TSTP Solution File: GRP586-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP586-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n066.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 00:23:32 EDT 2014
% Result : Unsatisfiable 3.30s
% Output : Refutation 3.30s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP586-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n066.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 21:06:08 CDT 2014
% % CPUTime : 3.30
% Processing problem /tmp/CiME_36154_n066.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a2,b2 : constant; multiply : 2; inverse : 1; double_divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C;
% multiply(A,B) = inverse(double_divide(B,A));
% ";
%
% let s1 = status F "
% a2 lr_lex;
% b2 lr_lex;
% multiply lr_lex;
% inverse lr_lex;
% double_divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > double_divide > inverse > b2 > a2";
%
% let s2 = status F "
% a2 mul;
% b2 mul;
% multiply mul;
% inverse mul;
% double_divide mul;
% ";
%
% let p2 = precedence F "
% multiply > double_divide > 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 = { double_divide(A,inverse(double_divide(inverse(
% double_divide(
% double_divide(A,B),
% inverse(C))),B)))
% = C,
% multiply(A,B) = inverse(double_divide(B,A)) }
% (2 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(A,B) -> inverse(double_divide(B,A))
% The conjecture has been reduced.
% Conjecture is now:
% inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) = a2
%
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 1
% New rule produced :
% [2]
% double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),
% inverse(C))),B))) -> C
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3]
% double_divide(inverse(double_divide(double_divide(double_divide(A,C),V_3),
% inverse(B))),V_3) ->
% double_divide(A,inverse(double_divide(inverse(B),C)))
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [4]
% double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(
% inverse(C),B)))))
% -> C
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [5]
% double_divide(double_divide(double_divide(inverse(A),B),inverse(double_divide(
% inverse(C),B))),
% inverse(C)) -> A
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6]
% double_divide(C,inverse(double_divide(inverse(B),V_3))) <->
% double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,
% inverse(double_divide(
% inverse(A),V_3)))))
% Current number of equations to process: 19
% Current number of ordered equations: 1
% Current number of rules: 6
% New rule produced :
% [7]
% double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,
% inverse(double_divide(
% inverse(A),V_3)))))
% <-> double_divide(C,inverse(double_divide(inverse(B),V_3)))
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8]
% double_divide(inverse(double_divide(A,inverse(B))),inverse(C)) <->
% double_divide(double_divide(inverse(A),V_3),inverse(double_divide(inverse(B),
% inverse(double_divide(
% inverse(C),V_3)))))
% Current number of equations to process: 60
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [9]
% double_divide(double_divide(inverse(A),V_3),inverse(double_divide(inverse(B),
% inverse(double_divide(
% inverse(C),V_3)))))
% <-> double_divide(inverse(double_divide(A,inverse(B))),inverse(C))
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10] double_divide(inverse(double_divide(B,inverse(B))),inverse(A)) -> A
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11]
% double_divide(double_divide(inverse(A),B),inverse(C)) <->
% double_divide(inverse(double_divide(A,inverse(V_3))),inverse(double_divide(
% double_divide(
% inverse(V_3),B),
% inverse(C))))
% Current number of equations to process: 90
% Current number of ordered equations: 1
% Current number of rules: 11
% New rule produced :
% [12]
% double_divide(inverse(double_divide(A,inverse(V_3))),inverse(double_divide(
% double_divide(
% inverse(V_3),B),
% inverse(C))))
% <-> double_divide(double_divide(inverse(A),B),inverse(C))
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13]
% double_divide(inverse(inverse(double_divide(A,inverse(A)))),inverse(B)) -> B
% Current number of equations to process: 103
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14] double_divide(inverse(double_divide(A,inverse(B))),inverse(A)) -> B
% Current number of equations to process: 103
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15] double_divide(A,inverse(double_divide(inverse(B),inverse(A)))) -> B
% Current number of equations to process: 106
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16] double_divide(A,inverse(A)) <-> double_divide(B,inverse(B))
% The conjecture has been reduced.
% Conjecture is now:
% inverse(double_divide(a2,inverse(double_divide(a2,inverse(a2))))) = a2
%
% Current number of equations to process: 107
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17]
% double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B) ->
% double_divide(inverse(C),inverse(A))
% Rule
% [2]
% double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),
% inverse(C))),B))) -> C
% collapsed.
% Rule
% [3]
% double_divide(inverse(double_divide(double_divide(double_divide(A,C),V_3),
% inverse(B))),V_3) ->
% double_divide(A,inverse(double_divide(inverse(B),C))) collapsed.
% Current number of equations to process: 107
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [18]
% double_divide(A,inverse(double_divide(inverse(B),C))) <->
% double_divide(inverse(B),inverse(double_divide(A,C)))
% Current number of equations to process: 106
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [19]
% double_divide(inverse(B),inverse(double_divide(A,C))) <->
% double_divide(A,inverse(double_divide(inverse(B),C)))
% Current number of equations to process: 106
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [20]
% double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,
% inverse(B))),C))) ->
% double_divide(inverse(B),C)
% Current number of equations to process: 109
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [21]
% double_divide(double_divide(double_divide(inverse(A),inverse(B)),inverse(B)),
% inverse(double_divide(C,inverse(C)))) -> A
% Current number of equations to process: 112
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [22]
% double_divide(double_divide(inverse(A),B),inverse(double_divide(inverse(C),B)))
% <->
% double_divide(inverse(double_divide(A,inverse(double_divide(V_3,inverse(V_3))))),
% inverse(C))
% Rule
% [5]
% double_divide(double_divide(double_divide(inverse(A),B),inverse(double_divide(
% inverse(C),B))),
% inverse(C)) -> A collapsed.
% Current number of equations to process: 116
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [23]
% double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(a2,
% inverse(a2)))),
% inverse(a2))),inverse(double_divide(double_divide(
% inverse(a2),
% inverse(C)),
% inverse(C)))) -> A
% Current number of equations to process: 115
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [24]
% double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(
% inverse(C),inverse(A))))))
% <->
% double_divide(inverse(double_divide(double_divide(V_3,inverse(V_3)),inverse(B))),
% inverse(C))
% Current number of equations to process: 118
% Current number of ordered equations: 3
% Current number of rules: 21
% New rule produced :
% [25]
% double_divide(inverse(double_divide(A,inverse(C))),inverse(double_divide(V_3,
% inverse(V_3))))
% <->
% double_divide(inverse(double_divide(A,inverse(double_divide(a2,inverse(a2))))),
% inverse(C))
% Current number of equations to process: 118
% Current number of ordered equations: 2
% Current number of rules: 22
% New rule produced :
% [26]
% double_divide(inverse(double_divide(double_divide(V_3,inverse(V_3)),inverse(B))),
% inverse(C)) <->
% double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(
% inverse(C),inverse(A))))))
% Current number of equations to process: 118
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [27]
% double_divide(inverse(double_divide(A,inverse(double_divide(a2,inverse(a2))))),
% inverse(C)) <->
% double_divide(inverse(double_divide(A,inverse(C))),inverse(double_divide(V_3,
% inverse(V_3))))
% Current number of equations to process: 118
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [28]
% double_divide(inverse(V_3),inverse(double_divide(double_divide(inverse(V_3),B),C)))
% <->
% double_divide(inverse(A),inverse(double_divide(double_divide(inverse(A),B),C)))
% Current number of equations to process: 134
% Current number of ordered equations: 0
% Current number of rules: 25
% Rule [25]
% double_divide(inverse(double_divide(A,inverse(C))),inverse(double_divide(V_3,
% inverse(V_3))))
% <->
% double_divide(inverse(double_divide(A,inverse(double_divide(a2,inverse(a2))))),
% inverse(C)) is composed into [25]
% double_divide(inverse(double_divide(A,
% inverse(C))),
% inverse(double_divide(V_3,inverse(V_3))))
% <->
% double_divide(inverse(double_divide(A,
% double_divide(a2,
% inverse(a2)))),
% inverse(C))
% New rule produced :
% [29] inverse(double_divide(B,inverse(B))) <-> double_divide(A,inverse(A))
% Rule
% [13]
% double_divide(inverse(inverse(double_divide(A,inverse(A)))),inverse(B)) -> B
% collapsed.
% Rule
% [23]
% double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(a2,
% inverse(a2)))),
% inverse(a2))),inverse(double_divide(double_divide(
% inverse(a2),
% inverse(C)),
% inverse(C)))) -> A collapsed.
% Rule
% [27]
% double_divide(inverse(double_divide(A,inverse(double_divide(a2,inverse(a2))))),
% inverse(C)) <->
% double_divide(inverse(double_divide(A,inverse(C))),inverse(double_divide(V_3,
% inverse(V_3))))
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% inverse(double_divide(a2,double_divide(a2,inverse(a2)))) = a2
%
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 23
% Rule [24]
% double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(
% inverse(C),
% inverse(A))))))
% <->
% double_divide(inverse(double_divide(double_divide(V_3,inverse(V_3)),
% inverse(B))),inverse(C)) is composed into
% [24]
% double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(
% inverse(C),inverse(A))))))
% -> double_divide(inverse(B),inverse(C))
% New rule produced :
% [30] double_divide(double_divide(A,inverse(A)),inverse(B)) -> B
% Rule
% [26]
% double_divide(inverse(double_divide(double_divide(V_3,inverse(V_3)),inverse(B))),
% inverse(C)) <->
% double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(
% inverse(C),inverse(A))))))
% collapsed.
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [31]
% double_divide(double_divide(inverse(A),inverse(inverse(B))),inverse(A)) -> B
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [32]
% double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,inverse(C))))
% -> double_divide(B,inverse(C))
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [33]
% double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(B))))) -> A
% Current number of equations to process: 161
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [34]
% double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(A))))) -> B
% Current number of equations to process: 165
% Current number of ordered equations: 0
% Current number of rules: 27
% Rule [25]
% double_divide(inverse(double_divide(A,inverse(C))),inverse(double_divide(V_3,
% inverse(V_3))))
% <->
% double_divide(inverse(double_divide(A,double_divide(a2,inverse(a2)))),
% inverse(C)) is composed into [25]
% double_divide(inverse(double_divide(A,
% inverse(C))),
% inverse(double_divide(V_3,inverse(V_3))))
% -> double_divide(A,inverse(C))
% New rule produced :
% [35]
% double_divide(inverse(double_divide(A,double_divide(a2,inverse(a2)))),
% inverse(B)) -> double_divide(A,inverse(B))
% Current number of equations to process: 169
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [36] double_divide(inverse(A),inverse(double_divide(B,inverse(B)))) -> A
% Rule
% [25]
% double_divide(inverse(double_divide(A,inverse(C))),inverse(double_divide(V_3,
% inverse(V_3)))) ->
% double_divide(A,inverse(C)) collapsed.
% Current number of equations to process: 180
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [37]
% double_divide(double_divide(double_divide(inverse(A),B),B),inverse(double_divide(C,
% inverse(C))))
% -> A
% Rule
% [21]
% double_divide(double_divide(double_divide(inverse(A),inverse(B)),inverse(B)),
% inverse(double_divide(C,inverse(C)))) -> A collapsed.
% Current number of equations to process: 189
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [38]
% double_divide(double_divide(inverse(A),inverse(inverse(B))),inverse(C)) ->
% double_divide(inverse(double_divide(A,inverse(B))),inverse(C))
% Rule
% [31]
% double_divide(double_divide(inverse(A),inverse(inverse(B))),inverse(A)) -> B
% collapsed.
% Current number of equations to process: 188
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [39]
% double_divide(inverse(double_divide(A,inverse(B))),inverse(C)) <->
% double_divide(inverse(double_divide(A,inverse(C))),inverse(B))
% Current number of equations to process: 187
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [40]
% double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(inverse(C)))))
% <-> double_divide(inverse(double_divide(C,inverse(A))),inverse(B))
% Current number of equations to process: 185
% Current number of ordered equations: 1
% Current number of rules: 30
% New rule produced :
% [41]
% double_divide(inverse(double_divide(C,inverse(A))),inverse(B)) <->
% double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(inverse(C)))))
% Rule [14] double_divide(inverse(double_divide(A,inverse(B))),inverse(A)) -> B
% collapsed.
% Current number of equations to process: 186
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [42] double_divide(inverse(B),double_divide(a2,inverse(a2))) -> B
% Current number of equations to process: 185
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [43]
% double_divide(double_divide(A,inverse(A)),B) <->
% double_divide(inverse(double_divide(C,B)),inverse(C))
% Current number of equations to process: 208
% Current number of ordered equations: 1
% Current number of rules: 32
% New rule produced :
% [44]
% double_divide(inverse(double_divide(C,B)),inverse(C)) <->
% double_divide(double_divide(A,inverse(A)),B)
% Current number of equations to process: 208
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [45] double_divide(B,inverse(double_divide(inverse(B),inverse(A)))) -> A
% Current number of equations to process: 209
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [46]
% double_divide(A,inverse(double_divide(inverse(B),inverse(C)))) <->
% double_divide(double_divide(C,inverse(A)),inverse(B))
% Current number of equations to process: 208
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [47]
% double_divide(double_divide(C,inverse(A)),inverse(B)) <->
% double_divide(A,inverse(double_divide(inverse(B),inverse(C))))
% Current number of equations to process: 208
% Current number of ordered equations: 0
% Current number of rules: 36
% Rule [40]
% double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(
% inverse(C)))))
% <-> double_divide(inverse(double_divide(C,inverse(A))),inverse(B)) is composed into
% [40]
% double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(inverse(C)))))
% <-> double_divide(inverse(A),inverse(double_divide(C,inverse(B))))
% Rule [38]
% double_divide(double_divide(inverse(A),inverse(inverse(B))),inverse(C))
% -> double_divide(inverse(double_divide(A,inverse(B))),inverse(C)) is composed into
% [38]
% double_divide(double_divide(inverse(A),inverse(inverse(B))),inverse(C)) ->
% double_divide(inverse(B),inverse(double_divide(A,inverse(C))))
% Rule [22]
% double_divide(double_divide(inverse(A),B),inverse(double_divide(
% inverse(C),B))) <->
% double_divide(inverse(double_divide(A,inverse(double_divide(V_3,
% inverse(V_3))))),inverse(C)) is composed into
% [22]
% double_divide(double_divide(inverse(A),B),inverse(double_divide(inverse(C),B)))
% <->
% double_divide(inverse(V_3),inverse(double_divide(V_3,inverse(double_divide(A,
% inverse(C))))))
% Rule [11]
% double_divide(double_divide(inverse(A),B),inverse(C)) <->
% double_divide(inverse(double_divide(A,inverse(V_3))),inverse(double_divide(
% double_divide(
% inverse(V_3),B),
% inverse(C)))) is composed into
% [11]
% double_divide(double_divide(inverse(A),B),inverse(C)) <->
% double_divide(inverse(V_3),inverse(double_divide(A,inverse(double_divide(
% double_divide(
% inverse(V_3),B),
% inverse(C))))))
% Rule [9]
% double_divide(double_divide(inverse(A),V_3),inverse(double_divide(
% inverse(B),inverse(
% double_divide(
% inverse(C),V_3)))))
% <-> double_divide(inverse(double_divide(A,inverse(B))),inverse(C)) is composed into
% [9]
% double_divide(double_divide(inverse(A),V_3),inverse(double_divide(inverse(B),
% inverse(double_divide(
% inverse(C),V_3)))))
% <-> double_divide(inverse(B),inverse(double_divide(A,inverse(C))))
% Rule [6]
% double_divide(C,inverse(double_divide(inverse(B),V_3))) <->
% double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,
% inverse(
% double_divide(
% inverse(A),V_3))))) is composed into
% [6]
% double_divide(C,inverse(double_divide(inverse(B),V_3))) <->
% double_divide(inverse(B),inverse(double_divide(A,inverse(double_divide(C,
% inverse(double_divide(
% inverse(A),V_3)))))))
% New rule produced :
% [48]
% double_divide(inverse(double_divide(A,inverse(B))),inverse(C)) ->
% double_divide(inverse(B),inverse(double_divide(A,inverse(C))))
% Rule
% [7]
% double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,
% inverse(double_divide(
% inverse(A),V_3)))))
% <-> double_divide(C,inverse(double_divide(inverse(B),V_3))) collapsed.
% Rule
% [8]
% double_divide(inverse(double_divide(A,inverse(B))),inverse(C)) <->
% double_divide(double_divide(inverse(A),V_3),inverse(double_divide(inverse(B),
% inverse(double_divide(
% inverse(C),V_3)))))
% collapsed.
% Rule [10] double_divide(inverse(double_divide(B,inverse(B))),inverse(A)) -> A
% collapsed.
% Rule
% [12]
% double_divide(inverse(double_divide(A,inverse(V_3))),inverse(double_divide(
% double_divide(
% inverse(V_3),B),
% inverse(C))))
% <-> double_divide(double_divide(inverse(A),B),inverse(C)) collapsed.
% Rule
% [39]
% double_divide(inverse(double_divide(A,inverse(B))),inverse(C)) <->
% double_divide(inverse(double_divide(A,inverse(C))),inverse(B)) collapsed.
% Rule
% [41]
% double_divide(inverse(double_divide(C,inverse(A))),inverse(B)) <->
% double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(inverse(C)))))
% collapsed.
% Current number of equations to process: 225
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [49]
% double_divide(inverse(C),inverse(double_divide(A,inverse(B)))) <->
% double_divide(inverse(B),inverse(double_divide(A,inverse(C))))
% Current number of equations to process: 224
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [50]
% double_divide(inverse(A),inverse(double_divide(inverse(double_divide(C,
% inverse(C))),B))) ->
% double_divide(inverse(A),B)
% Current number of equations to process: 223
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [51]
% double_divide(A,inverse(A)) <->
% double_divide(inverse(B),inverse(double_divide(double_divide(inverse(B),C),C)))
% Current number of equations to process: 234
% Current number of ordered equations: 1
% Current number of rules: 34
% Rule [51]
% double_divide(A,inverse(A)) <->
% double_divide(inverse(B),inverse(double_divide(double_divide(inverse(B),C),C))) is composed into
% [51] double_divide(A,inverse(A)) <-> double_divide(a2,inverse(a2))
% New rule produced :
% [52]
% double_divide(inverse(B),inverse(double_divide(double_divide(inverse(B),C),C)))
% <-> double_divide(A,inverse(A))
% Current number of equations to process: 234
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [53]
% double_divide(A,inverse(double_divide(B,inverse(B)))) <->
% double_divide(inverse(C),inverse(double_divide(A,inverse(inverse(C)))))
% Rule
% [37]
% double_divide(double_divide(double_divide(inverse(A),B),B),inverse(double_divide(C,
% inverse(C))))
% -> A collapsed.
% Current number of equations to process: 234
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [54]
% double_divide(inverse(C),inverse(double_divide(A,inverse(inverse(C))))) <->
% double_divide(A,inverse(double_divide(B,inverse(B))))
% Current number of equations to process: 234
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [55]
% double_divide(inverse(A),inverse(double_divide(double_divide(inverse(
% double_divide(B,
% inverse(A))),C),C)))
% -> B
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [56]
% double_divide(inverse(inverse(a2)),inverse(double_divide(double_divide(
% double_divide(
% inverse(A),B),B),
% inverse(a2)))) -> A
% Current number of equations to process: 249
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [57]
% double_divide(inverse(C),inverse(double_divide(inverse(double_divide(C,B)),
% inverse(inverse(inverse(A)))))) <->
% double_divide(inverse(A),B)
% Current number of equations to process: 248
% Current number of ordered equations: 1
% Current number of rules: 39
% New rule produced :
% [58]
% double_divide(inverse(A),B) <->
% double_divide(inverse(C),inverse(double_divide(inverse(double_divide(C,B)),
% inverse(inverse(inverse(A))))))
% Rule
% [17]
% double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B) ->
% double_divide(inverse(C),inverse(A)) collapsed.
% Current number of equations to process: 249
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [59]
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(
% inverse(B),inverse(
% inverse(C)))))))
% -> double_divide(A,inverse(B))
% Current number of equations to process: 248
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [60]
% double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),V_3)))))
% <->
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(B,V_3)))))
% Current number of equations to process: 247
% Current number of ordered equations: 1
% Current number of rules: 41
% New rule produced :
% [61]
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(B,V_3)))))
% <->
% double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),V_3)))))
% Current number of equations to process: 247
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [62]
% double_divide(inverse(double_divide(A,inverse(double_divide(inverse(C),B)))),V_3)
% ->
% double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(C),V_3)))
% Current number of equations to process: 246
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [63]
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(C,
% inverse(B)))))) ->
% double_divide(A,inverse(B))
% Current number of equations to process: 253
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [64]
% double_divide(inverse(double_divide(inverse(B),inverse(A))),C) ->
% double_divide(inverse(A),inverse(double_divide(inverse(B),C)))
% Current number of equations to process: 262
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [65]
% double_divide(inverse(A),inverse(double_divide(B,inverse(double_divide(
% inverse(B),C))))) ->
% double_divide(inverse(A),C)
% Current number of equations to process: 263
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [66]
% double_divide(double_divide(double_divide(inverse(A),B),B),inverse(double_divide(A,
% inverse(C))))
% -> C
% Current number of equations to process: 264
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [67]
% double_divide(inverse(C),inverse(double_divide(inverse(B),inverse(inverse(
% double_divide(A,
% inverse(C)))))))
% <-> double_divide(inverse(A),inverse(B))
% Current number of equations to process: 262
% Current number of ordered equations: 1
% Current number of rules: 48
% Rule [43]
% double_divide(double_divide(A,inverse(A)),B) <->
% double_divide(inverse(double_divide(C,B)),inverse(C)) is composed into
% [43]
% double_divide(double_divide(A,inverse(A)),B) <->
% double_divide(inverse(C),inverse(double_divide(inverse(C),inverse(inverse(
% double_divide(
% double_divide(C,B),
% inverse(C)))))))
% New rule produced :
% [68]
% double_divide(inverse(A),inverse(B)) <->
% double_divide(inverse(C),inverse(double_divide(inverse(B),inverse(inverse(
% double_divide(A,
% inverse(C)))))))
% Rule
% [44]
% double_divide(inverse(double_divide(C,B)),inverse(C)) <->
% double_divide(double_divide(A,inverse(A)),B) collapsed.
% Current number of equations to process: 263
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [69]
% double_divide(A,inverse(C)) <->
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(V_3,
% inverse(V_3))))))
% Current number of equations to process: 262
% Current number of ordered equations: 1
% Current number of rules: 49
% New rule produced :
% [70]
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(V_3,
% inverse(V_3))))))
% <-> double_divide(A,inverse(C))
% Current number of equations to process: 262
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [71]
% double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(
% inverse(C),
% inverse(V_3))))))
% <-> double_divide(double_divide(V_3,B),inverse(C))
% Current number of equations to process: 261
% Current number of ordered equations: 1
% Current number of rules: 51
% New rule produced :
% [72]
% double_divide(double_divide(V_3,B),inverse(C)) <->
% double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(
% inverse(C),
% inverse(V_3))))))
% Rule
% [56]
% double_divide(inverse(inverse(a2)),inverse(double_divide(double_divide(
% double_divide(
% inverse(A),B),B),
% inverse(a2)))) -> A collapsed.
% Current number of equations to process: 261
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [73]
% double_divide(A,inverse(double_divide(inverse(B),inverse(C)))) <->
% double_divide(inverse(B),inverse(double_divide(double_divide(C,V_3),inverse(
% double_divide(A,V_3)))))
% Current number of equations to process: 259
% Current number of ordered equations: 3
% Current number of rules: 52
% New rule produced :
% [74]
% double_divide(inverse(B),inverse(double_divide(double_divide(C,V_3),inverse(
% double_divide(A,V_3)))))
% <-> double_divide(A,inverse(double_divide(inverse(B),inverse(C))))
% Current number of equations to process: 259
% Current number of ordered equations: 2
% Current number of rules: 53
% New rule produced :
% [75]
% double_divide(inverse(double_divide(inverse(A),V_3)),inverse(B)) <->
% double_divide(inverse(double_divide(double_divide(B,C),V_3)),inverse(
% double_divide(
% inverse(A),C)))
% Current number of equations to process: 259
% Current number of ordered equations: 1
% Current number of rules: 54
% New rule produced :
% [76]
% double_divide(inverse(double_divide(double_divide(B,C),V_3)),inverse(
% double_divide(
% inverse(A),C)))
% <-> double_divide(inverse(double_divide(inverse(A),V_3)),inverse(B))
% Current number of equations to process: 259
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [77]
% double_divide(C,inverse(double_divide(inverse(A),inverse(double_divide(
% inverse(B),V_3)))))
% <->
% double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(double_divide(C,V_3)))))
% Current number of equations to process: 255
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [78]
% double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(double_divide(C,V_3)))))
% <->
% double_divide(C,inverse(double_divide(inverse(A),inverse(double_divide(
% inverse(B),V_3)))))
% Current number of equations to process: 255
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [79]
% double_divide(C,inverse(A)) <->
% double_divide(inverse(A),inverse(double_divide(B,inverse(double_divide(C,
% inverse(B))))))
% Current number of equations to process: 256
% Current number of ordered equations: 1
% Current number of rules: 58
% New rule produced :
% [80]
% double_divide(inverse(A),inverse(double_divide(B,inverse(double_divide(C,
% inverse(B)))))) <->
% double_divide(C,inverse(A))
% Current number of equations to process: 256
% Current number of ordered equations: 0
% Current number of rules: 59
% Rule [43]
% double_divide(double_divide(A,inverse(A)),B) <->
% double_divide(inverse(C),inverse(double_divide(inverse(C),inverse(
% inverse(
% double_divide(
% double_divide(C,B),
% inverse(C))))))) is composed into
% [43]
% double_divide(double_divide(A,inverse(A)),B) <->
% double_divide(inverse(C),inverse(double_divide(inverse(C),inverse(inverse(
% double_divide(
% inverse(C),
% inverse(
% inverse(
% double_divide(C,B)))))))))
% New rule produced :
% [81]
% double_divide(B,inverse(A)) <-> double_divide(inverse(A),inverse(inverse(B)))
% Current number of equations to process: 257
% Current number of ordered equations: 1
% Current number of rules: 60
% New rule produced :
% [82]
% double_divide(inverse(A),inverse(inverse(B))) <-> double_divide(B,inverse(A))
% Rule
% [40]
% double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(inverse(C)))))
% <-> double_divide(inverse(A),inverse(double_divide(C,inverse(B)))) collapsed.
% Current number of equations to process: 257
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [83]
% double_divide(B,inverse(A)) <->
% double_divide(inverse(A),inverse(double_divide(double_divide(inverse(B),C),C)))
% Current number of equations to process: 259
% Current number of ordered equations: 1
% Current number of rules: 61
% New rule produced :
% [84]
% double_divide(inverse(A),inverse(double_divide(double_divide(inverse(B),C),C)))
% <-> double_divide(B,inverse(A))
% Rule
% [52]
% double_divide(inverse(B),inverse(double_divide(double_divide(inverse(B),C),C)))
% <-> double_divide(A,inverse(A)) collapsed.
% Rule
% [55]
% double_divide(inverse(A),inverse(double_divide(double_divide(inverse(
% double_divide(B,
% inverse(A))),C),C)))
% -> B collapsed.
% Current number of equations to process: 259
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [85]
% double_divide(C,inverse(B)) <->
% double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(
% inverse(A),inverse(
% inverse(C)))))))
% Current number of equations to process: 263
% Current number of ordered equations: 1
% Current number of rules: 61
% New rule produced :
% [86]
% double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(
% inverse(A),inverse(
% inverse(C)))))))
% <-> double_divide(C,inverse(B))
% Current number of equations to process: 263
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [87]
% double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),V_3)
% ->
% double_divide(inverse(inverse(A)),inverse(double_divide(inverse(double_divide(
% inverse(B),C)),V_3)))
% Current number of equations to process: 263
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [88]
% double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(
% inverse(C),inverse(V_3))))))
% <->
% double_divide(inverse(B),inverse(double_divide(double_divide(V_3,inverse(A)),
% inverse(C))))
% Current number of equations to process: 261
% Current number of ordered equations: 5
% Current number of rules: 64
% New rule produced :
% [89]
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(B,
% inverse(V_3))))))
% <->
% double_divide(double_divide(inverse(A),inverse(B)),inverse(double_divide(
% inverse(C),
% inverse(V_3))))
% Current number of equations to process: 261
% Current number of ordered equations: 4
% Current number of rules: 65
% New rule produced :
% [90]
% double_divide(inverse(C),inverse(double_divide(double_divide(inverse(V_3),B),
% inverse(double_divide(A,inverse(V_3))))))
% <-> double_divide(double_divide(inverse(A),B),inverse(C))
% Current number of equations to process: 261
% Current number of ordered equations: 3
% Current number of rules: 66
% New rule produced :
% [91]
% double_divide(inverse(B),inverse(double_divide(double_divide(V_3,inverse(A)),
% inverse(C)))) <->
% double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(
% inverse(C),inverse(V_3))))))
% Current number of equations to process: 261
% Current number of ordered equations: 2
% Current number of rules: 67
% New rule produced :
% [92]
% double_divide(double_divide(inverse(A),B),inverse(C)) <->
% double_divide(inverse(C),inverse(double_divide(double_divide(inverse(V_3),B),
% inverse(double_divide(A,inverse(V_3))))))
% Current number of equations to process: 261
% Current number of ordered equations: 1
% Current number of rules: 68
% New rule produced :
% [93]
% double_divide(double_divide(inverse(A),inverse(B)),inverse(double_divide(
% inverse(C),
% inverse(V_3))))
% <->
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(B,
% inverse(V_3))))))
% Current number of equations to process: 261
% Current number of ordered equations: 0
% Current number of rules: 69
% Rule [6]
% double_divide(C,inverse(double_divide(inverse(B),V_3))) <->
% double_divide(inverse(B),inverse(double_divide(A,inverse(double_divide(C,
% inverse(
% double_divide(
% inverse(A),V_3))))))) is composed into
% [6]
% double_divide(C,inverse(double_divide(inverse(B),V_3))) <->
% double_divide(inverse(B),inverse(double_divide(C,V_3)))
% New rule produced :
% [94]
% double_divide(inverse(B),inverse(double_divide(A,inverse(double_divide(C,
% inverse(double_divide(
% inverse(A),V_3)))))))
% -> double_divide(inverse(B),inverse(double_divide(C,V_3)))
% Current number of equations to process: 260
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [95]
% double_divide(inverse(A),inverse(B)) <->
% double_divide(inverse(double_divide(C,V_3)),inverse(inverse(inverse(double_divide(
% double_divide(B,
% inverse(
% double_divide(C,V_3))),
% inverse(A))))))
% Current number of equations to process: 258
% Current number of ordered equations: 1
% Current number of rules: 71
% New rule produced :
% [96]
% double_divide(inverse(double_divide(C,V_3)),inverse(inverse(inverse(double_divide(
% double_divide(B,
% inverse(
% double_divide(C,V_3))),
% inverse(A))))))
% <-> double_divide(inverse(A),inverse(B))
% Current number of equations to process: 258
% Current number of ordered equations: 0
% Current number of rules: 72
% Rule [76]
% double_divide(inverse(double_divide(double_divide(B,C),V_3)),inverse(
% double_divide(
% inverse(A),C)))
% <-> double_divide(inverse(double_divide(inverse(A),V_3)),inverse(B)) is composed into
% [76]
% double_divide(inverse(double_divide(double_divide(B,C),V_3)),inverse(
% double_divide(
% inverse(A),C)))
% <->
% double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,V_3)),
% inverse(double_divide(inverse(A),inverse(B))))))
% New rule produced :
% [97]
% double_divide(inverse(double_divide(inverse(B),C)),V_3) <->
% double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,C)),
% inverse(double_divide(inverse(B),V_3)))))
% Rule
% [64]
% double_divide(inverse(double_divide(inverse(B),inverse(A))),C) ->
% double_divide(inverse(A),inverse(double_divide(inverse(B),C))) collapsed.
% Rule
% [75]
% double_divide(inverse(double_divide(inverse(A),V_3)),inverse(B)) <->
% double_divide(inverse(double_divide(double_divide(B,C),V_3)),inverse(
% double_divide(
% inverse(A),C)))
% collapsed.
% Rule
% [87]
% double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),V_3)
% ->
% double_divide(inverse(inverse(A)),inverse(double_divide(inverse(double_divide(
% inverse(B),C)),V_3)))
% collapsed.
% Current number of equations to process: 259
% Current number of ordered equations: 1
% Current number of rules: 70
% New rule produced :
% [98]
% double_divide(inverse(V_3),inverse(double_divide(A,inverse(double_divide(
% inverse(double_divide(V_3,
% inverse(B))),C)))))
% -> double_divide(A,inverse(double_divide(inverse(B),C)))
% Current number of equations to process: 258
% Current number of ordered equations: 2
% Current number of rules: 71
% New rule produced :
% [99]
% double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,C)),
% inverse(double_divide(inverse(B),V_3)))))
% <->
% double_divide(inverse(a2),inverse(double_divide(inverse(double_divide(a2,C)),
% inverse(double_divide(inverse(B),V_3)))))
% Current number of equations to process: 258
% Current number of ordered equations: 1
% Current number of rules: 72
% New rule produced :
% [100]
% double_divide(inverse(a2),inverse(double_divide(inverse(double_divide(a2,C)),
% inverse(double_divide(inverse(B),V_3)))))
% <->
% double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,C)),
% inverse(double_divide(inverse(B),V_3)))))
% Current number of equations to process: 258
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [101]
% double_divide(inverse(B),inverse(A)) <-> double_divide(inverse(A),inverse(B))
% Current number of equations to process: 261
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [102]
% double_divide(inverse(C),inverse(B)) <->
% double_divide(inverse(A),inverse(double_divide(double_divide(B,inverse(A)),
% inverse(C))))
% Current number of equations to process: 266
% Current number of ordered equations: 1
% Current number of rules: 75
% New rule produced :
% [103]
% double_divide(inverse(A),inverse(double_divide(double_divide(B,inverse(A)),
% inverse(C)))) <->
% double_divide(inverse(C),inverse(B))
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [104] double_divide(inverse(A),double_divide(B,inverse(B))) -> A
% Rule [42] double_divide(inverse(B),double_divide(a2,inverse(a2))) -> B
% collapsed.
% Current number of equations to process: 302
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [105]
% double_divide(A,inverse(double_divide(inverse(double_divide(C,inverse(C))),B)))
% -> double_divide(A,B)
% Rule
% [50]
% double_divide(inverse(A),inverse(double_divide(inverse(double_divide(C,
% inverse(C))),B))) ->
% double_divide(inverse(A),B) collapsed.
% Current number of equations to process: 306
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [106]
% double_divide(inverse(V_3),inverse(double_divide(double_divide(inverse(V_3),B),C)))
% <->
% double_divide(double_divide(inverse(a2),inverse(double_divide(inverse(a2),
% inverse(inverse(double_divide(
% inverse(a2),
% inverse(
% inverse(
% double_divide(a2,B))))))))),C)
% Current number of equations to process: 310
% Current number of ordered equations: 1
% Current number of rules: 77
% Rule [106]
% double_divide(inverse(V_3),inverse(double_divide(double_divide(inverse(V_3),B),C)))
% <->
% double_divide(double_divide(inverse(a2),inverse(double_divide(inverse(a2),
% inverse(inverse(
% double_divide(
% inverse(a2),
% inverse(
% inverse(
% double_divide(a2,B))))))))),C) is composed into
% [106]
% double_divide(inverse(V_3),inverse(double_divide(double_divide(inverse(V_3),B),C)))
% <->
% double_divide(inverse(a2),inverse(double_divide(double_divide(inverse(a2),B),C)))
% New rule produced :
% [107]
% double_divide(double_divide(inverse(a2),inverse(double_divide(inverse(a2),
% inverse(inverse(double_divide(
% inverse(a2),
% inverse(
% inverse(
% double_divide(a2,B))))))))),C)
% <->
% double_divide(inverse(V_3),inverse(double_divide(double_divide(inverse(V_3),B),C)))
% Current number of equations to process: 310
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [108]
% double_divide(C,inverse(double_divide(A,inverse(double_divide(inverse(V_3),B)))))
% <-> double_divide(double_divide(double_divide(A,B),inverse(C)),inverse(V_3))
% Current number of equations to process: 308
% Current number of ordered equations: 2
% Current number of rules: 79
% New rule produced :
% [109]
% double_divide(double_divide(double_divide(A,B),inverse(C)),inverse(V_3)) <->
% double_divide(C,inverse(double_divide(A,inverse(double_divide(inverse(V_3),B)))))
% Current number of equations to process: 308
% Current number of ordered equations: 1
% Current number of rules: 80
% New rule produced :
% [110]
% double_divide(double_divide(B,inverse(double_divide(inverse(A),C))),inverse(V_3))
% -> double_divide(A,inverse(double_divide(double_divide(B,C),inverse(V_3))))
% Current number of equations to process: 308
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [111]
% double_divide(inverse(A),inverse(double_divide(double_divide(inverse(A),
% inverse(B)),inverse(C)))) ->
% double_divide(B,inverse(C))
% Current number of equations to process: 310
% Current number of ordered equations: 0
% Current number of rules: 82
% Rule [69]
% double_divide(A,inverse(C)) <->
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(V_3,
% inverse(V_3)))))) is composed into
% [69]
% double_divide(A,inverse(C)) <->
% double_divide(inverse(C),inverse(double_divide(A,double_divide(V_3,inverse(V_3)))))
% Rule [54]
% double_divide(inverse(C),inverse(double_divide(A,inverse(inverse(C)))))
% <-> double_divide(A,inverse(double_divide(B,inverse(B)))) is composed into
% [54]
% double_divide(inverse(C),inverse(double_divide(A,inverse(inverse(C))))) <->
% double_divide(A,double_divide(B,inverse(B)))
% New rule produced :
% [112] inverse(double_divide(A,inverse(B))) <-> double_divide(B,inverse(A))
% Rule
% [29] inverse(double_divide(B,inverse(B))) <-> double_divide(A,inverse(A))
% collapsed.
% Rule
% [33]
% double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(B))))) -> A
% collapsed.
% Rule [36] double_divide(inverse(A),inverse(double_divide(B,inverse(B)))) -> A
% collapsed.
% Rule
% [53]
% double_divide(A,inverse(double_divide(B,inverse(B)))) <->
% double_divide(inverse(C),inverse(double_divide(A,inverse(inverse(C)))))
% collapsed.
% Rule
% [70]
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(V_3,
% inverse(V_3))))))
% <-> double_divide(A,inverse(C)) collapsed.
% Rule
% [105]
% double_divide(A,inverse(double_divide(inverse(double_divide(C,inverse(C))),B)))
% -> double_divide(A,B) collapsed.
% Current number of equations to process: 318
% Current number of ordered equations: 1
% Current number of rules: 77
% New rule produced :
% [113] double_divide(B,inverse(A)) <-> inverse(double_divide(A,inverse(B)))
% Current number of equations to process: 318
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [114]
% double_divide(A,inverse(double_divide(inverse(C),inverse(double_divide(
% inverse(C),inverse(
% inverse(
% double_divide(
% inverse(C),
% inverse(
% inverse(
% double_divide(C,B)))))))))))
% -> double_divide(A,B)
% Current number of equations to process: 317
% Current number of ordered equations: 0
% Current number of rules: 79
% Rule [89]
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(B,
% inverse(V_3))))))
% <->
% double_divide(double_divide(inverse(A),inverse(B)),inverse(double_divide(
% inverse(C),
% inverse(V_3)))) is composed into
% [89]
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(B,
% inverse(V_3))))))
% <->
% double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),
% inverse(V_3))))))
% New rule produced :
% [115]
% double_divide(double_divide(inverse(A),inverse(B)),inverse(C)) ->
% double_divide(A,inverse(double_divide(B,inverse(C))))
% Rule
% [38]
% double_divide(double_divide(inverse(A),inverse(inverse(B))),inverse(C)) ->
% double_divide(inverse(B),inverse(double_divide(A,inverse(C)))) collapsed.
% Rule
% [93]
% double_divide(double_divide(inverse(A),inverse(B)),inverse(double_divide(
% inverse(C),
% inverse(V_3))))
% <->
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(B,
% inverse(V_3))))))
% collapsed.
% Rule
% [111]
% double_divide(inverse(A),inverse(double_divide(double_divide(inverse(A),
% inverse(B)),inverse(C)))) ->
% double_divide(B,inverse(C)) collapsed.
% Current number of equations to process: 318
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [116]
% double_divide(inverse(double_divide(A,inverse(B))),C) ->
% double_divide(A,inverse(double_divide(inverse(B),C)))
% Rule
% [20]
% double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,
% inverse(B))),C))) ->
% double_divide(inverse(B),C) collapsed.
% Rule
% [48]
% double_divide(inverse(double_divide(A,inverse(B))),inverse(C)) ->
% double_divide(inverse(B),inverse(double_divide(A,inverse(C)))) collapsed.
% Rule
% [62]
% double_divide(inverse(double_divide(A,inverse(double_divide(inverse(C),B)))),V_3)
% ->
% double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(C),V_3)))
% collapsed.
% Rule
% [98]
% double_divide(inverse(V_3),inverse(double_divide(A,inverse(double_divide(
% inverse(double_divide(V_3,
% inverse(B))),C)))))
% -> double_divide(A,inverse(double_divide(inverse(B),C))) collapsed.
% Current number of equations to process: 319
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [117]
% double_divide(A,inverse(double_divide(inverse(B),inverse(C)))) <->
% double_divide(inverse(C),inverse(double_divide(A,inverse(B))))
% Current number of equations to process: 333
% Current number of ordered equations: 1
% Current number of rules: 75
% New rule produced :
% [118]
% double_divide(inverse(C),inverse(double_divide(A,inverse(B)))) <->
% double_divide(A,inverse(double_divide(inverse(B),inverse(C))))
% Current number of equations to process: 333
% Current number of ordered equations: 0
% Current number of rules: 76
% Rule [85]
% double_divide(C,inverse(B)) <->
% double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(
% inverse(A),
% inverse(
% inverse(C))))))) is composed into
% [85]
% double_divide(C,inverse(B)) <-> double_divide(inverse(B),inverse(inverse(C)))
% New rule produced :
% [119]
% double_divide(C,inverse(double_divide(A,inverse(double_divide(inverse(C),
% inverse(B)))))) ->
% double_divide(A,inverse(B))
% Rule
% [86]
% double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(
% inverse(A),inverse(
% inverse(C)))))))
% <-> double_divide(C,inverse(B)) collapsed.
% Current number of equations to process: 338
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [120]
% double_divide(inverse(C),B) <->
% double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),
% inverse(C))))
% Current number of equations to process: 337
% Current number of ordered equations: 1
% Current number of rules: 77
% New rule produced :
% [121]
% double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),
% inverse(C)))) <->
% double_divide(inverse(C),B)
% Current number of equations to process: 337
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [122]
% double_divide(A,inverse(double_divide(B,inverse(C)))) <->
% double_divide(B,inverse(inverse(double_divide(C,inverse(A)))))
% Current number of equations to process: 341
% Current number of ordered equations: 1
% Current number of rules: 79
% New rule produced :
% [123]
% double_divide(B,inverse(inverse(double_divide(C,inverse(A))))) <->
% double_divide(A,inverse(double_divide(B,inverse(C))))
% Rule
% [34]
% double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(A))))) -> B
% collapsed.
% Current number of equations to process: 341
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [124]
% double_divide(A,inverse(double_divide(B,inverse(A)))) <->
% double_divide(B,double_divide(a2,inverse(a2)))
% Current number of equations to process: 342
% Current number of ordered equations: 1
% Current number of rules: 80
% New rule produced :
% [125]
% double_divide(B,double_divide(a2,inverse(a2))) <->
% double_divide(A,inverse(double_divide(B,inverse(A))))
% Current number of equations to process: 342
% Current number of ordered equations: 0
% Current number of rules: 81
% Rule [68]
% double_divide(inverse(A),inverse(B)) <->
% double_divide(inverse(C),inverse(double_divide(inverse(B),inverse(
% inverse(
% double_divide(A,
% inverse(C))))))) is composed into
% [68]
% double_divide(inverse(A),inverse(B)) <-> double_divide(inverse(B),inverse(A))
% New rule produced :
% [126]
% double_divide(inverse(C),inverse(double_divide(A,inverse(inverse(double_divide(B,
% inverse(C)))))))
% -> double_divide(A,inverse(B))
% Rule
% [67]
% double_divide(inverse(C),inverse(double_divide(inverse(B),inverse(inverse(
% double_divide(A,
% inverse(C)))))))
% <-> double_divide(inverse(A),inverse(B)) collapsed.
% Current number of equations to process: 341
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [127]
% double_divide(C,inverse(B)) <->
% double_divide(A,inverse(double_divide(inverse(B),inverse(inverse(double_divide(A,
% inverse(C)))))))
% Current number of equations to process: 340
% Current number of ordered equations: 1
% Current number of rules: 82
% New rule produced :
% [128]
% double_divide(A,inverse(double_divide(inverse(B),inverse(inverse(double_divide(A,
% inverse(C)))))))
% <-> double_divide(C,inverse(B))
% Current number of equations to process: 340
% Current number of ordered equations: 0
% Current number of rules: 83
% Rule [76]
% double_divide(inverse(double_divide(double_divide(B,C),V_3)),inverse(
% double_divide(
% inverse(A),C)))
% <->
% double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,V_3)),
% inverse(double_divide(inverse(A),
% inverse(B)))))) is composed into
% [76]
% double_divide(inverse(double_divide(double_divide(B,C),V_3)),inverse(
% double_divide(
% inverse(A),C)))
% <->
% double_divide(inverse(A),inverse(double_divide(inverse(A),inverse(double_divide(
% inverse(
% double_divide(A,V_3)),
% inverse(B))))))
% Rule [72]
% double_divide(double_divide(V_3,B),inverse(C)) <->
% double_divide(double_divide(A,B),inverse(double_divide(A,inverse(
% double_divide(
% inverse(C),
% inverse(V_3)))))) is composed into
% [72]
% double_divide(double_divide(V_3,B),inverse(C)) <->
% double_divide(A,inverse(double_divide(double_divide(A,B),inverse(double_divide(
% inverse(C),
% inverse(V_3))))))
% Rule [22]
% double_divide(double_divide(inverse(A),B),inverse(double_divide(
% inverse(C),B))) <->
% double_divide(inverse(V_3),inverse(double_divide(V_3,inverse(double_divide(A,
% inverse(C)))))) is composed into
% [22]
% double_divide(double_divide(inverse(A),B),inverse(double_divide(inverse(C),B)))
% <->
% double_divide(V_3,inverse(double_divide(inverse(V_3),inverse(double_divide(A,
% inverse(C))))))
% New rule produced :
% [129]
% double_divide(A,inverse(double_divide(B,inverse(C)))) <->
% double_divide(B,inverse(double_divide(A,inverse(C))))
% Rule
% [4]
% double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(
% inverse(C),B)))))
% -> C collapsed.
% Rule
% [32]
% double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,inverse(C))))
% -> double_divide(B,inverse(C)) collapsed.
% Rule
% [66]
% double_divide(double_divide(double_divide(inverse(A),B),B),inverse(double_divide(A,
% inverse(C))))
% -> C collapsed.
% Rule
% [71]
% double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(
% inverse(C),
% inverse(V_3))))))
% <-> double_divide(double_divide(V_3,B),inverse(C)) collapsed.
% Current number of equations to process: 345
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [130]
% double_divide(A,inverse(double_divide(double_divide(A,inverse(B)),inverse(C))))
% -> double_divide(B,inverse(C))
% Current number of equations to process: 344
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [131]
% double_divide(A,inverse(double_divide(double_divide(A,B),inverse(double_divide(
% inverse(C),B)))))
% -> C
% Current number of equations to process: 343
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [132]
% double_divide(A,inverse(double_divide(double_divide(double_divide(inverse(A),B),B),
% inverse(C)))) -> C
% Current number of equations to process: 342
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [133]
% double_divide(A,inverse(A)) <->
% double_divide(B,inverse(inverse(double_divide(B,double_divide(a2,inverse(a2))))))
% Current number of equations to process: 349
% Current number of ordered equations: 2
% Current number of rules: 84
% Rule [133]
% double_divide(A,inverse(A)) <->
% double_divide(B,inverse(inverse(double_divide(B,double_divide(a2,
% inverse(a2)))))) is composed into
% [133] double_divide(A,inverse(A)) <-> double_divide(a2,inverse(a2))
% New rule produced :
% [134]
% double_divide(B,inverse(inverse(double_divide(B,double_divide(a2,inverse(a2))))))
% <-> double_divide(A,inverse(A))
% Current number of equations to process: 349
% Current number of ordered equations: 1
% Current number of rules: 85
% New rule produced :
% [135]
% double_divide(inverse(double_divide(A,double_divide(B,inverse(B)))),inverse(C))
% -> double_divide(A,inverse(C))
% Rule
% [35]
% double_divide(inverse(double_divide(A,double_divide(a2,inverse(a2)))),
% inverse(B)) -> double_divide(A,inverse(B)) collapsed.
% Current number of equations to process: 349
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [136]
% double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(
% inverse(A),C))))) ->
% double_divide(inverse(B),C)
% Current number of equations to process: 353
% Current number of ordered equations: 0
% Current number of rules: 86
% Rule [124]
% double_divide(A,inverse(double_divide(B,inverse(A)))) <->
% double_divide(B,double_divide(a2,inverse(a2))) is composed into
% [124] double_divide(A,inverse(double_divide(B,inverse(A)))) -> inverse(B)
% Rule [69]
% double_divide(A,inverse(C)) <->
% double_divide(inverse(C),inverse(double_divide(A,double_divide(V_3,
% inverse(V_3))))) is composed into
% [69]
% double_divide(A,inverse(C)) <-> double_divide(inverse(C),inverse(inverse(A)))
% Rule [54]
% double_divide(inverse(C),inverse(double_divide(A,inverse(inverse(C)))))
% <-> double_divide(A,double_divide(B,inverse(B))) is composed into
% [54]
% double_divide(inverse(C),inverse(double_divide(A,inverse(inverse(C))))) ->
% inverse(A)
% New rule produced :
% [137] double_divide(A,double_divide(B,inverse(B))) -> inverse(A)
% Rule [104] double_divide(inverse(A),double_divide(B,inverse(B))) -> A
% collapsed.
% Rule
% [125]
% double_divide(B,double_divide(a2,inverse(a2))) <->
% double_divide(A,inverse(double_divide(B,inverse(A)))) collapsed.
% Rule
% [134]
% double_divide(B,inverse(inverse(double_divide(B,double_divide(a2,inverse(a2))))))
% <-> double_divide(A,inverse(A)) collapsed.
% Rule
% [135]
% double_divide(inverse(double_divide(A,double_divide(B,inverse(B)))),inverse(C))
% -> double_divide(A,inverse(C)) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% inverse(inverse(a2)) = a2
%
% Current number of equations to process: 357
% Current number of ordered equations: 0
% Current number of rules: 83
% Rule [127]
% double_divide(C,inverse(B)) <->
% double_divide(A,inverse(double_divide(inverse(B),inverse(inverse(
% double_divide(A,
% inverse(C))))))) is composed into
% [127]
% double_divide(C,inverse(B)) <->
% double_divide(A,inverse(double_divide(inverse(B),double_divide(A,inverse(C)))))
% Rule [122]
% double_divide(A,inverse(double_divide(B,inverse(C)))) <->
% double_divide(B,inverse(inverse(double_divide(C,inverse(A))))) is composed into
% [122]
% double_divide(A,inverse(double_divide(B,inverse(C)))) <->
% double_divide(B,double_divide(C,inverse(A)))
% Rule [95]
% double_divide(inverse(A),inverse(B)) <->
% double_divide(inverse(double_divide(C,V_3)),inverse(inverse(inverse(
% double_divide(
% double_divide(B,
% inverse(
% double_divide(C,V_3))),
% inverse(A)))))) is composed into
% [95]
% double_divide(inverse(A),inverse(B)) <->
% double_divide(inverse(double_divide(C,V_3)),inverse(double_divide(double_divide(B,
% inverse(
% double_divide(C,V_3))),
% inverse(A))))
% Rule [85]
% double_divide(C,inverse(B)) <->
% double_divide(inverse(B),inverse(inverse(C))) is composed into [85]
% double_divide(C,
% inverse(B))
% <->
% double_divide(
% inverse(B),C)
% Rule [81]
% double_divide(B,inverse(A)) <->
% double_divide(inverse(A),inverse(inverse(B))) is composed into [81]
% double_divide(B,
% inverse(A))
% <->
% double_divide(
% inverse(A),B)
% Rule [69]
% double_divide(A,inverse(C)) <->
% double_divide(inverse(C),inverse(inverse(A))) is composed into [69]
% double_divide(A,
% inverse(C))
% <->
% double_divide(
% inverse(C),A)
% Rule [58]
% double_divide(inverse(A),B) <->
% double_divide(inverse(C),inverse(double_divide(inverse(double_divide(C,B)),
% inverse(inverse(inverse(A)))))) is composed into
% [58]
% double_divide(inverse(A),B) <->
% double_divide(inverse(C),inverse(double_divide(inverse(double_divide(C,B)),
% inverse(A))))
% Rule [43]
% double_divide(double_divide(A,inverse(A)),B) <->
% double_divide(inverse(C),inverse(double_divide(inverse(C),inverse(
% inverse(
% double_divide(
% inverse(C),
% inverse(
% inverse(
% double_divide(C,B))))))))) is composed into
% [43]
% double_divide(double_divide(A,inverse(A)),B) <->
% double_divide(inverse(C),inverse(double_divide(inverse(C),double_divide(
% inverse(C),
% double_divide(C,B)))))
% New rule produced : [138] inverse(inverse(A)) -> A
% Rule
% [54]
% double_divide(inverse(C),inverse(double_divide(A,inverse(inverse(C))))) ->
% inverse(A) collapsed.
% Rule
% [57]
% double_divide(inverse(C),inverse(double_divide(inverse(double_divide(C,B)),
% inverse(inverse(inverse(A)))))) <->
% double_divide(inverse(A),B) collapsed.
% Rule
% [59]
% double_divide(inverse(C),inverse(double_divide(A,inverse(double_divide(
% inverse(B),inverse(
% inverse(C)))))))
% -> double_divide(A,inverse(B)) collapsed.
% Rule
% [82]
% double_divide(inverse(A),inverse(inverse(B))) <-> double_divide(B,inverse(A))
% collapsed.
% Rule
% [96]
% double_divide(inverse(double_divide(C,V_3)),inverse(inverse(inverse(double_divide(
% double_divide(B,
% inverse(
% double_divide(C,V_3))),
% inverse(A))))))
% <-> double_divide(inverse(A),inverse(B)) collapsed.
% Rule
% [107]
% double_divide(double_divide(inverse(a2),inverse(double_divide(inverse(a2),
% inverse(inverse(double_divide(
% inverse(a2),
% inverse(
% inverse(
% double_divide(a2,B))))))))),C)
% <->
% double_divide(inverse(V_3),inverse(double_divide(double_divide(inverse(V_3),B),C)))
% collapsed.
% Rule
% [114]
% double_divide(A,inverse(double_divide(inverse(C),inverse(double_divide(
% inverse(C),inverse(
% inverse(
% double_divide(
% inverse(C),
% inverse(
% inverse(
% double_divide(C,B)))))))))))
% -> double_divide(A,B) collapsed.
% Rule
% [123]
% double_divide(B,inverse(inverse(double_divide(C,inverse(A))))) <->
% double_divide(A,inverse(double_divide(B,inverse(C)))) collapsed.
% Rule
% [126]
% double_divide(inverse(C),inverse(double_divide(A,inverse(inverse(double_divide(B,
% inverse(C)))))))
% -> double_divide(A,inverse(B)) collapsed.
% Rule
% [128]
% double_divide(A,inverse(double_divide(inverse(B),inverse(inverse(double_divide(A,
% inverse(C)))))))
% <-> double_divide(C,inverse(B)) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 364
% Current number of ordered equations: 0
% Current number of rules: 74
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 16 rules have been used:
% [1]
% multiply(A,B) -> inverse(double_divide(B,A)); trace = in the starting set
% [2] double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),
% inverse(C))),B))) -> C; trace = in the starting set
% [3] double_divide(inverse(double_divide(double_divide(double_divide(A,C),V_3),
% inverse(B))),V_3) ->
% double_divide(A,inverse(double_divide(inverse(B),C))); trace = Self cp of 2
% [4] double_divide(double_divide(A,B),inverse(double_divide(A,inverse(
% double_divide(
% inverse(C),B)))))
% -> C; trace = Cp of 3 and 2
% [5] double_divide(double_divide(double_divide(inverse(A),B),inverse(double_divide(
% inverse(C),B))),
% inverse(C)) -> A; trace = Self cp of 4
% [7] double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,
% inverse(
% double_divide(
% inverse(A),V_3)))))
% <-> double_divide(C,inverse(double_divide(inverse(B),V_3))); trace = Cp of 4 and 3
% [9] double_divide(double_divide(inverse(A),V_3),inverse(double_divide(
% inverse(B),inverse(
% double_divide(
% inverse(C),V_3)))))
% <-> double_divide(inverse(double_divide(A,inverse(B))),inverse(C)); trace = Cp of 7 and 4
% [10] double_divide(inverse(double_divide(B,inverse(B))),inverse(A)) -> A; trace = Cp of 9 and 4
% [13] double_divide(inverse(inverse(double_divide(A,inverse(A)))),inverse(B))
% -> B; trace = Self cp of 10
% [15] double_divide(A,inverse(double_divide(inverse(B),inverse(A)))) -> B; trace = Cp of 10 and 4
% [16] double_divide(A,inverse(A)) <-> double_divide(B,inverse(B)); trace = Cp of 10 and 5
% [18] double_divide(A,inverse(double_divide(inverse(B),C))) <->
% double_divide(inverse(B),inverse(double_divide(A,C))); trace = Self cp of 2
% [29] inverse(double_divide(B,inverse(B))) <-> double_divide(A,inverse(A)); trace = Cp of 13 and 4
% [45] double_divide(B,inverse(double_divide(inverse(B),inverse(A)))) -> A; trace = Cp of 18 and 4
% [137] double_divide(A,double_divide(B,inverse(B))) -> inverse(A); trace = Cp of 45 and 16
% [138] inverse(inverse(A)) -> A; trace = Cp of 29 and 15
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 2.170000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------