TSTP Solution File: LAT011-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : LAT011-1 : TPTP v6.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n080.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 00:26:08 EDT 2014
% Result : Unsatisfiable 3.45s
% Output : Refutation 3.45s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : LAT011-1 : TPTP v6.0.0. Released v2.2.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n080.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 15:58:58 CDT 2014
% % CPUTime : 3.45
% Processing problem /tmp/CiME_62861_n080.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " meet2,join,meet : AC; b,a : constant;";
% 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 meet2 X = X;
% X meet2 (X join Y) = X;
% X join (X meet2 Y) = X;
% ";
%
% let s1 = status F "
% b lr_lex;
% a lr_lex;
% meet2 mul;
% join mul;
% meet mul;
% ";
%
% let p1 = precedence F "
% meet > join > meet2 > a > b";
%
% let s2 = status F "
% b mul;
% a mul;
% meet2 mul;
% join mul;
% meet mul;
% ";
%
% let p2 = precedence F "
% meet > join > meet2 > a = b";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " a meet b = a meet2 b;"
% ;
% (*
% 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,
% X meet2 X = X,
% (X join Y) meet2 X = X,
% (X meet2 Y) join X = X } (7 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 meet a = b meet2 a } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] X meet2 X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 6
% 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: 5
% 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: 4
% Current number of rules: 3
% New rule produced : [4] (X join Y) meet2 X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 4
% New rule produced : [5] (X meet Y) join X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 5
% New rule produced : [6] (X meet2 Y) join X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 1
% 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: 0
% Current number of rules: 7
% New rule produced : [8] (X meet Y) meet2 X -> X meet Y
% Current number of equations to process: 139
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [9] (X meet2 Y) meet X -> X meet2 Y
% Current number of equations to process: 214
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [10] ((X meet2 Y) meet Z) join X -> X
% Current number of equations to process: 322
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] ((X meet Y) meet2 Z) join X -> X
% Current number of equations to process: 420
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] (X join Y) meet2 (X meet Z) -> X meet Z
% Current number of equations to process: 536
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] (X meet2 Y) meet (X join Z) -> X meet2 Y
% Current number of equations to process: 642
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [14] ((X meet2 Y) meet Z) meet2 X -> (X meet2 Y) meet Z
% Current number of equations to process: 751
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] (((X meet2 Y) meet Z) meet2 V_3) join X -> X
% Current number of equations to process: 799
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] ((X meet Y) meet2 Z) meet X -> (X meet Y) meet2 Z
% Current number of equations to process: 958
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] (((X meet Y) meet2 Z) meet V_3) join X -> X
% Current number of equations to process: 1008
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] ((X meet Y) meet2 Z) join (X meet2 Z) -> X meet2 Z
% Current number of equations to process: 1161
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] (X meet2 Y) join (X meet Y) -> X meet2 Y
% Current number of equations to process: 1264
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] X meet Y -> X meet2 Y
% Rule [3] X meet X -> X collapsed.
% Rule [5] (X meet Y) join X -> X collapsed.
% Rule [7] (X join Y) meet X -> X collapsed.
% Rule [8] (X meet Y) meet2 X -> X meet Y collapsed.
% Rule [9] (X meet2 Y) meet X -> X meet2 Y collapsed.
% Rule [10] ((X meet2 Y) meet Z) join X -> X collapsed.
% Rule [11] ((X meet Y) meet2 Z) join X -> X collapsed.
% Rule [12] (X join Y) meet2 (X meet Z) -> X meet Z collapsed.
% Rule [13] (X meet2 Y) meet (X join Z) -> X meet2 Y collapsed.
% Rule [14] ((X meet2 Y) meet Z) meet2 X -> (X meet2 Y) meet Z collapsed.
% Rule [15] (((X meet2 Y) meet Z) meet2 V_3) join X -> X collapsed.
% Rule [16] ((X meet Y) meet2 Z) meet X -> (X meet Y) meet2 Z collapsed.
% Rule [17] (((X meet Y) meet2 Z) meet V_3) join X -> X collapsed.
% Rule [18] ((X meet Y) meet2 Z) join (X meet2 Z) -> X meet2 Z collapsed.
% Rule [19] (X meet2 Y) join (X meet Y) -> X meet2 Y collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 1421
% Current number of ordered equations: 0
% Current number of rules: 5
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 8 rules have been used:
% [4]
% (X join Y) meet2 X -> X; trace = in the starting set
% [5] (X meet Y) join X -> X; trace = in the starting set
% [6] (X meet2 Y) join X -> X; trace = in the starting set
% [7] (X join Y) meet X -> X; trace = in the starting set
% [8] (X meet Y) meet2 X -> X meet Y; trace = Cp of 5 and 4
% [18] ((X meet Y) meet2 Z) join (X meet2 Z) -> X meet2 Z; trace = Cp of 8 and 6
% [19] (X meet2 Y) join (X meet Y) -> X meet2 Y; trace = Cp of 18 and 8
% [20] X meet Y -> X meet2 Y; trace = Cp of 19 and 7
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 2.340000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------