Vampire-SAT---5.0.1.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : ITP300_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:39:17 AM UTC 2026

% Result   : Theorem 10.72s 2.07s
% Output   : Refutation 10.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   24 (  17 unt;   0 typ;   0 def)
%            Number of atoms       :   52 (   8 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :   39 (  11   ~;   8   |;  18   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :   96 (  94 usr;   1 ari;   0 dat;   0 cdt)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   33 (  30 usr;   2 prp; 0-2 aty)
%            Number of functors    :  745 ( 745 usr;  99 con; 0-7 aty)
%            Number of variables   :    6 (   6   !;   0   ?;   6   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    'ZF_ZF_ZF_prod_fun$': $tType ).

tff(type_def_6,type,
    'Nat_set_set$': $tType ).

tff(type_def_7,type,
    'ZF_ZF_prod_ZF_ZF_prod_bool_fun_fun$': $tType ).

tff(type_def_8,type,
    'ZF_ZF_prod_ZF_prod_bool_fun$': $tType ).

tff(type_def_9,type,
    'Int_bool_fun$': $tType ).

tff(type_def_10,type,
    'ZF_set$': $tType ).

tff(type_def_11,type,
    'ZF_nat_set_fun$': $tType ).

tff(type_def_12,type,
    'ZF_ZF_prod_ZF_ZF_prod_prod_bool_fun$': $tType ).

tff(type_def_13,type,
    'Nat_set_set_ZF_set_set_fun$': $tType ).

tff(type_def_14,type,
    'Nat_ZF_prod_set$': $tType ).

tff(type_def_15,type,
    'ZF_ZF_prod_set$': $tType ).

tff(type_def_16,type,
    'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$': $tType ).

tff(type_def_17,type,
    'ZF_ZF_prod_set_set_ZF_set_set_fun$': $tType ).

tff(type_def_18,type,
    'ZF_set_set$': $tType ).

tff(type_def_19,type,
    'ZF_set_ZF_set_fun$': $tType ).

tff(type_def_20,type,
    'ZF_ZF_prod_ZF_ZF_prod_fun$': $tType ).

tff(type_def_21,type,
    'ZF_ZF_set_fun$': $tType ).

tff(type_def_22,type,
    'ZF_set_ZF_set_prod_set$': $tType ).

tff(type_def_23,type,
    'ZF_ZF_prod_ZF_fun$': $tType ).

tff(type_def_24,type,
    'ZF_nat_ZF_ZF_prod_set_fun_fun$': $tType ).

tff(type_def_25,type,
    'Nat_set_set_nat_set_fun$': $tType ).

tff(type_def_26,type,
    'ZF_ZF_ZF_prod_bool_fun_fun$': $tType ).

tff(type_def_27,type,
    'ZF_ZF_set_prod_set$': $tType ).

tff(type_def_28,type,
    'ZF_ZF_ZF_prod_prod_bool_fun$': $tType ).

tff(type_def_29,type,
    'ZF_nat_prod_ZF_ZF_prod_set_fun$': $tType ).

tff(type_def_30,type,
    'ZF_ZF_ZF_ZF_prod_fun_fun$': $tType ).

tff(type_def_31,type,
    'ZF_ZF_ZF_prod_set_fun$': $tType ).

tff(type_def_32,type,
    'ZF_ZF_prod_ZF_set_fun$': $tType ).

tff(type_def_33,type,
    'ZF_nat_ZF_set_fun_fun$': $tType ).

tff(type_def_34,type,
    'ZF_ZF_prod$': $tType ).

tff(type_def_35,type,
    'ZF_ZF_set_set_fun$': $tType ).

tff(type_def_36,type,
    'ZF_ZF_prod_ZF_set_set_fun$': $tType ).

tff(type_def_37,type,
    'Nat_ZF_set_prod_set$': $tType ).

tff(type_def_38,type,
    'ZF_ZF_prod_ZF_ZF_prod_prod_set$': $tType ).

tff(type_def_39,type,
    'Nat_nat_prod_set$': $tType ).

tff(type_def_40,type,
    'ZF_ZF_ZF_fun_fun$': $tType ).

tff(type_def_41,type,
    'ZF_ZF_ZF_set_fun_fun$': $tType ).

tff(type_def_42,type,
    'ZF_ZF_prod_ZF_ZF_prod_prod$': $tType ).

tff(type_def_43,type,
    'Nat_nat_fun$': $tType ).

tff(type_def_44,type,
    'ZF_set_set_set_ZF_set_set_fun$': $tType ).

tff(type_def_45,type,
    'Nat$': $tType ).

tff(type_def_46,type,
    'Nat_ZF_set_set_fun$': $tType ).

tff(type_def_47,type,
    'Nat_set_ZF_set_set_fun$': $tType ).

tff(type_def_48,type,
    'Nat_nat_prod_ZF_ZF_prod_set_fun$': $tType ).

tff(type_def_49,type,
    'Nat_ZF_ZF_prod_fun$': $tType ).

tff(type_def_50,type,
    'ZF_ZF_fun$': $tType ).

tff(type_def_51,type,
    'ZF_ZF_prod_bool_fun$': $tType ).

tff(type_def_52,type,
    'ZF_set_set_ZF_set_set_set_fun$': $tType ).

tff(type_def_53,type,
    'Nat_set_ZF_set_fun$': $tType ).

tff(type_def_54,type,
    'ZF_ZF_ZF_prod_prod_set$': $tType ).

tff(type_def_55,type,
    'ZF_set_ZF_set_prod_bool_fun$': $tType ).

tff(type_def_56,type,
    'Bool_ZF_fun$': $tType ).

tff(type_def_57,type,
    'ZF_ZF_prod_set_set$': $tType ).

tff(type_def_58,type,
    'Nat_ZF_set_fun$': $tType ).

tff(type_def_59,type,
    tlbool: $tType ).

tff(type_def_60,type,
    'ZF_nat_prod_set$': $tType ).

tff(type_def_61,type,
    'ZF_set_set_ZF_set_fun$': $tType ).

tff(type_def_62,type,
    'Nat_ZF_prod_ZF_ZF_prod_set_fun$': $tType ).

tff(type_def_63,type,
    'ZF_set_ZF_set_set_fun$': $tType ).

tff(type_def_64,type,
    'Nat_nat_set_fun$': $tType ).

tff(type_def_65,type,
    'ZF_ZF_ZF_ZF_prod_set_fun_fun$': $tType ).

tff(type_def_66,type,
    'Nat_nat_ZF_ZF_prod_set_fun_fun$': $tType ).

tff(type_def_67,type,
    'Nat_ZF_ZF_prod_set_fun$': $tType ).

tff(type_def_68,type,
    'ZF_ZF_unit_Category_ext$': $tType ).

tff(type_def_69,type,
    'Nat_nat_ZF_set_fun_fun$': $tType ).

tff(type_def_70,type,
    'ZF_ZF_prod_set_ZF_set_fun$': $tType ).

tff(type_def_71,type,
    'Bool_bool_fun$': $tType ).

tff(type_def_72,type,
    'ZF_set_ZF_prod_set$': $tType ).

tff(type_def_73,type,
    'ZF_set_ZF_set_prod$': $tType ).

tff(type_def_74,type,
    'ZF_set_ZF_fun$': $tType ).

tff(type_def_75,type,
    'ZF_ZF_prod_set_set_ZF_set_fun$': $tType ).

tff(type_def_76,type,
    'ZF_bool_fun$': $tType ).

tff(type_def_77,type,
    'ZF_ZF_prod_ZF_bool_fun_fun$': $tType ).

tff(type_def_78,type,
    'ZF_set_set_ZF_set_set_fun$': $tType ).

tff(type_def_79,type,
    'Nat_set_set_ZF_set_set_set_fun$': $tType ).

tff(type_def_80,type,
    'ZF_ZF_ZF_set_set_fun_fun$': $tType ).

tff(type_def_81,type,
    'ZF_nat_fun$': $tType ).

tff(type_def_82,type,
    'ZF_set_bool_fun$': $tType ).

tff(type_def_83,type,
    'ZF_ZF_prod_ZF_prod_set$': $tType ).

tff(type_def_84,type,
    'ZF_ZF_prod_ZF_set_prod_set$': $tType ).

tff(type_def_85,type,
    'Unit$': $tType ).

tff(type_def_86,type,
    'Nat_bool_fun$': $tType ).

tff(type_def_87,type,
    'Bool_set$': $tType ).

tff(type_def_88,type,
    'ZF$': $tType ).

tff(type_def_89,type,
    'ZF_set_set_set$': $tType ).

tff(type_def_90,type,
    'ZF_set_ZF_ZF_prod_fun$': $tType ).

tff(type_def_91,type,
    'ZF_set_ZF_ZF_prod_set_fun$': $tType ).

tff(type_def_92,type,
    'ZF_ZF_prod_set_bool_fun$': $tType ).

tff(type_def_93,type,
    'Nat_set$': $tType ).

tff(type_def_94,type,
    'Nat_ZF_fun$': $tType ).

tff(type_def_95,type,
    'ZF_ZF_prod_ZF_ZF_prod_set_fun$': $tType ).

tff(type_def_96,type,
    'Nat_ZF_ZF_ZF_prod_set_fun_fun$': $tType ).

tff(type_def_97,type,
    'Nat_ZF_ZF_set_fun_fun$': $tType ).

tff(type_def_98,type,
    'ZF_ZF_bool_fun_fun$': $tType ).

tff(func_def_0,type,
    'ext_ZF_n$': ( 'ZF_ZF_prod_set$' * 'ZF$' ) > 'Nat_ZF_fun$' ).

tff(func_def_1,type,
    'uxu$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_bool_fun$' ).

tff(func_def_2,type,
    'bind$c': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_set_fun$' ) > 'ZF_set$' ).

tff(func_def_3,type,
    'uzy$': 'Nat_ZF_fun$' > 'Nat_ZF_set_fun$' ).

tff(func_def_4,type,
    'uuh$': 'ZF$' > 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_5,type,
    'fun_app$as': ( 'ZF_set_ZF_ZF_prod_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_6,type,
    'domain$a': 'ZF_ZF_prod_set$' > 'ZF_set$' ).

tff(func_def_7,type,
    'uzw$': 'ZF_ZF_fun$' > 'ZF_ZF_set_fun$' ).

tff(func_def_8,type,
    'case_prod$g': 'ZF_ZF_prod_ZF_bool_fun_fun$' > 'ZF_ZF_prod_ZF_prod_bool_fun$' ).

tff(func_def_9,type,
    'fun_app$b': ( 'ZF_set_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set$' ).

tff(func_def_10,type,
    'fun_app$h': ( 'ZF_ZF_bool_fun_fun$' * 'ZF$' ) > 'ZF_bool_fun$' ).

tff(func_def_11,type,
    'uzd$': ( 'ZF_ZF_prod$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_12,type,
    'comp$f': ( 'ZF_set_set_ZF_set_fun$' * 'ZF_ZF_prod_set_set_ZF_set_set_fun$' ) > 'ZF_ZF_prod_set_set_ZF_set_fun$' ).

tff(func_def_13,type,
    'uut$': 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_14,type,
    'fun_app$ai': ( 'Nat_nat_ZF_set_fun_fun$' * 'Nat$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_15,type,
    'uyo$': 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_16,type,
    'uzp$': ( 'ZF_bool_fun$' * 'ZF_ZF_ZF_fun_fun$' ) > 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_17,type,
    'sigma$k': ( 'Nat_set$' * 'Nat_nat_set_fun$' ) > 'Nat_nat_prod_set$' ).

tff(func_def_18,type,
    'trancl$': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_set$' ).

tff(func_def_19,type,
    'eps$a': 'ZF_ZF_prod_bool_fun$' > 'ZF_ZF_prod$' ).

tff(func_def_20,type,
    'uwa$': 'Nat_bool_fun$' ).

tff(func_def_21,type,
    'sigma$a': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' ).

tff(func_def_22,type,
    'eps$b': 'ZF_set_bool_fun$' > 'ZF_set$' ).

tff(func_def_23,type,
    'uze$': ( 'ZF$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_24,type,
    'uuq$': ( 'ZF_set_set$' * 'ZF_set_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_25,type,
    'collect$': 'ZF_ZF_prod_bool_fun$' > 'ZF_ZF_prod_set$' ).

tff(func_def_26,type,
    'bot$a': 'ZF_ZF_prod_set$' ).

tff(func_def_27,type,
    'rec_set_unit$': ( 'ZF$' * 'Unit$' ) > 'ZF_bool_fun$' ).

tff(func_def_28,type,
    'relImage$b': ( 'Nat_nat_prod_set$' * 'Nat_ZF_set_fun$' ) > 'ZF_set_ZF_set_prod_set$' ).

tff(func_def_29,type,
    'case_prod$d': 'ZF_ZF_ZF_ZF_prod_set_fun_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' ).

tff(func_def_30,type,
    'uwo$': ( 'Nat_ZF_set_fun$' * 'Nat_set$' * 'ZF_set_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_31,type,
    'uxn$': ( 'Nat_ZF_set_fun$' * 'Nat_nat_fun$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_32,type,
    'case_nat$': ( tlbool * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).

tff(func_def_33,type,
    'image$d': 'ZF_ZF_fun$' > 'ZF_set_ZF_set_fun$' ).

tff(func_def_34,type,
    'least$c': 'ZF_set_bool_fun$' > 'ZF_set$' ).

tff(func_def_35,type,
    'less_eq$a': 'ZF_set$' > 'ZF_set_bool_fun$' ).

tff(func_def_36,type,
    'var$': ( 'ZF_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'ZF_nat_ZF_ZF_prod_set_fun_fun$' ).

tff(func_def_37,type,
    'vbk$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_ZF_set_fun_fun$' ).

tff(func_def_38,type,
    'fun_app$d': ( 'Nat_ZF_fun$' * 'Nat$' ) > 'ZF$' ).

tff(func_def_39,type,
    'case_prod$': 'ZF_ZF_ZF_fun_fun$' > 'ZF_ZF_prod_ZF_fun$' ).

tff(func_def_40,type,
    'field$': 'ZF_ZF_fun$' ).

tff(func_def_41,type,
    'least$b': 'ZF_ZF_prod_set_bool_fun$' > 'ZF_ZF_prod_set$' ).

tff(func_def_42,type,
    'fun_app$av': ( 'ZF_nat_ZF_ZF_prod_set_fun_fun$' * 'ZF$' ) > 'Nat_ZF_ZF_prod_set_fun$' ).

tff(func_def_43,type,
    'rec_unit$': ( 'ZF$' * 'Unit$' ) > 'ZF$' ).

tff(func_def_44,type,
    'fun_app$i': ( 'ZF_ZF_ZF_prod_set_fun$' * 'ZF$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_45,type,
    'pair$': 'ZF_ZF_ZF_ZF_prod_fun_fun$' ).

tff(func_def_46,type,
    'vag$': ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_47,type,
    'uua$': 'ZF_set$' > 'ZF_bool_fun$' ).

tff(func_def_48,type,
    'product$a': 'ZF_set$' > 'ZF_set_ZF_ZF_prod_set_fun$' ).

tff(func_def_49,type,
    'upair$': 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_50,type,
    'top$': 'ZF_set$' ).

tff(func_def_51,type,
    'uwt$': ( 'ZF_ZF_set_fun$' * 'ZF_set$' * 'ZF_set_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_52,type,
    'uwm$': ( 'ZF_ZF_fun$' * 'ZF_set$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_53,type,
    'fun_app$ak': ( 'Nat_ZF_ZF_prod_set_fun$' * 'Nat$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_54,type,
    'uwr$': ( 'ZF_set_ZF_set_fun$' * 'ZF_set_set$' * 'ZF_set_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_55,type,
    'uu$': 'ZF_set_set$' > 'ZF_set_bool_fun$' ).

tff(func_def_56,type,
    'uxb$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' * 'ZF_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_57,type,
    'uuw$': 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_58,type,
    'category_ext$': ( 'ZF_set$' * 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' * 'ZF_ZF_ZF_fun_fun$' * 'Unit$' ) > 'ZF_ZF_unit_Category_ext$' ).

tff(func_def_59,type,
    'case_prod$i': 'ZF_nat_ZF_ZF_prod_set_fun_fun$' > 'ZF_nat_prod_ZF_ZF_prod_set_fun$' ).

tff(func_def_60,type,
    'uwx$': ( 'ZF_set_ZF_fun$' * 'ZF_set_set$' * 'ZF_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_61,type,
    'vbm$': ( 'Nat_ZF_ZF_set_fun_fun$' * 'ZF_set$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_62,type,
    def_3: ( 'ZF_ZF_bool_fun_fun$' * 'ZF$' * 'ZF$' ) > tlbool ).

tff(func_def_63,type,
    'image$h': ( 'ZF_set_ZF_ZF_prod_fun$' * 'ZF_set_set$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_64,type,
    'top$b': 'ZF_ZF_prod_set$' ).

tff(func_def_65,type,
    'uys$': 'ZF_ZF_fun$' > 'ZF_bool_fun$' ).

tff(func_def_66,type,
    'uwc$': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' ).

tff(func_def_67,type,
    'fun_app$w': ( 'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set_set$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_68,type,
    'fun_app$ad': ( 'ZF_ZF_ZF_prod_bool_fun_fun$' * 'ZF$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_69,type,
    'case_prod$b': 'ZF_ZF_ZF_ZF_prod_fun_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_fun$' ).

tff(func_def_70,type,
    'vba$': ( 'Nat_ZF_set_fun$' * 'ZF_nat_set_fun$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_71,type,
    'uzv$': 'Nat_ZF_set_fun$' > 'Nat_ZF_set_set_fun$' ).

tff(func_def_72,type,
    'bot$': 'ZF_set$' ).

tff(func_def_73,type,
    'bind$b': ( 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_set$' ).

tff(func_def_74,type,
    'less_eq$b': 'Nat$' > 'Nat_bool_fun$' ).

tff(func_def_75,type,
    'image$n': ( 'Nat_ZF_ZF_prod_fun$' * 'Nat_set$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_76,type,
    'uzu$': 'ZF_ZF_set_fun$' > 'ZF_ZF_set_set_fun$' ).

tff(func_def_77,type,
    'top$e': 'Nat_nat_prod_set$' ).

tff(func_def_78,type,
    'top$d': 'Nat_ZF_prod_set$' ).

tff(func_def_79,type,
    'uue$': 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_80,type,
    'uwk$': ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set_ZF_set_set_fun$' ).

tff(func_def_81,type,
    'case_prod$c': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_prod_ZF_set_fun$' ).

tff(func_def_82,type,
    'uxe$': ( 'ZF_ZF_ZF_prod_fun$' * 'ZF_set$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_83,type,
    'pFun$': 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_84,type,
    'vbo$': ( 'Nat_ZF_ZF_set_fun_fun$' * 'Nat_set$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_85,type,
    'uwu$': ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' * 'ZF_set_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_86,type,
    'image$u': 'ZF_set_ZF_set_set_fun$' > 'ZF_set_set_ZF_set_set_set_fun$' ).

tff(func_def_87,type,
    'rec_bool$': ( 'ZF$' * 'ZF$' ) > 'Bool_ZF_fun$' ).

tff(func_def_88,type,
    'vai$': 'ZF_set_ZF_set_fun$' ).

tff(func_def_89,type,
    'uyh$': tlbool > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_90,type,
    'gr$': ( 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_set_prod_set$' ).

tff(func_def_91,type,
    'uvm$': 'ZF_ZF_prod_set$' > 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_92,type,
    'fun_app$ah': ( 'ZF_nat_ZF_set_fun_fun$' * 'ZF$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_93,type,
    'case_prod$f': 'ZF_ZF_ZF_prod_bool_fun_fun$' > 'ZF_ZF_ZF_prod_prod_bool_fun$' ).

tff(func_def_94,type,
    'case_prod$a': 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_95,type,
    'sigma$': ( 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_96,type,
    'image$k': ( 'Nat_ZF_fun$' * 'Nat_set$' ) > 'ZF_set$' ).

tff(func_def_97,type,
    'uvl$': 'ZF_ZF_prod_set$' > 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_98,type,
    'image$q': ( 'Nat_ZF_set_set_fun$' * 'Nat_set$' ) > 'ZF_set_set_set$' ).

tff(func_def_99,type,
    'uza$': 'ZF_ZF_prod_ZF_ZF_prod_bool_fun_fun$' ).

tff(func_def_100,type,
    'uzm$': ( 'ZF$' * 'ZF_set$' ) > 'ZF_bool_fun$' ).

tff(func_def_101,type,
    'singleton$': 'ZF_ZF_fun$' ).

tff(func_def_102,type,
    'uxm$': ( 'Nat_ZF_set_fun$' * 'ZF_nat_fun$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_103,type,
    'vaf$': 'ZF_ZF_prod_bool_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' ).

tff(func_def_104,type,
    'uvx$': 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_105,type,
    'seqSum$': 'Nat_ZF_fun$' > 'ZF$' ).

tff(func_def_106,type,
    'fun_app$at': ( 'ZF_set_set_ZF_set_set_fun$' * 'ZF_set_set$' ) > 'ZF_set_set$' ).

tff(func_def_107,type,
    'vce$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_ZF_prod_set_fun$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_108,type,
    'uzt$': 'ZF_set$' > 'ZF_bool_fun$' ).

tff(func_def_109,type,
    'sum$': 'ZF_ZF_fun$' ).

tff(func_def_110,type,
    'image$a': 'ZF_ZF_set_fun$' > 'ZF_set_ZF_set_set_fun$' ).

tff(func_def_111,type,
    'the$d': 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_112,type,
    'vby$': ( 'ZF_bool_fun$' * 'ZF_ZF_bool_fun_fun$' ) > 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_113,type,
    'uyu$': 'Nat_ZF_set_fun$' > 'ZF_set_bool_fun$' ).

tff(func_def_114,type,
    'vcg$': ( 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_set_set_fun$' ).

tff(func_def_115,type,
    def_7: ( 'ZF_ZF_bool_fun_fun$' * 'ZF_ZF_prod$' ) > tlbool ).

tff(func_def_116,type,
    'vay$': 'Nat_set$' > 'Nat_nat_set_fun$' ).

tff(func_def_117,type,
    'nat2nat$': 'ZF_nat_fun$' ).

tff(func_def_118,type,
    'uva$': ( 'ZF_ZF_bool_fun_fun$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_119,type,
    'comp$e': ( 'ZF_set_ZF_set_set_fun$' * 'ZF_set_set_ZF_set_fun$' ) > 'ZF_set_set_ZF_set_set_fun$' ).

tff(func_def_120,type,
    'collect$e': 'Nat_bool_fun$' > 'Nat_set$' ).

tff(func_def_121,type,
    'vci$': ( 'ZF_ZF_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_122,type,
    'app$': 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_123,type,
    'uzf$': ( 'ZF_ZF_prod$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_124,type,
    'set$': 'ZF_ZF_unit_Category_ext$' ).

tff(func_def_125,type,
    'natInterval$': 'Nat$' > 'Nat_ZF_fun$' ).

tff(func_def_126,type,
    'image2$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_127,type,
    'uvd$': 'ZF_set_bool_fun$' > 'ZF_set_bool_fun$' ).

tff(func_def_128,type,
    'fun_app$o': ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod$' ) > 'ZF_set$' ).

tff(func_def_129,type,
    'sigma$e': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_set_set_fun$' ) > 'ZF_ZF_prod_ZF_set_prod_set$' ).

tff(func_def_130,type,
    'image$': ( 'ZF_ZF_ZF_prod_set_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff(func_def_131,type,
    'vcd$': ( 'ZF_ZF_set_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_ZF_set_fun$' ).

tff(func_def_132,type,
    'gr$b': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_ZF_prod_set$' ).

tff(func_def_133,type,
    'uxg$': ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_134,type,
    'unity$': 'Unit$' ).

tff(func_def_135,type,
    'relInvImage$b': ( 'ZF_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_136,type,
    'vbq$': 'Nat_nat_ZF_set_fun_fun$' > 'Nat_nat_ZF_set_fun_fun$' ).

tff(func_def_137,type,
    'vcb$': 'ZF_ZF_set_fun$' > 'ZF_ZF_ZF_prod_set_fun$' ).

tff(func_def_138,type,
    'uus$': 'ZF_bool_fun$' ).

tff(func_def_139,type,
    'vau$': 'ZF_ZF_set_fun$' > 'ZF_ZF_ZF_set_fun_fun$' ).

tff(func_def_140,type,
    'fun_app$z': ( 'Nat_set_ZF_set_fun$' * 'Nat_set$' ) > 'ZF_set$' ).

tff(func_def_141,type,
    'uyc$': ( 'ZF_ZF_fun$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_142,type,
    'uxz$': ( 'ZF_set_ZF_ZF_prod_fun$' * 'ZF_set_set$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_143,type,
    'collect$c': 'ZF_ZF_prod_ZF_ZF_prod_prod_bool_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' ).

tff(func_def_144,type,
    'image$c': 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_set_ZF_set_fun$' ).

tff(func_def_145,type,
    'uwg$': 'ZF_ZF_prod_set$' > 'ZF_bool_fun$' ).

tff(func_def_146,type,
    'fun_app$aw': ( 'Nat_nat_ZF_ZF_prod_set_fun_fun$' * 'Nat$' ) > 'Nat_ZF_ZF_prod_set_fun$' ).

tff(func_def_147,type,
    'uzn$': ( 'ZF_ZF_prod$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_148,type,
    'empty$': 'ZF$' ).

tff(func_def_149,type,
    'uzj$': ( 'ZF$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_150,type,
    'vbf$': 'ZF_ZF_set_fun$' > 'ZF_set_ZF_set_fun$' ).

tff(func_def_151,type,
    'uxt$': ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_152,type,
    'image$m': ( 'Nat_nat_fun$' * 'Nat_set$' ) > 'Nat_set$' ).

tff(func_def_153,type,
    'pair$b': ( 'ZF_set$' * 'ZF_set$' ) > 'ZF_set_ZF_set_prod$' ).

tff(func_def_154,type,
    'fun_app$a': ( 'ZF_ZF_set_fun$' * 'ZF$' ) > 'ZF_set$' ).

tff(func_def_155,type,
    'uyj$': tlbool > 'Nat_bool_fun$' ).

tff(func_def_156,type,
    'repl$': ( 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).

tff(func_def_157,type,
    def_10: ( 'ZF_ZF_bool_fun_fun$' * 'ZF_ZF_prod$' ) > tlbool ).

tff(func_def_158,type,
    'uuo$': 'ZF_bool_fun$' > 'ZF_bool_fun$' ).

tff(func_def_159,type,
    'uun$': ( tlbool * 'ZF$' ) > 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_160,type,
    'vch$': ( 'ZF_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_set_set_fun$' ).

tff(func_def_161,type,
    'fun_app$t': ( 'ZF_ZF_ZF_fun_fun$' * 'ZF$' ) > 'ZF_ZF_fun$' ).

tff(func_def_162,type,
    'uwj$': 'ZF_set_set$' > 'ZF_ZF_set_set_fun$' ).

tff(func_def_163,type,
    'of_nat$': 'Nat$' > $int ).

tff(func_def_164,type,
    'sigma$h': ( 'Nat_set$' * 'Nat_ZF_set_set_fun$' ) > 'Nat_ZF_set_prod_set$' ).

tff(func_def_165,type,
    'vat$': ( 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_166,type,
    'relImage$c': ( 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_167,type,
    'vam$': 'ZF_ZF_set_fun$' ).

tff(func_def_168,type,
    'uxx$': ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_169,type,
    'vae$': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_bool_fun_fun$' ).

tff(func_def_170,type,
    'uwf$': 'ZF_set$' > 'ZF_ZF_set_fun$' ).

tff(func_def_171,type,
    'vaj$': 'ZF_ZF_bool_fun_fun$' > 'ZF_bool_fun$' ).

tff(func_def_172,type,
    'uxl$': ( 'ZF_ZF_set_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_173,type,
    'uxc$': ( 'ZF_set_ZF_ZF_prod_fun$' * 'ZF_set_set$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_174,type,
    'uxy$': ( 'ZF_ZF_ZF_prod_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_175,type,
    'image$w': ( 'Nat_ZF_prod_ZF_ZF_prod_set_fun$' * 'Nat_ZF_prod_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff(func_def_176,type,
    'zFfun$': ( 'ZF$' * 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).

tff(func_def_177,type,
    'image$z': ( 'Nat_nat_set_fun$' * 'Nat_set$' ) > 'Nat_set_set$' ).

tff(func_def_178,type,
    'fun_app$ax': ( 'Bool_ZF_fun$' * tlbool ) > 'ZF$' ).

tff(func_def_179,type,
    'gr$a': ( 'Nat_set$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_set_prod_set$' ).

tff(func_def_180,type,
    'uvu$': ( 'ZF_set_set$' * 'ZF_ZF_prod_set$' * 'ZF_set_ZF_fun$' ) > 'ZF_set_ZF_set_prod_bool_fun$' ).

tff(func_def_181,type,
    'collect$f': 'ZF_ZF_ZF_prod_prod_bool_fun$' > 'ZF_ZF_ZF_prod_prod_set$' ).

tff(func_def_182,type,
    'uxi$': ( 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_fun$' ).

tff(func_def_183,type,
    'uym$': 'Nat_ZF_set_fun$' ).

tff(func_def_184,type,
    'uzc$': 'ZF_set$' > 'Nat_ZF_set_fun$' ).

tff(func_def_185,type,
    'uya$': ( 'Nat_ZF_set_fun$' * 'Nat_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_186,type,
    'uwz$': ( 'ZF_ZF_fun$' * 'ZF_set$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_187,type,
    'relImage$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_188,type,
    'uxw$': ( 'ZF_set_ZF_fun$' * 'ZF_set_set$' ) > 'ZF_bool_fun$' ).

tff(func_def_189,type,
    'specialR$': 'ZF_ZF_prod_set$' ).

tff(func_def_190,type,
    'comp$c': ( 'Nat_set_ZF_set_set_fun$' * 'Nat_set_set_nat_set_fun$' ) > 'Nat_set_set_ZF_set_set_fun$' ).

tff(func_def_191,type,
    'collect$a': 'ZF_bool_fun$' > 'ZF_set$' ).

tff(func_def_192,type,
    'vbd$': ( 'ZF_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_193,type,
    'fun_app$y': ( 'ZF_set_ZF_set_set_fun$' * 'ZF_set$' ) > 'ZF_set_set$' ).

tff(func_def_194,type,
    'image$x': ( 'Nat_nat_prod_ZF_ZF_prod_set_fun$' * 'Nat_nat_prod_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff(func_def_195,type,
    'relInvImage$a': ( 'ZF_set_set$' * 'ZF_ZF_prod_set$' * 'ZF_set_ZF_fun$' ) > 'ZF_set_ZF_set_prod_set$' ).

tff(func_def_196,type,
    'universe$': 'ZF_bool_fun$' ).

tff(func_def_197,type,
    'comp$a': ( 'Nat_ZF_fun$' * 'ZF_nat_fun$' ) > 'ZF_ZF_fun$' ).

tff(func_def_198,type,
    'zFfunCod$': 'ZF_ZF_fun$' ).

tff(func_def_199,type,
    'pair$a': ( 'ZF_ZF_prod$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod_ZF_ZF_prod_prod$' ).

tff(func_def_200,type,
    'image$o': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_set$' ) > 'Bool_set$' ).

tff(func_def_201,type,
    'uug$': 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_202,type,
    'fun_app$ap': ( 'ZF_nat_set_fun$' * 'ZF$' ) > 'Nat_set$' ).

tff(func_def_203,type,
    'image$f': ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_set_set$' ).

tff(func_def_204,type,
    'fun_app$u': ( 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_205,type,
    def_1: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).

tff(func_def_206,type,
    'comp$i': ( 'ZF_set_ZF_set_fun$' * 'ZF_set_set_ZF_set_fun$' ) > 'ZF_set_set_ZF_set_fun$' ).

tff(func_def_207,type,
    'uvs$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_208,type,
    'image$r': ( 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff(func_def_209,type,
    'insert$': 'ZF$' > 'ZF_set_ZF_set_fun$' ).

tff(func_def_210,type,
    'snd$': 'ZF_ZF_fun$' ).

tff(func_def_211,type,
    'uyw$': 'Nat_ZF_ZF_prod_fun$' > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_212,type,
    'uzs$': 'ZF$' > 'ZF_set_ZF_fun$' ).

tff(func_def_213,type,
    'bot$d': 'ZF_set_ZF_prod_set$' ).

tff(func_def_214,type,
    'fun_app$p': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_215,type,
    'uvf$': 'Int_bool_fun$' > 'Int_bool_fun$' ).

tff(func_def_216,type,
    'uwh$': 'ZF_ZF_set_fun$' ).

tff(func_def_217,type,
    'set$a': 'ZF_ZF_unit_Category_ext$' ).

tff(func_def_218,type,
    'uwe$': 'ZF_ZF_prod_set$' > 'ZF_ZF_ZF_prod_set_fun$' ).

tff(func_def_219,type,
    'uvw$': 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_220,type,
    'uwn$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_221,type,
    'subsetFn$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_ZF_ZF_prod_fun$' ).

tff(func_def_222,type,
    'fun_app$f': ( 'ZF_ZF_ZF_prod_fun$' * 'ZF$' ) > 'ZF_ZF_prod$' ).

tff(func_def_223,type,
    'uzi$': 'ZF_ZF_prod_bool_fun$' > 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_224,type,
    tltrue: tlbool ).

tff(func_def_225,type,
    'uyy$': 'ZF_ZF_ZF_set_fun_fun$' ).

tff(func_def_226,type,
    'uvz$': ( 'Bool_bool_fun$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).

tff(func_def_227,type,
    'vcc$': 'ZF_ZF_ZF_ZF_prod_fun_fun$' ).

tff(func_def_228,type,
    'uxd$': ( 'ZF_set_ZF_ZF_prod_fun$' * 'ZF_set_set$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_229,type,
    'sup$d': 'ZF_set$' > 'ZF_set_ZF_set_fun$' ).

tff(func_def_230,type,
    'vbr$': ( 'Nat_nat_ZF_set_fun_fun$' * 'Nat_set$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_231,type,
    'ext_ZF$': 'ZF_ZF_prod_set$' > 'ZF_ZF_fun$' ).

tff(func_def_232,type,
    'is_Elem_of$': 'ZF_ZF_prod_set$' ).

tff(func_def_233,type,
    'uvc$': 'ZF_ZF_prod_set_bool_fun$' > 'ZF_ZF_prod_set_bool_fun$' ).

tff(func_def_234,type,
    'image$ac': 'ZF_ZF_prod_set_ZF_set_fun$' > 'ZF_ZF_prod_set_set_ZF_set_set_fun$' ).

tff(func_def_235,type,
    'member$a': 'ZF$' > 'ZF_set_bool_fun$' ).

tff(func_def_236,type,
    'image$aa': ( 'Nat_set_ZF_set_fun$' * 'Nat_set_set$' ) > 'ZF_set_set$' ).

tff(func_def_237,type,
    'comp$': ( 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_fun$' ).

tff(func_def_238,type,
    'uub$': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_239,type,
    'uyk$': 'ZF_ZF_set_fun$' ).

tff(func_def_240,type,
    'f$': 'ZF$' ).

tff(func_def_241,type,
    'sup$a': 'ZF_set_set_ZF_set_fun$' ).

tff(func_def_242,type,
    'uyr$': 'ZF_ZF_set_fun$' > 'ZF_set_bool_fun$' ).

tff(func_def_243,type,
    'fun_app$j': ( 'ZF_ZF_ZF_ZF_prod_set_fun_fun$' * 'ZF$' ) > 'ZF_ZF_ZF_prod_set_fun$' ).

tff(func_def_244,type,
    'uxh$': ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_245,type,
    'greatest$': 'Int_bool_fun$' > $int ).

tff(func_def_246,type,
    'vbe$': 'Nat_ZF_set_fun$' > 'Nat_set_ZF_set_fun$' ).

tff(func_def_247,type,
    'uuy$': 'ZF_bool_fun$' ).

tff(func_def_248,type,
    'image$p': ( 'ZF_ZF_set_set_fun$' * 'ZF_set$' ) > 'ZF_set_set_set$' ).

tff(func_def_249,type,
    'greatest$b': 'ZF_set_bool_fun$' > 'ZF_set$' ).

tff(func_def_250,type,
    'image$g': 'ZF_ZF_ZF_prod_fun$' > 'ZF_set_ZF_ZF_prod_set_fun$' ).

tff(func_def_251,type,
    'vao$': ( 'ZF$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_252,type,
    'sup$b': 'ZF_set_set_set_ZF_set_set_fun$' ).

tff(func_def_253,type,
    'insert$a': ( 'ZF_ZF_prod$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_254,type,
    'the$e': 'ZF_ZF_prod_bool_fun$' > 'ZF_ZF_prod$' ).

tff(func_def_255,type,
    'uww$': ( 'ZF_set_ZF_fun$' * 'ZF_set_set$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_256,type,
    'vac$': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF_ZF_prod_ZF_bool_fun_fun$' ).

tff(func_def_257,type,
    'sup$c': 'Nat_set_set_nat_set_fun$' ).

tff(func_def_258,type,
    'zFTThd$': 'ZF_ZF_fun$' ).

tff(func_def_259,type,
    'vbx$': 'ZF_ZF_prod_ZF_ZF_prod_bool_fun_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' ).

tff(func_def_260,type,
    'vbu$': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_ZF_bool_fun_fun$' ) > 'ZF_ZF_prod_ZF_bool_fun_fun$' ).

tff(func_def_261,type,
    'image$s': ( 'ZF_ZF_prod_ZF_set_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_set_set_set$' ).

tff(func_def_262,type,
    'vaz$': ( 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_ZF_ZF_prod_set_fun_fun$' ).

tff(func_def_263,type,
    'zFfunComp$': 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_264,type,
    'vbg$': ( 'ZF_ZF_ZF_set_fun_fun$' * 'ZF_set$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_265,type,
    'uyd$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_266,type,
    'the$': 'ZF_bool_fun$' > 'ZF$' ).

tff(func_def_267,type,
    'case_prod$e': 'ZF_ZF_ZF_set_set_fun_fun$' > 'ZF_ZF_prod_ZF_set_set_fun$' ).

tff(func_def_268,type,
    'subset$': 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_269,type,
    'relInvImage$d': ( 'Nat_set$' * 'ZF_set_ZF_set_prod_set$' * 'Nat_ZF_set_fun$' ) > 'Nat_nat_prod_set$' ).

tff(func_def_270,type,
    'uwy$': ( 'ZF_ZF_fun$' * 'ZF_set$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_271,type,
    'fun_app$x': ( 'ZF_set_set_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_272,type,
    'rec_set_bool$': ( 'ZF$' * 'ZF$' * tlbool ) > 'ZF_bool_fun$' ).

tff(func_def_273,type,
    'image$b': 'Nat_ZF_set_fun$' > 'Nat_set_ZF_set_set_fun$' ).

tff(func_def_274,type,
    'bot$b': 'ZF_set_set$' ).

tff(func_def_275,type,
    'fun_app$ag': ( 'Nat_ZF_ZF_set_fun_fun$' * 'Nat$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_276,type,
    'fun_app$bd': ( 'ZF_set_set_ZF_set_set_set_fun$' * 'ZF_set_set$' ) > 'ZF_set_set_set$' ).

tff(func_def_277,type,
    'ext_ZF_hull$': 'ZF_ZF_prod_set$' > 'ZF_ZF_fun$' ).

tff(func_def_278,type,
    'uvq$': ( 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_279,type,
    'uzr$': ( 'Bool_bool_fun$' * 'ZF_ZF_bool_fun_fun$' ) > 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_280,type,
    'uuz$': 'ZF_ZF_fun$' ).

tff(func_def_281,type,
    'uwq$': ( 'ZF_set_ZF_set_fun$' * 'ZF_set_set$' * 'ZF_set_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_282,type,
    'fst$': 'ZF_ZF_fun$' ).

tff(func_def_283,type,
    'ext$': 'ZF_ZF_prod_set$' > 'ZF_ZF_set_fun$' ).

tff(func_def_284,type,
    'gr$c': ( 'ZF_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_285,type,
    'uvv$': ( 'ZF_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_286,type,
    'vaq$': 'Nat_ZF_set_fun$' > 'Nat_ZF_ZF_set_fun_fun$' ).

tff(func_def_287,type,
    'uxa$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_288,type,
    'least$a': 'Int_bool_fun$' > $int ).

tff(func_def_289,type,
    'set_like$': 'ZF_ZF_prod_set_bool_fun$' ).

tff(func_def_290,type,
    'uxs$': ( 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_291,type,
    'bot$c': 'ZF_ZF_prod_ZF_prod_set$' ).

tff(func_def_292,type,
    'uwp$': ( 'Nat_ZF_set_fun$' * 'Nat_set$' * 'ZF_set_bool_fun$' ) > 'Nat_bool_fun$' ).

tff(func_def_293,type,
    'nat2Nat$': 'Nat_ZF_fun$' ).

tff(func_def_294,type,
    'comp$b': ( 'ZF_set_set_set_ZF_set_set_fun$' * 'Nat_set_set_ZF_set_set_set_fun$' ) > 'Nat_set_set_ZF_set_set_fun$' ).

tff(func_def_295,type,
    'uxv$': ( 'ZF_ZF_fun$' * 'ZF_set$' ) > 'ZF_bool_fun$' ).

tff(func_def_296,type,
    'uxq$': ( 'ZF_ZF_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_ZF_fun$' ).

tff(func_def_297,type,
    'uwl$': ( 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'ZF_set_ZF_set_set_fun$' ).

tff(func_def_298,type,
    'uux$': 'ZF$' > 'Nat_ZF_fun$' ).

tff(func_def_299,type,
    'fun_app$ao': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_300,type,
    'fun_app$q': ( 'ZF_ZF_set_set_fun$' * 'ZF$' ) > 'ZF_set_set$' ).

tff(func_def_301,type,
    'sigma$c': ( 'ZF_set$' * 'ZF_ZF_ZF_prod_set_fun$' ) > 'ZF_ZF_ZF_prod_prod_set$' ).

tff(func_def_302,type,
    'zFTFst$': 'ZF_ZF_fun$' ).

tff(func_def_303,type,
    'image$e': ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_304,type,
    'union$': 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_305,type,
    'vav$': ( 'Nat_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'Nat_ZF_ZF_ZF_prod_set_fun_fun$' ).

tff(func_def_306,type,
    'uve$': 'Nat_bool_fun$' > 'Nat_bool_fun$' ).

tff(func_def_307,type,
    'vcf$': ( 'ZF_ZF_prod_ZF_fun$' * 'Nat_ZF_ZF_prod_set_fun$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_308,type,
    def_6: ( 'ZF$' * 'ZF$' * 'ZF_ZF_bool_fun_fun$' ) > tlbool ).

tff(func_def_309,type,
    def_9: ( 'ZF_ZF_bool_fun_fun$' * 'ZF_ZF_prod$' ) > tlbool ).

tff(func_def_310,type,
    'fun_app$aa': ( 'Nat_set_ZF_set_set_fun$' * 'Nat_set$' ) > 'ZF_set_set$' ).

tff(func_def_311,type,
    'uwv$': ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' * 'ZF_set_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_312,type,
    'uui$': 'ZF$' > 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_313,type,
    'uvg$': 'ZF_ZF_prod_set_bool_fun$' > 'ZF_ZF_prod_set_bool_fun$' ).

tff(func_def_314,type,
    'the$b': 'ZF_ZF_prod_set_bool_fun$' > 'ZF_ZF_prod_set$' ).

tff(func_def_315,type,
    'relInvImage$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' ).

tff(func_def_316,type,
    'vbh$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_ZF_set_fun_fun$' ).

tff(func_def_317,type,
    'comp$h': ( 'ZF_set_set_ZF_set_fun$' * 'ZF_set_set_ZF_set_set_fun$' ) > 'ZF_set_set_ZF_set_fun$' ).

tff(func_def_318,type,
    'uye$': ( 'ZF_ZF_ZF_prod_fun$' * 'ZF_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_319,type,
    'comp$g': ( 'ZF_ZF_prod_set_ZF_set_fun$' * 'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$' ) > 'ZF_ZF_prod_set_set_ZF_set_fun$' ).

tff(func_def_320,type,
    'sigma$j': ( 'Nat_set$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_prod_set$' ).

tff(func_def_321,type,
    'collect$b': 'ZF_set_bool_fun$' > 'ZF_set_set$' ).

tff(func_def_322,type,
    'relImage$a': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_set_ZF_set_prod_set$' ).

tff(func_def_323,type,
    'vbb$': ( 'Nat_ZF_set_fun$' * 'Nat_nat_set_fun$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_324,type,
    'fun_app$v': ( 'ZF_ZF_prod_ZF_ZF_prod_bool_fun_fun$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_325,type,
    'zFTSnd$': 'ZF_ZF_fun$' ).

tff(func_def_326,type,
    'member$': 'ZF_ZF_prod$' > 'ZF_ZF_prod_set_bool_fun$' ).

tff(func_def_327,type,
    'case_prod$k': 'Nat_nat_ZF_ZF_prod_set_fun_fun$' > 'Nat_nat_prod_ZF_ZF_prod_set_fun$' ).

tff(func_def_328,type,
    'uzx$': 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_ZF_set_fun$' ).

tff(func_def_329,type,
    'fun_app$ab': ( 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_330,type,
    'uxk$': ( 'ZF_ZF_set_fun$' * 'Nat_ZF_fun$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_331,type,
    'isOpair$': 'ZF_bool_fun$' ).

tff(func_def_332,type,
    'vbz$': 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_set_fun$' ).

tff(func_def_333,type,
    'uuu$': 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_334,type,
    'less_eq$': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_set_bool_fun$' ).

tff(func_def_335,type,
    'sucNat$': 'ZF_ZF_fun$' ).

tff(func_def_336,type,
    'fun_app$aq': ( 'Nat_nat_set_fun$' * 'Nat$' ) > 'Nat_set$' ).

tff(func_def_337,type,
    'vap$': 'ZF_ZF_set_fun$' > 'ZF_set_ZF_ZF_prod_set_fun$' ).

tff(func_def_338,type,
    'vcj$': ( 'ZF_ZF_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_339,type,
    'vbw$': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_bool_fun_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_bool_fun_fun$' ).

tff(func_def_340,type,
    'image$v': ( 'ZF_nat_prod_ZF_ZF_prod_set_fun$' * 'ZF_nat_prod_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff(func_def_341,type,
    'uuv$': 'ZF_ZF_fun$' ).

tff(func_def_342,type,
    'opair$': 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_343,type,
    'uvn$': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_344,type,
    'vas$': 'Nat_set$' > 'ZF_nat_set_fun$' ).

tff(func_def_345,type,
    'uxo$': ( 'ZF_set_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_346,type,
    'isFun$': 'ZF_bool_fun$' ).

tff(func_def_347,type,
    'uyq$': 'ZF_ZF_prod_ZF_fun$' > 'ZF_bool_fun$' ).

tff(func_def_348,type,
    'uzk$': ( 'ZF_ZF_prod$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_349,type,
    'uzq$': ( 'Bool_ZF_fun$' * 'ZF_ZF_bool_fun_fun$' ) > 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_350,type,
    def_5: ( 'Bool_bool_fun$' * tlbool ) > tlbool ).

tff(func_def_351,type,
    'regular$': 'ZF_ZF_prod_set_bool_fun$' ).

tff(func_def_352,type,
    'the_elem$': 'ZF_set_ZF_fun$' ).

tff(func_def_353,type,
    'uxr$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_ZF_prod_fun$' ) > 'ZF_ZF_fun$' ).

tff(func_def_354,type,
    'elem$': 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_355,type,
    'vbs$': ( 'ZF_bool_fun$' * 'ZF_ZF_ZF_prod_bool_fun_fun$' ) > 'ZF_ZF_ZF_prod_bool_fun_fun$' ).

tff(func_def_356,type,
    'zFfunDom$': 'ZF_ZF_fun$' ).

tff(func_def_357,type,
    'uuj$': 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_358,type,
    'uzz$': ( 'ZF$' * 'ZF$' ) > 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_359,type,
    'vbn$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_nat_ZF_set_fun_fun$' ).

tff(func_def_360,type,
    'uyg$': 'ZF_set_set$' > 'Nat_ZF_set_set_fun$' ).

tff(func_def_361,type,
    'image$i': ( 'ZF_set_ZF_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_362,type,
    'fun_app$be': ( 'Nat_set_set_nat_set_fun$' * 'Nat_set_set$' ) > 'Nat_set$' ).

tff(func_def_363,type,
    'fun_app$bf': ( 'Nat_set_set_ZF_set_set_set_fun$' * 'Nat_set_set$' ) > 'ZF_set_set_set$' ).

tff(func_def_364,type,
    'uvt$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_prod_bool_fun$' ).

tff(func_def_365,type,
    'zFfunApp$': 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_366,type,
    'fun_app$ae': ( 'Nat_ZF_ZF_prod_fun$' * 'Nat$' ) > 'ZF_ZF_prod$' ).

tff(func_def_367,type,
    'uyb$': ( 'ZF_ZF_set_fun$' * 'ZF_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_368,type,
    'bot$e': 'Nat_set$' ).

tff(func_def_369,type,
    'fun_app$s': ( 'Nat_ZF_set_set_fun$' * 'Nat$' ) > 'ZF_set_set$' ).

tff(func_def_370,type,
    'range$': 'ZF_ZF_fun$' ).

tff(func_def_371,type,
    'sup$': 'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$' ).

tff(func_def_372,type,
    'lambda$': ( 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).

tff(func_def_373,type,
    'uvp$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_374,type,
    def_2: ( 'ZF_ZF_bool_fun_fun$' * 'ZF$' * 'ZF$' ) > tlbool ).

tff(func_def_375,type,
    'vaa$': ( 'ZF_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_ZF_prod_bool_fun_fun$' ).

tff(func_def_376,type,
    'fun_app$af': ( 'ZF_ZF_ZF_set_fun_fun$' * 'ZF$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_377,type,
    def_8: ( 'ZF_ZF_bool_fun_fun$' * 'ZF$' * 'ZF$' ) > tlbool ).

tff(func_def_378,type,
    'fun_app$au': ( 'Nat_ZF_ZF_ZF_prod_set_fun_fun$' * 'Nat$' ) > 'ZF_ZF_ZF_prod_set_fun$' ).

tff(func_def_379,type,
    def_4: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).

tff(func_def_380,type,
    'uur$': ( 'ZF_set$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_381,type,
    'least$': ( 'ZF_ZF_bool_fun_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_382,type,
    'insert$b': ( 'ZF_set$' * 'ZF_set_set$' ) > 'ZF_set_set$' ).

tff(func_def_383,type,
    'uvi$': 'Nat_bool_fun$' > 'Nat_bool_fun$' ).

tff(func_def_384,type,
    'uuf$': 'ZF_ZF_fun$' > 'ZF_ZF_fun$' ).

tff(func_def_385,type,
    'uuk$': 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_386,type,
    'fun_app$ar': ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod$' ).

tff(func_def_387,type,
    'image$t': ( 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_set_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff(func_def_388,type,
    'uyz$': 'ZF_ZF_prod_ZF_ZF_prod_bool_fun_fun$' ).

tff(func_def_389,type,
    'wfzf$': 'ZF_ZF_prod_set_bool_fun$' ).

tff(func_def_390,type,
    'uul$': ( 'ZF$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_391,type,
    'bind$': ( 'ZF_set$' * 'ZF_ZF_set_set_fun$' ) > 'ZF_set_set$' ).

tff(func_def_392,type,
    'eps$': 'ZF_bool_fun$' > 'ZF$' ).

tff(func_def_393,type,
    tlfalse: tlbool ).

tff(func_def_394,type,
    'vbi$': ( 'ZF_ZF_ZF_set_fun_fun$' * 'ZF_set$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_395,type,
    'nat$': $int > 'Nat$' ).

tff(func_def_396,type,
    'least$d': 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_397,type,
    'fun$': 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_398,type,
    'image$ab': 'Nat_set_ZF_set_set_fun$' > 'Nat_set_set_ZF_set_set_set_fun$' ).

tff(func_def_399,type,
    'bind$a': ( 'Nat_set$' * 'Nat_ZF_set_set_fun$' ) > 'ZF_set_set$' ).

tff(func_def_400,type,
    'uxj$': ( 'ZF_set_ZF_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_fun$' ).

tff(func_def_401,type,
    'uzo$': ( 'ZF_ZF_fun$' * 'ZF_ZF_ZF_fun_fun$' ) > 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_402,type,
    'greatest$c': 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_403,type,
    'uvy$': 'ZF_bool_fun$' ).

tff(func_def_404,type,
    'uud$': 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_405,type,
    'uyi$': tlbool > 'ZF_bool_fun$' ).

tff(func_def_406,type,
    'uyf$': ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_407,type,
    'greatest$a': 'ZF_ZF_prod_set_bool_fun$' > 'ZF_ZF_prod_set$' ).

tff(func_def_408,type,
    'uws$': ( 'ZF_ZF_set_fun$' * 'ZF_set$' * 'ZF_set_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_409,type,
    'fun_app$am': ( 'ZF_set_ZF_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_410,type,
    'uwd$': 'ZF_set$' > 'ZF_ZF_prod_ZF_set_fun$' ).

tff(func_def_411,type,
    'inf$': 'ZF$' ).

tff(func_def_412,type,
    'collect$g': 'ZF_ZF_prod_ZF_prod_bool_fun$' > 'ZF_ZF_prod_ZF_prod_set$' ).

tff(func_def_413,type,
    'image2$b': ( 'ZF_set_set$' * 'ZF_set_ZF_fun$' * 'ZF_set_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_414,type,
    'collect$d': 'ZF_set_ZF_set_prod_bool_fun$' > 'ZF_set_ZF_set_prod_set$' ).

tff(func_def_415,type,
    'fun_app$': ( 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_416,type,
    'vak$': tlbool > 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_417,type,
    'vbp$': ( 'Nat_nat_ZF_set_fun_fun$' * 'Nat_set$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_418,type,
    'makeCat$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$' ).

tff(func_def_419,type,
    'inj_on$a': 'ZF_ZF_set_fun$' > 'ZF_set_bool_fun$' ).

tff(func_def_420,type,
    'uxp$': ( 'ZF_set_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_421,type,
    'vbj$': ( 'ZF_nat_ZF_set_fun_fun$' * 'Nat_set$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_422,type,
    'comp$d': ( 'ZF_set_set_set_ZF_set_set_fun$' * 'ZF_set_set_ZF_set_set_set_fun$' ) > 'ZF_set_set_ZF_set_set_fun$' ).

tff(func_def_423,type,
    'uyl$': 'ZF_nat_set_fun$' ).

tff(func_def_424,type,
    'fun_app$g': ( 'ZF_ZF_ZF_ZF_prod_fun_fun$' * 'ZF$' ) > 'ZF_ZF_ZF_prod_fun$' ).

tff(func_def_425,type,
    'uyp$': ( 'ZF_ZF_fun$' * 'Nat_ZF_fun$' ) > 'Nat_ZF_fun$' ).

tff(func_def_426,type,
    'case_prod$h': 'ZF_ZF_prod_ZF_ZF_prod_bool_fun_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_prod_bool_fun$' ).

tff(func_def_427,type,
    'vck$': 'ZF_ZF_bool_fun_fun$' ).

tff(func_def_428,type,
    'uvj$': 'Nat_bool_fun$' > 'Nat_bool_fun$' ).

tff(func_def_429,type,
    'power$': 'ZF_ZF_fun$' ).

tff(func_def_430,type,
    'sep$': ( 'ZF$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_431,type,
    'sigma$b': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_set_fun$' ) > 'ZF_ZF_prod_ZF_prod_set$' ).

tff(func_def_432,type,
    'sigma$f': ( 'ZF_set$' * 'ZF_ZF_set_set_fun$' ) > 'ZF_ZF_set_prod_set$' ).

tff(func_def_433,type,
    'uvr$': ( 'ZF_set_set$' * 'ZF_set_ZF_fun$' * 'ZF_set_ZF_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_434,type,
    'uzb$': 'ZF$' > 'ZF_ZF_prod_ZF_fun$' ).

tff(func_def_435,type,
    'top$c': 'ZF_nat_prod_set$' ).

tff(func_def_436,type,
    'uwi$': 'ZF_set_set$' > 'ZF_ZF_prod_ZF_set_set_fun$' ).

tff(func_def_437,type,
    'relInvImage$c': ( 'ZF_set$' * 'ZF_set_ZF_set_prod_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_438,type,
    'sigma$g': ( 'ZF_set_set$' * 'ZF_set_ZF_set_set_fun$' ) > 'ZF_set_ZF_set_prod_set$' ).

tff(func_def_439,type,
    'uvk$': 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_440,type,
    'domain$': 'ZF_ZF_fun$' ).

tff(func_def_441,type,
    'uzg$': ( 'ZF$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_442,type,
    'uyn$': 'Nat_nat_set_fun$' ).

tff(func_def_443,type,
    'uup$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_444,type,
    'uvo$': ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_445,type,
    'uzl$': ( 'ZF_set$' * 'ZF_set_set$' ) > 'ZF_set_bool_fun$' ).

tff(func_def_446,type,
    'val$': 'Nat_ZF_set_fun$' ).

tff(func_def_447,type,
    'the$c': 'ZF_set_bool_fun$' > 'ZF_set$' ).

tff(func_def_448,type,
    'uuc$': 'ZF$' > 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_449,type,
    'vab$': 'ZF_ZF_prod_bool_fun$' > 'ZF_ZF_ZF_prod_set_fun$' ).

tff(func_def_450,type,
    'uwb$': 'Nat_bool_fun$' ).

tff(func_def_451,type,
    'vah$': 'ZF_bool_fun$' > 'ZF_ZF_set_fun$' ).

tff(func_def_452,type,
    'vaw$': ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_453,type,
    'subsetFn$a': ( 'ZF_set$' * 'ZF_set$' ) > 'ZF_ZF_fun$' ).

tff(func_def_454,type,
    'uyx$': ( 'ZF_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_455,type,
    'sigma$d': ( 'ZF_set_set$' * 'ZF_set_ZF_set_fun$' ) > 'ZF_set_ZF_prod_set$' ).

tff(func_def_456,type,
    'fun_app$ac': ( 'ZF_ZF_prod_ZF_bool_fun_fun$' * 'ZF_ZF_prod$' ) > 'ZF_bool_fun$' ).

tff(func_def_457,type,
    'nat$a': 'ZF$' ).

tff(func_def_458,type,
    'uvb$': 'Int_bool_fun$' > 'Int_bool_fun$' ).

tff(func_def_459,type,
    'image$ad': ( 'Nat_ZF_ZF_prod_set_fun$' * 'Nat_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff(func_def_460,type,
    'vax$': ( 'Nat_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat_nat_ZF_ZF_prod_set_fun_fun$' ).

tff(func_def_461,type,
    'image2$a': ( 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_462,type,
    'vca$': 'ZF_ZF_ZF_ZF_prod_set_fun_fun$' ).

tff(func_def_463,type,
    'image$l': ( 'ZF_nat_fun$' * 'ZF_set$' ) > 'Nat_set$' ).

tff(func_def_464,type,
    'case_prod$j': 'Nat_ZF_ZF_ZF_prod_set_fun_fun$' > 'Nat_ZF_prod_ZF_ZF_prod_set_fun$' ).

tff(func_def_465,type,
    'fun_app$bb': ( 'ZF_set_set_set_ZF_set_set_fun$' * 'ZF_set_set_set$' ) > 'ZF_set_set$' ).

tff(func_def_466,type,
    'van$': ( 'ZF$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_467,type,
    'vbl$': ( 'ZF_nat_ZF_set_fun_fun$' * 'ZF_set$' ) > 'Nat_ZF_set_fun$' ).

tff(func_def_468,type,
    'image$j': 'ZF_set_ZF_set_fun$' > 'ZF_set_set_ZF_set_set_fun$' ).

tff(func_def_469,type,
    'vad$': 'ZF_bool_fun$' > 'ZF_ZF_prod_ZF_set_fun$' ).

tff(func_def_470,type,
    'sigma$i': ( 'ZF_set$' * 'ZF_nat_set_fun$' ) > 'ZF_nat_prod_set$' ).

tff(func_def_471,type,
    'image$y': ( 'ZF_nat_set_fun$' * 'ZF_set$' ) > 'Nat_set_set$' ).

tff(func_def_472,type,
    'implode$': 'ZF_set_ZF_fun$' ).

tff(func_def_473,type,
    'explode$': 'ZF_ZF_set_fun$' ).

tff(func_def_474,type,
    'isZFfun$': 'ZF_bool_fun$' ).

tff(func_def_475,type,
    'product$': 'ZF_ZF_fun$' ).

tff(func_def_476,type,
    'cartProd$': 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_477,type,
    'uyt$': 'ZF_ZF_ZF_prod_fun$' > 'ZF_ZF_prod_bool_fun$' ).

tff(func_def_478,type,
    'top$a': 'Nat_set$' ).

tff(func_def_479,type,
    'fun_app$aj': ( 'ZF_ZF_prod_set_ZF_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_set$' ).

tff(func_def_480,type,
    'fun_app$bc': ( 'ZF_ZF_ZF_set_set_fun_fun$' * 'ZF$' ) > 'ZF_ZF_set_set_fun$' ).

tff(func_def_481,type,
    'fun_app$an': ( 'ZF_nat_fun$' * 'ZF$' ) > 'Nat$' ).

tff(func_def_482,type,
    'uxf$': ( 'ZF_ZF_ZF_prod_fun$' * 'ZF_set$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_bool_fun$' ).

tff(func_def_483,type,
    'fun_app$ba': ( 'ZF_ZF_prod_ZF_set_set_fun$' * 'ZF_ZF_prod$' ) > 'ZF_set_set$' ).

tff(func_def_484,type,
    'fun_app$r': ( 'Nat_ZF_set_fun$' * 'Nat$' ) > 'ZF_set$' ).

tff(func_def_485,type,
    'zFTriple$': 'ZF$' > 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_486,type,
    'uyv$': 'Nat_ZF_fun$' > 'ZF_bool_fun$' ).

tff(func_def_487,type,
    'vbc$': ( 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_set_fun$' ).

tff(func_def_488,type,
    'uum$': ( 'ZF$' * 'ZF_bool_fun$' ) > 'ZF_ZF_fun$' ).

tff(func_def_489,type,
    'vbt$': 'ZF_ZF_ZF_prod_bool_fun_fun$' > 'ZF_ZF_ZF_prod_set_fun$' ).

tff(func_def_490,type,
    'the$a': 'Int_bool_fun$' > $int ).

tff(func_def_491,type,
    'vbv$': 'ZF_ZF_prod_ZF_bool_fun_fun$' > 'ZF_ZF_prod_ZF_set_fun$' ).

tff(func_def_492,type,
    'uzh$': 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_ZF_fun_fun$' ).

tff(func_def_493,type,
    'fun_app$bg': ( 'ZF_ZF_prod_set_set_ZF_set_set_fun$' * 'ZF_ZF_prod_set_set$' ) > 'ZF_set_set$' ).

tff(func_def_494,type,
    'uvh$': 'ZF_set_bool_fun$' > 'ZF_set_bool_fun$' ).

tff(func_def_499,type,
    sK0: 'ZF$' > 'Nat$' ).

tff(func_def_500,type,
    sK1: 'ZF_ZF_prod$' > 'ZF$' ).

tff(func_def_501,type,
    sK2: 'ZF_ZF_prod$' > 'ZF$' ).

tff(func_def_502,type,
    sK3: ( 'ZF_ZF_prod_set_bool_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_503,type,
    sK4: ( 'ZF_set_bool_fun$' * 'ZF_set$' ) > 'ZF_set$' ).

tff(func_def_504,type,
    sK5: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_505,type,
    sK6: ( 'Int_bool_fun$' * $int ) > $int ).

tff(func_def_506,type,
    sK7: ( 'ZF_ZF_prod_set_bool_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_507,type,
    sK8: ( 'ZF_set_bool_fun$' * 'ZF_set$' ) > 'ZF_set$' ).

tff(func_def_508,type,
    sK9: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_509,type,
    sK10: ( 'Int_bool_fun$' * $int ) > $int ).

tff(func_def_510,type,
    sK11: ( 'ZF_ZF_bool_fun_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_511,type,
    sK12: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_512,type,
    sK13: ( 'ZF_ZF_prod_set$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_513,type,
    sK14: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_514,type,
    sK15: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_515,type,
    sK16: ( 'ZF_ZF_prod_ZF_fun$' * 'ZF$' ) > 'ZF_ZF_prod$' ).

tff(func_def_516,type,
    sK17: ( 'ZF_ZF_ZF_prod_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_517,type,
    sK18: ( 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_518,type,
    sK19: ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_519,type,
    sK20: ( 'Nat_ZF_ZF_prod_fun$' * 'ZF_ZF_prod$' ) > 'Nat$' ).

tff(func_def_520,type,
    sK21: ( 'Nat_ZF_fun$' * 'ZF$' ) > 'Nat$' ).

tff(func_def_521,type,
    sK22: ( 'Nat_ZF_set_fun$' * 'ZF_set$' ) > 'Nat$' ).

tff(func_def_522,type,
    sK23: ( 'ZF_ZF_bool_fun_fun$' * 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_523,type,
    sK24: ( 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_524,type,
    sK25: ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod$' ).

tff(func_def_525,type,
    sK26: ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' * 'ZF$' ) > 'ZF_ZF_prod$' ).

tff(func_def_526,type,
    sK27: ( 'ZF_ZF_ZF_prod_fun$' * 'ZF_set$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_527,type,
    sK28: ( 'ZF_ZF_fun$' * 'ZF_set$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_528,type,
    sK29: ( 'ZF_ZF_set_fun$' * 'ZF_set$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_529,type,
    sK30: ( 'ZF_set_ZF_ZF_prod_fun$' * 'ZF_set_set$' * 'ZF_ZF_prod$' ) > 'ZF_set$' ).

tff(func_def_530,type,
    sK31: ( 'ZF_set_ZF_fun$' * 'ZF_set_set$' * 'ZF$' ) > 'ZF_set$' ).

tff(func_def_531,type,
    sK32: ( 'Nat_ZF_set_fun$' * 'Nat_set$' * 'ZF_set$' ) > 'Nat$' ).

tff(func_def_532,type,
    sK33: ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod$' ).

tff(func_def_533,type,
    sK34: ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_bool_fun$' * 'ZF$' ) > 'ZF_ZF_prod$' ).

tff(func_def_534,type,
    sK35: ( 'ZF_ZF_ZF_prod_fun$' * 'ZF_bool_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_535,type,
    sK36: ( 'ZF_ZF_fun$' * 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_536,type,
    sK37: ( 'ZF_ZF_set_fun$' * 'ZF_bool_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_537,type,
    sK38: ( 'Nat_ZF_set_fun$' * 'Nat_bool_fun$' * 'ZF_set$' ) > 'Nat$' ).

tff(func_def_538,type,
    sK39: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_539,type,
    sK40: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_540,type,
    sK41: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod$' ).

tff(func_def_541,type,
    sK42: ( 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_542,type,
    sK43: ( 'ZF_set_set$' * 'ZF_set_ZF_fun$' * 'ZF_set_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF_set$' ).

tff(func_def_543,type,
    sK44: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_prod$' ) > 'ZF_ZF_prod$' ).

tff(func_def_544,type,
    sK45: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_prod$' ) > 'ZF_ZF_prod$' ).

tff(func_def_545,type,
    sK46: ( 'ZF_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_546,type,
    sK47: ( 'ZF_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_547,type,
    sK48: ( 'ZF_set_set$' * 'ZF_ZF_prod_set$' * 'ZF_set_ZF_fun$' * 'ZF_set_ZF_set_prod$' ) > 'ZF_set$' ).

tff(func_def_548,type,
    sK49: ( 'ZF_set_set$' * 'ZF_ZF_prod_set$' * 'ZF_set_ZF_fun$' * 'ZF_set_ZF_set_prod$' ) > 'ZF_set$' ).

tff(func_def_549,type,
    sK50: 'ZF$' > 'ZF$' ).

tff(func_def_550,type,
    sK51: 'ZF$' > 'ZF$' ).

tff(func_def_551,type,
    sK52: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_552,type,
    sK53: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_553,type,
    sK54: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_554,type,
    sK55: ( 'ZF$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_555,type,
    sK56: 'ZF_bool_fun$' > 'ZF$' ).

tff(func_def_556,type,
    sK57: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_557,type,
    sK58: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_558,type,
    sK59: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod$' ).

tff(func_def_559,type,
    sK60: ( 'ZF$' * 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_560,type,
    sK61: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_561,type,
    sK62: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_562,type,
    sK63: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_563,type,
    sK64: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_564,type,
    sK65: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_565,type,
    sK66: 'ZF$' > 'ZF$' ).

tff(func_def_566,type,
    sK67: 'ZF$' > 'ZF$' ).

tff(func_def_567,type,
    sK68: 'ZF$' > 'ZF$' ).

tff(func_def_568,type,
    sK69: ( 'ZF$' * 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_569,type,
    sK70: ( 'ZF$' * 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_570,type,
    sK71: ( 'ZF$' * 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_571,type,
    sK72: ( 'ZF$' * 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_572,type,
    sK73: ( 'ZF$' * 'ZF$' ) > 'ZF_ZF_fun$' ).

tff(func_def_573,type,
    sK74: ( 'ZF$' * 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).

tff(func_def_574,type,
    sK75: ( 'ZF$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF$' ).

tff(func_def_575,type,
    sK76: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_576,type,
    sK77: 'ZF$' > 'ZF$' ).

tff(func_def_577,type,
    sK78: 'ZF$' > 'ZF$' ).

tff(func_def_578,type,
    sK79: 'ZF$' > 'ZF$' ).

tff(func_def_579,type,
    sK80: 'ZF$' > 'ZF$' ).

tff(func_def_580,type,
    sK81: 'ZF$' > 'ZF$' ).

tff(func_def_581,type,
    sK82: 'ZF$' > 'ZF$' ).

tff(func_def_582,type,
    sK84: 'ZF$' > 'ZF$' ).

tff(func_def_583,type,
    sK85: 'ZF$' > 'ZF$' ).

tff(func_def_584,type,
    sK86: 'ZF$' > 'ZF$' ).

tff(func_def_585,type,
    sK87: 'ZF$' > 'ZF$' ).

tff(func_def_586,type,
    sK88: 'ZF$' > 'ZF$' ).

tff(func_def_587,type,
    sK90: 'ZF$' > 'ZF$' ).

tff(func_def_588,type,
    sK91: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_589,type,
    sK92: ( 'ZF$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_590,type,
    sK93: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_591,type,
    sK94: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_592,type,
    sK95: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_593,type,
    sK96: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_594,type,
    sK97: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_595,type,
    sK98: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_596,type,
    sK99: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_597,type,
    sK100: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_598,type,
    sK101: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_599,type,
    sK102: 'ZF_bool_fun$' > 'ZF$' ).

tff(func_def_600,type,
    sK103: 'ZF_bool_fun$' > 'ZF$' ).

tff(func_def_601,type,
    sK104: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_602,type,
    sK105: 'ZF_bool_fun$' > 'ZF$' ).

tff(func_def_603,type,
    sK106: 'ZF_bool_fun$' > 'ZF$' ).

tff(func_def_604,type,
    sK107: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_605,type,
    sK108: 'ZF_bool_fun$' > 'ZF$' ).

tff(func_def_606,type,
    sK109: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_607,type,
    sK110: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod$' ).

tff(func_def_608,type,
    sK111: ( 'ZF_set_set$' * 'ZF_set_bool_fun$' * 'ZF_set_bool_fun$' ) > 'ZF_set$' ).

tff(func_def_609,type,
    sK112: ( 'ZF_set$' * 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_610,type,
    sK113: 'ZF_bool_fun$' > 'ZF$' ).

tff(func_def_611,type,
    sK114: 'ZF_bool_fun$' > 'ZF$' ).

tff(func_def_612,type,
    sK115: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_613,type,
    sK116: 'ZF_bool_fun$' > 'ZF$' ).

tff(func_def_614,type,
    sK117: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_615,type,
    sK118: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_616,type,
    sK119: ( 'ZF$' * 'Nat_ZF_fun$' ) > 'Nat$' ).

tff(func_def_617,type,
    sK120: ( 'ZF$' * 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_618,type,
    sK121: ( 'ZF_ZF_prod_set$' * 'ZF$' * 'ZF$' ) > 'Nat$' ).

tff(func_def_619,type,
    sK122: 'ZF_ZF_prod_set$' > 'ZF$' ).

tff(func_def_620,type,
    sK123: ( 'ZF_ZF_prod_set$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_621,type,
    sK124: ( 'ZF_ZF_prod_set$' * 'ZF$' ) > 'ZF$' ).

tff(func_def_622,type,
    sK125: ( 'ZF_set_set$' * 'ZF_set_bool_fun$' ) > 'ZF_set$' ).

tff(func_def_623,type,
    sK126: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod$' ).

tff(func_def_624,type,
    sK127: ( 'ZF_set$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_625,type,
    sK128: ( 'ZF_set_set$' * 'ZF_set_bool_fun$' * 'ZF_set_bool_fun$' ) > 'ZF_set$' ).

tff(func_def_626,type,
    sK129: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod$' ).

tff(func_def_627,type,
    sK130: ( 'ZF_set$' * 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).

tff(func_def_628,type,
    sK131: ( 'ZF_ZF_prod_set$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_629,type,
    sK132: ( 'ZF_set$' * 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF$' ).

tff(func_def_630,type,
    sK133: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_set_fun$' ) > 'ZF_ZF_prod$' ).

tff(func_def_631,type,
    sK134: ( 'ZF_set_set$' * 'ZF_set_ZF_set_fun$' ) > 'ZF_set$' ).

tff(func_def_632,type,
    sK135: ( 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF$' ).

tff(func_def_633,type,
    sK136: ( 'ZF_ZF_prod$' * 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_634,type,
    sK137: ( 'ZF_ZF_prod$' * 'ZF_ZF_ZF_prod_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_635,type,
    sK138: ( 'ZF_ZF_prod$' * 'ZF_set_ZF_ZF_prod_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_636,type,
    sK139: ( 'ZF$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_637,type,
    sK140: ( 'ZF$' * 'ZF_ZF_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_638,type,
    sK141: ( 'ZF$' * 'ZF_set_ZF_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_639,type,
    sK142: ( 'ZF_set$' * 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'Nat$' ).

tff(func_def_640,type,
    sK143: ( 'ZF_set$' * 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_641,type,
    sK144: ( 'ZF_set$' * 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_642,type,
    sK145: ( 'ZF_set$' * 'ZF_set_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_643,type,
    sK146: ( 'Nat_bool_fun$' * 'Nat_ZF_set_fun$' * 'ZF_set_set$' ) > 'Nat$' ).

tff(func_def_644,type,
    sK147: ( 'ZF_bool_fun$' * 'ZF_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF$' ).

tff(func_def_645,type,
    sK148: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_646,type,
    sK149: ( 'ZF_bool_fun$' * 'ZF_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF$' ).

tff(func_def_647,type,
    sK150: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_648,type,
    sK151: ( 'ZF_bool_fun$' * 'ZF_ZF_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_649,type,
    sK152: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_650,type,
    sK153: 'ZF_ZF_prod_set$' > 'ZF$' ).

tff(func_def_651,type,
    sK154: ( 'ZF$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod$' ).

tff(func_def_652,type,
    sK155: ( 'ZF_ZF_prod$' * 'ZF_ZF_ZF_prod_fun$' ) > 'ZF$' ).

tff(func_def_653,type,
    sK156: ( 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).

tff(func_def_654,type,
    sK157: ( 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF$' ).

tff(func_def_655,type,
    sK158: ( 'ZF_ZF_prod$' * 'Nat_ZF_ZF_prod_fun$' ) > 'Nat$' ).

tff(func_def_656,type,
    sK159: ( 'ZF$' * 'Nat_ZF_fun$' ) > 'Nat$' ).

tff(func_def_657,type,
    sK160: ( 'ZF_set$' * 'Nat_ZF_set_fun$' ) > 'Nat$' ).

tff(func_def_658,type,
    sK161: ( 'ZF_bool_fun$' * 'ZF_ZF_ZF_fun_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_659,type,
    sK162: ( 'ZF_bool_fun$' * 'ZF_ZF_ZF_fun_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_660,type,
    sK163: ( 'Bool_bool_fun$' * 'ZF_ZF_bool_fun_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_661,type,
    sK164: ( 'Bool_bool_fun$' * 'ZF_ZF_bool_fun_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_662,type,
    sK165: ( 'ZF_ZF_ZF_fun_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF$' ).

tff(func_def_663,type,
    sK166: ( 'ZF_ZF_ZF_fun_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF$' ).

tff(func_def_664,type,
    sK167: ( 'ZF_ZF_bool_fun_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF$' ).

tff(func_def_665,type,
    sK168: ( 'ZF_ZF_bool_fun_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF$' ).

tff(func_def_666,type,
    sK169: 'ZF_set_set$' > 'ZF_set$' ).

tff(func_def_667,type,
    sK170: 'ZF_ZF_prod_set$' > 'ZF_ZF_prod$' ).

tff(func_def_668,type,
    sK171: 'ZF_set$' > 'ZF$' ).

tff(func_def_669,type,
    sK172: ( 'ZF_ZF_prod$' * 'ZF_ZF_bool_fun_fun$' ) > 'ZF$' ).

tff(func_def_670,type,
    sK173: ( 'ZF_ZF_prod$' * 'ZF_ZF_bool_fun_fun$' ) > 'ZF$' ).

tff(func_def_671,type,
    sK174: ( 'ZF_ZF_prod$' * 'ZF_ZF_prod$' * 'ZF_ZF_ZF_ZF_prod_set_fun_fun$' ) > 'ZF$' ).

tff(func_def_672,type,
    sK175: ( 'ZF_ZF_prod$' * 'ZF_ZF_prod$' * 'ZF_ZF_ZF_ZF_prod_set_fun_fun$' ) > 'ZF$' ).

tff(func_def_673,type,
    sK176: ( 'ZF_ZF_prod$' * 'ZF$' * 'ZF_ZF_ZF_set_fun_fun$' ) > 'ZF$' ).

tff(func_def_674,type,
    sK177: ( 'ZF_ZF_prod$' * 'ZF$' * 'ZF_ZF_ZF_set_fun_fun$' ) > 'ZF$' ).

tff(func_def_675,type,
    sK178: ( 'ZF_ZF_prod$' * 'ZF_set$' * 'ZF_ZF_ZF_set_set_fun_fun$' ) > 'ZF$' ).

tff(func_def_676,type,
    sK179: ( 'ZF_ZF_prod$' * 'ZF_set$' * 'ZF_ZF_ZF_set_set_fun_fun$' ) > 'ZF$' ).

tff(func_def_677,type,
    sK180: ( 'ZF_ZF_prod$' * 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_678,type,
    sK181: ( 'ZF_ZF_prod$' * 'ZF_ZF_ZF_prod_set_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_679,type,
    sK182: ( 'ZF_ZF_prod$' * 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_680,type,
    sK183: ( 'ZF_set$' * 'ZF_ZF_prod_ZF_set_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_681,type,
    sK184: ( 'ZF_set$' * 'ZF_ZF_set_set_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_682,type,
    sK185: ( 'ZF_set$' * 'ZF_set_ZF_set_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_683,type,
    sK186: ( 'ZF$' * 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'Nat$' ).

tff(func_def_684,type,
    sK187: ( 'ZF$' * 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_685,type,
    sK188: ( 'ZF$' * 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_686,type,
    sK189: ( 'ZF$' * 'ZF_set_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_687,type,
    sK190: ( 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'Nat$' ).

tff(func_def_688,type,
    sK191: ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_689,type,
    sK192: ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_690,type,
    sK193: ( 'ZF_set_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_691,type,
    sK194: ( 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'Nat$' ).

tff(func_def_692,type,
    sK195: ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_693,type,
    sK196: ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_694,type,
    sK197: ( 'ZF_set_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_695,type,
    sK198: ( 'ZF_ZF_prod$' * 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_696,type,
    sK199: ( 'ZF_ZF_prod$' * 'ZF_ZF_ZF_prod_set_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_697,type,
    sK200: ( 'ZF_ZF_prod$' * 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_698,type,
    sK201: ( 'ZF_set$' * 'ZF_ZF_prod_ZF_set_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_699,type,
    sK202: ( 'ZF_set$' * 'ZF_ZF_set_set_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_700,type,
    sK203: ( 'ZF_set$' * 'ZF_set_ZF_set_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_701,type,
    sK204: ( 'ZF$' * 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'Nat$' ).

tff(func_def_702,type,
    sK205: ( 'ZF$' * 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_703,type,
    sK206: ( 'ZF$' * 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_704,type,
    sK207: ( 'ZF$' * 'ZF_set_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff(func_def_705,type,
    sK208: ( 'ZF_ZF_bool_fun_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_706,type,
    sK209: ( 'ZF_ZF_bool_fun_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff(func_def_707,type,
    sK210: ( 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_708,type,
    sK211: ( 'ZF_ZF_ZF_prod_set_fun$' * 'ZF_set$' * 'ZF_ZF_prod_set$' ) > 'ZF$' ).

tff(func_def_709,type,
    sK212: ( 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_set_set$' * 'ZF_ZF_prod_set$' ) > 'ZF_set$' ).

tff(func_def_710,type,
    sK213: ( 'Nat_ZF_set_fun$' * 'Nat_set$' * 'ZF_set$' ) > 'Nat$' ).

tff(func_def_711,type,
    sK214: ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' * 'ZF_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_712,type,
    sK215: ( 'ZF_ZF_set_fun$' * 'ZF_set$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_713,type,
    sK216: ( 'ZF_set_ZF_set_fun$' * 'ZF_set_set$' * 'ZF_set$' ) > 'ZF_set$' ).

tff(func_def_714,type,
    sK217: ( 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF$' ).

tff(func_def_715,type,
    sK218: ( 'Nat_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat$' ).

tff(func_def_716,type,
    sK219: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_717,type,
    sK220: ( 'ZF_set$' * 'ZF_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF$' ).

tff(func_def_718,type,
    sK221: ( 'ZF_set_set$' * 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_set$' ).

tff(func_def_719,type,
    sK222: ( 'Nat_set$' * 'Nat_ZF_set_fun$' * 'ZF_set$' ) > 'Nat$' ).

tff(func_def_720,type,
    sK223: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_721,type,
    sK224: ( 'ZF_set$' * 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_722,type,
    sK225: ( 'ZF_set_set$' * 'ZF_set_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set$' ).

tff(func_def_723,type,
    sK226: ( 'Nat_set$' * 'Nat_set$' * 'Nat_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat$' ).

tff(func_def_724,type,
    sK227: ( 'Nat_set$' * 'ZF_set$' * 'Nat_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'Nat$' ).

tff(func_def_725,type,
    sK228: ( 'ZF_set$' * 'Nat_set$' * 'ZF_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'ZF$' ).

tff(func_def_726,type,
    sK229: ( 'ZF_set$' * 'ZF_set$' * 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF$' ).

tff(func_def_727,type,
    sK230: ( 'Nat_set$' * 'ZF_set_set$' * 'Nat_ZF_set_fun$' * 'ZF_set_ZF_set_fun$' ) > 'Nat$' ).

tff(func_def_728,type,
    sK231: ( 'ZF_set$' * 'ZF_set_set$' * 'ZF_ZF_set_fun$' * 'ZF_set_ZF_set_fun$' ) > 'ZF$' ).

tff(func_def_729,type,
    sK232: ( 'ZF_set_set$' * 'Nat_set$' * 'ZF_set_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'ZF_set$' ).

tff(func_def_730,type,
    sK233: ( 'ZF_set_set$' * 'ZF_set$' * 'ZF_set_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_set$' ).

tff(func_def_731,type,
    sK234: ( 'ZF_set$' * 'ZF_set$' * 'ZF_ZF_ZF_prod_set_fun$' * 'ZF_ZF_ZF_prod_set_fun$' ) > 'ZF$' ).

tff(func_def_732,type,
    sK235: ( 'Nat_set$' * 'ZF_ZF_prod_set$' * 'Nat_ZF_set_fun$' * 'ZF_ZF_prod_ZF_set_fun$' ) > 'Nat$' ).

tff(func_def_733,type,
    sK236: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_734,type,
    sK237: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_735,type,
    sK238: ( 'ZF_set$' * 'ZF_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_736,type,
    sK239: ( 'ZF_set$' * 'ZF_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF$' ).

tff(func_def_737,type,
    sK240: ( 'ZF_set_set$' * 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).

tff(func_def_738,type,
    sK241: ( 'ZF_set_set$' * 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_set$' ).

tff(func_def_739,type,
    sK242: ( 'Nat_set$' * 'Nat_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set$' ).

tff(func_def_740,type,
    sK243: ( 'Nat_set$' * 'Nat_ZF_set_fun$' * 'ZF_set$' ) > 'Nat$' ).

tff(func_def_741,type,
    sK244: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set$' ).

tff(func_def_742,type,
    sK245: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod$' ).

tff(func_def_743,type,
    sK246: ( 'ZF_set$' * 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set$' ).

tff(func_def_744,type,
    sK247: ( 'ZF_set$' * 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff(func_def_745,type,
    sK248: ( 'ZF_set_set$' * 'ZF_set_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set$' ).

tff(func_def_746,type,
    sK249: ( 'ZF_set_set$' * 'ZF_set_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set$' ).

tff(func_def_747,type,
    sK250: ( 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF$' ).

tff(func_def_748,type,
    sK251: 'Nat_ZF_set_fun$' > 'Nat$' ).

tff(pred_def_1,type,
    'less_eq$h': ( 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' * 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' ) > $o ).

tff(pred_def_2,type,
    'less_eq$k': ( 'ZF_ZF_prod_ZF_set_prod_set$' * 'ZF_ZF_prod_ZF_set_prod_set$' ) > $o ).

tff(pred_def_3,type,
    'less_eq$n': ( 'Nat_ZF_set_prod_set$' * 'Nat_ZF_set_prod_set$' ) > $o ).

tff(pred_def_4,type,
    'fun_app$c': ( 'ZF_bool_fun$' * 'ZF$' ) > $o ).

tff(pred_def_5,type,
    'less_eq$f': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > $o ).

tff(pred_def_6,type,
    'fun_app$e': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod$' ) > $o ).

tff(pred_def_7,type,
    'fun_app$m': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).

tff(pred_def_8,type,
    'uniq$b': 'ZF_bool_fun$' > $o ).

tff(pred_def_9,type,
    'less_eq$i': ( 'ZF_ZF_prod_ZF_prod_set$' * 'ZF_ZF_prod_ZF_prod_set$' ) > $o ).

tff(pred_def_10,type,
    'member$c': ( 'Nat$' * 'Nat_set$' ) > $o ).

tff(pred_def_11,type,
    'fun_app$l': ( 'ZF_set_bool_fun$' * 'ZF_set$' ) > $o ).

tff(pred_def_12,type,
    'less_eq$j': ( 'ZF_ZF_ZF_prod_prod_set$' * 'ZF_ZF_ZF_prod_prod_set$' ) > $o ).

tff(pred_def_13,type,
    'less_eq$c': ( 'ZF_ZF_bool_fun_fun$' * 'ZF_ZF_bool_fun_fun$' ) > $o ).

tff(pred_def_14,type,
    'inj_on$': ( 'Nat_ZF_fun$' * 'Nat_set$' ) > $o ).

tff(pred_def_15,type,
    'fun_app$ay': ( 'ZF_ZF_prod_ZF_ZF_prod_prod_bool_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_prod$' ) > $o ).

tff(pred_def_16,type,
    'less_eq$e': ( 'ZF_set_set$' * 'ZF_set_set$' ) > $o ).

tff(pred_def_17,type,
    'uniq$a': 'ZF_ZF_prod_bool_fun$' > $o ).

tff(pred_def_18,type,
    'less_eq$d': ( 'ZF_set_bool_fun$' * 'ZF_set_bool_fun$' ) > $o ).

tff(pred_def_19,type,
    'uniq$': 'ZF_set_bool_fun$' > $o ).

tff(pred_def_20,type,
    'less_eq$l': ( 'ZF_ZF_set_prod_set$' * 'ZF_ZF_set_prod_set$' ) > $o ).

tff(pred_def_21,type,
    'member$d': ( tlbool * 'Bool_set$' ) > $o ).

tff(pred_def_22,type,
    'fun_app$k': ( 'ZF_ZF_prod_set_bool_fun$' * 'ZF_ZF_prod_set$' ) > $o ).

tff(pred_def_23,type,
    'fun_app$n': ( 'Int_bool_fun$' * $int ) > $o ).

tff(pred_def_24,type,
    'member$b': ( 'ZF_set$' * 'ZF_set_set$' ) > $o ).

tff(pred_def_25,type,
    'fun_app$az': ( 'ZF_set_ZF_set_prod_bool_fun$' * 'ZF_set_ZF_set_prod$' ) > $o ).

tff(pred_def_26,type,
    'less_eq$g': ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > $o ).

tff(pred_def_27,type,
    'less_eq$m': ( 'ZF_set_ZF_set_prod_set$' * 'ZF_set_ZF_set_prod_set$' ) > $o ).

tff(pred_def_28,type,
    'fun_app$al': ( 'Bool_bool_fun$' * tlbool ) > $o ).

tff(pred_def_31,type,
    sP83: ( 'ZF$' * 'ZF$' ) > $o ).

tff(pred_def_32,type,
    sP89: ( 'ZF$' * 'ZF$' ) > $o ).

tff(f221,conjecture,
    'fun_app$c'('fun_app$h'('subset$','fun_app$'('snd$','f$')),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('domain$','fun_app$'('snd$','f$'))),'fun_app$'('range$','fun_app$'('snd$','f$')))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture220) ).

tff(f222,negated_conjecture,
    ~ 'fun_app$c'('fun_app$h'('subset$','fun_app$'('snd$','f$')),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('domain$','fun_app$'('snd$','f$'))),'fun_app$'('range$','fun_app$'('snd$','f$')))),
    inference(negated_conjecture,[status(cth)],[f221]) ).

tff(f223,axiom,
    'fun_app$c'('isZFfun$','f$'),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom221) ).

tff(f224,axiom,
    'fun_app$'('zFfunDom$','f$') = 'fun_app$'('domain$','fun_app$'('snd$','f$')),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom222) ).

tff(f232,axiom,
    'zFTThd$' = 'snd$',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom230) ).

tff(f233,axiom,
    ! [X0: 'ZF$'] :
      ( ( 'fun_app$c'('isZFfun$',X0)
        & ( ( 'fun_app$c'('isOpair$',X0)
            & 'fun_app$c'('isOpair$','fun_app$'('fst$',X0))
            & 'fun_app$c'('isFun$','fun_app$'('snd$',X0))
            & 'fun_app$c'('fun_app$h'('subset$','fun_app$'('snd$',X0)),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('domain$','fun_app$'('snd$',X0))),'fun_app$'('range$','fun_app$'('snd$',X0))))
            & ( 'fun_app$'('domain$','fun_app$'('snd$',X0)) = 'fun_app$'('zFfunDom$',X0) )
            & 'fun_app$c'('fun_app$h'('subset$','fun_app$'('range$','fun_app$'('snd$',X0))),'fun_app$'('zFfunCod$',X0)) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom231) ).

tff(f887,plain,
    ~ 'fun_app$c'('fun_app$h'('subset$','fun_app$'('snd$','f$')),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('domain$','fun_app$'('snd$','f$'))),'fun_app$'('range$','fun_app$'('snd$','f$')))),
    inference(flattening,[],[f222]) ).

tff(f930,plain,
    ! [X0: 'ZF$'] :
      ( $false
      | ~ 'fun_app$c'('isZFfun$',X0)
      | ( $true
        & 'fun_app$c'('isOpair$',X0)
        & 'fun_app$c'('isOpair$','fun_app$'('fst$',X0))
        & 'fun_app$c'('isFun$','fun_app$'('snd$',X0))
        & 'fun_app$c'('fun_app$h'('subset$','fun_app$'('snd$',X0)),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('domain$','fun_app$'('snd$',X0))),'fun_app$'('range$','fun_app$'('snd$',X0))))
        & ( 'fun_app$'('domain$','fun_app$'('snd$',X0)) = 'fun_app$'('zFfunDom$',X0) )
        & 'fun_app$c'('fun_app$h'('subset$','fun_app$'('range$','fun_app$'('snd$',X0))),'fun_app$'('zFfunCod$',X0)) ) ),
    inference(ennf_transformation,[],[f233]) ).

tff(f931,plain,
    ! [X0: 'ZF$'] :
      ( $false
      | ~ 'fun_app$c'('isZFfun$',X0)
      | ( $true
        & 'fun_app$c'('isOpair$',X0)
        & 'fun_app$c'('isOpair$','fun_app$'('fst$',X0))
        & 'fun_app$c'('isFun$','fun_app$'('snd$',X0))
        & 'fun_app$c'('fun_app$h'('subset$','fun_app$'('snd$',X0)),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('domain$','fun_app$'('snd$',X0))),'fun_app$'('range$','fun_app$'('snd$',X0))))
        & ( 'fun_app$'('domain$','fun_app$'('snd$',X0)) = 'fun_app$'('zFfunDom$',X0) )
        & 'fun_app$c'('fun_app$h'('subset$','fun_app$'('range$','fun_app$'('snd$',X0))),'fun_app$'('zFfunCod$',X0)) ) ),
    inference(flattening,[],[f930]) ).

tff(f1757,plain,
    ~ 'fun_app$c'('fun_app$h'('subset$','fun_app$'('snd$','f$')),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('domain$','fun_app$'('snd$','f$'))),'fun_app$'('range$','fun_app$'('snd$','f$')))),
    inference(cnf_transformation,[],[f887]) ).

tff(f1758,plain,
    'fun_app$c'('isZFfun$','f$'),
    inference(cnf_transformation,[],[f223]) ).

tff(f1759,plain,
    'fun_app$'('domain$','fun_app$'('snd$','f$')) = 'fun_app$'('zFfunDom$','f$'),
    inference(cnf_transformation,[],[f224]) ).

tff(f1768,plain,
    'snd$' = 'zFTThd$',
    inference(cnf_transformation,[],[f232]) ).

tff(f1772,plain,
    ! [X0: 'ZF$'] :
      ( 'fun_app$c'('fun_app$h'('subset$','fun_app$'('snd$',X0)),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('domain$','fun_app$'('snd$',X0))),'fun_app$'('range$','fun_app$'('snd$',X0))))
      | ~ 'fun_app$c'('isZFfun$',X0) ),
    inference(cnf_transformation,[],[f931]) ).

tff(f2816,plain,
    ~ 'fun_app$c'('fun_app$h'('subset$','fun_app$'('zFTThd$','f$')),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('domain$','fun_app$'('zFTThd$','f$'))),'fun_app$'('range$','fun_app$'('zFTThd$','f$')))),
    inference(definition_unfolding,[],[f1757,f1768,f1768,f1768]) ).

tff(f2817,plain,
    'fun_app$'('zFfunDom$','f$') = 'fun_app$'('domain$','fun_app$'('zFTThd$','f$')),
    inference(definition_unfolding,[],[f1759,f1768]) ).

tff(f2823,plain,
    ! [X0: 'ZF$'] :
      ( 'fun_app$c'('fun_app$h'('subset$','fun_app$'('zFTThd$',X0)),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('domain$','fun_app$'('zFTThd$',X0))),'fun_app$'('range$','fun_app$'('zFTThd$',X0))))
      | ~ 'fun_app$c'('isZFfun$',X0) ),
    inference(definition_unfolding,[],[f1772,f1768,f1768,f1768]) ).

tff(f3372,plain,
    'fun_app$c'('fun_app$h'('subset$','fun_app$'('zFTThd$','f$')),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('domain$','fun_app$'('zFTThd$','f$'))),'fun_app$'('range$','fun_app$'('zFTThd$','f$')))),
    inference(consistent_polarity_flipping,[],[f2816]) ).

tff(f3373,plain,
    ~ 'fun_app$c'('isZFfun$','f$'),
    inference(consistent_polarity_flipping,[],[f1758]) ).

tff(f3381,plain,
    ! [X0: 'ZF$'] :
      ( ~ 'fun_app$c'('fun_app$h'('subset$','fun_app$'('zFTThd$',X0)),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('domain$','fun_app$'('zFTThd$',X0))),'fun_app$'('range$','fun_app$'('zFTThd$',X0))))
      | 'fun_app$c'('isZFfun$',X0) ),
    inference(consistent_polarity_flipping,[],[f2823]) ).

tff(f9438,plain,
    'fun_app$c'('fun_app$h'('subset$','fun_app$'('zFTThd$','f$')),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('zFfunDom$','f$')),'fun_app$'('range$','fun_app$'('zFTThd$','f$')))),
    inference(forward_demodulation,[],[f3372,f2817]) ).

tff(f29600,plain,
    ( ~ 'fun_app$c'('fun_app$h'('subset$','fun_app$'('zFTThd$','f$')),'fun_app$'('fun_app$t'('cartProd$','fun_app$'('zFfunDom$','f$')),'fun_app$'('range$','fun_app$'('zFTThd$','f$'))))
    | 'fun_app$c'('isZFfun$','f$') ),
    inference(superposition,[],[f3381,f2817]) ).

tff(f29604,plain,
    'fun_app$c'('isZFfun$','f$'),
    inference(forward_subsumption_resolution,[],[f29600,f9438]) ).

tff(f29605,plain,
    $false,
    inference(forward_subsumption_resolution,[],[f29604,f3373]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : ITP300_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/0.41  % Computer : n005.cluster.edu
% 0.17/0.41  % Model    : x86_64 x86_64
% 0.17/0.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41  % Memory   : 8046.5625MB
% 0.17/0.41  % OS       : Linux 6.8.0-71-generic
% 0.17/0.41  % CPULimit : 300
% 0.17/0.41  % WCLimit  : 300
% 0.17/0.41  % DateTime : Sun Sep 27 12:53:17 UTC 2026
% 0.17/0.42  % CPUTime  : 
% 0.17/0.42  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/0.47  Running first-order model finding
% 0.17/0.47  Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.20/1.48  % (3960391)Will run a generic schedule for satisfiability detection.
% 6.20/1.48  % (3960397)% WARNING: option uhcvi not known.
% 6.20/1.48  % (3960396)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=104755247_2999 on theBenchmark for (2999ds/0Mi)
% 6.20/1.48  % (3960397)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=39889311:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.20/1.48  % (3960399)dis+10_1_sil=32000:sp=arity:random_seed=3597628571:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.20/1.48  % (3960398)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1422020791:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.20/1.48  % (3960400)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4024556402:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.20/1.48  % (3960401)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1300896106:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.20/1.48  % (3960402)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4079760337:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.20/1.48  % (3960396)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 6.20/1.48  % (3960396)Terminated due to inappropriate strategy.
% 6.20/1.48  % (3960396)------------------------------
% 6.20/1.48  % (3960396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.20/1.48  % (3960396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.48  % (3960396)CaDiCaL version: 2.1.3
% 6.20/1.48  % (3960396)Termination reason: Inappropriate
% 6.20/1.48  % (3960396)Time elapsed: 0.052 s
% 6.20/1.48  % (3960396)Peak memory usage: 14 MB
% 6.20/1.48  % (3960396)Instructions burned: 109 (million)
% 6.20/1.48  % (3960396)------------------------------
% 6.20/1.48  % (3960396)------------------------------
% 6.20/1.48  % (3960410)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1112781941:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 6.20/1.48  % (3960399)Instruction limit reached! 
% 6.20/1.48  % (3960399)------------------------------
% 6.20/1.48  % (3960399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.20/1.48  % (3960399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.48  % (3960399)CaDiCaL version: 2.1.3
% 6.20/1.48  % (3960399)Termination reason: Instruction limit
% 6.20/1.48  % (3960399)Termination phase: Saturation
% 6.20/1.48  % (3960399)Time elapsed: 0.092 s
% 6.20/1.48  % (3960399)Peak memory usage: 14 MB
% 6.20/1.48  % (3960399)Instructions burned: 103 (million)
% 6.20/1.48  % (3960400)Instruction limit reached! 
% 6.20/1.48  % (3960400)------------------------------
% 6.20/1.48  % (3960400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.20/1.48  % (3960400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.48  % (3960400)CaDiCaL version: 2.1.3
% 6.20/1.48  % (3960400)Termination reason: Instruction limit
% 6.20/1.48  % (3960400)Termination phase: Property scanning
% 6.20/1.48  % (3960400)Time elapsed: 0.103 s
% 6.20/1.48  % (3960400)Peak memory usage: 14 MB
% 6.20/1.48  % (3960400)Instructions burned: 116 (million)
% 6.20/1.48  % (3960412)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2823312845:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 6.20/1.48  % (3960401)Instruction limit reached! 
% 6.20/1.48  % (3960401)------------------------------
% 6.20/1.48  % (3960401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.20/1.48  % (3960401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.48  % (3960401)CaDiCaL version: 2.1.3
% 6.20/1.48  % (3960401)Termination reason: Instruction limit
% 6.20/1.48  % (3960401)Termination phase: Saturation
% 6.20/1.48  % (3960401)Time elapsed: 0.120 s
% 6.20/1.48  % (3960401)Peak memory usage: 14 MB
% 6.20/1.48  % (3960401)Instructions burned: 131 (million)
% 6.20/1.48  % (3960413)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1346430306:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2997 on theBenchmark for (2997ds/684Mi)
% 6.20/1.48  % (3960415)ott-21_1_sil=16000:fs=off:random_seed=856567867:i=180:av=off:fsr=off_2997 on theBenchmark for (2997ds/180Mi)
% 6.20/1.48  % (3960410)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 6.20/1.48  % (3960410)Terminated due to inappropriate strategy.
% 7.95/1.83  % (3960410)------------------------------
% 7.95/1.83  % (3960410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.95/1.83  % (3960410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.95/1.83  % (3960410)CaDiCaL version: 2.1.3
% 7.95/1.83  % (3960410)Termination reason: Inappropriate
% 7.95/1.83  % (3960410)Time elapsed: 0.082 s
% 7.95/1.83  % (3960410)Peak memory usage: 13 MB
% 7.95/1.83  % (3960410)Instructions burned: 87 (million)
% 7.95/1.83  % (3960402)Instruction limit reached! 
% 7.95/1.83  % (3960402)------------------------------
% 7.95/1.83  % (3960402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.95/1.83  % (3960402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.95/1.83  % (3960402)CaDiCaL version: 2.1.3
% 7.95/1.83  % (3960402)Termination reason: Instruction limit
% 7.95/1.83  % (3960402)Termination phase: Saturation
% 7.95/1.83  % (3960402)Time elapsed: 0.158 s
% 7.95/1.83  % (3960402)Peak memory usage: 16 MB
% 7.95/1.83  % (3960402)Instructions burned: 159 (million)
% 7.95/1.83  % (3960410)------------------------------
% 7.95/1.83  % (3960410)------------------------------
% 7.95/1.83  % (3960412)Instruction limit reached! 
% 7.95/1.83  % (3960412)------------------------------
% 7.95/1.83  % (3960412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.95/1.83  % (3960412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.95/1.83  % (3960412)CaDiCaL version: 2.1.3
% 7.95/1.83  % (3960412)Termination reason: Instruction limit
% 7.95/1.83  % (3960412)Termination phase: Saturation
% 7.95/1.83  % (3960412)Time elapsed: 0.063 s
% 7.95/1.83  % (3960412)Peak memory usage: 15 MB
% 7.95/1.83  % (3960412)Instructions burned: 132 (million)
% 7.95/1.83  % (3960421)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4280899529:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 7.95/1.83  % (3960418)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4124529538:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 7.95/1.83  % (3960419)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3678368493:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 7.95/1.83  % (3960419)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 7.95/1.83  % (3960419)Terminated due to inappropriate strategy.
% 7.95/1.83  % (3960419)------------------------------
% 7.95/1.83  % (3960419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.95/1.83  % (3960419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.95/1.83  % (3960419)CaDiCaL version: 2.1.3
% 7.95/1.83  % (3960419)Termination reason: Inappropriate
% 7.95/1.83  % (3960419)Time elapsed: 0.080 s
% 7.95/1.83  % (3960419)Peak memory usage: 13 MB
% 7.95/1.83  % (3960419)Instructions burned: 86 (million)
% 7.95/1.83  % (3960419)------------------------------
% 7.95/1.83  % (3960419)------------------------------
% 7.95/1.83  % (3960425)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=773125135:i=889:ins=1_2996 on theBenchmark for (2996ds/889Mi)
% 7.95/1.83  % (3960415)Instruction limit reached! 
% 7.95/1.83  % (3960415)------------------------------
% 7.95/1.83  % (3960415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.95/1.83  % (3960415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.95/1.83  % (3960415)CaDiCaL version: 2.1.3
% 7.95/1.83  % (3960415)Termination reason: Instruction limit
% 7.95/1.83  % (3960415)Termination phase: Saturation
% 7.95/1.83  % (3960415)Time elapsed: 0.168 s
% 7.95/1.83  % (3960415)Peak memory usage: 15 MB
% 7.95/1.83  % (3960415)Instructions burned: 181 (million)
% 7.95/1.83  % (3960427)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=286971471:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2995 on theBenchmark for (2995ds/692Mi)
% 7.95/1.83  % (3960425)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 7.95/1.83  % (3960425)Terminated due to inappropriate strategy.
% 7.95/1.83  % (3960425)------------------------------
% 7.95/1.83  % (3960425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.95/1.83  % (3960425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.95/1.83  % (3960425)CaDiCaL version: 2.1.3
% 7.95/1.83  % (3960425)Termination reason: Inappropriate
% 7.95/1.83  % (3960425)Time elapsed: 0.056 s
% 7.95/1.83  % (3960425)Peak memory usage: 13 MB
% 10.72/2.07  % (3960425)Instructions burned: 87 (million)
% 10.72/2.07  % (3960425)------------------------------
% 10.72/2.07  % (3960425)------------------------------
% 10.72/2.07  % (3960429)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1303994989:i=879:kws=inv_precedence:fsr=off_2995 on theBenchmark for (2995ds/879Mi)
% 10.72/2.07  % (3960418)Instruction limit reached! 
% 10.72/2.07  % (3960418)------------------------------
% 10.72/2.07  % (3960418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.07  % (3960418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.07  % (3960418)CaDiCaL version: 2.1.3
% 10.72/2.07  % (3960418)Termination reason: Instruction limit
% 10.72/2.07  % (3960418)Termination phase: Saturation
% 10.72/2.07  % (3960418)Time elapsed: 0.529 s
% 10.72/2.07  % (3960418)Peak memory usage: 17 MB
% 10.72/2.07  % (3960418)Instructions burned: 478 (million)
% 10.72/2.07  % (3960433)fmb+10_1_sil=64000:random_seed=41279063:i=22061:nm=2:gsp=on_2991 on theBenchmark for (2991ds/22061Mi)
% 10.72/2.07  % (3960413)Instruction limit reached! 
% 10.72/2.07  % (3960413)------------------------------
% 10.72/2.07  % (3960413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.07  % (3960413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.07  % (3960413)CaDiCaL version: 2.1.3
% 10.72/2.07  % (3960413)Termination reason: Instruction limit
% 10.72/2.07  % (3960413)Termination phase: Saturation
% 10.72/2.07  % (3960413)Time elapsed: 0.624 s
% 10.72/2.07  % (3960413)Peak memory usage: 18 MB
% 10.72/2.07  % (3960413)Instructions burned: 684 (million)
% 10.72/2.07  % (3960433)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 10.72/2.07  % (3960433)Terminated due to inappropriate strategy.
% 10.72/2.07  % (3960433)------------------------------
% 10.72/2.07  % (3960433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.07  % (3960433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.07  % (3960433)CaDiCaL version: 2.1.3
% 10.72/2.07  % (3960433)Termination reason: Inappropriate
% 10.72/2.07  % (3960433)Time elapsed: 0.052 s
% 10.72/2.07  % (3960433)Peak memory usage: 13 MB
% 10.72/2.07  % (3960433)Instructions burned: 94 (million)
% 10.72/2.07  % (3960433)------------------------------
% 10.72/2.07  % (3960433)------------------------------
% 10.72/2.07  % (3960435)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2540236657:i=9515:nm=5_2991 on theBenchmark for (2991ds/9515Mi)
% 10.72/2.07  % (3960436)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=452732247:fmbsr=1.7:i=920_2990 on theBenchmark for (2990ds/920Mi)
% 10.72/2.07  % (3960421)Instruction limit reached! 
% 10.72/2.07  % (3960421)------------------------------
% 10.72/2.07  % (3960421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.07  % (3960421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.07  % (3960421)CaDiCaL version: 2.1.3
% 10.72/2.07  % (3960421)Termination reason: Instruction limit
% 10.72/2.07  % (3960421)Termination phase: Saturation
% 10.72/2.07  % (3960421)Time elapsed: 0.668 s
% 10.72/2.07  % (3960421)Peak memory usage: 29 MB
% 10.72/2.07  % (3960421)Instructions burned: 1180 (million)
% 10.72/2.07  % (3960436)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 10.72/2.07  % (3960436)Terminated due to inappropriate strategy.
% 10.72/2.07  % (3960436)------------------------------
% 10.72/2.07  % (3960436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.07  % (3960436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.07  % (3960436)CaDiCaL version: 2.1.3
% 10.72/2.07  % (3960436)Termination reason: Inappropriate
% 10.72/2.07  % (3960436)Time elapsed: 0.049 s
% 10.72/2.07  % (3960436)Peak memory usage: 13 MB
% 10.72/2.07  % (3960436)Instructions burned: 87 (million)
% 10.72/2.07  % (3960436)------------------------------
% 10.72/2.07  % (3960436)------------------------------
% 10.72/2.07  % (3960441)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4124326041:i=5131_2990 on theBenchmark for (2990ds/5131Mi)
% 10.72/2.07  % (3960435)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 10.72/2.07  % (3960435)Terminated due to inappropriate strategy.
% 10.72/2.07  % (3960435)------------------------------
% 10.72/2.07  % (3960435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.07  % (3960435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.07  % (3960435)CaDiCaL version: 2.1.3
% 10.72/2.07  % (3960435)Termination reason: Inappropriate
% 10.72/2.07  % (3960435)Time elapsed: 0.088 s
% 10.72/2.07  % (3960435)Peak memory usage: 13 MB
% 10.72/2.07  % (3960435)Instructions burned: 87 (million)
% 10.72/2.07  % (3960442)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2970855784:i=1472:ins=7:fdi=8:gsp=on_2990 on theBenchmark for (2990ds/1472Mi)
% 10.72/2.07  % (3960435)------------------------------
% 10.72/2.07  % (3960435)------------------------------
% 10.72/2.07  % (3960445)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1003530968:i=6324_2989 on theBenchmark for (2989ds/6324Mi)
% 10.72/2.07  % (3960445)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 10.72/2.07  % (3960445)Terminated due to inappropriate strategy.
% 10.72/2.07  % (3960445)------------------------------
% 10.72/2.07  % (3960445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.07  % (3960445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.07  % (3960445)CaDiCaL version: 2.1.3
% 10.72/2.07  % (3960445)Termination reason: Inappropriate
% 10.72/2.07  % (3960445)Time elapsed: 0.056 s
% 10.72/2.07  % (3960445)Peak memory usage: 14 MB
% 10.72/2.07  % (3960445)Instructions burned: 108 (million)
% 10.72/2.07  % (3960445)------------------------------
% 10.72/2.07  % (3960445)------------------------------
% 10.72/2.07  % (3960447)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1793061882:fmbsr=2.30978:i=2174_2989 on theBenchmark for (2989ds/2174Mi)
% 10.72/2.07  % (3960447)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 10.72/2.07  % (3960447)Terminated due to inappropriate strategy.
% 10.72/2.07  % (3960447)------------------------------
% 10.72/2.07  % (3960447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.07  % (3960447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.07  % (3960447)CaDiCaL version: 2.1.3
% 10.72/2.07  % (3960447)Termination reason: Inappropriate
% 10.72/2.07  % (3960447)Time elapsed: 0.046 s
% 10.72/2.07  % (3960447)Peak memory usage: 13 MB
% 10.72/2.07  % (3960447)Instructions burned: 87 (million)
% 10.72/2.07  % (3960447)------------------------------
% 10.72/2.07  % (3960447)------------------------------
% 10.72/2.07  % (3960427)Instruction limit reached! 
% 10.72/2.07  % (3960427)------------------------------
% 10.72/2.07  % (3960427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.07  % (3960427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.07  % (3960427)CaDiCaL version: 2.1.3
% 10.72/2.07  % (3960427)Termination reason: Instruction limit
% 10.72/2.07  % (3960427)Termination phase: Saturation
% 10.72/2.07  % (3960427)Time elapsed: 0.702 s
% 10.72/2.07  % (3960427)Peak memory usage: 20 MB
% 10.72/2.07  % (3960427)Instructions burned: 692 (million)
% 10.72/2.07  % (3960449)ott-2_1_sil=16000:newcnf=on:random_seed=2081397646:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2988 on theBenchmark for (2988ds/869Mi)
% 10.72/2.07  % (3960450)ott+10_1_sil=32000:tgt=ground:random_seed=3369756105:i=5114:av=off_2988 on theBenchmark for (2988ds/5114Mi)
% 10.72/2.07  % (3960429)Instruction limit reached! 
% 10.72/2.07  % (3960429)------------------------------
% 10.72/2.07  % (3960429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.07  % (3960429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.07  % (3960429)CaDiCaL version: 2.1.3
% 10.72/2.07  % (3960429)Termination reason: Instruction limit
% 10.72/2.07  % (3960429)Termination phase: Saturation
% 10.72/2.07  % (3960429)Time elapsed: 0.714 s
% 10.72/2.07  % (3960429)Peak memory usage: 19 MB
% 10.72/2.07  % (3960429)Instructions burned: 879 (million)
% 10.72/2.07  % (3960454)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2327173386:i=54282_2987 on theBenchmark for (2987ds/54282Mi)
% 10.72/2.07  % (3960454)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 10.72/2.07  % (3960454)Terminated due to inappropriate strategy.
% 10.72/2.07  % (3960454)------------------------------
% 10.72/2.07  % (3960454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.07  % (3960454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.07  % (3960454)CaDiCaL version: 2.1.3
% 10.72/2.07  % (3960454)Termination reason: Inappropriate
% 10.72/2.07  % (3960454)Time elapsed: 0.101 s
% 10.72/2.07  % (3960454)Peak memory usage: 14 MB
% 10.72/2.07  % (3960454)Instructions burned: 109 (million)
% 10.72/2.07  % (3960454)------------------------------
% 10.72/2.07  % (3960454)------------------------------
% 10.72/2.07  % (3960457)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2129141468:i=3512:aac=none_2986 on theBenchmark for (2986ds/3512Mi)
% 10.72/2.07  % (3960397) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3960391-3960397"...
% 10.72/2.07  % (3960397)...printing done.
% 10.72/2.07  % (3960397)Refutation found. Thanks to Tanya!
% 10.72/2.07  % SZS status Theorem for theBenchmark
% 10.72/2.07  % SZS output start Proof for theBenchmark
% See solution above
% 10.72/2.07  % (3960397)------------------------------
% 10.72/2.07  % (3960397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.72/2.07  % (3960397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.07  % (3960397)CaDiCaL version: 2.1.3
% 10.72/2.07  % (3960397)Termination reason: Refutation
% 10.72/2.07  % (3960397)Time elapsed: 1.485 s
% 10.72/2.07  % (3960397)Peak memory usage: 30 MB
% 10.72/2.07  % (3960397)Instructions burned: 1646 (million)
% 10.72/2.07  % (3960391)Success in time 1.587 s
% 10.72/2.08  % Vampire exiting
%------------------------------------------------------------------------------