%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : COL003-17 : TPTP v6.0.0. Released v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n086.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 00:19:35 EDT 2014

% Result   : Unsatisfiable 77.32s
% Output   : Refutation 77.32s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : COL003-17 : TPTP v6.0.0. Released v2.1.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n086.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 15:51:58 CDT 2014
% % CPUTime  : 77.32 
% Processing problem /tmp/CiME_56338_n086.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " fixed_pt,strong_fixed_point,w,b : constant;  apply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z));
% apply(apply(w,X),Y) = apply(apply(X,Y),Y);
% strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),b)),b);
% ";
% 
% let s1 = status F "
% fixed_pt lr_lex;
% strong_fixed_point lr_lex;
% w lr_lex;
% apply lr_lex;
% b lr_lex;
% ";
% 
% let p1 = precedence F "
% apply > b > w > strong_fixed_point > fixed_pt";
% 
% let s2 = status F "
% fixed_pt mul;
% strong_fixed_point mul;
% w mul;
% apply mul;
% b mul;
% ";
% 
% let p2 = precedence F "
% apply > b = w = strong_fixed_point = fixed_pt";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt));"
% ;
% (*
% 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 = { apply(apply(apply(b,X),Y),Z) =
% apply(X,apply(Y,Z)),
% apply(apply(w,X),Y) = apply(apply(X,Y),Y),
% strong_fixed_point =
% apply(apply(b,apply(apply(b,apply(apply(b,
% apply(w,w)),
% apply(b,w))),b)),b) }
% (3 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% 
% [fixed_pt] = 1;
% [strong_fixed_point] = 2;
% [w] = 3;
% [b] = 4;
% [apply](x1,x2) = 1 + x1 + x2;
% Chosen ordering : KBO
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { apply(strong_fixed_point,fixed_pt) =
% apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) }
% (1 equation(s))
% time is now on
% 
% Initializing completion ...
% New rule produced : [1] apply(apply(X,Y),Y) <-> apply(apply(w,X),Y)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 1
% New rule produced : [2] apply(apply(w,X),Y) <-> apply(apply(X,Y),Y)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 2
% New rule produced : [3] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced :
% [4]
% apply(apply(b,apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),b)),b) ->
% strong_fixed_point
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [5] apply(apply(w,w),X) <-> apply(apply(X,X),X)
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced : [6] apply(apply(X,X),X) <-> apply(apply(w,w),X)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] apply(X,apply(X,Y)) <-> apply(apply(apply(w,b),X),Y)
% Current number of equations to process: 3
% Current number of ordered equations: 3
% Current number of rules: 7
% New rule produced : [8] apply(X,apply(Y,Y)) <-> apply(apply(w,apply(b,X)),Y)
% Current number of equations to process: 3
% Current number of ordered equations: 2
% Current number of rules: 8
% New rule produced : [9] apply(apply(apply(w,b),X),Y) <-> apply(X,apply(X,Y))
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced : [10] apply(apply(w,apply(b,X)),Y) <-> apply(X,apply(Y,Y))
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11] apply(apply(apply(w,X),Y),Y) -> apply(apply(w,apply(X,Y)),Y)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12] apply(apply(apply(X,Y),Y),Y) <-> apply(apply(w,apply(w,X)),Y)
% Current number of equations to process: 1
% Current number of ordered equations: 1
% Current number of rules: 12
% New rule produced :
% [13] apply(apply(w,apply(w,X)),Y) <-> apply(apply(apply(X,Y),Y),Y)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14] apply(apply(X,apply(Y,Z)),Z) <-> apply(apply(w,apply(apply(b,X),Y)),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [15] apply(apply(w,apply(apply(b,X),Y)),Z) <-> apply(apply(X,apply(Y,Z)),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16] apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(w,w)),X)
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [17] apply(apply(w,apply(w,w)),X) <-> apply(apply(apply(X,X),X),X)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18] apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(X,X)),X)
% Current number of equations to process: 5
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced :
% [19] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(w,X)),X)
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20] apply(apply(w,apply(X,Y)),Y) <-> apply(apply(w,apply(w,X)),Y)
% Rule [19] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(w,X)),X)
% collapsed.
% Current number of equations to process: 13
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [21] apply(apply(w,apply(w,X)),Y) <-> apply(apply(w,apply(X,Y)),Y)
% Rule [18] apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(X,X)),X)
% collapsed.
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [22] apply(X,apply(apply(b,X),apply(b,X))) <-> apply(apply(w,w),apply(b,X))
% Current number of equations to process: 12
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [23] apply(apply(w,w),apply(b,X)) <-> apply(X,apply(apply(b,X),apply(b,X)))
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [24] apply(apply(apply(w,apply(b,w)),X),Y) <-> apply(apply(apply(X,X),Y),Y)
% Current number of equations to process: 22
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [25] apply(apply(apply(X,X),Y),Y) <-> apply(apply(apply(w,apply(b,w)),X),Y)
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [26] apply(X,apply(X,X)) <-> apply(apply(w,apply(w,b)),X)
% Current number of equations to process: 26
% Current number of ordered equations: 2
% Current number of rules: 24
% New rule produced : [27] apply(apply(apply(w,w),b),X) -> apply(b,apply(b,X))
% Current number of equations to process: 26
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced : [28] apply(apply(w,apply(w,b)),X) <-> apply(X,apply(X,X))
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [29] apply(apply(X,apply(X,Y)),Y) <-> apply(apply(w,apply(apply(w,b),X)),Y)
% Current number of equations to process: 25
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [30] apply(apply(w,apply(apply(w,b),X)),Y) <-> apply(apply(X,apply(X,Y)),Y)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [31] apply(apply(X,apply(Y,Y)),Y) <-> apply(apply(w,apply(w,apply(b,X))),Y)
% Current number of equations to process: 31
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [32] apply(apply(w,apply(w,apply(b,X))),Y) <-> apply(apply(X,apply(Y,Y)),Y)
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [33]
% apply(apply(apply(w,b),X),apply(X,Y)) ->
% apply(X,apply(apply(apply(w,b),X),Y))
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [34]
% apply(apply(X,Y),apply(apply(w,X),Y)) <->
% apply(apply(apply(w,b),apply(X,Y)),Y)
% Current number of equations to process: 32
% Current number of ordered equations: 1
% Current number of rules: 32
% New rule produced :
% [35]
% apply(apply(apply(w,b),apply(X,Y)),Y) <->
% apply(apply(X,Y),apply(apply(w,X),Y))
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [36]
% apply(apply(w,X),apply(apply(X,Y),Y)) <->
% apply(apply(apply(w,b),apply(w,X)),Y)
% Current number of equations to process: 31
% Current number of ordered equations: 1
% Current number of rules: 34
% New rule produced :
% [37]
% apply(apply(apply(w,b),apply(w,X)),Y) <->
% apply(apply(w,X),apply(apply(X,Y),Y))
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [38]
% apply(apply(apply(w,b),apply(X,X)),X) ->
% apply(apply(X,X),apply(apply(w,w),X))
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [39]
% apply(apply(X,apply(Y,Y)),apply(Y,Y)) <->
% apply(apply(w,apply(b,apply(w,X))),Y)
% Current number of equations to process: 29
% Current number of ordered equations: 1
% Current number of rules: 37
% New rule produced :
% [40]
% apply(apply(w,apply(b,apply(w,X))),Y) <->
% apply(apply(X,apply(Y,Y)),apply(Y,Y))
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [41]
% apply(X,apply(apply(w,apply(b,X)),Y)) <->
% apply(apply(apply(w,b),X),apply(Y,Y))
% Current number of equations to process: 28
% Current number of ordered equations: 1
% Current number of rules: 39
% New rule produced :
% [42]
% apply(apply(apply(w,b),X),apply(Y,Y)) <->
% apply(X,apply(apply(w,apply(b,X)),Y))
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [43]
% apply(apply(w,apply(apply(w,X),Y)),Y) ->
% apply(apply(w,apply(w,apply(X,Y))),Y)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [44]
% apply(apply(apply(apply(X,Y),Y),Y),Y) <->
% apply(apply(w,apply(w,apply(w,X))),Y)
% Current number of equations to process: 35
% Current number of ordered equations: 1
% Current number of rules: 42
% New rule produced :
% [45]
% apply(apply(w,apply(w,apply(w,X))),Y) <->
% apply(apply(apply(apply(X,Y),Y),Y),Y)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [46] apply(apply(w,apply(w,w)),X) <-> apply(apply(w,apply(X,X)),X)
% Current number of equations to process: 46
% Current number of ordered equations: 1
% Current number of rules: 44
% New rule produced :
% [47] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(w,w)),X)
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [48] apply(apply(X,apply(X,X)),X) <-> apply(apply(w,apply(w,apply(w,b))),X)
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 46
% New rule produced :
% [49] apply(apply(w,apply(w,apply(w,b))),X) <-> apply(apply(X,apply(X,X)),X)
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [50]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Current number of equations to process: 44
% Current number of ordered equations: 1
% Current number of rules: 48
% New rule produced :
% [51]
% apply(apply(w,apply(w,apply(w,w))),X) <->
% apply(apply(apply(apply(X,X),X),X),X)
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [52]
% apply(apply(w,apply(apply(X,Y),Y)),Y) <->
% apply(apply(w,apply(w,apply(w,X))),Y)
% Current number of equations to process: 43
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced :
% [53]
% apply(apply(w,apply(w,apply(w,X))),Y) <->
% apply(apply(w,apply(apply(X,Y),Y)),Y)
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [54] apply(apply(apply(X,Y),Y),Y) <-> apply(apply(w,apply(apply(b,w),X)),Y)
% Current number of equations to process: 56
% Current number of ordered equations: 1
% Current number of rules: 52
% New rule produced :
% [55] apply(apply(w,apply(apply(b,w),X)),Y) <-> apply(apply(apply(X,Y),Y),Y)
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [56]
% apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,b)))) ->
% apply(strong_fixed_point,b)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [57]
% apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X)))) ->
% apply(strong_fixed_point,X)
% Rule
% [56]
% apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,b)))) ->
% apply(strong_fixed_point,b) collapsed.
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [58]
% apply(apply(apply(apply(w,b),X),Y),apply(X,Y)) ->
% apply(apply(w,X),apply(X,Y))
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [59]
% apply(X,apply(X,apply(Y,Z))) <->
% apply(apply(apply(apply(w,b),apply(b,X)),Y),Z)
% Current number of equations to process: 49
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [60]
% apply(apply(apply(apply(w,b),apply(b,X)),Y),Z) <->
% apply(X,apply(X,apply(Y,Z)))
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [61]
% apply(apply(apply(w,apply(b,X)),Y),apply(Y,Y)) ->
% apply(apply(w,X),apply(Y,Y))
% Current number of equations to process: 47
% Current number of ordered equations: 1
% Current number of rules: 58
% New rule produced :
% [62]
% apply(apply(w,apply(b,apply(X,apply(Y,Y)))),Y) ->
% apply(apply(w,X),apply(Y,Y))
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [63]
% apply(X,apply(Y,apply(Z,Z))) <->
% apply(apply(w,apply(b,apply(apply(b,X),Y))),Z)
% Current number of equations to process: 44
% Current number of ordered equations: 5
% Current number of rules: 60
% New rule produced :
% [64]
% apply(X,apply(apply(Y,Y),Z)) <->
% apply(apply(apply(w,apply(b,apply(b,X))),Y),Z)
% Current number of equations to process: 44
% Current number of ordered equations: 4
% Current number of rules: 61
% New rule produced :
% [65]
% apply(apply(X,X),apply(Y,Z)) <->
% apply(apply(apply(apply(w,apply(b,b)),X),Y),Z)
% Current number of equations to process: 44
% Current number of ordered equations: 3
% Current number of rules: 62
% New rule produced :
% [66]
% apply(apply(apply(apply(w,apply(b,b)),X),Y),Z) <->
% apply(apply(X,X),apply(Y,Z))
% Current number of equations to process: 44
% Current number of ordered equations: 2
% Current number of rules: 63
% New rule produced :
% [67]
% apply(apply(apply(w,apply(b,apply(b,X))),Y),Z) <->
% apply(X,apply(apply(Y,Y),Z))
% Current number of equations to process: 44
% Current number of ordered equations: 1
% Current number of rules: 64
% New rule produced :
% [68]
% apply(apply(w,apply(b,apply(apply(b,X),Y))),Z) <->
% apply(X,apply(Y,apply(Z,Z)))
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [69]
% apply(X,apply(X,apply(Y,Y))) <->
% apply(apply(w,apply(b,apply(apply(w,b),X))),Y)
% Current number of equations to process: 43
% Current number of ordered equations: 1
% Current number of rules: 66
% New rule produced :
% [70]
% apply(apply(w,apply(b,apply(apply(w,b),X))),Y) <->
% apply(X,apply(X,apply(Y,Y)))
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [71]
% apply(apply(X,X),apply(Y,Y)) <->
% apply(apply(w,apply(apply(w,apply(b,b)),X)),Y)
% Current number of equations to process: 42
% Current number of ordered equations: 1
% Current number of rules: 68
% New rule produced :
% [72]
% apply(apply(w,apply(apply(w,apply(b,b)),X)),Y) <->
% apply(apply(X,X),apply(Y,Y))
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [73]
% apply(X,apply(apply(Y,Z),Z)) <->
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Z)
% Current number of equations to process: 40
% Current number of ordered equations: 3
% Current number of rules: 70
% New rule produced :
% [74]
% apply(apply(X,Y),apply(Y,Z)) <->
% apply(apply(apply(w,apply(apply(b,b),X)),Y),Z)
% Current number of equations to process: 40
% Current number of ordered equations: 2
% Current number of rules: 71
% New rule produced :
% [75]
% apply(apply(apply(w,apply(apply(b,b),X)),Y),Z) <->
% apply(apply(X,Y),apply(Y,Z))
% Current number of equations to process: 40
% Current number of ordered equations: 1
% Current number of rules: 72
% New rule produced :
% [76]
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Z) <->
% apply(X,apply(apply(Y,Z),Z))
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [77] apply(X,apply(X,X)) <-> apply(apply(w,apply(apply(b,w),b)),X)
% Current number of equations to process: 56
% Current number of ordered equations: 1
% Current number of rules: 74
% New rule produced :
% [78] apply(apply(w,apply(apply(b,w),b)),X) <-> apply(X,apply(X,X))
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [79] apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(apply(w,b),w)),X)
% Current number of equations to process: 57
% Current number of ordered equations: 1
% Current number of rules: 76
% New rule produced :
% [80] apply(apply(w,apply(apply(w,b),w)),X) <-> apply(apply(apply(X,X),X),X)
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [81]
% apply(apply(apply(apply(w,b),X),Y),Y) <->
% apply(apply(w,apply(apply(b,X),X)),Y)
% Current number of equations to process: 56
% Current number of ordered equations: 1
% Current number of rules: 78
% New rule produced :
% [82]
% apply(apply(w,apply(apply(b,X),X)),Y) <->
% apply(apply(apply(apply(w,b),X),Y),Y)
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [83]
% apply(apply(w,apply(w,apply(w,X))),X) <->
% apply(apply(w,apply(w,apply(X,X))),X)
% Current number of equations to process: 69
% Current number of ordered equations: 1
% Current number of rules: 80
% New rule produced :
% [84]
% apply(apply(w,apply(w,apply(X,X))),X) <->
% apply(apply(w,apply(w,apply(w,X))),X)
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [85] apply(apply(w,apply(apply(b,w),X)),X) -> apply(apply(w,apply(w,X)),X)
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 82
% Rule [77] apply(X,apply(X,X)) <-> apply(apply(w,apply(apply(b,w),b)),X) is composed into 
% [77] apply(X,apply(X,X)) <-> apply(apply(w,apply(w,b)),X)
% Rule [54]
% apply(apply(apply(X,Y),Y),Y) <-> apply(apply(w,apply(apply(b,w),X)),Y) is composed into 
% [54] apply(apply(apply(X,Y),Y),Y) <-> apply(apply(w,apply(w,X)),Y)
% New rule produced :
% [86] apply(apply(w,apply(apply(b,w),X)),Y) -> apply(apply(w,apply(w,X)),Y)
% Rule
% [55] apply(apply(w,apply(apply(b,w),X)),Y) <-> apply(apply(apply(X,Y),Y),Y)
% collapsed.
% Rule [78] apply(apply(w,apply(apply(b,w),b)),X) <-> apply(X,apply(X,X))
% collapsed.
% Rule
% [85] apply(apply(w,apply(apply(b,w),X)),X) -> apply(apply(w,apply(w,X)),X)
% collapsed.
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [87]
% apply(apply(w,apply(w,apply(w,w))),X) <->
% apply(apply(w,apply(apply(X,X),X)),X)
% Current number of equations to process: 86
% Current number of ordered equations: 1
% Current number of rules: 81
% New rule produced :
% [88]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [89] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(apply(w,b),w)),X)
% Current number of equations to process: 100
% Current number of ordered equations: 1
% Current number of rules: 83
% New rule produced :
% [90] apply(apply(w,apply(apply(w,b),w)),X) <-> apply(apply(w,apply(X,X)),X)
% Current number of equations to process: 100
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [91] apply(apply(w,apply(w,X)),X) <-> apply(apply(apply(w,w),apply(b,w)),X)
% Current number of equations to process: 99
% Current number of ordered equations: 1
% Current number of rules: 85
% New rule produced :
% [92] apply(apply(apply(w,w),apply(b,w)),X) <-> apply(apply(w,apply(w,X)),X)
% Current number of equations to process: 99
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [93]
% apply(apply(w,apply(w,apply(X,Y))),Y) <->
% apply(apply(w,apply(w,apply(w,X))),Y)
% Rule
% [84]
% apply(apply(w,apply(w,apply(X,X))),X) <->
% apply(apply(w,apply(w,apply(w,X))),X) collapsed.
% Current number of equations to process: 98
% Current number of ordered equations: 1
% Current number of rules: 86
% New rule produced :
% [94]
% apply(apply(w,apply(w,apply(w,X))),Y) <->
% apply(apply(w,apply(w,apply(X,Y))),Y)
% Rule
% [83]
% apply(apply(w,apply(w,apply(w,X))),X) <->
% apply(apply(w,apply(w,apply(X,X))),X) collapsed.
% Current number of equations to process: 98
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [95] apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(w,apply(b,w))),X)
% Current number of equations to process: 116
% Current number of ordered equations: 1
% Current number of rules: 87
% New rule produced :
% [96] apply(apply(w,apply(w,apply(b,w))),X) <-> apply(apply(apply(X,X),X),X)
% Current number of equations to process: 116
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced : [97] apply(apply(w,apply(w,w)),b) -> apply(b,apply(b,b))
% Current number of equations to process: 166
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [98] apply(apply(b,apply(b,X)),X) <-> apply(apply(w,apply(apply(w,w),b)),X)
% Current number of equations to process: 165
% Current number of ordered equations: 1
% Current number of rules: 90
% New rule produced :
% [99] apply(apply(w,apply(apply(w,w),b)),X) <-> apply(apply(b,apply(b,X)),X)
% Current number of equations to process: 165
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [100]
% apply(apply(w,apply(w,apply(w,w))),X) <->
% apply(apply(w,apply(w,apply(X,X))),X)
% Current number of equations to process: 188
% Current number of ordered equations: 1
% Current number of rules: 92
% New rule produced :
% [101]
% apply(apply(w,apply(w,apply(X,X))),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Current number of equations to process: 188
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [102]
% apply(apply(apply(w,apply(w,b)),X),apply(X,X)) ->
% apply(apply(w,X),apply(X,X))
% Current number of equations to process: 187
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [103]
% apply(b,apply(b,apply(X,X))) <->
% apply(apply(w,apply(b,apply(apply(w,w),b))),X)
% Current number of equations to process: 184
% Current number of ordered equations: 1
% Current number of rules: 95
% New rule produced :
% [104]
% apply(apply(w,apply(b,apply(apply(w,w),b))),X) <->
% apply(b,apply(b,apply(X,X)))
% Current number of equations to process: 184
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [105]
% apply(apply(b,X),apply(X,X)) <->
% apply(apply(w,apply(w,apply(apply(w,w),b))),X)
% Current number of equations to process: 183
% Current number of ordered equations: 1
% Current number of rules: 97
% New rule produced :
% [106]
% apply(apply(w,apply(w,apply(apply(w,w),b))),X) <->
% apply(apply(b,X),apply(X,X))
% Current number of equations to process: 183
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [107]
% apply(X,apply(X,apply(Y,Y))) <->
% apply(apply(w,apply(apply(w,b),apply(b,X))),Y)
% Current number of equations to process: 181
% Current number of ordered equations: 3
% Current number of rules: 99
% New rule produced :
% [108]
% apply(apply(b,X),apply(X,Y)) <->
% apply(apply(apply(w,apply(apply(w,w),b)),X),Y)
% Current number of equations to process: 181
% Current number of ordered equations: 2
% Current number of rules: 100
% New rule produced :
% [109]
% apply(apply(apply(w,apply(apply(w,w),b)),X),Y) <->
% apply(apply(b,X),apply(X,Y))
% Current number of equations to process: 181
% Current number of ordered equations: 1
% Current number of rules: 101
% New rule produced :
% [110]
% apply(apply(w,apply(apply(w,b),apply(b,X))),Y) <->
% apply(X,apply(X,apply(Y,Y)))
% Current number of equations to process: 181
% Current number of ordered equations: 0
% Current number of rules: 102
% Rule [89]
% apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(apply(w,b),w)),X) is composed into 
% [89] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(w,w)),X)
% Rule [79]
% apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(apply(w,b),w)),X) is composed into 
% [79] apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(w,w)),X)
% New rule produced :
% [111] apply(apply(w,apply(apply(w,b),w)),X) -> apply(apply(w,apply(w,w)),X)
% Rule
% [80] apply(apply(w,apply(apply(w,b),w)),X) <-> apply(apply(apply(X,X),X),X)
% collapsed.
% Rule
% [90] apply(apply(w,apply(apply(w,b),w)),X) <-> apply(apply(w,apply(X,X)),X)
% collapsed.
% Current number of equations to process: 204
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [112]
% apply(X,apply(apply(Y,Y),Y)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y)
% Current number of equations to process: 225
% Current number of ordered equations: 3
% Current number of rules: 102
% New rule produced :
% [113]
% apply(apply(X,X),apply(X,Y)) <->
% apply(apply(apply(w,apply(w,apply(b,b))),X),Y)
% Current number of equations to process: 225
% Current number of ordered equations: 2
% Current number of rules: 103
% New rule produced :
% [114]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) <->
% apply(X,apply(apply(Y,Y),Y))
% Current number of equations to process: 225
% Current number of ordered equations: 1
% Current number of rules: 104
% New rule produced :
% [115]
% apply(apply(apply(w,apply(w,apply(b,b))),X),Y) <->
% apply(apply(X,X),apply(X,Y))
% Current number of equations to process: 225
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [116] apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(w,apply(b,w))),X)
% Current number of equations to process: 250
% Current number of ordered equations: 1
% Current number of rules: 106
% New rule produced :
% [117] apply(apply(w,apply(w,apply(b,w))),X) <-> apply(apply(w,apply(w,X)),X)
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [118]
% apply(X,apply(Y,apply(X,apply(Y,Z)))) <->
% apply(apply(apply(w,b),apply(apply(b,X),Y)),Z)
% Current number of equations to process: 600
% Current number of ordered equations: 1
% Current number of rules: 108
% New rule produced :
% [119]
% apply(apply(apply(w,b),apply(apply(b,X),Y)),Z) <->
% apply(X,apply(Y,apply(X,apply(Y,Z))))
% Current number of equations to process: 600
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [120]
% apply(X,apply(apply(w,apply(b,apply(Y,Y))),Y)) ->
% apply(apply(w,apply(b,X)),apply(Y,Y))
% Current number of equations to process: 599
% Current number of ordered equations: 0
% Current number of rules: 110
% Rule [116]
% apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(w,apply(b,w))),X) is composed into 
% [116] apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(w,w)),X)
% Rule [95]
% apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(w,apply(b,w))),X) is composed into 
% [95] apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(w,w)),X)
% New rule produced :
% [121] apply(apply(w,apply(w,apply(b,w))),X) -> apply(apply(w,apply(w,w)),X)
% Rule
% [96] apply(apply(w,apply(w,apply(b,w))),X) <-> apply(apply(apply(X,X),X),X)
% collapsed.
% Rule
% [117] apply(apply(w,apply(w,apply(b,w))),X) <-> apply(apply(w,apply(w,X)),X)
% collapsed.
% Current number of equations to process: 695
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [122]
% apply(apply(X,X),apply(apply(X,X),Y)) <->
% apply(apply(apply(w,apply(b,apply(w,b))),X),Y)
% Current number of equations to process: 829
% Current number of ordered equations: 1
% Current number of rules: 110
% New rule produced :
% [123]
% apply(apply(apply(w,apply(b,apply(w,b))),X),Y) <->
% apply(apply(X,X),apply(apply(X,X),Y))
% Current number of equations to process: 829
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [124]
% apply(X,apply(apply(Y,Y),apply(Y,Y))) <->
% apply(apply(w,apply(b,apply(w,apply(b,X)))),Y)
% Current number of equations to process: 828
% Current number of ordered equations: 1
% Current number of rules: 112
% New rule produced :
% [125]
% apply(apply(w,apply(b,apply(w,apply(b,X)))),Y) <->
% apply(X,apply(apply(Y,Y),apply(Y,Y)))
% Current number of equations to process: 828
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [126]
% apply(apply(apply(apply(w,apply(b,w)),X),Y),Y) <->
% apply(apply(w,apply(apply(X,X),Y)),Y)
% Current number of equations to process: 827
% Current number of ordered equations: 1
% Current number of rules: 114
% New rule produced :
% [127]
% apply(apply(w,apply(apply(X,X),Y)),Y) <->
% apply(apply(apply(apply(w,apply(b,w)),X),Y),Y)
% Current number of equations to process: 827
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [128]
% apply(apply(apply(X,apply(Y,Z)),Z),Z) <->
% apply(apply(w,apply(w,apply(apply(b,X),Y))),Z)
% Current number of equations to process: 826
% Current number of ordered equations: 1
% Current number of rules: 116
% New rule produced :
% [129]
% apply(apply(w,apply(w,apply(apply(b,X),Y))),Z) <->
% apply(apply(apply(X,apply(Y,Z)),Z),Z)
% Current number of equations to process: 826
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [130]
% apply(apply(apply(X,apply(X,Y)),Y),Y) <->
% apply(apply(w,apply(w,apply(apply(w,b),X))),Y)
% Current number of equations to process: 825
% Current number of ordered equations: 1
% Current number of rules: 118
% New rule produced :
% [131]
% apply(apply(w,apply(w,apply(apply(w,b),X))),Y) <->
% apply(apply(apply(X,apply(X,Y)),Y),Y)
% Current number of equations to process: 825
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [132]
% apply(apply(apply(X,apply(Y,Y)),Y),Y) <->
% apply(apply(w,apply(w,apply(w,apply(b,X)))),Y)
% Current number of equations to process: 824
% Current number of ordered equations: 1
% Current number of rules: 120
% New rule produced :
% [133]
% apply(apply(w,apply(w,apply(w,apply(b,X)))),Y) <->
% apply(apply(apply(X,apply(Y,Y)),Y),Y)
% Current number of equations to process: 824
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [134]
% apply(apply(apply(apply(X,X),Y),Y),Y) <->
% apply(apply(w,apply(apply(w,apply(b,w)),X)),Y)
% Current number of equations to process: 823
% Current number of ordered equations: 1
% Current number of rules: 122
% New rule produced :
% [135]
% apply(apply(w,apply(apply(w,apply(b,w)),X)),Y) <->
% apply(apply(apply(apply(X,X),Y),Y),Y)
% Current number of equations to process: 823
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [136]
% apply(apply(w,apply(apply(b,X),apply(Y,Z))),Z) ->
% apply(apply(X,apply(apply(w,Y),Z)),Z)
% Current number of equations to process: 822
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [137]
% apply(apply(w,apply(apply(b,X),apply(w,Y))),Z) <->
% apply(apply(X,apply(apply(Y,Z),Z)),Z)
% Current number of equations to process: 821
% Current number of ordered equations: 1
% Current number of rules: 125
% New rule produced :
% [138]
% apply(apply(X,apply(apply(Y,Z),Z)),Z) <->
% apply(apply(w,apply(apply(b,X),apply(w,Y))),Z)
% Current number of equations to process: 821
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [139]
% apply(apply(X,apply(apply(Y,Y),Y)),Y) <->
% apply(apply(w,apply(apply(b,X),apply(w,w))),Y)
% Current number of equations to process: 820
% Current number of ordered equations: 1
% Current number of rules: 127
% New rule produced :
% [140]
% apply(apply(w,apply(apply(b,X),apply(w,w))),Y) <->
% apply(apply(X,apply(apply(Y,Y),Y)),Y)
% Current number of equations to process: 820
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [141]
% apply(apply(X,Y),apply(apply(X,Y),Y)) <->
% apply(apply(w,apply(apply(b,apply(w,b)),X)),Y)
% Current number of equations to process: 818
% Current number of ordered equations: 1
% Current number of rules: 129
% New rule produced :
% [142]
% apply(apply(w,apply(apply(b,apply(w,b)),X)),Y) <->
% apply(apply(X,Y),apply(apply(X,Y),Y))
% Current number of equations to process: 818
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [143]
% apply(apply(apply(w,apply(b,w)),apply(b,X)),Y) <->
% apply(apply(X,apply(apply(b,X),Y)),Y)
% Current number of equations to process: 816
% Current number of ordered equations: 1
% Current number of rules: 131
% New rule produced :
% [144]
% apply(apply(X,apply(apply(b,X),Y)),Y) <->
% apply(apply(apply(w,apply(b,w)),apply(b,X)),Y)
% Current number of equations to process: 816
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [145]
% apply(apply(w,apply(w,apply(apply(b,X),Y))),Z) <->
% apply(apply(w,apply(X,apply(Y,Z))),Z)
% Current number of equations to process: 815
% Current number of ordered equations: 1
% Current number of rules: 133
% New rule produced :
% [146]
% apply(apply(w,apply(X,apply(Y,Z))),Z) <->
% apply(apply(w,apply(w,apply(apply(b,X),Y))),Z)
% Current number of equations to process: 815
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [147]
% apply(apply(w,apply(X,apply(X,Y))),Y) <->
% apply(apply(w,apply(w,apply(apply(w,b),X))),Y)
% Current number of equations to process: 814
% Current number of ordered equations: 1
% Current number of rules: 135
% New rule produced :
% [148]
% apply(apply(w,apply(w,apply(apply(w,b),X))),Y) <->
% apply(apply(w,apply(X,apply(X,Y))),Y)
% Current number of equations to process: 814
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [149]
% apply(apply(w,apply(X,apply(Y,Y))),Y) <->
% apply(apply(w,apply(w,apply(w,apply(b,X)))),Y)
% Current number of equations to process: 813
% Current number of ordered equations: 1
% Current number of rules: 137
% New rule produced :
% [150]
% apply(apply(w,apply(w,apply(w,apply(b,X)))),Y) <->
% apply(apply(w,apply(X,apply(Y,Y))),Y)
% Current number of equations to process: 813
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [151]
% apply(apply(w,apply(apply(X,X),Y)),Y) <->
% apply(apply(w,apply(apply(w,apply(b,w)),X)),Y)
% Current number of equations to process: 812
% Current number of ordered equations: 1
% Current number of rules: 139
% New rule produced :
% [152]
% apply(apply(w,apply(apply(w,apply(b,w)),X)),Y) <->
% apply(apply(w,apply(apply(X,X),Y)),Y)
% Current number of equations to process: 812
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [153]
% apply(apply(apply(apply(w,w),apply(b,b)),X),Y) ->
% apply(b,apply(apply(b,b),apply(X,Y)))
% Current number of equations to process: 811
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [154]
% apply(b,apply(apply(b,b),apply(X,X))) <->
% apply(apply(w,apply(apply(w,w),apply(b,b))),X)
% Current number of equations to process: 810
% Current number of ordered equations: 1
% Current number of rules: 142
% New rule produced :
% [155]
% apply(apply(w,apply(apply(w,w),apply(b,b))),X) <->
% apply(b,apply(apply(b,b),apply(X,X)))
% Current number of equations to process: 810
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [156]
% apply(apply(w,apply(w,apply(X,X))),X) <->
% apply(apply(w,apply(apply(w,w),apply(b,w))),X)
% Current number of equations to process: 809
% Current number of ordered equations: 1
% Current number of rules: 144
% New rule produced :
% [157]
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) <->
% apply(apply(w,apply(w,apply(X,X))),X)
% Current number of equations to process: 809
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [158]
% apply(apply(apply(apply(w,apply(b,w)),X),Y),Y) <->
% apply(apply(w,apply(w,apply(X,X))),Y)
% Current number of equations to process: 805
% Current number of ordered equations: 1
% Current number of rules: 146
% New rule produced :
% [159]
% apply(apply(w,apply(w,apply(X,X))),Y) <->
% apply(apply(apply(apply(w,apply(b,w)),X),Y),Y)
% Current number of equations to process: 805
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [160]
% apply(X,apply(X,apply(apply(b,X),Y))) <->
% apply(apply(apply(w,apply(w,b)),apply(b,X)),Y)
% Current number of equations to process: 804
% Current number of ordered equations: 1
% Current number of rules: 148
% New rule produced :
% [161]
% apply(apply(apply(w,apply(w,b)),apply(b,X)),Y) <->
% apply(X,apply(X,apply(apply(b,X),Y)))
% Current number of equations to process: 804
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [162]
% apply(apply(apply(w,b),apply(apply(w,w),b)),X) ->
% apply(b,apply(b,apply(b,apply(b,X))))
% Current number of equations to process: 802
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [163]
% apply(apply(w,apply(b,apply(b,X))),X) <->
% apply(apply(w,apply(w,apply(apply(w,w),b))),X)
% Current number of equations to process: 801
% Current number of ordered equations: 1
% Current number of rules: 151
% New rule produced :
% [164]
% apply(apply(w,apply(w,apply(apply(w,w),b))),X) <->
% apply(apply(w,apply(b,apply(b,X))),X)
% Current number of equations to process: 801
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [165]
% apply(apply(w,apply(X,apply(X,X))),X) <->
% apply(apply(w,apply(w,apply(w,apply(w,b)))),X)
% Current number of equations to process: 800
% Current number of ordered equations: 1
% Current number of rules: 153
% New rule produced :
% [166]
% apply(apply(w,apply(w,apply(w,apply(w,b)))),X) <->
% apply(apply(w,apply(X,apply(X,X))),X)
% Current number of equations to process: 800
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [167]
% apply(apply(apply(X,apply(X,Y)),Y),Y) <->
% apply(apply(w,apply(apply(apply(w,b),X),Y)),Y)
% Current number of equations to process: 798
% Current number of ordered equations: 1
% Current number of rules: 155
% New rule produced :
% [168]
% apply(apply(w,apply(apply(apply(w,b),X),Y)),Y) <->
% apply(apply(apply(X,apply(X,Y)),Y),Y)
% Current number of equations to process: 798
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [169]
% apply(apply(X,X),apply(apply(X,X),X)) <->
% apply(apply(w,apply(w,apply(b,apply(w,b)))),X)
% Current number of equations to process: 796
% Current number of ordered equations: 1
% Current number of rules: 157
% New rule produced :
% [170]
% apply(apply(w,apply(w,apply(b,apply(w,b)))),X) <->
% apply(apply(X,X),apply(apply(X,X),X))
% Current number of equations to process: 796
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [171]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(w,apply(apply(b,w),X))),X)
% Current number of equations to process: 795
% Current number of ordered equations: 1
% Current number of rules: 159
% New rule produced :
% [172]
% apply(apply(w,apply(w,apply(apply(b,w),X))),X) <->
% apply(apply(w,apply(apply(X,X),X)),X)
% Current number of equations to process: 795
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [173]
% apply(X,apply(apply(w,apply(b,X)),X)) <->
% apply(apply(w,apply(b,apply(apply(w,b),X))),X)
% Current number of equations to process: 791
% Current number of ordered equations: 1
% Current number of rules: 161
% New rule produced :
% [174]
% apply(apply(w,apply(b,apply(apply(w,b),X))),X) <->
% apply(X,apply(apply(w,apply(b,X)),X))
% Current number of equations to process: 791
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [175]
% apply(apply(X,X),apply(apply(w,X),X)) <->
% apply(apply(w,apply(apply(b,apply(w,b)),X)),X)
% Current number of equations to process: 788
% Current number of ordered equations: 1
% Current number of rules: 163
% New rule produced :
% [176]
% apply(apply(w,apply(apply(b,apply(w,b)),X)),X) <->
% apply(apply(X,X),apply(apply(w,X),X))
% Current number of equations to process: 788
% Current number of ordered equations: 0
% Current number of rules: 164
% New rule produced :
% [177]
% apply(apply(X,Y),apply(apply(w,X),Y)) <->
% apply(apply(w,apply(apply(b,apply(w,b)),X)),Y)
% Rule
% [175]
% apply(apply(X,X),apply(apply(w,X),X)) <->
% apply(apply(w,apply(apply(b,apply(w,b)),X)),X) collapsed.
% Current number of equations to process: 787
% Current number of ordered equations: 1
% Current number of rules: 164
% New rule produced :
% [178]
% apply(apply(w,apply(apply(b,apply(w,b)),X)),Y) <->
% apply(apply(X,Y),apply(apply(w,X),Y))
% Rule
% [176]
% apply(apply(w,apply(apply(b,apply(w,b)),X)),X) <->
% apply(apply(X,X),apply(apply(w,X),X)) collapsed.
% Current number of equations to process: 787
% Current number of ordered equations: 0
% Current number of rules: 164
% New rule produced :
% [179]
% apply(apply(X,X),apply(apply(w,X),X)) <->
% apply(apply(w,apply(w,apply(b,apply(w,b)))),X)
% Current number of equations to process: 786
% Current number of ordered equations: 1
% Current number of rules: 165
% New rule produced :
% [180]
% apply(apply(w,apply(w,apply(b,apply(w,b)))),X) <->
% apply(apply(X,X),apply(apply(w,X),X))
% Current number of equations to process: 786
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [181]
% apply(X,apply(X,apply(X,apply(X,Y)))) <->
% apply(apply(apply(w,b),apply(apply(w,b),X)),Y)
% Current number of equations to process: 784
% Current number of ordered equations: 1
% Current number of rules: 167
% New rule produced :
% [182]
% apply(apply(apply(w,b),apply(apply(w,b),X)),Y) <->
% apply(X,apply(X,apply(X,apply(X,Y))))
% Current number of equations to process: 784
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced :
% [183]
% apply(apply(w,X),apply(apply(X,X),X)) <->
% apply(apply(w,apply(apply(b,apply(w,b)),w)),X)
% Current number of equations to process: 783
% Current number of ordered equations: 1
% Current number of rules: 169
% New rule produced :
% [184]
% apply(apply(w,apply(apply(b,apply(w,b)),w)),X) <->
% apply(apply(w,X),apply(apply(X,X),X))
% Current number of equations to process: 783
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced :
% [185]
% apply(apply(X,X),apply(apply(w,w),X)) <->
% apply(apply(w,apply(apply(b,apply(w,b)),X)),X)
% Current number of equations to process: 782
% Current number of ordered equations: 1
% Current number of rules: 171
% New rule produced :
% [186]
% apply(apply(w,apply(apply(b,apply(w,b)),X)),X) <->
% apply(apply(X,X),apply(apply(w,w),X))
% Current number of equations to process: 782
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [187]
% apply(apply(X,X),apply(apply(w,w),X)) <->
% apply(apply(w,apply(w,apply(b,apply(w,b)))),X)
% Current number of equations to process: 781
% Current number of ordered equations: 1
% Current number of rules: 173
% New rule produced :
% [188]
% apply(apply(w,apply(w,apply(b,apply(w,b)))),X) <->
% apply(apply(X,X),apply(apply(w,w),X))
% Current number of equations to process: 781
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced :
% [189]
% apply(X,apply(apply(w,apply(b,X)),Y)) <->
% apply(apply(w,apply(b,apply(apply(w,b),X))),Y)
% Rule
% [173]
% apply(X,apply(apply(w,apply(b,X)),X)) <->
% apply(apply(w,apply(b,apply(apply(w,b),X))),X) collapsed.
% Current number of equations to process: 777
% Current number of ordered equations: 1
% Current number of rules: 174
% New rule produced :
% [190]
% apply(apply(w,apply(b,apply(apply(w,b),X))),Y) <->
% apply(X,apply(apply(w,apply(b,X)),Y))
% Rule
% [174]
% apply(apply(w,apply(b,apply(apply(w,b),X))),X) <->
% apply(X,apply(apply(w,apply(b,X)),X)) collapsed.
% Current number of equations to process: 777
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced :
% [191]
% apply(apply(apply(X,apply(X,X)),X),X) <->
% apply(apply(w,apply(w,apply(w,apply(w,b)))),X)
% Current number of equations to process: 771
% Current number of ordered equations: 1
% Current number of rules: 175
% New rule produced :
% [192]
% apply(apply(w,apply(w,apply(w,apply(w,b)))),X) <->
% apply(apply(apply(X,apply(X,X)),X),X)
% Current number of equations to process: 771
% Current number of ordered equations: 0
% Current number of rules: 176
% Rule [59]
% apply(X,apply(X,apply(Y,Z))) <->
% apply(apply(apply(apply(w,b),apply(b,X)),Y),Z) is composed into 
% [59] apply(X,apply(X,apply(Y,Z))) <-> apply(apply(apply(w,b),X),apply(Y,Z))
% New rule produced :
% [193]
% apply(apply(apply(apply(w,b),apply(b,X)),Y),Z) ->
% apply(apply(apply(w,b),X),apply(Y,Z))
% Rule
% [60]
% apply(apply(apply(apply(w,b),apply(b,X)),Y),Z) <->
% apply(X,apply(X,apply(Y,Z))) collapsed.
% Current number of equations to process: 961
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced :
% [194]
% apply(X,apply(apply(w,w),apply(b,X))) <->
% apply(apply(w,apply(w,apply(w,b))),apply(b,X))
% Current number of equations to process: 961
% Current number of ordered equations: 1
% Current number of rules: 177
% New rule produced :
% [195]
% apply(apply(w,apply(w,apply(w,b))),apply(b,X)) <->
% apply(X,apply(apply(w,w),apply(b,X)))
% Current number of equations to process: 961
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [196]
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Y) ->
% apply(X,apply(apply(w,Y),Y))
% Current number of equations to process: 1180
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [197]
% apply(apply(apply(w,b),X),apply(Y,Y)) <->
% apply(apply(w,apply(b,apply(apply(b,X),X))),Y)
% Current number of equations to process: 1178
% Current number of ordered equations: 2
% Current number of rules: 180
% New rule produced :
% [198]
% apply(apply(w,apply(b,apply(apply(b,X),Y))),Y) ->
% apply(X,apply(apply(w,apply(b,Y)),Y))
% Current number of equations to process: 1178
% Current number of ordered equations: 1
% Current number of rules: 181
% New rule produced :
% [199]
% apply(apply(w,apply(b,apply(apply(b,X),X))),Y) <->
% apply(apply(apply(w,b),X),apply(Y,Y))
% Current number of equations to process: 1178
% Current number of ordered equations: 0
% Current number of rules: 182
% Rule [197]
% apply(apply(apply(w,b),X),apply(Y,Y)) <->
% apply(apply(w,apply(b,apply(apply(b,X),X))),Y) is composed into 
% [197]
% apply(apply(apply(w,b),X),apply(Y,Y)) <->
% apply(X,apply(apply(w,apply(b,X)),Y))
% Rule [63]
% apply(X,apply(Y,apply(Z,Z))) <->
% apply(apply(w,apply(b,apply(apply(b,X),Y))),Z) is composed into 
% [63] apply(X,apply(Y,apply(Z,Z))) <-> apply(X,apply(apply(w,apply(b,Y)),Z))
% New rule produced :
% [200]
% apply(apply(w,apply(b,apply(apply(b,X),Y))),Z) ->
% apply(X,apply(apply(w,apply(b,Y)),Z))
% Rule
% [68]
% apply(apply(w,apply(b,apply(apply(b,X),Y))),Z) <->
% apply(X,apply(Y,apply(Z,Z))) collapsed.
% Rule
% [198]
% apply(apply(w,apply(b,apply(apply(b,X),Y))),Y) ->
% apply(X,apply(apply(w,apply(b,Y)),Y)) collapsed.
% Rule
% [199]
% apply(apply(w,apply(b,apply(apply(b,X),X))),Y) <->
% apply(apply(apply(w,b),X),apply(Y,Y)) collapsed.
% Current number of equations to process: 1177
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [201]
% apply(apply(apply(apply(w,apply(b,b)),X),Y),Y) <->
% apply(apply(w,apply(b,apply(X,X))),Y)
% Current number of equations to process: 1392
% Current number of ordered equations: 1
% Current number of rules: 181
% New rule produced :
% [202]
% apply(apply(w,apply(b,apply(X,X))),Y) <->
% apply(apply(apply(apply(w,apply(b,b)),X),Y),Y)
% Current number of equations to process: 1392
% Current number of ordered equations: 0
% Current number of rules: 182
% New rule produced :
% [203]
% apply(apply(w,apply(b,apply(apply(w,b),X))),X) ->
% apply(X,apply(apply(w,apply(w,b)),X))
% Current number of equations to process: 1600
% Current number of ordered equations: 0
% Current number of rules: 183
% New rule produced :
% [204]
% apply(apply(X,X),apply(X,X)) <->
% apply(apply(w,apply(w,apply(w,apply(b,b)))),X)
% Current number of equations to process: 1789
% Current number of ordered equations: 1
% Current number of rules: 184
% New rule produced :
% [205]
% apply(apply(w,apply(w,apply(w,apply(b,b)))),X) <->
% apply(apply(X,X),apply(X,X))
% Current number of equations to process: 1789
% Current number of ordered equations: 0
% Current number of rules: 185
% New rule produced :
% [206]
% apply(apply(X,X),apply(X,X)) <->
% apply(apply(w,apply(w,apply(apply(b,b),X))),X)
% Current number of equations to process: 1788
% Current number of ordered equations: 1
% Current number of rules: 186
% New rule produced :
% [207]
% apply(apply(w,apply(w,apply(apply(b,b),X))),X) <->
% apply(apply(X,X),apply(X,X))
% Current number of equations to process: 1788
% Current number of ordered equations: 0
% Current number of rules: 187
% Rule [73]
% apply(X,apply(apply(Y,Z),Z)) <->
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Z) is composed into 
% [73] apply(X,apply(apply(Y,Z),Z)) <-> apply(X,apply(apply(w,Y),Z))
% New rule produced :
% [208]
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Z) ->
% apply(X,apply(apply(w,Y),Z))
% Rule
% [76]
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Z) <->
% apply(X,apply(apply(Y,Z),Z)) collapsed.
% Rule
% [196]
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Y) ->
% apply(X,apply(apply(w,Y),Y)) collapsed.
% Current number of equations to process: 1787
% Current number of ordered equations: 0
% Current number of rules: 186
% New rule produced :
% [209]
% apply(X,apply(X,apply(apply(w,Y),Z))) <->
% apply(apply(apply(w,b),X),apply(apply(Y,Z),Z))
% Current number of equations to process: 1897
% Current number of ordered equations: 1
% Current number of rules: 187
% New rule produced :
% [210]
% apply(apply(apply(w,b),X),apply(apply(Y,Z),Z)) <->
% apply(X,apply(X,apply(apply(w,Y),Z)))
% Current number of equations to process: 1897
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [211]
% apply(X,apply(X,apply(apply(Y,Z),Z))) <->
% apply(apply(apply(w,b),X),apply(apply(w,Y),Z))
% Current number of equations to process: 1896
% Current number of ordered equations: 1
% Current number of rules: 189
% New rule produced :
% [212]
% apply(apply(apply(w,b),X),apply(apply(w,Y),Z)) <->
% apply(X,apply(X,apply(apply(Y,Z),Z)))
% Current number of equations to process: 1896
% Current number of ordered equations: 0
% Current number of rules: 190
% New rule produced :
% [213]
% apply(apply(apply(X,Y),Y),apply(Z,Z)) <->
% apply(apply(w,apply(b,apply(apply(w,X),Y))),Z)
% Current number of equations to process: 1895
% Current number of ordered equations: 1
% Current number of rules: 191
% New rule produced :
% [214]
% apply(apply(w,apply(b,apply(apply(w,X),Y))),Z) <->
% apply(apply(apply(X,Y),Y),apply(Z,Z))
% Current number of equations to process: 1895
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced :
% [215]
% apply(apply(X,apply(X,Y)),apply(X,Y)) <->
% apply(apply(apply(w,apply(apply(b,b),w)),X),Y)
% Current number of equations to process: 1893
% Current number of ordered equations: 1
% Current number of rules: 193
% New rule produced :
% [216]
% apply(apply(apply(w,apply(apply(b,b),w)),X),Y) <->
% apply(apply(X,apply(X,Y)),apply(X,Y))
% Current number of equations to process: 1893
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [217]
% apply(apply(X,Y),apply(Y,Y)) <->
% apply(apply(w,apply(w,apply(apply(b,b),X))),Y)
% Rule
% [206]
% apply(apply(X,X),apply(X,X)) <->
% apply(apply(w,apply(w,apply(apply(b,b),X))),X) collapsed.
% Current number of equations to process: 2052
% Current number of ordered equations: 1
% Current number of rules: 194
% New rule produced :
% [218]
% apply(apply(w,apply(w,apply(apply(b,b),X))),Y) <->
% apply(apply(X,Y),apply(Y,Y))
% Rule
% [207]
% apply(apply(w,apply(w,apply(apply(b,b),X))),X) <->
% apply(apply(X,X),apply(X,X)) collapsed.
% Current number of equations to process: 2052
% Current number of ordered equations: 0
% Current number of rules: 194
% Rule [91]
% apply(apply(w,apply(w,X)),X) <-> apply(apply(apply(w,w),apply(b,w)),X) is composed into 
% [91] apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(w,w)),X)
% New rule produced :
% [219] apply(apply(apply(w,w),apply(b,w)),X) -> apply(apply(w,apply(w,w)),X)
% Rule
% [92] apply(apply(apply(w,w),apply(b,w)),X) <-> apply(apply(w,apply(w,X)),X)
% collapsed.
% Current number of equations to process: 2278
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [220] apply(apply(w,apply(w,apply(w,w))),b) -> apply(apply(b,apply(b,b)),b)
% Current number of equations to process: 2450
% Current number of ordered equations: 0
% Current number of rules: 195
% New rule produced :
% [221]
% apply(apply(w,apply(w,apply(w,apply(w,w)))),b) ->
% apply(apply(b,b),apply(b,b))
% Current number of equations to process: 2565
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [222]
% apply(X,apply(apply(w,X),X)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),X)
% Current number of equations to process: 2619
% Current number of ordered equations: 1
% Current number of rules: 197
% New rule produced :
% [223]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),X) <->
% apply(X,apply(apply(w,X),X))
% Current number of equations to process: 2619
% Current number of ordered equations: 0
% Current number of rules: 198
% New rule produced :
% [224]
% apply(apply(apply(w,b),X),apply(Y,Y)) <->
% apply(apply(w,apply(apply(w,b),apply(b,X))),Y)
% Current number of equations to process: 2678
% Current number of ordered equations: 1
% Current number of rules: 199
% New rule produced :
% [225]
% apply(apply(w,apply(apply(w,b),apply(b,X))),Y) <->
% apply(apply(apply(w,b),X),apply(Y,Y))
% Current number of equations to process: 2678
% Current number of ordered equations: 0
% Current number of rules: 200
% New rule produced :
% [226]
% apply(apply(apply(apply(apply(w,b),X),Y),Y),Y) <->
% apply(apply(w,apply(X,apply(X,Y))),Y)
% Current number of equations to process: 2677
% Current number of ordered equations: 1
% Current number of rules: 201
% New rule produced :
% [227]
% apply(apply(w,apply(X,apply(X,Y))),Y) <->
% apply(apply(apply(apply(apply(w,b),X),Y),Y),Y)
% Current number of equations to process: 2677
% Current number of ordered equations: 0
% Current number of rules: 202
% New rule produced :
% [228]
% apply(apply(w,apply(w,X)),apply(apply(b,w),X)) ->
% apply(apply(w,w),apply(apply(b,w),X))
% Current number of equations to process: 2676
% Current number of ordered equations: 0
% Current number of rules: 203
% Rule [171]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(w,apply(apply(b,w),X))),X) is composed into 
% [171]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(w,apply(w,X))),X)
% New rule produced :
% [229]
% apply(apply(w,apply(w,apply(apply(b,w),X))),X) ->
% apply(apply(w,apply(w,apply(w,X))),X)
% Rule
% [172]
% apply(apply(w,apply(w,apply(apply(b,w),X))),X) <->
% apply(apply(w,apply(apply(X,X),X)),X) collapsed.
% Current number of equations to process: 2675
% Current number of ordered equations: 0
% Current number of rules: 203
% Rule [103]
% apply(b,apply(b,apply(X,X))) <->
% apply(apply(w,apply(b,apply(apply(w,w),b))),X) is composed into 
% [103] apply(b,apply(b,apply(X,X))) <-> apply(b,apply(apply(w,apply(b,b)),X))
% New rule produced :
% [230]
% apply(apply(w,apply(b,apply(apply(w,w),b))),X) ->
% apply(b,apply(apply(w,apply(b,b)),X))
% Rule
% [104]
% apply(apply(w,apply(b,apply(apply(w,w),b))),X) <->
% apply(b,apply(b,apply(X,X))) collapsed.
% Current number of equations to process: 2754
% Current number of ordered equations: 0
% Current number of rules: 203
% New rule produced :
% [231]
% apply(X,apply(apply(w,apply(b,X)),X)) <->
% apply(apply(w,apply(apply(w,b),apply(b,X))),X)
% Current number of equations to process: 3003
% Current number of ordered equations: 1
% Current number of rules: 204
% New rule produced :
% [232]
% apply(apply(w,apply(apply(w,b),apply(b,X))),X) <->
% apply(X,apply(apply(w,apply(b,X)),X))
% Current number of equations to process: 3003
% Current number of ordered equations: 0
% Current number of rules: 205
% New rule produced :
% [233]
% apply(X,apply(apply(w,apply(b,X)),Y)) <->
% apply(apply(w,apply(apply(w,b),apply(b,X))),Y)
% Rule
% [231]
% apply(X,apply(apply(w,apply(b,X)),X)) <->
% apply(apply(w,apply(apply(w,b),apply(b,X))),X) collapsed.
% Current number of equations to process: 3002
% Current number of ordered equations: 1
% Current number of rules: 205
% New rule produced :
% [234]
% apply(apply(w,apply(apply(w,b),apply(b,X))),Y) <->
% apply(X,apply(apply(w,apply(b,X)),Y))
% Rule
% [232]
% apply(apply(w,apply(apply(w,b),apply(b,X))),X) <->
% apply(X,apply(apply(w,apply(b,X)),X)) collapsed.
% Current number of equations to process: 3002
% Current number of ordered equations: 0
% Current number of rules: 205
% New rule produced :
% [235]
% apply(apply(w,apply(apply(w,b),apply(b,X))),X) ->
% apply(X,apply(apply(w,apply(w,b)),X))
% Current number of equations to process: 3001
% Current number of ordered equations: 0
% Current number of rules: 206
% New rule produced :
% [236]
% apply(X,apply(apply(w,Y),Y)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y)
% Rule
% [222]
% apply(X,apply(apply(w,X),X)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),X) collapsed.
% Current number of equations to process: 3279
% Current number of ordered equations: 1
% Current number of rules: 206
% New rule produced :
% [237]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) <->
% apply(X,apply(apply(w,Y),Y))
% Rule
% [223]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),X) <->
% apply(X,apply(apply(w,X),X)) collapsed.
% Current number of equations to process: 3279
% Current number of ordered equations: 0
% Current number of rules: 206
% New rule produced :
% [238]
% apply(apply(w,apply(w,w)),apply(apply(w,b),w)) ->
% apply(apply(w,w),apply(apply(w,b),w))
% Current number of equations to process: 3278
% Current number of ordered equations: 0
% Current number of rules: 207
% Rule [236]
% apply(X,apply(apply(w,Y),Y)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) is composed into 
% [236] apply(X,apply(apply(w,Y),Y)) <-> apply(X,apply(apply(w,w),Y))
% Rule [112]
% apply(X,apply(apply(Y,Y),Y)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) is composed into 
% [112] apply(X,apply(apply(Y,Y),Y)) <-> apply(X,apply(apply(w,w),Y))
% New rule produced :
% [239]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) ->
% apply(X,apply(apply(w,w),Y))
% Rule
% [114]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) <->
% apply(X,apply(apply(Y,Y),Y)) collapsed.
% Rule
% [237]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) <->
% apply(X,apply(apply(w,Y),Y)) collapsed.
% Current number of equations to process: 3430
% Current number of ordered equations: 0
% Current number of rules: 206
% New rule produced :
% [240]
% apply(apply(w,apply(w,w)),apply(w,apply(b,w))) ->
% apply(apply(w,w),apply(w,apply(b,w)))
% Current number of equations to process: 4273
% Current number of ordered equations: 2
% Current number of rules: 207
% New rule produced :
% [241]
% apply(apply(w,apply(w,apply(w,X))),X) <->
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X)
% Current number of equations to process: 4273
% Current number of ordered equations: 1
% Current number of rules: 208
% New rule produced :
% [242]
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X) <->
% apply(apply(w,apply(w,apply(w,X))),X)
% Current number of equations to process: 4273
% Current number of ordered equations: 0
% Current number of rules: 209
% New rule produced :
% [243]
% apply(apply(apply(apply(X,Y),Y),Y),Y) <->
% apply(apply(w,apply(w,apply(apply(b,w),X))),Y)
% Current number of equations to process: 4900
% Current number of ordered equations: 1
% Current number of rules: 210
% New rule produced :
% [244]
% apply(apply(w,apply(w,apply(apply(b,w),X))),Y) <->
% apply(apply(apply(apply(X,Y),Y),Y),Y)
% Current number of equations to process: 4900
% Current number of ordered equations: 0
% Current number of rules: 211
% New rule produced :
% [245]
% apply(X,apply(Y,apply(Z,apply(apply(b,Y),Z)))) <->
% apply(apply(w,apply(b,X)),apply(apply(b,Y),Z))
% Current number of equations to process: 4899
% Current number of ordered equations: 1
% Current number of rules: 212
% New rule produced :
% [246]
% apply(apply(w,apply(b,X)),apply(apply(b,Y),Z)) <->
% apply(X,apply(Y,apply(Z,apply(apply(b,Y),Z))))
% Current number of equations to process: 4899
% Current number of ordered equations: 0
% Current number of rules: 213
% New rule produced :
% [247]
% apply(apply(X,apply(X,X)),X) <->
% apply(apply(w,apply(w,apply(apply(b,w),b))),X)
% Current number of equations to process: 4994
% Current number of ordered equations: 1
% Current number of rules: 214
% New rule produced :
% [248]
% apply(apply(w,apply(w,apply(apply(b,w),b))),X) <->
% apply(apply(X,apply(X,X)),X)
% Current number of equations to process: 4994
% Current number of ordered equations: 0
% Current number of rules: 215
% New rule produced :
% [249]
% apply(apply(w,apply(apply(X,Y),Y)),Y) <->
% apply(apply(w,apply(w,apply(apply(b,w),X))),Y)
% Current number of equations to process: 2159
% Current number of ordered equations: 1
% Current number of rules: 216
% New rule produced :
% [250]
% apply(apply(w,apply(w,apply(apply(b,w),X))),Y) <->
% apply(apply(w,apply(apply(X,Y),Y)),Y)
% Current number of equations to process: 2159
% Current number of ordered equations: 0
% Current number of rules: 217
% New rule produced :
% [251]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(w,apply(w,apply(apply(w,b),w))),X)
% Current number of equations to process: 2158
% Current number of ordered equations: 1
% Current number of rules: 218
% New rule produced :
% [252]
% apply(apply(w,apply(w,apply(apply(w,b),w))),X) <->
% apply(apply(apply(apply(X,X),X),X),X)
% Current number of equations to process: 2158
% Current number of ordered equations: 0
% Current number of rules: 219
% New rule produced :
% [253]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(w,apply(apply(w,b),w))),X)
% Current number of equations to process: 2157
% Current number of ordered equations: 1
% Current number of rules: 220
% New rule produced :
% [254]
% apply(apply(w,apply(w,apply(apply(w,b),w))),X) <->
% apply(apply(w,apply(apply(X,X),X)),X)
% Current number of equations to process: 2157
% Current number of ordered equations: 0
% Current number of rules: 221
% New rule produced :
% [255]
% apply(apply(w,apply(w,apply(apply(w,b),w))),X) <->
% apply(apply(w,apply(w,apply(X,X))),X)
% Current number of equations to process: 2326
% Current number of ordered equations: 1
% Current number of rules: 222
% New rule produced :
% [256]
% apply(apply(w,apply(w,apply(X,X))),X) <->
% apply(apply(w,apply(w,apply(apply(w,b),w))),X)
% Current number of equations to process: 2326
% Current number of ordered equations: 0
% Current number of rules: 223
% New rule produced :
% [257]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X)
% Current number of equations to process: 2412
% Current number of ordered equations: 1
% Current number of rules: 224
% New rule produced :
% [258]
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X) <->
% apply(apply(apply(apply(X,X),X),X),X)
% Current number of equations to process: 2412
% Current number of ordered equations: 0
% Current number of rules: 225
% New rule produced :
% [259]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X)
% Current number of equations to process: 2518
% Current number of ordered equations: 1
% Current number of rules: 226
% New rule produced :
% [260]
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X) <->
% apply(apply(w,apply(apply(X,X),X)),X)
% Current number of equations to process: 2518
% Current number of ordered equations: 0
% Current number of rules: 227
% New rule produced :
% [261]
% apply(apply(X,apply(apply(w,b),X)),X) <->
% apply(apply(apply(w,apply(b,w)),apply(b,X)),X)
% Current number of equations to process: 2840
% Current number of ordered equations: 1
% Current number of rules: 228
% New rule produced :
% [262]
% apply(apply(apply(w,apply(b,w)),apply(b,X)),X) <->
% apply(apply(X,apply(apply(w,b),X)),X)
% Current number of equations to process: 2840
% Current number of ordered equations: 0
% Current number of rules: 229
% New rule produced :
% [263]
% apply(X,apply(X,apply(X,apply(X,X)))) <->
% apply(apply(w,apply(apply(w,b),apply(w,b))),X)
% Current number of equations to process: 3095
% Current number of ordered equations: 1
% Current number of rules: 230
% New rule produced :
% [264]
% apply(apply(w,apply(apply(w,b),apply(w,b))),X) <->
% apply(X,apply(X,apply(X,apply(X,X))))
% Current number of equations to process: 3095
% Current number of ordered equations: 0
% Current number of rules: 231
% New rule produced :
% [265]
% apply(X,apply(X,apply(apply(apply(w,b),X),Y))) <->
% apply(apply(apply(w,b),apply(apply(w,b),X)),Y)
% Current number of equations to process: 3093
% Current number of ordered equations: 1
% Current number of rules: 232
% New rule produced :
% [266]
% apply(apply(apply(w,b),apply(apply(w,b),X)),Y) <->
% apply(X,apply(X,apply(apply(apply(w,b),X),Y)))
% Current number of equations to process: 3093
% Current number of ordered equations: 0
% Current number of rules: 233
% New rule produced :
% [267]
% apply(X,apply(Y,apply(Y,apply(apply(w,b),Y)))) <->
% apply(apply(w,apply(b,X)),apply(apply(w,b),Y))
% Current number of equations to process: 3092
% Current number of ordered equations: 1
% Current number of rules: 234
% New rule produced :
% [268]
% apply(apply(w,apply(b,X)),apply(apply(w,b),Y)) <->
% apply(X,apply(Y,apply(Y,apply(apply(w,b),Y))))
% Current number of equations to process: 3092
% Current number of ordered equations: 0
% Current number of rules: 235
% New rule produced :
% [269]
% apply(apply(w,apply(b,X)),apply(X,apply(Y,Y))) <->
% apply(apply(apply(w,b),apply(w,apply(b,X))),Y)
% Current number of equations to process: 3091
% Current number of ordered equations: 1
% Current number of rules: 236
% New rule produced :
% [270]
% apply(apply(apply(w,b),apply(w,apply(b,X))),Y) <->
% apply(apply(w,apply(b,X)),apply(X,apply(Y,Y)))
% Current number of equations to process: 3091
% Current number of ordered equations: 0
% Current number of rules: 237
% New rule produced :
% [271]
% apply(apply(w,apply(w,apply(w,X))),X) <->
% apply(apply(w,apply(apply(w,w),apply(b,w))),X)
% Current number of equations to process: 3757
% Current number of ordered equations: 1
% Current number of rules: 238
% New rule produced :
% [272]
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) <->
% apply(apply(w,apply(w,apply(w,X))),X)
% Current number of equations to process: 3757
% Current number of ordered equations: 0
% Current number of rules: 239
% New rule produced :
% [273]
% apply(apply(X,apply(X,X)),apply(X,X)) <->
% apply(apply(w,apply(w,apply(apply(b,b),w))),X)
% Current number of equations to process: 4024
% Current number of ordered equations: 1
% Current number of rules: 240
% New rule produced :
% [274]
% apply(apply(w,apply(w,apply(apply(b,b),w))),X) <->
% apply(apply(X,apply(X,X)),apply(X,X))
% Current number of equations to process: 4024
% Current number of ordered equations: 0
% Current number of rules: 241
% Rule [249]
% apply(apply(w,apply(apply(X,Y),Y)),Y) <->
% apply(apply(w,apply(w,apply(apply(b,w),X))),Y) is composed into 
% [249]
% apply(apply(w,apply(apply(X,Y),Y)),Y) <->
% apply(apply(w,apply(w,apply(w,X))),Y)
% Rule [247]
% apply(apply(X,apply(X,X)),X) <->
% apply(apply(w,apply(w,apply(apply(b,w),b))),X) is composed into 
% [247] apply(apply(X,apply(X,X)),X) <-> apply(apply(w,apply(w,apply(w,b))),X)
% Rule [243]
% apply(apply(apply(apply(X,Y),Y),Y),Y) <->
% apply(apply(w,apply(w,apply(apply(b,w),X))),Y) is composed into 
% [243]
% apply(apply(apply(apply(X,Y),Y),Y),Y) <->
% apply(apply(w,apply(w,apply(w,X))),Y)
% New rule produced :
% [275]
% apply(apply(w,apply(w,apply(apply(b,w),X))),Y) ->
% apply(apply(w,apply(w,apply(w,X))),Y)
% Rule
% [229]
% apply(apply(w,apply(w,apply(apply(b,w),X))),X) ->
% apply(apply(w,apply(w,apply(w,X))),X) collapsed.
% Rule
% [244]
% apply(apply(w,apply(w,apply(apply(b,w),X))),Y) <->
% apply(apply(apply(apply(X,Y),Y),Y),Y) collapsed.
% Rule
% [248]
% apply(apply(w,apply(w,apply(apply(b,w),b))),X) <->
% apply(apply(X,apply(X,X)),X) collapsed.
% Rule
% [250]
% apply(apply(w,apply(w,apply(apply(b,w),X))),Y) <->
% apply(apply(w,apply(apply(X,Y),Y)),Y) collapsed.
% Current number of equations to process: 4023
% Current number of ordered equations: 0
% Current number of rules: 238
% New rule produced :
% [276]
% apply(apply(w,apply(apply(apply(X,Y),Y),Y)),Y) <->
% apply(apply(w,apply(w,apply(apply(w,X),Y))),Y)
% Current number of equations to process: 4022
% Current number of ordered equations: 1
% Current number of rules: 239
% New rule produced :
% [277]
% apply(apply(w,apply(w,apply(apply(w,X),Y))),Y) <->
% apply(apply(w,apply(apply(apply(X,Y),Y),Y)),Y)
% Current number of equations to process: 4022
% Current number of ordered equations: 0
% Current number of rules: 240
% Rule [256]
% apply(apply(w,apply(w,apply(X,X))),X) <->
% apply(apply(w,apply(w,apply(apply(w,b),w))),X) is composed into 
% [256]
% apply(apply(w,apply(w,apply(X,X))),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Rule [253]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(w,apply(apply(w,b),w))),X) is composed into 
% [253]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Rule [251]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(w,apply(w,apply(apply(w,b),w))),X) is composed into 
% [251]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% New rule produced :
% [278]
% apply(apply(w,apply(w,apply(apply(w,b),w))),X) ->
% apply(apply(w,apply(w,apply(w,w))),X)
% Rule
% [252]
% apply(apply(w,apply(w,apply(apply(w,b),w))),X) <->
% apply(apply(apply(apply(X,X),X),X),X) collapsed.
% Rule
% [254]
% apply(apply(w,apply(w,apply(apply(w,b),w))),X) <->
% apply(apply(w,apply(apply(X,X),X)),X) collapsed.
% Rule
% [255]
% apply(apply(w,apply(w,apply(apply(w,b),w))),X) <->
% apply(apply(w,apply(w,apply(X,X))),X) collapsed.
% Current number of equations to process: 4134
% Current number of ordered equations: 0
% Current number of rules: 238
% Rule [259]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X) is composed into 
% [259]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Rule [257]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X) is composed into 
% [257]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Rule [241]
% apply(apply(w,apply(w,apply(w,X))),X) <->
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X) is composed into 
% [241]
% apply(apply(w,apply(w,apply(w,X))),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% New rule produced :
% [279]
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X) ->
% apply(apply(w,apply(w,apply(w,w))),X)
% Rule
% [242]
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X) <->
% apply(apply(w,apply(w,apply(w,X))),X) collapsed.
% Rule
% [258]
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X) <->
% apply(apply(apply(apply(X,X),X),X),X) collapsed.
% Rule
% [260]
% apply(apply(w,apply(w,apply(w,apply(b,w)))),X) <->
% apply(apply(w,apply(apply(X,X),X)),X) collapsed.
% Current number of equations to process: 4360
% Current number of ordered equations: 0
% Current number of rules: 236
% New rule produced :
% [280]
% apply(apply(apply(X,apply(Y,Z)),apply(Y,Z)),Z) <->
% apply(apply(w,apply(apply(b,apply(w,X)),Y)),Z)
% Current number of equations to process: 4677
% Current number of ordered equations: 1
% Current number of rules: 237
% New rule produced :
% [281]
% apply(apply(w,apply(apply(b,apply(w,X)),Y)),Z) <->
% apply(apply(apply(X,apply(Y,Z)),apply(Y,Z)),Z)
% Current number of equations to process: 4677
% Current number of ordered equations: 0
% Current number of rules: 238
% New rule produced :
% [282]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(apply(w,w),apply(b,w))),X)
% Current number of equations to process: 4805
% Current number of ordered equations: 1
% Current number of rules: 239
% New rule produced :
% [283]
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) <->
% apply(apply(w,apply(apply(X,X),X)),X)
% Current number of equations to process: 4805
% Current number of ordered equations: 0
% Current number of rules: 240
% New rule produced :
% [284]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(w,apply(apply(w,w),apply(b,w))),X)
% Current number of equations to process: 4842
% Current number of ordered equations: 1
% Current number of rules: 241
% New rule produced :
% [285]
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) <->
% apply(apply(apply(apply(X,X),X),X),X)
% Current number of equations to process: 4842
% Current number of ordered equations: 0
% Current number of rules: 242
% Rule [284]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) is composed into 
% [284]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Rule [282]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) is composed into 
% [282]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Rule [271]
% apply(apply(w,apply(w,apply(w,X))),X) <->
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) is composed into 
% [271]
% apply(apply(w,apply(w,apply(w,X))),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Rule [156]
% apply(apply(w,apply(w,apply(X,X))),X) <->
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) is composed into 
% [156]
% apply(apply(w,apply(w,apply(X,X))),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% New rule produced :
% [286]
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) ->
% apply(apply(w,apply(w,apply(w,w))),X)
% Rule
% [157]
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) <->
% apply(apply(w,apply(w,apply(X,X))),X) collapsed.
% Rule
% [272]
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) <->
% apply(apply(w,apply(w,apply(w,X))),X) collapsed.
% Rule
% [283]
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) <->
% apply(apply(w,apply(apply(X,X),X)),X) collapsed.
% Rule
% [285]
% apply(apply(w,apply(apply(w,w),apply(b,w))),X) <->
% apply(apply(apply(apply(X,X),X),X),X) collapsed.
% Current number of equations to process: 4841
% Current number of ordered equations: 0
% Current number of rules: 239
% New rule produced :
% [287]
% apply(X,apply(X,apply(apply(w,b),X))) <->
% apply(apply(apply(w,apply(w,b)),apply(b,X)),X)
% Current number of equations to process: 4963
% Current number of ordered equations: 1
% Current number of rules: 240
% New rule produced :
% [288]
% apply(apply(apply(w,apply(w,b)),apply(b,X)),X) <->
% apply(X,apply(X,apply(apply(w,b),X)))
% Current number of equations to process: 4963
% Current number of ordered equations: 0
% Current number of rules: 241
% Rule [276]
% apply(apply(w,apply(apply(apply(X,Y),Y),Y)),Y) <->
% apply(apply(w,apply(w,apply(apply(w,X),Y))),Y) is composed into 
% [276]
% apply(apply(w,apply(apply(apply(X,Y),Y),Y)),Y) <->
% apply(apply(w,apply(w,apply(w,apply(X,Y)))),Y)
% New rule produced :
% [289]
% apply(apply(w,apply(w,apply(apply(w,X),Y))),Y) ->
% apply(apply(w,apply(w,apply(w,apply(X,Y)))),Y)
% Rule
% [277]
% apply(apply(w,apply(w,apply(apply(w,X),Y))),Y) <->
% apply(apply(w,apply(apply(apply(X,Y),Y),Y)),Y) collapsed.
% Current number of equations to process: 2894
% Current number of ordered equations: 0
% Current number of rules: 241
% New rule produced :
% [290]
% apply(apply(w,apply(apply(apply(X,Y),Y),Y)),Y) <->
% apply(apply(w,apply(w,apply(w,apply(w,X)))),Y)
% Current number of equations to process: 2893
% Current number of ordered equations: 1
% Current number of rules: 242
% New rule produced :
% [291]
% apply(apply(w,apply(w,apply(w,apply(w,X)))),Y) <->
% apply(apply(w,apply(apply(apply(X,Y),Y),Y)),Y)
% Current number of equations to process: 2893
% Current number of ordered equations: 0
% Current number of rules: 243
% New rule produced :
% [292]
% apply(apply(w,apply(apply(apply(X,X),X),X)),X) <->
% apply(apply(w,apply(w,apply(w,apply(w,w)))),X)
% Current number of equations to process: 3029
% Current number of ordered equations: 1
% Current number of rules: 244
% New rule produced :
% [293]
% apply(apply(w,apply(w,apply(w,apply(w,w)))),X) <->
% apply(apply(w,apply(apply(apply(X,X),X),X)),X)
% Current number of equations to process: 3029
% Current number of ordered equations: 0
% Current number of rules: 245
% New rule produced :
% [294]
% apply(apply(w,apply(X,apply(Y,Y))),apply(Y,Y)) <->
% apply(apply(w,apply(b,apply(w,apply(w,X)))),Y)
% Current number of equations to process: 3028
% Current number of ordered equations: 1
% Current number of rules: 246
% New rule produced :
% [295]
% apply(apply(w,apply(b,apply(w,apply(w,X)))),Y) <->
% apply(apply(w,apply(X,apply(Y,Y))),apply(Y,Y))
% Current number of equations to process: 3028
% Current number of ordered equations: 0
% Current number of rules: 247
% New rule produced :
% [296]
% apply(apply(w,apply(w,apply(apply(X,Y),Y))),Y) <->
% apply(apply(w,apply(w,apply(w,apply(w,X)))),Y)
% Current number of equations to process: 3027
% Current number of ordered equations: 1
% Current number of rules: 248
% New rule produced :
% [297]
% apply(apply(w,apply(w,apply(w,apply(w,X)))),Y) <->
% apply(apply(w,apply(w,apply(apply(X,Y),Y))),Y)
% Current number of equations to process: 3027
% Current number of ordered equations: 0
% Current number of rules: 249
% New rule produced :
% [298]
% apply(apply(X,apply(apply(b,X),apply(b,X))),X) <->
% apply(apply(w,apply(apply(b,apply(w,w)),b)),X)
% Current number of equations to process: 3532
% Current number of ordered equations: 1
% Current number of rules: 250
% New rule produced :
% [299]
% apply(apply(w,apply(apply(b,apply(w,w)),b)),X) <->
% apply(apply(X,apply(apply(b,X),apply(b,X))),X)
% Current number of equations to process: 3532
% Current number of ordered equations: 0
% Current number of rules: 251
% New rule produced :
% [300]
% apply(apply(w,apply(b,X)),apply(apply(w,w),b)) ->
% apply(X,apply(b,apply(b,apply(apply(w,w),b))))
% Current number of equations to process: 4252
% Current number of ordered equations: 0
% Current number of rules: 252
% New rule produced :
% [301]
% apply(apply(w,apply(w,b)),apply(X,apply(X,X))) <->
% apply(apply(apply(w,b),apply(w,apply(w,b))),X)
% Current number of equations to process: 4528
% Current number of ordered equations: 1
% Current number of rules: 253
% New rule produced :
% [302]
% apply(apply(apply(w,b),apply(w,apply(w,b))),X) <->
% apply(apply(w,apply(w,b)),apply(X,apply(X,X)))
% Current number of equations to process: 4528
% Current number of ordered equations: 0
% Current number of rules: 254
% New rule produced :
% [303]
% apply(apply(X,X),apply(apply(X,X),apply(X,X))) <->
% apply(apply(w,apply(b,apply(w,apply(w,b)))),X)
% Current number of equations to process: 4527
% Current number of ordered equations: 1
% Current number of rules: 255
% New rule produced :
% [304]
% apply(apply(w,apply(b,apply(w,apply(w,b)))),X) <->
% apply(apply(X,X),apply(apply(X,X),apply(X,X)))
% Current number of equations to process: 4527
% Current number of ordered equations: 0
% Current number of rules: 256
% New rule produced :
% [305]
% apply(apply(apply(X,Y),apply(apply(w,X),Y)),Y) <->
% apply(apply(w,apply(apply(w,b),apply(X,Y))),Y)
% Current number of equations to process: 4526
% Current number of ordered equations: 1
% Current number of rules: 257
% New rule produced :
% [306]
% apply(apply(w,apply(apply(w,b),apply(X,Y))),Y) <->
% apply(apply(apply(X,Y),apply(apply(w,X),Y)),Y)
% Current number of equations to process: 4526
% Current number of ordered equations: 0
% Current number of rules: 258
% New rule produced :
% [307]
% apply(apply(apply(w,X),apply(apply(X,Y),Y)),Y) <->
% apply(apply(w,apply(apply(w,b),apply(w,X))),Y)
% Current number of equations to process: 4525
% Current number of ordered equations: 1
% Current number of rules: 259
% New rule produced :
% [308]
% apply(apply(w,apply(apply(w,b),apply(w,X))),Y) <->
% apply(apply(apply(w,X),apply(apply(X,Y),Y)),Y)
% Current number of equations to process: 4525
% Current number of ordered equations: 0
% Current number of rules: 260
% New rule produced :
% [309]
% apply(apply(apply(w,w),apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(apply(w,b),apply(w,w))),X)
% Current number of equations to process: 4646
% Current number of ordered equations: 1
% Current number of rules: 261
% New rule produced :
% [310]
% apply(apply(w,apply(apply(w,b),apply(w,w))),X) <->
% apply(apply(apply(w,w),apply(apply(X,X),X)),X)
% Current number of equations to process: 4646
% Current number of ordered equations: 0
% Current number of rules: 262
% New rule produced :
% [311]
% apply(apply(apply(X,X),apply(apply(w,w),X)),X) <->
% apply(apply(w,apply(apply(w,b),apply(X,X))),X)
% Current number of equations to process: 4645
% Current number of ordered equations: 1
% Current number of rules: 263
% New rule produced :
% [312]
% apply(apply(w,apply(apply(w,b),apply(X,X))),X) <->
% apply(apply(apply(X,X),apply(apply(w,w),X)),X)
% Current number of equations to process: 4645
% Current number of ordered equations: 0
% Current number of rules: 264
% New rule produced :
% [313]
% apply(X,apply(apply(X,Y),Y)) <->
% apply(apply(w,apply(apply(w,apply(apply(w,w),b)),X)),Y)
% Current number of equations to process: 4644
% Current number of ordered equations: 1
% Current number of rules: 265
% New rule produced :
% [314]
% apply(apply(w,apply(apply(w,apply(apply(w,w),b)),X)),Y) <->
% apply(X,apply(apply(X,Y),Y))
% Current number of equations to process: 4644
% Current number of ordered equations: 0
% Current number of rules: 266
% New rule produced :
% [315]
% apply(apply(apply(X,apply(Y,Y)),apply(Y,Y)),Y) <->
% apply(apply(w,apply(w,apply(b,apply(w,X)))),Y)
% Current number of equations to process: 4643
% Current number of ordered equations: 1
% Current number of rules: 267
% New rule produced :
% [316]
% apply(apply(w,apply(w,apply(b,apply(w,X)))),Y) <->
% apply(apply(apply(X,apply(Y,Y)),apply(Y,Y)),Y)
% Current number of equations to process: 4643
% Current number of ordered equations: 0
% Current number of rules: 268
% New rule produced :
% [317]
% apply(X,apply(X,apply(apply(w,apply(b,X)),X))) <->
% apply(apply(apply(w,b),apply(apply(w,b),X)),X)
% Current number of equations to process: 4641
% Current number of ordered equations: 1
% Current number of rules: 269
% New rule produced :
% [318]
% apply(apply(apply(w,b),apply(apply(w,b),X)),X) <->
% apply(X,apply(X,apply(apply(w,apply(b,X)),X)))
% Current number of equations to process: 4641
% Current number of ordered equations: 0
% Current number of rules: 270
% New rule produced :
% [319]
% apply(X,apply(Y,apply(apply(w,apply(b,X)),Y))) <->
% apply(apply(apply(w,b),apply(apply(b,X),Y)),Y)
% Current number of equations to process: 4640
% Current number of ordered equations: 1
% Current number of rules: 271
% New rule produced :
% [320]
% apply(apply(apply(w,b),apply(apply(b,X),Y)),Y) <->
% apply(X,apply(Y,apply(apply(w,apply(b,X)),Y)))
% Current number of equations to process: 4640
% Current number of ordered equations: 0
% Current number of rules: 272
% New rule produced :
% [321]
% apply(X,apply(X,apply(apply(w,apply(w,b)),X))) <->
% apply(apply(apply(w,b),apply(apply(w,b),X)),X)
% Current number of equations to process: 4639
% Current number of ordered equations: 1
% Current number of rules: 273
% New rule produced :
% [322]
% apply(apply(apply(w,b),apply(apply(w,b),X)),X) <->
% apply(X,apply(X,apply(apply(w,apply(w,b)),X)))
% Current number of equations to process: 4639
% Current number of ordered equations: 0
% Current number of rules: 274
% New rule produced :
% [323]
% apply(apply(apply(w,apply(b,w)),X),apply(Y,Y)) <->
% apply(apply(w,apply(b,apply(w,apply(X,X)))),Y)
% Current number of equations to process: 4629
% Current number of ordered equations: 1
% Current number of rules: 275
% New rule produced :
% [324]
% apply(apply(w,apply(b,apply(w,apply(X,X)))),Y) <->
% apply(apply(apply(w,apply(b,w)),X),apply(Y,Y))
% Current number of equations to process: 4629
% Current number of ordered equations: 0
% Current number of rules: 276
% New rule produced :
% [325]
% apply(apply(apply(w,apply(b,b)),X),apply(Y,Y)) <->
% apply(apply(w,apply(b,apply(b,apply(X,X)))),Y)
% Current number of equations to process: 4902
% Current number of ordered equations: 1
% Current number of rules: 277
% New rule produced :
% [326]
% apply(apply(w,apply(b,apply(b,apply(X,X)))),Y) <->
% apply(apply(apply(w,apply(b,b)),X),apply(Y,Y))
% Current number of equations to process: 4902
% Current number of ordered equations: 0
% Current number of rules: 278
% New rule produced :
% [327]
% apply(apply(apply(apply(apply(X,Y),Y),Y),Y),Y) <->
% apply(apply(w,apply(w,apply(w,apply(w,X)))),Y)
% Current number of equations to process: 1406
% Current number of ordered equations: 1
% Current number of rules: 279
% New rule produced :
% [328]
% apply(apply(w,apply(w,apply(w,apply(w,X)))),Y) <->
% apply(apply(apply(apply(apply(X,Y),Y),Y),Y),Y)
% Current number of equations to process: 1406
% Current number of ordered equations: 0
% Current number of rules: 280
% New rule produced :
% [329]
% apply(apply(apply(apply(apply(X,X),X),X),X),X) <->
% apply(apply(w,apply(w,apply(w,apply(w,w)))),X)
% Current number of equations to process: 1405
% Current number of ordered equations: 1
% Current number of rules: 281
% New rule produced :
% [330]
% apply(apply(w,apply(w,apply(w,apply(w,w)))),X) <->
% apply(apply(apply(apply(apply(X,X),X),X),X),X)
% Current number of equations to process: 1405
% Current number of ordered equations: 0
% Current number of rules: 282
% New rule produced :
% [331]
% apply(apply(w,apply(w,apply(w,apply(apply(w,w),b)))),X) <->
% apply(X,apply(apply(X,X),X))
% Current number of equations to process: 1564
% Current number of ordered equations: 1
% Current number of rules: 283
% New rule produced :
% [332]
% apply(X,apply(apply(X,X),X)) <->
% apply(apply(w,apply(w,apply(w,apply(apply(w,w),b)))),X)
% Current number of equations to process: 1564
% Current number of ordered equations: 0
% Current number of rules: 284
% New rule produced :
% [333]
% apply(apply(w,apply(w,apply(apply(X,X),X))),X) <->
% apply(apply(w,apply(w,apply(w,apply(w,w)))),X)
% Current number of equations to process: 1560
% Current number of ordered equations: 1
% Current number of rules: 285
% New rule produced :
% [334]
% apply(apply(w,apply(w,apply(w,apply(w,w)))),X) <->
% apply(apply(w,apply(w,apply(apply(X,X),X))),X)
% Current number of equations to process: 1560
% Current number of ordered equations: 0
% Current number of rules: 286
% New rule produced :
% [335]
% apply(X,apply(X,apply(apply(w,w),Y))) <->
% apply(apply(apply(w,b),X),apply(apply(Y,Y),Y))
% Current number of equations to process: 1956
% Current number of ordered equations: 1
% Current number of rules: 287
% New rule produced :
% [336]
% apply(apply(apply(w,b),X),apply(apply(Y,Y),Y)) <->
% apply(X,apply(X,apply(apply(w,w),Y)))
% Current number of equations to process: 1956
% Current number of ordered equations: 0
% Current number of rules: 288
% New rule produced :
% [337]
% apply(apply(w,apply(w,apply(w,apply(w,X)))),X) <->
% apply(apply(w,apply(w,apply(w,apply(X,X)))),X)
% Current number of equations to process: 1955
% Current number of ordered equations: 1
% Current number of rules: 289
% New rule produced :
% [338]
% apply(apply(w,apply(w,apply(w,apply(X,X)))),X) <->
% apply(apply(w,apply(w,apply(w,apply(w,X)))),X)
% Current number of equations to process: 1955
% Current number of ordered equations: 0
% Current number of rules: 290
% New rule produced :
% [339]
% apply(X,apply(X,apply(apply(b,X),apply(b,X)))) <->
% apply(apply(w,apply(w,apply(w,b))),apply(b,X))
% Current number of equations to process: 1954
% Current number of ordered equations: 1
% Current number of rules: 291
% New rule produced :
% [340]
% apply(apply(w,apply(w,apply(w,b))),apply(b,X)) <->
% apply(X,apply(X,apply(apply(b,X),apply(b,X))))
% Current number of equations to process: 1954
% Current number of ordered equations: 0
% Current number of rules: 292
% New rule produced :
% [341]
% apply(X,apply(X,apply(apply(Y,Y),Y))) <->
% apply(apply(apply(w,b),X),apply(apply(w,w),Y))
% Current number of equations to process: 2402
% Current number of ordered equations: 1
% Current number of rules: 293
% New rule produced :
% [342]
% apply(apply(apply(w,b),X),apply(apply(w,w),Y)) <->
% apply(X,apply(X,apply(apply(Y,Y),Y)))
% Current number of equations to process: 2402
% Current number of ordered equations: 0
% Current number of rules: 294
% New rule produced :
% [343]
% apply(apply(apply(X,X),X),apply(Y,Y)) <->
% apply(apply(w,apply(b,apply(apply(w,w),X))),Y)
% Current number of equations to process: 2896
% Current number of ordered equations: 1
% Current number of rules: 295
% New rule produced :
% [344]
% apply(apply(w,apply(b,apply(apply(w,w),X))),Y) <->
% apply(apply(apply(X,X),X),apply(Y,Y))
% Current number of equations to process: 2896
% Current number of ordered equations: 0
% Current number of rules: 296
% New rule produced :
% [345]
% apply(apply(apply(w,w),X),apply(Y,Y)) <->
% apply(apply(w,apply(b,apply(apply(w,X),X))),Y)
% Current number of equations to process: 3056
% Current number of ordered equations: 1
% Current number of rules: 297
% New rule produced :
% [346]
% apply(apply(w,apply(b,apply(apply(w,X),X))),Y) <->
% apply(apply(apply(w,w),X),apply(Y,Y))
% Current number of equations to process: 3056
% Current number of ordered equations: 0
% Current number of rules: 298
% New rule produced :
% [347]
% apply(apply(apply(w,X),X),apply(Y,Y)) <->
% apply(apply(w,apply(b,apply(apply(X,X),X))),Y)
% Current number of equations to process: 3290
% Current number of ordered equations: 1
% Current number of rules: 299
% New rule produced :
% [348]
% apply(apply(w,apply(b,apply(apply(X,X),X))),Y) <->
% apply(apply(apply(w,X),X),apply(Y,Y))
% Current number of equations to process: 3290
% Current number of ordered equations: 0
% Current number of rules: 300
% New rule produced :
% [349]
% apply(apply(w,apply(w,apply(w,apply(w,w)))),X) <->
% apply(apply(w,apply(w,apply(w,apply(X,X)))),X)
% Current number of equations to process: 4192
% Current number of ordered equations: 1
% Current number of rules: 301
% New rule produced :
% [350]
% apply(apply(w,apply(w,apply(w,apply(X,X)))),X) <->
% apply(apply(w,apply(w,apply(w,apply(w,w)))),X)
% Current number of equations to process: 4192
% Current number of ordered equations: 0
% Current number of rules: 302
% New rule produced :
% [351]
% apply(apply(w,apply(b,apply(apply(w,apply(b,X)),Y))),Y) ->
% apply(apply(w,X),apply(Y,Y))
% Current number of equations to process: 4639
% Current number of ordered equations: 0
% Current number of rules: 303
% New rule produced :
% [352]
% apply(apply(w,apply(apply(w,apply(b,b)),apply(X,X))),X) ->
% apply(apply(w,w),apply(X,X))
% Current number of equations to process: 4636
% Current number of ordered equations: 0
% Current number of rules: 304
% New rule produced :
% [353]
% apply(apply(w,X),apply(X,X)) <->
% apply(apply(w,apply(b,apply(apply(w,apply(w,b)),X))),X)
% Current number of equations to process: 4635
% Current number of ordered equations: 1
% Current number of rules: 305
% New rule produced :
% [354]
% apply(apply(w,apply(b,apply(apply(w,apply(w,b)),X))),X) <->
% apply(apply(w,X),apply(X,X))
% Current number of equations to process: 4635
% Current number of ordered equations: 0
% Current number of rules: 306
% New rule produced :
% [355]
% apply(apply(apply(apply(w,apply(b,b)),apply(X,Y)),X),Y) ->
% apply(apply(w,w),apply(X,Y))
% Current number of equations to process: 4633
% Current number of ordered equations: 0
% Current number of rules: 307
% New rule produced :
% [356]
% apply(apply(w,apply(apply(w,w),X)),Y) <->
% apply(apply(apply(apply(w,X),X),Y),Y)
% Current number of equations to process: 1068
% Current number of ordered equations: 1
% Current number of rules: 308
% New rule produced :
% [357]
% apply(apply(apply(apply(w,X),X),Y),Y) <->
% apply(apply(w,apply(apply(w,w),X)),Y)
% Current number of equations to process: 1068
% Current number of ordered equations: 0
% Current number of rules: 309
% New rule produced :
% [358] apply(X,apply(strong_fixed_point,X)) -> apply(strong_fixed_point,X)
% The conjecture has been reduced. 
% Conjecture is now:
% Trivial
% 
% Current number of equations to process: 1429
% Current number of ordered equations: 0
% Current number of rules: 310
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% 
% The following 14 rules have been used:
% [1] 
% apply(apply(X,Y),Y) <-> apply(apply(w,X),Y); trace = in the starting set
% [2] apply(apply(w,X),Y) <-> apply(apply(X,Y),Y); trace = in the starting set
% [3] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z)); trace = in the starting set
% [6] apply(apply(X,X),X) <-> apply(apply(w,w),X); trace = Cp of 2 and 1
% [7] apply(X,apply(X,Y)) <-> apply(apply(apply(w,b),X),Y); trace = Cp of 3 and 1
% [10] apply(apply(w,apply(b,X)),Y) <-> apply(X,apply(Y,Y)); trace = Cp of 3 and 1
% [14] apply(apply(X,apply(Y,Z)),Z) <-> apply(apply(w,apply(apply(b,X),Y)),Z); trace = Cp of 3 and 1
% [20] apply(apply(w,apply(X,Y)),Y) <-> apply(apply(w,apply(w,X)),Y); trace = Cp of 7 and 2
% [31] apply(apply(X,apply(Y,Y)),Y) <-> apply(apply(w,apply(w,apply(b,X))),Y); trace = Cp of 10 and 1
% [86] apply(apply(w,apply(apply(b,w),X)),Y) -> apply(apply(w,apply(w,X)),Y); trace = Cp of 20 and 14
% [112] apply(X,apply(apply(Y,Y),Y)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y); trace = Cp of 31 and 3
% [228] apply(apply(w,apply(w,X)),apply(apply(b,w),X)) ->
% apply(apply(w,w),apply(apply(b,w),X)); trace = Cp of 86 and 1
% [239] apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) ->
% apply(X,apply(apply(w,w),Y)); trace = Cp of 112 and 6
% [358] apply(X,apply(strong_fixed_point,X)) -> apply(strong_fixed_point,X); trace = Cp of 239 and 228
% % SZS output end Refutation
% All conjectures have been proven
% 
% Execution time: 76.150000 sec
% res : bool = true
% time is now off
% 
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
% 
% EOF
%------------------------------------------------------------------------------