TSTP Solution File: LAT089-1 by CiME---2.01
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : LAT089-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n163.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 00:26:20 EDT 2014
% Result : Unsatisfiable 1.21s
% Output : Refutation 1.21s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----WARNING: CiME---2.01 format not known, defaulting to TPTP
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : LAT089-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n163.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 21:47:08 CDT 2014
% % CPUTime : 1.21
% Processing problem /tmp/CiME_10028_n163.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a,b : constant; join : 2; meet : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% join(meet(A,B),meet(A,join(A,B))) = A;
% join(meet(A,A),meet(B,join(A,A))) = A;
% join(meet(A,B),meet(B,join(A,B))) = B;
% meet(meet(join(A,B),join(C,A)),A) = A;
% join(join(meet(A,B),meet(C,A)),A) = A;
% ";
%
% let s1 = status F "
% a lr_lex;
% b lr_lex;
% join lr_lex;
% meet lr_lex;
% ";
%
% let p1 = precedence F "
% meet > join > b > a";
%
% let s2 = status F "
% a mul;
% b mul;
% join mul;
% meet mul;
% ";
%
% let p2 = precedence F "
% meet > join > b = a";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " meet(b,a) = meet(a,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 = { join(meet(A,B),meet(A,join(A,B))) = A,
% join(meet(A,A),meet(B,join(A,A))) = A,
% join(meet(A,B),meet(B,join(A,B))) = B,
% meet(meet(join(A,B),join(C,A)),A) = A,
% join(join(meet(A,B),meet(C,A)),A) = A }
% (5 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 = { meet(b,a) = meet(a,b) } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] join(meet(A,B),meet(A,join(A,B))) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 1
% New rule produced : [2] join(meet(A,B),meet(B,join(A,B))) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 2
% New rule produced : [3] join(meet(A,A),meet(B,join(A,A))) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 3
% New rule produced : [4] join(join(meet(A,B),meet(C,A)),A) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 4
% New rule produced : [5] meet(meet(join(A,B),join(C,A)),A) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [6] join(meet(A,A),join(A,A)) -> A
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] join(join(meet(A,B),A),A) -> A
% Current number of equations to process: 18
% Current number of ordered equations: 1
% Current number of rules: 7
% New rule produced : [8] meet(meet(join(A,B),A),A) -> A
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [9] meet(meet(A,meet(A,B)),meet(A,B)) -> meet(A,B)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [10] meet(meet(A,B),meet(A,B)) -> meet(A,B)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] meet(A,A) -> A
% Rule [3] join(meet(A,A),meet(B,join(A,A))) -> A collapsed.
% Rule [6] join(meet(A,A),join(A,A)) -> A collapsed.
% Rule [10] meet(meet(A,B),meet(A,B)) -> meet(A,B) collapsed.
% Current number of equations to process: 38
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [12] join(A,meet(B,join(A,A))) -> A
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [13] join(A,join(A,A)) -> A
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [14] meet(join(A,A),A) -> A
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [15] join(join(A,A),A) -> A
% Current number of equations to process: 38
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [16] join(join(A,meet(B,A)),A) -> A
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [17] meet(meet(A,join(B,A)),A) -> A
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [18] join(A,A) -> A
% Rule [12] join(A,meet(B,join(A,A))) -> A collapsed.
% Rule [13] join(A,join(A,A)) -> A collapsed.
% Rule [14] meet(join(A,A),A) -> A collapsed.
% Rule [15] join(join(A,A),A) -> A collapsed.
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [19] join(A,meet(B,A)) -> A
% Rule [16] join(join(A,meet(B,A)),A) -> A collapsed.
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [20] join(meet(A,meet(B,A)),A) -> A
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [21] meet(A,meet(A,join(B,A))) -> meet(A,join(B,A))
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [22] join(meet(meet(A,meet(B,A)),A),A) -> A
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [23] meet(meet(A,meet(B,A)),A) -> meet(A,meet(B,A))
% Rule [22] join(meet(meet(A,meet(B,A)),A),A) -> A collapsed.
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [24] join(A,meet(A,meet(B,A))) -> A
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [25] join(meet(A,meet(A,meet(B,A))),A) -> A
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [26] join(A,meet(A,meet(A,meet(B,A)))) -> A
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [27] meet(meet(A,meet(B,A)),meet(B,A)) -> meet(B,A)
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [28] meet(B,meet(A,B)) -> meet(A,B)
% Rule [20] join(meet(A,meet(B,A)),A) -> A collapsed.
% Rule [23] meet(meet(A,meet(B,A)),A) -> meet(A,meet(B,A)) collapsed.
% Rule [24] join(A,meet(A,meet(B,A))) -> A collapsed.
% Rule [25] join(meet(A,meet(A,meet(B,A))),A) -> A collapsed.
% Rule [26] join(A,meet(A,meet(A,meet(B,A)))) -> A collapsed.
% Rule [27] meet(meet(A,meet(B,A)),meet(B,A)) -> meet(B,A) collapsed.
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [29] join(meet(B,A),A) -> A
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [30] meet(meet(B,A),A) -> meet(B,A)
% Rule [8] meet(meet(join(A,B),A),A) -> A collapsed.
% Rule [9] meet(meet(A,meet(A,B)),meet(A,B)) -> meet(A,B) collapsed.
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [31] meet(join(A,B),A) -> A
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [32] meet(A,meet(A,B)) -> meet(A,B)
% Rule [21] meet(A,meet(A,join(B,A))) -> meet(A,join(B,A)) collapsed.
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [33] join(join(meet(A,B),meet(C,B)),B) -> B
% Current number of equations to process: 75
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [34] join(A,meet(A,join(join(A,B),A))) -> A
% Current number of equations to process: 77
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [35] meet(A,join(meet(A,B),A)) -> join(meet(A,B),A)
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [36] meet(join(meet(A,B),A),A) -> A
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [37] join(join(A,join(A,B)),join(A,B)) -> join(A,B)
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [38] meet(join(A,join(A,B)),join(A,B)) -> join(A,B)
% Current number of equations to process: 93
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [39] join(A,join(meet(A,join(B,A)),A)) -> A
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [40] join(meet(A,join(B,A)),A) -> A
% Rule [39] join(A,join(meet(A,join(B,A)),A)) -> A collapsed.
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [41] meet(A,join(join(A,B),A)) -> A
% Rule [34] join(A,meet(A,join(join(A,B),A))) -> A collapsed.
% Current number of equations to process: 98
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [42] meet(join(join(A,B),A),A) -> A
% Current number of equations to process: 109
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [43] join(A,meet(A,join(B,A))) -> meet(A,join(B,A))
% Current number of equations to process: 122
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [44] join(join(join(A,B),A),A) -> join(join(A,B),A)
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [45] join(A,join(join(A,B),A)) -> join(join(A,B),A)
% Current number of equations to process: 120
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [46] join(A,join(meet(A,B),A)) -> join(meet(A,B),A)
% Current number of equations to process: 122
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [47] meet(meet(A,B),join(A,meet(A,B))) -> meet(A,B)
% Current number of equations to process: 133
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [48] meet(join(A,meet(A,B)),meet(A,B)) -> meet(A,B)
% Current number of equations to process: 140
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [49] join(meet(A,B),meet(A,join(A,meet(A,B)))) -> A
% Current number of equations to process: 143
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [50] join(A,join(A,B)) -> join(A,B)
% Rule [37] join(join(A,join(A,B)),join(A,B)) -> join(A,B) collapsed.
% Rule [38] meet(join(A,join(A,B)),join(A,B)) -> join(A,B) collapsed.
% Current number of equations to process: 143
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [51] meet(A,join(B,A)) -> A
% Rule [2] join(meet(A,B),meet(B,join(A,B))) -> B collapsed.
% Rule [17] meet(meet(A,join(B,A)),A) -> A collapsed.
% Rule [35] meet(A,join(meet(A,B),A)) -> join(meet(A,B),A) collapsed.
% Rule [40] join(meet(A,join(B,A)),A) -> A collapsed.
% Rule [41] meet(A,join(join(A,B),A)) -> A collapsed.
% Rule [43] join(A,meet(A,join(B,A))) -> meet(A,join(B,A)) collapsed.
% Rule [47] meet(meet(A,B),join(A,meet(A,B))) -> meet(A,B) collapsed.
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [52] join(meet(A,B),A) -> A
% Rule [7] join(join(meet(A,B),A),A) -> A collapsed.
% Rule [36] meet(join(meet(A,B),A),A) -> A collapsed.
% Rule [46] join(A,join(meet(A,B),A)) -> join(meet(A,B),A) collapsed.
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [53] meet(A,join(A,B)) -> A
% Rule [1] join(meet(A,B),meet(A,join(A,B))) -> A collapsed.
% Rule [49] join(meet(A,B),meet(A,join(A,meet(A,B)))) -> A collapsed.
% Current number of equations to process: 152
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [54] join(join(A,B),B) -> join(A,B)
% Rule [44] join(join(join(A,B),A),A) -> join(join(A,B),A) collapsed.
% Current number of equations to process: 154
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [55] meet(join(A,B),B) -> B
% Rule [42] meet(join(join(A,B),A),A) -> A collapsed.
% Rule [48] meet(join(A,meet(A,B)),meet(A,B)) -> meet(A,B) collapsed.
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [56] join(A,join(B,A)) -> join(B,A)
% Rule [45] join(A,join(join(A,B),A)) -> join(join(A,B),A) collapsed.
% Current number of equations to process: 155
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [57] join(join(A,B),A) -> join(A,B)
% Current number of equations to process: 160
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [58] meet(meet(A,B),A) -> meet(A,B)
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [59] join(A,meet(A,B)) -> A
% Current number of equations to process: 167
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [60] meet(meet(join(A,B),join(C,B)),B) -> B
% Current number of equations to process: 171
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [61] meet(meet(join(A,B),join(A,C)),A) -> A
% Current number of equations to process: 179
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [62] join(A,join(meet(B,A),meet(C,A))) -> A
% Current number of equations to process: 191
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [63] join(A,join(meet(A,B),meet(C,A))) -> A
% Current number of equations to process: 201
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [64] meet(A,meet(join(A,B),join(C,A))) -> A
% Current number of equations to process: 213
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [65] join(join(meet(A,B),meet(B,C)),B) -> B
% Current number of equations to process: 230
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [66] join(join(meet(A,B),meet(A,C)),A) -> A
% Current number of equations to process: 245
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [67] meet(meet(join(A,B),join(B,C)),B) -> B
% Current number of equations to process: 261
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [68] meet(A,meet(join(B,A),join(C,A))) -> A
% Current number of equations to process: 278
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [69] meet(A,meet(join(A,B),join(A,C))) -> A
% Current number of equations to process: 293
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [70] join(A,join(meet(B,A),meet(A,C))) -> A
% Current number of equations to process: 312
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [71] join(A,join(meet(A,B),meet(A,C))) -> A
% Current number of equations to process: 332
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [72] meet(A,meet(join(B,A),join(A,C))) -> A
% Current number of equations to process: 346
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [73] meet(meet(A,join(B,meet(A,C))),meet(A,C)) -> meet(A,C)
% Current number of equations to process: 347
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [74] meet(meet(A,join(B,meet(C,A))),meet(C,A)) -> meet(C,A)
% Current number of equations to process: 364
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [75] meet(meet(A,B),meet(B,A)) -> meet(B,A)
% Current number of equations to process: 369
% Current number of ordered equations: 0
% Current number of rules: 37
% meet(A,B) = meet(B,A) (birth = 1419, lhs_size = 3, rhs_size = 3,trace = Cp of 75 and 58)
% Initializing completion ...
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% See solution above
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.110000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------