TSTP Solution File: COL045-1 by CiME---2.01
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- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL045-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n037.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 00:19:52 EDT 2014
% Result : Unsatisfiable 1.63s
% Output : Refutation 1.63s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL045-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n037.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 21:09:23 CDT 2014
% % CPUTime : 1.63
% Processing problem /tmp/CiME_38840_n037.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " combinator,m,b,s : constant; apply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z));
% apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z));
% apply(m,X) = apply(X,X);
% ";
%
% let s1 = status F "
% combinator lr_lex;
% m lr_lex;
% b lr_lex;
% apply lr_lex;
% s lr_lex;
% ";
%
% let p1 = precedence F "
% apply > s > b > m > combinator";
%
% let s2 = status F "
% combinator mul;
% m mul;
% b mul;
% apply mul;
% s mul;
% ";
%
% let p2 = precedence F "
% apply > s = b = m = 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(s,X),Y),Z) =
% apply(apply(X,Z),apply(Y,Z)),
% apply(apply(apply(b,X),Y),Z) =
% apply(X,apply(Y,Z)),
% apply(m,X) = apply(X,X) } (3 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
%
% [combinator] = 1;
% [m] = 2;
% [b] = 3;
% [s] = 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),apply(Y,Z)) <-> apply(apply(apply(s,X),Y),Z)
% Current number of equations to process: 9
% Current number of ordered equations: 7
% Current number of rules: 7
% New rule produced :
% [8] apply(apply(apply(s,X),Y),Z) <-> apply(apply(X,Z),apply(Y,Z))
% Current number of equations to process: 9
% Current number of ordered equations: 6
% Current number of rules: 8
% New rule produced : [9] (eq)(combinator,apply(m,combinator)) -> (false)
% Current number of equations to process: 9
% Current number of ordered equations: 5
% 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: 9
% Current number of ordered equations: 4
% Current number of rules: 10
% New rule produced : [11] apply(X,apply(m,Y)) <-> apply(apply(apply(b,X),Y),Y)
% Current number of equations to process: 9
% Current number of ordered equations: 3
% Current number of rules: 11
% New rule produced : [12] apply(apply(apply(b,X),Y),Y) <-> apply(X,apply(m,Y))
% Current number of equations to process: 9
% Current number of ordered equations: 2
% Current number of rules: 12
% New rule produced : [13] apply(X,apply(Y,Y)) <-> apply(apply(apply(b,X),m),Y)
% Current number of equations to process: 9
% Current number of ordered equations: 1
% Current number of rules: 13
% New rule produced : [14] apply(apply(apply(b,X),m),Y) <-> apply(X,apply(Y,Y))
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] apply(m,apply(X,Y)) -> apply(apply(apply(s,X),X),Y)
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16] (eq)(apply(m,X),apply(apply(apply(b,combinator),X),X)) -> (false)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17] (eq)(apply(X,X),apply(apply(apply(b,combinator),m),X)) -> (false)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(s,b),b),combinator),X))
% -> (false)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(b,combinator),X),
% apply(Y,Z))) -> (false)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(b,combinator),apply(apply(b,X),Y)),Z))
% -> (false)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21]
% (eq)(apply(apply(X,combinator),Y),apply(apply(apply(apply(s,b),X),combinator),Y))
% -> (false)
% Rule
% [18]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(s,b),b),combinator),X))
% -> (false) collapsed.
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [22]
% (eq)(apply(apply(apply(s,X),Y),Z),apply(apply(apply(b,combinator),apply(X,Z)),
% apply(Y,Z))) -> (false)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [23]
% (eq)(apply(apply(X,Y),apply(Z,Y)),apply(apply(apply(b,combinator),apply(
% apply(s,X),Z)),Y))
% -> (false)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [24]
% (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: 33
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [25]
% (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: 33
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [26]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(apply(apply(
% apply(
% apply(b,s),b),combinator),
% apply(b,combinator)),X))
% -> (false)
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [27]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(b,combinator),X),
% apply(m,Y))) -> (false)
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [28]
% (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: 45
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [29]
% (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: 45
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [30] (eq)(apply(X,X),apply(combinator,apply(m,X))) -> (false)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [31]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(b,combinator),apply(apply(b,X),Y)),Y))
% -> (false)
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [32]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(b,combinator),X),
% apply(Y,Y))) -> (false)
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [33]
% (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: 69
% Current number of ordered equations: 1
% Current number of rules: 32
% New rule produced :
% [34]
% (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: 69
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [35] (eq)(apply(m,X),apply(combinator,apply(X,X))) -> (false)
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [36]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(b,combinator),apply(apply(b,X),m)),Y))
% -> (false)
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [37]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(b,combinator),m),
% apply(X,Y))) -> (false)
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [38]
% (eq)(apply(apply(apply(s,b),b),combinator),apply(apply(apply(apply(s,b),b),combinator),
% apply(b,combinator))) -> (false)
% Current number of equations to process: 100
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [39]
% (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: 99
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [40]
% (eq)(apply(apply(apply(s,X),X),combinator),apply(apply(apply(apply(s,b),X),combinator),
% apply(X,combinator))) -> (false)
% Rule
% [38]
% (eq)(apply(apply(apply(s,b),b),combinator),apply(apply(apply(apply(s,b),b),combinator),
% apply(b,combinator))) -> (false)
% collapsed.
% Current number of equations to process: 99
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [41]
% (eq)(apply(apply(apply(b,m),m),X),apply(apply(apply(b,combinator),apply(X,X)),
% apply(X,X))) -> (false)
% Current number of equations to process: 104
% Current number of ordered equations: 0
% Current number of rules: 39
% 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: 107
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [43]
% (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: 106
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [44]
% (eq)(apply(apply(apply(apply(s,b),b),X),Y),apply(apply(apply(b,combinator),X),
% apply(apply(b,X),Y))) -> (false)
% Current number of equations to process: 105
% Current number of ordered equations: 0
% Current number of rules: 42
% 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: 112
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [46]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),apply(apply(
% apply(
% apply(s,b),b),combinator),
% apply(X,Y))) ->
% (false)
% Current number of equations to process: 111
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [47]
% (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: 109
% Current number of ordered equations: 1
% Current number of rules: 45
% New rule produced :
% [48]
% (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: 109
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [49]
% (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: 108
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [50]
% (eq)(apply(apply(apply(b,X),Y),X),apply(apply(apply(apply(apply(b,s),b),combinator),Y),X))
% -> (false)
% Rule
% [26]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(apply(apply(
% apply(
% apply(b,s),b),combinator),
% apply(b,combinator)),X))
% -> (false) collapsed.
% Current number of equations to process: 110
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [51]
% (eq)(apply(apply(apply(apply(s,b),X),Y),Z),apply(apply(apply(b,combinator),Y),
% apply(apply(X,Y),Z))) -> (false)
% Rule
% [44]
% (eq)(apply(apply(apply(apply(s,b),b),X),Y),apply(apply(apply(b,combinator),X),
% apply(apply(b,X),Y))) -> (false)
% collapsed.
% Current number of equations to process: 109
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [52]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(b,combinator),X),apply(Y,Y))) ->
% (false)
% Current number of equations to process: 115
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [53]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(b,combinator),X),apply(m,Y))) ->
% (false)
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [54]
% (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: 126
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [55]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),X),Y),Y))
% -> (false)
% Current number of equations to process: 125
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [56]
% (eq)(apply(apply(apply(b,X),apply(apply(b,Y),Z)),Z),apply(apply(apply(b,combinator),X),
% apply(Y,apply(m,Z)))) ->
% (false)
% Current number of equations to process: 124
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [57]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),X),m),Y))
% -> (false)
% Current number of equations to process: 123
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [58]
% (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: 121
% Current number of ordered equations: 1
% Current number of rules: 54
% New rule produced :
% [59]
% (eq)(apply(apply(apply(b,X),apply(apply(b,Y),m)),Z),apply(apply(apply(b,combinator),X),
% apply(Y,apply(Z,Z)))) ->
% (false)
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 55
% 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: 120
% Current number of ordered equations: 0
% Current number of rules: 56
% 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: 126
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [62]
% (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: 125
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [63]
% (eq)(apply(apply(apply(b,X),Y),apply(m,Z)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(b,Y),Z),Z))) ->
% (false)
% Current number of equations to process: 124
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [64]
% (eq)(apply(apply(apply(b,X),Y),apply(Z,Z)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(b,Y),m),Z))) ->
% (false)
% Current number of equations to process: 123
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [65]
% (eq)(apply(apply(apply(b,X),m),apply(Y,Z)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(s,Y),Y),Z))) ->
% (false)
% Current number of equations to process: 122
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [66]
% (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: 62
% New rule produced :
% [67]
% (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: 63
% New rule produced :
% [68]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(b,combinator),apply(
% apply(b,X),m)),Y))
% -> (false)
% Current number of equations to process: 125
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [69]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(b,combinator),apply(
% apply(b,X),Y)),Y))
% -> (false)
% Current number of equations to process: 129
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [70]
% (eq)(apply(apply(m,combinator),X),apply(apply(apply(apply(s,b),combinator),combinator),X))
% -> (false)
% Current number of equations to process: 135
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [71]
% (eq)(apply(apply(combinator,combinator),X),apply(apply(apply(apply(s,b),m),combinator),X))
% -> (false)
% Current number of equations to process: 134
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [72]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(b,combinator),apply(
% apply(b,m),X)),Y))
% -> (false)
% Current number of equations to process: 133
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [73]
% (eq)(apply(apply(apply(s,b),combinator),X),apply(apply(apply(apply(apply(s,s),s),b),combinator),X))
% -> (false)
% Current number of equations to process: 132
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [74]
% (eq)(apply(X,apply(combinator,Y)),apply(apply(apply(apply(s,b),apply(b,X)),combinator),Y))
% -> (false)
% Current number of equations to process: 136
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [75]
% (eq)(apply(apply(apply(apply(apply(b,b),X),combinator),Y),Z),apply(apply(
% apply(
% apply(s,b),X),combinator),
% apply(Y,Z))) ->
% (false)
% Rule
% [46]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),apply(apply(
% apply(
% apply(s,b),b),combinator),
% apply(X,Y))) ->
% (false) collapsed.
% Current number of equations to process: 135
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [76]
% (eq)(apply(apply(X,apply(Y,combinator)),Z),apply(apply(apply(apply(s,b),
% apply(apply(b,X),Y)),combinator),Z))
% -> (false)
% Current number of equations to process: 134
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [77]
% (eq)(apply(apply(apply(s,X),Y),combinator),apply(apply(apply(apply(s,b),X),combinator),
% apply(Y,combinator))) -> (false)
% Rule
% [40]
% (eq)(apply(apply(apply(s,X),X),combinator),apply(apply(apply(apply(s,b),X),combinator),
% apply(X,combinator))) -> (false)
% collapsed.
% Current number of equations to process: 135
% Current number of ordered equations: 1
% Current number of rules: 71
% New rule produced :
% [78]
% (eq)(apply(apply(apply(X,b),combinator),Y),apply(apply(apply(apply(apply(s,s),X),b),combinator),Y))
% -> (false)
% Rule
% [73]
% (eq)(apply(apply(apply(s,b),combinator),X),apply(apply(apply(apply(apply(s,s),s),b),combinator),X))
% -> (false) collapsed.
% Current number of equations to process: 135
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [79]
% (eq)(apply(apply(X,Y),apply(combinator,Y)),apply(apply(apply(apply(s,b),
% apply(s,X)),combinator),Y))
% -> (false)
% Current number of equations to process: 136
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [80]
% (eq)(apply(X,apply(m,combinator)),apply(apply(apply(apply(s,b),apply(b,X)),combinator),combinator))
% -> (false)
% Current number of equations to process: 140
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [81]
% (eq)(apply(apply(apply(s,X),Y),Y),apply(apply(apply(b,combinator),apply(X,Y)),
% apply(m,Y))) -> (false)
% Current number of equations to process: 148
% Current number of ordered equations: 2
% Current number of rules: 74
% New rule produced :
% [82]
% (eq)(apply(apply(apply(s,X),Y),X),apply(apply(apply(b,combinator),apply(m,X)),
% apply(Y,X))) -> (false)
% Current number of equations to process: 148
% Current number of ordered equations: 1
% Current number of rules: 75
% New rule produced :
% [83]
% (eq)(apply(apply(apply(m,s),X),Y),apply(apply(apply(b,combinator),apply(s,Y)),
% apply(X,Y))) -> (false)
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [84]
% (eq)(apply(apply(apply(s,X),m),Y),apply(apply(apply(b,combinator),apply(X,Y)),
% apply(Y,Y))) -> (false)
% Current number of equations to process: 146
% Current number of ordered equations: 1
% Current number of rules: 77
% New rule produced :
% [85]
% (eq)(apply(apply(apply(s,m),X),Y),apply(apply(apply(b,combinator),apply(Y,Y)),
% apply(X,Y))) -> (false)
% Current number of equations to process: 146
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [86]
% (eq)(apply(apply(apply(apply(apply(b,b),X),combinator),Y),Y),apply(apply(
% apply(
% apply(s,b),X),combinator),
% apply(m,Y))) ->
% (false)
% Current number of equations to process: 145
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [87]
% (eq)(apply(apply(X,apply(m,combinator)),Y),apply(apply(apply(apply(s,b),
% apply(apply(b,X),combinator)),combinator),Y))
% -> (false)
% Current number of equations to process: 144
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [88]
% (eq)(apply(apply(apply(apply(apply(b,b),X),combinator),m),Y),apply(apply(
% apply(
% apply(s,b),X),combinator),
% apply(Y,Y))) ->
% (false)
% Current number of equations to process: 143
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [89]
% (eq)(apply(apply(X,apply(combinator,combinator)),Y),apply(apply(apply(
% apply(s,b),
% apply(
% apply(b,X),m)),combinator),Y))
% -> (false)
% Current number of equations to process: 142
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [90]
% (eq)(apply(apply(apply(s,X),Y),Z),apply(combinator,apply(apply(X,Z),apply(Y,Z))))
% -> (false)
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [91]
% (eq)(apply(X,apply(apply(apply(b,Y),Z),Z)),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),
% apply(m,Z))) -> (false)
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [92]
% (eq)(apply(X,apply(apply(apply(b,Y),m),Z)),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),
% apply(Z,Z))) -> (false)
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [93]
% (eq)(apply(X,apply(apply(apply(s,Y),Y),Z)),apply(apply(apply(b,combinator),
% apply(apply(b,X),m)),
% apply(Y,Z))) -> (false)
% Current number of equations to process: 147
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [94]
% (eq)(apply(apply(apply(X,combinator),apply(Y,combinator)),Z),apply(apply(
% apply(
% apply(s,b),
% apply(
% apply(s,X),Y)),combinator),Z))
% -> (false)
% Current number of equations to process: 146
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [95]
% (eq)(apply(apply(apply(apply(s,s),s),X),Y),apply(apply(apply(b,combinator),
% apply(X,Y)),apply(apply(s,X),Y)))
% -> (false)
% Current number of equations to process: 145
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [96]
% (eq)(apply(apply(apply(apply(s,s),X),Y),Z),apply(apply(apply(b,combinator),
% apply(Y,Z)),apply(apply(X,Y),Z)))
% -> (false)
% Rule
% [95]
% (eq)(apply(apply(apply(apply(s,s),s),X),Y),apply(apply(apply(b,combinator),
% apply(X,Y)),apply(apply(s,X),Y)))
% -> (false) collapsed.
% Current number of equations to process: 146
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [97]
% (eq)(apply(apply(X,Y),apply(m,Y)),apply(apply(apply(b,combinator),apply(
% apply(s,X),Y)),Y))
% -> (false)
% Current number of equations to process: 167
% Current number of ordered equations: 2
% Current number of rules: 89
% New rule produced :
% [98]
% (eq)(apply(apply(m,X),apply(Y,X)),apply(apply(apply(b,combinator),apply(
% apply(s,X),Y)),X))
% -> (false)
% Current number of equations to process: 167
% Current number of ordered equations: 1
% Current number of rules: 90
% New rule produced :
% [99]
% (eq)(apply(apply(apply(s,s),X),Y),apply(apply(apply(b,combinator),apply(
% apply(m,s),X)),Y))
% -> (false)
% Current number of equations to process: 167
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [100]
% (eq)(apply(apply(X,Y),apply(Y,Y)),apply(apply(apply(b,combinator),apply(
% apply(s,X),m)),Y))
% -> (false)
% Current number of equations to process: 165
% Current number of ordered equations: 1
% Current number of rules: 92
% New rule produced :
% [101]
% (eq)(apply(apply(apply(s,X),Y),X),apply(apply(apply(b,combinator),apply(
% apply(s,m),Y)),X))
% -> (false)
% Current number of equations to process: 165
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [102]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Z),Y),apply(apply(apply(b,combinator),
% apply(apply(s,X),Z)),Y))
% -> (false)
% Current number of equations to process: 171
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [103]
% (eq)(apply(apply(X,Y),apply(Z,Y)),apply(combinator,apply(apply(apply(s,X),Z),Y)))
% -> (false)
% Current number of equations to process: 172
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [104]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Y),Y),apply(apply(apply(b,combinator),
% apply(apply(s,X),m)),Y))
% -> (false)
% Current number of equations to process: 178
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [105]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),m),Y),apply(apply(apply(b,combinator),
% apply(apply(s,X),Y)),Y))
% -> (false)
% Current number of equations to process: 183
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [106]
% (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: 191
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [107]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(X,Y))) -> (false)
% Current number of equations to process: 196
% Current number of ordered equations: 1
% Current number of rules: 99
% New rule produced :
% [108]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),
% apply(X,Y)),X),Y)) -> (false)
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [109]
% (eq)(apply(apply(apply(s,X),X),X),apply(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),
% apply(X,X))) -> (false)
% Current number of equations to process: 194
% Current number of ordered equations: 1
% Current number of rules: 101
% New rule produced :
% [110]
% (eq)(apply(apply(apply(s,X),X),X),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),
% apply(X,X)),m),X)) -> (false)
% Current number of equations to process: 194
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [111]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(apply(apply(
% apply(
% apply(b,b),
% apply(b,combinator)),m),X),Y))
% -> (false)
% Current number of equations to process: 193
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [112]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),Y),Z),V_3),apply(
% apply(
% apply(b,combinator),X),
% apply(
% apply(Y,Z),V_3)))
% -> (false)
% Current number of equations to process: 191
% Current number of ordered equations: 1
% Current number of rules: 104
% New rule produced :
% [113]
% (eq)(apply(apply(apply(apply(apply(b,b),apply(b,X)),Y),Z),V_3),apply(
% apply(
% apply(b,combinator),X),
% apply(Y,
% apply(Z,V_3))))
% -> (false)
% Current number of equations to process: 191
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [114]
% (eq)(apply(apply(apply(b,X),apply(Y,Z)),apply(V_3,Z)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(s,Y),V_3),Z)))
% -> (false)
% Current number of equations to process: 190
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [115]
% (eq)(apply(apply(apply(b,X),apply(apply(s,Y),Z)),V_3),apply(apply(apply(b,combinator),X),
% apply(apply(Y,V_3),
% apply(Z,V_3)))) ->
% (false)
% Current number of equations to process: 189
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [116]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),Y),Y),Z),apply(apply(
% apply(b,combinator),X),
% apply(apply(m,Y),Z)))
% -> (false)
% Current number of equations to process: 187
% Current number of ordered equations: 1
% Current number of rules: 108
% New rule produced :
% [117]
% (eq)(apply(apply(apply(apply(apply(b,b),apply(b,X)),Y),Z),Z),apply(apply(
% apply(b,combinator),X),
% apply(Y,
% apply(m,Z)))) ->
% (false)
% Current number of equations to process: 187
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [118]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),m),Y),Z),apply(apply(
% apply(b,combinator),X),
% apply(apply(Y,Y),Z)))
% -> (false)
% Current number of equations to process: 185
% Current number of ordered equations: 1
% Current number of rules: 110
% New rule produced :
% [119]
% (eq)(apply(apply(apply(apply(apply(b,b),apply(b,X)),Y),m),Z),apply(apply(
% apply(b,combinator),X),
% apply(Y,
% apply(Z,Z)))) ->
% (false)
% Current number of equations to process: 185
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [120]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(b,combinator),apply(
% apply(
% apply(
% apply(b,b),X),Y),X)),Y))
% -> (false)
% Current number of equations to process: 184
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [121]
% (eq)(apply(apply(X,Y),apply(Z,V_3)),apply(apply(apply(b,combinator),apply(
% apply(
% apply(
% apply(b,b),X),Y),Z)),V_3))
% -> (false)
% Current number of equations to process: 183
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [122]
% (eq)(apply(X,apply(Y,apply(Z,V_3))),apply(apply(apply(b,combinator),apply(
% apply(b,X),
% apply(
% apply(b,Y),Z))),V_3))
% -> (false)
% Current number of equations to process: 182
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [123]
% (eq)(apply(X,apply(Y,apply(m,Z))),apply(apply(apply(b,combinator),apply(
% apply(b,X),
% apply(
% apply(b,Y),Z))),Z))
% -> (false)
% Current number of equations to process: 181
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [124]
% (eq)(apply(X,apply(Y,apply(Z,Z))),apply(apply(apply(b,combinator),apply(
% apply(b,X),
% apply(
% apply(b,Y),m))),Z))
% -> (false)
% Current number of equations to process: 180
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [125]
% (eq)(apply(apply(apply(X,Y),combinator),Z),apply(apply(apply(apply(apply(
% apply(
% apply(b,b),s),b),X),Y),combinator),Z))
% -> (false)
% Current number of equations to process: 179
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [126]
% (eq)(apply(apply(apply(m,X),combinator),Y),apply(apply(apply(apply(apply(
% apply(
% apply(b,b),s),b),X),X),combinator),Y))
% -> (false)
% Current number of equations to process: 178
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [127]
% (eq)(apply(apply(apply(X,X),combinator),Y),apply(apply(apply(apply(apply(
% apply(
% apply(b,b),s),b),m),X),combinator),Y))
% -> (false)
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [128]
% (eq)(apply(apply(apply(s,X),Y),Z),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Z),
% apply(Y,Z))) -> (false)
% Rule
% [107]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(X,Y))) -> (false) collapsed.
% Current number of equations to process: 174
% Current number of ordered equations: 2
% Current number of rules: 119
% New rule produced :
% [129]
% (eq)(apply(apply(apply(s,X),Y),Z),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),
% apply(X,Z)),Y),Z)) -> (false)
% Rule
% [108]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),
% apply(X,Y)),X),Y)) -> (false)
% collapsed.
% Current number of equations to process: 174
% Current number of ordered equations: 1
% Current number of rules: 119
% New rule produced :
% [130]
% (eq)(apply(apply(apply(apply(apply(b,s),X),Y),Z),V_3),apply(apply(apply(b,combinator),
% apply(apply(X,Y),V_3)),
% apply(Z,V_3))) ->
% (false)
% Current number of equations to process: 174
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [131]
% (eq)(apply(apply(apply(s,X),apply(apply(b,Y),Z)),V_3),apply(apply(apply(b,combinator),
% apply(X,V_3)),
% apply(Y,apply(Z,V_3))))
% -> (false)
% Current number of equations to process: 173
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [132]
% (eq)(apply(apply(apply(s,X),m),Y),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),
% apply(X,Y)),Y),Y)) -> (false)
% Current number of equations to process: 171
% Current number of ordered equations: 1
% Current number of rules: 122
% New rule produced :
% [133]
% (eq)(apply(apply(apply(s,m),X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),Y),Y),
% apply(X,Y))) -> (false)
% Current number of equations to process: 171
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [134]
% (eq)(apply(apply(apply(s,X),apply(apply(b,Y),Z)),Z),apply(apply(apply(b,combinator),
% apply(X,Z)),
% apply(Y,apply(m,Z)))) ->
% (false)
% Current number of equations to process: 170
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [135]
% (eq)(apply(apply(apply(s,X),Y),Y),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),
% apply(X,Y)),m),Y)) -> (false)
% Rule
% [110]
% (eq)(apply(apply(apply(s,X),X),X),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),
% apply(X,X)),m),X)) -> (false)
% collapsed.
% Current number of equations to process: 168
% Current number of ordered equations: 1
% Current number of rules: 124
% New rule produced :
% [136]
% (eq)(apply(apply(apply(s,X),Y),X),apply(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),
% apply(Y,X))) -> (false)
% Rule
% [109]
% (eq)(apply(apply(apply(s,X),X),X),apply(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),
% apply(X,X))) -> (false) collapsed.
% Current number of equations to process: 168
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [137]
% (eq)(apply(apply(apply(s,X),apply(apply(b,Y),m)),Z),apply(apply(apply(b,combinator),
% apply(X,Z)),
% apply(Y,apply(Z,Z)))) ->
% (false)
% Current number of equations to process: 167
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [138]
% (eq)(apply(apply(X,Y),apply(Z,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(s,X)),Z),Y)) -> (false)
% Current number of equations to process: 166
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [139]
% (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: 186
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [140]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),m),X),Y))
% -> (false)
% Current number of equations to process: 185
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [141]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),Y),Y)) -> (false)
% Current number of equations to process: 201
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [142]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),m),Y)) -> (false)
% Current number of equations to process: 207
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [143]
% (eq)(apply(apply(apply(m,b),X),X),apply(apply(apply(b,combinator),b),
% apply(m,X))) -> (false)
% Current number of equations to process: 209
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [144]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(combinator,apply(X,apply(m,Y)))) ->
% (false)
% Current number of equations to process: 214
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [145]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Z),Z),apply(apply(apply(b,combinator),
% apply(X,Y)),
% apply(m,Z))) -> (false)
% Current number of equations to process: 213
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [146]
% (eq)(apply(apply(apply(b,X),X),X),apply(apply(apply(apply(apply(b,s),b),combinator),m),X))
% -> (false)
% Current number of equations to process: 214
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [147]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(apply(apply(m,b),apply(b,combinator)),X),Y),Y))
% -> (false)
% Current number of equations to process: 221
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [148]
% (eq)(apply(apply(apply(b,m),X),X),apply(combinator,apply(apply(apply(
% apply(
% apply(b,b),m),X),m),X)))
% -> (false)
% Current number of equations to process: 220
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [149]
% (eq)(apply(apply(apply(apply(s,b),b),X),apply(b,X)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(s,b),b),X)))
% -> (false)
% Current number of equations to process: 225
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [150]
% (eq)(apply(apply(apply(b,X),apply(Y,Z)),apply(Y,Z)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(b,m),Y),Z)))
% -> (false)
% Current number of equations to process: 224
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [151]
% (eq)(apply(apply(apply(apply(s,b),X),Y),apply(X,Y)),apply(apply(apply(b,combinator),Y),
% apply(apply(apply(s,X),X),Y)))
% -> (false)
% Rule
% [149]
% (eq)(apply(apply(apply(apply(s,b),b),X),apply(b,X)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(s,b),b),X)))
% -> (false) collapsed.
% Current number of equations to process: 223
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [152]
% (eq)(apply(apply(apply(b,X),apply(Y,Y)),apply(Y,Y)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(b,m),m),Y)))
% -> (false)
% Current number of equations to process: 222
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [153]
% (eq)(apply(apply(apply(apply(apply(b,b),m),X),m),X),apply(apply(apply(
% apply(
% apply(b,b),
% apply(b,combinator)),m),X),X))
% -> (false)
% Current number of equations to process: 221
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [154]
% (eq)(apply(apply(m,X),Y),apply(apply(apply(apply(apply(apply(m,b),b),combinator),X),X),Y))
% -> (false)
% Current number of equations to process: 234
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [155]
% (eq)(apply(apply(apply(b,b),m),X),apply(apply(apply(b,combinator),apply(
% apply(m,b),X)),X))
% -> (false)
% Current number of equations to process: 254
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [156]
% (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: 252
% Current number of ordered equations: 1
% Current number of rules: 143
% New rule produced :
% [157]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(combinator,
% apply(apply(apply(s,X),X),Y)))
% -> (false)
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [158]
% (eq)(apply(apply(apply(apply(apply(b,b),m),X),m),X),apply(apply(apply(b,combinator),
% apply(apply(b,m),X)),X))
% -> (false)
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [159]
% (eq)(apply(X,apply(m,Y)),apply(combinator,apply(apply(apply(b,X),Y),Y))) ->
% (false)
% Current number of equations to process: 255
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [160]
% (eq)(apply(apply(apply(m,b),m),X),apply(apply(apply(b,combinator),b),
% apply(X,X))) -> (false)
% Current number of equations to process: 260
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [161]
% (eq)(apply(apply(apply(b,X),m),Y),apply(combinator,apply(X,apply(Y,Y)))) ->
% (false)
% Current number of equations to process: 264
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [162]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),m),Z),apply(apply(apply(b,combinator),
% apply(X,Y)),
% apply(Z,Z))) -> (false)
% Current number of equations to process: 263
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [163]
% (eq)(apply(apply(apply(b,X),m),X),apply(apply(apply(apply(apply(b,s),b),combinator),X),X))
% -> (false)
% Current number of equations to process: 263
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [164]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(apply(apply(m,b),apply(b,combinator)),X),m),Y))
% -> (false)
% Current number of equations to process: 267
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [165]
% (eq)(apply(apply(apply(b,m),m),X),apply(combinator,apply(apply(apply(
% apply(
% apply(b,b),X),X),X),X)))
% -> (false)
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [166]
% (eq)(apply(apply(apply(s,m),m),X),apply(apply(apply(b,combinator),apply(
% apply(
% apply(
% apply(b,b),m),X),X)),X))
% -> (false)
% Current number of equations to process: 270
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [167]
% (eq)(apply(apply(X,Y),apply(m,Z)),apply(apply(apply(b,combinator),apply(
% apply(
% apply(
% apply(b,b),X),Y),Z)),Z))
% -> (false)
% Current number of equations to process: 269
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [168]
% (eq)(apply(apply(apply(apply(apply(b,b),X),X),X),X),apply(apply(apply(
% apply(
% apply(b,b),
% apply(b,combinator)),m),m),X))
% -> (false)
% Current number of equations to process: 268
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [169]
% (eq)(apply(apply(X,X),Y),apply(apply(apply(apply(apply(apply(m,b),b),combinator),m),X),Y))
% -> (false)
% Current number of equations to process: 278
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [170]
% (eq)(apply(apply(apply(s,X),X),X),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),m),m),X))
% -> (false)
% Current number of equations to process: 277
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [171]
% (eq)(apply(apply(apply(b,b),X),X),apply(apply(apply(b,combinator),apply(
% apply(m,b),m)),X))
% -> (false)
% Current number of equations to process: 290
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [172]
% (eq)(apply(apply(apply(s,X),X),Y),apply(combinator,apply(apply(apply(
% apply(
% apply(b,b),X),Y),X),Y)))
% -> (false)
% Current number of equations to process: 289
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [173]
% (eq)(apply(apply(apply(apply(apply(b,b),X),X),X),X),apply(apply(apply(b,combinator),
% apply(apply(b,m),m)),X))
% -> (false)
% Current number of equations to process: 288
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [174]
% (eq)(apply(X,apply(Y,Y)),apply(combinator,apply(apply(apply(b,X),m),Y))) ->
% (false)
% Current number of equations to process: 291
% Current number of ordered equations: 0
% Current number of rules: 161
% Rule [174]
% (eq)(apply(X,apply(Y,Y)),apply(combinator,apply(apply(apply(b,X),m),Y)))
% -> (false) is composed into [174]
% (eq)(apply(X,apply(Y,Y)),apply(combinator,
% apply(apply(
% apply(b,X),m),Y)))
% -> (true)
% Rule [173]
% (eq)(apply(apply(apply(apply(apply(b,b),X),X),X),X),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,m),m)),X))
% -> (false) is composed into [173]
% (eq)(apply(apply(apply(apply(apply(b,b),X),X),X),X),
% apply(apply(apply(b,combinator),apply(
% apply(b,m),m)),X))
% -> (true)
% Rule [172]
% (eq)(apply(apply(apply(s,X),X),Y),apply(combinator,apply(apply(apply(
% apply(
% apply(b,b),X),Y),X),Y)))
% -> (false) is composed into [172]
% (eq)(apply(apply(apply(s,X),X),Y),apply(combinator,
% apply(
% apply(
% apply(
% apply(
% apply(b,b),X),Y),X),Y)))
% -> (true)
% Rule [171]
% (eq)(apply(apply(apply(b,b),X),X),apply(apply(apply(b,combinator),
% apply(apply(m,b),m)),X)) ->
% (false) is composed into [171]
% (eq)(apply(apply(apply(b,b),X),X),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(m,b),m)),X))
% -> (true)
% Rule [170]
% (eq)(apply(apply(apply(s,X),X),X),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),m),m),X))
% -> (false) is composed into [170]
% (eq)(apply(apply(apply(s,X),X),X),apply(
% apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),m),m),X))
% -> (true)
% Rule [169]
% (eq)(apply(apply(X,X),Y),apply(apply(apply(apply(apply(apply(m,b),b),combinator),m),X),Y))
% -> (false) is composed into [169]
% (eq)(apply(apply(X,X),Y),apply(apply(
% apply(
% apply(
% apply(
% apply(m,b),b),combinator),m),X),Y))
% -> (true)
% Rule [168]
% (eq)(apply(apply(apply(apply(apply(b,b),X),X),X),X),apply(apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),m),m),X))
% -> (false) is composed into [168]
% (eq)(apply(apply(apply(apply(apply(b,b),X),X),X),X),
% apply(apply(apply(apply(apply(b,b),apply(b,combinator)),m),m),X))
% -> (true)
% Rule [167]
% (eq)(apply(apply(X,Y),apply(m,Z)),apply(apply(apply(b,combinator),
% apply(apply(apply(apply(b,b),X),Y),Z)),Z))
% -> (false) is composed into [167]
% (eq)(apply(apply(X,Y),apply(m,Z)),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(
% apply(
% apply(b,b),X),Y),Z)),Z))
% -> (true)
% Rule [166]
% (eq)(apply(apply(apply(s,m),m),X),apply(apply(apply(b,combinator),
% apply(apply(apply(apply(b,b),m),X),X)),X))
% -> (false) is composed into [166]
% (eq)(apply(apply(apply(s,m),m),X),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(
% apply(
% apply(b,b),m),X),X)),X))
% -> (true)
% Rule [165]
% (eq)(apply(apply(apply(b,m),m),X),apply(combinator,apply(apply(apply(
% apply(
% apply(b,b),X),X),X),X)))
% -> (false) is composed into [165]
% (eq)(apply(apply(apply(b,m),m),X),apply(combinator,
% apply(
% apply(
% apply(
% apply(
% apply(b,b),X),X),X),X)))
% -> (true)
% Rule [164]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(apply(apply(m,b),apply(b,combinator)),X),m),Y))
% -> (false) is composed into [164]
% (eq)(apply(X,apply(Y,Y)),apply(apply(
% apply(
% apply(
% apply(m,b),
% apply(b,combinator)),X),m),Y))
% -> (true)
% Rule [163]
% (eq)(apply(apply(apply(b,X),m),X),apply(apply(apply(apply(apply(b,s),b),combinator),X),X))
% -> (false) is composed into [163]
% (eq)(apply(apply(apply(b,X),m),X),apply(
% apply(
% apply(
% apply(
% apply(b,s),b),combinator),X),X))
% -> (true)
% Rule [162]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),m),Z),apply(apply(
% apply(b,combinator),
% apply(X,Y)),
% apply(Z,Z))) ->
% (false) is composed into [162]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),m),Z),
% apply(apply(apply(b,combinator),apply(X,Y)),
% apply(Z,Z))) -> (true)
% Rule [161]
% (eq)(apply(apply(apply(b,X),m),Y),apply(combinator,apply(X,apply(Y,Y))))
% -> (false) is composed into [161]
% (eq)(apply(apply(apply(b,X),m),Y),apply(combinator,
% apply(X,
% apply(Y,Y))))
% -> (true)
% Rule [160]
% (eq)(apply(apply(apply(m,b),m),X),apply(apply(apply(b,combinator),b),
% apply(X,X))) -> (false) is composed into
% [160]
% (eq)(apply(apply(apply(m,b),m),X),apply(apply(apply(b,combinator),b),
% apply(X,X))) -> (true)
% Rule [159]
% (eq)(apply(X,apply(m,Y)),apply(combinator,apply(apply(apply(b,X),Y),Y)))
% -> (false) is composed into [159]
% (eq)(apply(X,apply(m,Y)),apply(combinator,
% apply(apply(
% apply(b,X),Y),Y)))
% -> (true)
% Rule [158]
% (eq)(apply(apply(apply(apply(apply(b,b),m),X),m),X),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,m),X)),X))
% -> (false) is composed into [158]
% (eq)(apply(apply(apply(apply(apply(b,b),m),X),m),X),
% apply(apply(apply(b,combinator),apply(
% apply(b,m),X)),X))
% -> (true)
% Rule [157]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(combinator,
% apply(apply(
% apply(s,X),X),Y)))
% -> (false) is composed into [157]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(combinator,apply(apply(apply(s,X),X),Y)))
% -> (true)
% Rule [156]
% (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 [156]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(combinator,apply(apply(apply(b,m),X),Y)))
% -> (true)
% Rule [155]
% (eq)(apply(apply(apply(b,b),m),X),apply(apply(apply(b,combinator),
% apply(apply(m,b),X)),X)) ->
% (false) is composed into [155]
% (eq)(apply(apply(apply(b,b),m),X),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(m,b),X)),X))
% -> (true)
% Rule [154]
% (eq)(apply(apply(m,X),Y),apply(apply(apply(apply(apply(apply(m,b),b),combinator),X),X),Y))
% -> (false) is composed into [154]
% (eq)(apply(apply(m,X),Y),apply(apply(
% apply(
% apply(
% apply(
% apply(m,b),b),combinator),X),X),Y))
% -> (true)
% Rule [153]
% (eq)(apply(apply(apply(apply(apply(b,b),m),X),m),X),apply(apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),m),X),X))
% -> (false) is composed into [153]
% (eq)(apply(apply(apply(apply(apply(b,b),m),X),m),X),
% apply(apply(apply(apply(apply(b,b),apply(b,combinator)),m),X),X))
% -> (true)
% Rule [152]
% (eq)(apply(apply(apply(b,X),apply(Y,Y)),apply(Y,Y)),apply(apply(
% apply(b,combinator),X),
% apply(apply(
% apply(b,m),m),Y)))
% -> (false) is composed into [152]
% (eq)(apply(apply(apply(b,X),apply(Y,Y)),
% apply(Y,Y)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(b,m),m),Y)))
% -> (true)
% Rule [151]
% (eq)(apply(apply(apply(apply(s,b),X),Y),apply(X,Y)),apply(apply(
% apply(b,combinator),Y),
% apply(apply(
% apply(s,X),X),Y)))
% -> (false) is composed into [151]
% (eq)(apply(apply(apply(apply(s,b),X),Y),
% apply(X,Y)),apply(apply(apply(b,combinator),Y),
% apply(apply(apply(s,X),X),Y)))
% -> (true)
% Rule [150]
% (eq)(apply(apply(apply(b,X),apply(Y,Z)),apply(Y,Z)),apply(apply(
% apply(b,combinator),X),
% apply(apply(
% apply(b,m),Y),Z)))
% -> (false) is composed into [150]
% (eq)(apply(apply(apply(b,X),apply(Y,Z)),
% apply(Y,Z)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(b,m),Y),Z)))
% -> (true)
% Rule [148]
% (eq)(apply(apply(apply(b,m),X),X),apply(combinator,apply(apply(apply(
% apply(
% apply(b,b),m),X),m),X)))
% -> (false) is composed into [148]
% (eq)(apply(apply(apply(b,m),X),X),apply(combinator,
% apply(
% apply(
% apply(
% apply(
% apply(b,b),m),X),m),X)))
% -> (true)
% Rule [147]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(apply(apply(m,b),apply(b,combinator)),X),Y),Y))
% -> (false) is composed into [147]
% (eq)(apply(X,apply(m,Y)),apply(apply(
% apply(
% apply(
% apply(m,b),
% apply(b,combinator)),X),Y),Y))
% -> (true)
% Rule [146]
% (eq)(apply(apply(apply(b,X),X),X),apply(apply(apply(apply(apply(b,s),b),combinator),m),X))
% -> (false) is composed into [146]
% (eq)(apply(apply(apply(b,X),X),X),apply(
% apply(
% apply(
% apply(
% apply(b,s),b),combinator),m),X))
% -> (true)
% Rule [145]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Z),Z),apply(apply(
% apply(b,combinator),
% apply(X,Y)),
% apply(m,Z))) ->
% (false) is composed into [145]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Z),Z),
% apply(apply(apply(b,combinator),apply(X,Y)),
% apply(m,Z))) -> (true)
% Rule [144]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(combinator,apply(X,apply(m,Y))))
% -> (false) is composed into [144]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(combinator,
% apply(X,
% apply(m,Y))))
% -> (true)
% Rule [143]
% (eq)(apply(apply(apply(m,b),X),X),apply(apply(apply(b,combinator),b),
% apply(m,X))) -> (false) is composed into
% [143]
% (eq)(apply(apply(apply(m,b),X),X),apply(apply(apply(b,combinator),b),
% apply(m,X))) -> (true)
% Rule [142]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),m),Y)) -> (false) is composed into
% [142]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),m),Y)) -> (true)
% Rule [141]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),Y),Y)) -> (false) is composed into
% [141]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),Y),Y)) -> (true)
% Rule [140]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),m),X),Y))
% -> (false) is composed into [140]
% (eq)(apply(apply(apply(s,X),X),Y),apply(
% apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),m),X),Y))
% -> (true)
% Rule [139]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(m,b),b),combinator),X),Y),Z))
% -> (false) is composed into [139]
% (eq)(apply(apply(X,Y),Z),apply(apply(
% apply(
% apply(
% apply(
% apply(m,b),b),combinator),X),Y),Z))
% -> (true)
% Rule [138]
% (eq)(apply(apply(X,Y),apply(Z,Y)),apply(apply(apply(apply(apply(
% apply(b,b),b),combinator),
% apply(s,X)),Z),Y)) ->
% (false) is composed into [138]
% (eq)(apply(apply(X,Y),apply(Z,Y)),apply(
% apply(
% apply(
% apply(
% apply(
% apply(b,b),b),combinator),
% apply(s,X)),Z),Y))
% -> (true)
% Rule [137]
% (eq)(apply(apply(apply(s,X),apply(apply(b,Y),m)),Z),apply(apply(
% apply(b,combinator),
% apply(X,Z)),
% apply(Y,apply(Z,Z))))
% -> (false) is composed into [137]
% (eq)(apply(apply(apply(s,X),apply(apply(b,Y),m)),Z),
% apply(apply(apply(b,combinator),apply(X,Z)),
% apply(Y,apply(Z,Z)))) -> (true)
% Rule [136]
% (eq)(apply(apply(apply(s,X),Y),X),apply(apply(apply(apply(apply(
% apply(b,b),b),combinator),m),X),
% apply(Y,X))) -> (false) is composed into
% [136]
% (eq)(apply(apply(apply(s,X),Y),X),apply(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),
% apply(Y,X))) -> (true)
% Rule [135]
% (eq)(apply(apply(apply(s,X),Y),Y),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),
% apply(X,Y)),m),Y)) ->
% (false) is composed into [135]
% (eq)(apply(apply(apply(s,X),Y),Y),apply(
% apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),
% apply(X,Y)),m),Y))
% -> (true)
% Rule [134]
% (eq)(apply(apply(apply(s,X),apply(apply(b,Y),Z)),Z),apply(apply(
% apply(b,combinator),
% apply(X,Z)),
% apply(Y,apply(m,Z))))
% -> (false) is composed into [134]
% (eq)(apply(apply(apply(s,X),apply(apply(b,Y),Z)),Z),
% apply(apply(apply(b,combinator),apply(X,Z)),
% apply(Y,apply(m,Z)))) -> (true)
% Rule [133]
% (eq)(apply(apply(apply(s,m),X),Y),apply(apply(apply(apply(apply(
% apply(b,b),b),combinator),Y),Y),
% apply(X,Y))) -> (false) is composed into
% [133]
% (eq)(apply(apply(apply(s,m),X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),Y),Y),
% apply(X,Y))) -> (true)
% Rule [132]
% (eq)(apply(apply(apply(s,X),m),Y),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),
% apply(X,Y)),Y),Y)) ->
% (false) is composed into [132]
% (eq)(apply(apply(apply(s,X),m),Y),apply(
% apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),
% apply(X,Y)),Y),Y))
% -> (true)
% Rule [131]
% (eq)(apply(apply(apply(s,X),apply(apply(b,Y),Z)),V_3),apply(apply(
% apply(b,combinator),
% apply(X,V_3)),
% apply(Y,apply(Z,V_3))))
% -> (false) is composed into [131]
% (eq)(apply(apply(apply(s,X),apply(apply(b,Y),Z)),V_3),
% apply(apply(apply(b,combinator),apply(X,V_3)),
% apply(Y,apply(Z,V_3)))) -> (true)
% Rule [130]
% (eq)(apply(apply(apply(apply(apply(b,s),X),Y),Z),V_3),apply(apply(
% apply(b,combinator),
% apply(
% apply(X,Y),V_3)),
% apply(Z,V_3))) ->
% (false) is composed into [130]
% (eq)(apply(apply(apply(apply(apply(b,s),X),Y),Z),V_3),
% apply(apply(apply(b,combinator),apply(apply(X,Y),V_3)),
% apply(Z,V_3))) -> (true)
% Rule [129]
% (eq)(apply(apply(apply(s,X),Y),Z),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),
% apply(X,Z)),Y),Z)) ->
% (false) is composed into [129]
% (eq)(apply(apply(apply(s,X),Y),Z),apply(
% apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),
% apply(X,Z)),Y),Z))
% -> (true)
% Rule [128]
% (eq)(apply(apply(apply(s,X),Y),Z),apply(apply(apply(apply(apply(
% apply(b,b),b),combinator),X),Z),
% apply(Y,Z))) -> (false) is composed into
% [128]
% (eq)(apply(apply(apply(s,X),Y),Z),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Z),
% apply(Y,Z))) -> (true)
% Rule [127]
% (eq)(apply(apply(apply(X,X),combinator),Y),apply(apply(apply(apply(
% apply(
% apply(
% apply(b,b),s),b),m),X),combinator),Y))
% -> (false) is composed into [127]
% (eq)(apply(apply(apply(X,X),combinator),Y),
% apply(apply(apply(apply(apply(apply(
% apply(b,b),s),b),m),X),combinator),Y))
% -> (true)
% Rule [126]
% (eq)(apply(apply(apply(m,X),combinator),Y),apply(apply(apply(apply(
% apply(
% apply(
% apply(b,b),s),b),X),X),combinator),Y))
% -> (false) is composed into [126]
% (eq)(apply(apply(apply(m,X),combinator),Y),
% apply(apply(apply(apply(apply(apply(
% apply(b,b),s),b),X),X),combinator),Y))
% -> (true)
% Rule [125]
% (eq)(apply(apply(apply(X,Y),combinator),Z),apply(apply(apply(apply(
% apply(
% apply(
% apply(b,b),s),b),X),Y),combinator),Z))
% -> (false) is composed into [125]
% (eq)(apply(apply(apply(X,Y),combinator),Z),
% apply(apply(apply(apply(apply(apply(
% apply(b,b),s),b),X),Y),combinator),Z))
% -> (true)
% Rule [124]
% (eq)(apply(X,apply(Y,apply(Z,Z))),apply(apply(apply(b,combinator),
% apply(apply(b,X),apply(apply(b,Y),m))),Z))
% -> (false) is composed into [124]
% (eq)(apply(X,apply(Y,apply(Z,Z))),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(b,X),
% apply(
% apply(b,Y),m))),Z))
% -> (true)
% Rule [123]
% (eq)(apply(X,apply(Y,apply(m,Z))),apply(apply(apply(b,combinator),
% apply(apply(b,X),apply(apply(b,Y),Z))),Z))
% -> (false) is composed into [123]
% (eq)(apply(X,apply(Y,apply(m,Z))),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(b,X),
% apply(
% apply(b,Y),Z))),Z))
% -> (true)
% Rule [122]
% (eq)(apply(X,apply(Y,apply(Z,V_3))),apply(apply(apply(b,combinator),
% apply(apply(b,X),apply(
% apply(b,Y),Z))),V_3))
% -> (false) is composed into [122]
% (eq)(apply(X,apply(Y,apply(Z,V_3))),
% apply(apply(apply(b,combinator),apply(
% apply(b,X),
% apply(
% apply(b,Y),Z))),V_3))
% -> (true)
% Rule [121]
% (eq)(apply(apply(X,Y),apply(Z,V_3)),apply(apply(apply(b,combinator),
% apply(apply(apply(apply(b,b),X),Y),Z)),V_3))
% -> (false) is composed into [121]
% (eq)(apply(apply(X,Y),apply(Z,V_3)),
% apply(apply(apply(b,combinator),apply(
% apply(
% apply(
% apply(b,b),X),Y),Z)),V_3))
% -> (true)
% Rule [120]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(b,combinator),
% apply(apply(apply(apply(b,b),X),Y),X)),Y))
% -> (false) is composed into [120]
% (eq)(apply(apply(apply(s,X),X),Y),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(
% apply(
% apply(b,b),X),Y),X)),Y))
% -> (true)
% Rule [119]
% (eq)(apply(apply(apply(apply(apply(b,b),apply(b,X)),Y),m),Z),apply(
% apply(
% apply(b,combinator),X),
% apply(Y,
% apply(Z,Z))))
% -> (false) is composed into [119]
% (eq)(apply(apply(apply(apply(apply(b,b),
% apply(b,X)),Y),m),Z),
% apply(apply(apply(b,combinator),X),apply(Y,
% apply(Z,Z))))
% -> (true)
% Rule [118]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),m),Y),Z),apply(
% apply(
% apply(b,combinator),X),
% apply(
% apply(Y,Y),Z)))
% -> (false) is composed into [118]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),m),Y),Z),
% apply(apply(apply(b,combinator),X),apply(
% apply(Y,Y),Z)))
% -> (true)
% Rule [117]
% (eq)(apply(apply(apply(apply(apply(b,b),apply(b,X)),Y),Z),Z),apply(
% apply(
% apply(b,combinator),X),
% apply(Y,
% apply(m,Z))))
% -> (false) is composed into [117]
% (eq)(apply(apply(apply(apply(apply(b,b),
% apply(b,X)),Y),Z),Z),
% apply(apply(apply(b,combinator),X),apply(Y,
% apply(m,Z))))
% -> (true)
% Rule [116]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),Y),Y),Z),apply(
% apply(
% apply(b,combinator),X),
% apply(
% apply(m,Y),Z)))
% -> (false) is composed into [116]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),Y),Y),Z),
% apply(apply(apply(b,combinator),X),apply(
% apply(m,Y),Z)))
% -> (true)
% Rule [115]
% (eq)(apply(apply(apply(b,X),apply(apply(s,Y),Z)),V_3),apply(apply(
% apply(b,combinator),X),
% apply(apply(Y,V_3),
% apply(Z,V_3)))) ->
% (false) is composed into [115]
% (eq)(apply(apply(apply(b,X),apply(apply(s,Y),Z)),V_3),
% apply(apply(apply(b,combinator),X),apply(
% apply(Y,V_3),
% apply(Z,V_3))))
% -> (true)
% Rule [114]
% (eq)(apply(apply(apply(b,X),apply(Y,Z)),apply(V_3,Z)),apply(apply(
% apply(b,combinator),X),
% apply(apply(
% apply(s,Y),V_3),Z)))
% -> (false) is composed into [114]
% (eq)(apply(apply(apply(b,X),apply(Y,Z)),
% apply(V_3,Z)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(s,Y),V_3),Z)))
% -> (true)
% Rule [113]
% (eq)(apply(apply(apply(apply(apply(b,b),apply(b,X)),Y),Z),V_3),apply(
% apply(
% apply(b,combinator),X),
% apply(Y,
% apply(Z,V_3))))
% -> (false) is composed into [113]
% (eq)(apply(apply(apply(apply(apply(b,b),
% apply(b,X)),Y),Z),V_3),
% apply(apply(apply(b,combinator),X),apply(Y,
% apply(Z,V_3))))
% -> (true)
% Rule [112]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),Y),Z),V_3),apply(
% apply(
% apply(b,combinator),X),
% apply(
% apply(Y,Z),V_3)))
% -> (false) is composed into [112]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),Y),Z),V_3),
% apply(apply(apply(b,combinator),X),apply(
% apply(Y,Z),V_3)))
% -> (true)
% Rule [111]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),m),X),Y))
% -> (false) is composed into [111]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(apply(apply(apply(apply(b,b),apply(b,combinator)),m),X),Y))
% -> (true)
% Rule [106]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(m,b),apply(b,combinator)),X),Y),Z))
% -> (false) is composed into [106]
% (eq)(apply(X,apply(Y,Z)),apply(apply(
% apply(
% apply(
% apply(m,b),
% apply(b,combinator)),X),Y),Z))
% -> (true)
% Rule [105]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),m),Y),apply(apply(
% apply(b,combinator),
% apply(
% apply(s,X),Y)),Y))
% -> (false) is composed into [105]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),m),Y),
% apply(apply(apply(b,combinator),apply(
% apply(s,X),Y)),Y))
% -> (true)
% Rule [104]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Y),Y),apply(apply(
% apply(b,combinator),
% apply(
% apply(s,X),m)),Y))
% -> (false) is composed into [104]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Y),Y),
% apply(apply(apply(b,combinator),apply(
% apply(s,X),m)),Y))
% -> (true)
% Rule [103]
% (eq)(apply(apply(X,Y),apply(Z,Y)),apply(combinator,apply(apply(apply(s,X),Z),Y)))
% -> (false) is composed into [103]
% (eq)(apply(apply(X,Y),apply(Z,Y)),apply(combinator,
% apply(
% apply(
% apply(s,X),Z),Y)))
% -> (true)
% Rule [102]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Z),Y),apply(apply(
% apply(b,combinator),
% apply(
% apply(s,X),Z)),Y))
% -> (false) is composed into [102]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Z),Y),
% apply(apply(apply(b,combinator),apply(
% apply(s,X),Z)),Y))
% -> (true)
% Rule [101]
% (eq)(apply(apply(apply(s,X),Y),X),apply(apply(apply(b,combinator),
% apply(apply(s,m),Y)),X)) ->
% (false) is composed into [101]
% (eq)(apply(apply(apply(s,X),Y),X),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(s,m),Y)),X))
% -> (true)
% Rule [100]
% (eq)(apply(apply(X,Y),apply(Y,Y)),apply(apply(apply(b,combinator),
% apply(apply(s,X),m)),Y)) ->
% (false) is composed into [100]
% (eq)(apply(apply(X,Y),apply(Y,Y)),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(s,X),m)),Y))
% -> (true)
% Rule [99]
% (eq)(apply(apply(apply(s,s),X),Y),apply(apply(apply(b,combinator),
% apply(apply(m,s),X)),Y)) ->
% (false) is composed into [99]
% (eq)(apply(apply(apply(s,s),X),Y),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(m,s),X)),Y))
% -> (true)
% Rule [98]
% (eq)(apply(apply(m,X),apply(Y,X)),apply(apply(apply(b,combinator),
% apply(apply(s,X),Y)),X)) ->
% (false) is composed into [98]
% (eq)(apply(apply(m,X),apply(Y,X)),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(s,X),Y)),X))
% -> (true)
% Rule [97]
% (eq)(apply(apply(X,Y),apply(m,Y)),apply(apply(apply(b,combinator),
% apply(apply(s,X),Y)),Y)) ->
% (false) is composed into [97]
% (eq)(apply(apply(X,Y),apply(m,Y)),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(s,X),Y)),Y))
% -> (true)
% Rule [96]
% (eq)(apply(apply(apply(apply(s,s),X),Y),Z),apply(apply(apply(b,combinator),
% apply(Y,Z)),apply(
% apply(X,Y),Z)))
% -> (false) is composed into [96]
% (eq)(apply(apply(apply(apply(s,s),X),Y),Z),
% apply(apply(apply(b,combinator),apply(Y,Z)),
% apply(apply(X,Y),Z))) -> (true)
% Rule [94]
% (eq)(apply(apply(apply(X,combinator),apply(Y,combinator)),Z),apply(
% apply(
% apply(
% apply(s,b),
% apply(
% apply(s,X),Y)),combinator),Z))
% -> (false) is composed into [94]
% (eq)(apply(apply(apply(X,combinator),
% apply(Y,combinator)),Z),apply(
% apply(
% apply(
% apply(s,b),
% apply(
% apply(s,X),Y)),combinator),Z))
% -> (true)
% Rule [93]
% (eq)(apply(X,apply(apply(apply(s,Y),Y),Z)),apply(apply(apply(b,combinator),
% apply(apply(b,X),m)),
% apply(Y,Z))) -> (false) is composed into
% [93]
% (eq)(apply(X,apply(apply(apply(s,Y),Y),Z)),apply(apply(apply(b,combinator),
% apply(apply(b,X),m)),
% apply(Y,Z))) -> (true)
% Rule [92]
% (eq)(apply(X,apply(apply(apply(b,Y),m),Z)),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),
% apply(Z,Z))) -> (false) is composed into
% [92]
% (eq)(apply(X,apply(apply(apply(b,Y),m),Z)),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),
% apply(Z,Z))) -> (true)
% Rule [91]
% (eq)(apply(X,apply(apply(apply(b,Y),Z),Z)),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),
% apply(m,Z))) -> (false) is composed into
% [91]
% (eq)(apply(X,apply(apply(apply(b,Y),Z),Z)),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),
% apply(m,Z))) -> (true)
% Rule [90]
% (eq)(apply(apply(apply(s,X),Y),Z),apply(combinator,apply(apply(X,Z),
% apply(Y,Z)))) ->
% (false) is composed into [90]
% (eq)(apply(apply(apply(s,X),Y),Z),apply(combinator,
% apply(
% apply(X,Z),
% apply(Y,Z))))
% -> (true)
% Rule [89]
% (eq)(apply(apply(X,apply(combinator,combinator)),Y),apply(apply(
% apply(
% apply(s,b),
% apply(
% apply(b,X),m)),combinator),Y))
% -> (false) is composed into [89]
% (eq)(apply(apply(X,apply(combinator,combinator)),Y),
% apply(apply(apply(apply(s,b),apply(apply(b,X),m)),combinator),Y))
% -> (true)
% Rule [88]
% (eq)(apply(apply(apply(apply(apply(b,b),X),combinator),m),Y),apply(
% apply(
% apply(
% apply(s,b),X),combinator),
% apply(Y,Y)))
% -> (false) is composed into [88]
% (eq)(apply(apply(apply(apply(apply(b,b),X),combinator),m),Y),
% apply(apply(apply(apply(s,b),X),combinator),
% apply(Y,Y))) -> (true)
% Rule [87]
% (eq)(apply(apply(X,apply(m,combinator)),Y),apply(apply(apply(apply(s,b),
% apply(apply(b,X),combinator)),combinator),Y))
% -> (false) is composed into [87]
% (eq)(apply(apply(X,apply(m,combinator)),Y),
% apply(apply(apply(apply(s,b),apply(apply(b,X),combinator)),combinator),Y))
% -> (true)
% Rule [86]
% (eq)(apply(apply(apply(apply(apply(b,b),X),combinator),Y),Y),apply(
% apply(
% apply(
% apply(s,b),X),combinator),
% apply(m,Y)))
% -> (false) is composed into [86]
% (eq)(apply(apply(apply(apply(apply(b,b),X),combinator),Y),Y),
% apply(apply(apply(apply(s,b),X),combinator),
% apply(m,Y))) -> (true)
% Rule [85]
% (eq)(apply(apply(apply(s,m),X),Y),apply(apply(apply(b,combinator),
% apply(Y,Y)),apply(X,Y))) ->
% (false) is composed into [85]
% (eq)(apply(apply(apply(s,m),X),Y),apply(
% apply(
% apply(b,combinator),
% apply(Y,Y)),
% apply(X,Y)))
% -> (true)
% Rule [84]
% (eq)(apply(apply(apply(s,X),m),Y),apply(apply(apply(b,combinator),
% apply(X,Y)),apply(Y,Y))) ->
% (false) is composed into [84]
% (eq)(apply(apply(apply(s,X),m),Y),apply(
% apply(
% apply(b,combinator),
% apply(X,Y)),
% apply(Y,Y)))
% -> (true)
% Rule [83]
% (eq)(apply(apply(apply(m,s),X),Y),apply(apply(apply(b,combinator),
% apply(s,Y)),apply(X,Y))) ->
% (false) is composed into [83]
% (eq)(apply(apply(apply(m,s),X),Y),apply(
% apply(
% apply(b,combinator),
% apply(s,Y)),
% apply(X,Y)))
% -> (true)
% Rule [82]
% (eq)(apply(apply(apply(s,X),Y),X),apply(apply(apply(b,combinator),
% apply(m,X)),apply(Y,X))) ->
% (false) is composed into [82]
% (eq)(apply(apply(apply(s,X),Y),X),apply(
% apply(
% apply(b,combinator),
% apply(m,X)),
% apply(Y,X)))
% -> (true)
% Rule [81]
% (eq)(apply(apply(apply(s,X),Y),Y),apply(apply(apply(b,combinator),
% apply(X,Y)),apply(m,Y))) ->
% (false) is composed into [81]
% (eq)(apply(apply(apply(s,X),Y),Y),apply(
% apply(
% apply(b,combinator),
% apply(X,Y)),
% apply(m,Y)))
% -> (true)
% Rule [80]
% (eq)(apply(X,apply(m,combinator)),apply(apply(apply(apply(s,b),apply(b,X)),combinator),combinator))
% -> (false) is composed into [80]
% (eq)(apply(X,apply(m,combinator)),apply(
% apply(
% apply(
% apply(s,b),
% apply(b,X)),combinator),combinator))
% -> (true)
% Rule [79]
% (eq)(apply(apply(X,Y),apply(combinator,Y)),apply(apply(apply(apply(s,b),
% apply(s,X)),combinator),Y))
% -> (false) is composed into [79]
% (eq)(apply(apply(X,Y),apply(combinator,Y)),
% apply(apply(apply(apply(s,b),apply(s,X)),combinator),Y))
% -> (true)
% Rule [78]
% (eq)(apply(apply(apply(X,b),combinator),Y),apply(apply(apply(apply(
% apply(s,s),X),b),combinator),Y))
% -> (false) is composed into [78]
% (eq)(apply(apply(apply(X,b),combinator),Y),
% apply(apply(apply(apply(apply(s,s),X),b),combinator),Y))
% -> (true)
% Rule [77]
% (eq)(apply(apply(apply(s,X),Y),combinator),apply(apply(apply(apply(s,b),X),combinator),
% apply(Y,combinator))) ->
% (false) is composed into [77]
% (eq)(apply(apply(apply(s,X),Y),combinator),
% apply(apply(apply(apply(s,b),X),combinator),
% apply(Y,combinator))) -> (true)
% Rule [76]
% (eq)(apply(apply(X,apply(Y,combinator)),Z),apply(apply(apply(apply(s,b),
% apply(apply(b,X),Y)),combinator),Z))
% -> (false) is composed into [76]
% (eq)(apply(apply(X,apply(Y,combinator)),Z),
% apply(apply(apply(apply(s,b),apply(apply(b,X),Y)),combinator),Z))
% -> (true)
% Rule [75]
% (eq)(apply(apply(apply(apply(apply(b,b),X),combinator),Y),Z),apply(
% apply(
% apply(
% apply(s,b),X),combinator),
% apply(Y,Z)))
% -> (false) is composed into [75]
% (eq)(apply(apply(apply(apply(apply(b,b),X),combinator),Y),Z),
% apply(apply(apply(apply(s,b),X),combinator),
% apply(Y,Z))) -> (true)
% Rule [74]
% (eq)(apply(X,apply(combinator,Y)),apply(apply(apply(apply(s,b),apply(b,X)),combinator),Y))
% -> (false) is composed into [74]
% (eq)(apply(X,apply(combinator,Y)),apply(
% apply(
% apply(
% apply(s,b),
% apply(b,X)),combinator),Y))
% -> (true)
% Rule [72]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(b,combinator),
% apply(apply(b,m),X)),Y)) ->
% (false) is composed into [72]
% (eq)(apply(apply(apply(s,X),X),Y),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(b,m),X)),Y))
% -> (true)
% Rule [71]
% (eq)(apply(apply(combinator,combinator),X),apply(apply(apply(apply(s,b),m),combinator),X))
% -> (false) is composed into [71]
% (eq)(apply(apply(combinator,combinator),X),
% apply(apply(apply(apply(s,b),m),combinator),X))
% -> (true)
% Rule [70]
% (eq)(apply(apply(m,combinator),X),apply(apply(apply(apply(s,b),combinator),combinator),X))
% -> (false) is composed into [70]
% (eq)(apply(apply(m,combinator),X),apply(
% apply(
% apply(
% apply(s,b),combinator),combinator),X))
% -> (true)
% Rule [69]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),Y)) ->
% (false) is composed into [69]
% (eq)(apply(apply(apply(b,X),m),Y),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(b,X),Y)),Y))
% -> (true)
% Rule [68]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(b,combinator),
% apply(apply(b,X),m)),Y)) ->
% (false) is composed into [68]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(b,X),m)),Y))
% -> (true)
% Rule [67]
% (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
% [67]
% (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 [66]
% (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
% [66]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),Y),Z)) -> (true)
% Rule [65]
% (eq)(apply(apply(apply(b,X),m),apply(Y,Z)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(s,Y),Y),Z)))
% -> (false) is composed into [65]
% (eq)(apply(apply(apply(b,X),m),apply(Y,Z)),
% apply(apply(apply(b,combinator),X),apply(
% apply(
% apply(s,Y),Y),Z)))
% -> (true)
% Rule [64]
% (eq)(apply(apply(apply(b,X),Y),apply(Z,Z)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(b,Y),m),Z)))
% -> (false) is composed into [64]
% (eq)(apply(apply(apply(b,X),Y),apply(Z,Z)),
% apply(apply(apply(b,combinator),X),apply(
% apply(
% apply(b,Y),m),Z)))
% -> (true)
% Rule [63]
% (eq)(apply(apply(apply(b,X),Y),apply(m,Z)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(b,Y),Z),Z)))
% -> (false) is composed into [63]
% (eq)(apply(apply(apply(b,X),Y),apply(m,Z)),
% apply(apply(apply(b,combinator),X),apply(
% apply(
% apply(b,Y),Z),Z)))
% -> (true)
% Rule [62]
% (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 [62]
% (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 [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(b,Y),m)),Z),apply(apply(
% apply(b,combinator),X),
% apply(Y,apply(Z,Z))))
% -> (false) is composed into [59]
% (eq)(apply(apply(apply(b,X),apply(apply(b,Y),m)),Z),
% apply(apply(apply(b,combinator),X),apply(Y,
% apply(Z,Z))))
% -> (true)
% Rule [58]
% (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 [58]
% (eq)(apply(apply(apply(b,m),X),Y),apply(combinator,
% apply(
% apply(
% apply(
% apply(
% apply(b,b),X),Y),X),Y)))
% -> (true)
% Rule [57]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),X),m),Y))
% -> (false) is composed into [57]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(
% apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),m),Y))
% -> (true)
% Rule [56]
% (eq)(apply(apply(apply(b,X),apply(apply(b,Y),Z)),Z),apply(apply(
% apply(b,combinator),X),
% apply(Y,apply(m,Z))))
% -> (false) is composed into [56]
% (eq)(apply(apply(apply(b,X),apply(apply(b,Y),Z)),Z),
% apply(apply(apply(b,combinator),X),apply(Y,
% apply(m,Z))))
% -> (true)
% Rule [55]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),X),Y),Y))
% -> (false) is composed into [55]
% (eq)(apply(apply(apply(b,X),m),Y),apply(
% apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),Y),Y))
% -> (true)
% Rule [54]
% (eq)(apply(apply(apply(b,b),X),Y),apply(apply(apply(b,combinator),
% apply(apply(m,b),X)),Y)) ->
% (false) is composed into [54]
% (eq)(apply(apply(apply(b,b),X),Y),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(m,b),X)),Y))
% -> (true)
% Rule [53]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(b,combinator),X),apply(m,Y)))
% -> (false) is composed into [53]
% (eq)(apply(X,apply(Y,Y)),apply(apply(
% apply(b,combinator),X),
% apply(m,Y))) ->
% (true)
% Rule [52]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(b,combinator),X),apply(Y,Y)))
% -> (false) is composed into [52]
% (eq)(apply(X,apply(m,Y)),apply(apply(
% apply(b,combinator),X),
% apply(Y,Y))) ->
% (true)
% Rule [51]
% (eq)(apply(apply(apply(apply(s,b),X),Y),Z),apply(apply(apply(b,combinator),Y),
% apply(apply(X,Y),Z))) ->
% (false) is composed into [51]
% (eq)(apply(apply(apply(apply(s,b),X),Y),Z),
% apply(apply(apply(b,combinator),Y),apply(
% apply(X,Y),Z)))
% -> (true)
% Rule [50]
% (eq)(apply(apply(apply(b,X),Y),X),apply(apply(apply(apply(apply(b,s),b),combinator),Y),X))
% -> (false) is composed into [50]
% (eq)(apply(apply(apply(b,X),Y),X),apply(
% apply(
% apply(
% apply(
% apply(b,s),b),combinator),Y),X))
% -> (true)
% Rule [49]
% (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 [49]
% (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 [48]
% (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 [48]
% (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 [47]
% (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 [47]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(
% apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),Y),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 [43]
% (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 [43]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(apply(apply(b,combinator),m),apply(X,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,m),m),X),apply(apply(apply(b,combinator),
% apply(X,X)),apply(X,X))) ->
% (false) is composed into [41]
% (eq)(apply(apply(apply(b,m),m),X),apply(
% apply(
% apply(b,combinator),
% apply(X,X)),
% apply(X,X)))
% -> (true)
% Rule [39]
% (eq)(apply(apply(apply(b,m),X),Y),apply(apply(apply(b,combinator),
% apply(X,Y)),apply(X,Y))) ->
% (false) is composed into [39]
% (eq)(apply(apply(apply(b,m),X),Y),apply(
% apply(
% apply(b,combinator),
% apply(X,Y)),
% apply(X,Y)))
% -> (true)
% Rule [37]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(b,combinator),m),
% apply(X,Y))) -> (false) is composed into
% [37]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(b,combinator),m),
% apply(X,Y))) -> (true)
% Rule [36]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(b,combinator),apply(apply(b,X),m)),Y))
% -> (false) is composed into [36]
% (eq)(apply(X,apply(Y,Y)),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,X),m)),Y))
% -> (true)
% Rule [35] (eq)(apply(m,X),apply(combinator,apply(X,X))) -> (false) is composed into
% [35] (eq)(apply(m,X),apply(combinator,apply(X,X))) -> (true)
% Rule [34]
% (eq)(apply(apply(X,X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),Y))
% -> (false) is composed into [34]
% (eq)(apply(apply(X,X),Y),apply(apply(
% apply(
% apply(
% apply(
% apply(b,b),b),combinator),m),X),Y))
% -> (true)
% Rule [33]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),m),Y))
% -> (false) is composed into [33]
% (eq)(apply(X,apply(Y,Y)),apply(apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),m),Y))
% -> (true)
% Rule [32]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(b,combinator),X),
% apply(Y,Y))) -> (false) is composed into
% [32]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(b,combinator),X),
% apply(Y,Y))) -> (true)
% Rule [31]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(b,combinator),apply(apply(b,X),Y)),Y))
% -> (false) is composed into [31]
% (eq)(apply(X,apply(m,Y)),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,X),Y)),Y))
% -> (true)
% Rule [30] (eq)(apply(X,X),apply(combinator,apply(m,X))) -> (false) is composed into
% [30] (eq)(apply(X,X),apply(combinator,apply(m,X))) -> (true)
% Rule [29]
% (eq)(apply(apply(m,X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),X),Y))
% -> (false) is composed into [29]
% (eq)(apply(apply(m,X),Y),apply(apply(
% apply(
% apply(
% apply(
% apply(b,b),b),combinator),X),X),Y))
% -> (true)
% Rule [28]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),Y),Y))
% -> (false) is composed into [28]
% (eq)(apply(X,apply(m,Y)),apply(apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),Y),Y))
% -> (true)
% Rule [27]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(b,combinator),X),
% apply(m,Y))) -> (false) is composed into
% [27]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(b,combinator),X),
% apply(m,Y))) -> (true)
% Rule [25]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),Z))
% -> (false) is composed into [25]
% (eq)(apply(apply(X,Y),Z),apply(apply(
% apply(
% apply(
% apply(
% apply(b,b),b),combinator),X),Y),Z))
% -> (true)
% Rule [24]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),Y),Z))
% -> (false) is composed into [24]
% (eq)(apply(X,apply(Y,Z)),apply(apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),Y),Z))
% -> (true)
% Rule [23]
% (eq)(apply(apply(X,Y),apply(Z,Y)),apply(apply(apply(b,combinator),
% apply(apply(s,X),Z)),Y)) ->
% (false) is composed into [23]
% (eq)(apply(apply(X,Y),apply(Z,Y)),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(s,X),Z)),Y))
% -> (true)
% Rule [22]
% (eq)(apply(apply(apply(s,X),Y),Z),apply(apply(apply(b,combinator),
% apply(X,Z)),apply(Y,Z))) ->
% (false) is composed into [22]
% (eq)(apply(apply(apply(s,X),Y),Z),apply(
% apply(
% apply(b,combinator),
% apply(X,Z)),
% apply(Y,Z)))
% -> (true)
% Rule [21]
% (eq)(apply(apply(X,combinator),Y),apply(apply(apply(apply(s,b),X),combinator),Y))
% -> (false) is composed into [21]
% (eq)(apply(apply(X,combinator),Y),apply(
% apply(
% apply(
% apply(s,b),X),combinator),Y))
% -> (true)
% Rule [20]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(b,combinator),apply(apply(b,X),Y)),Z))
% -> (false) is composed into [20]
% (eq)(apply(X,apply(Y,Z)),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,X),Y)),Z))
% -> (true)
% Rule [19]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(b,combinator),X),
% apply(Y,Z))) -> (false) is composed into
% [19]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(b,combinator),X),
% apply(Y,Z))) -> (true)
% Rule [17] (eq)(apply(X,X),apply(apply(apply(b,combinator),m),X)) -> (false) is composed into
% [17] (eq)(apply(X,X),apply(apply(apply(b,combinator),m),X)) -> (true)
% Rule [16] (eq)(apply(m,X),apply(apply(apply(b,combinator),X),X)) -> (false) is composed into
% [16] (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 : [175] (false) -> (true)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 295
% Current number of ordered equations: 0
% Current number of rules: 162
% 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
% [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
% [7] apply(apply(X,Z),apply(Y,Z)) <-> apply(apply(apply(s,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
% [15] apply(m,apply(X,Y)) -> apply(apply(apply(s,X),X),Y); trace = Cp of 7 and 3
% [37] (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(b,combinator),m),
% apply(X,Y))) -> (false); trace = Cp of 15 and 10
% [175] (false) -> (true); trace = Cp of 37 and 3
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.510000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------