of ordered equations: 0
% Current number of rules: 259
% New rule produced :
% [295]
% multiply(X,multiply(Y,multiply(X,X))) <->
% multiply(Y,commutator(Y,multiply(X,multiply(Y,X))))
% Current number of equations to process: 1408
% Current number of ordered equations: 1
% Current number of rules: 260
% New rule produced :
% [296]
% multiply(Y,commutator(Y,multiply(X,multiply(Y,X)))) <->
% multiply(X,multiply(Y,multiply(X,X)))
% Current number of equations to process: 1408
% Current number of ordered equations: 0
% Current number of rules: 261
% New rule produced :
% [297]
% commutator(multiply(X,multiply(Y,Y)),Z) <->
% commutator(multiply(Y,multiply(X,X)),multiply(Z,Z))
% Current number of equations to process: 1386
% Current number of ordered equations: 1
% Current number of rules: 262
% New rule produced :
% [298]
% commutator(multiply(Y,multiply(X,X)),multiply(Z,Z)) <->
% commutator(multiply(X,multiply(Y,Y)),Z)
% Current number of equations to process: 1386
% Current number of ordered equations: 0
% Current number of rules: 263
% New rule produced :
% [299]
% commutator(X,multiply(Z,multiply(Y,Y))) <->
% commutator(multiply(X,X),multiply(Y,multiply(Z,Z)))
% Current number of equations to process: 1384
% Current number of ordered equations: 1
% Current number of rules: 264
% New rule produced :
% [300]
% commutator(multiply(X,X),multiply(Y,multiply(Z,Z))) <->
% commutator(X,multiply(Z,multiply(Y,Y)))
% Current number of equations to process: 1384
% Current number of ordered equations: 0
% Current number of rules: 265
% New rule produced :
% [301]
% commutator(multiply(Y,multiply(Y,X)),multiply(Z,Z)) <->
% commutator(multiply(X,multiply(X,Y)),Z)
% Current number of equations to process: 1381
% Current number of ordered equations: 1
% Current number of rules: 266
% New rule produced :
% [302]
% commutator(multiply(X,multiply(X,Y)),Z) <->
% commutator(multiply(Y,multiply(Y,X)),multiply(Z,Z))
% Current number of equations to process: 1381
% Current number of ordered equations: 0
% Current number of rules: 267
% New rule produced :
% [303]
% commutator(X,multiply(Y,multiply(Y,commutator(Z,Y)))) <->
% commutator(multiply(Y,commutator(Y,Z)),X)
% Rule [161] commutator(X,multiply(X,multiply(X,commutator(Y,X)))) -> identity
% collapsed.
% Current number of equations to process: 1380
% Current number of ordered equations: 1
% Current number of rules: 267
% New rule produced :
% [304]
% commutator(multiply(Y,commutator(Y,Z)),X) <->
% commutator(X,multiply(Y,multiply(Y,commutator(Z,Y))))
% Current number of equations to process: 1380
% Current number of ordered equations: 0
% Current number of rules: 268
% New rule produced :
% [305]
% commutator(X,multiply(Z,multiply(Z,Y))) <->
% commutator(multiply(X,X),multiply(Y,multiply(Y,Z)))
% Current number of equations to process: 1377
% Current number of ordered equations: 1
% Current number of rules: 269
% New rule produced :
% [306]
% commutator(multiply(X,X),multiply(Y,multiply(Y,Z))) <->
% commutator(X,multiply(Z,multiply(Z,Y)))
% Current number of equations to process: 1377
% Current number of ordered equations: 0
% Current number of rules: 270
% New rule produced :
% [307]
% commutator(Z,multiply(X,commutator(X,Y))) <->
% commutator(multiply(X,multiply(X,commutator(Y,X))),Z)
% Current number of equations to process: 1376
% Current number of ordered equations: 1
% Current number of rules: 271
% New rule produced :
% [308]
% commutator(multiply(X,multiply(X,commutator(Y,X))),Z) <->
% commutator(Z,multiply(X,commutator(X,Y)))
% Current number of equations to process: 1376
% Current number of ordered equations: 0
% Current number of rules: 272
% New rule produced :
% [309] commutator(X,multiply(X,commutator(X,commutator(Y,Z)))) -> identity
% Current number of equations to process: 4175
% Current number of ordered equations: 0
% Current number of rules: 273
% New rule produced :
% [310] commutator(X,multiply(X,commutator(X,Y))) -> identity
% Rule
% [179] commutator(commutator(X,multiply(X,commutator(X,Y))),Z) -> identity
% collapsed.
% Rule
% [180] commutator(X,commutator(Y,multiply(Y,commutator(Y,Z)))) -> identity
% collapsed.
% Rule
% [309] commutator(X,multiply(X,commutator(X,commutator(Y,Z)))) -> identity
% collapsed.
% Current number of equations to process: 4184
% Current number of ordered equations: 0
% Current number of rules: 271
% New rule produced :
% [311] commutator(X,multiply(Y,multiply(X,multiply(Y,Y)))) -> identity
% Rule
% [176]
% commutator(commutator(X,multiply(Y,multiply(X,multiply(Y,Y)))),Z) -> identity
% collapsed.
% Rule
% [177]
% commutator(X,commutator(Y,multiply(Z,multiply(Y,multiply(Z,Z))))) -> identity
% collapsed.
% Current number of equations to process: 4183
% Current number of ordered equations: 0
% Current number of rules: 270
% New rule produced :
% [312] commutator(X,multiply(Y,multiply(Y,multiply(X,Y)))) -> identity
% Rule
% [182]
% commutator(commutator(X,multiply(Y,multiply(Y,multiply(X,Y)))),Z) -> identity
% collapsed.
% Rule
% [184]
% commutator(X,commutator(Y,multiply(Z,multiply(Z,multiply(Y,Z))))) -> identity
% collapsed.
% Current number of equations to process: 4182
% Current number of ordered equations: 0
% Current number of rules: 269
% New rule produced :
% [313] commutator(X,multiply(X,commutator(multiply(X,X),Y))) -> identity
% Rule
% [183]
% commutator(commutator(X,multiply(X,commutator(multiply(X,X),Y))),Z) ->
% identity collapsed.
% Rule
% [185]
% commutator(X,commutator(Y,multiply(Y,commutator(multiply(Y,Y),Z)))) ->
% identity collapsed.
% Current number of equations to process: 4181
% Current number of ordered equations: 0
% Current number of rules: 268
% New rule produced :
% [314] commutator(X,multiply(X,commutator(Y,multiply(X,X)))) -> identity
% Rule
% [192]
% commutator(commutator(X,multiply(X,commutator(Y,multiply(X,X)))),Z) ->
% identity collapsed.
% Rule
% [193]
% commutator(X,commutator(Y,multiply(Y,commutator(Z,multiply(Y,Y))))) ->
% identity collapsed.
% Current number of equations to process: 4189
% Current number of ordered equations: 0
% Current number of rules: 267
% New rule produced :
% [315]
% commutator(multiply(X,multiply(Y,Y)),multiply(Y,multiply(X,Y))) -> identity
% Current number of equations to process: 4218
% Current number of ordered equations: 0
% Current number of rules: 268
% New rule produced :
% [316] commutator(multiply(X,multiply(Y,X)),Y) -> commutator(Y,X)
% Current number of equations to process: 3592
% Current number of ordered equations: 0
% Current number of rules: 269
% New rule produced :
% [317] commutator(multiply(X,X),multiply(Y,multiply(X,Y))) -> commutator(X,Y)
% Current number of equations to process: 3653
% Current number of ordered equations: 0
% Current number of rules: 270
% New rule produced :
% [318]
% commutator(X,multiply(X,multiply(Y,multiply(Z,X)))) ->
% commutator(X,multiply(Y,Z))
% Current number of equations to process: 3656
% Current number of ordered equations: 0
% Current number of rules: 271
% New rule produced :
% [319]
% commutator(multiply(X,multiply(Y,X)),multiply(Y,multiply(X,X))) -> identity
% Current number of equations to process: 3679
% Current number of ordered equations: 0
% Current number of rules: 272
% New rule produced :
% [320] commutator(multiply(X,X),multiply(X,multiply(Y,X))) -> commutator(Y,X)
% Current number of equations to process: 3811
% Current number of ordered equations: 0
% Current number of rules: 273
% New rule produced :
% [321]
% commutator(X,multiply(Y,multiply(X,multiply(X,commutator(X,Y))))) ->
% commutator(X,Y)
% Current number of equations to process: 3810
% Current number of ordered equations: 0
% Current number of rules: 274
% Rule [295]
% multiply(X,multiply(Y,multiply(X,X))) <->
% multiply(Y,commutator(Y,multiply(X,multiply(Y,X)))) is composed into
% [295] multiply(X,multiply(Y,multiply(X,X))) <-> multiply(Y,commutator(X,Y))
% New rule produced :
% [322]
% multiply(X,commutator(X,multiply(Y,multiply(X,Y)))) ->
% multiply(X,commutator(Y,X))
% Rule
% [296]
% multiply(Y,commutator(Y,multiply(X,multiply(Y,X)))) <->
% multiply(X,multiply(Y,multiply(X,X))) collapsed.
% Current number of equations to process: 3820
% Current number of ordered equations: 0
% Current number of rules: 274
% New rule produced :
% [323] commutator(Y,multiply(X,multiply(Y,X))) -> commutator(X,Y)
% Rule
% [322]
% multiply(X,commutator(X,multiply(Y,multiply(X,Y)))) ->
% multiply(X,commutator(Y,X)) collapsed.
% Current number of equations to process: 4037
% Current number of ordered equations: 0
% Current number of rules: 274
% New rule produced :
% [324]
% commutator(commutator(X,Y),multiply(X,Y)) <->
% commutator(commutator(X,Y),multiply(Y,X))
% Current number of equations to process: 4104
% Current number of ordered equations: 1
% Current number of rules: 275
% New rule produced :
% [325]
% commutator(commutator(X,Y),multiply(Y,X)) <->
% commutator(commutator(X,Y),multiply(X,Y))
% Current number of equations to process: 4104
% Current number of ordered equations: 0
% Current number of rules: 276
% New rule produced :
% [326]
% commutator(X,multiply(X,Y)) <-> commutator(X,multiply(Y,commutator(Y,X)))
% Current number of equations to process: 4114
% Current number of ordered equations: 1
% Current number of rules: 277
% New rule produced :
% [327]
% commutator(X,multiply(Y,commutator(Y,X))) <-> commutator(X,multiply(X,Y))
% Current number of equations to process: 4114
% Current number of ordered equations: 0
% Current number of rules: 278
% New rule produced :
% [328]
% commutator(X,multiply(Y,commutator(X,Y))) -> commutator(X,multiply(Y,X))
% Current number of equations to process: 4118
% Current number of ordered equations: 0
% Current number of rules: 279
% New rule produced :
% [329]
% commutator(X,multiply(Y,multiply(X,multiply(X,Y)))) ->
% commutator(X,multiply(Y,Y))
% Current number of equations to process: 4119
% Current number of ordered equations: 0
% Current number of rules: 280
% New rule produced :
% [330]
% commutator(X,multiply(X,Y)) <->
% commutator(X,multiply(Y,commutator(multiply(X,X),Y)))
% Current number of equations to process: 4118
% Current number of ordered equations: 1
% Current number of rules: 281
% New rule produced :
% [331]
% commutator(X,multiply(Y,commutator(multiply(X,X),Y))) <->
% commutator(X,multiply(X,Y))
% Current number of equations to process: 4118
% Current number of ordered equations: 0
% Current number of rules: 282
% New rule produced :
% [332]
% commutator(X,multiply(Y,commutator(multiply(Y,Y),X))) ->
% commutator(X,multiply(Y,X))
% Current number of equations to process: 4120
% Current number of ordered equations: 0
% Current number of rules: 283
% New rule produced :
% [333]
% commutator(X,multiply(X,Y)) <->
% commutator(X,multiply(Y,commutator(X,multiply(Y,Y))))
% Current number of equations to process: 4141
% Current number of ordered equations: 1
% Current number of rules: 284
% New rule produced :
% [334]
% commutator(X,multiply(Y,commutator(X,multiply(Y,Y)))) <->
% commutator(X,multiply(X,Y))
% Current number of equations to process: 4141
% Current number of ordered equations: 0
% Current number of rules: 285
% New rule produced :
% [335]
% commutator(X,multiply(Y,commutator(Y,multiply(X,X)))) ->
% commutator(X,multiply(Y,X))
% Current number of equations to process: 4140
% Current number of ordered equations: 0
% Current number of rules: 286
% New rule produced :
% [336]
% commutator(commutator(X,Y),multiply(X,multiply(Y,multiply(X,X)))) -> identity
% Current number of equations to process: 4291
% Current number of ordered equations: 0
% Current number of rules: 287
% New rule produced :
% [337]
% commutator(X,multiply(Y,multiply(Y,X))) ->
% commutator(multiply(Y,commutator(X,Y)),X)
% Current number of equations to process: 4372
% Current number of ordered equations: 0
% Current number of rules: 288
% New rule produced :
% [338] commutator(commutator(X,Y),multiply(Y,commutator(Y,X))) -> identity
% Current number of equations to process: 4425
% Current number of ordered equations: 0
% Current number of rules: 289
% New rule produced :
% [339]
% commutator(commutator(X,Y),multiply(Y,commutator(multiply(X,X),Y))) ->
% identity
% Current number of equations to process: 4647
% Current number of ordered equations: 0
% Current number of rules: 290
% New rule produced :
% [340]
% commutator(commutator(X,Y),multiply(Y,commutator(X,multiply(Y,Y)))) ->
% identity
% Current number of equations to process: 4646
% Current number of ordered equations: 0
% Current number of rules: 291
% New rule produced :
% [341]
% commutator(commutator(X,Y),multiply(X,multiply(X,multiply(Y,X)))) -> identity
% Current number of equations to process: 4645
% Current number of ordered equations: 0
% Current number of rules: 292
% New rule produced :
% [342]
% commutator(X,multiply(Y,multiply(X,X))) <->
% commutator(X,multiply(Y,commutator(Y,X)))
% Current number of equations to process: 4882
% Current number of ordered equations: 1
% Current number of rules: 293
% New rule produced :
% [343]
% commutator(X,multiply(Y,commutator(Y,X))) <->
% commutator(X,multiply(Y,multiply(X,X)))
% Current number of equations to process: 4882
% Current number of ordered equations: 0
% Current number of rules: 294
% New rule produced :
% [344] commutator(X,multiply(X,multiply(Y,Y))) -> commutator(multiply(X,Y),X)
% Current number of equations to process: 4908
% Current number of ordered equations: 0
% Current number of rules: 295
% New rule produced :
% [345] commutator(X,multiply(Y,X)) <-> commutator(X,multiply(X,multiply(X,Y)))
% Current number of equations to process: 2472
% Current number of ordered equations: 1
% Current number of rules: 296
% New rule produced :
% [346] commutator(X,multiply(X,multiply(X,Y))) <-> commutator(X,multiply(Y,X))
% Current number of equations to process: 2472
% Current number of ordered equations: 0
% Current number of rules: 297
% New rule produced : [347] commutator(X,commutator(Y,X)) -> identity
% Current number of equations to process: 2472
% Current number of ordered equations: 0
% Current number of rules: 298
% New rule produced :
% [348] commutator(commutator(X,Y),multiply(X,multiply(Y,X))) -> identity
% Current number of equations to process: 2475
% Current number of ordered equations: 0
% Current number of rules: 299
% New rule produced :
% [349] commutator(X,commutator(multiply(X,X),Y)) -> identity
% Current number of equations to process: 2482
% Current number of ordered equations: 0
% Current number of rules: 300
% New rule produced : [350] commutator(X,commutator(X,Y)) -> identity
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 2484
% Current number of ordered equations: 0
% Current number of rules: 301
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 38 rules have been used:
% [2]
% multiply(inverse(X),X) -> identity; trace = in the starting set
% [3] multiply(X,multiply(X,X)) -> identity; trace = in the starting set
% [4] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z)); trace = in the starting set
% [5] multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) ->
% commutator(X,Y); trace = in the starting set
% [6] multiply(inverse(Y),multiply(Y,X)) -> X; trace = Cp of 4 and 2
% [7] multiply(Y,multiply(Y,multiply(Y,X))) -> X; trace = Cp of 4 and 3
% [23] multiply(X,multiply(X,commutator(X,Y))) <->
% multiply(Y,multiply(X,multiply(X,multiply(Y,Y)))); trace = Cp of 6 and 5
% [24] multiply(Y,multiply(X,multiply(X,multiply(Y,Y)))) <->
% multiply(X,multiply(X,commutator(X,Y))); trace = Cp of 6 and 5
% [26] multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,multiply(Y,Z))))))
% -> Z; trace = Cp of 6 and 4
% [28] multiply(X,multiply(Y,multiply(X,multiply(Y,X)))) -> multiply(Y,Y); trace = Cp of 26 and 3
% [29] multiply(X,multiply(X,multiply(Y,Y))) <->
% multiply(Y,multiply(X,multiply(Y,X))); trace = Cp of 28 and 7
% [35] multiply(X,multiply(X,multiply(Y,multiply(X,Y)))) <->
% multiply(Y,multiply(Y,commutator(Y,X))); trace = Cp of 29 and 24
% [36] multiply(Y,multiply(Y,commutator(Y,X))) <->
% multiply(X,multiply(X,multiply(Y,multiply(X,Y)))); trace = Cp of 29 and 24
% [37] multiply(X,multiply(Y,multiply(Y,commutator(Y,X)))) <->
% multiply(Y,multiply(X,Y)); trace = Cp of 35 and 7
% [41] multiply(commutator(X,Y),Z) ->
% multiply(X,multiply(Y,multiply(X,multiply(X,multiply(Y,multiply(Y,Z)))))); trace = Cp of 5 and 4
% [46] multiply(Y,multiply(X,Y)) <->
% multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(X,X))))); trace = Cp of 37 and 23
% [47] multiply(X,multiply(X,multiply(Y,X))) <-> multiply(Y,commutator(Y,X)); trace = Cp of 46 and 29
% [48] multiply(Y,commutator(Y,X)) <-> multiply(X,multiply(X,multiply(Y,X))); trace = Cp of 46 and 29
% [50] multiply(X,multiply(Y,multiply(Y,X))) <->
% multiply(Y,multiply(X,multiply(X,Y))); trace = Cp of 47 and 46
% [52] multiply(Y,multiply(X,multiply(Y,Y))) <-> multiply(X,commutator(Y,X)); trace = Cp of 50 and 28
% [56] multiply(Y,multiply(X,X)) <->
% multiply(X,multiply(X,multiply(Y,commutator(X,Y)))); trace = Cp of 52 and 7
% [59] multiply(Y,multiply(X,commutator(multiply(Y,Y),X))) -> multiply(X,Y); trace = Self cp of 56
% [62] multiply(Y,commutator(multiply(X,X),Y)) <->
% multiply(X,multiply(X,multiply(Y,X))); trace = Cp of 59 and 7
% [63] multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(X,Y))))) ->
% commutator(X,Y); trace = Cp of 48 and 7
% [66] commutator(X,Y) <-> commutator(multiply(Y,Y),X); trace = Cp of 62 and 7
% [67] commutator(multiply(Y,Y),X) <-> commutator(X,Y); trace = Cp of 62 and 7
% [68] commutator(X,multiply(X,multiply(Y,multiply(Y,multiply(X,Y))))) ->
% identity; trace = Self cp of 63
% [78] commutator(commutator(X,Y),Z) <-> commutator(Z,commutator(Y,X)); trace = Cp of 67 and 41
% [79] commutator(multiply(X,X),multiply(Y,Y)) -> commutator(X,Y); trace = Cp of 67 and 66
% [84] commutator(X,multiply(X,multiply(X,commutator(X,Y)))) -> identity; trace = Cp of 68 and 47
% [107] commutator(Y,X) <-> commutator(X,multiply(Y,Y)); trace = Cp of 79 and 66
% [117] commutator(X,multiply(Y,multiply(Y,multiply(X,multiply(Y,X))))) ->
% identity; trace = Cp of 84 and 36
% [163] multiply(Y,multiply(Y,multiply(X,Y))) <->
% multiply(X,commutator(Y,multiply(X,X))); trace = Cp of 107 and 48
% [195] multiply(X,commutator(X,multiply(X,multiply(Y,X)))) ->
% multiply(X,commutator(X,Y)); trace = Self cp of 163
% [292] commutator(X,multiply(X,multiply(Y,X))) -> commutator(X,Y); trace = Cp of 195 and 7
% [318] commutator(X,multiply(X,multiply(Y,multiply(Z,X)))) ->
% commutator(X,multiply(Y,Z)); trace = Cp of 292 and 4
% [328] commutator(X,multiply(Y,commutator(X,Y))) ->
% commutator(X,multiply(Y,X)); trace = Cp of 318 and 52
% [350] commutator(X,commutator(X,Y)) -> identity; trace = Cp of 328 and 117
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 141.740000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------