%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP556-1 : TPTP v6.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n104.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 1.35s
% Output : Refutation 1.35s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP556-1 : TPTP v6.0.0. Bugfixed v2.7.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n104.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 19:24:48 CDT 2014
% % CPUTime : 1.35
% Processing problem /tmp/CiME_36757_n104.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b,a : 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 "
% b lr_lex;
% a lr_lex;
% multiply lr_lex;
% inverse lr_lex;
% divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > divide > inverse > a > b";
%
% let s2 = status F "
% b mul;
% a mul;
% multiply mul;
% inverse mul;
% divide mul;
% ";
%
% let p2 = precedence F "
% multiply > divide > inverse > a = b";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(a,b) = multiply(b,a);"
% ;
% (*
% 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(a,b) = multiply(b,a) }
% (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(a,inverse(b)) = divide(b,inverse(a))
%
% 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.
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [4]
% divide(b,inverse(divide(divide(B,divide(A,C)),divide(b,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(b,inverse(divide(divide(A,B),divide(b,B)))) -> A
% Rule
% [4]
% divide(b,inverse(divide(divide(B,divide(A,C)),divide(b,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(b,divide(A,
% inverse(
% divide(V_3,B))))),
% divide(V_3,divide(b,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(b,A))))) -> b
% 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(b,b)))),divide(B,divide(B,inverse(b))))
% -> b
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [9]
% divide(b,inverse(divide(b,divide(b,divide(A,divide(A,inverse(divide(b,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(b,inverse(divide(divide(A,divide(B,divide(B,inverse(divide(b,b))))),b)))
% -> 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(b,B))),divide(C,divide(C,inverse(A))))
% -> b
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [12]
% divide(b,divide(B,divide(B,inverse(divide(b,A))))) <->
% divide(b,inverse(divide(b,divide(b,divide(b,A)))))
% Current number of equations to process: 37
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced :
% [13]
% divide(b,inverse(divide(b,divide(b,divide(b,A))))) <->
% divide(b,divide(B,divide(B,inverse(divide(b,A)))))
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [14] divide(b,inverse(divide(b,b))) -> b
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [15]
% divide(divide(b,divide(A,divide(A,inverse(divide(b,B))))),divide(b,B)) -> b
% 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(b,b),A),divide(b,A))) -> b
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [17]
% divide(b,divide(A,divide(A,inverse(B)))) <->
% divide(b,inverse(divide(b,divide(b,B))))
% Rule
% [12]
% divide(b,divide(B,divide(B,inverse(divide(b,A))))) <->
% divide(b,inverse(divide(b,divide(b,divide(b,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(b,divide(b,divide(b,B)))) <->
% divide(A,divide(A,inverse(divide(b,B))))
% Rule
% [13]
% divide(b,inverse(divide(b,divide(b,divide(b,A))))) <->
% divide(b,divide(B,divide(B,inverse(divide(b,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(b,divide(b,b)) -> b
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [20] divide(divide(b,b),divide(A,divide(A,inverse(b)))) -> b
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [21] divide(b,inverse(divide(divide(A,divide(b,b)),b))) -> 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(b,b)),divide(A,divide(A,inverse(b)))) -> b
% 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(b,b),divide(B,divide(b,A))))) -> divide(b,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(b,divide(A,divide(A,inverse(B)))),B) -> b
% Rule
% [15]
% divide(divide(b,divide(A,divide(A,inverse(divide(b,B))))),divide(b,B)) -> b
% 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(b,divide(b,A))) <-> divide(B,divide(B,inverse(A)))
% Rule
% [18]
% inverse(divide(b,divide(b,divide(b,B)))) <->
% divide(A,divide(A,inverse(divide(b,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(b,divide(b,A)))
% Rule
% [17]
% divide(b,divide(A,divide(A,inverse(B)))) <->
% divide(b,inverse(divide(b,divide(b,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(b,b),divide(b,b)),b)) -> b
% Current number of equations to process: 113
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [28] inverse(divide(b,divide(b,divide(A,divide(A,inverse(b)))))) -> b
% Current number of equations to process: 117
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [29] inverse(divide(b,b)) -> divide(b,b)
% Rule
% [8]
% divide(divide(A,divide(A,inverse(divide(b,b)))),divide(B,divide(B,inverse(b))))
% -> b collapsed.
% Rule
% [10]
% divide(b,inverse(divide(divide(A,divide(B,divide(B,inverse(divide(b,b))))),b)))
% -> A collapsed.
% Rule [14] divide(b,inverse(divide(b,b))) -> b collapsed.
% Rule [22] divide(inverse(divide(b,b)),divide(A,divide(A,inverse(b)))) -> b
% collapsed.
% Current number of equations to process: 129
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [30] divide(b,divide(A,divide(A,divide(b,b)))) -> b
% 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(b,b),divide(A,B)))) -> B
% Rule
% [23]
% divide(B,inverse(divide(divide(b,b),divide(B,divide(b,A))))) -> divide(b,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(b))) -> inverse(b)
% Rule [20] divide(divide(b,b),divide(A,divide(A,inverse(b)))) -> b collapsed.
% Rule [28] inverse(divide(b,divide(b,divide(A,divide(A,inverse(b)))))) -> b
% 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(b)) -> b
% Current number of equations to process: 160
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [34] divide(divide(b,b),inverse(b)) -> b
% 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(b,b))) -> divide(b,b)
% Rule [30] divide(b,divide(A,divide(A,divide(b,b)))) -> b 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(b,divide(b,divide(b,A))))) -> b
% 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(b,divide(b,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(b,divide(b,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(b,b)),B) -> divide(A,B)
% Rule [21] divide(b,inverse(divide(divide(A,divide(b,b)),b))) -> A collapsed.
% Rule [27] inverse(divide(divide(divide(b,b),divide(b,b)),b)) -> b collapsed.
% Current number of equations to process: 191
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [40] divide(b,inverse(divide(A,b))) -> 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(b,b),b)) -> b
% 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(b,A)))) <-> divide(A,b)
% Current number of equations to process: 195
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [43] divide(A,b) <-> divide(B,divide(B,inverse(divide(b,A))))
% Rule [41] inverse(divide(divide(b,b),b)) -> b 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(b,B))) <->
% divide(b,inverse(divide(divide(b,b),A)))
% Rule [16] inverse(divide(divide(divide(b,b),A),divide(b,A))) -> b collapsed.
% Current number of equations to process: 196
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [46]
% divide(b,inverse(divide(divide(b,b),A))) <->
% inverse(divide(divide(A,B),divide(b,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,b)) -> b
% Rule [19] divide(b,divide(b,b)) -> b 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(b,A),divide(b,A))),inverse(b)) -> b
% 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(b,b)) -> A
% Rule [35] divide(A,divide(A,divide(b,b))) -> divide(b,b) collapsed.
% Rule [39] divide(divide(A,divide(b,b)),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(b,b)
% Rule [48] divide(inverse(divide(divide(b,A),divide(b,A))),inverse(b)) -> b
% collapsed.
% Current number of equations to process: 219
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced : [51] divide(b,b) <-> 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(b,b),inverse(inverse(divide(b,divide(b,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(b,b),divide(A,B))) <->
% divide(A,inverse(divide(divide(b,b),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(b,b),B))) <->
% inverse(divide(divide(b,b),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(b,inverse(divide(inverse(b),divide(b,divide(A,inverse(b)))))) -> 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(b,divide(b,A)),divide(A,b)) -> b
% Current number of equations to process: 219
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [57]
% divide(b,inverse(divide(b,divide(b,divide(A,b))))) -> divide(b,divide(b,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(b,divide(b,divide(b,A)))) <-> divide(A,b)
% Current number of equations to process: 229
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [59] divide(A,b) <-> inverse(divide(b,divide(b,divide(b,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(b,inverse(divide(b,divide(b,A)))))) -> b
% 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(b,divide(b,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(b,divide(b,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(b,divide(b,divide(A,b)))) -> divide(b,A)
% Rule
% [57]
% divide(b,inverse(divide(b,divide(b,divide(A,b))))) -> divide(b,divide(b,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,b)) <-> divide(b,inverse(divide(divide(b,b),A)))
% Current number of equations to process: 253
% Current number of ordered equations: 1
% Current number of rules: 42
% New rule produced :
% [67] divide(b,inverse(divide(divide(b,b),A))) <-> inverse(divide(A,b))
% 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,b)),divide(B,divide(B,inverse(A)))) -> b
% 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(b,divide(b,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(b,divide(b,A))))) is composed into
% [64]
% divide(B,divide(B,inverse(inverse(inverse(A))))) ->
% inverse(inverse(inverse(A)))
% Rule [59] divide(A,b) <-> inverse(divide(b,divide(b,divide(b,A)))) is composed into
% [59] divide(A,b) <-> inverse(divide(b,A))
% Rule [38]
% divide(B,divide(B,inverse(inverse(A)))) <->
% inverse(inverse(divide(b,divide(b,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(b,divide(b,A))) is composed into
% [26] divide(B,divide(B,inverse(A))) -> inverse(A)
% New rule produced : [70] divide(b,divide(b,A)) -> A
% Rule
% [9]
% divide(b,inverse(divide(b,divide(b,divide(A,divide(A,inverse(divide(b,B))))))))
% -> B collapsed.
% Rule [25] inverse(divide(b,divide(b,A))) <-> divide(B,divide(B,inverse(A)))
% collapsed.
% Rule [36] divide(A,inverse(divide(b,divide(b,divide(b,A))))) -> b collapsed.
% Rule
% [37]
% inverse(inverse(divide(b,divide(b,A)))) <->
% divide(B,divide(B,inverse(inverse(A)))) collapsed.
% Rule
% [52]
% divide(divide(b,b),inverse(inverse(divide(b,divide(b,A))))) -> inverse(A)
% collapsed.
% Rule [56] divide(divide(b,divide(b,A)),divide(A,b)) -> b collapsed.
% Rule [58] inverse(divide(b,divide(b,divide(b,A)))) <-> divide(A,b) collapsed.
% Rule
% [60]
% divide(inverse(A),inverse(divide(b,inverse(divide(b,divide(b,A)))))) -> b
% collapsed.
% Rule
% [63]
% inverse(inverse(inverse(divide(b,divide(b,A))))) <->
% divide(B,divide(B,inverse(inverse(inverse(A))))) collapsed.
% Rule [65] inverse(divide(b,divide(b,divide(A,b)))) -> divide(b,A) collapsed.
% Rule [69] inverse(divide(A,divide(A,inverse(divide(b,divide(b,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,b)) <-> divide(b,A)
% Rule [29] inverse(divide(b,b)) -> divide(b,b) collapsed.
% Current number of equations to process: 257
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced : [72] divide(b,A) <-> inverse(divide(A,b))
% 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(b,A))) -> b
% 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(b)) -> b 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,b) <-> divide(B,divide(B,inverse(divide(b,A)))) is composed into
% [43] divide(A,b) <-> inverse(divide(b,A))
% New rule produced : [75] divide(B,divide(B,A)) -> A
% Rule [7] divide(A,divide(B,divide(B,inverse(divide(b,A))))) -> b collapsed.
% Rule
% [11]
% divide(inverse(divide(divide(A,B),divide(b,B))),divide(C,divide(C,inverse(A))))
% -> b collapsed.
% Rule [24] divide(divide(b,divide(A,divide(A,inverse(B)))),B) -> b collapsed.
% Rule [26] divide(B,divide(B,inverse(A))) -> inverse(A) collapsed.
% Rule [32] divide(A,divide(A,inverse(b))) -> inverse(b) collapsed.
% Rule [42] divide(B,divide(B,inverse(divide(b,A)))) <-> divide(A,b) collapsed.
% Rule [44] divide(A,divide(A,inverse(B))) <-> divide(C,divide(C,inverse(B)))
% collapsed.
% Rule [47] divide(A,divide(A,b)) -> b collapsed.
% Rule [61] inverse(divide(A,divide(A,inverse(B)))) <-> divide(C,divide(C,B))
% collapsed.
% Rule [68] divide(inverse(divide(A,b)),divide(B,divide(B,inverse(A)))) -> b
% collapsed.
% Rule [70] divide(b,divide(b,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(b,inverse(divide(B,B))) -> b
% 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,b)),inverse(A)) -> b
% Current number of equations to process: 257
% Current number of ordered equations: 0
% Current number of rules: 26
% Rule [66] inverse(divide(A,b)) <-> divide(b,inverse(divide(divide(b,b),A))) is composed into
% [66] inverse(divide(A,b)) <-> divide(b,inverse(inverse(A)))
% Rule [45]
% inverse(divide(divide(A,B),divide(b,B))) <->
% divide(b,inverse(divide(divide(b,b),A))) is composed into [45]
% inverse(
% divide(
% divide(A,B),
% divide(b,B)))
% ->
% divide(b,
% inverse(
% inverse(A)))
% New rule produced : [78] divide(divide(b,b),A) -> inverse(A)
% Rule [31] divide(A,inverse(divide(divide(b,b),divide(A,B)))) -> B collapsed.
% Rule [34] divide(divide(b,b),inverse(b)) -> b collapsed.
% Rule
% [46]
% divide(b,inverse(divide(divide(b,b),A))) <->
% inverse(divide(divide(A,B),divide(b,B))) collapsed.
% Rule
% [53]
% inverse(divide(divide(b,b),divide(A,B))) <->
% divide(A,inverse(divide(divide(b,b),B))) collapsed.
% Rule
% [54]
% divide(A,inverse(divide(divide(b,b),B))) <->
% inverse(divide(divide(b,b),divide(A,B))) collapsed.
% Rule [67] divide(b,inverse(divide(divide(b,b),A))) <-> inverse(divide(A,b))
% 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(b,A),inverse(A)) -> b
% 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(b,B))) -> b
% 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(b),divide(C,divide(A,B))))) <->
% divide(divide(A,b),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(b),divide(C,divide(A,B))))) <->
% divide(divide(A,b),B) is composed into [81]
% divide(C,inverse(divide(inverse(b),
% divide(C,
% divide(A,B)))))
% <->
% divide(b,inverse(divide(inverse(b),
% divide(b,
% divide(A,B)))))
% New rule produced :
% [82]
% divide(divide(A,b),B) <->
% divide(C,inverse(divide(inverse(b),divide(C,divide(A,B)))))
% Rule [78] divide(divide(b,b),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(b),divide(C,divide(A,B))))) <->
% divide(b,inverse(divide(inverse(b),divide(b,divide(A,B))))) is composed into
% [81]
% divide(C,inverse(divide(inverse(b),divide(C,divide(A,B))))) ->
% inverse(divide(b,divide(A,B)))
% New rule produced :
% [83] divide(b,inverse(divide(inverse(b),A))) -> inverse(A)
% Rule
% [55]
% divide(b,inverse(divide(inverse(b),divide(b,divide(A,inverse(b)))))) -> 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(b,divide(A,inverse(b)))) -> 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(b,divide(B,inverse(A))))) -> divide(b,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(b,divide(A,b)),divide(b,A)) -> b
% 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(b,divide(A,divide(C,divide(b,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(b,divide(C,inverse(B)))) <->
% divide(A,inverse(divide(B,divide(A,divide(C,b)))))
% 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,b))))) <->
% inverse(divide(b,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(b,inverse(divide(divide(A,B),divide(b,B)))) -> A collapsed.
% Rule
% [6]
% divide(V_3,inverse(divide(divide(divide(B,divide(A,C)),divide(b,divide(A,
% inverse(
% divide(V_3,B))))),
% divide(V_3,divide(b,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(b,inverse(divide(A,b))) -> A collapsed.
% Rule [73] divide(A,inverse(divide(b,A))) -> b 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(b,b)) -> 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(b,b)
% Current number of equations to process: 249
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [94] divide(b,b) <-> 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(b,b)
% Current number of equations to process: 251
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced : [96] divide(b,b) <-> 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(b,B)) -> inverse(divide(b,A))
% Rule
% [45]
% inverse(divide(divide(A,B),divide(b,B))) -> divide(b,inverse(inverse(A)))
% collapsed.
% Rule [80] divide(A,divide(divide(A,B),divide(b,B))) -> b 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(b)) -> b
% 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,b)))) -> divide(b,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)
% Current number of equations to process: 256
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [101] divide(divide(A,A),inverse(b)) -> b
% Current number of equations to process: 257
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [102]
% divide(b,inverse(divide(A,inverse(divide(B,divide(A,inverse(B))))))) -> b
% Current number of equations to process: 257
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [103]
% divide(C,inverse(divide(A,divide(C,divide(b,B))))) <->
% divide(b,inverse(divide(A,B)))
% Current number of equations to process: 256
% Current number of ordered equations: 1
% Current number of rules: 37
% New rule produced :
% [104]
% divide(b,inverse(divide(A,B))) <->
% divide(C,inverse(divide(A,divide(C,divide(b,B)))))
% Current number of equations to process: 256
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [105]
% inverse(divide(b,divide(A,B))) <-> divide(A,inverse(divide(inverse(b),B)))
% Current number of equations to process: 262
% Current number of ordered equations: 2
% Current number of rules: 39
% New rule produced :
% [106]
% divide(A,inverse(divide(inverse(b),B))) <-> inverse(divide(b,divide(A,B)))
% Rule [83] divide(b,inverse(divide(inverse(b),A))) -> inverse(A) collapsed.
% Current number of equations to process: 262
% Current number of ordered equations: 1
% Current number of rules: 39
% New rule produced :
% [107]
% divide(inverse(b),inverse(divide(A,B))) -> inverse(divide(b,divide(A,B)))
% Current number of equations to process: 262
% Current number of ordered equations: 0
% Current number of rules: 40
% Rule [82]
% divide(divide(A,b),B) <->
% divide(C,inverse(divide(inverse(b),divide(C,divide(A,B))))) is composed into
% [82] divide(divide(A,b),B) -> inverse(divide(b,divide(A,B)))
% New rule produced :
% [108]
% divide(A,inverse(divide(inverse(b),divide(A,B)))) -> inverse(divide(b,B))
% Rule
% [81]
% divide(C,inverse(divide(inverse(b),divide(C,divide(A,B))))) ->
% inverse(divide(b,divide(A,B))) collapsed.
% Current number of equations to process: 261
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [109]
% inverse(divide(inverse(b),divide(A,divide(B,C)))) <->
% divide(A,inverse(divide(b,divide(B,C))))
% Current number of equations to process: 259
% Current number of ordered equations: 1
% Current number of rules: 41
% New rule produced :
% [110]
% divide(A,inverse(divide(b,divide(B,C)))) <->
% inverse(divide(inverse(b),divide(A,divide(B,C))))
% Current number of equations to process: 259
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [111] divide(inverse(divide(b,A)),B) -> inverse(divide(b,divide(A,B)))
% Current number of equations to process: 261
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced : [112] divide(divide(A,A),B) -> inverse(B)
% Rule [101] divide(divide(A,A),inverse(b)) -> b collapsed.
% Current number of equations to process: 261
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [113] inverse(divide(b,divide(A,inverse(divide(b,divide(A,B)))))) -> B
% Current number of equations to process: 261
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced : [114] divide(b,divide(A,inverse(b))) -> inverse(A)
% Rule [84] inverse(divide(b,divide(A,inverse(b)))) -> A collapsed.
% Current number of equations to process: 263
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced : [115] divide(inverse(A),inverse(b)) -> divide(b,A)
% Rule [98] divide(inverse(divide(A,A)),inverse(b)) -> b collapsed.
% Current number of equations to process: 265
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [116] inverse(divide(b,divide(A,inverse(B)))) <-> divide(A,divide(b,B))
% Current number of equations to process: 267
% Current number of ordered equations: 1
% Current number of rules: 45
% New rule produced :
% [117] divide(A,divide(b,B)) <-> inverse(divide(b,divide(A,inverse(B))))
% Rule [86] divide(divide(b,divide(A,b)),divide(b,A)) -> b collapsed.
% Rule [97] divide(divide(A,B),divide(b,B)) -> inverse(divide(b,A)) collapsed.
% Current number of equations to process: 268
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [118] divide(A,inverse(divide(b,divide(A,B)))) -> divide(b,inverse(B))
% Rule [85] divide(B,inverse(divide(b,divide(B,inverse(A))))) -> divide(b,A)
% collapsed.
% Rule [113] inverse(divide(b,divide(A,inverse(divide(b,divide(A,B)))))) -> B
% collapsed.
% Current number of equations to process: 267
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [119]
% inverse(divide(b,A)) <-> divide(A,inverse(divide(B,divide(b,inverse(B)))))
% Current number of equations to process: 266
% Current number of ordered equations: 1
% Current number of rules: 44
% New rule produced :
% [120]
% divide(A,inverse(divide(B,divide(b,inverse(B))))) <-> inverse(divide(b,A))
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [121] divide(B,b) <-> divide(A,divide(b,divide(B,A)))
% Current number of equations to process: 266
% Current number of ordered equations: 1
% Current number of rules: 46
% New rule produced : [122] divide(A,divide(b,divide(B,A))) <-> divide(B,b)
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced : [123] divide(divide(A,divide(b,B)),B) -> divide(A,b)
% Current number of equations to process: 269
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [124] inverse(divide(b,divide(divide(b,A),inverse(B)))) <-> divide(B,A)
% Current number of equations to process: 272
% Current number of ordered equations: 1
% Current number of rules: 49
% New rule produced :
% [125] divide(B,A) <-> inverse(divide(b,divide(divide(b,A),inverse(B))))
% Rule [123] divide(divide(A,divide(b,B)),B) -> divide(A,b) collapsed.
% Current number of equations to process: 273
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [126] divide(B,divide(b,C)) <-> divide(A,divide(b,divide(B,divide(A,C))))
% Current number of equations to process: 271
% Current number of ordered equations: 3
% Current number of rules: 50
% New rule produced :
% [127] divide(A,divide(B,C)) <-> divide(b,divide(B,divide(A,divide(b,C))))
% Current number of equations to process: 271
% Current number of ordered equations: 2
% Current number of rules: 51
% New rule produced :
% [128] divide(A,divide(b,divide(B,divide(A,C)))) <-> divide(B,divide(b,C))
% Current number of equations to process: 271
% Current number of ordered equations: 1
% Current number of rules: 52
% New rule produced :
% [129] divide(b,divide(B,divide(A,divide(b,C)))) <-> divide(A,divide(B,C))
% Current number of equations to process: 271
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [130]
% divide(B,inverse(divide(C,C))) <-> divide(A,divide(b,divide(B,divide(A,b))))
% Current number of equations to process: 270
% Current number of ordered equations: 1
% Current number of rules: 54
% New rule produced :
% [131]
% divide(A,divide(b,divide(B,divide(A,b)))) <-> divide(B,inverse(divide(C,C)))
% Current number of equations to process: 270
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [132]
% divide(A,inverse(divide(B,divide(A,inverse(divide(b,inverse(B))))))) ->
% inverse(b)
% Current number of equations to process: 279
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [133]
% inverse(divide(b,divide(A,inverse(B)))) <-> divide(A,inverse(divide(B,b)))
% Current number of equations to process: 287
% Current number of ordered equations: 3
% Current number of rules: 57
% New rule produced :
% [134]
% inverse(divide(b,divide(B,inverse(A)))) <-> divide(A,inverse(divide(B,b)))
% Current number of equations to process: 287
% Current number of ordered equations: 2
% Current number of rules: 58
% New rule produced :
% [135]
% divide(A,inverse(divide(B,b))) <-> inverse(divide(b,divide(A,inverse(B))))
% Rule [99] inverse(divide(divide(A,B),inverse(divide(B,b)))) -> divide(b,A)
% collapsed.
% Current number of equations to process: 288
% Current number of ordered equations: 1
% Current number of rules: 58
% New rule produced :
% [136]
% divide(A,inverse(divide(B,b))) <-> inverse(divide(b,divide(B,inverse(A))))
% Current number of equations to process: 288
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [137]
% inverse(divide(A,inverse(divide(B,divide(b,inverse(B)))))) <-> divide(b,A)
% Current number of equations to process: 287
% Current number of ordered equations: 1
% Current number of rules: 60
% New rule produced :
% [138]
% divide(b,A) <-> inverse(divide(A,inverse(divide(B,divide(b,inverse(B))))))
% Current number of equations to process: 287
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [139] inverse(divide(b,divide(B,inverse(divide(A,divide(B,b)))))) -> A
% Current number of equations to process: 286
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [140]
% inverse(divide(C,divide(A,divide(B,b)))) <->
% divide(A,inverse(divide(b,divide(B,inverse(C)))))
% Current number of equations to process: 285
% Current number of ordered equations: 1
% Current number of rules: 63
% New rule produced :
% [141]
% divide(A,inverse(divide(b,divide(B,inverse(C))))) <->
% inverse(divide(C,divide(A,divide(B,b))))
% Current number of equations to process: 285
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [142]
% divide(A,inverse(divide(B,inverse(divide(b,A))))) <-> divide(b,inverse(B))
% Current number of equations to process: 288
% Current number of ordered equations: 1
% Current number of rules: 65
% New rule produced :
% [143]
% divide(b,inverse(B)) <-> divide(A,inverse(divide(B,inverse(divide(b,A)))))
% Current number of equations to process: 288
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced : [144] divide(A,inverse(b)) <-> divide(b,inverse(A))
% Rule [115] divide(inverse(A),inverse(b)) -> divide(b,A) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 292
% Current number of ordered equations: 1
% Current number of rules: 66
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 21 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(b,inverse(divide(divide(B,divide(A,C)),divide(b,divide(A,C))))) ->
% B; trace = in the starting set
% [5] divide(b,inverse(divide(divide(A,B),divide(b,B)))) -> A; trace = Self cp of 4
% [6] divide(V_3,inverse(divide(divide(divide(B,divide(A,C)),divide(b,divide(A,
% inverse(
% divide(V_3,B))))),
% divide(V_3,divide(b,C))))) -> V_3; trace = Self cp of 2
% [7] divide(A,divide(B,divide(B,inverse(divide(b,A))))) -> b; trace = Cp of 6 and 5
% [9] divide(b,inverse(divide(b,divide(b,divide(A,divide(A,inverse(divide(b,B))))))))
% -> B; trace = Cp of 7 and 5
% [10] divide(b,inverse(divide(divide(A,divide(B,divide(B,inverse(divide(b,b))))),b)))
% -> A; trace = Cp of 7 and 5
% [12] divide(b,divide(B,divide(B,inverse(divide(b,A))))) <->
% divide(b,inverse(divide(b,divide(b,divide(b,A))))); trace = Self cp of 9
% [14] divide(b,inverse(divide(b,b))) -> b; trace = Cp of 9 and 7
% [17] divide(b,divide(A,divide(A,inverse(B)))) <->
% divide(b,inverse(divide(b,divide(b,B)))); trace = Cp of 12 and 5
% [19] divide(b,divide(b,b)) -> b; trace = Cp of 14 and 7
% [25] inverse(divide(b,divide(b,A))) <-> divide(B,divide(B,inverse(A))); trace = Cp of 17 and 9
% [26] divide(B,divide(B,inverse(A))) <-> inverse(divide(b,divide(b,A))); trace = Cp of 17 and 9
% [35] divide(A,divide(A,divide(b,b))) -> divide(b,b); trace = Cp of 25 and 19
% [40] divide(b,inverse(divide(A,b))) -> A; trace = Cp of 14 and 10
% [49] divide(A,divide(b,b)) -> A; trace = Cp of 35 and 5
% [72] divide(b,A) <-> inverse(divide(A,b)); trace = Cp of 40 and 26
% [90] divide(A,inverse(divide(B,divide(A,C)))) <-> divide(C,inverse(B)); trace = Cp of 49 and 3
% [144] divide(A,inverse(b)) <-> divide(b,inverse(A)); trace = Cp of 90 and 72
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.240000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------