TSTP Solution File: ALG006-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : ALG006-1 : TPTP v6.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n118.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 1.44s
% Output : Refutation 1.44s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : ALG006-1 : TPTP v6.0.0. Released v2.2.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n118.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 15:35:33 CDT 2014
% % CPUTime : 1.44
% Processing problem /tmp/CiME_18362_n118.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b,c,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),difference(Y,Z));
% ";
%
% let s1 = status F "
% b lr_lex;
% c lr_lex;
% a lr_lex;
% difference mul;
% ";
%
% let p1 = precedence F "
% difference > a > c > b";
%
% let s2 = status F "
% b mul;
% c mul;
% a mul;
% difference mul;
% ";
%
% let p2 = precedence F "
% difference > a = c = b";
%
% 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,c),b) = difference(difference(a,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),difference(Y,Z)) }
% (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,c),b) =
% difference(difference(a,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),difference(Y,Z))
% The conjecture has been reduced.
% Conjecture is now:
% difference(difference(a,b),difference(c,b)) = difference(difference(a,b),c)
%
% Current number of equations to process: 1
% Current number of ordered equations: 2
% Current number of rules: 3
% New rule produced :
% [4]
% difference(difference(X,Z),difference(Y,Z)) <-> difference(difference(X,Y),Z)
% Current number of equations to process: 1
% Current number of ordered equations: 1
% Current number of rules: 4
% New rule produced : [5] difference(difference(X,Y),Y) -> difference(X,Y)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6] difference(difference(X,Y),difference(X,Y)) -> difference(Y,Y)
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] difference(Y,Y) <-> difference(difference(X,X),Y)
% Current number of equations to process: 28
% Current number of ordered equations: 1
% Current number of rules: 7
% New rule produced : [8] difference(difference(X,X),Y) <-> difference(Y,Y)
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9] difference(difference(X,difference(X,Y)),Y) -> difference(Y,Y)
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [10] difference(difference(X,Y),X) -> difference(X,X)
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11] difference(Z,Z) <-> difference(difference(difference(X,X),Y),Z)
% Current number of equations to process: 43
% Current number of ordered equations: 2
% Current number of rules: 11
% New rule produced :
% [12] difference(difference(Y,Y),difference(Z,X)) -> difference(X,X)
% Current number of equations to process: 43
% Current number of ordered equations: 1
% Current number of rules: 12
% New rule produced :
% [13] difference(difference(difference(X,X),Y),Z) <-> difference(Z,Z)
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14] difference(X,difference(X,difference(Y,Y))) -> difference(X,X)
% Current number of equations to process: 41
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15] difference(difference(X,difference(Z,Z)),Y) -> difference(X,Y)
% Current number of equations to process: 38
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16] difference(difference(difference(X,Y),Z),X) -> difference(X,X)
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [17] difference(difference(X,difference(Y,Z)),Y) -> difference(X,Y)
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] difference(X,X) <-> difference(Y,Y)
% Rule [6] difference(difference(X,Y),difference(X,Y)) -> difference(Y,Y)
% collapsed.
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [19] difference(X,difference(Y,Y)) -> X
% Rule [14] difference(X,difference(X,difference(Y,Y))) -> difference(X,X)
% collapsed.
% Rule [15] difference(difference(X,difference(Z,Z)),Y) -> difference(X,Y)
% collapsed.
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 16
% Rule [11] difference(Z,Z) <-> difference(difference(difference(X,X),Y),Z) is composed into
% [11] difference(Z,Z) <-> difference(Y,Y)
% New rule produced :
% [20] difference(difference(difference(X,X),Y),Z) -> difference(Y,Y)
% Rule [13] difference(difference(difference(X,X),Y),Z) <-> difference(Z,Z)
% collapsed.
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [21] difference(Z,Z) <-> difference(difference(X,X),Y)
% Rule [7] difference(Y,Y) <-> difference(difference(X,X),Y) collapsed.
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [22] difference(X,difference(difference(Y,Y),Z)) -> X
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [23] difference(difference(X,X),Y) <-> difference(difference(Z,Z),V_3)
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [24] difference(X,difference(difference(Y,X),difference(Z,X))) -> X
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [25]
% difference(difference(X,difference(Y,Z)),Z) -> difference(difference(X,Y),Z)
% Rule [9] difference(difference(X,difference(X,Y)),Y) -> difference(Y,Y)
% collapsed.
% Current number of equations to process: 103
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [26]
% difference(difference(difference(X,Y),Z),Y) -> difference(difference(X,Z),Y)
% Current number of equations to process: 118
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [27]
% difference(difference(X,Y),difference(Y,difference(Y,X))) -> difference(X,Y)
% Current number of equations to process: 137
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [28]
% difference(difference(X,Y),difference(difference(Z,X),Y)) -> difference(X,Y)
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [29]
% difference(X,difference(Y,difference(Z,X))) ->
% difference(difference(X,Y),difference(Z,X))
% Rule [24] difference(X,difference(difference(Y,X),difference(Z,X))) -> X
% collapsed.
% Current number of equations to process: 167
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [30]
% difference(difference(difference(Y,difference(Y,X)),Z),X) -> difference(X,X)
% Current number of equations to process: 186
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [31]
% difference(difference(X,difference(Z,difference(Z,Y))),Y) -> difference(X,Y)
% Current number of equations to process: 186
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [32] difference(X,difference(X,difference(X,Y))) -> difference(X,Y)
% Current number of equations to process: 221
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [33] difference(difference(X,Y),difference(Y,X)) -> difference(X,Y)
% Current number of equations to process: 221
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [34]
% difference(difference(difference(X,Y),Z),difference(X,Z)) -> difference(Z,Z)
% Current number of equations to process: 248
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [35]
% difference(difference(X,difference(X,difference(Y,Z))),Y) -> difference(Y,Y)
% Current number of equations to process: 262
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [36]
% difference(difference(difference(difference(X,Y),Z),V_3),X) ->
% difference(X,X)
% Current number of equations to process: 283
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [37]
% difference(difference(X,difference(difference(Y,Z),V_3)),Y) ->
% difference(X,Y)
% Current number of equations to process: 283
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [38]
% difference(difference(X,Y),difference(X,difference(Y,Z))) -> difference(Y,Y)
% Current number of equations to process: 341
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [39]
% difference(difference(X,difference(Z,difference(X,Y))),Y) -> difference(X,Y)
% Current number of equations to process: 380
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [40]
% difference(X,difference(X,difference(difference(Y,X),Z))) -> difference(Y,Y)
% Current number of equations to process: 409
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [41] difference(X,difference(difference(Y,X),Z)) -> X
% Rule
% [40]
% difference(X,difference(X,difference(difference(Y,X),Z))) -> difference(Y,Y)
% collapsed.
% Current number of equations to process: 413
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [42] difference(difference(X,Y),Z) <-> difference(difference(X,Z),Y)
% Rule [17] difference(difference(X,difference(Y,Z)),Y) -> difference(X,Y)
% collapsed.
% Rule
% [25]
% difference(difference(X,difference(Y,Z)),Z) -> difference(difference(X,Y),Z)
% collapsed.
% Rule
% [31]
% difference(difference(X,difference(Z,difference(Z,Y))),Y) -> difference(X,Y)
% collapsed.
% Rule
% [35]
% difference(difference(X,difference(X,difference(Y,Z))),Y) -> difference(Y,Y)
% collapsed.
% Rule
% [37]
% difference(difference(X,difference(difference(Y,Z),V_3)),Y) ->
% difference(X,Y) collapsed.
% Rule
% [39]
% difference(difference(X,difference(Z,difference(X,Y))),Y) -> difference(X,Y)
% collapsed.
% Current number of equations to process: 420
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [43] difference(difference(X,Y),difference(Y,Z)) -> difference(X,Y)
% Rule
% [27]
% difference(difference(X,Y),difference(Y,difference(Y,X))) -> difference(X,Y)
% collapsed.
% Rule [33] difference(difference(X,Y),difference(Y,X)) -> difference(X,Y)
% collapsed.
% Current number of equations to process: 419
% Current number of ordered equations: 0
% Current number of rules: 27
% Rule [29]
% difference(X,difference(Y,difference(Z,X))) ->
% difference(difference(X,Y),difference(Z,X)) is composed into [29]
% difference(X,
% difference(Y,
% difference(Z,X)))
% ->
% difference(X,Y)
% New rule produced :
% [44] difference(difference(X,Y),difference(Z,X)) -> difference(X,Y)
% Current number of equations to process: 450
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [45] difference(X,difference(Y,difference(Y,difference(Z,X)))) -> X
% Current number of equations to process: 502
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [46] difference(X,difference(difference(Y,Z),difference(X,Z))) -> X
% Current number of equations to process: 502
% Current number of ordered equations: 0
% Current number of rules: 30
% Rule [3]
% difference(difference(X,Y),Z) <->
% difference(difference(X,Z),difference(Y,Z)) is composed into [3]
% difference(
% difference(X,Y),Z)
% <->
% difference(
% difference(X,Z),Y)
% New rule produced :
% [47]
% difference(difference(X,Y),difference(Z,Y)) -> difference(difference(X,Y),Z)
% Rule
% [4]
% difference(difference(X,Z),difference(Y,Z)) <-> difference(difference(X,Y),Z)
% collapsed.
% Rule
% [28]
% difference(difference(X,Y),difference(difference(Z,X),Y)) -> difference(X,Y)
% collapsed.
% Rule
% [34]
% difference(difference(difference(X,Y),Z),difference(X,Z)) -> difference(Z,Z)
% collapsed.
% Rule [46] difference(X,difference(difference(Y,Z),difference(X,Z))) -> X
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 501
% Current number of ordered equations: 0
% Current number of rules: 27
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 13 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),difference(Y,Z)); trace = in the starting set
% [4] difference(difference(X,Z),difference(Y,Z)) <->
% difference(difference(X,Y),Z); trace = in the starting set
% [5] difference(difference(X,Y),Y) -> difference(X,Y); trace = Self cp of 1
% [6] difference(difference(X,Y),difference(X,Y)) -> difference(Y,Y); trace = Cp of 5 and 2
% [10] difference(difference(X,Y),X) -> difference(X,X); trace = Cp of 6 and 5
% [17] difference(difference(X,difference(Y,Z)),Y) -> difference(X,Y); trace = Cp of 10 and 4
% [38] difference(difference(X,Y),difference(X,difference(Y,Z))) ->
% difference(Y,Y); trace = Cp of 17 and 10
% [40] difference(X,difference(X,difference(difference(Y,X),Z))) ->
% difference(Y,Y); trace = Cp of 38 and 1
% [41] difference(X,difference(difference(Y,X),Z)) -> X; trace = Cp of 40 and 2
% [42] difference(difference(X,Y),Z) <-> difference(difference(X,Z),Y); trace = Cp of 41 and 1
% [47] difference(difference(X,Y),difference(Z,Y)) ->
% difference(difference(X,Y),Z); trace = Cp of 42 and 3
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.320000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------