%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : REL015-1 : TPTP v6.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n119.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 00:30:56 EDT 2014
% Result : Unsatisfiable 15.15s
% Output : Refutation 15.15s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : REL015-1 : TPTP v6.0.0. Released v4.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n119.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 : Thu Jun 5 17:46:48 CDT 2014
% % CPUTime : 15.15
% Processing problem /tmp/CiME_3901_n119.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " join : AC; zero,top,one : constant; converse : 1; composition : 2; meet : 2; complement : 1;";
% let X = vars "A B C";
% let Axioms = equations F X "
% composition(composition(A,B),C) = composition(A,composition(B,C));
% A = complement(complement(A) join complement(B)) join complement(complement(A) join B);
% meet(A,B) = complement(complement(A) join complement(B));
% composition(A,one) = A;
% composition(A join B,C) = composition(A,C) join composition(B,C);
% converse(converse(A)) = A;
% converse(A join B) = converse(A) join converse(B);
% converse(composition(A,B)) = composition(converse(B),converse(A));
% composition(converse(A),complement(composition(A,B))) join complement(B) = complement(B);
% top = A join complement(A);
% zero = meet(A,complement(A));
% ";
%
% let s1 = status F "
% zero lr_lex;
% top lr_lex;
% converse lr_lex;
% one lr_lex;
% meet lr_lex;
% complement lr_lex;
% composition mul;
% join mul;
% ";
%
% let p1 = precedence F "
% meet > composition > complement > converse > join > one > top > zero";
%
% let s2 = status F "
% zero mul;
% top mul;
% converse mul;
% one mul;
% composition mul;
% meet mul;
% complement mul;
% join mul;
% ";
%
% let p2 = precedence F "
% meet > composition > complement > converse > join > one = top = zero";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " composition(top,top) = top;"
% ;
% (*
% 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 = { composition(composition(A,B),C) =
% composition(A,composition(B,C)),
% A =
% complement(complement(A) join complement(B)) join
% complement(complement(A) join B),
% meet(A,B) =
% complement(complement(A) join complement(B)),
% composition(A,one) = A,
% composition(A join B,C) =
% composition(A,C) join composition(B,C),
% converse(converse(A)) = A,
% converse(A join B) =
% converse(A) join converse(B),
% converse(composition(A,B)) =
% composition(converse(B),converse(A)),
% composition(converse(A),complement(composition(A,B))) join
% complement(B) = complement(B),
% top = complement(A) join A,
% zero = meet(A,complement(A)) } (11 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 = { composition(top,top) = top }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] converse(converse(A)) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 1
% New rule produced : [2] composition(A,one) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 2
% New rule produced : [3] complement(A) join A -> top
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 3
% New rule produced : [4] meet(A,complement(A)) -> zero
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 4
% New rule produced : [5] converse(A join B) -> converse(A) join converse(B)
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 5
% New rule produced :
% [6] composition(converse(B),converse(A)) -> converse(composition(A,B))
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 6
% New rule produced :
% [7] composition(A,composition(B,C)) <-> composition(composition(A,B),C)
% Current number of equations to process: 23
% Current number of ordered equations: 11
% Current number of rules: 7
% New rule produced :
% [8] composition(composition(A,B),C) <-> composition(A,composition(B,C))
% Current number of equations to process: 23
% Current number of ordered equations: 10
% Current number of rules: 8
% New rule produced :
% [9] meet(A,B) -> complement(complement(A) join complement(B))
% Rule [4] meet(A,complement(A)) -> zero collapsed.
% Current number of equations to process: 24
% Current number of ordered equations: 9
% Current number of rules: 8
% New rule produced : [10] complement(top) -> zero
% Current number of equations to process: 23
% Current number of ordered equations: 9
% Current number of rules: 9
% New rule produced :
% [11] composition(A join B,C) -> composition(A,C) join composition(B,C)
% Current number of equations to process: 23
% Current number of ordered equations: 8
% Current number of rules: 10
% New rule produced :
% [12]
% composition(converse(A),complement(composition(A,B))) join complement(B) ->
% complement(B)
% Current number of equations to process: 23
% Current number of ordered equations: 7
% Current number of rules: 11
% New rule produced :
% [13]
% complement(complement(A) join complement(B)) join complement(complement(A) join B)
% -> A
% Current number of equations to process: 23
% Current number of ordered equations: 6
% Current number of rules: 12
% New rule produced : [14] top join complement(complement(A)) -> top join A
% Current number of equations to process: 23
% Current number of ordered equations: 5
% Current number of rules: 13
% New rule produced :
% [15] converse(complement(A)) join converse(A) -> converse(top)
% Current number of equations to process: 23
% Current number of ordered equations: 4
% Current number of rules: 14
% New rule produced :
% [16] converse(composition(B,converse(A))) <-> composition(A,converse(B))
% Current number of equations to process: 23
% Current number of ordered equations: 3
% Current number of rules: 15
% New rule produced :
% [17] converse(composition(converse(B),A)) <-> composition(converse(A),B)
% Current number of equations to process: 23
% Current number of ordered equations: 2
% Current number of rules: 16
% New rule produced :
% [18] composition(A,converse(B)) <-> converse(composition(B,converse(A)))
% Current number of equations to process: 23
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced :
% [19] composition(converse(A),B) <-> converse(composition(converse(B),A))
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [20] composition(A,composition(one,B)) -> composition(A,B)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [21] zero join top -> top
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [22] composition(complement(B),A) join composition(B,A) -> composition(top,A)
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [23] top join composition(converse(A),complement(composition(A,B))) -> top
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [24] top join complement(A join B) join B -> top join complement(A)
% Current number of equations to process: 41
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [25]
% composition(A,converse(composition(B,C))) <->
% composition(composition(A,converse(C)),converse(B))
% Current number of equations to process: 40
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [26]
% composition(composition(A,converse(C)),converse(B)) <->
% composition(A,converse(composition(B,C)))
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [27]
% composition(converse(B),composition(converse(A),C)) <->
% composition(converse(composition(A,B)),C)
% Current number of equations to process: 39
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [28]
% composition(converse(composition(A,B)),C) <->
% composition(converse(B),composition(converse(A),C))
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [29] top join complement(complement(A join B) join B) -> top join A
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [30]
% composition(A,composition(composition(B,C),V_3)) <->
% composition(composition(A,B),composition(C,V_3))
% Current number of equations to process: 35
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [31]
% composition(composition(A,B),composition(C,V_3)) <->
% composition(A,composition(composition(B,C),V_3))
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [32]
% composition(A,composition(composition(B,C),V_3)) <->
% composition(composition(composition(A,B),C),V_3)
% Current number of equations to process: 32
% Current number of ordered equations: 5
% Current number of rules: 31
% New rule produced :
% [33]
% composition(A,composition(B,composition(C,V_3))) <->
% composition(composition(A,composition(B,C)),V_3)
% Current number of equations to process: 32
% Current number of ordered equations: 4
% Current number of rules: 32
% New rule produced :
% [34]
% composition(A,composition(B,composition(C,V_3))) <->
% composition(composition(composition(A,B),C),V_3)
% Current number of equations to process: 32
% Current number of ordered equations: 3
% Current number of rules: 33
% New rule produced :
% [35]
% composition(composition(A,composition(B,C)),V_3) <->
% composition(A,composition(B,composition(C,V_3)))
% Current number of equations to process: 32
% Current number of ordered equations: 2
% Current number of rules: 34
% New rule produced :
% [36]
% composition(composition(composition(A,B),C),V_3) <->
% composition(A,composition(composition(B,C),V_3))
% Current number of equations to process: 32
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [37]
% composition(composition(composition(A,B),C),V_3) <->
% composition(A,composition(B,composition(C,V_3)))
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [38]
% composition(composition(A,composition(B,C)),V_3) <->
% composition(composition(A,B),composition(C,V_3))
% Current number of equations to process: 31
% Current number of ordered equations: 1
% Current number of rules: 37
% New rule produced :
% [39]
% composition(composition(A,B),composition(C,V_3)) <->
% composition(composition(A,composition(B,C)),V_3)
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [40]
% composition(converse(A),complement(A)) join complement(one) ->
% complement(one)
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [41]
% zero join composition(converse(A),complement(composition(A,top))) -> zero
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [42] zero join complement(complement(A) join complement(A)) -> A
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [43] top join complement(complement(A) join B) -> top join complement(B)
% Rule [29] top join complement(complement(A join B) join B) -> top join A
% collapsed.
% Current number of equations to process: 71
% Current number of ordered equations: 1
% Current number of rules: 41
% New rule produced : [44] top join A <-> top join complement(B)
% Rule [14] top join complement(complement(A)) -> top join A collapsed.
% Rule
% [23] top join composition(converse(A),complement(composition(A,B))) -> top
% collapsed.
% Rule [24] top join complement(A join B) join B -> top join complement(A)
% collapsed.
% Rule [43] top join complement(complement(A) join B) -> top join complement(B)
% collapsed.
% Current number of equations to process: 72
% Current number of ordered equations: 2
% Current number of rules: 38
% Rule [44] top join A <-> top join complement(B) is composed into [44]
% top join A
% -> top
% New rule produced : [45] top join complement(B) -> top
% Current number of equations to process: 71
% Current number of ordered equations: 1
% Current number of rules: 39
% New rule produced :
% [46] zero join complement(complement(complement(A)) join A) -> complement(A)
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [47] complement(complement(A)) -> A
% Rule
% [46] zero join complement(complement(complement(A)) join A) -> complement(A)
% collapsed.
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [48] zero join complement(A join A) -> complement(A)
% Rule [42] zero join complement(complement(A) join complement(A)) -> A
% collapsed.
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [49]
% converse(composition(C,A join B)) ->
% converse(composition(C,A)) join converse(composition(C,B))
% Current number of equations to process: 66
% Current number of ordered equations: 1
% Current number of rules: 41
% New rule produced :
% [50]
% composition(converse(A),converse(B) join converse(C)) ->
% converse(composition(B,A)) join converse(composition(C,A))
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [51]
% composition(A,complement(composition(converse(A),B))) join complement(B) ->
% complement(B)
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [52]
% converse(complement(A join B)) join converse(A) join converse(B) ->
% converse(top)
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced : [53] zero join complement(zero join complement(A)) -> A
% Current number of equations to process: 75
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [54]
% complement(complement(A) join B) join B <->
% complement(complement(B) join A) join A
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [55] complement(zero join complement(A)) join complement(zero join A) -> top
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced : [56] converse(top) join complement(converse(A)) -> top
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [57] converse(complement(converse(A))) join A -> converse(top)
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced : [58] converse(zero) join converse(top) -> converse(top)
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced : [59] composition(converse(one),A) -> A
% Current number of equations to process: 101
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced : [60] converse(top) join converse(A) -> converse(top)
% Rule [58] converse(zero) join converse(top) -> converse(top) collapsed.
% Current number of equations to process: 134
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [61]
% converse(composition(converse(A),B)) <->
% composition(converse(composition(one,B)),A)
% Current number of equations to process: 156
% Current number of ordered equations: 1
% Current number of rules: 52
% New rule produced :
% [62]
% composition(converse(composition(one,B)),A) <->
% converse(composition(converse(A),B))
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [63] composition(zero,A) join composition(top,A) -> composition(top,A)
% Current number of equations to process: 155
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [64] composition(top,A) join complement(composition(B,A)) -> top
% Current number of equations to process: 154
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [65]
% composition(A,converse(composition(B,converse(one)))) ->
% composition(A,converse(B))
% Current number of equations to process: 152
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [66]
% converse(composition(converse(composition(one,A)),B)) <->
% composition(converse(B),A)
% Current number of equations to process: 151
% Current number of ordered equations: 1
% Current number of rules: 57
% New rule produced :
% [67]
% composition(converse(B),A) <->
% converse(composition(converse(composition(one,A)),B))
% Current number of equations to process: 151
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [68]
% composition(A,composition(composition(one,B),C)) ->
% composition(A,composition(B,C))
% Current number of equations to process: 155
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [69]
% converse(composition(A,composition(B,converse(C)))) <->
% composition(C,converse(composition(A,B)))
% Current number of equations to process: 151
% Current number of ordered equations: 1
% Current number of rules: 60
% New rule produced :
% [70]
% composition(C,converse(composition(A,B))) <->
% converse(composition(A,composition(B,converse(C))))
% Current number of equations to process: 151
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [71]
% converse(composition(composition(converse(A),B),C)) <->
% composition(converse(composition(B,C)),A)
% Current number of equations to process: 150
% Current number of ordered equations: 1
% Current number of rules: 62
% New rule produced :
% [72]
% composition(converse(composition(B,C)),A) <->
% converse(composition(composition(converse(A),B),C))
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [73]
% composition(A,converse(composition(B,converse(C)))) <->
% composition(composition(A,C),converse(B))
% Current number of equations to process: 149
% Current number of ordered equations: 1
% Current number of rules: 64
% New rule produced :
% [74]
% composition(composition(A,C),converse(B)) <->
% composition(A,converse(composition(B,converse(C))))
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [75]
% converse(composition(C,converse(composition(A,B)))) <->
% composition(A,composition(B,converse(C)))
% Current number of equations to process: 147
% Current number of ordered equations: 3
% Current number of rules: 66
% New rule produced :
% [76]
% composition(A,composition(B,converse(C))) <->
% converse(composition(C,converse(composition(A,B))))
% Current number of equations to process: 147
% Current number of ordered equations: 2
% Current number of rules: 67
% New rule produced :
% [77]
% composition(B,composition(converse(A),C)) <->
% composition(converse(composition(A,converse(B))),C)
% Current number of equations to process: 147
% Current number of ordered equations: 1
% Current number of rules: 68
% New rule produced :
% [78]
% composition(converse(composition(A,converse(B))),C) <->
% composition(B,composition(converse(A),C))
% Current number of equations to process: 147
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [79]
% converse(composition(converse(composition(B,C)),A)) <->
% composition(composition(converse(A),B),C)
% Current number of equations to process: 145
% Current number of ordered equations: 3
% Current number of rules: 70
% New rule produced :
% [80]
% composition(A,converse(composition(converse(B),C))) <->
% composition(composition(A,converse(C)),B)
% Current number of equations to process: 145
% Current number of ordered equations: 2
% Current number of rules: 71
% New rule produced :
% [81]
% composition(composition(converse(A),B),C) <->
% converse(composition(converse(composition(B,C)),A))
% Current number of equations to process: 145
% Current number of ordered equations: 1
% Current number of rules: 72
% New rule produced :
% [82]
% composition(composition(A,converse(C)),B) <->
% composition(A,converse(composition(converse(B),C)))
% Current number of equations to process: 145
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [83]
% composition(converse(B),composition(A,C)) <->
% composition(converse(composition(converse(A),B)),C)
% Current number of equations to process: 144
% Current number of ordered equations: 1
% Current number of rules: 74
% New rule produced :
% [84]
% composition(converse(composition(converse(A),B)),C) <->
% composition(converse(B),composition(A,C))
% Current number of equations to process: 144
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [85] converse(top) join complement(converse(A) join B) join B -> top
% Current number of equations to process: 145
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [86]
% converse(composition(C,composition(B,converse(A)))) <->
% composition(composition(A,converse(B)),converse(C))
% Current number of equations to process: 143
% Current number of ordered equations: 3
% Current number of rules: 77
% New rule produced :
% [87]
% converse(composition(composition(C,converse(B)),A)) <->
% composition(converse(A),composition(B,converse(C)))
% Current number of equations to process: 143
% Current number of ordered equations: 2
% Current number of rules: 78
% New rule produced :
% [88]
% composition(converse(A),composition(B,converse(C))) <->
% converse(composition(composition(C,converse(B)),A))
% Current number of equations to process: 143
% Current number of ordered equations: 1
% Current number of rules: 79
% New rule produced :
% [89]
% composition(composition(A,converse(B)),converse(C)) <->
% converse(composition(C,composition(B,converse(A))))
% Current number of equations to process: 143
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [90]
% converse(composition(C,composition(converse(B),A))) <->
% composition(composition(converse(A),B),converse(C))
% Current number of equations to process: 140
% Current number of ordered equations: 3
% Current number of rules: 81
% New rule produced :
% [91]
% converse(composition(composition(converse(C),B),A)) <->
% composition(converse(A),composition(converse(B),C))
% Current number of equations to process: 140
% Current number of ordered equations: 2
% Current number of rules: 82
% New rule produced :
% [92]
% composition(converse(A),composition(converse(B),C)) <->
% converse(composition(composition(converse(C),B),A))
% Current number of equations to process: 140
% Current number of ordered equations: 1
% Current number of rules: 83
% New rule produced :
% [93]
% composition(composition(converse(A),B),converse(C)) <->
% converse(composition(C,composition(converse(B),A)))
% Current number of equations to process: 140
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [94]
% composition(composition(A,converse(one)),converse(B)) ->
% composition(A,converse(B))
% Current number of equations to process: 147
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [95]
% converse(composition(composition(C,converse(B)),converse(A))) <->
% composition(A,composition(B,converse(C)))
% Current number of equations to process: 150
% Current number of ordered equations: 1
% Current number of rules: 86
% New rule produced :
% [96]
% composition(A,composition(B,converse(C))) <->
% converse(composition(composition(C,converse(B)),converse(A)))
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [97]
% converse(composition(composition(converse(C),B),converse(A))) <->
% composition(A,composition(converse(B),C))
% Current number of equations to process: 149
% Current number of ordered equations: 1
% Current number of rules: 88
% New rule produced :
% [98]
% composition(A,composition(converse(B),C)) <->
% converse(composition(composition(converse(C),B),converse(A)))
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [99]
% converse(composition(converse(C),composition(B,converse(A)))) <->
% composition(composition(A,converse(B)),C)
% Current number of equations to process: 148
% Current number of ordered equations: 1
% Current number of rules: 90
% New rule produced :
% [100]
% composition(composition(A,converse(B)),C) <->
% converse(composition(converse(C),composition(B,converse(A))))
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [101]
% converse(composition(converse(C),composition(converse(B),A))) <->
% composition(composition(converse(A),B),C)
% Current number of equations to process: 147
% Current number of ordered equations: 1
% Current number of rules: 92
% New rule produced :
% [102]
% composition(composition(converse(A),B),C) <->
% converse(composition(converse(C),composition(converse(B),A)))
% Current number of equations to process: 147
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [103]
% converse(composition(composition(A,B),converse(C))) <->
% composition(composition(C,converse(B)),converse(A))
% Current number of equations to process: 162
% Current number of ordered equations: 1
% Current number of rules: 94
% New rule produced :
% [104]
% composition(composition(C,converse(B)),converse(A)) <->
% converse(composition(composition(A,B),converse(C)))
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [105]
% converse(composition(composition(A,converse(B)),converse(C))) <->
% composition(composition(C,B),converse(A))
% Current number of equations to process: 161
% Current number of ordered equations: 1
% Current number of rules: 96
% New rule produced :
% [106]
% composition(composition(C,B),converse(A)) <->
% converse(composition(composition(A,converse(B)),converse(C)))
% Current number of equations to process: 161
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [107]
% converse(composition(A,converse(composition(B,C)))) <->
% composition(B,converse(composition(A,converse(C))))
% Current number of equations to process: 177
% Current number of ordered equations: 1
% Current number of rules: 98
% New rule produced :
% [108]
% composition(B,converse(composition(A,converse(C)))) <->
% converse(composition(A,converse(composition(B,C))))
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [109]
% converse(composition(A,converse(composition(B,converse(C))))) <->
% composition(B,converse(composition(A,C)))
% Current number of equations to process: 176
% Current number of ordered equations: 1
% Current number of rules: 100
% New rule produced :
% [110]
% composition(B,converse(composition(A,C))) <->
% converse(composition(A,converse(composition(B,converse(C)))))
% Current number of equations to process: 176
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [111]
% converse(composition(converse(composition(A,B)),C)) <->
% composition(converse(composition(converse(A),C)),B)
% Current number of equations to process: 191
% Current number of ordered equations: 1
% Current number of rules: 102
% New rule produced :
% [112]
% composition(converse(composition(converse(A),C)),B) <->
% converse(composition(converse(composition(A,B)),C))
% Current number of equations to process: 191
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [113]
% converse(composition(converse(composition(converse(A),B)),C)) <->
% composition(converse(composition(A,C)),B)
% Current number of equations to process: 190
% Current number of ordered equations: 1
% Current number of rules: 104
% New rule produced :
% [114]
% composition(converse(composition(A,C)),B) <->
% converse(composition(converse(composition(converse(A),B)),C))
% Current number of equations to process: 190
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [115]
% converse(composition(converse(A),composition(B,C))) <->
% composition(converse(C),composition(converse(B),A))
% Current number of equations to process: 210
% Current number of ordered equations: 1
% Current number of rules: 106
% New rule produced :
% [116]
% composition(converse(C),composition(converse(B),A)) <->
% converse(composition(converse(A),composition(B,C)))
% Current number of equations to process: 210
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [117]
% converse(composition(converse(A),composition(converse(B),C))) <->
% composition(converse(C),composition(B,A))
% Current number of equations to process: 211
% Current number of ordered equations: 1
% Current number of rules: 108
% New rule produced :
% [118]
% composition(converse(C),composition(B,A)) <->
% converse(composition(converse(A),composition(converse(B),C)))
% Current number of equations to process: 211
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [119]
% composition(A,complement(converse(A))) join complement(one) ->
% complement(one)
% Current number of equations to process: 731
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [120]
% converse(composition(converse(zero),top)) join complement(one) ->
% complement(one)
% Current number of equations to process: 730
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [121]
% complement(one) join complement(composition(converse(A),complement(A))) ->
% top
% Current number of equations to process: 732
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced : [122] zero join one -> one
% Current number of equations to process: 735
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [123]
% zero join composition(A,complement(composition(converse(A),top))) -> zero
% Current number of equations to process: 755
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [124]
% zero join complement(composition(converse(A),complement(composition(A,top))))
% -> top
% Current number of equations to process: 754
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [125] composition(top,A) join composition(B,A) -> composition(top,A)
% Rule [63] composition(zero,A) join composition(top,A) -> composition(top,A)
% collapsed.
% Current number of equations to process: 763
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced : [126] complement(zero) -> top
% Current number of equations to process: 765
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [127] complement(complement(A join A) join A) -> zero join zero
% Current number of equations to process: 784
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [128] complement(zero join A) join complement(B) join A -> top
% Current number of equations to process: 783
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced : [129] A join A <-> zero join A
% Current number of equations to process: 788
% Current number of ordered equations: 1
% Current number of rules: 119
% New rule produced : [130] zero join A <-> A join A
% Current number of equations to process: 788
% Current number of ordered equations: 0
% Current number of rules: 120
% Rule [127] complement(complement(A join A) join A) -> zero join zero is composed into
% [127] complement(complement(A join A) join A) -> zero
% New rule produced : [131] zero join zero -> zero
% Current number of equations to process: 796
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [132]
% converse(zero) join converse(complement(A join A)) -> converse(complement(A))
% Current number of equations to process: 794
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [133]
% converse(composition(converse(A),complement(A))) join complement(one) ->
% complement(one)
% Current number of equations to process: 793
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [134]
% composition(converse(A),complement(composition(A,complement(B)))) join B -> B
% Current number of equations to process: 792
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [135]
% complement(B join B) join complement(A) <->
% complement(A join A) join complement(B)
% Current number of equations to process: 791
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [136] complement(complement(A join A) join A join B) -> zero
% Current number of equations to process: 790
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [137]
% complement(complement(A) join B) join complement(A join B) -> complement(B)
% Rule
% [13]
% complement(complement(A) join complement(B)) join complement(complement(A) join B)
% -> A collapsed.
% Rule
% [55] complement(zero join complement(A)) join complement(zero join A) -> top
% collapsed.
% Current number of equations to process: 803
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [138] composition(A,B join C) -> composition(A,B) join composition(A,C)
% Rule
% [49]
% converse(composition(C,A join B)) ->
% converse(composition(C,A)) join converse(composition(C,B)) collapsed.
% Rule
% [50]
% composition(converse(A),converse(B) join converse(C)) ->
% converse(composition(B,A)) join converse(composition(C,A)) collapsed.
% Current number of equations to process: 811
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [139]
% composition(A,complement(composition(converse(A),complement(B)))) join B -> B
% Current number of equations to process: 854
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [140] converse(top) join complement(converse(A) join converse(B)) -> top
% Current number of equations to process: 863
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [141]
% composition(converse(B),complement(composition(B,top))) join complement(A) ->
% complement(A)
% Current number of equations to process: 875
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [142]
% converse(composition(converse(A),complement(A))) join converse(complement(one))
% -> converse(complement(one))
% Current number of equations to process: 878
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [143]
% complement(composition(A,complement(composition(converse(A),B)))) join
% complement(B) -> top
% Current number of equations to process: 875
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [144]
% complement(converse(complement(A join A)) join converse(A)) ->
% zero join complement(converse(top))
% Current number of equations to process: 873
% Current number of ordered equations: 0
% Current number of rules: 130
% Rule [144]
% complement(converse(complement(A join A)) join converse(A)) ->
% zero join complement(converse(top)) is composed into [144]
% complement(
% converse(complement(
% A join A)) join
% converse(A)) ->
% zero join complement(top)
% Rule [57] converse(complement(converse(A))) join A -> converse(top) is composed into
% [57] converse(complement(converse(A))) join A -> top
% Rule [52]
% converse(complement(A join B)) join converse(A) join converse(B) ->
% converse(top) is composed into [52]
% converse(complement(A join B)) join
% converse(A) join converse(B) -> top
% Rule [15] converse(complement(A)) join converse(A) -> converse(top) is composed into
% [15] converse(complement(A)) join converse(A) -> top
% New rule produced : [145] converse(top) -> top
% Rule [56] converse(top) join complement(converse(A)) -> top collapsed.
% Rule [60] converse(top) join converse(A) -> converse(top) collapsed.
% Rule [85] converse(top) join complement(converse(A) join B) join B -> top
% collapsed.
% Rule [140] converse(top) join complement(converse(A) join converse(B)) -> top
% collapsed.
% Current number of equations to process: 874
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced : [146] complement(zero join A) join A join B -> top
% Rule [128] complement(zero join A) join complement(B) join A -> top
% collapsed.
% Current number of equations to process: 878
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced : [147] zero join complement(zero join A) -> complement(A)
% Rule [53] zero join complement(zero join complement(A)) -> A collapsed.
% Current number of equations to process: 885
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [148] composition(converse(B),complement(composition(B,top))) join A -> A
% Rule
% [41]
% zero join composition(converse(A),complement(composition(A,top))) -> zero
% collapsed.
% Rule
% [141]
% composition(converse(B),complement(composition(B,top))) join complement(A) ->
% complement(A) collapsed.
% Current number of equations to process: 884
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced : [149] complement(zero join A) join A -> top
% Rule [146] complement(zero join A) join A join B -> top collapsed.
% Current number of equations to process: 884
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [150]
% converse(zero) join converse(complement(zero join complement(A))) ->
% converse(A)
% Current number of equations to process: 913
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced : [151] zero join A join A -> zero join A
% Current number of equations to process: 972
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [152]
% complement(zero join complement(A)) join complement(B) ->
% complement(B) join A
% Current number of equations to process: 970
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [153] converse(complement(converse(zero))) join complement(A) -> top
% Current number of equations to process: 1055
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced : [154] converse(one) -> one
% Rule [59] composition(converse(one),A) -> A collapsed.
% Rule
% [65]
% composition(A,converse(composition(B,converse(one)))) ->
% composition(A,converse(B)) collapsed.
% Rule
% [94]
% composition(composition(A,converse(one)),converse(B)) ->
% composition(A,converse(B)) collapsed.
% Current number of equations to process: 1070
% Current number of ordered equations: 0
% Current number of rules: 128
% Rule [67]
% composition(converse(B),A) <->
% converse(composition(converse(composition(one,A)),B)) is composed into
% [67] composition(converse(B),A) <-> converse(composition(converse(A),B))
% Rule [61]
% converse(composition(converse(A),B)) <->
% composition(converse(composition(one,B)),A) is composed into [61]
% converse(
% composition(
% converse(A),B))
% <->
% composition(
% converse(B),A)
% New rule produced : [155] composition(one,A) -> A
% Rule [20] composition(A,composition(one,B)) -> composition(A,B) collapsed.
% Rule
% [62]
% composition(converse(composition(one,B)),A) <->
% converse(composition(converse(A),B)) collapsed.
% Rule
% [66]
% converse(composition(converse(composition(one,A)),B)) <->
% composition(converse(B),A) collapsed.
% Rule
% [68]
% composition(A,composition(composition(one,B),C)) ->
% composition(A,composition(B,C)) collapsed.
% Current number of equations to process: 1069
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [156] composition(complement(one),A) join A -> composition(top,A)
% Current number of equations to process: 1068
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [157]
% converse(complement(converse(composition(A,B)))) join composition(top,B) ->
% top
% Current number of equations to process: 1211
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [158]
% converse(complement(converse(complement(A join A)))) join complement(A) ->
% top
% Current number of equations to process: 1210
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [159]
% converse(composition(top,A)) join converse(complement(composition(B,A))) ->
% top
% Current number of equations to process: 1209
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [160]
% composition(top,converse(A)) join complement(converse(composition(A,B))) ->
% top
% Current number of equations to process: 1208
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [161]
% composition(top,A) join complement(composition(B,composition(C,A))) -> top
% Current number of equations to process: 1207
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [162]
% converse(composition(A,top)) join complement(composition(B,converse(A))) ->
% top
% Current number of equations to process: 1206
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [163]
% composition(top,A) join complement(converse(composition(converse(A),B))) ->
% top
% Current number of equations to process: 1205
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [164]
% composition(B,converse(composition(converse(C),A))) <->
% composition(converse(composition(A,converse(B))),C)
% Current number of equations to process: 1204
% Current number of ordered equations: 1
% Current number of rules: 134
% New rule produced :
% [165]
% composition(converse(composition(A,converse(B))),C) <->
% composition(B,converse(composition(converse(C),A)))
% Current number of equations to process: 1204
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [166]
% converse(composition(composition(A,converse(B)),C)) <->
% composition(composition(converse(C),B),converse(A))
% Current number of equations to process: 1419
% Current number of ordered equations: 1
% Current number of rules: 136
% New rule produced :
% [167]
% composition(composition(converse(C),B),converse(A)) <->
% converse(composition(composition(A,converse(B)),C))
% Current number of equations to process: 1419
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [168]
% converse(composition(A,composition(converse(B),C))) <->
% composition(converse(C),composition(B,converse(A)))
% Current number of equations to process: 1534
% Current number of ordered equations: 1
% Current number of rules: 138
% New rule produced :
% [169]
% composition(converse(C),composition(B,converse(A))) <->
% converse(composition(A,composition(converse(B),C)))
% Current number of equations to process: 1534
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [170]
% converse(composition(converse(C),composition(B,converse(A)))) <->
% composition(A,composition(converse(B),C))
% Current number of equations to process: 2238
% Current number of ordered equations: 1
% Current number of rules: 140
% New rule produced :
% [171]
% composition(A,composition(converse(B),C)) <->
% converse(composition(converse(C),composition(B,converse(A))))
% Current number of equations to process: 2238
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [172]
% converse(composition(composition(converse(C),B),converse(A))) <->
% composition(composition(A,converse(B)),C)
% Current number of equations to process: 2237
% Current number of ordered equations: 1
% Current number of rules: 142
% New rule produced :
% [173]
% composition(composition(A,converse(B)),C) <->
% converse(composition(composition(converse(C),B),converse(A)))
% Current number of equations to process: 2237
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [174]
% complement(one) join complement(composition(A,complement(converse(A)))) ->
% top
% Current number of equations to process: 1673
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [175]
% complement(one) join complement(converse(composition(converse(zero),top))) ->
% top
% Current number of equations to process: 1747
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [176]
% converse(complement(one)) join composition(converse(zero),top) ->
% converse(complement(one))
% Current number of equations to process: 1746
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [177] composition(top,zero) join complement(one) -> complement(one)
% Current number of equations to process: 1749
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [178]
% converse(complement(composition(converse(zero),top))) join complement(one) ->
% top
% Current number of equations to process: 1748
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [179] complement(one) join complement(composition(top,zero)) -> top
% Current number of equations to process: 1763
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [180]
% complement(one) join complement(converse(composition(converse(A),complement(A))))
% -> top
% Current number of equations to process: 1770
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced : [181] one join converse(zero) -> one
% Current number of equations to process: 1829
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced : [182] composition(zero,A) join A -> A
% Current number of equations to process: 1831
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced : [183] one join converse(complement(one)) -> top
% Current number of equations to process: 1834
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [184] one join converse(complement(converse(zero))) -> top
% Current number of equations to process: 1843
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [185] one join complement(A join A) -> one join complement(A)
% Current number of equations to process: 1841
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [186] one join complement(zero join complement(A)) -> one join A
% Current number of equations to process: 1840
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [187]
% zero join composition(A,complement(converse(composition(top,A)))) -> zero
% Current number of equations to process: 1859
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [188]
% zero join complement(composition(A,complement(composition(converse(A),top))))
% -> top
% Current number of equations to process: 1860
% Current number of ordered equations: 0
% Current number of rules: 158
% Rule [144]
% complement(converse(complement(A join A)) join converse(A)) ->
% zero join complement(top) is composed into [144]
% complement(converse(complement(
% A join A)) join
% converse(A)) ->
% complement(top)
% Rule [129] A join A <-> zero join A is composed into [129] A join A -> A
% New rule produced : [189] zero join A -> A
% Rule [21] zero join top -> top collapsed.
% Rule [48] zero join complement(A join A) -> complement(A) collapsed.
% Rule [122] zero join one -> one collapsed.
% Rule
% [123]
% zero join composition(A,complement(composition(converse(A),top))) -> zero
% collapsed.
% Rule
% [124]
% zero join complement(composition(converse(A),complement(composition(A,top))))
% -> top collapsed.
% Rule [130] zero join A <-> A join A collapsed.
% Rule [131] zero join zero -> zero collapsed.
% Rule [147] zero join complement(zero join A) -> complement(A) collapsed.
% Rule [149] complement(zero join A) join A -> top collapsed.
% Rule
% [150]
% converse(zero) join converse(complement(zero join complement(A))) ->
% converse(A) collapsed.
% Rule [151] zero join A join A -> zero join A collapsed.
% Rule
% [152]
% complement(zero join complement(A)) join complement(B) ->
% complement(B) join A collapsed.
% Rule [186] one join complement(zero join complement(A)) -> one join A
% collapsed.
% Rule
% [187]
% zero join composition(A,complement(converse(composition(top,A)))) -> zero
% collapsed.
% Rule
% [188]
% zero join complement(composition(A,complement(composition(converse(A),top))))
% -> top collapsed.
% Current number of equations to process: 1872
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [190] composition(A,complement(composition(converse(A),top))) -> zero
% Current number of equations to process: 1872
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [191] composition(A,complement(converse(composition(top,A)))) -> zero
% Current number of equations to process: 1871
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced : [192] converse(zero) join converse(A) -> converse(A)
% Rule
% [132]
% converse(zero) join converse(complement(A join A)) -> converse(complement(A))
% collapsed.
% Current number of equations to process: 1870
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [193]
% complement(composition(converse(A),complement(composition(A,top)))) -> top
% Current number of equations to process: 1869
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [194] composition(converse(zero),top) join complement(one) -> complement(one)
% Current number of equations to process: 1965
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [195] complement(one) join complement(composition(converse(zero),top)) -> top
% Current number of equations to process: 1964
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [196] converse(composition(top,zero)) join complement(one) -> complement(one)
% Current number of equations to process: 1985
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [197]
% converse(composition(A,complement(converse(A)))) join complement(one) ->
% complement(one)
% Current number of equations to process: 1987
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [198]
% composition(top,A) join composition(B,composition(C,A)) -> composition(top,A)
% Current number of equations to process: 1992
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [199]
% converse(composition(converse(A),B)) join composition(top,A) ->
% composition(top,A)
% Current number of equations to process: 1991
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [200]
% converse(complement(one)) join composition(converse(A),complement(A)) ->
% converse(complement(one))
% Current number of equations to process: 1989
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [201]
% converse(complement(composition(converse(A),complement(A)))) join complement(one)
% -> top
% Current number of equations to process: 1988
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [202]
% converse(composition(top,A)) join converse(composition(B,A)) ->
% converse(composition(top,A))
% Current number of equations to process: 2097
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [203]
% converse(composition(A,B)) join composition(top,converse(A)) ->
% composition(top,converse(A))
% Current number of equations to process: 2096
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [204]
% converse(composition(A,top)) join composition(B,converse(A)) <->
% composition(top,converse(A))
% Current number of equations to process: 2095
% Current number of ordered equations: 1
% Current number of rules: 158
% Rule [204]
% converse(composition(A,top)) join composition(B,converse(A)) <->
% composition(top,converse(A)) is composed into [204]
% converse(composition(A,top)) join
% composition(B,converse(A))
% <->
% converse(composition(A,top)) join
% composition(zero,converse(A))
% New rule produced :
% [205]
% composition(top,converse(A)) <->
% converse(composition(A,top)) join composition(B,converse(A))
% Rule
% [160]
% composition(top,converse(A)) join complement(converse(composition(A,B))) ->
% top collapsed.
% Rule
% [203]
% converse(composition(A,B)) join composition(top,converse(A)) ->
% composition(top,converse(A)) collapsed.
% Current number of equations to process: 2097
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [206] complement(complement(A join B) join complement(B)) -> B
% Current number of equations to process: 2240
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [207] complement(complement(complement(A) join B) join A) -> complement(A)
% Current number of equations to process: 2239
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [208]
% complement(converse(A) join complement(converse(complement(A)))) ->
% complement(converse(A))
% Current number of equations to process: 2276
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [209]
% complement(converse(complement(A)) join complement(converse(A))) ->
% complement(converse(complement(A)))
% Current number of equations to process: 2275
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [210]
% complement(complement(complement(A join B) join B) join A) -> complement(A)
% Current number of equations to process: 2314
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced : [211] complement(A join B) join B -> complement(A) join B
% Rule
% [54]
% complement(complement(A) join B) join B <->
% complement(complement(B) join A) join A collapsed.
% Rule [127] complement(complement(A join A) join A) -> zero collapsed.
% Rule [136] complement(complement(A join A) join A join B) -> zero collapsed.
% Rule
% [210]
% complement(complement(complement(A join B) join B) join A) -> complement(A)
% collapsed.
% Current number of equations to process: 2425
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [212]
% complement(complement(converse(complement(converse(A)))) join A) ->
% complement(A)
% Current number of equations to process: 2445
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [213]
% complement(converse(complement(converse(A))) join complement(A)) ->
% complement(converse(complement(converse(A))))
% Current number of equations to process: 2455
% Current number of ordered equations: 1
% Current number of rules: 161
% New rule produced :
% [214]
% converse(complement(converse(complement(A join B)))) join complement(B) ->
% top
% Rule
% [158]
% converse(complement(converse(complement(A join A)))) join complement(A) ->
% top collapsed.
% Current number of equations to process: 2455
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [215] complement(A join B) join complement(A) -> complement(A)
% Rule [206] complement(complement(A join B) join complement(B)) -> B
% collapsed.
% Current number of equations to process: 2506
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [216]
% composition(A,top) join composition(A,complement(B)) -> composition(A,top)
% Current number of equations to process: 2589
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [217]
% composition(A,complement(B)) join composition(A,B) -> composition(A,top)
% Current number of equations to process: 2588
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [218] composition(A,top) join composition(A,B) -> composition(A,top)
% Rule
% [216]
% composition(A,top) join composition(A,complement(B)) -> composition(A,top)
% collapsed.
% Current number of equations to process: 2629
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [219]
% complement(converse(complement(converse(complement(A)))) join A) ->
% complement(converse(complement(converse(complement(A)))))
% Current number of equations to process: 2765
% Current number of ordered equations: 1
% Current number of rules: 164
% New rule produced :
% [220]
% complement(complement(converse(complement(converse(A))) join B) join A) ->
% complement(A)
% Current number of equations to process: 2765
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [221]
% one join complement(composition(A,complement(converse(A)))) ->
% complement(composition(A,complement(converse(A))))
% Current number of equations to process: 2764
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [222]
% one join complement(converse(composition(converse(zero),top))) ->
% complement(converse(composition(converse(zero),top)))
% Current number of equations to process: 2763
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced :
% [223]
% complement(composition(top,A)) join complement(composition(B,A)) ->
% complement(composition(B,A))
% Current number of equations to process: 2762
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced :
% [224]
% converse(composition(top,zero)) join converse(complement(one)) ->
% converse(complement(one))
% Current number of equations to process: 2915
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced :
% [225] converse(complement(converse(A) join converse(B))) join A join B -> top
% Current number of equations to process: 2922
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced :
% [226]
% composition(converse(complement(converse(B))),A) join composition(B,A) ->
% composition(top,A)
% Current number of equations to process: 2921
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [227]
% converse(complement(composition(A,converse(B)))) join composition(B,converse(A))
% -> top
% Current number of equations to process: 2920
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [228]
% converse(complement(composition(converse(A),B))) join composition(converse(B),A)
% -> top
% Current number of equations to process: 2919
% Current number of ordered equations: 0
% Current number of rules: 173
% New rule produced :
% [229]
% converse(complement(converse(composition(converse(A),complement(A))))) join
% complement(one) -> top
% Current number of equations to process: 2918
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced :
% [230]
% converse(composition(A,top)) join composition(zero,converse(A)) join
% complement(converse(composition(A,converse(B)))) -> top
% Current number of equations to process: 2915
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced :
% [231]
% converse(composition(A,complement(converse(A)))) join converse(complement(one))
% -> converse(complement(one))
% Current number of equations to process: 2913
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced :
% [232]
% converse(complement(converse(composition(A,complement(converse(A)))))) join
% complement(one) -> top
% Current number of equations to process: 2912
% Current number of ordered equations: 0
% Current number of rules: 177
% New rule produced :
% [233]
% converse(complement(one)) join converse(complement(composition(converse(A),
% complement(A)))) -> top
% Current number of equations to process: 2909
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [234]
% complement(composition(converse(A),complement(composition(A,complement(B))))) join B
% -> top
% Current number of equations to process: 2904
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [235]
% complement(converse(A) join complement(converse(complement(A)) join B)) ->
% complement(converse(A))
% Current number of equations to process: 2902
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [236]
% complement(one join complement(composition(converse(A),complement(A)))) ->
% composition(converse(A),complement(A))
% Current number of equations to process: 2898
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [237]
% composition(A,converse(complement(B))) join composition(A,converse(B)) ->
% composition(A,top)
% Current number of equations to process: 2897
% Current number of ordered equations: 0
% Current number of rules: 182
% New rule produced :
% [238]
% composition(A,converse(complement(converse(B)))) join composition(A,B) ->
% composition(A,top)
% Current number of equations to process: 2896
% Current number of ordered equations: 0
% Current number of rules: 183
% New rule produced :
% [239]
% complement(composition(A,complement(composition(converse(A),complement(B))))) join B
% -> top
% Current number of equations to process: 2895
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [240]
% composition(A,complement(converse(composition(converse(complement(B)),A)))) join B
% -> B
% Current number of equations to process: 2894
% Current number of ordered equations: 0
% Current number of rules: 185
% New rule produced :
% [241]
% converse(complement(one)) join complement(converse(composition(converse(A),
% complement(A)))) -> top
% Current number of equations to process: 2893
% Current number of ordered equations: 0
% Current number of rules: 186
% New rule produced :
% [242]
% converse(composition(converse(zero),top)) join converse(complement(one)) ->
% converse(complement(one))
% Current number of equations to process: 2934
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [243]
% complement(composition(converse(A),complement(composition(A,B)))) join
% complement(B) -> top
% Current number of equations to process: 2990
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [244] composition(converse(A),top) -> converse(composition(top,A))
% Rule
% [120]
% converse(composition(converse(zero),top)) join complement(one) ->
% complement(one) collapsed.
% Rule
% [175]
% complement(one) join complement(converse(composition(converse(zero),top))) ->
% top collapsed.
% Rule
% [176]
% converse(complement(one)) join composition(converse(zero),top) ->
% converse(complement(one)) collapsed.
% Rule
% [178]
% converse(complement(composition(converse(zero),top))) join complement(one) ->
% top collapsed.
% Rule [190] composition(A,complement(composition(converse(A),top))) -> zero
% collapsed.
% Rule
% [194] composition(converse(zero),top) join complement(one) -> complement(one)
% collapsed.
% Rule
% [195] complement(one) join complement(composition(converse(zero),top)) -> top
% collapsed.
% Rule
% [222]
% one join complement(converse(composition(converse(zero),top))) ->
% complement(converse(composition(converse(zero),top))) collapsed.
% Rule
% [242]
% converse(composition(converse(zero),top)) join converse(complement(one)) ->
% converse(complement(one)) collapsed.
% Current number of equations to process: 3108
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [245] complement(one) join complement(converse(composition(top,zero))) -> top
% Current number of equations to process: 3147
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [246]
% composition(A,converse(composition(B,top))) <->
% composition(composition(A,top),converse(B))
% Current number of equations to process: 3145
% Current number of ordered equations: 2
% Current number of rules: 182
% New rule produced :
% [247]
% composition(composition(A,converse(B)),top) ->
% composition(A,converse(composition(top,B)))
% Current number of equations to process: 3145
% Current number of ordered equations: 1
% Current number of rules: 183
% New rule produced :
% [248]
% composition(composition(A,top),converse(B)) <->
% composition(A,converse(composition(B,top)))
% Current number of equations to process: 3145
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [249]
% composition(converse(A),composition(top,B)) <->
% composition(converse(composition(top,A)),B)
% Current number of equations to process: 3143
% Current number of ordered equations: 2
% Current number of rules: 185
% New rule produced :
% [250]
% composition(top,composition(converse(A),B)) ->
% composition(converse(composition(A,top)),B)
% Current number of equations to process: 3143
% Current number of ordered equations: 1
% Current number of rules: 186
% New rule produced :
% [251]
% composition(converse(composition(top,A)),B) <->
% composition(converse(A),composition(top,B))
% Current number of equations to process: 3143
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [252]
% converse(complement(converse(composition(top,zero)))) join complement(one) ->
% top
% Current number of equations to process: 3137
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [253] composition(top,complement(composition(top,complement(A)))) join A -> A
% Current number of equations to process: 3136
% Current number of ordered equations: 0
% Current number of rules: 189
% New rule produced :
% [254]
% composition(top,complement(composition(top,A))) join complement(A) ->
% complement(A)
% Current number of equations to process: 3135
% Current number of ordered equations: 0
% Current number of rules: 190
% New rule produced :
% [255]
% converse(composition(composition(B,top),converse(A))) <->
% composition(composition(A,top),converse(B))
% Current number of equations to process: 3130
% Current number of ordered equations: 1
% Current number of rules: 191
% New rule produced :
% [256]
% composition(composition(A,top),converse(B)) <->
% converse(composition(composition(B,top),converse(A)))
% Current number of equations to process: 3130
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced :
% [257]
% converse(composition(B,converse(composition(A,top)))) <->
% composition(A,converse(composition(B,top)))
% Current number of equations to process: 3128
% Current number of ordered equations: 1
% Current number of rules: 193
% New rule produced :
% [258]
% composition(A,converse(composition(B,top))) <->
% converse(composition(B,converse(composition(A,top))))
% Current number of equations to process: 3128
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [259]
% converse(composition(converse(composition(top,B)),A)) <->
% composition(converse(composition(top,A)),B)
% Current number of equations to process: 3126
% Current number of ordered equations: 1
% Current number of rules: 195
% New rule produced :
% [260]
% composition(converse(composition(top,A)),B) <->
% converse(composition(converse(composition(top,B)),A))
% Current number of equations to process: 3126
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [261]
% converse(composition(converse(B),composition(top,A))) <->
% composition(converse(A),composition(top,B))
% Current number of equations to process: 3123
% Current number of ordered equations: 1
% Current number of rules: 197
% New rule produced :
% [262]
% composition(converse(A),composition(top,B)) <->
% converse(composition(converse(B),composition(top,A)))
% Current number of equations to process: 3123
% Current number of ordered equations: 0
% Current number of rules: 198
% New rule produced :
% [263]
% converse(complement(one)) join composition(top,zero) ->
% converse(complement(one))
% Current number of equations to process: 3121
% Current number of ordered equations: 0
% Current number of rules: 199
% New rule produced :
% [264]
% converse(composition(zero,converse(A))) join composition(A,top) ->
% composition(A,top)
% Current number of equations to process: 3120
% Current number of ordered equations: 0
% Current number of rules: 200
% New rule produced :
% [265]
% complement(composition(top,complement(composition(top,A)))) join complement(A)
% -> top
% Current number of equations to process: 3118
% Current number of ordered equations: 0
% Current number of rules: 201
% New rule produced :
% [266]
% converse(complement(converse(composition(converse(A),complement(composition(A,top))))))
% -> top
% Current number of equations to process: 3117
% Current number of ordered equations: 0
% Current number of rules: 202
% New rule produced :
% [267] composition(top,complement(composition(top,top))) join A -> A
% Current number of equations to process: 3130
% Current number of ordered equations: 0
% Current number of rules: 203
% New rule produced :
% [268] converse(complement(A)) join complement(converse(zero)) -> top
% Current number of equations to process: 3133
% Current number of ordered equations: 0
% Current number of rules: 204
% New rule produced : [269] converse(complement(converse(zero))) join A -> top
% Rule [153] converse(complement(converse(zero))) join complement(A) -> top
% collapsed.
% Rule [184] one join converse(complement(converse(zero))) -> top collapsed.
% Current number of equations to process: 3137
% Current number of ordered equations: 0
% Current number of rules: 203
% New rule produced :
% [270] converse(complement(one)) join complement(one) -> complement(one)
% Current number of equations to process: 3140
% Current number of ordered equations: 0
% Current number of rules: 204
% New rule produced : [271] composition(top,A) join complement(A) -> top
% Current number of equations to process: 3141
% Current number of ordered equations: 0
% Current number of rules: 205
% New rule produced : [272] composition(top,A) join A -> composition(top,A)
% Current number of equations to process: 3142
% Current number of ordered equations: 0
% Current number of rules: 206
% New rule produced :
% [273] converse(complement(converse(A))) join composition(top,A) -> top
% Current number of equations to process: 3141
% Current number of ordered equations: 0
% Current number of rules: 207
% New rule produced : [274] composition(top,top) join complement(A) -> top
% Current number of equations to process: 3146
% Current number of ordered equations: 0
% Current number of rules: 208
% New rule produced : [275] composition(top,complement(A)) join A -> top
% Current number of equations to process: 3148
% Current number of ordered equations: 0
% Current number of rules: 209
% New rule produced :
% [276] converse(composition(complement(A),top)) join converse(A) -> top
% Current number of equations to process: 3166
% Current number of ordered equations: 0
% Current number of rules: 210
% New rule produced : [277] composition(top,top) -> top
% Rule [267] composition(top,complement(composition(top,top))) join A -> A
% collapsed.
% Rule [274] composition(top,top) join complement(A) -> top collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 3175
% Current number of ordered equations: 0
% Current number of rules: 209
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 11 rules have been used:
% [1]
% converse(converse(A)) -> A; trace = in the starting set
% [2] composition(A,one) -> A; trace = in the starting set
% [3] complement(A) join A -> top; trace = in the starting set
% [6] composition(converse(B),converse(A)) -> converse(composition(A,B)); trace = in the starting set
% [11] composition(A join B,C) -> composition(A,C) join composition(B,C); trace = in the starting set
% [17] converse(composition(converse(B),A)) <-> composition(converse(A),B); trace = Cp of 6 and 1
% [22] composition(complement(B),A) join composition(B,A) -> composition(top,A); trace = Cp of 11 and 3
% [44] top join A -> top; trace = Self cp of 3
% [59] composition(converse(one),A) -> A; trace = Cp of 17 and 2
% [156] composition(complement(one),A) join A -> composition(top,A); trace = Cp of 59 and 22
% [277] composition(top,top) -> top; trace = Cp of 156 and 44
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 13.990000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------