CiME---2.01.UNS-Ref.s

%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : COL075-2 : TPTP v6.0.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n151.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 00:20:04 EDT 2014

% Result   : Unsatisfiable 8.74s
% Output   : Refutation 8.74s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : COL075-2 : TPTP v6.0.0. Released v1.2.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n151.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 : Fri Jun  6 01:22:53 CDT 2014
% % CPUTime  : 8.74 
% Processing problem /tmp/CiME_8954_n151.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " abstraction,k : constant;  c : 1;  b : 1;  apply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% apply(apply(k,X),Y) = X;
% apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z));
% ";
% 
% let s1 = status F "
% c lr_lex;
% b lr_lex;
% abstraction lr_lex;
% apply lr_lex;
% k lr_lex;
% ";
% 
% let p1 = precedence F "
% apply > b > c > k > abstraction";
% 
% let s2 = status F "
% c mul;
% b mul;
% abstraction mul;
% apply mul;
% k mul;
% ";
% 
% let p2 = precedence F "
% apply > b > c > k = abstraction";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " apply(apply(Y,b(Y)),c(Y)) = apply(b(Y),b(Y));"
% ;
% (*
% 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(k,X),Y) = X,
% apply(apply(apply(abstraction,X),Y),Z) =
% apply(apply(X,apply(k,Z)),apply(Y,Z)) }
% (2 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% 
% [abstraction] = 1;
% [k] = 2;
% [c](x1) = 3 + x1;
% [b](x1) = 4 + x1;
% [apply](x1,x2) = 1 + x1 + x2;
% Chosen ordering : RPO
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { apply(apply(Y,b(Y)),c(Y)) =
% apply(b(Y),b(Y)) } (1 equation(s))
% time is now on
% 
% Initializing completion ...
% New rule produced : [1] (eq)(X,X) -> (true)
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 1
% New rule produced :
% [2] (eq)(apply(apply(Y,b(Y)),c(Y)),apply(b(Y),b(Y))) -> (false)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 2
% New rule produced : [3] apply(apply(k,X),Y) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 3
% New rule produced :
% [4]
% apply(apply(X,apply(k,Z)),apply(Y,Z)) <->
% apply(apply(apply(abstraction,X),Y),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 4
% New rule produced :
% [5]
% apply(apply(apply(abstraction,X),Y),Z) <->
% apply(apply(X,apply(k,Z)),apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 5
% New rule produced : [6] (eq)(b(k),apply(b(k),b(k))) -> (false)
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 6
% New rule produced :
% [7]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(k,X)))) -> (false)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [8] apply(apply(apply(abstraction,k),Y),X) -> apply(k,X)
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9] apply(X,apply(Y,Z)) <-> apply(apply(apply(abstraction,apply(k,X)),Y),Z)
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced :
% [10] apply(apply(apply(abstraction,apply(k,X)),Y),Z) <-> apply(X,apply(Y,Z))
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11] (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12]
% (eq)(apply(k,c(apply(abstraction,k))),apply(b(apply(abstraction,k)),b(
% apply(abstraction,k))))
% -> (false)
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13]
% (eq)(b(apply(apply(abstraction,k),X)),apply(b(apply(apply(abstraction,k),X)),
% b(apply(apply(abstraction,k),X)))) ->
% (false)
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14]
% (eq)(apply(k,c(apply(k,apply(apply(abstraction,k),X)))),apply(b(apply(k,
% apply(
% apply(abstraction,k),X))),
% b(apply(k,apply(
% apply(abstraction,k),X)))))
% -> (false)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15]
% apply(k,apply(X,Y)) <->
% apply(apply(apply(abstraction,apply(abstraction,k)),X),Y)
% Rule
% [14]
% (eq)(apply(k,c(apply(k,apply(apply(abstraction,k),X)))),apply(b(apply(k,
% apply(
% apply(abstraction,k),X))),
% b(apply(k,apply(
% apply(abstraction,k),X)))))
% -> (false) collapsed.
% Current number of equations to process: 17
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [16]
% apply(apply(apply(abstraction,apply(abstraction,k)),X),Y) <->
% apply(k,apply(X,Y))
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [17] apply(apply(apply(abstraction,apply(k,apply(k,X))),Y),Z) -> X
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [18]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,apply(X,Y))))) -> (false)
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [19]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),apply(b(apply(apply(apply(abstraction,
% apply(k,k)),X),Y)),
% b(apply(k,apply(X,Y))))) ->
% (false)
% Current number of equations to process: 28
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced :
% [20]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),apply(b(apply(k,apply(X,Y))),
% b(apply(apply(apply(abstraction,
% apply(k,k)),X),Y))))
% -> (false)
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [21]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),b(apply(k,
% apply(k,X)))))
% -> (false)
% Current number of equations to process: 39
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [22]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,apply(k,k)),k),X))))
% -> (false)
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [23]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,apply(X,Y))))) -> (false)
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [24]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),X),Y)),
% b(apply(k,apply(X,Y))))) ->
% (false)
% Current number of equations to process: 51
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [25]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),apply(b(apply(k,apply(X,Y))),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),X),Y))))
% -> (false)
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [26]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 58
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [27]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X))))
% -> (false)
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [28]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(abstraction,
% apply(k,apply(k,X))))))
% -> (false)
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [29] apply(apply(apply(apply(abstraction,abstraction),X),apply(k,Y)),Z) -> Y
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [30]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false)
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [31]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(abstraction,apply(k,k)),
% apply(k,X)),Y)),b(apply(k,X)))) ->
% (false)
% Current number of equations to process: 99
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [32]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(abstraction,k),Y)),X)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 107
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [33]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y)))) ->
% (false)
% Current number of equations to process: 117
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [34]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,apply(k,k)),
% apply(apply(abstraction,k),Y)),X))))
% -> (false)
% Current number of equations to process: 125
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [35]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),k),X)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 139
% Current number of ordered equations: 1
% Current number of rules: 34
% New rule produced :
% [36]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X))))
% -> (false)
% Current number of equations to process: 139
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [37]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (false)
% Current number of equations to process: 138
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [38]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false)
% Current number of equations to process: 143
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [39]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),k),X))))
% -> (false)
% Current number of equations to process: 142
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [40]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false)
% Current number of equations to process: 141
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [41]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y)),b(apply(k,X)))) ->
% (false)
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [42]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(
% apply(abstraction,k),Y)),X)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 164
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [43]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y)))) ->
% (false)
% Current number of equations to process: 173
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [44]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(apply(abstraction,k),Y)),X))))
% -> (false)
% Current number of equations to process: 180
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [45]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),k),X)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 194
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [46]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false)
% Current number of equations to process: 193
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [47]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),k),X))))
% -> (false)
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [48]
% (eq)(X,apply(b(apply(abstraction,apply(apply(apply(abstraction,apply(k,k)),k),X))),
% b(apply(abstraction,apply(k,apply(k,X)))))) -> (false)
% Current number of equations to process: 202
% Current number of ordered equations: 3
% Current number of rules: 47
% New rule produced :
% [49]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(k,X))),b(apply(abstraction,apply(k,apply(k,X)))))) ->
% (false)
% Current number of equations to process: 202
% Current number of ordered equations: 2
% Current number of rules: 48
% New rule produced :
% [50]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(abstraction,
% apply(apply(
% apply(abstraction,
% apply(k,k)),k),X)))))
% -> (false)
% Current number of equations to process: 202
% Current number of ordered equations: 1
% Current number of rules: 49
% New rule produced :
% [51]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),k),
% apply(k,X))))) ->
% (false)
% Current number of equations to process: 202
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [52]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(b(apply(apply(apply(abstraction,apply(k,k)),X),Y)),b(apply(k,apply(X,Y)))))
% -> (false)
% Current number of equations to process: 201
% Current number of ordered equations: 1
% Current number of rules: 51
% New rule produced :
% [53]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(apply(apply(abstraction,apply(k,k)),X),Y))))
% -> (false)
% Current number of equations to process: 201
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [54]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y)),b(
% apply(k,
% apply(X,Y)))))
% -> (false)
% Current number of equations to process: 199
% Current number of ordered equations: 1
% Current number of rules: 53
% New rule produced :
% [55]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))))
% -> (false)
% Current number of equations to process: 199
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [56]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(b(apply(apply(apply(abstraction,apply(k,k)),X),Y)),b(apply(k,apply(X,Y)))))
% -> (false)
% Current number of equations to process: 195
% Current number of ordered equations: 1
% Current number of rules: 55
% New rule produced :
% [57]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(apply(apply(abstraction,apply(k,k)),X),Y))))
% -> (false)
% Current number of equations to process: 195
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [58]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y)),b(
% apply(k,
% apply(X,Y)))))
% -> (false)
% Current number of equations to process: 193
% Current number of ordered equations: 1
% Current number of rules: 57
% New rule produced :
% [59]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))))
% -> (false)
% Current number of equations to process: 193
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [60]
% apply(apply(apply(apply(abstraction,apply(abstraction,abstraction)),k),X),Y)
% -> X
% Current number of equations to process: 191
% Current number of ordered equations: 1
% Current number of rules: 59
% New rule produced :
% [61]
% apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X)),Y),Z)
% -> Z
% Current number of equations to process: 191
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [62]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(k,k)),b(apply(k,k)))) -> (false)
% Current number of equations to process: 199
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [63]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),X))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false)
% Current number of equations to process: 198
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [64]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,apply(k,X))),Y)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 208
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [65]
% (eq)(apply(k,c(apply(k,k))),apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),X)),
% b(apply(k,k)))) -> (false)
% Current number of equations to process: 209
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [66]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),Y),X)),
% b(apply(k,X)))) -> (false)
% Current number of equations to process: 208
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [67]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),
% apply(k,X)),Y))),apply(b(apply(k,X)),b(apply(k,X)))) ->
% (false)
% Current number of equations to process: 217
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [68]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,abstraction),apply(abstraction,k)),k),X)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 217
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [69]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,apply(k,k)),
% apply(k,apply(k,X))),Y)))) ->
% (false)
% Current number of equations to process: 225
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [70]
% (eq)(apply(k,c(apply(k,k))),apply(b(apply(k,k)),b(apply(apply(apply(apply(abstraction,abstraction),k),k),X))))
% -> (false)
% Current number of equations to process: 226
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [71]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))))
% -> (false)
% Current number of equations to process: 225
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [72]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,k)),k),X))))
% -> (false)
% Current number of equations to process: 235
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [73]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),X))),apply(b(apply(k,X)),
% b(apply(k,X)))) ->
% (false)
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [74]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),
% apply(k,X)),Y))),apply(b(apply(k,X)),b(apply(k,X)))) ->
% (false)
% Current number of equations to process: 265
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [75]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,
% apply(k,X))),Y)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 273
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [76]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,apply(k,X))),Y)))) ->
% (false)
% Current number of equations to process: 292
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [77]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(k,X)),Y)),b(apply(k,X)))) ->
% (false)
% Current number of equations to process: 354
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [78]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(k,X)),Y)))) ->
% (false)
% Current number of equations to process: 353
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [79]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),X)),
% b(apply(k,X)))) -> (false)
% Current number of equations to process: 352
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [80]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(k,X)),Y)),b(apply(k,X)))) ->
% (false)
% Current number of equations to process: 351
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [81]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),X))))
% -> (false)
% Current number of equations to process: 350
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [82]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(k,X)),Y)))) ->
% (false)
% Current number of equations to process: 349
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [83]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y)),b(apply(k,X))))
% -> (false)
% Current number of equations to process: 348
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [84]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))))
% -> (false)
% Current number of equations to process: 365
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [85]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y)),
% b(apply(k,X)))) -> (false)
% Current number of equations to process: 382
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [86]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y)))) -> (false)
% Current number of equations to process: 397
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [87]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y))),
% apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y)),b(apply(k,X))))
% -> (false)
% Current number of equations to process: 413
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [88]
% (eq)(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(abstraction,k)),X),Y)),apply(b(apply(apply(abstraction,k),
% apply(X,Y))),
% b(apply(apply(abstraction,k),
% apply(X,Y))))) -> (false)
% Current number of equations to process: 412
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [89]
% (eq)(apply(apply(apply(abstraction,apply(k,k)),b(apply(abstraction,apply(abstraction,k)))),
% c(apply(abstraction,apply(abstraction,k)))),apply(b(apply(abstraction,
% apply(abstraction,k))),
% b(apply(abstraction,
% apply(abstraction,k)))))
% -> (false)
% Current number of equations to process: 411
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [90]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))))
% -> (false)
% Current number of equations to process: 427
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [91]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y)),
% b(apply(k,X)))) -> (false)
% Current number of equations to process: 443
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [92]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y)))) -> (false)
% Current number of equations to process: 457
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [93]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),apply(
% b(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),k)),
% b(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),k))))
% -> (false)
% Current number of equations to process: 473
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [94]
% (eq)(apply(apply(apply(X,k),Y),c(apply(apply(apply(apply(abstraction,abstraction),X),k),Y))),
% apply(b(apply(k,apply(apply(X,k),Y))),b(apply(k,apply(apply(X,k),Y))))) ->
% (false)
% Current number of equations to process: 472
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [95]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,apply(X,Y))))) -> (false)
% Current number of equations to process: 471
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [96]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),apply(
% b(
% apply(abstraction,
% apply(
% apply(abstraction,abstraction),X))),
% b(
% apply(abstraction,
% apply(
% apply(abstraction,abstraction),X)))))
% -> (false)
% Current number of equations to process: 480
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [97]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(k,k)),Y),X))),apply(b(apply(k,X)),b(
% apply(k,X))))
% -> (false)
% Current number of equations to process: 500
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [98]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),
% apply(k,X))),b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 500
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [99]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(k,k)),Y),X)),b(
% apply(k,X))))
% -> (false)
% Current number of equations to process: 521
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [100]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,abstraction),apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false)
% Current number of equations to process: 536
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [101]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,abstraction),apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false)
% Current number of equations to process: 535
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [102]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),Y),
% apply(k,X))))) -> (false)
% Current number of equations to process: 535
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [103]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),b(apply(
% apply(
% apply(
% apply(abstraction,abstraction),
% apply(abstraction,k)),k),X))))
% -> (false)
% Current number of equations to process: 562
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [104]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(apply(abstraction,abstraction),apply(abstraction,k)),k),X))))
% -> (false)
% Current number of equations to process: 561
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [105]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(k,k)),Y),X))))
% -> (false)
% Current number of equations to process: 560
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [106]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,apply(X,Y))))) -> (false)
% Current number of equations to process: 615
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [107]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,abstraction)),apply(
% apply(abstraction,
% apply(abstraction,k)),k)),X)),
% b(apply(abstraction,apply(k,apply(k,X)))))) -> (false)
% Current number of equations to process: 624
% Current number of ordered equations: 1
% Current number of rules: 106
% New rule produced :
% [108]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),
% apply(
% apply(abstraction,
% apply(abstraction,k)),k)),X))))
% -> (false)
% Current number of equations to process: 624
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [109]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),
% apply(apply(abstraction,k),Y)),X)),b(apply(k,apply(k,X)))))
% -> (false)
% Current number of equations to process: 663
% Current number of ordered equations: 1
% Current number of rules: 108
% New rule produced :
% [110]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(abstraction,k),Y)),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false)
% Current number of equations to process: 663
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [111]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(abstraction,k),Y)),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false)
% Current number of equations to process: 662
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [112]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),
% apply(
% apply(abstraction,k),Y)),X))))
% -> (false)
% Current number of equations to process: 660
% Current number of ordered equations: 1
% Current number of rules: 111
% New rule produced :
% [113]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(apply(abstraction,k),Y)),X))))
% -> (false)
% Current number of equations to process: 660
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [114]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(abstraction,k),Y)),X))))
% -> (false)
% Current number of equations to process: 659
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [115]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,k)),X))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),X)),b(
% apply(k,k))))
% -> (false)
% Current number of equations to process: 662
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [116]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,k)),X)),b(apply(k,k))))
% -> (false)
% Current number of equations to process: 661
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [117]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false)
% Current number of equations to process: 673
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [118]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false)
% Current number of equations to process: 672
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [119]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,k)),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(apply(abstraction,abstraction),k),k),X))))
% -> (false)
% Current number of equations to process: 675
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [120]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(abstraction,apply(k,k)),apply(k,k)),X))))
% -> (false)
% Current number of equations to process: 674
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [121]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),b(apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),k),k),k),X))))
% -> (false)
% Current number of equations to process: 685
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [122]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,k)),X)),
% b(apply(k,k)))) -> (false)
% Current number of equations to process: 687
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [123]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),b(apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),k),X))))
% -> (false)
% Current number of equations to process: 698
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [124]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,k)),X)))) -> (false)
% Current number of equations to process: 700
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [125]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,k)),X))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),X)),b(
% apply(k,k))))
% -> (false)
% Current number of equations to process: 715
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [126]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),k),X))))
% -> (false)
% Current number of equations to process: 726
% Current number of ordered equations: 1
% Current number of rules: 125
% New rule produced :
% [127]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false)
% Current number of equations to process: 726
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [128]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),
% apply(apply(abstraction,k),Y)),X)),b(apply(k,apply(k,X)))))
% -> (false)
% Current number of equations to process: 724
% Current number of ordered equations: 1
% Current number of rules: 127
% New rule produced :
% [129]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(
% apply(abstraction,k),Y)),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false)
% Current number of equations to process: 724
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [130]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(
% apply(abstraction,k),Y)),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false)
% Current number of equations to process: 723
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [131]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),
% apply(
% apply(abstraction,k),Y)),X))))
% -> (false)
% Current number of equations to process: 721
% Current number of ordered equations: 1
% Current number of rules: 130
% New rule produced :
% [132]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(apply(abstraction,k),Y)),X))))
% -> (false)
% Current number of equations to process: 721
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [133]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(apply(abstraction,k),Y)),X))))
% -> (false)
% Current number of equations to process: 720
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [134]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false)
% Current number of equations to process: 717
% Current number of ordered equations: 1
% Current number of rules: 133
% New rule produced :
% [135]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),k),X))))
% -> (false)
% Current number of equations to process: 717
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [136]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,abstraction)),apply(
% apply(abstraction,
% apply(k,k)),k)),X)),
% b(apply(abstraction,apply(k,apply(k,X)))))) -> (false)
% Current number of equations to process: 714
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [137]
% (eq)(X,apply(b(apply(abstraction,apply(apply(apply(abstraction,apply(k,k)),k),X))),
% b(apply(apply(apply(abstraction,apply(k,abstraction)),k),apply(k,X)))))
% -> (false)
% Current number of equations to process: 712
% Current number of ordered equations: 1
% Current number of rules: 136
% New rule produced :
% [138]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(k,X))),b(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(k,X))))) -> (false)
% Current number of equations to process: 710
% Current number of ordered equations: 2
% Current number of rules: 137
% New rule produced :
% [139]
% (eq)(X,apply(b(apply(abstraction,apply(apply(apply(abstraction,apply(k,k)),k),X))),
% b(apply(abstraction,apply(apply(apply(abstraction,apply(k,k)),k),X)))))
% -> (false)
% Current number of equations to process: 709
% Current number of ordered equations: 2
% Current number of rules: 138
% New rule produced :
% [140]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(k,X))),b(apply(abstraction,apply(apply(apply(abstraction,
% apply(k,k)),k),X)))))
% -> (false)
% Current number of equations to process: 709
% Current number of ordered equations: 1
% Current number of rules: 139
% New rule produced :
% [141]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),
% apply(
% apply(abstraction,
% apply(k,k)),k)),X))))
% -> (false)
% Current number of equations to process: 709
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [142]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),
% apply(k,apply(k,X))),Y)),b(apply(k,apply(k,X))))) ->
% (false)
% Current number of equations to process: 704
% Current number of ordered equations: 2
% Current number of rules: 141
% New rule produced :
% [143]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(
% apply(abstraction,
% apply(k,k)),k),X)),Y)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 704
% Current number of ordered equations: 1
% Current number of rules: 142
% New rule produced :
% [144]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,apply(k,X))),Y)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false)
% Current number of equations to process: 704
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [145]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(
% apply(abstraction,
% apply(abstraction,k)),k),X)),Y)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 702
% Current number of ordered equations: 1
% Current number of rules: 144
% New rule produced :
% [146]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,apply(k,X))),Y)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false)
% Current number of equations to process: 702
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [147]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,
% apply(k,X))),Y))))
% -> (false)
% Current number of equations to process: 699
% Current number of ordered equations: 2
% Current number of rules: 146
% New rule produced :
% [148]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(k,apply(k,X))),Y)))) ->
% (false)
% Current number of equations to process: 699
% Current number of ordered equations: 1
% Current number of rules: 147
% New rule produced :
% [149]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,apply(k,k)),
% apply(apply(apply(abstraction,
% apply(k,k)),k),X)),Y))))
% -> (false)
% Current number of equations to process: 699
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [150]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),apply(k,apply(k,X))),Y))))
% -> (false)
% Current number of equations to process: 697
% Current number of ordered equations: 1
% Current number of rules: 149
% New rule produced :
% [151]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,apply(k,k)),
% apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X)),Y))))
% -> (false)
% Current number of equations to process: 697
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [152]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,apply(k,abstraction))),abstraction),k),Y),X))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false)
% Current number of equations to process: 696
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [153]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),apply(k,X))),b(apply(k,
% apply(k,X)))))
% -> (false)
% Current number of equations to process: 695
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [154]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),
% apply(k,apply(k,X))),Y)),b(apply(k,apply(k,X))))) ->
% (false)
% Current number of equations to process: 692
% Current number of ordered equations: 2
% Current number of rules: 153
% New rule produced :
% [155]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X)),Y)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 692
% Current number of ordered equations: 1
% Current number of rules: 154
% New rule produced :
% [156]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,
% apply(k,X))),Y)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false)
% Current number of equations to process: 692
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [157]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X)),Y)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 690
% Current number of ordered equations: 1
% Current number of rules: 156
% New rule produced :
% [158]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,
% apply(k,X))),Y)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false)
% Current number of equations to process: 690
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [159]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),
% apply(k,X))))) -> (false)
% Current number of equations to process: 689
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [160]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),
% apply(k,
% apply(k,X))),Y))))
% -> (false)
% Current number of equations to process: 686
% Current number of ordered equations: 2
% Current number of rules: 159
% New rule produced :
% [161]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(k,apply(k,X))),Y)))) ->
% (false)
% Current number of equations to process: 686
% Current number of ordered equations: 1
% Current number of rules: 160
% New rule produced :
% [162]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(apply(apply(abstraction,
% apply(k,k)),k),X)),Y))))
% -> (false)
% Current number of equations to process: 686
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [163]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,
% apply(k,X))),Y))))
% -> (false)
% Current number of equations to process: 684
% Current number of ordered equations: 1
% Current number of rules: 162
% New rule produced :
% [164]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X)),Y))))
% -> (false)
% Current number of equations to process: 684
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [165]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),
% apply(Y,X)))),apply(b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),Y),X)),
% b(apply(k,X)))) -> (false)
% Current number of equations to process: 677
% Current number of ordered equations: 0
% Current number of rules: 164
% New rule produced :
% [166]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),
% apply(Y,X)))),apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))))
% -> (false)
% Current number of equations to process: 676
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [167]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),
% apply(Y,X)))),apply(b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),Y),X)),
% b(apply(k,X)))) -> (false)
% Current number of equations to process: 675
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced :
% [168]
% (eq)(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(abstraction,k)),apply(k,X)),Y)),apply(b(apply(
% apply(abstraction,k),X)),
% b(apply(apply(abstraction,k),X))))
% -> (false)
% Current number of equations to process: 674
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced :
% [169]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,k)),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(apply(abstraction,abstraction),k),k),X))))
% -> (false)
% Current number of equations to process: 703
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced :
% [170]
% (eq)(b(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),abstraction),k)),
% apply(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),b(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),k))))
% -> (false)
% Current number of equations to process: 748
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced :
% [171]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))),apply(b(apply(k,
% apply(X,Y))),
% b(apply(k,apply(X,Y)))))
% -> (false)
% Current number of equations to process: 748
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced :
% [172]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),
% apply(Y,X)))),apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))))
% -> (false)
% Current number of equations to process: 747
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [173]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),apply(
% b(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),abstraction),k)),
% b(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),k))))
% -> (false)
% Current number of equations to process: 745
% Current number of ordered equations: 1
% Current number of rules: 172
% New rule produced :
% [174]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),apply(
% b(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),k)),
% b(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),abstraction),k))))
% -> (false)
% Current number of equations to process: 745
% Current number of ordered equations: 0
% Current number of rules: 173
% New rule produced :
% [175]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),apply(
% apply(abstraction,k),X)),k),Y))),
% apply(b(apply(k,k)),b(apply(k,k)))) -> (false)
% Current number of equations to process: 753
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced :
% [176]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(b(apply(abstraction,apply(apply(abstraction,abstraction),X))),b(
% apply(abstraction,
% apply(
% apply(abstraction,abstraction),X)))))
% -> (false)
% Current number of equations to process: 784
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced :
% [177]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),apply(
% b(
% apply(
% apply(
% apply(
% apply(abstraction,abstraction),abstraction),abstraction),X)),
% b(
% apply(abstraction,
% apply(
% apply(abstraction,abstraction),X)))))
% -> (false)
% Current number of equations to process: 782
% Current number of ordered equations: 1
% Current number of rules: 176
% New rule produced :
% [178]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),apply(
% b(
% apply(abstraction,
% apply(
% apply(abstraction,abstraction),X))),
% b(
% apply(
% apply(
% apply(
% apply(abstraction,abstraction),abstraction),abstraction),X))))
% -> (false)
% Current number of equations to process: 782
% Current number of ordered equations: 0
% Current number of rules: 177
% New rule produced :
% [179]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(abstraction,apply(k,k))),k),X)),b(apply(k,
% apply(k,X)))))
% -> (false)
% Current number of equations to process: 852
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [180]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(k,k)),Y),apply(k,X))),b(apply(k,apply(k,X)))))
% -> (false)
% Current number of equations to process: 850
% Current number of ordered equations: 1
% Current number of rules: 179
% New rule produced :
% [181]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),
% apply(k,X))),b(apply(apply(apply(abstraction,apply(k,k)),k),X))))
% -> (false)
% Current number of equations to process: 850
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [182]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),
% apply(k,X))),b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X))))
% -> (false)
% Current number of equations to process: 849
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [183]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,apply(k,k))),k),X))))
% -> (false)
% Current number of equations to process: 847
% Current number of ordered equations: 0
% Current number of rules: 182
% New rule produced :
% [184]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),
% apply(k,X)))))
% -> (false)
% Current number of equations to process: 845
% Current number of ordered equations: 1
% Current number of rules: 183
% New rule produced :
% [185]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(k,k)),Y),apply(k,X)))))
% -> (false)
% Current number of equations to process: 845
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [186]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),
% apply(k,X))))) -> (false)
% Current number of equations to process: 844
% Current number of ordered equations: 0
% Current number of rules: 185
% New rule produced :
% [187]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),X)),b(
% apply(k,k))))
% -> (false)
% Current number of equations to process: 912
% Current number of ordered equations: 0
% Current number of rules: 186
% New rule produced :
% [188]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),X),k))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),apply(X,k))),
% b(apply(k,k)))) -> (false)
% Current number of equations to process: 915
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [189]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),
% apply(X,k)))),apply(b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),X),k)),
% b(apply(k,k)))) -> (false)
% Current number of equations to process: 915
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [190]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(apply(abstraction,abstraction),k),k),X))))
% -> (false)
% Current number of equations to process: 926
% Current number of ordered equations: 0
% Current number of rules: 189
% New rule produced :
% [191]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),X),k))),
% apply(b(apply(k,k)),b(apply(apply(apply(apply(abstraction,abstraction),k),k),
% apply(X,k))))) -> (false)
% Current number of equations to process: 929
% Current number of ordered equations: 0
% Current number of rules: 190
% New rule produced :
% [192]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),
% apply(X,k)))),apply(b(apply(k,k)),b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),X),k))))
% -> (false)
% Current number of equations to process: 929
% Current number of ordered equations: 0
% Current number of rules: 191
% New rule produced :
% [193]
% (eq)(k,apply(b(apply(apply(apply(apply(abstraction,abstraction),apply(
% apply(abstraction,
% apply(k,k)),k)),k),X)),
% b(apply(k,apply(k,k))))) -> (false)
% Current number of equations to process: 1050
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced :
% [194]
% (eq)(k,apply(b(apply(apply(apply(apply(abstraction,abstraction),apply(
% apply(abstraction,
% apply(abstraction,k)),k)),k),X)),
% b(apply(k,apply(k,k))))) -> (false)
% Current number of equations to process: 1068
% Current number of ordered equations: 0
% Current number of rules: 193
% New rule produced :
% [195]
% (eq)(k,apply(b(apply(k,apply(k,k))),b(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(abstraction,
% apply(k,k)),k)),k),X))))
% -> (false)
% Current number of equations to process: 1105
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [196]
% (eq)(k,apply(b(apply(k,apply(k,k))),b(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(abstraction,
% apply(abstraction,k)),k)),k),X))))
% -> (false)
% Current number of equations to process: 1122
% Current number of ordered equations: 0
% Current number of rules: 195
% New rule produced :
% [197]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),X))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),X)),
% b(apply(k,X)))) -> (false)
% Current number of equations to process: 1260
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [198]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),X))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),Y),X)))) ->
% (false)
% Current number of equations to process: 1283
% Current number of ordered equations: 0
% Current number of rules: 197
% New rule produced :
% [199]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,X))),k),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false)
% Current number of equations to process: 1343
% Current number of ordered equations: 0
% Current number of rules: 198
% New rule produced :
% [200]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))),apply(b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),X),Y)),
% b(apply(k,apply(X,Y)))))
% -> (false)
% Current number of equations to process: 1361
% Current number of ordered equations: 1
% Current number of rules: 199
% New rule produced :
% [201]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))),apply(b(apply(k,
% apply(X,Y))),
% b(apply(apply(
% apply(abstraction,
% apply(k,k)),X),Y))))
% -> (false)
% Current number of equations to process: 1361
% Current number of ordered equations: 0
% Current number of rules: 200
% New rule produced :
% [202]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))),apply(b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y)),
% b(apply(k,apply(X,Y)))))
% -> (false)
% Current number of equations to process: 1359
% Current number of ordered equations: 1
% Current number of rules: 201
% New rule produced :
% [203]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))),apply(b(apply(k,
% apply(X,Y))),
% b(apply(apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y))))
% -> (false)
% Current number of equations to process: 1359
% Current number of ordered equations: 0
% Current number of rules: 202
% New rule produced :
% [204]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% b(apply(abstraction,apply(apply(abstraction,abstraction),X))))) -> (false)
% Current number of equations to process: 1391
% Current number of ordered equations: 1
% Current number of rules: 203
% New rule produced :
% [205]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(b(apply(abstraction,apply(apply(abstraction,abstraction),X))),b(
% apply(
% apply(
% apply(
% apply(abstraction,abstraction),abstraction),abstraction),X))))
% -> (false)
% Current number of equations to process: 1391
% Current number of ordered equations: 0
% Current number of rules: 204
% New rule produced :
% [206]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),apply(
% b(
% apply(
% apply(
% apply(
% apply(abstraction,abstraction),abstraction),abstraction),X)),
% b(
% apply(
% apply(
% apply(
% apply(abstraction,abstraction),abstraction),abstraction),X))))
% -> (false)
% Current number of equations to process: 1397
% Current number of ordered equations: 0
% Current number of rules: 205
% New rule produced :
% [207]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,X)),k))),apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),X)),
% b(apply(k,k)))) -> (false)
% Current number of equations to process: 1470
% Current number of ordered equations: 0
% Current number of rules: 206
% New rule produced :
% [208]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,X)),k))),apply(b(apply(k,k)),b(apply(apply(
% apply(
% apply(abstraction,abstraction),k),k),X))))
% -> (false)
% Current number of equations to process: 1498
% Current number of ordered equations: 0
% Current number of rules: 207
% New rule produced :
% [209]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,X)),k)),b(apply(k,k)))) -> (false)
% Current number of equations to process: 1584
% Current number of ordered equations: 0
% Current number of rules: 208
% New rule produced :
% [210]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),apply(k,X)),k))))
% -> (false)
% Current number of equations to process: 1583
% Current number of ordered equations: 0
% Current number of rules: 209
% New rule produced :
% [211]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X)),k),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false)
% Current number of equations to process: 1582
% Current number of ordered equations: 0
% Current number of rules: 210
% New rule produced :
% [212]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X)),k),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false)
% Current number of equations to process: 1581
% Current number of ordered equations: 0
% Current number of rules: 211
% New rule produced :
% [213]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,X))),k),Y))),
% apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y)),b(apply(k,X))))
% -> (false)
% Current number of equations to process: 1580
% Current number of ordered equations: 0
% Current number of rules: 212
% New rule produced :
% [214]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,X))),k),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))))
% -> (false)
% Current number of equations to process: 1597
% Current number of ordered equations: 0
% Current number of rules: 213
% New rule produced :
% [215]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,X))),k),Y))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y)),
% b(apply(k,X)))) -> (false)
% Current number of equations to process: 1614
% Current number of ordered equations: 0
% Current number of rules: 214
% New rule produced :
% [216]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,X))),k),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y)))) -> (false)
% Current number of equations to process: 1630
% Current number of ordered equations: 0
% Current number of rules: 215
% New rule produced :
% [217]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,X)),k))),apply(b(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,k)),X)),b(
% apply(k,k))))
% -> (false)
% Current number of equations to process: 1670
% Current number of ordered equations: 0
% Current number of rules: 216
% New rule produced :
% [218]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,X)),k))),apply(b(apply(k,k)),b(apply(apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,k)),X))))
% -> (false)
% Current number of equations to process: 1669
% Current number of ordered equations: 0
% Current number of rules: 217
% New rule produced :
% [219]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,k))),k),X))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),X)),b(
% apply(k,k))))
% -> (false)
% Current number of equations to process: 1704
% Current number of ordered equations: 0
% Current number of rules: 218
% New rule produced :
% [220]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,k))),k),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(apply(abstraction,abstraction),k),k),X))))
% -> (false)
% Current number of equations to process: 1718
% Current number of ordered equations: 0
% Current number of rules: 219
% New rule produced :
% [221]
% apply(apply(X,apply(k,Y)),Z) <->
% apply(apply(apply(abstraction,X),apply(k,Z)),Y)
% Current number of equations to process: 1786
% Current number of ordered equations: 1
% Current number of rules: 220
% New rule produced :
% [222]
% apply(apply(apply(abstraction,X),apply(k,Z)),Y) <->
% apply(apply(X,apply(k,Y)),Z)
% Rule
% [199]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,X))),k),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false) collapsed.
% Rule
% [207]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,X)),k))),apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),X)),
% b(apply(k,k)))) -> (false) collapsed.
% Rule
% [208]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,X)),k))),apply(b(apply(k,k)),b(apply(apply(
% apply(
% apply(abstraction,abstraction),k),k),X))))
% -> (false) collapsed.
% Rule
% [209]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,X)),k)),b(apply(k,k)))) -> (false) collapsed.
% Rule
% [210]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),apply(k,X)),k))))
% -> (false) collapsed.
% Rule
% [213]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,X))),k),Y))),
% apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y)),b(apply(k,X))))
% -> (false) collapsed.
% Rule
% [214]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,X))),k),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))))
% -> (false) collapsed.
% Rule
% [215]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,X))),k),Y))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y)),
% b(apply(k,X)))) -> (false) collapsed.
% Rule
% [216]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,X))),k),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y)))) -> (false) collapsed.
% Rule
% [217]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,X)),k))),apply(b(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,k)),X)),b(
% apply(k,k))))
% -> (false) collapsed.
% Rule
% [218]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,X)),k))),apply(b(apply(k,k)),b(apply(apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,k)),X))))
% -> (false) collapsed.
% Rule
% [219]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,k))),k),X))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),X)),b(
% apply(k,k))))
% -> (false) collapsed.
% Rule
% [220]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),apply(k,
% apply(k,k))),k),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(apply(abstraction,abstraction),k),k),X))))
% -> (false) collapsed.
% Current number of equations to process: 1786
% Current number of ordered equations: 0
% Current number of rules: 208
% New rule produced :
% [223]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),apply(b(apply(apply(apply(
% apply(abstraction,abstraction),
% apply(k,X)),k),Y)),
% b(apply(k,apply(X,Y))))) ->
% (false)
% Current number of equations to process: 1828
% Current number of ordered equations: 0
% Current number of rules: 209
% New rule produced :
% [224]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),apply(b(apply(k,apply(X,Y))),
% b(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))))
% -> (false)
% Current number of equations to process: 1827
% Current number of ordered equations: 0
% Current number of rules: 210
% New rule produced :
% [225]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,k)),abstraction),k),k),X)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 1832
% Current number of ordered equations: 0
% Current number of rules: 211
% New rule produced :
% [226]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,k)),abstraction),k),k),X))))
% -> (false)
% Current number of equations to process: 1833
% Current number of ordered equations: 0
% Current number of rules: 212
% New rule produced :
% [227]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,abstraction),apply(k,k)),abstraction),
% apply(k,X))),b(apply(abstraction,apply(k,apply(k,X)))))) ->
% (false)
% Current number of equations to process: 1833
% Current number of ordered equations: 0
% Current number of rules: 213
% New rule produced :
% [228]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,k)),abstraction),
% apply(k,X))))) ->
% (false)
% Current number of equations to process: 1833
% Current number of ordered equations: 0
% Current number of rules: 214
% New rule produced :
% [229]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,k)),abstraction),k),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false)
% Current number of equations to process: 1897
% Current number of ordered equations: 0
% Current number of rules: 215
% New rule produced :
% [230]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,Y)),X))),apply(b(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y)),b(
% apply(k,X))))
% -> (false)
% Current number of equations to process: 1896
% Current number of ordered equations: 0
% Current number of rules: 216
% New rule produced :
% [231]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,Y)),X))),apply(b(apply(k,X)),b(apply(apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y))))
% -> (false)
% Current number of equations to process: 1895
% Current number of ordered equations: 0
% Current number of rules: 217
% New rule produced :
% [232]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,Y)),X))),apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y)),b(
% apply(k,X))))
% -> (false)
% Current number of equations to process: 1894
% Current number of ordered equations: 0
% Current number of rules: 218
% New rule produced :
% [233]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,Y)),X))),apply(b(apply(k,X)),b(apply(apply(
% apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y))))
% -> (false)
% Current number of equations to process: 1893
% Current number of ordered equations: 0
% Current number of rules: 219
% New rule produced :
% [234]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,apply(abstraction,abstraction)),
% apply(k,k)),X),Y))),apply(b(apply(k,
% apply(X,Y))),
% b(apply(k,apply(X,Y)))))
% -> (false)
% Current number of equations to process: 1980
% Current number of ordered equations: 0
% Current number of rules: 220
% New rule produced :
% [235]
% apply(X,X) <-> apply(apply(apply(apply(abstraction,abstraction),k),X),Y)
% Rule
% [46]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false) collapsed.
% Rule
% [89]
% (eq)(apply(apply(apply(abstraction,apply(k,k)),b(apply(abstraction,apply(abstraction,k)))),
% c(apply(abstraction,apply(abstraction,k)))),apply(b(apply(abstraction,
% apply(abstraction,k))),
% b(apply(abstraction,
% apply(abstraction,k)))))
% -> (false) collapsed.
% Rule
% [93]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),apply(
% b(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),k)),
% b(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),k))))
% -> (false) collapsed.
% Rule
% [96]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),apply(
% b(
% apply(abstraction,
% apply(
% apply(abstraction,abstraction),X))),
% b(
% apply(abstraction,
% apply(
% apply(abstraction,abstraction),X)))))
% -> (false) collapsed.
% Rule
% [138]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(k,X))),b(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(k,X))))) -> (false) collapsed.
% Rule
% [139]
% (eq)(X,apply(b(apply(abstraction,apply(apply(apply(abstraction,apply(k,k)),k),X))),
% b(apply(abstraction,apply(apply(apply(abstraction,apply(k,k)),k),X)))))
% -> (false) collapsed.
% Rule
% [170]
% (eq)(b(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),abstraction),k)),
% apply(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),b(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),k))))
% -> (false) collapsed.
% Rule
% [176]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(b(apply(abstraction,apply(apply(abstraction,abstraction),X))),b(
% apply(abstraction,
% apply(
% apply(abstraction,abstraction),X)))))
% -> (false) collapsed.
% Current number of equations to process: 2035
% Current number of ordered equations: 1
% Current number of rules: 213
% New rule produced :
% [236]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(
% apply(abstraction,
% apply(abstraction,k)),k),X))),abstraction))
% -> (false)
% Current number of equations to process: 2034
% Current number of ordered equations: 1
% Current number of rules: 214
% New rule produced :
% [237]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),k),
% apply(k,X)))),abstraction))
% -> (false)
% Current number of equations to process: 2033
% Current number of ordered equations: 1
% Current number of rules: 215
% New rule produced :
% [238]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(abstraction,
% apply(apply(
% apply(abstraction,
% apply(k,k)),k),X)))),abstraction))
% -> (false)
% Current number of equations to process: 2032
% Current number of ordered equations: 1
% Current number of rules: 216
% New rule produced :
% [239]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),apply(
% apply(
% apply(
% apply(abstraction,abstraction),k),
% b(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),k))),abstraction))
% -> (false)
% Current number of equations to process: 2031
% Current number of ordered equations: 1
% Current number of rules: 217
% New rule produced :
% [240]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),apply(
% apply(
% apply(
% apply(abstraction,abstraction),k),
% b(
% apply(abstraction,
% apply(
% apply(abstraction,abstraction),X)))),abstraction))
% -> (false)
% Current number of equations to process: 2030
% Current number of ordered equations: 1
% Current number of rules: 218
% New rule produced :
% [241]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(abstraction,
% apply(apply(abstraction,abstraction),X)))),abstraction))
% -> (false)
% Current number of equations to process: 2029
% Current number of ordered equations: 1
% Current number of rules: 219
% New rule produced :
% [242]
% apply(apply(apply(apply(abstraction,abstraction),k),X),Y) <-> apply(X,X)
% Rule
% [62]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(k,k)),b(apply(k,k)))) -> (false) collapsed.
% Rule
% [65]
% (eq)(apply(k,c(apply(k,k))),apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),X)),
% b(apply(k,k)))) -> (false) collapsed.
% Rule
% [70]
% (eq)(apply(k,c(apply(k,k))),apply(b(apply(k,k)),b(apply(apply(apply(apply(abstraction,abstraction),k),k),X))))
% -> (false) collapsed.
% Rule
% [115]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,k)),X))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),X)),b(
% apply(k,k))))
% -> (false) collapsed.
% Rule
% [116]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,k)),X)),b(apply(k,k))))
% -> (false) collapsed.
% Rule
% [119]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,k)),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(apply(abstraction,abstraction),k),k),X))))
% -> (false) collapsed.
% Rule
% [120]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(abstraction,apply(k,k)),apply(k,k)),X))))
% -> (false) collapsed.
% Rule
% [122]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,k)),X)),
% b(apply(k,k)))) -> (false) collapsed.
% Rule
% [124]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,k)),X)))) -> (false) collapsed.
% Rule
% [125]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,k)),X))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),X)),b(
% apply(k,k))))
% -> (false) collapsed.
% Rule
% [169]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,k)),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(apply(abstraction,abstraction),k),k),X))))
% -> (false) collapsed.
% Rule
% [187]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),X)),b(
% apply(k,k))))
% -> (false) collapsed.
% Rule
% [188]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),X),k))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),k),k),apply(X,k))),
% b(apply(k,k)))) -> (false) collapsed.
% Rule
% [189]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),
% apply(X,k)))),apply(b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),X),k)),
% b(apply(k,k)))) -> (false) collapsed.
% Rule
% [190]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),X))),
% apply(b(apply(k,k)),b(apply(apply(apply(apply(abstraction,abstraction),k),k),X))))
% -> (false) collapsed.
% Rule
% [191]
% (eq)(apply(k,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),X),k))),
% apply(b(apply(k,k)),b(apply(apply(apply(apply(abstraction,abstraction),k),k),
% apply(X,k))))) -> (false) collapsed.
% Rule
% [192]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),k),k),
% apply(X,k)))),apply(b(apply(k,k)),b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),X),k))))
% -> (false) collapsed.
% Current number of equations to process: 2029
% Current number of ordered equations: 0
% Current number of rules: 203
% New rule produced :
% [243]
% (eq)(b(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),abstraction),k)),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,
% apply(abstraction,abstraction)),k))),abstraction))
% -> (false)
% Current number of equations to process: 2028
% Current number of ordered equations: 0
% Current number of rules: 204
% New rule produced :
% [244]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(apply(abstraction,apply(abstraction,abstraction)),
% apply(k,abstraction)),k),k),k),X)),
% b(apply(k,apply(k,X))))) -> (false)
% Current number of equations to process: 2124
% Current number of ordered equations: 0
% Current number of rules: 205
% New rule produced :
% [245]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(apply(abstraction,
% apply(abstraction,abstraction)),
% apply(k,abstraction)),k),k),k),X))))
% -> (false)
% Current number of equations to process: 2123
% Current number of ordered equations: 0
% Current number of rules: 206
% New rule produced :
% [246]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,apply(abstraction,abstraction)),
% apply(k,abstraction)),k),apply(k,X))),b(apply(abstraction,
% apply(k,
% apply(k,X))))))
% -> (false)
% Current number of equations to process: 2122
% Current number of ordered equations: 0
% Current number of rules: 207
% New rule produced :
% [247]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(apply(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),
% apply(k,abstraction)),k),
% apply(k,X))))) ->
% (false)
% Current number of equations to process: 2121
% Current number of ordered equations: 0
% Current number of rules: 208
% New rule produced :
% [248]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,apply(abstraction,abstraction)),
% apply(k,k)),apply(k,X)),Y))),apply(b(apply(k,X)),
% b(apply(k,X)))) ->
% (false)
% Current number of equations to process: 2210
% Current number of ordered equations: 0
% Current number of rules: 209
% New rule produced :
% [249]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),apply(
% apply(
% apply(
% apply(abstraction,abstraction),k),
% b(
% apply(
% apply(
% apply(
% apply(abstraction,abstraction),abstraction),abstraction),X))),Y))
% -> (false)
% Current number of equations to process: 2235
% Current number of ordered equations: 0
% Current number of rules: 210
% New rule produced :
% [250]
% (eq)(b(apply(apply(abstraction,k),X)),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(abstraction,k),X))),Y))
% -> (false)
% Current number of equations to process: 2242
% Current number of ordered equations: 0
% Current number of rules: 211
% New rule produced :
% [251]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),apply(
% apply(abstraction,k),X)),k),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,k))),Z)) ->
% (false)
% Current number of equations to process: 2240
% Current number of ordered equations: 0
% Current number of rules: 212
% New rule produced :
% [252]
% (eq)(apply(apply(X,b(X)),c(X)),apply(apply(apply(apply(abstraction,abstraction),k),
% b(X)),Y)) -> (false)
% Current number of equations to process: 2244
% Current number of ordered equations: 0
% Current number of rules: 213
% New rule produced :
% [253]
% (eq)(b(k),apply(apply(apply(apply(abstraction,abstraction),k),b(k)),X)) ->
% (false)
% Current number of equations to process: 2246
% Current number of ordered equations: 0
% Current number of rules: 214
% New rule produced :
% [254]
% (eq)(apply(X,c(apply(k,X))),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Y)) -> (false)
% Current number of equations to process: 2246
% Current number of ordered equations: 0
% Current number of rules: 215
% New rule produced :
% [255]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,
% apply(k,X)))),Y))
% -> (false)
% Current number of equations to process: 2249
% Current number of ordered equations: 0
% Current number of rules: 216
% New rule produced :
% [256]
% (eq)(apply(k,c(apply(abstraction,k))),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(abstraction,k))),X)) ->
% (false)
% Current number of equations to process: 2249
% Current number of ordered equations: 0
% Current number of rules: 217
% New rule produced :
% [257]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(abstraction,
% apply(k,
% apply(k,X))))),Y))
% -> (false)
% Current number of equations to process: 2274
% Current number of ordered equations: 0
% Current number of rules: 218
% New rule produced :
% [258]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,apply(X,Y)))),Z))
% -> (false)
% Current number of equations to process: 2273
% Current number of ordered equations: 0
% Current number of rules: 219
% New rule produced :
% [259]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,apply(X,Y)))),Z))
% -> (false)
% Current number of equations to process: 2272
% Current number of ordered equations: 0
% Current number of rules: 220
% New rule produced :
% [260]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,X))),Z)) ->
% (false)
% Current number of equations to process: 2275
% Current number of ordered equations: 0
% Current number of rules: 221
% New rule produced :
% [261]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(
% apply(abstraction,
% apply(k,k)),k),X))),Y))
% -> (false)
% Current number of equations to process: 2278
% Current number of ordered equations: 0
% Current number of rules: 222
% New rule produced :
% [262]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,X))),Z)) ->
% (false)
% Current number of equations to process: 2281
% Current number of ordered equations: 0
% Current number of rules: 223
% New rule produced :
% [263]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),X))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,X))),Z)) ->
% (false)
% Current number of equations to process: 2306
% Current number of ordered equations: 0
% Current number of rules: 224
% New rule produced :
% [264]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),k),X))),abstraction))
% -> (false)
% Current number of equations to process: 2471
% Current number of ordered equations: 0
% Current number of rules: 225
% New rule produced :
% [265]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,k)),abstraction),
% apply(k,X)))),abstraction))
% -> (false)
% Current number of equations to process: 2475
% Current number of ordered equations: 0
% Current number of rules: 226
% New rule produced :
% [266]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))),apply(apply(apply(
% apply(abstraction,abstraction),k),
% b(apply(k,
% apply(X,Y)))),Z))
% -> (false)
% Current number of equations to process: 2500
% Current number of ordered equations: 0
% Current number of rules: 227
% New rule produced :
% [267]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(apply(
% apply(abstraction,abstraction),abstraction),abstraction),X))),abstraction))
% -> (false)
% Current number of equations to process: 2499
% Current number of ordered equations: 0
% Current number of rules: 228
% New rule produced :
% [268]
% (eq)(apply(apply(apply(apply(apply(abstraction,abstraction),k),X),Y),
% c(apply(k,apply(X,X)))),apply(b(apply(apply(apply(abstraction,apply(k,k)),X),X)),
% b(apply(k,apply(X,X))))) -> (false)
% Current number of equations to process: 2500
% Current number of ordered equations: 0
% Current number of rules: 229
% New rule produced :
% [269]
% (eq)(apply(apply(apply(apply(apply(abstraction,abstraction),k),X),Y),
% c(apply(k,apply(X,X)))),apply(b(apply(k,apply(X,X))),b(apply(apply(
% apply(abstraction,
% apply(k,k)),X),X))))
% -> (false)
% Current number of equations to process: 2499
% Current number of ordered equations: 0
% Current number of rules: 230
% New rule produced :
% [270]
% (eq)(apply(apply(apply(apply(apply(abstraction,abstraction),k),X),Y),
% c(apply(k,apply(X,X)))),apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),X),X)),
% b(apply(k,apply(X,X))))) -> (false)
% Current number of equations to process: 2498
% Current number of ordered equations: 0
% Current number of rules: 231
% New rule produced :
% [271]
% (eq)(apply(apply(apply(apply(apply(abstraction,abstraction),k),X),Y),
% c(apply(k,apply(X,X)))),apply(b(apply(k,apply(X,X))),b(apply(apply(
% apply(abstraction,
% apply(abstraction,k)),X),X))))
% -> (false)
% Current number of equations to process: 2497
% Current number of ordered equations: 0
% Current number of rules: 232
% New rule produced :
% [272]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),k),apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,X))),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false)
% Current number of equations to process: 2496
% Current number of ordered equations: 0
% Current number of rules: 233
% New rule produced :
% [273]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),k),apply(
% apply(abstraction,
% apply(abstraction,k)),
% apply(k,X))),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false)
% Current number of equations to process: 2495
% Current number of ordered equations: 0
% Current number of rules: 234
% New rule produced :
% [274]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,abstraction),k),
% apply(abstraction,apply(abstraction,apply(k,k)))),Y),X))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false)
% Current number of equations to process: 2494
% Current number of ordered equations: 0
% Current number of rules: 235
% New rule produced :
% [275]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),
% apply(k,X)),Y))),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Z)) -> (false)
% Current number of equations to process: 2493
% Current number of ordered equations: 0
% Current number of rules: 236
% New rule produced :
% [276]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),X))),apply(apply(
% apply(
% apply(abstraction,abstraction),k),
% b(apply(k,X))),Z))
% -> (false)
% Current number of equations to process: 2492
% Current number of ordered equations: 0
% Current number of rules: 237
% New rule produced :
% [277]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),
% apply(k,X)),Y))),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Z)) -> (false)
% Current number of equations to process: 2491
% Current number of ordered equations: 0
% Current number of rules: 238
% New rule produced :
% [278]
% (eq)(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(abstraction,k)),X),Y)),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(abstraction,k),
% apply(X,Y)))),Z)) ->
% (false)
% Current number of equations to process: 2489
% Current number of ordered equations: 0
% Current number of rules: 239
% New rule produced :
% [279]
% (eq)(apply(apply(apply(X,k),Y),c(apply(apply(apply(apply(abstraction,abstraction),X),k),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,apply(apply(X,k),Y)))),Z))
% -> (false)
% Current number of equations to process: 2488
% Current number of ordered equations: 0
% Current number of rules: 240
% New rule produced :
% [280]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(k,k)),Y),X))),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Z)) ->
% (false)
% Current number of equations to process: 2487
% Current number of ordered equations: 0
% Current number of rules: 241
% New rule produced :
% [281]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),
% apply(
% apply(abstraction,
% apply(k,k)),k)),X))),abstraction))
% -> (false)
% Current number of equations to process: 2486
% Current number of ordered equations: 0
% Current number of rules: 242
% New rule produced :
% [282]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),apply(
% apply(
% apply(
% apply(abstraction,abstraction),k),
% b(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),abstraction),k))),abstraction))
% -> (false)
% Current number of equations to process: 2485
% Current number of ordered equations: 0
% Current number of rules: 243
% New rule produced :
% [283]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(apply(
% apply(abstraction,abstraction),abstraction),abstraction),X))),Y))
% -> (false)
% Rule
% [267]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(apply(
% apply(abstraction,abstraction),abstraction),abstraction),X))),abstraction))
% -> (false) collapsed.
% Current number of equations to process: 2545
% Current number of ordered equations: 0
% Current number of rules: 243
% New rule produced :
% [284]
% (eq)(b(apply(apply(abstraction,k),X)),apply(apply(apply(apply(abstraction,abstraction),k),
% apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(abstraction,k),X)))),Y))
% -> (false)
% Current number of equations to process: 2549
% Current number of ordered equations: 0
% Current number of rules: 244
% Rule [284]
% (eq)(b(apply(apply(abstraction,k),X)),apply(apply(apply(apply(abstraction,abstraction),k),
% apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(abstraction,k),X)))),Y))
% -> (false) is composed into [284]
% (eq)(b(apply(apply(abstraction,k),X)),
% apply(apply(apply(apply(abstraction,abstraction),k),
% apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(abstraction,k),X)))),Y))
% -> (true)
% Rule [283]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(
% apply(
% apply(abstraction,abstraction),abstraction),abstraction),X))),Y))
% -> (false) is composed into [283]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X))),Y))
% -> (true)
% Rule [282]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),abstraction),k))),abstraction))
% -> (false) is composed into [282]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),abstraction),k))),abstraction))
% -> (true)
% Rule [281]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),
% apply(
% apply(abstraction,
% apply(k,k)),k)),X))),abstraction))
% -> (false) is composed into [281]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(apply(abstraction,
% apply(k,abstraction)),
% apply(apply(abstraction,
% apply(k,k)),k)),X))),abstraction))
% -> (true)
% Rule [280]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(k,k)),Y),X))),apply(apply(apply(
% apply(abstraction,abstraction),k),
% b(apply(k,X))),Z))
% -> (false) is composed into [280]
% (eq)(apply(X,c(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(k,k)),Y),X))),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Z)) -> (true)
% Rule [279]
% (eq)(apply(apply(apply(X,k),Y),c(apply(apply(apply(apply(abstraction,abstraction),X),k),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,apply(
% apply(X,k),Y)))),Z))
% -> (false) is composed into [279]
% (eq)(apply(apply(apply(X,k),Y),c(apply(
% apply(
% apply(
% apply(abstraction,abstraction),X),k),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,apply(apply(X,k),Y)))),Z))
% -> (true)
% Rule [278]
% (eq)(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(abstraction,k)),X),Y)),apply(apply(apply(
% apply(abstraction,abstraction),k),
% b(apply(apply(abstraction,k),
% apply(X,Y)))),Z))
% -> (false) is composed into [278]
% (eq)(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),
% apply(abstraction,k)),X),Y)),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(abstraction,k),apply(X,Y)))),Z))
% -> (true)
% Rule [277]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),
% apply(k,X)),Y))),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Z)) ->
% (false) is composed into [277]
% (eq)(apply(X,c(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(k,X)),Y))),apply(
% apply(
% apply(
% apply(abstraction,abstraction),k),
% b(
% apply(k,X))),Z))
% -> (true)
% Rule [276]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),X))),apply(apply(
% apply(
% apply(abstraction,abstraction),k),
% b(
% apply(k,X))),Z))
% -> (false) is composed into [276]
% (eq)(apply(X,c(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),X))),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Z)) -> (true)
% Rule [275]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),
% apply(k,X)),Y))),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Z)) ->
% (false) is composed into [275]
% (eq)(apply(X,c(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(k,X)),Y))),apply(
% apply(
% apply(
% apply(abstraction,abstraction),k),
% b(
% apply(k,X))),Z))
% -> (true)
% Rule [274]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,abstraction),k),
% apply(abstraction,apply(abstraction,apply(k,k)))),Y),X))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false) is composed into 
% [274]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,abstraction),k),
% apply(abstraction,apply(abstraction,apply(k,k)))),Y),X))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (true)
% Rule [273]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),k),
% apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X))),Y))),apply(b(apply(k,X)),b(apply(k,X))))
% -> (false) is composed into [273]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),k),
% apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X))),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) ->
% (true)
% Rule [272]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),k),
% apply(apply(abstraction,apply(k,k)),apply(k,X))),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false) is composed into 
% [272]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),k),apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,X))),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (true)
% Rule [271]
% (eq)(apply(apply(apply(apply(apply(abstraction,abstraction),k),X),Y),
% c(apply(k,apply(X,X)))),apply(b(apply(k,apply(X,X))),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),X),X))))
% -> (false) is composed into [271]
% (eq)(apply(apply(apply(apply(apply(abstraction,abstraction),k),X),Y),
% c(apply(k,apply(X,X)))),apply(b(
% apply(k,
% apply(X,X))),
% b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),X),X))))
% -> (true)
% Rule [270]
% (eq)(apply(apply(apply(apply(apply(abstraction,abstraction),k),X),Y),
% c(apply(k,apply(X,X)))),apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),X),X)),
% b(apply(k,apply(X,X))))) -> (false) is composed into 
% [270]
% (eq)(apply(apply(apply(apply(apply(abstraction,abstraction),k),X),Y),
% c(apply(k,apply(X,X)))),apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),X),X)),
% b(apply(k,apply(X,X))))) -> (true)
% Rule [269]
% (eq)(apply(apply(apply(apply(apply(abstraction,abstraction),k),X),Y),
% c(apply(k,apply(X,X)))),apply(b(apply(k,apply(X,X))),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),X),X))))
% -> (false) is composed into [269]
% (eq)(apply(apply(apply(apply(apply(abstraction,abstraction),k),X),Y),
% c(apply(k,apply(X,X)))),apply(b(
% apply(k,
% apply(X,X))),
% b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),X),X))))
% -> (true)
% Rule [268]
% (eq)(apply(apply(apply(apply(apply(abstraction,abstraction),k),X),Y),
% c(apply(k,apply(X,X)))),apply(b(apply(apply(apply(abstraction,
% apply(k,k)),X),X)),
% b(apply(k,apply(X,X))))) -> (false) is composed into 
% [268]
% (eq)(apply(apply(apply(apply(apply(abstraction,abstraction),k),X),Y),
% c(apply(k,apply(X,X)))),apply(b(apply(apply(apply(abstraction,apply(k,k)),X),X)),
% b(apply(k,apply(X,X))))) -> (true)
% Rule [266]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))),apply(apply(
% apply(
% apply(abstraction,abstraction),k),
% b(
% apply(k,
% apply(X,Y)))),Z))
% -> (false) is composed into [266]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,X)),k),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,apply(X,Y)))),Z)) -> (true)
% Rule [265]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(
% apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,k)),abstraction),
% apply(k,X)))),abstraction))
% -> (false) is composed into [265]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,k)),abstraction),
% apply(k,X)))),abstraction))
% -> (true)
% Rule [264]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),k),X))),abstraction))
% -> (false) is composed into [264]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),k),X))),abstraction))
% -> (true)
% Rule [263]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),X))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,X))),Z))
% -> (false) is composed into [263]
% (eq)(apply(X,c(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Z)) -> (true)
% Rule [262]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y))),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Z)) ->
% (false) is composed into [262]
% (eq)(apply(X,c(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y))),apply(
% apply(
% apply(
% apply(abstraction,abstraction),k),
% b(
% apply(k,X))),Z))
% -> (true)
% Rule [261]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X))),Y))
% -> (false) is composed into [261]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(apply(abstraction,
% apply(k,k)),k),X))),Y))
% -> (true)
% Rule [260]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,X))),Z))
% -> (false) is composed into [260]
% (eq)(apply(X,c(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Z)) -> (true)
% Rule [259]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,apply(X,Y)))),Z))
% -> (false) is composed into [259]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,apply(X,Y)))),Z)) -> (true)
% Rule [258]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,apply(X,Y)))),Z))
% -> (false) is composed into [258]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(abstraction,
% apply(k,k)),X),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,apply(X,Y)))),Z)) -> (true)
% Rule [257]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(abstraction,
% apply(k,
% apply(k,X))))),Y))
% -> (false) is composed into [257]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(abstraction,apply(k,
% apply(k,X))))),Y))
% -> (true)
% Rule [256]
% (eq)(apply(k,c(apply(abstraction,k))),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(abstraction,k))),X))
% -> (false) is composed into [256]
% (eq)(apply(k,c(apply(abstraction,k))),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(abstraction,k))),X)) -> (true)
% Rule [255]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,
% apply(k,X)))),Y))
% -> (false) is composed into [255]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,apply(k,X)))),Y)) ->
% (true)
% Rule [254]
% (eq)(apply(X,c(apply(k,X))),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Y)) -> (false) is composed into 
% [254]
% (eq)(apply(X,c(apply(k,X))),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,X))),Y)) -> (true)
% Rule [253]
% (eq)(b(k),apply(apply(apply(apply(abstraction,abstraction),k),b(k)),X))
% -> (false) is composed into [253]
% (eq)(b(k),apply(apply(apply(apply(abstraction,abstraction),k),
% b(k)),X)) -> (true)
% Rule [252]
% (eq)(apply(apply(X,b(X)),c(X)),apply(apply(apply(apply(abstraction,abstraction),k),
% b(X)),Y)) -> (false) is composed into 
% [252]
% (eq)(apply(apply(X,b(X)),c(X)),apply(apply(apply(apply(abstraction,abstraction),k),
% b(X)),Y)) -> (true)
% Rule [251]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(abstraction,k),X)),k),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(k,k))),Z))
% -> (false) is composed into [251]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(abstraction,k),X)),k),Y))),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(k,k))),Z)) -> (true)
% Rule [250]
% (eq)(b(apply(apply(abstraction,k),X)),apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(abstraction,k),X))),Y))
% -> (false) is composed into [250]
% (eq)(b(apply(apply(abstraction,k),X)),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(abstraction,k),X))),Y))
% -> (true)
% Rule [249]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(
% apply(
% apply(abstraction,abstraction),abstraction),abstraction),X))),Y))
% -> (false) is composed into [249]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X))),Y))
% -> (true)
% Rule [248]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,apply(abstraction,abstraction)),
% apply(k,k)),apply(k,X)),Y))),apply(b(
% apply(k,X)),
% b(apply(k,X))))
% -> (false) is composed into [248]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,
% apply(abstraction,abstraction)),
% apply(k,k)),
% apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) ->
% (true)
% Rule [247]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(apply(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),
% apply(k,abstraction)),k),
% apply(k,X)))))
% -> (false) is composed into [247]
% (eq)(X,apply(b(apply(abstraction,apply(k,
% apply(k,X)))),
% b(apply(apply(apply(apply(abstraction,
% apply(abstraction,abstraction)),
% apply(k,abstraction)),k),
% apply(k,X))))) -> (true)
% Rule [246]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,apply(abstraction,abstraction)),
% apply(k,abstraction)),k),apply(k,X))),
% b(apply(abstraction,apply(k,apply(k,X)))))) -> (false) is composed into 
% [246]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,apply(abstraction,abstraction)),
% apply(k,abstraction)),k),apply(k,X))),b(apply(abstraction,
% apply(k,
% apply(k,X))))))
% -> (true)
% Rule [245]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(
% apply(abstraction,
% apply(abstraction,abstraction)),
% apply(k,abstraction)),k),k),k),X))))
% -> (false) is composed into [245]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(apply(apply(
% apply(abstraction,
% apply(abstraction,abstraction)),
% apply(k,abstraction)),k),k),k),X))))
% -> (true)
% Rule [244]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(apply(abstraction,apply(abstraction,abstraction)),
% apply(k,abstraction)),k),k),k),X)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [244]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),
% apply(k,abstraction)),k),k),k),X)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [243]
% (eq)(b(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),abstraction),k)),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,
% apply(abstraction,abstraction)),k))),abstraction))
% -> (false) is composed into [243]
% (eq)(b(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),abstraction),k)),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(abstraction,apply(abstraction,abstraction)),k))),abstraction))
% -> (true)
% Rule [241]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(abstraction,
% apply(apply(abstraction,abstraction),X)))),abstraction))
% -> (false) is composed into [241]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(abstraction,apply(apply(abstraction,abstraction),X)))),abstraction))
% -> (true)
% Rule [240]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(abstraction,
% apply(apply(abstraction,abstraction),X)))),abstraction))
% -> (false) is composed into [240]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(abstraction,apply(apply(abstraction,abstraction),X)))),abstraction))
% -> (true)
% Rule [239]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),
% apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,
% apply(abstraction,abstraction)),k))),abstraction))
% -> (false) is composed into [239]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),
% apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(abstraction,apply(abstraction,abstraction)),k))),abstraction))
% -> (true)
% Rule [238]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(abstraction,
% apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X)))),abstraction))
% -> (false) is composed into [238]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(abstraction,apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X)))),abstraction))
% -> (true)
% Rule [237]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),k),
% apply(k,X)))),abstraction))
% -> (false) is composed into [237]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),
% apply(k,X)))),abstraction))
% -> (true)
% Rule [236]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X))),abstraction))
% -> (false) is composed into [236]
% (eq)(X,apply(apply(apply(apply(abstraction,abstraction),k),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X))),abstraction))
% -> (true)
% Rule [234]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,apply(abstraction,abstraction)),
% apply(k,k)),X),Y))),apply(b(
% apply(k,
% apply(X,Y))),
% b(apply(k,
% apply(X,Y)))))
% -> (false) is composed into [234]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(
% apply(abstraction,
% apply(abstraction,abstraction)),
% apply(k,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,
% apply(X,Y)))))
% -> (true)
% Rule [233]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,Y)),X))),apply(b(apply(k,X)),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y))))
% -> (false) is composed into [233]
% (eq)(apply(X,c(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),
% apply(k,Y)),X))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y))))
% -> (true)
% Rule [232]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,Y)),X))),apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y)),
% b(apply(k,X)))) -> (false) is composed into 
% [232]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,Y)),X))),apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y)),b(
% apply(k,X))))
% -> (true)
% Rule [231]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,Y)),X))),apply(b(apply(k,X)),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y))))
% -> (false) is composed into [231]
% (eq)(apply(X,c(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),
% apply(k,Y)),X))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y))))
% -> (true)
% Rule [230]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,Y)),X))),apply(b(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y)),
% b(apply(k,X)))) -> (false) is composed into 
% [230]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),
% apply(k,Y)),X))),apply(b(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y)),b(
% apply(k,X))))
% -> (true)
% Rule [229]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,k)),abstraction),k),
% apply(k,X)),Y))),apply(b(apply(k,X)),b(apply(k,X))))
% -> (false) is composed into [229]
% (eq)(apply(X,c(apply(apply(apply(apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,k)),abstraction),k),
% apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) ->
% (true)
% Rule [228]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,k)),abstraction),
% apply(k,X)))))
% -> (false) is composed into [228]
% (eq)(X,apply(b(apply(abstraction,apply(k,
% apply(k,X)))),
% b(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,k)),abstraction),
% apply(k,X))))) -> (true)
% Rule [227]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,k)),abstraction),apply(k,X))),
% b(apply(abstraction,apply(k,apply(k,X)))))) -> (false) is composed into 
% [227]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,abstraction),apply(k,k)),abstraction),
% apply(k,X))),b(apply(abstraction,apply(k,apply(k,X)))))) ->
% (true)
% Rule [226]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(
% apply(abstraction,abstraction),
% apply(k,k)),abstraction),k),k),X))))
% -> (false) is composed into [226]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(apply(apply(
% apply(abstraction,abstraction),
% apply(k,k)),abstraction),k),k),X))))
% -> (true)
% Rule [225]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,k)),abstraction),k),k),X)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [225]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(
% apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,k)),abstraction),k),k),X)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [224]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),apply(b(apply(k,apply(X,Y))),
% b(apply(apply(apply(
% apply(abstraction,abstraction),
% apply(k,X)),k),Y))))
% -> (false) is composed into [224]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),
% apply(b(apply(k,apply(X,Y))),b(apply(
% apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,X)),k),Y))))
% -> (true)
% Rule [223]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),apply(b(apply(apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,X)),k),Y)),
% b(apply(k,apply(X,Y)))))
% -> (false) is composed into [223]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y)),
% b(apply(k,apply(X,Y))))) -> (true)
% Rule [212]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),k),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false) is composed into 
% [212]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X)),k),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (true)
% Rule [211]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(apply(abstraction,apply(k,k)),k),X)),k),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false) is composed into 
% [211]
% (eq)(apply(X,c(apply(apply(apply(apply(abstraction,abstraction),apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X)),k),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (true)
% Rule [206]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X))))
% -> (false) is composed into [206]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X))))
% -> (true)
% Rule [205]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(b(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X))))
% -> (false) is composed into [205]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(b(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X))))
% -> (true)
% Rule [204]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% b(apply(abstraction,apply(apply(abstraction,abstraction),X))))) ->
% (false) is composed into [204]
% (eq)(c(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% b(apply(abstraction,apply(apply(abstraction,abstraction),X)))))
% -> (true)
% Rule [203]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))),apply(b(
% apply(k,
% apply(X,Y))),
% b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y))))
% -> (false) is composed into [203]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,X)),k),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y))))
% -> (true)
% Rule [202]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))),apply(b(
% apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y)),
% b(apply(k,
% apply(X,Y)))))
% -> (false) is composed into [202]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,X)),k),Y))),
% apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),X),Y)),
% b(apply(k,apply(X,Y))))) -> (true)
% Rule [201]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))),apply(b(
% apply(k,
% apply(X,Y))),
% b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),X),Y))))
% -> (false) is composed into [201]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,X)),k),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),X),Y))))
% -> (true)
% Rule [200]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))),apply(b(
% apply(
% apply(
% apply(abstraction,
% apply(k,k)),X),Y)),
% b(apply(k,
% apply(X,Y)))))
% -> (false) is composed into [200]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,X)),k),Y))),
% apply(b(apply(apply(apply(abstraction,
% apply(k,k)),X),Y)),
% b(apply(k,apply(X,Y))))) -> (true)
% Rule [198]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),X))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),Y),X))))
% -> (false) is composed into [198]
% (eq)(apply(X,c(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))))
% -> (true)
% Rule [197]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),X))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),X)),
% b(apply(k,X)))) -> (false) is composed into [197]
% (eq)(apply(X,c(apply(
% apply(
% apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))),
% apply(b(apply(apply(
% apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X)),
% b(apply(k,X)))) -> (true)
% Rule [196]
% (eq)(k,apply(b(apply(k,apply(k,k))),b(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(abstraction,
% apply(abstraction,k)),k)),k),X))))
% -> (false) is composed into [196]
% (eq)(k,apply(b(apply(k,apply(k,k))),
% b(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(abstraction,
% apply(abstraction,k)),k)),k),X))))
% -> (true)
% Rule [195]
% (eq)(k,apply(b(apply(k,apply(k,k))),b(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(abstraction,
% apply(k,k)),k)),k),X))))
% -> (false) is composed into [195]
% (eq)(k,apply(b(apply(k,apply(k,k))),
% b(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(abstraction,
% apply(k,k)),k)),k),X))))
% -> (true)
% Rule [194]
% (eq)(k,apply(b(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(abstraction,apply(abstraction,k)),k)),k),X)),
% b(apply(k,apply(k,k))))) -> (false) is composed into [194]
% (eq)(k,
% apply(
% b(apply(
% apply(
% apply(
% apply(abstraction,abstraction),
% apply(
% apply(abstraction,
% apply(abstraction,k)),k)),k),X)),
% b(apply(k,
% apply(k,k)))))
% -> (true)
% Rule [193]
% (eq)(k,apply(b(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(abstraction,apply(k,k)),k)),k),X)),
% b(apply(k,apply(k,k))))) -> (false) is composed into [193]
% (eq)(k,
% apply(
% b(apply(
% apply(
% apply(
% apply(abstraction,abstraction),
% apply(
% apply(abstraction,
% apply(k,k)),k)),k),X)),
% b(apply(k,
% apply(k,k)))))
% -> (true)
% Rule [186]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),
% apply(k,X))))) -> (false) is composed into [186]
% (eq)(X,apply(
% b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X)),
% b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),
% apply(k,X)))))
% -> (true)
% Rule [185]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(k,k)),Y),
% apply(k,X))))) -> (false) is composed into 
% [185]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(k,k)),Y),apply(k,X)))))
% -> (true)
% Rule [184]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),
% apply(k,X))))) -> (false) is composed into [184]
% (eq)(X,apply(
% b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X)),
% b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),
% apply(k,X)))))
% -> (true)
% Rule [183]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,
% apply(k,k))),k),X))))
% -> (false) is composed into [183]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,
% apply(k,k))),k),X))))
% -> (true)
% Rule [182]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),
% apply(k,X))),b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X))))
% -> (false) is composed into [182]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),
% apply(k,X))),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [181]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),
% apply(k,X))),b(apply(apply(apply(abstraction,apply(k,k)),k),X))))
% -> (false) is composed into [181]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),
% apply(k,X))),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X))))
% -> (true)
% Rule [180]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(k,k)),Y),apply(k,X))),b(apply(k,
% apply(k,X)))))
% -> (false) is composed into [180]
% (eq)(X,apply(b(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(k,k)),Y),
% apply(k,X))),b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [179]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(abstraction,apply(k,k))),k),X)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [179]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,
% apply(k,k))),k),X)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [178]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% apply(b(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X))))
% -> (false) is composed into [178]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% apply(b(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X))))
% -> (true)
% Rule [177]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% b(apply(abstraction,apply(apply(abstraction,abstraction),X))))) ->
% (false) is composed into [177]
% (eq)(c(apply(abstraction,apply(apply(abstraction,abstraction),X))),
% apply(b(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),X)),
% b(apply(abstraction,apply(apply(abstraction,abstraction),X)))))
% -> (true)
% Rule [175]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),
% apply(apply(abstraction,k),X)),k),Y))),
% apply(b(apply(k,k)),b(apply(k,k)))) -> (false) is composed into 
% [175]
% (eq)(apply(k,c(apply(apply(apply(apply(abstraction,abstraction),apply(
% apply(abstraction,k),X)),k),Y))),
% apply(b(apply(k,k)),b(apply(k,k)))) -> (true)
% Rule [174]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),
% apply(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),
% b(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),abstraction),k))))
% -> (false) is composed into [174]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),
% apply(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),
% b(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),abstraction),k))))
% -> (true)
% Rule [173]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),
% apply(b(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),abstraction),k)),
% b(apply(apply(abstraction,apply(abstraction,abstraction)),k)))) ->
% (false) is composed into [173]
% (eq)(b(apply(apply(abstraction,apply(abstraction,abstraction)),k)),
% apply(b(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),abstraction),k)),
% b(apply(apply(abstraction,apply(abstraction,abstraction)),k))))
% -> (true)
% Rule [172]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),apply(Y,X)))),apply(b(apply(k,X)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))))
% -> (false) is composed into [172]
% (eq)(apply(X,c(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),apply(Y,X)))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))))
% -> (true)
% Rule [171]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(abstraction,abstraction),
% apply(k,X)),k),Y))),apply(b(
% apply(k,
% apply(X,Y))),
% b(apply(k,
% apply(X,Y)))))
% -> (false) is composed into [171]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(
% apply(abstraction,abstraction),
% apply(k,X)),k),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,
% apply(X,Y)))))
% -> (true)
% Rule [168]
% (eq)(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(abstraction,k)),apply(k,X)),Y)),apply(b(
% apply(
% apply(abstraction,k),X)),
% b(apply(
% apply(abstraction,k),X))))
% -> (false) is composed into [168]
% (eq)(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),
% apply(abstraction,k)),
% apply(k,X)),Y)),apply(b(
% apply(
% apply(abstraction,k),X)),
% b(apply(
% apply(abstraction,k),X))))
% -> (true)
% Rule [167]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),apply(Y,X)))),apply(b(apply(apply(
% apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X)),
% b(apply(k,X)))) ->
% (false) is composed into [167]
% (eq)(apply(X,c(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),apply(Y,X)))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),Y),X)),
% b(apply(k,X)))) -> (true)
% Rule [166]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),
% apply(Y,X)))),apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))))
% -> (false) is composed into [166]
% (eq)(apply(X,c(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,X)),apply(Y,X)))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))))
% -> (true)
% Rule [165]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),
% apply(Y,X)))),apply(b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X)),
% b(apply(k,X)))) -> (false) is composed into 
% [165]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),
% apply(Y,X)))),apply(b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),Y),X)),
% b(apply(k,X)))) -> (true)
% Rule [164]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X)),Y))))
% -> (false) is composed into [164]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X)),Y))))
% -> (true)
% Rule [163]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,
% apply(k,X))),Y))))
% -> (false) is composed into [163]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,apply(k,X))),Y)))) ->
% (true)
% Rule [162]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(apply(apply(abstraction,
% apply(k,k)),k),X)),Y))))
% -> (false) is composed into [162]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(apply(apply(abstraction,
% apply(k,k)),k),X)),Y))))
% -> (true)
% Rule [161]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(k,apply(k,X))),Y))))
% -> (false) is composed into [161]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(k,apply(k,X))),Y)))) ->
% (true)
% Rule [160]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,
% apply(k,X))),Y))))
% -> (false) is composed into [160]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(k,k)),k),X)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,apply(k,X))),Y)))) ->
% (true)
% Rule [159]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),
% apply(k,X))))) -> (false) is composed into 
% [159]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),
% apply(k,X))))) -> (true)
% Rule [158]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,apply(k,X))),Y)),b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (false) is composed into [158]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,apply(k,X))),Y)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [157]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),Y)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [157]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),
% apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X)),Y)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [156]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,apply(k,X))),Y)),b(apply(apply(apply(abstraction,
% apply(k,k)),k),X))))
% -> (false) is composed into [156]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,apply(k,X))),Y)),
% b(apply(apply(apply(abstraction,
% apply(k,k)),k),X)))) ->
% (true)
% Rule [155]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(apply(apply(abstraction,apply(k,k)),k),X)),Y)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [155]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),
% apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X)),Y)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [154]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),
% apply(k,apply(k,X))),Y)),b(apply(k,apply(k,X)))))
% -> (false) is composed into [154]
% (eq)(X,apply(b(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(k,apply(k,X))),Y)),
% b(apply(k,apply(k,X))))) -> (true)
% Rule [153]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),apply(k,X))),
% b(apply(k,apply(k,X))))) -> (false) is composed into [153]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),
% apply(k,X))),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [152]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,apply(k,abstraction))),abstraction),k),Y),X))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false) is composed into 
% [152]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,apply(k,abstraction))),abstraction),k),Y),X))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (true)
% Rule [151]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,
% apply(k,k)),apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X)),Y))))
% -> (false) is composed into [151]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(abstraction,
% apply(k,k)),apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X)),Y))))
% -> (true)
% Rule [150]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),apply(k,apply(k,X))),Y))))
% -> (false) is composed into [150]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,
% apply(k,k)),apply(k,
% apply(k,X))),Y))))
% -> (true)
% Rule [149]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,
% apply(k,k)),apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X)),Y))))
% -> (false) is composed into [149]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(abstraction,
% apply(k,k)),apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X)),Y))))
% -> (true)
% Rule [148]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(k,apply(k,X))),Y))))
% -> (false) is composed into [148]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(k,apply(k,X))),Y)))) ->
% (true)
% Rule [147]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),apply(k,apply(k,X))),Y))))
% -> (false) is composed into [147]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(k,k)),k),X)),
% b(apply(apply(apply(abstraction,
% apply(k,k)),apply(k,
% apply(k,X))),Y))))
% -> (true)
% Rule [146]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,
% apply(k,X))),Y)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false) is composed into [146]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,apply(k,X))),Y)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [145]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(
% apply(abstraction,
% apply(abstraction,k)),k),X)),Y)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [145]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),
% apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X)),Y)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [144]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,
% apply(k,X))),Y)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false) is composed into 
% [144]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,apply(k,X))),Y)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (true)
% Rule [143]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(
% apply(abstraction,
% apply(k,k)),k),X)),Y)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [143]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),
% apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X)),Y)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [142]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),
% apply(k,apply(k,X))),Y)),b(apply(k,apply(k,X)))))
% -> (false) is composed into [142]
% (eq)(X,apply(b(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(k,apply(k,X))),Y)),
% b(apply(k,apply(k,X))))) -> (true)
% Rule [141]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),
% apply(
% apply(abstraction,
% apply(k,k)),k)),X))))
% -> (false) is composed into [141]
% (eq)(X,apply(b(apply(abstraction,apply(k,
% apply(k,X)))),
% b(apply(apply(apply(abstraction,
% apply(k,abstraction)),
% apply(apply(abstraction,
% apply(k,k)),k)),X))))
% -> (true)
% Rule [140]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(k,X))),b(apply(abstraction,apply(apply(apply(abstraction,
% apply(k,k)),k),X)))))
% -> (false) is composed into [140]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),
% apply(k,X))),b(apply(abstraction,
% apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X)))))
% -> (true)
% Rule [137]
% (eq)(X,apply(b(apply(abstraction,apply(apply(apply(abstraction,apply(k,k)),k),X))),
% b(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(k,X))))) -> (false) is composed into [137]
% (eq)(X,apply(
% b(apply(abstraction,
% apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X))),
% b(apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),k),
% apply(k,X)))))
% -> (true)
% Rule [136]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,abstraction)),
% apply(apply(abstraction,apply(k,k)),k)),X)),
% b(apply(abstraction,apply(k,apply(k,X)))))) -> (false) is composed into 
% [136]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,abstraction)),apply(
% apply(abstraction,
% apply(k,k)),k)),X)),
% b(apply(abstraction,apply(k,apply(k,X)))))) -> (true)
% Rule [135]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),k),X))))
% -> (false) is composed into [135]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X)),
% b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),k),X))))
% -> (true)
% Rule [134]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false) is composed into [134]
% (eq)(X,apply(b(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),k),X)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [133]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(
% apply(abstraction,k),Y)),X))))
% -> (false) is composed into [133]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(apply(abstraction,k),Y)),X))))
% -> (true)
% Rule [132]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(apply(abstraction,k),Y)),X))))
% -> (false) is composed into [132]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(apply(abstraction,k),Y)),X))))
% -> (true)
% Rule [131]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(
% apply(abstraction,k),Y)),X))))
% -> (false) is composed into [131]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(k,k)),k),X)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(apply(abstraction,k),Y)),X))))
% -> (true)
% Rule [130]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(apply(abstraction,k),Y)),X)),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (false) is composed into [130]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(apply(abstraction,k),Y)),X)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [129]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(apply(abstraction,k),Y)),X)),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X))))
% -> (false) is composed into [129]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(apply(abstraction,k),Y)),X)),
% b(apply(apply(apply(abstraction,
% apply(k,k)),k),X)))) ->
% (true)
% Rule [128]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),
% apply(apply(abstraction,k),Y)),X)),b(apply(k,
% apply(k,X)))))
% -> (false) is composed into [128]
% (eq)(X,apply(b(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(apply(abstraction,k),Y)),X)),
% b(apply(k,apply(k,X))))) -> (true)
% Rule [127]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false) is composed into 
% [127]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (true)
% Rule [126]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),k),X))))
% -> (false) is composed into [126]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X)),
% b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),k),X))))
% -> (true)
% Rule [123]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),
% b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),k),X))))
% -> (false) is composed into [123]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(k,k)),k),X)),
% b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),k),X))))
% -> (true)
% Rule [121]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),
% b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),k),X))))
% -> (false) is composed into [121]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(k,k)),k),X)),
% b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),k),X))))
% -> (true)
% Rule [118]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false) is composed into [118]
% (eq)(X,apply(b(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),k),k),k),X)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [117]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false) is composed into 
% [117]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (true)
% Rule [114]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(abstraction,k),Y)),X))))
% -> (false) is composed into [114]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,
% apply(k,k)),apply(
% apply(abstraction,k),Y)),X))))
% -> (true)
% Rule [113]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(apply(abstraction,k),Y)),X))))
% -> (false) is composed into [113]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(apply(abstraction,k),Y)),X))))
% -> (true)
% Rule [112]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(abstraction,k),Y)),X))))
% -> (false) is composed into [112]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(k,k)),k),X)),
% b(apply(apply(apply(abstraction,
% apply(k,k)),apply(
% apply(abstraction,k),Y)),X))))
% -> (true)
% Rule [111]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(abstraction,k),Y)),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false) is composed into [111]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(apply(abstraction,k),Y)),X)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [110]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(abstraction,k),Y)),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false) is composed into 
% [110]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(abstraction,k),Y)),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (true)
% Rule [109]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),
% apply(apply(abstraction,k),Y)),X)),b(apply(k,
% apply(k,X)))))
% -> (false) is composed into [109]
% (eq)(X,apply(b(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(apply(abstraction,k),Y)),X)),
% b(apply(k,apply(k,X))))) -> (true)
% Rule [108]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),
% apply(
% apply(abstraction,
% apply(abstraction,k)),k)),X))))
% -> (false) is composed into [108]
% (eq)(X,apply(b(apply(abstraction,apply(k,
% apply(k,X)))),
% b(apply(apply(apply(abstraction,
% apply(k,abstraction)),
% apply(apply(abstraction,
% apply(abstraction,k)),k)),X))))
% -> (true)
% Rule [107]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,abstraction)),
% apply(apply(abstraction,apply(abstraction,k)),k)),X)),
% b(apply(abstraction,apply(k,apply(k,X)))))) -> (false) is composed into 
% [107]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,abstraction)),apply(
% apply(abstraction,
% apply(abstraction,k)),k)),X)),
% b(apply(abstraction,apply(k,apply(k,X)))))) -> (true)
% Rule [106]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,apply(X,Y))))) -> (false) is composed into 
% [106]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,apply(X,Y))))) -> (true)
% Rule [105]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(k,k)),Y),X))))
% -> (false) is composed into [105]
% (eq)(apply(X,c(apply(k,X))),apply(b(
% apply(k,X)),
% b(apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(k,k)),Y),X))))
% -> (true)
% Rule [104]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(apply(abstraction,abstraction),apply(abstraction,k)),k),X))))
% -> (false) is composed into [104]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X)),
% b(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [103]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),
% b(apply(apply(apply(apply(abstraction,abstraction),apply(abstraction,k)),k),X))))
% -> (false) is composed into [103]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(k,k)),k),X)),
% b(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [102]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),
% apply(k,X))))) -> (false) is composed into 
% [102]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),Y),
% apply(k,X))))) -> (true)
% Rule [101]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,k)),k),X)),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (false) is composed into [101]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [100]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,k)),k),X)),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X))))
% -> (false) is composed into [100]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,
% apply(k,k)),k),X)))) ->
% (true)
% Rule [99]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(k,k)),Y),X)),
% b(apply(k,X)))) -> (false) is composed into 
% [99]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(k,k)),Y),X)),b(
% apply(k,X))))
% -> (true)
% Rule [98]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),
% apply(k,X))),b(apply(k,apply(k,X))))) -> (false) is composed into 
% [98]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),
% apply(k,X))),b(apply(k,apply(k,X))))) -> (true)
% Rule [97]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(k,k)),Y),X))),apply(b(apply(k,X)),
% b(apply(k,X)))) ->
% (false) is composed into [97]
% (eq)(apply(X,c(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(k,k)),Y),X))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (true)
% Rule [95]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,apply(X,Y))))) -> (false) is composed into 
% [95]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,apply(X,Y))))) -> (true)
% Rule [94]
% (eq)(apply(apply(apply(X,k),Y),c(apply(apply(apply(apply(abstraction,abstraction),X),k),Y))),
% apply(b(apply(k,apply(apply(X,k),Y))),b(apply(k,apply(apply(X,k),Y)))))
% -> (false) is composed into [94]
% (eq)(apply(apply(apply(X,k),Y),c(apply(
% apply(
% apply(
% apply(abstraction,abstraction),X),k),Y))),
% apply(b(apply(k,apply(apply(X,k),Y))),
% b(apply(k,apply(apply(X,k),Y))))) -> (true)
% Rule [92]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y))),apply(b(apply(k,X)),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y))))
% -> (false) is composed into [92]
% (eq)(apply(X,c(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y))))
% -> (true)
% Rule [91]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y))),apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y)),
% b(apply(k,X)))) -> (false) is composed into 
% [91]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y)),
% b(apply(k,X)))) -> (true)
% Rule [90]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y))),apply(b(apply(k,X)),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y))))
% -> (false) is composed into [90]
% (eq)(apply(X,c(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y))))
% -> (true)
% Rule [88]
% (eq)(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(abstraction,k)),X),Y)),apply(b(apply(apply(abstraction,k),
% apply(X,Y))),
% b(apply(apply(abstraction,k),
% apply(X,Y))))) ->
% (false) is composed into [88]
% (eq)(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),
% apply(abstraction,k)),X),Y)),
% apply(b(apply(apply(abstraction,k),apply(X,Y))),
% b(apply(apply(abstraction,k),apply(X,Y))))) ->
% (true)
% Rule [87]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y))),apply(b(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y)),
% b(apply(k,X)))) -> (false) is composed into 
% [87]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y))),
% apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y)),b(apply(k,X))))
% -> (true)
% Rule [86]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y)))) -> (false) is composed into 
% [86]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y)))) -> (true)
% Rule [85]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),apply(k,X)),Y)),
% b(apply(k,X)))) -> (false) is composed into [85]
% (eq)(apply(X,c(apply(
% apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y))),
% apply(b(apply(apply(
% apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y)),
% b(apply(k,X)))) -> (true)
% Rule [84]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(k,k)),
% apply(k,X)),Y)))) -> (false) is composed into 
% [84]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))))
% -> (true)
% Rule [83]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y)),
% b(apply(k,X)))) -> (false) is composed into [83]
% (eq)(apply(X,c(apply(
% apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y))),
% apply(b(apply(apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y)),
% b(apply(k,X)))) -> (true)
% Rule [82]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(k,X)),Y))))
% -> (false) is composed into [82]
% (eq)(apply(X,c(apply(k,X))),apply(b(
% apply(k,X)),
% b(apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(k,X)),Y))))
% -> (true)
% Rule [81]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),X))))
% -> (false) is composed into [81]
% (eq)(apply(X,c(apply(k,X))),apply(b(
% apply(k,X)),
% b(apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),X))))
% -> (true)
% Rule [80]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(k,X)),Y)),b(apply(k,X))))
% -> (false) is composed into [80]
% (eq)(apply(X,c(apply(k,X))),apply(b(
% apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(k,X)),Y)),
% b(apply(k,X))))
% -> (true)
% Rule [79]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),X)),
% b(apply(k,X)))) -> (false) is composed into 
% [79]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),X)),
% b(apply(k,X)))) -> (true)
% Rule [78]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(k,X)),Y))))
% -> (false) is composed into [78]
% (eq)(apply(X,c(apply(k,X))),apply(b(
% apply(k,X)),
% b(apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(k,X)),Y))))
% -> (true)
% Rule [77]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(k,X)),Y)),b(apply(k,X))))
% -> (false) is composed into [77]
% (eq)(apply(X,c(apply(k,X))),apply(b(
% apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(k,X)),Y)),
% b(apply(k,X))))
% -> (true)
% Rule [76]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,apply(k,X))),Y))))
% -> (false) is composed into [76]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,apply(k,X))),Y)))) ->
% (true)
% Rule [75]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,apply(k,X))),Y)),b(apply(k,apply(k,X)))))
% -> (false) is composed into [75]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,apply(k,X))),Y)),
% b(apply(k,apply(k,X))))) -> (true)
% Rule [74]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),
% apply(k,X)),Y))),apply(b(apply(k,X)),b(apply(k,X))))
% -> (false) is composed into [74]
% (eq)(apply(X,c(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),
% apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) ->
% (true)
% Rule [73]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),X))),apply(b(
% apply(k,X)),
% b(apply(k,X))))
% -> (false) is composed into [73]
% (eq)(apply(X,c(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),
% apply(abstraction,k)),Y),X))),
% apply(b(apply(k,X)),b(apply(k,X)))) ->
% (true)
% Rule [72]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,k)),k),X))))
% -> (false) is composed into [72]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [71]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))))
% -> (false) is composed into [71]
% (eq)(apply(X,c(apply(k,X))),apply(b(
% apply(k,X)),
% b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X))))
% -> (true)
% Rule [69]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,
% apply(k,k)),apply(k,
% apply(k,X))),Y))))
% -> (false) is composed into [69]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(abstraction,
% apply(k,k)),apply(k,
% apply(k,X))),Y))))
% -> (true)
% Rule [68]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,k)),k),X)),b(apply(k,
% apply(k,X)))))
% -> (false) is composed into [68]
% (eq)(X,apply(b(apply(apply(apply(apply(abstraction,abstraction),
% apply(abstraction,k)),k),X)),
% b(apply(k,apply(k,X))))) -> (true)
% Rule [67]
% (eq)(apply(X,c(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),
% apply(k,X)),Y))),apply(b(apply(k,X)),b(apply(k,X))))
% -> (false) is composed into [67]
% (eq)(apply(X,c(apply(apply(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),k),k),
% apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) ->
% (true)
% Rule [66]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(abstraction,
% apply(abstraction,
% apply(k,k))),Y),X)),
% b(apply(k,X)))) -> (false) is composed into 
% [66]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(abstraction,apply(abstraction,
% apply(k,k))),Y),X)),
% b(apply(k,X)))) -> (true)
% Rule [64]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(k,
% apply(k,X))),Y)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [64]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,
% apply(k,X))),Y)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [63]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),X))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false) is composed into 
% [63]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,apply(k,k))),Y),X))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (true)
% Rule [59]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))))
% -> (false) is composed into [59]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y))))
% -> (true)
% Rule [58]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y)),
% b(apply(k,apply(X,Y))))) -> (false) is composed into [58]
% (eq)(apply(
% apply(X,Y),
% c(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y))),
% apply(b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y)),
% b(apply(k,apply(X,Y)))))
% -> (true)
% Rule [57]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(apply(apply(abstraction,apply(k,k)),X),Y))))
% -> (false) is composed into [57]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),X),Y))))
% -> (true)
% Rule [56]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(b(apply(apply(apply(abstraction,apply(k,k)),X),Y)),b(apply(k,
% apply(X,Y)))))
% -> (false) is composed into [56]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y))),
% apply(b(apply(apply(apply(abstraction,
% apply(k,k)),X),Y)),
% b(apply(k,apply(X,Y))))) -> (true)
% Rule [55]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))))
% -> (false) is composed into [55]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(abstraction,
% apply(k,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y))))
% -> (true)
% Rule [54]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y)),
% b(apply(k,apply(X,Y))))) -> (false) is composed into [54]
% (eq)(apply(
% apply(X,Y),
% c(apply(
% apply(
% apply(abstraction,
% apply(k,k)),X),Y))),
% apply(b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y)),
% b(apply(k,apply(X,Y)))))
% -> (true)
% Rule [53]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(apply(apply(abstraction,apply(k,k)),X),Y))))
% -> (false) is composed into [53]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(abstraction,
% apply(k,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),X),Y))))
% -> (true)
% Rule [52]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(b(apply(apply(apply(abstraction,apply(k,k)),X),Y)),b(apply(k,
% apply(X,Y)))))
% -> (false) is composed into [52]
% (eq)(apply(apply(X,Y),c(apply(apply(
% apply(abstraction,
% apply(k,k)),X),Y))),
% apply(b(apply(apply(apply(abstraction,
% apply(k,k)),X),Y)),
% b(apply(k,apply(X,Y))))) -> (true)
% Rule [51]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(apply(
% apply(abstraction,
% apply(k,abstraction)),k),
% apply(k,X)))))
% -> (false) is composed into [51]
% (eq)(X,apply(b(apply(abstraction,apply(k,
% apply(k,X)))),
% b(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),
% apply(k,X))))) -> (true)
% Rule [50]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(abstraction,
% apply(apply(
% apply(abstraction,
% apply(k,k)),k),X)))))
% -> (false) is composed into [50]
% (eq)(X,apply(b(apply(abstraction,apply(k,
% apply(k,X)))),
% b(apply(abstraction,apply(apply(
% apply(abstraction,
% apply(k,k)),k),X)))))
% -> (true)
% Rule [49]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,abstraction)),k),
% apply(k,X))),b(apply(abstraction,apply(k,apply(k,X))))))
% -> (false) is composed into [49]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),
% apply(k,X))),b(apply(abstraction,
% apply(k,
% apply(k,X))))))
% -> (true)
% Rule [48]
% (eq)(X,apply(b(apply(abstraction,apply(apply(apply(abstraction,apply(k,k)),k),X))),
% b(apply(abstraction,apply(k,apply(k,X)))))) -> (false) is composed into 
% [48]
% (eq)(X,apply(b(apply(abstraction,apply(apply(apply(abstraction,apply(k,k)),k),X))),
% b(apply(abstraction,apply(k,apply(k,X)))))) -> (true)
% Rule [47]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),k),X))))
% -> (false) is composed into [47]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),abstraction),k),k),X))))
% -> (true)
% Rule [45]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),abstraction),k),k),X)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [45]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),abstraction),k),k),X)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [44]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(apply(abstraction,k),Y)),X))))
% -> (false) is composed into [44]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(apply(abstraction,k),Y)),X))))
% -> (true)
% Rule [43]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y))))
% -> (false) is composed into [43]
% (eq)(apply(X,c(apply(k,X))),apply(b(
% apply(k,X)),
% b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y))))
% -> (true)
% Rule [42]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(apply(abstraction,k),Y)),X)),b(apply(k,
% apply(k,X)))))
% -> (false) is composed into [42]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(apply(abstraction,k),Y)),X)),
% b(apply(k,apply(k,X))))) -> (true)
% Rule [41]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y)),b(apply(k,X))))
% -> (false) is composed into [41]
% (eq)(apply(X,c(apply(k,X))),apply(b(
% apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y)),
% b(apply(k,X))))
% -> (true)
% Rule [40]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false) is composed into 
% [40]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (true)
% Rule [39]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),k),X))))
% -> (false) is composed into [39]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(apply(apply(abstraction,
% apply(k,abstraction)),k),k),k),X))))
% -> (true)
% Rule [38]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(abstraction,k)),
% apply(k,X)),Y))),apply(b(apply(k,X)),b(apply(k,X))))
% -> (false) is composed into [38]
% (eq)(apply(X,c(apply(apply(apply(abstraction,
% apply(abstraction,k)),
% apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) ->
% (true)
% Rule [37]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)))) ->
% (false) is composed into [37]
% (eq)(X,apply(b(apply(apply(apply(abstraction,
% apply(k,k)),k),X)),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [36]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),
% b(apply(apply(apply(abstraction,apply(k,k)),k),X)))) -> (false) is composed into 
% [36]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X))))
% -> (true)
% Rule [35]
% (eq)(X,apply(b(apply(apply(apply(apply(apply(abstraction,apply(k,abstraction)),k),k),k),X)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [35]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(
% apply(
% apply(abstraction,
% apply(k,abstraction)),k),k),k),X)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [34]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,
% apply(k,k)),apply(
% apply(abstraction,k),Y)),X))))
% -> (false) is composed into [34]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(abstraction,
% apply(k,k)),apply(
% apply(abstraction,k),Y)),X))))
% -> (true)
% Rule [33]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(apply(apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y))))
% -> (false) is composed into [33]
% (eq)(apply(X,c(apply(k,X))),apply(b(
% apply(k,X)),
% b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),
% apply(k,X)),Y))))
% -> (true)
% Rule [32]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),apply(apply(abstraction,k),Y)),X)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [32]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),
% apply(
% apply(abstraction,k),Y)),X)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [31]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(abstraction,
% apply(k,k)),apply(k,X)),Y)),
% b(apply(k,X)))) -> (false) is composed into 
% [31]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(apply(apply(abstraction,apply(k,k)),
% apply(k,X)),Y)),b(apply(k,X)))) ->
% (true)
% Rule [30]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (false) is composed into 
% [30]
% (eq)(apply(X,c(apply(apply(apply(abstraction,apply(k,k)),apply(k,X)),Y))),
% apply(b(apply(k,X)),b(apply(k,X)))) -> (true)
% Rule [28]
% (eq)(X,apply(b(apply(abstraction,apply(k,apply(k,X)))),b(apply(abstraction,
% apply(k,
% apply(k,X))))))
% -> (false) is composed into [28]
% (eq)(X,apply(b(apply(abstraction,apply(k,
% apply(k,X)))),
% b(apply(abstraction,apply(k,apply(k,X))))))
% -> (true)
% Rule [27]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (false) is composed into [27]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),k),X))))
% -> (true)
% Rule [26]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(abstraction,k)),k),X)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [26]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),k),X)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [25]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),apply(b(apply(k,apply(X,Y))),
% b(apply(apply(apply(abstraction,
% apply(abstraction,k)),X),Y))))
% -> (false) is composed into [25]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),
% apply(b(apply(k,apply(X,Y))),b(apply(
% apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y))))
% -> (true)
% Rule [24]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),apply(b(apply(apply(
% apply(abstraction,
% apply(abstraction,k)),X),Y)),
% b(apply(k,apply(X,Y)))))
% -> (false) is composed into [24]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),
% apply(b(apply(apply(apply(abstraction,
% apply(abstraction,k)),X),Y)),
% b(apply(k,apply(X,Y))))) -> (true)
% Rule [23]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,apply(X,Y))))) -> (false) is composed into 
% [23]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(abstraction,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,apply(X,Y))))) -> (true)
% Rule [22]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(apply(apply(abstraction,
% apply(k,k)),k),X))))
% -> (false) is composed into [22]
% (eq)(X,apply(b(apply(k,apply(k,X))),
% b(apply(apply(apply(abstraction,
% apply(k,k)),k),X)))) ->
% (true)
% Rule [21]
% (eq)(X,apply(b(apply(apply(apply(abstraction,apply(k,k)),k),X)),
% b(apply(k,apply(k,X))))) -> (false) is composed into [21]
% (eq)(X,
% apply(
% b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),k),X)),
% b(apply(k,
% apply(k,X)))))
% -> (true)
% Rule [20]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),apply(b(apply(k,apply(X,Y))),
% b(apply(apply(apply(abstraction,
% apply(k,k)),X),Y))))
% -> (false) is composed into [20]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),
% apply(b(apply(k,apply(X,Y))),b(apply(
% apply(
% apply(abstraction,
% apply(k,k)),X),Y))))
% -> (true)
% Rule [19]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),apply(b(apply(apply(
% apply(abstraction,
% apply(k,k)),X),Y)),
% b(apply(k,apply(X,Y)))))
% -> (false) is composed into [19]
% (eq)(apply(apply(X,Y),c(apply(k,apply(X,Y)))),
% apply(b(apply(apply(apply(abstraction,
% apply(k,k)),X),Y)),
% b(apply(k,apply(X,Y))))) -> (true)
% Rule [18]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,apply(X,Y))))) -> (false) is composed into 
% [18]
% (eq)(apply(apply(X,Y),c(apply(apply(apply(abstraction,apply(k,k)),X),Y))),
% apply(b(apply(k,apply(X,Y))),b(apply(k,apply(X,Y))))) -> (true)
% Rule [13]
% (eq)(b(apply(apply(abstraction,k),X)),apply(b(apply(apply(abstraction,k),X)),
% b(apply(apply(abstraction,k),X))))
% -> (false) is composed into [13]
% (eq)(b(apply(apply(abstraction,k),X)),
% apply(b(apply(apply(abstraction,k),X)),
% b(apply(apply(abstraction,k),X)))) -> (true)
% Rule [12]
% (eq)(apply(k,c(apply(abstraction,k))),apply(b(apply(abstraction,k)),
% b(apply(abstraction,k)))) ->
% (false) is composed into [12]
% (eq)(apply(k,c(apply(abstraction,k))),apply(
% b(
% apply(abstraction,k)),
% b(
% apply(abstraction,k))))
% -> (true)
% Rule [11]
% (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(k,apply(k,X))))) -> (false) is composed into 
% [11] (eq)(X,apply(b(apply(k,apply(k,X))),b(apply(k,apply(k,X))))) -> (true)
% Rule [7]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),b(apply(k,X)))) ->
% (false) is composed into [7]
% (eq)(apply(X,c(apply(k,X))),apply(b(apply(k,X)),
% b(apply(k,X)))) ->
% (true)
% Rule [6] (eq)(b(k),apply(b(k),b(k))) -> (false) is composed into [6]
% (eq)(
% b(k),
% apply(
% b(k),
% b(k))) ->
% (true)
% Rule [2] (eq)(apply(apply(Y,b(Y)),c(Y)),apply(b(Y),b(Y))) -> (false) is composed into 
% [2] (eq)(apply(apply(Y,b(Y)),c(Y)),apply(b(Y),b(Y))) -> (true)
% New rule produced : [285] (false) -> (true)
% The conjecture has been reduced. 
% Conjecture is now:
% Trivial
% 
% Current number of equations to process: 2558
% Current number of ordered equations: 0
% Current number of rules: 245
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% 
% The following 8 rules have been used:
% [1] 
% (eq)(X,X) -> (true); trace = in the starting set
% [2] (eq)(apply(apply(Y,b(Y)),c(Y)),apply(b(Y),b(Y))) -> (false); trace = in the starting set
% [3] apply(apply(k,X),Y) -> X; trace = in the starting set
% [4] apply(apply(X,apply(k,Z)),apply(Y,Z)) <->
% apply(apply(apply(abstraction,X),Y),Z); trace = in the starting set
% [222] apply(apply(apply(abstraction,X),apply(k,Z)),Y) <->
% apply(apply(X,apply(k,Y)),Z); trace = Cp of 4 and 3
% [235] apply(X,X) <->
% apply(apply(apply(apply(abstraction,abstraction),k),X),Y); trace = Cp of 222 and 4
% [252] (eq)(apply(apply(X,b(X)),c(X)),apply(apply(apply(apply(abstraction,abstraction),k),
% b(X)),Y)) -> (false); trace = Cp of 235 and 2
% [285] (false) -> (true); trace = Cp of 252 and 1
% % SZS output end Refutation
% All conjectures have been proven
% 
% Execution time: 7.590000 sec
% res : bool = true
% time is now off
% 
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
% 
% EOF
%------------------------------------------------------------------------------