TSTP Solution File: ALG007-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : ALG007-1 : TPTP v6.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n085.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 00:18:01 EDT 2014
% Result : Unsatisfiable 3.50s
% Output : Refutation 3.50s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : ALG007-1 : TPTP v6.0.0. Released v2.2.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n085.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 15:39:08 CDT 2014
% % CPUTime : 3.50
% Processing problem /tmp/CiME_19923_n085.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " c,b,a : constant; difference : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% difference(X,difference(Y,X)) = X;
% difference(X,difference(X,Y)) = difference(Y,difference(Y,X));
% difference(difference(X,Y),Z) = difference(difference(X,Z),Y);
% ";
%
% let s1 = status F "
% c lr_lex;
% b lr_lex;
% a lr_lex;
% difference lr_lex;
% ";
%
% let p1 = precedence F "
% difference > a > b > c";
%
% let s2 = status F "
% c mul;
% b mul;
% a mul;
% difference mul;
% ";
%
% let p2 = precedence F "
% difference > a = b = c";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " difference(difference(a,b),c) = difference(difference(a,c),difference(b,c));"
% ;
% (*
% 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 = { difference(X,difference(Y,X)) = X,
% difference(X,difference(X,Y)) =
% difference(Y,difference(Y,X)),
% difference(difference(X,Y),Z) =
% difference(difference(X,Z),Y) } (3 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 = { difference(difference(a,b),c) =
% difference(difference(a,c),difference(b,c)) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] difference(X,difference(Y,X)) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 1
% New rule produced :
% [2] difference(X,difference(X,Y)) <-> difference(Y,difference(Y,X))
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 2
% New rule produced :
% [3] difference(difference(X,Y),Z) <-> difference(difference(X,Z),Y)
% The conjecture has been reduced.
% Conjecture is now:
% difference(difference(a,c),b) = difference(difference(a,c),difference(b,c))
%
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced : [4] difference(difference(X,Y),Y) -> difference(X,Y)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [5] difference(X,difference(difference(Y,X),Z)) -> X
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6] difference(difference(Y,X),difference(Y,X)) -> difference(X,X)
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] difference(X,X) <-> difference(Y,Y)
% Rule [6] difference(difference(Y,X),difference(Y,X)) -> difference(X,X)
% collapsed.
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [8] difference(X,difference(Y,Y)) -> X
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [9] difference(Y,Y) <-> difference(difference(X,X),Y)
% Current number of equations to process: 29
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced : [10] difference(difference(X,X),Y) <-> difference(Y,Y)
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 9
% Rule [9] difference(Y,Y) <-> difference(difference(X,X),Y) is composed into
% [9] difference(Y,Y) <-> difference(X,X)
% New rule produced : [11] difference(difference(X,X),Y) -> difference(X,X)
% Rule [10] difference(difference(X,X),Y) <-> difference(Y,Y) collapsed.
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [12] difference(X,X) <-> difference(difference(Y,Z),Y)
% Current number of equations to process: 28
% Current number of ordered equations: 1
% Current number of rules: 10
% Rule [12] difference(X,X) <-> difference(difference(Y,Z),Y) is composed into
% [12] difference(X,X) <-> difference(c,c)
% New rule produced : [13] difference(difference(Y,Z),Y) <-> difference(X,X)
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [14] difference(difference(X,Y),difference(Z,X)) -> difference(X,Y)
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [15] difference(difference(X,Y),difference(Y,Z)) -> difference(X,Y)
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [16] difference(X,difference(X,difference(X,Y))) -> difference(X,Y)
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [17] difference(X,X) <-> difference(difference(difference(Y,Z),V_3),Y)
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 15
% Rule [17] difference(X,X) <-> difference(difference(difference(Y,Z),V_3),Y) is composed into
% [17] difference(X,X) <-> difference(c,c)
% New rule produced :
% [18] difference(difference(difference(Y,Z),V_3),Y) <-> difference(X,X)
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [19] difference(X,difference(Y,difference(Y,X))) -> difference(X,Y)
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [20]
% difference(difference(difference(X,Y),Z),Y) -> difference(difference(X,Y),Z)
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [21] difference(X,difference(Y,difference(Y,difference(Z,X)))) -> X
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [22] difference(X,difference(difference(difference(Y,X),Z),V_3)) -> X
% Current number of equations to process: 78
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [23]
% difference(difference(difference(X,Y),Z),V_3) <->
% difference(difference(difference(X,Z),V_3),Y)
% Current number of equations to process: 89
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [24]
% difference(difference(difference(X,Z),V_3),Y) <->
% difference(difference(difference(X,Y),Z),V_3)
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [25]
% difference(difference(X,difference(X,Y)),Z) <->
% difference(difference(Y,Z),difference(Y,X))
% Current number of equations to process: 179
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [26]
% difference(difference(Y,Z),difference(Y,X)) <->
% difference(difference(X,difference(X,Y)),Z)
% Current number of equations to process: 181
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [27]
% difference(difference(X,Y),difference(difference(Z,X),V_3)) ->
% difference(X,Y)
% Current number of equations to process: 264
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [28]
% difference(difference(difference(X,Y),Z),difference(X,Z)) <->
% difference(V_3,V_3)
% Current number of equations to process: 297
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [29]
% difference(difference(X,Y),difference(difference(Y,Z),V_3)) ->
% difference(X,Y)
% Current number of equations to process: 331
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [30]
% difference(difference(X,Y),difference(Z,difference(Z,Y))) -> difference(X,Y)
% Current number of equations to process: 368
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [31]
% difference(difference(X,Y),difference(X,difference(Y,Z))) <->
% difference(V_3,V_3)
% Current number of equations to process: 403
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [32]
% difference(X,X) <->
% difference(difference(difference(difference(Y,Z),V_3),V_4),Y)
% Current number of equations to process: 434
% Current number of ordered equations: 1
% Current number of rules: 30
% Rule [32]
% difference(X,X) <->
% difference(difference(difference(difference(Y,Z),V_3),V_4),Y) is composed into
% [32] difference(X,X) <-> difference(c,c)
% New rule produced :
% [33]
% difference(difference(difference(difference(Y,Z),V_3),V_4),Y) <->
% difference(X,X)
% Current number of equations to process: 434
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [34]
% difference(difference(difference(X,Y),Z),V_3) <->
% difference(difference(difference(X,V_3),Z),Y)
% Current number of equations to process: 450
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [35]
% difference(difference(X,Y),difference(X,Z)) <->
% difference(difference(Z,Y),difference(Z,X))
% Current number of equations to process: 522
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [36]
% difference(difference(difference(X,Y),Z),difference(Y,V_3)) ->
% difference(difference(X,Y),Z)
% Current number of equations to process: 596
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [37]
% difference(difference(X,difference(X,Y)),difference(Z,Y)) ->
% difference(Y,difference(Y,X))
% Current number of equations to process: 633
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [38]
% difference(difference(difference(X,Y),Z),difference(V_3,X)) ->
% difference(difference(X,Y),Z)
% Current number of equations to process: 708
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [39]
% difference(difference(X,Y),Z) <->
% difference(difference(X,Z),difference(X,difference(X,Y)))
% Current number of equations to process: 759
% Current number of ordered equations: 1
% Current number of rules: 37
% New rule produced :
% [40]
% difference(difference(X,Z),difference(X,difference(X,Y))) <->
% difference(difference(X,Y),Z)
% Current number of equations to process: 760
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [41]
% difference(X,difference(X,difference(difference(X,Y),Z))) ->
% difference(difference(X,Y),Z)
% Current number of equations to process: 893
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [42]
% difference(difference(X,Y),Z) <->
% difference(difference(X,Z),difference(Y,difference(Y,X)))
% Current number of equations to process: 938
% Current number of ordered equations: 1
% Current number of rules: 40
% New rule produced :
% [43]
% difference(difference(X,Z),difference(Y,difference(Y,X))) <->
% difference(difference(X,Y),Z)
% Current number of equations to process: 940
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [44]
% difference(X,difference(difference(Y,difference(Y,difference(Z,X))),V_3)) ->
% X
% Current number of equations to process: 1100
% Current number of ordered equations: 1
% Current number of rules: 42
% New rule produced :
% [45]
% difference(X,difference(Y,difference(Y,difference(difference(Z,X),V_3)))) ->
% X
% Current number of equations to process: 1181
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [46]
% difference(X,difference(difference(difference(difference(Y,X),Z),V_3),V_4))
% -> X
% Current number of equations to process: 1259
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [47]
% difference(difference(Y,difference(Z,X)),difference(Y,X)) ->
% difference(X,difference(X,Y))
% Current number of equations to process: 1327
% Current number of ordered equations: 0
% Current number of rules: 45
% Rule [26]
% difference(difference(Y,Z),difference(Y,X)) <->
% difference(difference(X,difference(X,Y)),Z) is composed into [26]
% difference(
% difference(Y,Z),
% difference(Y,X))
% <->
% difference(X,
% difference(X,
% difference(Y,Z)))
% New rule produced :
% [48]
% difference(difference(X,difference(X,Y)),Z) ->
% difference(X,difference(X,difference(Y,Z)))
% Rule
% [25]
% difference(difference(X,difference(X,Y)),Z) <->
% difference(difference(Y,Z),difference(Y,X)) collapsed.
% Rule
% [37]
% difference(difference(X,difference(X,Y)),difference(Z,Y)) ->
% difference(Y,difference(Y,X)) collapsed.
% Rule
% [44]
% difference(X,difference(difference(Y,difference(Y,difference(Z,X))),V_3)) ->
% X collapsed.
% Current number of equations to process: 1371
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [49]
% difference(X,difference(X,difference(Z,Y))) <->
% difference(difference(X,Y),difference(X,Z))
% Current number of equations to process: 1381
% Current number of ordered equations: 1
% Current number of rules: 44
% New rule produced :
% [50]
% difference(difference(X,Y),difference(X,Z)) <->
% difference(X,difference(X,difference(Z,Y)))
% Rule
% [47]
% difference(difference(Y,difference(Z,X)),difference(Y,X)) ->
% difference(X,difference(X,Y)) collapsed.
% Current number of equations to process: 1381
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [51]
% difference(X,difference(X,difference(Y,Z))) <->
% difference(Y,difference(Y,difference(X,Z)))
% Current number of equations to process: 1441
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [52]
% difference(X,difference(difference(Y,Z),difference(Y,difference(V_3,X)))) ->
% X
% Current number of equations to process: 1756
% Current number of ordered equations: 0
% Current number of rules: 46
% Rule [39]
% difference(difference(X,Y),Z) <->
% difference(difference(X,Z),difference(X,difference(X,Y))) is composed into
% [39] difference(difference(X,Y),Z) <-> difference(difference(X,Z),Y)
% New rule produced :
% [53]
% difference(difference(X,Y),difference(X,difference(X,Z))) ->
% difference(difference(X,Y),Z)
% Rule
% [40]
% difference(difference(X,Z),difference(X,difference(X,Y))) <->
% difference(difference(X,Y),Z) collapsed.
% Current number of equations to process: 1840
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [54]
% difference(X,difference(difference(Y,Z),difference(X,difference(X,Y)))) -> X
% Current number of equations to process: 1894
% Current number of ordered equations: 0
% Current number of rules: 47
% Rule [42]
% difference(difference(X,Y),Z) <->
% difference(difference(X,Z),difference(Y,difference(Y,X))) is composed into
% [42] difference(difference(X,Y),Z) <-> difference(difference(X,Z),Y)
% New rule produced :
% [55]
% difference(difference(X,Y),difference(Z,difference(Z,X))) ->
% difference(difference(X,Y),Z)
% Rule
% [43]
% difference(difference(X,Z),difference(Y,difference(Y,X))) <->
% difference(difference(X,Y),Z) collapsed.
% Rule
% [54]
% difference(X,difference(difference(Y,Z),difference(X,difference(X,Y)))) -> X
% collapsed.
% Current number of equations to process: 1956
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [56]
% difference(X,difference(X,difference(Y,difference(Z,X)))) ->
% difference(X,difference(X,Y))
% Current number of equations to process: 2011
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [57] difference(X,difference(Y,difference(Z,X))) -> difference(X,Y)
% Rule [19] difference(X,difference(Y,difference(Y,X))) -> difference(X,Y)
% collapsed.
% Rule
% [56]
% difference(X,difference(X,difference(Y,difference(Z,X)))) ->
% difference(X,difference(X,Y)) collapsed.
% Current number of equations to process: 2028
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [58]
% difference(difference(X,Y),difference(Z,Y)) -> difference(difference(X,Y),Z)
% Rule
% [28]
% difference(difference(difference(X,Y),Z),difference(X,Z)) <->
% difference(V_3,V_3) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 2074
% Current number of ordered equations: 0
% Current number of rules: 46
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 11 rules have been used:
% [1]
% difference(X,difference(Y,X)) -> X; trace = in the starting set
% [2] difference(X,difference(X,Y)) <-> difference(Y,difference(Y,X)); trace = in the starting set
% [3] difference(difference(X,Y),Z) <-> difference(difference(X,Z),Y); trace = in the starting set
% [14] difference(difference(X,Y),difference(Z,X)) -> difference(X,Y); trace = Cp of 3 and 1
% [25] difference(difference(X,difference(X,Y)),Z) <->
% difference(difference(Y,Z),difference(Y,X)); trace = Cp of 3 and 2
% [26] difference(difference(Y,Z),difference(Y,X)) <->
% difference(difference(X,difference(X,Y)),Z); trace = Cp of 3 and 2
% [47] difference(difference(Y,difference(Z,X)),difference(Y,X)) ->
% difference(X,difference(X,Y)); trace = Cp of 25 and 14
% [48] difference(difference(X,difference(X,Y)),Z) ->
% difference(X,difference(X,difference(Y,Z))); trace = Cp of 47 and 26
% [56] difference(X,difference(X,difference(Y,difference(Z,X)))) ->
% difference(X,difference(X,Y)); trace = Cp of 48 and 14
% [57] difference(X,difference(Y,difference(Z,X))) -> difference(X,Y); trace = Cp of 56 and 1
% [58] difference(difference(X,Y),difference(Z,Y)) ->
% difference(difference(X,Y),Z); trace = Cp of 57 and 1
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 2.370000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------