TSTP Solution File: LAT028-1 by CiME---2.01

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : LAT028-1 : TPTP v6.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n037.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 00:26:09 EDT 2014

% Result   : Unsatisfiable 1.33s
% Output   : Refutation 1.33s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : LAT028-1 : TPTP v6.0.0. Released v2.2.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n037.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 16:49:18 CDT 2014
% % CPUTime  : 1.33 
% Processing problem /tmp/CiME_35361_n037.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " meet2,join,meet : infix commutative; b,a : constant;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% X meet X = X;
% X join X = X;
% ((X join Y) meet (Z join Y)) meet Y = Y;
% ((X meet Y) join (Z meet Y)) join Y = Y;
% X meet2 X = X;
% ((X join Y) meet2 (Z join Y)) meet2 Y = Y;
% ((X meet2 Y) join (Z meet2 Y)) join Y = Y;
% ";
% 
% 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 (Y join Z)) meet Y = Y,
% ((X meet Y) join (Y meet Z)) join Y = Y,
% X meet2 X = X,
% ((X join Y) meet2 (Y join Z)) meet2 Y = Y,
% ((X meet2 Y) join (Y meet2 Z)) join Y = Y }
% (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 (Y join Z)) meet2 Y -> Y
% 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 (Y meet Z)) join Y -> Y
% 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 (Y meet2 Z)) join Y -> Y
% 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 (Y join Z)) meet Y -> Y
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [8] (X join Y) meet2 Y -> Y
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [9] (X meet Y) join Y -> Y
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [10] (X meet2 Y) join Y -> Y
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] (X join Y) meet Y -> Y
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] (X meet Y) meet2 X -> X meet Y
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] (X meet2 Y) meet2 X -> X meet2 Y
% Current number of equations to process: 23
% Current number of ordered equations: 1
% Current number of rules: 13
% New rule produced : [14] (X join Y) join Y -> X join Y
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] (X meet Y) meet Y -> X meet Y
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] (X meet2 Y) meet Y -> X meet2 Y
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] ((X meet2 Y) join (X meet Z)) join X -> X
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] ((X join Y) meet (Y join Z)) meet2 Y -> Y
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] ((X join Y) meet2 (Y join Z)) meet Y -> Y
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20] ((X meet Y) join (Y meet Z)) meet2 Y -> (X meet Y) join (Y meet Z)
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21] ((X meet2 Y) join (Y meet2 Z)) meet2 Y -> (X meet2 Y) join (Y meet2 Z)
% Current number of equations to process: 57
% Current number of ordered equations: 2
% Current number of rules: 21
% New rule produced :
% [22] (((X join Y) meet2 Z) join X) join (X join Y) -> X join Y
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [23] (((X meet Y) join Z) meet2 X) meet2 (X meet Y) -> X meet Y
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [24] (X meet2 Y) meet2 (X meet Y) -> X meet Y
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [25] (X meet2 Y) join (X meet Y) -> X meet2 Y
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [26] (X meet2 Y) meet (X meet Y) -> X meet Y
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [27] ((X join Y) meet (Y join Z)) join Y -> (X join Y) meet (Y join Z)
% Current number of equations to process: 97
% Current number of ordered equations: 2
% Current number of rules: 27
% New rule produced :
% [28] (((X meet Y) join Z) meet X) meet (X meet Y) -> X meet Y
% Current number of equations to process: 97
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [29] ((X join Y) meet2 (Y join Z)) join Y -> (X join Y) meet2 (Y join Z)
% Current number of equations to process: 126
% Current number of ordered equations: 2
% Current number of rules: 29
% New rule produced :
% [30] (((X meet2 Y) join Z) meet2 X) meet2 (X meet2 Y) -> X meet2 Y
% Current number of equations to process: 126
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [31] (X meet2 Y) meet (((X meet2 Y) join Z) meet X) -> X meet2 Y
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [32] X meet Y -> X meet2 Y
% Rule [3] X meet X -> X collapsed.
% Rule [5] ((X meet Y) join (Y meet Z)) join Y -> Y collapsed.
% Rule [7] ((X join Y) meet (Y join Z)) meet Y -> Y collapsed.
% Rule [9] (X meet Y) join Y -> Y collapsed.
% Rule [11] (X join Y) meet Y -> Y collapsed.
% Rule [12] (X meet Y) meet2 X -> X meet Y collapsed.
% Rule [15] (X meet Y) meet Y -> X meet Y collapsed.
% Rule [16] (X meet2 Y) meet Y -> X meet2 Y collapsed.
% Rule [17] ((X meet2 Y) join (X meet Z)) join X -> X collapsed.
% Rule [18] ((X join Y) meet (Y join Z)) meet2 Y -> Y collapsed.
% Rule [19] ((X join Y) meet2 (Y join Z)) meet Y -> Y collapsed.
% Rule [20] ((X meet Y) join (Y meet Z)) meet2 Y -> (X meet Y) join (Y meet Z)
% collapsed.
% Rule [23] (((X meet Y) join Z) meet2 X) meet2 (X meet Y) -> X meet Y
% collapsed.
% Rule [24] (X meet2 Y) meet2 (X meet Y) -> X meet Y collapsed.
% Rule [25] (X meet2 Y) join (X meet Y) -> X meet2 Y collapsed.
% Rule [26] (X meet2 Y) meet (X meet Y) -> X meet Y collapsed.
% Rule [27] ((X join Y) meet (Y join Z)) join Y -> (X join Y) meet (Y join Z)
% collapsed.
% Rule [28] (((X meet Y) join Z) meet X) meet (X meet Y) -> X meet Y collapsed.
% Rule [31] (X meet2 Y) meet (((X meet2 Y) join Z) meet X) -> X meet2 Y
% collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% Trivial
% 
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 13
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% 
% The following 6 rules have been used:
% [2] 
% X join X -> X; trace = in the starting set
% [6] ((X meet2 Y) join (Y meet2 Z)) join Y -> Y; trace = in the starting set
% [7] ((X join Y) meet (Y join Z)) meet Y -> Y; trace = in the starting set
% [10] (X meet2 Y) join Y -> Y; trace = Cp of 6 and 2
% [31] (X meet2 Y) meet (((X meet2 Y) join Z) meet X) -> X meet2 Y; trace = Cp of 10 and 7
% [32] X meet Y -> X meet2 Y; trace = Cp of 31 and 10
% % SZS output end Refutation
% All conjectures have been proven
% 
% Execution time: 0.210000 sec
% res : bool = true
% time is now off
% 
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
% 
% EOF
%------------------------------------------------------------------------------