CiME---2.01.UNS-Ref.s

%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : COL024-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n139.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.11.2.el6.x86_64
% CPULimit : 300s
% DateTime : Tue Jun 10 00:19:44 EDT 2014

% Result   : Unsatisfiable 1.54s
% Output   : Refutation 1.54s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : COL024-1 : TPTP v6.0.0. Released v1.0.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n139.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jun  5 17:48:08 CDT 2014
% % CPUTime  : 1.54 
% Processing problem /tmp/CiME_64342_n139.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " combinator,c,m,b : constant;  apply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z));
% apply(m,X) = apply(X,X);
% apply(apply(apply(c,X),Y),Z) = apply(apply(X,Z),Y);
% ";
% 
% let s1 = status F "
% combinator lr_lex;
% c lr_lex;
% m lr_lex;
% apply lr_lex;
% b lr_lex;
% ";
% 
% let p1 = precedence F "
% apply > b > m > c > combinator";
% 
% let s2 = status F "
% combinator mul;
% c mul;
% m mul;
% apply mul;
% b mul;
% ";
% 
% let p2 = precedence F "
% apply > b = m = c = combinator";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " Y = apply(combinator,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(apply(b,X),Y),Z) =
% apply(X,apply(Y,Z)),
% apply(m,X) = apply(X,X),
% apply(apply(apply(c,X),Y),Z) =
% apply(apply(X,Z),Y) } (3 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% 
% [combinator] = 1;
% [c] = 2;
% [m] = 3;
% [b] = 4;
% [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 = { Y = apply(combinator,Y) } (1 equation(s))
% time is now on
% 
% Initializing completion ...
% New rule produced : [1] (eq)(Y,apply(combinator,Y)) -> (false)
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 1
% New rule produced : [2] (eq)(X,X) -> (true)
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 2
% New rule produced : [3] apply(X,X) <-> apply(m,X)
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 3
% New rule produced : [4] apply(m,X) <-> apply(X,X)
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 4
% New rule produced : [5] apply(X,apply(Y,Z)) <-> apply(apply(apply(b,X),Y),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 5
% New rule produced : [6] apply(apply(apply(b,X),Y),Z) <-> apply(X,apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 6
% New rule produced : [7] apply(apply(X,Z),Y) <-> apply(apply(apply(c,X),Y),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 7
% New rule produced : [8] apply(apply(apply(c,X),Y),Z) <-> apply(apply(X,Z),Y)
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced : [9] (eq)(combinator,apply(m,combinator)) -> (false)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10] (eq)(apply(X,Y),apply(apply(apply(b,combinator),X),Y)) -> (false)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11] (eq)(apply(m,X),apply(apply(apply(b,combinator),X),X)) -> (false)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12] (eq)(apply(X,X),apply(apply(apply(b,combinator),m),X)) -> (false)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13]
% (eq)(apply(apply(b,combinator),X),apply(apply(m,apply(b,combinator)),X)) ->
% (false)
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(m,apply(apply(b,combinator),X)))
% -> (false)
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(b,combinator),X),
% apply(Y,Z))) -> (false)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(b,combinator),apply(apply(b,X),Y)),Z))
% -> (false)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17]
% (eq)(apply(X,Y),apply(apply(apply(apply(c,b),X),combinator),Y)) -> (false)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(apply(apply(b,combinator),apply(X,Z)),Y))
% -> (false)
% Current number of equations to process: 33
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced :
% [19]
% (eq)(apply(X,Y),apply(apply(apply(apply(apply(b,c),b),combinator),Y),X)) ->
% (false)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20]
% (eq)(apply(m,apply(b,combinator)),apply(apply(m,apply(b,combinator)),
% apply(b,combinator))) -> (false)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(b,combinator),apply(apply(c,X),Z)),Y))
% -> (false)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22] (eq)(apply(m,X),apply(combinator,apply(X,X))) -> (false)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [23]
% (eq)(apply(m,X),apply(apply(apply(apply(c,b),X),combinator),X)) -> (false)
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [24]
% (eq)(apply(m,X),apply(apply(apply(apply(apply(b,c),b),combinator),X),X)) ->
% (false)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [25] (eq)(apply(X,X),apply(combinator,apply(m,X))) -> (false)
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [26]
% (eq)(apply(X,X),apply(apply(apply(apply(c,b),m),combinator),X)) -> (false)
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [27]
% (eq)(apply(X,X),apply(apply(apply(apply(apply(b,c),b),combinator),X),m)) ->
% (false)
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [28]
% (eq)(apply(apply(apply(b,m),X),Y),apply(apply(apply(b,combinator),apply(X,Y)),
% apply(X,Y))) -> (false)
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [29]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(b,m),b),combinator),X))
% -> (false)
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [30]
% (eq)(apply(apply(apply(c,b),X),combinator),apply(apply(m,apply(b,combinator)),X))
% -> (false)
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [31]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(c,m),X),apply(b,combinator)))
% -> (false)
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [32]
% (eq)(apply(apply(m,apply(b,combinator)),combinator),apply(m,apply(apply(b,combinator),combinator)))
% -> (false)
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [33]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),apply(m,apply(apply(b,combinator),b)))
% -> (false)
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [34]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),Y),Z))
% -> (false)
% Current number of equations to process: 42
% Current number of ordered equations: 1
% Current number of rules: 34
% New rule produced :
% [35]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),Z))
% -> (false)
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [36]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(apply(apply(b,combinator),m),
% apply(X,Y))) -> (false)
% Current number of equations to process: 41
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [37]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),apply(apply(m,
% apply(b,combinator)),
% apply(X,Y))) ->
% (false)
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [38]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(apply(apply(b,m),
% apply(b,combinator)),X))
% -> (false)
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [39]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(m,apply(apply(
% apply(c,b),X),combinator)))
% -> (false)
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [40]
% (eq)(apply(apply(apply(apply(c,b),apply(b,combinator)),X),X),apply(m,
% apply(apply(b,combinator),X)))
% -> (false)
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [41]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(b,combinator),X),
% apply(m,Y))) -> (false)
% Current number of equations to process: 46
% Current number of ordered equations: 1
% Current number of rules: 41
% New rule produced :
% [42]
% (eq)(apply(apply(apply(m,b),X),Y),apply(apply(apply(b,combinator),b),
% apply(X,Y))) -> (false)
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [43]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(b,combinator),X),
% apply(Y,Y))) -> (false)
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [44]
% (eq)(apply(apply(m,apply(b,X)),Y),apply(apply(apply(b,combinator),X),
% apply(apply(b,X),Y))) -> (false)
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [45]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(combinator,apply(X,apply(Y,Z)))) ->
% (false)
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [46]
% (eq)(apply(apply(apply(apply(c,b),X),Y),Z),apply(apply(apply(b,combinator),Y),
% apply(X,Z))) -> (false)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [47]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(apply(c,b),X),combinator),
% apply(Y,Z))) -> (false)
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [48]
% (eq)(apply(apply(apply(apply(apply(b,c),b),X),Y),Z),apply(apply(apply(b,combinator),X),
% apply(Z,Y))) -> (false)
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [49]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(b,combinator),apply(apply(b,X),Y)),Y))
% -> (false)
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [50]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(b,combinator),apply(apply(b,X),m)),Y))
% -> (false)
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [51]
% (eq)(apply(apply(apply(b,b),X),Y),apply(apply(apply(b,combinator),apply(
% apply(m,b),X)),Y))
% -> (false)
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [52]
% (eq)(apply(apply(b,combinator),apply(X,Y)),apply(apply(apply(apply(apply(b,b),m),
% apply(b,combinator)),X),Y))
% -> (false)
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [53]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),b),combinator),X),
% apply(m,apply(apply(b,combinator),X))) -> (false)
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [54]
% (eq)(apply(apply(apply(apply(apply(b,c),b),X),X),apply(b,combinator)),
% apply(m,apply(apply(b,combinator),X))) -> (false)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [55]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),X),Y),Z))
% -> (false)
% Current number of equations to process: 53
% Current number of ordered equations: 1
% Current number of rules: 55
% New rule produced :
% [56]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Z),V_3),apply(apply(apply(b,combinator),
% apply(X,Y)),
% apply(Z,V_3))) ->
% (false)
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [57]
% (eq)(apply(apply(apply(b,X),apply(apply(b,Y),Z)),V_3),apply(apply(apply(b,combinator),X),
% apply(Y,apply(Z,V_3))))
% -> (false)
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [58]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(apply(apply(b,c),b),combinator),
% apply(Y,Z)),X)) -> (false)
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [59]
% (eq)(apply(apply(apply(b,X),apply(apply(c,Y),Z)),V_3),apply(apply(apply(b,combinator),X),
% apply(apply(Y,V_3),Z)))
% -> (false)
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [60]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(apply(apply(b,combinator),
% apply(apply(b,m),X)),Y))
% -> (false)
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [61]
% (eq)(apply(X,apply(Y,Z)),apply(combinator,apply(apply(apply(b,X),Y),Z))) ->
% (false)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [62]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(b,combinator),apply(apply(
% apply(c,b),Y),X)),Z))
% -> (false)
% Current number of equations to process: 57
% Current number of ordered equations: 1
% Current number of rules: 62
% New rule produced :
% [63]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(c,b),apply(apply(b,X),Y)),combinator),Z))
% -> (false)
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [64]
% (eq)(apply(apply(c,b),X),apply(apply(apply(m,apply(c,b)),combinator),X)) ->
% (false)
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [65]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(apply(apply(apply(c,b),apply(X,Z)),combinator),Y))
% -> (false)
% Current number of equations to process: 62
% Current number of ordered equations: 1
% Current number of rules: 65
% New rule produced :
% [66]
% (eq)(apply(X,Y),apply(apply(apply(apply(apply(apply(b,c),c),b),combinator),X),Y))
% -> (false)
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [67]
% (eq)(apply(apply(apply(c,X),Y),X),apply(apply(apply(b,combinator),apply(m,X)),Y))
% -> (false)
% Current number of equations to process: 67
% Current number of ordered equations: 1
% Current number of rules: 67
% New rule produced :
% [68]
% (eq)(apply(apply(apply(m,c),X),Y),apply(apply(apply(b,combinator),apply(c,Y)),X))
% -> (false)
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [69]
% (eq)(apply(apply(apply(c,m),X),Y),apply(apply(apply(b,combinator),apply(Y,Y)),X))
% -> (false)
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [70]
% (eq)(apply(apply(m,apply(c,X)),Y),apply(apply(apply(b,combinator),apply(X,Y)),
% apply(c,X))) -> (false)
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [71]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(c,b),apply(apply(c,X),Z)),combinator),Y))
% -> (false)
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [72]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(combinator,apply(apply(X,Z),Y))) ->
% (false)
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [73]
% (eq)(apply(apply(apply(apply(c,c),X),Y),Z),apply(apply(apply(b,combinator),
% apply(Y,Z)),X)) -> (false)
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [74]
% (eq)(apply(apply(apply(apply(apply(b,c),c),X),Y),Z),apply(apply(apply(b,combinator),
% apply(X,Y)),Z)) ->
% (false)
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [75]
% (eq)(apply(X,apply(apply(apply(b,c),b),combinator)),apply(apply(m,apply(
% apply(
% apply(b,c),b),combinator)),X))
% -> (false)
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [76]
% (eq)(apply(apply(apply(b,m),b),combinator),apply(apply(m,apply(b,combinator)),
% apply(b,combinator))) -> (false)
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [77]
% (eq)(apply(m,apply(b,combinator)),apply(apply(apply(apply(b,m),b),combinator),
% apply(b,combinator))) -> (false)
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [78]
% (eq)(apply(m,apply(b,combinator)),apply(apply(apply(apply(apply(b,b),m),
% apply(b,combinator)),b),combinator))
% -> (false)
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [79]
% (eq)(apply(apply(c,X),Y),apply(apply(apply(b,combinator),apply(apply(m,c),Y)),X))
% -> (false)
% Current number of equations to process: 84
% Current number of ordered equations: 1
% Current number of rules: 79
% New rule produced :
% [80]
% (eq)(apply(apply(m,X),Y),apply(apply(apply(b,combinator),apply(apply(c,X),Y)),X))
% -> (false)
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [81]
% (eq)(apply(apply(X,X),Y),apply(apply(apply(b,combinator),apply(apply(c,m),Y)),X))
% -> (false)
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [82]
% (eq)(apply(apply(X,Y),apply(c,X)),apply(apply(apply(b,combinator),apply(m,
% apply(c,X))),Y))
% -> (false)
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [83]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(b,combinator),apply(apply(c,X),
% apply(X,Y))),Y)) ->
% (false)
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [84]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Z),Y))
% -> (false)
% Current number of equations to process: 79
% Current number of ordered equations: 1
% Current number of rules: 84
% New rule produced :
% [85]
% (eq)(apply(apply(apply(apply(apply(b,c),X),Y),Z),V_3),apply(apply(apply(b,combinator),
% apply(apply(X,Y),V_3)),Z))
% -> (false)
% Current number of equations to process: 79
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [86]
% (eq)(apply(apply(apply(apply(apply(b,c),b),combinator),X),X),apply(m,
% apply(apply(
% apply(
% apply(b,c),b),combinator),X)))
% -> (false)
% Current number of equations to process: 77
% Current number of ordered equations: 1
% Current number of rules: 86
% New rule produced :
% [87]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(apply(apply(apply(apply(b,c),b),combinator),Y),
% apply(X,Z))) -> (false)
% Current number of equations to process: 76
% Current number of ordered equations: 1
% Current number of rules: 87
% New rule produced :
% [88]
% (eq)(apply(X,Y),apply(apply(apply(apply(apply(apply(apply(b,c),b),c),combinator),b),Y),X))
% -> (false)
% Current number of equations to process: 76
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [89]
% (eq)(apply(apply(X,Y),Z),apply(combinator,apply(apply(apply(c,X),Z),Y))) ->
% (false)
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [90]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(b,combinator),apply(apply(
% apply(c,c),Z),X)),Y))
% -> (false)
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [91]
% (eq)(apply(m,apply(c,b)),apply(apply(apply(m,apply(c,b)),combinator),
% apply(c,b))) -> (false)
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [92]
% (eq)(apply(m,X),apply(apply(apply(apply(apply(apply(b,c),c),b),combinator),X),X))
% -> (false)
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [93]
% (eq)(apply(m,apply(X,Y)),apply(combinator,apply(apply(apply(apply(apply(b,b),X),Y),X),Y)))
% -> (false)
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [94]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(combinator,
% apply(m,apply(X,Y)))) ->
% (false)
% Current number of equations to process: 97
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [95]
% (eq)(apply(X,X),apply(apply(apply(apply(apply(apply(b,c),c),b),combinator),m),X))
% -> (false)
% Current number of equations to process: 100
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [96]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(combinator,
% apply(apply(apply(b,m),X),Y)))
% -> (false)
% Current number of equations to process: 100
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [97]
% (eq)(apply(apply(apply(b,m),X),X),apply(apply(apply(b,combinator),apply(m,X)),
% apply(X,X))) -> (false)
% Current number of equations to process: 109
% Current number of ordered equations: 1
% Current number of rules: 97
% New rule produced :
% [98]
% (eq)(apply(apply(apply(b,m),X),X),apply(apply(apply(b,combinator),apply(X,X)),
% apply(m,X))) -> (false)
% Current number of equations to process: 109
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [99]
% (eq)(apply(apply(apply(b,m),m),X),apply(apply(apply(b,combinator),apply(m,X)),
% apply(X,X))) -> (false)
% Current number of equations to process: 107
% Current number of ordered equations: 1
% Current number of rules: 99
% New rule produced :
% [100]
% (eq)(apply(apply(apply(b,m),m),X),apply(apply(apply(b,combinator),apply(X,X)),
% apply(m,X))) -> (false)
% Current number of equations to process: 107
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [101]
% (eq)(apply(apply(apply(b,m),X),Y),apply(combinator,apply(apply(apply(
% apply(
% apply(b,b),X),Y),X),Y)))
% -> (false)
% Current number of equations to process: 106
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [102]
% (eq)(apply(apply(apply(b,m),X),Y),apply(apply(apply(apply(c,b),apply(X,Y)),combinator),
% apply(X,Y))) -> (false)
% Current number of equations to process: 105
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [103]
% (eq)(apply(m,X),apply(apply(apply(apply(apply(apply(apply(b,c),b),c),combinator),b),X),X))
% -> (false)
% Current number of equations to process: 104
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [104]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(apply(apply(
% apply(c,b),m),combinator),
% apply(X,Y))) -> (false)
% Current number of equations to process: 103
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [105]
% (eq)(apply(X,X),apply(apply(apply(apply(apply(apply(apply(b,c),b),c),combinator),b),X),m))
% -> (false)
% Current number of equations to process: 102
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [106]
% (eq)(apply(apply(apply(apply(c,b),X),m),Y),apply(apply(apply(b,combinator),
% apply(X,Y)),apply(X,Y))) ->
% (false)
% Current number of equations to process: 114
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [107]
% (eq)(apply(apply(apply(apply(apply(b,c),b),m),X),Y),apply(apply(apply(b,combinator),
% apply(Y,X)),
% apply(Y,X))) -> (false)
% Current number of equations to process: 113
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [108]
% (eq)(apply(apply(apply(c,b),X),combinator),apply(apply(apply(apply(b,m),b),combinator),X))
% -> (false)
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [109]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(apply(c,b),b),m),combinator),X))
% -> (false)
% Current number of equations to process: 120
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [110]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(apply(apply(b,c),b),m),combinator),b),X))
% -> (false)
% Current number of equations to process: 118
% Current number of ordered equations: 1
% Current number of rules: 110
% New rule produced :
% [111]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(apply(b,c),
% apply(b,m)),b),X),combinator))
% -> (false)
% Current number of equations to process: 118
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [112]
% (eq)(apply(apply(m,apply(c,b)),combinator),apply(apply(m,apply(b,combinator)),
% apply(c,b))) -> (false)
% Current number of equations to process: 119
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [113]
% (eq)(apply(apply(apply(c,b),X),combinator),apply(apply(apply(c,m),X),
% apply(b,combinator))) -> (false)
% Current number of equations to process: 122
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [114]
% (eq)(apply(apply(apply(apply(apply(b,c),c),b),combinator),X),apply(apply(m,
% apply(b,combinator)),X))
% -> (false)
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [115]
% (eq)(apply(apply(b,combinator),apply(c,m)),apply(apply(apply(apply(b,m),c),m),
% apply(b,combinator))) -> (false)
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [116]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(apply(b,b),
% apply(c,m)),X),b),combinator))
% -> (false)
% Current number of equations to process: 123
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [117]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(c,c),X),m),
% apply(b,combinator))) -> (false)
% Current number of equations to process: 124
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [118]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(apply(b,c),c),m),
% apply(b,combinator)),X)) -> (false)
% Current number of equations to process: 123
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [119]
% (eq)(apply(apply(m,apply(b,combinator)),combinator),apply(apply(apply(b,m),
% apply(b,combinator)),combinator))
% -> (false)
% Current number of equations to process: 124
% Current number of ordered equations: 1
% Current number of rules: 119
% New rule produced :
% [120]
% (eq)(apply(apply(apply(apply(b,m),b),combinator),combinator),apply(m,
% apply(apply(b,combinator),combinator)))
% -> (false)
% Current number of equations to process: 124
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [121]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),apply(apply(apply(b,m),
% apply(b,combinator)),b))
% -> (false)
% Current number of equations to process: 126
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [122]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),apply(m,apply(apply(
% apply(c,b),b),combinator)))
% -> (false)
% Current number of equations to process: 128
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [123]
% (eq)(apply(apply(apply(apply(c,m),apply(b,combinator)),b),b),apply(m,
% apply(apply(b,combinator),b)))
% -> (false)
% Current number of equations to process: 127
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [124]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(m,b),apply(b,combinator)),X),Y),Z))
% -> (false)
% Current number of equations to process: 133
% Current number of ordered equations: 1
% Current number of rules: 124
% New rule produced :
% [125]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),Y),Y))
% -> (false)
% Current number of equations to process: 133
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [126]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),m),Y))
% -> (false)
% Current number of equations to process: 132
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [127]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),apply(apply(
% apply(
% apply(b,m),b),combinator),
% apply(X,Y))) ->
% (false)
% Current number of equations to process: 131
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [128]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),apply(apply(
% apply(c,m),
% apply(X,Y)),
% apply(b,combinator)))
% -> (false)
% Current number of equations to process: 130
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [129]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),m),b),b),combinator),b),
% apply(m,apply(apply(b,combinator),b))) -> (false)
% Current number of equations to process: 129
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [130]
% (eq)(apply(apply(apply(apply(apply(b,c),m),b),b),apply(b,combinator)),
% apply(m,apply(apply(b,combinator),b))) -> (false)
% Current number of equations to process: 128
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [131]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(X,Y))) -> (false)
% Current number of equations to process: 126
% Current number of ordered equations: 1
% Current number of rules: 131
% New rule produced :
% [132]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),
% apply(X,Y)),X),Y)) -> (false)
% Current number of equations to process: 126
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [133]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),m),apply(b,combinator)),
% apply(apply(apply(b,m),m),apply(b,combinator))) -> (false)
% Current number of equations to process: 125
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [134]
% (eq)(apply(apply(apply(b,X),Y),apply(Z,V_3)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(b,Y),Z),V_3)))
% -> (false)
% Current number of equations to process: 124
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [135]
% (eq)(apply(apply(apply(b,X),apply(Y,Z)),V_3),apply(apply(apply(b,combinator),X),
% apply(apply(apply(c,Y),V_3),Z)))
% -> (false)
% Current number of equations to process: 123
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [136]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(b,combinator),apply(apply(
% apply(
% apply(b,b),X),Y),X)),Y))
% -> (false)
% Current number of equations to process: 122
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [137]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),Y),Z)) -> (false)
% Current number of equations to process: 120
% Current number of ordered equations: 1
% Current number of rules: 137
% New rule produced :
% [138]
% (eq)(apply(X,apply(apply(apply(b,Y),Z),V_3)),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),
% apply(Z,V_3))) -> (false)
% Current number of equations to process: 120
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [139]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(b,c),b),combinator),Z),
% apply(apply(b,X),Y))) -> (false)
% Current number of equations to process: 118
% Current number of ordered equations: 1
% Current number of rules: 139
% New rule produced :
% [140]
% (eq)(apply(X,apply(apply(apply(c,Y),Z),V_3)),apply(apply(apply(b,combinator),
% apply(apply(b,X),apply(Y,V_3))),Z))
% -> (false)
% Current number of equations to process: 118
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [141]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(apply(b,b),c),b),X),Y),combinator),Z))
% -> (false)
% Current number of equations to process: 117
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [142]
% (eq)(apply(apply(apply(c,X),Y),apply(Z,V_3)),apply(apply(apply(b,combinator),
% apply(apply(apply(b,X),Z),V_3)),Y))
% -> (false)
% Current number of equations to process: 116
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [143]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(b,c),b),combinator),Y),
% apply(apply(c,X),Z))) -> (false)
% Current number of equations to process: 114
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [144]
% (eq)(apply(apply(apply(apply(b,X),Y),Z),V_3),apply(apply(apply(b,combinator),
% apply(apply(c,X),V_3)),
% apply(Y,Z))) -> (false)
% Current number of equations to process: 111
% Current number of ordered equations: 1
% Current number of rules: 144
% New rule produced :
% [145]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(c,X)),Z),Y)) -> (false)
% Current number of equations to process: 111
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [146]
% (eq)(apply(apply(apply(c,b),apply(X,Y)),combinator),apply(apply(apply(
% apply(
% apply(b,b),m),
% apply(b,combinator)),X),Y))
% -> (false)
% Current number of equations to process: 108
% Current number of ordered equations: 1
% Current number of rules: 146
% New rule produced :
% [147]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),c),b),X),Y),combinator),
% apply(apply(m,apply(b,combinator)),apply(X,Y))) -> (false)
% Current number of equations to process: 108
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [148]
% (eq)(apply(apply(m,X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),X),Y))
% -> (false)
% Current number of equations to process: 125
% Current number of ordered equations: 1
% Current number of rules: 148
% New rule produced :
% [149]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(m,b),b),combinator),X),Y),Z))
% -> (false)
% Current number of equations to process: 125
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [150]
% (eq)(apply(apply(X,X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),Y))
% -> (false)
% Current number of equations to process: 124
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [151]
% (eq)(apply(apply(apply(apply(apply(b,b),X),X),X),X),apply(apply(apply(b,combinator),m),
% apply(m,X))) -> (false)
% Current number of equations to process: 140
% Current number of ordered equations: 1
% Current number of rules: 151
% New rule produced :
% [152]
% (eq)(apply(apply(apply(apply(apply(m,b),X),Y),X),Y),apply(apply(apply(b,combinator),m),
% apply(X,Y))) -> (false)
% Current number of equations to process: 140
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [153]
% (eq)(apply(apply(apply(apply(apply(b,b),m),X),m),X),apply(apply(apply(b,combinator),m),
% apply(X,X))) -> (false)
% Current number of equations to process: 139
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [154]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),X),apply(apply(m,
% apply(b,combinator)),
% apply(m,X))) ->
% (false)
% Current number of equations to process: 156
% Current number of ordered equations: 1
% Current number of rules: 154
% New rule produced :
% [155]
% (eq)(apply(apply(apply(apply(apply(m,b),b),combinator),X),Y),apply(apply(m,
% apply(b,combinator)),
% apply(X,Y))) ->
% (false)
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [156]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),apply(apply(m,
% apply(b,combinator)),
% apply(X,X))) ->
% (false)
% Current number of equations to process: 155
% Current number of ordered equations: 0
% Current number of rules: 156
% Rule [156]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),apply(
% apply(m,
% apply(b,combinator)),
% apply(X,X)))
% -> (false) is composed into [156]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),
% apply(apply(m,apply(b,combinator)),apply(X,X)))
% -> (true)
% Rule [155]
% (eq)(apply(apply(apply(apply(apply(m,b),b),combinator),X),Y),apply(
% apply(m,
% apply(b,combinator)),
% apply(X,Y)))
% -> (false) is composed into [155]
% (eq)(apply(apply(apply(apply(apply(m,b),b),combinator),X),Y),
% apply(apply(m,apply(b,combinator)),apply(X,Y)))
% -> (true)
% Rule [154]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),X),apply(
% apply(m,
% apply(b,combinator)),
% apply(m,X)))
% -> (false) is composed into [154]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),X),
% apply(apply(m,apply(b,combinator)),apply(m,X)))
% -> (true)
% Rule [153]
% (eq)(apply(apply(apply(apply(apply(b,b),m),X),m),X),apply(apply(
% apply(b,combinator),m),
% apply(X,X))) ->
% (false) is composed into [153]
% (eq)(apply(apply(apply(apply(apply(b,b),m),X),m),X),
% apply(apply(apply(b,combinator),m),apply(X,X)))
% -> (true)
% Rule [152]
% (eq)(apply(apply(apply(apply(apply(m,b),X),Y),X),Y),apply(apply(
% apply(b,combinator),m),
% apply(X,Y))) ->
% (false) is composed into [152]
% (eq)(apply(apply(apply(apply(apply(m,b),X),Y),X),Y),
% apply(apply(apply(b,combinator),m),apply(X,Y)))
% -> (true)
% Rule [151]
% (eq)(apply(apply(apply(apply(apply(b,b),X),X),X),X),apply(apply(
% apply(b,combinator),m),
% apply(m,X))) ->
% (false) is composed into [151]
% (eq)(apply(apply(apply(apply(apply(b,b),X),X),X),X),
% apply(apply(apply(b,combinator),m),apply(m,X)))
% -> (true)
% Rule [150]
% (eq)(apply(apply(X,X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),Y))
% -> (false) is composed into [150]
% (eq)(apply(apply(X,X),Y),apply(apply(
% apply(
% apply(
% apply(
% apply(b,b),b),combinator),m),X),Y))
% -> (true)
% Rule [149]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(m,b),b),combinator),X),Y),Z))
% -> (false) is composed into [149]
% (eq)(apply(apply(X,Y),Z),apply(apply(
% apply(
% apply(
% apply(
% apply(m,b),b),combinator),X),Y),Z))
% -> (true)
% Rule [148]
% (eq)(apply(apply(m,X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),X),Y))
% -> (false) is composed into [148]
% (eq)(apply(apply(m,X),Y),apply(apply(
% apply(
% apply(
% apply(
% apply(b,b),b),combinator),X),X),Y))
% -> (true)
% Rule [147]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),c),b),X),Y),combinator),
% apply(apply(m,apply(b,combinator)),apply(X,Y))) -> (false) is composed into 
% [147]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),c),b),X),Y),combinator),
% apply(apply(m,apply(b,combinator)),apply(X,Y))) -> (true)
% Rule [146]
% (eq)(apply(apply(apply(c,b),apply(X,Y)),combinator),apply(apply(
% apply(
% apply(
% apply(b,b),m),
% apply(b,combinator)),X),Y))
% -> (false) is composed into [146]
% (eq)(apply(apply(apply(c,b),apply(X,Y)),combinator),
% apply(apply(apply(apply(apply(b,b),m),
% apply(b,combinator)),X),Y)) ->
% (true)
% Rule [145]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(c,X)),Z),Y)) -> (false) is composed into 
% [145]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(c,X)),Z),Y)) -> (true)
% Rule [144]
% (eq)(apply(apply(apply(apply(b,X),Y),Z),V_3),apply(apply(apply(b,combinator),
% apply(apply(c,X),V_3)),
% apply(Y,Z))) -> (false) is composed into 
% [144]
% (eq)(apply(apply(apply(apply(b,X),Y),Z),V_3),apply(apply(apply(b,combinator),
% apply(apply(c,X),V_3)),
% apply(Y,Z))) -> (true)
% Rule [143]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(b,c),b),combinator),Y),
% apply(apply(c,X),Z))) -> (false) is composed into 
% [143]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(b,c),b),combinator),Y),
% apply(apply(c,X),Z))) -> (true)
% Rule [142]
% (eq)(apply(apply(apply(c,X),Y),apply(Z,V_3)),apply(apply(apply(b,combinator),
% apply(apply(apply(b,X),Z),V_3)),Y))
% -> (false) is composed into [142]
% (eq)(apply(apply(apply(c,X),Y),apply(Z,V_3)),
% apply(apply(apply(b,combinator),apply(
% apply(
% apply(b,X),Z),V_3)),Y))
% -> (true)
% Rule [141]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(apply(b,b),c),b),X),Y),combinator),Z))
% -> (false) is composed into [141]
% (eq)(apply(apply(X,Y),Z),apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(b,b),c),b),X),Y),combinator),Z))
% -> (true)
% Rule [140]
% (eq)(apply(X,apply(apply(apply(c,Y),Z),V_3)),apply(apply(apply(b,combinator),
% apply(apply(b,X),
% apply(Y,V_3))),Z)) ->
% (false) is composed into [140]
% (eq)(apply(X,apply(apply(apply(c,Y),Z),V_3)),
% apply(apply(apply(b,combinator),apply(apply(b,X),
% apply(Y,V_3))),Z))
% -> (true)
% Rule [139]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(b,c),b),combinator),Z),
% apply(apply(b,X),Y))) -> (false) is composed into 
% [139]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(b,c),b),combinator),Z),
% apply(apply(b,X),Y))) -> (true)
% Rule [138]
% (eq)(apply(X,apply(apply(apply(b,Y),Z),V_3)),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),
% apply(Z,V_3))) -> (false) is composed into 
% [138]
% (eq)(apply(X,apply(apply(apply(b,Y),Z),V_3)),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),
% apply(Z,V_3))) -> (true)
% Rule [137]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),Y),Z)) -> (false) is composed into 
% [137]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),Y),Z)) -> (true)
% Rule [136]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(b,combinator),apply(apply(
% apply(
% apply(b,b),X),Y),X)),Y))
% -> (false) is composed into [136]
% (eq)(apply(m,apply(X,Y)),apply(apply(
% apply(b,combinator),
% apply(
% apply(
% apply(
% apply(b,b),X),Y),X)),Y))
% -> (true)
% Rule [135]
% (eq)(apply(apply(apply(b,X),apply(Y,Z)),V_3),apply(apply(apply(b,combinator),X),
% apply(apply(apply(c,Y),V_3),Z)))
% -> (false) is composed into [135]
% (eq)(apply(apply(apply(b,X),apply(Y,Z)),V_3),
% apply(apply(apply(b,combinator),X),apply(
% apply(
% apply(c,Y),V_3),Z)))
% -> (true)
% Rule [134]
% (eq)(apply(apply(apply(b,X),Y),apply(Z,V_3)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(b,Y),Z),V_3)))
% -> (false) is composed into [134]
% (eq)(apply(apply(apply(b,X),Y),apply(Z,V_3)),
% apply(apply(apply(b,combinator),X),apply(
% apply(
% apply(b,Y),Z),V_3)))
% -> (true)
% Rule [133]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),m),apply(b,combinator)),
% apply(apply(apply(b,m),m),apply(b,combinator))) -> (false) is composed into 
% [133]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),m),apply(b,combinator)),
% apply(apply(apply(b,m),m),apply(b,combinator))) -> (true)
% Rule [132]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),
% apply(X,Y)),X),Y)) -> (false) is composed into 
% [132]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),
% apply(X,Y)),X),Y)) -> (true)
% Rule [131]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(X,Y))) -> (false) is composed into 
% [131]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(X,Y))) -> (true)
% Rule [130]
% (eq)(apply(apply(apply(apply(apply(b,c),m),b),b),apply(b,combinator)),
% apply(m,apply(apply(b,combinator),b))) -> (false) is composed into 
% [130]
% (eq)(apply(apply(apply(apply(apply(b,c),m),b),b),apply(b,combinator)),
% apply(m,apply(apply(b,combinator),b))) -> (true)
% Rule [129]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),m),b),b),combinator),b),
% apply(m,apply(apply(b,combinator),b))) -> (false) is composed into 
% [129]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),m),b),b),combinator),b),
% apply(m,apply(apply(b,combinator),b))) -> (true)
% Rule [128]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),apply(
% apply(
% apply(c,m),
% apply(X,Y)),
% apply(b,combinator)))
% -> (false) is composed into [128]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(apply(apply(c,m),apply(X,Y)),apply(b,combinator)))
% -> (true)
% Rule [127]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),apply(
% apply(
% apply(
% apply(b,m),b),combinator),
% apply(X,Y)))
% -> (false) is composed into [127]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(apply(apply(apply(b,m),b),combinator),
% apply(X,Y))) -> (true)
% Rule [126]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),m),Y))
% -> (false) is composed into [126]
% (eq)(apply(X,apply(Y,Y)),apply(apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),m),Y))
% -> (true)
% Rule [125]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),Y),Y))
% -> (false) is composed into [125]
% (eq)(apply(X,apply(m,Y)),apply(apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),Y),Y))
% -> (true)
% Rule [124]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(m,b),apply(b,combinator)),X),Y),Z))
% -> (false) is composed into [124]
% (eq)(apply(X,apply(Y,Z)),apply(apply(
% apply(
% apply(
% apply(m,b),
% apply(b,combinator)),X),Y),Z))
% -> (true)
% Rule [123]
% (eq)(apply(apply(apply(apply(c,m),apply(b,combinator)),b),b),apply(m,
% apply(
% apply(b,combinator),b)))
% -> (false) is composed into [123]
% (eq)(apply(apply(apply(apply(c,m),apply(b,combinator)),b),b),
% apply(m,apply(apply(b,combinator),b))) ->
% (true)
% Rule [122]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),apply(m,apply(
% apply(
% apply(c,b),b),combinator)))
% -> (false) is composed into [122]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),
% apply(m,apply(apply(apply(c,b),b),combinator)))
% -> (true)
% Rule [121]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),apply(apply(
% apply(b,m),
% apply(b,combinator)),b))
% -> (false) is composed into [121]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),
% apply(apply(apply(b,m),apply(b,combinator)),b))
% -> (true)
% Rule [120]
% (eq)(apply(apply(apply(apply(b,m),b),combinator),combinator),apply(m,
% apply(
% apply(b,combinator),combinator)))
% -> (false) is composed into [120]
% (eq)(apply(apply(apply(apply(b,m),b),combinator),combinator),
% apply(m,apply(apply(b,combinator),combinator)))
% -> (true)
% Rule [119]
% (eq)(apply(apply(m,apply(b,combinator)),combinator),apply(apply(
% apply(b,m),
% apply(b,combinator)),combinator))
% -> (false) is composed into [119]
% (eq)(apply(apply(m,apply(b,combinator)),combinator),
% apply(apply(apply(b,m),apply(b,combinator)),combinator))
% -> (true)
% Rule [118]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(apply(b,c),c),m),
% apply(b,combinator)),X)) ->
% (false) is composed into [118]
% (eq)(apply(apply(b,combinator),X),apply(
% apply(
% apply(
% apply(
% apply(b,c),c),m),
% apply(b,combinator)),X))
% -> (true)
% Rule [117]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(c,c),X),m),
% apply(b,combinator))) -> (false) is composed into 
% [117]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(c,c),X),m),
% apply(b,combinator))) -> (true)
% Rule [116]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(apply(b,b),
% apply(c,m)),X),b),combinator))
% -> (false) is composed into [116]
% (eq)(apply(apply(b,combinator),X),apply(
% apply(
% apply(
% apply(
% apply(b,b),
% apply(c,m)),X),b),combinator))
% -> (true)
% Rule [115]
% (eq)(apply(apply(b,combinator),apply(c,m)),apply(apply(apply(apply(b,m),c),m),
% apply(b,combinator))) ->
% (false) is composed into [115]
% (eq)(apply(apply(b,combinator),apply(c,m)),
% apply(apply(apply(apply(b,m),c),m),apply(b,combinator)))
% -> (true)
% Rule [114]
% (eq)(apply(apply(apply(apply(apply(b,c),c),b),combinator),X),apply(
% apply(m,
% apply(b,combinator)),X))
% -> (false) is composed into [114]
% (eq)(apply(apply(apply(apply(apply(b,c),c),b),combinator),X),
% apply(apply(m,apply(b,combinator)),X)) ->
% (true)
% Rule [113]
% (eq)(apply(apply(apply(c,b),X),combinator),apply(apply(apply(c,m),X),
% apply(b,combinator))) ->
% (false) is composed into [113]
% (eq)(apply(apply(apply(c,b),X),combinator),
% apply(apply(apply(c,m),X),apply(b,combinator)))
% -> (true)
% Rule [112]
% (eq)(apply(apply(m,apply(c,b)),combinator),apply(apply(m,apply(b,combinator)),
% apply(c,b))) -> (false) is composed into 
% [112]
% (eq)(apply(apply(m,apply(c,b)),combinator),apply(apply(m,apply(b,combinator)),
% apply(c,b))) -> (true)
% Rule [111]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(apply(b,c),
% apply(b,m)),b),X),combinator))
% -> (false) is composed into [111]
% (eq)(apply(apply(b,combinator),X),apply(
% apply(
% apply(
% apply(
% apply(b,c),
% apply(b,m)),b),X),combinator))
% -> (true)
% Rule [110]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(apply(
% apply(b,c),b),m),combinator),b),X))
% -> (false) is composed into [110]
% (eq)(apply(apply(b,combinator),X),apply(
% apply(
% apply(
% apply(
% apply(
% apply(b,c),b),m),combinator),b),X))
% -> (true)
% Rule [109]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(apply(c,b),b),m),combinator),X))
% -> (false) is composed into [109]
% (eq)(apply(apply(b,combinator),X),apply(
% apply(
% apply(
% apply(
% apply(c,b),b),m),combinator),X))
% -> (true)
% Rule [108]
% (eq)(apply(apply(apply(c,b),X),combinator),apply(apply(apply(apply(b,m),b),combinator),X))
% -> (false) is composed into [108]
% (eq)(apply(apply(apply(c,b),X),combinator),
% apply(apply(apply(apply(b,m),b),combinator),X))
% -> (true)
% Rule [107]
% (eq)(apply(apply(apply(apply(apply(b,c),b),m),X),Y),apply(apply(
% apply(b,combinator),
% apply(Y,X)),
% apply(Y,X))) ->
% (false) is composed into [107]
% (eq)(apply(apply(apply(apply(apply(b,c),b),m),X),Y),
% apply(apply(apply(b,combinator),apply(Y,X)),
% apply(Y,X))) -> (true)
% Rule [106]
% (eq)(apply(apply(apply(apply(c,b),X),m),Y),apply(apply(apply(b,combinator),
% apply(X,Y)),apply(X,Y)))
% -> (false) is composed into [106]
% (eq)(apply(apply(apply(apply(c,b),X),m),Y),
% apply(apply(apply(b,combinator),apply(X,Y)),
% apply(X,Y))) -> (true)
% Rule [105]
% (eq)(apply(X,X),apply(apply(apply(apply(apply(apply(apply(b,c),b),c),combinator),b),X),m))
% -> (false) is composed into [105]
% (eq)(apply(X,X),apply(apply(apply(apply(
% apply(
% apply(
% apply(b,c),b),c),combinator),b),X),m))
% -> (true)
% Rule [104]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(apply(
% apply(
% apply(c,b),m),combinator),
% apply(X,Y))) ->
% (false) is composed into [104]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(apply(apply(apply(c,b),m),combinator),
% apply(X,Y))) -> (true)
% Rule [103]
% (eq)(apply(m,X),apply(apply(apply(apply(apply(apply(apply(b,c),b),c),combinator),b),X),X))
% -> (false) is composed into [103]
% (eq)(apply(m,X),apply(apply(apply(apply(
% apply(
% apply(
% apply(b,c),b),c),combinator),b),X),X))
% -> (true)
% Rule [102]
% (eq)(apply(apply(apply(b,m),X),Y),apply(apply(apply(apply(c,b),apply(X,Y)),combinator),
% apply(X,Y))) -> (false) is composed into 
% [102]
% (eq)(apply(apply(apply(b,m),X),Y),apply(apply(apply(apply(c,b),apply(X,Y)),combinator),
% apply(X,Y))) -> (true)
% Rule [101]
% (eq)(apply(apply(apply(b,m),X),Y),apply(combinator,apply(apply(apply(
% apply(
% apply(b,b),X),Y),X),Y)))
% -> (false) is composed into [101]
% (eq)(apply(apply(apply(b,m),X),Y),apply(combinator,
% apply(
% apply(
% apply(
% apply(
% apply(b,b),X),Y),X),Y)))
% -> (true)
% Rule [100]
% (eq)(apply(apply(apply(b,m),m),X),apply(apply(apply(b,combinator),
% apply(X,X)),apply(m,X))) ->
% (false) is composed into [100]
% (eq)(apply(apply(apply(b,m),m),X),apply(
% apply(
% apply(b,combinator),
% apply(X,X)),
% apply(m,X)))
% -> (true)
% Rule [99]
% (eq)(apply(apply(apply(b,m),m),X),apply(apply(apply(b,combinator),
% apply(m,X)),apply(X,X))) ->
% (false) is composed into [99]
% (eq)(apply(apply(apply(b,m),m),X),apply(
% apply(
% apply(b,combinator),
% apply(m,X)),
% apply(X,X)))
% -> (true)
% Rule [98]
% (eq)(apply(apply(apply(b,m),X),X),apply(apply(apply(b,combinator),
% apply(X,X)),apply(m,X))) ->
% (false) is composed into [98]
% (eq)(apply(apply(apply(b,m),X),X),apply(
% apply(
% apply(b,combinator),
% apply(X,X)),
% apply(m,X)))
% -> (true)
% Rule [97]
% (eq)(apply(apply(apply(b,m),X),X),apply(apply(apply(b,combinator),
% apply(m,X)),apply(X,X))) ->
% (false) is composed into [97]
% (eq)(apply(apply(apply(b,m),X),X),apply(
% apply(
% apply(b,combinator),
% apply(m,X)),
% apply(X,X)))
% -> (true)
% Rule [96]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(combinator,
% apply(apply(
% apply(b,m),X),Y)))
% -> (false) is composed into [96]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(combinator,apply(apply(apply(b,m),X),Y)))
% -> (true)
% Rule [95]
% (eq)(apply(X,X),apply(apply(apply(apply(apply(apply(b,c),c),b),combinator),m),X))
% -> (false) is composed into [95]
% (eq)(apply(X,X),apply(apply(apply(apply(
% apply(
% apply(b,c),c),b),combinator),m),X))
% -> (true)
% Rule [94]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(combinator,
% apply(m,apply(X,Y))))
% -> (false) is composed into [94]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(combinator,apply(m,apply(X,Y)))) ->
% (true)
% Rule [93]
% (eq)(apply(m,apply(X,Y)),apply(combinator,apply(apply(apply(apply(
% apply(b,b),X),Y),X),Y)))
% -> (false) is composed into [93]
% (eq)(apply(m,apply(X,Y)),apply(combinator,
% apply(apply(
% apply(
% apply(
% apply(b,b),X),Y),X),Y)))
% -> (true)
% Rule [92]
% (eq)(apply(m,X),apply(apply(apply(apply(apply(apply(b,c),c),b),combinator),X),X))
% -> (false) is composed into [92]
% (eq)(apply(m,X),apply(apply(apply(apply(
% apply(
% apply(b,c),c),b),combinator),X),X))
% -> (true)
% Rule [91]
% (eq)(apply(m,apply(c,b)),apply(apply(apply(m,apply(c,b)),combinator),
% apply(c,b))) -> (false) is composed into 
% [91]
% (eq)(apply(m,apply(c,b)),apply(apply(apply(m,apply(c,b)),combinator),
% apply(c,b))) -> (true)
% Rule [90]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(b,combinator),apply(apply(
% apply(c,c),Z),X)),Y))
% -> (false) is composed into [90]
% (eq)(apply(apply(X,Y),Z),apply(apply(
% apply(b,combinator),
% apply(
% apply(
% apply(c,c),Z),X)),Y))
% -> (true)
% Rule [89]
% (eq)(apply(apply(X,Y),Z),apply(combinator,apply(apply(apply(c,X),Z),Y)))
% -> (false) is composed into [89]
% (eq)(apply(apply(X,Y),Z),apply(combinator,
% apply(apply(
% apply(c,X),Z),Y)))
% -> (true)
% Rule [88]
% (eq)(apply(X,Y),apply(apply(apply(apply(apply(apply(apply(b,c),b),c),combinator),b),Y),X))
% -> (false) is composed into [88]
% (eq)(apply(X,Y),apply(apply(apply(apply(
% apply(
% apply(
% apply(b,c),b),c),combinator),b),Y),X))
% -> (true)
% Rule [87]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(apply(apply(apply(apply(b,c),b),combinator),Y),
% apply(X,Z))) -> (false) is composed into 
% [87]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(apply(apply(apply(apply(b,c),b),combinator),Y),
% apply(X,Z))) -> (true)
% Rule [86]
% (eq)(apply(apply(apply(apply(apply(b,c),b),combinator),X),X),apply(m,
% apply(
% apply(
% apply(
% apply(b,c),b),combinator),X)))
% -> (false) is composed into [86]
% (eq)(apply(apply(apply(apply(apply(b,c),b),combinator),X),X),
% apply(m,apply(apply(apply(apply(b,c),b),combinator),X)))
% -> (true)
% Rule [85]
% (eq)(apply(apply(apply(apply(apply(b,c),X),Y),Z),V_3),apply(apply(
% apply(b,combinator),
% apply(
% apply(X,Y),V_3)),Z))
% -> (false) is composed into [85]
% (eq)(apply(apply(apply(apply(apply(b,c),X),Y),Z),V_3),
% apply(apply(apply(b,combinator),apply(
% apply(X,Y),V_3)),Z))
% -> (true)
% Rule [84]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(apply(apply(apply(apply(
% apply(b,b),b),combinator),X),Z),Y))
% -> (false) is composed into [84]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(
% apply(
% apply(
% apply(
% apply(
% apply(b,b),b),combinator),X),Z),Y))
% -> (true)
% Rule [83]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(b,combinator),apply(apply(c,X),
% apply(X,Y))),Y))
% -> (false) is composed into [83]
% (eq)(apply(m,apply(X,Y)),apply(apply(
% apply(b,combinator),
% apply(
% apply(c,X),
% apply(X,Y))),Y))
% -> (true)
% Rule [82]
% (eq)(apply(apply(X,Y),apply(c,X)),apply(apply(apply(b,combinator),
% apply(m,apply(c,X))),Y)) ->
% (false) is composed into [82]
% (eq)(apply(apply(X,Y),apply(c,X)),apply(
% apply(
% apply(b,combinator),
% apply(m,
% apply(c,X))),Y))
% -> (true)
% Rule [81]
% (eq)(apply(apply(X,X),Y),apply(apply(apply(b,combinator),apply(apply(c,m),Y)),X))
% -> (false) is composed into [81]
% (eq)(apply(apply(X,X),Y),apply(apply(
% apply(b,combinator),
% apply(
% apply(c,m),Y)),X))
% -> (true)
% Rule [80]
% (eq)(apply(apply(m,X),Y),apply(apply(apply(b,combinator),apply(apply(c,X),Y)),X))
% -> (false) is composed into [80]
% (eq)(apply(apply(m,X),Y),apply(apply(
% apply(b,combinator),
% apply(
% apply(c,X),Y)),X))
% -> (true)
% Rule [79]
% (eq)(apply(apply(c,X),Y),apply(apply(apply(b,combinator),apply(apply(m,c),Y)),X))
% -> (false) is composed into [79]
% (eq)(apply(apply(c,X),Y),apply(apply(
% apply(b,combinator),
% apply(
% apply(m,c),Y)),X))
% -> (true)
% Rule [78]
% (eq)(apply(m,apply(b,combinator)),apply(apply(apply(apply(apply(b,b),m),
% apply(b,combinator)),b),combinator))
% -> (false) is composed into [78]
% (eq)(apply(m,apply(b,combinator)),apply(
% apply(
% apply(
% apply(
% apply(b,b),m),
% apply(b,combinator)),b),combinator))
% -> (true)
% Rule [77]
% (eq)(apply(m,apply(b,combinator)),apply(apply(apply(apply(b,m),b),combinator),
% apply(b,combinator))) -> (false) is composed into 
% [77]
% (eq)(apply(m,apply(b,combinator)),apply(apply(apply(apply(b,m),b),combinator),
% apply(b,combinator))) -> (true)
% Rule [76]
% (eq)(apply(apply(apply(b,m),b),combinator),apply(apply(m,apply(b,combinator)),
% apply(b,combinator))) ->
% (false) is composed into [76]
% (eq)(apply(apply(apply(b,m),b),combinator),
% apply(apply(m,apply(b,combinator)),apply(b,combinator)))
% -> (true)
% Rule [75]
% (eq)(apply(X,apply(apply(apply(b,c),b),combinator)),apply(apply(m,
% apply(
% apply(
% apply(b,c),b),combinator)),X))
% -> (false) is composed into [75]
% (eq)(apply(X,apply(apply(apply(b,c),b),combinator)),
% apply(apply(m,apply(apply(apply(b,c),b),combinator)),X))
% -> (true)
% Rule [74]
% (eq)(apply(apply(apply(apply(apply(b,c),c),X),Y),Z),apply(apply(
% apply(b,combinator),
% apply(X,Y)),Z))
% -> (false) is composed into [74]
% (eq)(apply(apply(apply(apply(apply(b,c),c),X),Y),Z),
% apply(apply(apply(b,combinator),apply(X,Y)),Z))
% -> (true)
% Rule [73]
% (eq)(apply(apply(apply(apply(c,c),X),Y),Z),apply(apply(apply(b,combinator),
% apply(Y,Z)),X)) ->
% (false) is composed into [73]
% (eq)(apply(apply(apply(apply(c,c),X),Y),Z),
% apply(apply(apply(b,combinator),apply(Y,Z)),X))
% -> (true)
% Rule [72]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(combinator,apply(apply(X,Z),Y)))
% -> (false) is composed into [72]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(combinator,
% apply(
% apply(X,Z),Y)))
% -> (true)
% Rule [71]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(c,b),apply(apply(c,X),Z)),combinator),Y))
% -> (false) is composed into [71]
% (eq)(apply(apply(X,Y),Z),apply(apply(
% apply(
% apply(c,b),
% apply(
% apply(c,X),Z)),combinator),Y))
% -> (true)
% Rule [70]
% (eq)(apply(apply(m,apply(c,X)),Y),apply(apply(apply(b,combinator),
% apply(X,Y)),apply(c,X))) ->
% (false) is composed into [70]
% (eq)(apply(apply(m,apply(c,X)),Y),apply(
% apply(
% apply(b,combinator),
% apply(X,Y)),
% apply(c,X)))
% -> (true)
% Rule [69]
% (eq)(apply(apply(apply(c,m),X),Y),apply(apply(apply(b,combinator),
% apply(Y,Y)),X)) -> (false) is composed into 
% [69]
% (eq)(apply(apply(apply(c,m),X),Y),apply(apply(apply(b,combinator),apply(Y,Y)),X))
% -> (true)
% Rule [68]
% (eq)(apply(apply(apply(m,c),X),Y),apply(apply(apply(b,combinator),
% apply(c,Y)),X)) -> (false) is composed into 
% [68]
% (eq)(apply(apply(apply(m,c),X),Y),apply(apply(apply(b,combinator),apply(c,Y)),X))
% -> (true)
% Rule [67]
% (eq)(apply(apply(apply(c,X),Y),X),apply(apply(apply(b,combinator),
% apply(m,X)),Y)) -> (false) is composed into 
% [67]
% (eq)(apply(apply(apply(c,X),Y),X),apply(apply(apply(b,combinator),apply(m,X)),Y))
% -> (true)
% Rule [66]
% (eq)(apply(X,Y),apply(apply(apply(apply(apply(apply(b,c),c),b),combinator),X),Y))
% -> (false) is composed into [66]
% (eq)(apply(X,Y),apply(apply(apply(apply(
% apply(
% apply(b,c),c),b),combinator),X),Y))
% -> (true)
% Rule [65]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(apply(apply(apply(c,b),apply(X,Z)),combinator),Y))
% -> (false) is composed into [65]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(
% apply(
% apply(
% apply(c,b),
% apply(X,Z)),combinator),Y))
% -> (true)
% Rule [64]
% (eq)(apply(apply(c,b),X),apply(apply(apply(m,apply(c,b)),combinator),X))
% -> (false) is composed into [64]
% (eq)(apply(apply(c,b),X),apply(apply(
% apply(m,
% apply(c,b)),combinator),X))
% -> (true)
% Rule [63]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(c,b),apply(apply(b,X),Y)),combinator),Z))
% -> (false) is composed into [63]
% (eq)(apply(X,apply(Y,Z)),apply(apply(
% apply(
% apply(c,b),
% apply(
% apply(b,X),Y)),combinator),Z))
% -> (true)
% Rule [62]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(b,combinator),apply(apply(
% apply(c,b),Y),X)),Z))
% -> (false) is composed into [62]
% (eq)(apply(X,apply(Y,Z)),apply(apply(
% apply(b,combinator),
% apply(
% apply(
% apply(c,b),Y),X)),Z))
% -> (true)
% Rule [61]
% (eq)(apply(X,apply(Y,Z)),apply(combinator,apply(apply(apply(b,X),Y),Z)))
% -> (false) is composed into [61]
% (eq)(apply(X,apply(Y,Z)),apply(combinator,
% apply(apply(
% apply(b,X),Y),Z)))
% -> (true)
% Rule [60]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,m),X)),Y))
% -> (false) is composed into [60]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(apply(apply(b,combinator),apply(
% apply(b,m),X)),Y))
% -> (true)
% Rule [59]
% (eq)(apply(apply(apply(b,X),apply(apply(c,Y),Z)),V_3),apply(apply(
% apply(b,combinator),X),
% apply(apply(Y,V_3),Z)))
% -> (false) is composed into [59]
% (eq)(apply(apply(apply(b,X),apply(apply(c,Y),Z)),V_3),
% apply(apply(apply(b,combinator),X),apply(
% apply(Y,V_3),Z)))
% -> (true)
% Rule [58]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(apply(apply(b,c),b),combinator),
% apply(Y,Z)),X)) -> (false) is composed into 
% [58]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(apply(apply(b,c),b),combinator),
% apply(Y,Z)),X)) -> (true)
% Rule [57]
% (eq)(apply(apply(apply(b,X),apply(apply(b,Y),Z)),V_3),apply(apply(
% apply(b,combinator),X),
% apply(Y,apply(Z,V_3))))
% -> (false) is composed into [57]
% (eq)(apply(apply(apply(b,X),apply(apply(b,Y),Z)),V_3),
% apply(apply(apply(b,combinator),X),apply(Y,
% apply(Z,V_3))))
% -> (true)
% Rule [56]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Z),V_3),apply(apply(
% apply(b,combinator),
% apply(X,Y)),
% apply(Z,V_3))) ->
% (false) is composed into [56]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Z),V_3),
% apply(apply(apply(b,combinator),apply(X,Y)),
% apply(Z,V_3))) -> (true)
% Rule [55]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),X),Y),Z))
% -> (false) is composed into [55]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(
% apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),Y),Z))
% -> (true)
% Rule [54]
% (eq)(apply(apply(apply(apply(apply(b,c),b),X),X),apply(b,combinator)),
% apply(m,apply(apply(b,combinator),X))) -> (false) is composed into 
% [54]
% (eq)(apply(apply(apply(apply(apply(b,c),b),X),X),apply(b,combinator)),
% apply(m,apply(apply(b,combinator),X))) -> (true)
% Rule [53]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),b),combinator),X),
% apply(m,apply(apply(b,combinator),X))) -> (false) is composed into 
% [53]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),b),combinator),X),
% apply(m,apply(apply(b,combinator),X))) -> (true)
% Rule [52]
% (eq)(apply(apply(b,combinator),apply(X,Y)),apply(apply(apply(apply(
% apply(b,b),m),
% apply(b,combinator)),X),Y))
% -> (false) is composed into [52]
% (eq)(apply(apply(b,combinator),apply(X,Y)),
% apply(apply(apply(apply(apply(b,b),m),
% apply(b,combinator)),X),Y)) ->
% (true)
% Rule [51]
% (eq)(apply(apply(apply(b,b),X),Y),apply(apply(apply(b,combinator),
% apply(apply(m,b),X)),Y)) ->
% (false) is composed into [51]
% (eq)(apply(apply(apply(b,b),X),Y),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(m,b),X)),Y))
% -> (true)
% Rule [50]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(b,combinator),apply(apply(b,X),m)),Y))
% -> (false) is composed into [50]
% (eq)(apply(X,apply(Y,Y)),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,X),m)),Y))
% -> (true)
% Rule [49]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(b,combinator),apply(apply(b,X),Y)),Y))
% -> (false) is composed into [49]
% (eq)(apply(X,apply(m,Y)),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,X),Y)),Y))
% -> (true)
% Rule [48]
% (eq)(apply(apply(apply(apply(apply(b,c),b),X),Y),Z),apply(apply(
% apply(b,combinator),X),
% apply(Z,Y))) ->
% (false) is composed into [48]
% (eq)(apply(apply(apply(apply(apply(b,c),b),X),Y),Z),
% apply(apply(apply(b,combinator),X),apply(Z,Y)))
% -> (true)
% Rule [47]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(apply(c,b),X),combinator),
% apply(Y,Z))) -> (false) is composed into 
% [47]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(apply(c,b),X),combinator),
% apply(Y,Z))) -> (true)
% Rule [46]
% (eq)(apply(apply(apply(apply(c,b),X),Y),Z),apply(apply(apply(b,combinator),Y),
% apply(X,Z))) -> (false) is composed into 
% [46]
% (eq)(apply(apply(apply(apply(c,b),X),Y),Z),apply(apply(apply(b,combinator),Y),
% apply(X,Z))) -> (true)
% Rule [45]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(combinator,apply(X,apply(Y,Z))))
% -> (false) is composed into [45]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(combinator,
% apply(X,
% apply(Y,Z))))
% -> (true)
% Rule [44]
% (eq)(apply(apply(m,apply(b,X)),Y),apply(apply(apply(b,combinator),X),
% apply(apply(b,X),Y))) -> (false) is composed into 
% [44]
% (eq)(apply(apply(m,apply(b,X)),Y),apply(apply(apply(b,combinator),X),
% apply(apply(b,X),Y))) -> (true)
% Rule [43]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(b,combinator),X),
% apply(Y,Y))) -> (false) is composed into 
% [43]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(b,combinator),X),
% apply(Y,Y))) -> (true)
% Rule [42]
% (eq)(apply(apply(apply(m,b),X),Y),apply(apply(apply(b,combinator),b),
% apply(X,Y))) -> (false) is composed into 
% [42]
% (eq)(apply(apply(apply(m,b),X),Y),apply(apply(apply(b,combinator),b),
% apply(X,Y))) -> (true)
% Rule [41]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(b,combinator),X),
% apply(m,Y))) -> (false) is composed into 
% [41]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(b,combinator),X),
% apply(m,Y))) -> (true)
% Rule [40]
% (eq)(apply(apply(apply(apply(c,b),apply(b,combinator)),X),X),apply(m,
% apply(
% apply(b,combinator),X)))
% -> (false) is composed into [40]
% (eq)(apply(apply(apply(apply(c,b),apply(b,combinator)),X),X),
% apply(m,apply(apply(b,combinator),X))) ->
% (true)
% Rule [39]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(m,apply(
% apply(
% apply(c,b),X),combinator)))
% -> (false) is composed into [39]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),
% apply(m,apply(apply(apply(c,b),X),combinator)))
% -> (true)
% Rule [38]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(apply(
% apply(b,m),
% apply(b,combinator)),X))
% -> (false) is composed into [38]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),
% apply(apply(apply(b,m),apply(b,combinator)),X))
% -> (true)
% Rule [37]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),apply(
% apply(m,
% apply(b,combinator)),
% apply(X,Y)))
% -> (false) is composed into [37]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(apply(m,apply(b,combinator)),apply(X,Y)))
% -> (true)
% Rule [36]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(apply(
% apply(b,combinator),m),
% apply(X,Y))) ->
% (false) is composed into [36]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(apply(apply(b,combinator),m),apply(X,Y)))
% -> (true)
% Rule [35]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),Z))
% -> (false) is composed into [35]
% (eq)(apply(apply(X,Y),Z),apply(apply(
% apply(
% apply(
% apply(
% apply(b,b),b),combinator),X),Y),Z))
% -> (true)
% Rule [34]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),Y),Z))
% -> (false) is composed into [34]
% (eq)(apply(X,apply(Y,Z)),apply(apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),Y),Z))
% -> (true)
% Rule [33]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),apply(m,apply(
% apply(b,combinator),b)))
% -> (false) is composed into [33]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),
% apply(m,apply(apply(b,combinator),b))) ->
% (true)
% Rule [32]
% (eq)(apply(apply(m,apply(b,combinator)),combinator),apply(m,apply(
% apply(b,combinator),combinator)))
% -> (false) is composed into [32]
% (eq)(apply(apply(m,apply(b,combinator)),combinator),
% apply(m,apply(apply(b,combinator),combinator)))
% -> (true)
% Rule [31]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(c,m),X),apply(b,combinator)))
% -> (false) is composed into [31]
% (eq)(apply(apply(b,combinator),X),apply(
% apply(
% apply(c,m),X),
% apply(b,combinator)))
% -> (true)
% Rule [30]
% (eq)(apply(apply(apply(c,b),X),combinator),apply(apply(m,apply(b,combinator)),X))
% -> (false) is composed into [30]
% (eq)(apply(apply(apply(c,b),X),combinator),
% apply(apply(m,apply(b,combinator)),X)) ->
% (true)
% Rule [29]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(b,m),b),combinator),X))
% -> (false) is composed into [29]
% (eq)(apply(apply(b,combinator),X),apply(
% apply(
% apply(
% apply(b,m),b),combinator),X))
% -> (true)
% Rule [28]
% (eq)(apply(apply(apply(b,m),X),Y),apply(apply(apply(b,combinator),
% apply(X,Y)),apply(X,Y))) ->
% (false) is composed into [28]
% (eq)(apply(apply(apply(b,m),X),Y),apply(
% apply(
% apply(b,combinator),
% apply(X,Y)),
% apply(X,Y)))
% -> (true)
% Rule [27]
% (eq)(apply(X,X),apply(apply(apply(apply(apply(b,c),b),combinator),X),m))
% -> (false) is composed into [27]
% (eq)(apply(X,X),apply(apply(apply(apply(
% apply(b,c),b),combinator),X),m))
% -> (true)
% Rule [26]
% (eq)(apply(X,X),apply(apply(apply(apply(c,b),m),combinator),X)) ->
% (false) is composed into [26]
% (eq)(apply(X,X),apply(apply(apply(apply(c,b),m),combinator),X))
% -> (true)
% Rule [25] (eq)(apply(X,X),apply(combinator,apply(m,X))) -> (false) is composed into 
% [25] (eq)(apply(X,X),apply(combinator,apply(m,X))) -> (true)
% Rule [24]
% (eq)(apply(m,X),apply(apply(apply(apply(apply(b,c),b),combinator),X),X))
% -> (false) is composed into [24]
% (eq)(apply(m,X),apply(apply(apply(apply(
% apply(b,c),b),combinator),X),X))
% -> (true)
% Rule [23]
% (eq)(apply(m,X),apply(apply(apply(apply(c,b),X),combinator),X)) ->
% (false) is composed into [23]
% (eq)(apply(m,X),apply(apply(apply(apply(c,b),X),combinator),X))
% -> (true)
% Rule [22] (eq)(apply(m,X),apply(combinator,apply(X,X))) -> (false) is composed into 
% [22] (eq)(apply(m,X),apply(combinator,apply(X,X))) -> (true)
% Rule [21]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(b,combinator),apply(apply(c,X),Z)),Y))
% -> (false) is composed into [21]
% (eq)(apply(apply(X,Y),Z),apply(apply(
% apply(b,combinator),
% apply(
% apply(c,X),Z)),Y))
% -> (true)
% Rule [20]
% (eq)(apply(m,apply(b,combinator)),apply(apply(m,apply(b,combinator)),
% apply(b,combinator))) -> (false) is composed into 
% [20]
% (eq)(apply(m,apply(b,combinator)),apply(apply(m,apply(b,combinator)),
% apply(b,combinator))) -> (true)
% Rule [19]
% (eq)(apply(X,Y),apply(apply(apply(apply(apply(b,c),b),combinator),Y),X))
% -> (false) is composed into [19]
% (eq)(apply(X,Y),apply(apply(apply(apply(
% apply(b,c),b),combinator),Y),X))
% -> (true)
% Rule [18]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(apply(apply(b,combinator),
% apply(X,Z)),Y)) -> (false) is composed into 
% [18]
% (eq)(apply(apply(apply(c,X),Y),Z),apply(apply(apply(b,combinator),apply(X,Z)),Y))
% -> (true)
% Rule [17]
% (eq)(apply(X,Y),apply(apply(apply(apply(c,b),X),combinator),Y)) ->
% (false) is composed into [17]
% (eq)(apply(X,Y),apply(apply(apply(apply(c,b),X),combinator),Y))
% -> (true)
% Rule [16]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(b,combinator),apply(apply(b,X),Y)),Z))
% -> (false) is composed into [16]
% (eq)(apply(X,apply(Y,Z)),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,X),Y)),Z))
% -> (true)
% Rule [15]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(b,combinator),X),
% apply(Y,Z))) -> (false) is composed into 
% [15]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(b,combinator),X),
% apply(Y,Z))) -> (true)
% Rule [14]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(m,apply(
% apply(b,combinator),X)))
% -> (false) is composed into [14]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),
% apply(m,apply(apply(b,combinator),X))) ->
% (true)
% Rule [13]
% (eq)(apply(apply(b,combinator),X),apply(apply(m,apply(b,combinator)),X))
% -> (false) is composed into [13]
% (eq)(apply(apply(b,combinator),X),apply(
% apply(m,
% apply(b,combinator)),X))
% -> (true)
% Rule [12] (eq)(apply(X,X),apply(apply(apply(b,combinator),m),X)) -> (false) is composed into 
% [12] (eq)(apply(X,X),apply(apply(apply(b,combinator),m),X)) -> (true)
% Rule [11] (eq)(apply(m,X),apply(apply(apply(b,combinator),X),X)) -> (false) is composed into 
% [11] (eq)(apply(m,X),apply(apply(apply(b,combinator),X),X)) -> (true)
% Rule [10] (eq)(apply(X,Y),apply(apply(apply(b,combinator),X),Y)) -> (false) is composed into 
% [10] (eq)(apply(X,Y),apply(apply(apply(b,combinator),X),Y)) -> (true)
% Rule [9] (eq)(combinator,apply(m,combinator)) -> (false) is composed into 
% [9] (eq)(combinator,apply(m,combinator)) -> (true)
% Rule [1] (eq)(Y,apply(combinator,Y)) -> (false) is composed into [1]
% (eq)(Y,
% apply(combinator,Y))
% -> (true)
% New rule produced : [157] (false) -> (true)
% The conjecture has been reduced. 
% Conjecture is now:
% Trivial
% 
% Current number of equations to process: 165
% Current number of ordered equations: 0
% Current number of rules: 157
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% 
% The following 8 rules have been used:
% [1] 
% (eq)(Y,apply(combinator,Y)) -> (false); trace = in the starting set
% [2] (eq)(X,X) -> (true); trace = in the starting set
% [3] apply(X,X) <-> apply(m,X); trace = in the starting set
% [5] apply(X,apply(Y,Z)) <-> apply(apply(apply(b,X),Y),Z); trace = in the starting set
% [10] (eq)(apply(X,Y),apply(apply(apply(b,combinator),X),Y)) -> (false); trace = Cp of 5 and 1
% [14] (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(m,apply(
% apply(b,combinator),X)))
% -> (false); trace = Cp of 10 and 3
% [38] (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(apply(
% apply(b,m),
% apply(b,combinator)),X))
% -> (false); trace = Cp of 14 and 5
% [157] (false) -> (true); trace = Cp of 38 and 2
% % SZS output end Refutation
% All conjectures have been proven
% 
% Execution time: 0.420000 sec
% res : bool = true
% time is now off
% 
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
% 
% EOF
%------------------------------------------------------------------------------