TSTP Solution File: GRP554-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP554-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n150.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 00:23:27 EDT 2014
% Result : Unsatisfiable 1.27s
% Output : Refutation 1.27s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP554-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n150.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 19:15:58 CDT 2014
% % CPUTime : 1.27
% Processing problem /tmp/CiME_22506_n150.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a2,b2 : constant; multiply : 2; inverse : 1; divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% divide(divide(A,inverse(divide(B,divide(A,C)))),C) = B;
% multiply(A,B) = divide(A,inverse(B));
% ";
%
% let s1 = status F "
% a2 lr_lex;
% b2 lr_lex;
% multiply lr_lex;
% inverse lr_lex;
% divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > divide > inverse > b2 > a2";
%
% let s2 = status F "
% a2 mul;
% b2 mul;
% multiply mul;
% inverse mul;
% divide mul;
% ";
%
% let p2 = precedence F "
% multiply > 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 = { divide(divide(A,inverse(divide(B,divide(A,C)))),C)
% = B,
% multiply(A,B) = divide(A,inverse(B)) }
% (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) -> divide(A,inverse(B))
% The conjecture has been reduced.
% Conjecture is now:
% divide(divide(inverse(b2),inverse(b2)),inverse(a2)) = a2
%
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 1
% New rule produced :
% [2] divide(divide(A,inverse(divide(B,divide(A,C)))),C) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3]
% divide(divide(A,inverse(B)),C) <->
% divide(V_3,inverse(divide(B,divide(V_3,divide(A,C)))))
% Rule [2] divide(divide(A,inverse(divide(B,divide(A,C)))),C) -> B collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% divide(a2,inverse(divide(b2,divide(a2,divide(inverse(b2),inverse(a2)))))) = a2
%
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [4]
% divide(a2,inverse(divide(divide(B,divide(A,C)),divide(a2,divide(A,C))))) -> B
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [5] divide(a2,inverse(divide(divide(A,B),divide(a2,B)))) -> A
% Rule
% [4]
% divide(a2,inverse(divide(divide(B,divide(A,C)),divide(a2,divide(A,C))))) -> B
% collapsed.
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [6]
% divide(V_3,inverse(divide(divide(divide(B,divide(A,C)),divide(a2,divide(A,
% inverse(
% divide(V_3,B))))),
% divide(V_3,divide(a2,C))))) -> V_3
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [7] divide(A,divide(B,divide(B,inverse(divide(a2,A))))) -> a2
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [8]
% divide(divide(A,divide(A,inverse(divide(a2,a2)))),divide(B,divide(B,inverse(a2))))
% -> a2
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [9]
% divide(a2,inverse(divide(a2,divide(a2,divide(A,divide(A,inverse(divide(a2,B))))))))
% -> B
% Current number of equations to process: 33
% Current number of ordered equations: 2
% Current number of rules: 7
% New rule produced :
% [10]
% divide(a2,inverse(divide(divide(A,divide(B,divide(B,inverse(divide(a2,a2))))),a2)))
% -> A
% Current number of equations to process: 35
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [11]
% divide(inverse(divide(divide(A,B),divide(a2,B))),divide(C,divide(C,inverse(A))))
% -> a2
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [12]
% divide(a2,divide(B,divide(B,inverse(divide(a2,A))))) <->
% divide(a2,inverse(divide(a2,divide(a2,divide(a2,A)))))
% Current number of equations to process: 37
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced :
% [13]
% divide(a2,inverse(divide(a2,divide(a2,divide(a2,A))))) <->
% divide(a2,divide(B,divide(B,inverse(divide(a2,A)))))
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [14] divide(a2,inverse(divide(a2,a2))) -> a2
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [15]
% divide(divide(a2,divide(A,divide(A,inverse(divide(a2,B))))),divide(a2,B)) ->
% a2
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [16] inverse(divide(divide(divide(a2,a2),A),divide(a2,A))) -> a2
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [17]
% divide(a2,divide(A,divide(A,inverse(B)))) <->
% divide(a2,inverse(divide(a2,divide(a2,B))))
% Rule
% [12]
% divide(a2,divide(B,divide(B,inverse(divide(a2,A))))) <->
% divide(a2,inverse(divide(a2,divide(a2,divide(a2,A))))) collapsed.
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [18]
% inverse(divide(a2,divide(a2,divide(a2,B)))) <->
% divide(A,divide(A,inverse(divide(a2,B))))
% Rule
% [13]
% divide(a2,inverse(divide(a2,divide(a2,divide(a2,A))))) <->
% divide(a2,divide(B,divide(B,inverse(divide(a2,A))))) collapsed.
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [19] divide(a2,divide(a2,a2)) -> a2
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [20] divide(divide(a2,a2),divide(A,divide(A,inverse(a2)))) -> a2
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [21] divide(a2,inverse(divide(divide(A,divide(a2,a2)),a2))) -> A
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [22] divide(inverse(divide(a2,a2)),divide(A,divide(A,inverse(a2)))) -> a2
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [23]
% divide(B,inverse(divide(divide(a2,a2),divide(B,divide(a2,A))))) ->
% divide(a2,A)
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [24] divide(divide(a2,divide(A,divide(A,inverse(B)))),B) -> a2
% Rule
% [15]
% divide(divide(a2,divide(A,divide(A,inverse(divide(a2,B))))),divide(a2,B)) ->
% a2 collapsed.
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [25] inverse(divide(a2,divide(a2,A))) <-> divide(B,divide(B,inverse(A)))
% Rule
% [18]
% inverse(divide(a2,divide(a2,divide(a2,B)))) <->
% divide(A,divide(A,inverse(divide(a2,B)))) collapsed.
% Current number of equations to process: 106
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [26] divide(B,divide(B,inverse(A))) <-> inverse(divide(a2,divide(a2,A)))
% Rule
% [17]
% divide(a2,divide(A,divide(A,inverse(B)))) <->
% divide(a2,inverse(divide(a2,divide(a2,B)))) collapsed.
% Current number of equations to process: 106
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [27] inverse(divide(divide(divide(a2,a2),divide(a2,a2)),a2)) -> a2
% Current number of equations to process: 113
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [28] inverse(divide(a2,divide(a2,divide(A,divide(A,inverse(a2)))))) -> a2
% Current number of equations to process: 117
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [29] inverse(divide(a2,a2)) -> divide(a2,a2)
% Rule
% [8]
% divide(divide(A,divide(A,inverse(divide(a2,a2)))),divide(B,divide(B,inverse(a2))))
% -> a2 collapsed.
% Rule
% [10]
% divide(a2,inverse(divide(divide(A,divide(B,divide(B,inverse(divide(a2,a2))))),a2)))
% -> A collapsed.
% Rule [14] divide(a2,inverse(divide(a2,a2))) -> a2 collapsed.
% Rule
% [22] divide(inverse(divide(a2,a2)),divide(A,divide(A,inverse(a2)))) -> a2
% collapsed.
% Current number of equations to process: 129
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [30] divide(a2,divide(A,divide(A,divide(a2,a2)))) -> a2
% Current number of equations to process: 128
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [31] divide(A,inverse(divide(divide(a2,a2),divide(A,B)))) -> B
% Rule
% [23]
% divide(B,inverse(divide(divide(a2,a2),divide(B,divide(a2,A))))) ->
% divide(a2,A) collapsed.
% Current number of equations to process: 130
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [32] divide(A,divide(A,inverse(a2))) -> inverse(a2)
% Rule [20] divide(divide(a2,a2),divide(A,divide(A,inverse(a2)))) -> a2
% collapsed.
% Rule
% [28] inverse(divide(a2,divide(a2,divide(A,divide(A,inverse(a2)))))) -> a2
% collapsed.
% Current number of equations to process: 161
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [33] inverse(inverse(a2)) -> a2
% Current number of equations to process: 160
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [34] divide(divide(a2,a2),inverse(a2)) -> a2
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [35] divide(A,divide(A,divide(a2,a2))) -> divide(a2,a2)
% Rule [30] divide(a2,divide(A,divide(A,divide(a2,a2)))) -> a2 collapsed.
% Current number of equations to process: 158
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [36] divide(A,inverse(divide(a2,divide(a2,divide(a2,A))))) -> a2
% Current number of equations to process: 174
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [37]
% inverse(inverse(divide(a2,divide(a2,A)))) <->
% divide(B,divide(B,inverse(inverse(A))))
% Current number of equations to process: 184
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [38]
% divide(B,divide(B,inverse(inverse(A)))) <->
% inverse(inverse(divide(a2,divide(a2,A))))
% Current number of equations to process: 184
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [39] divide(divide(A,divide(a2,a2)),B) -> divide(A,B)
% Rule [21] divide(a2,inverse(divide(divide(A,divide(a2,a2)),a2))) -> A
% collapsed.
% Rule [27] inverse(divide(divide(divide(a2,a2),divide(a2,a2)),a2)) -> a2
% collapsed.
% Current number of equations to process: 191
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [40] divide(a2,inverse(divide(A,a2))) -> A
% Current number of equations to process: 190
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [41] inverse(divide(divide(a2,a2),a2)) -> a2
% Current number of equations to process: 189
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [42] divide(B,divide(B,inverse(divide(a2,A)))) <-> divide(A,a2)
% Current number of equations to process: 195
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [43] divide(A,a2) <-> divide(B,divide(B,inverse(divide(a2,A))))
% Rule [41] inverse(divide(divide(a2,a2),a2)) -> a2 collapsed.
% Current number of equations to process: 195
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [44] divide(A,divide(A,inverse(B))) <-> divide(C,divide(C,inverse(B)))
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [45]
% inverse(divide(divide(A,B),divide(a2,B))) <->
% divide(a2,inverse(divide(divide(a2,a2),A)))
% Rule [16] inverse(divide(divide(divide(a2,a2),A),divide(a2,A))) -> a2
% collapsed.
% Current number of equations to process: 196
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [46]
% divide(a2,inverse(divide(divide(a2,a2),A))) <->
% inverse(divide(divide(A,B),divide(a2,B)))
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [47] divide(A,divide(A,a2)) -> a2
% Rule [19] divide(a2,divide(a2,a2)) -> a2 collapsed.
% Current number of equations to process: 216
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [48] divide(inverse(divide(divide(a2,A),divide(a2,A))),inverse(a2)) -> a2
% Current number of equations to process: 217
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [49] divide(A,divide(a2,a2)) -> A
% Rule [35] divide(A,divide(A,divide(a2,a2))) -> divide(a2,a2) collapsed.
% Rule [39] divide(divide(A,divide(a2,a2)),B) -> divide(A,B) collapsed.
% Current number of equations to process: 220
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [50] divide(A,A) <-> divide(a2,a2)
% Rule
% [48] divide(inverse(divide(divide(a2,A),divide(a2,A))),inverse(a2)) -> a2
% collapsed.
% Current number of equations to process: 219
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced : [51] divide(a2,a2) <-> divide(A,A)
% Current number of equations to process: 219
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [52]
% divide(divide(a2,a2),inverse(inverse(divide(a2,divide(a2,A))))) -> inverse(A)
% Current number of equations to process: 218
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [53]
% inverse(divide(divide(a2,a2),divide(A,B))) <->
% divide(A,inverse(divide(divide(a2,a2),B)))
% Current number of equations to process: 217
% Current number of ordered equations: 1
% Current number of rules: 30
% New rule produced :
% [54]
% divide(A,inverse(divide(divide(a2,a2),B))) <->
% inverse(divide(divide(a2,a2),divide(A,B)))
% Current number of equations to process: 217
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [55]
% divide(a2,inverse(divide(inverse(a2),divide(a2,divide(A,inverse(a2)))))) -> A
% Current number of equations to process: 216
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [56] divide(divide(a2,divide(a2,A)),divide(A,a2)) -> a2
% Current number of equations to process: 219
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [57]
% divide(a2,inverse(divide(a2,divide(a2,divide(A,a2))))) ->
% divide(a2,divide(a2,A))
% Current number of equations to process: 221
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [58] inverse(divide(a2,divide(a2,divide(a2,A)))) <-> divide(A,a2)
% Current number of equations to process: 229
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [59] divide(A,a2) <-> inverse(divide(a2,divide(a2,divide(a2,A))))
% Current number of equations to process: 229
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [60]
% divide(inverse(A),inverse(divide(a2,inverse(divide(a2,divide(a2,A)))))) -> a2
% Current number of equations to process: 228
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [61]
% inverse(divide(A,divide(A,inverse(B)))) <->
% divide(C,divide(C,inverse(inverse(B))))
% Current number of equations to process: 237
% Current number of ordered equations: 1
% Current number of rules: 38
% New rule produced :
% [62]
% divide(C,divide(C,inverse(inverse(B)))) <->
% inverse(divide(A,divide(A,inverse(B))))
% Current number of equations to process: 237
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [63]
% inverse(inverse(inverse(divide(a2,divide(a2,A))))) <->
% divide(B,divide(B,inverse(inverse(inverse(A)))))
% Current number of equations to process: 236
% Current number of ordered equations: 1
% Current number of rules: 40
% New rule produced :
% [64]
% divide(B,divide(B,inverse(inverse(inverse(A))))) <->
% inverse(inverse(inverse(divide(a2,divide(a2,A)))))
% Current number of equations to process: 236
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [65] inverse(divide(a2,divide(a2,divide(A,a2)))) -> divide(a2,A)
% Rule
% [57]
% divide(a2,inverse(divide(a2,divide(a2,divide(A,a2))))) ->
% divide(a2,divide(a2,A)) collapsed.
% Current number of equations to process: 246
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [66] inverse(divide(A,a2)) <-> divide(a2,inverse(divide(divide(a2,a2),A)))
% Current number of equations to process: 253
% Current number of ordered equations: 1
% Current number of rules: 42
% New rule produced :
% [67] divide(a2,inverse(divide(divide(a2,a2),A))) <-> inverse(divide(A,a2))
% Current number of equations to process: 253
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [68] divide(inverse(divide(A,a2)),divide(B,divide(B,inverse(A)))) -> a2
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [69] inverse(divide(A,divide(A,inverse(divide(a2,divide(a2,B)))))) -> B
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 45
% Rule [64]
% divide(B,divide(B,inverse(inverse(inverse(A))))) <->
% inverse(inverse(inverse(divide(a2,divide(a2,A))))) is composed into
% [64]
% divide(B,divide(B,inverse(inverse(inverse(A))))) ->
% inverse(inverse(inverse(A)))
% Rule [59] divide(A,a2) <-> inverse(divide(a2,divide(a2,divide(a2,A)))) is composed into
% [59] divide(A,a2) <-> inverse(divide(a2,A))
% Rule [38]
% divide(B,divide(B,inverse(inverse(A)))) <->
% inverse(inverse(divide(a2,divide(a2,A)))) is composed into [38]
% divide(B,
% divide(B,
% inverse(
% inverse(A))))
% ->
% inverse(
% inverse(A))
% Rule [26] divide(B,divide(B,inverse(A))) <-> inverse(divide(a2,divide(a2,A))) is composed into
% [26] divide(B,divide(B,inverse(A))) -> inverse(A)
% New rule produced : [70] divide(a2,divide(a2,A)) -> A
% Rule
% [9]
% divide(a2,inverse(divide(a2,divide(a2,divide(A,divide(A,inverse(divide(a2,B))))))))
% -> B collapsed.
% Rule [25] inverse(divide(a2,divide(a2,A))) <-> divide(B,divide(B,inverse(A)))
% collapsed.
% Rule [36] divide(A,inverse(divide(a2,divide(a2,divide(a2,A))))) -> a2
% collapsed.
% Rule
% [37]
% inverse(inverse(divide(a2,divide(a2,A)))) <->
% divide(B,divide(B,inverse(inverse(A)))) collapsed.
% Rule
% [52]
% divide(divide(a2,a2),inverse(inverse(divide(a2,divide(a2,A))))) -> inverse(A)
% collapsed.
% Rule [56] divide(divide(a2,divide(a2,A)),divide(A,a2)) -> a2 collapsed.
% Rule [58] inverse(divide(a2,divide(a2,divide(a2,A)))) <-> divide(A,a2)
% collapsed.
% Rule
% [60]
% divide(inverse(A),inverse(divide(a2,inverse(divide(a2,divide(a2,A)))))) -> a2
% collapsed.
% Rule
% [63]
% inverse(inverse(inverse(divide(a2,divide(a2,A))))) <->
% divide(B,divide(B,inverse(inverse(inverse(A))))) collapsed.
% Rule [65] inverse(divide(a2,divide(a2,divide(A,a2)))) -> divide(a2,A)
% collapsed.
% Rule [69] inverse(divide(A,divide(A,inverse(divide(a2,divide(a2,B)))))) -> B
% collapsed.
% Current number of equations to process: 259
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [71] inverse(divide(A,a2)) <-> divide(a2,A)
% Rule [29] inverse(divide(a2,a2)) -> divide(a2,a2) collapsed.
% Current number of equations to process: 257
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced : [72] divide(a2,A) <-> inverse(divide(A,a2))
% Current number of equations to process: 257
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [73] divide(A,inverse(divide(a2,A))) -> a2
% Current number of equations to process: 256
% Current number of ordered equations: 0
% Current number of rules: 37
% Rule [61]
% inverse(divide(A,divide(A,inverse(B)))) <->
% divide(C,divide(C,inverse(inverse(B)))) is composed into [61]
% inverse(
% divide(A,
% divide(A,
% inverse(B))))
% <->
% divide(C,
% divide(C,B))
% New rule produced : [74] inverse(inverse(B)) -> B
% Rule [33] inverse(inverse(a2)) -> a2 collapsed.
% Rule [38] divide(B,divide(B,inverse(inverse(A)))) -> inverse(inverse(A))
% collapsed.
% Rule
% [62]
% divide(C,divide(C,inverse(inverse(B)))) <->
% inverse(divide(A,divide(A,inverse(B)))) collapsed.
% Rule
% [64]
% divide(B,divide(B,inverse(inverse(inverse(A))))) ->
% inverse(inverse(inverse(A))) collapsed.
% Current number of equations to process: 257
% Current number of ordered equations: 0
% Current number of rules: 34
% Rule [43] divide(A,a2) <-> divide(B,divide(B,inverse(divide(a2,A)))) is composed into
% [43] divide(A,a2) <-> inverse(divide(a2,A))
% New rule produced : [75] divide(B,divide(B,A)) -> A
% Rule [7] divide(A,divide(B,divide(B,inverse(divide(a2,A))))) -> a2 collapsed.
% Rule
% [11]
% divide(inverse(divide(divide(A,B),divide(a2,B))),divide(C,divide(C,inverse(A))))
% -> a2 collapsed.
% Rule [24] divide(divide(a2,divide(A,divide(A,inverse(B)))),B) -> a2
% collapsed.
% Rule [26] divide(B,divide(B,inverse(A))) -> inverse(A) collapsed.
% Rule [32] divide(A,divide(A,inverse(a2))) -> inverse(a2) collapsed.
% Rule [42] divide(B,divide(B,inverse(divide(a2,A)))) <-> divide(A,a2)
% collapsed.
% Rule [44] divide(A,divide(A,inverse(B))) <-> divide(C,divide(C,inverse(B)))
% collapsed.
% Rule [47] divide(A,divide(A,a2)) -> a2 collapsed.
% Rule [61] inverse(divide(A,divide(A,inverse(B)))) <-> divide(C,divide(C,B))
% collapsed.
% Rule [68] divide(inverse(divide(A,a2)),divide(B,divide(B,inverse(A)))) -> a2
% collapsed.
% Rule [70] divide(a2,divide(a2,A)) -> A collapsed.
% Current number of equations to process: 260
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [76] divide(a2,inverse(divide(B,B))) -> a2
% Current number of equations to process: 258
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [77] divide(inverse(divide(A,a2)),inverse(A)) -> a2
% Current number of equations to process: 257
% Current number of ordered equations: 0
% Current number of rules: 26
% Rule [66]
% inverse(divide(A,a2)) <-> divide(a2,inverse(divide(divide(a2,a2),A))) is composed into
% [66] inverse(divide(A,a2)) <-> divide(a2,inverse(inverse(A)))
% Rule [45]
% inverse(divide(divide(A,B),divide(a2,B))) <->
% divide(a2,inverse(divide(divide(a2,a2),A))) is composed into [45]
% inverse(
% divide(
% divide(A,B),
% divide(a2,B)))
% ->
% divide(a2,
% inverse(
% inverse(A)))
% New rule produced : [78] divide(divide(a2,a2),A) -> inverse(A)
% Rule [31] divide(A,inverse(divide(divide(a2,a2),divide(A,B)))) -> B
% collapsed.
% Rule [34] divide(divide(a2,a2),inverse(a2)) -> a2 collapsed.
% Rule
% [46]
% divide(a2,inverse(divide(divide(a2,a2),A))) <->
% inverse(divide(divide(A,B),divide(a2,B))) collapsed.
% Rule
% [53]
% inverse(divide(divide(a2,a2),divide(A,B))) <->
% divide(A,inverse(divide(divide(a2,a2),B))) collapsed.
% Rule
% [54]
% divide(A,inverse(divide(divide(a2,a2),B))) <->
% inverse(divide(divide(a2,a2),divide(A,B))) collapsed.
% Rule
% [67] divide(a2,inverse(divide(divide(a2,a2),A))) <-> inverse(divide(A,a2))
% collapsed.
% Current number of equations to process: 256
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [79] divide(divide(a2,A),inverse(A)) -> a2
% Current number of equations to process: 253
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [80] divide(A,divide(divide(A,B),divide(a2,B))) -> a2
% Current number of equations to process: 258
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [81]
% divide(C,inverse(divide(inverse(a2),divide(C,divide(A,B))))) <->
% divide(divide(A,a2),B)
% Current number of equations to process: 251
% Current number of ordered equations: 1
% Current number of rules: 24
% Rule [81]
% divide(C,inverse(divide(inverse(a2),divide(C,divide(A,B))))) <->
% divide(divide(A,a2),B) is composed into [81]
% divide(C,inverse(divide(
% inverse(a2),
% divide(C,
% divide(A,B)))))
% <->
% divide(a2,inverse(divide(
% inverse(a2),
% divide(a2,
% divide(A,B)))))
% New rule produced :
% [82]
% divide(divide(A,a2),B) <->
% divide(C,inverse(divide(inverse(a2),divide(C,divide(A,B)))))
% Rule [78] divide(divide(a2,a2),A) -> inverse(A) collapsed.
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 24
% Rule [81]
% divide(C,inverse(divide(inverse(a2),divide(C,divide(A,B))))) <->
% divide(a2,inverse(divide(inverse(a2),divide(a2,divide(A,B))))) is composed into
% [81]
% divide(C,inverse(divide(inverse(a2),divide(C,divide(A,B))))) ->
% inverse(divide(a2,divide(A,B)))
% New rule produced :
% [83] divide(a2,inverse(divide(inverse(a2),A))) -> inverse(A)
% Rule
% [55]
% divide(a2,inverse(divide(inverse(a2),divide(a2,divide(A,inverse(a2)))))) -> A
% collapsed.
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [84] inverse(divide(a2,divide(A,inverse(a2)))) -> A
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [85] divide(B,inverse(divide(a2,divide(B,inverse(A))))) -> divide(a2,A)
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [86] divide(divide(a2,divide(A,a2)),divide(a2,A)) -> a2
% Current number of equations to process: 249
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [87] divide(C,divide(a2,divide(A,divide(C,divide(a2,B))))) -> divide(A,B)
% Current number of equations to process: 247
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [88]
% inverse(divide(a2,divide(C,inverse(B)))) <->
% divide(A,inverse(divide(B,divide(A,divide(C,a2)))))
% Current number of equations to process: 246
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [89]
% divide(A,inverse(divide(B,divide(A,divide(C,a2))))) <->
% inverse(divide(a2,divide(C,inverse(B))))
% Current number of equations to process: 246
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [90] divide(A,inverse(divide(B,divide(A,C)))) <-> divide(C,inverse(B))
% Rule [5] divide(a2,inverse(divide(divide(A,B),divide(a2,B)))) -> A collapsed.
% Rule
% [6]
% divide(V_3,inverse(divide(divide(divide(B,divide(A,C)),divide(a2,divide(A,
% inverse(
% divide(V_3,B))))),
% divide(V_3,divide(a2,C))))) -> V_3 collapsed.
% Current number of equations to process: 249
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced : [91] divide(B,inverse(divide(A,B))) -> A
% Rule [40] divide(a2,inverse(divide(A,a2))) -> A collapsed.
% Rule [73] divide(A,inverse(divide(a2,A))) -> a2 collapsed.
% Current number of equations to process: 248
% Current number of ordered equations: 1
% Current number of rules: 28
% New rule produced : [92] divide(A,divide(B,B)) -> A
% Rule [49] divide(A,divide(a2,a2)) -> A collapsed.
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [93] divide(A,inverse(divide(B,divide(A,inverse(B))))) <-> divide(a2,a2)
% Current number of equations to process: 249
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [94] divide(a2,a2) <-> divide(A,inverse(divide(B,divide(A,inverse(B)))))
% Current number of equations to process: 249
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [95] inverse(divide(A,A)) <-> divide(a2,a2)
% Current number of equations to process: 251
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced : [96] divide(a2,a2) <-> inverse(divide(A,A))
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [97] divide(divide(A,B),divide(a2,B)) -> inverse(divide(a2,A))
% Rule
% [45]
% inverse(divide(divide(A,B),divide(a2,B))) -> divide(a2,inverse(inverse(A)))
% collapsed.
% Rule [80] divide(A,divide(divide(A,B),divide(a2,B))) -> a2 collapsed.
% Current number of equations to process: 254
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [98] divide(inverse(divide(A,A)),inverse(a2)) -> a2
% Current number of equations to process: 258
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [99] inverse(divide(divide(A,B),inverse(divide(B,a2)))) -> divide(a2,A)
% Current number of equations to process: 257
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [100]
% divide(B,inverse(divide(C,divide(B,divide(inverse(C),A))))) -> inverse(A)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 256
% Current number of ordered equations: 0
% Current number of rules: 34
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 15 rules have been used:
% [1]
% multiply(A,B) -> divide(A,inverse(B)); trace = in the starting set
% [2] divide(divide(A,inverse(divide(B,divide(A,C)))),C) -> B; trace = in the starting set
% [3] divide(divide(A,inverse(B)),C) <->
% divide(V_3,inverse(divide(B,divide(V_3,divide(A,C))))); trace = Self cp of 2
% [4] divide(a2,inverse(divide(divide(B,divide(A,C)),divide(a2,divide(A,C)))))
% -> B; trace = in the starting set
% [5] divide(a2,inverse(divide(divide(A,B),divide(a2,B)))) -> A; trace = Self cp of 4
% [6] divide(V_3,inverse(divide(divide(divide(B,divide(A,C)),divide(a2,
% divide(A,inverse(
% divide(V_3,B))))),
% divide(V_3,divide(a2,C))))) -> V_3; trace = Self cp of 2
% [7] divide(A,divide(B,divide(B,inverse(divide(a2,A))))) -> a2; trace = Cp of 6 and 5
% [9] divide(a2,inverse(divide(a2,divide(a2,divide(A,divide(A,inverse(divide(a2,B))))))))
% -> B; trace = Cp of 7 and 5
% [12] divide(a2,divide(B,divide(B,inverse(divide(a2,A))))) <->
% divide(a2,inverse(divide(a2,divide(a2,divide(a2,A))))); trace = Self cp of 9
% [14] divide(a2,inverse(divide(a2,a2))) -> a2; trace = Cp of 9 and 7
% [17] divide(a2,divide(A,divide(A,inverse(B)))) <->
% divide(a2,inverse(divide(a2,divide(a2,B)))); trace = Cp of 12 and 5
% [19] divide(a2,divide(a2,a2)) -> a2; trace = Cp of 14 and 7
% [25] inverse(divide(a2,divide(a2,A))) <-> divide(B,divide(B,inverse(A))); trace = Cp of 17 and 9
% [50] divide(A,A) <-> divide(a2,a2); trace = Cp of 25 and 19
% [100] divide(B,inverse(divide(C,divide(B,divide(inverse(C),A))))) ->
% inverse(A); trace = Cp of 50 and 3
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.140000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------