TSTP Solution File: GRP452-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP452-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n090.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 00:23:12 EDT 2014
% Result : Unsatisfiable 1.90s
% Output : Refutation 1.90s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP452-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n090.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 13:46:23 CDT 2014
% % CPUTime : 1.90
% Processing problem /tmp/CiME_55423_n090.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a2,b2 : constant; inverse : 1; multiply : 2; divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B;
% multiply(A,B) = divide(A,divide(divide(C,C),B));
% inverse(A) = divide(divide(B,B),A);
% ";
%
% let s1 = status F "
% a2 lr_lex;
% b2 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > inverse > divide > b2 > a2";
%
% let s2 = status F "
% a2 mul;
% b2 mul;
% inverse mul;
% multiply mul;
% divide mul;
% ";
%
% let p2 = precedence F "
% multiply > inverse > divide > 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 = { divide(divide(divide(A,A),divide(A,divide(B,
% divide(
% divide(
% divide(A,A),A),C)))),C)
% = B,
% multiply(A,B) = divide(A,divide(divide(C,C),B)),
% inverse(A) = divide(divide(B,B),A) }
% (3 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { multiply(multiply(inverse(b2),b2),a2) = a2 }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] inverse(A) <-> divide(divide(B,B),A)
% The conjecture has been reduced.
% Conjecture is now:
% multiply(multiply(divide(divide(a2,a2),b2),b2),a2) = a2
%
% Current number of equations to process: 1
% Current number of ordered equations: 3
% Current number of rules: 1
% New rule produced : [2] divide(divide(B,B),A) <-> divide(divide(a2,a2),A)
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 2
% New rule produced : [3] divide(divide(a2,a2),A) <-> divide(divide(B,B),A)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 3
% New rule produced : [4] multiply(A,B) <-> divide(A,divide(divide(C,C),B))
% The conjecture has been reduced.
% Conjecture is now:
% divide(divide(a2,a2),divide(divide(a2,a2),a2)) = a2
%
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 4
% New rule produced :
% [5]
% divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C)
% -> B
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6] divide(divide(divide(a2,a2),divide(A,A)),B) -> divide(divide(a2,a2),B)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7] divide(divide(divide(A,A),divide(a2,a2)),B) -> divide(divide(a2,a2),B)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [8] divide(A,A) <-> divide(a2,a2)
% Rule [2] divide(divide(B,B),A) <-> divide(divide(a2,a2),A) collapsed.
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [9] divide(divide(divide(A,A),divide(B,B)),C) -> divide(divide(a2,a2),C)
% Rule
% [6] divide(divide(divide(a2,a2),divide(A,A)),B) -> divide(divide(a2,a2),B)
% collapsed.
% Rule
% [7] divide(divide(divide(A,A),divide(a2,a2)),B) -> divide(divide(a2,a2),B)
% collapsed.
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [10] divide(divide(A,A),divide(a2,a2)) -> divide(a2,a2)
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [11] divide(divide(A,A),divide(B,B)) -> divide(a2,a2)
% Rule [9] divide(divide(divide(A,A),divide(B,B)),C) -> divide(divide(a2,a2),C)
% collapsed.
% Rule [10] divide(divide(A,A),divide(a2,a2)) -> divide(a2,a2) collapsed.
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [12]
% divide(divide(divide(A,A),divide(A,divide(a2,a2))),B) ->
% divide(divide(divide(A,A),A),B)
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [13] divide(divide(A,A),divide(A,divide(a2,a2))) -> divide(divide(A,A),A)
% Rule
% [12]
% divide(divide(divide(A,A),divide(A,divide(a2,a2))),B) ->
% divide(divide(divide(A,A),A),B) collapsed.
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [14] divide(divide(A,A),A) <-> divide(divide(a2,a2),divide(A,divide(a2,a2)))
% Current number of equations to process: 17
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [15] divide(divide(a2,a2),divide(A,divide(a2,a2))) <-> divide(divide(A,A),A)
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [16]
% divide(divide(A,A),divide(a2,divide(a2,a2))) <-> divide(divide(a2,a2),a2)
% Current number of equations to process: 16
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced :
% [17]
% divide(divide(a2,a2),a2) <-> divide(divide(A,A),divide(a2,divide(a2,a2)))
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 11
% Rule [14]
% divide(divide(A,A),A) <-> divide(divide(a2,a2),divide(A,divide(a2,a2))) is composed into
% [14] divide(divide(A,A),A) <-> divide(divide(a2,a2),A)
% New rule produced :
% [18] divide(divide(a2,a2),divide(A,divide(a2,a2))) -> divide(divide(a2,a2),A)
% Rule
% [15] divide(divide(a2,a2),divide(A,divide(a2,a2))) <-> divide(divide(A,A),A)
% collapsed.
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [19] divide(divide(A,A),a2) <-> divide(divide(B,B),divide(a2,divide(a2,a2)))
% Rule
% [17]
% divide(divide(a2,a2),a2) <-> divide(divide(A,A),divide(a2,divide(a2,a2)))
% collapsed.
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [20] divide(divide(A,A),divide(B,divide(a2,a2))) <-> divide(divide(a2,a2),B)
% Rule
% [16]
% divide(divide(A,A),divide(a2,divide(a2,a2))) <-> divide(divide(a2,a2),a2)
% collapsed.
% Rule
% [18] divide(divide(a2,a2),divide(A,divide(a2,a2))) -> divide(divide(a2,a2),A)
% collapsed.
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [21]
% divide(divide(divide(a2,a2),divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C)
% -> B
% Current number of equations to process: 15
% Current number of ordered equations: 2
% Current number of rules: 11
% New rule produced :
% [22]
% divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(a2,a2),A),C)))),C)
% -> B
% Current number of equations to process: 15
% Current number of ordered equations: 1
% Current number of rules: 12
% New rule produced :
% [23]
% divide(divide(divide(a2,a2),divide(divide(A,A),divide(B,divide(divide(a2,a2),C)))),C)
% -> B
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [24]
% divide(divide(divide(a2,a2),divide(a2,divide(A,divide(divide(divide(B,B),a2),C)))),C)
% -> A
% Current number of equations to process: 47
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [25]
% divide(divide(divide(A,A),divide(a2,divide(B,divide(divide(divide(a2,a2),a2),C)))),C)
% -> B
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [26]
% divide(divide(divide(A,A),divide(A,divide(B,divide(a2,a2)))),divide(divide(A,A),A))
% -> B
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [27]
% divide(divide(divide(a2,a2),divide(divide(A,A),B)),a2) ->
% divide(divide(a2,a2),divide(a2,divide(B,divide(a2,a2))))
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [28]
% divide(divide(divide(A,A),divide(divide(B,B),C)),a2) ->
% divide(divide(a2,a2),divide(a2,divide(C,divide(a2,a2))))
% Rule
% [27]
% divide(divide(divide(a2,a2),divide(divide(A,A),B)),a2) ->
% divide(divide(a2,a2),divide(a2,divide(B,divide(a2,a2)))) collapsed.
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [29]
% divide(divide(divide(a2,a2),divide(A,divide(B,divide(a2,a2)))),divide(
% divide(A,A),A))
% -> B
% Current number of equations to process: 90
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced :
% [30] divide(divide(divide(a2,a2),A),divide(divide(A,A),A)) -> divide(a2,a2)
% Current number of equations to process: 92
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [31] divide(divide(divide(a2,a2),a2),divide(divide(A,A),a2)) -> divide(a2,a2)
% Current number of equations to process: 100
% Current number of ordered equations: 2
% Current number of rules: 20
% New rule produced :
% [32] divide(divide(divide(A,A),B),divide(divide(B,B),B)) -> divide(a2,a2)
% Rule
% [30] divide(divide(divide(a2,a2),A),divide(divide(A,A),A)) -> divide(a2,a2)
% collapsed.
% Current number of equations to process: 100
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [33] divide(divide(divide(A,A),a2),divide(divide(B,B),a2)) -> divide(a2,a2)
% Rule
% [31] divide(divide(divide(a2,a2),a2),divide(divide(A,A),a2)) -> divide(a2,a2)
% collapsed.
% Current number of equations to process: 103
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [34] divide(divide(divide(A,A),B),divide(divide(a2,a2),B)) -> divide(a2,a2)
% Current number of equations to process: 105
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [35] divide(divide(divide(A,A),B),divide(divide(C,C),B)) -> divide(a2,a2)
% Rule
% [32] divide(divide(divide(A,A),B),divide(divide(B,B),B)) -> divide(a2,a2)
% collapsed.
% Rule
% [33] divide(divide(divide(A,A),a2),divide(divide(B,B),a2)) -> divide(a2,a2)
% collapsed.
% Rule
% [34] divide(divide(divide(A,A),B),divide(divide(a2,a2),B)) -> divide(a2,a2)
% collapsed.
% Current number of equations to process: 111
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [36]
% divide(divide(divide(a2,a2),a2),divide(divide(A,A),divide(a2,divide(a2,a2))))
% -> divide(a2,a2)
% Current number of equations to process: 120
% Current number of ordered equations: 2
% Current number of rules: 20
% New rule produced :
% [37]
% divide(divide(divide(A,A),divide(a2,divide(a2,a2))),divide(divide(a2,a2),a2))
% -> divide(a2,a2)
% Current number of equations to process: 120
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [38]
% divide(divide(divide(A,A),divide(a2,divide(a2,a2))),divide(divide(B,B),a2))
% -> divide(a2,a2)
% Rule
% [37]
% divide(divide(divide(A,A),divide(a2,divide(a2,a2))),divide(divide(a2,a2),a2))
% -> divide(a2,a2) collapsed.
% Current number of equations to process: 118
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [39]
% divide(divide(divide(A,A),a2),divide(divide(B,B),divide(a2,divide(a2,a2))))
% -> divide(a2,a2)
% Rule
% [36]
% divide(divide(divide(a2,a2),a2),divide(divide(A,A),divide(a2,divide(a2,a2))))
% -> divide(a2,a2) collapsed.
% Current number of equations to process: 115
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [40]
% divide(divide(divide(A,A),divide(B,divide(a2,a2))),divide(divide(a2,a2),B))
% -> divide(a2,a2)
% Current number of equations to process: 112
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [41]
% divide(divide(divide(A,A),A),divide(divide(B,B),divide(A,divide(a2,a2)))) ->
% divide(a2,a2)
% Current number of equations to process: 110
% Current number of ordered equations: 2
% Current number of rules: 23
% New rule produced :
% [42]
% divide(divide(divide(A,A),divide(B,divide(a2,a2))),divide(divide(B,B),B)) ->
% divide(a2,a2)
% Current number of equations to process: 110
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [43]
% divide(divide(divide(a2,a2),A),divide(divide(B,B),divide(A,divide(a2,a2))))
% -> divide(a2,a2)
% Current number of equations to process: 106
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [44]
% divide(divide(divide(A,A),divide(B,divide(a2,a2))),divide(divide(C,C),B)) ->
% divide(a2,a2)
% Rule
% [38]
% divide(divide(divide(A,A),divide(a2,divide(a2,a2))),divide(divide(B,B),a2))
% -> divide(a2,a2) collapsed.
% Rule
% [40]
% divide(divide(divide(A,A),divide(B,divide(a2,a2))),divide(divide(a2,a2),B))
% -> divide(a2,a2) collapsed.
% Rule
% [42]
% divide(divide(divide(A,A),divide(B,divide(a2,a2))),divide(divide(B,B),B)) ->
% divide(a2,a2) collapsed.
% Current number of equations to process: 108
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [45]
% divide(divide(divide(A,A),B),divide(divide(C,C),divide(B,divide(a2,a2)))) ->
% divide(a2,a2)
% Rule
% [39]
% divide(divide(divide(A,A),a2),divide(divide(B,B),divide(a2,divide(a2,a2))))
% -> divide(a2,a2) collapsed.
% Rule
% [41]
% divide(divide(divide(A,A),A),divide(divide(B,B),divide(A,divide(a2,a2)))) ->
% divide(a2,a2) collapsed.
% Rule
% [43]
% divide(divide(divide(a2,a2),A),divide(divide(B,B),divide(A,divide(a2,a2))))
% -> divide(a2,a2) collapsed.
% Current number of equations to process: 111
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [46]
% divide(divide(divide(a2,a2),divide(A,divide(B,divide(divide(divide(a2,a2),A),C)))),C)
% -> B
% Current number of equations to process: 118
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [47]
% divide(divide(divide(A,A),divide(B,divide(C,divide(divide(divide(B,B),B),V_3)))),V_3)
% -> C
% Rule
% [5]
% divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C)
% -> B collapsed.
% Rule
% [21]
% divide(divide(divide(a2,a2),divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C)
% -> B collapsed.
% Rule
% [25]
% divide(divide(divide(A,A),divide(a2,divide(B,divide(divide(divide(a2,a2),a2),C)))),C)
% -> B collapsed.
% Current number of equations to process: 146
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [48]
% divide(divide(divide(B,B),B),C) <->
% divide(divide(divide(A,A),divide(B,divide(a2,a2))),C)
% Current number of equations to process: 155
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [49]
% divide(divide(divide(A,A),divide(B,divide(a2,a2))),C) <->
% divide(divide(divide(B,B),B),C)
% Current number of equations to process: 155
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [50] divide(divide(A,A),divide(B,divide(a2,a2))) <-> divide(divide(B,B),B)
% Rule
% [13] divide(divide(A,A),divide(A,divide(a2,a2))) -> divide(divide(A,A),A)
% collapsed.
% Rule
% [49]
% divide(divide(divide(A,A),divide(B,divide(a2,a2))),C) <->
% divide(divide(divide(B,B),B),C) collapsed.
% Current number of equations to process: 166
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [51] divide(divide(B,B),B) <-> divide(divide(A,A),divide(B,divide(a2,a2)))
% Rule
% [48]
% divide(divide(divide(B,B),B),C) <->
% divide(divide(divide(A,A),divide(B,divide(a2,a2))),C) collapsed.
% Current number of equations to process: 166
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [52]
% divide(divide(A,A),divide(a2,divide(a2,a2))) <->
% divide(divide(B,B),divide(a2,divide(a2,a2)))
% Current number of equations to process: 175
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [53]
% divide(divide(divide(A,A),divide(A,divide(B,divide(a2,a2)))),divide(divide(a2,a2),A))
% -> B
% Current number of equations to process: 176
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [54] divide(divide(divide(a2,a2),divide(divide(a2,a2),A)),divide(a2,a2)) -> A
% Current number of equations to process: 179
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [55]
% divide(divide(C,C),divide(C,divide(B,divide(a2,a2)))) <->
% divide(divide(divide(a2,a2),divide(divide(A,A),B)),C)
% Current number of equations to process: 186
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [56]
% divide(divide(divide(a2,a2),divide(divide(A,A),B)),C) <->
% divide(divide(C,C),divide(C,divide(B,divide(a2,a2))))
% Rule
% [54] divide(divide(divide(a2,a2),divide(divide(a2,a2),A)),divide(a2,a2)) -> A
% collapsed.
% Current number of equations to process: 187
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [57]
% divide(divide(a2,a2),divide(A,divide(B,divide(a2,a2)))) <->
% divide(divide(divide(a2,a2),divide(divide(C,C),B)),A)
% Current number of equations to process: 196
% Current number of ordered equations: 2
% Current number of rules: 26
% New rule produced :
% [58]
% divide(divide(divide(a2,a2),divide(divide(A,A),B)),divide(B,divide(a2,a2)))
% -> divide(a2,a2)
% Current number of equations to process: 196
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [59]
% divide(divide(divide(a2,a2),divide(divide(C,C),B)),A) <->
% divide(divide(a2,a2),divide(A,divide(B,divide(a2,a2))))
% Rule
% [23]
% divide(divide(divide(a2,a2),divide(divide(A,A),divide(B,divide(divide(a2,a2),C)))),C)
% -> B collapsed.
% Current number of equations to process: 197
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [60]
% divide(divide(V_3,V_3),divide(V_3,divide(C,divide(a2,a2)))) <->
% divide(divide(divide(A,A),divide(divide(B,B),C)),V_3)
% Rule
% [55]
% divide(divide(C,C),divide(C,divide(B,divide(a2,a2)))) <->
% divide(divide(divide(a2,a2),divide(divide(A,A),B)),C) collapsed.
% Current number of equations to process: 208
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [61]
% divide(divide(divide(A,A),divide(divide(B,B),C)),V_3) <->
% divide(divide(V_3,V_3),divide(V_3,divide(C,divide(a2,a2))))
% Rule
% [28]
% divide(divide(divide(A,A),divide(divide(B,B),C)),a2) ->
% divide(divide(a2,a2),divide(a2,divide(C,divide(a2,a2)))) collapsed.
% Rule
% [56]
% divide(divide(divide(a2,a2),divide(divide(A,A),B)),C) <->
% divide(divide(C,C),divide(C,divide(B,divide(a2,a2)))) collapsed.
% Current number of equations to process: 208
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [62]
% divide(divide(A,A),divide(B,divide(C,divide(a2,a2)))) <->
% divide(divide(divide(a2,a2),divide(divide(V_3,V_3),C)),B)
% Rule
% [57]
% divide(divide(a2,a2),divide(A,divide(B,divide(a2,a2)))) <->
% divide(divide(divide(a2,a2),divide(divide(C,C),B)),A) collapsed.
% Current number of equations to process: 212
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [63]
% divide(divide(divide(A,A),divide(divide(B,B),C)),divide(C,divide(a2,a2))) ->
% divide(a2,a2)
% Rule
% [58]
% divide(divide(divide(a2,a2),divide(divide(A,A),B)),divide(B,divide(a2,a2)))
% -> divide(a2,a2) collapsed.
% Current number of equations to process: 215
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [64]
% divide(divide(a2,a2),divide(V_3,divide(C,divide(a2,a2)))) <->
% divide(divide(divide(A,A),divide(divide(B,B),C)),V_3)
% Current number of equations to process: 219
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [65]
% divide(divide(divide(A,A),divide(divide(B,B),C)),V_3) <->
% divide(divide(a2,a2),divide(V_3,divide(C,divide(a2,a2))))
% Rule
% [59]
% divide(divide(divide(a2,a2),divide(divide(C,C),B)),A) <->
% divide(divide(a2,a2),divide(A,divide(B,divide(a2,a2)))) collapsed.
% Current number of equations to process: 219
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [66]
% divide(divide(divide(A,A),divide(divide(B,B),C)),V_3) <->
% divide(divide(divide(a2,a2),divide(divide(V_4,V_4),C)),V_3)
% Current number of equations to process: 270
% Current number of ordered equations: 1
% Current number of rules: 28
% New rule produced :
% [67]
% divide(divide(divide(a2,a2),divide(divide(V_4,V_4),C)),V_3) <->
% divide(divide(divide(A,A),divide(divide(B,B),C)),V_3)
% Current number of equations to process: 270
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [68]
% divide(divide(A,A),divide(B,divide(C,divide(a2,a2)))) <->
% divide(divide(divide(V_3,V_3),divide(divide(V_4,V_4),C)),B)
% Rule
% [60]
% divide(divide(V_3,V_3),divide(V_3,divide(C,divide(a2,a2)))) <->
% divide(divide(divide(A,A),divide(divide(B,B),C)),V_3) collapsed.
% Rule
% [62]
% divide(divide(A,A),divide(B,divide(C,divide(a2,a2)))) <->
% divide(divide(divide(a2,a2),divide(divide(V_3,V_3),C)),B) collapsed.
% Rule
% [64]
% divide(divide(a2,a2),divide(V_3,divide(C,divide(a2,a2)))) <->
% divide(divide(divide(A,A),divide(divide(B,B),C)),V_3) collapsed.
% Current number of equations to process: 297
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [69]
% divide(divide(C,C),divide(divide(V_3,V_3),B)) <->
% divide(divide(a2,a2),divide(divide(A,A),B))
% Rule
% [66]
% divide(divide(divide(A,A),divide(divide(B,B),C)),V_3) <->
% divide(divide(divide(a2,a2),divide(divide(V_4,V_4),C)),V_3) collapsed.
% Current number of equations to process: 311
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [70]
% divide(divide(divide(A,A),divide(divide(B,B),C)),V_3) <->
% divide(divide(divide(V_4,V_4),divide(divide(V_5,V_5),C)),V_3)
% Rule
% [67]
% divide(divide(divide(a2,a2),divide(divide(V_4,V_4),C)),V_3) <->
% divide(divide(divide(A,A),divide(divide(B,B),C)),V_3) collapsed.
% Current number of equations to process: 315
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [71]
% divide(divide(A,A),divide(divide(B,B),C)) <->
% divide(divide(V_3,V_3),divide(divide(V_4,V_4),C))
% Rule
% [69]
% divide(divide(C,C),divide(divide(V_3,V_3),B)) <->
% divide(divide(a2,a2),divide(divide(A,A),B)) collapsed.
% Rule
% [70]
% divide(divide(divide(A,A),divide(divide(B,B),C)),V_3) <->
% divide(divide(divide(V_4,V_4),divide(divide(V_5,V_5),C)),V_3) collapsed.
% Current number of equations to process: 361
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [72]
% divide(divide(a2,a2),divide(C,divide(divide(B,divide(divide(a2,a2),C)),
% divide(a2,a2)))) -> B
% Current number of equations to process: 371
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [73]
% divide(B,B) <->
% divide(divide(a2,a2),divide(A,divide(divide(a2,a2),divide(divide(a2,a2),A))))
% Current number of equations to process: 375
% Current number of ordered equations: 1
% Current number of rules: 28
% Rule [73]
% divide(B,B) <->
% divide(divide(a2,a2),divide(A,divide(divide(a2,a2),divide(divide(a2,a2),A)))) is composed into
% [73] divide(B,B) <-> divide(a2,a2)
% New rule produced :
% [74]
% divide(divide(a2,a2),divide(A,divide(divide(a2,a2),divide(divide(a2,a2),A))))
% <-> divide(B,B)
% Current number of equations to process: 375
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [75]
% divide(divide(A,A),divide(B,divide(divide(a2,a2),divide(divide(a2,a2),B))))
% <-> divide(C,C)
% Rule
% [74]
% divide(divide(a2,a2),divide(A,divide(divide(a2,a2),divide(divide(a2,a2),A))))
% <-> divide(B,B) collapsed.
% Current number of equations to process: 410
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [76]
% divide(divide(A,A),divide(B,divide(divide(a2,a2),divide(divide(C,C),B)))) <->
% divide(V_3,V_3)
% Rule
% [75]
% divide(divide(A,A),divide(B,divide(divide(a2,a2),divide(divide(a2,a2),B))))
% <-> divide(C,C) collapsed.
% Current number of equations to process: 418
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [77]
% divide(divide(A,A),divide(B,divide(divide(C,C),divide(divide(V_3,V_3),B))))
% <-> divide(V_4,V_4)
% Rule
% [76]
% divide(divide(A,A),divide(B,divide(divide(a2,a2),divide(divide(C,C),B)))) <->
% divide(V_3,V_3) collapsed.
% Current number of equations to process: 427
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [78] divide(B,B) <-> divide(A,A)
% Rule [3] divide(divide(a2,a2),A) <-> divide(divide(B,B),A) collapsed.
% Rule [8] divide(A,A) <-> divide(a2,a2) collapsed.
% Rule [14] divide(divide(A,A),A) <-> divide(divide(a2,a2),A) collapsed.
% Rule
% [52]
% divide(divide(A,A),divide(a2,divide(a2,a2))) <->
% divide(divide(B,B),divide(a2,divide(a2,a2))) collapsed.
% Rule
% [71]
% divide(divide(A,A),divide(divide(B,B),C)) <->
% divide(divide(V_3,V_3),divide(divide(V_4,V_4),C)) collapsed.
% Rule [73] divide(B,B) <-> divide(a2,a2) collapsed.
% Current number of equations to process: 429
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [79] divide(divide(A,A),B) <-> divide(divide(C,C),divide(B,divide(a2,a2)))
% Rule
% [19] divide(divide(A,A),a2) <-> divide(divide(B,B),divide(a2,divide(a2,a2)))
% collapsed.
% Rule
% [51] divide(divide(B,B),B) <-> divide(divide(A,A),divide(B,divide(a2,a2)))
% collapsed.
% Current number of equations to process: 470
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [80] divide(divide(A,A),divide(B,divide(C,C))) <-> divide(divide(a2,a2),B)
% Rule
% [20] divide(divide(A,A),divide(B,divide(a2,a2))) <-> divide(divide(a2,a2),B)
% collapsed.
% Current number of equations to process: 469
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [81] divide(divide(A,A),divide(B,divide(C,C))) <-> divide(divide(B,B),B)
% Rule
% [50] divide(divide(A,A),divide(B,divide(a2,a2))) <-> divide(divide(B,B),B)
% collapsed.
% Current number of equations to process: 468
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [82]
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(a2,a2))) <->
% divide(divide(a2,a2),B)
% Current number of equations to process: 510
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [83]
% divide(divide(a2,a2),B) <->
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(a2,a2)))
% Current number of equations to process: 510
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [84]
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(a2,a2))) <->
% divide(divide(B,B),B)
% Current number of equations to process: 509
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [85]
% divide(divide(B,B),B) <->
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(a2,a2)))
% Current number of equations to process: 509
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [86]
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(V_3,V_3))) <->
% divide(divide(a2,a2),B)
% Rule
% [82]
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(a2,a2))) <->
% divide(divide(a2,a2),B) collapsed.
% Current number of equations to process: 522
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [87]
% divide(divide(A,A),B) <->
% divide(divide(C,C),divide(divide(B,divide(V_3,V_3)),divide(a2,a2)))
% Rule
% [83]
% divide(divide(a2,a2),B) <->
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(a2,a2))) collapsed.
% Rule
% [85]
% divide(divide(B,B),B) <->
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(a2,a2))) collapsed.
% Current number of equations to process: 535
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [88]
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(V_3,V_3))) <->
% divide(divide(B,B),B)
% Rule
% [84]
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(a2,a2))) <->
% divide(divide(B,B),B) collapsed.
% Current number of equations to process: 548
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [89]
% divide(divide(A,A),divide(B,divide(C,divide(V_3,V_3)))) <->
% divide(divide(divide(V_4,V_4),divide(divide(V_5,V_5),C)),B)
% Rule
% [68]
% divide(divide(A,A),divide(B,divide(C,divide(a2,a2)))) <->
% divide(divide(divide(V_3,V_3),divide(divide(V_4,V_4),C)),B) collapsed.
% Current number of equations to process: 592
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [90]
% divide(divide(divide(A,A),divide(divide(B,B),C)),divide(C,divide(V_3,V_3)))
% -> divide(a2,a2)
% Rule
% [63]
% divide(divide(divide(A,A),divide(divide(B,B),C)),divide(C,divide(a2,a2))) ->
% divide(a2,a2) collapsed.
% Current number of equations to process: 591
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [91]
% divide(divide(divide(A,A),divide(B,divide(C,C))),divide(divide(V_3,V_3),B))
% -> divide(a2,a2)
% Rule
% [44]
% divide(divide(divide(A,A),divide(B,divide(a2,a2))),divide(divide(C,C),B)) ->
% divide(a2,a2) collapsed.
% Current number of equations to process: 590
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [92]
% divide(divide(divide(A,A),B),divide(divide(C,C),divide(B,divide(V_3,V_3))))
% -> divide(a2,a2)
% Rule
% [45]
% divide(divide(divide(A,A),B),divide(divide(C,C),divide(B,divide(a2,a2)))) ->
% divide(a2,a2) collapsed.
% Current number of equations to process: 589
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [93]
% divide(divide(A,A),divide(divide(A,divide(B,B)),divide(A,divide(a2,a2)))) ->
% divide(a2,a2)
% Current number of equations to process: 612
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [94]
% divide(divide(a2,a2),divide(divide(A,divide(B,B)),divide(A,divide(a2,a2))))
% -> divide(a2,a2)
% Current number of equations to process: 612
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [95]
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(B,divide(a2,a2)))) ->
% divide(a2,a2)
% Rule
% [93]
% divide(divide(A,A),divide(divide(A,divide(B,B)),divide(A,divide(a2,a2)))) ->
% divide(a2,a2) collapsed.
% Rule
% [94]
% divide(divide(a2,a2),divide(divide(A,divide(B,B)),divide(A,divide(a2,a2))))
% -> divide(a2,a2) collapsed.
% Current number of equations to process: 671
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [96]
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(B,divide(V_3,V_3))))
% -> divide(a2,a2)
% Rule
% [95]
% divide(divide(A,A),divide(divide(B,divide(C,C)),divide(B,divide(a2,a2)))) ->
% divide(a2,a2) collapsed.
% Current number of equations to process: 684
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [97]
% divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(C,C),A),V_3)))),V_3)
% -> B
% Rule
% [22]
% divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(a2,a2),A),C)))),C)
% -> B collapsed.
% Rule
% [24]
% divide(divide(divide(a2,a2),divide(a2,divide(A,divide(divide(divide(B,B),a2),C)))),C)
% -> A collapsed.
% Current number of equations to process: 696
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [98]
% divide(divide(divide(a2,a2),divide(divide(A,A),divide(B,divide(a2,a2)))),
% divide(C,C)) -> B
% Current number of equations to process: 739
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [99] divide(divide(divide(a2,a2),divide(divide(A,A),A)),divide(B,B)) -> A
% Current number of equations to process: 741
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [100] divide(divide(a2,a2),divide(divide(a2,a2),A)) -> A
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 743
% Current number of ordered equations: 0
% Current number of rules: 29
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 17 rules have been used:
% [1]
% inverse(A) <-> divide(divide(B,B),A); trace = in the starting set
% [2] divide(divide(B,B),A) <-> divide(divide(a2,a2),A); trace = in the starting set
% [3] divide(divide(a2,a2),A) <-> divide(divide(B,B),A); trace = in the starting set
% [4] multiply(A,B) <-> divide(A,divide(divide(C,C),B)); trace = in the starting set
% [5] divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C)
% -> B; trace = in the starting set
% [6] divide(divide(divide(a2,a2),divide(A,A)),B) -> divide(divide(a2,a2),B); trace = Self cp of 2
% [8] divide(A,A) <-> divide(a2,a2); trace = Cp of 5 and 2
% [9] divide(divide(divide(A,A),divide(B,B)),C) -> divide(divide(a2,a2),C); trace = Cp of 6 and 3
% [11] divide(divide(A,A),divide(B,B)) -> divide(a2,a2); trace = Cp of 9 and 5
% [22] divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(a2,a2),A),C)))),C)
% -> B; trace = Cp of 5 and 2
% [23] divide(divide(divide(a2,a2),divide(divide(A,A),divide(B,divide(divide(a2,a2),C)))),C)
% -> B; trace = Cp of 5 and 2
% [53] divide(divide(divide(A,A),divide(A,divide(B,divide(a2,a2)))),divide(
% divide(a2,a2),A))
% -> B; trace = Cp of 22 and 8
% [55] divide(divide(C,C),divide(C,divide(B,divide(a2,a2)))) <->
% divide(divide(divide(a2,a2),divide(divide(A,A),B)),C); trace = Cp of 53 and 23
% [59] divide(divide(divide(a2,a2),divide(divide(C,C),B)),A) <->
% divide(divide(a2,a2),divide(A,divide(B,divide(a2,a2)))); trace = Cp of 55 and 8
% [65] divide(divide(divide(A,A),divide(divide(B,B),C)),V_3) <->
% divide(divide(a2,a2),divide(V_3,divide(C,divide(a2,a2)))); trace = Cp of 59 and 3
% [98] divide(divide(divide(a2,a2),divide(divide(A,A),divide(B,divide(a2,a2)))),
% divide(C,C)) -> B; trace = Cp of 23 and 11
% [100] divide(divide(a2,a2),divide(divide(a2,a2),A)) -> A; trace = Cp of 98 and 65
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.780000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------