%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : REL008-1 : TPTP v6.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n142.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 00:30:50 EDT 2014
% Result : Unsatisfiable 2.03s
% Output : Refutation 2.03s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : REL008-1 : TPTP v6.0.0. Released v4.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n142.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 16:26:03 CDT 2014
% % CPUTime : 2.03
% Processing problem /tmp/CiME_48819_n142.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " join : AC; sk3,sk2,sk1,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 "
% sk3 lr_lex;
% sk2 lr_lex;
% sk1 lr_lex;
% 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 > sk1 > sk2 > sk3";
%
% let s2 = status F "
% sk3 mul;
% sk2 mul;
% sk1 mul;
% 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 = sk1 = sk2 = sk3";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " composition(sk1,sk2 join sk3) = composition(sk1,sk2) join composition(sk1,sk3);"
% ;
% (*
% 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(sk1,sk3 join sk2) =
% composition(sk1,sk3) join composition(sk1,sk2) }
% (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.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 811
% Current number of ordered equations: 0
% Current number of rules: 124
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 5 rules have been used:
% [1]
% converse(converse(A)) -> A; trace = in the starting set
% [5] converse(A join B) -> converse(A) join converse(B); trace = in the starting set
% [6] composition(converse(B),converse(A)) -> converse(composition(A,B)); trace = in the starting set
% [49] converse(composition(C,A join B)) ->
% converse(composition(C,A)) join converse(composition(C,B)); trace = Cp of 6 and 5
% [138] composition(A,B join C) -> composition(A,B) join composition(A,C); trace = Cp of 49 and 1
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.910000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------