TSTP Solution File: GRP559-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP559-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n121.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 00:23:28 EDT 2014
% Result : Unsatisfiable 1.23s
% Output : Refutation 1.23s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP559-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n121.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 19:40:08 CDT 2014
% % CPUTime : 1.23
% Processing problem /tmp/CiME_5365_n121.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " c3,b3,a3 : constant; multiply : 2; inverse : 1; divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% divide(A,inverse(divide(divide(B,C),divide(A,C)))) = B;
% multiply(A,B) = divide(A,inverse(B));
% ";
%
% let s1 = status F "
% c3 lr_lex;
% b3 lr_lex;
% a3 lr_lex;
% multiply lr_lex;
% inverse lr_lex;
% divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > divide > inverse > a3 > b3 > c3";
%
% let s2 = status F "
% c3 mul;
% b3 mul;
% a3 mul;
% multiply mul;
% inverse mul;
% divide mul;
% ";
%
% let p2 = precedence F "
% multiply > divide > inverse > a3 = b3 = c3";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3));"
% ;
% (*
% 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(A,inverse(divide(divide(B,C),divide(A,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(a3,b3),c3) =
% multiply(a3,multiply(b3,c3)) }
% (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(a3,inverse(b3)),inverse(c3)) = divide(a3,inverse(divide(b3,
% inverse(c3))))
%
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 1
% New rule produced :
% [2] divide(A,inverse(divide(divide(B,C),divide(A,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(A,inverse(divide(B,divide(A,inverse(divide(divide(B,C),divide(V_3,C)))))))
% -> V_3
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced :
% [4]
% divide(A,inverse(divide(divide(B,inverse(divide(divide(C,V_3),divide(A,V_3)))),C)))
% -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [5] divide(A,inverse(divide(B,B))) -> A
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [6] divide(A,inverse(inverse(divide(B,B)))) -> A
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] divide(A,inverse(divide(B,A))) -> B
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8] divide(A,inverse(inverse(inverse(inverse(divide(B,B)))))) -> A
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [9] divide(inverse(divide(A,B)),inverse(A)) -> B
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10] divide(A,inverse(inverse(inverse(divide(B,B))))) -> A
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11] divide(divide(A,B),inverse(divide(C,divide(C,B)))) -> A
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] divide(inverse(divide(A,A)),inverse(B)) -> B
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13] divide(inverse(inverse(divide(A,A))),inverse(B)) -> B
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14] divide(A,inverse(divide(divide(B,C),B))) -> divide(A,C)
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15] divide(A,inverse(divide(B,divide(A,inverse(divide(B,C)))))) -> C
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16] divide(A,inverse(divide(divide(B,inverse(divide(C,A))),C))) -> B
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17] divide(inverse(divide(divide(A,B),divide(C,B))),inverse(A)) -> C
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18] divide(inverse(A),inverse(inverse(divide(B,A)))) -> inverse(B)
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19] divide(A,inverse(inverse(inverse(inverse(inverse(divide(B,B))))))) -> A
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20] divide(inverse(inverse(inverse(inverse(divide(A,A))))),inverse(B)) -> B
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21]
% inverse(divide(divide(A,C),divide(B,C))) -> divide(inverse(A),inverse(B))
% Rule [2] divide(A,inverse(divide(divide(B,C),divide(A,C)))) -> B collapsed.
% Rule
% [3]
% divide(A,inverse(divide(B,divide(A,inverse(divide(divide(B,C),divide(V_3,C)))))))
% -> V_3 collapsed.
% Rule
% [4]
% divide(A,inverse(divide(divide(B,inverse(divide(divide(C,V_3),divide(A,V_3)))),C)))
% -> B collapsed.
% Rule [17] divide(inverse(divide(divide(A,B),divide(C,B))),inverse(A)) -> C
% collapsed.
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [22] divide(A,divide(inverse(B),inverse(A))) -> B
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [23] inverse(divide(divide(A,A),B)) -> B
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [24] inverse(divide(B,B)) <-> divide(inverse(A),inverse(A))
% Current number of equations to process: 28
% Current number of ordered equations: 1
% Current number of rules: 20
% Rule [24] inverse(divide(B,B)) <-> divide(inverse(A),inverse(A)) is composed into
% [24] inverse(divide(B,B)) <-> inverse(divide(c3,c3))
% New rule produced :
% [25] divide(inverse(A),inverse(A)) <-> inverse(divide(B,B))
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [26] inverse(inverse(divide(A,A))) <-> inverse(divide(c3,c3))
% Current number of equations to process: 30
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [27] inverse(divide(c3,c3)) <-> inverse(inverse(divide(A,A)))
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 23
% Rule [21]
% inverse(divide(divide(A,C),divide(B,C))) ->
% divide(inverse(A),inverse(B)) is composed into [21]
% inverse(divide(divide(A,C),
% divide(B,C))) ->
% inverse(divide(A,B))
% New rule produced :
% [28] divide(inverse(A),inverse(B)) -> inverse(divide(A,B))
% Rule [9] divide(inverse(divide(A,B)),inverse(A)) -> B collapsed.
% Rule [12] divide(inverse(divide(A,A)),inverse(B)) -> B collapsed.
% Rule [13] divide(inverse(inverse(divide(A,A))),inverse(B)) -> B collapsed.
% Rule [18] divide(inverse(A),inverse(inverse(divide(B,A)))) -> inverse(B)
% collapsed.
% Rule
% [20] divide(inverse(inverse(inverse(inverse(divide(A,A))))),inverse(B)) -> B
% collapsed.
% Rule [22] divide(A,divide(inverse(B),inverse(A))) -> B collapsed.
% Rule [25] divide(inverse(A),inverse(A)) <-> inverse(divide(B,B)) collapsed.
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [29] inverse(divide(B,B)) <-> inverse(divide(A,A))
% Rule [24] inverse(divide(B,B)) <-> inverse(divide(c3,c3)) collapsed.
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [30] inverse(divide(divide(A,B),A)) -> B
% Rule [14] divide(A,inverse(divide(divide(B,C),B))) -> divide(A,C) collapsed.
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [31] inverse(divide(inverse(divide(A,A)),B)) -> B
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [32] inverse(divide(inverse(inverse(divide(A,A))),B)) -> B
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [33] inverse(divide(inverse(inverse(inverse(divide(A,A)))),B)) -> B
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [34] inverse(divide(divide(A,divide(A,B)),C)) <-> divide(C,B)
% Current number of equations to process: 30
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [35] divide(C,B) <-> inverse(divide(divide(A,divide(A,B)),C))
% The conjecture has been reduced.
% Conjecture is now:
% inverse(divide(divide(c3,divide(c3,inverse(c3))),divide(a3,inverse(b3)))) =
% divide(a3,inverse(divide(b3,inverse(c3))))
%
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [36] divide(divide(A,inverse(divide(B,divide(B,C)))),C) -> A
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [37] divide(C,B) <-> divide(divide(A,B),inverse(divide(C,A)))
% Current number of equations to process: 40
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [38] divide(divide(A,B),inverse(divide(C,A))) <-> divide(C,B)
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [39]
% inverse(divide(C,B)) <-> divide(A,inverse(divide(B,divide(A,inverse(C)))))
% Rule [16] divide(A,inverse(divide(divide(B,inverse(divide(C,A))),C))) -> B
% collapsed.
% Rule [30] inverse(divide(divide(A,B),A)) -> B collapsed.
% Current number of equations to process: 40
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [40]
% divide(A,inverse(divide(B,divide(A,inverse(C))))) <-> inverse(divide(C,B))
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [41] inverse(divide(inverse(inverse(inverse(inverse(divide(A,A))))),B)) -> B
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [42]
% inverse(inverse(inverse(inverse(inverse(divide(B,B)))))) <->
% inverse(divide(A,A))
% Current number of equations to process: 42
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [43]
% inverse(divide(A,A)) <->
% inverse(inverse(inverse(inverse(inverse(divide(B,B))))))
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [44] divide(B,B) <-> divide(A,A)
% Rule [29] inverse(divide(B,B)) <-> inverse(divide(A,A)) collapsed.
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 28
% Rule [27] inverse(divide(c3,c3)) <-> inverse(inverse(divide(A,A))) is composed into
% [27] inverse(divide(c3,c3)) <-> inverse(divide(A,A))
% New rule produced :
% [45] inverse(inverse(divide(B,B))) <-> inverse(divide(A,A))
% Rule [26] inverse(inverse(divide(A,A))) <-> inverse(divide(c3,c3)) collapsed.
% Rule [32] inverse(divide(inverse(inverse(divide(A,A))),B)) -> B collapsed.
% Rule [33] inverse(divide(inverse(inverse(inverse(divide(A,A)))),B)) -> B
% collapsed.
% Rule
% [41] inverse(divide(inverse(inverse(inverse(inverse(divide(A,A))))),B)) -> B
% collapsed.
% Current number of equations to process: 51
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [46] inverse(divide(A,A)) <-> inverse(inverse(divide(B,B)))
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [47] inverse(divide(A,divide(B,B))) -> inverse(A)
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [48] inverse(inverse(inverse(divide(B,B)))) <-> inverse(divide(A,A))
% Current number of equations to process: 51
% Current number of ordered equations: 1
% Current number of rules: 28
% New rule produced :
% [49] inverse(divide(A,A)) <-> inverse(inverse(inverse(divide(B,B))))
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [50] inverse(divide(B,divide(B,A))) -> inverse(A)
% Rule [11] divide(divide(A,B),inverse(divide(C,divide(C,B)))) -> A collapsed.
% Rule [36] divide(divide(A,inverse(divide(B,divide(B,C)))),C) -> A collapsed.
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [51] divide(divide(A,B),inverse(B)) -> A
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [52] divide(divide(A,inverse(C)),C) -> A
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 30
% Rule [35] divide(C,B) <-> inverse(divide(divide(A,divide(A,B)),C)) is composed into
% [35] divide(C,B) <-> inverse(divide(B,C))
% New rule produced : [53] divide(A,divide(A,B)) -> B
% Rule [34] inverse(divide(divide(A,divide(A,B)),C)) <-> divide(C,B) collapsed.
% Rule [50] inverse(divide(B,divide(B,A))) -> inverse(A) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% inverse(divide(inverse(c3),divide(a3,inverse(b3)))) = divide(a3,inverse(
% divide(b3,
% inverse(c3))))
%
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [54] inverse(inverse(inverse(inverse(divide(B,B))))) <-> inverse(divide(A,A))
% Current number of equations to process: 52
% Current number of ordered equations: 1
% Current number of rules: 30
% New rule produced :
% [55] inverse(divide(A,A)) <-> inverse(inverse(inverse(inverse(divide(B,B)))))
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [56] inverse(divide(B,divide(A,inverse(B)))) -> A
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 32
% Rule [54]
% inverse(inverse(inverse(inverse(divide(B,B))))) <-> inverse(divide(A,A)) is composed into
% [54] inverse(inverse(inverse(inverse(divide(B,B))))) <-> divide(A,A)
% Rule [48] inverse(inverse(inverse(divide(B,B)))) <-> inverse(divide(A,A)) is composed into
% [48] inverse(inverse(inverse(divide(B,B)))) <-> divide(A,A)
% Rule [42]
% inverse(inverse(inverse(inverse(inverse(divide(B,B)))))) <->
% inverse(divide(A,A)) is composed into [42]
% inverse(inverse(inverse(inverse(
% inverse(
% divide(B,B))))))
% <-> divide(A,A)
% New rule produced : [57] inverse(divide(B,B)) <-> divide(A,A)
% Rule [27] inverse(divide(c3,c3)) <-> inverse(divide(A,A)) collapsed.
% Rule [31] inverse(divide(inverse(divide(A,A)),B)) -> B collapsed.
% Rule
% [43]
% inverse(divide(A,A)) <->
% inverse(inverse(inverse(inverse(inverse(divide(B,B)))))) collapsed.
% Rule [45] inverse(inverse(divide(B,B))) <-> inverse(divide(A,A)) collapsed.
% Rule [46] inverse(divide(A,A)) <-> inverse(inverse(divide(B,B))) collapsed.
% Rule [49] inverse(divide(A,A)) <-> inverse(inverse(inverse(divide(B,B))))
% collapsed.
% Rule
% [55] inverse(divide(A,A)) <-> inverse(inverse(inverse(inverse(divide(B,B)))))
% collapsed.
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [58] inverse(inverse(divide(B,B))) <-> divide(A,A)
% Current number of equations to process: 63
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced : [59] divide(A,A) <-> inverse(inverse(divide(B,B)))
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [60] divide(divide(A,B),divide(divide(C,C),B)) -> A
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 29
% Rule [59] divide(A,A) <-> inverse(inverse(divide(B,B))) is composed into
% [59] divide(A,A) <-> divide(B,B)
% New rule produced : [61] inverse(inverse(A)) -> A
% Rule [6] divide(A,inverse(inverse(divide(B,B)))) -> A collapsed.
% Rule [8] divide(A,inverse(inverse(inverse(inverse(divide(B,B)))))) -> A
% collapsed.
% Rule [10] divide(A,inverse(inverse(inverse(divide(B,B))))) -> A collapsed.
% Rule
% [19] divide(A,inverse(inverse(inverse(inverse(inverse(divide(B,B))))))) -> A
% collapsed.
% Rule
% [42] inverse(inverse(inverse(inverse(inverse(divide(B,B)))))) <-> divide(A,A)
% collapsed.
% Rule [48] inverse(inverse(inverse(divide(B,B)))) <-> divide(A,A) collapsed.
% Rule [54] inverse(inverse(inverse(inverse(divide(B,B))))) <-> divide(A,A)
% collapsed.
% Rule [58] inverse(inverse(divide(B,B))) <-> divide(A,A) collapsed.
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [62] divide(A,divide(B,B)) -> A
% Rule [47] inverse(divide(A,divide(B,B))) -> inverse(A) collapsed.
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [63] inverse(divide(inverse(divide(B,B)),A)) -> A
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [64] inverse(divide(A,divide(divide(C,C),B))) <-> divide(inverse(A),B)
% Current number of equations to process: 59
% Current number of ordered equations: 2
% Current number of rules: 24
% New rule produced :
% [65] inverse(divide(divide(divide(C,C),A),B)) -> divide(A,inverse(B))
% Current number of equations to process: 59
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [66] divide(inverse(A),B) <-> inverse(divide(A,divide(divide(C,C),B)))
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 26
% Rule [66] divide(inverse(A),B) <-> inverse(divide(A,divide(divide(C,C),B))) is composed into
% [66] divide(inverse(A),B) -> inverse(divide(A,inverse(B)))
% New rule produced : [67] divide(divide(B,B),A) -> inverse(A)
% Rule [23] inverse(divide(divide(A,A),B)) -> B collapsed.
% Rule [60] divide(divide(A,B),divide(divide(C,C),B)) -> A collapsed.
% Rule [64] inverse(divide(A,divide(divide(C,C),B))) <-> divide(inverse(A),B)
% collapsed.
% Rule [65] inverse(divide(divide(divide(C,C),A),B)) -> divide(A,inverse(B))
% collapsed.
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [68] divide(B,inverse(divide(A,C))) <-> divide(A,inverse(divide(B,C)))
% The conjecture has been reduced.
% Conjecture is now:
% divide(c3,inverse(divide(a3,inverse(b3)))) = divide(b3,inverse(divide(a3,
% inverse(c3))))
%
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [69] inverse(divide(divide(A,B),divide(A,C))) -> divide(B,C)
% Current number of equations to process: 72
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [70] divide(A,divide(divide(A,B),inverse(C))) -> divide(B,C)
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 26
% Rule [37] divide(C,B) <-> divide(divide(A,B),inverse(divide(C,A))) is composed into
% [37] divide(C,B) <-> inverse(divide(B,C))
% New rule produced :
% [71] divide(divide(C,A),inverse(divide(B,C))) -> inverse(divide(A,B))
% Rule [38] divide(divide(A,B),inverse(divide(C,A))) <-> divide(C,B) collapsed.
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [72] divide(A,inverse(divide(B,divide(A,divide(C,B))))) -> C
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [73]
% inverse(divide(C,B)) <-> inverse(divide(A,divide(B,inverse(divide(A,C)))))
% Current number of equations to process: 69
% Current number of ordered equations: 1
% Current number of rules: 28
% New rule produced :
% [74]
% inverse(divide(A,divide(B,inverse(divide(A,C))))) <-> inverse(divide(C,B))
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [75]
% inverse(divide(B,inverse(divide(divide(A,B),C)))) -> inverse(divide(A,C))
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [76] divide(A,B) <-> divide(C,divide(B,inverse(divide(C,A))))
% Rule [51] divide(divide(A,B),inverse(B)) -> A collapsed.
% Rule [52] divide(divide(A,inverse(C)),C) -> A collapsed.
% Rule
% [73]
% inverse(divide(C,B)) <-> inverse(divide(A,divide(B,inverse(divide(A,C)))))
% collapsed.
% Current number of equations to process: 74
% Current number of ordered equations: 1
% Current number of rules: 28
% New rule produced :
% [77] divide(C,divide(B,inverse(divide(C,A)))) <-> divide(A,B)
% Rule
% [74]
% inverse(divide(A,divide(B,inverse(divide(A,C))))) <-> inverse(divide(C,B))
% collapsed.
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 28
% Rule [39]
% inverse(divide(C,B)) <->
% divide(A,inverse(divide(B,divide(A,inverse(C))))) is composed into
% [39] inverse(divide(C,B)) <-> divide(B,C)
% New rule produced :
% [78] divide(C,inverse(divide(A,divide(C,inverse(B))))) -> divide(A,B)
% Rule [15] divide(A,inverse(divide(B,divide(A,inverse(divide(B,C)))))) -> C
% collapsed.
% Rule
% [40]
% divide(A,inverse(divide(B,divide(A,inverse(C))))) <-> inverse(divide(C,B))
% collapsed.
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [79] divide(A,divide(B,divide(C,A))) -> inverse(divide(B,C))
% Rule [72] divide(A,inverse(divide(B,divide(A,divide(C,B))))) -> C collapsed.
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [80] divide(B,divide(A,inverse(B))) -> inverse(A)
% Rule [56] inverse(divide(B,divide(A,inverse(B)))) -> A collapsed.
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [81] divide(divide(A,C),divide(B,C)) -> divide(A,B)
% Rule [21] inverse(divide(divide(A,C),divide(B,C))) -> inverse(divide(A,B))
% collapsed.
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [82] inverse(divide(A,inverse(B))) <-> inverse(divide(B,inverse(A)))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 28
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 16 rules have been used:
% [1]
% multiply(A,B) -> divide(A,inverse(B)); trace = in the starting set
% [2] divide(A,inverse(divide(divide(B,C),divide(A,C)))) -> B; trace = in the starting set
% [3] divide(A,inverse(divide(B,divide(A,inverse(divide(divide(B,C),divide(V_3,C)))))))
% -> V_3; trace = Self cp of 2
% [5] divide(A,inverse(divide(B,B))) -> A; trace = Cp of 3 and 2
% [7] divide(A,inverse(divide(B,A))) -> B; trace = Cp of 5 and 2
% [9] divide(inverse(divide(A,B)),inverse(A)) -> B; trace = Self cp of 7
% [11] divide(divide(A,B),inverse(divide(C,divide(C,B)))) -> A; trace = Cp of 7 and 3
% [15] divide(A,inverse(divide(B,divide(A,inverse(divide(B,C)))))) -> C; trace = Cp of 5 and 3
% [23] inverse(divide(divide(A,A),B)) -> B; trace = Cp of 9 and 5
% [28] divide(inverse(A),inverse(B)) -> inverse(divide(A,B)); trace = Cp of 9 and 7
% [35] divide(C,B) <-> inverse(divide(B,C)); trace = Cp of 11 and 7
% [38] divide(divide(A,B),inverse(divide(C,A))) <-> divide(C,B); trace = Cp of 15 and 11
% [53] divide(A,divide(A,B)) -> B; trace = Cp of 23 and 15
% [66] divide(inverse(A),B) -> inverse(divide(A,inverse(B))); trace = Cp of 28 and 23
% [68] divide(B,inverse(divide(A,C))) <-> divide(A,inverse(divide(B,C))); trace = Cp of 38 and 7
% [82] inverse(divide(A,inverse(B))) <-> inverse(divide(B,inverse(A))); trace = Cp of 66 and 35
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.120000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------