%------------------------------------------------------------------------------
% File     : NUM795+4 : TPTP v8.2.0. Released v7.3.0.
% Domain   : Number theory
% Problem  : Grundlagen problem satz99c
% Version  : [Bro17] axioms : Especial.
% English  :

% Refs     : [Bro17] Brown (2017), Email to G. Sutcliffe
% Source   : [Br017]
% Names    :

% Status   : Theorem
% Rating   : 1.00 v7.3.0
% Syntax   : Number of formulae    : 1412 ( 464 unt;   0 def)
%            Number of atoms       : 2758 ( 167 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives : 1364 (  18   ~;  16   |;  25   &)
%                                         ( 899 <=>; 406  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :   12 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    : 1063 (1063 usr; 652 con; 0-5 aty)
%            Number of variables   : 2347 (2340   !;   7   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Translated by Isabelle from the THF version.
%------------------------------------------------------------------------------
% Explicit typings (32)
fof(gsy_c_HOL_Oundefined_001t__HOL__Obool,axiom,
    gg_bool(undefined_bool(bool)) ).

fof(gsy_c_HOL_Oundefined_001t__TPTP____Interpret__Oind,axiom,
    gg_TPTP_ind(undefined_TPTP_ind(tPTP_ind)) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__amone,axiom,
    ! [B_1,B_2] : gg_bool(scratc1875410914_amone(B_1,B_2)) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__d__428__id,axiom,
    gg_TPTP_ind(scratc394302153428_id) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__d__and,axiom,
    ! [B_1,B_2] : gg_bool(scratc520525675_d_and(B_1,B_2)) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__d__not,axiom,
    ! [B_1] : gg_bool(scratc627990855_d_not(B_1)) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__ec3,axiom,
    ! [B_1,B_2,B_3] : gg_bool(scratc408216893nd_ec3(B_1,B_2,B_3)) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__ect,axiom,
    ! [B_1,B_2] : gg_TPTP_ind(scratc408216958nd_ect(B_1,B_2)) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__emptyset,axiom,
    gg_TPTP_ind(scratc1884736269ptyset) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__eps,axiom,
    ! [B_1] : gg_TPTP_ind(scratc409069744nd_eps(B_1)) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__frac,axiom,
    gg_TPTP_ind(scratc406400774d_frac) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__ind,axiom,
    ! [B_1,B_2] : gg_TPTP_ind(scratc441984551nd_ind(B_1,B_2)) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__l__ec,axiom,
    ! [B_1,B_2] : gg_bool(scratc1202139186d_l_ec(B_1,B_2)) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__n__1,axiom,
    gg_TPTP_ind(scratc51547579nd_n_1) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__n__1o,axiom,
    gg_TPTP_ind(scratc1330372980d_n_1o) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__n__1t,axiom,
    gg_TPTP_ind(scratc1330372985d_n_1t) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__n__2,axiom,
    gg_TPTP_ind(scratc51547580nd_n_2) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__n__2t,axiom,
    gg_TPTP_ind(scratc1330438584d_n_2t) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__nat,axiom,
    gg_TPTP_ind(scratc482439305nd_nat) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__omega,axiom,
    gg_TPTP_ind(scratc566367529_omega) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__or3,axiom,
    ! [B_1,B_2,B_3] : gg_bool(scratc491815928nd_or3(B_1,B_2,B_3)) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__plusfrt,axiom,
    gg_TPTP_ind(scratc2083963126lusfrt) ).

fof(gsy_c_Scratch__tptp__translate__64633__6546_ONUM795__thf__4__p_Obnd__rat,axiom,
    gg_TPTP_ind(scratc515485325nd_rat) ).

fof(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool,axiom,
    ! [B_1,B_2] : gg_bool(aa_bool_bool(B_1,B_2)) ).

fof(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool,axiom,
    ! [B_1,B_2] : gg_bool(aa_TPTP_ind_bool(B_1,B_2)) ).

fof(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind,axiom,
    ! [B_1,B_2] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) ).

fof(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool,hypothesis,
    ! [B_1,B_2] : gg_bool(aa_fun171081125l_bool(B_1,B_2)) ).

fof(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind,axiom,
    ! [B_1,B_2] : gg_TPTP_ind(aa_fun1431113780TP_ind(B_1,B_2)) ).

fof(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__TPTP____Interpret__Oind_J_001t__TPTP____Interpret__Oind,axiom,
    ! [B_1,B_2] : gg_TPTP_ind(aa_fun277296641TP_ind(B_1,B_2)) ).

fof(gsy_c_fEx_001t__TPTP____Interpret__Oind,axiom,
    ! [B_1] : gg_bool(fEx_TPTP_ind(B_1)) ).

fof(gsy_c_fFalse,axiom,
    gg_bool(fFalse) ).

fof(gsy_c_fTrue,axiom,
    gg_bool(fTrue) ).

% Relevant facts (1364)
fof(fact_def__rt__pl,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc2041718494indrat(X,Xa,scratc515485325nd_rat),scratc2083963126lusfrt) ).

% def_rt_pl
fof(fact_def__plusfrt,axiom,
    scratc2083963126lusfrt = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,scratc406400774d_frac),aTP_Lamm_af) ).

% def_plusfrt
fof(fact_def__rt__lessis,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,X),Xa))
    <=> pp(aa_bool_bool(scratc1202795191d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,X),Xa))) ) ).

% def_rt_lessis
fof(fact_def__rt__moreis,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1066042873moreis,X),Xa))
    <=> pp(aa_bool_bool(scratc1202795191d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,X),Xa))) ) ).

% def_rt_moreis
fof(fact_def__propl,axiom,
    ! [X,Xa,Xb,Xc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1397105969_propl(X,Xa),Xb),Xc))
    <=> scratc765582804d_and3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441984553nd_inf,Xb),aa_TPTP_ind_TPTP_ind(scratc1111135584_class,X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441984553nd_inf,Xc),aa_TPTP_ind_TPTP_ind(scratc1111135584_class,Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Xb),Xc)) ) ).

% def_propl
fof(fact_def__rt__less,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,X),Xa))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(scratc406400774d_frac),aa_TPT43085870d_bool(aTP_Lamm_ah(X),Xa))) ) ).

% def_rt_less
fof(fact_def__propm,axiom,
    ! [X,Xa,Xb,Xc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1397105970_propm(X,Xa),Xb),Xc))
    <=> scratc765582804d_and3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441984553nd_inf,Xb),aa_TPTP_ind_TPTP_ind(scratc1111135584_class,X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441984553nd_inf,Xc),aa_TPTP_ind_TPTP_ind(scratc1111135584_class,Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Xb),Xc)) ) ).

% def_propm
fof(fact_def__rt__more,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,X),Xa))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(scratc406400774d_frac),aa_TPT43085870d_bool(aTP_Lamm_aj(X),Xa))) ) ).

% def_rt_more
fof(fact_def__indrat,axiom,
    ! [X,Xa,Xb,Xc] : aa_TPTP_ind_TPTP_ind(scratc2041718494indrat(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1935368447indeq2(scratc406400774d_frac,scratc1333784130d_n_eq,Xb,Xc,X),Xa) ).

% def_indrat
fof(fact_def__fixf,axiom,
    scratc333556009d_fixf = scratc4374950fixfu2(scratc406400774d_frac,scratc1333784130d_n_eq) ).

% def_fixf
fof(fact_def__class,axiom,
    scratc1111135584_class = scratc691943104_ecect(scratc406400774d_frac,scratc1333784130d_n_eq) ).

% def_class
fof(fact_def__ratof,axiom,
    scratc1184912324_ratof = scratc401199599ectelt(scratc406400774d_frac,scratc1333784130d_n_eq) ).

% def_ratof
fof(fact_def__rt__in,axiom,
    scratc1725338559_rt_in = scratc1782805115d_esti(scratc515485325nd_rat) ).

% def_rt_in
fof(fact_def__rt__one,axiom,
    scratc1703000428rt_one = scratc491553582nd_one(scratc515485325nd_rat) ).

% def_rt_one
fof(fact_def__rt__all,axiom,
    scratc1587208167rt_all = scratc375761321nd_all(scratc515485325nd_rat) ).

% def_rt_all
fof(fact_def__rt__some,axiom,
    scratc1861875310t_some = scratc828602088l_some(scratc515485325nd_rat) ).

% def_rt_some
fof(fact_def__rt__nis,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1694410942rt_nis,X),Xa))
    <=> pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,X),Xa))) ) ).

% def_rt_nis
fof(fact_def__rt__is,axiom,
    scratc1725338564_rt_is = scratc1815386167d_e_is(scratc515485325nd_rat) ).

% def_rt_is
fof(fact_def__rat,axiom,
    scratc515485325nd_rat = scratc408216958nd_ect(scratc406400774d_frac,scratc1333784130d_n_eq) ).

% def_rat
fof(fact_def__inf,axiom,
    scratc441984553nd_inf = scratc1782805115d_esti(scratc406400774d_frac) ).

% def_inf
fof(fact_def__d__477__v,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc13799086_477_v(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,Xa))) ).

% def_d_477_v
fof(fact_def__n__tf,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,Xa))),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,Xa))) ).

% def_n_tf
fof(fact_def__d__367__w,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc649711215_367_w(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1445449089367_vo(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,Xa))) ).

% def_d_367_w
fof(fact_def__d__367__vo,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc1445449089367_vo(X),Xa) = scratc441984551nd_ind(scratc482439305nd_nat,aa_TPT43085870d_bool(scratc1019149568ffprop(aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,X)))) ).

% def_d_367_vo
fof(fact_def__n__pf,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,X)))),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,Xa))) ).

% def_n_pf
fof(fact_def__lesseq,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,X),Xa))
    <=> pp(aa_bool_bool(scratc1202795191d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,X),Xa))) ) ).

% def_lesseq
fof(fact_def__moreq,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,X),Xa))
    <=> pp(aa_bool_bool(scratc1202795191d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,X),Xa))) ) ).

% def_moreq
fof(fact_def__lessf,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,X),Xa))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,X)))) ) ).

% def_lessf
fof(fact_def__moref,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,X),Xa))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,X)))) ) ).

% def_moref
fof(fact_def__n__eq,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,X),Xa))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,X)))) ) ).

% def_n_eq
fof(fact_def__den,axiom,
    scratc400086645nd_den = scratc1722379013econd1(scratc482439305nd_nat) ).

% def_den
fof(fact_def__num,axiom,
    scratc483751278nd_num = scratc1870636665first1(scratc482439305nd_nat) ).

% def_num
fof(fact_def__n__fr,axiom,
    scratc1333849730d_n_fr = scratc962587583_pair1(scratc482439305nd_nat) ).

% def_n_fr
fof(fact_def__frac,axiom,
    scratc406400774d_frac = aa_TPTP_ind_TPTP_ind(scratc1946932025r1type,scratc482439305nd_nat) ).

% def_frac
fof(fact_def__left__f2,axiom,
    ! [X,Xa,Xb,Xc] : aa_TPTP_ind_TPTP_ind(scratc322305355eft_f2(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc687885119d_left(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(scratc322305354eft_f1(X,Xa,Xb),Xc)) ).

% def_left_f2
fof(fact_def__left__f1,axiom,
    ! [X,Xa,Xb] : scratc322305354eft_f1(X,Xa,Xb) = scratc687885119d_left(X,Xb,Xa) ).

% def_left_f1
fof(fact_def__right,axiom,
    ! [X,Xa,Xb,Xc] : aa_TPTP_ind_TPTP_ind(scratc879300228_right(X,Xa,Xb),Xc) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,aa_TPTP_ind_TPTP_ind(scratc124367040_d_1to,Xb)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ak(Xa),Xb),Xc)) ).

% def_right
fof(fact_def__left,axiom,
    ! [X,Xa,Xb,Xc] : aa_TPTP_ind_TPTP_ind(scratc687885119d_left(X,Xa,Xb),Xc) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,aa_TPTP_ind_TPTP_ind(scratc124367040_d_1to,Xb)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_al(Xa),Xb),Xc)) ).

% def_left
fof(fact_def__right1to,axiom,
    ! [X,Xa,Xb] : aa_TPTP_ind_TPTP_ind(scratc1608132904ght1to(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1015265528d_outn(aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc441984561nd_inn(Xa),Xb))) ).

% def_right1to
fof(fact_def__left1to,axiom,
    ! [X,Xa,Xb] : aa_TPTP_ind_TPTP_ind(scratc569010349eft1to(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1015265528d_outn(X),aa_TPTP_ind_TPTP_ind(scratc441984561nd_inn(Xa),Xb)) ).

% def_left1to
fof(fact_def__xout,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc1548595950d_xout,X) = aa_TPTP_ind_TPTP_ind(scratc1015265528d_outn(X),X) ).

% def_xout
fof(fact_def__d__1out,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc22164393d_1out,X) = aa_TPTP_ind_TPTP_ind(scratc1015265528d_outn(X),scratc51547579nd_n_1) ).

% def_d_1out
fof(fact_def__pair__q0,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc25719473air_q0(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc962587583_pair1(X),aa_TPTP_ind_TPTP_ind(scratc1870636665first1(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1722379013econd1(X),Xa)) ).

% def_pair_q0
fof(fact_def__second1,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc1722379013econd1(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Xa),scratc1330438584d_n_2t) ).

% def_second1
fof(fact_def__first1,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc1870636665first1(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Xa),scratc1330372985d_n_1t) ).

% def_first1
fof(fact_def__pair1,axiom,
    ! [X,Xa,Xb] : aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc962587583_pair1(X),Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,aa_TPTP_ind_TPTP_ind(scratc124367040_d_1to,scratc51547580nd_n_2)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_am(X),Xa),Xb)) ).

% def_pair1
fof(fact_def__pair1type,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc1946932025r1type,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,aa_TPTP_ind_TPTP_ind(scratc124367040_d_1to,scratc51547580nd_n_2)),aTP_Lamm_an(X)) ).

% def_pair1type
fof(fact_def__pair__u0,axiom,
    scratc25981869air_u0 = scratc441984561nd_inn(scratc51547580nd_n_2) ).

% def_pair_u0
fof(fact_def__n__2t,axiom,
    scratc1330438584d_n_2t = aa_TPTP_ind_TPTP_ind(scratc1015265528d_outn(scratc51547580nd_n_2),scratc51547580nd_n_2) ).

% def_n_2t
fof(fact_def__n__1t,axiom,
    scratc1330372985d_n_1t = aa_TPTP_ind_TPTP_ind(scratc1015265528d_outn(scratc51547580nd_n_2),scratc51547579nd_n_1) ).

% def_n_1t
fof(fact_def__n__2,axiom,
    scratc51547580nd_n_2 = aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(scratc51547579nd_n_1),scratc51547579nd_n_1) ).

% def_n_2
fof(fact_def__singlet__u0,axiom,
    scratc534552911let_u0 = scratc441984561nd_inn(scratc51547579nd_n_1) ).

% def_singlet_u0
fof(fact_def__n__1o,axiom,
    scratc1330372980d_n_1o = aa_TPTP_ind_TPTP_ind(scratc1015265528d_outn(scratc51547579nd_n_1),scratc51547579nd_n_1) ).

% def_n_1o
fof(fact_def__inn,axiom,
    ! [X] : scratc441984561nd_inn(X) = scratc1815386162d_e_in(scratc482439305nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ao,X)) ).

% def_inn
fof(fact_def__outn,axiom,
    ! [X] : scratc1015265528d_outn(X) = scratc492012790nd_out(scratc482439305nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ao,X)) ).

% def_outn
fof(fact_def__d__1to,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc124367040_d_1to,X) = aa_fun1431113780TP_ind(scratc404274226_d_Sep(scratc482439305nd_nat),aa_TPT43085870d_bool(aTP_Lamm_ao,X)) ).

% def_d_1to
fof(fact_def__n__mn,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc1334308919d_n_mn(X),Xa) = scratc441984551nd_ind(scratc482439305nd_nat,aa_TPT43085870d_bool(scratc1019149568ffprop(X),Xa)) ).

% def_n_mn
fof(fact_def__d__431__prop1,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1861455336_prop1(X),Xa),Xb))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(X),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Xa),Xb)))) ) ).

% def_d_431_prop1
fof(fact_def__d__430__prop1,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1273093161_prop1(X),Xa),Xb))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(X),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Xa),Xb))),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(X),Xb)))) ) ).

% def_d_430_prop1
fof(fact_def__d__429__prop1,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879189471_prop1,X),Xa))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Xa),X))) ) ).

% def_d_429_prop1
fof(fact_def__n__ts,axiom,
    ! [X] : scratc1334768117d_n_ts(X) = aa_TPT1424761345TP_ind(scratc468400007bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1060317390_times,X)) ).

% def_n_ts
fof(fact_def__times,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc1060317390_times,X) = scratc441984551nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,scratc482439305nd_nat),aTP_Lamm_ap),aa_TPT43085870d_bool(scratc290827297_prop2,X)) ).

% def_times
fof(fact_def__d__428__g,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc1539015769_428_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,scratc482439305nd_nat),aTP_Lamm_aq(X)) ).

% def_d_428_g
fof(fact_def__d__428__id,axiom,
    scratc394302153428_id = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,scratc482439305nd_nat),aTP_Lamm_ar) ).

% def_d_428_id
fof(fact_def__d__428__prop4,axiom,
    ! [X] :
      ( pp(aa_TPTP_ind_bool(scratc290827299_prop4,X))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,scratc482439305nd_nat),aTP_Lamm_ap)),aa_TPT43085870d_bool(scratc290827297_prop2,X))) ) ).

% def_d_428_prop4
fof(fact_def__d__428__prop2,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc290827297_prop2,X),Xa))
    <=> pp(scratc520525675_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Xa),scratc51547579nd_n_1)),X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc290827296_prop1,X),Xa))) ) ).

% def_d_428_prop2
fof(fact_def__d__428__prop1,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc290827296_prop1,X),Xa))
    <=> pp(aa_fun171081125l_bool(scratc2092983147_n_all,aa_TPT43085870d_bool(aTP_Lamm_as(X),Xa))) ) ).

% def_d_428_prop1
fof(fact_def__min,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(scratc474702586nd_min(X),Xa))
    <=> pp(scratc520525675_d_and(aa_TPTP_ind_bool(scratc1334243308d_n_lb(X),Xa),aa_TPTP_ind_bool(X,Xa))) ) ).

% def_min
fof(fact_def__n__lb,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(scratc1334243308d_n_lb(X),Xa))
    <=> pp(aa_fun171081125l_bool(scratc2092983147_n_all,aa_TPT43085870d_bool(scratc998417137lbprop(X),Xa))) ) ).

% def_n_lb
fof(fact_def__lbprop,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc998417137lbprop(X),Xa),Xb))
    <=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc441918964nd_imp,aa_TPTP_ind_bool(X,Xb)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Xa),Xb))) ) ).

% def_lbprop
fof(fact_def__lessis,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,X),Xa))
    <=> pp(aa_bool_bool(scratc1202795191d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,X),Xa))) ) ).

% def_lessis
fof(fact_def__moreis,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,X),Xa))
    <=> pp(aa_bool_bool(scratc1202795191d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,X),Xa))) ) ).

% def_moreis
fof(fact_def__d__29__prop1,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc980344891_prop1,X),Xa))
    <=> pp(scratc491815928nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,X),Xa))) ) ).

% def_d_29_prop1
fof(fact_def__iii,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,X),Xa))
    <=> pp(aa_fun171081125l_bool(scratc1572426730n_some,aa_TPT43085870d_bool(scratc1019149568ffprop(Xa),X))) ) ).

% def_iii
fof(fact_def__d__29__ii,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,X),Xa))
    <=> pp(aa_fun171081125l_bool(scratc1572426730n_some,aa_TPT43085870d_bool(scratc1019149568ffprop(X),Xa))) ) ).

% def_d_29_ii
fof(fact_def__diffprop,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1019149568ffprop(X),Xa),Xb))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Xa),Xb))) ) ).

% def_diffprop
fof(fact_def__d__28__prop1,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc391982716_prop1(X),Xa),Xb))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(X),Xb))) ) ).

% def_d_28_prop1
fof(fact_def__d__27__prop1,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1951104189_prop1,X),Xa))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(X),Xa))) ) ).

% def_d_27_prop1
fof(fact_def__d__26__prop1,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1362742014_prop1,X),Xa))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Xa),X))) ) ).

% def_d_26_prop1
fof(fact_def__d__25__prop1,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc774379839_prop1(X),Xa),Xb))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Xa),Xb)))) ) ).

% def_d_25_prop1
fof(fact_def__n__pl,axiom,
    ! [X] : scratc1334505714d_n_pl(X) = aa_TPT1424761345TP_ind(scratc468400007bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1721564786d_plus,X)) ).

% def_n_pl
fof(fact_def__plus,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc1721564786d_plus,X) = scratc441984551nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,scratc482439305nd_nat),aTP_Lamm_ap),aa_TPT43085870d_bool(scratc186017665_prop2,X)) ).

% def_plus
fof(fact_def__d__24__g,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc114532281d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,scratc482439305nd_nat),aTP_Lamm_at(X)) ).

% def_d_24_g
fof(fact_def__prop4,axiom,
    ! [X] :
      ( pp(aa_TPTP_ind_bool(scratc1397105913_prop4,X))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,scratc482439305nd_nat),aTP_Lamm_ap)),aa_TPT43085870d_bool(scratc186017665_prop2,X))) ) ).

% def_prop4
fof(fact_def__prop3,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1397105912_prop3(X),Xa),Xb))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Xa),Xb))) ) ).

% def_prop3
fof(fact_def__d__24__prop2,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc186017665_prop2,X),Xa))
    <=> pp(scratc520525675_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Xa),scratc51547579nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,X)),aa_TPTP_ind_bool(scratc186017664_prop1,Xa))) ) ).

% def_d_24_prop2
fof(fact_def__d__24__prop1,axiom,
    ! [X] :
      ( pp(aa_TPTP_ind_bool(scratc186017664_prop1,X))
    <=> pp(aa_fun171081125l_bool(scratc2092983147_n_all,aa_TPT43085870d_bool(aTP_Lamm_au,X))) ) ).

% def_d_24_prop1
fof(fact_def__d__23__prop1,axiom,
    ! [X] :
      ( pp(aa_TPTP_ind_bool(scratc1745139137_prop1,X))
    <=> pp(aa_bool_bool(scratc1202795191d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,X),scratc51547579nd_n_1)),aa_fun171081125l_bool(scratc1572426730n_some,aa_TPT43085870d_bool(aTP_Lamm_av,X)))) ) ).

% def_d_23_prop1
fof(fact_def__d__22__prop1,axiom,
    ! [X] :
      ( pp(aa_TPTP_ind_bool(scratc1156776962_prop1,X))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,X)),X)) ) ).

% def_d_22_prop1
fof(fact_def__i1__s,axiom,
    scratc530747251d_i1_s = scratc404274226_d_Sep(scratc482439305nd_nat) ).

% def_i1_s
fof(fact_def__cond2,axiom,
    ! [X] :
      ( pp(aa_TPTP_ind_bool(scratc1411829048_cond2,X))
    <=> pp(aa_fun171081125l_bool(scratc2092983147_n_all,aa_TPT43085870d_bool(aTP_Lamm_aw,X))) ) ).

% def_cond2
fof(fact_def__cond1,axiom,
    scratc1411829047_cond1 = aa_TPT43085870d_bool(scratc1334046523d_n_in,scratc51547579nd_n_1) ).

% def_cond1
fof(fact_def__n__1,axiom,
    scratc51547579nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,scratc1884736269ptyset) ).

% def_n_1
fof(fact_def__n__one,axiom,
    scratc61291760_n_one = scratc491553582nd_one(scratc482439305nd_nat) ).

% def_n_one
fof(fact_def__n__all,axiom,
    scratc2092983147_n_all = scratc375761321nd_all(scratc482439305nd_nat) ).

% def_n_all
fof(fact_def__n__some,axiom,
    scratc1572426730n_some = scratc828602088l_some(scratc482439305nd_nat) ).

% def_n_some
fof(fact_def__n__in,axiom,
    scratc1334046523d_n_in = scratc1782805115d_esti(scratc482439305nd_nat) ).

% def_n_in
fof(fact_def__nis,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,X),Xa))
    <=> pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,X),Xa))) ) ).

% def_nis
fof(fact_def__n__is,axiom,
    scratc1334046528d_n_is = scratc1815386167d_e_is(scratc482439305nd_nat) ).

% def_n_is
fof(fact_def__nat,axiom,
    scratc482439305nd_nat = aa_fun1431113780TP_ind(scratc404274226_d_Sep(scratc566367529_omega),aTP_Lamm_ax) ).

% def_nat
fof(fact_def__indeq2,axiom,
    ! [X,Xa,Xb,Xc,Xd] : scratc1935368447indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc943627251_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc928173693d_11_i(X,Xa,Xb),Xc),Xd)) ).

% def_indeq2
fof(fact_def__d__11__i,axiom,
    ! [X,Xa,Xb] : scratc928173693d_11_i(X,Xa,Xb) = scratc943627251_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,X),aTP_Lamm_an(Xb))) ).

% def_d_11_i
fof(fact_def__fixfu2,axiom,
    ! [X,Xa,Xb,Xc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc4374950fixfu2(X,Xa),Xb),Xc))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_bc(X),Xa),Xb),Xc))) ) ).

% def_fixfu2
fof(fact_def__indeq,axiom,
    ! [X,Xa,Xb,Xc,Xd] : aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc943627251_indeq(X,Xa,Xb),Xc),Xd) = scratc441984551nd_ind(Xb,aa_TPT43085870d_bool(scratc1397105911_prop2(X,Xa,Xb,Xc),Xd)) ).

% def_indeq
fof(fact_def__prop2,axiom,
    ! [X,Xa,Xb,Xc,Xd,Xe] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1397105911_prop2(X,Xa,Xb,Xc),Xd),Xe))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(X),aa_TPT43085870d_bool(scratc733340291_prop1(X,Xa,Xb,Xc,Xd),Xe))) ) ).

% def_prop2
fof(fact_def__d__10__prop1,axiom,
    ! [X,Xa,Xb,Xc,Xd,Xe,Xf] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc733340291_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf))
    <=> pp(scratc520525675_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1782805115d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc691943104_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Xc),Xf)),Xe))) ) ).

% def_d_10_prop1
fof(fact_def__fixfu,axiom,
    ! [X,Xa,Xb,Xc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc229745036_fixfu(X,Xa),Xb),Xc))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_be(X),Xa),Xb),Xc))) ) ).

% def_fixfu
fof(fact_def__ecect,axiom,
    ! [X,Xa] : scratc691943104_ecect(X,Xa) = scratc1815386162d_e_in(aa_TPTP_ind_TPTP_ind(scratc1268198477_power,X),scratc765648451d_anec(X,Xa)) ).

% def_ecect
fof(fact_def__ectelt,axiom,
    ! [X,Xa,Xb] : aa_TPTP_ind_TPTP_ind(scratc401199599ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc516401476ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc692533495_ecelt(X,Xa),Xb)) ).

% def_ectelt
fof(fact_def__ectset,axiom,
    ! [X,Xa] : scratc516401476ectset(X,Xa) = scratc492012790nd_out(aa_TPTP_ind_TPTP_ind(scratc1268198477_power,X),scratc765648451d_anec(X,Xa)) ).

% def_ectset
fof(fact_def__ect,axiom,
    ! [X,Xa] : scratc408216958nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc404274226_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1268198477_power,X)),scratc765648451d_anec(X,Xa)) ).

% def_ect
fof(fact_def__anec,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(scratc765648451d_anec(X,Xa),Xb))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(X),aa_TPT43085870d_bool(scratc408216954nd_ecp(X,Xa),Xb))) ) ).

% def_anec
fof(fact_def__ecp,axiom,
    ! [X,Xa,Xb,Xc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc408216954nd_ecp(X,Xa),Xb),Xc))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(aa_TPTP_ind_TPTP_ind(scratc1268198477_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc692533495_ecelt(X,Xa),Xc))) ) ).

% def_ecp
fof(fact_def__ecelt,axiom,
    ! [X,Xa,Xb] : aa_TPTP_ind_TPTP_ind(scratc692533495_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc404274226_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb)) ).

% def_ecelt
fof(fact_def__unmore,axiom,
    ! [X,Xa,Xb] : aa_TPTP_ind_TPTP_ind(scratc622518822unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc404274226_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bg(X),Xa),Xb)) ).

% def_unmore
fof(fact_def__nissetprop,axiom,
    ! [X,Xa,Xb,Xc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc745198213etprop(X,Xa),Xb),Xc))
    <=> pp(scratc520525675_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1782805115d_esti(X),Xc),Xa),scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1782805115d_esti(X),Xc),Xb)))) ) ).

% def_nissetprop
fof(fact_def__st__disj,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1429672309t_disj(X),Xa),Xb))
    <=> pp(aa_fun171081125l_bool(scratc375761321nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bh(X),Xa),Xb))) ) ).

% def_st_disj
fof(fact_def__incl,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc567763910d_incl(X),Xa),Xb))
    <=> pp(aa_fun171081125l_bool(scratc375761321nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bi(X),Xa),Xb))) ) ).

% def_incl
fof(fact_def__nonempty,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc22847608nempty,X),Xa))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(X),aa_TPT43085870d_bool(aTP_Lamm_bj(X),Xa))) ) ).

% def_nonempty
fof(fact_def__empty,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2147355893_empty,X),Xa))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X)),scratc483357685nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_bj(X),Xa)))) ) ).

% def_empty
fof(fact_def__esti,axiom,
    ! [X] : scratc1782805115d_esti(X) = scratc468924797bnd_in ).

% def_esti
fof(fact_def__r__ec,axiom,
    ! [X,Xa] :
      ( scratc1597073976d_r_ec(X,Xa)
    <=> ( pp(X)
       => pp(scratc627990855_d_not(Xa)) ) ) ).

% def_r_ec
fof(fact_def__changef,axiom,
    ! [X,Xa,Xb,Xc,Xd] : aa_TPTP_ind_TPTP_ind(scratc212773854hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_bk(X),Xb),Xc),Xd)) ).

% def_changef
fof(fact_def__wissel,axiom,
    ! [X,Xa,Xb] : aa_TPTP_ind_TPTP_ind(scratc384428273wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X),scratc684567900sel_wb(X,Xa,Xb)) ).

% def_wissel
fof(fact_def__wissel__wb,axiom,
    ! [X,Xa,Xb,Xc] : aa_TPTP_ind_TPTP_ind(scratc684567900sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc442378146nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc684567899sel_wa(X,Xa,Xb),Xc)) ).

% def_wissel_wb
fof(fact_def__wissel__wa,axiom,
    ! [X,Xa,Xb,Xc] : aa_TPTP_ind_TPTP_ind(scratc684567899sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc442378146nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(X),Xc),Xa),X,Xb),Xc) ).

% def_wissel_wa
fof(fact_def__ite,axiom,
    ! [X,Xa,Xb,Xc] : aa_TPTP_ind_TPTP_ind(scratc442378146nd_ite(X,Xa,Xb),Xc) = scratc441984551nd_ind(Xa,aa_TPT43085870d_bool(scratc1397105910_prop1(X,Xa,Xb),Xc)) ).

% def_ite
fof(fact_def__prop1,axiom,
    ! [X,Xa,Xb,Xc,Xd] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1397105910_prop1(X,Xa,Xb),Xc),Xd))
    <=> pp(scratc520525675_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc441918964nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc441918964nd_imp,scratc627990855_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Xa),Xd),Xc)))) ) ).

% def_prop1
fof(fact_def__second,axiom,
    ! [X,Xa] : scratc1143644204second(X,Xa) = scratc1396712316_proj1 ).

% def_second
fof(fact_def__first,axiom,
    ! [X,Xa] : scratc181028792_first(X,Xa) = scratc1396712315_proj0 ).

% def_first
fof(fact_def__d__pair,axiom,
    ! [X,Xa] : scratc1838069414d_pair(X,Xa) = scratc1629901042d_pair ).

% def_d_pair
fof(fact_def__out,axiom,
    ! [X,Xa] : scratc492012790nd_out(X,Xa) = scratc1939643266d_soft(aa_fun1431113780TP_ind(scratc404274226_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,aa_fun1431113780TP_ind(scratc404274226_d_Sep(X),Xa)),scratc1815386162d_e_in(X,Xa))) ).

% def_out
fof(fact_def__e__in,axiom,
    ! [X,Xa,Xb] :
      ( gg_TPTP_ind(Xb)
     => aa_TPTP_ind_TPTP_ind(scratc1815386162d_e_in(X,Xa),Xb) = Xb ) ).

% def_e_in
fof(fact_def__inj__h,axiom,
    ! [X,Xa,Xb,Xc,Xd] : aa_TPTP_ind_TPTP_ind(scratc125690939_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_bl(Xc),Xd)) ).

% def_inj_h
fof(fact_def__invf,axiom,
    ! [X,Xa,Xb] : aa_TPTP_ind_TPTP_ind(scratc569010285d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,Xa),scratc1939643266d_soft(X,Xa,Xb)) ).

% def_invf
fof(fact_def__bijective,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936364301ective(X),Xa),Xb))
    <=> pp(scratc520525675_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1752645071ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc280943508ective(X),Xa),Xb))) ) ).

% def_bijective
fof(fact_def__surjective,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc280943508ective(X),Xa),Xb))
    <=> pp(aa_fun171081125l_bool(scratc375761321nd_all(Xa),aa_TPT43085870d_bool(scratc138386723_image(X,Xa),Xb))) ) ).

% def_surjective
fof(fact_def__inverse,axiom,
    ! [X,Xa,Xb] : aa_TPTP_ind_TPTP_ind(scratc198814904nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_bm(X),Xa),Xb)) ).

% def_inverse
fof(fact_def__soft,axiom,
    ! [X,Xa,Xb,Xc] : aa_TPTP_ind_TPTP_ind(scratc1939643266d_soft(X,Xa,Xb),Xc) = scratc441984551nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bn(Xa),Xb),Xc)) ).

% def_soft
fof(fact_def__tofs,axiom,
    ! [X,Xa] : scratc572746816d_tofs(X,Xa) = scratc468400007bnd_ap ).

% def_tofs
fof(fact_def__image,axiom,
    ! [X,Xa,Xb,Xc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc138386723_image(X,Xa),Xb),Xc))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bn(Xa),Xb),Xc))) ) ).

% def_image
fof(fact_def__injective,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1752645071ective(X),Xa),Xb))
    <=> pp(aa_fun171081125l_bool(scratc375761321nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(X),Xa),Xb))) ) ).

% def_injective
fof(fact_def__ind,axiom,
    ! [X,Xa] : scratc441984551nd_ind(X,Xa) = scratc409069744nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bq(X),Xa)) ).

% def_ind
fof(fact_def__one,axiom,
    ! [X,Xa] :
      ( pp(aa_fun171081125l_bool(scratc491553582nd_one(X),Xa))
    <=> pp(scratc520525675_d_and(scratc1875410914_amone(X,Xa),aa_fun171081125l_bool(scratc828602088l_some(X),Xa))) ) ).

% def_one
fof(fact_def__amone,axiom,
    ! [X,Xa] :
      ( pp(scratc1875410914_amone(X,Xa))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X)),aa_fun1584354236d_bool(aTP_Lamm_bs(X),Xa))) ) ).

% def_amone
fof(fact_def__e__is,axiom,
    ! [X] : scratc1815386167d_e_is(X) = fequal_TPTP_ind ).

% def_e_is
fof(fact_def__orec3,axiom,
    ! [X,Xa,Xb] :
      ( scratc174073786_orec3(X,Xa,Xb)
    <=> pp(scratc520525675_d_and(scratc491815928nd_or3(X,Xa,Xb),scratc408216893nd_ec3(X,Xa,Xb))) ) ).

% def_orec3
fof(fact_def__ec3,axiom,
    ! [X,Xa,Xb] :
      ( pp(scratc408216893nd_ec3(X,Xa,Xb))
    <=> scratc765582804d_and3(scratc1202139186d_l_ec(X,Xa),scratc1202139186d_l_ec(Xa,Xb),scratc1202139186d_l_ec(Xb,X)) ) ).

% def_ec3
fof(fact_def__and3,axiom,
    ! [X,Xa,Xb] :
      ( scratc765582804d_and3(X,Xa,Xb)
    <=> pp(scratc520525675_d_and(X,scratc520525675_d_and(Xa,Xb))) ) ).

% def_and3
fof(fact_def__or3,axiom,
    ! [X,Xa,Xb] :
      ( pp(scratc491815928nd_or3(X,Xa,Xb))
    <=> pp(aa_bool_bool(scratc1202795191d_l_or(X),aa_bool_bool(scratc1202795191d_l_or(Xa),Xb))) ) ).

% def_or3
fof(fact_def__l__some,axiom,
    ! [X,Xa] :
      ( pp(aa_fun171081125l_bool(scratc828602088l_some(X),Xa))
    <=> pp(scratc627990855_d_not(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X)),scratc483357685nd_non(X,Xa)))) ) ).

% def_l_some
fof(fact_def__non,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(scratc483357685nd_non(X,Xa),Xb))
    <=> pp(scratc627990855_d_not(aa_TPTP_ind_bool(Xa,Xb))) ) ).

% def_non
fof(fact_def__all,axiom,
    ! [X] : scratc375761321nd_all(X) = scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X)) ).

% def_all
fof(fact_def__l__iff,axiom,
    ! [X,Xa] :
      ( scratc1414667125_l_iff(X,Xa)
    <=> pp(scratc520525675_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc441918964nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc441918964nd_imp,Xa),X))) ) ).

% def_l_iff
fof(fact_def__orec,axiom,
    ! [X,Xa] :
      ( scratc989497017d_orec(X,Xa)
    <=> pp(scratc520525675_d_and(aa_bool_bool(scratc1202795191d_l_or(X),Xa),scratc1202139186d_l_ec(X,Xa))) ) ).

% def_orec
fof(fact_def__l__or,axiom,
    ! [X] : scratc1202795191d_l_or(X) = aa_boo1142376798l_bool(scratc441918964nd_imp,scratc627990855_d_not(X)) ).

% def_l_or
fof(fact_def__d__and,axiom,
    ! [X,Xa] :
      ( pp(scratc520525675_d_and(X,Xa))
    <=> pp(scratc627990855_d_not(scratc1202139186d_l_ec(X,Xa))) ) ).

% def_d_and
fof(fact_def__l__ec,axiom,
    ! [X,Xa] :
      ( pp(scratc1202139186d_l_ec(X,Xa))
    <=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc441918964nd_imp,X),scratc627990855_d_not(Xa))) ) ).

% def_l_ec
fof(fact_def__obvious,axiom,
    ( scratc1063897551bvious
  <=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc441918964nd_imp,fFalse),fFalse)) ) ).

% def_obvious
fof(fact_def__wel,axiom,
    ! [X] :
      ( scratc557055238nd_wel(X)
    <=> pp(scratc627990855_d_not(scratc627990855_d_not(X))) ) ).

% def_wel
fof(fact_def__d__not,axiom,
    ! [X] :
      ( pp(scratc627990855_d_not(X))
    <=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc441918964nd_imp,X),fFalse)) ) ).

% def_d_not
fof(fact_def__imp,axiom,
    scratc441918964nd_imp = fimplies ).

% def_imp
fof(fact_def__d__Pi,axiom,
    ! [X,Xa] : aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc404274226_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1268198477_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X),aTP_Lamm_bt(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bu(X),Xa)) ).

% def_d_Pi
fof(fact_def__pair__p,axiom,
    ! [X] :
      ( gg_TPTP_ind(X)
     => ( pp(aa_TPTP_ind_bool(scratc657317182pair_p,X))
      <=> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1629901042d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,X),scratc1884736269ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,scratc1884736269ptyset))) = X ) ) ).

% def_pair_p
fof(fact_def__ap,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1308658787eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bv,Xa)),scratc1396712316_proj1) ).

% def_ap
fof(fact_def__setprod,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc434490305etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X),aTP_Lamm_an(Xa)) ).

% def_setprod
fof(fact_def__d__Sigma,axiom,
    ! [X,Xa] : aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc102693173munion,X),aTP_Lamm_bw(Xa)) ).

% def_d_Sigma
fof(fact_def__proj1,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc1396712316_proj1,X) = aa_fun277296641TP_ind(scratc1308658787eplSep(X,aTP_Lamm_bx),scratc421387621_d_Unj) ).

% def_proj1
fof(fact_def__proj0,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc1396712315_proj0,X) = aa_fun277296641TP_ind(scratc1308658787eplSep(X,aTP_Lamm_by),scratc421387621_d_Unj) ).

% def_proj0
fof(fact_def__pair,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1629901042d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1096550272nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1077096999d_repl,X),scratc1567404823d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1077096999d_repl,Xa),scratc1567404824d_Inj1)) ).

% def_pair
fof(fact_def__d__Unj,axiom,
    scratc421387621_d_Unj = scratc1036422367In_rec(aTP_Lamm_bz) ).

% def_d_Unj
fof(fact_def__d__Inj0,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc1567404823d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1077096999d_repl,X),scratc1567404824d_Inj1) ).

% def_d_Inj0
fof(fact_def__d__Inj1,axiom,
    scratc1567404824d_Inj1 = scratc1036422367In_rec(aTP_Lamm_ca) ).

% def_d_Inj1
fof(fact_def__omega,axiom,
    scratc566367529_omega = aa_fun1431113780TP_ind(scratc404274226_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1852771061univof,scratc1884736269ptyset)),scratc1419714279_nat_p) ).

% def_omega
fof(fact_def__nat__p,axiom,
    ! [X] :
      ( pp(aa_TPTP_ind_bool(scratc1419714279_nat_p,X))
    <=> ! [X1] :
          ( pp(aa_TPTP_ind_bool(X1,scratc1884736269ptyset))
         => ( ! [X2] :
                ( gg_TPTP_ind(X2)
               => ( pp(aa_TPTP_ind_bool(X1,X2))
                 => pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,X2))) ) )
           => pp(aa_TPTP_ind_bool(X1,X)) ) ) ) ).

% def_nat_p
fof(fact_def__ordsucc,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1096550272nunion(X),aa_TPTP_ind_TPTP_ind(scratc742297147d_Sing,X)) ).

% def_ordsucc
fof(fact_def__d__In__rec,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc1036422367In_rec(X),Xa) = scratc409069744nd_eps(aa_TPT43085870d_bool(scratc1735992040_rec_G(X),Xa)) ).

% def_d_In_rec
fof(fact_def__d__In__rec__G,axiom,
    ! [X,Xa,Xb] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1735992040_rec_G(X),Xa),Xb))
    <=> ! [X3] :
          ( ! [X4,X5] :
              ( gg_TPTP_ind(X4)
             => ( ! [X6] :
                    ( gg_TPTP_ind(X6)
                   => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X6),X4))
                     => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X6),aa_TPTP_ind_TPTP_ind(X5,X6))) ) )
               => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X4),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(X,X4),X5))) ) )
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,Xa),Xb)) ) ) ).

% def_d_In_rec_G
fof(fact_def__setminus,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc1012835814tminus(X),Xa) = aa_fun1431113780TP_ind(scratc404274226_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_cb,Xa)) ).

% def_setminus
fof(fact_def__d__ReplSep,axiom,
    ! [X,Xa] : scratc1308658787eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc1077096999d_repl,aa_fun1431113780TP_ind(scratc404274226_d_Sep(X),Xa)) ).

% def_d_ReplSep
fof(fact_def__d__Sep,axiom,
    ! [X,Xa] : aa_fun1431113780TP_ind(scratc404274226_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc468924797bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1077096999d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_cc(X),Xa))),scratc1884736269ptyset) ).

% def_d_Sep
fof(fact_def__famunion,axiom,
    ! [X,Xa] : aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc102693173munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1775460343_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1077096999d_repl,X),Xa)) ).

% def_famunion
fof(fact_def__binunion,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc1096550272nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1775460343_union,aa_TPTP_ind_TPTP_ind(scratc1743360835_UPair(X),Xa)) ).

% def_binunion
fof(fact_def__d__Sing,axiom,
    ! [X] : aa_TPTP_ind_TPTP_ind(scratc742297147d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc1743360835_UPair(X),X) ).

% def_d_Sing
fof(fact_def__d__UPair,axiom,
    ! [X,Xa] : aa_TPTP_ind_TPTP_ind(scratc1743360835_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1077096999d_repl,aa_TPTP_ind_TPTP_ind(scratc1268198477_power,aa_TPTP_ind_TPTP_ind(scratc1268198477_power,scratc1884736269ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_cd(X),Xa)) ).

% def_d_UPair
fof(fact_def__nIn,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc480864923nd_nIn,X),Xa))
    <=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X),Xa)) ) ).

% def_nIn
fof(fact_def__if,axiom,
    ! [X,Xa,Xb] : aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(X,Xa),Xb) = scratc409069744nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ce(X),Xa),Xb)) ).

% def_if
fof(fact_def__d__ZF__closed,axiom,
    ! [X] :
      ( pp(aa_TPTP_ind_bool(scratc2034515940closed,X))
    <=> ( pp(aa_TPTP_ind_bool(scratc356465583closed,X))
        & pp(aa_TPTP_ind_bool(scratc521198597closed,X))
        & pp(aa_TPTP_ind_bool(scratc387744903closed,X)) ) ) ).

% def_d_ZF_closed
fof(fact_def__d__Repl__closed,axiom,
    ! [X] :
      ( pp(aa_TPTP_ind_bool(scratc387744903closed,X))
    <=> ! [X1] :
          ( gg_TPTP_ind(X1)
         => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X1),X))
           => ! [X2] :
                ( ! [X3] :
                    ( gg_TPTP_ind(X3)
                   => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X3),X1))
                     => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X)) ) )
               => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1077096999d_repl,X1),X2)),X)) ) ) ) ) ).

% def_d_Repl_closed
fof(fact_def__d__Power__closed,axiom,
    ! [X] :
      ( pp(aa_TPTP_ind_bool(scratc521198597closed,X))
    <=> ! [X1] :
          ( gg_TPTP_ind(X1)
         => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X1),X))
           => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_TPTP_ind_TPTP_ind(scratc1268198477_power,X1)),X)) ) ) ) ).

% def_d_Power_closed
fof(fact_def__d__Union__closed,axiom,
    ! [X] :
      ( pp(aa_TPTP_ind_bool(scratc356465583closed,X))
    <=> ! [X1] :
          ( gg_TPTP_ind(X1)
         => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X1),X))
           => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_TPTP_ind_TPTP_ind(scratc1775460343_union,X1)),X)) ) ) ) ).

% def_d_Union_closed
fof(fact_def__d__Subq,axiom,
    ! [X,Xa] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc840648029d_Subq,X),Xa))
    <=> ! [X2] :
          ( gg_TPTP_ind(X2)
         => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X2),X))
           => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X2),Xa)) ) ) ) ).

% def_d_Subq
fof(fact_def__all__of,axiom,
    ! [X,Xa] :
      ( pp(aa_fun171081125l_bool(scratc1717941280all_of(X),Xa))
    <=> ! [X2] :
          ( gg_TPTP_ind(X2)
         => ( scratc1533070073_is_of(X2,X)
           => pp(aa_TPTP_ind_bool(Xa,X2)) ) ) ) ).

% def_all_of
fof(fact_def__is__of,axiom,
    ! [X,Xa] :
      ( scratc1533070073_is_of(X,Xa)
    <=> pp(aa_TPTP_ind_bool(Xa,X)) ) ).

% def_is_of
fof(fact_satz99b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_ci)) ).

% satz99b
fof(fact_satz99a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_cm)) ).

% satz99a
fof(fact_satz98a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_cq)) ).

% satz98a
fof(fact_satz98,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_cu)) ).

% satz98
fof(fact_satz97c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_cx)) ).

% satz97c
fof(fact_satz97b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_da)) ).

% satz97b
fof(fact_satz97a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_dd)) ).

% satz97a
fof(fact_satz96f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_dg)) ).

% satz96f
fof(fact_satz96e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_dj)) ).

% satz96e
fof(fact_satz96d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_dm)) ).

% satz96d
fof(fact_satz96c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_dp)) ).

% satz96c
fof(fact_satz96b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_ds)) ).

% satz96b
fof(fact_satz95,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_dv)) ).

% satz95
fof(fact_satz94a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_dx)) ).

% satz94a
fof(fact_satz94,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_dz)) ).

% satz94
fof(fact_satz93,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_ec)) ).

% satz93
fof(fact_satz92,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_ee)) ).

% satz92
fof(fact_satz91,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_eh)) ).

% satz91
fof(fact_satz90,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_ej)) ).

% satz90
fof(fact_satz89,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_el)) ).

% satz89
fof(fact_satz88,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_eo)) ).

% satz88
fof(fact_satz87d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_er)) ).

% satz87d
fof(fact_satz87c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_eu)) ).

% satz87c
fof(fact_satz87b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_ex)) ).

% satz87b
fof(fact_satz87a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_fa)) ).

% satz87a
fof(fact_satz86,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_fd)) ).

% satz86
fof(fact_satz85,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_ff)) ).

% satz85
fof(fact_satz84,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_fh)) ).

% satz84
fof(fact_satz81k,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_fj)) ).

% satz81k
fof(fact_satz81j,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_fl)) ).

% satz81j
fof(fact_satz81h,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_fn)) ).

% satz81h
fof(fact_satz81g,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_fp)) ).

% satz81g
fof(fact_satz81f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_fr)) ).

% satz81f
fof(fact_satz81e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_ft)) ).

% satz81e
fof(fact_satz81d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_fv)) ).

% satz81d
fof(fact_satz81c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_fx)) ).

% satz81c
fof(fact_satz83,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_fz)) ).

% satz83
fof(fact_satz82,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_gb)) ).

% satz82
fof(fact_satz81b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_gd)) ).

% satz81b
fof(fact_satz81a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_gf)) ).

% satz81a
fof(fact_satz81,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_gh)) ).

% satz81
fof(fact_satz80,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_gk)) ).

% satz80
fof(fact_satz79,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_gm)) ).

% satz79
fof(fact_satz78,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_gn)) ).

% satz78
fof(fact_satz77a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_gr)) ).

% satz77a
fof(fact_satz77b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_gv)) ).

% satz77b
fof(fact_satz76a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_gz)) ).

% satz76a
fof(fact_satz76,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_hd)) ).

% satz76
fof(fact_satz75d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_hh)) ).

% satz75d
fof(fact_satz75c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_hl)) ).

% satz75c
fof(fact_satz75b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_hp)) ).

% satz75b
fof(fact_satz75a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ht)) ).

% satz75a
fof(fact_satz74a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_hx)) ).

% satz74a
fof(fact_satz74,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ib)) ).

% satz74
fof(fact_satz73f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ie)) ).

% satz73f
fof(fact_satz73e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ih)) ).

% satz73e
fof(fact_satz73d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ik)) ).

% satz73d
fof(fact_satz73c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_in)) ).

% satz73c
fof(fact_satz73b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_iq)) ).

% satz73b
fof(fact_satz73a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_it)) ).

% satz73a
fof(fact_satz72k,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ix)) ).

% satz72k
fof(fact_satz72j,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_jb)) ).

% satz72j
fof(fact_satz72h,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_jf)) ).

% satz72h
fof(fact_satz72g,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_jj)) ).

% satz72g
fof(fact_satz72f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_jm)) ).

% satz72f
fof(fact_satz72e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_jp)) ).

% satz72e
fof(fact_satz72d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_js)) ).

% satz72d
fof(fact_satz72c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_jv)) ).

% satz72c
fof(fact_satz72b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_jy)) ).

% satz72b
fof(fact_satz72a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_kb)) ).

% satz72a
fof(fact_satz71,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ke)) ).

% satz71
fof(fact_satz70,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_kh)) ).

% satz70
fof(fact_satz69,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_kj)) ).

% satz69
fof(fact_satz68,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_kn)) ).

% satz68
fof(fact_satz67e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_kq)) ).

% satz67e
fof(fact_satz67d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ks)) ).

% satz67d
fof(fact_k__satz67c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ku)) ).

% k_satz67c
fof(fact_satz67a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_kx)) ).

% satz67a
fof(fact_satz67b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_lb)) ).

% satz67b
fof(fact_satz66a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_lf)) ).

% satz66a
fof(fact_satz66,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_lj)) ).

% satz66
fof(fact_satz65d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ln)) ).

% satz65d
fof(fact_satz65c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_lr)) ).

% satz65c
fof(fact_satz65b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_lv)) ).

% satz65b
fof(fact_satz65a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_lz)) ).

% satz65a
fof(fact_satz64a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_md)) ).

% satz64a
fof(fact_satz64,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_mh)) ).

% satz64
fof(fact_satz63f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_mk)) ).

% satz63f
fof(fact_satz63e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_mn)) ).

% satz63e
fof(fact_satz63d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_mq)) ).

% satz63d
fof(fact_satz63c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_mt)) ).

% satz63c
fof(fact_satz63b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_mw)) ).

% satz63b
fof(fact_satz63a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_mz)) ).

% satz63a
fof(fact_satz62k,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_nd)) ).

% satz62k
fof(fact_satz62j,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_nh)) ).

% satz62j
fof(fact_satz62h,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_nl)) ).

% satz62h
fof(fact_satz62g,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_np)) ).

% satz62g
fof(fact_satz62f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ns)) ).

% satz62f
fof(fact_satz62e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_nv)) ).

% satz62e
fof(fact_satz62d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ny)) ).

% satz62d
fof(fact_satz62c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ob)) ).

% satz62c
fof(fact_satz62b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_oe)) ).

% satz62b
fof(fact_satz61,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_oh)) ).

% satz61
fof(fact_satz60a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_oj)) ).

% satz60a
fof(fact_satz60,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ol)) ).

% satz60
fof(fact_satz59,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_oo)) ).

% satz59
fof(fact_satz58,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_oq)) ).

% satz58
fof(fact_satz57a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ou)) ).

% satz57a
fof(fact_satz57,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ox)) ).

% satz57
fof(fact_satz56,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_pb)) ).

% satz56
fof(fact_satz55,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_pe)) ).

% satz55
fof(fact_satz54,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_pg)) ).

% satz54
fof(fact_satz53,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_pi)) ).

% satz53
fof(fact_satz52,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_pl)) ).

% satz52
fof(fact_satz51d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_po)) ).

% satz51d
fof(fact_satz51c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_pr)) ).

% satz51c
fof(fact_satz51b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_pu)) ).

% satz51b
fof(fact_satz51a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_px)) ).

% satz51a
fof(fact_satz50,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_qa)) ).

% satz50
fof(fact_satz49,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_qc)) ).

% satz49
fof(fact_satz48,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_qe)) ).

% satz48
fof(fact_satz47,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_qi)) ).

% satz47
fof(fact_satz46,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_qm)) ).

% satz46
fof(fact_satz41k,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_qo)) ).

% satz41k
fof(fact_satz41j,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_qq)) ).

% satz41j
fof(fact_satz41h,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_qs)) ).

% satz41h
fof(fact_satz41g,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_qu)) ).

% satz41g
fof(fact_satz41f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_qw)) ).

% satz41f
fof(fact_satz41e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_qy)) ).

% satz41e
fof(fact_satz41d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ra)) ).

% satz41d
fof(fact_satz41c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_rc)) ).

% satz41c
fof(fact_satz45,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_rg)) ).

% satz45
fof(fact_satz44,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_rk)) ).

% satz44
fof(fact_satz43,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_rm)) ).

% satz43
fof(fact_satz42,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ro)) ).

% satz42
fof(fact_satz41b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_rq)) ).

% satz41b
fof(fact_satz41a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_rs)) ).

% satz41a
fof(fact_satz41,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_ru)) ).

% satz41
fof(fact_satz40c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_rx)) ).

% satz40c
fof(fact_satz40b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_sa)) ).

% satz40b
fof(fact_satz40a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_sc)) ).

% satz40a
fof(fact_satz40,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_se)) ).

% satz40
fof(fact_satz39,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_sh)) ).

% satz39
fof(fact_satz38,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_sj)) ).

% satz38
fof(fact_satz37,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aTP_Lamm_sk)) ).

% satz37
fof(fact_satz36a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_so)) ).

% satz36a
fof(fact_satz36,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ss)) ).

% satz36
fof(fact_satz35d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_sw)) ).

% satz35d
fof(fact_satz35c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ta)) ).

% satz35c
fof(fact_satz35b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_te)) ).

% satz35b
fof(fact_satz35a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ti)) ).

% satz35a
fof(fact_satz34a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_tm)) ).

% satz34a
fof(fact_satz34,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_tq)) ).

% satz34
fof(fact_satz33c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_tt)) ).

% satz33c
fof(fact_satz33b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_tw)) ).

% satz33b
fof(fact_satz33a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_tz)) ).

% satz33a
fof(fact_satz32o,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_uc)) ).

% satz32o
fof(fact_satz32n,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_uf)) ).

% satz32n
fof(fact_satz32m,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ui)) ).

% satz32m
fof(fact_satz32l,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ul)) ).

% satz32l
fof(fact_satz32k,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_up)) ).

% satz32k
fof(fact_satz32j,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ut)) ).

% satz32j
fof(fact_satz32h,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ux)) ).

% satz32h
fof(fact_satz32g,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_vb)) ).

% satz32g
fof(fact_satz32f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ve)) ).

% satz32f
fof(fact_satz32e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_vh)) ).

% satz32e
fof(fact_satz32d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_vk)) ).

% satz32d
fof(fact_satz32c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_vn)) ).

% satz32c
fof(fact_satz32b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_vq)) ).

% satz32b
fof(fact_satz32a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_vt)) ).

% satz32a
fof(fact_satz31,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_vw)) ).

% satz31
fof(fact_satz30,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_vz)) ).

% satz30
fof(fact_satz29,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wb)) ).

% satz29
fof(fact_satz28h,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wd)) ).

% satz28h
fof(fact_satz28g,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_we)) ).

% satz28g
fof(fact_satz28f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wg)) ).

% satz28f
fof(fact_satz28e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wh)) ).

% satz28e
fof(fact_satz28d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wj)) ).

% satz28d
fof(fact_satz28c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wk)) ).

% satz28c
fof(fact_satz28b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wm)) ).

% satz28b
fof(fact_satz28a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wn)) ).

% satz28a
fof(fact_satz28,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wp)) ).

% satz28
fof(fact_satz27a,axiom,
    ! [X0] :
      ( pp(aa_fun171081125l_bool(scratc1572426730n_some,X0))
     => pp(aa_fun171081125l_bool(scratc61291760_n_one,scratc474702586nd_min(X0))) ) ).

% satz27a
fof(fact_satz27,axiom,
    ! [X0] :
      ( pp(aa_fun171081125l_bool(scratc1572426730n_some,X0))
     => pp(aa_fun171081125l_bool(scratc1572426730n_some,scratc474702586nd_min(X0))) ) ).

% satz27
fof(fact_satz26c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wr)) ).

% satz26c
fof(fact_satz26b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wt)) ).

% satz26b
fof(fact_satz26a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wv)) ).

% satz26a
fof(fact_satz26,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wx)) ).

% satz26
fof(fact_satz25c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_wz)) ).

% satz25c
fof(fact_satz25b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_xb)) ).

% satz25b
fof(fact_satz25a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_xd)) ).

% satz25a
fof(fact_satz25,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_xf)) ).

% satz25
fof(fact_satz24c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_xg)) ).

% satz24c
fof(fact_satz24b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_xh)) ).

% satz24b
fof(fact_satz24a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(scratc324288571lessis,scratc51547579nd_n_1))) ).

% satz24a
fof(fact_satz24,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_xi)) ).

% satz24
fof(fact_satz23a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_xm)) ).

% satz23a
fof(fact_satz23,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_xq)) ).

% satz23
fof(fact_satz22d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_xu)) ).

% satz22d
fof(fact_satz22c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_xy)) ).

% satz22c
fof(fact_satz22b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_yc)) ).

% satz22b
fof(fact_satz22a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_yg)) ).

% satz22a
fof(fact_satz21a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_yk)) ).

% satz21a
fof(fact_satz21,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_yo)) ).

% satz21
fof(fact_satz20f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_yr)) ).

% satz20f
fof(fact_satz20e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_yu)) ).

% satz20e
fof(fact_satz20d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_yx)) ).

% satz20d
fof(fact_satz20c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_za)) ).

% satz20c
fof(fact_satz20b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_zd)) ).

% satz20b
fof(fact_satz20a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_zg)) ).

% satz20a
fof(fact_satz19o,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_zj)) ).

% satz19o
fof(fact_satz19n,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_zm)) ).

% satz19n
fof(fact_satz19m,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_zp)) ).

% satz19m
fof(fact_satz19l,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_zs)) ).

% satz19l
fof(fact_satz19k,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_zw)) ).

% satz19k
fof(fact_satz19j,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aaa)) ).

% satz19j
fof(fact_satz19h,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aae)) ).

% satz19h
fof(fact_satz19g,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aai)) ).

% satz19g
fof(fact_satz19f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aal)) ).

% satz19f
fof(fact_satz19e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aao)) ).

% satz19e
fof(fact_satz19d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aar)) ).

% satz19d
fof(fact_satz19c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aau)) ).

% satz19c
fof(fact_satz19b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aax)) ).

% satz19b
fof(fact_satz19a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aba)) ).

% satz19a
fof(fact_satz18c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_abb)) ).

% satz18c
fof(fact_satz18b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_abc)) ).

% satz18b
fof(fact_satz18a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_abe)) ).

% satz18a
fof(fact_satz18,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_abg)) ).

% satz18
fof(fact_satz17,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_abj)) ).

% satz17
fof(fact_satz16d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_abm)) ).

% satz16d
fof(fact_satz16c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_abp)) ).

% satz16c
fof(fact_satz16b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_abs)) ).

% satz16b
fof(fact_satz16a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_abv)) ).

% satz16a
fof(fact_satz15,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aby)) ).

% satz15
fof(fact_satz10k,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aca)) ).

% satz10k
fof(fact_satz10j,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_acc)) ).

% satz10j
fof(fact_satz10h,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ace)) ).

% satz10h
fof(fact_satz10g,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_acg)) ).

% satz10g
fof(fact_satz10f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aci)) ).

% satz10f
fof(fact_satz10e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ack)) ).

% satz10e
fof(fact_satz10d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_acm)) ).

% satz10d
fof(fact_satz10c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aco)) ).

% satz10c
fof(fact_satz14,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_acq)) ).

% satz14
fof(fact_satz13,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_acs)) ).

% satz13
fof(fact_satz12,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_acu)) ).

% satz12
fof(fact_satz11,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_acw)) ).

% satz11
fof(fact_satz10b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_acy)) ).

% satz10b
fof(fact_satz10a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ada)) ).

% satz10a
fof(fact_satz10,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_adc)) ).

% satz10
fof(fact_satz9b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ade)) ).

% satz9b
fof(fact_satz9a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_adg)) ).

% satz9a
fof(fact_satz9,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_adk)) ).

% satz9
fof(fact_satz8b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_adm)) ).

% satz8b
fof(fact_satz8a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_adp)) ).

% satz8a
fof(fact_satz8,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ads)) ).

% satz8
fof(fact_satz7,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_adu)) ).

% satz7
fof(fact_satz6,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_adw)) ).

% satz6
fof(fact_satz5,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_adz)) ).

% satz5
fof(fact_satz4h,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aeb)) ).

% satz4h
fof(fact_satz4g,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aec)) ).

% satz4g
fof(fact_satz4f,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aee)) ).

% satz4f
fof(fact_satz4e,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aef)) ).

% satz4e
fof(fact_satz4d,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aeh)) ).

% satz4d
fof(fact_satz4c,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aei)) ).

% satz4c
fof(fact_satz4b,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aek)) ).

% satz4b
fof(fact_satz4a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_ael)) ).

% satz4a
fof(fact_satz4,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aen)) ).

% satz4
fof(fact_satz3a,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aeo)) ).

% satz3a
fof(fact_satz3,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aep)) ).

% satz3
fof(fact_satz2,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aeq)) ).

% satz2
fof(fact_satz1,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aes)) ).

% satz1
fof(fact_n__ax5,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_aet),aTP_Lamm_aev)) ).

% n_ax5
fof(fact_n__ax4,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aex)) ).

% n_ax4
fof(fact_n__ax3,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aey)) ).

% n_ax3
fof(fact_suc__p,axiom,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aTP_Lamm_aez)) ).

% suc_p
fof(fact_n__1__p,axiom,
    scratc1533070073_is_of(scratc51547579nd_n_1,aTP_Lamm_or) ).

% n_1_p
fof(fact_isseti,axiom,
    ! [X0] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_afa,X0)),aa_TPT43085870d_bool(aTP_Lamm_afc,X0))) ).

% isseti
fof(fact_estie,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X0)),aa_fun1584354236d_bool(aTP_Lamm_afd(X0),X12))) ).

% estie
fof(fact_estii,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X0)),aa_fun1584354236d_bool(aTP_Lamm_afe(X0),X12))) ).

% estii
fof(fact_setof__p,axiom,
    ! [X0,X12] : scratc1533070073_is_of(aa_fun1431113780TP_ind(scratc404274226_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_afa,X0)) ).

% setof_p
fof(fact_secondis1,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X0)),aa_TPT43085870d_bool(aTP_Lamm_afg(X0),X12))) ).

% secondis1
fof(fact_firstis1,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X0)),aa_TPT43085870d_bool(aTP_Lamm_afi(X0),X12))) ).

% firstis1
fof(fact_pairis1,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_afj(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_afk(X0),X12))) ).

% pairis1
fof(fact_second__p,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_afj(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_afl(X0),X12))) ).

% second_p
fof(fact_first__p,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_afj(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_afm(X0),X12))) ).

% first_p
fof(fact_e__pair__p,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X0)),aa_TPT43085870d_bool(aTP_Lamm_afo(X0),X12))) ).

% e_pair_p
fof(fact_otax2,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X0)),aa_fun1584354236d_bool(aTP_Lamm_afp(X0),X12))) ).

% otax2
fof(fact_otax1,axiom,
    ! [X0,X12] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1752645071ective(aa_fun1431113780TP_ind(scratc404274226_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,aa_fun1431113780TP_ind(scratc404274226_d_Sep(X0),X12)),scratc1815386162d_e_in(X0,X12)))) ).

% otax1
fof(fact_e__inp,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_fun1584354236d_bool(aTP_Lamm_afq(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_afr(X0),X12))) ).

% e_inp
fof(fact_e__in__p,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_fun1584354236d_bool(aTP_Lamm_afq(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_afs(X0),X12))) ).

% e_in_p
fof(fact_e__fisi,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_aft(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_afw(X0),X12))) ).

% e_fisi
fof(fact_oneax,axiom,
    ! [X0,X12] :
      ( pp(aa_fun171081125l_bool(scratc491553582nd_one(X0),X12))
     => pp(aa_TPTP_ind_bool(X12,scratc441984551nd_ind(X0,X12))) ) ).

% oneax
fof(fact_ind__p,axiom,
    ! [X0,X12] :
      ( pp(aa_fun171081125l_bool(scratc491553582nd_one(X0),X12))
     => scratc1533070073_is_of(scratc441984551nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_ay,X0)) ) ).

% ind_p
fof(fact_e__isp,axiom,
    ! [X0,X12] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X0)),aa_fun1584354236d_bool(aTP_Lamm_afy(X0),X12))) ).

% e_isp
fof(fact_refis,axiom,
    ! [X0] : pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,X0)),aa_TPT43085870d_bool(aTP_Lamm_afz,X0))) ).

% refis
fof(fact_l__et,axiom,
    ! [X0] :
      ( scratc557055238nd_wel(X0)
     => pp(X0) ) ).

% l_et
fof(fact_k__If__In__then__E,axiom,
    ! [X0,X12,X22,X32] :
      ( pp(X0)
     => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(X0,X22),X32)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X12),X22)) ) ) ).

% k_If_In_then_E
fof(fact_k__If__In__01,axiom,
    ! [X0,X12,X22] :
      ( ( pp(X0)
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X12),X22)) )
     => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(X0,X12),scratc1884736269ptyset)),aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,scratc1884736269ptyset)))) ) ).

% k_If_In_01
fof(fact_xi__ext,axiom,
    ! [X0,X12,X22] :
      ( ! [X33] :
          ( gg_TPTP_ind(X33)
         => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X33),X0))
           => aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33) ) )
     => aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X0),X22) ) ).

% xi_ext
fof(fact_k__Pi__ext,axiom,
    ! [X0,X12,X22] :
      ( gg_TPTP_ind(X22)
     => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,X0),X12)))
       => ! [X32] :
            ( gg_TPTP_ind(X32)
           => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,X0),X12)))
             => ( ! [X42] :
                    ( gg_TPTP_ind(X42)
                   => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X42),X0))
                     => aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,X32),X42) ) )
               => X22 = X32 ) ) ) ) ) ).

% k_Pi_ext
fof(fact_ap__Pi,axiom,
    ! [X0,X12,X22,X32] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,X0),X12)))
     => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X32),X0))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32))) ) ) ).

% ap_Pi
fof(fact_lam__Pi,axiom,
    ! [X0,X12,X22] :
      ( ! [X33] :
          ( gg_TPTP_ind(X33)
         => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X33),X0))
           => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33))) ) )
     => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,X0),X12))) ) ).

% lam_Pi
fof(fact_beta,axiom,
    ! [X0,X12,X22] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),X0))
     => aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22) ) ).

% beta
fof(fact_proj1__Sigma,axiom,
    ! [X0,X12,X22] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X0),X12)))
     => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_TPTP_ind_TPTP_ind(scratc1396712316_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1396712315_proj0,X22)))) ) ).

% proj1_Sigma
fof(fact_proj0__Sigma,axiom,
    ! [X0,X12,X22] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X0),X12)))
     => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_TPTP_ind_TPTP_ind(scratc1396712315_proj0,X22)),X0)) ) ).

% proj0_Sigma
fof(fact_proj__Sigma__eta,axiom,
    ! [X0,X12,X22] :
      ( gg_TPTP_ind(X22)
     => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X0),X12)))
       => aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1629901042d_pair,aa_TPTP_ind_TPTP_ind(scratc1396712315_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1396712316_proj1,X22)) = X22 ) ) ).

% proj_Sigma_eta
fof(fact_k__Sigma__eta__proj0__proj1,axiom,
    ! [X0,X12,X22] :
      ( gg_TPTP_ind(X22)
     => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X0),X12)))
       => ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1629901042d_pair,aa_TPTP_ind_TPTP_ind(scratc1396712315_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1396712316_proj1,X22)) = X22
          & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_TPTP_ind_TPTP_ind(scratc1396712315_proj0,X22)),X0))
          & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_TPTP_ind_TPTP_ind(scratc1396712316_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1396712315_proj0,X22)))) ) ) ) ).

% k_Sigma_eta_proj0_proj1
fof(fact_pair__Sigma,axiom,
    ! [X0,X12,X22] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),X0))
     => ! [X32] :
          ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22)))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1629901042d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,X0),X12))) ) ) ).

% pair_Sigma
fof(fact_proj1__pair__eq,axiom,
    ! [X0,X12] :
      ( gg_TPTP_ind(X12)
     => aa_TPTP_ind_TPTP_ind(scratc1396712316_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1629901042d_pair,X0),X12)) = X12 ) ).

% proj1_pair_eq
fof(fact_proj0__pair__eq,axiom,
    ! [X0,X12] :
      ( gg_TPTP_ind(X0)
     => aa_TPTP_ind_TPTP_ind(scratc1396712315_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1629901042d_pair,X0),X12)) = X0 ) ).

% proj0_pair_eq
fof(fact_nat__p__omega,axiom,
    ! [X0] :
      ( pp(aa_TPTP_ind_bool(scratc1419714279_nat_p,X0))
     => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X0),scratc566367529_omega)) ) ).

% nat_p_omega
fof(fact_omega__nat__p,axiom,
    ! [X0] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X0),scratc566367529_omega))
     => pp(aa_TPTP_ind_bool(scratc1419714279_nat_p,X0)) ) ).

% omega_nat_p
fof(fact_nat__inv,axiom,
    ! [X0] :
      ( gg_TPTP_ind(X0)
     => ( pp(aa_TPTP_ind_bool(scratc1419714279_nat_p,X0))
       => ( X0 = scratc1884736269ptyset
          | ? [X13] :
              ( gg_TPTP_ind(X13)
              & pp(aa_TPTP_ind_bool(scratc1419714279_nat_p,X13))
              & X0 = aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,X13) ) ) ) ) ).

% nat_inv
fof(fact_nat__ind,axiom,
    ! [X0] :
      ( pp(aa_TPTP_ind_bool(X0,scratc1884736269ptyset))
     => ( ! [X13] :
            ( gg_TPTP_ind(X13)
           => ( pp(aa_TPTP_ind_bool(scratc1419714279_nat_p,X13))
             => ( pp(aa_TPTP_ind_bool(X0,X13))
               => pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,X13))) ) ) )
       => ! [X12] :
            ( pp(aa_TPTP_ind_bool(scratc1419714279_nat_p,X12))
           => pp(aa_TPTP_ind_bool(X0,X12)) ) ) ) ).

% nat_ind
fof(fact_nat__1,axiom,
    pp(aa_TPTP_ind_bool(scratc1419714279_nat_p,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,scratc1884736269ptyset))) ).

% nat_1
fof(fact_nat__ordsucc,axiom,
    ! [X0] :
      ( pp(aa_TPTP_ind_bool(scratc1419714279_nat_p,X0))
     => pp(aa_TPTP_ind_bool(scratc1419714279_nat_p,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,X0))) ) ).

% nat_ordsucc
fof(fact_k__In__0__1,axiom,
    pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,scratc1884736269ptyset),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,scratc1884736269ptyset))) ).

% k_In_0_1
fof(fact_ordsucc__inj,axiom,
    ! [X0,X12] :
      ( ( gg_TPTP_ind(X0)
        & gg_TPTP_ind(X12) )
     => ( aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,X12)
       => X0 = X12 ) ) ).

% ordsucc_inj
fof(fact_neq__ordsucc__0,axiom,
    ! [X0] : aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,X0) != scratc1884736269ptyset ).

% neq_ordsucc_0
fof(fact_k__SepE2,axiom,
    ! [X0,X12,X22] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),aa_fun1431113780TP_ind(scratc404274226_d_Sep(X0),X12)))
     => pp(aa_TPTP_ind_bool(X12,X22)) ) ).

% k_SepE2
fof(fact_k__SepE1,axiom,
    ! [X0,X12,X22] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),aa_fun1431113780TP_ind(scratc404274226_d_Sep(X0),X12)))
     => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),X0)) ) ).

% k_SepE1
fof(fact_k__SepI,axiom,
    ! [X0,X12,X22] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),X0))
     => ( pp(aa_TPTP_ind_bool(X12,X22))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),aa_fun1431113780TP_ind(scratc404274226_d_Sep(X0),X12))) ) ) ).

% k_SepI
fof(fact_k__Self__In__Power,axiom,
    ! [X0] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1268198477_power,X0))) ).

% k_Self_In_Power
fof(fact_k__PowerI,axiom,
    ! [X0,X12] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc840648029d_Subq,X12),X0))
     => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1268198477_power,X0))) ) ).

% k_PowerI
fof(fact_k__PowerE,axiom,
    ! [X0,X12] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1268198477_power,X0)))
     => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc840648029d_Subq,X12),X0)) ) ).

% k_PowerE
fof(fact_if__i__or,axiom,
    ! [X0,X12,X22] :
      ( ( gg_TPTP_ind(X12)
        & gg_TPTP_ind(X22) )
     => ( aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(X0,X12),X22) = X12
        | aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(X0,X12),X22) = X22 ) ) ).

% if_i_or
fof(fact_if__i__1,axiom,
    ! [X0,X12,X22] :
      ( gg_TPTP_ind(X12)
     => ( pp(X0)
       => aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(X0,X12),X22) = X12 ) ) ).

% if_i_1
fof(fact_if__i__0,axiom,
    ! [X0,X12,X22] :
      ( gg_TPTP_ind(X22)
     => ( ~ pp(X0)
       => aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(X0,X12),X22) = X22 ) ) ).

% if_i_0
fof(fact_if__i__correct,axiom,
    ! [X0,X12,X22] :
      ( ( gg_TPTP_ind(X12)
        & gg_TPTP_ind(X22) )
     => ( ( pp(X0)
          & aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(X0,X12),X22) = X12 )
        | ( ~ pp(X0)
          & aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(X0,X12),X22) = X22 ) ) ) ).

% if_i_correct
fof(fact_k__UnivOf__ZF__closed,axiom,
    ! [X0] : pp(aa_TPTP_ind_bool(scratc2034515940closed,aa_TPTP_ind_TPTP_ind(scratc1852771061univof,X0))) ).

% k_UnivOf_ZF_closed
fof(fact_k__UnivOf__In,axiom,
    ! [X0] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1852771061univof,X0))) ).

% k_UnivOf_In
fof(fact_k__ReplEq,axiom,
    ! [X0,X12,X22] :
      ( gg_TPTP_ind(X22)
     => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1077096999d_repl,X0),X12)))
      <=> ? [X3] :
            ( gg_TPTP_ind(X3)
            & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X3),X0))
            & X22 = aa_TPTP_ind_TPTP_ind(X12,X3) ) ) ) ).

% k_ReplEq
fof(fact_k__PowerEq,axiom,
    ! [X0,X12] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1268198477_power,X0)))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc840648029d_Subq,X12),X0)) ) ).

% k_PowerEq
fof(fact_k__UnionEq,axiom,
    ! [X0,X12] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1775460343_union,X0)))
    <=> ? [X2] :
          ( gg_TPTP_ind(X2)
          & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X12),X2))
          & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X2),X0)) ) ) ).

% k_UnionEq
fof(fact_k__EmptyAx,axiom,
    ~ ? [X0] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X0),scratc1884736269ptyset)) ).

% k_EmptyAx
fof(fact_k__In__ind,axiom,
    ! [X0] :
      ( ! [X13] :
          ( gg_TPTP_ind(X13)
         => ( ! [X22] :
                ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X22),X13))
               => pp(aa_TPTP_ind_bool(X0,X22)) )
           => pp(aa_TPTP_ind_bool(X0,X13)) ) )
     => ! [X14] : pp(aa_TPTP_ind_bool(X0,X14)) ) ).

% k_In_ind
fof(fact_set__ext,axiom,
    ! [X0,X12] :
      ( ( gg_TPTP_ind(X0)
        & gg_TPTP_ind(X12) )
     => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc840648029d_Subq,X0),X12))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc840648029d_Subq,X12),X0))
         => X0 = X12 ) ) ) ).

% set_ext
fof(fact_ATP_Olambda__1,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aep,Uu))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,Uu),scratc51547579nd_n_1))
       => pp(aa_fun171081125l_bool(scratc1572426730n_some,aa_TPT43085870d_bool(aTP_Lamm_av,Uu))) ) ) ).

% ATP.lambda_1
fof(fact_ATP_Olambda__2,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aeo,Uu))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,Uu),scratc51547579nd_n_1))
       => pp(aa_fun171081125l_bool(scratc61291760_n_one,aa_TPT43085870d_bool(aTP_Lamm_av,Uu))) ) ) ).

% ATP.lambda_2
fof(fact_ATP_Olambda__3,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ael,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),scratc51547579nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu))) ) ).

% ATP.lambda_3
fof(fact_ATP_Olambda__4,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wn,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),scratc51547579nd_n_1)),Uu)) ) ).

% ATP.lambda_4
fof(fact_ATP_Olambda__5,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aei,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(scratc51547579nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu))) ) ).

% ATP.lambda_5
fof(fact_ATP_Olambda__6,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wk,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(scratc51547579nd_n_1),Uu)),Uu)) ) ).

% ATP.lambda_6
fof(fact_ATP_Olambda__7,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aen,Uu))
    <=> pp(aa_fun171081125l_bool(scratc491553582nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,scratc482439305nd_nat),aTP_Lamm_ap)),aa_TPT43085870d_bool(aTP_Lamm_aem,Uu))) ) ).

% ATP.lambda_7
fof(fact_ATP_Olambda__8,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wp,Uu))
    <=> pp(aa_fun171081125l_bool(scratc491553582nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,scratc482439305nd_nat),aTP_Lamm_ap)),aa_TPT43085870d_bool(aTP_Lamm_wo,Uu))) ) ).

% ATP.lambda_8
fof(fact_ATP_Olambda__9,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aev,Uu))
    <=> ( pp(aa_TPTP_ind_bool(scratc1411829047_cond1,Uu))
       => ( pp(aa_TPTP_ind_bool(scratc1411829048_cond2,Uu))
         => pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aeu,Uu))) ) ) ) ).

% ATP.lambda_9
fof(fact_ATP_Olambda__10,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aef,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),scratc51547579nd_n_1))) ) ).

% ATP.lambda_10
fof(fact_ATP_Olambda__11,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aec,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(scratc51547579nd_n_1),Uu))) ) ).

% ATP.lambda_11
fof(fact_ATP_Olambda__12,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_abc,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),Uu)) ) ).

% ATP.lambda_12
fof(fact_ATP_Olambda__13,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aeq,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),Uu)) ) ).

% ATP.lambda_13
fof(fact_ATP_Olambda__14,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aez,Uu))
    <=> scratc1533070073_is_of(aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu),aTP_Lamm_or) ) ).

% ATP.lambda_14
fof(fact_ATP_Olambda__15,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_xh,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),scratc51547579nd_n_1)) ) ).

% ATP.lambda_15
fof(fact_ATP_Olambda__16,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aey,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),scratc51547579nd_n_1)) ) ).

% ATP.lambda_16
fof(fact_ATP_Olambda__17,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wh,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),scratc51547579nd_n_1))) ) ).

% ATP.lambda_17
fof(fact_ATP_Olambda__18,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_we,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(scratc51547579nd_n_1),Uu))) ) ).

% ATP.lambda_18
fof(fact_ATP_Olambda__19,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_abb,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu))) ) ).

% ATP.lambda_19
fof(fact_ATP_Olambda__20,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aet,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1268198477_power,scratc482439305nd_nat))) ) ).

% ATP.lambda_20
fof(fact_ATP_Olambda__21,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gn,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,Uu),Uu)) ) ).

% ATP.lambda_21
fof(fact_ATP_Olambda__22,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_sk,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uu)) ) ).

% ATP.lambda_22
fof(fact_ATP_Olambda__23,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_xi,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),scratc51547579nd_n_1)) ) ).

% ATP.lambda_23
fof(fact_ATP_Olambda__24,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_go,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,Uu),scratc406400774d_frac)) ) ).

% ATP.lambda_24
fof(fact_ATP_Olambda__25,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,Uu),scratc515485325nd_rat)) ) ).

% ATP.lambda_25
fof(fact_ATP_Olambda__26,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_or,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,Uu),scratc482439305nd_nat)) ) ).

% ATP.lambda_26
fof(fact_ATP_Olambda__27,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aex,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aew,Uu))) ) ).

% ATP.lambda_27
fof(fact_ATP_Olambda__28,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aes,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aer,Uu))) ) ).

% ATP.lambda_28
fof(fact_ATP_Olambda__29,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aek,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aej,Uu))) ) ).

% ATP.lambda_29
fof(fact_ATP_Olambda__30,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aeh,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aeg,Uu))) ) ).

% ATP.lambda_30
fof(fact_ATP_Olambda__31,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aee,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aed,Uu))) ) ).

% ATP.lambda_31
fof(fact_ATP_Olambda__32,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aeb,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aea,Uu))) ) ).

% ATP.lambda_32
fof(fact_ATP_Olambda__33,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_adz,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ady,Uu))) ) ).

% ATP.lambda_33
fof(fact_ATP_Olambda__34,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_adw,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_adv,Uu))) ) ).

% ATP.lambda_34
fof(fact_ATP_Olambda__35,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_adu,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_adt,Uu))) ) ).

% ATP.lambda_35
fof(fact_ATP_Olambda__36,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ads,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_adr,Uu))) ) ).

% ATP.lambda_36
fof(fact_ATP_Olambda__37,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_adp,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ado,Uu))) ) ).

% ATP.lambda_37
fof(fact_ATP_Olambda__38,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_adm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_adl,Uu))) ) ).

% ATP.lambda_38
fof(fact_ATP_Olambda__39,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_adk,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_adj,Uu))) ) ).

% ATP.lambda_39
fof(fact_ATP_Olambda__40,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_adg,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_adf,Uu))) ) ).

% ATP.lambda_40
fof(fact_ATP_Olambda__41,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ade,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_add,Uu))) ) ).

% ATP.lambda_41
fof(fact_ATP_Olambda__42,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_adc,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_adb,Uu))) ) ).

% ATP.lambda_42
fof(fact_ATP_Olambda__43,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ada,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_acz,Uu))) ) ).

% ATP.lambda_43
fof(fact_ATP_Olambda__44,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_acy,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_acx,Uu))) ) ).

% ATP.lambda_44
fof(fact_ATP_Olambda__45,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_acw,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_acv,Uu))) ) ).

% ATP.lambda_45
fof(fact_ATP_Olambda__46,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_acu,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_act,Uu))) ) ).

% ATP.lambda_46
fof(fact_ATP_Olambda__47,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_acs,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_acr,Uu))) ) ).

% ATP.lambda_47
fof(fact_ATP_Olambda__48,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_acq,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_acp,Uu))) ) ).

% ATP.lambda_48
fof(fact_ATP_Olambda__49,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aco,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_acn,Uu))) ) ).

% ATP.lambda_49
fof(fact_ATP_Olambda__50,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_acm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_acl,Uu))) ) ).

% ATP.lambda_50
fof(fact_ATP_Olambda__51,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ack,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_acj,Uu))) ) ).

% ATP.lambda_51
fof(fact_ATP_Olambda__52,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aci,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ach,Uu))) ) ).

% ATP.lambda_52
fof(fact_ATP_Olambda__53,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_acg,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_acf,Uu))) ) ).

% ATP.lambda_53
fof(fact_ATP_Olambda__54,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ace,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_acd,Uu))) ) ).

% ATP.lambda_54
fof(fact_ATP_Olambda__55,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_acc,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_acb,Uu))) ) ).

% ATP.lambda_55
fof(fact_ATP_Olambda__56,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aca,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abz,Uu))) ) ).

% ATP.lambda_56
fof(fact_ATP_Olambda__57,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aby,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abx,Uu))) ) ).

% ATP.lambda_57
fof(fact_ATP_Olambda__58,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_abv,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abu,Uu))) ) ).

% ATP.lambda_58
fof(fact_ATP_Olambda__59,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_abs,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abr,Uu))) ) ).

% ATP.lambda_59
fof(fact_ATP_Olambda__60,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_abp,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abo,Uu))) ) ).

% ATP.lambda_60
fof(fact_ATP_Olambda__61,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_abm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abl,Uu))) ) ).

% ATP.lambda_61
fof(fact_ATP_Olambda__62,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_abj,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abi,Uu))) ) ).

% ATP.lambda_62
fof(fact_ATP_Olambda__63,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_abg,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abf,Uu))) ) ).

% ATP.lambda_63
fof(fact_ATP_Olambda__64,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_abe,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abd,Uu))) ) ).

% ATP.lambda_64
fof(fact_ATP_Olambda__65,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aba,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aaz,Uu))) ) ).

% ATP.lambda_65
fof(fact_ATP_Olambda__66,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aax,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aaw,Uu))) ) ).

% ATP.lambda_66
fof(fact_ATP_Olambda__67,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aau,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aat,Uu))) ) ).

% ATP.lambda_67
fof(fact_ATP_Olambda__68,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aar,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aaq,Uu))) ) ).

% ATP.lambda_68
fof(fact_ATP_Olambda__69,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aao,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aan,Uu))) ) ).

% ATP.lambda_69
fof(fact_ATP_Olambda__70,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aal,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aak,Uu))) ) ).

% ATP.lambda_70
fof(fact_ATP_Olambda__71,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aai,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aah,Uu))) ) ).

% ATP.lambda_71
fof(fact_ATP_Olambda__72,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aae,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aad,Uu))) ) ).

% ATP.lambda_72
fof(fact_ATP_Olambda__73,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aaa,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zz,Uu))) ) ).

% ATP.lambda_73
fof(fact_ATP_Olambda__74,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_zw,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zv,Uu))) ) ).

% ATP.lambda_74
fof(fact_ATP_Olambda__75,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_zs,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zr,Uu))) ) ).

% ATP.lambda_75
fof(fact_ATP_Olambda__76,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_zp,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zo,Uu))) ) ).

% ATP.lambda_76
fof(fact_ATP_Olambda__77,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_zm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zl,Uu))) ) ).

% ATP.lambda_77
fof(fact_ATP_Olambda__78,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_zj,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zi,Uu))) ) ).

% ATP.lambda_78
fof(fact_ATP_Olambda__79,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_zg,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zf,Uu))) ) ).

% ATP.lambda_79
fof(fact_ATP_Olambda__80,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_zd,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zc,Uu))) ) ).

% ATP.lambda_80
fof(fact_ATP_Olambda__81,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_za,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_yz,Uu))) ) ).

% ATP.lambda_81
fof(fact_ATP_Olambda__82,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_yx,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_yw,Uu))) ) ).

% ATP.lambda_82
fof(fact_ATP_Olambda__83,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_yu,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_yt,Uu))) ) ).

% ATP.lambda_83
fof(fact_ATP_Olambda__84,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_yr,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_yq,Uu))) ) ).

% ATP.lambda_84
fof(fact_ATP_Olambda__85,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_yo,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_yn,Uu))) ) ).

% ATP.lambda_85
fof(fact_ATP_Olambda__86,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_yk,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_yj,Uu))) ) ).

% ATP.lambda_86
fof(fact_ATP_Olambda__87,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_yg,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_yf,Uu))) ) ).

% ATP.lambda_87
fof(fact_ATP_Olambda__88,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_yc,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_yb,Uu))) ) ).

% ATP.lambda_88
fof(fact_ATP_Olambda__89,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_xy,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_xx,Uu))) ) ).

% ATP.lambda_89
fof(fact_ATP_Olambda__90,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_xu,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_xt,Uu))) ) ).

% ATP.lambda_90
fof(fact_ATP_Olambda__91,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_xq,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_xp,Uu))) ) ).

% ATP.lambda_91
fof(fact_ATP_Olambda__92,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_xm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_xl,Uu))) ) ).

% ATP.lambda_92
fof(fact_ATP_Olambda__93,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_xf,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_xe,Uu))) ) ).

% ATP.lambda_93
fof(fact_ATP_Olambda__94,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_xd,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_xc,Uu))) ) ).

% ATP.lambda_94
fof(fact_ATP_Olambda__95,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_xb,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_xa,Uu))) ) ).

% ATP.lambda_95
fof(fact_ATP_Olambda__96,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wz,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_wy,Uu))) ) ).

% ATP.lambda_96
fof(fact_ATP_Olambda__97,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wx,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ww,Uu))) ) ).

% ATP.lambda_97
fof(fact_ATP_Olambda__98,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wv,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_wu,Uu))) ) ).

% ATP.lambda_98
fof(fact_ATP_Olambda__99,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wt,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ws,Uu))) ) ).

% ATP.lambda_99
fof(fact_ATP_Olambda__100,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wr,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_wq,Uu))) ) ).

% ATP.lambda_100
fof(fact_ATP_Olambda__101,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_wl,Uu))) ) ).

% ATP.lambda_101
fof(fact_ATP_Olambda__102,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wj,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_wi,Uu))) ) ).

% ATP.lambda_102
fof(fact_ATP_Olambda__103,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wg,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_wf,Uu))) ) ).

% ATP.lambda_103
fof(fact_ATP_Olambda__104,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wd,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_wc,Uu))) ) ).

% ATP.lambda_104
fof(fact_ATP_Olambda__105,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_wb,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_wa,Uu))) ) ).

% ATP.lambda_105
fof(fact_ATP_Olambda__106,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_vz,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vy,Uu))) ) ).

% ATP.lambda_106
fof(fact_ATP_Olambda__107,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_vw,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vv,Uu))) ) ).

% ATP.lambda_107
fof(fact_ATP_Olambda__108,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_vt,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vs,Uu))) ) ).

% ATP.lambda_108
fof(fact_ATP_Olambda__109,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_vq,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vp,Uu))) ) ).

% ATP.lambda_109
fof(fact_ATP_Olambda__110,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_vn,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vm,Uu))) ) ).

% ATP.lambda_110
fof(fact_ATP_Olambda__111,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_vk,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vj,Uu))) ) ).

% ATP.lambda_111
fof(fact_ATP_Olambda__112,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_vh,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vg,Uu))) ) ).

% ATP.lambda_112
fof(fact_ATP_Olambda__113,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ve,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vd,Uu))) ) ).

% ATP.lambda_113
fof(fact_ATP_Olambda__114,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_vb,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_va,Uu))) ) ).

% ATP.lambda_114
fof(fact_ATP_Olambda__115,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ux,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_uw,Uu))) ) ).

% ATP.lambda_115
fof(fact_ATP_Olambda__116,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ut,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_us,Uu))) ) ).

% ATP.lambda_116
fof(fact_ATP_Olambda__117,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_up,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_uo,Uu))) ) ).

% ATP.lambda_117
fof(fact_ATP_Olambda__118,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ul,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_uk,Uu))) ) ).

% ATP.lambda_118
fof(fact_ATP_Olambda__119,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ui,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_uh,Uu))) ) ).

% ATP.lambda_119
fof(fact_ATP_Olambda__120,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_uf,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ue,Uu))) ) ).

% ATP.lambda_120
fof(fact_ATP_Olambda__121,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_uc,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ub,Uu))) ) ).

% ATP.lambda_121
fof(fact_ATP_Olambda__122,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_tz,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ty,Uu))) ) ).

% ATP.lambda_122
fof(fact_ATP_Olambda__123,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_tw,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_tv,Uu))) ) ).

% ATP.lambda_123
fof(fact_ATP_Olambda__124,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_tt,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ts,Uu))) ) ).

% ATP.lambda_124
fof(fact_ATP_Olambda__125,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_tq,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_tp,Uu))) ) ).

% ATP.lambda_125
fof(fact_ATP_Olambda__126,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_tm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_tl,Uu))) ) ).

% ATP.lambda_126
fof(fact_ATP_Olambda__127,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ti,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_th,Uu))) ) ).

% ATP.lambda_127
fof(fact_ATP_Olambda__128,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_te,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_td,Uu))) ) ).

% ATP.lambda_128
fof(fact_ATP_Olambda__129,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ta,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_sz,Uu))) ) ).

% ATP.lambda_129
fof(fact_ATP_Olambda__130,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_sw,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_sv,Uu))) ) ).

% ATP.lambda_130
fof(fact_ATP_Olambda__131,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ss,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_sr,Uu))) ) ).

% ATP.lambda_131
fof(fact_ATP_Olambda__132,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_so,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_sn,Uu))) ) ).

% ATP.lambda_132
fof(fact_ATP_Olambda__133,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_se,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_sd,Uu))) ) ).

% ATP.lambda_133
fof(fact_ATP_Olambda__134,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_sc,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_sb,Uu))) ) ).

% ATP.lambda_134
fof(fact_ATP_Olambda__135,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_sa,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_rz,Uu))) ) ).

% ATP.lambda_135
fof(fact_ATP_Olambda__136,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_rx,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_rw,Uu))) ) ).

% ATP.lambda_136
fof(fact_ATP_Olambda__137,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ox,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ow,Uu))) ) ).

% ATP.lambda_137
fof(fact_ATP_Olambda__138,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ou,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ot,Uu))) ) ).

% ATP.lambda_138
fof(fact_ATP_Olambda__139,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_sj,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_si,Uu))) ) ).

% ATP.lambda_139
fof(fact_ATP_Olambda__140,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_sh,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_sg,Uu))) ) ).

% ATP.lambda_140
fof(fact_ATP_Olambda__141,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ru,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_rt,Uu))) ) ).

% ATP.lambda_141
fof(fact_ATP_Olambda__142,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_rs,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_rr,Uu))) ) ).

% ATP.lambda_142
fof(fact_ATP_Olambda__143,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_rq,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_rp,Uu))) ) ).

% ATP.lambda_143
fof(fact_ATP_Olambda__144,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ro,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_rn,Uu))) ) ).

% ATP.lambda_144
fof(fact_ATP_Olambda__145,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_rm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_rl,Uu))) ) ).

% ATP.lambda_145
fof(fact_ATP_Olambda__146,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_rk,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_rj,Uu))) ) ).

% ATP.lambda_146
fof(fact_ATP_Olambda__147,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_rg,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_rf,Uu))) ) ).

% ATP.lambda_147
fof(fact_ATP_Olambda__148,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_rc,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_rb,Uu))) ) ).

% ATP.lambda_148
fof(fact_ATP_Olambda__149,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ra,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_qz,Uu))) ) ).

% ATP.lambda_149
fof(fact_ATP_Olambda__150,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_qy,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_qx,Uu))) ) ).

% ATP.lambda_150
fof(fact_ATP_Olambda__151,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_qw,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_qv,Uu))) ) ).

% ATP.lambda_151
fof(fact_ATP_Olambda__152,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_qu,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_qt,Uu))) ) ).

% ATP.lambda_152
fof(fact_ATP_Olambda__153,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_qs,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_qr,Uu))) ) ).

% ATP.lambda_153
fof(fact_ATP_Olambda__154,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_qq,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_qp,Uu))) ) ).

% ATP.lambda_154
fof(fact_ATP_Olambda__155,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_qo,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_qn,Uu))) ) ).

% ATP.lambda_155
fof(fact_ATP_Olambda__156,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_qm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ql,Uu))) ) ).

% ATP.lambda_156
fof(fact_ATP_Olambda__157,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_qi,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_qh,Uu))) ) ).

% ATP.lambda_157
fof(fact_ATP_Olambda__158,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_qe,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_qd,Uu))) ) ).

% ATP.lambda_158
fof(fact_ATP_Olambda__159,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_qc,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_qb,Uu))) ) ).

% ATP.lambda_159
fof(fact_ATP_Olambda__160,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_qa,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_pz,Uu))) ) ).

% ATP.lambda_160
fof(fact_ATP_Olambda__161,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_px,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_pw,Uu))) ) ).

% ATP.lambda_161
fof(fact_ATP_Olambda__162,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_pu,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_pt,Uu))) ) ).

% ATP.lambda_162
fof(fact_ATP_Olambda__163,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_pr,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_pq,Uu))) ) ).

% ATP.lambda_163
fof(fact_ATP_Olambda__164,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_po,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_pn,Uu))) ) ).

% ATP.lambda_164
fof(fact_ATP_Olambda__165,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_pl,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_pk,Uu))) ) ).

% ATP.lambda_165
fof(fact_ATP_Olambda__166,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_pe,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_pd,Uu))) ) ).

% ATP.lambda_166
fof(fact_ATP_Olambda__167,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_pb,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_pa,Uu))) ) ).

% ATP.lambda_167
fof(fact_ATP_Olambda__168,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_oq,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_op,Uu))) ) ).

% ATP.lambda_168
fof(fact_ATP_Olambda__169,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_oo,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_on,Uu))) ) ).

% ATP.lambda_169
fof(fact_ATP_Olambda__170,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ol,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ok,Uu))) ) ).

% ATP.lambda_170
fof(fact_ATP_Olambda__171,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_oj,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_oi,Uu))) ) ).

% ATP.lambda_171
fof(fact_ATP_Olambda__172,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_oh,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_og,Uu))) ) ).

% ATP.lambda_172
fof(fact_ATP_Olambda__173,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_oe,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_od,Uu))) ) ).

% ATP.lambda_173
fof(fact_ATP_Olambda__174,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ob,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_oa,Uu))) ) ).

% ATP.lambda_174
fof(fact_ATP_Olambda__175,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ny,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nx,Uu))) ) ).

% ATP.lambda_175
fof(fact_ATP_Olambda__176,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_nv,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nu,Uu))) ) ).

% ATP.lambda_176
fof(fact_ATP_Olambda__177,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ns,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nr,Uu))) ) ).

% ATP.lambda_177
fof(fact_ATP_Olambda__178,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_np,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_no,Uu))) ) ).

% ATP.lambda_178
fof(fact_ATP_Olambda__179,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_nl,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nk,Uu))) ) ).

% ATP.lambda_179
fof(fact_ATP_Olambda__180,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_nh,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ng,Uu))) ) ).

% ATP.lambda_180
fof(fact_ATP_Olambda__181,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_nd,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nc,Uu))) ) ).

% ATP.lambda_181
fof(fact_ATP_Olambda__182,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_mz,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_my,Uu))) ) ).

% ATP.lambda_182
fof(fact_ATP_Olambda__183,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_mw,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mv,Uu))) ) ).

% ATP.lambda_183
fof(fact_ATP_Olambda__184,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_mt,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ms,Uu))) ) ).

% ATP.lambda_184
fof(fact_ATP_Olambda__185,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_mq,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mp,Uu))) ) ).

% ATP.lambda_185
fof(fact_ATP_Olambda__186,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_mn,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mm,Uu))) ) ).

% ATP.lambda_186
fof(fact_ATP_Olambda__187,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_mk,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mj,Uu))) ) ).

% ATP.lambda_187
fof(fact_ATP_Olambda__188,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_mh,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mg,Uu))) ) ).

% ATP.lambda_188
fof(fact_ATP_Olambda__189,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_md,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mc,Uu))) ) ).

% ATP.lambda_189
fof(fact_ATP_Olambda__190,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_lz,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ly,Uu))) ) ).

% ATP.lambda_190
fof(fact_ATP_Olambda__191,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_lv,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_lu,Uu))) ) ).

% ATP.lambda_191
fof(fact_ATP_Olambda__192,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_lr,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_lq,Uu))) ) ).

% ATP.lambda_192
fof(fact_ATP_Olambda__193,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ln,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_lm,Uu))) ) ).

% ATP.lambda_193
fof(fact_ATP_Olambda__194,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_lj,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_li,Uu))) ) ).

% ATP.lambda_194
fof(fact_ATP_Olambda__195,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_lf,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_le,Uu))) ) ).

% ATP.lambda_195
fof(fact_ATP_Olambda__196,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_lb,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_la,Uu))) ) ).

% ATP.lambda_196
fof(fact_ATP_Olambda__197,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_kx,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_kw,Uu))) ) ).

% ATP.lambda_197
fof(fact_ATP_Olambda__198,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ku,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_kt,Uu))) ) ).

% ATP.lambda_198
fof(fact_ATP_Olambda__199,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ks,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_kr,Uu))) ) ).

% ATP.lambda_199
fof(fact_ATP_Olambda__200,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_kq,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_kp,Uu))) ) ).

% ATP.lambda_200
fof(fact_ATP_Olambda__201,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_kn,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_km,Uu))) ) ).

% ATP.lambda_201
fof(fact_ATP_Olambda__202,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_kj,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ki,Uu))) ) ).

% ATP.lambda_202
fof(fact_ATP_Olambda__203,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_kh,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_kg,Uu))) ) ).

% ATP.lambda_203
fof(fact_ATP_Olambda__204,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ke,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_kd,Uu))) ) ).

% ATP.lambda_204
fof(fact_ATP_Olambda__205,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_kb,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ka,Uu))) ) ).

% ATP.lambda_205
fof(fact_ATP_Olambda__206,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_jy,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_jx,Uu))) ) ).

% ATP.lambda_206
fof(fact_ATP_Olambda__207,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_jv,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ju,Uu))) ) ).

% ATP.lambda_207
fof(fact_ATP_Olambda__208,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_js,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_jr,Uu))) ) ).

% ATP.lambda_208
fof(fact_ATP_Olambda__209,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_jp,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_jo,Uu))) ) ).

% ATP.lambda_209
fof(fact_ATP_Olambda__210,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_jm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_jl,Uu))) ) ).

% ATP.lambda_210
fof(fact_ATP_Olambda__211,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_jj,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ji,Uu))) ) ).

% ATP.lambda_211
fof(fact_ATP_Olambda__212,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_jf,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_je,Uu))) ) ).

% ATP.lambda_212
fof(fact_ATP_Olambda__213,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_jb,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ja,Uu))) ) ).

% ATP.lambda_213
fof(fact_ATP_Olambda__214,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ix,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_iw,Uu))) ) ).

% ATP.lambda_214
fof(fact_ATP_Olambda__215,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_it,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_is,Uu))) ) ).

% ATP.lambda_215
fof(fact_ATP_Olambda__216,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_iq,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ip,Uu))) ) ).

% ATP.lambda_216
fof(fact_ATP_Olambda__217,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_in,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_im,Uu))) ) ).

% ATP.lambda_217
fof(fact_ATP_Olambda__218,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ik,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ij,Uu))) ) ).

% ATP.lambda_218
fof(fact_ATP_Olambda__219,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ih,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ig,Uu))) ) ).

% ATP.lambda_219
fof(fact_ATP_Olambda__220,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ie,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_id,Uu))) ) ).

% ATP.lambda_220
fof(fact_ATP_Olambda__221,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ib,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ia,Uu))) ) ).

% ATP.lambda_221
fof(fact_ATP_Olambda__222,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_hx,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_hw,Uu))) ) ).

% ATP.lambda_222
fof(fact_ATP_Olambda__223,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ht,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_hs,Uu))) ) ).

% ATP.lambda_223
fof(fact_ATP_Olambda__224,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_hp,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ho,Uu))) ) ).

% ATP.lambda_224
fof(fact_ATP_Olambda__225,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_hl,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_hk,Uu))) ) ).

% ATP.lambda_225
fof(fact_ATP_Olambda__226,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_hh,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_hg,Uu))) ) ).

% ATP.lambda_226
fof(fact_ATP_Olambda__227,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_hd,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_hc,Uu))) ) ).

% ATP.lambda_227
fof(fact_ATP_Olambda__228,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gz,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_gy,Uu))) ) ).

% ATP.lambda_228
fof(fact_ATP_Olambda__229,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gv,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_gu,Uu))) ) ).

% ATP.lambda_229
fof(fact_ATP_Olambda__230,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gr,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_gq,Uu))) ) ).

% ATP.lambda_230
fof(fact_ATP_Olambda__231,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gl,Uu))) ) ).

% ATP.lambda_231
fof(fact_ATP_Olambda__232,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gk,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gj,Uu))) ) ).

% ATP.lambda_232
fof(fact_ATP_Olambda__233,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gh,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gg,Uu))) ) ).

% ATP.lambda_233
fof(fact_ATP_Olambda__234,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gf,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ge,Uu))) ) ).

% ATP.lambda_234
fof(fact_ATP_Olambda__235,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gd,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gc,Uu))) ) ).

% ATP.lambda_235
fof(fact_ATP_Olambda__236,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gb,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ga,Uu))) ) ).

% ATP.lambda_236
fof(fact_ATP_Olambda__237,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_fz,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fy,Uu))) ) ).

% ATP.lambda_237
fof(fact_ATP_Olambda__238,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_fx,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fw,Uu))) ) ).

% ATP.lambda_238
fof(fact_ATP_Olambda__239,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_fv,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fu,Uu))) ) ).

% ATP.lambda_239
fof(fact_ATP_Olambda__240,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ft,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fs,Uu))) ) ).

% ATP.lambda_240
fof(fact_ATP_Olambda__241,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_fr,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fq,Uu))) ) ).

% ATP.lambda_241
fof(fact_ATP_Olambda__242,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_fp,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fo,Uu))) ) ).

% ATP.lambda_242
fof(fact_ATP_Olambda__243,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_fn,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fm,Uu))) ) ).

% ATP.lambda_243
fof(fact_ATP_Olambda__244,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_fl,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fk,Uu))) ) ).

% ATP.lambda_244
fof(fact_ATP_Olambda__245,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_fj,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fi,Uu))) ) ).

% ATP.lambda_245
fof(fact_ATP_Olambda__246,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_fh,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fg,Uu))) ) ).

% ATP.lambda_246
fof(fact_ATP_Olambda__247,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ff,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fe,Uu))) ) ).

% ATP.lambda_247
fof(fact_ATP_Olambda__248,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_fd,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fc,Uu))) ) ).

% ATP.lambda_248
fof(fact_ATP_Olambda__249,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_fa,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ez,Uu))) ) ).

% ATP.lambda_249
fof(fact_ATP_Olambda__250,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ew,Uu))) ) ).

% ATP.lambda_250
fof(fact_ATP_Olambda__251,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_eu,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_et,Uu))) ) ).

% ATP.lambda_251
fof(fact_ATP_Olambda__252,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eq,Uu))) ) ).

% ATP.lambda_252
fof(fact_ATP_Olambda__253,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_eo,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_en,Uu))) ) ).

% ATP.lambda_253
fof(fact_ATP_Olambda__254,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_eh,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eg,Uu))) ) ).

% ATP.lambda_254
fof(fact_ATP_Olambda__255,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ee,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ed,Uu))) ) ).

% ATP.lambda_255
fof(fact_ATP_Olambda__256,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ec,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eb,Uu))) ) ).

% ATP.lambda_256
fof(fact_ATP_Olambda__257,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_dz,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dy,Uu))) ) ).

% ATP.lambda_257
fof(fact_ATP_Olambda__258,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_dx,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dw,Uu))) ) ).

% ATP.lambda_258
fof(fact_ATP_Olambda__259,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_dv,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_du,Uu))) ) ).

% ATP.lambda_259
fof(fact_ATP_Olambda__260,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ds,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dr,Uu))) ) ).

% ATP.lambda_260
fof(fact_ATP_Olambda__261,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_dp,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_do,Uu))) ) ).

% ATP.lambda_261
fof(fact_ATP_Olambda__262,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_dm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dl,Uu))) ) ).

% ATP.lambda_262
fof(fact_ATP_Olambda__263,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_dj,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_di,Uu))) ) ).

% ATP.lambda_263
fof(fact_ATP_Olambda__264,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_dg,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_df,Uu))) ) ).

% ATP.lambda_264
fof(fact_ATP_Olambda__265,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_dd,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dc,Uu))) ) ).

% ATP.lambda_265
fof(fact_ATP_Olambda__266,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_da,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cz,Uu))) ) ).

% ATP.lambda_266
fof(fact_ATP_Olambda__267,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_cx,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cw,Uu))) ) ).

% ATP.lambda_267
fof(fact_ATP_Olambda__268,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_cu,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ct,Uu))) ) ).

% ATP.lambda_268
fof(fact_ATP_Olambda__269,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_cq,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cp,Uu))) ) ).

% ATP.lambda_269
fof(fact_ATP_Olambda__270,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_cm,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cl,Uu))) ) ).

% ATP.lambda_270
fof(fact_ATP_Olambda__271,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ci,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch,Uu))) ) ).

% ATP.lambda_271
fof(fact_ATP_Olambda__272,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ad,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ac,Uu))) ) ).

% ATP.lambda_272
fof(fact_ATP_Olambda__273,axiom,
    ! [Uu] : aa_TPTP_ind_TPTP_ind(aTP_Lamm_af,Uu) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,scratc406400774d_frac),aTP_Lamm_ae(Uu)) ).

% ATP.lambda_273
fof(fact_ATP_Olambda__274,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_pi,Uu))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(scratc406400774d_frac),aa_TPT43085870d_bool(aTP_Lamm_ph,Uu))) ) ).

% ATP.lambda_274
fof(fact_ATP_Olambda__275,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_pg,Uu))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(scratc406400774d_frac),aa_TPT43085870d_bool(aTP_Lamm_pf,Uu))) ) ).

% ATP.lambda_275
fof(fact_ATP_Olambda__276,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_xg,Uu))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,scratc51547579nd_n_1),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu))) ) ).

% ATP.lambda_276
fof(fact_ATP_Olambda__277,axiom,
    ! [Uu] : aa_TPT494704832TP_ind(aTP_Lamm_bz,Uu) = aa_TPT494704832TP_ind(scratc1077096999d_repl,aa_TPTP_ind_TPTP_ind(scratc1012835814tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc742297147d_Sing,scratc1884736269ptyset))) ).

% ATP.lambda_277
fof(fact_ATP_Olambda__278,axiom,
    ! [Uu] :
      ( gg_TPTP_ind(Uu)
     => ( pp(aa_TPTP_ind_bool(aTP_Lamm_ax,Uu))
      <=> Uu != scratc1884736269ptyset ) ) ).

% ATP.lambda_278
fof(fact_ATP_Olambda__279,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_el,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1861875310t_some,aa_TPT43085870d_bool(aTP_Lamm_ek,Uu))) ) ).

% ATP.lambda_279
fof(fact_ATP_Olambda__280,axiom,
    ! [Uu] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_ej,Uu))
    <=> pp(aa_fun171081125l_bool(scratc1861875310t_some,aa_TPT43085870d_bool(aTP_Lamm_ei,Uu))) ) ).

% ATP.lambda_280
fof(fact_ATP_Olambda__281,axiom,
    ! [Uu] :
      ( gg_TPTP_ind(Uu)
     => ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
      <=> ? [X2] :
            ( gg_TPTP_ind(X2)
            & aa_TPTP_ind_TPTP_ind(scratc1567404824d_Inj1,X2) = Uu ) ) ) ).

% ATP.lambda_281
fof(fact_ATP_Olambda__282,axiom,
    ! [Uu] :
      ( gg_TPTP_ind(Uu)
     => ( pp(aa_TPTP_ind_bool(aTP_Lamm_by,Uu))
      <=> ? [X2] :
            ( gg_TPTP_ind(X2)
            & aa_TPTP_ind_TPTP_ind(scratc1567404823d_Inj0,X2) = Uu ) ) ) ).

% ATP.lambda_282
fof(fact_ATP_Olambda__283,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gg,Uu),Uua))
    <=> scratc174073786_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua)) ) ).

% ATP.lambda_283
fof(fact_ATP_Olambda__284,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_adb,Uu),Uua))
    <=> scratc174073786_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua)) ) ).

% ATP.lambda_284
fof(fact_ATP_Olambda__285,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rt,Uu),Uua))
    <=> scratc174073786_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua)) ) ).

% ATP.lambda_285
fof(fact_ATP_Olambda__286,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ge,Uu),Uua))
    <=> pp(scratc491815928nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua))) ) ).

% ATP.lambda_286
fof(fact_ATP_Olambda__287,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acz,Uu),Uua))
    <=> pp(scratc491815928nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))) ) ).

% ATP.lambda_287
fof(fact_ATP_Olambda__288,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rr,Uu),Uua))
    <=> pp(scratc491815928nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))) ) ).

% ATP.lambda_288
fof(fact_ATP_Olambda__289,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gc,Uu),Uua))
    <=> pp(scratc408216893nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua))) ) ).

% ATP.lambda_289
fof(fact_ATP_Olambda__290,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acx,Uu),Uua))
    <=> pp(scratc408216893nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))) ) ).

% ATP.lambda_290
fof(fact_ATP_Olambda__291,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rp,Uu),Uua))
    <=> pp(scratc408216893nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))) ) ).

% ATP.lambda_291
fof(fact_ATP_Olambda__292,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_adj,Uu),Uua))
    <=> scratc174073786_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1572426730n_some,aa_TPT43085870d_bool(aTP_Lamm_adh(Uu),Uua)),aa_fun171081125l_bool(scratc1572426730n_some,aa_TPT43085870d_bool(aTP_Lamm_adi(Uu),Uua))) ) ).

% ATP.lambda_292
fof(fact_ATP_Olambda__293,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_adf,Uu),Uua))
    <=> pp(scratc491815928nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1572426730n_some,aa_TPT43085870d_bool(scratc1019149568ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1572426730n_some,aa_TPT43085870d_bool(scratc1019149568ffprop(Uua),Uu)))) ) ).

% ATP.lambda_293
fof(fact_ATP_Olambda__294,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_add,Uu),Uua))
    <=> pp(scratc408216893nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1572426730n_some,aa_TPT43085870d_bool(scratc1019149568ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1572426730n_some,aa_TPT43085870d_bool(scratc1019149568ffprop(Uua),Uu)))) ) ).

% ATP.lambda_294
fof(fact_ATP_Olambda__295,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_afz,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Uu),Uua),Uua)) ) ).

% ATP.lambda_295
fof(fact_ATP_Olambda__296,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sb,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,Uu)),Uua))),Uu)) ) ).

% ATP.lambda_296
fof(fact_ATP_Olambda__297,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wc,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uua)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),Uua))) ) ).

% ATP.lambda_297
fof(fact_ATP_Olambda__298,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wf,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uua)),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uua)))) ) ).

% ATP.lambda_298
fof(fact_ATP_Olambda__299,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aem,Uu),Uua))
    <=> pp(scratc520525675_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uua),scratc51547579nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),aa_fun171081125l_bool(scratc2092983147_n_all,aa_TPT43085870d_bool(aTP_Lamm_au,Uua)))) ) ).

% ATP.lambda_299
fof(fact_ATP_Olambda__300,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ws,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),scratc51547579nd_n_1)),Uu))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uua),Uu)) ) ) ).

% ATP.lambda_300
fof(fact_ATP_Olambda__301,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wo,Uu),Uua))
    <=> pp(scratc520525675_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uua),scratc51547579nd_n_1)),Uu),aa_fun171081125l_bool(scratc2092983147_n_all,aa_TPT43085870d_bool(aTP_Lamm_as(Uu),Uua)))) ) ).

% ATP.lambda_301
fof(fact_ATP_Olambda__302,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aew,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua)) ) ) ).

% ATP.lambda_302
fof(fact_ATP_Olambda__303,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wi,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uua)),Uua))) ) ).

% ATP.lambda_303
fof(fact_ATP_Olambda__304,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wq,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uua)),Uu))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uua),Uu)) ) ) ).

% ATP.lambda_304
fof(fact_ATP_Olambda__305,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aeg,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua)))) ) ).

% ATP.lambda_305
fof(fact_ATP_Olambda__306,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ww,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),scratc51547579nd_n_1)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uua),Uu)) ) ) ).

% ATP.lambda_306
fof(fact_ATP_Olambda__307,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wl,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uua)),Uu))) ) ).

% ATP.lambda_307
fof(fact_ATP_Olambda__308,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wu,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uua),Uu)) ) ) ).

% ATP.lambda_308
fof(fact_ATP_Olambda__309,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aej,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua)))) ) ).

% ATP.lambda_309
fof(fact_ATP_Olambda__310,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_au,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uu),Uua)))) ) ).

% ATP.lambda_310
fof(fact_ATP_Olambda__311,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kt,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),aa_TPTP_ind_TPTP_ind(scratc649711215_367_w(Uu),Uua))),Uu)) ) ) ).

% ATP.lambda_311
fof(fact_ATP_Olambda__312,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xa,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uua),Uu))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),scratc51547579nd_n_1)),Uu)) ) ) ).

% ATP.lambda_312
fof(fact_ATP_Olambda__313,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aer,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uua))) ) ) ).

% ATP.lambda_313
fof(fact_ATP_Olambda__314,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aw,Uu),Uua))
    <=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc441918964nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046523d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046523d_n_in,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uua)),Uu))) ) ).

% ATP.lambda_314
fof(fact_ATP_Olambda__315,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wy,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uua),Uu))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uua)),Uu)) ) ) ).

% ATP.lambda_315
fof(fact_ATP_Olambda__316,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kr,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),aa_TPTP_ind_TPTP_ind(scratc649711215_367_w(Uu),Uua)))) ) ) ).

% ATP.lambda_316
fof(fact_ATP_Olambda__317,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xe,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uua),Uu))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),scratc51547579nd_n_1))) ) ) ).

% ATP.lambda_317
fof(fact_ATP_Olambda__318,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xc,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uua),Uu))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu))) ) ) ).

% ATP.lambda_318
fof(fact_ATP_Olambda__319,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uu))) ) ).

% ATP.lambda_319
fof(fact_ATP_Olambda__320,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wa,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uu))) ) ).

% ATP.lambda_320
fof(fact_ATP_Olambda__321,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_adv,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uu))) ) ).

% ATP.lambda_321
fof(fact_ATP_Olambda__322,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ki,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uu))) ) ).

% ATP.lambda_322
fof(fact_ATP_Olambda__323,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_op,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uu))) ) ).

% ATP.lambda_323
fof(fact_ATP_Olambda__324,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fg,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1066042873moreis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,Uua),Uu)) ) ) ).

% ATP.lambda_324
fof(fact_ATP_Olambda__325,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fe,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1066042873moreis,Uua),Uu)) ) ) ).

% ATP.lambda_325
fof(fact_ATP_Olambda__326,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ga,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uua),Uu)) ) ) ).

% ATP.lambda_326
fof(fact_ATP_Olambda__327,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fy,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uua),Uu)) ) ) ).

% ATP.lambda_327
fof(fact_ATP_Olambda__328,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acv,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uua),Uu)) ) ) ).

% ATP.lambda_328
fof(fact_ATP_Olambda__329,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acr,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uua),Uu)) ) ) ).

% ATP.lambda_329
fof(fact_ATP_Olambda__330,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acp,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uua),Uu)) ) ) ).

% ATP.lambda_330
fof(fact_ATP_Olambda__331,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qb,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uua),Uu)) ) ) ).

% ATP.lambda_331
fof(fact_ATP_Olambda__332,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gl,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,Uua),Uu)) ) ) ).

% ATP.lambda_332
fof(fact_ATP_Olambda__333,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qd,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uua),Uu)) ) ) ).

% ATP.lambda_333
fof(fact_ATP_Olambda__334,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rn,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uua),Uu)) ) ) ).

% ATP.lambda_334
fof(fact_ATP_Olambda__335,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rl,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uua),Uu)) ) ) ).

% ATP.lambda_335
fof(fact_ATP_Olambda__336,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_si,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uua),Uu)) ) ) ).

% ATP.lambda_336
fof(fact_ATP_Olambda__337,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_act,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uua),Uu)) ) ) ).

% ATP.lambda_337
fof(fact_ATP_Olambda__338,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kw,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => pp(aa_fun171081125l_bool(scratc828602088l_some(scratc406400774d_frac),aa_TPT43085870d_bool(aTP_Lamm_kv(Uu),Uua))) ) ) ).

% ATP.lambda_338
fof(fact_ATP_Olambda__339,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pd,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => pp(aa_fun171081125l_bool(scratc828602088l_some(scratc406400774d_frac),aa_TPT43085870d_bool(aTP_Lamm_pc(Uu),Uua))) ) ) ).

% ATP.lambda_339
fof(fact_ATP_Olambda__340,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua))
       => pp(aa_fun171081125l_bool(scratc1861875310t_some,aa_TPT43085870d_bool(aTP_Lamm_ef(Uu),Uua))) ) ) ).

% ATP.lambda_340
fof(fact_ATP_Olambda__341,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fw,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1066042873moreis,Uu),Uua))
       => pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua))) ) ) ).

% ATP.lambda_341
fof(fact_ATP_Olambda__342,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fu,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,Uu),Uua))
       => pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua))) ) ) ).

% ATP.lambda_342
fof(fact_ATP_Olambda__343,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fo,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua))
       => pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,Uu),Uua))) ) ) ).

% ATP.lambda_343
fof(fact_ATP_Olambda__344,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fm,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua))
       => pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1066042873moreis,Uu),Uua))) ) ) ).

% ATP.lambda_344
fof(fact_ATP_Olambda__345,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acf,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua))
       => pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))) ) ) ).

% ATP.lambda_345
fof(fact_ATP_Olambda__346,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acn,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua))
       => pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))) ) ) ).

% ATP.lambda_346
fof(fact_ATP_Olambda__347,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acl,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))
       => pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua))) ) ) ).

% ATP.lambda_347
fof(fact_ATP_Olambda__348,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qz,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uua))
       => pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))) ) ) ).

% ATP.lambda_348
fof(fact_ATP_Olambda__349,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rb,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uu),Uua))
       => pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))) ) ) ).

% ATP.lambda_349
fof(fact_ATP_Olambda__350,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qt,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uua))) ) ) ).

% ATP.lambda_350
fof(fact_ATP_Olambda__351,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qr,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uu),Uua))) ) ) ).

% ATP.lambda_351
fof(fact_ATP_Olambda__352,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acd,Uu),Uua))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))
       => pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua))) ) ) ).

% ATP.lambda_352
fof(fact_ATP_Olambda__353,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uua)),Uu)) ) ).

% ATP.lambda_353
fof(fact_ATP_Olambda__354,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abf,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua)),Uu)) ) ).

% ATP.lambda_354
fof(fact_ATP_Olambda__355,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ok,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uua)),Uu)) ) ).

% ATP.lambda_355
fof(fact_ATP_Olambda__356,axiom,
    ! [Uu,Uua] : aa_TPTP_ind_TPTP_ind(aTP_Lamm_aq(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uu),Uua)),Uua) ).

% ATP.lambda_356
fof(fact_ATP_Olambda__357,axiom,
    ! [Uu,Uua] : aa_TPTP_ind_TPTP_ind(aTP_Lamm_bw(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1077096999d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1629901042d_pair,Uua)) ).

% ATP.lambda_357
fof(fact_ATP_Olambda__358,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_afc,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_afa,Uu)),aa_TPT43085870d_bool(aTP_Lamm_afb(Uu),Uua))) ) ).

% ATP.lambda_358
fof(fact_ATP_Olambda__359,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aea,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uu)),Uua))) ) ).

% ATP.lambda_359
fof(fact_ATP_Olambda__360,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aed,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uua)))) ) ).

% ATP.lambda_360
fof(fact_ATP_Olambda__361,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fk,Uu),Uua))
    <=> ( pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1066042873moreis,Uu),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua)) ) ) ).

% ATP.lambda_361
fof(fact_ATP_Olambda__362,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fi,Uu),Uua))
    <=> ( pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,Uu),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua)) ) ) ).

% ATP.lambda_362
fof(fact_ATP_Olambda__363,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fs,Uu),Uua))
    <=> ( pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,Uu),Uua)) ) ) ).

% ATP.lambda_363
fof(fact_ATP_Olambda__364,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fq,Uu),Uua))
    <=> ( pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1066042873moreis,Uu),Uua)) ) ) ).

% ATP.lambda_364
fof(fact_ATP_Olambda__365,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acj,Uu),Uua))
    <=> ( pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua)) ) ) ).

% ATP.lambda_365
fof(fact_ATP_Olambda__366,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acb,Uu),Uua))
    <=> ( pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua)) ) ) ).

% ATP.lambda_366
fof(fact_ATP_Olambda__367,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abz,Uu),Uua))
    <=> ( pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua)) ) ) ).

% ATP.lambda_367
fof(fact_ATP_Olambda__368,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qn,Uu),Uua))
    <=> ( pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua)) ) ) ).

% ATP.lambda_368
fof(fact_ATP_Olambda__369,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qp,Uu),Uua))
    <=> ( pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uu),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua)) ) ) ).

% ATP.lambda_369
fof(fact_ATP_Olambda__370,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qx,Uu),Uua))
    <=> ( pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uua)) ) ) ).

% ATP.lambda_370
fof(fact_ATP_Olambda__371,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qv,Uu),Uua))
    <=> ( pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uu),Uua)) ) ) ).

% ATP.lambda_371
fof(fact_ATP_Olambda__372,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ach,Uu),Uua))
    <=> ( pp(scratc627990855_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua)) ) ) ).

% ATP.lambda_372
fof(fact_ATP_Olambda__373,axiom,
    ! [Uu,Uua] : aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_ca,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1096550272nunion(aa_TPTP_ind_TPTP_ind(scratc742297147d_Sing,scratc1884736269ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1077096999d_repl,Uu),Uua)) ).

% ATP.lambda_373
fof(fact_ATP_Olambda__374,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sd,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc483751278nd_num,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc400086645nd_den,Uu)),Uua)))) ) ).

% ATP.lambda_374
fof(fact_ATP_Olambda__375,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dw,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uua))) ) ).

% ATP.lambda_375
fof(fact_ATP_Olambda__376,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oi,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uua))) ) ).

% ATP.lambda_376
fof(fact_ATP_Olambda__377,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_adt,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua))) ) ).

% ATP.lambda_377
fof(fact_ATP_Olambda__378,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abd,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua))) ) ).

% ATP.lambda_378
fof(fact_ATP_Olambda__379,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_av,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uua))) ) ).

% ATP.lambda_379
fof(fact_ATP_Olambda__380,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_afa,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1268198477_power,Uu))) ) ).

% ATP.lambda_380
fof(fact_ATP_Olambda__381,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uua),Uu)) ) ).

% ATP.lambda_381
fof(fact_ATP_Olambda__382,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ei,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uua),Uu)) ) ).

% ATP.lambda_382
fof(fact_ATP_Olambda__383,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ao,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uua),Uu)) ) ).

% ATP.lambda_383
fof(fact_ATP_Olambda__384,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ph,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uua),Uu)) ) ).

% ATP.lambda_384
fof(fact_ATP_Olambda__385,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pf,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uua),Uu)) ) ).

% ATP.lambda_385
fof(fact_ATP_Olambda__386,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aeu,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046523d_n_in,Uua),Uu)) ) ).

% ATP.lambda_386
fof(fact_ATP_Olambda__387,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cb,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc480864923nd_nIn,Uua),Uu)) ) ).

% ATP.lambda_387
fof(fact_ATP_Olambda__388,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ay,Uu),Uua))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,Uua),Uu)) ) ).

% ATP.lambda_388
fof(fact_ATP_Olambda__389,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ady,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_adx(Uu),Uua))) ) ).

% ATP.lambda_389
fof(fact_ATP_Olambda__390,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_adr,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_adq(Uu),Uua))) ) ).

% ATP.lambda_390
fof(fact_ATP_Olambda__391,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ado,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_adn(Uu),Uua))) ) ).

% ATP.lambda_391
fof(fact_ATP_Olambda__392,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abx,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abw(Uu),Uua))) ) ).

% ATP.lambda_392
fof(fact_ATP_Olambda__393,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abu,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abt(Uu),Uua))) ) ).

% ATP.lambda_393
fof(fact_ATP_Olambda__394,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abr,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abq(Uu),Uua))) ) ).

% ATP.lambda_394
fof(fact_ATP_Olambda__395,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abo,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abn(Uu),Uua))) ) ).

% ATP.lambda_395
fof(fact_ATP_Olambda__396,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abl,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abk(Uu),Uua))) ) ).

% ATP.lambda_396
fof(fact_ATP_Olambda__397,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abi,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_abh(Uu),Uua))) ) ).

% ATP.lambda_397
fof(fact_ATP_Olambda__398,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aaz,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aay(Uu),Uua))) ) ).

% ATP.lambda_398
fof(fact_ATP_Olambda__399,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aaw,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aav(Uu),Uua))) ) ).

% ATP.lambda_399
fof(fact_ATP_Olambda__400,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aat,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aas(Uu),Uua))) ) ).

% ATP.lambda_400
fof(fact_ATP_Olambda__401,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aaq,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aap(Uu),Uua))) ) ).

% ATP.lambda_401
fof(fact_ATP_Olambda__402,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aan,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aam(Uu),Uua))) ) ).

% ATP.lambda_402
fof(fact_ATP_Olambda__403,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aak,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aaj(Uu),Uua))) ) ).

% ATP.lambda_403
fof(fact_ATP_Olambda__404,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aah,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aag(Uu),Uua))) ) ).

% ATP.lambda_404
fof(fact_ATP_Olambda__405,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aad,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_aac(Uu),Uua))) ) ).

% ATP.lambda_405
fof(fact_ATP_Olambda__406,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zz,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zy(Uu),Uua))) ) ).

% ATP.lambda_406
fof(fact_ATP_Olambda__407,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zv,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zu(Uu),Uua))) ) ).

% ATP.lambda_407
fof(fact_ATP_Olambda__408,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zr,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zq(Uu),Uua))) ) ).

% ATP.lambda_408
fof(fact_ATP_Olambda__409,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zo,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zn(Uu),Uua))) ) ).

% ATP.lambda_409
fof(fact_ATP_Olambda__410,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zl,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zk(Uu),Uua))) ) ).

% ATP.lambda_410
fof(fact_ATP_Olambda__411,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zi,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zh(Uu),Uua))) ) ).

% ATP.lambda_411
fof(fact_ATP_Olambda__412,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zf,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ze(Uu),Uua))) ) ).

% ATP.lambda_412
fof(fact_ATP_Olambda__413,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zc,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_zb(Uu),Uua))) ) ).

% ATP.lambda_413
fof(fact_ATP_Olambda__414,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yz,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_yy(Uu),Uua))) ) ).

% ATP.lambda_414
fof(fact_ATP_Olambda__415,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yw,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_yv(Uu),Uua))) ) ).

% ATP.lambda_415
fof(fact_ATP_Olambda__416,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yt,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ys(Uu),Uua))) ) ).

% ATP.lambda_416
fof(fact_ATP_Olambda__417,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yq,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_yp(Uu),Uua))) ) ).

% ATP.lambda_417
fof(fact_ATP_Olambda__418,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yn,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ym(Uu),Uua))) ) ).

% ATP.lambda_418
fof(fact_ATP_Olambda__419,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yj,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_yi(Uu),Uua))) ) ).

% ATP.lambda_419
fof(fact_ATP_Olambda__420,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yf,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ye(Uu),Uua))) ) ).

% ATP.lambda_420
fof(fact_ATP_Olambda__421,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yb,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ya(Uu),Uua))) ) ).

% ATP.lambda_421
fof(fact_ATP_Olambda__422,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xx,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_xw(Uu),Uua))) ) ).

% ATP.lambda_422
fof(fact_ATP_Olambda__423,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xt,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_xs(Uu),Uua))) ) ).

% ATP.lambda_423
fof(fact_ATP_Olambda__424,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xp,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_xo(Uu),Uua))) ) ).

% ATP.lambda_424
fof(fact_ATP_Olambda__425,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xl,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_xk(Uu),Uua))) ) ).

% ATP.lambda_425
fof(fact_ATP_Olambda__426,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vy,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vx(Uu),Uua))) ) ).

% ATP.lambda_426
fof(fact_ATP_Olambda__427,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vv,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vu(Uu),Uua))) ) ).

% ATP.lambda_427
fof(fact_ATP_Olambda__428,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vs,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vr(Uu),Uua))) ) ).

% ATP.lambda_428
fof(fact_ATP_Olambda__429,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vp,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vo(Uu),Uua))) ) ).

% ATP.lambda_429
fof(fact_ATP_Olambda__430,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vm,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vl(Uu),Uua))) ) ).

% ATP.lambda_430
fof(fact_ATP_Olambda__431,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vj,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vi(Uu),Uua))) ) ).

% ATP.lambda_431
fof(fact_ATP_Olambda__432,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vg,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vf(Uu),Uua))) ) ).

% ATP.lambda_432
fof(fact_ATP_Olambda__433,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vd,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_vc(Uu),Uua))) ) ).

% ATP.lambda_433
fof(fact_ATP_Olambda__434,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_va,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_uz(Uu),Uua))) ) ).

% ATP.lambda_434
fof(fact_ATP_Olambda__435,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uw,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_uv(Uu),Uua))) ) ).

% ATP.lambda_435
fof(fact_ATP_Olambda__436,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_us,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ur(Uu),Uua))) ) ).

% ATP.lambda_436
fof(fact_ATP_Olambda__437,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uo,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_un(Uu),Uua))) ) ).

% ATP.lambda_437
fof(fact_ATP_Olambda__438,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uk,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_uj(Uu),Uua))) ) ).

% ATP.lambda_438
fof(fact_ATP_Olambda__439,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uh,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ug(Uu),Uua))) ) ).

% ATP.lambda_439
fof(fact_ATP_Olambda__440,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ue,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ud(Uu),Uua))) ) ).

% ATP.lambda_440
fof(fact_ATP_Olambda__441,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ub,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ua(Uu),Uua))) ) ).

% ATP.lambda_441
fof(fact_ATP_Olambda__442,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ty,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_tx(Uu),Uua))) ) ).

% ATP.lambda_442
fof(fact_ATP_Olambda__443,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tv,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_tu(Uu),Uua))) ) ).

% ATP.lambda_443
fof(fact_ATP_Olambda__444,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ts,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_tr(Uu),Uua))) ) ).

% ATP.lambda_444
fof(fact_ATP_Olambda__445,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tp,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_to(Uu),Uua))) ) ).

% ATP.lambda_445
fof(fact_ATP_Olambda__446,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tl,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_tk(Uu),Uua))) ) ).

% ATP.lambda_446
fof(fact_ATP_Olambda__447,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_th,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_tg(Uu),Uua))) ) ).

% ATP.lambda_447
fof(fact_ATP_Olambda__448,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_td,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_tc(Uu),Uua))) ) ).

% ATP.lambda_448
fof(fact_ATP_Olambda__449,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sz,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_sy(Uu),Uua))) ) ).

% ATP.lambda_449
fof(fact_ATP_Olambda__450,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sv,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_su(Uu),Uua))) ) ).

% ATP.lambda_450
fof(fact_ATP_Olambda__451,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sr,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_sq(Uu),Uua))) ) ).

% ATP.lambda_451
fof(fact_ATP_Olambda__452,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sn,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_sm(Uu),Uua))) ) ).

% ATP.lambda_452
fof(fact_ATP_Olambda__453,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rz,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ry(Uu),Uua))) ) ).

% ATP.lambda_453
fof(fact_ATP_Olambda__454,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rw,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_rv(Uu),Uua))) ) ).

% ATP.lambda_454
fof(fact_ATP_Olambda__455,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ow,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_ov(Uu),Uua))) ) ).

% ATP.lambda_455
fof(fact_ATP_Olambda__456,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ot,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aTP_Lamm_os(Uu),Uua))) ) ).

% ATP.lambda_456
fof(fact_ATP_Olambda__457,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sg,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_sf(Uu),Uua))) ) ).

% ATP.lambda_457
fof(fact_ATP_Olambda__458,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rj,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ri(Uu),Uua))) ) ).

% ATP.lambda_458
fof(fact_ATP_Olambda__459,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rf,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_re(Uu),Uua))) ) ).

% ATP.lambda_459
fof(fact_ATP_Olambda__460,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ql,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_qk(Uu),Uua))) ) ).

% ATP.lambda_460
fof(fact_ATP_Olambda__461,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qh,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_qg(Uu),Uua))) ) ).

% ATP.lambda_461
fof(fact_ATP_Olambda__462,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pz,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_py(Uu),Uua))) ) ).

% ATP.lambda_462
fof(fact_ATP_Olambda__463,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pw,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_pv(Uu),Uua))) ) ).

% ATP.lambda_463
fof(fact_ATP_Olambda__464,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pt,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ps(Uu),Uua))) ) ).

% ATP.lambda_464
fof(fact_ATP_Olambda__465,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pq,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_pp(Uu),Uua))) ) ).

% ATP.lambda_465
fof(fact_ATP_Olambda__466,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pn,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_pm(Uu),Uua))) ) ).

% ATP.lambda_466
fof(fact_ATP_Olambda__467,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pk,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_pj(Uu),Uua))) ) ).

% ATP.lambda_467
fof(fact_ATP_Olambda__468,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pa,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_oz(Uu),Uua))) ) ).

% ATP.lambda_468
fof(fact_ATP_Olambda__469,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_on,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_om(Uu),Uua))) ) ).

% ATP.lambda_469
fof(fact_ATP_Olambda__470,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_og,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_of(Uu),Uua))) ) ).

% ATP.lambda_470
fof(fact_ATP_Olambda__471,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_od,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_oc(Uu),Uua))) ) ).

% ATP.lambda_471
fof(fact_ATP_Olambda__472,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oa,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nz(Uu),Uua))) ) ).

% ATP.lambda_472
fof(fact_ATP_Olambda__473,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nx,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nw(Uu),Uua))) ) ).

% ATP.lambda_473
fof(fact_ATP_Olambda__474,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nu,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nt(Uu),Uua))) ) ).

% ATP.lambda_474
fof(fact_ATP_Olambda__475,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nr,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nq(Uu),Uua))) ) ).

% ATP.lambda_475
fof(fact_ATP_Olambda__476,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_no,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nn(Uu),Uua))) ) ).

% ATP.lambda_476
fof(fact_ATP_Olambda__477,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nk,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nj(Uu),Uua))) ) ).

% ATP.lambda_477
fof(fact_ATP_Olambda__478,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ng,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nf(Uu),Uua))) ) ).

% ATP.lambda_478
fof(fact_ATP_Olambda__479,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nc,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_nb(Uu),Uua))) ) ).

% ATP.lambda_479
fof(fact_ATP_Olambda__480,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_my,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mx(Uu),Uua))) ) ).

% ATP.lambda_480
fof(fact_ATP_Olambda__481,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mv,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mu(Uu),Uua))) ) ).

% ATP.lambda_481
fof(fact_ATP_Olambda__482,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ms,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mr(Uu),Uua))) ) ).

% ATP.lambda_482
fof(fact_ATP_Olambda__483,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mp,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mo(Uu),Uua))) ) ).

% ATP.lambda_483
fof(fact_ATP_Olambda__484,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mm,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ml(Uu),Uua))) ) ).

% ATP.lambda_484
fof(fact_ATP_Olambda__485,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mj,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mi(Uu),Uua))) ) ).

% ATP.lambda_485
fof(fact_ATP_Olambda__486,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mg,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mf(Uu),Uua))) ) ).

% ATP.lambda_486
fof(fact_ATP_Olambda__487,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mc,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_mb(Uu),Uua))) ) ).

% ATP.lambda_487
fof(fact_ATP_Olambda__488,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ly,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_lx(Uu),Uua))) ) ).

% ATP.lambda_488
fof(fact_ATP_Olambda__489,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lu,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_lt(Uu),Uua))) ) ).

% ATP.lambda_489
fof(fact_ATP_Olambda__490,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lq,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_lp(Uu),Uua))) ) ).

% ATP.lambda_490
fof(fact_ATP_Olambda__491,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lm,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ll(Uu),Uua))) ) ).

% ATP.lambda_491
fof(fact_ATP_Olambda__492,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_li,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_lh(Uu),Uua))) ) ).

% ATP.lambda_492
fof(fact_ATP_Olambda__493,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_le,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ld(Uu),Uua))) ) ).

% ATP.lambda_493
fof(fact_ATP_Olambda__494,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_la,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_kz(Uu),Uua))) ) ).

% ATP.lambda_494
fof(fact_ATP_Olambda__495,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kp,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ko(Uu),Uua))) ) ).

% ATP.lambda_495
fof(fact_ATP_Olambda__496,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_km,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_kl(Uu),Uua))) ) ).

% ATP.lambda_496
fof(fact_ATP_Olambda__497,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kg,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_kf(Uu),Uua))) ) ).

% ATP.lambda_497
fof(fact_ATP_Olambda__498,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kd,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_kc(Uu),Uua))) ) ).

% ATP.lambda_498
fof(fact_ATP_Olambda__499,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ka,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_jz(Uu),Uua))) ) ).

% ATP.lambda_499
fof(fact_ATP_Olambda__500,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jx,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_jw(Uu),Uua))) ) ).

% ATP.lambda_500
fof(fact_ATP_Olambda__501,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ju,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_jt(Uu),Uua))) ) ).

% ATP.lambda_501
fof(fact_ATP_Olambda__502,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jr,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_jq(Uu),Uua))) ) ).

% ATP.lambda_502
fof(fact_ATP_Olambda__503,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jo,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_jn(Uu),Uua))) ) ).

% ATP.lambda_503
fof(fact_ATP_Olambda__504,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jl,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_jk(Uu),Uua))) ) ).

% ATP.lambda_504
fof(fact_ATP_Olambda__505,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ji,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_jh(Uu),Uua))) ) ).

% ATP.lambda_505
fof(fact_ATP_Olambda__506,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_je,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_jd(Uu),Uua))) ) ).

% ATP.lambda_506
fof(fact_ATP_Olambda__507,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ja,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_iz(Uu),Uua))) ) ).

% ATP.lambda_507
fof(fact_ATP_Olambda__508,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iw,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_iv(Uu),Uua))) ) ).

% ATP.lambda_508
fof(fact_ATP_Olambda__509,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_is,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ir(Uu),Uua))) ) ).

% ATP.lambda_509
fof(fact_ATP_Olambda__510,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ip,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_io(Uu),Uua))) ) ).

% ATP.lambda_510
fof(fact_ATP_Olambda__511,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_im,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_il(Uu),Uua))) ) ).

% ATP.lambda_511
fof(fact_ATP_Olambda__512,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ij,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ii(Uu),Uua))) ) ).

% ATP.lambda_512
fof(fact_ATP_Olambda__513,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ig,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_if(Uu),Uua))) ) ).

% ATP.lambda_513
fof(fact_ATP_Olambda__514,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_id,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_ic(Uu),Uua))) ) ).

% ATP.lambda_514
fof(fact_ATP_Olambda__515,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ia,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_hz(Uu),Uua))) ) ).

% ATP.lambda_515
fof(fact_ATP_Olambda__516,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hw,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_hv(Uu),Uua))) ) ).

% ATP.lambda_516
fof(fact_ATP_Olambda__517,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hs,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_hr(Uu),Uua))) ) ).

% ATP.lambda_517
fof(fact_ATP_Olambda__518,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ho,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_hn(Uu),Uua))) ) ).

% ATP.lambda_518
fof(fact_ATP_Olambda__519,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hk,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_hj(Uu),Uua))) ) ).

% ATP.lambda_519
fof(fact_ATP_Olambda__520,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hg,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_hf(Uu),Uua))) ) ).

% ATP.lambda_520
fof(fact_ATP_Olambda__521,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hc,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_hb(Uu),Uua))) ) ).

% ATP.lambda_521
fof(fact_ATP_Olambda__522,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gy,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_gx(Uu),Uua))) ) ).

% ATP.lambda_522
fof(fact_ATP_Olambda__523,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gu,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aTP_Lamm_gt(Uu),Uua))) ) ).

% ATP.lambda_523
fof(fact_ATP_Olambda__524,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gj,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gi(Uu),Uua))) ) ).

% ATP.lambda_524
fof(fact_ATP_Olambda__525,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fc,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fb(Uu),Uua))) ) ).

% ATP.lambda_525
fof(fact_ATP_Olambda__526,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ez,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ey(Uu),Uua))) ) ).

% ATP.lambda_526
fof(fact_ATP_Olambda__527,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ew,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ev(Uu),Uua))) ) ).

% ATP.lambda_527
fof(fact_ATP_Olambda__528,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_et,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua))) ) ).

% ATP.lambda_528
fof(fact_ATP_Olambda__529,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eq,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ep(Uu),Uua))) ) ).

% ATP.lambda_529
fof(fact_ATP_Olambda__530,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_en,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua))) ) ).

% ATP.lambda_530
fof(fact_ATP_Olambda__531,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eb,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua))) ) ).

% ATP.lambda_531
fof(fact_ATP_Olambda__532,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua))) ) ).

% ATP.lambda_532
fof(fact_ATP_Olambda__533,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dr,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dq(Uu),Uua))) ) ).

% ATP.lambda_533
fof(fact_ATP_Olambda__534,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_do,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dn(Uu),Uua))) ) ).

% ATP.lambda_534
fof(fact_ATP_Olambda__535,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dl,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dk(Uu),Uua))) ) ).

% ATP.lambda_535
fof(fact_ATP_Olambda__536,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dh(Uu),Uua))) ) ).

% ATP.lambda_536
fof(fact_ATP_Olambda__537,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua))) ) ).

% ATP.lambda_537
fof(fact_ATP_Olambda__538,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dc,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_db(Uu),Uua))) ) ).

% ATP.lambda_538
fof(fact_ATP_Olambda__539,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua))) ) ).

% ATP.lambda_539
fof(fact_ATP_Olambda__540,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cw,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cv(Uu),Uua))) ) ).

% ATP.lambda_540
fof(fact_ATP_Olambda__541,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cs(Uu),Uua))) ) ).

% ATP.lambda_541
fof(fact_ATP_Olambda__542,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_co(Uu),Uua))) ) ).

% ATP.lambda_542
fof(fact_ATP_Olambda__543,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cl,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ck(Uu),Uua))) ) ).

% ATP.lambda_543
fof(fact_ATP_Olambda__544,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua))) ) ).

% ATP.lambda_544
fof(fact_ATP_Olambda__545,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ac,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ab(Uu),Uua))) ) ).

% ATP.lambda_545
fof(fact_ATP_Olambda__546,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gq,Uu),Uua))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(scratc406400774d_frac),aa_TPT43085870d_bool(aTP_Lamm_gp(Uu),Uua))) ) ).

% ATP.lambda_546
fof(fact_ATP_Olambda__547,axiom,
    ! [Uu,Uua] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_adl,Uu),Uua))
    <=> pp(scratc1875410914_amone(scratc482439305nd_nat,aa_TPT43085870d_bool(aTP_Lamm_adh(Uu),Uua))) ) ).

% ATP.lambda_547
fof(fact_ATP_Olambda__548,axiom,
    ! [Uu,Uua] : aa_TPTP_ind_TPTP_ind(aTP_Lamm_at(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uu),Uua)) ).

% ATP.lambda_548
fof(fact_ATP_Olambda__549,axiom,
    ! [Uu,Uua] : aa_TPTP_ind_TPTP_ind(aTP_Lamm_ae(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1184912324_ratof,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uua)) ).

% ATP.lambda_549
fof(fact_ATP_Olambda__550,axiom,
    ! [Uu,Uua] : aa_TPTP_ind_TPTP_ind(aTP_Lamm_bt(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1775460343_union,aa_TPTP_ind_TPTP_ind(Uu,Uua)) ).

% ATP.lambda_550
fof(fact_ATP_Olambda__551,axiom,
    ! [Uu,Uua] :
      ( gg_TPTP_ind(Uua)
     => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bv,Uu),Uua))
      <=> ? [X3] :
            ( gg_TPTP_ind(X3)
            & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1629901042d_pair,Uu),X3) ) ) ) ).

% ATP.lambda_551
fof(fact_ATP_Olambda__552,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_afk(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(aa_TPTP_ind_TPTP_ind(scratc434490305etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1838069414d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc181028792_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1143644204second(Uu,Uua),Uub))),Uub)) ) ).

% ATP.lambda_552
fof(fact_ATP_Olambda__553,axiom,
    ! [Uu,Uua,Uub] : aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_cd(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,scratc1884736269ptyset),Uub),Uu),Uua) ).

% ATP.lambda_553
fof(fact_ATP_Olambda__554,axiom,
    ! [Uu,Uua,Uub] : aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_cc(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc409069744nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bq(Uu),Uua))) ).

% ATP.lambda_554
fof(fact_ATP_Olambda__555,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bj(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1782805115d_esti(Uu),Uub),Uua)) ) ).

% ATP.lambda_555
fof(fact_ATP_Olambda__556,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_afd(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1782805115d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc404274226_d_Sep(Uu),Uua)))
       => pp(aa_TPTP_ind_bool(Uua,Uub)) ) ) ).

% ATP.lambda_556
fof(fact_ATP_Olambda__557,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_afb(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc567763910d_incl(Uu),Uua),Uub))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc567763910d_incl(Uu),Uub),Uua))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(aa_TPTP_ind_TPTP_ind(scratc1268198477_power,Uu)),Uua),Uub)) ) ) ) ).

% ATP.lambda_557
fof(fact_ATP_Olambda__558,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_afl(Uu),Uua),Uub))
    <=> scratc1533070073_is_of(aa_TPTP_ind_TPTP_ind(scratc1143644204second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ay,Uua)) ) ).

% ATP.lambda_558
fof(fact_ATP_Olambda__559,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_afm(Uu),Uua),Uub))
    <=> scratc1533070073_is_of(aa_TPTP_ind_TPTP_ind(scratc181028792_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ay,Uu)) ) ).

% ATP.lambda_559
fof(fact_ATP_Olambda__560,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_afs(Uu),Uua),Uub))
    <=> scratc1533070073_is_of(aa_TPTP_ind_TPTP_ind(scratc1815386162d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ay,Uu)) ) ).

% ATP.lambda_560
fof(fact_ATP_Olambda__561,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_afw(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_aft(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_afv(Uu),Uua),Uub))) ) ).

% ATP.lambda_561
fof(fact_ATP_Olambda__562,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ov(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,Uu),Uub)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,Uua),Uub))),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua)),Uub))) ) ).

% ATP.lambda_562
fof(fact_ATP_Olambda__563,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rv(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uub))),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,Uu),Uua))) ) ).

% ATP.lambda_563
fof(fact_ATP_Olambda__564,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_db(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua)) ) ) ).

% ATP.lambda_564
fof(fact_ATP_Olambda__565,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua)) ) ) ).

% ATP.lambda_565
fof(fact_ATP_Olambda__566,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tx(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua)) ) ) ).

% ATP.lambda_566
fof(fact_ATP_Olambda__567,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ze(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua)) ) ) ).

% ATP.lambda_567
fof(fact_ATP_Olambda__568,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yv(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua)) ) ) ).

% ATP.lambda_568
fof(fact_ATP_Olambda__569,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,Uu),Uua)) ) ) ).

% ATP.lambda_569
fof(fact_ATP_Olambda__570,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ir(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua)) ) ) ).

% ATP.lambda_570
fof(fact_ATP_Olambda__571,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ii(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua)) ) ) ).

% ATP.lambda_571
fof(fact_ATP_Olambda__572,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mx(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua)) ) ) ).

% ATP.lambda_572
fof(fact_ATP_Olambda__573,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mo(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua)) ) ) ).

% ATP.lambda_573
fof(fact_ATP_Olambda__574,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_il(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua)) ) ) ).

% ATP.lambda_574
fof(fact_ATP_Olambda__575,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ic(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua)) ) ) ).

% ATP.lambda_575
fof(fact_ATP_Olambda__576,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mr(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua)) ) ) ).

% ATP.lambda_576
fof(fact_ATP_Olambda__577,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mi(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua)) ) ) ).

% ATP.lambda_577
fof(fact_ATP_Olambda__578,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tu(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua)) ) ) ).

% ATP.lambda_578
fof(fact_ATP_Olambda__579,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_adn(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uua),Uub)) ) ) ).

% ATP.lambda_579
fof(fact_ATP_Olambda__580,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zb(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua)) ) ) ).

% ATP.lambda_580
fof(fact_ATP_Olambda__581,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ys(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua)) ) ) ).

% ATP.lambda_581
fof(fact_ATP_Olambda__582,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_io(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua)) ) ) ).

% ATP.lambda_582
fof(fact_ATP_Olambda__583,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_if(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua)) ) ) ).

% ATP.lambda_583
fof(fact_ATP_Olambda__584,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mu(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua)) ) ) ).

% ATP.lambda_584
fof(fact_ATP_Olambda__585,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ml(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua)) ) ) ).

% ATP.lambda_585
fof(fact_ATP_Olambda__586,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tr(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua)) ) ) ).

% ATP.lambda_586
fof(fact_ATP_Olambda__587,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yy(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uub)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua)) ) ) ).

% ATP.lambda_587
fof(fact_ATP_Olambda__588,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yp(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uua)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua)) ) ) ).

% ATP.lambda_588
fof(fact_ATP_Olambda__589,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_os(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,Uu),Uub)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,Uua),Uub)))) ) ).

% ATP.lambda_589
fof(fact_ATP_Olambda__590,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uub)))) ) ).

% ATP.lambda_590
fof(fact_ATP_Olambda__591,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vu(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uub)))) ) ).

% ATP.lambda_591
fof(fact_ATP_Olambda__592,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_adx(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uub)))) ) ).

% ATP.lambda_592
fof(fact_ATP_Olambda__593,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kf(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uub)))) ) ).

% ATP.lambda_593
fof(fact_ATP_Olambda__594,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_om(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uub)))) ) ).

% ATP.lambda_594
fof(fact_ATP_Olambda__595,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vx(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uub))),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)))) ) ).

% ATP.lambda_595
fof(fact_ATP_Olambda__596,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kc(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uub))),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)))) ) ).

% ATP.lambda_596
fof(fact_ATP_Olambda__597,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_as(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(scratc800567211rdsucc,Uub))),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uua),Uub)),Uu))) ) ).

% ATP.lambda_597
fof(fact_ATP_Olambda__598,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ko(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uub)),Uu))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uub),aa_TPTP_ind_TPTP_ind(scratc649711215_367_w(Uu),Uua))) ) ) ) ).

% ATP.lambda_598
fof(fact_ATP_Olambda__599,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ry(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1333849730d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uub)))) ) ).

% ATP.lambda_599
fof(fact_ATP_Olambda__600,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1066042873moreis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uub)) ) ) ) ).

% ATP.lambda_600
fof(fact_ATP_Olambda__601,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,Uu),Uub)) ) ) ) ).

% ATP.lambda_601
fof(fact_ATP_Olambda__602,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ey(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uub)) ) ) ) ).

% ATP.lambda_602
fof(fact_ATP_Olambda__603,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uub))) ) ) ).

% ATP.lambda_603
fof(fact_ATP_Olambda__604,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uub),Uua))) ) ) ).

% ATP.lambda_604
fof(fact_ATP_Olambda__605,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1066042873moreis,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uub)) ) ) ) ).

% ATP.lambda_605
fof(fact_ATP_Olambda__606,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dn(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uub))) ) ) ).

% ATP.lambda_606
fof(fact_ATP_Olambda__607,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uub),Uua))) ) ) ).

% ATP.lambda_607
fof(fact_ATP_Olambda__608,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uub)) ) ) ) ).

% ATP.lambda_608
fof(fact_ATP_Olambda__609,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fb(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uub)) ) ) ) ).

% ATP.lambda_609
fof(fact_ATP_Olambda__610,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vr(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uub))) ) ) ).

% ATP.lambda_610
fof(fact_ATP_Olambda__611,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vi(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uub),Uua))) ) ) ).

% ATP.lambda_611
fof(fact_ATP_Olambda__612,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aay(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uub))) ) ) ).

% ATP.lambda_612
fof(fact_ATP_Olambda__613,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aap(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uua))) ) ) ).

% ATP.lambda_613
fof(fact_ATP_Olambda__614,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abk(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uub)) ) ) ) ).

% ATP.lambda_614
fof(fact_ATP_Olambda__615,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uj(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uub))) ) ) ).

% ATP.lambda_615
fof(fact_ATP_Olambda__616,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ug(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uub),Uua))) ) ) ).

% ATP.lambda_616
fof(fact_ATP_Olambda__617,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zq(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uub))) ) ) ).

% ATP.lambda_617
fof(fact_ATP_Olambda__618,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zn(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uua))) ) ) ).

% ATP.lambda_618
fof(fact_ATP_Olambda__619,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abn(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uub)) ) ) ) ).

% ATP.lambda_619
fof(fact_ATP_Olambda__620,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ud(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uub))) ) ) ).

% ATP.lambda_620
fof(fact_ATP_Olambda__621,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ua(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uub),Uua))) ) ) ).

% ATP.lambda_621
fof(fact_ATP_Olambda__622,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zk(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uub))) ) ) ).

% ATP.lambda_622
fof(fact_ATP_Olambda__623,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zh(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uua))) ) ) ).

% ATP.lambda_623
fof(fact_ATP_Olambda__624,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abh(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uub)) ) ) ) ).

% ATP.lambda_624
fof(fact_ATP_Olambda__625,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abt(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uub)) ) ) ) ).

% ATP.lambda_625
fof(fact_ATP_Olambda__626,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pj(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uub)) ) ) ) ).

% ATP.lambda_626
fof(fact_ATP_Olambda__627,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pv(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uub)) ) ) ) ).

% ATP.lambda_627
fof(fact_ATP_Olambda__628,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uub))) ) ) ).

% ATP.lambda_628
fof(fact_ATP_Olambda__629,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dh(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uub),Uua))) ) ) ).

% ATP.lambda_629
fof(fact_ATP_Olambda__630,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gi(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725338564_rt_is,Uu),Uub)) ) ) ) ).

% ATP.lambda_630
fof(fact_ATP_Olambda__631,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pp(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uub)) ) ) ) ).

% ATP.lambda_631
fof(fact_ATP_Olambda__632,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jz(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uub))) ) ) ).

% ATP.lambda_632
fof(fact_ATP_Olambda__633,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jq(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uua))) ) ) ).

% ATP.lambda_633
fof(fact_ATP_Olambda__634,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_of(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uub))) ) ) ).

% ATP.lambda_634
fof(fact_ATP_Olambda__635,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nw(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uua))) ) ) ).

% ATP.lambda_635
fof(fact_ATP_Olambda__636,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pm(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uub)) ) ) ) ).

% ATP.lambda_636
fof(fact_ATP_Olambda__637,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jt(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uub))) ) ) ).

% ATP.lambda_637
fof(fact_ATP_Olambda__638,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jk(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uua))) ) ) ).

% ATP.lambda_638
fof(fact_ATP_Olambda__639,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nz(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uub))) ) ) ).

% ATP.lambda_639
fof(fact_ATP_Olambda__640,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nq(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uua))) ) ) ).

% ATP.lambda_640
fof(fact_ATP_Olambda__641,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ps(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uub)) ) ) ) ).

% ATP.lambda_641
fof(fact_ATP_Olambda__642,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_py(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uub)) ) ) ) ).

% ATP.lambda_642
fof(fact_ATP_Olambda__643,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vo(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uub))) ) ) ).

% ATP.lambda_643
fof(fact_ATP_Olambda__644,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vf(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uub),Uua))) ) ) ).

% ATP.lambda_644
fof(fact_ATP_Olambda__645,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aav(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uub))) ) ) ).

% ATP.lambda_645
fof(fact_ATP_Olambda__646,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aam(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uua))) ) ) ).

% ATP.lambda_646
fof(fact_ATP_Olambda__647,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jw(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uub))) ) ) ).

% ATP.lambda_647
fof(fact_ATP_Olambda__648,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jn(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uua))) ) ) ).

% ATP.lambda_648
fof(fact_ATP_Olambda__649,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oc(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uub))) ) ) ).

% ATP.lambda_649
fof(fact_ATP_Olambda__650,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nt(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uua))) ) ) ).

% ATP.lambda_650
fof(fact_ATP_Olambda__651,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sf(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uub)) ) ) ) ).

% ATP.lambda_651
fof(fact_ATP_Olambda__652,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_adq(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,Uua),Uub))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc482964096nd_nis,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub))) ) ) ).

% ATP.lambda_652
fof(fact_ATP_Olambda__653,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vl(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uub))) ) ) ).

% ATP.lambda_653
fof(fact_ATP_Olambda__654,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vc(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uub),Uua))) ) ) ).

% ATP.lambda_654
fof(fact_ATP_Olambda__655,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aas(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uub))) ) ) ).

% ATP.lambda_655
fof(fact_ATP_Olambda__656,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aaj(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uua))) ) ) ).

% ATP.lambda_656
fof(fact_ATP_Olambda__657,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abq(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uub)) ) ) ) ).

% ATP.lambda_657
fof(fact_ATP_Olambda__658,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abw(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uua),Uub))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uub)) ) ) ) ).

% ATP.lambda_658
fof(fact_ATP_Olambda__659,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ef(Uu),Uua),Uub))
    <=> pp(scratc520525675_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uub),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uub),Uua))) ) ).

% ATP.lambda_659
fof(fact_ATP_Olambda__660,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pc(Uu),Uua),Uub))
    <=> pp(scratc520525675_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uub),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uub),Uua))) ) ).

% ATP.lambda_660
fof(fact_ATP_Olambda__661,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bq(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,Uub),Uu))
        & pp(aa_TPTP_ind_bool(Uua,Uub)) ) ) ).

% ATP.lambda_661
fof(fact_ATP_Olambda__662,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gp(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uub)),Uu)) ) ).

% ATP.lambda_662
fof(fact_ATP_Olambda__663,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kv(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uub)),Uu)) ) ).

% ATP.lambda_663
fof(fact_ATP_Olambda__664,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_afp(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(Uua,Uub))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc138386723_image(aa_fun1431113780TP_ind(scratc404274226_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1848874457_Sigma,aa_fun1431113780TP_ind(scratc404274226_d_Sep(Uu),Uua)),scratc1815386162d_e_in(Uu,Uua))),Uub)) ) ) ).

% ATP.lambda_664
fof(fact_ATP_Olambda__665,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_afe(Uu),Uua),Uub))
    <=> ( pp(aa_TPTP_ind_bool(Uua,Uub))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1782805115d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc404274226_d_Sep(Uu),Uua))) ) ) ).

% ATP.lambda_665
fof(fact_ATP_Olambda__666,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_afy(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_afx(Uu),Uua),Uub))) ) ).

% ATP.lambda_666
fof(fact_ATP_Olambda__667,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bs(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_br(Uu),Uua),Uub))) ) ).

% ATP.lambda_667
fof(fact_ATP_Olambda__668,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_afo(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_afn(Uu),Uua),Uub))) ) ).

% ATP.lambda_668
fof(fact_ATP_Olambda__669,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_afi(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_afh(Uu),Uua),Uub))) ) ).

% ATP.lambda_669
fof(fact_ATP_Olambda__670,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_afg(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aff(Uu),Uua),Uub))) ) ).

% ATP.lambda_670
fof(fact_ATP_Olambda__671,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aft(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,Uu),aTP_Lamm_an(Uua)))) ) ).

% ATP.lambda_671
fof(fact_ATP_Olambda__672,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_adh(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uub))) ) ).

% ATP.lambda_672
fof(fact_ATP_Olambda__673,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_adi(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub))) ) ).

% ATP.lambda_673
fof(fact_ATP_Olambda__674,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_afj(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc434490305etprod(Uu),Uua))) ) ).

% ATP.lambda_674
fof(fact_ATP_Olambda__675,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_afq(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,Uub),aa_fun1431113780TP_ind(scratc404274226_d_Sep(Uu),Uua))) ) ).

% ATP.lambda_675
fof(fact_ATP_Olambda__676,axiom,
    ! [Uu,Uua,Uub] : aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bl(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uu),Uub)) ).

% ATP.lambda_676
fof(fact_ATP_Olambda__677,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aag(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aaf(Uu),Uua),Uub))) ) ).

% ATP.lambda_677
fof(fact_ATP_Olambda__678,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aac(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aab(Uu),Uua),Uub))) ) ).

% ATP.lambda_678
fof(fact_ATP_Olambda__679,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zy(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_zx(Uu),Uua),Uub))) ) ).

% ATP.lambda_679
fof(fact_ATP_Olambda__680,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zu(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_zt(Uu),Uua),Uub))) ) ).

% ATP.lambda_680
fof(fact_ATP_Olambda__681,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ym(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_yl(Uu),Uua),Uub))) ) ).

% ATP.lambda_681
fof(fact_ATP_Olambda__682,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yi(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_yh(Uu),Uua),Uub))) ) ).

% ATP.lambda_682
fof(fact_ATP_Olambda__683,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ye(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_yd(Uu),Uua),Uub))) ) ).

% ATP.lambda_683
fof(fact_ATP_Olambda__684,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ya(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_xz(Uu),Uua),Uub))) ) ).

% ATP.lambda_684
fof(fact_ATP_Olambda__685,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xw(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_xv(Uu),Uua),Uub))) ) ).

% ATP.lambda_685
fof(fact_ATP_Olambda__686,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xs(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_xr(Uu),Uua),Uub))) ) ).

% ATP.lambda_686
fof(fact_ATP_Olambda__687,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xo(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_xn(Uu),Uua),Uub))) ) ).

% ATP.lambda_687
fof(fact_ATP_Olambda__688,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xk(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_xj(Uu),Uua),Uub))) ) ).

% ATP.lambda_688
fof(fact_ATP_Olambda__689,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uz(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uy(Uu),Uua),Uub))) ) ).

% ATP.lambda_689
fof(fact_ATP_Olambda__690,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uv(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uu(Uu),Uua),Uub))) ) ).

% ATP.lambda_690
fof(fact_ATP_Olambda__691,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ur(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uq(Uu),Uua),Uub))) ) ).

% ATP.lambda_691
fof(fact_ATP_Olambda__692,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_un(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_um(Uu),Uua),Uub))) ) ).

% ATP.lambda_692
fof(fact_ATP_Olambda__693,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_to(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tn(Uu),Uua),Uub))) ) ).

% ATP.lambda_693
fof(fact_ATP_Olambda__694,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tk(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tj(Uu),Uua),Uub))) ) ).

% ATP.lambda_694
fof(fact_ATP_Olambda__695,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tg(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tf(Uu),Uua),Uub))) ) ).

% ATP.lambda_695
fof(fact_ATP_Olambda__696,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tc(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tb(Uu),Uua),Uub))) ) ).

% ATP.lambda_696
fof(fact_ATP_Olambda__697,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sy(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_sx(Uu),Uua),Uub))) ) ).

% ATP.lambda_697
fof(fact_ATP_Olambda__698,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_su(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_st(Uu),Uua),Uub))) ) ).

% ATP.lambda_698
fof(fact_ATP_Olambda__699,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sq(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_sp(Uu),Uua),Uub))) ) ).

% ATP.lambda_699
fof(fact_ATP_Olambda__700,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sm(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_or),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_sl(Uu),Uua),Uub))) ) ).

% ATP.lambda_700
fof(fact_ATP_Olambda__701,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ri(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rh(Uu),Uua),Uub))) ) ).

% ATP.lambda_701
fof(fact_ATP_Olambda__702,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_re(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rd(Uu),Uua),Uub))) ) ).

% ATP.lambda_702
fof(fact_ATP_Olambda__703,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qk(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qj(Uu),Uua),Uub))) ) ).

% ATP.lambda_703
fof(fact_ATP_Olambda__704,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qg(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qf(Uu),Uua),Uub))) ) ).

% ATP.lambda_704
fof(fact_ATP_Olambda__705,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oz(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_oy(Uu),Uua),Uub))) ) ).

% ATP.lambda_705
fof(fact_ATP_Olambda__706,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nn(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_nm(Uu),Uua),Uub))) ) ).

% ATP.lambda_706
fof(fact_ATP_Olambda__707,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nj(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ni(Uu),Uua),Uub))) ) ).

% ATP.lambda_707
fof(fact_ATP_Olambda__708,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nf(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ne(Uu),Uua),Uub))) ) ).

% ATP.lambda_708
fof(fact_ATP_Olambda__709,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nb(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_na(Uu),Uua),Uub))) ) ).

% ATP.lambda_709
fof(fact_ATP_Olambda__710,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mf(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_me(Uu),Uua),Uub))) ) ).

% ATP.lambda_710
fof(fact_ATP_Olambda__711,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mb(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ma(Uu),Uua),Uub))) ) ).

% ATP.lambda_711
fof(fact_ATP_Olambda__712,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lx(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lw(Uu),Uua),Uub))) ) ).

% ATP.lambda_712
fof(fact_ATP_Olambda__713,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lt(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ls(Uu),Uua),Uub))) ) ).

% ATP.lambda_713
fof(fact_ATP_Olambda__714,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lp(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lo(Uu),Uua),Uub))) ) ).

% ATP.lambda_714
fof(fact_ATP_Olambda__715,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ll(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lk(Uu),Uua),Uub))) ) ).

% ATP.lambda_715
fof(fact_ATP_Olambda__716,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lh(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lg(Uu),Uua),Uub))) ) ).

% ATP.lambda_716
fof(fact_ATP_Olambda__717,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ld(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lc(Uu),Uua),Uub))) ) ).

% ATP.lambda_717
fof(fact_ATP_Olambda__718,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kz(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ky(Uu),Uua),Uub))) ) ).

% ATP.lambda_718
fof(fact_ATP_Olambda__719,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kl(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kk(Uu),Uua),Uub))) ) ).

% ATP.lambda_719
fof(fact_ATP_Olambda__720,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jh(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jg(Uu),Uua),Uub))) ) ).

% ATP.lambda_720
fof(fact_ATP_Olambda__721,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jd(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jc(Uu),Uua),Uub))) ) ).

% ATP.lambda_721
fof(fact_ATP_Olambda__722,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iz(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_iy(Uu),Uua),Uub))) ) ).

% ATP.lambda_722
fof(fact_ATP_Olambda__723,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iv(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_iu(Uu),Uua),Uub))) ) ).

% ATP.lambda_723
fof(fact_ATP_Olambda__724,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hz(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hy(Uu),Uua),Uub))) ) ).

% ATP.lambda_724
fof(fact_ATP_Olambda__725,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hv(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hu(Uu),Uua),Uub))) ) ).

% ATP.lambda_725
fof(fact_ATP_Olambda__726,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hr(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hq(Uu),Uua),Uub))) ) ).

% ATP.lambda_726
fof(fact_ATP_Olambda__727,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hm(Uu),Uua),Uub))) ) ).

% ATP.lambda_727
fof(fact_ATP_Olambda__728,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hj(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hi(Uu),Uua),Uub))) ) ).

% ATP.lambda_728
fof(fact_ATP_Olambda__729,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hf(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_he(Uu),Uua),Uub))) ) ).

% ATP.lambda_729
fof(fact_ATP_Olambda__730,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hb(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ha(Uu),Uua),Uub))) ) ).

% ATP.lambda_730
fof(fact_ATP_Olambda__731,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gw(Uu),Uua),Uub))) ) ).

% ATP.lambda_731
fof(fact_ATP_Olambda__732,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_go),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gs(Uu),Uua),Uub))) ) ).

% ATP.lambda_732
fof(fact_ATP_Olambda__733,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cr(Uu),Uua),Uub))) ) ).

% ATP.lambda_733
fof(fact_ATP_Olambda__734,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_co(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cn(Uu),Uua),Uub))) ) ).

% ATP.lambda_734
fof(fact_ATP_Olambda__735,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cj(Uu),Uua),Uub))) ) ).

% ATP.lambda_735
fof(fact_ATP_Olambda__736,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cf(Uu),Uua),Uub))) ) ).

% ATP.lambda_736
fof(fact_ATP_Olambda__737,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ab(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aa(Uu),Uua),Uub))) ) ).

% ATP.lambda_737
fof(fact_ATP_Olambda__738,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aj(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(scratc406400774d_frac),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ai(Uu),Uua),Uub))) ) ).

% ATP.lambda_738
fof(fact_ATP_Olambda__739,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ah(Uu),Uua),Uub))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(scratc406400774d_frac),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ag(Uu),Uua),Uub))) ) ).

% ATP.lambda_739
fof(fact_ATP_Olambda__740,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_afr(Uu),Uua),Uub))
    <=> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc1815386162d_e_in(Uu,Uua),Uub))) ) ).

% ATP.lambda_740
fof(fact_ATP_Olambda__741,axiom,
    ! [Uu,Uua,Uub] :
      ( pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bu(Uu),Uua),Uub))
    <=> ! [X3] :
          ( gg_TPTP_ind(X3)
         => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,X3),Uu))
           => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468924797bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3))) ) ) ) ).

% ATP.lambda_741
fof(fact_ATP_Olambda__742,axiom,
    ! [Uu,Uua,Uub,Uuc] : aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_am(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc442378146nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(aa_TPTP_ind_TPTP_ind(scratc124367040_d_1to,scratc51547580nd_n_2)),Uuc),scratc1330372985d_n_1t),Uu,Uua),Uub) ).

% ATP.lambda_742
fof(fact_ATP_Olambda__743,axiom,
    ! [Uu,Uua,Uub,Uuc] : aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_bm(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc468924789bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc138386723_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1939643266d_soft(Uu,Uua,Uub),Uuc)),scratc1884736269ptyset) ).

% ATP.lambda_743
fof(fact_ATP_Olambda__744,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ai(Uu),Uua),Uub),Uuc))
    <=> scratc765582804d_and3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441984553nd_inf,Uub),aa_TPTP_ind_TPTP_ind(scratc1111135584_class,Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441984553nd_inf,Uuc),aa_TPTP_ind_TPTP_ind(scratc1111135584_class,Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uub),Uuc)) ) ).

% ATP.lambda_744
fof(fact_ATP_Olambda__745,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ag(Uu),Uua),Uub),Uuc))
    <=> scratc765582804d_and3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441984553nd_inf,Uub),aa_TPTP_ind_TPTP_ind(scratc1111135584_class,Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441984553nd_inf,Uuc),aa_TPTP_ind_TPTP_ind(scratc1111135584_class,Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uub),Uuc)) ) ).

% ATP.lambda_745
fof(fact_ATP_Olambda__746,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_afh(Uu),Uua),Uub),Uuc))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc181028792_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1838069414d_pair(Uu,Uua),Uub),Uuc))),Uub)) ) ).

% ATP.lambda_746
fof(fact_ATP_Olambda__747,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aff(Uu),Uua),Uub),Uuc))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1143644204second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1838069414d_pair(Uu,Uua),Uub),Uuc))),Uuc)) ) ).

% ATP.lambda_747
fof(fact_ATP_Olambda__748,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_afu(Uu),Uua),Uub),Uuc))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uub),Uuc))) ) ).

% ATP.lambda_748
fof(fact_ATP_Olambda__749,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bf(Uu),Uua),Uub),Uuc))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1782805115d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uua),Uuc))) ) ).

% ATP.lambda_749
fof(fact_ATP_Olambda__750,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bn(Uu),Uua),Uub),Uuc))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uua),Uuc))) ) ).

% ATP.lambda_750
fof(fact_ATP_Olambda__751,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_afn(Uu),Uua),Uub),Uuc))
    <=> scratc1533070073_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1838069414d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_afj(Uu),Uua)) ) ).

% ATP.lambda_751
fof(fact_ATP_Olambda__752,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bh(Uu),Uua),Uub),Uuc))
    <=> pp(scratc1202139186d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1782805115d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1782805115d_esti(Uu),Uuc),Uub))) ) ).

% ATP.lambda_752
fof(fact_ATP_Olambda__753,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bi(Uu),Uua),Uub),Uuc))
    <=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc441918964nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1782805115d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1782805115d_esti(Uu),Uuc),Uub))) ) ).

% ATP.lambda_753
fof(fact_ATP_Olambda__754,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gs(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uub)),Uu))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uuc)),Uu))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uub),Uuc)) ) ) ) ).

% ATP.lambda_754
fof(fact_ATP_Olambda__755,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ky(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uub)),Uu))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uuc)),Uu))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uub),Uuc)) ) ) ) ).

% ATP.lambda_755
fof(fact_ATP_Olambda__756,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_afv(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_afu(Uua),Uub),Uuc)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc674181893d_d_Pi,Uu),aTP_Lamm_an(Uua))),Uub),Uuc)) ) ) ).

% ATP.lambda_756
fof(fact_ATP_Olambda__757,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( ( gg_TPTP_ind(Uua)
        & gg_TPTP_ind(Uub)
        & gg_TPTP_ind(Uuc) )
     => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ce(Uu),Uua),Uub),Uuc))
      <=> ( ( pp(Uu)
            & Uuc = Uua )
          | ( ~ pp(Uu)
            & Uuc = Uub ) ) ) ) ).

% ATP.lambda_757
fof(fact_ATP_Olambda__758,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cj(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1066042873moreis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_758
fof(fact_ATP_Olambda__759,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aa(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc932059261lessis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_759
fof(fact_ATP_Olambda__760,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cf(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1066042873moreis,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_760
fof(fact_ATP_Olambda__761,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cr(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1473647407t_more,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_761
fof(fact_ATP_Olambda__762,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cn(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc610510771t_less,aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1725797750_rt_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_762
fof(fact_ATP_Olambda__763,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tn(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uuc))) ) ) ) ).

% ATP.lambda_763
fof(fact_ATP_Olambda__764,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_yl(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_764
fof(fact_ATP_Olambda__765,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tb(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uuc))) ) ) ) ).

% ATP.lambda_765
fof(fact_ATP_Olambda__766,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_xz(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_766
fof(fact_ATP_Olambda__767,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tf(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uuc))) ) ) ) ).

% ATP.lambda_767
fof(fact_ATP_Olambda__768,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_yd(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_768
fof(fact_ATP_Olambda__769,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_sp(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uuc))) ) ) ) ).

% ATP.lambda_769
fof(fact_ATP_Olambda__770,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_xn(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc458272183moreis,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_770
fof(fact_ATP_Olambda__771,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_sl(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uuc))) ) ) ) ).

% ATP.lambda_771
fof(fact_ATP_Olambda__772,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_xj(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_772
fof(fact_ATP_Olambda__773,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_sx(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uuc))) ) ) ) ).

% ATP.lambda_773
fof(fact_ATP_Olambda__774,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_xv(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_774
fof(fact_ATP_Olambda__775,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gw(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_775
fof(fact_ATP_Olambda__776,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lc(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_776
fof(fact_ATP_Olambda__777,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hi(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_777
fof(fact_ATP_Olambda__778,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lo(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_778
fof(fact_ATP_Olambda__779,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qf(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uub))
         => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uua),Uuc))
           => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uub),Uuc)) ) ) ) ) ).

% ATP.lambda_779
fof(fact_ATP_Olambda__780,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ha(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_780
fof(fact_ATP_Olambda__781,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lg(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_781
fof(fact_ATP_Olambda__782,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hq(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_782
fof(fact_ATP_Olambda__783,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lw(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_783
fof(fact_ATP_Olambda__784,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qj(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uub))
         => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uua),Uuc))
           => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uub),Uuc)) ) ) ) ) ).

% ATP.lambda_784
fof(fact_ATP_Olambda__785,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hm(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_785
fof(fact_ATP_Olambda__786,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ls(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165380_moreq,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_786
fof(fact_ATP_Olambda__787,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hy(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_787
fof(fact_ATP_Olambda__788,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_me(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_788
fof(fact_ATP_Olambda__789,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rh(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uub))
         => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uua),Uuc))
           => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uub),Uuc)) ) ) ) ) ).

% ATP.lambda_789
fof(fact_ATP_Olambda__790,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_he(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_790
fof(fact_ATP_Olambda__791,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lk(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324026173lesseq,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_791
fof(fact_ATP_Olambda__792,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hu(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_792
fof(fact_ATP_Olambda__793,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ma(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_793
fof(fact_ATP_Olambda__794,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rd(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uub))
         => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uua),Uuc))
           => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uub),Uuc)) ) ) ) ) ).

% ATP.lambda_794
fof(fact_ATP_Olambda__795,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uy(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uuc))) ) ) ) ).

% ATP.lambda_795
fof(fact_ATP_Olambda__796,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uu(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uuc),Uua))) ) ) ) ).

% ATP.lambda_796
fof(fact_ATP_Olambda__797,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aaf(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_797
fof(fact_ATP_Olambda__798,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aab(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc560802419_29_ii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uuc),Uua))) ) ) ) ).

% ATP.lambda_798
fof(fact_ATP_Olambda__799,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uq(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uuc))) ) ) ) ).

% ATP.lambda_799
fof(fact_ATP_Olambda__800,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_um(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uuc),Uua))) ) ) ) ).

% ATP.lambda_800
fof(fact_ATP_Olambda__801,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_zx(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_801
fof(fact_ATP_Olambda__802,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_zt(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1334046528d_n_is,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uuc),Uua))) ) ) ) ).

% ATP.lambda_802
fof(fact_ATP_Olambda__803,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jg(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_803
fof(fact_ATP_Olambda__804,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jc(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uuc),Uua))) ) ) ) ).

% ATP.lambda_804
fof(fact_ATP_Olambda__805,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_nm(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_805
fof(fact_ATP_Olambda__806,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ni(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2103165369_moref,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uuc),Uua))) ) ) ) ).

% ATP.lambda_806
fof(fact_ATP_Olambda__807,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_iy(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_807
fof(fact_ATP_Olambda__808,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_iu(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uuc),Uua))) ) ) ) ).

% ATP.lambda_808
fof(fact_ATP_Olambda__809,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ne(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_809
fof(fact_ATP_Olambda__810,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_na(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756843573_lessf,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uuc),Uua))) ) ) ) ).

% ATP.lambda_810
fof(fact_ATP_Olambda__811,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kk(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768104d_n_tf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_811
fof(fact_ATP_Olambda__812,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_oy(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1333784130d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505708d_n_pf(Uua),Uuc))) ) ) ) ).

% ATP.lambda_812
fof(fact_ATP_Olambda__813,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_st(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uuc))) ) ) ) ).

% ATP.lambda_813
fof(fact_ATP_Olambda__814,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_xr(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc324288571lessis,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_814
fof(fact_ATP_Olambda__815,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tj(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334768117d_n_ts(Uua),Uuc))) ) ) ) ).

% ATP.lambda_815
fof(fact_ATP_Olambda__816,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_yh(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uu),Uua))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,Uub),Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441656561nd_iii,aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1334505714d_n_pl(Uua),Uuc))) ) ) ) ).

% ATP.lambda_816
fof(fact_ATP_Olambda__817,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_afx(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(Uua,Uub))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Uu),Uub),Uuc))
         => pp(aa_TPTP_ind_bool(Uua,Uuc)) ) ) ) ).

% ATP.lambda_817
fof(fact_ATP_Olambda__818,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_br(Uu),Uua),Uub),Uuc))
    <=> ( pp(aa_TPTP_ind_bool(Uua,Uub))
       => ( pp(aa_TPTP_ind_bool(Uua,Uuc))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Uu),Uub),Uuc)) ) ) ) ).

% ATP.lambda_818
fof(fact_ATP_Olambda__819,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(Uu),Uua),Uub),Uuc))
    <=> pp(aa_fun171081125l_bool(scratc375761321nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bo(Uu),Uua),Uub),Uuc))) ) ).

% ATP.lambda_819
fof(fact_ATP_Olambda__820,axiom,
    ! [Uu,Uua,Uub,Uuc] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bg(Uu),Uua),Uub),Uuc))
    <=> pp(aa_fun171081125l_bool(scratc828602088l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bf(Uu),Uub),Uuc))) ) ).

% ATP.lambda_820
fof(fact_ATP_Olambda__821,axiom,
    ! [Uu,Uua,Uub,Uuc] : aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ak(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uub),aa_TPTP_ind_TPTP_ind(scratc1608132904ght1to(Uu,Uua),Uuc)) ).

% ATP.lambda_821
fof(fact_ATP_Olambda__822,axiom,
    ! [Uu,Uua,Uub,Uuc] : aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_al(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uub),aa_TPTP_ind_TPTP_ind(scratc569010349eft1to(Uu,Uua),Uuc)) ).

% ATP.lambda_822
fof(fact_ATP_Olambda__823,axiom,
    ! [Uu,Uua,Uub,Uuc,Uud] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bo(Uu),Uua),Uub),Uuc),Uud))
    <=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc441918964nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Uu),Uuc),Uud))) ) ).

% ATP.lambda_823
fof(fact_ATP_Olambda__824,axiom,
    ! [Uu,Uua,Uub,Uuc,Uud] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bd(Uu),Uua),Uub),Uuc),Uud))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uub),Uud))) ) ) ).

% ATP.lambda_824
fof(fact_ATP_Olambda__825,axiom,
    ! [Uu,Uua,Uub,Uuc,Uud] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc),Uud))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_bb(Uu),Uua),Uub),Uuc),Uud))) ) ).

% ATP.lambda_825
fof(fact_ATP_Olambda__826,axiom,
    ! [Uu,Uua,Uub,Uuc,Uud] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_be(Uu),Uua),Uub),Uuc),Uud))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bd(Uua),Uub),Uuc),Uud))) ) ).

% ATP.lambda_826
fof(fact_ATP_Olambda__827,axiom,
    ! [Uu,Uua,Uub,Uuc,Uud] : aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_bk(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,aa_TPTP_ind_TPTP_ind(scratc384428273wissel(Uu,Uub),Uuc)),Uud)) ).

% ATP.lambda_827
fof(fact_ATP_Olambda__828,axiom,
    ! [Uu,Uua,Uub,Uuc,Uud,Uue] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_bb(Uu),Uua),Uub),Uuc),Uud),Uue))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc),Uud),Uue))) ) ).

% ATP.lambda_828
fof(fact_ATP_Olambda__829,axiom,
    ! [Uu,Uua,Uub,Uuc,Uud,Uue,Uuf] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud))
       => ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uue),Uuf))
         => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1815386167d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc468400007bnd_ap,Uub),Uud)),Uuf))) ) ) ) ).

% ATP.lambda_829
fof(fact_ATP_Olambda__830,axiom,
    ! [Uu,Uua,Uub,Uuc,Uud,Uue,Uuf] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf))
    <=> pp(aa_fun171081125l_bool(scratc1717941280all_of(aa_TPT43085870d_bool(aTP_Lamm_ay,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_az(Uua),Uub),Uuc),Uud),Uue),Uuf))) ) ).

% ATP.lambda_830
fof(fact_ATP_Olambda__831,axiom,
    ! [Uu,Uua] :
      ( gg_TPTP_ind(Uu)
     => aa_TPTP_ind_TPTP_ind(aTP_Lamm_an(Uu),Uua) = Uu ) ).

% ATP.lambda_831
fof(fact_ATP_Olambda__832,axiom,
    ! [Uu] :
      ( gg_TPTP_ind(Uu)
     => aa_TPTP_ind_TPTP_ind(aTP_Lamm_ar,Uu) = Uu ) ).

% ATP.lambda_832
fof(fact_ATP_Olambda__833,axiom,
    ! [Uu] : aa_TPTP_ind_TPTP_ind(aTP_Lamm_ap,Uu) = scratc482439305nd_nat ).

% ATP.lambda_833

% Helper facts (15)
fof(help_pp_2_1_U,axiom,
    pp(fTrue) ).

fof(help_fconj_3_1_U,axiom,
    ! [P,Q] :
      ( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q))
      | pp(Q) ) ).

fof(help_fconj_2_1_U,axiom,
    ! [P,Q] :
      ( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q))
      | pp(P) ) ).

fof(help_fconj_1_1_U,axiom,
    ! [P,Q] :
      ( ~ pp(P)
      | ~ pp(Q)
      | pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) ) ).

fof(help_fFalse_1_1_T,axiom,
    ! [P] :
      ( gg_bool(P)
     => ( P = fTrue
        | P = fFalse ) ) ).

fof(help_fFalse_1_1_U,axiom,
    ~ pp(fFalse) ).

fof(help_fimplies_3_1_U,axiom,
    ! [P,Q] :
      ( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q))
      | ~ pp(P)
      | pp(Q) ) ).

fof(help_fimplies_2_1_U,axiom,
    ! [Q,P] :
      ( ~ pp(Q)
      | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ) ).

fof(help_fimplies_1_1_U,axiom,
    ! [P,Q] :
      ( pp(P)
      | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ) ).

fof(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U,axiom,
    ! [P,X7] :
      ( ~ pp(aa_TPTP_ind_bool(P,X7))
      | pp(fEx_TPTP_ind(P)) ) ).

fof(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T,axiom,
    ! [X7,Y] :
      ( X7 != Y
      | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ) ).

fof(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T,axiom,
    ! [X7,Y] :
      ( ( gg_TPTP_ind(X7)
        & gg_TPTP_ind(Y) )
     => ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
        | X7 = Y ) ) ).

fof(help_COMBS_1_1_COMBS_001t__TPTP____Interpret__Oind_001t__HOL__Obool_001t__HOL__Obool_U,axiom,
    ! [P,Q,R] : aa_TPTP_ind_bool(cOMBS_2003118649l_bool(P,Q),R) = aa_bool_bool(aa_TPT2142672771l_bool(P,R),aa_TPTP_ind_bool(Q,R)) ).

fof(help_COMBC_1_1_COMBC_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind_001t__HOL__Obool_U,axiom,
    ! [P,Q,R] : aa_TPTP_ind_bool(aa_TPT43085870d_bool(cOMBC_1555011498d_bool(P),Q),R) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(P,R),Q) ).

fof(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind_U,axiom,
    ! [P,Q,R] : aa_TPT2142672771l_bool(cOMBB_658106424TP_ind(P,Q),R) = aa_boo1142376798l_bool(P,aa_TPTP_ind_bool(Q,R)) ).

% Conjectures (1)
fof(conj_0,conjecture,
    pp(aa_fun171081125l_bool(scratc1717941280all_of(aTP_Lamm_a),aTP_Lamm_ad)) ).

%------------------------------------------------------------------------------