TSTP Solution File: LAT044-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : LAT044-1 : TPTP v6.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n139.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 00:26:11 EDT 2014
% Result : Unsatisfiable 28.02s
% Output : Refutation 28.02s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : LAT044-1 : TPTP v6.0.0. Released v2.5.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n139.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 17:37:48 CDT 2014
% % CPUTime : 28.02
% Processing problem /tmp/CiME_62413_n139.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " join,meet : AC; b,a,n0,n1 : constant; complement : 1;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% X meet X = X;
% X join X = X;
% X meet (X join Y) = X;
% X join (X meet Y) = X;
% complement(X join Y) = complement(X) meet complement(Y);
% complement(X meet Y) = complement(X) join complement(Y);
% complement(X) join X = n1;
% complement(X) meet X = n0;
% complement(complement(X)) = X;
% X join (complement(X) meet (X join Y)) = X join Y;
% ";
%
% let s1 = status F "
% b lr_lex;
% a lr_lex;
% n0 lr_lex;
% n1 lr_lex;
% complement lr_lex;
% join mul;
% meet mul;
% ";
%
% let p1 = precedence F "
% complement > meet > join > n1 > n0 > a > b";
%
% let s2 = status F "
% b mul;
% a mul;
% n0 mul;
% n1 mul;
% complement mul;
% join mul;
% meet mul;
% ";
%
% let p2 = precedence F "
% complement > meet > join > n1 = n0 = a = b";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " (complement(a) meet (a join b)) join (complement(b) join (a meet b)) = n1;"
% ;
% (*
% 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 = { X meet X = X,
% X join X = X,
% (X join Y) meet X = X,
% (X meet Y) join X = X,
% complement(X join Y) =
% complement(X) meet complement(Y),
% complement(X meet Y) =
% complement(X) join complement(Y),
% complement(X) join X = n1,
% complement(X) meet X = n0,
% complement(complement(X)) = X,
% ((X join Y) meet complement(X)) join X =
% X join Y } (10 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 = { ((b join a) meet complement(a)) join
% (b meet a) join complement(b) = n1 }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] complement(complement(X)) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 1
% New rule produced : [2] X join X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 2
% New rule produced : [3] X meet X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 3
% New rule produced : [4] complement(X) join X -> n1
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 4
% New rule produced : [5] complement(X) meet X -> n0
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 5
% New rule produced : [6] (X meet Y) join X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 6
% New rule produced : [7] (X join Y) meet X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 7
% New rule produced :
% [8] complement(X join Y) -> complement(X) meet complement(Y)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 8
% New rule produced :
% [9] complement(X meet Y) -> complement(X) join complement(Y)
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced : [10] ((X join Y) meet complement(X)) join X -> X join Y
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] n1 join X -> n1
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] n0 meet X -> n0
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] n0 join X -> X
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [14] n1 meet X -> X
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] complement(n1) -> n0
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] complement(n0) -> n1
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17] (complement(X) meet complement(Y)) join X join Y -> n1
% Current number of equations to process: 105
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18] (X join Y) meet complement(X) meet complement(Y) -> n0
% Current number of equations to process: 112
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19] (X meet Y) join complement(X) join complement(Y) -> n1
% Current number of equations to process: 119
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20] (complement(X) join complement(Y)) meet X meet Y -> n0
% Current number of equations to process: 131
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21] (complement(X) meet Y) join complement(Y) join X -> n1
% Current number of equations to process: 135
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22] (complement(X) join Y) meet complement(Y) meet X -> n0
% Current number of equations to process: 145
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [23]
% ((complement(X) join Y) meet X) join complement(X) -> complement(X) join Y
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [24]
% ((complement(X) meet Y) join complement(Y)) meet Y -> complement(X) meet Y
% Current number of equations to process: 161
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [25] ((X meet Y) join complement(Y)) meet Y -> X meet Y
% Rule
% [24]
% ((complement(X) meet Y) join complement(Y)) meet Y -> complement(X) meet Y
% collapsed.
% Current number of equations to process: 186
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [26]
% ((complement(X) meet Y) join X) meet complement(X) -> complement(X) meet Y
% Current number of equations to process: 229
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [27] ((X join Y) meet Z) join (X meet Z) -> (X join Y) meet Z
% Current number of equations to process: 237
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [28] ((X meet Y) join Z) meet (X join Z) -> (X meet Y) join Z
% Current number of equations to process: 245
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [29] ((complement(X) join complement(Y)) meet X) join (X meet Y) -> X
% Current number of equations to process: 502
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [30] ((complement(X) join complement(Y)) meet Y) join X -> X join Y
% Current number of equations to process: 552
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [31]
% ((complement(X) join Y) meet complement(Y)) join X -> complement(Y) join X
% Current number of equations to process: 630
% Current number of ordered equations: 1
% Current number of rules: 30
% New rule produced :
% [32]
% ((complement(X) join Y) meet X) join complement(Y) -> complement(Y) join X
% Current number of equations to process: 634
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [33]
% ((complement(Y) meet X) join Y) meet complement(X) -> complement(X) meet Y
% Current number of equations to process: 658
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [34]
% ((complement(Y) meet X) join complement(X)) meet Y -> complement(X) meet Y
% Current number of equations to process: 712
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [35] ((complement(X) meet complement(Y)) join Y) meet X -> X meet Y
% Current number of equations to process: 763
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [36] ((complement(X) meet complement(Y)) join X) meet (X join Y) -> X
% Current number of equations to process: 869
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [37] ((complement(X) join Z) meet (X join Y)) join X -> X join Y
% Current number of equations to process: 964
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [38] ((complement(X) join Y) meet complement(Z)) join X join Z -> n1
% Current number of equations to process: 1041
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [39] ((X join Y) meet Z) join complement(X) join complement(Z) -> n1
% Current number of equations to process: 1057
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [40] ((complement(X) join Y) meet Z) join complement(Z) join X -> n1
% Current number of equations to process: 1109
% Current number of ordered equations: 1
% Current number of rules: 39
% New rule produced :
% [41] ((X join Y) meet complement(Z)) join complement(X) join Z -> n1
% Current number of equations to process: 1109
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [42] ((X meet Y) join Z) meet complement(X) meet complement(Z) -> n0
% Current number of equations to process: 1166
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [43] ((complement(X) meet Y) join complement(Z)) meet X meet Z -> n0
% Current number of equations to process: 1204
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [44] ((complement(X) meet Y) join Z) meet complement(Z) meet X -> n0
% Current number of equations to process: 1214
% Current number of ordered equations: 1
% Current number of rules: 43
% New rule produced :
% [45] ((X meet Y) join complement(Z)) meet complement(X) meet Z -> n0
% Current number of equations to process: 1214
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [46] ((complement(X) meet Z) join (X meet Y)) meet X -> X meet Y
% Current number of equations to process: 1252
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [47] ((complement(X) join Y) meet X) join (complement(Y) meet X) -> X
% Current number of equations to process: 1316
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [48]
% ((X meet Y) join complement(Y)) meet complement(X) ->
% complement(X) meet complement(Y)
% Current number of equations to process: 1379
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [49]
% ((X join Y) meet complement(Y)) join complement(X) ->
% complement(X) join complement(Y)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 1460
% Current number of ordered equations: 0
% Current number of rules: 48
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 7 rules have been used:
% [1]
% complement(complement(X)) -> X; trace = in the starting set
% [6] (X meet Y) join X -> X; trace = in the starting set
% [10] ((X join Y) meet complement(X)) join X -> X join Y; trace = in the starting set
% [29] ((complement(X) join complement(Y)) meet X) join (X meet Y) -> X; trace = Cp of 10 and 6
% [30] ((complement(X) join complement(Y)) meet Y) join X -> X join Y; trace = Cp of 29 and 6
% [31] ((complement(X) join Y) meet complement(Y)) join X ->
% complement(Y) join X; trace = Cp of 30 and 1
% [49] ((X join Y) meet complement(Y)) join complement(X) ->
% complement(X) join complement(Y); trace = Cp of 31 and 1
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 26.850000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------