TSTP Solution File: GRP433-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP433-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n135.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 00:23:05 EDT 2014
% Result : Unsatisfiable 1.31s
% Output : Refutation 1.31s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP433-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n135.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Fri Jun 6 13:20:03 CDT 2014
% % CPUTime : 1.31
% Processing problem /tmp/CiME_64107_n135.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b1,a1 : constant; inverse : 1; multiply : 2;";
% let X = vars "A B C D";
% let Axioms = equations F X "
% inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D)))) = C;
% ";
%
% let s1 = status F "
% b1 lr_lex;
% a1 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > inverse > a1 > b1";
%
% let s2 = status F "
% b1 mul;
% a1 mul;
% inverse mul;
% multiply mul;
% ";
%
% let p2 = precedence F "
% multiply > inverse > a1 = b1";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(inverse(a1),a1) = multiply(inverse(b1),b1);"
% ;
% (*
% 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 = { inverse(multiply(multiply(multiply(inverse(
% multiply(
% multiply(A,B),C)),A),B),
% multiply(D,inverse(D)))) = C }
% (1 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(inverse(a1),a1) =
% multiply(inverse(b1),b1) } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced :
% [1]
% inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),
% multiply(D,inverse(D)))) -> C
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 1
% New rule produced :
% [2]
% inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),
% multiply(D,inverse(D)))) <-> multiply(V_4,inverse(V_4))
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3] multiply(b1,inverse(b1)) <-> multiply(V_4,inverse(V_4))
% Current number of equations to process: 1
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced :
% [4] multiply(V_4,inverse(V_4)) <-> multiply(b1,inverse(b1))
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [5]
% inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),B)),b1),
% inverse(b1)),multiply(C,inverse(C)))) -> B
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6]
% inverse(multiply(multiply(multiply(inverse(multiply(b1,inverse(b1))),A),B),
% multiply(C,inverse(C)))) -> inverse(multiply(A,B))
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7]
% inverse(multiply(multiply(multiply(inverse(multiply(multiply(b1,inverse(b1)),A)),B),
% inverse(B)),multiply(C,inverse(C)))) -> A
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8]
% multiply(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),
% multiply(D,inverse(D))),C) -> multiply(b1,inverse(b1))
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9]
% inverse(multiply(multiply(inverse(multiply(multiply(B,C),inverse(multiply(b1,
% inverse(b1))))),B),C))
% <-> multiply(A,inverse(A))
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10]
% inverse(multiply(multiply(multiply(inverse(multiply(A,inverse(A))),B),C),
% multiply(D,inverse(D)))) -> inverse(multiply(B,C))
% Rule
% [6]
% inverse(multiply(multiply(multiply(inverse(multiply(b1,inverse(b1))),A),B),
% multiply(C,inverse(C)))) -> inverse(multiply(A,B)) collapsed.
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [11]
% inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),B)),C),
% inverse(C)),multiply(D,inverse(D)))) -> B
% Rule
% [5]
% inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),B)),b1),
% inverse(b1)),multiply(C,inverse(C)))) -> B collapsed.
% Rule
% [7]
% inverse(multiply(multiply(multiply(inverse(multiply(multiply(b1,inverse(b1)),A)),B),
% inverse(B)),multiply(C,inverse(C)))) -> A collapsed.
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [12]
% inverse(multiply(multiply(inverse(multiply(multiply(A,B),inverse(multiply(C,
% inverse(C))))),A),B))
% <-> multiply(D,inverse(D))
% Rule
% [9]
% inverse(multiply(multiply(inverse(multiply(multiply(B,C),inverse(multiply(b1,
% inverse(b1))))),B),C))
% <-> multiply(A,inverse(A)) collapsed.
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [13] multiply(A,inverse(A)) <-> multiply(B,inverse(B))
% Rule [3] multiply(b1,inverse(b1)) <-> multiply(V_4,inverse(V_4)) collapsed.
% Rule [4] multiply(V_4,inverse(V_4)) <-> multiply(b1,inverse(b1)) collapsed.
% Current number of equations to process: 41
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [14]
% inverse(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),inverse(
% multiply(b1,
% inverse(b1))))),b1),
% inverse(b1))) <-> multiply(B,inverse(B))
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [15]
% inverse(multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(B))) <->
% multiply(C,inverse(C))
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [16]
% inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(D))),C)))) <->
% inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B))))
% Current number of equations to process: 87
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced :
% [17]
% inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))) <->
% inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(D))),C))))
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [18]
% inverse(multiply(inverse(inverse(multiply(D,inverse(D)))),B)) <->
% inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(C,inverse(C))))
% Current number of equations to process: 86
% Current number of ordered equations: 1
% Current number of rules: 12
% Rule [18]
% inverse(multiply(inverse(inverse(multiply(D,inverse(D)))),B)) <->
% inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(C,inverse(C)))) is composed into
% [18]
% inverse(multiply(inverse(inverse(multiply(D,inverse(D)))),B)) <->
% inverse(multiply(inverse(inverse(multiply(b1,inverse(b1)))),B))
% New rule produced :
% [19]
% inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(C,inverse(C))))
% <-> inverse(multiply(inverse(inverse(multiply(D,inverse(D)))),B))
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [20]
% inverse(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),inverse(
% multiply(B,
% inverse(B))))),C),
% inverse(C))) <-> multiply(D,inverse(D))
% Rule
% [14]
% inverse(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),inverse(
% multiply(b1,
% inverse(b1))))),b1),
% inverse(b1))) <-> multiply(B,inverse(B)) collapsed.
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [21]
% inverse(multiply(inverse(inverse(multiply(b1,inverse(b1)))),inverse(multiply(A,
% inverse(A)))))
% <-> multiply(B,inverse(B))
% Current number of equations to process: 100
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [22]
% inverse(multiply(multiply(A,inverse(A)),inverse(inverse(inverse(multiply(B,
% inverse(B)))))))
% <-> multiply(C,inverse(C))
% Current number of equations to process: 99
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [23]
% multiply(D,inverse(D)) <->
% multiply(multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(B)),
% multiply(C,inverse(C)))
% Current number of equations to process: 98
% Current number of ordered equations: 1
% Current number of rules: 16
% Rule [23]
% multiply(D,inverse(D)) <->
% multiply(multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(B)),
% multiply(C,inverse(C))) is composed into [23]
% multiply(D,inverse(D)) <->
% multiply(b1,inverse(b1))
% New rule produced :
% [24]
% multiply(multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(B)),
% multiply(C,inverse(C))) <-> multiply(D,inverse(D))
% Current number of equations to process: 98
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [25]
% inverse(multiply(inverse(multiply(B,inverse(B))),multiply(C,inverse(C)))) <->
% multiply(A,inverse(A))
% Current number of equations to process: 105
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [26]
% inverse(multiply(multiply(C,inverse(C)),multiply(D,inverse(D)))) <->
% inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(B,
% inverse(B)))))
% Current number of equations to process: 122
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [27]
% inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(B,
% inverse(B)))))
% <-> inverse(multiply(multiply(C,inverse(C)),multiply(D,inverse(D))))
% Rule
% [21]
% inverse(multiply(inverse(inverse(multiply(b1,inverse(b1)))),inverse(multiply(A,
% inverse(A)))))
% <-> multiply(B,inverse(B)) collapsed.
% Current number of equations to process: 123
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [28]
% inverse(multiply(multiply(b1,inverse(b1)),multiply(b1,inverse(b1)))) <->
% multiply(B,inverse(B))
% Current number of equations to process: 122
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [29]
% inverse(multiply(A,inverse(A))) <->
% inverse(multiply(inverse(inverse(multiply(b1,inverse(b1)))),inverse(inverse(
% inverse(
% multiply(B,
% inverse(B)))))))
% Current number of equations to process: 129
% Current number of ordered equations: 1
% Current number of rules: 21
% Rule [29]
% inverse(multiply(A,inverse(A))) <->
% inverse(multiply(inverse(inverse(multiply(b1,inverse(b1)))),inverse(
% inverse(
% inverse(
% multiply(B,
% inverse(B))))))) is composed into
% [29] inverse(multiply(A,inverse(A))) <-> inverse(multiply(b1,inverse(b1)))
% New rule produced :
% [30]
% inverse(multiply(inverse(inverse(multiply(b1,inverse(b1)))),inverse(inverse(
% inverse(
% multiply(B,
% inverse(B)))))))
% <-> inverse(multiply(A,inverse(A)))
% Current number of equations to process: 129
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [31]
% inverse(multiply(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,
% inverse(B)))),C),
% multiply(D,inverse(D)))) -> inverse(C)
% Current number of equations to process: 144
% Current number of ordered equations: 0
% Current number of rules: 23
% Rule [27]
% inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(
% multiply(B,
% inverse(B)))))
% <-> inverse(multiply(multiply(C,inverse(C)),multiply(D,inverse(D)))) is composed into
% [27]
% inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(B,
% inverse(B)))))
% -> multiply(b1,inverse(b1))
% Rule [16]
% inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(D))),C))))
% <-> inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))) is composed into
% [16]
% inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(D))),C)))) ->
% multiply(b1,inverse(b1))
% New rule produced :
% [32]
% inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))) ->
% multiply(b1,inverse(b1))
% Rule
% [17]
% inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))) <->
% inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(D))),C))))
% collapsed.
% Rule
% [26]
% inverse(multiply(multiply(C,inverse(C)),multiply(D,inverse(D)))) <->
% inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(B,
% inverse(B)))))
% collapsed.
% Rule
% [28]
% inverse(multiply(multiply(b1,inverse(b1)),multiply(b1,inverse(b1)))) <->
% multiply(B,inverse(B)) collapsed.
% Current number of equations to process: 180
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [33]
% multiply(D,inverse(D)) <->
% multiply(multiply(inverse(multiply(A,inverse(A))),multiply(B,inverse(B))),
% multiply(C,inverse(C)))
% Current number of equations to process: 208
% Current number of ordered equations: 1
% Current number of rules: 22
% Rule [33]
% multiply(D,inverse(D)) <->
% multiply(multiply(inverse(multiply(A,inverse(A))),multiply(B,inverse(B))),
% multiply(C,inverse(C))) is composed into [33]
% multiply(D,inverse(D)) <->
% multiply(b1,inverse(b1))
% New rule produced :
% [34]
% multiply(multiply(inverse(multiply(A,inverse(A))),multiply(B,inverse(B))),
% multiply(C,inverse(C))) <-> multiply(D,inverse(D))
% Current number of equations to process: 208
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [35]
% inverse(inverse(inverse(multiply(D,inverse(D))))) <->
% inverse(multiply(multiply(multiply(multiply(A,inverse(A)),B),inverse(B)),
% multiply(C,inverse(C))))
% Current number of equations to process: 206
% Current number of ordered equations: 1
% Current number of rules: 24
% Rule [35]
% inverse(inverse(inverse(multiply(D,inverse(D))))) <->
% inverse(multiply(multiply(multiply(multiply(A,inverse(A)),B),inverse(B)),
% multiply(C,inverse(C)))) is composed into [35]
% inverse(inverse(
% inverse(
% multiply(D,
% inverse(D)))))
% <->
% inverse(inverse(
% inverse(
% multiply(b1,
% inverse(b1)))))
% New rule produced :
% [36]
% inverse(multiply(multiply(multiply(multiply(A,inverse(A)),B),inverse(B)),
% multiply(C,inverse(C)))) <->
% inverse(inverse(inverse(multiply(D,inverse(D)))))
% Current number of equations to process: 206
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [37]
% multiply(B,inverse(B)) <->
% multiply(multiply(A,inverse(A)),inverse(multiply(b1,inverse(b1))))
% Current number of equations to process: 215
% Current number of ordered equations: 1
% Current number of rules: 26
% Rule [37]
% multiply(B,inverse(B)) <->
% multiply(multiply(A,inverse(A)),inverse(multiply(b1,inverse(b1)))) is composed into
% [37] multiply(B,inverse(B)) <-> multiply(b1,inverse(b1))
% New rule produced :
% [38]
% multiply(multiply(A,inverse(A)),inverse(multiply(b1,inverse(b1)))) <->
% multiply(B,inverse(B))
% Current number of equations to process: 215
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [39]
% inverse(multiply(C,inverse(C))) <->
% inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(inverse(
% inverse(
% multiply(B,
% inverse(B)))))))
% Current number of equations to process: 221
% Current number of ordered equations: 1
% Current number of rules: 28
% Rule [39]
% inverse(multiply(C,inverse(C))) <->
% inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(
% inverse(
% inverse(
% multiply(B,
% inverse(B))))))) is composed into
% [39] inverse(multiply(C,inverse(C))) <-> inverse(multiply(b1,inverse(b1)))
% New rule produced :
% [40]
% inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(inverse(
% inverse(
% multiply(B,
% inverse(B)))))))
% <-> inverse(multiply(C,inverse(C)))
% Rule
% [30]
% inverse(multiply(inverse(inverse(multiply(b1,inverse(b1)))),inverse(inverse(
% inverse(
% multiply(B,
% inverse(B)))))))
% <-> inverse(multiply(A,inverse(A))) collapsed.
% Current number of equations to process: 221
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [41]
% multiply(D,inverse(D)) <->
% multiply(multiply(multiply(A,inverse(A)),inverse(inverse(inverse(multiply(B,
% inverse(B)))))),
% multiply(C,inverse(C)))
% Current number of equations to process: 220
% Current number of ordered equations: 1
% Current number of rules: 29
% Rule [41]
% multiply(D,inverse(D)) <->
% multiply(multiply(multiply(A,inverse(A)),inverse(inverse(inverse(
% multiply(B,
% inverse(B)))))),
% multiply(C,inverse(C))) is composed into [41]
% multiply(D,inverse(D)) <->
% multiply(b1,inverse(b1))
% New rule produced :
% [42]
% multiply(multiply(multiply(A,inverse(A)),inverse(inverse(inverse(multiply(B,
% inverse(B)))))),
% multiply(C,inverse(C))) <-> multiply(D,inverse(D))
% Current number of equations to process: 220
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [43]
% multiply(C,inverse(C)) <->
% multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(B,
% inverse(B)))),
% multiply(b1,inverse(b1)))
% Current number of equations to process: 217
% Current number of ordered equations: 1
% Current number of rules: 31
% Rule [43]
% multiply(C,inverse(C)) <->
% multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(
% multiply(B,
% inverse(B)))),
% multiply(b1,inverse(b1))) is composed into [43]
% multiply(C,inverse(C)) <->
% multiply(b1,inverse(b1))
% New rule produced :
% [44]
% multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(B,
% inverse(B)))),
% multiply(b1,inverse(b1))) <-> multiply(C,inverse(C))
% Current number of equations to process: 217
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [45]
% inverse(multiply(multiply(inverse(multiply(A,inverse(A))),multiply(B,
% inverse(B))),
% inverse(multiply(b1,inverse(b1))))) <-> multiply(C,inverse(C))
% Current number of equations to process: 215
% Current number of ordered equations: 0
% Current number of rules: 33
% Rule [18]
% inverse(multiply(inverse(inverse(multiply(D,inverse(D)))),B)) <->
% inverse(multiply(inverse(inverse(multiply(b1,inverse(b1)))),B)) is composed into
% [18]
% inverse(multiply(inverse(inverse(multiply(D,inverse(D)))),B)) -> inverse(B)
% New rule produced :
% [46]
% inverse(multiply(inverse(inverse(multiply(b1,inverse(b1)))),A)) -> inverse(A)
% Current number of equations to process: 222
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [47]
% inverse(inverse(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B))))))
% -> multiply(b1,inverse(b1))
% Current number of equations to process: 221
% Current number of ordered equations: 0
% Current number of rules: 35
% Rule [35]
% inverse(inverse(inverse(multiply(D,inverse(D))))) <->
% inverse(inverse(inverse(multiply(b1,inverse(b1))))) is composed into
% [35]
% inverse(inverse(inverse(multiply(D,inverse(D))))) <->
% multiply(b1,inverse(b1))
% New rule produced :
% [48]
% inverse(inverse(inverse(multiply(b1,inverse(b1))))) <->
% multiply(A,inverse(A))
% Current number of equations to process: 235
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [49]
% multiply(C,inverse(C)) <->
% multiply(multiply(multiply(A,inverse(A)),multiply(B,inverse(B))),multiply(b1,
% inverse(b1)))
% Current number of equations to process: 238
% Current number of ordered equations: 1
% Current number of rules: 37
% Rule [49]
% multiply(C,inverse(C)) <->
% multiply(multiply(multiply(A,inverse(A)),multiply(B,inverse(B))),
% multiply(b1,inverse(b1))) is composed into [49]
% multiply(C,inverse(C)) <->
% multiply(b1,inverse(b1))
% New rule produced :
% [50]
% multiply(multiply(multiply(A,inverse(A)),multiply(B,inverse(B))),multiply(b1,
% inverse(b1)))
% <-> multiply(C,inverse(C))
% Current number of equations to process: 238
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [51] inverse(inverse(multiply(b1,inverse(b1)))) -> multiply(b1,inverse(b1))
% Rule
% [46]
% inverse(multiply(inverse(inverse(multiply(b1,inverse(b1)))),A)) -> inverse(A)
% collapsed.
% Rule
% [48]
% inverse(inverse(inverse(multiply(b1,inverse(b1))))) <->
% multiply(A,inverse(A)) collapsed.
% Current number of equations to process: 239
% Current number of ordered equations: 2
% Current number of rules: 37
% Rule [39]
% inverse(multiply(C,inverse(C))) <-> inverse(multiply(b1,inverse(b1))) is composed into
% [39] inverse(multiply(C,inverse(C))) <-> multiply(b1,inverse(b1))
% Rule [29]
% inverse(multiply(A,inverse(A))) <-> inverse(multiply(b1,inverse(b1))) is composed into
% [29] inverse(multiply(A,inverse(A))) <-> multiply(b1,inverse(b1))
% New rule produced :
% [52] inverse(multiply(b1,inverse(b1))) <-> multiply(A,inverse(A))
% Rule
% [38]
% multiply(multiply(A,inverse(A)),inverse(multiply(b1,inverse(b1)))) <->
% multiply(B,inverse(B)) collapsed.
% Rule
% [45]
% inverse(multiply(multiply(inverse(multiply(A,inverse(A))),multiply(B,
% inverse(B))),
% inverse(multiply(b1,inverse(b1))))) <-> multiply(C,inverse(C))
% collapsed.
% Rule
% [51] inverse(inverse(multiply(b1,inverse(b1)))) -> multiply(b1,inverse(b1))
% collapsed.
% Current number of equations to process: 239
% Current number of ordered equations: 2
% Current number of rules: 35
% New rule produced :
% [53] inverse(multiply(multiply(b1,inverse(b1)),A)) -> inverse(A)
% Current number of equations to process: 238
% Current number of ordered equations: 2
% Current number of rules: 36
% New rule produced :
% [54] inverse(inverse(multiply(A,inverse(A)))) <-> multiply(b1,inverse(b1))
% Current number of equations to process: 238
% Current number of ordered equations: 1
% Current number of rules: 37
% New rule produced :
% [55] multiply(b1,inverse(b1)) <-> inverse(inverse(multiply(A,inverse(A))))
% Current number of equations to process: 238
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [56]
% multiply(B,inverse(B)) <->
% multiply(multiply(A,inverse(A)),multiply(b1,inverse(b1)))
% Current number of equations to process: 237
% Current number of ordered equations: 1
% Current number of rules: 39
% Rule [56]
% multiply(B,inverse(B)) <->
% multiply(multiply(A,inverse(A)),multiply(b1,inverse(b1))) is composed into
% [56] multiply(B,inverse(B)) <-> multiply(b1,inverse(b1))
% New rule produced :
% [57]
% multiply(multiply(A,inverse(A)),multiply(b1,inverse(b1))) <->
% multiply(B,inverse(B))
% Current number of equations to process: 237
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [58]
% multiply(multiply(A,inverse(multiply(inverse(multiply(B,inverse(B))),A))),
% multiply(b1,inverse(b1))) -> multiply(b1,inverse(b1))
% Current number of equations to process: 237
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [59]
% inverse(multiply(multiply(multiply(A,multiply(inverse(A),B)),inverse(B)),
% multiply(C,inverse(C)))) <-> multiply(D,inverse(D))
% Current number of equations to process: 238
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [60]
% multiply(multiply(multiply(multiply(inverse(A),B),inverse(B)),multiply(C,
% inverse(C))),A)
% -> multiply(b1,inverse(b1))
% Current number of equations to process: 238
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [61]
% inverse(multiply(multiply(multiply(b1,inverse(b1)),A),inverse(A))) <->
% multiply(B,inverse(B))
% Current number of equations to process: 240
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [62]
% inverse(multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),B),
% inverse(B))) <-> multiply(C,inverse(C))
% Current number of equations to process: 239
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [63]
% inverse(multiply(multiply(multiply(inverse(A),B),inverse(B)),multiply(C,
% inverse(C)))) ->
% A
% Rule
% [11]
% inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),B)),C),
% inverse(C)),multiply(D,inverse(D)))) -> B collapsed.
% Current number of equations to process: 240
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [64] multiply(multiply(A,inverse(A)),B) -> B
% Rule
% [19]
% inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(C,inverse(C))))
% <-> inverse(multiply(inverse(inverse(multiply(D,inverse(D)))),B)) collapsed.
% Rule
% [20]
% inverse(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),inverse(
% multiply(B,
% inverse(B))))),C),
% inverse(C))) <-> multiply(D,inverse(D)) collapsed.
% Rule
% [22]
% inverse(multiply(multiply(A,inverse(A)),inverse(inverse(inverse(multiply(B,
% inverse(B)))))))
% <-> multiply(C,inverse(C)) collapsed.
% Rule
% [31]
% inverse(multiply(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,
% inverse(B)))),C),
% multiply(D,inverse(D)))) -> inverse(C) collapsed.
% Rule
% [32]
% inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))) ->
% multiply(b1,inverse(b1)) collapsed.
% Rule
% [36]
% inverse(multiply(multiply(multiply(multiply(A,inverse(A)),B),inverse(B)),
% multiply(C,inverse(C)))) <->
% inverse(inverse(inverse(multiply(D,inverse(D))))) collapsed.
% Rule
% [42]
% multiply(multiply(multiply(A,inverse(A)),inverse(inverse(inverse(multiply(B,
% inverse(B)))))),
% multiply(C,inverse(C))) <-> multiply(D,inverse(D)) collapsed.
% Rule
% [47]
% inverse(inverse(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B))))))
% -> multiply(b1,inverse(b1)) collapsed.
% Rule
% [50]
% multiply(multiply(multiply(A,inverse(A)),multiply(B,inverse(B))),multiply(b1,
% inverse(b1)))
% <-> multiply(C,inverse(C)) collapsed.
% Rule [53] inverse(multiply(multiply(b1,inverse(b1)),A)) -> inverse(A)
% collapsed.
% Rule
% [57]
% multiply(multiply(A,inverse(A)),multiply(b1,inverse(b1))) <->
% multiply(B,inverse(B)) collapsed.
% Rule
% [61]
% inverse(multiply(multiply(multiply(b1,inverse(b1)),A),inverse(A))) <->
% multiply(B,inverse(B)) collapsed.
% Current number of equations to process: 245
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [65] inverse(multiply(A,inverse(A))) <-> multiply(B,inverse(B))
% Rule
% [25]
% inverse(multiply(inverse(multiply(B,inverse(B))),multiply(C,inverse(C)))) <->
% multiply(A,inverse(A)) collapsed.
% Rule
% [27]
% inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(B,
% inverse(B)))))
% -> multiply(b1,inverse(b1)) collapsed.
% Rule [29] inverse(multiply(A,inverse(A))) <-> multiply(b1,inverse(b1))
% collapsed.
% Rule [39] inverse(multiply(C,inverse(C))) <-> multiply(b1,inverse(b1))
% collapsed.
% Rule
% [40]
% inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(inverse(
% inverse(
% multiply(B,
% inverse(B)))))))
% <-> inverse(multiply(C,inverse(C))) collapsed.
% Rule
% [44]
% multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(B,
% inverse(B)))),
% multiply(b1,inverse(b1))) <-> multiply(C,inverse(C)) collapsed.
% Rule [52] inverse(multiply(b1,inverse(b1))) <-> multiply(A,inverse(A))
% collapsed.
% Rule
% [58]
% multiply(multiply(A,inverse(multiply(inverse(multiply(B,inverse(B))),A))),
% multiply(b1,inverse(b1))) -> multiply(b1,inverse(b1)) collapsed.
% Current number of equations to process: 246
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [66] multiply(B,inverse(B)) <-> inverse(multiply(A,inverse(A)))
% Current number of equations to process: 246
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [67]
% inverse(multiply(C,inverse(C))) <->
% inverse(inverse(inverse(multiply(D,inverse(D)))))
% Current number of equations to process: 245
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [68]
% inverse(inverse(inverse(multiply(D,inverse(D))))) <->
% inverse(multiply(C,inverse(C)))
% Current number of equations to process: 245
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [69] inverse(multiply(B,multiply(C,inverse(C)))) -> inverse(B)
% Rule
% [1]
% inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),
% multiply(D,inverse(D)))) -> C collapsed.
% Rule
% [2]
% inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),
% multiply(D,inverse(D)))) <-> multiply(V_4,inverse(V_4)) collapsed.
% Rule
% [10]
% inverse(multiply(multiply(multiply(inverse(multiply(A,inverse(A))),B),C),
% multiply(D,inverse(D)))) -> inverse(multiply(B,C)) collapsed.
% Rule
% [59]
% inverse(multiply(multiply(multiply(A,multiply(inverse(A),B)),inverse(B)),
% multiply(C,inverse(C)))) <-> multiply(D,inverse(D)) collapsed.
% Rule
% [63]
% inverse(multiply(multiply(multiply(inverse(A),B),inverse(B)),multiply(C,
% inverse(C)))) ->
% A collapsed.
% Current number of equations to process: 248
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [70] inverse(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B)) -> C
% Rule
% [12]
% inverse(multiply(multiply(inverse(multiply(multiply(A,B),inverse(multiply(C,
% inverse(C))))),A),B))
% <-> multiply(D,inverse(D)) collapsed.
% Current number of equations to process: 247
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [71] inverse(multiply(multiply(inverse(A),B),inverse(B))) -> A
% Rule
% [15]
% inverse(multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(B))) <->
% multiply(C,inverse(C)) collapsed.
% Rule
% [62]
% inverse(multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),B),
% inverse(B))) <-> multiply(C,inverse(C)) collapsed.
% Current number of equations to process: 246
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [72]
% inverse(multiply(multiply(inverse(multiply(A,inverse(A))),B),C)) ->
% inverse(multiply(B,C))
% Current number of equations to process: 245
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [73]
% inverse(multiply(multiply(A,multiply(inverse(A),B)),inverse(B))) <->
% multiply(D,inverse(D))
% Current number of equations to process: 244
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [74]
% inverse(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C))
% <-> multiply(V_4,inverse(V_4))
% Current number of equations to process: 240
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [75]
% multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),B),inverse(B)) ->
% multiply(b1,inverse(b1))
% Current number of equations to process: 240
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [76]
% multiply(C,inverse(C)) <->
% multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),multiply(B,
% inverse(B))),
% multiply(b1,inverse(b1)))
% Current number of equations to process: 239
% Current number of ordered equations: 1
% Current number of rules: 30
% Rule [76]
% multiply(C,inverse(C)) <->
% multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),multiply(B,
% inverse(B))),
% multiply(b1,inverse(b1))) is composed into [76]
% multiply(C,inverse(C)) <->
% multiply(b1,inverse(b1))
% New rule produced :
% [77]
% multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),multiply(B,
% inverse(B))),
% multiply(b1,inverse(b1))) <-> multiply(C,inverse(C))
% Current number of equations to process: 239
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [78]
% multiply(B,inverse(B)) <->
% multiply(inverse(inverse(multiply(A,inverse(A)))),multiply(b1,inverse(b1)))
% Current number of equations to process: 239
% Current number of ordered equations: 1
% Current number of rules: 32
% Rule [78]
% multiply(B,inverse(B)) <->
% multiply(inverse(inverse(multiply(A,inverse(A)))),multiply(b1,inverse(b1))) is composed into
% [78] multiply(B,inverse(B)) <-> multiply(b1,inverse(b1))
% New rule produced :
% [79]
% multiply(inverse(inverse(multiply(A,inverse(A)))),multiply(b1,inverse(b1)))
% <-> multiply(B,inverse(B))
% Current number of equations to process: 239
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [80]
% inverse(inverse(inverse(inverse(multiply(A,inverse(A)))))) <->
% multiply(b1,inverse(b1))
% Current number of equations to process: 244
% Current number of ordered equations: 1
% Current number of rules: 34
% New rule produced :
% [81]
% multiply(b1,inverse(b1)) <->
% inverse(inverse(inverse(inverse(multiply(A,inverse(A))))))
% Current number of equations to process: 244
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [82]
% multiply(multiply(inverse(inverse(inverse(A))),multiply(B,inverse(B))),A) ->
% multiply(b1,inverse(b1))
% Current number of equations to process: 246
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [83] multiply(inverse(inverse(multiply(A,inverse(A)))),B) -> B
% Rule
% [18]
% inverse(multiply(inverse(inverse(multiply(D,inverse(D)))),B)) -> inverse(B)
% collapsed.
% Rule
% [75]
% multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),B),inverse(B)) ->
% multiply(b1,inverse(b1)) collapsed.
% Rule
% [77]
% multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),multiply(B,
% inverse(B))),
% multiply(b1,inverse(b1))) <-> multiply(C,inverse(C)) collapsed.
% Rule
% [79]
% multiply(inverse(inverse(multiply(A,inverse(A)))),multiply(b1,inverse(b1)))
% <-> multiply(B,inverse(B)) collapsed.
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [84]
% inverse(inverse(inverse(multiply(A,inverse(A))))) <-> multiply(B,inverse(B))
% Rule
% [35]
% inverse(inverse(inverse(multiply(D,inverse(D))))) <->
% multiply(b1,inverse(b1)) collapsed.
% Current number of equations to process: 251
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [85]
% multiply(B,inverse(B)) <-> inverse(inverse(inverse(multiply(A,inverse(A)))))
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [86] inverse(inverse(multiply(A,inverse(A)))) <-> multiply(B,inverse(B))
% Rule
% [54] inverse(inverse(multiply(A,inverse(A)))) <-> multiply(b1,inverse(b1))
% collapsed.
% Rule
% [68]
% inverse(inverse(inverse(multiply(D,inverse(D))))) <->
% inverse(multiply(C,inverse(C))) collapsed.
% Current number of equations to process: 255
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [87] multiply(B,inverse(B)) <-> inverse(inverse(multiply(A,inverse(A))))
% Rule
% [55] multiply(b1,inverse(b1)) <-> inverse(inverse(multiply(A,inverse(A))))
% collapsed.
% Rule
% [67]
% inverse(multiply(C,inverse(C))) <->
% inverse(inverse(inverse(multiply(D,inverse(D))))) collapsed.
% Current number of equations to process: 255
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [88] multiply(inverse(multiply(A,inverse(A))),B) -> B
% Rule
% [16]
% inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(D))),C)))) ->
% multiply(b1,inverse(b1)) collapsed.
% Rule
% [24]
% multiply(multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(B)),
% multiply(C,inverse(C))) <-> multiply(D,inverse(D)) collapsed.
% Rule
% [34]
% multiply(multiply(inverse(multiply(A,inverse(A))),multiply(B,inverse(B))),
% multiply(C,inverse(C))) <-> multiply(D,inverse(D)) collapsed.
% Rule
% [72]
% inverse(multiply(multiply(inverse(multiply(A,inverse(A))),B),C)) ->
% inverse(multiply(B,C)) collapsed.
% Current number of equations to process: 256
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [89]
% multiply(multiply(A,multiply(B,inverse(B))),inverse(A)) ->
% multiply(b1,inverse(b1))
% Current number of equations to process: 258
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [90]
% multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),C) ->
% multiply(b1,inverse(b1))
% Current number of equations to process: 262
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [91]
% inverse(multiply(multiply(inverse(multiply(A,B)),A),B)) <->
% multiply(C,inverse(C))
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [92] inverse(multiply(multiply(A,inverse(multiply(multiply(B,C),A))),B)) -> C
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [93]
% inverse(multiply(multiply(inverse(multiply(A,B)),multiply(C,inverse(C))),A))
% -> B
% Current number of equations to process: 267
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [94]
% inverse(multiply(inverse(multiply(multiply(A,multiply(B,inverse(B))),C)),A))
% -> C
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 35
% Rule [81]
% multiply(b1,inverse(b1)) <->
% inverse(inverse(inverse(inverse(multiply(A,inverse(A)))))) is composed into
% [81] multiply(b1,inverse(b1)) <-> multiply(A,inverse(A))
% New rule produced : [95] inverse(inverse(inverse(inverse(A)))) -> A
% Rule
% [80]
% inverse(inverse(inverse(inverse(multiply(A,inverse(A)))))) <->
% multiply(b1,inverse(b1)) collapsed.
% Current number of equations to process: 267
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [96]
% multiply(multiply(multiply(inverse(A),B),inverse(B)),A) ->
% multiply(b1,inverse(b1))
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 36
% Rule [87] multiply(B,inverse(B)) <-> inverse(inverse(multiply(A,inverse(A)))) is composed into
% [87] multiply(B,inverse(B)) <-> multiply(A,inverse(A))
% Rule [85]
% multiply(B,inverse(B)) <->
% inverse(inverse(inverse(multiply(A,inverse(A))))) is composed into
% [85] multiply(B,inverse(B)) <-> inverse(multiply(A,inverse(A)))
% New rule produced : [97] inverse(inverse(A)) -> A
% Rule
% [82]
% multiply(multiply(inverse(inverse(inverse(A))),multiply(B,inverse(B))),A) ->
% multiply(b1,inverse(b1)) collapsed.
% Rule [83] multiply(inverse(inverse(multiply(A,inverse(A)))),B) -> B
% collapsed.
% Rule
% [84]
% inverse(inverse(inverse(multiply(A,inverse(A))))) <-> multiply(B,inverse(B))
% collapsed.
% Rule [86] inverse(inverse(multiply(A,inverse(A)))) <-> multiply(B,inverse(B))
% collapsed.
% Rule [95] inverse(inverse(inverse(inverse(A)))) -> A collapsed.
% Current number of equations to process: 267
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [98] multiply(A,multiply(B,inverse(B))) -> A
% Rule
% [8]
% multiply(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),
% multiply(D,inverse(D))),C) -> multiply(b1,inverse(b1)) collapsed.
% Rule
% [60]
% multiply(multiply(multiply(multiply(inverse(A),B),inverse(B)),multiply(C,
% inverse(C))),A)
% -> multiply(b1,inverse(b1)) collapsed.
% Rule [69] inverse(multiply(B,multiply(C,inverse(C)))) -> inverse(B)
% collapsed.
% Rule
% [89]
% multiply(multiply(A,multiply(B,inverse(B))),inverse(A)) ->
% multiply(b1,inverse(b1)) collapsed.
% Rule
% [93]
% inverse(multiply(multiply(inverse(multiply(A,B)),multiply(C,inverse(C))),A))
% -> B collapsed.
% Rule
% [94]
% inverse(multiply(inverse(multiply(multiply(A,multiply(B,inverse(B))),C)),A))
% -> C collapsed.
% Current number of equations to process: 270
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [99] inverse(multiply(inverse(multiply(A,B)),A)) -> B
% Current number of equations to process: 269
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [100]
% inverse(multiply(multiply(A,B),inverse(B))) <->
% multiply(multiply(inverse(A),C),inverse(C))
% Current number of equations to process: 271
% Current number of ordered equations: 1
% Current number of rules: 29
% Rule [100]
% inverse(multiply(multiply(A,B),inverse(B))) <->
% multiply(multiply(inverse(A),C),inverse(C)) is composed into [100]
% inverse(
% multiply(
% multiply(A,B),
% inverse(B)))
% <->
% inverse(
% multiply(
% multiply(A,b1),
% inverse(b1)))
% New rule produced :
% [101]
% multiply(multiply(inverse(A),C),inverse(C)) <->
% inverse(multiply(multiply(A,B),inverse(B)))
% Rule [71] inverse(multiply(multiply(inverse(A),B),inverse(B))) -> A
% collapsed.
% Rule
% [96]
% multiply(multiply(multiply(inverse(A),B),inverse(B)),A) ->
% multiply(b1,inverse(b1)) collapsed.
% Current number of equations to process: 273
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [102] multiply(multiply(A,B),inverse(B)) -> A
% Rule
% [100]
% inverse(multiply(multiply(A,B),inverse(B))) <->
% inverse(multiply(multiply(A,b1),inverse(b1))) collapsed.
% Rule
% [101]
% multiply(multiply(inverse(A),C),inverse(C)) <->
% inverse(multiply(multiply(A,B),inverse(B))) collapsed.
% Current number of equations to process: 272
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [103] multiply(inverse(A),A) -> multiply(b1,inverse(b1))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 271
% 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 15 rules have been used:
% [1]
% inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),
% multiply(D,inverse(D)))) -> C; trace = in the starting set
% [2] inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),
% multiply(D,inverse(D)))) <-> multiply(V_4,inverse(V_4)); trace = Self cp of 1
% [3] multiply(b1,inverse(b1)) <-> multiply(V_4,inverse(V_4)); trace = Self cp of 1
% [4] multiply(V_4,inverse(V_4)) <-> multiply(b1,inverse(b1)); trace = Self cp of 1
% [6] inverse(multiply(multiply(multiply(inverse(multiply(b1,inverse(b1))),A),B),
% multiply(C,inverse(C)))) -> inverse(multiply(A,B)); trace = Cp of 4 and 1
% [7] inverse(multiply(multiply(multiply(inverse(multiply(multiply(b1,inverse(b1)),A)),B),
% inverse(B)),multiply(C,inverse(C)))) -> A; trace = Cp of 4 and 1
% [8] multiply(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),
% multiply(D,inverse(D))),C) -> multiply(b1,inverse(b1)); trace = Cp of 4 and 1
% [10] inverse(multiply(multiply(multiply(inverse(multiply(A,inverse(A))),B),C),
% multiply(D,inverse(D)))) -> inverse(multiply(B,C)); trace = Cp of 6 and 3
% [11] inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),B)),C),
% inverse(C)),multiply(D,inverse(D)))) -> B; trace = Cp of 7 and 3
% [13] multiply(A,inverse(A)) <-> multiply(B,inverse(B)); trace = Cp of 10 and 2
% [16] inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(D))),C))))
% <-> inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))); trace = Cp of 13 and 10
% [25] inverse(multiply(inverse(multiply(B,inverse(B))),multiply(C,inverse(C))))
% <-> multiply(A,inverse(A)); trace = Cp of 16 and 11
% [33] multiply(D,inverse(D)) <-> multiply(b1,inverse(b1)); trace = Cp of 25 and 13
% [60] multiply(multiply(multiply(multiply(inverse(A),B),inverse(B)),multiply(C,
% inverse(C))),A)
% -> multiply(b1,inverse(b1)); trace = Cp of 33 and 8
% [103] multiply(inverse(A),A) -> multiply(b1,inverse(b1)); trace = Cp of 60 and 13
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.200000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------