TSTP Solution File: LAT090-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : LAT090-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n108.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 1.12s
% Output : Refutation 1.12s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : LAT090-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n108.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 21:52:43 CDT 2014
% % CPUTime : 1.12
% Processing problem /tmp/CiME_10994_n108.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a : 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;
% join lr_lex;
% meet lr_lex;
% ";
%
% let p1 = precedence F "
% meet > join > a";
%
% let s2 = status F "
% a mul;
% join mul;
% meet mul;
% ";
%
% let p2 = precedence F "
% meet > join > a";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " join(a,a) = a;"
% ;
% (*
% 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 = { join(a,a) = a } (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.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 11
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 9 rules have been used:
% [1]
% join(meet(A,B),meet(A,join(A,B))) -> A; trace = in the starting set
% [2] join(meet(A,B),meet(B,join(A,B))) -> B; trace = in the starting set
% [4] join(join(meet(A,B),meet(C,A)),A) -> A; trace = in the starting set
% [5] meet(meet(join(A,B),join(C,A)),A) -> A; trace = in the starting set
% [8] meet(meet(join(A,B),A),A) -> A; trace = Cp of 5 and 4
% [9] meet(meet(A,meet(A,B)),meet(A,B)) -> meet(A,B); trace = Cp of 8 and 1
% [11] meet(A,A) -> A; trace = Cp of 9 and 5
% [14] meet(join(A,A),A) -> A; trace = Cp of 11 and 5
% [18] join(A,A) -> A; trace = Cp of 14 and 2
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.010000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
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