%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : COL061-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n100.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 00:19:56 EDT 2014

% Result   : Unsatisfiable 3.52s
% Output   : Refutation 3.52s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : COL061-1 : TPTP v6.0.0. Released v1.0.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n100.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 23:37:33 CDT 2014
% % CPUTime  : 3.52 
% Processing problem /tmp/CiME_40822_n100.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " t,b : constant;  h : 1;  g : 1;  f : 1;  apply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z));
% apply(apply(t,X),Y) = apply(Y,X);
% ";
% 
% let s1 = status F "
% h lr_lex;
% g lr_lex;
% f lr_lex;
% t lr_lex;
% apply lr_lex;
% b lr_lex;
% ";
% 
% let p1 = precedence F "
% apply > f > g > h > b > t";
% 
% let s2 = status F "
% h mul;
% g mul;
% f mul;
% t mul;
% apply mul;
% b mul;
% ";
% 
% let p2 = precedence F "
% apply > f > g > h > b = t";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " apply(apply(apply(X,f(X)),g(X)),h(X)) = apply(f(X),apply(h(X),g(X)));"
% ;
% (*
% let Red_Axioms = normalize_equations Defining_rules Axioms;
% 
% let Red_Conjectures =  normalize_equations Defining_rules Conjectures;
% *)
% #time on;
% 
% let res = prove_conj_by_ordered_completion o Axioms Conjectures;
% 
% #time off;
% 
% 
% let status = if res then "unsatisfiable" else "satisfiable";
% #quit;
% Verbose level is now 1
% 
% F : signature = <signature>
% X : variable_set = <variable set>
% 
% Axioms : (F,X) equations = { apply(apply(apply(b,X),Y),Z) =
% apply(X,apply(Y,Z)),
% apply(apply(t,X),Y) = apply(Y,X) }
% (2 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% 
% [t] = 1;
% [b] = 2;
% [h](x1) = 3 + x1;
% [g](x1) = 4 + x1;
% [f](x1) = 5 + x1;
% [apply](x1,x2) = 1 + x1 + x2;
% Chosen ordering : KBO
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { apply(apply(apply(X,f(X)),g(X)),h(X)) =
% apply(f(X),apply(h(X),g(X))) }
% (1 equation(s))
% time is now on
% 
% Initializing completion ...
% New rule produced : [1] (eq)(X,X) -> (true)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 1
% New rule produced : [2] apply(apply(t,X),Y) -> apply(Y,X)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 2
% New rule produced :
% [3]
% (eq)(apply(apply(apply(X,f(X)),g(X)),h(X)),apply(f(X),apply(h(X),g(X)))) ->
% (false)
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced : [4] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [5]
% (eq)(apply(apply(g(t),f(t)),h(t)),apply(f(t),apply(h(t),g(t)))) -> (false)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6]
% (eq)(apply(f(b),apply(g(b),h(b))),apply(f(b),apply(h(b),g(b)))) -> (false)
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7]
% (eq)(apply(apply(apply(f(apply(t,X)),X),g(apply(t,X))),h(apply(t,X))),
% apply(f(apply(t,X)),apply(h(apply(t,X)),g(apply(t,X))))) -> (false)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8]
% (eq)(apply(apply(X,apply(f(apply(b,X)),g(apply(b,X)))),h(apply(b,X))),
% apply(f(apply(b,X)),apply(h(apply(b,X)),g(apply(b,X))))) -> (false)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9]
% (eq)(apply(h(apply(b,t)),apply(f(apply(b,t)),g(apply(b,t)))),apply(f(
% apply(b,t)),
% apply(h(
% apply(b,t)),
% g(apply(b,t)))))
% -> (false)
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10]
% (eq)(apply(apply(apply(f(apply(b,apply(t,X))),g(apply(b,apply(t,X)))),X),
% h(apply(b,apply(t,X)))),apply(f(apply(b,apply(t,X))),apply(h(apply(b,
% apply(t,X))),
% g(apply(b,apply(t,X))))))
% -> (false)
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11]
% (eq)(apply(X,apply(apply(f(apply(b,apply(b,X))),g(apply(b,apply(b,X)))),
% h(apply(b,apply(b,X))))),apply(f(apply(b,apply(b,X))),apply(
% h(
% apply(b,
% apply(b,X))),
% g(
% apply(b,
% apply(b,X))))))
% -> (false)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12]
% (eq)(apply(apply(apply(X,apply(Y,f(apply(apply(b,X),Y)))),g(apply(apply(b,X),Y))),
% h(apply(apply(b,X),Y))),apply(f(apply(apply(b,X),Y)),apply(h(apply(
% apply(b,X),Y)),
% g(apply(apply(b,X),Y)))))
% -> (false)
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13]
% (eq)(apply(apply(g(apply(apply(b,t),X)),apply(X,f(apply(apply(b,t),X)))),
% h(apply(apply(b,t),X))),apply(f(apply(apply(b,t),X)),apply(h(apply(
% apply(b,t),X)),
% g(apply(apply(b,t),X)))))
% -> (false)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14]
% (eq)(apply(apply(X,f(apply(apply(b,b),X))),apply(g(apply(apply(b,b),X)),
% h(apply(apply(b,b),X)))),apply(
% f(
% apply(
% apply(b,b),X)),
% apply(
% h(
% apply(
% apply(b,b),X)),
% g(
% apply(
% apply(b,b),X)))))
% -> (false)
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15]
% (eq)(apply(apply(g(apply(apply(b,b),t)),h(apply(apply(b,b),t))),f(apply(
% apply(b,b),t))),
% apply(f(apply(apply(b,b),t)),apply(h(apply(apply(b,b),t)),g(apply(apply(b,b),t)))))
% -> (false)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16]
% (eq)(apply(apply(apply(f(apply(b,apply(b,apply(t,X)))),g(apply(b,apply(b,
% apply(t,X))))),
% h(apply(b,apply(b,apply(t,X))))),X),apply(f(apply(b,apply(b,
% apply(t,X)))),
% apply(h(apply(b,apply(b,
% apply(t,X)))),
% g(apply(b,apply(b,apply(t,X)))))))
% -> (false)
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17]
% (eq)(apply(apply(g(apply(apply(b,t),apply(t,X))),apply(f(apply(apply(b,t),
% apply(t,X))),X)),
% h(apply(apply(b,t),apply(t,X)))),apply(f(apply(apply(b,t),apply(t,X))),
% apply(h(apply(apply(b,t),apply(t,X))),
% g(apply(apply(b,t),apply(t,X)))))) ->
% (false)
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18]
% (eq)(apply(apply(f(apply(apply(b,b),apply(t,X))),X),apply(g(apply(apply(b,b),
% apply(t,X))),
% h(apply(apply(b,b),
% apply(t,X))))),
% apply(f(apply(apply(b,b),apply(t,X))),apply(h(apply(apply(b,b),apply(t,X))),
% g(apply(apply(b,b),apply(t,X)))))) ->
% (false)
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19]
% (eq)(apply(X,apply(f(apply(apply(b,b),apply(b,X))),apply(g(apply(apply(b,b),
% apply(b,X))),
% h(apply(apply(b,b),
% apply(b,X)))))),
% apply(f(apply(apply(b,b),apply(b,X))),apply(h(apply(apply(b,b),apply(b,X))),
% g(apply(apply(b,b),apply(b,X)))))) ->
% (false)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20]
% (eq)(apply(apply(X,apply(Y,apply(f(apply(b,apply(apply(b,X),Y))),g(apply(b,
% apply(
% apply(b,X),Y)))))),
% h(apply(b,apply(apply(b,X),Y)))),apply(f(apply(b,apply(apply(b,X),Y))),
% apply(h(apply(b,apply(apply(b,X),Y))),
% g(apply(b,apply(apply(b,X),Y)))))) ->
% (false)
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21]
% (eq)(apply(h(apply(b,apply(apply(b,t),X))),apply(X,apply(f(apply(b,apply(
% apply(b,t),X))),
% g(apply(b,apply(apply(b,t),X)))))),
% apply(f(apply(b,apply(apply(b,t),X))),apply(h(apply(b,apply(apply(b,t),X))),
% g(apply(b,apply(apply(b,t),X)))))) ->
% (false)
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22]
% (eq)(apply(apply(apply(X,apply(f(apply(apply(b,X),apply(t,Y))),Y)),g(
% apply(
% apply(b,X),
% apply(t,Y)))),
% h(apply(apply(b,X),apply(t,Y)))),apply(f(apply(apply(b,X),apply(t,Y))),
% apply(h(apply(apply(b,X),apply(t,Y))),
% g(apply(apply(b,X),apply(t,Y)))))) ->
% (false)
% Current number of equations to process: 15
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [23]
% (eq)(apply(apply(apply(apply(X,f(apply(apply(b,apply(t,Y)),X))),Y),g(
% apply(
% apply(b,
% apply(t,Y)),X))),
% h(apply(apply(b,apply(t,Y)),X))),apply(f(apply(apply(b,apply(t,Y)),X)),
% apply(h(apply(apply(b,apply(t,Y)),X)),
% g(apply(apply(b,apply(t,Y)),X))))) ->
% (false)
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [24]
% (eq)(apply(apply(apply(X,f(apply(apply(b,apply(t,X)),t))),g(apply(apply(b,
% apply(t,X)),t))),
% h(apply(apply(b,apply(t,X)),t))),apply(f(apply(apply(b,apply(t,X)),t)),
% apply(h(apply(apply(b,apply(t,X)),t)),
% g(apply(apply(b,apply(t,X)),t))))) ->
% (false)
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [25]
% (eq)(apply(apply(f(apply(apply(b,apply(t,X)),b)),apply(X,g(apply(apply(b,
% apply(t,X)),b)))),
% h(apply(apply(b,apply(t,X)),b))),apply(f(apply(apply(b,apply(t,X)),b)),
% apply(h(apply(apply(b,apply(t,X)),b)),
% g(apply(apply(b,apply(t,X)),b))))) ->
% (false)
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [26]
% (eq)(apply(apply(g(apply(apply(b,apply(t,t)),t)),f(apply(apply(b,apply(t,t)),t))),
% h(apply(apply(b,apply(t,t)),t))),apply(f(apply(apply(b,apply(t,t)),t)),
% apply(h(apply(apply(b,apply(t,t)),t)),
% g(apply(apply(b,apply(t,t)),t))))) ->
% (false)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [27]
% (eq)(apply(f(apply(apply(b,apply(t,b)),t)),apply(g(apply(apply(b,apply(t,b)),t)),
% h(apply(apply(b,apply(t,b)),t)))),
% apply(f(apply(apply(b,apply(t,b)),t)),apply(h(apply(apply(b,apply(t,b)),t)),
% g(apply(apply(b,apply(t,b)),t))))) ->
% (false)
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [28]
% (eq)(apply(apply(X,apply(apply(Y,f(apply(apply(b,apply(b,X)),Y))),g(apply(
% apply(b,
% apply(b,X)),Y)))),
% h(apply(apply(b,apply(b,X)),Y))),apply(f(apply(apply(b,apply(b,X)),Y)),
% apply(h(apply(apply(b,apply(b,X)),Y)),
% g(apply(apply(b,apply(b,X)),Y))))) ->
% (false)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [29]
% (eq)(apply(apply(X,apply(g(apply(apply(b,apply(b,X)),t)),f(apply(apply(b,
% apply(b,X)),t)))),
% h(apply(apply(b,apply(b,X)),t))),apply(f(apply(apply(b,apply(b,X)),t)),
% apply(h(apply(apply(b,apply(b,X)),t)),
% g(apply(apply(b,apply(b,X)),t))))) ->
% (false)
% Current number of equations to process: 31
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [30]
% (eq)(apply(h(apply(apply(b,apply(b,t)),X)),apply(apply(X,f(apply(apply(b,
% apply(b,t)),X))),
% g(apply(apply(b,apply(b,t)),X)))),
% apply(f(apply(apply(b,apply(b,t)),X)),apply(h(apply(apply(b,apply(b,t)),X)),
% g(apply(apply(b,apply(b,t)),X))))) ->
% (false)
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [31]
% (eq)(apply(h(apply(apply(b,apply(b,t)),t)),apply(g(apply(apply(b,apply(b,t)),t)),
% f(apply(apply(b,apply(b,t)),t)))),
% apply(f(apply(apply(b,apply(b,t)),t)),apply(h(apply(apply(b,apply(b,t)),t)),
% g(apply(apply(b,apply(b,t)),t))))) ->
% (false)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [32]
% (eq)(apply(apply(f(apply(apply(b,b),apply(b,apply(t,X)))),apply(g(apply(
% apply(b,b),
% apply(b,
% apply(t,X)))),
% h(apply(apply(b,b),
% apply(b,apply(t,X)))))),X),
% apply(f(apply(apply(b,b),apply(b,apply(t,X)))),apply(h(apply(apply(b,b),
% apply(b,apply(t,X)))),
% g(apply(apply(b,b),apply(b,
% apply(t,X)))))))
% -> (false)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [33]
% (eq)(apply(h(apply(b,apply(apply(b,t),apply(t,X)))),apply(apply(f(apply(b,
% apply(
% apply(b,t),
% apply(t,X)))),
% g(apply(b,apply(
% apply(b,t),
% apply(t,X))))),X)),
% apply(f(apply(b,apply(apply(b,t),apply(t,X)))),apply(h(apply(b,apply(
% apply(b,t),
% apply(t,X)))),
% g(apply(b,apply(apply(b,t),
% apply(t,X))))))) ->
% (false)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [34]
% (eq)(apply(apply(apply(f(apply(apply(b,apply(t,apply(t,X))),t)),X),g(
% apply(
% apply(b,
% apply(t,
% apply(t,X))),t))),
% h(apply(apply(b,apply(t,apply(t,X))),t))),apply(f(apply(apply(b,
% apply(t,
% apply(t,X))),t)),
% apply(h(apply(apply(b,
% apply(t,
% apply(t,X))),t)),
% g(apply(apply(b,apply(t,
% apply(t,X))),t)))))
% -> (false)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [35]
% (eq)(apply(apply(X,apply(f(apply(apply(b,apply(t,apply(b,X))),t)),g(apply(
% apply(b,
% apply(t,
% apply(b,X))),t)))),
% h(apply(apply(b,apply(t,apply(b,X))),t))),apply(f(apply(apply(b,
% apply(t,
% apply(b,X))),t)),
% apply(h(apply(apply(b,
% apply(t,
% apply(b,X))),t)),
% g(apply(apply(b,apply(t,
% apply(b,X))),t)))))
% -> (false)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [36]
% (eq)(apply(h(apply(apply(b,apply(t,apply(b,t))),t)),apply(f(apply(apply(b,
% apply(t,
% apply(b,t))),t)),
% g(apply(apply(b,apply(t,
% apply(b,t))),t)))),
% apply(f(apply(apply(b,apply(t,apply(b,t))),t)),apply(h(apply(apply(b,
% apply(t,
% apply(b,t))),t)),
% g(apply(apply(b,apply(t,
% apply(b,t))),t)))))
% -> (false)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [37]
% (eq)(apply(apply(f(apply(apply(b,apply(t,apply(t,X))),b)),apply(g(apply(
% apply(b,
% apply(t,
% apply(t,X))),b)),X)),
% h(apply(apply(b,apply(t,apply(t,X))),b))),apply(f(apply(apply(b,
% apply(t,
% apply(t,X))),b)),
% apply(h(apply(apply(b,
% apply(t,
% apply(t,X))),b)),
% g(apply(apply(b,apply(t,
% apply(t,X))),b)))))
% -> (false)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [38]
% (eq)(apply(apply(apply(g(apply(apply(b,apply(b,apply(t,X))),t)),f(apply(
% apply(b,
% apply(b,
% apply(t,X))),t))),X),
% h(apply(apply(b,apply(b,apply(t,X))),t))),apply(f(apply(apply(b,
% apply(b,
% apply(t,X))),t)),
% apply(h(apply(apply(b,
% apply(b,
% apply(t,X))),t)),
% g(apply(apply(b,apply(b,
% apply(t,X))),t)))))
% -> (false)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [39]
% (eq)(apply(X,apply(apply(g(apply(apply(b,apply(b,apply(b,X))),t)),f(apply(
% apply(b,
% apply(b,
% apply(b,X))),t))),
% h(apply(apply(b,apply(b,apply(b,X))),t)))),apply(f(apply(
% apply(b,
% apply(b,
% apply(b,X))),t)),
% apply(h(apply(
% apply(b,
% apply(b,
% apply(b,X))),t)),
% g(apply(apply(b,
% apply(b,
% apply(b,X))),t)))))
% -> (false)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [40]
% (eq)(apply(h(apply(apply(b,apply(b,t)),apply(t,X))),apply(apply(f(apply(
% apply(b,
% apply(b,t)),
% apply(t,X))),X),
% g(apply(apply(b,apply(b,t)),
% apply(t,X))))),
% apply(f(apply(apply(b,apply(b,t)),apply(t,X))),apply(h(apply(apply(b,
% apply(b,t)),
% apply(t,X))),g(
% apply(
% apply(b,
% apply(b,t)),
% apply(t,X))))))
% -> (false)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [41]
% (eq)(apply(h(apply(apply(b,apply(b,t)),apply(b,X))),apply(X,apply(f(apply(
% apply(b,
% apply(b,t)),
% apply(b,X))),
% g(apply(apply(b,
% apply(b,t)),
% apply(b,X)))))),
% apply(f(apply(apply(b,apply(b,t)),apply(b,X))),apply(h(apply(apply(b,
% apply(b,t)),
% apply(b,X))),g(
% apply(
% apply(b,
% apply(b,t)),
% apply(b,X))))))
% -> (false)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [42]
% (eq)(apply(X,apply(Y,apply(apply(f(apply(b,apply(b,apply(apply(b,X),Y)))),
% g(apply(b,apply(b,apply(apply(b,X),Y))))),
% h(apply(b,apply(b,apply(apply(b,X),Y))))))),apply(
% f(apply(b,
% apply(b,
% apply(
% apply(b,X),Y)))),
% apply(
% h(apply(b,
% apply(b,
% apply(
% apply(b,X),Y)))),
% g(apply(b,
% apply(b,
% apply(
% apply(b,X),Y)))))))
% -> (false)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [43]
% (eq)(apply(apply(g(apply(apply(b,t),apply(apply(b,X),Y))),apply(X,apply(Y,
% f(apply(
% apply(b,t),
% apply(
% apply(b,X),Y)))))),
% h(apply(apply(b,t),apply(apply(b,X),Y)))),apply(f(apply(apply(b,t),
% apply(apply(b,X),Y))),
% apply(h(apply(apply(b,t),
% apply(apply(b,X),Y))),
% g(apply(apply(b,t),apply(
% apply(b,X),Y))))))
% -> (false)
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [44]
% (eq)(apply(apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X),Y))))),
% apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),
% apply(apply(b,X),Y))))),
% apply(f(apply(apply(b,b),apply(apply(b,X),Y))),apply(h(apply(apply(b,b),
% apply(apply(b,X),Y))),
% g(apply(apply(b,b),apply(
% apply(b,X),Y))))))
% -> (false)
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [45]
% (eq)(apply(apply(g(apply(apply(b,b),apply(apply(b,t),X))),h(apply(apply(b,b),
% apply(apply(b,t),X)))),
% apply(X,f(apply(apply(b,b),apply(apply(b,t),X))))),apply(f(apply(
% apply(b,b),
% apply(
% apply(b,t),X))),
% apply(h(apply(
% apply(b,b),
% apply(
% apply(b,t),X))),
% g(apply(apply(b,b),
% apply(apply(b,t),X))))))
% -> (false)
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [46]
% (eq)(apply(apply(X,apply(apply(f(apply(b,apply(apply(b,X),apply(t,Y)))),
% g(apply(b,apply(apply(b,X),apply(t,Y))))),Y)),
% h(apply(b,apply(apply(b,X),apply(t,Y))))),apply(f(apply(b,apply(
% apply(b,X),
% apply(t,Y)))),
% apply(h(apply(b,apply(
% apply(b,X),
% apply(t,Y)))),
% g(apply(b,apply(apply(b,X),
% apply(t,Y))))))) ->
% (false)
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 46
% New rule produced :
% [47]
% (eq)(apply(apply(apply(X,apply(f(apply(b,apply(apply(b,apply(t,Y)),X))),
% g(apply(b,apply(apply(b,apply(t,Y)),X))))),Y),
% h(apply(b,apply(apply(b,apply(t,Y)),X)))),apply(f(apply(b,apply(
% apply(b,
% apply(t,Y)),X))),
% apply(h(apply(b,apply(
% apply(b,
% apply(t,Y)),X))),
% g(apply(b,apply(apply(b,
% apply(t,Y)),X))))))
% -> (false)
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [48]
% (eq)(apply(apply(X,apply(f(apply(b,apply(apply(b,apply(t,X)),t))),g(apply(b,
% apply(
% apply(b,
% apply(t,X)),t))))),
% h(apply(b,apply(apply(b,apply(t,X)),t)))),apply(f(apply(b,apply(
% apply(b,
% apply(t,X)),t))),
% apply(h(apply(b,apply(
% apply(b,
% apply(t,X)),t))),
% g(apply(b,apply(apply(b,
% apply(t,X)),t))))))
% -> (false)
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [49]
% (eq)(apply(apply(f(apply(b,apply(apply(b,apply(t,X)),b))),g(apply(b,apply(
% apply(b,
% apply(t,X)),b)))),
% apply(X,h(apply(b,apply(apply(b,apply(t,X)),b))))),apply(f(apply(b,
% apply(
% apply(b,
% apply(t,X)),b))),
% apply(h(apply(b,
% apply(
% apply(b,
% apply(t,X)),b))),
% g(apply(b,apply(
% apply(b,
% apply(t,X)),b))))))
% -> (false)
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [50]
% (eq)(apply(h(apply(b,apply(apply(b,apply(t,t)),t))),apply(f(apply(b,apply(
% apply(b,
% apply(t,t)),t))),
% g(apply(b,apply(apply(b,
% apply(t,t)),t))))),
% apply(f(apply(b,apply(apply(b,apply(t,t)),t))),apply(h(apply(b,apply(
% apply(b,
% apply(t,t)),t))),
% g(apply(b,apply(apply(b,
% apply(t,t)),t))))))
% -> (false)
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [51]
% (eq)(apply(X,apply(apply(Y,apply(f(apply(b,apply(apply(b,apply(b,X)),Y))),
% g(apply(b,apply(apply(b,apply(b,X)),Y))))),
% h(apply(b,apply(apply(b,apply(b,X)),Y))))),apply(f(apply(b,
% apply(
% apply(b,
% apply(b,X)),Y))),
% apply(h(apply(b,
% apply(
% apply(b,
% apply(b,X)),Y))),
% g(apply(b,apply(
% apply(b,
% apply(b,X)),Y))))))
% -> (false)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [52]
% (eq)(apply(X,apply(h(apply(b,apply(apply(b,apply(b,X)),t))),apply(f(apply(b,
% apply(
% apply(b,
% apply(b,X)),t))),
% g(apply(b,
% apply(apply(b,
% apply(b,X)),t)))))),
% apply(f(apply(b,apply(apply(b,apply(b,X)),t))),apply(h(apply(b,apply(
% apply(b,
% apply(b,X)),t))),
% g(apply(b,apply(apply(b,
% apply(b,X)),t))))))
% -> (false)
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [53]
% (eq)(apply(apply(apply(apply(f(apply(apply(b,apply(t,X)),apply(t,Y))),Y),X),
% g(apply(apply(b,apply(t,X)),apply(t,Y)))),h(apply(apply(b,
% apply(t,X)),
% apply(t,Y)))),
% apply(f(apply(apply(b,apply(t,X)),apply(t,Y))),apply(h(apply(apply(b,
% apply(t,X)),
% apply(t,Y))),g(
% apply(
% apply(b,
% apply(t,X)),
% apply(t,Y))))))
% -> (false)
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [54]
% (eq)(apply(apply(X,apply(apply(f(apply(apply(b,apply(b,X)),apply(t,Y))),Y),
% g(apply(apply(b,apply(b,X)),apply(t,Y))))),h(apply(
% apply(b,
% apply(b,X)),
% apply(t,Y)))),
% apply(f(apply(apply(b,apply(b,X)),apply(t,Y))),apply(h(apply(apply(b,
% apply(b,X)),
% apply(t,Y))),g(
% apply(
% apply(b,
% apply(b,X)),
% apply(t,Y))))))
% -> (false)
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [55]
% (eq)(apply(apply(apply(X,apply(f(apply(apply(b,apply(t,Y)),apply(b,X))),Y)),
% g(apply(apply(b,apply(t,Y)),apply(b,X)))),h(apply(apply(b,
% apply(t,Y)),
% apply(b,X)))),
% apply(f(apply(apply(b,apply(t,Y)),apply(b,X))),apply(h(apply(apply(b,
% apply(t,Y)),
% apply(b,X))),g(
% apply(
% apply(b,
% apply(t,Y)),
% apply(b,X))))))
% -> (false)
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [56]
% (eq)(apply(apply(g(apply(apply(b,apply(t,X)),apply(b,t))),apply(f(apply(
% apply(b,
% apply(t,X)),
% apply(b,t))),X)),
% h(apply(apply(b,apply(t,X)),apply(b,t)))),apply(f(apply(apply(b,
% apply(t,X)),
% apply(b,t))),apply(
% h(
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t))),
% g(
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t))))))
% -> (false)
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [57]
% (eq)(apply(apply(f(apply(apply(b,apply(t,X)),apply(b,b))),X),apply(g(
% apply(
% apply(b,
% apply(t,X)),
% apply(b,b))),
% h(apply(
% apply(b,
% apply(t,X)),
% apply(b,b))))),
% apply(f(apply(apply(b,apply(t,X)),apply(b,b))),apply(h(apply(apply(b,
% apply(t,X)),
% apply(b,b))),g(
% apply(
% apply(b,
% apply(t,X)),
% apply(b,b))))))
% -> (false)
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [58]
% (eq)(apply(apply(apply(apply(X,f(apply(apply(b,apply(b,apply(t,Y))),X))),
% g(apply(apply(b,apply(b,apply(t,Y))),X))),Y),h(apply(
% apply(b,
% apply(b,
% apply(t,Y))),X))),
% apply(f(apply(apply(b,apply(b,apply(t,Y))),X)),apply(h(apply(apply(b,
% apply(b,
% apply(t,Y))),X)),
% g(apply(apply(b,apply(b,
% apply(t,Y))),X)))))
% -> (false)
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [59]
% (eq)(apply(apply(f(apply(apply(b,apply(b,apply(t,X))),b)),apply(g(apply(
% apply(b,
% apply(b,
% apply(t,X))),b)),X)),
% h(apply(apply(b,apply(b,apply(t,X))),b))),apply(f(apply(apply(b,
% apply(b,
% apply(t,X))),b)),
% apply(h(apply(apply(b,
% apply(b,
% apply(t,X))),b)),
% g(apply(apply(b,apply(b,
% apply(t,X))),b)))))
% -> (false)
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [60]
% (eq)(apply(apply(X,apply(Y,apply(f(apply(apply(b,apply(b,X)),apply(b,Y))),
% g(apply(apply(b,apply(b,X)),apply(b,Y)))))),
% h(apply(apply(b,apply(b,X)),apply(b,Y)))),apply(f(apply(apply(b,
% apply(b,X)),
% apply(b,Y))),apply(
% h(
% apply(
% apply(b,
% apply(b,X)),
% apply(b,Y))),
% g(
% apply(
% apply(b,
% apply(b,X)),
% apply(b,Y))))))
% -> (false)
% Current number of equations to process: 63
% Current number of ordered equations: 1
% Current number of rules: 60
% New rule produced :
% [61]
% (eq)(apply(X,apply(apply(apply(Y,f(apply(apply(b,apply(b,apply(b,X))),Y))),
% g(apply(apply(b,apply(b,apply(b,X))),Y))),h(apply(
% apply(b,
% apply(b,
% apply(b,X))),Y)))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),Y)),apply(h(apply(apply(b,
% apply(b,
% apply(b,X))),Y)),
% g(apply(apply(b,apply(b,
% apply(b,X))),Y)))))
% -> (false)
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [62]
% (eq)(apply(X,apply(f(apply(apply(b,apply(b,apply(b,X))),b)),apply(g(apply(
% apply(b,
% apply(b,
% apply(b,X))),b)),
% h(apply(apply(b,
% apply(b,
% apply(b,X))),b))))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),b)),apply(h(apply(apply(b,
% apply(b,
% apply(b,X))),b)),
% g(apply(apply(b,apply(b,
% apply(b,X))),b)))))
% -> (false)
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [63]
% (eq)(apply(apply(apply(X,apply(Y,apply(Z,f(apply(apply(b,X),apply(apply(b,Y),Z)))))),
% g(apply(apply(b,X),apply(apply(b,Y),Z)))),h(apply(apply(b,X),
% apply(apply(b,Y),Z)))),
% apply(f(apply(apply(b,X),apply(apply(b,Y),Z))),apply(h(apply(apply(b,X),
% apply(apply(b,Y),Z))),
% g(apply(apply(b,X),apply(
% apply(b,Y),Z))))))
% -> (false)
% Current number of equations to process: 72
% Current number of ordered equations: 1
% Current number of rules: 63
% New rule produced :
% [64]
% (eq)(apply(apply(apply(X,apply(Y,apply(Z,f(apply(apply(b,apply(apply(b,X),Y)),Z))))),
% g(apply(apply(b,apply(apply(b,X),Y)),Z))),h(apply(apply(b,
% apply(apply(b,X),Y)),Z))),
% apply(f(apply(apply(b,apply(apply(b,X),Y)),Z)),apply(h(apply(apply(b,
% apply(apply(b,X),Y)),Z)),
% g(apply(apply(b,apply(
% apply(b,X),Y)),Z)))))
% -> (false)
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [65]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,t),X)),Y)),apply(X,apply(Y,
% f(apply(
% apply(b,
% apply(
% apply(b,t),X)),Y))))),
% h(apply(apply(b,apply(apply(b,t),X)),Y))),apply(f(apply(apply(b,
% apply(apply(b,t),X)),Y)),
% apply(h(apply(apply(b,
% apply(apply(b,t),X)),Y)),
% g(apply(apply(b,apply(
% apply(b,t),X)),Y)))))
% -> (false)
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [66]
% (eq)(apply(apply(X,apply(Y,f(apply(apply(b,apply(apply(b,b),X)),Y)))),
% apply(g(apply(apply(b,apply(apply(b,b),X)),Y)),h(apply(apply(b,apply(
% apply(b,b),X)),Y)))),
% apply(f(apply(apply(b,apply(apply(b,b),X)),Y)),apply(h(apply(apply(b,
% apply(apply(b,b),X)),Y)),
% g(apply(apply(b,apply(
% apply(b,b),X)),Y)))))
% -> (false)
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [67]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,b),t)),X)),h(apply(apply(b,
% apply(
% apply(b,b),t)),X))),
% apply(X,f(apply(apply(b,apply(apply(b,b),t)),X)))),apply(f(apply(
% apply(b,
% apply(
% apply(b,b),t)),X)),
% apply(h(apply(
% apply(b,
% apply(
% apply(b,b),t)),X)),
% g(apply(apply(b,
% apply(
% apply(b,b),t)),X)))))
% -> (false)
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [68]
% (eq)(apply(apply(apply(f(apply(apply(b,apply(t,apply(b,apply(t,X)))),t)),
% g(apply(apply(b,apply(t,apply(b,apply(t,X)))),t))),X),
% h(apply(apply(b,apply(t,apply(b,apply(t,X)))),t))),apply(f(apply(
% apply(b,
% apply(t,
% apply(b,
% apply(t,X)))),t)),
% apply(h(apply(
% apply(b,
% apply(t,
% apply(b,
% apply(t,X)))),t)),
% g(apply(apply(b,
% apply(t,
% apply(b,
% apply(t,X)))),t)))))
% -> (false)
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [69]
% (eq)(apply(X,apply(apply(f(apply(apply(b,apply(t,apply(b,apply(b,X)))),t)),
% g(apply(apply(b,apply(t,apply(b,apply(b,X)))),t))),
% h(apply(apply(b,apply(t,apply(b,apply(b,X)))),t)))),apply(
% f(apply(
% apply(b,
% apply(t,
% apply(b,
% apply(b,X)))),t)),
% apply(
% h(apply(
% apply(b,
% apply(t,
% apply(b,
% apply(b,X)))),t)),
% g(apply(
% apply(b,
% apply(t,
% apply(b,
% apply(b,X)))),t)))))
% -> (false)
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [70]
% (eq)(apply(apply(apply(g(apply(apply(b,apply(b,apply(b,apply(t,X)))),t)),
% f(apply(apply(b,apply(b,apply(b,apply(t,X)))),t))),h(
% apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,X)))),t))),X),
% apply(f(apply(apply(b,apply(b,apply(b,apply(t,X)))),t)),apply(h(apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,X)))),t)),
% g(apply(apply(b,
% apply(b,
% apply(b,
% apply(t,X)))),t)))))
% -> (false)
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [71]
% (eq)(apply(h(apply(apply(b,apply(b,t)),apply(b,apply(t,X)))),apply(apply(
% f(
% apply(
% apply(b,
% apply(b,t)),
% apply(b,
% apply(t,X)))),
% g(
% apply(
% apply(b,
% apply(b,t)),
% apply(b,
% apply(t,X))))),X)),
% apply(f(apply(apply(b,apply(b,t)),apply(b,apply(t,X)))),apply(h(apply(
% apply(b,
% apply(b,t)),
% apply(b,
% apply(t,X)))),
% g(apply(apply(b,
% apply(b,t)),
% apply(b,apply(t,X)))))))
% -> (false)
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [72]
% (eq)(apply(apply(g(apply(apply(b,b),apply(apply(b,t),apply(t,X)))),h(
% apply(
% apply(b,b),
% apply(
% apply(b,t),
% apply(t,X))))),
% apply(f(apply(apply(b,b),apply(apply(b,t),apply(t,X)))),X)),apply(
% f(apply(
% apply(b,b),
% apply(
% apply(b,t),
% apply(t,X)))),
% apply(
% h(apply(
% apply(b,b),
% apply(
% apply(b,t),
% apply(t,X)))),
% g(apply(
% apply(b,b),
% apply(
% apply(b,t),
% apply(t,X)))))))
% -> (false)
% Current number of equations to process: 93
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [73]
% (eq)(apply(apply(apply(f(apply(b,apply(apply(b,apply(t,apply(t,X))),t))),
% g(apply(b,apply(apply(b,apply(t,apply(t,X))),t)))),X),
% h(apply(b,apply(apply(b,apply(t,apply(t,X))),t)))),apply(f(apply(b,
% apply(
% apply(b,
% apply(t,
% apply(t,X))),t))),
% apply(h(apply(b,
% apply(
% apply(b,
% apply(t,
% apply(t,X))),t))),
% g(apply(b,apply(
% apply(b,
% apply(t,
% apply(t,X))),t))))))
% -> (false)
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [74]
% (eq)(apply(X,apply(apply(f(apply(b,apply(apply(b,apply(t,apply(b,X))),t))),
% g(apply(b,apply(apply(b,apply(t,apply(b,X))),t)))),
% h(apply(b,apply(apply(b,apply(t,apply(b,X))),t))))),apply(
% f(apply(b,
% apply(
% apply(b,
% apply(t,
% apply(b,X))),t))),
% apply(
% h(apply(b,
% apply(
% apply(b,
% apply(t,
% apply(b,X))),t))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,
% apply(b,X))),t))))))
% -> (false)
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [75]
% (eq)(apply(apply(f(apply(b,apply(apply(b,apply(t,apply(t,X))),b))),g(
% apply(b,
% apply(
% apply(b,
% apply(t,
% apply(t,X))),b)))),
% apply(h(apply(b,apply(apply(b,apply(t,apply(t,X))),b))),X)),apply(
% f(apply(b,
% apply(
% apply(b,
% apply(t,
% apply(t,X))),b))),
% apply(
% h(apply(b,
% apply(
% apply(b,
% apply(t,
% apply(t,X))),b))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,
% apply(t,X))),b))))))
% -> (false)
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [76]
% (eq)(apply(apply(h(apply(b,apply(apply(b,apply(b,apply(t,X))),t))),apply(
% f(
% apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,X))),t))),
% g(
% apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,X))),t))))),X),
% apply(f(apply(b,apply(apply(b,apply(b,apply(t,X))),t))),apply(h(apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,X))),t))),
% g(apply(b,apply(
% apply(b,
% apply(b,
% apply(t,X))),t))))))
% -> (false)
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [77]
% (eq)(apply(apply(f(apply(apply(b,apply(b,apply(b,apply(t,X)))),b)),apply(
% g(
% apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,X)))),b)),
% h(
% apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,X)))),b)))),X),
% apply(f(apply(apply(b,apply(b,apply(b,apply(t,X)))),b)),apply(h(apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,X)))),b)),
% g(apply(apply(b,
% apply(b,
% apply(b,
% apply(t,X)))),b)))))
% -> (false)
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [78]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,b),t)),apply(t,X))),h(
% apply(
% apply(b,
% apply(
% apply(b,b),t)),
% apply(t,X)))),
% apply(f(apply(apply(b,apply(apply(b,b),t)),apply(t,X))),X)),apply(
% f(apply(
% apply(b,
% apply(
% apply(b,b),t)),
% apply(t,X))),
% apply(
% h(apply(
% apply(b,
% apply(
% apply(b,b),t)),
% apply(t,X))),
% g(apply(
% apply(b,
% apply(
% apply(b,b),t)),
% apply(t,X))))))
% -> (false)
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [79]
% (eq)(apply(X,apply(Y,apply(f(apply(apply(b,b),apply(b,apply(apply(b,X),Y)))),
% apply(g(apply(apply(b,b),apply(b,apply(apply(b,X),Y)))),
% h(apply(apply(b,b),apply(b,apply(apply(b,X),Y)))))))),
% apply(f(apply(apply(b,b),apply(b,apply(apply(b,X),Y)))),apply(h(apply(
% apply(b,b),
% apply(b,
% apply(
% apply(b,X),Y)))),
% g(apply(apply(b,b),
% apply(b,apply(
% apply(b,X),Y)))))))
% -> (false)
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [80]
% (eq)(apply(h(apply(b,apply(apply(b,t),apply(apply(b,X),Y)))),apply(X,
% apply(Y,
% apply(f(
% apply(b,
% apply(
% apply(b,t),
% apply(
% apply(b,X),Y)))),
% g(apply(b,
% apply(
% apply(b,t),
% apply(
% apply(b,X),Y)))))))),
% apply(f(apply(b,apply(apply(b,t),apply(apply(b,X),Y)))),apply(h(apply(b,
% apply(
% apply(b,t),
% apply(
% apply(b,X),Y)))),
% g(apply(b,apply(
% apply(b,t),
% apply(
% apply(b,X),Y)))))))
% -> (false)
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [81]
% (eq)(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,apply(apply(b,X),Y))),t)))),
% g(apply(apply(b,apply(t,apply(apply(b,X),Y))),t))),h(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),t))),
% apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),t)),apply(h(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),t)),
% g(apply(apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),t)))))
% -> (false)
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [82]
% (eq)(apply(apply(g(apply(apply(b,apply(t,apply(apply(b,t),X))),t)),apply(X,
% f(
% apply(
% apply(b,
% apply(t,
% apply(
% apply(b,t),X))),t)))),
% h(apply(apply(b,apply(t,apply(apply(b,t),X))),t))),apply(f(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,t),X))),t)),
% apply(h(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,t),X))),t)),
% g(apply(apply(b,
% apply(t,
% apply(
% apply(b,t),X))),t)))))
% -> (false)
% Current number of equations to process: 100
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [83]
% (eq)(apply(apply(X,f(apply(apply(b,apply(t,apply(apply(b,b),X))),t))),
% apply(g(apply(apply(b,apply(t,apply(apply(b,b),X))),t)),h(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,b),X))),t)))),
% apply(f(apply(apply(b,apply(t,apply(apply(b,b),X))),t)),apply(h(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,b),X))),t)),
% g(apply(apply(b,
% apply(t,
% apply(
% apply(b,b),X))),t)))))
% -> (false)
% Current number of equations to process: 99
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [84]
% (eq)(apply(apply(g(apply(apply(b,apply(t,apply(apply(b,b),t))),t)),h(
% apply(
% apply(b,
% apply(t,
% apply(
% apply(b,b),t))),t))),
% f(apply(apply(b,apply(t,apply(apply(b,b),t))),t))),apply(f(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,b),t))),t)),
% apply(h(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,b),t))),t)),
% g(apply(apply(b,
% apply(t,
% apply(
% apply(b,b),t))),t)))))
% -> (false)
% Current number of equations to process: 104
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [85]
% (eq)(apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(X,
% apply(Y,
% g(
% apply(
% apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),b))))),
% h(apply(apply(b,apply(t,apply(apply(b,X),Y))),b))),apply(f(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),b)),
% apply(h(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),b)),
% g(apply(apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),b)))))
% -> (false)
% Current number of equations to process: 103
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [86]
% (eq)(apply(apply(X,apply(Y,apply(g(apply(apply(b,apply(b,apply(apply(b,X),Y))),t)),
% f(apply(apply(b,apply(b,apply(apply(b,X),Y))),t))))),
% h(apply(apply(b,apply(b,apply(apply(b,X),Y))),t))),apply(f(apply(
% apply(b,
% apply(b,
% apply(
% apply(b,X),Y))),t)),
% apply(h(apply(
% apply(b,
% apply(b,
% apply(
% apply(b,X),Y))),t)),
% g(apply(apply(b,
% apply(b,
% apply(
% apply(b,X),Y))),t)))))
% -> (false)
% Current number of equations to process: 106
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [87]
% (eq)(apply(h(apply(apply(b,apply(b,apply(apply(b,t),X))),t)),apply(X,
% apply(g(
% apply(
% apply(b,
% apply(b,
% apply(
% apply(b,t),X))),t)),
% f(apply(
% apply(b,
% apply(b,
% apply(
% apply(b,t),X))),t))))),
% apply(f(apply(apply(b,apply(b,apply(apply(b,t),X))),t)),apply(h(apply(
% apply(b,
% apply(b,
% apply(
% apply(b,t),X))),t)),
% g(apply(apply(b,
% apply(b,
% apply(
% apply(b,t),X))),t)))))
% -> (false)
% Current number of equations to process: 111
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [88]
% (eq)(apply(h(apply(apply(b,apply(b,t)),apply(apply(b,X),Y))),apply(apply(X,
% apply(Y,
% f(
% apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,X),Y))))),
% g(apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,X),Y))))),
% apply(f(apply(apply(b,apply(b,t)),apply(apply(b,X),Y))),apply(h(apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,X),Y))),
% g(apply(apply(b,
% apply(b,t)),
% apply(apply(b,X),Y))))))
% -> (false)
% Current number of equations to process: 112
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [89]
% (eq)(apply(h(apply(apply(b,apply(b,t)),apply(apply(b,t),X))),apply(g(
% apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,t),X))),
% apply(X,
% f(apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,t),X)))))),
% apply(f(apply(apply(b,apply(b,t)),apply(apply(b,t),X))),apply(h(apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,t),X))),
% g(apply(apply(b,
% apply(b,t)),
% apply(apply(b,t),X))))))
% -> (false)
% Current number of equations to process: 117
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [90]
% (eq)(apply(X,apply(apply(apply(f(apply(b,apply(b,apply(apply(b,X),apply(t,Y))))),
% g(apply(b,apply(b,apply(apply(b,X),apply(t,Y)))))),
% h(apply(b,apply(b,apply(apply(b,X),apply(t,Y)))))),Y)),
% apply(f(apply(b,apply(b,apply(apply(b,X),apply(t,Y))))),apply(h(apply(b,
% apply(b,
% apply(
% apply(b,X),
% apply(t,Y))))),
% g(apply(b,apply(b,
% apply(
% apply(b,X),
% apply(t,Y))))))))
% -> (false)
% Current number of equations to process: 117
% Current number of ordered equations: 1
% Current number of rules: 90
% New rule produced :
% [91]
% (eq)(apply(apply(X,apply(apply(f(apply(b,apply(b,apply(apply(b,apply(t,Y)),X)))),
% g(apply(b,apply(b,apply(apply(b,apply(t,Y)),X))))),
% h(apply(b,apply(b,apply(apply(b,apply(t,Y)),X)))))),Y),
% apply(f(apply(b,apply(b,apply(apply(b,apply(t,Y)),X)))),apply(h(apply(b,
% apply(b,
% apply(
% apply(b,
% apply(t,Y)),X)))),
% g(apply(b,apply(b,
% apply(
% apply(b,
% apply(t,Y)),X)))))))
% -> (false)
% Current number of equations to process: 117
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [92]
% (eq)(apply(X,apply(apply(f(apply(b,apply(b,apply(apply(b,apply(t,X)),t)))),
% g(apply(b,apply(b,apply(apply(b,apply(t,X)),t))))),
% h(apply(b,apply(b,apply(apply(b,apply(t,X)),t)))))),apply(
% f(apply(b,
% apply(b,
% apply(
% apply(b,
% apply(t,X)),t)))),
% apply(
% h(apply(b,
% apply(b,
% apply(
% apply(b,
% apply(t,X)),t)))),
% g(apply(b,
% apply(b,
% apply(
% apply(b,
% apply(t,X)),t)))))))
% -> (false)
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [93]
% (eq)(apply(apply(g(apply(apply(b,t),apply(apply(b,X),apply(t,Y)))),apply(X,
% apply(
% f(
% apply(
% apply(b,t),
% apply(
% apply(b,X),
% apply(t,Y)))),Y))),
% h(apply(apply(b,t),apply(apply(b,X),apply(t,Y))))),apply(f(apply(
% apply(b,t),
% apply(
% apply(b,X),
% apply(t,Y)))),
% apply(h(apply(
% apply(b,t),
% apply(
% apply(b,X),
% apply(t,Y)))),
% g(apply(apply(b,t),
% apply(apply(b,X),
% apply(t,Y))))))) ->
% (false)
% Current number of equations to process: 121
% Current number of ordered equations: 1
% Current number of rules: 93
% New rule produced :
% [94]
% (eq)(apply(apply(g(apply(apply(b,t),apply(apply(b,apply(t,X)),Y))),apply(
% apply(Y,
% f(
% apply(
% apply(b,t),
% apply(
% apply(b,
% apply(t,X)),Y)))),X)),
% h(apply(apply(b,t),apply(apply(b,apply(t,X)),Y)))),apply(f(apply(
% apply(b,t),
% apply(
% apply(b,
% apply(t,X)),Y))),
% apply(h(apply(
% apply(b,t),
% apply(
% apply(b,
% apply(t,X)),Y))),
% g(apply(apply(b,t),
% apply(apply(b,
% apply(t,X)),Y))))))
% -> (false)
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [95]
% (eq)(apply(apply(g(apply(apply(b,t),apply(apply(b,apply(t,X)),t))),apply(X,
% f(
% apply(
% apply(b,t),
% apply(
% apply(b,
% apply(t,X)),t))))),
% h(apply(apply(b,t),apply(apply(b,apply(t,X)),t)))),apply(f(apply(
% apply(b,t),
% apply(
% apply(b,
% apply(t,X)),t))),
% apply(h(apply(
% apply(b,t),
% apply(
% apply(b,
% apply(t,X)),t))),
% g(apply(apply(b,t),
% apply(apply(b,
% apply(t,X)),t))))))
% -> (false)
% Current number of equations to process: 125
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [96]
% (eq)(apply(apply(X,apply(f(apply(apply(b,b),apply(apply(b,X),apply(t,Y)))),Y)),
% apply(g(apply(apply(b,b),apply(apply(b,X),apply(t,Y)))),h(apply(
% apply(b,b),
% apply(
% apply(b,X),
% apply(t,Y)))))),
% apply(f(apply(apply(b,b),apply(apply(b,X),apply(t,Y)))),apply(h(apply(
% apply(b,b),
% apply(
% apply(b,X),
% apply(t,Y)))),
% g(apply(apply(b,b),
% apply(apply(b,X),
% apply(t,Y))))))) ->
% (false)
% Current number of equations to process: 125
% Current number of ordered equations: 1
% Current number of rules: 96
% New rule produced :
% [97]
% (eq)(apply(apply(apply(X,f(apply(apply(b,b),apply(apply(b,apply(t,Y)),X)))),Y),
% apply(g(apply(apply(b,b),apply(apply(b,apply(t,Y)),X))),h(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,Y)),X))))),
% apply(f(apply(apply(b,b),apply(apply(b,apply(t,Y)),X))),apply(h(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,Y)),X))),
% g(apply(apply(b,b),
% apply(apply(b,
% apply(t,Y)),X))))))
% -> (false)
% Current number of equations to process: 125
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [98]
% (eq)(apply(apply(X,f(apply(apply(b,b),apply(apply(b,apply(t,X)),t)))),
% apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),t))),h(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,X)),t))))),
% apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),t))),apply(h(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,X)),t))),
% g(apply(apply(b,b),
% apply(apply(b,
% apply(t,X)),t))))))
% -> (false)
% Current number of equations to process: 132
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [99]
% (eq)(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),b))),apply(X,
% apply(g(
% apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,X)),b))),
% h(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,X)),b)))))),
% apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),b))),apply(h(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,X)),b))),
% g(apply(apply(b,b),
% apply(apply(b,
% apply(t,X)),b))))))
% -> (false)
% Current number of equations to process: 131
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [100]
% (eq)(apply(apply(g(apply(apply(b,b),apply(apply(b,apply(t,t)),t))),h(
% apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,t)),t)))),
% f(apply(apply(b,b),apply(apply(b,apply(t,t)),t)))),apply(f(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,t)),t))),
% apply(h(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,t)),t))),
% g(apply(apply(b,b),
% apply(apply(b,
% apply(t,t)),t))))))
% -> (false)
% Current number of equations to process: 134
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [101]
% (eq)(apply(X,apply(apply(Y,f(apply(apply(b,b),apply(apply(b,apply(b,X)),Y)))),
% apply(g(apply(apply(b,b),apply(apply(b,apply(b,X)),Y))),
% h(apply(apply(b,b),apply(apply(b,apply(b,X)),Y)))))),apply(
% f(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(b,X)),Y))),
% apply(
% h(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(b,X)),Y))),
% g(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(b,X)),Y))))))
% -> (false)
% Current number of equations to process: 135
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [102]
% (eq)(apply(X,apply(apply(g(apply(apply(b,b),apply(apply(b,apply(b,X)),t))),
% h(apply(apply(b,b),apply(apply(b,apply(b,X)),t)))),
% f(apply(apply(b,b),apply(apply(b,apply(b,X)),t))))),apply(
% f(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(b,X)),t))),
% apply(
% h(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(b,X)),t))),
% g(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(b,X)),t))))))
% -> (false)
% Current number of equations to process: 140
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [103]
% (eq)(apply(apply(apply(apply(f(apply(b,apply(apply(b,apply(t,X)),apply(t,Y)))),
% g(apply(b,apply(apply(b,apply(t,X)),apply(t,Y))))),Y),X),
% h(apply(b,apply(apply(b,apply(t,X)),apply(t,Y))))),apply(f(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(t,Y)))),
% apply(h(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(t,Y)))),
% g(apply(b,apply(
% apply(b,
% apply(t,X)),
% apply(t,Y)))))))
% -> (false)
% Current number of equations to process: 141
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [104]
% (eq)(apply(X,apply(apply(apply(f(apply(b,apply(apply(b,apply(b,X)),apply(t,Y)))),
% g(apply(b,apply(apply(b,apply(b,X)),apply(t,Y))))),Y),
% h(apply(b,apply(apply(b,apply(b,X)),apply(t,Y)))))),apply(
% f(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(t,Y)))),
% apply(
% h(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(t,Y)))),
% g(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(t,Y)))))))
% -> (false)
% Current number of equations to process: 140
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [105]
% (eq)(apply(apply(X,apply(apply(f(apply(b,apply(apply(b,apply(t,Y)),apply(b,X)))),
% g(apply(b,apply(apply(b,apply(t,Y)),apply(b,X))))),Y)),
% h(apply(b,apply(apply(b,apply(t,Y)),apply(b,X))))),apply(f(apply(b,
% apply(
% apply(b,
% apply(t,Y)),
% apply(b,X)))),
% apply(h(apply(b,
% apply(
% apply(b,
% apply(t,Y)),
% apply(b,X)))),
% g(apply(b,apply(
% apply(b,
% apply(t,Y)),
% apply(b,X)))))))
% -> (false)
% Current number of equations to process: 140
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [106]
% (eq)(apply(h(apply(b,apply(apply(b,apply(t,X)),apply(b,t)))),apply(apply(
% f(
% apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t)))),
% g(
% apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t))))),X)),
% apply(f(apply(b,apply(apply(b,apply(t,X)),apply(b,t)))),apply(h(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t)))),
% g(apply(b,apply(
% apply(b,
% apply(t,X)),
% apply(b,t)))))))
% -> (false)
% Current number of equations to process: 143
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [107]
% (eq)(apply(apply(apply(X,apply(f(apply(b,apply(apply(b,apply(b,apply(t,Y))),X))),
% g(apply(b,apply(apply(b,apply(b,apply(t,Y))),X))))),
% h(apply(b,apply(apply(b,apply(b,apply(t,Y))),X)))),Y),apply(
% f(apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,Y))),X))),
% apply(
% h(apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,Y))),X))),
% g(apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,Y))),X))))))
% -> (false)
% Current number of equations to process: 141
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [108]
% (eq)(apply(apply(f(apply(b,apply(apply(b,apply(b,apply(t,X))),b))),g(
% apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,X))),b)))),
% apply(h(apply(b,apply(apply(b,apply(b,apply(t,X))),b))),X)),apply(
% f(apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,X))),b))),
% apply(
% h(apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,X))),b))),
% g(apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,X))),b))))))
% -> (false)
% Current number of equations to process: 144
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [109]
% (eq)(apply(X,apply(Y,apply(apply(f(apply(b,apply(apply(b,apply(b,X)),
% apply(b,Y)))),g(apply(b,apply(
% apply(b,
% apply(b,X)),
% apply(b,Y))))),
% h(apply(b,apply(apply(b,apply(b,X)),apply(b,Y))))))),
% apply(f(apply(b,apply(apply(b,apply(b,X)),apply(b,Y)))),apply(h(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(b,Y)))),
% g(apply(b,apply(
% apply(b,
% apply(b,X)),
% apply(b,Y)))))))
% -> (false)
% Current number of equations to process: 143
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [110]
% (eq)(apply(apply(apply(apply(f(apply(apply(b,apply(b,apply(t,X))),apply(t,Y))),Y),
% g(apply(apply(b,apply(b,apply(t,X))),apply(t,Y)))),X),
% h(apply(apply(b,apply(b,apply(t,X))),apply(t,Y)))),apply(f(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(t,Y))),
% apply(h(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(t,Y))),
% g(apply(apply(b,
% apply(b,
% apply(t,X))),
% apply(t,Y)))))) ->
% (false)
% Current number of equations to process: 145
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [111]
% (eq)(apply(X,apply(apply(apply(f(apply(apply(b,apply(b,apply(b,X))),apply(t,Y))),Y),
% g(apply(apply(b,apply(b,apply(b,X))),apply(t,Y)))),
% h(apply(apply(b,apply(b,apply(b,X))),apply(t,Y))))),apply(
% f(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(t,Y))),
% apply(
% h(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(t,Y))),
% g(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(t,Y))))))
% -> (false)
% Current number of equations to process: 144
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [112]
% (eq)(apply(apply(apply(apply(f(apply(apply(b,apply(t,X)),apply(b,apply(t,Y)))),X),Y),
% g(apply(apply(b,apply(t,X)),apply(b,apply(t,Y))))),h(apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(t,Y))))),
% apply(f(apply(apply(b,apply(t,X)),apply(b,apply(t,Y)))),apply(h(apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(t,Y)))),
% g(apply(apply(b,
% apply(t,X)),
% apply(b,apply(t,Y)))))))
% -> (false)
% Current number of equations to process: 145
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [113]
% (eq)(apply(apply(X,apply(apply(f(apply(apply(b,apply(t,Y)),apply(b,apply(b,X)))),Y),
% g(apply(apply(b,apply(t,Y)),apply(b,apply(b,X)))))),
% h(apply(apply(b,apply(t,Y)),apply(b,apply(b,X))))),apply(f(apply(
% apply(b,
% apply(t,Y)),
% apply(b,
% apply(b,X)))),
% apply(h(apply(
% apply(b,
% apply(t,Y)),
% apply(b,
% apply(b,X)))),
% g(apply(apply(b,
% apply(t,Y)),
% apply(b,apply(b,X)))))))
% -> (false)
% Current number of equations to process: 144
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [114]
% (eq)(apply(h(apply(apply(b,apply(t,X)),apply(b,apply(b,t)))),apply(apply(
% f(
% apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(b,t)))),X),
% g(apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(b,t)))))),
% apply(f(apply(apply(b,apply(t,X)),apply(b,apply(b,t)))),apply(h(apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(b,t)))),
% g(apply(apply(b,
% apply(t,X)),
% apply(b,apply(b,t)))))))
% -> (false)
% Current number of equations to process: 147
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [115]
% (eq)(apply(apply(apply(X,apply(f(apply(apply(b,apply(b,apply(t,Y))),apply(b,X))),
% g(apply(apply(b,apply(b,apply(t,Y))),apply(b,X))))),Y),
% h(apply(apply(b,apply(b,apply(t,Y))),apply(b,X)))),apply(f(apply(
% apply(b,
% apply(b,
% apply(t,Y))),
% apply(b,X))),
% apply(h(apply(
% apply(b,
% apply(b,
% apply(t,Y))),
% apply(b,X))),
% g(apply(apply(b,
% apply(b,
% apply(t,Y))),
% apply(b,X)))))) ->
% (false)
% Current number of equations to process: 144
% Current number of ordered equations: 1
% Current number of rules: 115
% New rule produced :
% [116]
% (eq)(apply(apply(X,apply(apply(f(apply(apply(b,apply(b,X)),apply(b,apply(t,Y)))),
% g(apply(apply(b,apply(b,X)),apply(b,apply(t,Y))))),Y)),
% h(apply(apply(b,apply(b,X)),apply(b,apply(t,Y))))),apply(f(apply(
% apply(b,
% apply(b,X)),
% apply(b,
% apply(t,Y)))),
% apply(h(apply(
% apply(b,
% apply(b,X)),
% apply(b,
% apply(t,Y)))),
% g(apply(apply(b,
% apply(b,X)),
% apply(b,apply(t,Y)))))))
% -> (false)
% Current number of equations to process: 144
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [117]
% (eq)(apply(apply(X,apply(f(apply(apply(b,apply(b,apply(t,X))),apply(b,t))),
% g(apply(apply(b,apply(b,apply(t,X))),apply(b,t))))),
% h(apply(apply(b,apply(b,apply(t,X))),apply(b,t)))),apply(f(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,t))),
% apply(h(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,t))),
% g(apply(apply(b,
% apply(b,
% apply(t,X))),
% apply(b,t)))))) ->
% (false)
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [118]
% (eq)(apply(apply(f(apply(apply(b,apply(b,apply(t,X))),apply(b,b))),g(
% apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,b)))),
% apply(X,h(apply(apply(b,apply(b,apply(t,X))),apply(b,b))))),apply(
% f(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,b))),
% apply(
% h(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,b))),
% g(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,b))))))
% -> (false)
% Current number of equations to process: 147
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [119]
% (eq)(apply(h(apply(apply(b,apply(b,apply(t,t))),apply(b,t))),apply(f(
% apply(
% apply(b,
% apply(b,
% apply(t,t))),
% apply(b,t))),
% g(apply(
% apply(b,
% apply(b,
% apply(t,t))),
% apply(b,t))))),
% apply(f(apply(apply(b,apply(b,apply(t,t))),apply(b,t))),apply(h(apply(
% apply(b,
% apply(b,
% apply(t,t))),
% apply(b,t))),
% g(apply(apply(b,
% apply(b,
% apply(t,t))),
% apply(b,t)))))) ->
% (false)
% Current number of equations to process: 152
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [120]
% (eq)(apply(X,apply(apply(Y,apply(f(apply(apply(b,apply(b,apply(b,X))),
% apply(b,Y))),g(apply(apply(b,apply(b,
% apply(b,X))),
% apply(b,Y))))),h(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,Y))))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),apply(b,Y))),apply(h(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,Y))),
% g(apply(apply(b,
% apply(b,
% apply(b,X))),
% apply(b,Y)))))) ->
% (false)
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [121]
% (eq)(apply(X,apply(h(apply(apply(b,apply(b,apply(b,X))),apply(b,t))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),apply(b,t))),
% g(apply(apply(b,apply(b,apply(b,X))),apply(b,t)))))),apply(
% f(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,t))),
% apply(
% h(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,t))),
% g(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,t))))))
% -> (false)
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [122]
% (eq)(apply(apply(apply(apply(X,f(apply(apply(b,apply(b,apply(b,apply(t,Y)))),X))),
% g(apply(apply(b,apply(b,apply(b,apply(t,Y)))),X))),h(
% apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,Y)))),X))),Y),
% apply(f(apply(apply(b,apply(b,apply(b,apply(t,Y)))),X)),apply(h(apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,Y)))),X)),
% g(apply(apply(b,
% apply(b,
% apply(b,
% apply(t,Y)))),X)))))
% -> (false)
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [123]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,t),X)),apply(t,Y))),apply(X,
% apply(
% f(
% apply(
% apply(b,
% apply(
% apply(b,t),X)),
% apply(t,Y))),Y))),
% h(apply(apply(b,apply(apply(b,t),X)),apply(t,Y)))),apply(f(apply(
% apply(b,
% apply(
% apply(b,t),X)),
% apply(t,Y))),
% apply(h(apply(
% apply(b,
% apply(
% apply(b,t),X)),
% apply(t,Y))),
% g(apply(apply(b,
% apply(
% apply(b,t),X)),
% apply(t,Y)))))) ->
% (false)
% Current number of equations to process: 157
% Current number of ordered equations: 1
% Current number of rules: 123
% New rule produced :
% [124]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,t),apply(t,X))),Y)),apply(
% apply(Y,
% f(
% apply(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))),Y))),X)),
% h(apply(apply(b,apply(apply(b,t),apply(t,X))),Y))),apply(f(apply(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))),Y)),
% apply(h(apply(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))),Y)),
% g(apply(apply(b,
% apply(
% apply(b,t),
% apply(t,X))),Y)))))
% -> (false)
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [125]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,t),apply(t,X))),t)),apply(X,
% f(
% apply(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))),t)))),
% h(apply(apply(b,apply(apply(b,t),apply(t,X))),t))),apply(f(apply(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))),t)),
% apply(h(apply(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))),t)),
% g(apply(apply(b,
% apply(
% apply(b,t),
% apply(t,X))),t)))))
% -> (false)
% Current number of equations to process: 161
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [126]
% (eq)(apply(apply(X,apply(f(apply(apply(b,apply(apply(b,b),X)),apply(t,Y))),Y)),
% apply(g(apply(apply(b,apply(apply(b,b),X)),apply(t,Y))),h(apply(
% apply(b,
% apply(
% apply(b,b),X)),
% apply(t,Y))))),
% apply(f(apply(apply(b,apply(apply(b,b),X)),apply(t,Y))),apply(h(apply(
% apply(b,
% apply(
% apply(b,b),X)),
% apply(t,Y))),
% g(apply(apply(b,
% apply(
% apply(b,b),X)),
% apply(t,Y)))))) ->
% (false)
% Current number of equations to process: 161
% Current number of ordered equations: 1
% Current number of rules: 126
% New rule produced :
% [127]
% (eq)(apply(apply(apply(X,f(apply(apply(b,apply(apply(b,b),apply(t,Y))),X))),Y),
% apply(g(apply(apply(b,apply(apply(b,b),apply(t,Y))),X)),h(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,Y))),X)))),
% apply(f(apply(apply(b,apply(apply(b,b),apply(t,Y))),X)),apply(h(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,Y))),X)),
% g(apply(apply(b,
% apply(
% apply(b,b),
% apply(t,Y))),X)))))
% -> (false)
% Current number of equations to process: 161
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [128]
% (eq)(apply(apply(X,f(apply(apply(b,apply(apply(b,b),apply(t,X))),t))),
% apply(g(apply(apply(b,apply(apply(b,b),apply(t,X))),t)),h(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,X))),t)))),
% apply(f(apply(apply(b,apply(apply(b,b),apply(t,X))),t)),apply(h(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,X))),t)),
% g(apply(apply(b,
% apply(
% apply(b,b),
% apply(t,X))),t)))))
% -> (false)
% Current number of equations to process: 168
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [129]
% (eq)(apply(f(apply(apply(b,apply(apply(b,b),apply(t,X))),b)),apply(X,
% apply(g(
% apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,X))),b)),
% h(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,X))),b))))),
% apply(f(apply(apply(b,apply(apply(b,b),apply(t,X))),b)),apply(h(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,X))),b)),
% g(apply(apply(b,
% apply(
% apply(b,b),
% apply(t,X))),b)))))
% -> (false)
% Current number of equations to process: 167
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [130]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,b),apply(t,t))),t)),h(
% apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,t))),t))),
% f(apply(apply(b,apply(apply(b,b),apply(t,t))),t))),apply(f(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,t))),t)),
% apply(h(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,t))),t)),
% g(apply(apply(b,
% apply(
% apply(b,b),
% apply(t,t))),t)))))
% -> (false)
% Current number of equations to process: 170
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [131]
% (eq)(apply(X,apply(apply(Y,f(apply(apply(b,apply(apply(b,b),apply(b,X))),Y))),
% apply(g(apply(apply(b,apply(apply(b,b),apply(b,X))),Y)),
% h(apply(apply(b,apply(apply(b,b),apply(b,X))),Y))))),apply(
% f(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(b,X))),Y)),
% apply(
% h(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(b,X))),Y)),
% g(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(b,X))),Y)))))
% -> (false)
% Current number of equations to process: 171
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [132]
% (eq)(apply(X,apply(apply(g(apply(apply(b,apply(apply(b,b),apply(b,X))),t)),
% h(apply(apply(b,apply(apply(b,b),apply(b,X))),t))),
% f(apply(apply(b,apply(apply(b,b),apply(b,X))),t)))),apply(
% f(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(b,X))),t)),
% apply(
% h(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(b,X))),t)),
% g(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(b,X))),t)))))
% -> (false)
% Current number of equations to process: 176
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [133]
% (eq)(apply(apply(X,apply(Y,apply(Z,apply(f(apply(b,apply(apply(b,X),apply(
% apply(b,Y),Z)))),
% g(apply(b,apply(apply(b,X),apply(apply(b,Y),Z)))))))),
% h(apply(b,apply(apply(b,X),apply(apply(b,Y),Z))))),apply(f(apply(b,
% apply(
% apply(b,X),
% apply(
% apply(b,Y),Z)))),
% apply(h(apply(b,
% apply(
% apply(b,X),
% apply(
% apply(b,Y),Z)))),
% g(apply(b,apply(
% apply(b,X),
% apply(
% apply(b,Y),Z)))))))
% -> (false)
% Current number of equations to process: 176
% Current number of ordered equations: 1
% Current number of rules: 133
% New rule produced :
% [134]
% (eq)(apply(apply(X,apply(Y,apply(Z,apply(f(apply(b,apply(apply(b,apply(
% apply(b,X),Y)),Z))),
% g(apply(b,apply(apply(b,apply(apply(b,X),Y)),Z))))))),
% h(apply(b,apply(apply(b,apply(apply(b,X),Y)),Z)))),apply(f(apply(b,
% apply(
% apply(b,
% apply(
% apply(b,X),Y)),Z))),
% apply(h(apply(b,
% apply(
% apply(b,
% apply(
% apply(b,X),Y)),Z))),
% g(apply(b,apply(
% apply(b,
% apply(
% apply(b,X),Y)),Z))))))
% -> (false)
% Current number of equations to process: 176
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [135]
% (eq)(apply(h(apply(b,apply(apply(b,apply(apply(b,t),X)),Y))),apply(X,
% apply(Y,
% apply(f(
% apply(b,
% apply(
% apply(b,
% apply(
% apply(b,t),X)),Y))),
% g(apply(b,
% apply(
% apply(b,
% apply(
% apply(b,t),X)),Y))))))),
% apply(f(apply(b,apply(apply(b,apply(apply(b,t),X)),Y))),apply(h(apply(b,
% apply(
% apply(b,
% apply(
% apply(b,t),X)),Y))),
% g(apply(b,apply(
% apply(b,
% apply(
% apply(b,t),X)),Y))))))
% -> (false)
% Current number of equations to process: 189
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [136]
% (eq)(apply(apply(apply(X,apply(Y,apply(f(apply(apply(b,apply(apply(b,X),Y)),
% apply(t,Z))),Z))),g(apply(apply(b,
% apply(
% apply(b,X),Y)),
% apply(t,Z)))),
% h(apply(apply(b,apply(apply(b,X),Y)),apply(t,Z)))),apply(f(apply(
% apply(b,
% apply(
% apply(b,X),Y)),
% apply(t,Z))),
% apply(h(apply(
% apply(b,
% apply(
% apply(b,X),Y)),
% apply(t,Z))),
% g(apply(apply(b,
% apply(
% apply(b,X),Y)),
% apply(t,Z)))))) ->
% (false)
% Current number of equations to process: 192
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [137]
% (eq)(apply(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,Z)),apply(
% apply(b,X),Y))))),Z),
% g(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y)))),h(apply(
% apply(b,
% apply(t,Z)),
% apply(
% apply(b,X),Y)))),
% apply(f(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y))),apply(h(apply(
% apply(b,
% apply(t,Z)),
% apply(
% apply(b,X),Y))),
% g(apply(apply(b,
% apply(t,Z)),
% apply(apply(b,X),Y))))))
% -> (false)
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [138]
% (eq)(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,X)),apply(apply(b,t),Y))))),
% g(apply(apply(b,apply(t,X)),apply(apply(b,t),Y)))),h(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,t),Y)))),
% apply(f(apply(apply(b,apply(t,X)),apply(apply(b,t),Y))),apply(h(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,t),Y))),
% g(apply(apply(b,
% apply(t,X)),
% apply(apply(b,t),Y))))))
% -> (false)
% Current number of equations to process: 202
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [139]
% (eq)(apply(apply(apply(X,f(apply(apply(b,apply(t,Y)),apply(apply(b,b),X)))),
% apply(Y,g(apply(apply(b,apply(t,Y)),apply(apply(b,b),X))))),
% h(apply(apply(b,apply(t,Y)),apply(apply(b,b),X)))),apply(f(apply(
% apply(b,
% apply(t,Y)),
% apply(
% apply(b,b),X))),
% apply(h(apply(
% apply(b,
% apply(t,Y)),
% apply(
% apply(b,b),X))),
% g(apply(apply(b,
% apply(t,Y)),
% apply(apply(b,b),X))))))
% -> (false)
% Current number of equations to process: 201
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [140]
% (eq)(apply(apply(g(apply(apply(b,apply(t,t)),apply(apply(b,t),X))),apply(X,
% f(
% apply(
% apply(b,
% apply(t,t)),
% apply(
% apply(b,t),X))))),
% h(apply(apply(b,apply(t,t)),apply(apply(b,t),X)))),apply(f(apply(
% apply(b,
% apply(t,t)),
% apply(
% apply(b,t),X))),
% apply(h(apply(
% apply(b,
% apply(t,t)),
% apply(
% apply(b,t),X))),
% g(apply(apply(b,
% apply(t,t)),
% apply(apply(b,t),X))))))
% -> (false)
% Current number of equations to process: 207
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [141]
% (eq)(apply(apply(X,f(apply(apply(b,apply(t,b)),apply(apply(b,t),X)))),
% apply(g(apply(apply(b,apply(t,b)),apply(apply(b,t),X))),h(apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,t),X))))),
% apply(f(apply(apply(b,apply(t,b)),apply(apply(b,t),X))),apply(h(apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,t),X))),
% g(apply(apply(b,
% apply(t,b)),
% apply(apply(b,t),X))))))
% -> (false)
% Current number of equations to process: 206
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [142]
% (eq)(apply(apply(apply(X,g(apply(apply(b,apply(t,X)),apply(apply(b,b),t)))),
% f(apply(apply(b,apply(t,X)),apply(apply(b,b),t)))),h(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),t)))),
% apply(f(apply(apply(b,apply(t,X)),apply(apply(b,b),t))),apply(h(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),t))),
% g(apply(apply(b,
% apply(t,X)),
% apply(apply(b,b),t))))))
% -> (false)
% Current number of equations to process: 212
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [143]
% (eq)(apply(f(apply(apply(b,apply(t,X)),apply(apply(b,b),b))),apply(apply(X,
% g(
% apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b)))),
% h(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b))))),
% apply(f(apply(apply(b,apply(t,X)),apply(apply(b,b),b))),apply(h(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b))),
% g(apply(apply(b,
% apply(t,X)),
% apply(apply(b,b),b))))))
% -> (false)
% Current number of equations to process: 211
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [144]
% (eq)(apply(apply(g(apply(apply(b,apply(t,b)),apply(apply(b,t),t))),h(
% apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,t),t)))),
% f(apply(apply(b,apply(t,b)),apply(apply(b,t),t)))),apply(f(apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,t),t))),
% apply(h(apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,t),t))),
% g(apply(apply(b,
% apply(t,b)),
% apply(apply(b,t),t))))))
% -> (false)
% Current number of equations to process: 216
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [145]
% (eq)(apply(apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),t))),g(
% apply(
% apply(b,
% apply(t,t)),
% apply(
% apply(b,b),t)))),
% h(apply(apply(b,apply(t,t)),apply(apply(b,b),t)))),apply(f(apply(
% apply(b,
% apply(t,t)),
% apply(
% apply(b,b),t))),
% apply(h(apply(
% apply(b,
% apply(t,t)),
% apply(
% apply(b,b),t))),
% g(apply(apply(b,
% apply(t,t)),
% apply(apply(b,b),t))))))
% -> (false)
% Current number of equations to process: 220
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [146]
% (eq)(apply(g(apply(apply(b,apply(t,b)),apply(apply(b,b),t))),apply(f(
% apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,b),t))),
% h(apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,b),t))))),
% apply(f(apply(apply(b,apply(t,b)),apply(apply(b,b),t))),apply(h(apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,b),t))),
% g(apply(apply(b,
% apply(t,b)),
% apply(apply(b,b),t))))))
% -> (false)
% Current number of equations to process: 219
% Current number of ordered equations: 0
% Current number of rules: 146
% Rule [146]
% (eq)(apply(g(apply(apply(b,apply(t,b)),apply(apply(b,b),t))),apply(
% f(apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,b),t))),
% h(apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,b),t))))),
% apply(f(apply(apply(b,apply(t,b)),apply(apply(b,b),t))),apply(h(
% apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,b),t))),
% g(apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,b),t))))))
% -> (false) is composed into [146]
% (eq)(apply(g(apply(apply(b,apply(t,b)),
% apply(apply(b,b),t))),apply(
% f(
% apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,b),t))),
% h(
% apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,b),t))))),
% apply(f(apply(apply(b,apply(t,b)),apply(
% apply(b,b),t))),
% apply(h(apply(apply(b,apply(t,b)),apply(
% apply(b,b),t))),
% g(apply(apply(b,apply(t,b)),apply(apply(b,b),t))))))
% -> (true)
% Rule [145]
% (eq)(apply(apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),t))),
% g(apply(apply(b,apply(t,t)),apply(apply(b,b),t)))),h(
% apply(
% apply(b,
% apply(t,t)),
% apply(
% apply(b,b),t)))),
% apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),t))),apply(h(
% apply(
% apply(b,
% apply(t,t)),
% apply(
% apply(b,b),t))),
% g(apply(
% apply(b,
% apply(t,t)),
% apply(
% apply(b,b),t))))))
% -> (false) is composed into [145]
% (eq)(apply(apply(f(apply(apply(b,apply(t,t)),
% apply(apply(b,b),t))),
% g(apply(apply(b,apply(t,t)),
% apply(apply(b,b),t)))),
% h(apply(apply(b,apply(t,t)),apply(
% apply(b,b),t)))),
% apply(f(apply(apply(b,apply(t,t)),apply(
% apply(b,b),t))),
% apply(h(apply(apply(b,apply(t,t)),apply(
% apply(b,b),t))),
% g(apply(apply(b,apply(t,t)),apply(apply(b,b),t))))))
% -> (true)
% Rule [144]
% (eq)(apply(apply(g(apply(apply(b,apply(t,b)),apply(apply(b,t),t))),
% h(apply(apply(b,apply(t,b)),apply(apply(b,t),t)))),f(
% apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,t),t)))),
% apply(f(apply(apply(b,apply(t,b)),apply(apply(b,t),t))),apply(h(
% apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,t),t))),
% g(apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,t),t))))))
% -> (false) is composed into [144]
% (eq)(apply(apply(g(apply(apply(b,apply(t,b)),
% apply(apply(b,t),t))),
% h(apply(apply(b,apply(t,b)),
% apply(apply(b,t),t)))),
% f(apply(apply(b,apply(t,b)),apply(
% apply(b,t),t)))),
% apply(f(apply(apply(b,apply(t,b)),apply(
% apply(b,t),t))),
% apply(h(apply(apply(b,apply(t,b)),apply(
% apply(b,t),t))),
% g(apply(apply(b,apply(t,b)),apply(apply(b,t),t))))))
% -> (true)
% Rule [143]
% (eq)(apply(f(apply(apply(b,apply(t,X)),apply(apply(b,b),b))),apply(
% apply(X,
% g(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b)))),
% h(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b))))),
% apply(f(apply(apply(b,apply(t,X)),apply(apply(b,b),b))),apply(h(
% apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b))),
% g(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b))))))
% -> (false) is composed into [143]
% (eq)(apply(f(apply(apply(b,apply(t,X)),
% apply(apply(b,b),b))),apply(
% apply(X,
% g(
% apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b)))),
% h(
% apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b))))),
% apply(f(apply(apply(b,apply(t,X)),apply(
% apply(b,b),b))),
% apply(h(apply(apply(b,apply(t,X)),apply(
% apply(b,b),b))),
% g(apply(apply(b,apply(t,X)),apply(apply(b,b),b))))))
% -> (true)
% Rule [142]
% (eq)(apply(apply(apply(X,g(apply(apply(b,apply(t,X)),apply(apply(b,b),t)))),
% f(apply(apply(b,apply(t,X)),apply(apply(b,b),t)))),h(
% apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),t)))),
% apply(f(apply(apply(b,apply(t,X)),apply(apply(b,b),t))),apply(h(
% apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),t))),
% g(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),t))))))
% -> (false) is composed into [142]
% (eq)(apply(apply(apply(X,g(apply(apply(b,
% apply(t,X)),
% apply(apply(b,b),t)))),
% f(apply(apply(b,apply(t,X)),
% apply(apply(b,b),t)))),
% h(apply(apply(b,apply(t,X)),apply(
% apply(b,b),t)))),
% apply(f(apply(apply(b,apply(t,X)),apply(
% apply(b,b),t))),
% apply(h(apply(apply(b,apply(t,X)),apply(
% apply(b,b),t))),
% g(apply(apply(b,apply(t,X)),apply(apply(b,b),t))))))
% -> (true)
% Rule [141]
% (eq)(apply(apply(X,f(apply(apply(b,apply(t,b)),apply(apply(b,t),X)))),
% apply(g(apply(apply(b,apply(t,b)),apply(apply(b,t),X))),h(apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,t),X))))),
% apply(f(apply(apply(b,apply(t,b)),apply(apply(b,t),X))),apply(h(
% apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,t),X))),
% g(apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,t),X))))))
% -> (false) is composed into [141]
% (eq)(apply(apply(X,f(apply(apply(b,apply(t,b)),
% apply(apply(b,t),X)))),
% apply(g(apply(apply(b,apply(t,b)),
% apply(apply(b,t),X))),h(
% apply(
% apply(b,
% apply(t,b)),
% apply(
% apply(b,t),X))))),
% apply(f(apply(apply(b,apply(t,b)),apply(
% apply(b,t),X))),
% apply(h(apply(apply(b,apply(t,b)),apply(
% apply(b,t),X))),
% g(apply(apply(b,apply(t,b)),apply(apply(b,t),X))))))
% -> (true)
% Rule [140]
% (eq)(apply(apply(g(apply(apply(b,apply(t,t)),apply(apply(b,t),X))),
% apply(X,f(apply(apply(b,apply(t,t)),apply(apply(b,t),X))))),
% h(apply(apply(b,apply(t,t)),apply(apply(b,t),X)))),apply(f(
% apply(
% apply(b,
% apply(t,t)),
% apply(
% apply(b,t),X))),
% apply(h(
% apply(
% apply(b,
% apply(t,t)),
% apply(
% apply(b,t),X))),
% g(apply(
% apply(b,
% apply(t,t)),
% apply(
% apply(b,t),X))))))
% -> (false) is composed into [140]
% (eq)(apply(apply(g(apply(apply(b,apply(t,t)),
% apply(apply(b,t),X))),
% apply(X,f(apply(apply(b,apply(t,t)),
% apply(apply(b,t),X))))),
% h(apply(apply(b,apply(t,t)),apply(
% apply(b,t),X)))),
% apply(f(apply(apply(b,apply(t,t)),apply(
% apply(b,t),X))),
% apply(h(apply(apply(b,apply(t,t)),apply(
% apply(b,t),X))),
% g(apply(apply(b,apply(t,t)),apply(apply(b,t),X))))))
% -> (true)
% Rule [139]
% (eq)(apply(apply(apply(X,f(apply(apply(b,apply(t,Y)),apply(apply(b,b),X)))),
% apply(Y,g(apply(apply(b,apply(t,Y)),apply(apply(b,b),X))))),
% h(apply(apply(b,apply(t,Y)),apply(apply(b,b),X)))),apply(f(
% apply(
% apply(b,
% apply(t,Y)),
% apply(
% apply(b,b),X))),
% apply(h(
% apply(
% apply(b,
% apply(t,Y)),
% apply(
% apply(b,b),X))),
% g(apply(
% apply(b,
% apply(t,Y)),
% apply(
% apply(b,b),X))))))
% -> (false) is composed into [139]
% (eq)(apply(apply(apply(X,f(apply(apply(b,
% apply(t,Y)),
% apply(apply(b,b),X)))),
% apply(Y,g(apply(apply(b,apply(t,Y)),
% apply(apply(b,b),X))))),
% h(apply(apply(b,apply(t,Y)),apply(
% apply(b,b),X)))),
% apply(f(apply(apply(b,apply(t,Y)),apply(
% apply(b,b),X))),
% apply(h(apply(apply(b,apply(t,Y)),apply(
% apply(b,b),X))),
% g(apply(apply(b,apply(t,Y)),apply(apply(b,b),X))))))
% -> (true)
% Rule [138]
% (eq)(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,X)),apply(
% apply(b,t),Y))))),
% g(apply(apply(b,apply(t,X)),apply(apply(b,t),Y)))),h(
% apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,t),Y)))),
% apply(f(apply(apply(b,apply(t,X)),apply(apply(b,t),Y))),apply(h(
% apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,t),Y))),
% g(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,t),Y))))))
% -> (false) is composed into [138]
% (eq)(apply(apply(apply(X,apply(Y,f(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,t),Y))))),
% g(apply(apply(b,apply(t,X)),
% apply(apply(b,t),Y)))),
% h(apply(apply(b,apply(t,X)),apply(
% apply(b,t),Y)))),
% apply(f(apply(apply(b,apply(t,X)),apply(
% apply(b,t),Y))),
% apply(h(apply(apply(b,apply(t,X)),apply(
% apply(b,t),Y))),
% g(apply(apply(b,apply(t,X)),apply(apply(b,t),Y))))))
% -> (true)
% Rule [137]
% (eq)(apply(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,Z)),
% apply(apply(b,X),Y))))),Z),
% g(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y)))),h(
% apply(
% apply(b,
% apply(t,Z)),
% apply(
% apply(b,X),Y)))),
% apply(f(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y))),apply(h(
% apply(
% apply(b,
% apply(t,Z)),
% apply(
% apply(b,X),Y))),
% g(apply(
% apply(b,
% apply(t,Z)),
% apply(
% apply(b,X),Y))))))
% -> (false) is composed into [137]
% (eq)(apply(apply(apply(apply(X,apply(Y,
% f(apply(
% apply(b,
% apply(t,Z)),
% apply(
% apply(b,X),Y))))),Z),
% g(apply(apply(b,apply(t,Z)),
% apply(apply(b,X),Y)))),
% h(apply(apply(b,apply(t,Z)),apply(
% apply(b,X),Y)))),
% apply(f(apply(apply(b,apply(t,Z)),apply(
% apply(b,X),Y))),
% apply(h(apply(apply(b,apply(t,Z)),apply(
% apply(b,X),Y))),
% g(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y))))))
% -> (true)
% Rule [136]
% (eq)(apply(apply(apply(X,apply(Y,apply(f(apply(apply(b,apply(apply(b,X),Y)),
% apply(t,Z))),Z))),g(apply(
% apply(b,
% apply(
% apply(b,X),Y)),
% apply(t,Z)))),
% h(apply(apply(b,apply(apply(b,X),Y)),apply(t,Z)))),apply(f(
% apply(
% apply(b,
% apply(
% apply(b,X),Y)),
% apply(t,Z))),
% apply(h(
% apply(
% apply(b,
% apply(
% apply(b,X),Y)),
% apply(t,Z))),
% g(apply(
% apply(b,
% apply(
% apply(b,X),Y)),
% apply(t,Z))))))
% -> (false) is composed into [136]
% (eq)(apply(apply(apply(X,apply(Y,apply(
% f(apply(
% apply(b,
% apply(
% apply(b,X),Y)),
% apply(t,Z))),Z))),
% g(apply(apply(b,apply(apply(b,X),Y)),
% apply(t,Z)))),h(apply(apply(b,
% apply(
% apply(b,X),Y)),
% apply(t,Z)))),
% apply(f(apply(apply(b,apply(apply(b,X),Y)),
% apply(t,Z))),apply(h(apply(apply(b,
% apply(
% apply(b,X),Y)),
% apply(t,Z))),
% g(apply(apply(b,
% apply(apply(b,X),Y)),
% apply(t,Z)))))) ->
% (true)
% Rule [135]
% (eq)(apply(h(apply(b,apply(apply(b,apply(apply(b,t),X)),Y))),apply(X,
% apply(Y,
% apply(
% f(apply(b,
% apply(
% apply(b,
% apply(
% apply(b,t),X)),Y))),
% g(apply(b,
% apply(
% apply(b,
% apply(
% apply(b,t),X)),Y))))))),
% apply(f(apply(b,apply(apply(b,apply(apply(b,t),X)),Y))),apply(h(
% apply(b,
% apply(
% apply(b,
% apply(
% apply(b,t),X)),Y))),
% g(apply(b,
% apply(
% apply(b,
% apply(
% apply(b,t),X)),Y))))))
% -> (false) is composed into [135]
% (eq)(apply(h(apply(b,apply(apply(b,apply(
% apply(b,t),X)),Y))),
% apply(X,apply(Y,apply(f(apply(b,
% apply(apply(b,
% apply(
% apply(b,t),X)),Y))),
% g(apply(b,apply(
% apply(b,
% apply(
% apply(b,t),X)),Y))))))),
% apply(f(apply(b,apply(apply(b,apply(
% apply(b,t),X)),Y))),
% apply(h(apply(b,apply(apply(b,apply(
% apply(b,t),X)),Y))),
% g(apply(b,apply(apply(b,apply(apply(b,t),X)),Y))))))
% -> (true)
% Rule [134]
% (eq)(apply(apply(X,apply(Y,apply(Z,apply(f(apply(b,apply(apply(b,
% apply(apply(b,X),Y)),Z))),
% g(apply(b,apply(apply(b,apply(
% apply(b,X),Y)),Z))))))),
% h(apply(b,apply(apply(b,apply(apply(b,X),Y)),Z)))),apply(f(
% apply(b,
% apply(
% apply(b,
% apply(
% apply(b,X),Y)),Z))),
% apply(h(
% apply(b,
% apply(
% apply(b,
% apply(
% apply(b,X),Y)),Z))),
% g(apply(b,
% apply(
% apply(b,
% apply(
% apply(b,X),Y)),Z))))))
% -> (false) is composed into [134]
% (eq)(apply(apply(X,apply(Y,apply(Z,apply(
% f(
% apply(b,
% apply(
% apply(b,
% apply(
% apply(b,X),Y)),Z))),
% g(
% apply(b,
% apply(
% apply(b,
% apply(
% apply(b,X),Y)),Z))))))),
% h(apply(b,apply(apply(b,apply(apply(b,X),Y)),Z)))),
% apply(f(apply(b,apply(apply(b,apply(
% apply(b,X),Y)),Z))),
% apply(h(apply(b,apply(apply(b,apply(
% apply(b,X),Y)),Z))),
% g(apply(b,apply(apply(b,apply(apply(b,X),Y)),Z))))))
% -> (true)
% Rule [133]
% (eq)(apply(apply(X,apply(Y,apply(Z,apply(f(apply(b,apply(apply(b,X),
% apply(apply(b,Y),Z)))),
% g(apply(b,apply(apply(b,X),apply(
% apply(b,Y),Z)))))))),
% h(apply(b,apply(apply(b,X),apply(apply(b,Y),Z))))),apply(f(
% apply(b,
% apply(
% apply(b,X),
% apply(
% apply(b,Y),Z)))),
% apply(h(
% apply(b,
% apply(
% apply(b,X),
% apply(
% apply(b,Y),Z)))),
% g(apply(b,
% apply(
% apply(b,X),
% apply(
% apply(b,Y),Z)))))))
% -> (false) is composed into [133]
% (eq)(apply(apply(X,apply(Y,apply(Z,apply(
% f(
% apply(b,
% apply(
% apply(b,X),
% apply(
% apply(b,Y),Z)))),
% g(
% apply(b,
% apply(
% apply(b,X),
% apply(
% apply(b,Y),Z)))))))),
% h(apply(b,apply(apply(b,X),apply(
% apply(b,Y),Z))))),
% apply(f(apply(b,apply(apply(b,X),apply(
% apply(b,Y),Z)))),
% apply(h(apply(b,apply(apply(b,X),apply(
% apply(b,Y),Z)))),
% g(apply(b,apply(apply(b,X),apply(apply(b,Y),Z)))))))
% -> (true)
% Rule [132]
% (eq)(apply(X,apply(apply(g(apply(apply(b,apply(apply(b,b),apply(b,X))),t)),
% h(apply(apply(b,apply(apply(b,b),apply(b,X))),t))),
% f(apply(apply(b,apply(apply(b,b),apply(b,X))),t)))),
% apply(f(apply(apply(b,apply(apply(b,b),apply(b,X))),t)),apply(h(
% apply(
% apply(b,
% apply(
% apply(b,b),
% apply(b,X))),t)),
% g(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(b,X))),t)))))
% -> (false) is composed into [132]
% (eq)(apply(X,apply(apply(g(apply(apply(b,
% apply(
% apply(b,b),
% apply(b,X))),t)),
% h(apply(apply(b,apply(
% apply(b,b),
% apply(b,X))),t))),
% f(apply(apply(b,apply(apply(b,b),
% apply(b,X))),t)))),
% apply(f(apply(apply(b,apply(apply(b,b),
% apply(b,X))),t)),
% apply(h(apply(apply(b,apply(apply(b,b),
% apply(b,X))),t)),
% g(apply(apply(b,apply(apply(b,b),apply(b,X))),t)))))
% -> (true)
% Rule [131]
% (eq)(apply(X,apply(apply(Y,f(apply(apply(b,apply(apply(b,b),apply(b,X))),Y))),
% apply(g(apply(apply(b,apply(apply(b,b),apply(b,X))),Y)),
% h(apply(apply(b,apply(apply(b,b),apply(b,X))),Y))))),
% apply(f(apply(apply(b,apply(apply(b,b),apply(b,X))),Y)),apply(h(
% apply(
% apply(b,
% apply(
% apply(b,b),
% apply(b,X))),Y)),
% g(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(b,X))),Y)))))
% -> (false) is composed into [131]
% (eq)(apply(X,apply(apply(Y,f(apply(apply(b,
% apply(
% apply(b,b),
% apply(b,X))),Y))),
% apply(g(apply(apply(b,apply(
% apply(b,b),
% apply(b,X))),Y)),
% h(apply(apply(b,apply(apply(b,b),
% apply(b,X))),Y))))),
% apply(f(apply(apply(b,apply(apply(b,b),
% apply(b,X))),Y)),
% apply(h(apply(apply(b,apply(apply(b,b),
% apply(b,X))),Y)),
% g(apply(apply(b,apply(apply(b,b),apply(b,X))),Y)))))
% -> (true)
% Rule [130]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,b),apply(t,t))),t)),
% h(apply(apply(b,apply(apply(b,b),apply(t,t))),t))),f(
% apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,t))),t))),
% apply(f(apply(apply(b,apply(apply(b,b),apply(t,t))),t)),apply(h(
% apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,t))),t)),
% g(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,t))),t)))))
% -> (false) is composed into [130]
% (eq)(apply(apply(g(apply(apply(b,apply(
% apply(b,b),
% apply(t,t))),t)),
% h(apply(apply(b,apply(apply(b,b),
% apply(t,t))),t))),
% f(apply(apply(b,apply(apply(b,b),
% apply(t,t))),t))),
% apply(f(apply(apply(b,apply(apply(b,b),
% apply(t,t))),t)),
% apply(h(apply(apply(b,apply(apply(b,b),
% apply(t,t))),t)),
% g(apply(apply(b,apply(apply(b,b),apply(t,t))),t)))))
% -> (true)
% Rule [129]
% (eq)(apply(f(apply(apply(b,apply(apply(b,b),apply(t,X))),b)),apply(X,
% apply(
% g(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,X))),b)),
% h(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,X))),b))))),
% apply(f(apply(apply(b,apply(apply(b,b),apply(t,X))),b)),apply(h(
% apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,X))),b)),
% g(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,X))),b)))))
% -> (false) is composed into [129]
% (eq)(apply(f(apply(apply(b,apply(apply(b,b),
% apply(t,X))),b)),
% apply(X,apply(g(apply(apply(b,apply(
% apply(b,b),
% apply(t,X))),b)),
% h(apply(apply(b,apply(apply(b,b),
% apply(t,X))),b))))),
% apply(f(apply(apply(b,apply(apply(b,b),
% apply(t,X))),b)),
% apply(h(apply(apply(b,apply(apply(b,b),
% apply(t,X))),b)),
% g(apply(apply(b,apply(apply(b,b),apply(t,X))),b)))))
% -> (true)
% Rule [128]
% (eq)(apply(apply(X,f(apply(apply(b,apply(apply(b,b),apply(t,X))),t))),
% apply(g(apply(apply(b,apply(apply(b,b),apply(t,X))),t)),h(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,X))),t)))),
% apply(f(apply(apply(b,apply(apply(b,b),apply(t,X))),t)),apply(h(
% apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,X))),t)),
% g(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,X))),t)))))
% -> (false) is composed into [128]
% (eq)(apply(apply(X,f(apply(apply(b,apply(
% apply(b,b),
% apply(t,X))),t))),
% apply(g(apply(apply(b,apply(apply(b,b),
% apply(t,X))),t)),
% h(apply(apply(b,apply(apply(b,b),
% apply(t,X))),t)))),
% apply(f(apply(apply(b,apply(apply(b,b),
% apply(t,X))),t)),
% apply(h(apply(apply(b,apply(apply(b,b),
% apply(t,X))),t)),
% g(apply(apply(b,apply(apply(b,b),apply(t,X))),t)))))
% -> (true)
% Rule [127]
% (eq)(apply(apply(apply(X,f(apply(apply(b,apply(apply(b,b),apply(t,Y))),X))),Y),
% apply(g(apply(apply(b,apply(apply(b,b),apply(t,Y))),X)),h(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,Y))),X)))),
% apply(f(apply(apply(b,apply(apply(b,b),apply(t,Y))),X)),apply(h(
% apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,Y))),X)),
% g(apply(
% apply(b,
% apply(
% apply(b,b),
% apply(t,Y))),X)))))
% -> (false) is composed into [127]
% (eq)(apply(apply(apply(X,f(apply(apply(b,
% apply(
% apply(b,b),
% apply(t,Y))),X))),Y),
% apply(g(apply(apply(b,apply(apply(b,b),
% apply(t,Y))),X)),
% h(apply(apply(b,apply(apply(b,b),
% apply(t,Y))),X)))),
% apply(f(apply(apply(b,apply(apply(b,b),
% apply(t,Y))),X)),
% apply(h(apply(apply(b,apply(apply(b,b),
% apply(t,Y))),X)),
% g(apply(apply(b,apply(apply(b,b),apply(t,Y))),X)))))
% -> (true)
% Rule [126]
% (eq)(apply(apply(X,apply(f(apply(apply(b,apply(apply(b,b),X)),apply(t,Y))),Y)),
% apply(g(apply(apply(b,apply(apply(b,b),X)),apply(t,Y))),h(apply(
% apply(b,
% apply(
% apply(b,b),X)),
% apply(t,Y))))),
% apply(f(apply(apply(b,apply(apply(b,b),X)),apply(t,Y))),apply(h(
% apply(
% apply(b,
% apply(
% apply(b,b),X)),
% apply(t,Y))),
% g(apply(
% apply(b,
% apply(
% apply(b,b),X)),
% apply(t,Y))))))
% -> (false) is composed into [126]
% (eq)(apply(apply(X,apply(f(apply(apply(b,
% apply(
% apply(b,b),X)),
% apply(t,Y))),Y)),
% apply(g(apply(apply(b,apply(apply(b,b),X)),
% apply(t,Y))),h(apply(apply(b,
% apply(
% apply(b,b),X)),
% apply(t,Y))))),
% apply(f(apply(apply(b,apply(apply(b,b),X)),
% apply(t,Y))),apply(h(apply(apply(b,
% apply(
% apply(b,b),X)),
% apply(t,Y))),
% g(apply(apply(b,
% apply(apply(b,b),X)),
% apply(t,Y)))))) ->
% (true)
% Rule [125]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,t),apply(t,X))),t)),
% apply(X,f(apply(apply(b,apply(apply(b,t),apply(t,X))),t)))),
% h(apply(apply(b,apply(apply(b,t),apply(t,X))),t))),apply(f(
% apply(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))),t)),
% apply(h(
% apply(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))),t)),
% g(apply(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))),t)))))
% -> (false) is composed into [125]
% (eq)(apply(apply(g(apply(apply(b,apply(
% apply(b,t),
% apply(t,X))),t)),
% apply(X,f(apply(apply(b,apply(
% apply(b,t),
% apply(t,X))),t)))),
% h(apply(apply(b,apply(apply(b,t),
% apply(t,X))),t))),
% apply(f(apply(apply(b,apply(apply(b,t),
% apply(t,X))),t)),
% apply(h(apply(apply(b,apply(apply(b,t),
% apply(t,X))),t)),
% g(apply(apply(b,apply(apply(b,t),apply(t,X))),t)))))
% -> (true)
% Rule [124]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,t),apply(t,X))),Y)),
% apply(apply(Y,f(apply(apply(b,apply(apply(b,t),apply(t,X))),Y))),X)),
% h(apply(apply(b,apply(apply(b,t),apply(t,X))),Y))),apply(f(
% apply(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))),Y)),
% apply(h(
% apply(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))),Y)),
% g(apply(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))),Y)))))
% -> (false) is composed into [124]
% (eq)(apply(apply(g(apply(apply(b,apply(
% apply(b,t),
% apply(t,X))),Y)),
% apply(apply(Y,f(apply(apply(b,
% apply(
% apply(b,t),
% apply(t,X))),Y))),X)),
% h(apply(apply(b,apply(apply(b,t),
% apply(t,X))),Y))),
% apply(f(apply(apply(b,apply(apply(b,t),
% apply(t,X))),Y)),
% apply(h(apply(apply(b,apply(apply(b,t),
% apply(t,X))),Y)),
% g(apply(apply(b,apply(apply(b,t),apply(t,X))),Y)))))
% -> (true)
% Rule [123]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,t),X)),apply(t,Y))),
% apply(X,apply(f(apply(apply(b,apply(apply(b,t),X)),apply(t,Y))),Y))),
% h(apply(apply(b,apply(apply(b,t),X)),apply(t,Y)))),apply(f(
% apply(
% apply(b,
% apply(
% apply(b,t),X)),
% apply(t,Y))),
% apply(h(
% apply(
% apply(b,
% apply(
% apply(b,t),X)),
% apply(t,Y))),
% g(apply(
% apply(b,
% apply(
% apply(b,t),X)),
% apply(t,Y))))))
% -> (false) is composed into [123]
% (eq)(apply(apply(g(apply(apply(b,apply(
% apply(b,t),X)),
% apply(t,Y))),apply(X,
% apply(
% f(apply(
% apply(b,
% apply(
% apply(b,t),X)),
% apply(t,Y))),Y))),
% h(apply(apply(b,apply(apply(b,t),X)),
% apply(t,Y)))),apply(f(apply(apply(b,
% apply(
% apply(b,t),X)),
% apply(t,Y))),
% apply(h(apply(apply(b,
% apply(
% apply(b,t),X)),
% apply(t,Y))),
% g(apply(apply(b,
% apply(apply(b,t),X)),
% apply(t,Y)))))) ->
% (true)
% Rule [122]
% (eq)(apply(apply(apply(apply(X,f(apply(apply(b,apply(b,apply(b,apply(t,Y)))),X))),
% g(apply(apply(b,apply(b,apply(b,apply(t,Y)))),X))),
% h(apply(apply(b,apply(b,apply(b,apply(t,Y)))),X))),Y),
% apply(f(apply(apply(b,apply(b,apply(b,apply(t,Y)))),X)),apply(h(
% apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,Y)))),X)),
% g(apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,Y)))),X)))))
% -> (false) is composed into [122]
% (eq)(apply(apply(apply(apply(X,f(apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,Y)))),X))),
% g(apply(apply(b,apply(b,
% apply(b,
% apply(t,Y)))),X))),
% h(apply(apply(b,apply(b,apply(b,
% apply(t,Y)))),X))),Y),
% apply(f(apply(apply(b,apply(b,apply(b,
% apply(t,Y)))),X)),
% apply(h(apply(apply(b,apply(b,apply(b,
% apply(t,Y)))),X)),
% g(apply(apply(b,apply(b,apply(b,apply(t,Y)))),X)))))
% -> (true)
% Rule [121]
% (eq)(apply(X,apply(h(apply(apply(b,apply(b,apply(b,X))),apply(b,t))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),apply(b,t))),
% g(apply(apply(b,apply(b,apply(b,X))),apply(b,t)))))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),apply(b,t))),apply(h(
% apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,t))),
% g(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,t))))))
% -> (false) is composed into [121]
% (eq)(apply(X,apply(h(apply(apply(b,apply(b,
% apply(b,X))),
% apply(b,t))),apply(
% f(
% apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,t))),
% g(
% apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,t)))))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),
% apply(b,t))),apply(h(apply(apply(b,
% apply(b,
% apply(b,X))),
% apply(b,t))),
% g(apply(apply(b,
% apply(b,
% apply(b,X))),
% apply(b,t)))))) ->
% (true)
% Rule [120]
% (eq)(apply(X,apply(apply(Y,apply(f(apply(apply(b,apply(b,apply(b,X))),
% apply(b,Y))),g(apply(apply(b,
% apply(b,
% apply(b,X))),
% apply(b,Y))))),
% h(apply(apply(b,apply(b,apply(b,X))),apply(b,Y))))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),apply(b,Y))),apply(h(
% apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,Y))),
% g(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,Y))))))
% -> (false) is composed into [120]
% (eq)(apply(X,apply(apply(Y,apply(f(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,Y))),
% g(apply(apply(b,
% apply(b,
% apply(b,X))),
% apply(b,Y))))),
% h(apply(apply(b,apply(b,
% apply(b,X))),
% apply(b,Y))))),apply(
% f(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,Y))),
% apply(
% h(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,Y))),
% g(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(b,Y))))))
% -> (true)
% Rule [119]
% (eq)(apply(h(apply(apply(b,apply(b,apply(t,t))),apply(b,t))),apply(
% f(apply(
% apply(b,
% apply(b,
% apply(t,t))),
% apply(b,t))),
% g(apply(
% apply(b,
% apply(b,
% apply(t,t))),
% apply(b,t))))),
% apply(f(apply(apply(b,apply(b,apply(t,t))),apply(b,t))),apply(h(
% apply(
% apply(b,
% apply(b,
% apply(t,t))),
% apply(b,t))),
% g(apply(
% apply(b,
% apply(b,
% apply(t,t))),
% apply(b,t))))))
% -> (false) is composed into [119]
% (eq)(apply(h(apply(apply(b,apply(b,apply(t,t))),
% apply(b,t))),apply(f(apply(
% apply(b,
% apply(b,
% apply(t,t))),
% apply(b,t))),
% g(apply(apply(b,
% apply(b,
% apply(t,t))),
% apply(b,t))))),
% apply(f(apply(apply(b,apply(b,apply(t,t))),
% apply(b,t))),apply(h(apply(apply(b,
% apply(b,
% apply(t,t))),
% apply(b,t))),
% g(apply(apply(b,
% apply(b,
% apply(t,t))),
% apply(b,t)))))) ->
% (true)
% Rule [118]
% (eq)(apply(apply(f(apply(apply(b,apply(b,apply(t,X))),apply(b,b))),
% g(apply(apply(b,apply(b,apply(t,X))),apply(b,b)))),apply(X,
% h(
% apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,b))))),
% apply(f(apply(apply(b,apply(b,apply(t,X))),apply(b,b))),apply(h(
% apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,b))),
% g(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,b))))))
% -> (false) is composed into [118]
% (eq)(apply(apply(f(apply(apply(b,apply(b,
% apply(t,X))),
% apply(b,b))),g(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,b)))),
% apply(X,h(apply(apply(b,apply(b,
% apply(t,X))),
% apply(b,b))))),apply(
% f(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,b))),
% apply(
% h(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,b))),
% g(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,b))))))
% -> (true)
% Rule [117]
% (eq)(apply(apply(X,apply(f(apply(apply(b,apply(b,apply(t,X))),apply(b,t))),
% g(apply(apply(b,apply(b,apply(t,X))),apply(b,t))))),
% h(apply(apply(b,apply(b,apply(t,X))),apply(b,t)))),apply(f(
% apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,t))),
% apply(h(
% apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,t))),
% g(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(b,t))))))
% -> (false) is composed into [117]
% (eq)(apply(apply(X,apply(f(apply(apply(b,
% apply(b,
% apply(t,X))),
% apply(b,t))),
% g(apply(apply(b,apply(b,
% apply(t,X))),
% apply(b,t))))),
% h(apply(apply(b,apply(b,apply(t,X))),
% apply(b,t)))),apply(f(apply(apply(b,
% apply(b,
% apply(t,X))),
% apply(b,t))),
% apply(h(apply(apply(b,
% apply(b,
% apply(t,X))),
% apply(b,t))),
% g(apply(apply(b,
% apply(b,
% apply(t,X))),
% apply(b,t)))))) ->
% (true)
% Rule [116]
% (eq)(apply(apply(X,apply(apply(f(apply(apply(b,apply(b,X)),apply(b,
% apply(t,Y)))),
% g(apply(apply(b,apply(b,X)),apply(b,apply(t,Y))))),Y)),
% h(apply(apply(b,apply(b,X)),apply(b,apply(t,Y))))),apply(f(
% apply(
% apply(b,
% apply(b,X)),
% apply(b,
% apply(t,Y)))),
% apply(h(
% apply(
% apply(b,
% apply(b,X)),
% apply(b,
% apply(t,Y)))),
% g(apply(
% apply(b,
% apply(b,X)),
% apply(b,
% apply(t,Y)))))))
% -> (false) is composed into [116]
% (eq)(apply(apply(X,apply(apply(f(apply(
% apply(b,
% apply(b,X)),
% apply(b,
% apply(t,Y)))),
% g(apply(apply(b,
% apply(b,X)),
% apply(b,apply(t,Y))))),Y)),
% h(apply(apply(b,apply(b,X)),apply(b,
% apply(t,Y))))),
% apply(f(apply(apply(b,apply(b,X)),apply(b,
% apply(t,Y)))),
% apply(h(apply(apply(b,apply(b,X)),apply(b,
% apply(t,Y)))),
% g(apply(apply(b,apply(b,X)),apply(b,
% apply(t,Y)))))))
% -> (true)
% Rule [115]
% (eq)(apply(apply(apply(X,apply(f(apply(apply(b,apply(b,apply(t,Y))),
% apply(b,X))),g(apply(apply(b,apply(b,
% apply(t,Y))),
% apply(b,X))))),Y),
% h(apply(apply(b,apply(b,apply(t,Y))),apply(b,X)))),apply(f(
% apply(
% apply(b,
% apply(b,
% apply(t,Y))),
% apply(b,X))),
% apply(h(
% apply(
% apply(b,
% apply(b,
% apply(t,Y))),
% apply(b,X))),
% g(apply(
% apply(b,
% apply(b,
% apply(t,Y))),
% apply(b,X))))))
% -> (false) is composed into [115]
% (eq)(apply(apply(apply(X,apply(f(apply(
% apply(b,
% apply(b,
% apply(t,Y))),
% apply(b,X))),
% g(apply(apply(b,
% apply(b,
% apply(t,Y))),
% apply(b,X))))),Y),
% h(apply(apply(b,apply(b,apply(t,Y))),
% apply(b,X)))),apply(f(apply(apply(b,
% apply(b,
% apply(t,Y))),
% apply(b,X))),
% apply(h(apply(apply(b,
% apply(b,
% apply(t,Y))),
% apply(b,X))),
% g(apply(apply(b,
% apply(b,
% apply(t,Y))),
% apply(b,X)))))) ->
% (true)
% Rule [114]
% (eq)(apply(h(apply(apply(b,apply(t,X)),apply(b,apply(b,t)))),apply(
% apply(
% f(apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(b,t)))),X),
% g(apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(b,t)))))),
% apply(f(apply(apply(b,apply(t,X)),apply(b,apply(b,t)))),apply(h(
% apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(b,t)))),
% g(apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(b,t)))))))
% -> (false) is composed into [114]
% (eq)(apply(h(apply(apply(b,apply(t,X)),
% apply(b,apply(b,t)))),apply(
% apply(
% f(
% apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(b,t)))),X),
% g(
% apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(b,t)))))),
% apply(f(apply(apply(b,apply(t,X)),apply(b,
% apply(b,t)))),
% apply(h(apply(apply(b,apply(t,X)),apply(b,
% apply(b,t)))),
% g(apply(apply(b,apply(t,X)),apply(b,
% apply(b,t)))))))
% -> (true)
% Rule [113]
% (eq)(apply(apply(X,apply(apply(f(apply(apply(b,apply(t,Y)),apply(b,
% apply(b,X)))),Y),
% g(apply(apply(b,apply(t,Y)),apply(b,apply(b,X)))))),
% h(apply(apply(b,apply(t,Y)),apply(b,apply(b,X))))),apply(f(
% apply(
% apply(b,
% apply(t,Y)),
% apply(b,
% apply(b,X)))),
% apply(h(
% apply(
% apply(b,
% apply(t,Y)),
% apply(b,
% apply(b,X)))),
% g(apply(
% apply(b,
% apply(t,Y)),
% apply(b,
% apply(b,X)))))))
% -> (false) is composed into [113]
% (eq)(apply(apply(X,apply(apply(f(apply(
% apply(b,
% apply(t,Y)),
% apply(b,
% apply(b,X)))),Y),
% g(apply(apply(b,apply(t,Y)),
% apply(b,apply(b,X)))))),
% h(apply(apply(b,apply(t,Y)),apply(b,
% apply(b,X))))),
% apply(f(apply(apply(b,apply(t,Y)),apply(b,
% apply(b,X)))),
% apply(h(apply(apply(b,apply(t,Y)),apply(b,
% apply(b,X)))),
% g(apply(apply(b,apply(t,Y)),apply(b,
% apply(b,X)))))))
% -> (true)
% Rule [112]
% (eq)(apply(apply(apply(apply(f(apply(apply(b,apply(t,X)),apply(b,
% apply(t,Y)))),X),Y),
% g(apply(apply(b,apply(t,X)),apply(b,apply(t,Y))))),h(
% apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(t,Y))))),
% apply(f(apply(apply(b,apply(t,X)),apply(b,apply(t,Y)))),apply(h(
% apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(t,Y)))),
% g(apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(t,Y)))))))
% -> (false) is composed into [112]
% (eq)(apply(apply(apply(apply(f(apply(
% apply(b,
% apply(t,X)),
% apply(b,
% apply(t,Y)))),X),Y),
% g(apply(apply(b,apply(t,X)),
% apply(b,apply(t,Y))))),
% h(apply(apply(b,apply(t,X)),apply(b,
% apply(t,Y))))),
% apply(f(apply(apply(b,apply(t,X)),apply(b,
% apply(t,Y)))),
% apply(h(apply(apply(b,apply(t,X)),apply(b,
% apply(t,Y)))),
% g(apply(apply(b,apply(t,X)),apply(b,
% apply(t,Y)))))))
% -> (true)
% Rule [111]
% (eq)(apply(X,apply(apply(apply(f(apply(apply(b,apply(b,apply(b,X))),
% apply(t,Y))),Y),g(apply(apply(b,
% apply(b,
% apply(b,X))),
% apply(t,Y)))),
% h(apply(apply(b,apply(b,apply(b,X))),apply(t,Y))))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),apply(t,Y))),apply(h(
% apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(t,Y))),
% g(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(t,Y))))))
% -> (false) is composed into [111]
% (eq)(apply(X,apply(apply(apply(f(apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(t,Y))),Y),
% g(apply(apply(b,apply(b,
% apply(b,X))),
% apply(t,Y)))),h(
% apply(
% apply(b,
% apply(b,
% apply(b,X))),
% apply(t,Y))))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),
% apply(t,Y))),apply(h(apply(apply(b,
% apply(b,
% apply(b,X))),
% apply(t,Y))),
% g(apply(apply(b,
% apply(b,
% apply(b,X))),
% apply(t,Y)))))) ->
% (true)
% Rule [110]
% (eq)(apply(apply(apply(apply(f(apply(apply(b,apply(b,apply(t,X))),
% apply(t,Y))),Y),g(apply(apply(b,apply(b,
% apply(t,X))),
% apply(t,Y)))),X),
% h(apply(apply(b,apply(b,apply(t,X))),apply(t,Y)))),apply(f(
% apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(t,Y))),
% apply(h(
% apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(t,Y))),
% g(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(t,Y))))))
% -> (false) is composed into [110]
% (eq)(apply(apply(apply(apply(f(apply(
% apply(b,
% apply(b,
% apply(t,X))),
% apply(t,Y))),Y),
% g(apply(apply(b,apply(b,
% apply(t,X))),
% apply(t,Y)))),X),
% h(apply(apply(b,apply(b,apply(t,X))),
% apply(t,Y)))),apply(f(apply(apply(b,
% apply(b,
% apply(t,X))),
% apply(t,Y))),
% apply(h(apply(apply(b,
% apply(b,
% apply(t,X))),
% apply(t,Y))),
% g(apply(apply(b,
% apply(b,
% apply(t,X))),
% apply(t,Y)))))) ->
% (true)
% Rule [109]
% (eq)(apply(X,apply(Y,apply(apply(f(apply(b,apply(apply(b,apply(b,X)),
% apply(b,Y)))),g(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(b,Y))))),
% h(apply(b,apply(apply(b,apply(b,X)),apply(b,Y))))))),
% apply(f(apply(b,apply(apply(b,apply(b,X)),apply(b,Y)))),apply(h(
% apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(b,Y)))),
% g(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(b,Y)))))))
% -> (false) is composed into [109]
% (eq)(apply(X,apply(Y,apply(apply(f(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(b,Y)))),
% g(apply(b,
% apply(apply(b,
% apply(b,X)),
% apply(b,Y))))),
% h(apply(b,apply(
% apply(b,
% apply(b,X)),
% apply(b,Y))))))),
% apply(f(apply(b,apply(apply(b,apply(b,X)),
% apply(b,Y)))),apply(
% h(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(b,Y)))),
% g(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(b,Y)))))))
% -> (true)
% Rule [108]
% (eq)(apply(apply(f(apply(b,apply(apply(b,apply(b,apply(t,X))),b))),
% g(apply(b,apply(apply(b,apply(b,apply(t,X))),b)))),apply(
% h(
% apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,X))),b))),X)),
% apply(f(apply(b,apply(apply(b,apply(b,apply(t,X))),b))),apply(h(
% apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,X))),b))),
% g(apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,X))),b))))))
% -> (false) is composed into [108]
% (eq)(apply(apply(f(apply(b,apply(apply(b,
% apply(b,
% apply(t,X))),b))),
% g(apply(b,apply(apply(b,apply(b,
% apply(t,X))),b)))),
% apply(h(apply(b,apply(apply(b,apply(b,
% apply(t,X))),b))),X)),
% apply(f(apply(b,apply(apply(b,apply(b,
% apply(t,X))),b))),
% apply(h(apply(b,apply(apply(b,apply(b,
% apply(t,X))),b))),
% g(apply(b,apply(apply(b,apply(b,apply(t,X))),b))))))
% -> (true)
% Rule [107]
% (eq)(apply(apply(apply(X,apply(f(apply(b,apply(apply(b,apply(b,apply(t,Y))),X))),
% g(apply(b,apply(apply(b,apply(b,apply(t,Y))),X))))),
% h(apply(b,apply(apply(b,apply(b,apply(t,Y))),X)))),Y),
% apply(f(apply(b,apply(apply(b,apply(b,apply(t,Y))),X))),apply(h(
% apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,Y))),X))),
% g(apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,Y))),X))))))
% -> (false) is composed into [107]
% (eq)(apply(apply(apply(X,apply(f(apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,Y))),X))),
% g(apply(b,apply(
% apply(b,
% apply(b,
% apply(t,Y))),X))))),
% h(apply(b,apply(apply(b,apply(b,
% apply(t,Y))),X)))),Y),
% apply(f(apply(b,apply(apply(b,apply(b,
% apply(t,Y))),X))),
% apply(h(apply(b,apply(apply(b,apply(b,
% apply(t,Y))),X))),
% g(apply(b,apply(apply(b,apply(b,apply(t,Y))),X))))))
% -> (true)
% Rule [106]
% (eq)(apply(h(apply(b,apply(apply(b,apply(t,X)),apply(b,t)))),apply(
% apply(
% f(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t)))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t))))),X)),
% apply(f(apply(b,apply(apply(b,apply(t,X)),apply(b,t)))),apply(h(
% apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t)))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t)))))))
% -> (false) is composed into [106]
% (eq)(apply(h(apply(b,apply(apply(b,apply(t,X)),
% apply(b,t)))),apply(
% apply(
% f(
% apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t)))),
% g(
% apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t))))),X)),
% apply(f(apply(b,apply(apply(b,apply(t,X)),
% apply(b,t)))),apply(
% h(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t)))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t)))))))
% -> (true)
% Rule [105]
% (eq)(apply(apply(X,apply(apply(f(apply(b,apply(apply(b,apply(t,Y)),
% apply(b,X)))),g(apply(b,
% apply(apply(b,
% apply(t,Y)),
% apply(b,X))))),Y)),
% h(apply(b,apply(apply(b,apply(t,Y)),apply(b,X))))),apply(f(
% apply(b,
% apply(
% apply(b,
% apply(t,Y)),
% apply(b,X)))),
% apply(h(
% apply(b,
% apply(
% apply(b,
% apply(t,Y)),
% apply(b,X)))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,Y)),
% apply(b,X)))))))
% -> (false) is composed into [105]
% (eq)(apply(apply(X,apply(apply(f(apply(b,
% apply(
% apply(b,
% apply(t,Y)),
% apply(b,X)))),
% g(apply(b,apply(
% apply(b,
% apply(t,Y)),
% apply(b,X))))),Y)),
% h(apply(b,apply(apply(b,apply(t,Y)),
% apply(b,X))))),apply(
% f(apply(b,
% apply(
% apply(b,
% apply(t,Y)),
% apply(b,X)))),
% apply(
% h(apply(b,
% apply(
% apply(b,
% apply(t,Y)),
% apply(b,X)))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,Y)),
% apply(b,X)))))))
% -> (true)
% Rule [104]
% (eq)(apply(X,apply(apply(apply(f(apply(b,apply(apply(b,apply(b,X)),
% apply(t,Y)))),g(apply(b,
% apply(apply(b,
% apply(b,X)),
% apply(t,Y))))),Y),
% h(apply(b,apply(apply(b,apply(b,X)),apply(t,Y)))))),
% apply(f(apply(b,apply(apply(b,apply(b,X)),apply(t,Y)))),apply(h(
% apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(t,Y)))),
% g(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(t,Y)))))))
% -> (false) is composed into [104]
% (eq)(apply(X,apply(apply(apply(f(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(t,Y)))),
% g(apply(b,apply(
% apply(b,
% apply(b,X)),
% apply(t,Y))))),Y),
% h(apply(b,apply(apply(b,
% apply(b,X)),
% apply(t,Y)))))),
% apply(f(apply(b,apply(apply(b,apply(b,X)),
% apply(t,Y)))),apply(
% h(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(t,Y)))),
% g(apply(b,
% apply(
% apply(b,
% apply(b,X)),
% apply(t,Y)))))))
% -> (true)
% Rule [103]
% (eq)(apply(apply(apply(apply(f(apply(b,apply(apply(b,apply(t,X)),
% apply(t,Y)))),g(apply(b,apply(
% apply(b,
% apply(t,X)),
% apply(t,Y))))),Y),X),
% h(apply(b,apply(apply(b,apply(t,X)),apply(t,Y))))),apply(f(
% apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(t,Y)))),
% apply(h(
% apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(t,Y)))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(t,Y)))))))
% -> (false) is composed into [103]
% (eq)(apply(apply(apply(apply(f(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(t,Y)))),
% g(apply(b,apply(
% apply(b,
% apply(t,X)),
% apply(t,Y))))),Y),X),
% h(apply(b,apply(apply(b,apply(t,X)),
% apply(t,Y))))),apply(
% f(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(t,Y)))),
% apply(
% h(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(t,Y)))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,X)),
% apply(t,Y)))))))
% -> (true)
% Rule [102]
% (eq)(apply(X,apply(apply(g(apply(apply(b,b),apply(apply(b,apply(b,X)),t))),
% h(apply(apply(b,b),apply(apply(b,apply(b,X)),t)))),
% f(apply(apply(b,b),apply(apply(b,apply(b,X)),t))))),
% apply(f(apply(apply(b,b),apply(apply(b,apply(b,X)),t))),apply(h(
% apply(
% apply(b,b),
% apply(
% apply(b,
% apply(b,X)),t))),
% g(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(b,X)),t))))))
% -> (false) is composed into [102]
% (eq)(apply(X,apply(apply(g(apply(apply(b,b),
% apply(apply(b,
% apply(b,X)),t))),
% h(apply(apply(b,b),
% apply(apply(b,apply(b,X)),t)))),
% f(apply(apply(b,b),apply(
% apply(b,
% apply(b,X)),t))))),
% apply(f(apply(apply(b,b),apply(apply(b,
% apply(b,X)),t))),
% apply(h(apply(apply(b,b),apply(apply(b,
% apply(b,X)),t))),
% g(apply(apply(b,b),apply(apply(b,apply(b,X)),t))))))
% -> (true)
% Rule [101]
% (eq)(apply(X,apply(apply(Y,f(apply(apply(b,b),apply(apply(b,apply(b,X)),Y)))),
% apply(g(apply(apply(b,b),apply(apply(b,apply(b,X)),Y))),
% h(apply(apply(b,b),apply(apply(b,apply(b,X)),Y)))))),
% apply(f(apply(apply(b,b),apply(apply(b,apply(b,X)),Y))),apply(h(
% apply(
% apply(b,b),
% apply(
% apply(b,
% apply(b,X)),Y))),
% g(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(b,X)),Y))))))
% -> (false) is composed into [101]
% (eq)(apply(X,apply(apply(Y,f(apply(apply(b,b),
% apply(apply(b,
% apply(b,X)),Y)))),
% apply(g(apply(apply(b,b),
% apply(apply(b,apply(b,X)),Y))),
% h(apply(apply(b,b),apply(
% apply(b,
% apply(b,X)),Y)))))),
% apply(f(apply(apply(b,b),apply(apply(b,
% apply(b,X)),Y))),
% apply(h(apply(apply(b,b),apply(apply(b,
% apply(b,X)),Y))),
% g(apply(apply(b,b),apply(apply(b,apply(b,X)),Y))))))
% -> (true)
% Rule [100]
% (eq)(apply(apply(g(apply(apply(b,b),apply(apply(b,apply(t,t)),t))),
% h(apply(apply(b,b),apply(apply(b,apply(t,t)),t)))),f(
% apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,t)),t)))),
% apply(f(apply(apply(b,b),apply(apply(b,apply(t,t)),t))),apply(h(
% apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,t)),t))),
% g(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,t)),t))))))
% -> (false) is composed into [100]
% (eq)(apply(apply(g(apply(apply(b,b),
% apply(apply(b,apply(t,t)),t))),
% h(apply(apply(b,b),apply(
% apply(b,
% apply(t,t)),t)))),
% f(apply(apply(b,b),apply(apply(b,
% apply(t,t)),t)))),
% apply(f(apply(apply(b,b),apply(apply(b,
% apply(t,t)),t))),
% apply(h(apply(apply(b,b),apply(apply(b,
% apply(t,t)),t))),
% g(apply(apply(b,b),apply(apply(b,apply(t,t)),t))))))
% -> (true)
% Rule [99]
% (eq)(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),b))),apply(X,
% apply(
% g(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,X)),b))),
% h(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,X)),b)))))),
% apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),b))),apply(h(
% apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,X)),b))),
% g(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,X)),b))))))
% -> (false) is composed into [99]
% (eq)(apply(f(apply(apply(b,b),apply(
% apply(b,
% apply(t,X)),b))),
% apply(X,apply(g(apply(apply(b,b),
% apply(apply(b,apply(t,X)),b))),
% h(apply(apply(b,b),apply(
% apply(b,
% apply(t,X)),b)))))),
% apply(f(apply(apply(b,b),apply(apply(b,
% apply(t,X)),b))),
% apply(h(apply(apply(b,b),apply(apply(b,
% apply(t,X)),b))),
% g(apply(apply(b,b),apply(apply(b,apply(t,X)),b))))))
% -> (true)
% Rule [98]
% (eq)(apply(apply(X,f(apply(apply(b,b),apply(apply(b,apply(t,X)),t)))),
% apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),t))),h(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,X)),t))))),
% apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),t))),apply(h(
% apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,X)),t))),
% g(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,X)),t))))))
% -> (false) is composed into [98]
% (eq)(apply(apply(X,f(apply(apply(b,b),
% apply(apply(b,apply(t,X)),t)))),
% apply(g(apply(apply(b,b),apply(
% apply(b,
% apply(t,X)),t))),
% h(apply(apply(b,b),apply(apply(b,
% apply(t,X)),t))))),
% apply(f(apply(apply(b,b),apply(apply(b,
% apply(t,X)),t))),
% apply(h(apply(apply(b,b),apply(apply(b,
% apply(t,X)),t))),
% g(apply(apply(b,b),apply(apply(b,apply(t,X)),t))))))
% -> (true)
% Rule [97]
% (eq)(apply(apply(apply(X,f(apply(apply(b,b),apply(apply(b,apply(t,Y)),X)))),Y),
% apply(g(apply(apply(b,b),apply(apply(b,apply(t,Y)),X))),h(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,Y)),X))))),
% apply(f(apply(apply(b,b),apply(apply(b,apply(t,Y)),X))),apply(h(
% apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,Y)),X))),
% g(apply(
% apply(b,b),
% apply(
% apply(b,
% apply(t,Y)),X))))))
% -> (false) is composed into [97]
% (eq)(apply(apply(apply(X,f(apply(apply(b,b),
% apply(apply(b,
% apply(t,Y)),X)))),Y),
% apply(g(apply(apply(b,b),apply(
% apply(b,
% apply(t,Y)),X))),
% h(apply(apply(b,b),apply(apply(b,
% apply(t,Y)),X))))),
% apply(f(apply(apply(b,b),apply(apply(b,
% apply(t,Y)),X))),
% apply(h(apply(apply(b,b),apply(apply(b,
% apply(t,Y)),X))),
% g(apply(apply(b,b),apply(apply(b,apply(t,Y)),X))))))
% -> (true)
% Rule [96]
% (eq)(apply(apply(X,apply(f(apply(apply(b,b),apply(apply(b,X),apply(t,Y)))),Y)),
% apply(g(apply(apply(b,b),apply(apply(b,X),apply(t,Y)))),h(apply(
% apply(b,b),
% apply(
% apply(b,X),
% apply(t,Y)))))),
% apply(f(apply(apply(b,b),apply(apply(b,X),apply(t,Y)))),apply(h(
% apply(
% apply(b,b),
% apply(
% apply(b,X),
% apply(t,Y)))),
% g(apply(
% apply(b,b),
% apply(
% apply(b,X),
% apply(t,Y)))))))
% -> (false) is composed into [96]
% (eq)(apply(apply(X,apply(f(apply(apply(b,b),
% apply(apply(b,X),
% apply(t,Y)))),Y)),
% apply(g(apply(apply(b,b),apply(
% apply(b,X),
% apply(t,Y)))),
% h(apply(apply(b,b),apply(apply(b,X),
% apply(t,Y)))))),
% apply(f(apply(apply(b,b),apply(apply(b,X),
% apply(t,Y)))),
% apply(h(apply(apply(b,b),apply(apply(b,X),
% apply(t,Y)))),
% g(apply(apply(b,b),apply(apply(b,X),
% apply(t,Y))))))) ->
% (true)
% Rule [95]
% (eq)(apply(apply(g(apply(apply(b,t),apply(apply(b,apply(t,X)),t))),
% apply(X,f(apply(apply(b,t),apply(apply(b,apply(t,X)),t))))),
% h(apply(apply(b,t),apply(apply(b,apply(t,X)),t)))),apply(f(
% apply(
% apply(b,t),
% apply(
% apply(b,
% apply(t,X)),t))),
% apply(h(
% apply(
% apply(b,t),
% apply(
% apply(b,
% apply(t,X)),t))),
% g(apply(
% apply(b,t),
% apply(
% apply(b,
% apply(t,X)),t))))))
% -> (false) is composed into [95]
% (eq)(apply(apply(g(apply(apply(b,t),
% apply(apply(b,apply(t,X)),t))),
% apply(X,f(apply(apply(b,t),
% apply(apply(b,apply(t,X)),t))))),
% h(apply(apply(b,t),apply(apply(b,
% apply(t,X)),t)))),
% apply(f(apply(apply(b,t),apply(apply(b,
% apply(t,X)),t))),
% apply(h(apply(apply(b,t),apply(apply(b,
% apply(t,X)),t))),
% g(apply(apply(b,t),apply(apply(b,apply(t,X)),t))))))
% -> (true)
% Rule [94]
% (eq)(apply(apply(g(apply(apply(b,t),apply(apply(b,apply(t,X)),Y))),
% apply(apply(Y,f(apply(apply(b,t),apply(apply(b,apply(t,X)),Y)))),X)),
% h(apply(apply(b,t),apply(apply(b,apply(t,X)),Y)))),apply(f(
% apply(
% apply(b,t),
% apply(
% apply(b,
% apply(t,X)),Y))),
% apply(h(
% apply(
% apply(b,t),
% apply(
% apply(b,
% apply(t,X)),Y))),
% g(apply(
% apply(b,t),
% apply(
% apply(b,
% apply(t,X)),Y))))))
% -> (false) is composed into [94]
% (eq)(apply(apply(g(apply(apply(b,t),
% apply(apply(b,apply(t,X)),Y))),
% apply(apply(Y,f(apply(apply(b,t),
% apply(apply(b,
% apply(t,X)),Y)))),X)),
% h(apply(apply(b,t),apply(apply(b,
% apply(t,X)),Y)))),
% apply(f(apply(apply(b,t),apply(apply(b,
% apply(t,X)),Y))),
% apply(h(apply(apply(b,t),apply(apply(b,
% apply(t,X)),Y))),
% g(apply(apply(b,t),apply(apply(b,apply(t,X)),Y))))))
% -> (true)
% Rule [93]
% (eq)(apply(apply(g(apply(apply(b,t),apply(apply(b,X),apply(t,Y)))),
% apply(X,apply(f(apply(apply(b,t),apply(apply(b,X),apply(t,Y)))),Y))),
% h(apply(apply(b,t),apply(apply(b,X),apply(t,Y))))),apply(f(
% apply(
% apply(b,t),
% apply(
% apply(b,X),
% apply(t,Y)))),
% apply(h(
% apply(
% apply(b,t),
% apply(
% apply(b,X),
% apply(t,Y)))),
% g(apply(
% apply(b,t),
% apply(
% apply(b,X),
% apply(t,Y)))))))
% -> (false) is composed into [93]
% (eq)(apply(apply(g(apply(apply(b,t),
% apply(apply(b,X),
% apply(t,Y)))),apply(X,
% apply(
% f(apply(
% apply(b,t),
% apply(
% apply(b,X),
% apply(t,Y)))),Y))),
% h(apply(apply(b,t),apply(apply(b,X),
% apply(t,Y))))),
% apply(f(apply(apply(b,t),apply(apply(b,X),
% apply(t,Y)))),
% apply(h(apply(apply(b,t),apply(apply(b,X),
% apply(t,Y)))),
% g(apply(apply(b,t),apply(apply(b,X),
% apply(t,Y))))))) ->
% (true)
% Rule [92]
% (eq)(apply(X,apply(apply(f(apply(b,apply(b,apply(apply(b,apply(t,X)),t)))),
% g(apply(b,apply(b,apply(apply(b,apply(t,X)),t))))),
% h(apply(b,apply(b,apply(apply(b,apply(t,X)),t)))))),
% apply(f(apply(b,apply(b,apply(apply(b,apply(t,X)),t)))),apply(h(
% apply(b,
% apply(b,
% apply(
% apply(b,
% apply(t,X)),t)))),
% g(apply(b,
% apply(b,
% apply(
% apply(b,
% apply(t,X)),t)))))))
% -> (false) is composed into [92]
% (eq)(apply(X,apply(apply(f(apply(b,apply(b,
% apply(
% apply(b,
% apply(t,X)),t)))),
% g(apply(b,apply(b,
% apply(apply(b,
% apply(t,X)),t))))),
% h(apply(b,apply(b,apply(
% apply(b,
% apply(t,X)),t)))))),
% apply(f(apply(b,apply(b,apply(apply(b,
% apply(t,X)),t)))),
% apply(h(apply(b,apply(b,apply(apply(b,
% apply(t,X)),t)))),
% g(apply(b,apply(b,apply(apply(b,apply(t,X)),t)))))))
% -> (true)
% Rule [91]
% (eq)(apply(apply(X,apply(apply(f(apply(b,apply(b,apply(apply(b,apply(t,Y)),X)))),
% g(apply(b,apply(b,apply(apply(b,apply(t,Y)),X))))),
% h(apply(b,apply(b,apply(apply(b,apply(t,Y)),X)))))),Y),
% apply(f(apply(b,apply(b,apply(apply(b,apply(t,Y)),X)))),apply(h(
% apply(b,
% apply(b,
% apply(
% apply(b,
% apply(t,Y)),X)))),
% g(apply(b,
% apply(b,
% apply(
% apply(b,
% apply(t,Y)),X)))))))
% -> (false) is composed into [91]
% (eq)(apply(apply(X,apply(apply(f(apply(b,
% apply(b,
% apply(
% apply(b,
% apply(t,Y)),X)))),
% g(apply(b,apply(b,
% apply(
% apply(b,
% apply(t,Y)),X))))),
% h(apply(b,apply(b,
% apply(apply(b,
% apply(t,Y)),X)))))),Y),
% apply(f(apply(b,apply(b,apply(apply(b,
% apply(t,Y)),X)))),
% apply(h(apply(b,apply(b,apply(apply(b,
% apply(t,Y)),X)))),
% g(apply(b,apply(b,apply(apply(b,apply(t,Y)),X)))))))
% -> (true)
% Rule [90]
% (eq)(apply(X,apply(apply(apply(f(apply(b,apply(b,apply(apply(b,X),
% apply(t,Y))))),
% g(apply(b,apply(b,apply(apply(b,X),apply(t,Y)))))),
% h(apply(b,apply(b,apply(apply(b,X),apply(t,Y)))))),Y)),
% apply(f(apply(b,apply(b,apply(apply(b,X),apply(t,Y))))),apply(h(
% apply(b,
% apply(b,
% apply(
% apply(b,X),
% apply(t,Y))))),
% g(apply(b,
% apply(b,
% apply(
% apply(b,X),
% apply(t,Y))))))))
% -> (false) is composed into [90]
% (eq)(apply(X,apply(apply(apply(f(apply(b,
% apply(b,
% apply(
% apply(b,X),
% apply(t,Y))))),
% g(apply(b,apply(b,
% apply(
% apply(b,X),
% apply(t,Y)))))),
% h(apply(b,apply(b,
% apply(apply(b,X),
% apply(t,Y)))))),Y)),
% apply(f(apply(b,apply(b,apply(apply(b,X),
% apply(t,Y))))),
% apply(h(apply(b,apply(b,apply(apply(b,X),
% apply(t,Y))))),
% g(apply(b,apply(b,apply(apply(b,X),apply(t,Y))))))))
% -> (true)
% Rule [89]
% (eq)(apply(h(apply(apply(b,apply(b,t)),apply(apply(b,t),X))),apply(
% g(apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,t),X))),
% apply(X,
% f(apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,t),X)))))),
% apply(f(apply(apply(b,apply(b,t)),apply(apply(b,t),X))),apply(h(
% apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,t),X))),
% g(apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,t),X))))))
% -> (false) is composed into [89]
% (eq)(apply(h(apply(apply(b,apply(b,t)),
% apply(apply(b,t),X))),apply(
% g(
% apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,t),X))),
% apply(X,
% f(
% apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,t),X)))))),
% apply(f(apply(apply(b,apply(b,t)),apply(
% apply(b,t),X))),
% apply(h(apply(apply(b,apply(b,t)),apply(
% apply(b,t),X))),
% g(apply(apply(b,apply(b,t)),apply(apply(b,t),X))))))
% -> (true)
% Rule [88]
% (eq)(apply(h(apply(apply(b,apply(b,t)),apply(apply(b,X),Y))),apply(
% apply(X,
% apply(Y,
% f(apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,X),Y))))),
% g(apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,X),Y))))),
% apply(f(apply(apply(b,apply(b,t)),apply(apply(b,X),Y))),apply(h(
% apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,X),Y))),
% g(apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,X),Y))))))
% -> (false) is composed into [88]
% (eq)(apply(h(apply(apply(b,apply(b,t)),
% apply(apply(b,X),Y))),apply(
% apply(X,
% apply(Y,
% f(
% apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,X),Y))))),
% g(
% apply(
% apply(b,
% apply(b,t)),
% apply(
% apply(b,X),Y))))),
% apply(f(apply(apply(b,apply(b,t)),apply(
% apply(b,X),Y))),
% apply(h(apply(apply(b,apply(b,t)),apply(
% apply(b,X),Y))),
% g(apply(apply(b,apply(b,t)),apply(apply(b,X),Y))))))
% -> (true)
% Rule [87]
% (eq)(apply(h(apply(apply(b,apply(b,apply(apply(b,t),X))),t)),apply(X,
% apply(
% g(apply(
% apply(b,
% apply(b,
% apply(
% apply(b,t),X))),t)),
% f(apply(
% apply(b,
% apply(b,
% apply(
% apply(b,t),X))),t))))),
% apply(f(apply(apply(b,apply(b,apply(apply(b,t),X))),t)),apply(h(
% apply(
% apply(b,
% apply(b,
% apply(
% apply(b,t),X))),t)),
% g(apply(
% apply(b,
% apply(b,
% apply(
% apply(b,t),X))),t)))))
% -> (false) is composed into [87]
% (eq)(apply(h(apply(apply(b,apply(b,apply(
% apply(b,t),X))),t)),
% apply(X,apply(g(apply(apply(b,apply(b,
% apply(
% apply(b,t),X))),t)),
% f(apply(apply(b,apply(b,
% apply(apply(b,t),X))),t))))),
% apply(f(apply(apply(b,apply(b,apply(
% apply(b,t),X))),t)),
% apply(h(apply(apply(b,apply(b,apply(
% apply(b,t),X))),t)),
% g(apply(apply(b,apply(b,apply(apply(b,t),X))),t)))))
% -> (true)
% Rule [86]
% (eq)(apply(apply(X,apply(Y,apply(g(apply(apply(b,apply(b,apply(apply(b,X),Y))),t)),
% f(apply(apply(b,apply(b,apply(apply(b,X),Y))),t))))),
% h(apply(apply(b,apply(b,apply(apply(b,X),Y))),t))),apply(f(
% apply(
% apply(b,
% apply(b,
% apply(
% apply(b,X),Y))),t)),
% apply(h(
% apply(
% apply(b,
% apply(b,
% apply(
% apply(b,X),Y))),t)),
% g(apply(
% apply(b,
% apply(b,
% apply(
% apply(b,X),Y))),t)))))
% -> (false) is composed into [86]
% (eq)(apply(apply(X,apply(Y,apply(g(apply(
% apply(b,
% apply(b,
% apply(
% apply(b,X),Y))),t)),
% f(apply(apply(b,
% apply(b,
% apply(
% apply(b,X),Y))),t))))),
% h(apply(apply(b,apply(b,apply(apply(b,X),Y))),t))),
% apply(f(apply(apply(b,apply(b,apply(
% apply(b,X),Y))),t)),
% apply(h(apply(apply(b,apply(b,apply(
% apply(b,X),Y))),t)),
% g(apply(apply(b,apply(b,apply(apply(b,X),Y))),t)))))
% -> (true)
% Rule [85]
% (eq)(apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),
% apply(X,apply(Y,g(apply(apply(b,apply(t,apply(apply(b,X),Y))),b))))),
% h(apply(apply(b,apply(t,apply(apply(b,X),Y))),b))),apply(f(
% apply(
% apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),b)),
% apply(h(
% apply(
% apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),b)),
% g(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),b)))))
% -> (false) is composed into [85]
% (eq)(apply(apply(f(apply(apply(b,apply(t,
% apply(
% apply(b,X),Y))),b)),
% apply(X,apply(Y,g(apply(apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),b))))),
% h(apply(apply(b,apply(t,apply(apply(b,X),Y))),b))),
% apply(f(apply(apply(b,apply(t,apply(
% apply(b,X),Y))),b)),
% apply(h(apply(apply(b,apply(t,apply(
% apply(b,X),Y))),b)),
% g(apply(apply(b,apply(t,apply(apply(b,X),Y))),b)))))
% -> (true)
% Rule [84]
% (eq)(apply(apply(g(apply(apply(b,apply(t,apply(apply(b,b),t))),t)),
% h(apply(apply(b,apply(t,apply(apply(b,b),t))),t))),f(
% apply(
% apply(b,
% apply(t,
% apply(
% apply(b,b),t))),t))),
% apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),t)),apply(h(
% apply(
% apply(b,
% apply(t,
% apply(
% apply(b,b),t))),t)),
% g(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,b),t))),t)))))
% -> (false) is composed into [84]
% (eq)(apply(apply(g(apply(apply(b,apply(t,
% apply(
% apply(b,b),t))),t)),
% h(apply(apply(b,apply(t,apply(
% apply(b,b),t))),t))),
% f(apply(apply(b,apply(t,apply(apply(b,b),t))),t))),
% apply(f(apply(apply(b,apply(t,apply(
% apply(b,b),t))),t)),
% apply(h(apply(apply(b,apply(t,apply(
% apply(b,b),t))),t)),
% g(apply(apply(b,apply(t,apply(apply(b,b),t))),t)))))
% -> (true)
% Rule [83]
% (eq)(apply(apply(X,f(apply(apply(b,apply(t,apply(apply(b,b),X))),t))),
% apply(g(apply(apply(b,apply(t,apply(apply(b,b),X))),t)),h(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,b),X))),t)))),
% apply(f(apply(apply(b,apply(t,apply(apply(b,b),X))),t)),apply(h(
% apply(
% apply(b,
% apply(t,
% apply(
% apply(b,b),X))),t)),
% g(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,b),X))),t)))))
% -> (false) is composed into [83]
% (eq)(apply(apply(X,f(apply(apply(b,apply(t,
% apply(
% apply(b,b),X))),t))),
% apply(g(apply(apply(b,apply(t,apply(
% apply(b,b),X))),t)),
% h(apply(apply(b,apply(t,apply(apply(b,b),X))),t)))),
% apply(f(apply(apply(b,apply(t,apply(
% apply(b,b),X))),t)),
% apply(h(apply(apply(b,apply(t,apply(
% apply(b,b),X))),t)),
% g(apply(apply(b,apply(t,apply(apply(b,b),X))),t)))))
% -> (true)
% Rule [82]
% (eq)(apply(apply(g(apply(apply(b,apply(t,apply(apply(b,t),X))),t)),
% apply(X,f(apply(apply(b,apply(t,apply(apply(b,t),X))),t)))),
% h(apply(apply(b,apply(t,apply(apply(b,t),X))),t))),apply(f(
% apply(
% apply(b,
% apply(t,
% apply(
% apply(b,t),X))),t)),
% apply(h(
% apply(
% apply(b,
% apply(t,
% apply(
% apply(b,t),X))),t)),
% g(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,t),X))),t)))))
% -> (false) is composed into [82]
% (eq)(apply(apply(g(apply(apply(b,apply(t,
% apply(
% apply(b,t),X))),t)),
% apply(X,f(apply(apply(b,apply(t,
% apply(
% apply(b,t),X))),t)))),
% h(apply(apply(b,apply(t,apply(apply(b,t),X))),t))),
% apply(f(apply(apply(b,apply(t,apply(
% apply(b,t),X))),t)),
% apply(h(apply(apply(b,apply(t,apply(
% apply(b,t),X))),t)),
% g(apply(apply(b,apply(t,apply(apply(b,t),X))),t)))))
% -> (true)
% Rule [81]
% (eq)(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,apply(apply(b,X),Y))),t)))),
% g(apply(apply(b,apply(t,apply(apply(b,X),Y))),t))),h(
% apply(
% apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),t))),
% apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),t)),apply(h(
% apply(
% apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),t)),
% g(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),t)))))
% -> (false) is composed into [81]
% (eq)(apply(apply(apply(X,apply(Y,f(apply(
% apply(b,
% apply(t,
% apply(
% apply(b,X),Y))),t)))),
% g(apply(apply(b,apply(t,apply(
% apply(b,X),Y))),t))),
% h(apply(apply(b,apply(t,apply(apply(b,X),Y))),t))),
% apply(f(apply(apply(b,apply(t,apply(
% apply(b,X),Y))),t)),
% apply(h(apply(apply(b,apply(t,apply(
% apply(b,X),Y))),t)),
% g(apply(apply(b,apply(t,apply(apply(b,X),Y))),t)))))
% -> (true)
% Rule [80]
% (eq)(apply(h(apply(b,apply(apply(b,t),apply(apply(b,X),Y)))),apply(X,
% apply(Y,
% apply(
% f(apply(b,
% apply(
% apply(b,t),
% apply(
% apply(b,X),Y)))),
% g(apply(b,
% apply(
% apply(b,t),
% apply(
% apply(b,X),Y)))))))),
% apply(f(apply(b,apply(apply(b,t),apply(apply(b,X),Y)))),apply(h(
% apply(b,
% apply(
% apply(b,t),
% apply(
% apply(b,X),Y)))),
% g(apply(b,
% apply(
% apply(b,t),
% apply(
% apply(b,X),Y)))))))
% -> (false) is composed into [80]
% (eq)(apply(h(apply(b,apply(apply(b,t),
% apply(apply(b,X),Y)))),
% apply(X,apply(Y,apply(f(apply(b,
% apply(apply(b,t),
% apply(apply(b,X),Y)))),
% g(apply(b,apply(
% apply(b,t),
% apply(
% apply(b,X),Y)))))))),
% apply(f(apply(b,apply(apply(b,t),apply(
% apply(b,X),Y)))),
% apply(h(apply(b,apply(apply(b,t),apply(
% apply(b,X),Y)))),
% g(apply(b,apply(apply(b,t),apply(apply(b,X),Y)))))))
% -> (true)
% Rule [79]
% (eq)(apply(X,apply(Y,apply(f(apply(apply(b,b),apply(b,apply(apply(b,X),Y)))),
% apply(g(apply(apply(b,b),apply(b,apply(apply(b,X),Y)))),
% h(apply(apply(b,b),apply(b,apply(apply(b,X),Y)))))))),
% apply(f(apply(apply(b,b),apply(b,apply(apply(b,X),Y)))),apply(h(
% apply(
% apply(b,b),
% apply(b,
% apply(
% apply(b,X),Y)))),
% g(apply(
% apply(b,b),
% apply(b,
% apply(
% apply(b,X),Y)))))))
% -> (false) is composed into [79]
% (eq)(apply(X,apply(Y,apply(f(apply(apply(b,b),
% apply(b,
% apply(apply(b,X),Y)))),
% apply(g(apply(apply(b,b),
% apply(b,
% apply(apply(b,X),Y)))),
% h(apply(apply(b,b),
% apply(b,apply(
% apply(b,X),Y)))))))),
% apply(f(apply(apply(b,b),apply(b,apply(
% apply(b,X),Y)))),
% apply(h(apply(apply(b,b),apply(b,apply(
% apply(b,X),Y)))),
% g(apply(apply(b,b),apply(b,apply(apply(b,X),Y)))))))
% -> (true)
% Rule [78]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,b),t)),apply(t,X))),
% h(apply(apply(b,apply(apply(b,b),t)),apply(t,X)))),apply(
% f(
% apply(
% apply(b,
% apply(
% apply(b,b),t)),
% apply(t,X))),X)),
% apply(f(apply(apply(b,apply(apply(b,b),t)),apply(t,X))),apply(h(
% apply(
% apply(b,
% apply(
% apply(b,b),t)),
% apply(t,X))),
% g(apply(
% apply(b,
% apply(
% apply(b,b),t)),
% apply(t,X))))))
% -> (false) is composed into [78]
% (eq)(apply(apply(g(apply(apply(b,apply(
% apply(b,b),t)),
% apply(t,X))),h(apply(
% apply(b,
% apply(
% apply(b,b),t)),
% apply(t,X)))),
% apply(f(apply(apply(b,apply(apply(b,b),t)),
% apply(t,X))),X)),apply(
% f(apply(
% apply(b,
% apply(
% apply(b,b),t)),
% apply(t,X))),
% apply(
% h(apply(
% apply(b,
% apply(
% apply(b,b),t)),
% apply(t,X))),
% g(apply(
% apply(b,
% apply(
% apply(b,b),t)),
% apply(t,X))))))
% -> (true)
% Rule [77]
% (eq)(apply(apply(f(apply(apply(b,apply(b,apply(b,apply(t,X)))),b)),
% apply(g(apply(apply(b,apply(b,apply(b,apply(t,X)))),b)),
% h(apply(apply(b,apply(b,apply(b,apply(t,X)))),b)))),X),
% apply(f(apply(apply(b,apply(b,apply(b,apply(t,X)))),b)),apply(h(
% apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,X)))),b)),
% g(apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,X)))),b)))))
% -> (false) is composed into [77]
% (eq)(apply(apply(f(apply(apply(b,apply(b,
% apply(b,
% apply(t,X)))),b)),
% apply(g(apply(apply(b,apply(b,
% apply(b,
% apply(t,X)))),b)),
% h(apply(apply(b,apply(b,apply(b,
% apply(t,X)))),b)))),X),
% apply(f(apply(apply(b,apply(b,apply(b,
% apply(t,X)))),b)),
% apply(h(apply(apply(b,apply(b,apply(b,
% apply(t,X)))),b)),
% g(apply(apply(b,apply(b,apply(b,apply(t,X)))),b)))))
% -> (true)
% Rule [76]
% (eq)(apply(apply(h(apply(b,apply(apply(b,apply(b,apply(t,X))),t))),
% apply(f(apply(b,apply(apply(b,apply(b,apply(t,X))),t))),
% g(apply(b,apply(apply(b,apply(b,apply(t,X))),t))))),X),
% apply(f(apply(b,apply(apply(b,apply(b,apply(t,X))),t))),apply(h(
% apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,X))),t))),
% g(apply(b,
% apply(
% apply(b,
% apply(b,
% apply(t,X))),t))))))
% -> (false) is composed into [76]
% (eq)(apply(apply(h(apply(b,apply(apply(b,
% apply(b,
% apply(t,X))),t))),
% apply(f(apply(b,apply(apply(b,
% apply(b,
% apply(t,X))),t))),
% g(apply(b,apply(apply(b,apply(b,
% apply(t,X))),t))))),X),
% apply(f(apply(b,apply(apply(b,apply(b,
% apply(t,X))),t))),
% apply(h(apply(b,apply(apply(b,apply(b,
% apply(t,X))),t))),
% g(apply(b,apply(apply(b,apply(b,apply(t,X))),t))))))
% -> (true)
% Rule [75]
% (eq)(apply(apply(f(apply(b,apply(apply(b,apply(t,apply(t,X))),b))),
% g(apply(b,apply(apply(b,apply(t,apply(t,X))),b)))),apply(
% h(
% apply(b,
% apply(
% apply(b,
% apply(t,
% apply(t,X))),b))),X)),
% apply(f(apply(b,apply(apply(b,apply(t,apply(t,X))),b))),apply(h(
% apply(b,
% apply(
% apply(b,
% apply(t,
% apply(t,X))),b))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,
% apply(t,X))),b))))))
% -> (false) is composed into [75]
% (eq)(apply(apply(f(apply(b,apply(apply(b,
% apply(t,
% apply(t,X))),b))),
% g(apply(b,apply(apply(b,apply(t,
% apply(t,X))),b)))),
% apply(h(apply(b,apply(apply(b,apply(t,
% apply(t,X))),b))),X)),
% apply(f(apply(b,apply(apply(b,apply(t,
% apply(t,X))),b))),
% apply(h(apply(b,apply(apply(b,apply(t,
% apply(t,X))),b))),
% g(apply(b,apply(apply(b,apply(t,apply(t,X))),b))))))
% -> (true)
% Rule [74]
% (eq)(apply(X,apply(apply(f(apply(b,apply(apply(b,apply(t,apply(b,X))),t))),
% g(apply(b,apply(apply(b,apply(t,apply(b,X))),t)))),
% h(apply(b,apply(apply(b,apply(t,apply(b,X))),t))))),
% apply(f(apply(b,apply(apply(b,apply(t,apply(b,X))),t))),apply(h(
% apply(b,
% apply(
% apply(b,
% apply(t,
% apply(b,X))),t))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,
% apply(b,X))),t))))))
% -> (false) is composed into [74]
% (eq)(apply(X,apply(apply(f(apply(b,apply(
% apply(b,
% apply(t,
% apply(b,X))),t))),
% g(apply(b,apply(apply(b,
% apply(t,
% apply(b,X))),t)))),
% h(apply(b,apply(apply(b,
% apply(t,
% apply(b,X))),t))))),
% apply(f(apply(b,apply(apply(b,apply(t,
% apply(b,X))),t))),
% apply(h(apply(b,apply(apply(b,apply(t,
% apply(b,X))),t))),
% g(apply(b,apply(apply(b,apply(t,apply(b,X))),t))))))
% -> (true)
% Rule [73]
% (eq)(apply(apply(apply(f(apply(b,apply(apply(b,apply(t,apply(t,X))),t))),
% g(apply(b,apply(apply(b,apply(t,apply(t,X))),t)))),X),
% h(apply(b,apply(apply(b,apply(t,apply(t,X))),t)))),apply(f(
% apply(b,
% apply(
% apply(b,
% apply(t,
% apply(t,X))),t))),
% apply(h(
% apply(b,
% apply(
% apply(b,
% apply(t,
% apply(t,X))),t))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,
% apply(t,X))),t))))))
% -> (false) is composed into [73]
% (eq)(apply(apply(apply(f(apply(b,apply(
% apply(b,
% apply(t,
% apply(t,X))),t))),
% g(apply(b,apply(apply(b,
% apply(t,
% apply(t,X))),t)))),X),
% h(apply(b,apply(apply(b,apply(t,
% apply(t,X))),t)))),
% apply(f(apply(b,apply(apply(b,apply(t,
% apply(t,X))),t))),
% apply(h(apply(b,apply(apply(b,apply(t,
% apply(t,X))),t))),
% g(apply(b,apply(apply(b,apply(t,apply(t,X))),t))))))
% -> (true)
% Rule [72]
% (eq)(apply(apply(g(apply(apply(b,b),apply(apply(b,t),apply(t,X)))),
% h(apply(apply(b,b),apply(apply(b,t),apply(t,X))))),apply(
% f(
% apply(
% apply(b,b),
% apply(
% apply(b,t),
% apply(t,X)))),X)),
% apply(f(apply(apply(b,b),apply(apply(b,t),apply(t,X)))),apply(h(
% apply(
% apply(b,b),
% apply(
% apply(b,t),
% apply(t,X)))),
% g(apply(
% apply(b,b),
% apply(
% apply(b,t),
% apply(t,X)))))))
% -> (false) is composed into [72]
% (eq)(apply(apply(g(apply(apply(b,b),
% apply(apply(b,t),
% apply(t,X)))),h(apply(
% apply(b,b),
% apply(
% apply(b,t),
% apply(t,X))))),
% apply(f(apply(apply(b,b),apply(
% apply(b,t),
% apply(t,X)))),X)),
% apply(f(apply(apply(b,b),apply(apply(b,t),
% apply(t,X)))),
% apply(h(apply(apply(b,b),apply(apply(b,t),
% apply(t,X)))),
% g(apply(apply(b,b),apply(apply(b,t),
% apply(t,X))))))) ->
% (true)
% Rule [71]
% (eq)(apply(h(apply(apply(b,apply(b,t)),apply(b,apply(t,X)))),apply(
% apply(
% f(apply(
% apply(b,
% apply(b,t)),
% apply(b,
% apply(t,X)))),
% g(apply(
% apply(b,
% apply(b,t)),
% apply(b,
% apply(t,X))))),X)),
% apply(f(apply(apply(b,apply(b,t)),apply(b,apply(t,X)))),apply(h(
% apply(
% apply(b,
% apply(b,t)),
% apply(b,
% apply(t,X)))),
% g(apply(
% apply(b,
% apply(b,t)),
% apply(b,
% apply(t,X)))))))
% -> (false) is composed into [71]
% (eq)(apply(h(apply(apply(b,apply(b,t)),
% apply(b,apply(t,X)))),apply(
% apply(
% f(
% apply(
% apply(b,
% apply(b,t)),
% apply(b,
% apply(t,X)))),
% g(
% apply(
% apply(b,
% apply(b,t)),
% apply(b,
% apply(t,X))))),X)),
% apply(f(apply(apply(b,apply(b,t)),apply(b,
% apply(t,X)))),
% apply(h(apply(apply(b,apply(b,t)),apply(b,
% apply(t,X)))),
% g(apply(apply(b,apply(b,t)),apply(b,
% apply(t,X)))))))
% -> (true)
% Rule [70]
% (eq)(apply(apply(apply(g(apply(apply(b,apply(b,apply(b,apply(t,X)))),t)),
% f(apply(apply(b,apply(b,apply(b,apply(t,X)))),t))),
% h(apply(apply(b,apply(b,apply(b,apply(t,X)))),t))),X),
% apply(f(apply(apply(b,apply(b,apply(b,apply(t,X)))),t)),apply(h(
% apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,X)))),t)),
% g(apply(
% apply(b,
% apply(b,
% apply(b,
% apply(t,X)))),t)))))
% -> (false) is composed into [70]
% (eq)(apply(apply(apply(g(apply(apply(b,
% apply(b,
% apply(b,
% apply(t,X)))),t)),
% f(apply(apply(b,apply(b,
% apply(b,
% apply(t,X)))),t))),
% h(apply(apply(b,apply(b,apply(b,
% apply(t,X)))),t))),X),
% apply(f(apply(apply(b,apply(b,apply(b,
% apply(t,X)))),t)),
% apply(h(apply(apply(b,apply(b,apply(b,
% apply(t,X)))),t)),
% g(apply(apply(b,apply(b,apply(b,apply(t,X)))),t)))))
% -> (true)
% Rule [69]
% (eq)(apply(X,apply(apply(f(apply(apply(b,apply(t,apply(b,apply(b,X)))),t)),
% g(apply(apply(b,apply(t,apply(b,apply(b,X)))),t))),
% h(apply(apply(b,apply(t,apply(b,apply(b,X)))),t)))),
% apply(f(apply(apply(b,apply(t,apply(b,apply(b,X)))),t)),apply(h(
% apply(
% apply(b,
% apply(t,
% apply(b,
% apply(b,X)))),t)),
% g(apply(
% apply(b,
% apply(t,
% apply(b,
% apply(b,X)))),t)))))
% -> (false) is composed into [69]
% (eq)(apply(X,apply(apply(f(apply(apply(b,
% apply(t,
% apply(b,
% apply(b,X)))),t)),
% g(apply(apply(b,apply(t,
% apply(b,
% apply(b,X)))),t))),
% h(apply(apply(b,apply(t,
% apply(b,
% apply(b,X)))),t)))),
% apply(f(apply(apply(b,apply(t,apply(b,
% apply(b,X)))),t)),
% apply(h(apply(apply(b,apply(t,apply(b,
% apply(b,X)))),t)),
% g(apply(apply(b,apply(t,apply(b,apply(b,X)))),t)))))
% -> (true)
% Rule [68]
% (eq)(apply(apply(apply(f(apply(apply(b,apply(t,apply(b,apply(t,X)))),t)),
% g(apply(apply(b,apply(t,apply(b,apply(t,X)))),t))),X),
% h(apply(apply(b,apply(t,apply(b,apply(t,X)))),t))),apply(f(
% apply(
% apply(b,
% apply(t,
% apply(b,
% apply(t,X)))),t)),
% apply(h(
% apply(
% apply(b,
% apply(t,
% apply(b,
% apply(t,X)))),t)),
% g(apply(
% apply(b,
% apply(t,
% apply(b,
% apply(t,X)))),t)))))
% -> (false) is composed into [68]
% (eq)(apply(apply(apply(f(apply(apply(b,
% apply(t,
% apply(b,
% apply(t,X)))),t)),
% g(apply(apply(b,apply(t,
% apply(b,
% apply(t,X)))),t))),X),
% h(apply(apply(b,apply(t,apply(b,
% apply(t,X)))),t))),
% apply(f(apply(apply(b,apply(t,apply(b,
% apply(t,X)))),t)),
% apply(h(apply(apply(b,apply(t,apply(b,
% apply(t,X)))),t)),
% g(apply(apply(b,apply(t,apply(b,apply(t,X)))),t)))))
% -> (true)
% Rule [67]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,b),t)),X)),h(apply(
% apply(b,
% apply(
% apply(b,b),t)),X))),
% apply(X,f(apply(apply(b,apply(apply(b,b),t)),X)))),apply(f(
% apply(
% apply(b,
% apply(
% apply(b,b),t)),X)),
% apply(h(
% apply(
% apply(b,
% apply(
% apply(b,b),t)),X)),
% g(apply(
% apply(b,
% apply(
% apply(b,b),t)),X)))))
% -> (false) is composed into [67]
% (eq)(apply(apply(g(apply(apply(b,apply(
% apply(b,b),t)),X)),
% h(apply(apply(b,apply(apply(b,b),t)),X))),
% apply(X,f(apply(apply(b,apply(apply(b,b),t)),X)))),
% apply(f(apply(apply(b,apply(apply(b,b),t)),X)),
% apply(h(apply(apply(b,apply(apply(b,b),t)),X)),
% g(apply(apply(b,apply(apply(b,b),t)),X)))))
% -> (true)
% Rule [66]
% (eq)(apply(apply(X,apply(Y,f(apply(apply(b,apply(apply(b,b),X)),Y)))),
% apply(g(apply(apply(b,apply(apply(b,b),X)),Y)),h(apply(apply(b,
% apply(
% apply(b,b),X)),Y)))),
% apply(f(apply(apply(b,apply(apply(b,b),X)),Y)),apply(h(apply(apply(b,
% apply(
% apply(b,b),X)),Y)),
% g(apply(apply(b,apply(
% apply(b,b),X)),Y)))))
% -> (false) is composed into [66]
% (eq)(apply(apply(X,apply(Y,f(apply(apply(b,
% apply(
% apply(b,b),X)),Y)))),
% apply(g(apply(apply(b,apply(apply(b,b),X)),Y)),
% h(apply(apply(b,apply(apply(b,b),X)),Y)))),
% apply(f(apply(apply(b,apply(apply(b,b),X)),Y)),
% apply(h(apply(apply(b,apply(apply(b,b),X)),Y)),
% g(apply(apply(b,apply(apply(b,b),X)),Y)))))
% -> (true)
% Rule [65]
% (eq)(apply(apply(g(apply(apply(b,apply(apply(b,t),X)),Y)),apply(X,
% apply(Y,
% f(apply(
% apply(b,
% apply(
% apply(b,t),X)),Y))))),
% h(apply(apply(b,apply(apply(b,t),X)),Y))),apply(f(apply(apply(b,
% apply(
% apply(b,t),X)),Y)),
% apply(h(apply(apply(b,
% apply(
% apply(b,t),X)),Y)),
% g(apply(apply(b,apply(
% apply(b,t),X)),Y)))))
% -> (false) is composed into [65]
% (eq)(apply(apply(g(apply(apply(b,apply(
% apply(b,t),X)),Y)),
% apply(X,apply(Y,f(apply(apply(b,
% apply(
% apply(b,t),X)),Y))))),
% h(apply(apply(b,apply(apply(b,t),X)),Y))),
% apply(f(apply(apply(b,apply(apply(b,t),X)),Y)),
% apply(h(apply(apply(b,apply(apply(b,t),X)),Y)),
% g(apply(apply(b,apply(apply(b,t),X)),Y)))))
% -> (true)
% Rule [64]
% (eq)(apply(apply(apply(X,apply(Y,apply(Z,f(apply(apply(b,apply(apply(b,X),Y)),Z))))),
% g(apply(apply(b,apply(apply(b,X),Y)),Z))),h(apply(apply(b,
% apply(
% apply(b,X),Y)),Z))),
% apply(f(apply(apply(b,apply(apply(b,X),Y)),Z)),apply(h(apply(apply(b,
% apply(
% apply(b,X),Y)),Z)),
% g(apply(apply(b,apply(
% apply(b,X),Y)),Z)))))
% -> (false) is composed into [64]
% (eq)(apply(apply(apply(X,apply(Y,apply(Z,
% f(apply(
% apply(b,
% apply(
% apply(b,X),Y)),Z))))),
% g(apply(apply(b,apply(apply(b,X),Y)),Z))),
% h(apply(apply(b,apply(apply(b,X),Y)),Z))),
% apply(f(apply(apply(b,apply(apply(b,X),Y)),Z)),
% apply(h(apply(apply(b,apply(apply(b,X),Y)),Z)),
% g(apply(apply(b,apply(apply(b,X),Y)),Z)))))
% -> (true)
% Rule [63]
% (eq)(apply(apply(apply(X,apply(Y,apply(Z,f(apply(apply(b,X),apply(
% apply(b,Y),Z)))))),
% g(apply(apply(b,X),apply(apply(b,Y),Z)))),h(apply(apply(b,X),
% apply(apply(b,Y),Z)))),
% apply(f(apply(apply(b,X),apply(apply(b,Y),Z))),apply(h(apply(apply(b,X),
% apply(apply(b,Y),Z))),
% g(apply(apply(b,X),
% apply(apply(b,Y),Z))))))
% -> (false) is composed into [63]
% (eq)(apply(apply(apply(X,apply(Y,apply(Z,
% f(apply(
% apply(b,X),
% apply(
% apply(b,Y),Z)))))),
% g(apply(apply(b,X),apply(
% apply(b,Y),Z)))),
% h(apply(apply(b,X),apply(apply(b,Y),Z)))),
% apply(f(apply(apply(b,X),apply(apply(b,Y),Z))),
% apply(h(apply(apply(b,X),apply(apply(b,Y),Z))),
% g(apply(apply(b,X),apply(apply(b,Y),Z))))))
% -> (true)
% Rule [62]
% (eq)(apply(X,apply(f(apply(apply(b,apply(b,apply(b,X))),b)),apply(
% g(apply(
% apply(b,
% apply(b,
% apply(b,X))),b)),
% h(apply(
% apply(b,
% apply(b,
% apply(b,X))),b))))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),b)),apply(h(apply(apply(b,
% apply(b,
% apply(b,X))),b)),
% g(apply(apply(b,apply(b,
% apply(b,X))),b)))))
% -> (false) is composed into [62]
% (eq)(apply(X,apply(f(apply(apply(b,apply(b,
% apply(b,X))),b)),
% apply(g(apply(apply(b,apply(b,
% apply(b,X))),b)),
% h(apply(apply(b,apply(b,
% apply(b,X))),b))))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),b)),
% apply(h(apply(apply(b,apply(b,apply(b,X))),b)),
% g(apply(apply(b,apply(b,apply(b,X))),b)))))
% -> (true)
% Rule [61]
% (eq)(apply(X,apply(apply(apply(Y,f(apply(apply(b,apply(b,apply(b,X))),Y))),
% g(apply(apply(b,apply(b,apply(b,X))),Y))),h(apply(
% apply(b,
% apply(b,
% apply(b,X))),Y)))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),Y)),apply(h(apply(apply(b,
% apply(b,
% apply(b,X))),Y)),
% g(apply(apply(b,apply(b,
% apply(b,X))),Y)))))
% -> (false) is composed into [61]
% (eq)(apply(X,apply(apply(apply(Y,f(apply(
% apply(b,
% apply(b,
% apply(b,X))),Y))),
% g(apply(apply(b,apply(b,
% apply(b,X))),Y))),
% h(apply(apply(b,apply(b,
% apply(b,X))),Y)))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),Y)),
% apply(h(apply(apply(b,apply(b,apply(b,X))),Y)),
% g(apply(apply(b,apply(b,apply(b,X))),Y)))))
% -> (true)
% Rule [60]
% (eq)(apply(apply(X,apply(Y,apply(f(apply(apply(b,apply(b,X)),apply(b,Y))),
% g(apply(apply(b,apply(b,X)),apply(b,Y)))))),
% h(apply(apply(b,apply(b,X)),apply(b,Y)))),apply(f(apply(apply(b,
% apply(b,X)),
% apply(b,Y))),
% apply(h(apply(apply(b,
% apply(b,X)),
% apply(b,Y))),
% g(apply(apply(b,apply(b,X)),
% apply(b,Y)))))) ->
% (false) is composed into [60]
% (eq)(apply(apply(X,apply(Y,apply(f(apply(
% apply(b,
% apply(b,X)),
% apply(b,Y))),
% g(apply(apply(b,
% apply(b,X)),
% apply(b,Y)))))),
% h(apply(apply(b,apply(b,X)),apply(b,Y)))),
% apply(f(apply(apply(b,apply(b,X)),apply(b,Y))),
% apply(h(apply(apply(b,apply(b,X)),apply(b,Y))),
% g(apply(apply(b,apply(b,X)),apply(b,Y)))))) ->
% (true)
% Rule [59]
% (eq)(apply(apply(f(apply(apply(b,apply(b,apply(t,X))),b)),apply(
% g(apply(
% apply(b,
% apply(b,
% apply(t,X))),b)),X)),
% h(apply(apply(b,apply(b,apply(t,X))),b))),apply(f(apply(apply(b,
% apply(b,
% apply(t,X))),b)),
% apply(h(apply(apply(b,
% apply(b,
% apply(t,X))),b)),
% g(apply(apply(b,apply(b,
% apply(t,X))),b)))))
% -> (false) is composed into [59]
% (eq)(apply(apply(f(apply(apply(b,apply(b,
% apply(t,X))),b)),
% apply(g(apply(apply(b,apply(b,
% apply(t,X))),b)),X)),
% h(apply(apply(b,apply(b,apply(t,X))),b))),
% apply(f(apply(apply(b,apply(b,apply(t,X))),b)),
% apply(h(apply(apply(b,apply(b,apply(t,X))),b)),
% g(apply(apply(b,apply(b,apply(t,X))),b)))))
% -> (true)
% Rule [58]
% (eq)(apply(apply(apply(apply(X,f(apply(apply(b,apply(b,apply(t,Y))),X))),
% g(apply(apply(b,apply(b,apply(t,Y))),X))),Y),h(
% apply(
% apply(b,
% apply(b,
% apply(t,Y))),X))),
% apply(f(apply(apply(b,apply(b,apply(t,Y))),X)),apply(h(apply(apply(b,
% apply(b,
% apply(t,Y))),X)),
% g(apply(apply(b,apply(b,
% apply(t,Y))),X)))))
% -> (false) is composed into [58]
% (eq)(apply(apply(apply(apply(X,f(apply(
% apply(b,
% apply(b,
% apply(t,Y))),X))),
% g(apply(apply(b,apply(b,
% apply(t,Y))),X))),Y),
% h(apply(apply(b,apply(b,apply(t,Y))),X))),
% apply(f(apply(apply(b,apply(b,apply(t,Y))),X)),
% apply(h(apply(apply(b,apply(b,apply(t,Y))),X)),
% g(apply(apply(b,apply(b,apply(t,Y))),X)))))
% -> (true)
% Rule [57]
% (eq)(apply(apply(f(apply(apply(b,apply(t,X)),apply(b,b))),X),apply(
% g(apply(
% apply(b,
% apply(t,X)),
% apply(b,b))),
% h(apply(
% apply(b,
% apply(t,X)),
% apply(b,b))))),
% apply(f(apply(apply(b,apply(t,X)),apply(b,b))),apply(h(apply(apply(b,
% apply(t,X)),
% apply(b,b))),
% g(apply(apply(b,apply(t,X)),
% apply(b,b)))))) ->
% (false) is composed into [57]
% (eq)(apply(apply(f(apply(apply(b,apply(t,X)),
% apply(b,b))),X),apply(
% g(apply(
% apply(b,
% apply(t,X)),
% apply(b,b))),
% h(apply(
% apply(b,
% apply(t,X)),
% apply(b,b))))),
% apply(f(apply(apply(b,apply(t,X)),apply(b,b))),
% apply(h(apply(apply(b,apply(t,X)),apply(b,b))),
% g(apply(apply(b,apply(t,X)),apply(b,b)))))) ->
% (true)
% Rule [56]
% (eq)(apply(apply(g(apply(apply(b,apply(t,X)),apply(b,t))),apply(
% f(apply(
% apply(b,
% apply(t,X)),
% apply(b,t))),X)),
% h(apply(apply(b,apply(t,X)),apply(b,t)))),apply(f(apply(apply(b,
% apply(t,X)),
% apply(b,t))),
% apply(h(apply(apply(b,
% apply(t,X)),
% apply(b,t))),
% g(apply(apply(b,apply(t,X)),
% apply(b,t)))))) ->
% (false) is composed into [56]
% (eq)(apply(apply(g(apply(apply(b,apply(t,X)),
% apply(b,t))),apply(f(
% apply(
% apply(b,
% apply(t,X)),
% apply(b,t))),X)),
% h(apply(apply(b,apply(t,X)),apply(b,t)))),
% apply(f(apply(apply(b,apply(t,X)),apply(b,t))),
% apply(h(apply(apply(b,apply(t,X)),apply(b,t))),
% g(apply(apply(b,apply(t,X)),apply(b,t)))))) ->
% (true)
% Rule [55]
% (eq)(apply(apply(apply(X,apply(f(apply(apply(b,apply(t,Y)),apply(b,X))),Y)),
% g(apply(apply(b,apply(t,Y)),apply(b,X)))),h(apply(apply(b,
% apply(t,Y)),
% apply(b,X)))),
% apply(f(apply(apply(b,apply(t,Y)),apply(b,X))),apply(h(apply(apply(b,
% apply(t,Y)),
% apply(b,X))),
% g(apply(apply(b,apply(t,Y)),
% apply(b,X)))))) ->
% (false) is composed into [55]
% (eq)(apply(apply(apply(X,apply(f(apply(
% apply(b,
% apply(t,Y)),
% apply(b,X))),Y)),
% g(apply(apply(b,apply(t,Y)),
% apply(b,X)))),h(apply(apply(b,
% apply(t,Y)),
% apply(b,X)))),
% apply(f(apply(apply(b,apply(t,Y)),apply(b,X))),
% apply(h(apply(apply(b,apply(t,Y)),apply(b,X))),
% g(apply(apply(b,apply(t,Y)),apply(b,X)))))) ->
% (true)
% Rule [54]
% (eq)(apply(apply(X,apply(apply(f(apply(apply(b,apply(b,X)),apply(t,Y))),Y),
% g(apply(apply(b,apply(b,X)),apply(t,Y))))),h(
% apply(
% apply(b,
% apply(b,X)),
% apply(t,Y)))),
% apply(f(apply(apply(b,apply(b,X)),apply(t,Y))),apply(h(apply(apply(b,
% apply(b,X)),
% apply(t,Y))),
% g(apply(apply(b,apply(b,X)),
% apply(t,Y)))))) ->
% (false) is composed into [54]
% (eq)(apply(apply(X,apply(apply(f(apply(
% apply(b,
% apply(b,X)),
% apply(t,Y))),Y),
% g(apply(apply(b,apply(b,X)),
% apply(t,Y))))),h(apply(
% apply(b,
% apply(b,X)),
% apply(t,Y)))),
% apply(f(apply(apply(b,apply(b,X)),apply(t,Y))),
% apply(h(apply(apply(b,apply(b,X)),apply(t,Y))),
% g(apply(apply(b,apply(b,X)),apply(t,Y)))))) ->
% (true)
% Rule [53]
% (eq)(apply(apply(apply(apply(f(apply(apply(b,apply(t,X)),apply(t,Y))),Y),X),
% g(apply(apply(b,apply(t,X)),apply(t,Y)))),h(apply(apply(b,
% apply(t,X)),
% apply(t,Y)))),
% apply(f(apply(apply(b,apply(t,X)),apply(t,Y))),apply(h(apply(apply(b,
% apply(t,X)),
% apply(t,Y))),
% g(apply(apply(b,apply(t,X)),
% apply(t,Y)))))) ->
% (false) is composed into [53]
% (eq)(apply(apply(apply(apply(f(apply(apply(b,
% apply(t,X)),
% apply(t,Y))),Y),X),
% g(apply(apply(b,apply(t,X)),
% apply(t,Y)))),h(apply(apply(b,
% apply(t,X)),
% apply(t,Y)))),
% apply(f(apply(apply(b,apply(t,X)),apply(t,Y))),
% apply(h(apply(apply(b,apply(t,X)),apply(t,Y))),
% g(apply(apply(b,apply(t,X)),apply(t,Y)))))) ->
% (true)
% Rule [52]
% (eq)(apply(X,apply(h(apply(b,apply(apply(b,apply(b,X)),t))),apply(
% f(apply(b,
% apply(
% apply(b,
% apply(b,X)),t))),
% g(apply(b,
% apply(
% apply(b,
% apply(b,X)),t)))))),
% apply(f(apply(b,apply(apply(b,apply(b,X)),t))),apply(h(apply(b,apply(
% apply(b,
% apply(b,X)),t))),
% g(apply(b,apply(apply(b,
% apply(b,X)),t))))))
% -> (false) is composed into [52]
% (eq)(apply(X,apply(h(apply(b,apply(apply(b,
% apply(b,X)),t))),
% apply(f(apply(b,apply(apply(b,
% apply(b,X)),t))),
% g(apply(b,apply(apply(b,
% apply(b,X)),t)))))),
% apply(f(apply(b,apply(apply(b,apply(b,X)),t))),
% apply(h(apply(b,apply(apply(b,apply(b,X)),t))),
% g(apply(b,apply(apply(b,apply(b,X)),t))))))
% -> (true)
% Rule [51]
% (eq)(apply(X,apply(apply(Y,apply(f(apply(b,apply(apply(b,apply(b,X)),Y))),
% g(apply(b,apply(apply(b,apply(b,X)),Y))))),
% h(apply(b,apply(apply(b,apply(b,X)),Y))))),apply(f(
% apply(b,
% apply(
% apply(b,
% apply(b,X)),Y))),
% apply(h(
% apply(b,
% apply(
% apply(b,
% apply(b,X)),Y))),
% g(apply(b,
% apply(
% apply(b,
% apply(b,X)),Y))))))
% -> (false) is composed into [51]
% (eq)(apply(X,apply(apply(Y,apply(f(apply(b,
% apply(
% apply(b,
% apply(b,X)),Y))),
% g(apply(b,
% apply(apply(b,
% apply(b,X)),Y))))),
% h(apply(b,apply(apply(b,
% apply(b,X)),Y))))),
% apply(f(apply(b,apply(apply(b,apply(b,X)),Y))),
% apply(h(apply(b,apply(apply(b,apply(b,X)),Y))),
% g(apply(b,apply(apply(b,apply(b,X)),Y))))))
% -> (true)
% Rule [50]
% (eq)(apply(h(apply(b,apply(apply(b,apply(t,t)),t))),apply(f(apply(b,
% apply(
% apply(b,
% apply(t,t)),t))),
% g(apply(b,apply(
% apply(b,
% apply(t,t)),t))))),
% apply(f(apply(b,apply(apply(b,apply(t,t)),t))),apply(h(apply(b,apply(
% apply(b,
% apply(t,t)),t))),
% g(apply(b,apply(apply(b,
% apply(t,t)),t))))))
% -> (false) is composed into [50]
% (eq)(apply(h(apply(b,apply(apply(b,apply(t,t)),t))),
% apply(f(apply(b,apply(apply(b,apply(t,t)),t))),
% g(apply(b,apply(apply(b,apply(t,t)),t))))),
% apply(f(apply(b,apply(apply(b,apply(t,t)),t))),
% apply(h(apply(b,apply(apply(b,apply(t,t)),t))),
% g(apply(b,apply(apply(b,apply(t,t)),t))))))
% -> (true)
% Rule [49]
% (eq)(apply(apply(f(apply(b,apply(apply(b,apply(t,X)),b))),g(apply(b,
% apply(
% apply(b,
% apply(t,X)),b)))),
% apply(X,h(apply(b,apply(apply(b,apply(t,X)),b))))),apply(f(
% apply(b,
% apply(
% apply(b,
% apply(t,X)),b))),
% apply(h(
% apply(b,
% apply(
% apply(b,
% apply(t,X)),b))),
% g(apply(b,
% apply(
% apply(b,
% apply(t,X)),b))))))
% -> (false) is composed into [49]
% (eq)(apply(apply(f(apply(b,apply(apply(b,
% apply(t,X)),b))),
% g(apply(b,apply(apply(b,apply(t,X)),b)))),
% apply(X,h(apply(b,apply(apply(b,
% apply(t,X)),b))))),
% apply(f(apply(b,apply(apply(b,apply(t,X)),b))),
% apply(h(apply(b,apply(apply(b,apply(t,X)),b))),
% g(apply(b,apply(apply(b,apply(t,X)),b))))))
% -> (true)
% Rule [48]
% (eq)(apply(apply(X,apply(f(apply(b,apply(apply(b,apply(t,X)),t))),
% g(apply(b,apply(apply(b,apply(t,X)),t))))),h(
% apply(b,
% apply(
% apply(b,
% apply(t,X)),t)))),
% apply(f(apply(b,apply(apply(b,apply(t,X)),t))),apply(h(apply(b,apply(
% apply(b,
% apply(t,X)),t))),
% g(apply(b,apply(apply(b,
% apply(t,X)),t))))))
% -> (false) is composed into [48]
% (eq)(apply(apply(X,apply(f(apply(b,apply(
% apply(b,
% apply(t,X)),t))),
% g(apply(b,apply(apply(b,
% apply(t,X)),t))))),
% h(apply(b,apply(apply(b,apply(t,X)),t)))),
% apply(f(apply(b,apply(apply(b,apply(t,X)),t))),
% apply(h(apply(b,apply(apply(b,apply(t,X)),t))),
% g(apply(b,apply(apply(b,apply(t,X)),t))))))
% -> (true)
% Rule [47]
% (eq)(apply(apply(apply(X,apply(f(apply(b,apply(apply(b,apply(t,Y)),X))),
% g(apply(b,apply(apply(b,apply(t,Y)),X))))),Y),
% h(apply(b,apply(apply(b,apply(t,Y)),X)))),apply(f(apply(b,apply(
% apply(b,
% apply(t,Y)),X))),
% apply(h(apply(b,apply(
% apply(b,
% apply(t,Y)),X))),
% g(apply(b,apply(apply(b,
% apply(t,Y)),X))))))
% -> (false) is composed into [47]
% (eq)(apply(apply(apply(X,apply(f(apply(b,
% apply(
% apply(b,
% apply(t,Y)),X))),
% g(apply(b,apply(
% apply(b,
% apply(t,Y)),X))))),Y),
% h(apply(b,apply(apply(b,apply(t,Y)),X)))),
% apply(f(apply(b,apply(apply(b,apply(t,Y)),X))),
% apply(h(apply(b,apply(apply(b,apply(t,Y)),X))),
% g(apply(b,apply(apply(b,apply(t,Y)),X))))))
% -> (true)
% Rule [46]
% (eq)(apply(apply(X,apply(apply(f(apply(b,apply(apply(b,X),apply(t,Y)))),
% g(apply(b,apply(apply(b,X),apply(t,Y))))),Y)),
% h(apply(b,apply(apply(b,X),apply(t,Y))))),apply(f(apply(b,apply(
% apply(b,X),
% apply(t,Y)))),
% apply(h(apply(b,apply(
% apply(b,X),
% apply(t,Y)))),
% g(apply(b,apply(apply(b,X),
% apply(t,Y)))))))
% -> (false) is composed into [46]
% (eq)(apply(apply(X,apply(apply(f(apply(b,
% apply(
% apply(b,X),
% apply(t,Y)))),
% g(apply(b,apply(
% apply(b,X),
% apply(t,Y))))),Y)),
% h(apply(b,apply(apply(b,X),apply(t,Y))))),
% apply(f(apply(b,apply(apply(b,X),apply(t,Y)))),
% apply(h(apply(b,apply(apply(b,X),apply(t,Y)))),
% g(apply(b,apply(apply(b,X),apply(t,Y)))))))
% -> (true)
% Rule [45]
% (eq)(apply(apply(g(apply(apply(b,b),apply(apply(b,t),X))),h(apply(
% apply(b,b),
% apply(
% apply(b,t),X)))),
% apply(X,f(apply(apply(b,b),apply(apply(b,t),X))))),apply(f(
% apply(
% apply(b,b),
% apply(
% apply(b,t),X))),
% apply(h(
% apply(
% apply(b,b),
% apply(
% apply(b,t),X))),
% g(apply(
% apply(b,b),
% apply(
% apply(b,t),X))))))
% -> (false) is composed into [45]
% (eq)(apply(apply(g(apply(apply(b,b),
% apply(apply(b,t),X))),
% h(apply(apply(b,b),apply(
% apply(b,t),X)))),
% apply(X,f(apply(apply(b,b),apply(
% apply(b,t),X))))),
% apply(f(apply(apply(b,b),apply(apply(b,t),X))),
% apply(h(apply(apply(b,b),apply(apply(b,t),X))),
% g(apply(apply(b,b),apply(apply(b,t),X))))))
% -> (true)
% Rule [44]
% (eq)(apply(apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X),Y))))),
% apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),
% apply(apply(b,X),Y))))),
% apply(f(apply(apply(b,b),apply(apply(b,X),Y))),apply(h(apply(apply(b,b),
% apply(apply(b,X),Y))),
% g(apply(apply(b,b),
% apply(apply(b,X),Y))))))
% -> (false) is composed into [44]
% (eq)(apply(apply(X,apply(Y,f(apply(apply(b,b),
% apply(apply(b,X),Y))))),
% apply(g(apply(apply(b,b),apply(
% apply(b,X),Y))),
% h(apply(apply(b,b),apply(apply(b,X),Y))))),
% apply(f(apply(apply(b,b),apply(apply(b,X),Y))),
% apply(h(apply(apply(b,b),apply(apply(b,X),Y))),
% g(apply(apply(b,b),apply(apply(b,X),Y))))))
% -> (true)
% Rule [43]
% (eq)(apply(apply(g(apply(apply(b,t),apply(apply(b,X),Y))),apply(X,
% apply(Y,
% f(apply(
% apply(b,t),
% apply(
% apply(b,X),Y)))))),
% h(apply(apply(b,t),apply(apply(b,X),Y)))),apply(f(apply(apply(b,t),
% apply(apply(b,X),Y))),
% apply(h(apply(apply(b,t),
% apply(apply(b,X),Y))),
% g(apply(apply(b,t),
% apply(apply(b,X),Y))))))
% -> (false) is composed into [43]
% (eq)(apply(apply(g(apply(apply(b,t),
% apply(apply(b,X),Y))),
% apply(X,apply(Y,f(apply(apply(b,t),
% apply(apply(b,X),Y)))))),
% h(apply(apply(b,t),apply(apply(b,X),Y)))),
% apply(f(apply(apply(b,t),apply(apply(b,X),Y))),
% apply(h(apply(apply(b,t),apply(apply(b,X),Y))),
% g(apply(apply(b,t),apply(apply(b,X),Y))))))
% -> (true)
% Rule [42]
% (eq)(apply(X,apply(Y,apply(apply(f(apply(b,apply(b,apply(apply(b,X),Y)))),
% g(apply(b,apply(b,apply(apply(b,X),Y))))),
% h(apply(b,apply(b,apply(apply(b,X),Y))))))),
% apply(f(apply(b,apply(b,apply(apply(b,X),Y)))),apply(h(apply(b,apply(b,
% apply(
% apply(b,X),Y)))),
% g(apply(b,apply(b,
% apply(apply(b,X),Y)))))))
% -> (false) is composed into [42]
% (eq)(apply(X,apply(Y,apply(apply(f(apply(b,
% apply(b,
% apply(
% apply(b,X),Y)))),
% g(apply(b,
% apply(b,
% apply(apply(b,X),Y))))),
% h(apply(b,apply(b,
% apply(
% apply(b,X),Y))))))),
% apply(f(apply(b,apply(b,apply(apply(b,X),Y)))),
% apply(h(apply(b,apply(b,apply(apply(b,X),Y)))),
% g(apply(b,apply(b,apply(apply(b,X),Y)))))))
% -> (true)
% Rule [41]
% (eq)(apply(h(apply(apply(b,apply(b,t)),apply(b,X))),apply(X,apply(
% f(apply(
% apply(b,
% apply(b,t)),
% apply(b,X))),
% g(apply(
% apply(b,
% apply(b,t)),
% apply(b,X)))))),
% apply(f(apply(apply(b,apply(b,t)),apply(b,X))),apply(h(apply(apply(b,
% apply(b,t)),
% apply(b,X))),
% g(apply(apply(b,apply(b,t)),
% apply(b,X)))))) ->
% (false) is composed into [41]
% (eq)(apply(h(apply(apply(b,apply(b,t)),
% apply(b,X))),apply(X,apply(
% f(apply(
% apply(b,
% apply(b,t)),
% apply(b,X))),
% g(apply(
% apply(b,
% apply(b,t)),
% apply(b,X)))))),
% apply(f(apply(apply(b,apply(b,t)),apply(b,X))),
% apply(h(apply(apply(b,apply(b,t)),apply(b,X))),
% g(apply(apply(b,apply(b,t)),apply(b,X)))))) ->
% (true)
% Rule [40]
% (eq)(apply(h(apply(apply(b,apply(b,t)),apply(t,X))),apply(apply(
% f(apply(
% apply(b,
% apply(b,t)),
% apply(t,X))),X),
% g(apply(apply(b,
% apply(b,t)),
% apply(t,X))))),
% apply(f(apply(apply(b,apply(b,t)),apply(t,X))),apply(h(apply(apply(b,
% apply(b,t)),
% apply(t,X))),
% g(apply(apply(b,apply(b,t)),
% apply(t,X)))))) ->
% (false) is composed into [40]
% (eq)(apply(h(apply(apply(b,apply(b,t)),
% apply(t,X))),apply(apply(f(
% apply(
% apply(b,
% apply(b,t)),
% apply(t,X))),X),
% g(apply(apply(b,
% apply(b,t)),
% apply(t,X))))),
% apply(f(apply(apply(b,apply(b,t)),apply(t,X))),
% apply(h(apply(apply(b,apply(b,t)),apply(t,X))),
% g(apply(apply(b,apply(b,t)),apply(t,X)))))) ->
% (true)
% Rule [39]
% (eq)(apply(X,apply(apply(g(apply(apply(b,apply(b,apply(b,X))),t)),
% f(apply(apply(b,apply(b,apply(b,X))),t))),h(apply(
% apply(b,
% apply(b,
% apply(b,X))),t)))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),t)),apply(h(apply(apply(b,
% apply(b,
% apply(b,X))),t)),
% g(apply(apply(b,apply(b,
% apply(b,X))),t)))))
% -> (false) is composed into [39]
% (eq)(apply(X,apply(apply(g(apply(apply(b,
% apply(b,
% apply(b,X))),t)),
% f(apply(apply(b,apply(b,
% apply(b,X))),t))),
% h(apply(apply(b,apply(b,
% apply(b,X))),t)))),
% apply(f(apply(apply(b,apply(b,apply(b,X))),t)),
% apply(h(apply(apply(b,apply(b,apply(b,X))),t)),
% g(apply(apply(b,apply(b,apply(b,X))),t)))))
% -> (true)
% Rule [38]
% (eq)(apply(apply(apply(g(apply(apply(b,apply(b,apply(t,X))),t)),
% f(apply(apply(b,apply(b,apply(t,X))),t))),X),h(
% apply(
% apply(b,
% apply(b,
% apply(t,X))),t))),
% apply(f(apply(apply(b,apply(b,apply(t,X))),t)),apply(h(apply(apply(b,
% apply(b,
% apply(t,X))),t)),
% g(apply(apply(b,apply(b,
% apply(t,X))),t)))))
% -> (false) is composed into [38]
% (eq)(apply(apply(apply(g(apply(apply(b,
% apply(b,
% apply(t,X))),t)),
% f(apply(apply(b,apply(b,
% apply(t,X))),t))),X),
% h(apply(apply(b,apply(b,apply(t,X))),t))),
% apply(f(apply(apply(b,apply(b,apply(t,X))),t)),
% apply(h(apply(apply(b,apply(b,apply(t,X))),t)),
% g(apply(apply(b,apply(b,apply(t,X))),t)))))
% -> (true)
% Rule [37]
% (eq)(apply(apply(f(apply(apply(b,apply(t,apply(t,X))),b)),apply(
% g(apply(
% apply(b,
% apply(t,
% apply(t,X))),b)),X)),
% h(apply(apply(b,apply(t,apply(t,X))),b))),apply(f(apply(apply(b,
% apply(t,
% apply(t,X))),b)),
% apply(h(apply(apply(b,
% apply(t,
% apply(t,X))),b)),
% g(apply(apply(b,apply(t,
% apply(t,X))),b)))))
% -> (false) is composed into [37]
% (eq)(apply(apply(f(apply(apply(b,apply(t,
% apply(t,X))),b)),
% apply(g(apply(apply(b,apply(t,
% apply(t,X))),b)),X)),
% h(apply(apply(b,apply(t,apply(t,X))),b))),
% apply(f(apply(apply(b,apply(t,apply(t,X))),b)),
% apply(h(apply(apply(b,apply(t,apply(t,X))),b)),
% g(apply(apply(b,apply(t,apply(t,X))),b)))))
% -> (true)
% Rule [36]
% (eq)(apply(h(apply(apply(b,apply(t,apply(b,t))),t)),apply(f(apply(
% apply(b,
% apply(t,
% apply(b,t))),t)),
% g(apply(apply(b,
% apply(t,
% apply(b,t))),t)))),
% apply(f(apply(apply(b,apply(t,apply(b,t))),t)),apply(h(apply(apply(b,
% apply(t,
% apply(b,t))),t)),
% g(apply(apply(b,apply(t,
% apply(b,t))),t)))))
% -> (false) is composed into [36]
% (eq)(apply(h(apply(apply(b,apply(t,apply(b,t))),t)),
% apply(f(apply(apply(b,apply(t,apply(b,t))),t)),
% g(apply(apply(b,apply(t,apply(b,t))),t)))),
% apply(f(apply(apply(b,apply(t,apply(b,t))),t)),
% apply(h(apply(apply(b,apply(t,apply(b,t))),t)),
% g(apply(apply(b,apply(t,apply(b,t))),t)))))
% -> (true)
% Rule [35]
% (eq)(apply(apply(X,apply(f(apply(apply(b,apply(t,apply(b,X))),t)),
% g(apply(apply(b,apply(t,apply(b,X))),t)))),h(
% apply(
% apply(b,
% apply(t,
% apply(b,X))),t))),
% apply(f(apply(apply(b,apply(t,apply(b,X))),t)),apply(h(apply(apply(b,
% apply(t,
% apply(b,X))),t)),
% g(apply(apply(b,apply(t,
% apply(b,X))),t)))))
% -> (false) is composed into [35]
% (eq)(apply(apply(X,apply(f(apply(apply(b,
% apply(t,
% apply(b,X))),t)),
% g(apply(apply(b,apply(t,
% apply(b,X))),t)))),
% h(apply(apply(b,apply(t,apply(b,X))),t))),
% apply(f(apply(apply(b,apply(t,apply(b,X))),t)),
% apply(h(apply(apply(b,apply(t,apply(b,X))),t)),
% g(apply(apply(b,apply(t,apply(b,X))),t)))))
% -> (true)
% Rule [34]
% (eq)(apply(apply(apply(f(apply(apply(b,apply(t,apply(t,X))),t)),X),
% g(apply(apply(b,apply(t,apply(t,X))),t))),h(apply(apply(b,
% apply(t,
% apply(t,X))),t))),
% apply(f(apply(apply(b,apply(t,apply(t,X))),t)),apply(h(apply(apply(b,
% apply(t,
% apply(t,X))),t)),
% g(apply(apply(b,apply(t,
% apply(t,X))),t)))))
% -> (false) is composed into [34]
% (eq)(apply(apply(apply(f(apply(apply(b,
% apply(t,
% apply(t,X))),t)),X),
% g(apply(apply(b,apply(t,apply(t,X))),t))),
% h(apply(apply(b,apply(t,apply(t,X))),t))),
% apply(f(apply(apply(b,apply(t,apply(t,X))),t)),
% apply(h(apply(apply(b,apply(t,apply(t,X))),t)),
% g(apply(apply(b,apply(t,apply(t,X))),t)))))
% -> (true)
% Rule [33]
% (eq)(apply(h(apply(b,apply(apply(b,t),apply(t,X)))),apply(apply(
% f(apply(b,
% apply(
% apply(b,t),
% apply(t,X)))),
% g(apply(b,
% apply(
% apply(b,t),
% apply(t,X))))),X)),
% apply(f(apply(b,apply(apply(b,t),apply(t,X)))),apply(h(apply(b,apply(
% apply(b,t),
% apply(t,X)))),
% g(apply(b,apply(apply(b,t),
% apply(t,X)))))))
% -> (false) is composed into [33]
% (eq)(apply(h(apply(b,apply(apply(b,t),
% apply(t,X)))),apply(
% apply(
% f(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X)))),
% g(
% apply(b,
% apply(
% apply(b,t),
% apply(t,X))))),X)),
% apply(f(apply(b,apply(apply(b,t),apply(t,X)))),
% apply(h(apply(b,apply(apply(b,t),apply(t,X)))),
% g(apply(b,apply(apply(b,t),apply(t,X)))))))
% -> (true)
% Rule [32]
% (eq)(apply(apply(f(apply(apply(b,b),apply(b,apply(t,X)))),apply(
% g(apply(
% apply(b,b),
% apply(b,
% apply(t,X)))),
% h(apply(
% apply(b,b),
% apply(b,
% apply(t,X)))))),X),
% apply(f(apply(apply(b,b),apply(b,apply(t,X)))),apply(h(apply(apply(b,b),
% apply(b,apply(t,X)))),
% g(apply(apply(b,b),
% apply(b,apply(t,X)))))))
% -> (false) is composed into [32]
% (eq)(apply(apply(f(apply(apply(b,b),
% apply(b,apply(t,X)))),
% apply(g(apply(apply(b,b),
% apply(b,apply(t,X)))),
% h(apply(apply(b,b),apply(b,
% apply(t,X)))))),X),
% apply(f(apply(apply(b,b),apply(b,apply(t,X)))),
% apply(h(apply(apply(b,b),apply(b,apply(t,X)))),
% g(apply(apply(b,b),apply(b,apply(t,X)))))))
% -> (true)
% Rule [31]
% (eq)(apply(h(apply(apply(b,apply(b,t)),t)),apply(g(apply(apply(b,
% apply(b,t)),t)),
% f(apply(apply(b,apply(b,t)),t)))),
% apply(f(apply(apply(b,apply(b,t)),t)),apply(h(apply(apply(b,apply(b,t)),t)),
% g(apply(apply(b,apply(b,t)),t)))))
% -> (false) is composed into [31]
% (eq)(apply(h(apply(apply(b,apply(b,t)),t)),
% apply(g(apply(apply(b,apply(b,t)),t)),
% f(apply(apply(b,apply(b,t)),t)))),
% apply(f(apply(apply(b,apply(b,t)),t)),
% apply(h(apply(apply(b,apply(b,t)),t)),
% g(apply(apply(b,apply(b,t)),t))))) -> (true)
% Rule [30]
% (eq)(apply(h(apply(apply(b,apply(b,t)),X)),apply(apply(X,f(apply(
% apply(b,
% apply(b,t)),X))),
% g(apply(apply(b,apply(b,t)),X)))),
% apply(f(apply(apply(b,apply(b,t)),X)),apply(h(apply(apply(b,apply(b,t)),X)),
% g(apply(apply(b,apply(b,t)),X)))))
% -> (false) is composed into [30]
% (eq)(apply(h(apply(apply(b,apply(b,t)),X)),
% apply(apply(X,f(apply(apply(b,apply(b,t)),X))),
% g(apply(apply(b,apply(b,t)),X)))),
% apply(f(apply(apply(b,apply(b,t)),X)),
% apply(h(apply(apply(b,apply(b,t)),X)),
% g(apply(apply(b,apply(b,t)),X))))) -> (true)
% Rule [29]
% (eq)(apply(apply(X,apply(g(apply(apply(b,apply(b,X)),t)),f(apply(
% apply(b,
% apply(b,X)),t)))),
% h(apply(apply(b,apply(b,X)),t))),apply(f(apply(apply(b,apply(b,X)),t)),
% apply(h(apply(apply(b,apply(b,X)),t)),
% g(apply(apply(b,apply(b,X)),t)))))
% -> (false) is composed into [29]
% (eq)(apply(apply(X,apply(g(apply(apply(b,
% apply(b,X)),t)),
% f(apply(apply(b,apply(b,X)),t)))),
% h(apply(apply(b,apply(b,X)),t))),
% apply(f(apply(apply(b,apply(b,X)),t)),
% apply(h(apply(apply(b,apply(b,X)),t)),
% g(apply(apply(b,apply(b,X)),t))))) -> (true)
% Rule [28]
% (eq)(apply(apply(X,apply(apply(Y,f(apply(apply(b,apply(b,X)),Y))),
% g(apply(apply(b,apply(b,X)),Y)))),h(apply(apply(b,
% apply(b,X)),Y))),
% apply(f(apply(apply(b,apply(b,X)),Y)),apply(h(apply(apply(b,apply(b,X)),Y)),
% g(apply(apply(b,apply(b,X)),Y)))))
% -> (false) is composed into [28]
% (eq)(apply(apply(X,apply(apply(Y,f(apply(
% apply(b,
% apply(b,X)),Y))),
% g(apply(apply(b,apply(b,X)),Y)))),
% h(apply(apply(b,apply(b,X)),Y))),
% apply(f(apply(apply(b,apply(b,X)),Y)),
% apply(h(apply(apply(b,apply(b,X)),Y)),
% g(apply(apply(b,apply(b,X)),Y))))) -> (true)
% Rule [27]
% (eq)(apply(f(apply(apply(b,apply(t,b)),t)),apply(g(apply(apply(b,
% apply(t,b)),t)),
% h(apply(apply(b,apply(t,b)),t)))),
% apply(f(apply(apply(b,apply(t,b)),t)),apply(h(apply(apply(b,apply(t,b)),t)),
% g(apply(apply(b,apply(t,b)),t)))))
% -> (false) is composed into [27]
% (eq)(apply(f(apply(apply(b,apply(t,b)),t)),
% apply(g(apply(apply(b,apply(t,b)),t)),
% h(apply(apply(b,apply(t,b)),t)))),
% apply(f(apply(apply(b,apply(t,b)),t)),
% apply(h(apply(apply(b,apply(t,b)),t)),
% g(apply(apply(b,apply(t,b)),t))))) -> (true)
% Rule [26]
% (eq)(apply(apply(g(apply(apply(b,apply(t,t)),t)),f(apply(apply(b,
% apply(t,t)),t))),
% h(apply(apply(b,apply(t,t)),t))),apply(f(apply(apply(b,apply(t,t)),t)),
% apply(h(apply(apply(b,apply(t,t)),t)),
% g(apply(apply(b,apply(t,t)),t)))))
% -> (false) is composed into [26]
% (eq)(apply(apply(g(apply(apply(b,apply(t,t)),t)),
% f(apply(apply(b,apply(t,t)),t))),
% h(apply(apply(b,apply(t,t)),t))),
% apply(f(apply(apply(b,apply(t,t)),t)),
% apply(h(apply(apply(b,apply(t,t)),t)),
% g(apply(apply(b,apply(t,t)),t))))) -> (true)
% Rule [25]
% (eq)(apply(apply(f(apply(apply(b,apply(t,X)),b)),apply(X,g(apply(
% apply(b,
% apply(t,X)),b)))),
% h(apply(apply(b,apply(t,X)),b))),apply(f(apply(apply(b,apply(t,X)),b)),
% apply(h(apply(apply(b,apply(t,X)),b)),
% g(apply(apply(b,apply(t,X)),b)))))
% -> (false) is composed into [25]
% (eq)(apply(apply(f(apply(apply(b,apply(t,X)),b)),
% apply(X,g(apply(apply(b,apply(t,X)),b)))),
% h(apply(apply(b,apply(t,X)),b))),
% apply(f(apply(apply(b,apply(t,X)),b)),
% apply(h(apply(apply(b,apply(t,X)),b)),
% g(apply(apply(b,apply(t,X)),b))))) -> (true)
% Rule [24]
% (eq)(apply(apply(apply(X,f(apply(apply(b,apply(t,X)),t))),g(apply(
% apply(b,
% apply(t,X)),t))),
% h(apply(apply(b,apply(t,X)),t))),apply(f(apply(apply(b,apply(t,X)),t)),
% apply(h(apply(apply(b,apply(t,X)),t)),
% g(apply(apply(b,apply(t,X)),t)))))
% -> (false) is composed into [24]
% (eq)(apply(apply(apply(X,f(apply(apply(b,
% apply(t,X)),t))),
% g(apply(apply(b,apply(t,X)),t))),
% h(apply(apply(b,apply(t,X)),t))),
% apply(f(apply(apply(b,apply(t,X)),t)),
% apply(h(apply(apply(b,apply(t,X)),t)),
% g(apply(apply(b,apply(t,X)),t))))) -> (true)
% Rule [23]
% (eq)(apply(apply(apply(apply(X,f(apply(apply(b,apply(t,Y)),X))),Y),
% g(apply(apply(b,apply(t,Y)),X))),h(apply(apply(b,apply(t,Y)),X))),
% apply(f(apply(apply(b,apply(t,Y)),X)),apply(h(apply(apply(b,apply(t,Y)),X)),
% g(apply(apply(b,apply(t,Y)),X)))))
% -> (false) is composed into [23]
% (eq)(apply(apply(apply(apply(X,f(apply(
% apply(b,
% apply(t,Y)),X))),Y),
% g(apply(apply(b,apply(t,Y)),X))),
% h(apply(apply(b,apply(t,Y)),X))),
% apply(f(apply(apply(b,apply(t,Y)),X)),
% apply(h(apply(apply(b,apply(t,Y)),X)),
% g(apply(apply(b,apply(t,Y)),X))))) -> (true)
% Rule [22]
% (eq)(apply(apply(apply(X,apply(f(apply(apply(b,X),apply(t,Y))),Y)),
% g(apply(apply(b,X),apply(t,Y)))),h(apply(apply(b,X),apply(t,Y)))),
% apply(f(apply(apply(b,X),apply(t,Y))),apply(h(apply(apply(b,X),apply(t,Y))),
% g(apply(apply(b,X),apply(t,Y))))))
% -> (false) is composed into [22]
% (eq)(apply(apply(apply(X,apply(f(apply(
% apply(b,X),
% apply(t,Y))),Y)),
% g(apply(apply(b,X),apply(t,Y)))),
% h(apply(apply(b,X),apply(t,Y)))),
% apply(f(apply(apply(b,X),apply(t,Y))),
% apply(h(apply(apply(b,X),apply(t,Y))),
% g(apply(apply(b,X),apply(t,Y)))))) -> (true)
% Rule [21]
% (eq)(apply(h(apply(b,apply(apply(b,t),X))),apply(X,apply(f(apply(b,
% apply(
% apply(b,t),X))),
% g(apply(b,apply(
% apply(b,t),X)))))),
% apply(f(apply(b,apply(apply(b,t),X))),apply(h(apply(b,apply(apply(b,t),X))),
% g(apply(b,apply(apply(b,t),X))))))
% -> (false) is composed into [21]
% (eq)(apply(h(apply(b,apply(apply(b,t),X))),
% apply(X,apply(f(apply(b,apply(apply(b,t),X))),
% g(apply(b,apply(apply(b,t),X)))))),
% apply(f(apply(b,apply(apply(b,t),X))),
% apply(h(apply(b,apply(apply(b,t),X))),
% g(apply(b,apply(apply(b,t),X)))))) -> (true)
% Rule [20]
% (eq)(apply(apply(X,apply(Y,apply(f(apply(b,apply(apply(b,X),Y))),
% g(apply(b,apply(apply(b,X),Y)))))),h(
% apply(b,
% apply(
% apply(b,X),Y)))),
% apply(f(apply(b,apply(apply(b,X),Y))),apply(h(apply(b,apply(apply(b,X),Y))),
% g(apply(b,apply(apply(b,X),Y))))))
% -> (false) is composed into [20]
% (eq)(apply(apply(X,apply(Y,apply(f(apply(b,
% apply(
% apply(b,X),Y))),
% g(apply(b,
% apply(apply(b,X),Y)))))),
% h(apply(b,apply(apply(b,X),Y)))),
% apply(f(apply(b,apply(apply(b,X),Y))),
% apply(h(apply(b,apply(apply(b,X),Y))),
% g(apply(b,apply(apply(b,X),Y)))))) -> (true)
% Rule [19]
% (eq)(apply(X,apply(f(apply(apply(b,b),apply(b,X))),apply(g(apply(
% apply(b,b),
% apply(b,X))),
% h(apply(apply(b,b),
% apply(b,X)))))),
% apply(f(apply(apply(b,b),apply(b,X))),apply(h(apply(apply(b,b),apply(b,X))),
% g(apply(apply(b,b),apply(b,X))))))
% -> (false) is composed into [19]
% (eq)(apply(X,apply(f(apply(apply(b,b),
% apply(b,X))),apply(
% g(
% apply(
% apply(b,b),
% apply(b,X))),
% h(
% apply(
% apply(b,b),
% apply(b,X)))))),
% apply(f(apply(apply(b,b),apply(b,X))),
% apply(h(apply(apply(b,b),apply(b,X))),
% g(apply(apply(b,b),apply(b,X)))))) -> (true)
% Rule [18]
% (eq)(apply(apply(f(apply(apply(b,b),apply(t,X))),X),apply(g(apply(
% apply(b,b),
% apply(t,X))),
% h(apply(apply(b,b),
% apply(t,X))))),
% apply(f(apply(apply(b,b),apply(t,X))),apply(h(apply(apply(b,b),apply(t,X))),
% g(apply(apply(b,b),apply(t,X))))))
% -> (false) is composed into [18]
% (eq)(apply(apply(f(apply(apply(b,b),
% apply(t,X))),X),apply(
% g(
% apply(
% apply(b,b),
% apply(t,X))),
% h(
% apply(
% apply(b,b),
% apply(t,X))))),
% apply(f(apply(apply(b,b),apply(t,X))),
% apply(h(apply(apply(b,b),apply(t,X))),
% g(apply(apply(b,b),apply(t,X)))))) -> (true)
% Rule [17]
% (eq)(apply(apply(g(apply(apply(b,t),apply(t,X))),apply(f(apply(apply(b,t),
% apply(t,X))),X)),
% h(apply(apply(b,t),apply(t,X)))),apply(f(apply(apply(b,t),apply(t,X))),
% apply(h(apply(apply(b,t),apply(t,X))),
% g(apply(apply(b,t),apply(t,X))))))
% -> (false) is composed into [17]
% (eq)(apply(apply(g(apply(apply(b,t),
% apply(t,X))),apply(
% f(apply(
% apply(b,t),
% apply(t,X))),X)),
% h(apply(apply(b,t),apply(t,X)))),
% apply(f(apply(apply(b,t),apply(t,X))),
% apply(h(apply(apply(b,t),apply(t,X))),
% g(apply(apply(b,t),apply(t,X)))))) -> (true)
% Rule [16]
% (eq)(apply(apply(apply(f(apply(b,apply(b,apply(t,X)))),g(apply(b,
% apply(b,
% apply(t,X))))),
% h(apply(b,apply(b,apply(t,X))))),X),apply(f(apply(b,apply(b,
% apply(t,X)))),
% apply(h(apply(b,apply(b,
% apply(t,X)))),
% g(apply(b,apply(b,
% apply(t,X)))))))
% -> (false) is composed into [16]
% (eq)(apply(apply(apply(f(apply(b,apply(b,
% apply(t,X)))),
% g(apply(b,apply(b,apply(t,X))))),
% h(apply(b,apply(b,apply(t,X))))),X),
% apply(f(apply(b,apply(b,apply(t,X)))),
% apply(h(apply(b,apply(b,apply(t,X)))),
% g(apply(b,apply(b,apply(t,X))))))) -> (true)
% Rule [15]
% (eq)(apply(apply(g(apply(apply(b,b),t)),h(apply(apply(b,b),t))),
% f(apply(apply(b,b),t))),apply(f(apply(apply(b,b),t)),apply(
% h(apply(
% apply(b,b),t)),
% g(apply(
% apply(b,b),t)))))
% -> (false) is composed into [15]
% (eq)(apply(apply(g(apply(apply(b,b),t)),
% h(apply(apply(b,b),t))),f(
% apply(
% apply(b,b),t))),
% apply(f(apply(apply(b,b),t)),apply(h(
% apply(
% apply(b,b),t)),
% g(apply(
% apply(b,b),t)))))
% -> (true)
% Rule [14]
% (eq)(apply(apply(X,f(apply(apply(b,b),X))),apply(g(apply(apply(b,b),X)),
% h(apply(apply(b,b),X)))),
% apply(f(apply(apply(b,b),X)),apply(h(apply(apply(b,b),X)),g(apply(
% apply(b,b),X)))))
% -> (false) is composed into [14]
% (eq)(apply(apply(X,f(apply(apply(b,b),X))),
% apply(g(apply(apply(b,b),X)),h(
% apply(
% apply(b,b),X)))),
% apply(f(apply(apply(b,b),X)),apply(h(
% apply(
% apply(b,b),X)),
% g(apply(
% apply(b,b),X)))))
% -> (true)
% Rule [13]
% (eq)(apply(apply(g(apply(apply(b,t),X)),apply(X,f(apply(apply(b,t),X)))),
% h(apply(apply(b,t),X))),apply(f(apply(apply(b,t),X)),apply(
% h(apply(
% apply(b,t),X)),
% g(apply(
% apply(b,t),X)))))
% -> (false) is composed into [13]
% (eq)(apply(apply(g(apply(apply(b,t),X)),
% apply(X,f(apply(apply(b,t),X)))),
% h(apply(apply(b,t),X))),apply(f(
% apply(
% apply(b,t),X)),
% apply(h(
% apply(
% apply(b,t),X)),
% g(apply(
% apply(b,t),X)))))
% -> (true)
% Rule [12]
% (eq)(apply(apply(apply(X,apply(Y,f(apply(apply(b,X),Y)))),g(apply(
% apply(b,X),Y))),
% h(apply(apply(b,X),Y))),apply(f(apply(apply(b,X),Y)),apply(
% h(apply(
% apply(b,X),Y)),
% g(apply(
% apply(b,X),Y)))))
% -> (false) is composed into [12]
% (eq)(apply(apply(apply(X,apply(Y,f(apply(
% apply(b,X),Y)))),
% g(apply(apply(b,X),Y))),h(
% apply(
% apply(b,X),Y))),
% apply(f(apply(apply(b,X),Y)),apply(h(
% apply(
% apply(b,X),Y)),
% g(apply(
% apply(b,X),Y)))))
% -> (true)
% Rule [11]
% (eq)(apply(X,apply(apply(f(apply(b,apply(b,X))),g(apply(b,apply(b,X)))),
% h(apply(b,apply(b,X))))),apply(f(apply(b,apply(b,X))),
% apply(h(apply(b,apply(b,X))),
% g(apply(b,apply(b,X)))))) ->
% (false) is composed into [11]
% (eq)(apply(X,apply(apply(f(apply(b,apply(b,X))),
% g(apply(b,apply(b,X)))),
% h(apply(b,apply(b,X))))),apply(
% f(
% apply(b,
% apply(b,X))),
% apply(
% h(
% apply(b,
% apply(b,X))),
% g(
% apply(b,
% apply(b,X))))))
% -> (true)
% Rule [10]
% (eq)(apply(apply(apply(f(apply(b,apply(t,X))),g(apply(b,apply(t,X)))),X),
% h(apply(b,apply(t,X)))),apply(f(apply(b,apply(t,X))),apply(
% h(apply(b,
% apply(t,X))),
% g(apply(b,
% apply(t,X))))))
% -> (false) is composed into [10]
% (eq)(apply(apply(apply(f(apply(b,apply(t,X))),
% g(apply(b,apply(t,X)))),X),
% h(apply(b,apply(t,X)))),apply(f(
% apply(b,
% apply(t,X))),
% apply(h(
% apply(b,
% apply(t,X))),
% g(apply(b,
% apply(t,X))))))
% -> (true)
% Rule [9]
% (eq)(apply(h(apply(b,t)),apply(f(apply(b,t)),g(apply(b,t)))),apply(
% f(apply(b,t)),
% apply(
% h(apply(b,t)),
% g(apply(b,t)))))
% -> (false) is composed into [9]
% (eq)(apply(h(apply(b,t)),apply(f(apply(b,t)),
% g(apply(b,t)))),
% apply(f(apply(b,t)),apply(h(apply(b,t)),
% g(apply(b,t))))) ->
% (true)
% Rule [8]
% (eq)(apply(apply(X,apply(f(apply(b,X)),g(apply(b,X)))),h(apply(b,X))),
% apply(f(apply(b,X)),apply(h(apply(b,X)),g(apply(b,X))))) -> (false) is composed into 
% [8]
% (eq)(apply(apply(X,apply(f(apply(b,X)),g(apply(b,X)))),h(apply(b,X))),
% apply(f(apply(b,X)),apply(h(apply(b,X)),g(apply(b,X))))) -> (true)
% Rule [7]
% (eq)(apply(apply(apply(f(apply(t,X)),X),g(apply(t,X))),h(apply(t,X))),
% apply(f(apply(t,X)),apply(h(apply(t,X)),g(apply(t,X))))) -> (false) is composed into 
% [7]
% (eq)(apply(apply(apply(f(apply(t,X)),X),g(apply(t,X))),h(apply(t,X))),
% apply(f(apply(t,X)),apply(h(apply(t,X)),g(apply(t,X))))) -> (true)
% Rule [6]
% (eq)(apply(f(b),apply(g(b),h(b))),apply(f(b),apply(h(b),g(b)))) ->
% (false) is composed into [6]
% (eq)(apply(f(b),apply(g(b),h(b))),apply(
% f(b),
% apply(
% h(b),
% g(b)))) ->
% (true)
% Rule [5]
% (eq)(apply(apply(g(t),f(t)),h(t)),apply(f(t),apply(h(t),g(t)))) ->
% (false) is composed into [5]
% (eq)(apply(apply(g(t),f(t)),h(t)),apply(
% f(t),
% apply(
% h(t),
% g(t)))) ->
% (true)
% Rule [3]
% (eq)(apply(apply(apply(X,f(X)),g(X)),h(X)),apply(f(X),apply(h(X),g(X))))
% -> (false) is composed into [3]
% (eq)(apply(apply(apply(X,f(X)),g(X)),h(X)),
% apply(f(X),apply(h(X),g(X)))) -> (true)
% New rule produced : [147] (false) -> (true)
% The conjecture has been reduced. 
% Conjecture is now:
% Trivial
% 
% Current number of equations to process: 220
% Current number of ordered equations: 0
% Current number of rules: 147
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% 
% The following 9 rules have been used:
% [2] 
% apply(apply(t,X),Y) -> apply(Y,X); trace = in the starting set
% [3] (eq)(apply(apply(apply(X,f(X)),g(X)),h(X)),apply(f(X),apply(h(X),g(X))))
% -> (false); trace = in the starting set
% [4] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z)); trace = in the starting set
% [12] (eq)(apply(apply(apply(X,apply(Y,f(apply(apply(b,X),Y)))),g(apply(
% apply(b,X),Y))),
% h(apply(apply(b,X),Y))),apply(f(apply(apply(b,X),Y)),apply(
% h(apply(
% apply(b,X),Y)),
% g(apply(
% apply(b,X),Y)))))
% -> (false); trace = Cp of 4 and 3
% [23] (eq)(apply(apply(apply(apply(X,f(apply(apply(b,apply(t,Y)),X))),Y),
% g(apply(apply(b,apply(t,Y)),X))),h(apply(apply(b,apply(t,Y)),X))),
% apply(f(apply(apply(b,apply(t,Y)),X)),apply(h(apply(apply(b,apply(t,Y)),X)),
% g(apply(apply(b,apply(t,Y)),X)))))
% -> (false); trace = Cp of 12 and 2
% [137] (eq)(apply(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,Z)),
% apply(apply(b,X),Y))))),Z),
% g(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y)))),h(
% apply(
% apply(b,
% apply(t,Z)),
% apply(
% apply(b,X),Y)))),
% apply(f(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y))),apply(h(
% apply(
% apply(b,
% apply(t,Z)),
% apply(
% apply(b,X),Y))),
% g(apply(
% apply(b,
% apply(t,Z)),
% apply(
% apply(b,X),Y))))))
% -> (false); trace = Cp of 23 and 4
% [139] (eq)(apply(apply(apply(X,f(apply(apply(b,apply(t,Y)),apply(apply(b,b),X)))),
% apply(Y,g(apply(apply(b,apply(t,Y)),apply(apply(b,b),X))))),
% h(apply(apply(b,apply(t,Y)),apply(apply(b,b),X)))),apply(f(
% apply(
% apply(b,
% apply(t,Y)),
% apply(
% apply(b,b),X))),
% apply(h(
% apply(
% apply(b,
% apply(t,Y)),
% apply(
% apply(b,b),X))),
% g(apply(
% apply(b,
% apply(t,Y)),
% apply(
% apply(b,b),X))))))
% -> (false); trace = Cp of 137 and 4
% [143] (eq)(apply(f(apply(apply(b,apply(t,X)),apply(apply(b,b),b))),apply(
% apply(X,
% g(
% apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b)))),
% h(
% apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b))))),
% apply(f(apply(apply(b,apply(t,X)),apply(apply(b,b),b))),apply(h(
% apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b))),
% g(apply(
% apply(b,
% apply(t,X)),
% apply(
% apply(b,b),b))))))
% -> (false); trace = Cp of 139 and 4
% [147] (false) -> (true); trace = Cp of 143 and 2
% % SZS output end Refutation
% All conjectures have been proven
% 
% Execution time: 2.390000 sec
% res : bool = true
% time is now off
% 
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
% 
% EOF
%------------------------------------------------------------------------------