%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP203-1 : TPTP v6.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n059.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 00:22:39 EDT 2014

% Result   : Unsatisfiable 59.05s
% Output   : Refutation 59.05s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP203-1 : TPTP v6.0.0. Released v2.2.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n059.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Fri Jun  6 07:33:28 CDT 2014
% % CPUTime  : 59.05 
% Processing problem /tmp/CiME_17350_n059.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " c,b,a,identity : constant;  left_inverse : 1;  multiply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% multiply(identity,X) = X;
% multiply(left_inverse(X),X) = identity;
% multiply(multiply(multiply(X,Y),X),Z) = multiply(X,multiply(Y,multiply(X,Z)));
% ";
% 
% let s1 = status F "
% c lr_lex;
% b lr_lex;
% a lr_lex;
% left_inverse lr_lex;
% multiply lr_lex;
% identity lr_lex;
% ";
% 
% let p1 = precedence F "
% left_inverse > multiply > identity > a > b > c";
% 
% let s2 = status F "
% c mul;
% b mul;
% a mul;
% left_inverse mul;
% multiply mul;
% identity mul;
% ";
% 
% let p2 = precedence F "
% left_inverse > multiply > identity = a = b = c";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " multiply(multiply(multiply(a,b),c),b) = multiply(a,multiply(b,multiply(c,b)));"
% ;
% (*
% 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(identity,X) = X,
% multiply(left_inverse(X),X) = identity,
% multiply(multiply(multiply(X,Y),X),Z) =
% multiply(X,multiply(Y,multiply(X,Z))) }
% (3 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { multiply(multiply(multiply(a,b),c),b) =
% multiply(a,multiply(b,multiply(c,b))) }
% (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: 2
% Current number of rules: 1
% New rule produced : [2] multiply(left_inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 2
% New rule produced :
% [3]
% multiply(multiply(multiply(X,Y),X),Z) ->
% multiply(X,multiply(Y,multiply(X,Z)))
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced : [4] multiply(multiply(X,identity),Y) -> multiply(X,Y)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [5] multiply(left_inverse(identity),X) -> X
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6] multiply(multiply(X,X),Y) -> multiply(X,multiply(X,Y))
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7] multiply(multiply(X,left_inverse(identity)),Y) -> multiply(X,Y)
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [8] multiply(left_inverse(left_inverse(identity)),X) -> X
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [9] left_inverse(identity) -> identity
% Rule [5] multiply(left_inverse(identity),X) -> X collapsed.
% Rule [7] multiply(multiply(X,left_inverse(identity)),Y) -> multiply(X,Y)
% collapsed.
% Rule [8] multiply(left_inverse(left_inverse(identity)),X) -> X collapsed.
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [10]
% multiply(multiply(X,multiply(X,identity)),Y) -> multiply(X,multiply(X,Y))
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [11]
% multiply(multiply(X,multiply(X,X)),Y) ->
% multiply(X,multiply(X,multiply(X,Y)))
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [12]
% multiply(left_inverse(X),multiply(X,multiply(left_inverse(X),Y))) ->
% multiply(left_inverse(X),Y)
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [13] multiply(left_inverse(X),multiply(X,identity)) -> identity
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [14]
% multiply(left_inverse(multiply(X,X)),multiply(X,multiply(X,identity))) ->
% identity
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [15]
% multiply(multiply(X,multiply(Y,multiply(X,identity))),Z) ->
% multiply(X,multiply(Y,multiply(X,Z)))
% Current number of equations to process: 28
% Current number of ordered equations: 1
% Current number of rules: 12
% New rule produced :
% [16]
% multiply(multiply(multiply(X,Y),multiply(X,identity)),Z) ->
% multiply(X,multiply(Y,multiply(X,Z)))
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [17]
% multiply(X,multiply(left_inverse(multiply(X,identity)),multiply(X,Y))) ->
% multiply(X,Y)
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [18] multiply(X,multiply(left_inverse(X),multiply(X,Y))) -> multiply(X,Y)
% Current number of equations to process: 41
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [19]
% multiply(left_inverse(X),multiply(left_inverse(multiply(left_inverse(X),identity)),identity))
% -> identity
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [20]
% multiply(left_inverse(X),multiply(left_inverse(left_inverse(X)),identity)) ->
% identity
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [21]
% multiply(multiply(X,multiply(X,multiply(X,X))),Y) ->
% multiply(X,multiply(X,multiply(X,multiply(X,Y))))
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [22]
% multiply(left_inverse(multiply(multiply(X,Y),X)),multiply(X,multiply(Y,
% multiply(X,identity))))
% -> identity
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [23]
% multiply(left_inverse(multiply(multiply(X,left_inverse(X)),X)),multiply(X,identity))
% -> identity
% Current number of equations to process: 98
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [24]
% multiply(left_inverse(multiply(multiply(X,left_inverse(multiply(X,identity))),X)),
% multiply(X,identity)) -> identity
% Current number of equations to process: 105
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [25]
% multiply(left_inverse(multiply(X,multiply(X,X))),multiply(X,multiply(X,
% multiply(X,identity))))
% -> identity
% Current number of equations to process: 128
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [26]
% multiply(X,multiply(left_inverse(multiply(multiply(X,left_inverse(X)),X)),
% multiply(X,Y))) -> multiply(X,Y)
% Current number of equations to process: 133
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [27]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,identity)))),Y) ->
% multiply(X,multiply(X,multiply(X,multiply(X,Y))))
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [28]
% multiply(multiply(X,multiply(Y,multiply(Y,multiply(X,identity)))),Z) ->
% multiply(X,multiply(Y,multiply(Y,multiply(X,Z))))
% Rule
% [27]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,identity)))),Y) ->
% multiply(X,multiply(X,multiply(X,multiply(X,Y)))) collapsed.
% Current number of equations to process: 164
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [29]
% multiply(multiply(X,multiply(left_inverse(X),identity)),Y) ->
% multiply(X,multiply(left_inverse(X),multiply(left_inverse(X),multiply(X,Y))))
% Current number of equations to process: 197
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [30]
% multiply(multiply(X,multiply(left_inverse(X),multiply(left_inverse(X),
% multiply(X,X)))),Y) ->
% multiply(X,Y)
% Current number of equations to process: 217
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [31]
% multiply(X,multiply(multiply(Y,multiply(X,identity)),multiply(X,Z))) <->
% multiply(multiply(X,multiply(Y,multiply(X,X))),Z)
% Current number of equations to process: 250
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [32]
% multiply(multiply(X,multiply(Y,multiply(X,X))),Z) <->
% multiply(X,multiply(multiply(Y,multiply(X,identity)),multiply(X,Z)))
% Rule
% [21]
% multiply(multiply(X,multiply(X,multiply(X,X))),Y) ->
% multiply(X,multiply(X,multiply(X,multiply(X,Y)))) collapsed.
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [33]
% multiply(X,multiply(multiply(left_inverse(X),multiply(X,Y)),multiply(X,Z)))
% -> multiply(X,multiply(Y,multiply(X,Z)))
% Current number of equations to process: 341
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [34]
% multiply(left_inverse(multiply(multiply(X,left_inverse(multiply(X,identity))),
% multiply(X,identity))),multiply(X,identity)) ->
% identity
% Current number of equations to process: 371
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [35]
% multiply(left_inverse(X),multiply(left_inverse(multiply(multiply(left_inverse(X),
% left_inverse(
% left_inverse(X))),
% left_inverse(X))),identity))
% -> identity
% Current number of equations to process: 387
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [36]
% multiply(left_inverse(left_inverse(Y)),multiply(left_inverse(Y),multiply(
% left_inverse(Y),
% multiply(
% left_inverse(
% left_inverse(Y)),X))))
% -> X
% Current number of equations to process: 389
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [37]
% multiply(left_inverse(left_inverse(left_inverse(X))),identity) ->
% multiply(left_inverse(left_inverse(X)),multiply(left_inverse(X),multiply(
% left_inverse(X),identity)))
% Current number of equations to process: 390
% Current number of ordered equations: 0
% Current number of rules: 32
% Rule [37]
% multiply(left_inverse(left_inverse(left_inverse(X))),identity) ->
% multiply(left_inverse(left_inverse(X)),multiply(left_inverse(X),
% multiply(left_inverse(X),identity))) is composed into 
% [37]
% multiply(left_inverse(left_inverse(left_inverse(X))),identity) ->
% left_inverse(X)
% New rule produced :
% [38]
% multiply(left_inverse(left_inverse(X)),multiply(left_inverse(X),multiply(
% left_inverse(X),identity)))
% -> left_inverse(X)
% Current number of equations to process: 392
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [39] multiply(left_inverse(Y),multiply(left_inverse(left_inverse(Y)),X)) -> X
% Rule
% [20]
% multiply(left_inverse(X),multiply(left_inverse(left_inverse(X)),identity)) ->
% identity collapsed.
% Rule
% [36]
% multiply(left_inverse(left_inverse(Y)),multiply(left_inverse(Y),multiply(
% left_inverse(Y),
% multiply(
% left_inverse(
% left_inverse(Y)),X))))
% -> X collapsed.
% Current number of equations to process: 394
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [40] multiply(left_inverse(left_inverse(Y)),multiply(left_inverse(Y),X)) -> X
% Rule
% [38]
% multiply(left_inverse(left_inverse(X)),multiply(left_inverse(X),multiply(
% left_inverse(X),identity)))
% -> left_inverse(X) collapsed.
% Current number of equations to process: 394
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [41] multiply(left_inverse(X),identity) -> left_inverse(X)
% Rule
% [19]
% multiply(left_inverse(X),multiply(left_inverse(multiply(left_inverse(X),identity)),identity))
% -> identity collapsed.
% Rule
% [29]
% multiply(multiply(X,multiply(left_inverse(X),identity)),Y) ->
% multiply(X,multiply(left_inverse(X),multiply(left_inverse(X),multiply(X,Y))))
% collapsed.
% Rule
% [35]
% multiply(left_inverse(X),multiply(left_inverse(multiply(multiply(left_inverse(X),
% left_inverse(
% left_inverse(X))),
% left_inverse(X))),identity))
% -> identity collapsed.
% Rule
% [37]
% multiply(left_inverse(left_inverse(left_inverse(X))),identity) ->
% left_inverse(X) collapsed.
% Current number of equations to process: 397
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [42] left_inverse(left_inverse(left_inverse(X))) -> left_inverse(X)
% Current number of equations to process: 396
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [43] multiply(left_inverse(X),left_inverse(left_inverse(X))) -> identity
% Current number of equations to process: 395
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [44] multiply(left_inverse(X),multiply(X,Y)) -> Y
% Rule
% [12]
% multiply(left_inverse(X),multiply(X,multiply(left_inverse(X),Y))) ->
% multiply(left_inverse(X),Y) collapsed.
% Rule [13] multiply(left_inverse(X),multiply(X,identity)) -> identity
% collapsed.
% Rule
% [18] multiply(X,multiply(left_inverse(X),multiply(X,Y))) -> multiply(X,Y)
% collapsed.
% Rule
% [30]
% multiply(multiply(X,multiply(left_inverse(X),multiply(left_inverse(X),
% multiply(X,X)))),Y) ->
% multiply(X,Y) collapsed.
% Rule
% [33]
% multiply(X,multiply(multiply(left_inverse(X),multiply(X,Y)),multiply(X,Z)))
% -> multiply(X,multiply(Y,multiply(X,Z))) collapsed.
% Rule
% [40] multiply(left_inverse(left_inverse(Y)),multiply(left_inverse(Y),X)) -> X
% collapsed.
% Current number of equations to process: 396
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [45] multiply(left_inverse(left_inverse(X)),Y) -> multiply(X,Y)
% Rule
% [39] multiply(left_inverse(Y),multiply(left_inverse(left_inverse(Y)),X)) -> X
% collapsed.
% Current number of equations to process: 400
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [46]
% multiply(multiply(X,left_inverse(X)),Y) ->
% multiply(X,multiply(left_inverse(X),Y))
% Rule
% [23]
% multiply(left_inverse(multiply(multiply(X,left_inverse(X)),X)),multiply(X,identity))
% -> identity collapsed.
% Rule
% [26]
% multiply(X,multiply(left_inverse(multiply(multiply(X,left_inverse(X)),X)),
% multiply(X,Y))) -> multiply(X,Y) collapsed.
% Current number of equations to process: 402
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [47] left_inverse(left_inverse(X)) -> X
% Rule [42] left_inverse(left_inverse(left_inverse(X))) -> left_inverse(X)
% collapsed.
% Rule [43] multiply(left_inverse(X),left_inverse(left_inverse(X))) -> identity
% collapsed.
% Rule [45] multiply(left_inverse(left_inverse(X)),Y) -> multiply(X,Y)
% collapsed.
% Current number of equations to process: 407
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [48] multiply(left_inverse(multiply(Y,identity)),multiply(Y,X)) -> X
% Rule
% [17]
% multiply(X,multiply(left_inverse(multiply(X,identity)),multiply(X,Y))) ->
% multiply(X,Y) collapsed.
% Current number of equations to process: 409
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [49] multiply(left_inverse(multiply(X,X)),multiply(X,multiply(X,Y))) -> Y
% Rule
% [14]
% multiply(left_inverse(multiply(X,X)),multiply(X,multiply(X,identity))) ->
% identity collapsed.
% Current number of equations to process: 409
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [50] multiply(X,left_inverse(X)) -> identity
% Rule
% [46]
% multiply(multiply(X,left_inverse(X)),Y) ->
% multiply(X,multiply(left_inverse(X),Y)) collapsed.
% Current number of equations to process: 411
% Current number of ordered equations: 0
% Current number of rules: 23
% Rule [32]
% multiply(multiply(X,multiply(Y,multiply(X,X))),Z) <->
% multiply(X,multiply(multiply(Y,multiply(X,identity)),multiply(X,Z))) is composed into 
% [32]
% multiply(multiply(X,multiply(Y,multiply(X,X))),Z) ->
% multiply(X,multiply(multiply(Y,X),multiply(X,Z)))
% New rule produced : [51] multiply(X,identity) -> X
% Rule [4] multiply(multiply(X,identity),Y) -> multiply(X,Y) collapsed.
% Rule
% [10]
% multiply(multiply(X,multiply(X,identity)),Y) -> multiply(X,multiply(X,Y))
% collapsed.
% Rule
% [15]
% multiply(multiply(X,multiply(Y,multiply(X,identity))),Z) ->
% multiply(X,multiply(Y,multiply(X,Z))) collapsed.
% Rule
% [16]
% multiply(multiply(multiply(X,Y),multiply(X,identity)),Z) ->
% multiply(X,multiply(Y,multiply(X,Z))) collapsed.
% Rule
% [22]
% multiply(left_inverse(multiply(multiply(X,Y),X)),multiply(X,multiply(Y,
% multiply(X,identity))))
% -> identity collapsed.
% Rule
% [24]
% multiply(left_inverse(multiply(multiply(X,left_inverse(multiply(X,identity))),X)),
% multiply(X,identity)) -> identity collapsed.
% Rule
% [25]
% multiply(left_inverse(multiply(X,multiply(X,X))),multiply(X,multiply(X,
% multiply(X,identity))))
% -> identity collapsed.
% Rule
% [28]
% multiply(multiply(X,multiply(Y,multiply(Y,multiply(X,identity)))),Z) ->
% multiply(X,multiply(Y,multiply(Y,multiply(X,Z)))) collapsed.
% Rule
% [31]
% multiply(X,multiply(multiply(Y,multiply(X,identity)),multiply(X,Z))) <->
% multiply(multiply(X,multiply(Y,multiply(X,X))),Z) collapsed.
% Rule
% [34]
% multiply(left_inverse(multiply(multiply(X,left_inverse(multiply(X,identity))),
% multiply(X,identity))),multiply(X,identity)) ->
% identity collapsed.
% Rule [41] multiply(left_inverse(X),identity) -> left_inverse(X) collapsed.
% Rule [48] multiply(left_inverse(multiply(Y,identity)),multiply(Y,X)) -> X
% collapsed.
% Current number of equations to process: 414
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [52] multiply(X,multiply(left_inverse(X),Y)) -> Y
% Current number of equations to process: 413
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [53]
% multiply(left_inverse(multiply(left_inverse(X),left_inverse(X))),left_inverse(X))
% -> X
% Current number of equations to process: 415
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [54]
% multiply(multiply(X,multiply(Y,X)),Z) ->
% multiply(X,multiply(Y,multiply(X,Z)))
% Rule
% [11]
% multiply(multiply(X,multiply(X,X)),Y) ->
% multiply(X,multiply(X,multiply(X,Y))) collapsed.
% Current number of equations to process: 414
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [55]
% multiply(left_inverse(multiply(multiply(X,Y),X)),multiply(X,multiply(Y,X)))
% -> identity
% Current number of equations to process: 415
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [56]
% multiply(left_inverse(multiply(left_inverse(X),left_inverse(X))),multiply(
% left_inverse(X),Y))
% -> multiply(X,Y)
% Current number of equations to process: 413
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [57] multiply(X,multiply(X,left_inverse(multiply(X,X)))) -> identity
% Current number of equations to process: 415
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [58] multiply(left_inverse(multiply(X,X)),X) -> left_inverse(X)
% Rule
% [53]
% multiply(left_inverse(multiply(left_inverse(X),left_inverse(X))),left_inverse(X))
% -> X collapsed.
% Current number of equations to process: 417
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [59] multiply(multiply(X,Y),X) -> multiply(X,multiply(Y,X))
% Rule
% [3]
% multiply(multiply(multiply(X,Y),X),Z) ->
% multiply(X,multiply(Y,multiply(X,Z))) collapsed.
% Rule
% [55]
% multiply(left_inverse(multiply(multiply(X,Y),X)),multiply(X,multiply(Y,X)))
% -> identity collapsed.
% Current number of equations to process: 416
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [60]
% multiply(X,multiply(multiply(Y,X),X)) ->
% multiply(X,multiply(Y,multiply(X,X)))
% Current number of equations to process: 417
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [61] multiply(X,multiply(X,multiply(left_inverse(multiply(X,X)),Y))) -> Y
% Current number of equations to process: 416
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [62]
% multiply(left_inverse(multiply(X,X)),multiply(X,Y)) ->
% multiply(left_inverse(X),Y)
% Rule
% [49] multiply(left_inverse(multiply(X,X)),multiply(X,multiply(X,Y))) -> Y
% collapsed.
% Rule
% [56]
% multiply(left_inverse(multiply(left_inverse(X),left_inverse(X))),multiply(
% left_inverse(X),Y))
% -> multiply(X,Y) collapsed.
% Current number of equations to process: 422
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [63]
% multiply(X,multiply(Y,multiply(X,left_inverse(multiply(X,multiply(Y,X))))))
% -> identity
% Current number of equations to process: 421
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [64] multiply(X,left_inverse(multiply(X,X))) -> left_inverse(X)
% Rule [57] multiply(X,multiply(X,left_inverse(multiply(X,X)))) -> identity
% collapsed.
% Current number of equations to process: 429
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [65] multiply(left_inverse(multiply(X,Y)),multiply(X,multiply(Y,X))) -> X
% Current number of equations to process: 435
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [66]
% multiply(left_inverse(Y),multiply(multiply(Y,X),left_inverse(Y))) ->
% multiply(X,left_inverse(Y))
% Current number of equations to process: 434
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [67] multiply(Y,multiply(multiply(left_inverse(Y),X),Y)) -> multiply(X,Y)
% Current number of equations to process: 439
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [68] multiply(multiply(X,Y),Y) -> multiply(X,multiply(Y,Y))
% Rule
% [60]
% multiply(X,multiply(multiply(Y,X),X)) ->
% multiply(X,multiply(Y,multiply(X,X))) collapsed.
% Current number of equations to process: 444
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [69]
% multiply(X,multiply(left_inverse(multiply(X,X)),Y)) ->
% multiply(left_inverse(X),Y)
% Rule
% [61] multiply(X,multiply(X,multiply(left_inverse(multiply(X,X)),Y))) -> Y
% collapsed.
% Current number of equations to process: 446
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [70]
% multiply(left_inverse(multiply(X,X)),Y) ->
% multiply(left_inverse(X),multiply(left_inverse(X),Y))
% Rule [58] multiply(left_inverse(multiply(X,X)),X) -> left_inverse(X)
% collapsed.
% Rule
% [62]
% multiply(left_inverse(multiply(X,X)),multiply(X,Y)) ->
% multiply(left_inverse(X),Y) collapsed.
% Rule
% [69]
% multiply(X,multiply(left_inverse(multiply(X,X)),Y)) ->
% multiply(left_inverse(X),Y) collapsed.
% Current number of equations to process: 446
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [71]
% multiply(left_inverse(X),left_inverse(multiply(X,X))) ->
% multiply(left_inverse(X),multiply(left_inverse(X),left_inverse(X)))
% Current number of equations to process: 447
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [72]
% multiply(Y,multiply(X,left_inverse(multiply(X,multiply(Y,X))))) ->
% left_inverse(X)
% Rule
% [63]
% multiply(X,multiply(Y,multiply(X,left_inverse(multiply(X,multiply(Y,X))))))
% -> identity collapsed.
% Current number of equations to process: 451
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [73] left_inverse(multiply(left_inverse(X),left_inverse(X))) -> multiply(X,X)
% Current number of equations to process: 451
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [74] left_inverse(multiply(X,X)) -> multiply(left_inverse(X),left_inverse(X))
% Rule [64] multiply(X,left_inverse(multiply(X,X))) -> left_inverse(X)
% collapsed.
% Rule
% [70]
% multiply(left_inverse(multiply(X,X)),Y) ->
% multiply(left_inverse(X),multiply(left_inverse(X),Y)) collapsed.
% Rule
% [71]
% multiply(left_inverse(X),left_inverse(multiply(X,X))) ->
% multiply(left_inverse(X),multiply(left_inverse(X),left_inverse(X)))
% collapsed.
% Rule
% [73] left_inverse(multiply(left_inverse(X),left_inverse(X))) -> multiply(X,X)
% collapsed.
% Current number of equations to process: 452
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [75]
% multiply(multiply(X,Y),left_inverse(X)) ->
% multiply(X,multiply(Y,left_inverse(X)))
% Rule
% [66]
% multiply(left_inverse(Y),multiply(multiply(Y,X),left_inverse(Y))) ->
% multiply(X,left_inverse(Y)) collapsed.
% Current number of equations to process: 463
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [76] multiply(multiply(X,left_inverse(Y)),Y) -> X
% Current number of equations to process: 466
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [77]
% multiply(multiply(left_inverse(X),Y),X) ->
% multiply(left_inverse(X),multiply(Y,X))
% Rule
% [67] multiply(Y,multiply(multiply(left_inverse(Y),X),Y)) -> multiply(X,Y)
% collapsed.
% Current number of equations to process: 466
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [78] multiply(left_inverse(multiply(X,Y)),multiply(X,multiply(Y,Y))) -> Y
% Current number of equations to process: 488
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [79]
% multiply(multiply(X,multiply(X,Y)),Y) ->
% multiply(X,multiply(X,multiply(Y,Y)))
% Current number of equations to process: 487
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [80]
% multiply(multiply(X,Y),multiply(X,X)) ->
% multiply(X,multiply(Y,multiply(X,X)))
% Current number of equations to process: 486
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [81]
% multiply(multiply(X,multiply(Y,Y)),Y) ->
% multiply(multiply(X,Y),multiply(Y,Y))
% Current number of equations to process: 485
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [82]
% multiply(Y,left_inverse(multiply(Y,multiply(X,Y)))) ->
% multiply(left_inverse(X),left_inverse(Y))
% Rule
% [72]
% multiply(Y,multiply(X,left_inverse(multiply(X,multiply(Y,X))))) ->
% left_inverse(X) collapsed.
% Current number of equations to process: 484
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [83] multiply(X,multiply(multiply(Y,X),left_inverse(X))) -> multiply(X,Y)
% Current number of equations to process: 491
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [84]
% multiply(left_inverse(multiply(X,Y)),multiply(X,multiply(Y,left_inverse(X))))
% -> left_inverse(X)
% Current number of equations to process: 492
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [85] multiply(left_inverse(multiply(X,left_inverse(Y))),X) -> Y
% Current number of equations to process: 502
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [86] multiply(multiply(X,Y),left_inverse(Y)) -> X
% Rule
% [83] multiply(X,multiply(multiply(Y,X),left_inverse(X))) -> multiply(X,Y)
% collapsed.
% Current number of equations to process: 504
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [87] multiply(multiply(X,multiply(X,left_inverse(Y))),Y) -> multiply(X,X)
% Current number of equations to process: 509
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [88] multiply(multiply(X,left_inverse(Y)),multiply(Y,Y)) -> multiply(X,Y)
% Current number of equations to process: 508
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [89]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(Y))),Y) ->
% multiply(X,left_inverse(Y))
% Current number of equations to process: 510
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [90]
% multiply(left_inverse(multiply(X,multiply(Y,left_inverse(X)))),multiply(X,Y))
% -> X
% Current number of equations to process: 509
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [91]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(Y))),multiply(Y,Y))
% -> X
% Current number of equations to process: 508
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [92]
% multiply(multiply(left_inverse(X),Y),multiply(X,X)) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,X)))
% Current number of equations to process: 507
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [93]
% multiply(Y,multiply(multiply(left_inverse(Y),X),multiply(Y,Z))) <->
% multiply(multiply(X,Y),Z)
% Current number of equations to process: 520
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [94]
% multiply(multiply(X,Y),Z) <->
% multiply(Y,multiply(multiply(left_inverse(Y),X),multiply(Y,Z)))
% Current number of equations to process: 520
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [95]
% multiply(left_inverse(Y),multiply(multiply(Y,X),multiply(Y,X))) ->
% multiply(X,multiply(Y,X))
% Current number of equations to process: 519
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [96]
% multiply(multiply(X,multiply(Y,left_inverse(X))),multiply(X,Y)) ->
% multiply(X,multiply(Y,Y))
% Current number of equations to process: 518
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [97]
% multiply(X,multiply(multiply(Y,multiply(X,X)),left_inverse(X))) ->
% multiply(X,multiply(Y,X))
% Current number of equations to process: 517
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [98]
% multiply(X,multiply(multiply(Y,left_inverse(X)),multiply(X,Z))) <->
% multiply(multiply(X,Y),Z)
% Current number of equations to process: 515
% Current number of ordered equations: 2
% Current number of rules: 38
% New rule produced :
% [99]
% multiply(multiply(X,Y),Z) <->
% multiply(X,multiply(multiply(Y,left_inverse(X)),multiply(X,Z)))
% Current number of equations to process: 515
% Current number of ordered equations: 1
% Current number of rules: 39
% New rule produced :
% [100]
% multiply(multiply(X,multiply(Y,multiply(X,left_inverse(Z)))),Z) ->
% multiply(X,multiply(Y,X))
% Current number of equations to process: 515
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [101]
% multiply(left_inverse(multiply(left_inverse(X),Y)),multiply(left_inverse(X),
% multiply(Y,X))) -> X
% Current number of equations to process: 513
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [102]
% multiply(multiply(left_inverse(X),Y),multiply(X,Y)) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,Y)))
% Current number of equations to process: 531
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [103]
% multiply(multiply(X,left_inverse(Y)),multiply(X,Y)) ->
% multiply(X,multiply(left_inverse(Y),multiply(X,Y)))
% Current number of equations to process: 552
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [104]
% left_inverse(multiply(left_inverse(X),multiply(Y,left_inverse(X)))) ->
% multiply(X,multiply(left_inverse(Y),X))
% Current number of equations to process: 589
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [105]
% multiply(Y,multiply(left_inverse(multiply(Y,multiply(X,Y))),Y)) ->
% left_inverse(X)
% Current number of equations to process: 588
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [106]
% left_inverse(multiply(X,multiply(Y,X))) ->
% multiply(left_inverse(X),multiply(left_inverse(Y),left_inverse(X)))
% Rule
% [82]
% multiply(Y,left_inverse(multiply(Y,multiply(X,Y)))) ->
% multiply(left_inverse(X),left_inverse(Y)) collapsed.
% Rule
% [104]
% left_inverse(multiply(left_inverse(X),multiply(Y,left_inverse(X)))) ->
% multiply(X,multiply(left_inverse(Y),X)) collapsed.
% Rule
% [105]
% multiply(Y,multiply(left_inverse(multiply(Y,multiply(X,Y))),Y)) ->
% left_inverse(X) collapsed.
% Current number of equations to process: 604
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [107]
% multiply(left_inverse(X),left_inverse(multiply(Y,left_inverse(X)))) <->
% multiply(left_inverse(multiply(X,Y)),X)
% Current number of equations to process: 603
% Current number of ordered equations: 1
% Current number of rules: 44
% New rule produced :
% [108]
% multiply(left_inverse(multiply(X,Y)),X) <->
% multiply(left_inverse(X),left_inverse(multiply(Y,left_inverse(X))))
% Current number of equations to process: 603
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [109]
% multiply(X,left_inverse(multiply(X,Y))) <->
% multiply(left_inverse(multiply(Y,left_inverse(X))),left_inverse(X))
% Current number of equations to process: 602
% Current number of ordered equations: 1
% Current number of rules: 46
% New rule produced :
% [110]
% multiply(left_inverse(multiply(Y,left_inverse(X))),left_inverse(X)) <->
% multiply(X,left_inverse(multiply(X,Y)))
% Current number of equations to process: 602
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [111]
% multiply(X,left_inverse(multiply(Y,X))) <->
% multiply(left_inverse(multiply(left_inverse(X),Y)),left_inverse(X))
% Current number of equations to process: 601
% Current number of ordered equations: 1
% Current number of rules: 48
% New rule produced :
% [112]
% multiply(left_inverse(multiply(left_inverse(X),Y)),left_inverse(X)) <->
% multiply(X,left_inverse(multiply(Y,X)))
% Current number of equations to process: 601
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [113]
% multiply(multiply(left_inverse(X),left_inverse(Y)),multiply(Y,multiply(X,Y)))
% -> Y
% Current number of equations to process: 609
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [114]
% multiply(multiply(X,Y),left_inverse(multiply(X,multiply(Y,Y)))) ->
% multiply(X,left_inverse(multiply(X,Y)))
% Current number of equations to process: 608
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [115]
% multiply(multiply(X,multiply(Y,multiply(Y,X))),Z) ->
% multiply(X,multiply(Y,multiply(Y,multiply(X,Z))))
% Current number of equations to process: 607
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [116]
% multiply(multiply(X,multiply(X,multiply(Y,X))),Z) ->
% multiply(X,multiply(multiply(X,Y),multiply(X,Z)))
% Current number of equations to process: 602
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [117]
% multiply(multiply(X,Y),multiply(X,multiply(X,Y))) ->
% multiply(X,multiply(Y,multiply(X,multiply(X,Y))))
% Current number of equations to process: 599
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [118]
% multiply(X,multiply(multiply(Y,X),multiply(Y,X))) ->
% multiply(X,multiply(Y,multiply(X,multiply(Y,X))))
% Current number of equations to process: 596
% Current number of ordered equations: 1
% Current number of rules: 55
% New rule produced :
% [119]
% multiply(multiply(X,multiply(Y,multiply(X,Z))),Z) ->
% multiply(X,multiply(Y,multiply(X,multiply(Z,Z))))
% Current number of equations to process: 596
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [120]
% multiply(multiply(X,multiply(Y,Y)),multiply(X,Y)) ->
% multiply(multiply(X,Y),multiply(Y,multiply(X,Y)))
% Current number of equations to process: 595
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [121]
% multiply(multiply(X,Y),multiply(left_inverse(X),left_inverse(X))) ->
% multiply(X,multiply(Y,multiply(left_inverse(X),left_inverse(X))))
% Current number of equations to process: 594
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [122]
% multiply(multiply(X,multiply(X,multiply(Y,Y))),Y) ->
% multiply(multiply(X,multiply(X,Y)),multiply(Y,Y))
% Current number of equations to process: 593
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [123]
% multiply(X,multiply(multiply(Y,X),multiply(X,X))) ->
% multiply(X,multiply(Y,multiply(X,multiply(X,X))))
% Current number of equations to process: 592
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [124]
% multiply(left_inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(X,X))))
% -> multiply(X,X)
% Current number of equations to process: 591
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [125]
% multiply(X,left_inverse(multiply(X,multiply(Y,multiply(X,X))))) ->
% multiply(left_inverse(multiply(Y,X)),left_inverse(X))
% Current number of equations to process: 589
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [126]
% multiply(X,left_inverse(multiply(X,multiply(X,multiply(Y,X))))) ->
% multiply(left_inverse(multiply(X,Y)),left_inverse(X))
% Current number of equations to process: 588
% Current number of ordered equations: 0
% Current number of rules: 63
% Rule [111]
% multiply(X,left_inverse(multiply(Y,X))) <->
% multiply(left_inverse(multiply(left_inverse(X),Y)),left_inverse(X)) is composed into 
% [111] multiply(X,left_inverse(multiply(Y,X))) -> left_inverse(Y)
% Rule [107]
% multiply(left_inverse(X),left_inverse(multiply(Y,left_inverse(X)))) <->
% multiply(left_inverse(multiply(X,Y)),X) is composed into [107]
% multiply(
% left_inverse(X),
% left_inverse(
% multiply(Y,
% left_inverse(X))))
% ->
% left_inverse(Y)
% New rule produced :
% [127] multiply(left_inverse(multiply(X,Y)),X) -> left_inverse(Y)
% Rule [85] multiply(left_inverse(multiply(X,left_inverse(Y))),X) -> Y
% collapsed.
% Rule
% [108]
% multiply(left_inverse(multiply(X,Y)),X) <->
% multiply(left_inverse(X),left_inverse(multiply(Y,left_inverse(X))))
% collapsed.
% Rule
% [112]
% multiply(left_inverse(multiply(left_inverse(X),Y)),left_inverse(X)) <->
% multiply(X,left_inverse(multiply(Y,X))) collapsed.
% Current number of equations to process: 611
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [128]
% left_inverse(multiply(Y,X)) -> multiply(left_inverse(X),left_inverse(Y))
% Rule
% [65] multiply(left_inverse(multiply(X,Y)),multiply(X,multiply(Y,X))) -> X
% collapsed.
% Rule
% [74] left_inverse(multiply(X,X)) -> multiply(left_inverse(X),left_inverse(X))
% collapsed.
% Rule
% [78] multiply(left_inverse(multiply(X,Y)),multiply(X,multiply(Y,Y))) -> Y
% collapsed.
% Rule
% [84]
% multiply(left_inverse(multiply(X,Y)),multiply(X,multiply(Y,left_inverse(X))))
% -> left_inverse(X) collapsed.
% Rule
% [90]
% multiply(left_inverse(multiply(X,multiply(Y,left_inverse(X)))),multiply(X,Y))
% -> X collapsed.
% Rule
% [101]
% multiply(left_inverse(multiply(left_inverse(X),Y)),multiply(left_inverse(X),
% multiply(Y,X))) -> X
% collapsed.
% Rule
% [106]
% left_inverse(multiply(X,multiply(Y,X))) ->
% multiply(left_inverse(X),multiply(left_inverse(Y),left_inverse(X)))
% collapsed.
% Rule
% [107]
% multiply(left_inverse(X),left_inverse(multiply(Y,left_inverse(X)))) ->
% left_inverse(Y) collapsed.
% Rule
% [109]
% multiply(X,left_inverse(multiply(X,Y))) <->
% multiply(left_inverse(multiply(Y,left_inverse(X))),left_inverse(X))
% collapsed.
% Rule
% [110]
% multiply(left_inverse(multiply(Y,left_inverse(X))),left_inverse(X)) <->
% multiply(X,left_inverse(multiply(X,Y))) collapsed.
% Rule [111] multiply(X,left_inverse(multiply(Y,X))) -> left_inverse(Y)
% collapsed.
% Rule
% [114]
% multiply(multiply(X,Y),left_inverse(multiply(X,multiply(Y,Y)))) ->
% multiply(X,left_inverse(multiply(X,Y))) collapsed.
% Rule
% [124]
% multiply(left_inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(X,X))))
% -> multiply(X,X) collapsed.
% Rule
% [125]
% multiply(X,left_inverse(multiply(X,multiply(Y,multiply(X,X))))) ->
% multiply(left_inverse(multiply(Y,X)),left_inverse(X)) collapsed.
% Rule
% [126]
% multiply(X,left_inverse(multiply(X,multiply(X,multiply(Y,X))))) ->
% multiply(left_inverse(multiply(X,Y)),left_inverse(X)) collapsed.
% Rule [127] multiply(left_inverse(multiply(X,Y)),X) -> left_inverse(Y)
% collapsed.
% Current number of equations to process: 624
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [129] multiply(multiply(X,multiply(Y,Y)),left_inverse(Y)) -> multiply(X,Y)
% Rule
% [97]
% multiply(X,multiply(multiply(Y,multiply(X,X)),left_inverse(X))) ->
% multiply(X,multiply(Y,X)) collapsed.
% Current number of equations to process: 623
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [130] multiply(multiply(X,multiply(X,Y)),left_inverse(Y)) -> multiply(X,X)
% Current number of equations to process: 629
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [131]
% multiply(multiply(X,Y),multiply(left_inverse(Y),left_inverse(Y))) ->
% multiply(X,left_inverse(Y))
% Current number of equations to process: 632
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [132]
% multiply(multiply(left_inverse(Y),left_inverse(X)),multiply(X,multiply(Y,Y)))
% -> Y
% Current number of equations to process: 631
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [133] multiply(multiply(X,left_inverse(Y)),multiply(Y,X)) -> multiply(X,X)
% Current number of equations to process: 644
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [134]
% multiply(multiply(X,Y),multiply(X,Y)) ->
% multiply(X,multiply(Y,multiply(X,Y)))
% Rule
% [95]
% multiply(left_inverse(Y),multiply(multiply(Y,X),multiply(Y,X))) ->
% multiply(X,multiply(Y,X)) collapsed.
% Rule
% [118]
% multiply(X,multiply(multiply(Y,X),multiply(Y,X))) ->
% multiply(X,multiply(Y,multiply(X,multiply(Y,X)))) collapsed.
% Current number of equations to process: 643
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [135]
% multiply(multiply(X,multiply(X,left_inverse(Y))),multiply(Y,left_inverse(X)))
% -> X
% Current number of equations to process: 654
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [136]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(X))),multiply(X,Y))
% -> X
% Current number of equations to process: 653
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [137]
% multiply(multiply(X,Y),multiply(left_inverse(Y),multiply(X,Y))) ->
% multiply(X,multiply(X,Y))
% Current number of equations to process: 652
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [138]
% multiply(multiply(X,multiply(Y,multiply(X,Z))),left_inverse(Z)) ->
% multiply(X,multiply(Y,X))
% Current number of equations to process: 651
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [139]
% multiply(multiply(X,multiply(X,multiply(Y,Y))),left_inverse(Y)) ->
% multiply(X,multiply(X,Y))
% Current number of equations to process: 650
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [140]
% multiply(multiply(X,multiply(X,left_inverse(Y))),multiply(Y,Y)) ->
% multiply(X,multiply(X,Y))
% Current number of equations to process: 649
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [141]
% multiply(multiply(left_inverse(Y),left_inverse(X)),multiply(X,multiply(Y,
% left_inverse(X))))
% -> left_inverse(X)
% Current number of equations to process: 648
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [142]
% multiply(multiply(left_inverse(X),multiply(left_inverse(Y),X)),multiply(
% left_inverse(X),Y))
% -> left_inverse(X)
% Current number of equations to process: 647
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [143]
% multiply(multiply(X,multiply(Y,Y)),multiply(left_inverse(Y),left_inverse(Y)))
% -> X
% Current number of equations to process: 668
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [144]
% multiply(multiply(left_inverse(Y),X),multiply(left_inverse(X),multiply(Y,X)))
% -> X
% Current number of equations to process: 666
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [145]
% multiply(multiply(X,left_inverse(Y)),multiply(left_inverse(Y),X)) ->
% multiply(X,multiply(left_inverse(Y),multiply(left_inverse(Y),X)))
% Current number of equations to process: 663
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [146]
% multiply(X,multiply(multiply(left_inverse(X),Y),Z)) <->
% multiply(multiply(Y,X),multiply(left_inverse(X),Z))
% Current number of equations to process: 677
% Current number of ordered equations: 1
% Current number of rules: 61
% New rule produced :
% [147]
% multiply(multiply(Y,X),multiply(left_inverse(X),Z)) <->
% multiply(X,multiply(multiply(left_inverse(X),Y),Z))
% Current number of equations to process: 677
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [148]
% multiply(left_inverse(X),multiply(multiply(X,Y),Z)) <->
% multiply(multiply(Y,left_inverse(X)),multiply(X,Z))
% Current number of equations to process: 675
% Current number of ordered equations: 3
% Current number of rules: 63
% New rule produced :
% [149]
% multiply(left_inverse(X),multiply(multiply(Y,X),Z)) <->
% multiply(multiply(left_inverse(X),Y),multiply(X,Z))
% Current number of equations to process: 675
% Current number of ordered equations: 2
% Current number of rules: 64
% New rule produced :
% [150]
% multiply(multiply(left_inverse(X),Y),multiply(X,Z)) <->
% multiply(left_inverse(X),multiply(multiply(Y,X),Z))
% Current number of equations to process: 675
% Current number of ordered equations: 1
% Current number of rules: 65
% New rule produced :
% [151]
% multiply(multiply(Y,left_inverse(X)),multiply(X,Z)) <->
% multiply(left_inverse(X),multiply(multiply(X,Y),Z))
% Current number of equations to process: 675
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [152]
% multiply(X,multiply(multiply(Y,left_inverse(X)),Z)) <->
% multiply(multiply(X,Y),multiply(left_inverse(X),Z))
% Current number of equations to process: 785
% Current number of ordered equations: 1
% Current number of rules: 67
% New rule produced :
% [153]
% multiply(multiply(X,Y),multiply(left_inverse(X),Z)) <->
% multiply(X,multiply(multiply(Y,left_inverse(X)),Z))
% Current number of equations to process: 785
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [154]
% multiply(multiply(X,Y),multiply(X,multiply(Y,X))) ->
% multiply(X,multiply(Y,multiply(X,multiply(Y,X))))
% Current number of equations to process: 784
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [155]
% multiply(X,multiply(multiply(left_inverse(Y),left_inverse(X)),multiply(X,Y)))
% -> X
% Current number of equations to process: 850
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [156]
% multiply(X,multiply(multiply(Y,left_inverse(X)),multiply(X,left_inverse(Y))))
% -> X
% Current number of equations to process: 849
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [157]
% multiply(multiply(multiply(X,Y),multiply(Z,X)),Y) ->
% multiply(multiply(X,Y),multiply(Z,multiply(X,Y)))
% Current number of equations to process: 912
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [158]
% multiply(multiply(X,Y),multiply(left_inverse(X),Y)) ->
% multiply(X,multiply(Y,multiply(left_inverse(X),Y)))
% Current number of equations to process: 929
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [159]
% multiply(multiply(X,Y),multiply(X,left_inverse(Y))) ->
% multiply(X,multiply(Y,multiply(X,left_inverse(Y))))
% Current number of equations to process: 964
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [160]
% multiply(multiply(X,left_inverse(Y)),multiply(Y,multiply(left_inverse(X),Y)))
% -> Y
% Current number of equations to process: 988
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [161]
% multiply(multiply(left_inverse(X),Y),multiply(left_inverse(Y),multiply(X,
% left_inverse(Y))))
% -> left_inverse(Y)
% Current number of equations to process: 987
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [162]
% multiply(left_inverse(Y),multiply(multiply(Y,X),multiply(left_inverse(Y),Z)))
% <-> multiply(multiply(X,left_inverse(Y)),Z)
% Current number of equations to process: 1021
% Current number of ordered equations: 1
% Current number of rules: 77
% New rule produced :
% [163]
% multiply(multiply(X,left_inverse(Y)),Z) <->
% multiply(left_inverse(Y),multiply(multiply(Y,X),multiply(left_inverse(Y),Z)))
% Current number of equations to process: 1021
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [164]
% multiply(multiply(X,left_inverse(Y)),multiply(Y,multiply(X,left_inverse(Y))))
% -> multiply(X,multiply(X,left_inverse(Y)))
% Current number of equations to process: 1016
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [165]
% multiply(multiply(left_inverse(X),multiply(Y,X)),multiply(left_inverse(X),Y))
% -> multiply(left_inverse(X),multiply(Y,Y))
% Current number of equations to process: 1015
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [166]
% multiply(multiply(X,multiply(X,multiply(left_inverse(Y),left_inverse(Y)))),Y)
% -> multiply(X,multiply(X,left_inverse(Y)))
% Current number of equations to process: 1014
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [167]
% multiply(left_inverse(X),multiply(multiply(Y,X),multiply(left_inverse(X),Z)))
% <-> multiply(multiply(left_inverse(X),Y),Z)
% Current number of equations to process: 1011
% Current number of ordered equations: 1
% Current number of rules: 82
% New rule produced :
% [168]
% multiply(multiply(left_inverse(X),Y),Z) <->
% multiply(left_inverse(X),multiply(multiply(Y,X),multiply(left_inverse(X),Z)))
% Current number of equations to process: 1011
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [169]
% multiply(Y,multiply(multiply(left_inverse(Y),X),multiply(Y,left_inverse(X))))
% -> multiply(X,multiply(Y,left_inverse(X)))
% Current number of equations to process: 1008
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [170]
% multiply(Y,multiply(multiply(left_inverse(Y),left_inverse(X)),multiply(Y,X)))
% -> multiply(left_inverse(X),multiply(Y,X))
% Current number of equations to process: 1007
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [171]
% multiply(multiply(X,multiply(Y,Y)),multiply(left_inverse(Y),left_inverse(X)))
% -> multiply(X,multiply(Y,left_inverse(X)))
% Current number of equations to process: 1005
% Current number of ordered equations: 0
% Current number of rules: 86
% Rule [81]
% multiply(multiply(X,multiply(Y,Y)),Y) ->
% multiply(multiply(X,Y),multiply(Y,Y)) is composed into [81]
% multiply(
% multiply(X,
% multiply(Y,Y)),Y)
% ->
% multiply(X,
% multiply(Y,
% multiply(Y,Y)))
% New rule produced :
% [172]
% multiply(multiply(X,Y),multiply(Y,Y)) ->
% multiply(X,multiply(Y,multiply(Y,Y)))
% Rule
% [123]
% multiply(X,multiply(multiply(Y,X),multiply(X,X))) ->
% multiply(X,multiply(Y,multiply(X,multiply(X,X)))) collapsed.
% Current number of equations to process: 1446
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [173]
% multiply(multiply(left_inverse(X),left_inverse(Y)),multiply(Y,X)) -> identity
% Rule
% [155]
% multiply(X,multiply(multiply(left_inverse(Y),left_inverse(X)),multiply(X,Y)))
% -> X collapsed.
% Current number of equations to process: 1464
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [174]
% multiply(multiply(X,Y),multiply(left_inverse(Y),left_inverse(X))) -> identity
% Current number of equations to process: 1463
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [175]
% multiply(multiply(X,Y),multiply(multiply(left_inverse(Y),left_inverse(X)),Z))
% -> Z
% Current number of equations to process: 1483
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [176]
% multiply(multiply(left_inverse(X),left_inverse(Y)),multiply(multiply(Y,X),Z))
% -> Z
% Current number of equations to process: 1482
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [177]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(Z))),multiply(Z,Y))
% -> X
% Rule
% [91]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(Y))),multiply(Y,Y))
% -> X collapsed.
% Rule
% [136]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(X))),multiply(X,Y))
% -> X collapsed.
% Current number of equations to process: 1481
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [178]
% multiply(multiply(X,multiply(Y,Z)),multiply(left_inverse(Z),left_inverse(Y)))
% -> X
% Rule
% [143]
% multiply(multiply(X,multiply(Y,Y)),multiply(left_inverse(Y),left_inverse(Y)))
% -> X collapsed.
% Current number of equations to process: 1480
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [179]
% multiply(multiply(X,Y),multiply(Y,X)) ->
% multiply(X,multiply(Y,multiply(Y,X)))
% Rule
% [145]
% multiply(multiply(X,left_inverse(Y)),multiply(left_inverse(Y),X)) ->
% multiply(X,multiply(left_inverse(Y),multiply(left_inverse(Y),X))) collapsed.
% Current number of equations to process: 1485
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [180] multiply(multiply(X,Y),multiply(left_inverse(Y),X)) -> multiply(X,X)
% Current number of equations to process: 1510
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [181]
% multiply(multiply(left_inverse(X),Y),multiply(left_inverse(Y),multiply(X,X)))
% -> X
% Current number of equations to process: 1585
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [182]
% multiply(multiply(X,left_inverse(Y)),multiply(Y,multiply(left_inverse(X),
% left_inverse(X)))) ->
% left_inverse(X)
% Current number of equations to process: 1584
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [183]
% multiply(multiply(left_inverse(X),Y),multiply(Y,X)) ->
% multiply(left_inverse(X),multiply(Y,multiply(Y,X)))
% Current number of equations to process: 1676
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [184]
% multiply(multiply(X,Y),multiply(Y,left_inverse(X))) ->
% multiply(X,multiply(Y,multiply(Y,left_inverse(X))))
% Current number of equations to process: 1719
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [185]
% multiply(X,multiply(multiply(X,left_inverse(Y)),multiply(Y,left_inverse(X))))
% -> X
% Current number of equations to process: 1730
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [186]
% multiply(multiply(X,multiply(Y,multiply(X,Y))),Z) ->
% multiply(multiply(X,Y),multiply(multiply(X,Y),Z))
% Current number of equations to process: 1773
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [187]
% multiply(multiply(X,multiply(Y,Z)),multiply(left_inverse(Z),X)) ->
% multiply(X,multiply(Y,X))
% Current number of equations to process: 1827
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [188]
% multiply(multiply(X,left_inverse(Y)),multiply(Y,multiply(X,Y))) ->
% multiply(X,multiply(X,Y))
% Current number of equations to process: 1939
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [189]
% multiply(multiply(X,Y),multiply(X,multiply(Y,Y))) ->
% multiply(X,multiply(Y,multiply(X,multiply(Y,Y))))
% Current number of equations to process: 1961
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [190]
% multiply(multiply(X,multiply(X,Y)),multiply(left_inverse(Y),left_inverse(Y)))
% -> multiply(X,multiply(X,left_inverse(Y)))
% Current number of equations to process: 1960
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [191]
% multiply(multiply(X,left_inverse(Y)),multiply(Y,left_inverse(X))) -> identity
% Rule
% [156]
% multiply(X,multiply(multiply(Y,left_inverse(X)),multiply(X,left_inverse(Y))))
% -> X collapsed.
% Rule
% [185]
% multiply(X,multiply(multiply(X,left_inverse(Y)),multiply(Y,left_inverse(X))))
% -> X collapsed.
% Current number of equations to process: 1969
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [192]
% multiply(multiply(X,left_inverse(Y)),multiply(Y,multiply(left_inverse(X),
% left_inverse(Y)))) ->
% left_inverse(Y)
% Current number of equations to process: 1971
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [193]
% multiply(multiply(X,Y),multiply(left_inverse(Y),multiply(left_inverse(X),Y)))
% -> Y
% Current number of equations to process: 2014
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [194]
% multiply(multiply(left_inverse(X),multiply(left_inverse(X),Y)),multiply(
% left_inverse(Y),X))
% -> left_inverse(X)
% Current number of equations to process: 2048
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [195]
% multiply(multiply(left_inverse(X),Y),multiply(left_inverse(Y),X)) -> identity
% Current number of equations to process: 2049
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [196]
% multiply(multiply(X,Y),multiply(left_inverse(Y),multiply(left_inverse(X),
% left_inverse(X)))) ->
% left_inverse(X)
% Current number of equations to process: 2095
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [197]
% multiply(multiply(X,multiply(X,left_inverse(Y))),multiply(Y,X)) ->
% multiply(X,multiply(X,X))
% Current number of equations to process: 2146
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [198]
% multiply(multiply(X,left_inverse(Y)),multiply(Y,multiply(Y,Y))) ->
% multiply(X,multiply(Y,Y))
% Current number of equations to process: 2167
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [199]
% multiply(multiply(X,multiply(Y,left_inverse(X))),multiply(X,left_inverse(Y)))
% -> X
% Current number of equations to process: 2181
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [200]
% multiply(multiply(X,left_inverse(Y)),multiply(Y,multiply(Y,X))) ->
% multiply(X,multiply(Y,X))
% Current number of equations to process: 2188
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [201]
% multiply(multiply(left_inverse(X),left_inverse(Y)),multiply(X,Y)) ->
% multiply(left_inverse(X),multiply(left_inverse(Y),multiply(X,Y)))
% Rule
% [170]
% multiply(Y,multiply(multiply(left_inverse(Y),left_inverse(X)),multiply(Y,X)))
% -> multiply(left_inverse(X),multiply(Y,X)) collapsed.
% Current number of equations to process: 2215
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [202]
% multiply(multiply(left_inverse(X),Y),multiply(X,left_inverse(Y))) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,left_inverse(Y))))
% Rule
% [169]
% multiply(Y,multiply(multiply(left_inverse(Y),X),multiply(Y,left_inverse(X))))
% -> multiply(X,multiply(Y,left_inverse(X))) collapsed.
% Current number of equations to process: 2277
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [203]
% multiply(multiply(X,left_inverse(Y)),multiply(left_inverse(X),Y)) ->
% multiply(X,multiply(left_inverse(Y),multiply(left_inverse(X),Y)))
% Current number of equations to process: 2399
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [204]
% multiply(multiply(X,Y),multiply(left_inverse(X),left_inverse(Y))) ->
% multiply(X,multiply(Y,multiply(left_inverse(X),left_inverse(Y))))
% Current number of equations to process: 2455
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [205]
% multiply(multiply(X,Y),multiply(left_inverse(Y),multiply(left_inverse(Y),X)))
% -> multiply(X,multiply(left_inverse(Y),X))
% Current number of equations to process: 2514
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [206]
% multiply(multiply(left_inverse(X),left_inverse(Y)),multiply(Y,multiply(Y,X)))
% -> multiply(left_inverse(X),multiply(Y,X))
% Current number of equations to process: 2513
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [207]
% multiply(multiply(X,multiply(Y,left_inverse(Z))),multiply(Z,X)) ->
% multiply(X,multiply(Y,X))
% Rule
% [197]
% multiply(multiply(X,multiply(X,left_inverse(Y))),multiply(Y,X)) ->
% multiply(X,multiply(X,X)) collapsed.
% Current number of equations to process: 2627
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [208]
% multiply(multiply(X,Y),multiply(left_inverse(Y),multiply(left_inverse(X),
% left_inverse(Y)))) ->
% left_inverse(Y)
% Current number of equations to process: 2887
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [209]
% multiply(multiply(X,left_inverse(Y)),multiply(Y,multiply(Y,left_inverse(X))))
% -> multiply(X,multiply(Y,left_inverse(X)))
% Current number of equations to process: 2892
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [210]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(X))),multiply(X,
% multiply(Y,Y)))
% -> multiply(X,Y)
% Current number of equations to process: 2927
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [211]
% multiply(multiply(left_inverse(Y),multiply(left_inverse(Y),left_inverse(X))),
% multiply(X,multiply(Y,multiply(Y,X)))) -> X
% Current number of equations to process: 2926
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [212]
% multiply(multiply(left_inverse(Y),multiply(left_inverse(X),left_inverse(X))),
% multiply(X,multiply(X,multiply(Y,X)))) -> X
% Current number of equations to process: 2925
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [213]
% multiply(multiply(left_inverse(Y),multiply(left_inverse(Y),left_inverse(X))),
% multiply(X,multiply(Y,multiply(Y,Y)))) -> Y
% Current number of equations to process: 2923
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [214]
% multiply(multiply(left_inverse(Y),multiply(left_inverse(X),left_inverse(X))),
% multiply(X,multiply(X,multiply(Y,Y)))) -> Y
% Current number of equations to process: 2920
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [215]
% multiply(multiply(left_inverse(Y),left_inverse(X)),multiply(X,multiply(Y,
% multiply(X,X))))
% -> multiply(X,X)
% Current number of equations to process: 2919
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [216]
% multiply(multiply(X,multiply(X,multiply(left_inverse(Y),left_inverse(Y)))),
% multiply(Y,Y)) -> multiply(X,X)
% Current number of equations to process: 2916
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [217]
% multiply(multiply(left_inverse(X),Y),multiply(left_inverse(Y),multiply(X,
% multiply(Y,Y))))
% -> multiply(Y,Y)
% Current number of equations to process: 2915
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [218]
% multiply(multiply(left_inverse(X),Y),multiply(left_inverse(Y),multiply(X,
% multiply(Y,X))))
% -> multiply(Y,X)
% Current number of equations to process: 2912
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [219]
% multiply(multiply(X,left_inverse(Y)),multiply(Y,multiply(left_inverse(X),
% multiply(Y,X)))) ->
% multiply(Y,X)
% Current number of equations to process: 2911
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [220]
% multiply(multiply(X,multiply(X,multiply(left_inverse(Y),left_inverse(Z)))),
% multiply(Z,Y)) -> multiply(X,X)
% Rule
% [216]
% multiply(multiply(X,multiply(X,multiply(left_inverse(Y),left_inverse(Y)))),
% multiply(Y,Y)) -> multiply(X,X) collapsed.
% Current number of equations to process: 2910
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [221]
% multiply(multiply(X,multiply(X,multiply(Y,Z))),multiply(left_inverse(Z),
% left_inverse(Y))) ->
% multiply(X,X)
% Current number of equations to process: 2908
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [222]
% multiply(multiply(X,multiply(Y,multiply(Y,Y))),multiply(left_inverse(Y),
% left_inverse(Y))) ->
% multiply(X,Y)
% Current number of equations to process: 2907
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [223]
% multiply(multiply(X,multiply(X,multiply(X,left_inverse(Y)))),multiply(Y,
% left_inverse(X)))
% -> multiply(X,X)
% Current number of equations to process: 2905
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [224]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(X))),multiply(X,
% multiply(Y,X)))
% -> multiply(X,X)
% Current number of equations to process: 2904
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [225]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(Y))),multiply(Y,
% multiply(Y,X)))
% -> multiply(X,X)
% Current number of equations to process: 2903
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [226]
% multiply(multiply(left_inverse(X),left_inverse(Y)),multiply(Y,multiply(X,
% multiply(X,X))))
% -> multiply(X,X)
% Current number of equations to process: 2902
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [227]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(Z))),multiply(
% multiply(Z,Y),X))
% -> multiply(X,X)
% Current number of equations to process: 2900
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [228]
% multiply(multiply(left_inverse(X),Y),multiply(left_inverse(Y),multiply(X,
% multiply(X,Y))))
% -> multiply(X,Y)
% Current number of equations to process: 2896
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [229]
% multiply(multiply(X,multiply(X,Y)),multiply(left_inverse(Y),multiply(
% left_inverse(X),Y)))
% -> multiply(X,Y)
% Current number of equations to process: 2894
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [230]
% multiply(multiply(left_inverse(X),multiply(Y,Y)),multiply(left_inverse(Y),
% multiply(left_inverse(Y),X)))
% -> identity
% Current number of equations to process: 2889
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [231]
% multiply(multiply(Y,X),multiply(left_inverse(X),multiply(left_inverse(Y),
% multiply(X,Y)))) ->
% multiply(X,Y)
% Current number of equations to process: 2888
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [232]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(X))),multiply(X,
% multiply(Y,
% left_inverse(X))))
% -> identity
% Current number of equations to process: 2885
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [233]
% multiply(multiply(X,multiply(Y,multiply(Y,left_inverse(X)))),multiply(X,
% left_inverse(Y)))
% -> multiply(X,Y)
% Current number of equations to process: 2883
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [234]
% multiply(multiply(Y,left_inverse(X)),multiply(X,multiply(left_inverse(Y),
% multiply(X,X)))) ->
% multiply(X,X)
% Current number of equations to process: 2878
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [235]
% multiply(multiply(X,multiply(Y,Y)),multiply(left_inverse(Y),multiply(
% left_inverse(Y),X)))
% -> multiply(X,X)
% Current number of equations to process: 3113
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [236]
% multiply(multiply(left_inverse(X),multiply(Y,multiply(X,left_inverse(Y)))),Y)
% -> multiply(left_inverse(X),multiply(Y,X))
% Current number of equations to process: 3312
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [237]
% multiply(multiply(left_inverse(X),Y),multiply(multiply(left_inverse(Y),X),Z))
% -> Z
% Current number of equations to process: 3485
% Current number of ordered equations: 1
% Current number of rules: 140
% New rule produced :
% [238]
% multiply(multiply(X,left_inverse(Y)),multiply(multiply(Y,left_inverse(X)),Z))
% -> Z
% Current number of equations to process: 3485
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [239]
% multiply(multiply(X,multiply(Y,multiply(Y,Y))),left_inverse(Y)) ->
% multiply(X,multiply(Y,Y))
% Current number of equations to process: 3484
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [240]
% multiply(multiply(X,Y),multiply(left_inverse(Y),multiply(X,X))) ->
% multiply(X,multiply(X,X))
% Current number of equations to process: 3483
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [241]
% multiply(multiply(X,left_inverse(Y)),multiply(Y,multiply(X,X))) ->
% multiply(X,multiply(X,X))
% Current number of equations to process: 3482
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [242]
% multiply(multiply(X,multiply(Y,left_inverse(Z))),multiply(Z,left_inverse(Y)))
% -> X
% Rule
% [135]
% multiply(multiply(X,multiply(X,left_inverse(Y))),multiply(Y,left_inverse(X)))
% -> X collapsed.
% Rule
% [199]
% multiply(multiply(X,multiply(Y,left_inverse(X))),multiply(X,left_inverse(Y)))
% -> X collapsed.
% Current number of equations to process: 3586
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [243]
% multiply(multiply(X,multiply(left_inverse(Y),Z)),multiply(left_inverse(Z),Y))
% -> X
% Rule
% [142]
% multiply(multiply(left_inverse(X),multiply(left_inverse(Y),X)),multiply(
% left_inverse(X),Y))
% -> left_inverse(X) collapsed.
% Rule
% [194]
% multiply(multiply(left_inverse(X),multiply(left_inverse(X),Y)),multiply(
% left_inverse(Y),X))
% -> left_inverse(X) collapsed.
% Current number of equations to process: 3597
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [244]
% multiply(multiply(left_inverse(X),multiply(Y,X)),Y) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,Y)))
% Current number of equations to process: 3746
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [245]
% multiply(multiply(X,multiply(Y,left_inverse(X))),Y) ->
% multiply(X,multiply(Y,multiply(left_inverse(X),Y)))
% Current number of equations to process: 3745
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [246]
% multiply(multiply(X,multiply(Y,multiply(Y,Y))),Y) ->
% multiply(multiply(X,Y),multiply(Y,multiply(Y,Y)))
% Current number of equations to process: 3932
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [247]
% multiply(multiply(X,Y),multiply(X,multiply(X,X))) ->
% multiply(X,multiply(Y,multiply(X,multiply(X,X))))
% Current number of equations to process: 3931
% Current number of ordered equations: 0
% Current number of rules: 146
% Rule [246]
% multiply(multiply(X,multiply(Y,multiply(Y,Y))),Y) ->
% multiply(multiply(X,Y),multiply(Y,multiply(Y,Y))) is composed into 
% [246]
% multiply(multiply(X,multiply(Y,multiply(Y,Y))),Y) ->
% multiply(X,multiply(Y,multiply(Y,multiply(Y,Y))))
% New rule produced :
% [248]
% multiply(multiply(X,Y),multiply(Y,multiply(Y,Y))) ->
% multiply(X,multiply(Y,multiply(Y,multiply(Y,Y))))
% Current number of equations to process: 3930
% Current number of ordered equations: 0
% Current number of rules: 147
% Rule [122]
% multiply(multiply(X,multiply(X,multiply(Y,Y))),Y) ->
% multiply(multiply(X,multiply(X,Y)),multiply(Y,Y)) is composed into 
% [122]
% multiply(multiply(X,multiply(X,multiply(Y,Y))),Y) ->
% multiply(X,multiply(X,multiply(Y,multiply(Y,Y))))
% New rule produced :
% [249]
% multiply(multiply(X,multiply(X,Y)),multiply(Y,Y)) ->
% multiply(X,multiply(X,multiply(Y,multiply(Y,Y))))
% Current number of equations to process: 3929
% Current number of ordered equations: 0
% Current number of rules: 148
% Rule [120]
% multiply(multiply(X,multiply(Y,Y)),multiply(X,Y)) ->
% multiply(multiply(X,Y),multiply(Y,multiply(X,Y))) is composed into 
% [120]
% multiply(multiply(X,multiply(Y,Y)),multiply(X,Y)) ->
% multiply(X,multiply(Y,multiply(Y,multiply(X,Y))))
% New rule produced :
% [250]
% multiply(multiply(X,Y),multiply(Y,multiply(X,Y))) ->
% multiply(X,multiply(Y,multiply(Y,multiply(X,Y))))
% Current number of equations to process: 3928
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [251]
% multiply(multiply(left_inverse(X),multiply(Y,Y)),multiply(left_inverse(Y),X))
% -> multiply(left_inverse(X),multiply(Y,X))
% Current number of equations to process: 3927
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [252]
% multiply(X,multiply(multiply(Y,multiply(left_inverse(Z),left_inverse(X))),X))
% <-> multiply(multiply(X,Y),left_inverse(Z))
% Current number of equations to process: 3926
% Current number of ordered equations: 1
% Current number of rules: 151
% New rule produced :
% [253]
% multiply(multiply(X,Y),left_inverse(Z)) <->
% multiply(X,multiply(multiply(Y,multiply(left_inverse(Z),left_inverse(X))),X))
% Current number of equations to process: 3926
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [254]
% multiply(left_inverse(X),multiply(multiply(Y,multiply(Z,X)),left_inverse(X)))
% <-> multiply(multiply(left_inverse(X),Y),Z)
% Current number of equations to process: 3925
% Current number of ordered equations: 1
% Current number of rules: 153
% New rule produced :
% [255]
% multiply(multiply(left_inverse(X),Y),Z) <->
% multiply(left_inverse(X),multiply(multiply(Y,multiply(Z,X)),left_inverse(X)))
% Current number of equations to process: 3925
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [256]
% multiply(multiply(X,Y),multiply(left_inverse(Y),multiply(X,left_inverse(Y))))
% -> multiply(X,multiply(X,left_inverse(Y)))
% Current number of equations to process: 3924
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [257]
% multiply(multiply(X,Y),multiply(multiply(left_inverse(Y),Z),X)) ->
% multiply(X,multiply(Z,X))
% Current number of equations to process: 4261
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [258]
% multiply(X,multiply(multiply(Y,left_inverse(Z)),X)) <->
% multiply(multiply(X,Y),multiply(left_inverse(Z),X))
% Current number of equations to process: 4272
% Current number of ordered equations: 1
% Current number of rules: 157
% New rule produced :
% [259]
% multiply(multiply(X,Y),multiply(left_inverse(Z),X)) <->
% multiply(X,multiply(multiply(Y,left_inverse(Z)),X))
% Current number of equations to process: 4272
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [260]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(Y))),multiply(Y,
% multiply(Y,Y)))
% -> multiply(X,Y)
% Current number of equations to process: 4486
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [261]
% multiply(multiply(left_inverse(Y),left_inverse(X)),multiply(X,multiply(Y,
% multiply(X,Y))))
% -> multiply(X,Y)
% Current number of equations to process: 4484
% Current number of ordered equations: 1
% Current number of rules: 160
% New rule produced :
% [262]
% multiply(multiply(left_inverse(X),multiply(left_inverse(X),left_inverse(Y))),
% multiply(Y,multiply(X,X))) -> identity
% Current number of equations to process: 4484
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [263]
% multiply(multiply(left_inverse(X),multiply(left_inverse(Y),X)),multiply(
% left_inverse(X),
% multiply(Y,X)))
% -> identity
% Current number of equations to process: 4483
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [264]
% multiply(multiply(left_inverse(X),multiply(left_inverse(Y),left_inverse(Y))),
% multiply(Y,multiply(Y,X))) -> identity
% Current number of equations to process: 4482
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [265]
% multiply(multiply(multiply(left_inverse(X),left_inverse(Y)),left_inverse(Z)),
% multiply(Z,multiply(Y,X))) -> identity
% Current number of equations to process: 4479
% Current number of ordered equations: 1
% Current number of rules: 164
% New rule produced :
% [266]
% multiply(multiply(left_inverse(X),multiply(left_inverse(Y),left_inverse(Z))),
% multiply(multiply(Z,Y),X)) -> identity
% Current number of equations to process: 4479
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [267]
% multiply(multiply(X,multiply(Y,Y)),multiply(left_inverse(Y),multiply(
% left_inverse(Y),
% left_inverse(X))))
% -> identity
% Current number of equations to process: 4478
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [268]
% multiply(multiply(left_inverse(X),multiply(Y,X)),multiply(left_inverse(X),
% multiply(left_inverse(Y),X)))
% -> identity
% Current number of equations to process: 4477
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced :
% [269]
% multiply(multiply(X,multiply(X,Y)),multiply(left_inverse(Y),multiply(
% left_inverse(X),
% left_inverse(X))))
% -> identity
% Current number of equations to process: 4476
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced :
% [270]
% multiply(multiply(multiply(X,Y),Z),multiply(left_inverse(Z),multiply(
% left_inverse(Y),
% left_inverse(X))))
% -> identity
% Current number of equations to process: 4473
% Current number of ordered equations: 1
% Current number of rules: 169
% New rule produced :
% [271]
% multiply(multiply(X,multiply(Y,Z)),multiply(multiply(left_inverse(Z),
% left_inverse(Y)),left_inverse(X)))
% -> identity
% Current number of equations to process: 4473
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced :
% [272]
% multiply(multiply(X,Y),multiply(left_inverse(Y),multiply(left_inverse(X),
% multiply(Y,Y)))) ->
% multiply(Y,Y)
% Current number of equations to process: 4472
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [273]
% multiply(multiply(X,Y),multiply(left_inverse(Y),multiply(multiply(left_inverse(X),Y),Z)))
% -> multiply(Y,Z)
% Current number of equations to process: 4471
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [274]
% multiply(multiply(X,Y),multiply(left_inverse(X),multiply(multiply(X,left_inverse(Y)),Z)))
% -> multiply(X,Z)
% Current number of equations to process: 4470
% Current number of ordered equations: 0
% Current number of rules: 173
% New rule produced :
% [275]
% multiply(multiply(left_inverse(Z),X),multiply(left_inverse(X),multiply(
% multiply(Z,X),Y)))
% -> multiply(X,Y)
% Current number of equations to process: 4468
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced :
% [276]
% multiply(multiply(X,left_inverse(Z)),multiply(left_inverse(X),multiply(
% multiply(X,Z),Y)))
% -> multiply(X,Y)
% Current number of equations to process: 4467
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced :
% [277]
% multiply(multiply(multiply(left_inverse(X),left_inverse(Y)),Z),multiply(
% left_inverse(Z),
% multiply(Y,X)))
% -> identity
% Current number of equations to process: 4465
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced :
% [278]
% multiply(multiply(X,multiply(Y,Z)),multiply(multiply(left_inverse(Z),
% left_inverse(Y)),X)) ->
% multiply(X,X)
% Current number of equations to process: 4463
% Current number of ordered equations: 0
% Current number of rules: 177
% New rule produced :
% [279]
% multiply(multiply(multiply(X,Y),left_inverse(Z)),multiply(Z,multiply(
% left_inverse(Y),
% left_inverse(X))))
% -> identity
% Current number of equations to process: 4461
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [280]
% multiply(multiply(left_inverse(X),left_inverse(Y)),multiply(Y,multiply(X,
% multiply(X,Y))))
% -> multiply(X,Y)
% Current number of equations to process: 4460
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [281]
% multiply(multiply(left_inverse(X),Y),multiply(left_inverse(Y),multiply(X,
% multiply(X,X))))
% -> multiply(X,X)
% Current number of equations to process: 4458
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [282]
% multiply(multiply(multiply(X,Z),left_inverse(Y)),multiply(Y,multiply(
% left_inverse(Z),Y)))
% -> multiply(X,Y)
% Current number of equations to process: 4456
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [283]
% multiply(multiply(left_inverse(X),multiply(left_inverse(Y),X)),Y) ->
% multiply(left_inverse(X),multiply(left_inverse(Y),multiply(X,Y)))
% Current number of equations to process: 4793
% Current number of ordered equations: 0
% Current number of rules: 182
% New rule produced :
% [284]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(X))),Y) ->
% multiply(X,multiply(left_inverse(Y),multiply(left_inverse(X),Y)))
% Current number of equations to process: 4792
% Current number of ordered equations: 0
% Current number of rules: 183
% New rule produced :
% [285]
% multiply(multiply(X,multiply(Y,left_inverse(X))),left_inverse(Y)) ->
% multiply(X,multiply(Y,multiply(left_inverse(X),left_inverse(Y))))
% Current number of equations to process: 4899
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [286]
% multiply(multiply(left_inverse(X),multiply(Y,X)),left_inverse(Y)) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,left_inverse(Y))))
% Current number of equations to process: 4898
% Current number of ordered equations: 0
% Current number of rules: 185
% New rule produced :
% [287]
% multiply(multiply(X,multiply(X,left_inverse(Y))),multiply(Y,multiply(
% left_inverse(X),
% left_inverse(X))))
% -> identity
% Current number of equations to process: 4979
% Current number of ordered equations: 1
% Current number of rules: 186
% New rule produced :
% [288]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(Y))),multiply(Y,
% multiply(Y,
% left_inverse(X))))
% -> identity
% Current number of equations to process: 4979
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [289]
% multiply(multiply(X,multiply(Y,left_inverse(X))),multiply(X,multiply(
% left_inverse(Y),
% left_inverse(X))))
% -> identity
% Current number of equations to process: 4976
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [290]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(Z))),multiply(
% multiply(Z,Y),
% left_inverse(X)))
% -> identity
% Current number of equations to process: 4975
% Current number of ordered equations: 0
% Current number of rules: 189
% New rule produced :
% [291]
% multiply(multiply(left_inverse(X),multiply(Y,Z)),multiply(multiply(left_inverse(Z),
% left_inverse(Y)),X))
% -> identity
% Current number of equations to process: 4974
% Current number of ordered equations: 0
% Current number of rules: 190
% New rule produced :
% [292]
% multiply(multiply(X,multiply(X,left_inverse(Y))),multiply(Y,multiply(
% left_inverse(X),Y)))
% -> multiply(X,Y)
% Current number of equations to process: 4973
% Current number of ordered equations: 0
% Current number of rules: 191
% New rule produced :
% [293]
% multiply(multiply(X,multiply(Y,multiply(left_inverse(X),left_inverse(Y)))),
% multiply(Y,X)) -> multiply(X,Y)
% Current number of equations to process: 4972
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced :
% [294]
% multiply(X,multiply(multiply(Y,Z),X)) <->
% multiply(multiply(X,Y),multiply(Z,X))
% Rule
% [258]
% multiply(X,multiply(multiply(Y,left_inverse(Z)),X)) <->
% multiply(multiply(X,Y),multiply(left_inverse(Z),X)) collapsed.
% Current number of equations to process: 1699
% Current number of ordered equations: 1
% Current number of rules: 192
% New rule produced :
% [295]
% multiply(multiply(X,Y),multiply(Z,X)) <->
% multiply(X,multiply(multiply(Y,Z),X))
% Rule
% [259]
% multiply(multiply(X,Y),multiply(left_inverse(Z),X)) <->
% multiply(X,multiply(multiply(Y,left_inverse(Z)),X)) collapsed.
% Current number of equations to process: 1699
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced :
% [296]
% multiply(X,multiply(multiply(Y,multiply(Z,Z)),X)) <->
% multiply(multiply(X,multiply(Y,Z)),multiply(Z,X))
% Current number of equations to process: 1778
% Current number of ordered equations: 1
% Current number of rules: 193
% New rule produced :
% [297]
% multiply(multiply(X,multiply(Y,Z)),multiply(Z,X)) <->
% multiply(X,multiply(multiply(Y,multiply(Z,Z)),X))
% Current number of equations to process: 1778
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [298]
% multiply(X,multiply(multiply(Y,multiply(Y,Z)),X)) <->
% multiply(multiply(X,multiply(Y,Y)),multiply(Z,X))
% Current number of equations to process: 1777
% Current number of ordered equations: 1
% Current number of rules: 195
% New rule produced :
% [299]
% multiply(multiply(X,multiply(Y,Y)),multiply(Z,X)) <->
% multiply(X,multiply(multiply(Y,multiply(Y,Z)),X))
% Current number of equations to process: 1777
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [300]
% multiply(multiply(multiply(X,left_inverse(Z)),left_inverse(Y)),multiply(Y,
% multiply(Z,Y)))
% -> multiply(X,Y)
% Current number of equations to process: 1822
% Current number of ordered equations: 0
% Current number of rules: 197
% New rule produced :
% [301]
% multiply(multiply(X,multiply(X,multiply(Y,left_inverse(Z)))),multiply(Z,
% left_inverse(Y)))
% -> multiply(X,X)
% Rule
% [223]
% multiply(multiply(X,multiply(X,multiply(X,left_inverse(Y)))),multiply(Y,
% left_inverse(X)))
% -> multiply(X,X) collapsed.
% Current number of equations to process: 2359
% Current number of ordered equations: 0
% Current number of rules: 197
% New rule produced :
% [302]
% multiply(left_inverse(X),multiply(multiply(X,Y),multiply(left_inverse(Y),
% multiply(left_inverse(Y),
% left_inverse(X))))) ->
% multiply(left_inverse(Y),left_inverse(X))
% Current number of equations to process: 2357
% Current number of ordered equations: 0
% Current number of rules: 198
% New rule produced :
% [303]
% multiply(multiply(X,Y),multiply(X,multiply(left_inverse(Y),left_inverse(X))))
% ->
% multiply(X,multiply(Y,multiply(X,multiply(left_inverse(Y),left_inverse(X)))))
% Current number of equations to process: 2354
% Current number of ordered equations: 0
% Current number of rules: 199
% New rule produced :
% [304]
% multiply(multiply(X,multiply(X,multiply(left_inverse(Y),Z))),multiply(
% left_inverse(Z),Y))
% -> multiply(X,X)
% Current number of equations to process: 2454
% Current number of ordered equations: 0
% Current number of rules: 200
% New rule produced :
% [305]
% multiply(multiply(X,multiply(Y,left_inverse(X))),multiply(X,multiply(
% left_inverse(Y),X)))
% -> multiply(X,X)
% Current number of equations to process: 2638
% Current number of ordered equations: 0
% Current number of rules: 201
% New rule produced :
% [306]
% multiply(multiply(X,multiply(Y,left_inverse(Z))),multiply(multiply(Z,
% left_inverse(Y)),X))
% -> multiply(X,X)
% Current number of equations to process: 2763
% Current number of ordered equations: 0
% Current number of rules: 202
% New rule produced :
% [307]
% multiply(multiply(X,multiply(left_inverse(Y),Z)),multiply(multiply(left_inverse(Z),Y),X))
% -> multiply(X,X)
% Current number of equations to process: 2851
% Current number of ordered equations: 0
% Current number of rules: 203
% New rule produced :
% [308]
% multiply(X,multiply(multiply(left_inverse(X),Y),multiply(X,Z))) <->
% multiply(Y,multiply(multiply(X,left_inverse(Y)),multiply(Y,Z)))
% Current number of equations to process: 3160
% Current number of ordered equations: 1
% Current number of rules: 204
% New rule produced :
% [309]
% multiply(Y,multiply(multiply(X,left_inverse(Y)),multiply(Y,Z))) <->
% multiply(X,multiply(multiply(left_inverse(X),Y),multiply(X,Z)))
% Current number of equations to process: 3160
% Current number of ordered equations: 0
% Current number of rules: 205
% New rule produced :
% [310]
% multiply(multiply(left_inverse(X),multiply(Y,Z)),multiply(X,Z)) ->
% multiply(left_inverse(X),multiply(Y,multiply(Z,multiply(X,Z))))
% Current number of equations to process: 3196
% Current number of ordered equations: 0
% Current number of rules: 206
% New rule produced :
% [311]
% multiply(multiply(X,multiply(Y,Z)),multiply(left_inverse(X),Z)) ->
% multiply(X,multiply(Y,multiply(Z,multiply(left_inverse(X),Z))))
% Current number of equations to process: 3195
% Current number of ordered equations: 0
% Current number of rules: 207
% New rule produced :
% [312]
% multiply(multiply(multiply(X,left_inverse(Y)),multiply(Z,X)),Y) ->
% multiply(multiply(X,left_inverse(Y)),multiply(Z,multiply(X,Y)))
% Current number of equations to process: 3194
% Current number of ordered equations: 0
% Current number of rules: 208
% New rule produced :
% [313]
% multiply(multiply(multiply(X,Y),multiply(Z,X)),left_inverse(Y)) ->
% multiply(multiply(X,Y),multiply(Z,multiply(X,left_inverse(Y))))
% Current number of equations to process: 3193
% Current number of ordered equations: 0
% Current number of rules: 209
% New rule produced :
% [314]
% multiply(multiply(X,multiply(Y,multiply(left_inverse(X),left_inverse(Y)))),Y)
% -> multiply(X,multiply(Y,left_inverse(X)))
% Current number of equations to process: 3288
% Current number of ordered equations: 0
% Current number of rules: 210
% New rule produced :
% [315]
% multiply(X,multiply(multiply(Y,multiply(Z,left_inverse(X))),X)) <->
% multiply(multiply(X,Y),Z)
% Rule
% [252]
% multiply(X,multiply(multiply(Y,multiply(left_inverse(Z),left_inverse(X))),X))
% <-> multiply(multiply(X,Y),left_inverse(Z)) collapsed.
% Current number of equations to process: 3579
% Current number of ordered equations: 1
% Current number of rules: 210
% New rule produced :
% [316]
% multiply(multiply(X,Y),Z) <->
% multiply(X,multiply(multiply(Y,multiply(Z,left_inverse(X))),X))
% Rule
% [253]
% multiply(multiply(X,Y),left_inverse(Z)) <->
% multiply(X,multiply(multiply(Y,multiply(left_inverse(Z),left_inverse(X))),X))
% collapsed.
% Current number of equations to process: 3579
% Current number of ordered equations: 0
% Current number of rules: 210
% New rule produced :
% [317]
% multiply(multiply(left_inverse(X),multiply(Y,multiply(X,Y))),left_inverse(Y))
% -> multiply(left_inverse(X),multiply(Y,X))
% Current number of equations to process: 3887
% Current number of ordered equations: 0
% Current number of rules: 211
% New rule produced :
% [318]
% multiply(multiply(X,multiply(Y,multiply(left_inverse(X),Y))),left_inverse(Y))
% -> multiply(X,multiply(Y,left_inverse(X)))
% Current number of equations to process: 3886
% Current number of ordered equations: 0
% Current number of rules: 212
% New rule produced :
% [319]
% multiply(multiply(X,multiply(Y,multiply(left_inverse(X),Y))),multiply(
% left_inverse(Y),X))
% -> multiply(X,Y)
% Current number of equations to process: 4308
% Current number of ordered equations: 0
% Current number of rules: 213
% New rule produced :
% [320]
% multiply(multiply(multiply(X,left_inverse(Y)),Z),multiply(left_inverse(Z),
% multiply(Y,left_inverse(X))))
% -> identity
% Current number of equations to process: 4307
% Current number of ordered equations: 0
% Current number of rules: 214
% New rule produced :
% [321]
% multiply(multiply(multiply(X,left_inverse(Y)),left_inverse(Z)),multiply(Z,
% multiply(Y,
% left_inverse(X))))
% -> identity
% Current number of equations to process: 4306
% Current number of ordered equations: 0
% Current number of rules: 215
% New rule produced :
% [322]
% multiply(multiply(X,multiply(Y,multiply(X,left_inverse(Y)))),multiply(Y,
% left_inverse(X)))
% -> multiply(X,Y)
% Current number of equations to process: 4305
% Current number of ordered equations: 0
% Current number of rules: 216
% New rule produced :
% [323]
% multiply(multiply(multiply(left_inverse(X),Y),Z),multiply(left_inverse(Z),
% multiply(left_inverse(Y),X)))
% -> identity
% Current number of equations to process: 4304
% Current number of ordered equations: 0
% Current number of rules: 217
% New rule produced :
% [324]
% multiply(multiply(multiply(left_inverse(X),Y),left_inverse(Z)),multiply(Z,
% multiply(
% left_inverse(Y),X)))
% -> identity
% Current number of equations to process: 4303
% Current number of ordered equations: 0
% Current number of rules: 218
% New rule produced :
% [325]
% multiply(multiply(multiply(left_inverse(X),Y),Z),X) ->
% multiply(left_inverse(X),multiply(Y,multiply(Z,X)))
% Current number of equations to process: 4354
% Current number of ordered equations: 0
% Current number of rules: 219
% New rule produced :
% [326]
% multiply(X,multiply(multiply(left_inverse(X),Y),Z)) <->
% multiply(multiply(Y,multiply(Z,X)),left_inverse(X))
% Current number of equations to process: 4359
% Current number of ordered equations: 1
% Current number of rules: 220
% New rule produced :
% [327]
% multiply(multiply(Y,multiply(Z,X)),left_inverse(X)) <->
% multiply(X,multiply(multiply(left_inverse(X),Y),Z))
% Current number of equations to process: 4359
% Current number of ordered equations: 0
% Current number of rules: 221
% New rule produced :
% [328]
% multiply(left_inverse(Z),multiply(multiply(multiply(Z,X),multiply(Y,Z)),
% left_inverse(Z))) -> multiply(X,Y)
% Current number of equations to process: 4448
% Current number of ordered equations: 0
% Current number of rules: 222
% New rule produced :
% [329]
% multiply(multiply(X,multiply(Y,multiply(Z,Y))),left_inverse(Y)) ->
% multiply(multiply(X,Y),Z)
% Rule
% [239]
% multiply(multiply(X,multiply(Y,multiply(Y,Y))),left_inverse(Y)) ->
% multiply(X,multiply(Y,Y)) collapsed.
% Rule
% [317]
% multiply(multiply(left_inverse(X),multiply(Y,multiply(X,Y))),left_inverse(Y))
% -> multiply(left_inverse(X),multiply(Y,X)) collapsed.
% Rule
% [318]
% multiply(multiply(X,multiply(Y,multiply(left_inverse(X),Y))),left_inverse(Y))
% -> multiply(X,multiply(Y,left_inverse(X))) collapsed.
% Current number of equations to process: 4455
% Current number of ordered equations: 0
% Current number of rules: 220
% New rule produced :
% [330]
% multiply(multiply(X,Z),multiply(left_inverse(Z),Y)) <->
% multiply(multiply(X,multiply(Y,Z)),left_inverse(Z))
% Current number of equations to process: 4478
% Current number of ordered equations: 1
% Current number of rules: 221
% New rule produced :
% [331]
% multiply(multiply(X,multiply(Y,Z)),left_inverse(Z)) <->
% multiply(multiply(X,Z),multiply(left_inverse(Z),Y))
% Current number of equations to process: 4478
% Current number of ordered equations: 0
% Current number of rules: 222
% New rule produced :
% [332]
% multiply(X,multiply(multiply(multiply(left_inverse(X),Y),Z),Y)) ->
% multiply(Y,multiply(Z,Y))
% Current number of equations to process: 4666
% Current number of ordered equations: 0
% Current number of rules: 223
% New rule produced :
% [333]
% multiply(multiply(X,left_inverse(Y)),multiply(multiply(Y,Z),X)) ->
% multiply(X,multiply(Z,X))
% Current number of equations to process: 4665
% Current number of ordered equations: 0
% Current number of rules: 224
% New rule produced :
% [334]
% multiply(multiply(left_inverse(X),Z),Y) <->
% multiply(multiply(left_inverse(X),left_inverse(Y)),multiply(Y,multiply(Z,Y)))
% Rule
% [236]
% multiply(multiply(left_inverse(X),multiply(Y,multiply(X,left_inverse(Y)))),Y)
% -> multiply(left_inverse(X),multiply(Y,X)) collapsed.
% Rule
% [283]
% multiply(multiply(left_inverse(X),multiply(left_inverse(Y),X)),Y) ->
% multiply(left_inverse(X),multiply(left_inverse(Y),multiply(X,Y))) collapsed.
% Current number of equations to process: 4746
% Current number of ordered equations: 1
% Current number of rules: 223
% New rule produced :
% [335]
% multiply(multiply(left_inverse(X),left_inverse(Y)),multiply(Y,multiply(Z,Y)))
% <-> multiply(multiply(left_inverse(X),Z),Y)
% Current number of equations to process: 4746
% Current number of ordered equations: 0
% Current number of rules: 224
% New rule produced :
% [336]
% multiply(multiply(Z,left_inverse(Y)),multiply(Y,multiply(multiply(left_inverse(Z),X),Y)))
% -> multiply(X,Y)
% Current number of equations to process: 4758
% Current number of ordered equations: 0
% Current number of rules: 225
% New rule produced :
% [337]
% multiply(multiply(left_inverse(X),multiply(left_inverse(X),Y)),multiply(
% left_inverse(Y),
% multiply(X,X)))
% -> identity
% Current number of equations to process: 4843
% Current number of ordered equations: 0
% Current number of rules: 226
% New rule produced :
% [338]
% multiply(multiply(left_inverse(X),multiply(left_inverse(Y),Z)),multiply(
% multiply(
% left_inverse(Z),Y),X))
% -> identity
% Current number of equations to process: 1979
% Current number of ordered equations: 1
% Current number of rules: 227
% New rule produced :
% [339]
% multiply(multiply(left_inverse(X),multiply(Y,left_inverse(Z))),multiply(
% multiply(Z,
% left_inverse(Y)),X))
% -> identity
% Current number of equations to process: 1979
% Current number of ordered equations: 0
% Current number of rules: 228
% New rule produced :
% [340]
% multiply(multiply(X,multiply(Y,left_inverse(Z))),multiply(multiply(Z,
% left_inverse(Y)),
% left_inverse(X))) ->
% identity
% Current number of equations to process: 2237
% Current number of ordered equations: 1
% Current number of rules: 229
% New rule produced :
% [341]
% multiply(multiply(X,multiply(left_inverse(Y),Z)),multiply(multiply(left_inverse(Z),Y),
% left_inverse(X))) ->
% identity
% Current number of equations to process: 2237
% Current number of ordered equations: 0
% Current number of rules: 230
% New rule produced :
% [342]
% multiply(multiply(multiply(X,Y),multiply(left_inverse(Y),Z)),Y) ->
% multiply(X,multiply(Z,Y))
% Current number of equations to process: 2982
% Current number of ordered equations: 0
% Current number of rules: 231
% New rule produced :
% [343]
% multiply(Y,multiply(multiply(left_inverse(Y),multiply(X,Y)),Z)) <->
% multiply(multiply(X,multiply(Y,Y)),multiply(left_inverse(Y),Z))
% Current number of equations to process: 2980
% Current number of ordered equations: 1
% Current number of rules: 232
% New rule produced :
% [344]
% multiply(multiply(X,multiply(Y,Y)),multiply(left_inverse(Y),Z)) <->
% multiply(Y,multiply(multiply(left_inverse(Y),multiply(X,Y)),Z))
% Current number of equations to process: 2980
% Current number of ordered equations: 0
% Current number of rules: 233
% New rule produced :
% [345]
% multiply(Y,multiply(multiply(left_inverse(Y),multiply(X,X)),Z)) <->
% multiply(multiply(X,multiply(X,Y)),multiply(left_inverse(Y),Z))
% Current number of equations to process: 3212
% Current number of ordered equations: 1
% Current number of rules: 234
% New rule produced :
% [346]
% multiply(multiply(X,multiply(X,Y)),multiply(left_inverse(Y),Z)) <->
% multiply(Y,multiply(multiply(left_inverse(Y),multiply(X,X)),Z))
% Current number of equations to process: 3212
% Current number of ordered equations: 0
% Current number of rules: 235
% New rule produced :
% [347]
% multiply(multiply(multiply(X,left_inverse(Y)),multiply(Y,Z)),Y) <->
% multiply(left_inverse(Y),multiply(multiply(multiply(Y,X),Z),Y))
% Current number of equations to process: 3210
% Current number of ordered equations: 1
% Current number of rules: 236
% New rule produced :
% [348]
% multiply(left_inverse(Y),multiply(multiply(multiply(Y,X),Z),Y)) <->
% multiply(multiply(multiply(X,left_inverse(Y)),multiply(Y,Z)),Y)
% Current number of equations to process: 3210
% Current number of ordered equations: 0
% Current number of rules: 237
% New rule produced :
% [349]
% multiply(multiply(X,Y),multiply(left_inverse(X),multiply(Y,X))) ->
% multiply(X,multiply(Y,multiply(left_inverse(X),multiply(Y,X))))
% Current number of equations to process: 3208
% Current number of ordered equations: 0
% Current number of rules: 238
% New rule produced :
% [350]
% multiply(multiply(X,left_inverse(Y)),multiply(X,multiply(Y,Y))) ->
% multiply(X,multiply(left_inverse(Y),multiply(X,multiply(Y,Y))))
% Current number of equations to process: 3207
% Current number of ordered equations: 0
% Current number of rules: 239
% New rule produced :
% [351]
% multiply(left_inverse(X),multiply(multiply(multiply(Y,X),Z),X)) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,multiply(Z,X))))
% Current number of equations to process: 3206
% Current number of ordered equations: 0
% Current number of rules: 240
% New rule produced :
% [352]
% multiply(left_inverse(X),multiply(multiply(Y,multiply(X,X)),Z)) <->
% multiply(multiply(left_inverse(X),multiply(Y,X)),multiply(X,Z))
% Current number of equations to process: 3205
% Current number of ordered equations: 1
% Current number of rules: 241
% New rule produced :
% [353]
% multiply(multiply(left_inverse(X),multiply(Y,X)),multiply(X,Z)) <->
% multiply(left_inverse(X),multiply(multiply(Y,multiply(X,X)),Z))
% Current number of equations to process: 3205
% Current number of ordered equations: 0
% Current number of rules: 242
% New rule produced :
% [354]
% multiply(left_inverse(X),multiply(multiply(Y,multiply(Y,X)),Z)) <->
% multiply(multiply(left_inverse(X),multiply(Y,Y)),multiply(X,Z))
% Current number of equations to process: 3204
% Current number of ordered equations: 1
% Current number of rules: 243
% New rule produced :
% [355]
% multiply(multiply(left_inverse(X),multiply(Y,Y)),multiply(X,Z)) <->
% multiply(left_inverse(X),multiply(multiply(Y,multiply(Y,X)),Z))
% Current number of equations to process: 3204
% Current number of ordered equations: 0
% Current number of rules: 244
% New rule produced :
% [356]
% multiply(multiply(left_inverse(X),Y),multiply(X,multiply(Y,Y))) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,multiply(Y,Y))))
% Current number of equations to process: 3203
% Current number of ordered equations: 0
% Current number of rules: 245
% New rule produced :
% [357]
% multiply(multiply(left_inverse(X),Y),multiply(X,multiply(Y,X))) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,multiply(Y,X))))
% Current number of equations to process: 3201
% Current number of ordered equations: 0
% Current number of rules: 246
% New rule produced :
% [358]
% multiply(left_inverse(Y),multiply(multiply(Y,multiply(X,X)),Z)) <->
% multiply(multiply(X,multiply(X,left_inverse(Y))),multiply(Y,Z))
% Current number of equations to process: 3391
% Current number of ordered equations: 1
% Current number of rules: 247
% New rule produced :
% [359]
% multiply(multiply(X,multiply(X,left_inverse(Y))),multiply(Y,Z)) <->
% multiply(left_inverse(Y),multiply(multiply(Y,multiply(X,X)),Z))
% Current number of equations to process: 3391
% Current number of ordered equations: 0
% Current number of rules: 248
% New rule produced :
% [360]
% multiply(left_inverse(X),multiply(multiply(X,multiply(X,Y)),Z)) <->
% multiply(multiply(X,multiply(Y,left_inverse(X))),multiply(X,Z))
% Current number of equations to process: 3390
% Current number of ordered equations: 1
% Current number of rules: 249
% New rule produced :
% [361]
% multiply(multiply(X,multiply(Y,left_inverse(X))),multiply(X,Z)) <->
% multiply(left_inverse(X),multiply(multiply(X,multiply(X,Y)),Z))
% Current number of equations to process: 3390
% Current number of ordered equations: 0
% Current number of rules: 250
% New rule produced :
% [362]
% multiply(multiply(multiply(X,Y),multiply(left_inverse(X),Z)),X) ->
% multiply(multiply(X,multiply(Y,left_inverse(X))),multiply(Z,X))
% Current number of equations to process: 3387
% Current number of ordered equations: 0
% Current number of rules: 251
% New rule produced :
% [363]
% multiply(X,multiply(multiply(Y,multiply(Y,left_inverse(X))),Z)) <->
% multiply(multiply(X,multiply(Y,Y)),multiply(left_inverse(X),Z))
% Current number of equations to process: 3386
% Current number of ordered equations: 1
% Current number of rules: 252
% New rule produced :
% [364]
% multiply(multiply(X,multiply(Y,Y)),multiply(left_inverse(X),Z)) <->
% multiply(X,multiply(multiply(Y,multiply(Y,left_inverse(X))),Z))
% Current number of equations to process: 3386
% Current number of ordered equations: 0
% Current number of rules: 253
% New rule produced :
% [365]
% multiply(X,multiply(multiply(X,multiply(Y,left_inverse(X))),Z)) <->
% multiply(multiply(X,multiply(X,Y)),multiply(left_inverse(X),Z))
% Current number of equations to process: 3385
% Current number of ordered equations: 1
% Current number of rules: 254
% New rule produced :
% [366]
% multiply(multiply(X,multiply(X,Y)),multiply(left_inverse(X),Z)) <->
% multiply(X,multiply(multiply(X,multiply(Y,left_inverse(X))),Z))
% Current number of equations to process: 3385
% Current number of ordered equations: 0
% Current number of rules: 255
% New rule produced :
% [367]
% multiply(multiply(X,Y),multiply(left_inverse(X),multiply(Y,Y))) ->
% multiply(X,multiply(Y,multiply(left_inverse(X),multiply(Y,Y))))
% Current number of equations to process: 3384
% Current number of ordered equations: 0
% Current number of rules: 256
% New rule produced :
% [368]
% multiply(multiply(left_inverse(X),multiply(Y,left_inverse(Z))),left_inverse(Y))
% ->
% multiply(multiply(left_inverse(X),Y),multiply(left_inverse(Z),left_inverse(Y)))
% Current number of equations to process: 3437
% Current number of ordered equations: 0
% Current number of rules: 257
% New rule produced :
% [369]
% multiply(left_inverse(X),multiply(multiply(X,Y),multiply(Z,X))) <->
% multiply(multiply(Y,Z),X)
% Current number of equations to process: 3890
% Current number of ordered equations: 1
% Current number of rules: 258
% Rule [348]
% multiply(left_inverse(Y),multiply(multiply(multiply(Y,X),Z),Y)) <->
% multiply(multiply(multiply(X,left_inverse(Y)),multiply(Y,Z)),Y) is composed into 
% [348]
% multiply(left_inverse(Y),multiply(multiply(multiply(Y,X),Z),Y)) <->
% multiply(left_inverse(Y),multiply(multiply(Y,multiply(X,left_inverse(Y))),
% multiply(multiply(Y,Z),Y)))
% New rule produced :
% [370]
% multiply(multiply(Y,Z),X) <->
% multiply(left_inverse(X),multiply(multiply(X,Y),multiply(Z,X)))
% Rule
% [77]
% multiply(multiply(left_inverse(X),Y),X) ->
% multiply(left_inverse(X),multiply(Y,X)) collapsed.
% Rule
% [284]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(X))),Y) ->
% multiply(X,multiply(left_inverse(Y),multiply(left_inverse(X),Y))) collapsed.
% Rule
% [312]
% multiply(multiply(multiply(X,left_inverse(Y)),multiply(Z,X)),Y) ->
% multiply(multiply(X,left_inverse(Y)),multiply(Z,multiply(X,Y))) collapsed.
% Rule
% [314]
% multiply(multiply(X,multiply(Y,multiply(left_inverse(X),left_inverse(Y)))),Y)
% -> multiply(X,multiply(Y,left_inverse(X))) collapsed.
% Rule
% [325]
% multiply(multiply(multiply(left_inverse(X),Y),Z),X) ->
% multiply(left_inverse(X),multiply(Y,multiply(Z,X))) collapsed.
% Rule
% [342]
% multiply(multiply(multiply(X,Y),multiply(left_inverse(Y),Z)),Y) ->
% multiply(X,multiply(Z,Y)) collapsed.
% Rule
% [347]
% multiply(multiply(multiply(X,left_inverse(Y)),multiply(Y,Z)),Y) <->
% multiply(left_inverse(Y),multiply(multiply(multiply(Y,X),Z),Y)) collapsed.
% Rule
% [362]
% multiply(multiply(multiply(X,Y),multiply(left_inverse(X),Z)),X) ->
% multiply(multiply(X,multiply(Y,left_inverse(X))),multiply(Z,X)) collapsed.
% Current number of equations to process: 3894
% Current number of ordered equations: 0
% Current number of rules: 251
% New rule produced :
% [371]
% multiply(multiply(multiply(X,Y),multiply(Z,X)),left_inverse(X)) ->
% multiply(X,multiply(Y,Z))
% Rule
% [328]
% multiply(left_inverse(Z),multiply(multiply(multiply(Z,X),multiply(Y,Z)),
% left_inverse(Z))) -> multiply(X,Y) collapsed.
% Current number of equations to process: 3893
% Current number of ordered equations: 0
% Current number of rules: 251
% Rule [316]
% multiply(multiply(X,Y),Z) <->
% multiply(X,multiply(multiply(Y,multiply(Z,left_inverse(X))),X)) is composed into 
% [316]
% multiply(multiply(X,Y),Z) <->
% multiply(X,multiply(multiply(Y,left_inverse(X)),multiply(X,multiply(multiply(Z,
% left_inverse(X)),X))))
% New rule produced :
% [372]
% multiply(multiply(X,Y),Z) <->
% multiply(multiply(X,left_inverse(Z)),multiply(Z,multiply(Y,Z)))
% Rule
% [87] multiply(multiply(X,multiply(X,left_inverse(Y))),Y) -> multiply(X,X)
% collapsed.
% Rule
% [89]
% multiply(multiply(X,multiply(left_inverse(Y),left_inverse(Y))),Y) ->
% multiply(X,left_inverse(Y)) collapsed.
% Rule
% [100]
% multiply(multiply(X,multiply(Y,multiply(X,left_inverse(Z)))),Z) ->
% multiply(X,multiply(Y,X)) collapsed.
% Rule
% [166]
% multiply(multiply(X,multiply(X,multiply(left_inverse(Y),left_inverse(Y)))),Y)
% -> multiply(X,multiply(X,left_inverse(Y))) collapsed.
% Rule
% [315]
% multiply(X,multiply(multiply(Y,multiply(Z,left_inverse(X))),X)) <->
% multiply(multiply(X,Y),Z) collapsed.
% Rule
% [334]
% multiply(multiply(left_inverse(X),Z),Y) <->
% multiply(multiply(left_inverse(X),left_inverse(Y)),multiply(Y,multiply(Z,Y)))
% collapsed.
% Current number of equations to process: 4185
% Current number of ordered equations: 1
% Current number of rules: 246
% New rule produced :
% [373]
% multiply(multiply(X,left_inverse(Z)),multiply(Z,multiply(Y,Z))) <->
% multiply(multiply(X,Y),Z)
% Rule
% [198]
% multiply(multiply(X,left_inverse(Y)),multiply(Y,multiply(Y,Y))) ->
% multiply(X,multiply(Y,Y)) collapsed.
% Rule
% [335]
% multiply(multiply(left_inverse(X),left_inverse(Y)),multiply(Y,multiply(Z,Y)))
% <-> multiply(multiply(left_inverse(X),Z),Y) collapsed.
% Current number of equations to process: 4185
% Current number of ordered equations: 0
% Current number of rules: 245
% New rule produced :
% [374]
% multiply(multiply(X,Y),multiply(multiply(Z,Y),X)) ->
% multiply(X,multiply(Y,multiply(Z,multiply(Y,X))))
% Current number of equations to process: 4183
% Current number of ordered equations: 1
% Current number of rules: 246
% New rule produced :
% [375]
% multiply(multiply(multiply(X,Y),multiply(Z,X)),V_3) ->
% multiply(X,multiply(multiply(Y,Z),multiply(X,V_3)))
% Rule
% [157]
% multiply(multiply(multiply(X,Y),multiply(Z,X)),Y) ->
% multiply(multiply(X,Y),multiply(Z,multiply(X,Y))) collapsed.
% Rule
% [313]
% multiply(multiply(multiply(X,Y),multiply(Z,X)),left_inverse(Y)) ->
% multiply(multiply(X,Y),multiply(Z,multiply(X,left_inverse(Y)))) collapsed.
% Rule
% [371]
% multiply(multiply(multiply(X,Y),multiply(Z,X)),left_inverse(X)) ->
% multiply(X,multiply(Y,Z)) collapsed.
% Current number of equations to process: 4184
% Current number of ordered equations: 0
% Current number of rules: 244
% New rule produced :
% [376]
% multiply(multiply(X,multiply(Y,Z)),multiply(Y,X)) ->
% multiply(X,multiply(Y,multiply(Z,multiply(Y,X))))
% Rule
% [293]
% multiply(multiply(X,multiply(Y,multiply(left_inverse(X),left_inverse(Y)))),
% multiply(Y,X)) -> multiply(X,Y) collapsed.
% Current number of equations to process: 4182
% Current number of ordered equations: 0
% Current number of rules: 244
% New rule produced :
% [377]
% multiply(multiply(X,Y),multiply(Y,multiply(X,X))) ->
% multiply(X,multiply(Y,multiply(Y,multiply(X,X))))
% Current number of equations to process: 4181
% Current number of ordered equations: 0
% Current number of rules: 245
% New rule produced :
% [378]
% multiply(multiply(X,multiply(X,Y)),multiply(Y,X)) ->
% multiply(X,multiply(X,multiply(Y,multiply(Y,X))))
% Current number of equations to process: 4179
% Current number of ordered equations: 0
% Current number of rules: 246
% New rule produced :
% [379]
% multiply(X,multiply(multiply(Y,multiply(Z,X)),X)) <->
% multiply(multiply(X,Y),multiply(Z,multiply(X,X)))
% Current number of equations to process: 4178
% Current number of ordered equations: 1
% Current number of rules: 247
% New rule produced :
% [380]
% multiply(multiply(X,Y),multiply(Z,multiply(X,X))) <->
% multiply(X,multiply(multiply(Y,multiply(Z,X)),X))
% Current number of equations to process: 4178
% Current number of ordered equations: 0
% Current number of rules: 248
% New rule produced :
% [381]
% multiply(X,multiply(multiply(Y,multiply(Z,Z)),X)) <->
% multiply(multiply(X,Y),multiply(Z,multiply(Z,X)))
% Current number of equations to process: 4177
% Current number of ordered equations: 1
% Current number of rules: 249
% New rule produced :
% [382]
% multiply(multiply(X,Y),multiply(Z,multiply(Z,X))) <->
% multiply(X,multiply(multiply(Y,multiply(Z,Z)),X))
% Current number of equations to process: 4177
% Current number of ordered equations: 0
% Current number of rules: 250
% New rule produced :
% [383]
% multiply(X,multiply(multiply(Y,Z),multiply(X,Y))) <->
% multiply(multiply(X,Y),multiply(Z,multiply(X,Y)))
% Current number of equations to process: 4175
% Current number of ordered equations: 3
% Current number of rules: 251
% New rule produced :
% [384]
% multiply(multiply(X,Y),multiply(Z,multiply(X,Y))) <->
% multiply(X,multiply(multiply(Y,Z),multiply(X,Y)))
% Current number of equations to process: 4175
% Current number of ordered equations: 2
% Current number of rules: 252
% New rule produced :
% [385]
% multiply(X,multiply(multiply(Y,multiply(X,Z)),X)) <->
% multiply(multiply(X,Y),multiply(X,multiply(Z,X)))
% Current number of equations to process: 4175
% Current number of ordered equations: 1
% Current number of rules: 253
% New rule produced :
% [386]
% multiply(multiply(X,Y),multiply(X,multiply(Z,X))) <->
% multiply(X,multiply(multiply(Y,multiply(X,Z)),X))
% Current number of equations to process: 4175
% Current number of ordered equations: 0
% Current number of rules: 254
% New rule produced :
% [387]
% multiply(X,multiply(multiply(left_inverse(X),Y),multiply(Z,left_inverse(X))))
% <-> multiply(multiply(Y,Z),left_inverse(X))
% Current number of equations to process: 4188
% Current number of ordered equations: 1
% Current number of rules: 255
% New rule produced :
% [388]
% multiply(multiply(Y,Z),left_inverse(X)) <->
% multiply(X,multiply(multiply(left_inverse(X),Y),multiply(Z,left_inverse(X))))
% Current number of equations to process: 4188
% Current number of ordered equations: 0
% Current number of rules: 256
% New rule produced :
% [389]
% multiply(left_inverse(Z),multiply(multiply(multiply(Z,X),Y),left_inverse(Z)))
% -> multiply(X,multiply(Y,left_inverse(Z)))
% Current number of equations to process: 4187
% Current number of ordered equations: 0
% Current number of rules: 257
% New rule produced :
% [390]
% multiply(multiply(X,Z),multiply(left_inverse(Z),multiply(Y,left_inverse(Z))))
% <-> multiply(multiply(X,Y),left_inverse(Z))
% Current number of equations to process: 4186
% Current number of ordered equations: 1
% Current number of rules: 258
% New rule produced :
% [391]
% multiply(multiply(X,Y),left_inverse(Z)) <->
% multiply(multiply(X,Z),multiply(left_inverse(Z),multiply(Y,left_inverse(Z))))
% Current number of equations to process: 4186
% Current number of ordered equations: 0
% Current number of rules: 259
% Rule [296]
% multiply(X,multiply(multiply(Y,multiply(Z,Z)),X)) <->
% multiply(multiply(X,multiply(Y,Z)),multiply(Z,X)) is composed into 
% [296]
% multiply(X,multiply(multiply(Y,multiply(Z,Z)),X)) <->
% multiply(multiply(X,Y),multiply(Z,multiply(Z,X)))
% New rule produced :
% [392]
% multiply(multiply(X,multiply(Y,Z)),multiply(Z,X)) ->
% multiply(multiply(X,Y),multiply(Z,multiply(Z,X)))
% Rule
% [297]
% multiply(multiply(X,multiply(Y,Z)),multiply(Z,X)) <->
% multiply(X,multiply(multiply(Y,multiply(Z,Z)),X)) collapsed.
% Rule
% [378]
% multiply(multiply(X,multiply(X,Y)),multiply(Y,X)) ->
% multiply(X,multiply(X,multiply(Y,multiply(Y,X)))) collapsed.
% Current number of equations to process: 4270
% Current number of ordered equations: 0
% Current number of rules: 258
% New rule produced :
% [393]
% multiply(multiply(X,Y),multiply(Y,multiply(Y,X))) ->
% multiply(X,multiply(Y,multiply(Y,multiply(Y,X))))
% Current number of equations to process: 4299
% Current number of ordered equations: 0
% Current number of rules: 259
% New rule produced :
% [394]
% multiply(multiply(X,Y),multiply(multiply(Y,Z),X)) <->
% multiply(multiply(X,multiply(Y,Y)),multiply(Z,X))
% Current number of equations to process: 4512
% Current number of ordered equations: 1
% Current number of rules: 260
% New rule produced :
% [395]
% multiply(multiply(X,multiply(Y,Y)),multiply(Z,X)) <->
% multiply(multiply(X,Y),multiply(multiply(Y,Z),X))
% Current number of equations to process: 4512
% Current number of ordered equations: 0
% Current number of rules: 261
% New rule produced :
% [396]
% multiply(multiply(left_inverse(X),left_inverse(Y)),multiply(Y,multiply(
% multiply(X,Z),Y)))
% -> multiply(Z,Y)
% Current number of equations to process: 4748
% Current number of ordered equations: 0
% Current number of rules: 262
% New rule produced :
% [397]
% multiply(X,multiply(multiply(Y,Z),multiply(X,left_inverse(Y)))) <->
% multiply(multiply(X,Y),multiply(Z,multiply(X,left_inverse(Y))))
% Current number of equations to process: 4747
% Current number of ordered equations: 1
% Current number of rules: 263
% New rule produced :
% [398]
% multiply(multiply(X,Y),multiply(Z,multiply(X,left_inverse(Y)))) <->
% multiply(X,multiply(multiply(Y,Z),multiply(X,left_inverse(Y))))
% Current number of equations to process: 4747
% Current number of ordered equations: 0
% Current number of rules: 264
% New rule produced :
% [399]
% multiply(multiply(left_inverse(X),Y),multiply(X,multiply(X,X))) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,multiply(X,X))))
% Current number of equations to process: 4910
% Current number of ordered equations: 0
% Current number of rules: 265
% New rule produced :
% [400]
% multiply(multiply(X,Y),multiply(Y,multiply(X,left_inverse(Y)))) ->
% multiply(X,multiply(Y,multiply(Y,multiply(X,left_inverse(Y)))))
% Current number of equations to process: 4909
% Current number of ordered equations: 0
% Current number of rules: 266
% New rule produced :
% [401]
% multiply(multiply(left_inverse(X),Y),multiply(X,multiply(X,Y))) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,multiply(X,Y))))
% Current number of equations to process: 4908
% Current number of ordered equations: 0
% Current number of rules: 267
% New rule produced :
% [402]
% multiply(multiply(X,Y),multiply(X,multiply(Y,left_inverse(X)))) ->
% multiply(X,multiply(Y,multiply(X,multiply(Y,left_inverse(X)))))
% Current number of equations to process: 4907
% Current number of ordered equations: 0
% Current number of rules: 268
% New rule produced :
% [403]
% multiply(multiply(left_inverse(X),multiply(Y,multiply(X,Y))),Y) ->
% multiply(multiply(left_inverse(X),multiply(Y,X)),multiply(Y,Y))
% Current number of equations to process: 4903
% Current number of ordered equations: 0
% Current number of rules: 269
% New rule produced :
% [404]
% multiply(multiply(X,multiply(Y,multiply(left_inverse(X),Y))),Y) ->
% multiply(multiply(X,multiply(Y,left_inverse(X))),multiply(Y,Y))
% Current number of equations to process: 4902
% Current number of ordered equations: 0
% Current number of rules: 270
% New rule produced :
% [405]
% multiply(multiply(left_inverse(X),multiply(multiply(Y,X),Z)),Y) ->
% multiply(left_inverse(X),multiply(multiply(Y,X),multiply(Z,Y)))
% Current number of equations to process: 4899
% Current number of ordered equations: 0
% Current number of rules: 271
% New rule produced :
% [406]
% multiply(left_inverse(X),multiply(multiply(Y,multiply(Z,X)),X)) <->
% multiply(multiply(multiply(left_inverse(X),Y),Z),multiply(X,X))
% Current number of equations to process: 4898
% Current number of ordered equations: 1
% Current number of rules: 272
% New rule produced :
% [407]
% multiply(multiply(multiply(left_inverse(X),Y),Z),multiply(X,X)) <->
% multiply(left_inverse(X),multiply(multiply(Y,multiply(Z,X)),X))
% Current number of equations to process: 4898
% Current number of ordered equations: 0
% Current number of rules: 273
% New rule produced :
% [408]
% multiply(left_inverse(X),multiply(multiply(Y,multiply(Z,X)),V_3)) <->
% multiply(multiply(multiply(left_inverse(X),Y),Z),multiply(X,V_3))
% Rule
% [406]
% multiply(left_inverse(X),multiply(multiply(Y,multiply(Z,X)),X)) <->
% multiply(multiply(multiply(left_inverse(X),Y),Z),multiply(X,X)) collapsed.
% Current number of equations to process: 4897
% Current number of ordered equations: 1
% Current number of rules: 273
% New rule produced :
% [409]
% multiply(multiply(multiply(left_inverse(X),Y),Z),multiply(X,V_3)) <->
% multiply(left_inverse(X),multiply(multiply(Y,multiply(Z,X)),V_3))
% Rule
% [407]
% multiply(multiply(multiply(left_inverse(X),Y),Z),multiply(X,X)) <->
% multiply(left_inverse(X),multiply(multiply(Y,multiply(Z,X)),X)) collapsed.
% Current number of equations to process: 4897
% Current number of ordered equations: 0
% Current number of rules: 273
% New rule produced :
% [410]
% multiply(X,multiply(multiply(Y,multiply(Z,left_inverse(Y))),X)) <->
% multiply(multiply(X,multiply(Y,Z)),multiply(left_inverse(Y),X))
% Current number of equations to process: 4891
% Current number of ordered equations: 1
% Current number of rules: 274
% New rule produced :
% [411]
% multiply(multiply(X,multiply(Y,Z)),multiply(left_inverse(Y),X)) <->
% multiply(X,multiply(multiply(Y,multiply(Z,left_inverse(Y))),X))
% Current number of equations to process: 4891
% Current number of ordered equations: 0
% Current number of rules: 275
% New rule produced :
% [412]
% multiply(multiply(X,left_inverse(Y)),multiply(X,multiply(Y,X))) ->
% multiply(X,multiply(left_inverse(Y),multiply(X,multiply(Y,X))))
% Current number of equations to process: 4890
% Current number of ordered equations: 0
% Current number of rules: 276
% New rule produced :
% [413]
% multiply(multiply(X,Y),multiply(X,multiply(left_inverse(Y),X))) ->
% multiply(X,multiply(Y,multiply(X,multiply(left_inverse(Y),X))))
% Current number of equations to process: 4889
% Current number of ordered equations: 0
% Current number of rules: 277
% New rule produced :
% [414]
% multiply(left_inverse(X),multiply(Y,multiply(multiply(X,Z),Y))) <->
% multiply(multiply(left_inverse(X),Y),multiply(X,multiply(Z,Y)))
% Current number of equations to process: 4887
% Current number of ordered equations: 1
% Current number of rules: 278
% New rule produced :
% [415]
% multiply(multiply(left_inverse(X),Y),multiply(X,multiply(Z,Y))) <->
% multiply(left_inverse(X),multiply(Y,multiply(multiply(X,Z),Y)))
% Rule
% [356]
% multiply(multiply(left_inverse(X),Y),multiply(X,multiply(Y,Y))) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,multiply(Y,Y)))) collapsed.
% Rule
% [401]
% multiply(multiply(left_inverse(X),Y),multiply(X,multiply(X,Y))) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,multiply(X,Y)))) collapsed.
% Current number of equations to process: 4887
% Current number of ordered equations: 0
% Current number of rules: 277
% New rule produced :
% [416]
% multiply(X,multiply(Y,multiply(multiply(left_inverse(X),Z),Y))) <->
% multiply(multiply(X,Y),multiply(left_inverse(X),multiply(Z,Y)))
% Current number of equations to process: 4886
% Current number of ordered equations: 1
% Current number of rules: 278
% New rule produced :
% [417]
% multiply(multiply(X,Y),multiply(left_inverse(X),multiply(Z,Y))) <->
% multiply(X,multiply(Y,multiply(multiply(left_inverse(X),Z),Y)))
% Current number of equations to process: 4886
% Current number of ordered equations: 0
% Current number of rules: 279
% New rule produced :
% [418]
% multiply(multiply(left_inverse(X),multiply(Y,multiply(Y,X))),Y) ->
% multiply(multiply(left_inverse(X),Y),multiply(Y,multiply(X,Y)))
% Current number of equations to process: 4885
% Current number of ordered equations: 0
% Current number of rules: 280
% New rule produced :
% [419]
% multiply(multiply(X,multiply(Y,multiply(Y,left_inverse(X)))),Y) ->
% multiply(multiply(X,Y),multiply(Y,multiply(left_inverse(X),Y)))
% Current number of equations to process: 4884
% Current number of ordered equations: 0
% Current number of rules: 281
% New rule produced :
% [420]
% multiply(multiply(multiply(X,Y),Z),Y) ->
% multiply(X,multiply(Y,multiply(Z,Y)))
% Rule
% [332]
% multiply(X,multiply(multiply(multiply(left_inverse(X),Y),Z),Y)) ->
% multiply(Y,multiply(Z,Y)) collapsed.
% Rule
% [351]
% multiply(left_inverse(X),multiply(multiply(multiply(Y,X),Z),X)) ->
% multiply(left_inverse(X),multiply(Y,multiply(X,multiply(Z,X)))) collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% Trivial
% 
% Current number of equations to process: 1717
% Current number of ordered equations: 0
% Current number of rules: 280
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% 
% The following 28 rules have been used:
% [1] 
% multiply(identity,X) -> X; trace = in the starting set
% [2] multiply(left_inverse(X),X) -> identity; trace = in the starting set
% [3] multiply(multiply(multiply(X,Y),X),Z) ->
% multiply(X,multiply(Y,multiply(X,Z))); trace = in the starting set
% [4] multiply(multiply(X,identity),Y) -> multiply(X,Y); trace = Cp of 3 and 1
% [6] multiply(multiply(X,X),Y) -> multiply(X,multiply(X,Y)); trace = Cp of 4 and 3
% [12] multiply(left_inverse(X),multiply(X,multiply(left_inverse(X),Y))) ->
% multiply(left_inverse(X),Y); trace = Cp of 3 and 2
% [13] multiply(left_inverse(X),multiply(X,identity)) -> identity; trace = Cp of 12 and 2
% [15] multiply(multiply(X,multiply(Y,multiply(X,identity))),Z) ->
% multiply(X,multiply(Y,multiply(X,Z))); trace = Cp of 4 and 3
% [18] multiply(X,multiply(left_inverse(X),multiply(X,Y))) -> multiply(X,Y); trace = Cp of 15 and 13
% [20] multiply(left_inverse(X),multiply(left_inverse(left_inverse(X)),identity))
% -> identity; trace = Cp of 18 and 2
% [28] multiply(multiply(X,multiply(Y,multiply(Y,multiply(X,identity)))),Z) ->
% multiply(X,multiply(Y,multiply(Y,multiply(X,Z)))); trace = Cp of 15 and 6
% [32] multiply(multiply(X,multiply(Y,multiply(X,X))),Z) ->
% multiply(X,multiply(multiply(Y,X),multiply(X,Z))); trace = Cp of 15 and 3
% [36] multiply(left_inverse(left_inverse(Y)),multiply(left_inverse(Y),
% multiply(left_inverse(Y),
% multiply(left_inverse(left_inverse(Y)),X))))
% -> X; trace = Cp of 28 and 20
% [39] multiply(left_inverse(Y),multiply(left_inverse(left_inverse(Y)),X)) -> X; trace = Cp of 36 and 12
% [41] multiply(left_inverse(X),identity) -> left_inverse(X); trace = Cp of 36 and 2
% [44] multiply(left_inverse(X),multiply(X,Y)) -> Y; trace = Cp of 39 and 12
% [47] left_inverse(left_inverse(X)) -> X; trace = Cp of 44 and 2
% [51] multiply(X,identity) -> X; trace = Cp of 47 and 41
% [52] multiply(X,multiply(left_inverse(X),Y)) -> Y; trace = Cp of 47 and 44
% [54] multiply(multiply(X,multiply(Y,X)),Z) ->
% multiply(X,multiply(Y,multiply(X,Z))); trace = Cp of 4 and 3
% [59] multiply(multiply(X,Y),X) -> multiply(X,multiply(Y,X)); trace = Cp of 51 and 3
% [60] multiply(X,multiply(multiply(Y,X),X)) ->
% multiply(X,multiply(Y,multiply(X,X))); trace = Cp of 51 and 32
% [67] multiply(Y,multiply(multiply(left_inverse(Y),X),Y)) -> multiply(X,Y); trace = Cp of 59 and 52
% [68] multiply(multiply(X,Y),Y) -> multiply(X,multiply(Y,Y)); trace = Cp of 60 and 44
% [93] multiply(Y,multiply(multiply(left_inverse(Y),X),multiply(Y,Z))) <->
% multiply(multiply(X,Y),Z); trace = Cp of 67 and 54
% [119] multiply(multiply(X,multiply(Y,multiply(X,Z))),Z) ->
% multiply(X,multiply(Y,multiply(X,multiply(Z,Z)))); trace = Cp of 68 and 54
% [310] multiply(multiply(left_inverse(X),multiply(Y,Z)),multiply(X,Z)) ->
% multiply(left_inverse(X),multiply(Y,multiply(Z,multiply(X,Z)))); trace = Cp of 119 and 44
% [420] multiply(multiply(multiply(X,Y),Z),Y) ->
% multiply(X,multiply(Y,multiply(Z,Y))); trace = Cp of 310 and 93
% % SZS output end Refutation
% All conjectures have been proven
% 
% Execution time: 57.860000 sec
% res : bool = true
% time is now off
% 
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
% 
% EOF
%------------------------------------------------------------------------------