TSTP Solution File: BOO075-1 by CiME---2.01
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- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : BOO075-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n092.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 00:19:21 EDT 2014
% Result : Unsatisfiable 1.42s
% Output : Refutation 1.42s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : BOO075-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n092.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 22:53:18 CDT 2014
% % CPUTime : 1.42
% Processing problem /tmp/CiME_61771_n092.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b,a : constant; nand : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A))) = B;
% ";
%
% let s1 = status F "
% b lr_lex;
% a lr_lex;
% nand lr_lex;
% ";
%
% let p1 = precedence F "
% nand > a > b";
%
% let s2 = status F "
% b mul;
% a mul;
% nand mul;
% ";
%
% let p2 = precedence F "
% nand > a = b";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " nand(nand(a,a),nand(b,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 = { nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A)))
% = B } (1 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 = { nand(nand(a,a),nand(b,a)) = a }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced :
% [1] nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A))) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 1
% New rule produced :
% [2]
% nand(nand(nand(A,nand(B,C)),nand(nand(V_3,nand(A,nand(B,C))),nand(A,nand(B,C)))),
% nand(V_3,A)) -> V_3
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3] nand(nand(nand(A,B),nand(nand(C,nand(A,B)),nand(A,B))),nand(C,A)) -> C
% Rule
% [2]
% nand(nand(nand(A,nand(B,C)),nand(nand(V_3,nand(A,nand(B,C))),nand(A,nand(B,C)))),
% nand(V_3,A)) -> V_3 collapsed.
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [4] nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,nand(nand(A,C),C)))) -> B
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [5]
% nand(nand(A,nand(nand(nand(B,nand(nand(B,B),B)),A),A)),B) ->
% nand(B,nand(nand(B,B),B))
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [6] nand(nand(A,nand(nand(B,A),A)),nand(B,nand(nand(B,B),B))) -> B
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [7] nand(A,nand(nand(B,nand(nand(A,B),B)),A)) -> nand(B,nand(nand(A,B),B))
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [8] nand(nand(A,nand(nand(A,A),A)),nand(B,nand(nand(A,B),B))) -> A
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [9] nand(nand(A,nand(nand(B,A),A)),nand(B,nand(A,nand(nand(B,A),A)))) -> B
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [10]
% nand(nand(nand(A,nand(B,A)),nand(A,nand(A,nand(B,A)))),A) ->
% nand(A,nand(nand(A,A),A))
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 9
% Rule [10]
% nand(nand(nand(A,nand(B,A)),nand(A,nand(A,nand(B,A)))),A) ->
% nand(A,nand(nand(A,A),A)) is composed into [10]
% nand(nand(nand(A,nand(B,A)),
% nand(A,nand(A,nand(B,A)))),A)
% -> nand(A,A)
% New rule produced : [11] nand(A,nand(nand(A,A),A)) -> nand(A,A)
% Rule
% [5]
% nand(nand(A,nand(nand(nand(B,nand(nand(B,B),B)),A),A)),B) ->
% nand(B,nand(nand(B,B),B)) collapsed.
% Rule [6] nand(nand(A,nand(nand(B,A),A)),nand(B,nand(nand(B,B),B))) -> B
% collapsed.
% Rule [8] nand(nand(A,nand(nand(A,A),A)),nand(B,nand(nand(A,B),B))) -> A
% collapsed.
% Current number of equations to process: 96
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [12] nand(nand(A,nand(nand(B,A),A)),nand(B,B)) -> B
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [13] nand(nand(A,A),nand(B,nand(nand(A,B),B))) -> A
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [14] nand(nand(A,nand(nand(nand(B,B),A),A)),B) -> nand(B,B)
% Current number of equations to process: 93
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [15] nand(nand(A,A),nand(A,A)) -> A
% Current number of equations to process: 99
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [16] nand(nand(A,A),nand(A,nand(B,A))) -> A
% Current number of equations to process: 98
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [17] nand(nand(A,A),nand(A,nand(B,nand(nand(A,B),B)))) -> A
% Current number of equations to process: 109
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [18] nand(nand(nand(A,B),nand(A,B)),nand(nand(A,B),A)) -> nand(A,B)
% Current number of equations to process: 115
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [19] nand(A,nand(nand(A,A),B)) -> nand(A,A)
% Rule [11] nand(A,nand(nand(A,A),A)) -> nand(A,A) collapsed.
% Current number of equations to process: 123
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [20] nand(A,nand(B,nand(nand(nand(A,A),B),B))) -> nand(A,A)
% Current number of equations to process: 140
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [21] nand(nand(A,A),nand(A,B)) -> A
% Rule [15] nand(nand(A,A),nand(A,A)) -> A collapsed.
% Rule [16] nand(nand(A,A),nand(A,nand(B,A))) -> A collapsed.
% Rule [17] nand(nand(A,A),nand(A,nand(B,nand(nand(A,B),B)))) -> A collapsed.
% Rule [18] nand(nand(nand(A,B),nand(A,B)),nand(nand(A,B),A)) -> nand(A,B)
% collapsed.
% Current number of equations to process: 182
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [22] nand(nand(nand(A,B),nand(A,nand(A,B))),A) -> nand(A,A)
% Rule
% [10] nand(nand(nand(A,nand(B,A)),nand(A,nand(A,nand(B,A)))),A) -> nand(A,A)
% collapsed.
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [23] nand(A,nand(nand(A,B),nand(A,nand(A,B)))) -> nand(A,A)
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [24] nand(nand(nand(A,nand(nand(nand(A,A),A),A)),nand(A,A)),A) -> nand(A,A)
% Current number of equations to process: 220
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [25] nand(nand(nand(A,B),nand(A,nand(A,B))),nand(nand(A,A),A)) -> nand(A,A)
% Current number of equations to process: 219
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [26] nand(A,nand(nand(A,nand(nand(nand(A,A),A),A)),nand(A,A))) -> nand(A,A)
% Current number of equations to process: 217
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [27]
% nand(nand(A,nand(nand(nand(B,nand(nand(A,B),B)),A),A)),A) ->
% nand(B,nand(nand(A,B),B))
% Current number of equations to process: 256
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [28]
% nand(A,nand(nand(B,nand(nand(A,B),B)),nand(C,nand(A,A)))) ->
% nand(B,nand(nand(A,B),B))
% Current number of equations to process: 277
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [29]
% nand(nand(nand(nand(A,A),nand(nand(A,nand(A,A)),nand(A,A))),A),nand(A,A)) ->
% A
% Current number of equations to process: 306
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [30]
% nand(nand(A,A),nand(nand(nand(A,A),nand(nand(A,nand(A,A)),nand(A,A))),A)) ->
% A
% Current number of equations to process: 315
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [31]
% nand(A,nand(nand(B,nand(nand(A,B),B)),nand(B,nand(nand(A,B),B)))) ->
% nand(B,nand(nand(A,B),B))
% Current number of equations to process: 320
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [32]
% nand(nand(nand(A,nand(nand(B,A),A)),nand(A,nand(nand(B,A),A))),B) ->
% nand(A,nand(nand(B,A),A))
% Current number of equations to process: 333
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [33]
% nand(nand(nand(A,B),nand(A,nand(A,B))),nand(nand(A,A),nand(C,nand(A,B)))) ->
% nand(A,A)
% Current number of equations to process: 343
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [34]
% nand(nand(nand(A,nand(nand(nand(A,A),A),A)),nand(A,A)),nand(nand(A,A),A)) ->
% nand(A,A)
% Current number of equations to process: 370
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [35]
% nand(nand(nand(nand(A,A),A),nand(nand(A,A),nand(nand(A,A),A))),nand(A,
% nand(A,A))) ->
% A
% Current number of equations to process: 386
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [36]
% nand(nand(A,A),nand(nand(B,nand(nand(nand(A,A),B),B)),nand(C,A))) ->
% nand(B,nand(nand(nand(A,A),B),B))
% Current number of equations to process: 404
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [37] nand(B,nand(nand(nand(nand(A,B),nand(A,B)),B),B)) -> nand(A,B)
% Current number of equations to process: 411
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [38] nand(nand(A,nand(B,C)),nand(A,nand(A,nand(B,C)))) -> A
% Current number of equations to process: 444
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [39] nand(nand(A,B),nand(A,nand(A,B))) -> A
% Rule [22] nand(nand(nand(A,B),nand(A,nand(A,B))),A) -> nand(A,A) collapsed.
% Rule [23] nand(A,nand(nand(A,B),nand(A,nand(A,B)))) -> nand(A,A) collapsed.
% Rule
% [25] nand(nand(nand(A,B),nand(A,nand(A,B))),nand(nand(A,A),A)) -> nand(A,A)
% collapsed.
% Rule
% [33]
% nand(nand(nand(A,B),nand(A,nand(A,B))),nand(nand(A,A),nand(C,nand(A,B)))) ->
% nand(A,A) collapsed.
% Rule
% [35]
% nand(nand(nand(nand(A,A),A),nand(nand(A,A),nand(nand(A,A),A))),nand(A,
% nand(A,A))) ->
% A collapsed.
% Rule [38] nand(nand(A,nand(B,C)),nand(A,nand(A,nand(B,C)))) -> A collapsed.
% Current number of equations to process: 452
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [40] nand(A,nand(B,nand(A,A))) -> nand(A,A)
% Rule
% [26] nand(A,nand(nand(A,nand(nand(nand(A,A),A),A)),nand(A,A))) -> nand(A,A)
% collapsed.
% Current number of equations to process: 454
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [41] nand(nand(A,A),nand(B,A)) -> A
% Rule
% [30]
% nand(nand(A,A),nand(nand(nand(A,A),nand(nand(A,nand(A,A)),nand(A,A))),A)) ->
% A collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 455
% Current number of ordered equations: 0
% Current number of rules: 23
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 17 rules have been used:
% [1]
% nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A))) -> B; trace = in the starting set
% [2] nand(nand(nand(A,nand(B,C)),nand(nand(V_3,nand(A,nand(B,C))),nand(A,
% nand(B,C)))),
% nand(V_3,A)) -> V_3; trace = Self cp of 1
% [3] nand(nand(nand(A,B),nand(nand(C,nand(A,B)),nand(A,B))),nand(C,A)) -> C; trace = Self cp of 2
% [4] nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,nand(nand(A,C),C)))) -> B; trace = Cp of 3 and 1
% [5] nand(nand(A,nand(nand(nand(B,nand(nand(B,B),B)),A),A)),B) ->
% nand(B,nand(nand(B,B),B)); trace = Cp of 4 and 1
% [6] nand(nand(A,nand(nand(B,A),A)),nand(B,nand(nand(B,B),B))) -> B; trace = Cp of 5 and 1
% [7] nand(A,nand(nand(B,nand(nand(A,B),B)),A)) -> nand(B,nand(nand(A,B),B)); trace = Cp of 6 and 3
% [10] nand(nand(nand(A,nand(B,A)),nand(A,nand(A,nand(B,A)))),A) ->
% nand(A,nand(nand(A,A),A)); trace = Cp of 5 and 1
% [11] nand(A,nand(nand(A,A),A)) -> nand(A,A); trace = Cp of 10 and 4
% [13] nand(nand(A,A),nand(B,nand(nand(A,B),B))) -> A; trace = Cp of 7 and 1
% [14] nand(nand(A,nand(nand(nand(B,B),A),A)),B) -> nand(B,B); trace = Cp of 4 and 1
% [15] nand(nand(A,A),nand(A,A)) -> A; trace = Cp of 11 and 1
% [19] nand(A,nand(nand(A,A),B)) -> nand(A,A); trace = Cp of 13 and 3
% [21] nand(nand(A,A),nand(A,B)) -> A; trace = Cp of 19 and 15
% [36] nand(nand(A,A),nand(nand(B,nand(nand(nand(A,A),B),B)),nand(C,A))) ->
% nand(B,nand(nand(nand(A,A),B),B)); trace = Cp of 14 and 1
% [37] nand(B,nand(nand(nand(nand(A,B),nand(A,B)),B),B)) -> nand(A,B); trace = Cp of 36 and 1
% [41] nand(nand(A,A),nand(B,A)) -> A; trace = Cp of 37 and 21
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.310000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------