%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP002-4 : TPTP v6.0.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n087.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 125.29s
% Output   : Refutation 125.29s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP002-4 : TPTP v6.0.0. Released v1.0.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n087.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 15:43:23 CDT 2014
% % CPUTime  : 125.29 
% Processing problem /tmp/CiME_50373_n087.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;
% multiply(X,identity) = X;
% multiply(X,inverse(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,
% multiply(X,identity) = X,
% multiply(X,inverse(X)) = identity,
% commutator(X,Y) =
% multiply(X,multiply(Y,multiply(inverse(X),
% inverse(Y)))),
% multiply(X,multiply(X,X)) = identity }
% (7 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(X,identity) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 1
% New rule produced : [2] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 2
% New rule produced : [3] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 3
% New rule produced : [4] multiply(inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 4
% New rule produced : [5] multiply(X,multiply(X,X)) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 5
% New rule produced :
% [6] 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: 6
% New rule produced :
% [7]
% 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: 7
% New rule produced : [8] inverse(identity) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [9] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [10] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] multiply(Y,multiply(Y,multiply(Y,X))) -> X
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] commutator(X,inverse(X)) -> identity
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [14] commutator(inverse(X),X) -> identity
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] commutator(identity,X) -> identity
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] inverse(inverse(X)) -> X
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] multiply(inverse(X),inverse(X)) -> X
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] inverse(X) -> multiply(X,X)
% Rule [3] multiply(X,inverse(X)) -> identity collapsed.
% Rule [4] multiply(inverse(X),X) -> identity collapsed.
% Rule
% [7]
% multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) -> commutator(X,Y)
% collapsed.
% Rule [8] inverse(identity) -> identity collapsed.
% Rule [9] multiply(Y,multiply(inverse(Y),X)) -> X collapsed.
% Rule [10] multiply(inverse(Y),multiply(Y,X)) -> X collapsed.
% Rule [12] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% collapsed.
% Rule [13] commutator(X,inverse(X)) -> identity collapsed.
% Rule [14] commutator(inverse(X),X) -> identity collapsed.
% Rule [16] inverse(inverse(X)) -> X collapsed.
% Rule [17] multiply(inverse(X),inverse(X)) -> X collapsed.
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [19]
% multiply(X,multiply(Y,multiply(X,multiply(X,multiply(Y,Y))))) ->
% commutator(X,Y)
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [20] commutator(X,multiply(X,X)) -> identity
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [21] commutator(multiply(X,X),X) -> identity
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [22]
% 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: 11
% New rule produced :
% [23]
% 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: 12
% New rule produced : [24] commutator(X,identity) -> identity
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [25] multiply(X,multiply(Y,multiply(X,multiply(Y,X)))) -> multiply(Y,Y)
% Rule
% [23]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,Y))))) -> identity
% collapsed.
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [26]
% multiply(X,multiply(X,multiply(Y,Y))) <->
% multiply(Y,multiply(X,multiply(Y,X)))
% Current number of equations to process: 20
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [27]
% multiply(Y,multiply(X,multiply(Y,X))) <->
% multiply(X,multiply(X,multiply(Y,Y)))
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [28]
% commutator(multiply(X,Y),multiply(X,multiply(Y,multiply(X,Y)))) -> identity
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [29]
% commutator(multiply(X,multiply(Y,multiply(X,Y))),multiply(X,Y)) -> identity
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [30]
% multiply(X,multiply(Y,multiply(X,commutator(Y,X)))) ->
% multiply(Y,multiply(X,X))
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [31]
% commutator(multiply(X,Y),multiply(Y,multiply(Y,multiply(X,X)))) -> identity
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [32] commutator(X,X) -> identity
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [33]
% commutator(multiply(X,multiply(X,multiply(Y,Y))),multiply(Y,X)) -> identity
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [34]
% multiply(X,multiply(X,commutator(X,Y))) <->
% multiply(Y,multiply(X,multiply(X,multiply(Y,Y))))
% Current number of equations to process: 38
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [35]
% multiply(Y,multiply(X,multiply(X,multiply(Y,Y)))) <->
% multiply(X,multiply(X,commutator(X,Y)))
% Current number of equations to process: 38
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [36]
% multiply(X,multiply(Y,multiply(Y,multiply(X,multiply(Y,X))))) ->
% commutator(X,Y)
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [37]
% multiply(X,multiply(X,multiply(Y,multiply(X,X)))) <->
% multiply(Y,multiply(X,commutator(Y,X)))
% Current number of equations to process: 51
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [38]
% multiply(Y,multiply(X,commutator(Y,X))) <->
% multiply(X,multiply(X,multiply(Y,multiply(X,X))))
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [39]
% multiply(X,multiply(X,multiply(Y,multiply(X,Y)))) <->
% multiply(Y,multiply(Y,commutator(Y,X)))
% Current number of equations to process: 59
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [40]
% multiply(Y,multiply(Y,commutator(Y,X))) <->
% multiply(X,multiply(X,multiply(Y,multiply(X,Y))))
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [41]
% multiply(X,multiply(Y,multiply(Y,commutator(Y,X)))) <->
% multiply(Y,multiply(X,Y))
% Current number of equations to process: 64
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [42]
% multiply(Y,multiply(X,Y)) <->
% multiply(X,multiply(Y,multiply(Y,commutator(Y,X))))
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [43]
% multiply(commutator(X,Y),Z) ->
% multiply(X,multiply(Y,multiply(X,multiply(X,multiply(Y,multiply(Y,Z))))))
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [44]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,Z))))) ->
% multiply(Y,multiply(Y,Z))
% Rule
% [22]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,multiply(Y,Z)))))) ->
% Z collapsed.
% Current number of equations to process: 129
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [45]
% multiply(X,multiply(Y,multiply(X,multiply(Y,Z)))) <->
% multiply(Y,multiply(Y,multiply(X,multiply(X,Z))))
% Current number of equations to process: 150
% Current number of ordered equations: 1
% Current number of rules: 32
% New rule produced :
% [46]
% multiply(Y,multiply(Y,multiply(X,multiply(X,Z)))) <->
% multiply(X,multiply(Y,multiply(X,multiply(Y,Z))))
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [47]
% multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(X,X))))) <->
% multiply(Y,multiply(X,Y))
% Current number of equations to process: 202
% Current number of ordered equations: 1
% Current number of rules: 34
% New rule produced :
% [48]
% multiply(Y,multiply(X,Y)) <->
% multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(X,X)))))
% Current number of equations to process: 202
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [49] multiply(X,multiply(X,multiply(Y,X))) <-> multiply(Y,commutator(Y,X))
% Current number of equations to process: 218
% Current number of ordered equations: 1
% Current number of rules: 36
% New rule produced :
% [50] multiply(Y,commutator(Y,X)) <-> multiply(X,multiply(X,multiply(Y,X)))
% Current number of equations to process: 218
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [51] multiply(X,multiply(Y,commutator(Y,X))) -> multiply(Y,X)
% Current number of equations to process: 224
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [52]
% multiply(X,multiply(Y,multiply(Y,X))) <->
% multiply(Y,multiply(X,multiply(X,Y)))
% Current number of equations to process: 249
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [53] multiply(X,commutator(Y,X)) <-> multiply(Y,multiply(X,multiply(Y,Y)))
% Current number of equations to process: 278
% Current number of ordered equations: 1
% Current number of rules: 40
% New rule produced :
% [54] multiply(Y,multiply(X,multiply(Y,Y))) <-> multiply(X,commutator(Y,X))
% Current number of equations to process: 278
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [55]
% multiply(X,multiply(Y,commutator(X,Y))) <->
% multiply(Y,multiply(X,commutator(Y,X)))
% Current number of equations to process: 278
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [56]
% multiply(X,multiply(X,multiply(Y,commutator(X,Y)))) <->
% multiply(Y,multiply(X,X))
% Current number of equations to process: 331
% Current number of ordered equations: 1
% Current number of rules: 43
% New rule produced :
% [57]
% multiply(Y,multiply(X,X)) <->
% multiply(X,multiply(X,multiply(Y,commutator(X,Y))))
% Current number of equations to process: 331
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [58]
% multiply(X,multiply(Y,multiply(Y,commutator(X,Y)))) ->
% multiply(Y,multiply(Y,X))
% Current number of equations to process: 330
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [59] multiply(Y,multiply(X,commutator(multiply(Y,Y),X))) -> multiply(X,Y)
% Current number of equations to process: 349
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [60]
% multiply(X,multiply(X,multiply(Y,X))) <->
% multiply(Y,commutator(multiply(X,X),Y))
% Current number of equations to process: 378
% Current number of ordered equations: 1
% Current number of rules: 47
% New rule produced :
% [61]
% multiply(Y,commutator(multiply(X,X),Y)) <->
% multiply(X,multiply(X,multiply(Y,X)))
% Current number of equations to process: 378
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [62] multiply(X,commutator(X,Y)) <-> multiply(X,commutator(multiply(Y,Y),X))
% Current number of equations to process: 400
% Current number of ordered equations: 1
% Current number of rules: 49
% New rule produced :
% [63] multiply(X,commutator(multiply(Y,Y),X)) <-> multiply(X,commutator(X,Y))
% Current number of equations to process: 400
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced : [64] commutator(Y,X) <-> commutator(multiply(X,X),Y)
% Rule
% [62] multiply(X,commutator(X,Y)) <-> multiply(X,commutator(multiply(Y,Y),X))
% collapsed.
% Current number of equations to process: 416
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [65]
% multiply(X,commutator(multiply(X,X),Y)) <->
% multiply(Y,multiply(X,multiply(Y,Y)))
% Current number of equations to process: 438
% Current number of ordered equations: 1
% Current number of rules: 51
% New rule produced :
% [66]
% multiply(Y,multiply(X,multiply(Y,Y))) <->
% multiply(X,commutator(multiply(X,X),Y))
% Current number of equations to process: 438
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [67]
% multiply(X,commutator(multiply(X,X),multiply(Y,Y))) ->
% multiply(X,commutator(X,Y))
% Current number of equations to process: 440
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [68] commutator(multiply(X,X),multiply(Y,Y)) -> commutator(X,Y)
% Rule
% [67]
% multiply(X,commutator(multiply(X,X),multiply(Y,Y))) ->
% multiply(X,commutator(X,Y)) collapsed.
% Current number of equations to process: 463
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced : [69] commutator(X,multiply(Y,Y)) <-> commutator(Y,X)
% Rule [20] commutator(X,multiply(X,X)) -> identity collapsed.
% Current number of equations to process: 469
% Current number of ordered equations: 1
% Current number of rules: 53
% New rule produced : [70] commutator(Y,X) <-> commutator(X,multiply(Y,Y))
% Current number of equations to process: 469
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [71] commutator(X,multiply(Y,Y)) <-> commutator(multiply(X,X),Y)
% Current number of equations to process: 487
% Current number of ordered equations: 1
% Current number of rules: 55
% New rule produced :
% [72] commutator(multiply(X,X),Y) <-> commutator(X,multiply(Y,Y))
% Rule [21] commutator(multiply(X,X),X) -> identity collapsed.
% Current number of equations to process: 487
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [73]
% multiply(X,commutator(Y,multiply(X,X))) <->
% multiply(Y,multiply(Y,multiply(X,Y)))
% Current number of equations to process: 502
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [74]
% multiply(Y,multiply(Y,multiply(X,Y))) <->
% multiply(X,commutator(Y,multiply(X,X)))
% Current number of equations to process: 502
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [75] multiply(X,multiply(Y,commutator(X,multiply(Y,Y)))) -> multiply(Y,X)
% Current number of equations to process: 504
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [76]
% multiply(X,commutator(X,multiply(Y,Y))) <->
% multiply(Y,multiply(X,multiply(Y,Y)))
% Current number of equations to process: 503
% Current number of ordered equations: 1
% Current number of rules: 59
% New rule produced :
% [77]
% multiply(Y,multiply(X,multiply(Y,Y))) <->
% multiply(X,commutator(X,multiply(Y,Y)))
% Current number of equations to process: 503
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [78]
% commutator(X,multiply(Y,multiply(Z,multiply(Y,Z)))) <->
% commutator(multiply(Y,Z),X)
% Rule
% [28]
% commutator(multiply(X,Y),multiply(X,multiply(Y,multiply(X,Y)))) -> identity
% collapsed.
% Current number of equations to process: 500
% Current number of ordered equations: 1
% Current number of rules: 60
% New rule produced :
% [79]
% commutator(multiply(Y,Z),X) <->
% commutator(X,multiply(Y,multiply(Z,multiply(Y,Z))))
% Current number of equations to process: 500
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [80]
% commutator(X,multiply(Y,multiply(Y,multiply(Z,Z)))) <->
% commutator(multiply(Z,Y),X)
% Current number of equations to process: 565
% Current number of ordered equations: 1
% Current number of rules: 62
% New rule produced :
% [81]
% commutator(multiply(Z,Y),X) <->
% commutator(X,multiply(Y,multiply(Y,multiply(Z,Z))))
% Current number of equations to process: 565
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [82]
% multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(X,Y))))) ->
% commutator(X,Y)
% Current number of equations to process: 568
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [83]
% multiply(X,multiply(Y,multiply(X,multiply(X,Y)))) <->
% multiply(Y,multiply(Y,commutator(X,Y)))
% Current number of equations to process: 570
% Current number of ordered equations: 1
% Current number of rules: 65
% New rule produced :
% [84]
% multiply(Y,multiply(Y,commutator(X,Y))) <->
% multiply(X,multiply(Y,multiply(X,multiply(X,Y))))
% Current number of equations to process: 570
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [85]
% multiply(Y,multiply(X,multiply(Y,multiply(X,multiply(X,Y))))) ->
% commutator(X,Y)
% Current number of equations to process: 569
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [86]
% multiply(X,multiply(X,multiply(Y,multiply(X,multiply(Y,Y))))) ->
% commutator(Y,X)
% Current number of equations to process: 568
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [87]
% multiply(X,multiply(X,commutator(Y,X))) <->
% multiply(Y,multiply(Y,multiply(X,multiply(X,Y))))
% Current number of equations to process: 567
% Current number of ordered equations: 1
% Current number of rules: 69
% New rule produced :
% [88]
% multiply(Y,multiply(Y,multiply(X,multiply(X,Y)))) <->
% multiply(X,multiply(X,commutator(Y,X)))
% Current number of equations to process: 567
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [89] commutator(Z,commutator(Y,X)) <-> commutator(commutator(X,Y),Z)
% Current number of equations to process: 574
% Current number of ordered equations: 1
% Current number of rules: 71
% New rule produced :
% [90] 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: 574
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [91]
% commutator(Z,multiply(Y,X)) <->
% commutator(multiply(X,multiply(X,multiply(Y,Y))),Z)
% Current number of equations to process: 579
% Current number of ordered equations: 1
% Current number of rules: 73
% New rule produced :
% [92]
% commutator(multiply(X,multiply(X,multiply(Y,Y))),Z) <->
% commutator(Z,multiply(Y,X))
% Current number of equations to process: 579
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [93]
% commutator(Z,multiply(Y,multiply(X,Y))) <->
% commutator(multiply(X,multiply(Y,X)),Z)
% Current number of equations to process: 587
% Current number of ordered equations: 1
% Current number of rules: 75
% New rule produced :
% [94]
% commutator(multiply(X,multiply(Y,X)),Z) <->
% commutator(Z,multiply(Y,multiply(X,Y)))
% Current number of equations to process: 587
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [95]
% multiply(X,multiply(Y,commutator(X,Y))) <->
% multiply(Y,multiply(X,commutator(multiply(X,X),Y)))
% Current number of equations to process: 631
% Current number of ordered equations: 1
% Current number of rules: 77
% New rule produced :
% [96]
% multiply(Y,multiply(X,commutator(multiply(X,X),Y))) <->
% multiply(X,multiply(Y,commutator(X,Y)))
% Current number of equations to process: 631
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [97]
% commutator(Z,multiply(Y,multiply(X,X))) <->
% commutator(multiply(X,multiply(Y,Y)),Z)
% Current number of equations to process: 644
% Current number of ordered equations: 1
% Current number of rules: 79
% New rule produced :
% [98]
% commutator(multiply(X,multiply(Y,Y)),Z) <->
% commutator(Z,multiply(Y,multiply(X,X)))
% Current number of equations to process: 644
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [99]
% commutator(Z,multiply(X,Y)) <->
% commutator(multiply(X,multiply(Y,multiply(X,Y))),Z)
% Current number of equations to process: 643
% Current number of ordered equations: 1
% Current number of rules: 81
% New rule produced :
% [100]
% commutator(multiply(X,multiply(Y,multiply(X,Y))),Z) <->
% commutator(Z,multiply(X,Y))
% Rule
% [29]
% commutator(multiply(X,multiply(Y,multiply(X,Y))),multiply(X,Y)) -> identity
% collapsed.
% Current number of equations to process: 643
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [101]
% commutator(X,multiply(X,multiply(Y,multiply(Y,multiply(X,Y))))) -> identity
% Current number of equations to process: 688
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [102]
% commutator(X,multiply(Y,multiply(X,multiply(X,multiply(Y,Y))))) -> identity
% Current number of equations to process: 691
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [103]
% multiply(X,multiply(Y,commutator(Y,multiply(X,X)))) <->
% multiply(Y,multiply(X,commutator(Y,X)))
% Current number of equations to process: 685
% Current number of ordered equations: 1
% Current number of rules: 84
% New rule produced :
% [104]
% multiply(Y,multiply(X,commutator(Y,X))) <->
% multiply(X,multiply(Y,commutator(Y,multiply(X,X))))
% Current number of equations to process: 685
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [105]
% commutator(X,multiply(Y,multiply(Z,multiply(Y,Z)))) <->
% commutator(multiply(X,X),multiply(Y,Z))
% Current number of equations to process: 684
% Current number of ordered equations: 1
% Current number of rules: 86
% New rule produced :
% [106]
% commutator(multiply(X,X),multiply(Y,Z)) <->
% commutator(X,multiply(Y,multiply(Z,multiply(Y,Z))))
% Current number of equations to process: 684
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [107]
% commutator(multiply(X,Y),multiply(Z,Z)) <->
% commutator(multiply(X,multiply(Y,multiply(X,Y))),Z)
% Current number of equations to process: 683
% Current number of ordered equations: 1
% Current number of rules: 88
% New rule produced :
% [108]
% commutator(multiply(X,multiply(Y,multiply(X,Y))),Z) <->
% commutator(multiply(X,Y),multiply(Z,Z))
% Current number of equations to process: 683
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [109]
% commutator(X,multiply(Z,multiply(Z,multiply(Y,Y)))) <->
% commutator(multiply(X,X),multiply(Y,Z))
% Current number of equations to process: 680
% Current number of ordered equations: 1
% Current number of rules: 90
% New rule produced :
% [110]
% commutator(multiply(X,X),multiply(Y,Z)) <->
% commutator(X,multiply(Z,multiply(Z,multiply(Y,Y))))
% Current number of equations to process: 680
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [111] commutator(Y,multiply(X,multiply(Y,Y))) <-> commutator(multiply(X,X),Y)
% Current number of equations to process: 722
% Current number of ordered equations: 1
% Current number of rules: 92
% New rule produced :
% [112] commutator(multiply(X,X),Y) <-> commutator(Y,multiply(X,multiply(Y,Y)))
% Current number of equations to process: 722
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [113]
% multiply(X,multiply(Y,multiply(Y,multiply(X,multiply(X,Y))))) ->
% commutator(Y,X)
% Current number of equations to process: 740
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [114] commutator(commutator(X,Y),commutator(Y,X)) -> identity
% Current number of equations to process: 781
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [115]
% commutator(X,commutator(multiply(Y,Y),Z)) <-> commutator(commutator(Y,Z),X)
% Current number of equations to process: 802
% Current number of ordered equations: 1
% Current number of rules: 96
% New rule produced :
% [116]
% commutator(commutator(Y,Z),X) <-> commutator(X,commutator(multiply(Y,Y),Z))
% Current number of equations to process: 802
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [117]
% commutator(X,commutator(Y,Z)) <-> commutator(commutator(multiply(Y,Y),Z),X)
% Current number of equations to process: 801
% Current number of ordered equations: 1
% Current number of rules: 98
% New rule produced :
% [118]
% commutator(commutator(multiply(Y,Y),Z),X) <-> commutator(X,commutator(Y,Z))
% Current number of equations to process: 801
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [119]
% commutator(X,commutator(Y,multiply(Z,Z))) <-> commutator(commutator(Y,Z),X)
% Current number of equations to process: 799
% Current number of ordered equations: 3
% Current number of rules: 100
% New rule produced :
% [120]
% commutator(commutator(X,Y),multiply(Z,Z)) <-> commutator(commutator(Y,X),Z)
% Current number of equations to process: 799
% Current number of ordered equations: 2
% Current number of rules: 101
% New rule produced :
% [121]
% commutator(commutator(Y,X),Z) <-> commutator(commutator(X,Y),multiply(Z,Z))
% Current number of equations to process: 799
% Current number of ordered equations: 1
% Current number of rules: 102
% New rule produced :
% [122]
% commutator(commutator(Y,Z),X) <-> commutator(X,commutator(Y,multiply(Z,Z)))
% Current number of equations to process: 799
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [123]
% commutator(X,commutator(Z,Y)) <-> commutator(multiply(X,X),commutator(Y,Z))
% Current number of equations to process: 819
% Current number of ordered equations: 1
% Current number of rules: 104
% New rule produced :
% [124]
% commutator(multiply(X,X),commutator(Y,Z)) <-> commutator(X,commutator(Z,Y))
% Current number of equations to process: 819
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [125]
% commutator(Z,commutator(X,Y)) <-> commutator(commutator(X,multiply(Y,Y)),Z)
% Current number of equations to process: 817
% Current number of ordered equations: 1
% Current number of rules: 106
% New rule produced :
% [126]
% commutator(commutator(X,multiply(Y,Y)),Z) <-> commutator(Z,commutator(X,Y))
% Current number of equations to process: 817
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [127]
% commutator(X,commutator(commutator(Y,Z),V_3)) <->
% commutator(commutator(commutator(Z,Y),V_3),X)
% Current number of equations to process: 821
% Current number of ordered equations: 1
% Current number of rules: 108
% New rule produced :
% [128]
% commutator(commutator(commutator(Z,Y),V_3),X) <->
% commutator(X,commutator(commutator(Y,Z),V_3))
% Current number of equations to process: 821
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [129]
% commutator(X,commutator(multiply(Y,Y),Z)) <->
% commutator(commutator(multiply(Z,Z),Y),X)
% Current number of equations to process: 820
% Current number of ordered equations: 1
% Current number of rules: 110
% New rule produced :
% [130]
% commutator(commutator(multiply(Z,Z),Y),X) <->
% commutator(X,commutator(multiply(Y,Y),Z))
% Current number of equations to process: 820
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [131]
% commutator(X,commutator(Y,multiply(Z,Z))) <->
% commutator(commutator(Z,multiply(Y,Y)),X)
% Current number of equations to process: 819
% Current number of ordered equations: 1
% Current number of rules: 112
% New rule produced :
% [132]
% commutator(commutator(Z,multiply(Y,Y)),X) <->
% commutator(X,commutator(Y,multiply(Z,Z)))
% Current number of equations to process: 819
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [133]
% commutator(V_3,commutator(X,commutator(Z,Y))) <->
% commutator(commutator(X,commutator(Y,Z)),V_3)
% Current number of equations to process: 818
% Current number of ordered equations: 1
% Current number of rules: 114
% New rule produced :
% [134]
% commutator(commutator(X,commutator(Y,Z)),V_3) <->
% commutator(V_3,commutator(X,commutator(Z,Y)))
% Current number of equations to process: 818
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [135]
% commutator(commutator(X,Y),commutator(Z,V_3)) <->
% commutator(commutator(Y,X),commutator(V_3,Z))
% Current number of equations to process: 813
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [136]
% commutator(multiply(X,multiply(Y,X)),multiply(Y,multiply(X,Y))) -> identity
% Current number of equations to process: 901
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [137]
% commutator(X,multiply(Y,multiply(Y,commutator(Y,Z)))) <->
% commutator(multiply(Y,commutator(Z,Y)),X)
% Current number of equations to process: 954
% Current number of ordered equations: 1
% Current number of rules: 118
% New rule produced :
% [138]
% commutator(multiply(Y,commutator(Z,Y)),X) <->
% commutator(X,multiply(Y,multiply(Y,commutator(Y,Z))))
% Current number of equations to process: 954
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [139]
% commutator(multiply(X,Y),multiply(Z,Z)) <->
% commutator(multiply(Y,multiply(Y,multiply(X,X))),Z)
% Current number of equations to process: 953
% Current number of ordered equations: 1
% Current number of rules: 120
% New rule produced :
% [140]
% commutator(multiply(Y,multiply(Y,multiply(X,X))),Z) <->
% commutator(multiply(X,Y),multiply(Z,Z))
% Current number of equations to process: 953
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [141]
% commutator(multiply(Y,multiply(X,Y)),Z) <->
% commutator(multiply(X,multiply(Y,X)),multiply(Z,Z))
% Current number of equations to process: 952
% Current number of ordered equations: 1
% Current number of rules: 122
% New rule produced :
% [142]
% commutator(multiply(X,multiply(Y,X)),multiply(Z,Z)) <->
% commutator(multiply(Y,multiply(X,Y)),Z)
% Current number of equations to process: 952
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [143]
% commutator(X,multiply(Z,multiply(Y,Z))) <->
% commutator(multiply(X,X),multiply(Y,multiply(Z,Y)))
% Current number of equations to process: 951
% Current number of ordered equations: 1
% Current number of rules: 124
% New rule produced :
% [144]
% commutator(multiply(X,X),multiply(Y,multiply(Z,Y))) <->
% commutator(X,multiply(Z,multiply(Y,Z)))
% Current number of equations to process: 951
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [145]
% commutator(multiply(X,multiply(Y,Y)),multiply(Y,multiply(X,X))) -> identity
% Current number of equations to process: 994
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [146] commutator(multiply(X,X),multiply(X,commutator(Y,X))) -> identity
% Current number of equations to process: 1146
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [147]
% commutator(X,multiply(X,multiply(X,commutator(multiply(Y,Y),X)))) -> identity
% Current number of equations to process: 1147
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [148]
% commutator(X,multiply(X,multiply(X,commutator(Y,multiply(X,X))))) -> identity
% Current number of equations to process: 1146
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [149] commutator(multiply(X,multiply(Y,multiply(X,X))),Y) -> identity
% Current number of equations to process: 1148
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [150]
% commutator(X,multiply(Y,multiply(Y,multiply(X,multiply(Y,X))))) -> identity
% Current number of equations to process: 1150
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [151]
% commutator(multiply(X,multiply(Y,Y)),multiply(Z,Z)) <->
% commutator(multiply(Y,multiply(X,X)),Z)
% Current number of equations to process: 1162
% Current number of ordered equations: 1
% Current number of rules: 132
% New rule produced :
% [152]
% commutator(multiply(Y,multiply(X,X)),Z) <->
% commutator(multiply(X,multiply(Y,Y)),multiply(Z,Z))
% Current number of equations to process: 1162
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [153]
% commutator(X,multiply(Z,multiply(Y,Y))) <->
% commutator(multiply(X,X),multiply(Y,multiply(Z,Z)))
% Current number of equations to process: 1161
% Current number of ordered equations: 1
% Current number of rules: 134
% New rule produced :
% [154]
% commutator(multiply(X,X),multiply(Y,multiply(Z,Z))) <->
% commutator(X,multiply(Z,multiply(Y,Y)))
% Current number of equations to process: 1161
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [155] commutator(multiply(X,multiply(Y,Y)),X) -> commutator(multiply(Y,Y),X)
% Current number of equations to process: 1458
% Current number of ordered equations: 0
% Current number of rules: 136
% Rule [112]
% commutator(multiply(X,X),Y) <-> commutator(Y,multiply(X,multiply(Y,Y))) is composed into 
% [112] commutator(multiply(X,X),Y) <-> commutator(Y,X)
% New rule produced :
% [156] commutator(X,multiply(Y,multiply(X,X))) -> commutator(X,Y)
% Rule
% [111] commutator(Y,multiply(X,multiply(Y,Y))) <-> commutator(multiply(X,X),Y)
% collapsed.
% Current number of equations to process: 1467
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [157] commutator(X,commutator(X,multiply(Y,Y))) -> identity
% Current number of equations to process: 1469
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [158]
% commutator(commutator(X,Y),multiply(Z,commutator(Y,X))) <->
% commutator(multiply(Z,Z),commutator(X,Y))
% Current number of equations to process: 1474
% Current number of ordered equations: 1
% Current number of rules: 138
% New rule produced :
% [159]
% commutator(multiply(Z,Z),commutator(X,Y)) <->
% commutator(commutator(X,Y),multiply(Z,commutator(Y,X)))
% Current number of equations to process: 1474
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [160] commutator(commutator(X,Y),commutator(Y,multiply(X,X))) -> identity
% Current number of equations to process: 1490
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [161] commutator(commutator(X,Y),commutator(multiply(Y,Y),X)) -> identity
% Current number of equations to process: 1489
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [162]
% commutator(commutator(X,Y),multiply(Z,Z)) <->
% commutator(commutator(multiply(X,X),Y),Z)
% Current number of equations to process: 1551
% Current number of ordered equations: 1
% Current number of rules: 142
% New rule produced :
% [163]
% commutator(commutator(multiply(X,X),Y),Z) <->
% commutator(commutator(X,Y),multiply(Z,Z))
% Current number of equations to process: 1551
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [164]
% commutator(X,commutator(multiply(Y,Y),Z)) <->
% commutator(multiply(X,X),commutator(Y,Z))
% Current number of equations to process: 1571
% Current number of ordered equations: 1
% Current number of rules: 144
% New rule produced :
% [165]
% commutator(multiply(X,X),commutator(Y,Z)) <->
% commutator(X,commutator(multiply(Y,Y),Z))
% Current number of equations to process: 1571
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [166]
% commutator(commutator(X,Y),multiply(Z,Z)) <->
% commutator(commutator(X,multiply(Y,Y)),Z)
% Current number of equations to process: 1729
% Current number of ordered equations: 1
% Current number of rules: 146
% New rule produced :
% [167]
% commutator(commutator(X,multiply(Y,Y)),Z) <->
% commutator(commutator(X,Y),multiply(Z,Z))
% Current number of equations to process: 1729
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [168]
% commutator(multiply(X,X),commutator(Y,Z)) <->
% commutator(commutator(Z,multiply(Y,Y)),X)
% Current number of equations to process: 1782
% Current number of ordered equations: 1
% Current number of rules: 148
% New rule produced :
% [169]
% commutator(commutator(Z,multiply(Y,Y)),X) <->
% commutator(multiply(X,X),commutator(Y,Z))
% Current number of equations to process: 1782
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [170]
% commutator(X,commutator(multiply(Y,Y),Z)) <->
% commutator(commutator(Z,Y),multiply(X,X))
% Current number of equations to process: 1838
% Current number of ordered equations: 1
% Current number of rules: 150
% New rule produced :
% [171]
% commutator(commutator(Z,Y),multiply(X,X)) <->
% commutator(X,commutator(multiply(Y,Y),Z))
% Current number of equations to process: 1838
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [172]
% commutator(X,commutator(Y,multiply(Z,Z))) <->
% commutator(multiply(X,X),commutator(Y,Z))
% Current number of equations to process: 1856
% Current number of ordered equations: 1
% Current number of rules: 152
% New rule produced :
% [173]
% commutator(multiply(X,X),commutator(Y,Z)) <->
% commutator(X,commutator(Y,multiply(Z,Z)))
% Current number of equations to process: 1856
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [174] commutator(X,commutator(Y,multiply(Y,commutator(Z,Y)))) -> identity
% Current number of equations to process: 1874
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [175]
% commutator(Z,commutator(Y,multiply(X,X))) <->
% commutator(commutator(X,Y),multiply(Z,Z))
% Current number of equations to process: 1899
% Current number of ordered equations: 1
% Current number of rules: 155
% New rule produced :
% [176]
% commutator(commutator(X,Y),multiply(Z,Z)) <->
% commutator(Z,commutator(Y,multiply(X,X)))
% Current number of equations to process: 1899
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [177]
% commutator(multiply(Z,Z),commutator(Y,X)) <->
% commutator(commutator(multiply(X,X),Y),Z)
% Current number of equations to process: 1958
% Current number of ordered equations: 1
% Current number of rules: 157
% New rule produced :
% [178]
% commutator(commutator(multiply(X,X),Y),Z) <->
% commutator(multiply(Z,Z),commutator(Y,X))
% Current number of equations to process: 1958
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [179] commutator(commutator(X,multiply(X,commutator(Y,X))),Z) -> identity
% Current number of equations to process: 2038
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [180]
% commutator(commutator(multiply(X,X),Y),commutator(multiply(Y,Y),X)) ->
% identity
% Current number of equations to process: 2122
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [181]
% commutator(commutator(X,multiply(Y,Y)),commutator(Y,multiply(X,X))) ->
% identity
% Current number of equations to process: 2121
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [182]
% commutator(commutator(commutator(X,Y),Z),commutator(commutator(Y,X),Z)) ->
% identity
% Current number of equations to process: 2120
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [183]
% commutator(commutator(X,commutator(Y,Z)),commutator(X,commutator(Z,Y))) ->
% identity
% Current number of equations to process: 2119
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [184]
% commutator(commutator(multiply(X,X),Y),multiply(Z,Z)) ->
% commutator(commutator(X,Y),Z)
% Current number of equations to process: 2118
% Current number of ordered equations: 0
% Current number of rules: 164
% New rule produced :
% [185]
% commutator(multiply(X,X),commutator(multiply(Y,Y),Z)) ->
% commutator(X,commutator(Y,Z))
% Current number of equations to process: 2117
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [186]
% commutator(commutator(X,multiply(Y,Y)),multiply(Z,Z)) ->
% commutator(commutator(X,Y),Z)
% Current number of equations to process: 2112
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [187]
% commutator(multiply(X,X),commutator(Y,multiply(Z,Z))) ->
% commutator(X,commutator(Y,Z))
% Current number of equations to process: 2105
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced :
% [188]
% commutator(X,commutator(Y,multiply(Z,multiply(Y,multiply(Z,Z))))) -> identity
% Current number of equations to process: 2103
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced :
% [189]
% commutator(commutator(X,multiply(Y,multiply(X,multiply(Y,Y)))),Z) -> identity
% Current number of equations to process: 2093
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced :
% [190]
% commutator(commutator(commutator(X,Y),Z),commutator(Z,commutator(Y,X))) ->
% identity
% Current number of equations to process: 2188
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced :
% [191]
% commutator(commutator(X,commutator(Y,Z)),commutator(commutator(Z,Y),X)) ->
% identity
% Current number of equations to process: 2304
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [192]
% commutator(commutator(commutator(multiply(Y,Y),Z),V_3),X) <->
% commutator(X,commutator(commutator(Y,Z),V_3))
% Current number of equations to process: 2927
% Current number of ordered equations: 3
% Current number of rules: 172
% New rule produced :
% [193]
% commutator(X,commutator(commutator(Y,Z),V_3)) <->
% commutator(commutator(commutator(multiply(Y,Y),Z),V_3),X)
% Current number of equations to process: 2927
% Current number of ordered equations: 2
% Current number of rules: 173
% New rule produced :
% [194]
% 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: 2927
% Current number of ordered equations: 1
% Current number of rules: 174
% New rule produced :
% [195]
% 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: 2927
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced :
% [196]
% commutator(commutator(X,Y),commutator(V_3,Z)) <->
% commutator(commutator(multiply(X,X),Y),commutator(Z,V_3))
% Current number of equations to process: 2925
% Current number of ordered equations: 3
% Current number of rules: 176
% New rule produced :
% [197]
% commutator(V_3,commutator(commutator(multiply(X,X),Y),Z)) <->
% commutator(commutator(commutator(X,Y),Z),V_3)
% Current number of equations to process: 2925
% Current number of ordered equations: 2
% Current number of rules: 177
% New rule produced :
% [198]
% commutator(commutator(commutator(X,Y),Z),V_3) <->
% commutator(V_3,commutator(commutator(multiply(X,X),Y),Z))
% Current number of equations to process: 2925
% Current number of ordered equations: 1
% Current number of rules: 178
% New rule produced :
% [199]
% commutator(commutator(multiply(X,X),Y),commutator(Z,V_3)) <->
% commutator(commutator(X,Y),commutator(V_3,Z))
% Rule
% [180]
% commutator(commutator(multiply(X,X),Y),commutator(multiply(Y,Y),X)) ->
% identity collapsed.
% Current number of equations to process: 2925
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [200]
% commutator(X,commutator(Y,commutator(multiply(Z,Z),V_3))) <->
% commutator(commutator(Y,commutator(Z,V_3)),X)
% Current number of equations to process: 2922
% Current number of ordered equations: 5
% Current number of rules: 179
% New rule produced :
% [201]
% commutator(commutator(X,Y),commutator(Z,V_3)) <->
% commutator(commutator(Y,X),commutator(multiply(Z,Z),V_3))
% Current number of equations to process: 2922
% Current number of ordered equations: 4
% Current number of rules: 180
% New rule produced :
% [202]
% commutator(V_3,commutator(multiply(Z,Z),commutator(Y,X))) <->
% commutator(commutator(commutator(X,Y),Z),V_3)
% Current number of equations to process: 2922
% Current number of ordered equations: 3
% Current number of rules: 181
% New rule produced :
% [203]
% commutator(commutator(Y,X),commutator(multiply(Z,Z),V_3)) <->
% commutator(commutator(X,Y),commutator(Z,V_3))
% Current number of equations to process: 2922
% Current number of ordered equations: 2
% Current number of rules: 182
% New rule produced :
% [204]
% commutator(commutator(Y,commutator(Z,V_3)),X) <->
% commutator(X,commutator(Y,commutator(multiply(Z,Z),V_3)))
% Current number of equations to process: 2922
% Current number of ordered equations: 1
% Current number of rules: 183
% New rule produced :
% [205]
% commutator(commutator(commutator(X,Y),Z),V_3) <->
% commutator(V_3,commutator(multiply(Z,Z),commutator(Y,X)))
% Current number of equations to process: 2922
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [206]
% commutator(V_3,commutator(X,commutator(Y,Z))) <->
% commutator(commutator(X,commutator(multiply(Y,Y),Z)),V_3)
% Current number of equations to process: 2921
% Current number of ordered equations: 1
% Current number of rules: 185
% New rule produced :
% [207]
% commutator(commutator(X,commutator(multiply(Y,Y),Z)),V_3) <->
% commutator(V_3,commutator(X,commutator(Y,Z)))
% Current number of equations to process: 2921
% Current number of ordered equations: 0
% Current number of rules: 186
% 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: 2920
% Current number of ordered equations: 1
% Current number of rules: 187
% 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: 2920
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [210]
% 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: 2918
% Current number of ordered equations: 1
% Current number of rules: 189
% New rule produced :
% [211]
% 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: 2918
% Current number of ordered equations: 0
% Current number of rules: 190
% New rule produced :
% [212]
% commutator(X,commutator(Y,commutator(multiply(Z,Z),V_3))) <->
% commutator(commutator(commutator(V_3,Z),Y),X)
% Current number of equations to process: 2915
% Current number of ordered equations: 1
% Current number of rules: 191
% New rule produced :
% [213]
% commutator(commutator(commutator(V_3,Z),Y),X) <->
% commutator(X,commutator(Y,commutator(multiply(Z,Z),V_3)))
% Current number of equations to process: 2915
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced :
% [214]
% commutator(V_3,commutator(Z,commutator(Y,X))) <->
% commutator(commutator(commutator(X,Y),multiply(Z,Z)),V_3)
% Current number of equations to process: 2912
% Current number of ordered equations: 1
% Current number of rules: 193
% New rule produced :
% [215]
% commutator(commutator(commutator(X,Y),multiply(Z,Z)),V_3) <->
% commutator(V_3,commutator(Z,commutator(Y,X)))
% Current number of equations to process: 2912
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [216]
% commutator(commutator(commutator(Y,multiply(Z,Z)),V_3),X) <->
% commutator(X,commutator(commutator(Y,Z),V_3))
% Current number of equations to process: 2910
% Current number of ordered equations: 1
% Current number of rules: 195
% New rule produced :
% [217]
% commutator(X,commutator(commutator(Y,Z),V_3)) <->
% commutator(commutator(commutator(Y,multiply(Z,Z)),V_3),X)
% Current number of equations to process: 2910
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [218]
% commutator(commutator(X,Y),commutator(V_3,Z)) <->
% commutator(commutator(X,multiply(Y,Y)),commutator(Z,V_3))
% Current number of equations to process: 2907
% Current number of ordered equations: 3
% Current number of rules: 197
% New rule produced :
% [219]
% commutator(V_3,commutator(commutator(X,multiply(Y,Y)),Z)) <->
% commutator(commutator(commutator(X,Y),Z),V_3)
% Current number of equations to process: 2907
% Current number of ordered equations: 2
% Current number of rules: 198
% New rule produced :
% [220]
% commutator(commutator(commutator(X,Y),Z),V_3) <->
% commutator(V_3,commutator(commutator(X,multiply(Y,Y)),Z))
% Current number of equations to process: 2907
% Current number of ordered equations: 1
% Current number of rules: 199
% New rule produced :
% [221]
% commutator(commutator(X,multiply(Y,Y)),commutator(Z,V_3)) <->
% commutator(commutator(X,Y),commutator(V_3,Z))
% Current number of equations to process: 2907
% Current number of ordered equations: 0
% Current number of rules: 200
% New rule produced :
% [222]
% commutator(commutator(commutator(Y,X),Z),V_3) <->
% commutator(commutator(commutator(X,Y),Z),multiply(V_3,V_3))
% Current number of equations to process: 2903
% Current number of ordered equations: 1
% Current number of rules: 201
% New rule produced :
% [223]
% commutator(commutator(commutator(X,Y),Z),multiply(V_3,V_3)) <->
% commutator(commutator(commutator(Y,X),Z),V_3)
% Current number of equations to process: 2903
% Current number of ordered equations: 0
% Current number of rules: 202
% New rule produced :
% [224]
% commutator(commutator(X,commutator(Z,Y)),V_3) <->
% commutator(commutator(X,commutator(Y,Z)),multiply(V_3,V_3))
% Current number of equations to process: 2901
% Current number of ordered equations: 1
% Current number of rules: 203
% New rule produced :
% [225]
% commutator(commutator(X,commutator(Y,Z)),multiply(V_3,V_3)) <->
% commutator(commutator(X,commutator(Z,Y)),V_3)
% Current number of equations to process: 2901
% Current number of ordered equations: 0
% Current number of rules: 204
% New rule produced :
% [226]
% commutator(commutator(multiply(X,X),Y),commutator(Z,V_3)) <->
% commutator(commutator(V_3,Z),commutator(Y,X))
% Current number of equations to process: 2894
% Current number of ordered equations: 1
% Current number of rules: 205
% New rule produced :
% [227]
% commutator(commutator(V_3,Z),commutator(Y,X)) <->
% commutator(commutator(multiply(X,X),Y),commutator(Z,V_3))
% Current number of equations to process: 2894
% Current number of ordered equations: 0
% Current number of rules: 206
% New rule produced :
% [228]
% commutator(X,commutator(Y,commutator(Z,multiply(V_3,V_3)))) <->
% commutator(commutator(Y,commutator(Z,V_3)),X)
% Current number of equations to process: 2892
% Current number of ordered equations: 3
% Current number of rules: 207
% New rule produced :
% [229]
% commutator(commutator(X,Y),commutator(Z,V_3)) <->
% commutator(commutator(Y,X),commutator(Z,multiply(V_3,V_3)))
% Current number of equations to process: 2892
% Current number of ordered equations: 2
% Current number of rules: 208
% New rule produced :
% [230]
% commutator(commutator(Y,X),commutator(Z,multiply(V_3,V_3))) <->
% commutator(commutator(X,Y),commutator(Z,V_3))
% Current number of equations to process: 2892
% Current number of ordered equations: 1
% Current number of rules: 209
% New rule produced :
% [231]
% commutator(commutator(Y,commutator(Z,V_3)),X) <->
% commutator(X,commutator(Y,commutator(Z,multiply(V_3,V_3))))
% Current number of equations to process: 2892
% Current number of ordered equations: 0
% Current number of rules: 210
% New rule produced :
% [232]
% commutator(V_3,commutator(X,commutator(Y,Z))) <->
% commutator(commutator(X,commutator(Y,multiply(Z,Z))),V_3)
% Current number of equations to process: 2890
% Current number of ordered equations: 1
% Current number of rules: 211
% New rule produced :
% [233]
% commutator(commutator(X,commutator(Y,multiply(Z,Z))),V_3) <->
% commutator(V_3,commutator(X,commutator(Y,Z)))
% Current number of equations to process: 2890
% Current number of ordered equations: 0
% Current number of rules: 212
% New rule produced :
% [234]
% commutator(V_3,commutator(commutator(Z,Y),X)) <->
% commutator(commutator(X,commutator(Y,multiply(Z,Z))),V_3)
% Current number of equations to process: 2889
% Current number of ordered equations: 1
% Current number of rules: 213
% New rule produced :
% [235]
% commutator(commutator(X,commutator(Y,multiply(Z,Z))),V_3) <->
% commutator(V_3,commutator(commutator(Z,Y),X))
% Current number of equations to process: 2889
% Current number of ordered equations: 0
% Current number of rules: 214
% New rule produced :
% [236]
% 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: 2887
% Current number of ordered equations: 3
% Current number of rules: 215
% New rule produced :
% [237]
% commutator(V_3,commutator(Z,commutator(Y,X))) <->
% commutator(commutator(commutator(multiply(X,X),Y),Z),V_3)
% Current number of equations to process: 2887
% Current number of ordered equations: 2
% Current number of rules: 216
% New rule produced :
% [238]
% commutator(commutator(commutator(multiply(X,X),Y),Z),V_3) <->
% commutator(V_3,commutator(Z,commutator(Y,X)))
% Current number of equations to process: 2887
% Current number of ordered equations: 1
% Current number of rules: 217
% New rule produced :
% [239]
% 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: 2887
% Current number of ordered equations: 0
% Current number of rules: 218
% New rule produced :
% [240]
% commutator(X,commutator(commutator(Y,Z),V_3)) <->
% commutator(multiply(X,X),commutator(commutator(Z,Y),V_3))
% Current number of equations to process: 2883
% Current number of ordered equations: 1
% Current number of rules: 219
% New rule produced :
% [241]
% commutator(multiply(X,X),commutator(commutator(Z,Y),V_3)) <->
% commutator(X,commutator(commutator(Y,Z),V_3))
% Current number of equations to process: 2883
% Current number of ordered equations: 0
% Current number of rules: 220
% New rule produced :
% [242]
% commutator(X,commutator(Y,commutator(Z,V_3))) <->
% commutator(multiply(X,X),commutator(Y,commutator(V_3,Z)))
% Current number of equations to process: 2881
% Current number of ordered equations: 1
% Current number of rules: 221
% New rule produced :
% [243]
% commutator(multiply(X,X),commutator(Y,commutator(V_3,Z))) <->
% commutator(X,commutator(Y,commutator(Z,V_3)))
% Current number of equations to process: 2881
% Current number of ordered equations: 0
% Current number of rules: 222
% New rule produced :
% [244]
% commutator(commutator(X,Y),commutator(multiply(Z,Z),V_3)) <->
% commutator(commutator(V_3,Z),commutator(Y,X))
% Rule
% [161] commutator(commutator(X,Y),commutator(multiply(Y,Y),X)) -> identity
% collapsed.
% Current number of equations to process: 2880
% Current number of ordered equations: 1
% Current number of rules: 222
% New rule produced :
% [245]
% commutator(commutator(V_3,Z),commutator(Y,X)) <->
% commutator(commutator(X,Y),commutator(multiply(Z,Z),V_3))
% Current number of equations to process: 2880
% Current number of ordered equations: 0
% Current number of rules: 223
% New rule produced :
% [246]
% commutator(commutator(X,Y),commutator(Z,multiply(V_3,V_3))) <->
% commutator(commutator(V_3,Z),commutator(Y,X))
% Rule
% [160] commutator(commutator(X,Y),commutator(Y,multiply(X,X))) -> identity
% collapsed.
% Rule
% [181]
% commutator(commutator(X,multiply(Y,Y)),commutator(Y,multiply(X,X))) ->
% identity collapsed.
% Current number of equations to process: 2879
% Current number of ordered equations: 1
% Current number of rules: 222
% New rule produced :
% [247]
% commutator(commutator(V_3,Z),commutator(Y,X)) <->
% commutator(commutator(X,Y),commutator(Z,multiply(V_3,V_3)))
% Current number of equations to process: 2879
% Current number of ordered equations: 0
% Current number of rules: 223
% New rule produced :
% [248]
% commutator(X,commutator(commutator(multiply(Y,Y),Z),V_3)) <->
% commutator(commutator(V_3,commutator(Z,Y)),X)
% Current number of equations to process: 2868
% Current number of ordered equations: 1
% Current number of rules: 224
% New rule produced :
% [249]
% commutator(commutator(V_3,commutator(Z,Y)),X) <->
% commutator(X,commutator(commutator(multiply(Y,Y),Z),V_3))
% Current number of equations to process: 2868
% Current number of ordered equations: 0
% Current number of rules: 225
% New rule produced :
% [250]
% commutator(commutator(X,Y),commutator(Z,V_3)) <->
% commutator(commutator(V_3,multiply(Z,Z)),commutator(Y,X))
% Current number of equations to process: 2867
% Current number of ordered equations: 1
% Current number of rules: 226
% New rule produced :
% [251]
% commutator(commutator(V_3,multiply(Z,Z)),commutator(Y,X)) <->
% commutator(commutator(X,Y),commutator(Z,V_3))
% Current number of equations to process: 2867
% Current number of ordered equations: 0
% Current number of rules: 227
% New rule produced :
% [252]
% commutator(V_3,commutator(Z,commutator(Y,X))) <->
% commutator(commutator(commutator(X,multiply(Y,Y)),Z),V_3)
% Current number of equations to process: 2866
% Current number of ordered equations: 1
% Current number of rules: 228
% New rule produced :
% [253]
% commutator(commutator(commutator(X,multiply(Y,Y)),Z),V_3) <->
% commutator(V_3,commutator(Z,commutator(Y,X)))
% Current number of equations to process: 2866
% Current number of ordered equations: 0
% Current number of rules: 229
% New rule produced :
% [254]
% commutator(X,commutator(commutator(Y,multiply(Z,Z)),V_3)) <->
% commutator(commutator(V_3,commutator(Z,Y)),X)
% Current number of equations to process: 2865
% Current number of ordered equations: 1
% Current number of rules: 230
% New rule produced :
% [255]
% commutator(commutator(V_3,commutator(Z,Y)),X) <->
% commutator(X,commutator(commutator(Y,multiply(Z,Z)),V_3))
% Current number of equations to process: 2865
% Current number of ordered equations: 0
% Current number of rules: 231
% New rule produced :
% [256]
% commutator(multiply(X,X),commutator(Y,commutator(Z,V_3))) <->
% commutator(commutator(commutator(V_3,Z),Y),X)
% Current number of equations to process: 2849
% Current number of ordered equations: 1
% Current number of rules: 232
% New rule produced :
% [257]
% commutator(commutator(commutator(V_3,Z),Y),X) <->
% commutator(multiply(X,X),commutator(Y,commutator(Z,V_3)))
% Current number of equations to process: 2849
% Current number of ordered equations: 0
% Current number of rules: 233
% New rule produced :
% [258]
% commutator(X,commutator(Y,commutator(Z,V_3))) <->
% commutator(commutator(commutator(V_3,Z),Y),multiply(X,X))
% Current number of equations to process: 2848
% Current number of ordered equations: 1
% Current number of rules: 234
% New rule produced :
% [259]
% commutator(commutator(commutator(V_3,Z),Y),multiply(X,X)) <->
% commutator(X,commutator(Y,commutator(Z,V_3)))
% Current number of equations to process: 2848
% Current number of ordered equations: 0
% Current number of rules: 235
% New rule produced :
% [260]
% 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: 2836
% Current number of ordered equations: 1
% Current number of rules: 236
% New rule produced :
% [261]
% 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: 2836
% Current number of ordered equations: 0
% Current number of rules: 237
% New rule produced :
% [262]
% 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: 2835
% Current number of ordered equations: 1
% Current number of rules: 238
% New rule produced :
% [263]
% 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: 2835
% Current number of ordered equations: 0
% Current number of rules: 239
% New rule produced :
% [264] commutator(multiply(X,X),multiply(X,commutator(X,Y))) -> identity
% Current number of equations to process: 3288
% Current number of ordered equations: 0
% Current number of rules: 240
% New rule produced :
% [265]
% commutator(multiply(X,X),multiply(Y,multiply(Y,multiply(X,Y)))) -> identity
% Current number of equations to process: 3299
% Current number of ordered equations: 0
% Current number of rules: 241
% New rule produced :
% [266]
% commutator(multiply(X,X),multiply(Y,multiply(X,multiply(Y,Y)))) -> identity
% Current number of equations to process: 3298
% Current number of ordered equations: 0
% Current number of rules: 242
% New rule produced :
% [267]
% commutator(multiply(X,X),multiply(X,commutator(multiply(X,X),Y))) -> identity
% Current number of equations to process: 3297
% Current number of ordered equations: 0
% Current number of rules: 243
% New rule produced :
% [268]
% commutator(multiply(X,X),multiply(X,commutator(Y,multiply(X,X)))) -> identity
% Current number of equations to process: 3296
% Current number of ordered equations: 0
% Current number of rules: 244
% New rule produced :
% [269]
% commutator(X,multiply(X,multiply(X,commutator(commutator(Y,Z),X)))) ->
% identity
% Current number of equations to process: 3300
% Current number of ordered equations: 0
% Current number of rules: 245
% New rule produced :
% [270] commutator(X,multiply(X,multiply(X,commutator(Y,X)))) -> identity
% Rule
% [147]
% commutator(X,multiply(X,multiply(X,commutator(multiply(Y,Y),X)))) -> identity
% collapsed.
% Rule
% [269]
% commutator(X,multiply(X,multiply(X,commutator(commutator(Y,Z),X)))) ->
% identity collapsed.
% Current number of equations to process: 3322
% Current number of ordered equations: 0
% Current number of rules: 244
% New rule produced :
% [271]
% commutator(multiply(X,commutator(Y,Z)),X) -> commutator(commutator(Y,Z),X)
% Current number of equations to process: 3565
% Current number of ordered equations: 0
% Current number of rules: 245
% New rule produced :
% [272] commutator(X,commutator(multiply(X,X),Y)) -> identity
% Current number of equations to process: 3614
% Current number of ordered equations: 0
% Current number of rules: 246
% New rule produced :
% [273] commutator(X,commutator(X,commutator(Y,Z))) -> identity
% Current number of equations to process: 3619
% Current number of ordered equations: 0
% Current number of rules: 247
% New rule produced : [274] commutator(X,commutator(Y,X)) -> identity
% Current number of equations to process: 3621
% Current number of ordered equations: 0
% Current number of rules: 248
% New rule produced :
% [275] commutator(X,commutator(Y,commutator(Y,Z))) -> identity
% Current number of equations to process: 3632
% Current number of ordered equations: 0
% Current number of rules: 249
% New rule produced :
% [276] commutator(commutator(X,commutator(X,Y)),Z) -> identity
% Current number of equations to process: 3632
% Current number of ordered equations: 0
% Current number of rules: 250
% New rule produced :
% [277] commutator(commutator(X,Y),commutator(commutator(Y,X),Z)) -> identity
% Current number of equations to process: 3642
% Current number of ordered equations: 0
% Current number of rules: 251
% New rule produced :
% [278] commutator(multiply(X,X),multiply(X,multiply(Y,Y))) -> commutator(X,Y)
% Current number of equations to process: 3649
% Current number of ordered equations: 0
% Current number of rules: 252
% New rule produced :
% [279]
% commutator(commutator(Y,multiply(Y,multiply(X,X))),Z) ->
% commutator(commutator(X,Y),Z)
% Current number of equations to process: 3647
% Current number of ordered equations: 0
% Current number of rules: 253
% New rule produced :
% [280]
% commutator(X,commutator(Z,multiply(Z,multiply(Y,Y)))) ->
% commutator(X,commutator(Y,Z))
% Current number of equations to process: 3646
% Current number of ordered equations: 0
% Current number of rules: 254
% New rule produced :
% [281]
% commutator(X,multiply(Y,multiply(Z,multiply(X,X)))) ->
% commutator(X,multiply(Y,Z))
% Current number of equations to process: 3645
% Current number of ordered equations: 0
% Current number of rules: 255
% Rule [159]
% commutator(multiply(Z,Z),commutator(X,Y)) <->
% commutator(commutator(X,Y),multiply(Z,commutator(Y,X))) is composed into 
% [159]
% commutator(multiply(Z,Z),commutator(X,Y)) <-> commutator(commutator(X,Y),Z)
% New rule produced :
% [282]
% commutator(commutator(X,Y),multiply(Z,commutator(Y,X))) ->
% commutator(commutator(X,Y),Z)
% Rule
% [158]
% commutator(commutator(X,Y),multiply(Z,commutator(Y,X))) <->
% commutator(multiply(Z,Z),commutator(X,Y)) collapsed.
% Current number of equations to process: 3644
% Current number of ordered equations: 0
% Current number of rules: 255
% New rule produced :
% [283]
% commutator(X,commutator(X,multiply(Y,multiply(Z,multiply(Y,Z))))) -> identity
% Current number of equations to process: 3643
% Current number of ordered equations: 0
% Current number of rules: 256
% New rule produced :
% [284]
% commutator(commutator(X,Y),commutator(multiply(Z,Z),commutator(Y,X))) ->
% identity
% Current number of equations to process: 3642
% Current number of ordered equations: 0
% Current number of rules: 257
% New rule produced :
% [285]
% commutator(commutator(multiply(X,X),Y),commutator(Z,commutator(Y,X))) ->
% identity
% Current number of equations to process: 3641
% Current number of ordered equations: 0
% Current number of rules: 258
% New rule produced :
% [286]
% commutator(commutator(X,multiply(Y,Y)),commutator(Z,commutator(Y,X))) ->
% identity
% Current number of equations to process: 3640
% Current number of ordered equations: 0
% Current number of rules: 259
% New rule produced :
% [287]
% commutator(X,multiply(X,multiply(X,multiply(Y,commutator(X,Y))))) ->
% commutator(X,Y)
% Current number of equations to process: 3637
% Current number of ordered equations: 0
% Current number of rules: 260
% New rule produced :
% [288]
% commutator(commutator(X,Y),commutator(commutator(multiply(X,X),Y),Z)) ->
% identity
% Current number of equations to process: 3764
% Current number of ordered equations: 0
% Current number of rules: 261
% New rule produced :
% [289]
% commutator(commutator(multiply(X,X),Y),commutator(commutator(X,Y),Z)) ->
% identity
% Current number of equations to process: 3841
% Current number of ordered equations: 0
% Current number of rules: 262
% New rule produced :
% [290]
% commutator(commutator(X,Y),commutator(commutator(X,multiply(Y,Y)),Z)) ->
% identity
% Current number of equations to process: 4059
% Current number of ordered equations: 0
% Current number of rules: 263
% New rule produced :
% [291]
% commutator(commutator(X,multiply(Y,Y)),commutator(commutator(X,Y),Z)) ->
% identity
% Current number of equations to process: 4131
% Current number of ordered equations: 0
% Current number of rules: 264
% New rule produced :
% [292]
% commutator(commutator(X,Y),commutator(Z,commutator(multiply(Y,Y),X))) ->
% identity
% Current number of equations to process: 4436
% Current number of ordered equations: 0
% Current number of rules: 265
% New rule produced :
% [293] commutator(X,commutator(Y,multiply(Y,commutator(Y,Z)))) -> identity
% Current number of equations to process: 4601
% Current number of ordered equations: 0
% Current number of rules: 266
% New rule produced :
% [294]
% commutator(X,commutator(Y,multiply(Z,multiply(Z,multiply(Y,Z))))) -> identity
% Current number of equations to process: 4634
% Current number of ordered equations: 0
% Current number of rules: 267
% New rule produced :
% [295]
% commutator(X,commutator(Y,multiply(Y,commutator(multiply(Y,Y),Z)))) ->
% identity
% Current number of equations to process: 4633
% Current number of ordered equations: 0
% Current number of rules: 268
% New rule produced :
% [296]
% commutator(X,commutator(Y,multiply(Y,commutator(Z,multiply(Y,Y))))) ->
% identity
% Current number of equations to process: 4632
% Current number of ordered equations: 0
% Current number of rules: 269
% New rule produced :
% [297]
% commutator(commutator(X,Y),commutator(Z,commutator(Y,multiply(X,X)))) ->
% identity
% Current number of equations to process: 4786
% Current number of ordered equations: 0
% Current number of rules: 270
% New rule produced :
% [298] commutator(commutator(X,multiply(X,commutator(X,Y))),Z) -> identity
% Current number of equations to process: 4977
% Current number of ordered equations: 0
% Current number of rules: 271
% New rule produced :
% [299]
% commutator(commutator(X,multiply(Y,multiply(Y,multiply(X,Y)))),Z) -> identity
% Current number of equations to process: 2736
% Current number of ordered equations: 0
% Current number of rules: 272
% New rule produced :
% [300]
% commutator(commutator(X,multiply(X,commutator(multiply(X,X),Y))),Z) ->
% identity
% Current number of equations to process: 2735
% Current number of ordered equations: 0
% Current number of rules: 273
% New rule produced :
% [301]
% commutator(commutator(X,multiply(X,commutator(Y,multiply(X,X)))),Z) ->
% identity
% Current number of equations to process: 2734
% Current number of ordered equations: 0
% Current number of rules: 274
% New rule produced :
% [302]
% commutator(X,multiply(Y,multiply(X,multiply(Y,multiply(Y,X))))) -> identity
% Current number of equations to process: 4933
% Current number of ordered equations: 0
% Current number of rules: 275
% New rule produced :
% [303] commutator(multiply(X,multiply(X,multiply(Y,X))),Y) -> identity
% Current number of equations to process: 4941
% Current number of ordered equations: 0
% Current number of rules: 276
% New rule produced :
% [304]
% commutator(X,multiply(Y,multiply(Y,multiply(X,multiply(X,Y))))) -> identity
% Current number of equations to process: 4940
% Current number of ordered equations: 0
% Current number of rules: 277
% New rule produced : [305] commutator(X,commutator(X,Y)) -> identity
% Rule [157] commutator(X,commutator(X,multiply(Y,Y))) -> identity collapsed.
% Rule [273] commutator(X,commutator(X,commutator(Y,Z))) -> identity collapsed.
% Rule [275] commutator(X,commutator(Y,commutator(Y,Z))) -> identity collapsed.
% Rule [276] commutator(commutator(X,commutator(X,Y)),Z) -> identity collapsed.
% Rule
% [283]
% commutator(X,commutator(X,multiply(Y,multiply(Z,multiply(Y,Z))))) -> identity
% collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% Trivial
% 
% Current number of equations to process: 4969
% Current number of ordered equations: 0
% Current number of rules: 273
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% 
% The following 38 rules have been used:
% [3] 
% multiply(X,inverse(X)) -> identity; trace = in the starting set
% [5] multiply(X,multiply(X,X)) -> identity; trace = in the starting set
% [6] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z)); trace = in the starting set
% [9] multiply(Y,multiply(inverse(Y),X)) -> X; trace = Cp of 6 and 3
% [11] multiply(Y,multiply(Y,multiply(Y,X))) -> X; trace = Cp of 6 and 5
% [19] multiply(X,multiply(Y,multiply(X,multiply(X,multiply(Y,Y))))) ->
% commutator(X,Y); trace = in the starting set
% [22] multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,multiply(Y,Z))))))
% -> Z; trace = Cp of 9 and 6
% [25] multiply(X,multiply(Y,multiply(X,multiply(Y,X)))) -> multiply(Y,Y); trace = Cp of 22 and 5
% [26] multiply(X,multiply(X,multiply(Y,Y))) <->
% multiply(Y,multiply(X,multiply(Y,X))); trace = Cp of 25 and 11
% [27] multiply(Y,multiply(X,multiply(Y,X))) <->
% multiply(X,multiply(X,multiply(Y,Y))); trace = Cp of 25 and 11
% [34] multiply(X,multiply(X,commutator(X,Y))) <->
% multiply(Y,multiply(X,multiply(X,multiply(Y,Y)))); trace = Cp of 19 and 11
% [35] multiply(Y,multiply(X,multiply(X,multiply(Y,Y)))) <->
% multiply(X,multiply(X,commutator(X,Y))); trace = Cp of 19 and 11
% [39] multiply(X,multiply(X,multiply(Y,multiply(X,Y)))) <->
% multiply(Y,multiply(Y,commutator(Y,X))); trace = Cp of 35 and 26
% [41] multiply(X,multiply(Y,multiply(Y,commutator(Y,X)))) <->
% multiply(Y,multiply(X,Y)); trace = Cp of 39 and 11
% [48] multiply(Y,multiply(X,Y)) <->
% multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(X,X))))); trace = Cp of 41 and 34
% [49] multiply(X,multiply(X,multiply(Y,X))) <-> multiply(Y,commutator(Y,X)); trace = Cp of 48 and 26
% [50] multiply(Y,commutator(Y,X)) <-> multiply(X,multiply(X,multiply(Y,X))); trace = Cp of 48 and 26
% [52] multiply(X,multiply(Y,multiply(Y,X))) <->
% multiply(Y,multiply(X,multiply(X,Y))); trace = Cp of 49 and 48
% [54] multiply(Y,multiply(X,multiply(Y,Y))) <-> multiply(X,commutator(Y,X)); trace = Cp of 52 and 25
% [57] multiply(Y,multiply(X,X)) <->
% multiply(X,multiply(X,multiply(Y,commutator(X,Y)))); trace = Cp of 54 and 11
% [59] multiply(Y,multiply(X,commutator(multiply(Y,Y),X))) -> multiply(X,Y); trace = Self cp of 57
% [60] multiply(X,multiply(X,multiply(Y,X))) <->
% multiply(Y,commutator(multiply(X,X),Y)); trace = Cp of 59 and 11
% [62] multiply(X,commutator(X,Y)) <-> multiply(X,commutator(multiply(Y,Y),X)); trace = Cp of 60 and 49
% [63] multiply(X,commutator(multiply(Y,Y),X)) <-> multiply(X,commutator(X,Y)); trace = Cp of 60 and 49
% [64] commutator(Y,X) <-> commutator(multiply(X,X),Y); trace = Cp of 62 and 11
% [67] multiply(X,commutator(multiply(X,X),multiply(Y,Y))) ->
% multiply(X,commutator(X,Y)); trace = Cp of 64 and 63
% [68] commutator(multiply(X,X),multiply(Y,Y)) -> commutator(X,Y); trace = Cp of 67 and 11
% [69] commutator(X,multiply(Y,Y)) <-> commutator(Y,X); trace = Cp of 68 and 64
% [78] commutator(X,multiply(Y,multiply(Z,multiply(Y,Z)))) <->
% commutator(multiply(Y,Z),X); trace = Cp of 69 and 6
% [79] commutator(multiply(Y,Z),X) <->
% commutator(X,multiply(Y,multiply(Z,multiply(Y,Z)))); trace = Cp of 69 and 6
% [81] commutator(multiply(Z,Y),X) <->
% commutator(X,multiply(Y,multiply(Y,multiply(Z,Z)))); trace = Cp of 78 and 27
% [82] multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(X,Y))))) ->
% commutator(X,Y); trace = Cp of 50 and 11
% [90] commutator(commutator(X,Y),Z) <-> commutator(Z,commutator(Y,X)); trace = Cp of 79 and 19
% [101] commutator(X,multiply(X,multiply(Y,multiply(Y,multiply(X,Y))))) ->
% identity; trace = Self cp of 82
% [110] commutator(multiply(X,X),multiply(Y,Z)) <->
% commutator(X,multiply(Z,multiply(Z,multiply(Y,Y)))); trace = Cp of 81 and 64
% [146] commutator(multiply(X,X),multiply(X,commutator(Y,X))) -> identity; trace = Cp of 101 and 49
% [267] commutator(multiply(X,X),multiply(X,commutator(multiply(X,X),Y))) ->
% identity; trace = Cp of 146 and 64
% [305] commutator(X,commutator(X,Y)) -> identity; trace = Cp of 267 and 110
% % SZS output end Refutation
% All conjectures have been proven
% 
% Execution time: 124.100000 sec
% res : bool = true
% time is now off
% 
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
% 
% EOF
%------------------------------------------------------------------------------