TSTP Solution File: LAT043-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : LAT043-1 : TPTP v6.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n049.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 00:26:10 EDT 2014
% Result : Unsatisfiable 2.18s
% Output : Refutation 2.18s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : LAT043-1 : TPTP v6.0.0. Released v2.5.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n049.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 17:34:38 CDT 2014
% % CPUTime : 2.18
% Processing problem /tmp/CiME_10068_n049.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " join,meet : AC; d,c,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;
% X meet (Y join Z) = (X meet Y) join (X meet Z);
% complement(X) join X = n1;
% complement(X) meet X = n0;
% complement(complement(X)) = X;
% ";
%
% let s1 = status F "
% d lr_lex;
% c lr_lex;
% n0 lr_lex;
% n1 lr_lex;
% complement lr_lex;
% join mul;
% meet mul;
% ";
%
% let p1 = precedence F "
% complement > meet > join > n1 > n0 > c > d";
%
% let s2 = status F "
% d mul;
% c mul;
% n0 mul;
% n1 mul;
% complement mul;
% join mul;
% meet mul;
% ";
%
% let p2 = precedence F "
% complement > meet > join > n1 = n0 = c = d";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " complement(c join d) = complement(c) meet complement(d);"
% ;
% (*
% 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,
% (Y join Z) meet X = (X meet Y) join (X meet Z),
% complement(X) join X = n1,
% complement(X) meet X = n0,
% complement(complement(X)) = X } (8 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 = { complement(d join c) =
% complement(d) meet complement(c) }
% (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: 7
% 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: 6
% 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: 5
% 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: 4
% 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: 3
% 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: 2
% 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: 1
% Current number of rules: 7
% New rule produced : [8] (Y join Z) meet X -> (X meet Y) join (X meet Z)
% Rule [7] (X join Y) meet X -> X collapsed.
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [9] n1 join X -> n1
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [10] n0 meet X -> n0
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [11] n0 join X -> X
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [12] complement(X meet Y) join X -> n1
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [13] n1 meet X meet Y -> X meet Y
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [14] complement(n0) -> n1
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [15] n1 meet X -> X
% Rule [13] n1 meet X meet Y -> X meet Y collapsed.
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [16] complement(n1) -> n0
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [17] (complement(Y) meet X) join (X meet Y) -> X
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [18] (complement(X) meet Y) join X -> X join Y
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [19] (X meet Y) join complement(Y) -> complement(Y) join X
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [20] complement(complement(X) meet Y) meet X -> X
% Current number of equations to process: 132
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [21] complement(X meet Y) meet complement(Y) -> complement(Y)
% Current number of equations to process: 131
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [22] complement(X meet Y) join complement(Y) -> complement(X meet Y)
% Current number of equations to process: 413
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [23] (complement(X meet Y) meet Z) join X -> X join Z
% Current number of equations to process: 452
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [24] complement(complement(X meet Y) meet Y) meet X -> X
% Current number of equations to process: 505
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [25] complement(X meet Y) meet Y -> complement(X) meet Y
% Rule [24] complement(complement(X meet Y) meet Y) meet X -> X collapsed.
% Current number of equations to process: 580
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [26] complement(X meet Y) -> complement(X) join complement(Y)
% Rule [12] complement(X meet Y) join X -> n1 collapsed.
% Rule [20] complement(complement(X) meet Y) meet X -> X collapsed.
% Rule [21] complement(X meet Y) meet complement(Y) -> complement(Y) collapsed.
% Rule [22] complement(X meet Y) join complement(Y) -> complement(X meet Y)
% collapsed.
% Rule [23] (complement(X meet Y) meet Z) join X -> X join Z collapsed.
% Rule [25] complement(X meet Y) meet Y -> complement(X) meet Y collapsed.
% Current number of equations to process: 670
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [27] complement(complement(X) join complement(Y)) -> X meet Y
% Current number of equations to process: 670
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [28] complement(complement(X) join Y) -> complement(Y) meet X
% Rule [27] complement(complement(X) join complement(Y)) -> X meet Y collapsed.
% Current number of equations to process: 677
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [29] complement(X join Y) meet Y -> n0
% Current number of equations to process: 681
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [30] complement(X join Y) -> complement(X) meet complement(Y)
% Rule [28] complement(complement(X) join Y) -> complement(Y) meet X collapsed.
% Rule [29] complement(X join Y) meet Y -> n0 collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 680
% Current number of ordered equations: 0
% Current number of rules: 18
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 13 rules have been used:
% [1]
% complement(complement(X)) -> X; trace = in the starting set
% [4] complement(X) join X -> n1; trace = in the starting set
% [5] complement(X) meet X -> n0; trace = in the starting set
% [6] (X meet Y) join X -> X; trace = in the starting set
% [8] (Y join Z) meet X -> (X meet Y) join (X meet Z); trace = in the starting set
% [17] (complement(Y) meet X) join (X meet Y) -> X; trace = Cp of 8 and 4
% [19] (X meet Y) join complement(Y) -> complement(Y) join X; trace = Cp of 17 and 6
% [24] complement(complement(X meet Y) meet Y) meet X -> X; trace = Cp of 17 and 5
% [25] complement(X meet Y) meet Y -> complement(X) meet Y; trace = Cp of 24 and 5
% [26] complement(X meet Y) -> complement(X) join complement(Y); trace = Cp of 25 and 19
% [27] complement(complement(X) join complement(Y)) -> X meet Y; trace = Cp of 26 and 1
% [28] complement(complement(X) join Y) -> complement(Y) meet X; trace = Cp of 27 and 1
% [30] complement(X join Y) -> complement(X) meet complement(Y); trace = Cp of 28 and 1
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 1.070000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------