TSTP Solution File: GRP410-1 by CiME---2.01

%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP410-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n109.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 00:22:55 EDT 2014

% Result   : Unsatisfiable 3.49s
% Output   : Refutation 3.49s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP410-1 : TPTP v6.0.0. Released v2.6.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n109.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 12:44:48 CDT 2014
% % CPUTime  : 3.49 
% Processing problem /tmp/CiME_43397_n109.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a2,b2 : constant;  inverse : 1;  multiply : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))) = B;
% ";
% 
% let s1 = status F "
% a2 lr_lex;
% b2 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% ";
% 
% let p1 = precedence F "
% multiply > inverse > b2 > a2";
% 
% let s2 = status F "
% a2 mul;
% b2 mul;
% inverse mul;
% multiply mul;
% ";
% 
% let p2 = precedence F "
% multiply > inverse > b2 = a2";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " multiply(multiply(inverse(b2),b2),a2) = a2;"
% ;
% (*
% let Red_Axioms = normalize_equations Defining_rules Axioms;
% 
% let Red_Conjectures =  normalize_equations Defining_rules Conjectures;
% *)
% #time on;
% 
% let res = prove_conj_by_ordered_completion o Axioms Conjectures;
% 
% #time off;
% 
% 
% let status = if res then "unsatisfiable" else "satisfiable";
% #quit;
% Verbose level is now 1
% 
% F : signature = <signature>
% X : variable_set = <variable set>
% 
% Axioms : (F,X) equations = { multiply(multiply(inverse(multiply(A,inverse(
% multiply(B,C)))),
% multiply(A,inverse(C))),inverse(
% multiply(
% inverse(C),C)))
% = B } (1 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(inverse(b2),b2),a2) = a2 }
% (1 equation(s))
% time is now on
% 
% Initializing completion ...
% New rule produced :
% [1]
% multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,
% inverse(C))),
% inverse(multiply(inverse(C),C))) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 1
% New rule produced :
% [2]
% multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(
% multiply(A,C)))),
% multiply(B,inverse(C))),inverse(C))),
% inverse(multiply(inverse(C),C))) -> inverse(C)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3]
% multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(B),multiply(
% multiply(
% inverse(
% multiply(C,
% inverse(
% multiply(B,A)))),
% multiply(C,
% inverse(A))),
% inverse(A))),
% inverse(A))),inverse(multiply(inverse(A),A)))
% -> inverse(A)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [4]
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(
% inverse(C),C)))))
% Current number of equations to process: 20
% Current number of ordered equations: 1
% Current number of rules: 4
% Rule [4]
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,
% inverse(C))) <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(
% multiply(
% inverse(C),C))))) is composed into 
% [4]
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% <->
% multiply(inverse(multiply(a2,inverse(multiply(B,C)))),multiply(a2,inverse(C)))
% New rule produced :
% [5]
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(a2,inverse(B))),multiply(a2,inverse(inverse(
% multiply(
% inverse(C),C)))))
% Current number of equations to process: 24
% Current number of ordered equations: 1
% Current number of rules: 6
% New rule produced :
% [7]
% multiply(inverse(multiply(a2,inverse(B))),multiply(a2,inverse(inverse(
% multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(C),C)))))
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8]
% multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),
% multiply(B,inverse(C))),inverse(C))) ->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(C),C)))),multiply(a2,
% inverse(C)))
% Rule
% [2]
% multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(
% multiply(A,C)))),
% multiply(B,inverse(C))),inverse(C))),
% inverse(multiply(inverse(C),C))) -> inverse(C) collapsed.
% Rule
% [3]
% multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(B),multiply(
% multiply(
% inverse(
% multiply(C,
% inverse(
% multiply(B,A)))),
% multiply(C,
% inverse(A))),
% inverse(A))),
% inverse(A))),inverse(multiply(inverse(A),A)))
% -> inverse(A) collapsed.
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [9]
% multiply(inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(
% inverse(C),C))),C)))),
% multiply(B,inverse(C))) -> A
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [10]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(A),A)))))
% <->
% multiply(inverse(multiply(C,inverse(B))),multiply(C,inverse(inverse(multiply(
% inverse(A),A)))))
% Current number of equations to process: 24
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [11]
% multiply(inverse(multiply(C,inverse(B))),multiply(C,inverse(inverse(multiply(
% inverse(A),A)))))
% <->
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(A),A)))))
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [12]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),
% multiply(A,inverse(C))),inverse(multiply(V_3,
% multiply(inverse(C),C))))),B)
% ->
% multiply(inverse(multiply(a2,inverse(multiply(V_3,multiply(inverse(C),C))))),
% multiply(a2,inverse(multiply(inverse(C),C))))
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [13]
% multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C)))
% <->
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% Rule
% [4]
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% <->
% multiply(inverse(multiply(a2,inverse(multiply(B,C)))),multiply(a2,inverse(C)))
% collapsed.
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [14]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(V_3,inverse(B))),multiply(V_3,inverse(inverse(
% multiply(
% inverse(C),C)))))
% Rule
% [6]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(a2,inverse(B))),multiply(a2,inverse(inverse(
% multiply(
% inverse(C),C)))))
% collapsed.
% Rule
% [7]
% multiply(inverse(multiply(a2,inverse(B))),multiply(a2,inverse(inverse(
% multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(C),C)))))
% collapsed.
% Rule
% [10]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(A),A)))))
% <->
% multiply(inverse(multiply(C,inverse(B))),multiply(C,inverse(inverse(multiply(
% inverse(A),A)))))
% collapsed.
% Rule
% [11]
% multiply(inverse(multiply(C,inverse(B))),multiply(C,inverse(inverse(multiply(
% inverse(A),A)))))
% <->
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(A),A)))))
% collapsed.
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [15]
% multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),
% multiply(B,inverse(C))),inverse(inverse(
% multiply(
% inverse(V_3),V_3)))))
% ->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(C),C)))),multiply(a2,
% inverse(
% inverse(
% multiply(
% inverse(V_3),V_3)))))
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [16]
% inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(V_3),V_3))),V_3))))
% <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(multiply(C,inverse(V_3))),multiply(C,inverse(V_3)))))
% Current number of equations to process: 58
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced :
% [17]
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(multiply(C,inverse(V_3))),multiply(C,inverse(V_3)))))
% <->
% inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(V_3),V_3))),V_3))))
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [18]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,
% inverse(C))))),
% multiply(A,inverse(inverse(C)))),inverse(V_3))),B)
% ->
% multiply(inverse(multiply(a2,inverse(V_3))),multiply(a2,inverse(multiply(
% inverse(
% inverse(C)),
% inverse(C)))))
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [19]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,
% inverse(V_3)))))
% <->
% multiply(inverse(multiply(V_4,inverse(B))),multiply(V_4,inverse(multiply(C,
% inverse(V_3)))))
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [20]
% multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,
% inverse(multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(multiply(C,inverse(V_3))),multiply(C,
% inverse(V_3))))),
% multiply(C,inverse(V_3))) -> B
% Current number of equations to process: 126
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [21]
% multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,
% inverse(C))),
% inverse(multiply(inverse(C),C))),C) -> B
% Rule
% [20]
% multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,
% inverse(multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(multiply(C,inverse(V_3))),multiply(C,
% inverse(V_3))))),
% multiply(C,inverse(V_3))) -> B collapsed.
% Current number of equations to process: 129
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [22]
% inverse(multiply(B,inverse(multiply(multiply(multiply(A,multiply(B,inverse(C))),
% inverse(multiply(inverse(C),C))),C)))) ->
% A
% Current number of equations to process: 145
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [23]
% multiply(inverse(A),A) <->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(inverse(B)),inverse(B))))),
% multiply(a2,inverse(multiply(inverse(inverse(B)),inverse(B)))))
% Current number of equations to process: 174
% Current number of ordered equations: 1
% Current number of rules: 15
% Rule [23]
% multiply(inverse(A),A) <->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(inverse(B)),
% inverse(B))))),multiply(a2,
% inverse(multiply(
% inverse(
% inverse(B)),
% inverse(B))))) is composed into 
% [23] multiply(inverse(A),A) <-> multiply(inverse(a2),a2)
% New rule produced :
% [24]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(inverse(B)),inverse(B))))),
% multiply(a2,inverse(multiply(inverse(inverse(B)),inverse(B))))) <->
% multiply(inverse(A),A)
% Current number of equations to process: 174
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [25]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) <->
% multiply(inverse(multiply(V_3,inverse(B))),multiply(V_3,inverse(C)))
% Rule
% [13]
% multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C)))
% <->
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% collapsed.
% Rule
% [14]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(V_3,inverse(B))),multiply(V_3,inverse(inverse(
% multiply(
% inverse(C),C)))))
% collapsed.
% Rule
% [19]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,
% inverse(V_3)))))
% <->
% multiply(inverse(multiply(V_4,inverse(B))),multiply(V_4,inverse(multiply(C,
% inverse(V_3)))))
% collapsed.
% Current number of equations to process: 203
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [26]
% multiply(multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,inverse(V_3)))))),
% multiply(A,inverse(multiply(C,inverse(V_3))))),inverse(multiply(
% inverse(a2),a2)))
% -> B
% Current number of equations to process: 204
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [27]
% multiply(multiply(multiply(A,multiply(B,inverse(C))),inverse(multiply(
% inverse(C),C))),C)
% <->
% multiply(multiply(multiply(A,multiply(B,inverse(V_3))),inverse(multiply(
% inverse(V_3),V_3))),V_3)
% Current number of equations to process: 248
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [28]
% multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,
% inverse(C))),
% inverse(multiply(inverse(a2),a2))) -> B
% Rule
% [26]
% multiply(multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,inverse(V_3)))))),
% multiply(A,inverse(multiply(C,inverse(V_3))))),inverse(multiply(
% inverse(a2),a2)))
% -> B collapsed.
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [29]
% multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(a2),a2)))),
% multiply(A,inverse(B))),inverse(multiply(inverse(B),B))) ->
% inverse(B)
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [30]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(
% multiply(A,B))),
% inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% -> A
% Current number of equations to process: 248
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced :
% [31]
% multiply(multiply(inverse(multiply(inverse(inverse(A)),inverse(multiply(B,A)))),
% multiply(inverse(a2),a2)),inverse(multiply(inverse(A),A))) -> B
% Current number of equations to process: 248
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [32]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),
% multiply(A,inverse(C))),inverse(V_3))),B) ->
% multiply(inverse(multiply(a2,inverse(V_3))),multiply(a2,inverse(multiply(
% inverse(C),C))))
% Rule
% [12]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),
% multiply(A,inverse(C))),inverse(multiply(V_3,
% multiply(inverse(C),C))))),B)
% ->
% multiply(inverse(multiply(a2,inverse(multiply(V_3,multiply(inverse(C),C))))),
% multiply(a2,inverse(multiply(inverse(C),C)))) collapsed.
% Rule
% [18]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,
% inverse(C))))),
% multiply(A,inverse(inverse(C)))),inverse(V_3))),B)
% ->
% multiply(inverse(multiply(a2,inverse(V_3))),multiply(a2,inverse(multiply(
% inverse(
% inverse(C)),
% inverse(C)))))
% collapsed.
% Current number of equations to process: 247
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [33]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,
% inverse(C))))),
% multiply(A,inverse(inverse(C)))),V_3)),B) ->
% multiply(inverse(multiply(a2,V_3)),multiply(a2,inverse(multiply(inverse(a2),a2))))
% Current number of equations to process: 246
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [34]
% multiply(V_3,inverse(multiply(multiply(multiply(B,multiply(V_3,inverse(V_4))),
% inverse(multiply(inverse(V_4),V_4))),V_4))) <->
% multiply(multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),
% inverse(multiply(inverse(C),C))),C)
% Current number of equations to process: 245
% Current number of ordered equations: 1
% Current number of rules: 20
% Rule [34]
% multiply(V_3,inverse(multiply(multiply(multiply(B,multiply(V_3,inverse(V_4))),
% inverse(multiply(inverse(V_4),V_4))),V_4)))
% <->
% multiply(multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),
% inverse(multiply(inverse(C),C))),C) is composed into [34]
% multiply(V_3,
% inverse(
% multiply(
% multiply(
% multiply(B,
% multiply(V_3,
% inverse(V_4))),
% inverse(
% multiply(
% inverse(V_4),V_4))),V_4)))
% <->
% multiply(a2,
% inverse(
% multiply(
% multiply(
% multiply(B,
% multiply(a2,
% inverse(a2))),
% inverse(
% multiply(
% inverse(a2),a2))),a2)))
% New rule produced :
% [35]
% multiply(multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),
% inverse(multiply(inverse(C),C))),C) <->
% multiply(V_3,inverse(multiply(multiply(multiply(B,multiply(V_3,inverse(V_4))),
% inverse(multiply(inverse(V_4),V_4))),V_4)))
% Rule
% [21]
% multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,
% inverse(C))),
% inverse(multiply(inverse(C),C))),C) -> B collapsed.
% Current number of equations to process: 246
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [36]
% multiply(a2,inverse(multiply(multiply(multiply(inverse(B),multiply(a2,
% inverse(a2))),
% inverse(multiply(inverse(a2),a2))),a2))) -> B
% Current number of equations to process: 245
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [37]
% multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(a2),a2),B)))),
% multiply(A,inverse(B))) -> inverse(inverse(multiply(inverse(B),B)))
% Current number of equations to process: 255
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [38]
% multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(
% inverse(a2),a2))),C)))),
% multiply(A,inverse(C))) -> B
% Current number of equations to process: 254
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [39]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% multiply(A,
% inverse(
% multiply(
% inverse(B),B))),B))),
% inverse(B))) -> A
% Current number of equations to process: 252
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [40]
% multiply(inverse(multiply(inverse(inverse(A)),inverse(multiply(multiply(B,
% inverse(
% multiply(
% inverse(A),A))),A)))),
% multiply(inverse(a2),a2)) -> B
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [41]
% multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),B)))),
% multiply(A,inverse(B))) ->
% multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(a2),a2)))
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [42]
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(a2),a2)))
% Current number of equations to process: 252
% Current number of ordered equations: 3
% Current number of rules: 27
% Rule [42]
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,
% inverse(C))) <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(a2),a2))) is composed into [42]
% multiply(inverse(
% multiply(V_3,
% inverse(
% multiply(B,C)))),
% multiply(V_3,
% inverse(C))) <->
% multiply(inverse(
% multiply(a2,
% inverse(
% multiply(B,C)))),
% multiply(a2,
% inverse(C)))
% New rule produced :
% [43]
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(a2),a2))) <->
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% Current number of equations to process: 254
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [44]
% multiply(inverse(multiply(C,inverse(multiply(B,V_3)))),multiply(C,inverse(V_3)))
% <->
% multiply(inverse(multiply(a2,inverse(multiply(B,a2)))),multiply(a2,inverse(a2)))
% Current number of equations to process: 252
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [45]
% multiply(inverse(multiply(a2,inverse(multiply(B,a2)))),multiply(a2,inverse(a2)))
% <->
% multiply(inverse(multiply(C,inverse(multiply(B,V_3)))),multiply(C,inverse(V_3)))
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [46]
% multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(inverse(inverse(multiply(A,B))),
% inverse(B))),inverse(B))) ->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(B),B)))),multiply(a2,
% inverse(B)))
% Current number of equations to process: 252
% Current number of ordered equations: 3
% Current number of rules: 31
% New rule produced :
% [47]
% multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(inverse(B)),
% inverse(multiply(A,B)))),
% multiply(inverse(a2),a2)),inverse(B))) ->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(B),B)))),multiply(a2,
% inverse(B)))
% Current number of equations to process: 252
% Current number of ordered equations: 2
% Current number of rules: 32
% New rule produced :
% [48]
% multiply(inverse(inverse(A)),multiply(multiply(inverse(multiply(B,inverse(
% multiply(
% inverse(a2),a2)))),
% multiply(B,inverse(A))),inverse(A)))
% <->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),multiply(a2,
% inverse(A)))
% Current number of equations to process: 252
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [49]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),multiply(a2,
% inverse(A)))
% <->
% multiply(inverse(inverse(A)),multiply(multiply(inverse(multiply(B,inverse(
% multiply(
% inverse(a2),a2)))),
% multiply(B,inverse(A))),inverse(A)))
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [50]
% multiply(multiply(inverse(multiply(V_3,inverse(B))),multiply(V_3,inverse(
% multiply(A,
% inverse(C))))),
% inverse(multiply(inverse(a2),a2))) ->
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(a2),a2))),C))))
% Current number of equations to process: 255
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [51]
% inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(a2),a2),
% inverse(multiply(inverse(B),B))),B)))) ->
% inverse(multiply(A,inverse(B)))
% Current number of equations to process: 261
% Current number of ordered equations: 1
% Current number of rules: 36
% New rule produced :
% [52]
% inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),
% inverse(multiply(inverse(a2),a2))),C))))
% -> B
% Current number of equations to process: 261
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [53]
% inverse(multiply(inverse(inverse(A)),inverse(multiply(multiply(multiply(B,
% multiply(
% inverse(a2),a2)),
% inverse(multiply(
% inverse(A),A))),A))))
% -> B
% Current number of equations to process: 260
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [54]
% inverse(multiply(A,inverse(multiply(multiply(multiply(A,inverse(B)),inverse(
% multiply(
% inverse(B),B))),B))))
% -> multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(a2),a2)))
% Current number of equations to process: 259
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [55]
% multiply(A,multiply(B,inverse(multiply(multiply(multiply(A,multiply(B,
% inverse(C))),
% inverse(multiply(inverse(C),C))),C))))
% -> multiply(inverse(a2),a2)
% Current number of equations to process: 258
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [56]
% inverse(multiply(inverse(inverse(C)),inverse(multiply(multiply(B,inverse(
% multiply(
% inverse(C),C))),C))))
% <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(
% inverse(a2),a2)))),
% inverse(multiply(inverse(a2),a2)))
% Current number of equations to process: 257
% Current number of ordered equations: 1
% Current number of rules: 41
% Rule [56]
% inverse(multiply(inverse(inverse(C)),inverse(multiply(multiply(B,
% inverse(multiply(
% inverse(C),C))),C))))
% <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(
% inverse(a2),a2)))),
% inverse(multiply(inverse(a2),a2))) is composed into [56]
% inverse(multiply(
% inverse(
% inverse(C)),
% inverse(
% multiply(
% multiply(B,
% inverse(
% multiply(
% inverse(C),C))),C))))
% <->
% inverse(multiply(
% inverse(
% inverse(a2)),
% inverse(
% multiply(
% multiply(B,
% inverse(
% multiply(
% inverse(a2),a2))),a2))))
% New rule produced :
% [57]
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(
% inverse(a2),a2)))),
% inverse(multiply(inverse(a2),a2))) <->
% inverse(multiply(inverse(inverse(C)),inverse(multiply(multiply(B,inverse(
% multiply(
% inverse(C),C))),C))))
% Current number of equations to process: 257
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [58]
% inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(inverse(C),C))),C))))
% <->
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(A)),
% inverse(multiply(B,
% inverse(C))))),
% inverse(multiply(inverse(a2),a2)))
% Current number of equations to process: 255
% Current number of ordered equations: 2
% Current number of rules: 43
% New rule produced :
% [59]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(A)),
% inverse(multiply(B,
% inverse(C))))),
% inverse(multiply(inverse(a2),a2))) <->
% inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(inverse(C),C))),C))))
% Current number of equations to process: 255
% Current number of ordered equations: 1
% Current number of rules: 44
% New rule produced :
% [60]
% multiply(multiply(inverse(multiply(inverse(inverse(multiply(A,inverse(B)))),
% inverse(C))),multiply(inverse(a2),a2)),inverse(
% multiply(
% inverse(a2),a2)))
% ->
% inverse(multiply(A,inverse(multiply(multiply(C,inverse(multiply(inverse(B),B))),B))))
% Current number of equations to process: 255
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [61]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,C)) <->
% multiply(inverse(multiply(V_3,inverse(B))),multiply(V_3,C))
% Rule
% [25]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) <->
% multiply(inverse(multiply(V_3,inverse(B))),multiply(V_3,inverse(C)))
% collapsed.
% Rule
% [42]
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% <->
% multiply(inverse(multiply(a2,inverse(multiply(B,C)))),multiply(a2,inverse(C)))
% collapsed.
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [62]
% multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),
% multiply(B,inverse(C))),inverse(V_3))) <->
% multiply(inverse(multiply(V_4,inverse(multiply(inverse(C),C)))),multiply(V_4,
% inverse(V_3)))
% Rule
% [8]
% multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),
% multiply(B,inverse(C))),inverse(C))) ->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(C),C)))),multiply(a2,
% inverse(C)))
% collapsed.
% Rule
% [15]
% multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),
% multiply(B,inverse(C))),inverse(inverse(
% multiply(
% inverse(V_3),V_3)))))
% ->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(C),C)))),multiply(a2,
% inverse(
% inverse(
% multiply(
% inverse(V_3),V_3)))))
% collapsed.
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [63]
% multiply(inverse(multiply(V_3,inverse(multiply(multiply(multiply(A,multiply(B,
% inverse(V_4))),
% inverse(multiply(inverse(V_4),V_4))),V_4)))),
% multiply(V_3,inverse(C))) -> multiply(A,multiply(B,inverse(C)))
% Current number of equations to process: 265
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [64]
% multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(
% inverse(a2),a2))),C)))),
% multiply(A,inverse(V_3))) <->
% multiply(inverse(multiply(V_4,inverse(multiply(multiply(B,inverse(multiply(
% inverse(C),C))),C)))),
% multiply(V_4,inverse(V_3)))
% Current number of equations to process: 264
% Current number of ordered equations: 1
% Current number of rules: 45
% New rule produced :
% [65]
% multiply(inverse(multiply(V_4,inverse(multiply(multiply(B,inverse(multiply(
% inverse(C),C))),C)))),
% multiply(V_4,inverse(V_3))) <->
% multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(
% inverse(a2),a2))),C)))),
% multiply(A,inverse(V_3)))
% Current number of equations to process: 264
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [66]
% multiply(multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(A),A))),A)
% -> A
% Rule
% [51]
% inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(a2),a2),
% inverse(multiply(inverse(B),B))),B)))) ->
% inverse(multiply(A,inverse(B))) collapsed.
% Current number of equations to process: 270
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [67]
% multiply(multiply(multiply(A,multiply(B,inverse(V_3))),inverse(multiply(
% inverse(V_3),V_3))),V_3)
% <->
% multiply(multiply(multiply(A,multiply(B,inverse(C))),inverse(multiply(
% inverse(a2),a2))),C)
% Current number of equations to process: 269
% Current number of ordered equations: 1
% Current number of rules: 47
% New rule produced :
% [68]
% multiply(multiply(multiply(A,multiply(B,inverse(C))),inverse(multiply(
% inverse(a2),a2))),C)
% <->
% multiply(multiply(multiply(A,multiply(B,inverse(V_3))),inverse(multiply(
% inverse(V_3),V_3))),V_3)
% Current number of equations to process: 269
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [69]
% multiply(multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),
% multiply(a2,inverse(a2))),inverse(multiply(inverse(a2),a2))) ->
% inverse(a2)
% Current number of equations to process: 270
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [70]
% multiply(multiply(multiply(A,multiply(inverse(inverse(B)),inverse(C))),
% inverse(multiply(inverse(C),C))),C) ->
% multiply(multiply(multiply(A,multiply(inverse(a2),a2)),inverse(multiply(
% inverse(B),B))),B)
% Current number of equations to process: 269
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [71]
% multiply(multiply(inverse(multiply(a2,inverse(multiply(A,multiply(inverse(a2),a2))))),
% multiply(a2,inverse(multiply(inverse(B),B)))),inverse(multiply(
% inverse(a2),a2)))
% -> A
% Current number of equations to process: 268
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [72]
% multiply(inverse(multiply(C,inverse(multiply(B,V_3)))),multiply(C,inverse(V_3)))
% <->
% multiply(inverse(multiply(A,inverse(multiply(B,a2)))),multiply(A,inverse(a2)))
% Rule
% [33]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,
% inverse(C))))),
% multiply(A,inverse(inverse(C)))),V_3)),B) ->
% multiply(inverse(multiply(a2,V_3)),multiply(a2,inverse(multiply(inverse(a2),a2))))
% collapsed.
% Rule
% [44]
% multiply(inverse(multiply(C,inverse(multiply(B,V_3)))),multiply(C,inverse(V_3)))
% <->
% multiply(inverse(multiply(a2,inverse(multiply(B,a2)))),multiply(a2,inverse(a2)))
% collapsed.
% Current number of equations to process: 270
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced :
% [73]
% multiply(inverse(multiply(A,inverse(multiply(B,a2)))),multiply(A,inverse(a2)))
% <->
% multiply(inverse(multiply(C,inverse(multiply(B,V_3)))),multiply(C,inverse(V_3)))
% Rule
% [45]
% multiply(inverse(multiply(a2,inverse(multiply(B,a2)))),multiply(a2,inverse(a2)))
% <->
% multiply(inverse(multiply(C,inverse(multiply(B,V_3)))),multiply(C,inverse(V_3)))
% collapsed.
% Current number of equations to process: 270
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [74]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,a2)))),
% multiply(A,inverse(a2))),V_3)),B) ->
% multiply(inverse(multiply(a2,V_3)),multiply(a2,inverse(multiply(inverse(a2),a2))))
% Current number of equations to process: 268
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [75]
% multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(a2),a2)))),
% multiply(A,inverse(B))),inverse(multiply(inverse(a2),a2))) ->
% inverse(B)
% Current number of equations to process: 273
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [76]
% inverse(multiply(inverse(A),A)) <->
% multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(a2),a2)))
% Current number of equations to process: 273
% Current number of ordered equations: 1
% Current number of rules: 53
% Rule [76]
% inverse(multiply(inverse(A),A)) <->
% multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(a2),a2))) is composed into 
% [76] inverse(multiply(inverse(A),A)) <-> inverse(multiply(inverse(a2),a2))
% Rule [54]
% inverse(multiply(A,inverse(multiply(multiply(multiply(A,inverse(B)),
% inverse(multiply(inverse(B),B))),B))))
% -> multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(a2),a2))) is composed into 
% [54]
% inverse(multiply(A,inverse(multiply(multiply(multiply(A,inverse(B)),inverse(
% multiply(
% inverse(B),B))),B))))
% -> inverse(multiply(inverse(a2),a2))
% Rule [41]
% multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),B)))),
% multiply(A,inverse(B))) ->
% multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(a2),a2))) is composed into 
% [41]
% multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),B)))),
% multiply(A,inverse(B))) -> inverse(multiply(inverse(a2),a2))
% New rule produced :
% [77]
% multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(a2),a2))) <->
% inverse(multiply(inverse(A),A))
% Current number of equations to process: 273
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [78]
% inverse(multiply(inverse(B),B)) <->
% multiply(multiply(inverse(A),A),inverse(multiply(inverse(a2),a2)))
% Current number of equations to process: 274
% Current number of ordered equations: 1
% Current number of rules: 55
% Rule [78]
% inverse(multiply(inverse(B),B)) <->
% multiply(multiply(inverse(A),A),inverse(multiply(inverse(a2),a2))) is composed into 
% [78] inverse(multiply(inverse(B),B)) <-> inverse(multiply(inverse(a2),a2))
% New rule produced :
% [79]
% multiply(multiply(inverse(A),A),inverse(multiply(inverse(a2),a2))) <->
% inverse(multiply(inverse(B),B))
% Rule
% [77]
% multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(a2),a2))) <->
% inverse(multiply(inverse(A),A)) collapsed.
% Current number of equations to process: 275
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [80]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(
% multiply(A,B))),
% inverse(B))),inverse(
% multiply(
% inverse(a2),a2)))
% -> A
% Current number of equations to process: 272
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [81]
% multiply(multiply(inverse(multiply(inverse(inverse(A)),inverse(multiply(B,A)))),
% multiply(inverse(a2),a2)),inverse(multiply(inverse(a2),a2))) -> B
% Current number of equations to process: 272
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [82]
% multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,
% inverse(B)))
% <->
% multiply(inverse(multiply(C,inverse(multiply(inverse(a2),a2)))),multiply(C,
% inverse(B)))
% Current number of equations to process: 272
% Current number of ordered equations: 1
% Current number of rules: 58
% New rule produced :
% [83]
% multiply(inverse(multiply(C,inverse(multiply(inverse(a2),a2)))),multiply(C,
% inverse(B)))
% <->
% multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,
% inverse(B)))
% Current number of equations to process: 272
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [84]
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C))))
% <->
% inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(multiply(B,inverse(multiply(inverse(a2),a2))),C)))))
% Current number of equations to process: 273
% Current number of ordered equations: 1
% Current number of rules: 60
% New rule produced :
% [85]
% inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(multiply(B,inverse(multiply(inverse(a2),a2))),C)))))
% <->
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C))))
% Current number of equations to process: 273
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [86]
% multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(a2),a2)))),
% multiply(A,B)),inverse(multiply(inverse(a2),a2))) -> B
% Rule
% [75]
% multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(a2),a2)))),
% multiply(A,inverse(B))),inverse(multiply(inverse(a2),a2))) ->
% inverse(B) collapsed.
% Current number of equations to process: 273
% Current number of ordered equations: 0
% Current number of rules: 61
% Rule [16]
% inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(
% inverse(V_3),V_3))),V_3))))
% <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(multiply(C,inverse(V_3))),multiply(C,inverse(V_3))))) is composed into 
% [16]
% inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(V_3),V_3))),V_3))))
% <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(a2),a2)))
% New rule produced : [87] multiply(inverse(B),B) <-> multiply(inverse(A),A)
% Rule
% [5]
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% collapsed.
% Rule
% [17]
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(multiply(C,inverse(V_3))),multiply(C,inverse(V_3)))))
% <->
% inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(V_3),V_3))),V_3))))
% collapsed.
% Rule [23] multiply(inverse(A),A) <-> multiply(inverse(a2),a2) collapsed.
% Rule
% [24]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(inverse(B)),inverse(B))))),
% multiply(a2,inverse(multiply(inverse(inverse(B)),inverse(B))))) <->
% multiply(inverse(A),A) collapsed.
% Rule
% [76] inverse(multiply(inverse(A),A)) <-> inverse(multiply(inverse(a2),a2))
% collapsed.
% Rule
% [78] inverse(multiply(inverse(B),B)) <-> inverse(multiply(inverse(a2),a2))
% collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% multiply(multiply(inverse(a2),a2),a2) = a2
% 
% Current number of equations to process: 275
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [88]
% multiply(multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),
% multiply(a2,inverse(B))),inverse(multiply(inverse(B),B))) ->
% inverse(B)
% Rule
% [69]
% multiply(multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),
% multiply(a2,inverse(a2))),inverse(multiply(inverse(a2),a2))) ->
% inverse(a2) collapsed.
% Current number of equations to process: 277
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [89]
% multiply(inverse(multiply(a2,inverse(multiply(A,B)))),multiply(a2,inverse(B)))
% <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(A,B))),
% inverse(B)))
% Current number of equations to process: 281
% Current number of ordered equations: 1
% Current number of rules: 57
% New rule produced :
% [90]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(A,B))),
% inverse(B))) <->
% multiply(inverse(multiply(a2,inverse(multiply(A,B)))),multiply(a2,inverse(B)))
% Current number of equations to process: 281
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [91]
% multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C)))
% <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(B,C))),
% inverse(C)))
% Rule
% [9]
% multiply(inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(
% inverse(C),C))),C)))),
% multiply(B,inverse(C))) -> A collapsed.
% Rule
% [37]
% multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(a2),a2),B)))),
% multiply(A,inverse(B))) -> inverse(inverse(multiply(inverse(B),B)))
% collapsed.
% Rule
% [38]
% multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(
% inverse(a2),a2))),C)))),
% multiply(A,inverse(C))) -> B collapsed.
% Rule
% [41]
% multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),B)))),
% multiply(A,inverse(B))) -> inverse(multiply(inverse(a2),a2)) collapsed.
% Rule
% [89]
% multiply(inverse(multiply(a2,inverse(multiply(A,B)))),multiply(a2,inverse(B)))
% <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(A,B))),
% inverse(B))) collapsed.
% Current number of equations to process: 283
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [92]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% multiply(
% inverse(a2),a2),B))),
% inverse(B))) ->
% inverse(inverse(multiply(inverse(B),B)))
% Current number of equations to process: 282
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [93]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% inverse(
% multiply(
% inverse(B),B)),B))),
% inverse(B))) ->
% inverse(multiply(inverse(a2),a2))
% Current number of equations to process: 281
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [94]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% multiply(B,
% inverse(
% multiply(
% inverse(a2),a2))),C))),
% inverse(C))) -> B
% Current number of equations to process: 280
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [95]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(
% multiply(
% inverse(a2),a2))),
% inverse(A))),inverse(
% multiply(
% inverse(A),A)))
% -> inverse(A)
% Current number of equations to process: 278
% Current number of ordered equations: 1
% Current number of rules: 58
% New rule produced :
% [96]
% multiply(multiply(inverse(multiply(inverse(inverse(A)),inverse(multiply(
% inverse(a2),a2)))),
% multiply(inverse(a2),a2)),inverse(multiply(inverse(A),A))) ->
% inverse(A)
% Current number of equations to process: 278
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [97]
% multiply(multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(A),A))),
% multiply(A,B)) -> multiply(A,B)
% Current number of equations to process: 285
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [98]
% multiply(inverse(multiply(inverse(inverse(B)),inverse(multiply(A,B)))),
% multiply(inverse(a2),a2)) ->
% multiply(inverse(multiply(a2,inverse(multiply(A,B)))),multiply(a2,inverse(B)))
% Rule
% [31]
% multiply(multiply(inverse(multiply(inverse(inverse(A)),inverse(multiply(B,A)))),
% multiply(inverse(a2),a2)),inverse(multiply(inverse(A),A))) -> B
% collapsed.
% Rule
% [40]
% multiply(inverse(multiply(inverse(inverse(A)),inverse(multiply(multiply(B,
% inverse(
% multiply(
% inverse(A),A))),A)))),
% multiply(inverse(a2),a2)) -> B collapsed.
% Rule
% [47]
% multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(inverse(B)),
% inverse(multiply(A,B)))),
% multiply(inverse(a2),a2)),inverse(B))) ->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(B),B)))),multiply(a2,
% inverse(B)))
% collapsed.
% Rule
% [81]
% multiply(multiply(inverse(multiply(inverse(inverse(A)),inverse(multiply(B,A)))),
% multiply(inverse(a2),a2)),inverse(multiply(inverse(a2),a2))) -> B
% collapsed.
% Current number of equations to process: 292
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [99]
% multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(multiply(B,
% inverse(
% multiply(
% inverse(a2),a2)))),
% multiply(B,inverse(A))),
% inverse(A))),inverse(multiply(inverse(A),A)))
% -> inverse(A)
% Current number of equations to process: 293
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [100]
% multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(multiply(B,
% inverse(
% multiply(
% inverse(a2),a2)))),
% multiply(B,inverse(A))),
% inverse(A))),inverse(multiply(inverse(a2),a2)))
% -> inverse(A)
% Current number of equations to process: 292
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [101]
% multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(inverse(inverse(multiply(A,a2))),
% inverse(a2))),inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% -> inverse(B)
% Current number of equations to process: 291
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [102]
% multiply(inverse(A),A) <->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))),multiply(a2,
% inverse(
% multiply(
% inverse(B),B))))
% Current number of equations to process: 303
% Current number of ordered equations: 1
% Current number of rules: 61
% Rule [102]
% multiply(inverse(A),A) <->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))),
% multiply(a2,inverse(multiply(inverse(B),B)))) is composed into [102]
% multiply(
% inverse(A),A)
% <->
% multiply(
% inverse(a2),a2)
% New rule produced :
% [103]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))),multiply(a2,
% inverse(
% multiply(
% inverse(B),B))))
% <-> multiply(inverse(A),A)
% Current number of equations to process: 303
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [104]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),
% multiply(A,inverse(C))),V_3)),B) ->
% multiply(inverse(multiply(a2,V_3)),multiply(a2,inverse(multiply(inverse(C),C))))
% Rule
% [32]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),
% multiply(A,inverse(C))),inverse(V_3))),B) ->
% multiply(inverse(multiply(a2,inverse(V_3))),multiply(a2,inverse(multiply(
% inverse(C),C))))
% collapsed.
% Rule
% [74]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,a2)))),
% multiply(A,inverse(a2))),V_3)),B) ->
% multiply(inverse(multiply(a2,V_3)),multiply(a2,inverse(multiply(inverse(a2),a2))))
% collapsed.
% Current number of equations to process: 309
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [105]
% multiply(inverse(multiply(multiply(inverse(multiply(a2,inverse(multiply(
% inverse(A),A)))),
% multiply(a2,inverse(a2))),inverse(B))),inverse(a2))
% ->
% multiply(inverse(multiply(a2,inverse(B))),multiply(a2,inverse(multiply(
% inverse(a2),a2))))
% Current number of equations to process: 310
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [106]
% multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,inverse(A)))
% <->
% multiply(multiply(inverse(multiply(inverse(inverse(inverse(multiply(inverse(A),A)))),
% inverse(B))),multiply(inverse(a2),a2)),inverse(
% multiply(
% inverse(a2),a2)))
% Current number of equations to process: 307
% Current number of ordered equations: 3
% Current number of rules: 63
% Rule [106]
% multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,
% inverse(A))) <->
% multiply(multiply(inverse(multiply(inverse(inverse(inverse(multiply(
% inverse(A),A)))),
% inverse(B))),multiply(inverse(a2),a2)),
% inverse(multiply(inverse(a2),a2))) is composed into [106]
% multiply(inverse(
% multiply(C,
% inverse(
% multiply(B,A)))),
% multiply(C,inverse(A)))
% <->
% multiply(inverse(
% multiply(a2,
% inverse(
% multiply(B,A)))),
% multiply(a2,
% inverse(A)))
% New rule produced :
% [107]
% multiply(multiply(inverse(multiply(inverse(inverse(inverse(multiply(inverse(A),A)))),
% inverse(B))),multiply(inverse(a2),a2)),inverse(
% multiply(
% inverse(a2),a2)))
% <->
% multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,inverse(A)))
% Current number of equations to process: 307
% Current number of ordered equations: 2
% Current number of rules: 64
% New rule produced :
% [108]
% multiply(inverse(multiply(C,inverse(multiply(A,B)))),multiply(C,inverse(B)))
% <->
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(A)),
% inverse(inverse(multiply(
% inverse(B),B))))),
% inverse(multiply(inverse(a2),a2)))
% Current number of equations to process: 307
% Current number of ordered equations: 1
% Current number of rules: 65
% Rule [108]
% multiply(inverse(multiply(C,inverse(multiply(A,B)))),multiply(C,
% inverse(B))) <->
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(A)),
% inverse(inverse(
% multiply(
% inverse(B),B))))),
% inverse(multiply(inverse(a2),a2))) is composed into [108]
% multiply(inverse(
% multiply(C,
% inverse(
% multiply(A,B)))),
% multiply(C,inverse(B)))
% <->
% multiply(inverse(
% multiply(a2,
% inverse(
% multiply(A,B)))),
% multiply(a2,
% inverse(B)))
% New rule produced :
% [109]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(A)),
% inverse(inverse(multiply(
% inverse(B),B))))),
% inverse(multiply(inverse(a2),a2))) <->
% multiply(inverse(multiply(C,inverse(multiply(A,B)))),multiply(C,inverse(B)))
% Current number of equations to process: 307
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [110]
% multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,inverse(A)))
% <->
% multiply(multiply(inverse(multiply(inverse(inverse(inverse(multiply(inverse(A),A)))),
% inverse(B))),multiply(inverse(a2),a2)),inverse(
% multiply(
% inverse(A),A)))
% Current number of equations to process: 305
% Current number of ordered equations: 1
% Current number of rules: 67
% Rule [110]
% multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,
% inverse(A))) <->
% multiply(multiply(inverse(multiply(inverse(inverse(inverse(multiply(
% inverse(A),A)))),
% inverse(B))),multiply(inverse(a2),a2)),
% inverse(multiply(inverse(A),A))) is composed into [110]
% multiply(inverse(
% multiply(C,
% inverse(
% multiply(B,A)))),
% multiply(C,inverse(A)))
% <->
% multiply(inverse(
% multiply(a2,
% inverse(
% multiply(B,A)))),
% multiply(a2,inverse(A)))
% New rule produced :
% [111]
% multiply(multiply(inverse(multiply(inverse(inverse(inverse(multiply(inverse(A),A)))),
% inverse(B))),multiply(inverse(a2),a2)),inverse(
% multiply(
% inverse(A),A)))
% <->
% multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,inverse(A)))
% Current number of equations to process: 305
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [112]
% multiply(C,inverse(multiply(multiply(multiply(inverse(multiply(A,B)),
% multiply(C,inverse(V_3))),inverse(
% multiply(
% inverse(V_3),V_3))),V_3)))
% -> multiply(A,B)
% Current number of equations to process: 313
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [113]
% multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),inverse(
% multiply(
% inverse(C),C)))
% <->
% multiply(multiply(inverse(multiply(V_3,B)),multiply(V_3,inverse(C))),
% inverse(multiply(inverse(C),C)))
% Current number of equations to process: 312
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [114]
% inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(C,B)),
% multiply(C,inverse(V_3))),
% inverse(multiply(inverse(a2),a2))),V_3))))
% -> inverse(multiply(A,B))
% Current number of equations to process: 313
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [115]
% multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),inverse(
% multiply(
% inverse(a2),a2)))
% <->
% multiply(multiply(inverse(multiply(V_3,B)),multiply(V_3,inverse(C))),
% inverse(multiply(inverse(C),C)))
% Current number of equations to process: 316
% Current number of ordered equations: 1
% Current number of rules: 72
% New rule produced :
% [116]
% multiply(multiply(inverse(multiply(V_3,B)),multiply(V_3,inverse(C))),
% inverse(multiply(inverse(C),C))) <->
% multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),inverse(
% multiply(
% inverse(a2),a2)))
% Current number of equations to process: 316
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [117]
% multiply(multiply(inverse(multiply(C,A)),multiply(C,inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% <->
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(A),
% inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% Rule
% [29]
% multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(a2),a2)))),
% multiply(A,inverse(B))),inverse(multiply(inverse(B),B))) ->
% inverse(B) collapsed.
% Current number of equations to process: 320
% Current number of ordered equations: 1
% Current number of rules: 73
% New rule produced :
% [118]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(A),
% inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% <->
% multiply(multiply(inverse(multiply(C,A)),multiply(C,inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% Current number of equations to process: 320
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [119]
% multiply(a2,inverse(multiply(multiply(multiply(inverse(A),multiply(a2,
% inverse(B))),
% inverse(multiply(inverse(B),B))),B))) -> A
% Rule
% [36]
% multiply(a2,inverse(multiply(multiply(multiply(inverse(B),multiply(a2,
% inverse(a2))),
% inverse(multiply(inverse(a2),a2))),a2))) -> B
% collapsed.
% Current number of equations to process: 324
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [120]
% inverse(multiply(inverse(inverse(multiply(multiply(A,inverse(multiply(
% inverse(B),B))),B))),
% inverse(multiply(multiply(A,inverse(multiply(inverse(a2),a2))),B))))
% -> inverse(multiply(inverse(a2),a2))
% Current number of equations to process: 323
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [121]
% multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C)))
% <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(A,a2))),
% inverse(a2)))
% Current number of equations to process: 327
% Current number of ordered equations: 1
% Current number of rules: 76
% New rule produced :
% [122]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(A,a2))),
% inverse(a2))) <->
% multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C)))
% Current number of equations to process: 327
% Current number of ordered equations: 0
% Current number of rules: 77
% Rule [82]
% multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,
% inverse(B)))
% <->
% multiply(inverse(multiply(C,inverse(multiply(inverse(a2),a2)))),
% multiply(C,inverse(B))) is composed into [82]
% multiply(inverse(multiply(A,
% inverse(
% multiply(
% inverse(B),B)))),
% multiply(A,inverse(B))) <->
% multiply(inverse(multiply(
% inverse(a2),a2)),
% multiply(inverse(inverse(
% multiply(
% inverse(a2),a2))),
% inverse(B)))
% Rule [49]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),multiply(a2,
% inverse(A)))
% <->
% multiply(inverse(inverse(A)),multiply(multiply(inverse(multiply(B,
% inverse(multiply(
% inverse(a2),a2)))),
% multiply(B,inverse(A))),inverse(A))) is composed into 
% [49]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),multiply(a2,
% inverse(A)))
% <->
% multiply(inverse(inverse(A)),multiply(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(inverse(inverse(multiply(
% inverse(a2),a2))),
% inverse(A))),inverse(A)))
% New rule produced :
% [123]
% multiply(inverse(multiply(C,A)),multiply(C,inverse(B))) <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(A),inverse(B)))
% Rule
% [48]
% multiply(inverse(inverse(A)),multiply(multiply(inverse(multiply(B,inverse(
% multiply(
% inverse(a2),a2)))),
% multiply(B,inverse(A))),inverse(A)))
% <->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),multiply(a2,
% inverse(A)))
% collapsed.
% Rule
% [63]
% multiply(inverse(multiply(V_3,inverse(multiply(multiply(multiply(A,multiply(B,
% inverse(V_4))),
% inverse(multiply(inverse(V_4),V_4))),V_4)))),
% multiply(V_3,inverse(C))) -> multiply(A,multiply(B,inverse(C))) collapsed.
% Rule
% [64]
% multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(
% inverse(a2),a2))),C)))),
% multiply(A,inverse(V_3))) <->
% multiply(inverse(multiply(V_4,inverse(multiply(multiply(B,inverse(multiply(
% inverse(C),C))),C)))),
% multiply(V_4,inverse(V_3))) collapsed.
% Rule
% [65]
% multiply(inverse(multiply(V_4,inverse(multiply(multiply(B,inverse(multiply(
% inverse(C),C))),C)))),
% multiply(V_4,inverse(V_3))) <->
% multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(
% inverse(a2),a2))),C)))),
% multiply(A,inverse(V_3))) collapsed.
% Rule
% [71]
% multiply(multiply(inverse(multiply(a2,inverse(multiply(A,multiply(inverse(a2),a2))))),
% multiply(a2,inverse(multiply(inverse(B),B)))),inverse(multiply(
% inverse(a2),a2)))
% -> A collapsed.
% Rule
% [83]
% multiply(inverse(multiply(C,inverse(multiply(inverse(a2),a2)))),multiply(C,
% inverse(B)))
% <->
% multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,
% inverse(B)))
% collapsed.
% Rule
% [91]
% multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C)))
% <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(B,C))),
% inverse(C))) collapsed.
% Rule
% [99]
% multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(multiply(B,
% inverse(
% multiply(
% inverse(a2),a2)))),
% multiply(B,inverse(A))),
% inverse(A))),inverse(multiply(inverse(A),A)))
% -> inverse(A) collapsed.
% Rule
% [100]
% multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(multiply(B,
% inverse(
% multiply(
% inverse(a2),a2)))),
% multiply(B,inverse(A))),
% inverse(A))),inverse(multiply(inverse(a2),a2)))
% -> inverse(A) collapsed.
% Rule
% [103]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))),multiply(a2,
% inverse(
% multiply(
% inverse(B),B))))
% <-> multiply(inverse(A),A) collapsed.
% Rule
% [117]
% multiply(multiply(inverse(multiply(C,A)),multiply(C,inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% <->
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(A),
% inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% collapsed.
% Current number of equations to process: 335
% Current number of ordered equations: 1
% Current number of rules: 67
% New rule produced :
% [124]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(A),inverse(B)))
% <-> multiply(inverse(multiply(C,A)),multiply(C,inverse(B)))
% Rule
% [90]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(A,B))),
% inverse(B))) <->
% multiply(inverse(multiply(a2,inverse(multiply(A,B)))),multiply(a2,inverse(B)))
% collapsed.
% Rule
% [118]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(A),
% inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% <->
% multiply(multiply(inverse(multiply(C,A)),multiply(C,inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% collapsed.
% Current number of equations to process: 335
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [125]
% multiply(inverse(A),A) <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% inverse(a2),a2))),
% inverse(multiply(inverse(B),B))))
% Current number of equations to process: 334
% Current number of ordered equations: 1
% Current number of rules: 67
% Rule [125]
% multiply(inverse(A),A) <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(
% multiply(
% inverse(a2),a2))),
% inverse(multiply(inverse(B),B)))) is composed into 
% [125] multiply(inverse(A),A) <-> multiply(inverse(a2),a2)
% New rule produced :
% [126]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% inverse(a2),a2))),
% inverse(multiply(inverse(B),B))))
% <-> multiply(inverse(A),A)
% Current number of equations to process: 334
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [127]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(
% multiply(A,
% multiply(
% inverse(a2),a2)))),
% inverse(multiply(
% inverse(B),B)))),
% inverse(multiply(inverse(a2),a2))) -> A
% Current number of equations to process: 335
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [128]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% multiply(
% multiply(A,
% multiply(B,
% inverse(V_4))),
% inverse(
% multiply(
% inverse(V_4),V_4))),V_4))),
% inverse(C))) ->
% multiply(A,multiply(B,inverse(C)))
% Current number of equations to process: 334
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [129]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% multiply(
% inverse(A),A),B))),
% inverse(B))) ->
% inverse(inverse(multiply(inverse(B),B)))
% Rule
% [92]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% multiply(
% inverse(a2),a2),B))),
% inverse(B))) ->
% inverse(inverse(multiply(inverse(B),B))) collapsed.
% Current number of equations to process: 337
% Current number of ordered equations: 0
% Current number of rules: 70
% Rule [49]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),multiply(a2,
% inverse(A)))
% <->
% multiply(inverse(inverse(A)),multiply(multiply(inverse(multiply(
% inverse(a2),a2)),
% multiply(inverse(inverse(multiply(
% inverse(a2),a2))),
% inverse(A))),inverse(A))) is composed into 
% [49]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),multiply(a2,
% inverse(A)))
% <->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))),multiply(a2,
% inverse(A)))
% New rule produced :
% [130]
% multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(inverse(inverse(multiply(inverse(a2),a2))),A)),A))
% ->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))),multiply(a2,A))
% Current number of equations to process: 362
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [131]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(A,inverse(B))),
% inverse(multiply(inverse(B),B))) ->
% multiply(multiply(A,inverse(B)),inverse(multiply(inverse(B),B)))
% Rule
% [30]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(
% multiply(A,B))),
% inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% -> A collapsed.
% Rule
% [95]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(
% multiply(
% inverse(a2),a2))),
% inverse(A))),inverse(
% multiply(
% inverse(A),A)))
% -> inverse(A) collapsed.
% Current number of equations to process: 448
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [132]
% multiply(multiply(inverse(inverse(multiply(A,B))),inverse(B)),inverse(
% multiply(
% inverse(B),B)))
% -> A
% Current number of equations to process: 447
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [133]
% multiply(multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(A)),
% inverse(multiply(inverse(A),A))) -> inverse(A)
% Current number of equations to process: 446
% Current number of ordered equations: 0
% Current number of rules: 72
% Rule [58]
% inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(
% inverse(C),C))),C))))
% <->
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(A)),
% inverse(multiply(B,
% inverse(C))))),
% inverse(multiply(inverse(a2),a2))) is composed into [58]
% inverse(multiply(B,
% inverse(
% multiply(
% multiply(A,
% inverse(
% multiply(
% inverse(C),C))),C))))
% <->
% multiply(multiply(
% inverse(
% inverse(A)),
% inverse(
% multiply(B,
% inverse(C)))),
% inverse(multiply(
% inverse(
% multiply(B,
% inverse(C))),
% multiply(B,
% inverse(C)))))
% New rule produced :
% [134]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(A,inverse(B))),
% inverse(multiply(inverse(a2),a2))) ->
% multiply(multiply(A,inverse(B)),inverse(multiply(inverse(B),B)))
% Rule
% [59]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(A)),
% inverse(multiply(B,
% inverse(C))))),
% inverse(multiply(inverse(a2),a2))) <->
% inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(inverse(C),C))),C))))
% collapsed.
% Rule
% [80]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(
% multiply(A,B))),
% inverse(B))),inverse(
% multiply(
% inverse(a2),a2)))
% -> A collapsed.
% Rule
% [109]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(A)),
% inverse(inverse(multiply(
% inverse(B),B))))),
% inverse(multiply(inverse(a2),a2))) <->
% multiply(inverse(multiply(C,inverse(multiply(A,B)))),multiply(C,inverse(B)))
% collapsed.
% Rule
% [127]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(
% inverse(
% multiply(A,
% multiply(
% inverse(a2),a2)))),
% inverse(multiply(
% inverse(B),B)))),
% inverse(multiply(inverse(a2),a2))) -> A collapsed.
% Current number of equations to process: 457
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [135]
% multiply(multiply(multiply(A,inverse(C)),inverse(multiply(inverse(C),C))),C)
% <->
% multiply(multiply(multiply(A,inverse(B)),inverse(multiply(inverse(B),B))),B)
% Current number of equations to process: 459
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [136]
% inverse(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,
% inverse(inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(B,multiply(inverse(a2),a2))))) ->
% inverse(multiply(inverse(a2),a2))
% Current number of equations to process: 478
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [137]
% inverse(multiply(inverse(inverse(A)),inverse(multiply(B,A)))) <->
% inverse(multiply(inverse(inverse(a2)),inverse(multiply(B,a2))))
% Current number of equations to process: 487
% Current number of ordered equations: 1
% Current number of rules: 72
% New rule produced :
% [138]
% inverse(multiply(inverse(inverse(a2)),inverse(multiply(B,a2)))) <->
% inverse(multiply(inverse(inverse(A)),inverse(multiply(B,A))))
% Current number of equations to process: 487
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [139]
% inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(multiply(multiply(B,multiply(A,inverse(C))),
% inverse(multiply(inverse(C),C))),C)))))
% -> B
% Current number of equations to process: 486
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [140]
% multiply(multiply(inverse(inverse(multiply(A,multiply(inverse(a2),a2)))),
% inverse(multiply(inverse(B),B))),inverse(multiply(inverse(a2),a2)))
% -> A
% Current number of equations to process: 485
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [141]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(multiply(multiply(A,
% multiply(B,
% inverse(C))),
% inverse(multiply(
% inverse(C),C))),C))
% <->
% multiply(multiply(multiply(A,multiply(B,inverse(V_3))),inverse(multiply(
% inverse(V_3),V_3))),V_3)
% Current number of equations to process: 484
% Current number of ordered equations: 1
% Current number of rules: 76
% New rule produced :
% [142]
% multiply(multiply(multiply(A,multiply(B,inverse(V_3))),inverse(multiply(
% inverse(V_3),V_3))),V_3)
% <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(multiply(multiply(A,
% multiply(B,
% inverse(C))),
% inverse(multiply(
% inverse(C),C))),C))
% Current number of equations to process: 484
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [143]
% inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(inverse(C),C))),C))))
% <->
% multiply(multiply(inverse(inverse(A)),inverse(multiply(B,inverse(C)))),
% inverse(multiply(inverse(a2),a2)))
% Current number of equations to process: 483
% Current number of ordered equations: 1
% Current number of rules: 78
% New rule produced :
% [144]
% multiply(multiply(inverse(inverse(A)),inverse(multiply(B,inverse(C)))),
% inverse(multiply(inverse(a2),a2))) <->
% inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(inverse(C),C))),C))))
% Current number of equations to process: 483
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [145]
% inverse(multiply(inverse(inverse(a2)),inverse(multiply(multiply(multiply(
% inverse(
% multiply(C,B)),
% multiply(C,
% inverse(A))),
% inverse(multiply(
% inverse(a2),a2))),a2))))
% -> inverse(multiply(inverse(inverse(A)),B))
% Current number of equations to process: 494
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [146]
% inverse(multiply(inverse(inverse(A)),inverse(multiply(multiply(multiply(
% inverse(B),B),
% inverse(multiply(
% inverse(A),A))),A))))
% -> inverse(multiply(inverse(a2),a2))
% Current number of equations to process: 521
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [147]
% inverse(multiply(inverse(inverse(B)),inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(B),B))),B))))
% <->
% inverse(multiply(inverse(inverse(A)),inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(A),A))),A))))
% Current number of equations to process: 520
% Current number of ordered equations: 1
% Current number of rules: 82
% New rule produced :
% [148]
% inverse(multiply(inverse(inverse(A)),inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(A),A))),A))))
% <->
% inverse(multiply(inverse(inverse(B)),inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(B),B))),B))))
% Current number of equations to process: 520
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [149]
% inverse(multiply(inverse(inverse(C)),inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(C),C))),C))))
% <->
% multiply(multiply(inverse(multiply(a2,inverse(A))),multiply(a2,inverse(
% multiply(
% inverse(B),B)))),
% inverse(multiply(inverse(a2),a2)))
% Current number of equations to process: 553
% Current number of ordered equations: 1
% Current number of rules: 84
% Rule [149]
% inverse(multiply(inverse(inverse(C)),inverse(multiply(multiply(A,
% inverse(multiply(
% inverse(C),C))),C))))
% <->
% multiply(multiply(inverse(multiply(a2,inverse(A))),multiply(a2,inverse(
% multiply(
% inverse(B),B)))),
% inverse(multiply(inverse(a2),a2))) is composed into [149]
% inverse(multiply(
% inverse(
% inverse(C)),
% inverse(
% multiply(
% multiply(A,
% inverse(
% multiply(
% inverse(C),C))),C))))
% <->
% inverse(multiply(
% inverse(
% inverse(a2)),
% inverse(
% multiply(
% multiply(A,
% inverse(
% multiply(
% inverse(a2),a2))),a2))))
% New rule produced :
% [150]
% multiply(multiply(inverse(multiply(a2,inverse(A))),multiply(a2,inverse(
% multiply(
% inverse(B),B)))),
% inverse(multiply(inverse(a2),a2))) <->
% inverse(multiply(inverse(inverse(C)),inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(C),C))),C))))
% Current number of equations to process: 553
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [151]
% inverse(multiply(A,inverse(multiply(multiply(inverse(inverse(multiply(
% inverse(B),B))),
% inverse(multiply(inverse(a2),a2))),B))))
% -> inverse(multiply(A,inverse(multiply(multiply(inverse(a2),a2),B))))
% Current number of equations to process: 551
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [152]
% multiply(multiply(inverse(inverse(A)),inverse(inverse(multiply(inverse(B),B)))),
% inverse(multiply(inverse(a2),a2))) ->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(A,B))),
% inverse(B)))
% Current number of equations to process: 548
% Current number of ordered equations: 0
% Current number of rules: 87
% Rule [143]
% inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(
% inverse(C),C))),C))))
% <->
% multiply(multiply(inverse(inverse(A)),inverse(multiply(B,inverse(C)))),
% inverse(multiply(inverse(a2),a2))) is composed into [143]
% inverse(multiply(B,
% inverse(
% multiply(
% multiply(A,
% inverse(
% multiply(
% inverse(C),C))),C))))
% <->
% inverse(multiply(B,
% inverse(
% multiply(
% multiply(A,
% inverse(
% multiply(
% inverse(a2),a2))),C))))
% New rule produced :
% [153]
% multiply(multiply(inverse(inverse(B)),inverse(multiply(A,inverse(C)))),
% inverse(multiply(inverse(a2),a2))) ->
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(a2),a2))),C))))
% Rule
% [144]
% multiply(multiply(inverse(inverse(A)),inverse(multiply(B,inverse(C)))),
% inverse(multiply(inverse(a2),a2))) <->
% inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(inverse(C),C))),C))))
% collapsed.
% Current number of equations to process: 547
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [154]
% multiply(multiply(multiply(inverse(inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(a2),a2))),B))),
% inverse(C)),inverse(multiply(inverse(C),C))),C) ->
% multiply(multiply(A,inverse(multiply(inverse(B),B))),B)
% Current number of equations to process: 556
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [155]
% multiply(multiply(inverse(inverse(A)),inverse(multiply(inverse(a2),a2))),
% inverse(multiply(inverse(a2),a2))) ->
% inverse(multiply(inverse(inverse(a2)),inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(a2),a2))),a2))))
% Current number of equations to process: 568
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [156]
% inverse(multiply(inverse(inverse(a2)),inverse(multiply(inverse(multiply(A,
% inverse(
% multiply(
% multiply(B,
% inverse(
% multiply(
% inverse(C),C))),C)))),a2))))
% -> inverse(multiply(inverse(inverse(multiply(A,inverse(C)))),inverse(B)))
% Current number of equations to process: 600
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [157]
% multiply(inverse(multiply(V_3,B)),multiply(V_3,C)) <->
% multiply(inverse(multiply(A,B)),multiply(A,C))
% Rule
% [61]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,C)) <->
% multiply(inverse(multiply(V_3,inverse(B))),multiply(V_3,C)) collapsed.
% Rule
% [106]
% multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,inverse(A)))
% <->
% multiply(inverse(multiply(a2,inverse(multiply(B,A)))),multiply(a2,inverse(A)))
% collapsed.
% Rule
% [108]
% multiply(inverse(multiply(C,inverse(multiply(A,B)))),multiply(C,inverse(B)))
% <->
% multiply(inverse(multiply(a2,inverse(multiply(A,B)))),multiply(a2,inverse(B)))
% collapsed.
% Rule
% [110]
% multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,inverse(A)))
% <->
% multiply(inverse(multiply(a2,inverse(multiply(B,A)))),multiply(a2,inverse(A)))
% collapsed.
% Rule
% [113]
% multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),inverse(
% multiply(
% inverse(C),C)))
% <->
% multiply(multiply(inverse(multiply(V_3,B)),multiply(V_3,inverse(C))),
% inverse(multiply(inverse(C),C))) collapsed.
% Current number of equations to process: 611
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [158]
% multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),
% multiply(B,inverse(C))),V_3)) <->
% multiply(inverse(multiply(V_4,inverse(multiply(inverse(C),C)))),multiply(V_4,V_3))
% Rule
% [62]
% multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),
% multiply(B,inverse(C))),inverse(V_3))) <->
% multiply(inverse(multiply(V_4,inverse(multiply(inverse(C),C)))),multiply(V_4,
% inverse(V_3)))
% collapsed.
% Current number of equations to process: 611
% Current number of ordered equations: 0
% Current number of rules: 86
% Rule [84]
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(
% inverse(C),C))),C))))
% <->
% inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(multiply(B,inverse(multiply(
% inverse(a2),a2))),C))))) is composed into 
% [84]
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C))))
% <->
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(a2),a2))),C))))
% New rule produced :
% [159]
% inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(a2),a2)),B))))
% -> inverse(multiply(A,inverse(B)))
% Rule
% [85]
% inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(multiply(B,inverse(multiply(inverse(a2),a2))),C)))))
% <->
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C))))
% collapsed.
% Rule
% [139]
% inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(multiply(multiply(B,multiply(A,inverse(C))),
% inverse(multiply(inverse(C),C))),C)))))
% -> B collapsed.
% Current number of equations to process: 612
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [160]
% multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(A),A))) ->
% inverse(multiply(inverse(a2),a2))
% Rule
% [66]
% multiply(multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(A),A))),A)
% -> A collapsed.
% Rule
% [97]
% multiply(multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(A),A))),
% multiply(A,B)) -> multiply(A,B) collapsed.
% Current number of equations to process: 615
% Current number of ordered equations: 0
% Current number of rules: 84
% Rule [152]
% multiply(multiply(inverse(inverse(A)),inverse(inverse(multiply(inverse(B),B)))),
% inverse(multiply(inverse(a2),a2))) ->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(
% multiply(A,B))),
% inverse(B))) is composed into 
% [152]
% multiply(multiply(inverse(inverse(A)),inverse(inverse(multiply(inverse(B),B)))),
% inverse(multiply(inverse(a2),a2))) ->
% multiply(inverse(inverse(multiply(A,B))),inverse(B))
% Rule [142]
% multiply(multiply(multiply(A,multiply(B,inverse(V_3))),inverse(multiply(
% inverse(V_3),V_3))),V_3)
% <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(multiply(multiply(A,
% multiply(B,
% inverse(C))),
% inverse(multiply(
% inverse(C),C))),C)) is composed into 
% [142]
% multiply(multiply(multiply(A,multiply(B,inverse(V_3))),inverse(multiply(
% inverse(V_3),V_3))),V_3)
% <->
% multiply(multiply(multiply(A,multiply(B,inverse(C))),inverse(multiply(
% inverse(C),C))),C)
% Rule [123]
% multiply(inverse(multiply(C,A)),multiply(C,inverse(B))) <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(A),inverse(B))) is composed into 
% [123]
% multiply(inverse(multiply(C,A)),multiply(C,inverse(B))) ->
% multiply(inverse(A),inverse(B))
% Rule [121]
% multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,
% inverse(C))) <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(
% multiply(A,a2))),
% inverse(a2))) is composed into 
% [121]
% multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C)))
% <-> multiply(inverse(inverse(multiply(A,a2))),inverse(a2))
% Rule [82]
% multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,
% inverse(B)))
% <->
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(
% multiply(
% inverse(a2),a2))),
% inverse(B))) is composed into 
% [82]
% multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,
% inverse(B)))
% <-> multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(B))
% New rule produced : [161] multiply(inverse(multiply(inverse(a2),a2)),A) -> A
% Rule
% [39]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% multiply(A,
% inverse(
% multiply(
% inverse(B),B))),B))),
% inverse(B))) -> A collapsed.
% Rule
% [46]
% multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(inverse(inverse(multiply(A,B))),
% inverse(B))),inverse(B))) ->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(B),B)))),multiply(a2,
% inverse(B)))
% collapsed.
% Rule
% [93]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% inverse(
% multiply(
% inverse(B),B)),B))),
% inverse(B))) ->
% inverse(multiply(inverse(a2),a2)) collapsed.
% Rule
% [94]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% multiply(B,
% inverse(
% multiply(
% inverse(a2),a2))),C))),
% inverse(C))) -> B collapsed.
% Rule
% [101]
% multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(inverse(inverse(multiply(A,a2))),
% inverse(a2))),inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% -> inverse(B) collapsed.
% Rule
% [122]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(A,a2))),
% inverse(a2))) <->
% multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C)))
% collapsed.
% Rule
% [124]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(A),inverse(B)))
% <-> multiply(inverse(multiply(C,A)),multiply(C,inverse(B))) collapsed.
% Rule
% [126]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% inverse(a2),a2))),
% inverse(multiply(inverse(B),B))))
% <-> multiply(inverse(A),A) collapsed.
% Rule
% [128]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% multiply(
% multiply(A,
% multiply(B,
% inverse(V_4))),
% inverse(
% multiply(
% inverse(V_4),V_4))),V_4))),
% inverse(C))) ->
% multiply(A,multiply(B,inverse(C))) collapsed.
% Rule
% [129]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(inverse(inverse(multiply(
% multiply(
% inverse(A),A),B))),
% inverse(B))) ->
% inverse(inverse(multiply(inverse(B),B))) collapsed.
% Rule
% [130]
% multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(a2),a2)),
% multiply(inverse(inverse(multiply(inverse(a2),a2))),A)),A))
% ->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))),multiply(a2,A))
% collapsed.
% Rule
% [131]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(A,inverse(B))),
% inverse(multiply(inverse(B),B))) ->
% multiply(multiply(A,inverse(B)),inverse(multiply(inverse(B),B))) collapsed.
% Rule
% [134]
% multiply(multiply(inverse(multiply(inverse(a2),a2)),multiply(A,inverse(B))),
% inverse(multiply(inverse(a2),a2))) ->
% multiply(multiply(A,inverse(B)),inverse(multiply(inverse(B),B))) collapsed.
% Rule
% [141]
% multiply(inverse(multiply(inverse(a2),a2)),multiply(multiply(multiply(A,
% multiply(B,
% inverse(C))),
% inverse(multiply(
% inverse(C),C))),C))
% <->
% multiply(multiply(multiply(A,multiply(B,inverse(V_3))),inverse(multiply(
% inverse(V_3),V_3))),V_3)
% collapsed.
% Rule
% [159]
% inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(a2),a2)),B))))
% -> inverse(multiply(A,inverse(B))) collapsed.
% Current number of equations to process: 624
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [162]
% multiply(inverse(A),A) <->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(
% inverse(B),B)))
% Current number of equations to process: 622
% Current number of ordered equations: 1
% Current number of rules: 71
% Rule [162]
% multiply(inverse(A),A) <->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(
% inverse(B),B))) is composed into 
% [162] multiply(inverse(A),A) <-> multiply(inverse(a2),a2)
% New rule produced :
% [163]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(
% inverse(B),B)))
% <-> multiply(inverse(A),A)
% Current number of equations to process: 622
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [164]
% multiply(inverse(inverse(multiply(multiply(inverse(A),A),B))),inverse(B)) ->
% inverse(inverse(multiply(inverse(B),B)))
% Current number of equations to process: 621
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [165]
% multiply(inverse(inverse(multiply(inverse(multiply(inverse(B),B)),B))),
% inverse(B)) -> inverse(multiply(inverse(a2),a2))
% Current number of equations to process: 620
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [166]
% multiply(inverse(inverse(multiply(multiply(A,inverse(multiply(inverse(B),B))),B))),
% inverse(B)) -> A
% Current number of equations to process: 618
% Current number of ordered equations: 1
% Current number of rules: 75
% New rule produced :
% [167]
% multiply(inverse(inverse(multiply(multiply(B,inverse(multiply(inverse(a2),a2))),C))),
% inverse(C)) -> B
% Current number of equations to process: 618
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [168]
% multiply(inverse(inverse(multiply(A,a2))),inverse(a2)) <->
% multiply(inverse(inverse(multiply(A,C))),inverse(C))
% Current number of equations to process: 617
% Current number of ordered equations: 1
% Current number of rules: 77
% New rule produced :
% [169]
% multiply(inverse(inverse(multiply(A,C))),inverse(C)) <->
% multiply(inverse(inverse(multiply(A,a2))),inverse(a2))
% Current number of equations to process: 617
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [170]
% multiply(inverse(A),multiply(multiply(inverse(inverse(multiply(inverse(a2),a2))),A),A))
% ->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))),multiply(a2,A))
% Current number of equations to process: 616
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [171]
% multiply(inverse(A),multiply(multiply(inverse(inverse(multiply(A,B))),
% inverse(B)),inverse(B))) ->
% multiply(inverse(inverse(multiply(inverse(B),B))),inverse(B))
% Current number of equations to process: 616
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [172]
% multiply(multiply(inverse(A),multiply(multiply(inverse(inverse(multiply(A,a2))),
% inverse(a2)),inverse(B))),inverse(
% multiply(
% inverse(B),B)))
% -> inverse(B)
% Current number of equations to process: 615
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [173]
% multiply(inverse(inverse(multiply(multiply(multiply(A,multiply(B,inverse(V_4))),
% inverse(multiply(inverse(V_4),V_4))),V_4))),
% inverse(C)) -> multiply(A,multiply(B,inverse(C)))
% Current number of equations to process: 614
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [174]
% multiply(multiply(inverse(inverse(multiply(inverse(multiply(A,inverse(B))),
% multiply(A,C)))),inverse(multiply(V_3,C))),
% inverse(multiply(inverse(a2),a2))) -> inverse(multiply(V_3,inverse(B)))
% Current number of equations to process: 613
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [175]
% multiply(inverse(multiply(V_3,inverse(multiply(multiply(multiply(A,multiply(B,
% inverse(V_4))),
% inverse(multiply(inverse(V_4),V_4))),V_4)))),
% multiply(V_3,C)) -> multiply(A,multiply(B,C))
% Current number of equations to process: 612
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [176]
% multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(
% inverse(a2),a2))),C)))),
% multiply(A,V_3)) <->
% multiply(inverse(multiply(V_4,inverse(multiply(multiply(B,inverse(multiply(
% inverse(C),C))),C)))),
% multiply(V_4,V_3))
% Current number of equations to process: 611
% Current number of ordered equations: 1
% Current number of rules: 85
% New rule produced :
% [177]
% multiply(inverse(multiply(V_4,inverse(multiply(multiply(B,inverse(multiply(
% inverse(C),C))),C)))),
% multiply(V_4,V_3)) <->
% multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(
% inverse(a2),a2))),C)))),
% multiply(A,V_3))
% Current number of equations to process: 611
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [178]
% multiply(A,multiply(B,inverse(multiply(multiply(multiply(A,multiply(B,
% inverse(C))),
% inverse(multiply(inverse(a2),a2))),C))))
% -> multiply(inverse(a2),a2)
% Current number of equations to process: 622
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [179]
% multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),
% inverse(multiply(inverse(a2),a2))),C))) <->
% multiply(a2,inverse(multiply(multiply(multiply(B,multiply(a2,inverse(a2))),
% inverse(multiply(inverse(a2),a2))),a2)))
% Current number of equations to process: 627
% Current number of ordered equations: 1
% Current number of rules: 88
% New rule produced :
% [180]
% multiply(a2,inverse(multiply(multiply(multiply(B,multiply(a2,inverse(a2))),
% inverse(multiply(inverse(a2),a2))),a2))) <->
% multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),
% inverse(multiply(inverse(a2),a2))),C)))
% Current number of equations to process: 627
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [181]
% inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(C,inverse(V_4))),
% inverse(multiply(inverse(a2),a2))),V_4))))
% <->
% inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(C,inverse(V_3))),
% inverse(multiply(inverse(a2),a2))),V_3))))
% Current number of equations to process: 667
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [182]
% multiply(multiply(inverse(inverse(multiply(A,a2))),inverse(a2)),inverse(
% multiply(
% inverse(B),B)))
% -> A
% Current number of equations to process: 687
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [183]
% multiply(multiply(multiply(A,multiply(inverse(inverse(B)),inverse(C))),
% inverse(multiply(inverse(a2),a2))),C) ->
% multiply(multiply(multiply(A,multiply(inverse(a2),a2)),inverse(multiply(
% inverse(B),B))),B)
% Current number of equations to process: 686
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [184]
% multiply(inverse(inverse(multiply(multiply(A,inverse(multiply(inverse(B),B))),a2))),
% inverse(a2)) -> A
% Current number of equations to process: 688
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [185]
% multiply(inverse(inverse(multiply(inverse(A),a2))),inverse(a2)) <->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(A))
% Current number of equations to process: 693
% Current number of ordered equations: 1
% Current number of rules: 94
% New rule produced :
% [186]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(A)) <->
% multiply(inverse(inverse(multiply(inverse(A),a2))),inverse(a2))
% Current number of equations to process: 693
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [187]
% multiply(multiply(inverse(inverse(multiply(A,B))),inverse(B)),inverse(
% multiply(
% inverse(a2),a2)))
% -> A
% Current number of equations to process: 709
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [188]
% multiply(inverse(inverse(multiply(multiply(multiply(A,multiply(B,inverse(C))),
% inverse(multiply(inverse(a2),a2))),C))),
% inverse(V_3)) -> multiply(A,multiply(B,inverse(V_3)))
% Current number of equations to process: 708
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [189]
% multiply(inverse(A),inverse(inverse(multiply(multiply(multiply(A,multiply(B,
% inverse(C))),
% inverse(multiply(inverse(C),C))),C))))
% -> multiply(inverse(inverse(multiply(B,a2))),inverse(a2))
% Current number of equations to process: 707
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [190]
% multiply(inverse(A),inverse(inverse(multiply(multiply(multiply(A,multiply(B,
% inverse(C))),
% inverse(multiply(inverse(a2),a2))),C))))
% -> multiply(inverse(inverse(multiply(B,a2))),inverse(a2))
% Current number of equations to process: 706
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [191]
% multiply(inverse(inverse(multiply(multiply(multiply(A,multiply(inverse(a2),a2)),
% inverse(multiply(inverse(B),B))),B))),
% inverse(C)) -> multiply(A,multiply(inverse(inverse(B)),inverse(C)))
% Current number of equations to process: 705
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [192]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,a2))),inverse(a2)))),
% inverse(multiply(B,inverse(C)))) <->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(B,
% inverse(multiply(A,C)))))
% Current number of equations to process: 704
% Current number of ordered equations: 1
% Current number of rules: 101
% New rule produced :
% [193]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(B,
% inverse(multiply(A,C)))))
% <->
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,a2))),inverse(a2)))),
% inverse(multiply(B,inverse(C))))
% Current number of equations to process: 704
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [194]
% multiply(inverse(A),inverse(inverse(multiply(multiply(multiply(A,multiply(
% inverse(a2),a2)),
% inverse(multiply(inverse(B),B))),B))))
% -> multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(inverse(B)))
% Current number of equations to process: 703
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [195]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(a2),a2))),
% inverse(A)))),inverse(multiply(a2,inverse(A)))) ->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(a2,
% inverse(multiply(
% inverse(A),A)))))
% Current number of equations to process: 702
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [196]
% inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),a2)))) ->
% inverse(multiply(A,inverse(a2)))
% Current number of equations to process: 709
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [197]
% multiply(inverse(inverse(inverse(multiply(inverse(A),A)))),inverse(inverse(
% multiply(
% inverse(a2),a2))))
% -> inverse(inverse(multiply(inverse(a2),a2)))
% Current number of equations to process: 725
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [198]
% multiply(inverse(inverse(multiply(inverse(A),A))),multiply(multiply(inverse(B),B),
% inverse(a2))) <->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(a2))
% Current number of equations to process: 724
% Current number of ordered equations: 1
% Current number of rules: 107
% New rule produced :
% [199]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(a2)) <->
% multiply(inverse(inverse(multiply(inverse(A),A))),multiply(multiply(inverse(B),B),
% inverse(a2)))
% Current number of equations to process: 724
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [200]
% multiply(inverse(inverse(multiply(inverse(a2),C))),inverse(C)) <->
% multiply(inverse(inverse(multiply(inverse(A),A))),multiply(multiply(inverse(B),B),
% inverse(a2)))
% Rule
% [199]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(a2)) <->
% multiply(inverse(inverse(multiply(inverse(A),A))),multiply(multiply(inverse(B),B),
% inverse(a2))) collapsed.
% Current number of equations to process: 723
% Current number of ordered equations: 1
% Current number of rules: 108
% New rule produced :
% [201]
% multiply(inverse(inverse(multiply(inverse(A),A))),multiply(multiply(inverse(B),B),
% inverse(a2))) <->
% multiply(inverse(inverse(multiply(inverse(a2),C))),inverse(C))
% Rule
% [198]
% multiply(inverse(inverse(multiply(inverse(A),A))),multiply(multiply(inverse(B),B),
% inverse(a2))) <->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(a2)) collapsed.
% Current number of equations to process: 723
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [202]
% multiply(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(
% inverse(B),B))),
% inverse(multiply(inverse(a2),a2))) -> inverse(multiply(inverse(a2),a2))
% Current number of equations to process: 722
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [203]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,B))),inverse(B)))),
% inverse(multiply(C,inverse(a2)))) <->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(C,
% inverse(multiply(A,a2)))))
% Current number of equations to process: 721
% Current number of ordered equations: 1
% Current number of rules: 110
% New rule produced :
% [204]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(C,
% inverse(multiply(A,a2)))))
% <->
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,B))),inverse(B)))),
% inverse(multiply(C,inverse(a2))))
% Current number of equations to process: 721
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [205]
% inverse(multiply(multiply(inverse(C),C),inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(a2),a2))),
% multiply(inverse(a2),a2)))))
% <-> multiply(inverse(inverse(multiply(A,B))),inverse(B))
% Current number of equations to process: 720
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [206]
% multiply(inverse(multiply(multiply(inverse(A),A),inverse(multiply(B,multiply(
% inverse(a2),a2))))),
% inverse(multiply(inverse(C),C))) ->
% multiply(inverse(inverse(multiply(B,a2))),inverse(a2))
% Current number of equations to process: 719
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [207]
% inverse(multiply(inverse(C),C)) <->
% multiply(multiply(A,inverse(multiply(multiply(multiply(A,inverse(B)),
% inverse(multiply(inverse(B),B))),B))),
% inverse(multiply(inverse(a2),a2)))
% Current number of equations to process: 718
% Current number of ordered equations: 1
% Current number of rules: 114
% Rule [207]
% inverse(multiply(inverse(C),C)) <->
% multiply(multiply(A,inverse(multiply(multiply(multiply(A,inverse(B)),
% inverse(multiply(inverse(B),B))),B))),
% inverse(multiply(inverse(a2),a2))) is composed into [207]
% inverse(multiply(
% inverse(C),C))
% <->
% inverse(multiply(
% inverse(a2),a2))
% New rule produced :
% [208]
% multiply(multiply(A,inverse(multiply(multiply(multiply(A,inverse(B)),
% inverse(multiply(inverse(B),B))),B))),
% inverse(multiply(inverse(a2),a2))) <-> inverse(multiply(inverse(C),C))
% Current number of equations to process: 718
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [209]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(inverse(multiply(
% multiply(
% multiply(A,
% inverse(B)),
% inverse(
% multiply(
% inverse(B),B))),B))))
% -> multiply(inverse(inverse(multiply(A,a2))),inverse(a2))
% Current number of equations to process: 717
% Current number of ordered equations: 0
% Current number of rules: 116
% Rule [170]
% multiply(inverse(A),multiply(multiply(inverse(inverse(multiply(inverse(a2),a2))),A),A))
% ->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))),
% multiply(a2,A)) is composed into [170]
% multiply(inverse(A),multiply(multiply(
% inverse(
% inverse(
% multiply(
% inverse(a2),a2))),A),A))
% ->
% multiply(inverse(inverse(multiply(
% inverse(a2),a2))),A)
% Rule [49]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),multiply(a2,
% inverse(A)))
% <->
% multiply(inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))),
% multiply(a2,inverse(A))) is composed into [49]
% multiply(inverse(multiply(a2,
% inverse(
% multiply(
% inverse(A),A)))),
% multiply(a2,inverse(A))) <->
% multiply(inverse(inverse(
% multiply(
% inverse(a2),a2))),
% inverse(A))
% New rule produced :
% [210]
% multiply(inverse(multiply(A,inverse(multiply(inverse(a2),a2)))),multiply(A,B))
% -> multiply(inverse(inverse(multiply(inverse(a2),a2))),B)
% Rule
% [86]
% multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(a2),a2)))),
% multiply(A,B)),inverse(multiply(inverse(a2),a2))) -> B collapsed.
% Current number of equations to process: 719
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [211]
% multiply(multiply(inverse(inverse(multiply(inverse(a2),a2))),B),inverse(
% multiply(
% inverse(a2),a2)))
% -> B
% Current number of equations to process: 718
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [212]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(a2),a2))),
% inverse(A)))),inverse(multiply(B,inverse(A)))) <->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(B,
% inverse(multiply(
% inverse(A),A)))))
% Rule
% [195]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(a2),a2))),
% inverse(A)))),inverse(multiply(a2,inverse(A)))) ->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(a2,
% inverse(multiply(
% inverse(A),A)))))
% collapsed.
% Current number of equations to process: 725
% Current number of ordered equations: 1
% Current number of rules: 117
% New rule produced :
% [213]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(B,
% inverse(multiply(
% inverse(A),A)))))
% <->
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(a2),a2))),
% inverse(A)))),inverse(multiply(B,inverse(A))))
% Current number of equations to process: 725
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [214]
% multiply(multiply(inverse(inverse(multiply(inverse(A),A))),multiply(multiply(
% inverse(B),B),
% inverse(multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(a2),a2))) -> inverse(multiply(C,inverse(V_3)))
% Current number of equations to process: 724
% Current number of ordered equations: 0
% Current number of rules: 119
% Rule [207]
% inverse(multiply(inverse(C),C)) <-> inverse(multiply(inverse(a2),a2)) is composed into 
% [207] inverse(multiply(inverse(C),C)) <-> multiply(inverse(a2),a2)
% Rule [203]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,B))),
% inverse(B)))),inverse(multiply(C,inverse(a2))))
% <->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(C,
% inverse(
% multiply(A,a2))))) is composed into 
% [203]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,B))),inverse(B)))),
% inverse(multiply(C,inverse(a2)))) <->
% multiply(multiply(inverse(a2),a2),inverse(multiply(C,inverse(multiply(A,a2)))))
% Rule [194]
% multiply(inverse(A),inverse(inverse(multiply(multiply(multiply(A,
% multiply(inverse(a2),a2)),
% inverse(multiply(inverse(B),B))),B))))
% ->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(inverse(B))) is composed into 
% [194]
% multiply(inverse(A),inverse(inverse(multiply(multiply(multiply(A,multiply(
% inverse(a2),a2)),
% inverse(multiply(inverse(B),B))),B))))
% -> multiply(multiply(inverse(a2),a2),inverse(inverse(B)))
% Rule [192]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,a2))),
% inverse(a2)))),inverse(multiply(B,inverse(C))))
% <->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(B,
% inverse(
% multiply(A,C))))) is composed into 
% [192]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,a2))),inverse(a2)))),
% inverse(multiply(B,inverse(C)))) <->
% multiply(multiply(inverse(a2),a2),inverse(multiply(B,inverse(multiply(A,C)))))
% Rule [185]
% multiply(inverse(inverse(multiply(inverse(A),a2))),inverse(a2)) <->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(A)) is composed into 
% [185]
% multiply(inverse(inverse(multiply(inverse(A),a2))),inverse(a2)) <->
% multiply(multiply(inverse(a2),a2),inverse(A))
% Rule [177]
% multiply(inverse(multiply(V_4,inverse(multiply(multiply(B,inverse(
% multiply(
% inverse(C),C))),C)))),
% multiply(V_4,V_3)) <->
% multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(
% multiply(
% inverse(a2),a2))),C)))),
% multiply(A,V_3)) is composed into [177]
% multiply(inverse(multiply(V_4,
% inverse(multiply(
% multiply(B,
% inverse(
% multiply(
% inverse(C),C))),C)))),
% multiply(V_4,V_3)) <->
% multiply(inverse(multiply(A,inverse(
% multiply(
% multiply(B,
% multiply(
% inverse(a2),a2)),C)))),
% multiply(A,V_3))
% Rule [165]
% multiply(inverse(inverse(multiply(inverse(multiply(inverse(B),B)),B))),
% inverse(B)) -> inverse(multiply(inverse(a2),a2)) is composed into 
% [165]
% multiply(inverse(inverse(multiply(inverse(multiply(inverse(B),B)),B))),
% inverse(B)) -> multiply(inverse(a2),a2)
% Rule [160]
% multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(A),A))) ->
% inverse(multiply(inverse(a2),a2)) is composed into [160]
% multiply(multiply(
% inverse(a2),a2),
% inverse(multiply(
% inverse(A),A)))
% ->
% multiply(inverse(a2),a2)
% Rule [149]
% inverse(multiply(inverse(inverse(C)),inverse(multiply(multiply(A,
% inverse(multiply(
% inverse(C),C))),C))))
% <->
% inverse(multiply(inverse(inverse(a2)),inverse(multiply(multiply(A,
% inverse(multiply(
% inverse(a2),a2))),a2)))) is composed into 
% [149]
% inverse(multiply(inverse(inverse(C)),inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(C),C))),C))))
% <->
% inverse(multiply(inverse(inverse(a2)),inverse(multiply(multiply(A,multiply(
% inverse(a2),a2)),a2))))
% Rule [146]
% inverse(multiply(inverse(inverse(A)),inverse(multiply(multiply(multiply(
% inverse(B),B),
% inverse(multiply(
% inverse(A),A))),A))))
% -> inverse(multiply(inverse(a2),a2)) is composed into [146]
% inverse(multiply(
% inverse(
% inverse(A)),
% inverse(
% multiply(
% multiply(
% multiply(
% inverse(B),B),
% inverse(
% multiply(
% inverse(A),A))),A))))
% ->
% multiply(inverse(a2),a2)
% Rule [143]
% inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(
% inverse(C),C))),C))))
% <->
% inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(
% inverse(a2),a2))),C)))) is composed into 
% [143]
% inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(inverse(C),C))),C))))
% <->
% inverse(multiply(B,inverse(multiply(multiply(A,multiply(inverse(a2),a2)),C))))
% Rule [136]
% inverse(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,
% inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(B,multiply(inverse(a2),a2))))) ->
% inverse(multiply(inverse(a2),a2)) is composed into [136]
% inverse(multiply(
% multiply(
% inverse(
% multiply(A,
% inverse(B))),
% multiply(A,
% inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(
% multiply(B,
% multiply(
% inverse(a2),a2)))))
% ->
% multiply(inverse(a2),a2)
% Rule [116]
% multiply(multiply(inverse(multiply(V_3,B)),multiply(V_3,inverse(C))),
% inverse(multiply(inverse(C),C))) <->
% multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),
% inverse(multiply(inverse(a2),a2))) is composed into [116]
% multiply(multiply(
% inverse(
% multiply(V_3,B)),
% multiply(V_3,
% inverse(C))),
% inverse(multiply(
% inverse(C),C)))
% <->
% multiply(multiply(
% inverse(
% multiply(A,B)),
% multiply(A,
% inverse(C))),
% multiply(inverse(a2),a2))
% Rule [105]
% multiply(inverse(multiply(multiply(inverse(multiply(a2,inverse(multiply(
% inverse(A),A)))),
% multiply(a2,inverse(a2))),inverse(B))),
% inverse(a2)) ->
% multiply(inverse(multiply(a2,inverse(B))),multiply(a2,inverse(multiply(
% inverse(a2),a2)))) is composed into 
% [105]
% multiply(inverse(multiply(multiply(inverse(multiply(a2,inverse(multiply(
% inverse(A),A)))),
% multiply(a2,inverse(a2))),inverse(B))),inverse(a2))
% ->
% multiply(inverse(multiply(a2,inverse(B))),multiply(a2,multiply(inverse(a2),a2)))
% Rule [84]
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(
% inverse(C),C))),C))))
% <->
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(
% inverse(a2),a2))),C)))) is composed into 
% [84]
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C))))
% <->
% inverse(multiply(A,inverse(multiply(multiply(B,multiply(inverse(a2),a2)),C))))
% Rule [82]
% multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,
% inverse(B)))
% <-> multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(B)) is composed into 
% [82]
% multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,
% inverse(B)))
% <-> multiply(multiply(inverse(a2),a2),inverse(B))
% Rule [67]
% multiply(multiply(multiply(A,multiply(B,inverse(V_3))),inverse(multiply(
% inverse(V_3),V_3))),V_3)
% <->
% multiply(multiply(multiply(A,multiply(B,inverse(C))),inverse(multiply(
% inverse(a2),a2))),C) is composed into 
% [67]
% multiply(multiply(multiply(A,multiply(B,inverse(V_3))),inverse(multiply(
% inverse(V_3),V_3))),V_3)
% <->
% multiply(multiply(multiply(A,multiply(B,inverse(C))),multiply(inverse(a2),a2)),C)
% Rule [56]
% inverse(multiply(inverse(inverse(C)),inverse(multiply(multiply(B,
% inverse(multiply(
% inverse(C),C))),C))))
% <->
% inverse(multiply(inverse(inverse(a2)),inverse(multiply(multiply(B,
% inverse(multiply(
% inverse(a2),a2))),a2)))) is composed into 
% [56]
% inverse(multiply(inverse(inverse(C)),inverse(multiply(multiply(B,inverse(
% multiply(
% inverse(C),C))),C))))
% <->
% inverse(multiply(inverse(inverse(a2)),inverse(multiply(multiply(B,multiply(
% inverse(a2),a2)),a2))))
% Rule [54]
% inverse(multiply(A,inverse(multiply(multiply(multiply(A,inverse(B)),
% inverse(multiply(inverse(B),B))),B))))
% -> inverse(multiply(inverse(a2),a2)) is composed into [54]
% inverse(multiply(A,
% inverse(
% multiply(
% multiply(
% multiply(A,
% inverse(B)),
% inverse(
% multiply(
% inverse(B),B))),B))))
% ->
% multiply(inverse(a2),a2)
% Rule [49]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),multiply(a2,
% inverse(A)))
% <-> multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(A)) is composed into 
% [49]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),multiply(a2,
% inverse(A)))
% <-> multiply(multiply(inverse(a2),a2),inverse(A))
% Rule [34]
% multiply(V_3,inverse(multiply(multiply(multiply(B,multiply(V_3,inverse(V_4))),
% inverse(multiply(inverse(V_4),V_4))),V_4)))
% <->
% multiply(a2,inverse(multiply(multiply(multiply(B,multiply(a2,inverse(a2))),
% inverse(multiply(inverse(a2),a2))),a2))) is composed into 
% [34]
% multiply(V_3,inverse(multiply(multiply(multiply(B,multiply(V_3,inverse(V_4))),
% inverse(multiply(inverse(V_4),V_4))),V_4))) <->
% multiply(a2,inverse(multiply(multiply(multiply(B,multiply(a2,inverse(a2))),
% multiply(inverse(a2),a2)),a2)))
% Rule [16]
% inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(
% inverse(V_3),V_3))),V_3))))
% <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(a2),a2))) is composed into [16]
% inverse(multiply(C,
% inverse(
% multiply(
% multiply(B,
% inverse(
% multiply(
% inverse(V_3),V_3))),V_3))))
% <->
% multiply(multiply(
% inverse(
% multiply(A,
% inverse(B))),
% multiply(A,
% inverse(
% multiply(C,
% inverse(V_3))))),
% multiply(inverse(a2),a2))
% New rule produced :
% [215] inverse(multiply(inverse(a2),a2)) -> multiply(inverse(a2),a2)
% Rule
% [28]
% multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,
% inverse(C))),
% inverse(multiply(inverse(a2),a2))) -> B collapsed.
% Rule
% [43]
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(a2),a2))) <->
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% collapsed.
% Rule
% [50]
% multiply(multiply(inverse(multiply(V_3,inverse(B))),multiply(V_3,inverse(
% multiply(A,
% inverse(C))))),
% inverse(multiply(inverse(a2),a2))) ->
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(a2),a2))),C))))
% collapsed.
% Rule
% [52]
% inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),
% inverse(multiply(inverse(a2),a2))),C))))
% -> B collapsed.
% Rule
% [57]
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(
% inverse(a2),a2)))),
% inverse(multiply(inverse(a2),a2))) <->
% inverse(multiply(inverse(inverse(C)),inverse(multiply(multiply(B,inverse(
% multiply(
% inverse(C),C))),C))))
% collapsed.
% Rule
% [60]
% multiply(multiply(inverse(multiply(inverse(inverse(multiply(A,inverse(B)))),
% inverse(C))),multiply(inverse(a2),a2)),inverse(
% multiply(
% inverse(a2),a2)))
% ->
% inverse(multiply(A,inverse(multiply(multiply(C,inverse(multiply(inverse(B),B))),B))))
% collapsed.
% Rule
% [68]
% multiply(multiply(multiply(A,multiply(B,inverse(C))),inverse(multiply(
% inverse(a2),a2))),C)
% <->
% multiply(multiply(multiply(A,multiply(B,inverse(V_3))),inverse(multiply(
% inverse(V_3),V_3))),V_3)
% collapsed.
% Rule
% [79]
% multiply(multiply(inverse(A),A),inverse(multiply(inverse(a2),a2))) <->
% inverse(multiply(inverse(B),B)) collapsed.
% Rule
% [96]
% multiply(multiply(inverse(multiply(inverse(inverse(A)),inverse(multiply(
% inverse(a2),a2)))),
% multiply(inverse(a2),a2)),inverse(multiply(inverse(A),A))) ->
% inverse(A) collapsed.
% Rule
% [107]
% multiply(multiply(inverse(multiply(inverse(inverse(inverse(multiply(inverse(A),A)))),
% inverse(B))),multiply(inverse(a2),a2)),inverse(
% multiply(
% inverse(a2),a2)))
% <->
% multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,inverse(A)))
% collapsed.
% Rule
% [114]
% inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(C,B)),
% multiply(C,inverse(V_3))),
% inverse(multiply(inverse(a2),a2))),V_3))))
% -> inverse(multiply(A,B)) collapsed.
% Rule
% [115]
% multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),inverse(
% multiply(
% inverse(a2),a2)))
% <->
% multiply(multiply(inverse(multiply(V_3,B)),multiply(V_3,inverse(C))),
% inverse(multiply(inverse(C),C))) collapsed.
% Rule
% [120]
% inverse(multiply(inverse(inverse(multiply(multiply(A,inverse(multiply(
% inverse(B),B))),B))),
% inverse(multiply(multiply(A,inverse(multiply(inverse(a2),a2))),B))))
% -> inverse(multiply(inverse(a2),a2)) collapsed.
% Rule
% [133]
% multiply(multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(A)),
% inverse(multiply(inverse(A),A))) -> inverse(A) collapsed.
% Rule
% [140]
% multiply(multiply(inverse(inverse(multiply(A,multiply(inverse(a2),a2)))),
% inverse(multiply(inverse(B),B))),inverse(multiply(inverse(a2),a2)))
% -> A collapsed.
% Rule
% [145]
% inverse(multiply(inverse(inverse(a2)),inverse(multiply(multiply(multiply(
% inverse(
% multiply(C,B)),
% multiply(C,
% inverse(A))),
% inverse(multiply(
% inverse(a2),a2))),a2))))
% -> inverse(multiply(inverse(inverse(A)),B)) collapsed.
% Rule
% [150]
% multiply(multiply(inverse(multiply(a2,inverse(A))),multiply(a2,inverse(
% multiply(
% inverse(B),B)))),
% inverse(multiply(inverse(a2),a2))) <->
% inverse(multiply(inverse(inverse(C)),inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(C),C))),C))))
% collapsed.
% Rule
% [151]
% inverse(multiply(A,inverse(multiply(multiply(inverse(inverse(multiply(
% inverse(B),B))),
% inverse(multiply(inverse(a2),a2))),B))))
% -> inverse(multiply(A,inverse(multiply(multiply(inverse(a2),a2),B))))
% collapsed.
% Rule
% [152]
% multiply(multiply(inverse(inverse(A)),inverse(inverse(multiply(inverse(B),B)))),
% inverse(multiply(inverse(a2),a2))) ->
% multiply(inverse(inverse(multiply(A,B))),inverse(B)) collapsed.
% Rule
% [153]
% multiply(multiply(inverse(inverse(B)),inverse(multiply(A,inverse(C)))),
% inverse(multiply(inverse(a2),a2))) ->
% inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(a2),a2))),C))))
% collapsed.
% Rule
% [154]
% multiply(multiply(multiply(inverse(inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(a2),a2))),B))),
% inverse(C)),inverse(multiply(inverse(C),C))),C) ->
% multiply(multiply(A,inverse(multiply(inverse(B),B))),B) collapsed.
% Rule
% [155]
% multiply(multiply(inverse(inverse(A)),inverse(multiply(inverse(a2),a2))),
% inverse(multiply(inverse(a2),a2))) ->
% inverse(multiply(inverse(inverse(a2)),inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(a2),a2))),a2))))
% collapsed.
% Rule [161] multiply(inverse(multiply(inverse(a2),a2)),A) -> A collapsed.
% Rule
% [163]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(
% inverse(B),B)))
% <-> multiply(inverse(A),A) collapsed.
% Rule
% [167]
% multiply(inverse(inverse(multiply(multiply(B,inverse(multiply(inverse(a2),a2))),C))),
% inverse(C)) -> B collapsed.
% Rule
% [170]
% multiply(inverse(A),multiply(multiply(inverse(inverse(multiply(inverse(a2),a2))),A),A))
% -> multiply(inverse(inverse(multiply(inverse(a2),a2))),A) collapsed.
% Rule
% [174]
% multiply(multiply(inverse(inverse(multiply(inverse(multiply(A,inverse(B))),
% multiply(A,C)))),inverse(multiply(V_3,C))),
% inverse(multiply(inverse(a2),a2))) -> inverse(multiply(V_3,inverse(B)))
% collapsed.
% Rule
% [176]
% multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(
% inverse(a2),a2))),C)))),
% multiply(A,V_3)) <->
% multiply(inverse(multiply(V_4,inverse(multiply(multiply(B,inverse(multiply(
% inverse(C),C))),C)))),
% multiply(V_4,V_3)) collapsed.
% Rule
% [178]
% multiply(A,multiply(B,inverse(multiply(multiply(multiply(A,multiply(B,
% inverse(C))),
% inverse(multiply(inverse(a2),a2))),C))))
% -> multiply(inverse(a2),a2) collapsed.
% Rule
% [179]
% multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),
% inverse(multiply(inverse(a2),a2))),C))) <->
% multiply(a2,inverse(multiply(multiply(multiply(B,multiply(a2,inverse(a2))),
% inverse(multiply(inverse(a2),a2))),a2)))
% collapsed.
% Rule
% [180]
% multiply(a2,inverse(multiply(multiply(multiply(B,multiply(a2,inverse(a2))),
% inverse(multiply(inverse(a2),a2))),a2))) <->
% multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),
% inverse(multiply(inverse(a2),a2))),C)))
% collapsed.
% Rule
% [181]
% inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(C,inverse(V_4))),
% inverse(multiply(inverse(a2),a2))),V_4))))
% <->
% inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(C,inverse(V_3))),
% inverse(multiply(inverse(a2),a2))),V_3))))
% collapsed.
% Rule
% [183]
% multiply(multiply(multiply(A,multiply(inverse(inverse(B)),inverse(C))),
% inverse(multiply(inverse(a2),a2))),C) ->
% multiply(multiply(multiply(A,multiply(inverse(a2),a2)),inverse(multiply(
% inverse(B),B))),B)
% collapsed.
% Rule
% [186]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(A)) <->
% multiply(inverse(inverse(multiply(inverse(A),a2))),inverse(a2)) collapsed.
% Rule
% [187]
% multiply(multiply(inverse(inverse(multiply(A,B))),inverse(B)),inverse(
% multiply(
% inverse(a2),a2)))
% -> A collapsed.
% Rule
% [188]
% multiply(inverse(inverse(multiply(multiply(multiply(A,multiply(B,inverse(C))),
% inverse(multiply(inverse(a2),a2))),C))),
% inverse(V_3)) -> multiply(A,multiply(B,inverse(V_3))) collapsed.
% Rule
% [190]
% multiply(inverse(A),inverse(inverse(multiply(multiply(multiply(A,multiply(B,
% inverse(C))),
% inverse(multiply(inverse(a2),a2))),C))))
% -> multiply(inverse(inverse(multiply(B,a2))),inverse(a2)) collapsed.
% Rule
% [193]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(B,
% inverse(multiply(A,C)))))
% <->
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,a2))),inverse(a2)))),
% inverse(multiply(B,inverse(C)))) collapsed.
% Rule
% [197]
% multiply(inverse(inverse(inverse(multiply(inverse(A),A)))),inverse(inverse(
% multiply(
% inverse(a2),a2))))
% -> inverse(inverse(multiply(inverse(a2),a2))) collapsed.
% Rule
% [202]
% multiply(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(
% inverse(B),B))),
% inverse(multiply(inverse(a2),a2))) -> inverse(multiply(inverse(a2),a2))
% collapsed.
% Rule
% [204]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(C,
% inverse(multiply(A,a2)))))
% <->
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,B))),inverse(B)))),
% inverse(multiply(C,inverse(a2)))) collapsed.
% Rule
% [205]
% inverse(multiply(multiply(inverse(C),C),inverse(multiply(multiply(A,inverse(
% multiply(
% inverse(a2),a2))),
% multiply(inverse(a2),a2)))))
% <-> multiply(inverse(inverse(multiply(A,B))),inverse(B)) collapsed.
% Rule
% [208]
% multiply(multiply(A,inverse(multiply(multiply(multiply(A,inverse(B)),
% inverse(multiply(inverse(B),B))),B))),
% inverse(multiply(inverse(a2),a2))) <-> inverse(multiply(inverse(C),C))
% collapsed.
% Rule
% [209]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(inverse(multiply(
% multiply(
% multiply(A,
% inverse(B)),
% inverse(
% multiply(
% inverse(B),B))),B))))
% -> multiply(inverse(inverse(multiply(A,a2))),inverse(a2)) collapsed.
% Rule
% [210]
% multiply(inverse(multiply(A,inverse(multiply(inverse(a2),a2)))),multiply(A,B))
% -> multiply(inverse(inverse(multiply(inverse(a2),a2))),B) collapsed.
% Rule
% [211]
% multiply(multiply(inverse(inverse(multiply(inverse(a2),a2))),B),inverse(
% multiply(
% inverse(a2),a2)))
% -> B collapsed.
% Rule
% [212]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(a2),a2))),
% inverse(A)))),inverse(multiply(B,inverse(A)))) <->
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(B,
% inverse(multiply(
% inverse(A),A)))))
% collapsed.
% Rule
% [213]
% multiply(inverse(inverse(multiply(inverse(a2),a2))),inverse(multiply(B,
% inverse(multiply(
% inverse(A),A)))))
% <->
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(a2),a2))),
% inverse(A)))),inverse(multiply(B,inverse(A))))
% collapsed.
% Rule
% [214]
% multiply(multiply(inverse(inverse(multiply(inverse(A),A))),multiply(multiply(
% inverse(B),B),
% inverse(multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(a2),a2))) -> inverse(multiply(C,inverse(V_3)))
% collapsed.
% Current number of equations to process: 769
% Current number of ordered equations: 0
% Current number of rules: 71
% Rule [203]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,B))),
% inverse(B)))),inverse(multiply(C,inverse(a2))))
% <->
% multiply(multiply(inverse(a2),a2),inverse(multiply(C,inverse(multiply(A,a2))))) is composed into 
% [203]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,B))),inverse(B)))),
% inverse(multiply(C,inverse(a2)))) <->
% inverse(multiply(C,inverse(multiply(A,a2))))
% Rule [194]
% multiply(inverse(A),inverse(inverse(multiply(multiply(multiply(A,
% multiply(inverse(a2),a2)),
% inverse(multiply(inverse(B),B))),B))))
% -> multiply(multiply(inverse(a2),a2),inverse(inverse(B))) is composed into 
% [194]
% multiply(inverse(A),inverse(inverse(multiply(multiply(multiply(A,multiply(
% inverse(a2),a2)),
% inverse(multiply(inverse(B),B))),B))))
% -> inverse(inverse(B))
% Rule [192]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,a2))),
% inverse(a2)))),inverse(multiply(B,inverse(C))))
% <->
% multiply(multiply(inverse(a2),a2),inverse(multiply(B,inverse(multiply(A,C))))) is composed into 
% [192]
% multiply(inverse(inverse(multiply(inverse(inverse(multiply(A,a2))),inverse(a2)))),
% inverse(multiply(B,inverse(C)))) <->
% inverse(multiply(B,inverse(multiply(A,C))))
% Rule [185]
% multiply(inverse(inverse(multiply(inverse(A),a2))),inverse(a2)) <->
% multiply(multiply(inverse(a2),a2),inverse(A)) is composed into [185]
% multiply(
% inverse(
% inverse(
% multiply(
% inverse(A),a2))),
% inverse(a2))
% ->
% inverse(A)
% Rule [82]
% multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,
% inverse(B)))
% <-> multiply(multiply(inverse(a2),a2),inverse(B)) is composed into 
% [82]
% multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,
% inverse(B))) ->
% inverse(B)
% Rule [49]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),multiply(a2,
% inverse(A)))
% <-> multiply(multiply(inverse(a2),a2),inverse(A)) is composed into 
% [49]
% multiply(inverse(multiply(a2,inverse(multiply(inverse(A),A)))),multiply(a2,
% inverse(A)))
% -> inverse(A)
% New rule produced : [216] multiply(multiply(inverse(a2),a2),A) -> A
% Rule
% [160]
% multiply(multiply(inverse(a2),a2),inverse(multiply(inverse(A),A))) ->
% multiply(inverse(a2),a2) collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% Trivial
% 
% Current number of equations to process: 768
% Current number of ordered equations: 0
% Current number of rules: 71
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% 
% The following 15 rules have been used:
% [1] 
% multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,
% inverse(C))),
% inverse(multiply(inverse(C),C))) -> B; trace = in the starting set
% [4] multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,
% inverse(C))) <->
% multiply(inverse(multiply(a2,inverse(multiply(B,C)))),multiply(a2,
% inverse(C))); trace = Self cp of 1
% [5] multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(
% multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,
% inverse(C))); trace = Self cp of 1
% [9] multiply(inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(
% inverse(C),C))),C)))),
% multiply(B,inverse(C))) -> A; trace = Cp of 5 and 1
% [12] multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),
% multiply(A,inverse(C))),inverse(multiply(V_3,
% multiply(
% inverse(C),C))))),B)
% ->
% multiply(inverse(multiply(a2,inverse(multiply(V_3,multiply(inverse(C),C))))),
% multiply(a2,inverse(multiply(inverse(C),C)))); trace = Cp of 4 and 1
% [16] inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(
% inverse(V_3),V_3))),V_3))))
% <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(multiply(C,inverse(V_3))),multiply(C,inverse(V_3))))); trace = Cp of 9 and 1
% [17] multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(multiply(C,inverse(V_3))),multiply(C,inverse(V_3)))))
% <->
% inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(
% inverse(V_3),V_3))),V_3)))); trace = Cp of 9 and 1
% [18] multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,
% inverse(C))))),
% multiply(A,inverse(inverse(C)))),inverse(V_3))),B)
% ->
% multiply(inverse(multiply(a2,inverse(V_3))),multiply(a2,inverse(
% multiply(
% inverse(
% inverse(C)),
% inverse(C))))); trace = Cp of 12 and 9
% [21] multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,
% inverse(C))),
% inverse(multiply(inverse(C),C))),C) -> B; trace = Cp of 16 and 12
% [22] inverse(multiply(B,inverse(multiply(multiply(multiply(A,multiply(B,
% inverse(C))),
% inverse(multiply(inverse(C),C))),C))))
% -> A; trace = Cp of 17 and 1
% [23] multiply(inverse(A),A) <-> multiply(inverse(a2),a2); trace = Cp of 18 and 1
% [27] multiply(multiply(multiply(A,multiply(B,inverse(C))),inverse(multiply(
% inverse(C),C))),C)
% <->
% multiply(multiply(multiply(A,multiply(B,inverse(V_3))),inverse(multiply(
% inverse(V_3),V_3))),V_3); trace = Cp of 22 and 21
% [29] multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(a2),a2)))),
% multiply(A,inverse(B))),inverse(multiply(inverse(B),B))) ->
% inverse(B); trace = Cp of 23 and 1
% [87] multiply(inverse(B),B) <-> multiply(inverse(A),A); trace = Cp of 29 and 27
% [216] multiply(multiply(inverse(a2),a2),A) -> A; trace = Cp of 27 and 23
% % SZS output end Refutation
% All conjectures have been proven
% 
% Execution time: 2.360000 sec
% res : bool = true
% time is now off
% 
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
% 
% EOF
%------------------------------------------------------------------------------