TSTP Solution File: GRP511-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP511-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n137.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 00:23:23 EDT 2014
% Result : Unsatisfiable 1.63s
% Output : Refutation 1.63s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----WARNING: CiME---2.01 format not known, defaulting to TPTP
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP511-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n137.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 15:12:03 CDT 2014
% % CPUTime : 1.63
% Processing problem /tmp/CiME_13988_n137.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " c3,b3,a3 : constant; inverse : 1; multiply : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B;
% ";
%
% let s1 = status F "
% c3 lr_lex;
% b3 lr_lex;
% a3 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% ";
%
% let p1 = precedence F "
% inverse > multiply > a3 > b3 > c3";
%
% let s2 = status F "
% c3 mul;
% b3 mul;
% a3 mul;
% inverse mul;
% multiply mul;
% ";
%
% let p2 = precedence F "
% inverse > multiply > 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 = { multiply(multiply(multiply(A,B),C),inverse(
% multiply(A,C)))
% = B } (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(multiply(a3,b3),c3) =
% multiply(a3,multiply(b3,c3)) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced :
% [1] multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 1
% New rule produced :
% [2] multiply(A,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) -> C
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3]
% inverse(multiply(multiply(V_3,C),inverse(multiply(V_3,A)))) <->
% multiply(multiply(A,B),inverse(multiply(C,B)))
% Rule
% [2] multiply(A,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) -> C
% collapsed.
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [4] multiply(A,multiply(multiply(C,B),inverse(multiply(A,B)))) -> C
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [5]
% multiply(multiply(A,B),inverse(multiply(C,B))) <->
% multiply(multiply(A,V_3),inverse(multiply(C,V_3)))
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [6]
% multiply(multiply(B,C),inverse(multiply(B,C))) <->
% multiply(multiply(A,A),inverse(multiply(A,A)))
% Current number of equations to process: 35
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced :
% [7] multiply(A,inverse(A)) <-> multiply(multiply(B,B),inverse(multiply(B,B)))
% Rule
% [6]
% multiply(multiply(B,C),inverse(multiply(B,C))) <->
% multiply(multiply(A,A),inverse(multiply(A,A))) collapsed.
% Current number of equations to process: 37
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced :
% [8] multiply(A,multiply(multiply(B,B),inverse(multiply(B,B)))) -> A
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 6
% New rule produced : [9] multiply(multiply(A,B),inverse(A)) -> B
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 7
% Rule [7]
% multiply(A,inverse(A)) <->
% multiply(multiply(B,B),inverse(multiply(B,B))) is composed into
% [7] multiply(A,inverse(A)) <-> multiply(B,inverse(B))
% Rule [3]
% inverse(multiply(multiply(V_3,C),inverse(multiply(V_3,A)))) <->
% multiply(multiply(A,B),inverse(multiply(C,B))) is composed into
% [3]
% inverse(multiply(multiply(V_3,C),inverse(multiply(V_3,A)))) ->
% multiply(A,inverse(C))
% New rule produced :
% [10] multiply(multiply(A,C),inverse(multiply(B,C))) -> multiply(A,inverse(B))
% Rule [1] multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) -> B
% collapsed.
% Rule [4] multiply(A,multiply(multiply(C,B),inverse(multiply(A,B)))) -> C
% collapsed.
% Rule
% [5]
% multiply(multiply(A,B),inverse(multiply(C,B))) <->
% multiply(multiply(A,V_3),inverse(multiply(C,V_3))) collapsed.
% Rule [8] multiply(A,multiply(multiply(B,B),inverse(multiply(B,B)))) -> A
% collapsed.
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [11] multiply(A,multiply(C,inverse(A))) -> C
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [12] multiply(A,multiply(B,inverse(B))) -> A
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [13] multiply(A,inverse(multiply(B,A))) -> inverse(B)
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [14] multiply(multiply(A,inverse(A)),inverse(B)) -> inverse(B)
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [15] inverse(multiply(A,inverse(B))) -> multiply(B,inverse(A))
% Rule
% [3]
% inverse(multiply(multiply(V_3,C),inverse(multiply(V_3,A)))) ->
% multiply(A,inverse(C)) collapsed.
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [16]
% multiply(multiply(V_3,A),inverse(multiply(V_3,C))) -> multiply(A,inverse(C))
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [17] inverse(multiply(A,B)) -> multiply(inverse(A),inverse(B))
% Rule
% [10] multiply(multiply(A,C),inverse(multiply(B,C))) -> multiply(A,inverse(B))
% collapsed.
% Rule [13] multiply(A,inverse(multiply(B,A))) -> inverse(B) collapsed.
% Rule [15] inverse(multiply(A,inverse(B))) -> multiply(B,inverse(A))
% collapsed.
% Rule
% [16]
% multiply(multiply(V_3,A),inverse(multiply(V_3,C))) -> multiply(A,inverse(C))
% collapsed.
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [18] multiply(B,inverse(A)) <-> multiply(inverse(A),inverse(inverse(B)))
% Current number of equations to process: 58
% Current number of ordered equations: 1
% Current number of rules: 7
% New rule produced :
% [19] multiply(inverse(A),inverse(inverse(B))) <-> multiply(B,inverse(A))
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [20] multiply(A,multiply(inverse(A),inverse(inverse(B)))) -> B
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [21] multiply(inverse(A),multiply(A,inverse(B))) -> inverse(B)
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [22] multiply(multiply(B,A),inverse(C)) -> multiply(A,multiply(B,inverse(C)))
% Rule [9] multiply(multiply(A,B),inverse(A)) -> B collapsed.
% Rule [14] multiply(multiply(A,inverse(A)),inverse(B)) -> inverse(B)
% collapsed.
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 9
% Rule [18] multiply(B,inverse(A)) <-> multiply(inverse(A),inverse(inverse(B))) is composed into
% [18] multiply(B,inverse(A)) <-> multiply(inverse(A),B)
% New rule produced : [23] inverse(inverse(A)) -> A
% Rule [19] multiply(inverse(A),inverse(inverse(B))) <-> multiply(B,inverse(A))
% collapsed.
% Rule [20] multiply(A,multiply(inverse(A),inverse(inverse(B)))) -> B
% collapsed.
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [24] multiply(A,multiply(inverse(A),B)) -> B
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [25] multiply(inverse(A),multiply(inverse(B),A)) -> inverse(B)
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 10
% multiply(B,A) = multiply(A,B) (birth = 134, lhs_size = 3, rhs_size = 3,trace = Cp of 23 and 18)
% Initializing completion ...
% New rule produced : [1] A <-> inverse(inverse(A))
% Current number of equations to process: 83
% Current number of ordered equations: 15
% Current number of rules: 1
% New rule produced : [2] inverse(inverse(A)) <-> A
% Current number of equations to process: 83
% Current number of ordered equations: 14
% Current number of rules: 2
% New rule produced : [3] A <-> (inverse(B) multiply B) multiply A
% Current number of equations to process: 82
% Current number of ordered equations: 17
% Current number of rules: 3
% New rule produced : [4] B <-> (inverse(A) multiply B) multiply A
% Current number of equations to process: 82
% Current number of ordered equations: 15
% Current number of rules: 4
% New rule produced : [5] (inverse(A) multiply B) multiply A <-> B
% Current number of equations to process: 82
% Current number of ordered equations: 13
% Current number of rules: 5
% New rule produced : [6] (inverse(B) multiply B) multiply A <-> A
% Current number of equations to process: 82
% Current number of ordered equations: 12
% Current number of rules: 6
% New rule produced :
% [7] inverse(A multiply B) <-> inverse(A) multiply inverse(B)
% Current number of equations to process: 110
% Current number of ordered equations: 17
% Current number of rules: 7
% New rule produced :
% [8] inverse(A) multiply inverse(B) <-> inverse(A multiply B)
% Current number of equations to process: 110
% Current number of ordered equations: 16
% Current number of rules: 8
% New rule produced :
% [9] inverse(B) <-> inverse(A) multiply (inverse(B) multiply A)
% Current number of equations to process: 123
% Current number of ordered equations: 31
% Current number of rules: 9
% New rule produced :
% [10] inverse(A) multiply (inverse(B) multiply A) <-> inverse(B)
% Current number of equations to process: 123
% Current number of ordered equations: 30
% Current number of rules: 10
% New rule produced :
% [11]
% inverse(C) multiply (A multiply B) <-> (inverse(C) multiply B) multiply A
% Current number of equations to process: 141
% Current number of ordered equations: 57
% Current number of rules: 11
% New rule produced :
% [12]
% (inverse(C) multiply B) multiply A <-> inverse(C) multiply (A multiply B)
% Current number of equations to process: 141
% Current number of ordered equations: 56
% Current number of rules: 12
% New rule produced :
% [13] B <-> inverse(A multiply C) multiply ((A multiply B) multiply C)
% Current number of equations to process: 164
% Current number of ordered equations: 117
% Current number of rules: 13
% New rule produced :
% [14] inverse(A multiply C) multiply ((A multiply B) multiply C) <-> B
% Current number of equations to process: 164
% Current number of ordered equations: 116
% Current number of rules: 14
% New rule produced : [15] A <-> inverse(inverse(inverse(inverse(A))))
% Current number of equations to process: 164
% Current number of ordered equations: 115
% Current number of rules: 15
% New rule produced : [16] inverse(inverse(inverse(inverse(A)))) <-> A
% Current number of equations to process: 164
% Current number of ordered equations: 114
% Current number of rules: 16
% New rule produced : [17] inverse(B) multiply B <-> inverse(A) multiply A
% Current number of equations to process: 164
% Current number of ordered equations: 106
% Current number of rules: 17
% New rule produced : [18] B <-> inverse(A) multiply (A multiply B)
% Rule [9] inverse(B) <-> inverse(A) multiply (inverse(B) multiply A)
% collapsed.
% Current number of equations to process: 164
% Current number of ordered equations: 96
% Current number of rules: 17
% New rule produced : [19] inverse(A) multiply (A multiply B) <-> B
% Rule [10] inverse(A) multiply (inverse(B) multiply A) <-> inverse(B)
% collapsed.
% Current number of equations to process: 164
% Current number of ordered equations: 74
% Current number of rules: 17
% New rule produced :
% [20] inverse(inverse(B) multiply A) <-> inverse(A) multiply B
% Current number of equations to process: 167
% Current number of ordered equations: 73
% Current number of rules: 18
% New rule produced :
% [21] inverse(A) multiply B <-> inverse(inverse(B) multiply A)
% Current number of equations to process: 167
% Current number of ordered equations: 72
% Current number of rules: 19
% New rule produced : [22] inverse(B) <-> inverse(A multiply B) multiply A
% Current number of equations to process: 167
% Current number of ordered equations: 70
% Current number of rules: 20
% New rule produced : [23] inverse(A multiply B) multiply A <-> inverse(B)
% Current number of equations to process: 167
% Current number of ordered equations: 68
% Current number of rules: 21
% New rule produced :
% [24] inverse(inverse(A)) <-> (inverse(B) multiply B) multiply A
% Current number of equations to process: 167
% Current number of ordered equations: 67
% Current number of rules: 22
% New rule produced :
% [25] (inverse(B) multiply B) multiply A <-> inverse(inverse(A))
% Current number of equations to process: 167
% Current number of ordered equations: 66
% Current number of rules: 23
% New rule produced :
% [26] inverse(inverse(A)) <-> (inverse(B) multiply A) multiply B
% Current number of equations to process: 167
% Current number of ordered equations: 65
% Current number of rules: 24
% New rule produced :
% [27] (inverse(B) multiply A) multiply B <-> inverse(inverse(A))
% Current number of equations to process: 167
% Current number of ordered equations: 64
% Current number of rules: 25
% New rule produced : [28] B <-> inverse(inverse(A) multiply A) multiply B
% Current number of equations to process: 167
% Current number of ordered equations: 60
% Current number of rules: 26
% New rule produced : [29] inverse(inverse(A) multiply A) multiply B <-> B
% Current number of equations to process: 167
% Current number of ordered equations: 56
% Current number of rules: 27
% New rule produced :
% [30] inverse(inverse(A) multiply inverse(B)) <-> A multiply B
% Current number of equations to process: 167
% Current number of ordered equations: 54
% Current number of rules: 28
% New rule produced :
% [31] A multiply B <-> inverse(inverse(A) multiply inverse(B))
% Current number of equations to process: 167
% Current number of ordered equations: 52
% Current number of rules: 29
% New rule produced :
% [32] A <-> inverse(inverse(A) multiply (inverse(B) multiply B))
% Current number of equations to process: 175
% Current number of ordered equations: 51
% Current number of rules: 30
% New rule produced :
% [33] A <-> inverse(inverse(A)) multiply (inverse(B) multiply B)
% Current number of equations to process: 175
% Current number of ordered equations: 50
% Current number of rules: 31
% New rule produced :
% [34] inverse(inverse(A) multiply (inverse(B) multiply B)) <-> A
% Current number of equations to process: 175
% Current number of ordered equations: 49
% Current number of rules: 32
% New rule produced :
% [35] inverse(inverse(A)) multiply (inverse(B) multiply B) <-> A
% Current number of equations to process: 175
% Current number of ordered equations: 48
% Current number of rules: 33
% New rule produced :
% [36] A <-> inverse((inverse(A) multiply inverse(B)) multiply B)
% Current number of equations to process: 175
% Current number of ordered equations: 47
% Current number of rules: 34
% New rule produced :
% [37] A <-> (inverse(inverse(A)) multiply inverse(B)) multiply B
% Current number of equations to process: 175
% Current number of ordered equations: 46
% Current number of rules: 35
% New rule produced :
% [38] inverse((inverse(A) multiply inverse(B)) multiply B) <-> A
% Current number of equations to process: 175
% Current number of ordered equations: 45
% Current number of rules: 36
% New rule produced :
% [39] (inverse(inverse(A)) multiply inverse(B)) multiply B <-> A
% Current number of equations to process: 175
% Current number of ordered equations: 44
% Current number of rules: 37
% New rule produced :
% [40] B <-> inverse(inverse((inverse(A) multiply B) multiply A))
% Current number of equations to process: 175
% Current number of ordered equations: 43
% Current number of rules: 38
% New rule produced :
% [41] B <-> inverse(inverse(inverse(A) multiply B)) multiply A
% Current number of equations to process: 175
% Current number of ordered equations: 42
% Current number of rules: 39
% New rule produced :
% [42] B <-> (inverse(inverse(inverse(A))) multiply B) multiply A
% Current number of equations to process: 175
% Current number of ordered equations: 41
% Current number of rules: 40
% New rule produced :
% [43] inverse(inverse((inverse(A) multiply B) multiply A)) <-> B
% Current number of equations to process: 175
% Current number of ordered equations: 40
% Current number of rules: 41
% New rule produced :
% [44] inverse(inverse(inverse(A) multiply B)) multiply A <-> B
% Current number of equations to process: 175
% Current number of ordered equations: 39
% Current number of rules: 42
% New rule produced :
% [45] (inverse(inverse(inverse(A))) multiply B) multiply A <-> B
% Current number of equations to process: 175
% Current number of ordered equations: 38
% Current number of rules: 43
% New rule produced :
% [46] B <-> inverse(inverse((inverse(A) multiply A) multiply B))
% Current number of equations to process: 175
% Current number of ordered equations: 37
% Current number of rules: 44
% New rule produced :
% [47] B <-> inverse(inverse(inverse(A) multiply A)) multiply B
% Current number of equations to process: 175
% Current number of ordered equations: 36
% Current number of rules: 45
% New rule produced :
% [48] B <-> (inverse(inverse(inverse(A))) multiply A) multiply B
% Current number of equations to process: 175
% Current number of ordered equations: 35
% Current number of rules: 46
% New rule produced :
% [49] inverse(inverse((inverse(A) multiply A) multiply B)) <-> B
% Current number of equations to process: 175
% Current number of ordered equations: 34
% Current number of rules: 47
% New rule produced :
% [50] inverse(inverse(inverse(A) multiply A)) multiply B <-> B
% Current number of equations to process: 175
% Current number of ordered equations: 33
% Current number of rules: 48
% New rule produced :
% [51] (inverse(inverse(inverse(A))) multiply A) multiply B <-> B
% Current number of equations to process: 175
% Current number of ordered equations: 32
% Current number of rules: 49
% New rule produced :
% [52]
% inverse(inverse(inverse(A multiply B))) <-> inverse(A) multiply inverse(B)
% Current number of equations to process: 175
% Current number of ordered equations: 31
% Current number of rules: 50
% New rule produced :
% [53]
% inverse(A) multiply inverse(B) <-> inverse(inverse(inverse(A multiply B)))
% Current number of equations to process: 175
% Current number of ordered equations: 30
% Current number of rules: 51
% New rule produced :
% [54]
% inverse(A) multiply (B multiply C) <-> (inverse(A) multiply B) multiply C
% Current number of equations to process: 179
% Current number of ordered equations: 29
% Current number of rules: 52
% New rule produced :
% [55]
% (inverse(A) multiply B) multiply C <-> inverse(A) multiply (B multiply C)
% Current number of equations to process: 179
% Current number of ordered equations: 28
% Current number of rules: 53
% New rule produced :
% [56]
% (inverse(A) multiply B) multiply A <-> (inverse(C) multiply B) multiply C
% Current number of equations to process: 179
% Current number of ordered equations: 26
% Current number of rules: 54
% New rule produced :
% [57]
% (inverse(A) multiply A) multiply B <-> (inverse(C) multiply B) multiply C
% Current number of equations to process: 179
% Current number of ordered equations: 25
% Current number of rules: 55
% New rule produced :
% [58]
% (inverse(C) multiply B) multiply C <-> (inverse(A) multiply A) multiply B
% Current number of equations to process: 179
% Current number of ordered equations: 24
% Current number of rules: 56
% New rule produced :
% [59]
% inverse(A multiply B) <-> inverse(inverse(inverse(A))) multiply inverse(B)
% Current number of equations to process: 179
% Current number of ordered equations: 23
% Current number of rules: 57
% New rule produced :
% [60]
% inverse(inverse(inverse(A))) multiply inverse(B) <-> inverse(A multiply B)
% Current number of equations to process: 179
% Current number of ordered equations: 22
% Current number of rules: 58
% New rule produced :
% [61]
% (inverse(A) multiply B) multiply C <-> (inverse(A) multiply C) multiply B
% Current number of equations to process: 179
% Current number of ordered equations: 20
% Current number of rules: 59
% New rule produced :
% [62]
% inverse(inverse(A)) <-> inverse(inverse(B)) multiply (inverse(B) multiply A)
% Current number of equations to process: 179
% Current number of ordered equations: 19
% Current number of rules: 60
% New rule produced :
% [63] B multiply C <-> ((inverse(A) multiply C) multiply B) multiply A
% Current number of equations to process: 179
% Current number of ordered equations: 18
% Current number of rules: 61
% New rule produced :
% [64]
% inverse(inverse(B)) multiply (inverse(B) multiply A) <-> inverse(inverse(A))
% Current number of equations to process: 179
% Current number of ordered equations: 17
% Current number of rules: 62
% New rule produced :
% [65] ((inverse(A) multiply C) multiply B) multiply A <-> B multiply C
% Current number of equations to process: 179
% Current number of ordered equations: 16
% Current number of rules: 63
% New rule produced :
% [66]
% inverse(inverse(A multiply B)) <->
% inverse(inverse(A)) multiply inverse(inverse(B))
% Current number of equations to process: 179
% Current number of ordered equations: 15
% Current number of rules: 64
% New rule produced :
% [67]
% inverse(inverse(A)) multiply inverse(inverse(B)) <->
% inverse(inverse(A multiply B))
% Current number of equations to process: 179
% Current number of ordered equations: 14
% Current number of rules: 65
% New rule produced :
% [68]
% (A multiply B) multiply C <-> (inverse(inverse(C)) multiply B) multiply A
% Current number of equations to process: 179
% Current number of ordered equations: 13
% Current number of rules: 66
% New rule produced :
% [69]
% (inverse(inverse(C)) multiply B) multiply A <-> (A multiply B) multiply C
% Current number of equations to process: 179
% Current number of ordered equations: 12
% Current number of rules: 67
% New rule produced :
% [70] B multiply C <-> ((inverse(A) multiply B) multiply C) multiply A
% Current number of equations to process: 179
% Current number of ordered equations: 11
% Current number of rules: 68
% New rule produced :
% [71] ((inverse(A) multiply B) multiply C) multiply A <-> B multiply C
% Current number of equations to process: 179
% Current number of ordered equations: 10
% Current number of rules: 69
% New rule produced :
% [72]
% (A multiply B) multiply C <-> inverse(inverse(A)) multiply (B multiply C)
% Current number of equations to process: 179
% Current number of ordered equations: 9
% Current number of rules: 70
% New rule produced :
% [73]
% inverse(inverse(A)) multiply (B multiply C) <-> (A multiply B) multiply C
% Current number of equations to process: 179
% Current number of ordered equations: 8
% Current number of rules: 71
% New rule produced :
% [74]
% inverse(B multiply C) multiply A <->
% inverse(C) multiply (inverse(B) multiply A)
% Current number of equations to process: 185
% Current number of ordered equations: 6
% Current number of rules: 72
% New rule produced :
% [75]
% inverse(B) multiply A <->
% inverse(inverse(inverse(B))) multiply inverse(inverse(A))
% Current number of equations to process: 185
% Current number of ordered equations: 5
% Current number of rules: 73
% New rule produced :
% [76]
% inverse(C) multiply (inverse(B) multiply A) <->
% inverse(B multiply C) multiply A
% Current number of equations to process: 185
% Current number of ordered equations: 3
% Current number of rules: 74
% New rule produced :
% [77]
% inverse(inverse(inverse(B))) multiply inverse(inverse(A)) <->
% inverse(B) multiply A
% Current number of equations to process: 185
% Current number of ordered equations: 2
% Current number of rules: 75
% New rule produced :
% [78]
% inverse(A multiply B) multiply C <->
% inverse(A) multiply (inverse(B) multiply C)
% Current number of equations to process: 185
% Current number of ordered equations: 1
% Current number of rules: 76
% New rule produced :
% [79]
% inverse(A) multiply (inverse(B) multiply C) <->
% inverse(A multiply B) multiply C
% Current number of equations to process: 185
% Current number of ordered equations: 0
% Current number of rules: 77
% (A multiply B) multiply C = (A multiply C) multiply B (birth = 239, lhs_size = 5, rhs_size = 5,trace = Cp of 14 and 5)
% Initializing completion ...
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% See solution above
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.510000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------