SET007 Axioms: SET007+695.ax


%------------------------------------------------------------------------------
% File     : SET007+695 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Characterizations of Compactness
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : yellow19 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   60 (   2 unit)
%            Number of atoms       :  560 (  13 equality)
%            Maximal formula depth :   17 (   9 average)
%            Number of connectives :  628 ( 128 ~  ;   1  |; 310  &)
%                                         (  32 <=>; 157 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   38 (   1 propositional; 0-3 arity)
%            Number of functors    :   27 (   1 constant; 0-3 arity)
%            Number of variables   :  188 (   0 singleton; 172 !;  16 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_yellow19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k1_yellow19(A,B))
        & v2_waybel_0(k1_yellow19(A,B),k3_yellow_1(k2_pre_topc(A)))
        & v13_waybel_0(k1_yellow19(A,B),k3_yellow_1(k2_pre_topc(A)))
        & v1_tex_2(k1_yellow19(A,B),k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) ) )).

fof(cc1_yellow19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_waybel_0(B,A) )
     => ! [C] :
          ( m1_yellow19(C,A,B)
         => ~ v1_xboole_0(C) ) ) )).

fof(fc2_yellow19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_waybel_0(B,A) )
     => ( ~ v1_xboole_0(k2_yellow19(A,B))
        & v13_waybel_0(k2_yellow19(A,B),k3_yellow_1(k2_pre_topc(A))) ) ) )).

fof(fc3_yellow19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A) )
     => ( ~ v1_xboole_0(k2_yellow19(A,B))
        & v2_waybel_0(k2_yellow19(A,B),k3_yellow_1(k2_pre_topc(A)))
        & v13_waybel_0(k2_yellow19(A,B),k3_yellow_1(k2_pre_topc(A)))
        & v1_tex_2(k2_yellow19(A,B),k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) ) )).

fof(fc4_yellow19,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & ~ v1_xboole_0(C)
        & v2_waybel_0(C,k3_yellow_1(B))
        & v13_waybel_0(C,k3_yellow_1(B))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) )
     => ( ~ v3_struct_0(k3_yellow19(A,B,C))
        & v2_orders_2(k3_yellow19(A,B,C))
        & v3_orders_2(k3_yellow19(A,B,C))
        & v6_waybel_0(k3_yellow19(A,B,C),A) ) ) )).

fof(fc5_yellow19,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & ~ v1_xboole_0(C)
        & v2_waybel_0(C,k3_yellow_1(B))
        & v13_waybel_0(C,k3_yellow_1(B))
        & v1_tex_2(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B))))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) )
     => ( ~ v3_struct_0(k3_yellow19(A,B,C))
        & v2_orders_2(k3_yellow19(A,B,C))
        & v3_orders_2(k3_yellow19(A,B,C))
        & v6_waybel_0(k3_yellow19(A,B,C),A)
        & v7_waybel_0(k3_yellow19(A,B,C)) ) ) )).

fof(cc2_yellow19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & v3_orders_2(B)
        & l1_waybel_0(B,A) )
     => ! [C] :
          ( m1_yellow_6(C,A,B)
         => ( v2_yellow_6(C,A,B)
           => ( v3_orders_2(C)
              & v2_yellow_6(C,A,B) ) ) ) ) )).

fof(rc1_yellow19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A) )
     => ? [C] :
          ( m1_yellow_6(C,A,B)
          & ~ v3_struct_0(C)
          & v6_waybel_0(C,A)
          & v7_waybel_0(C)
          & v2_yellow_6(C,A,B) ) ) )).

fof(fc6_yellow19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
        & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
        & v3_waybel_7(B,k3_yellow_1(k2_pre_topc(A)))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
     => ( ~ v3_struct_0(k3_yellow19(A,k2_pre_topc(A),B))
        & v2_orders_2(k3_yellow19(A,k2_pre_topc(A),B))
        & v3_orders_2(k3_yellow19(A,k2_pre_topc(A),B))
        & v6_waybel_0(k3_yellow19(A,k2_pre_topc(A),B),A)
        & v7_waybel_0(k3_yellow19(A,k2_pre_topc(A),B))
        & v1_yellow19(k3_yellow19(A,k2_pre_topc(A),B),A) ) ) )).

fof(t1_yellow19,axiom,(
    $true )).

fof(t2_yellow19,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_waybel_0(B,k3_yellow_1(A))
            & v13_waybel_0(B,k3_yellow_1(A))
            & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A))))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) )
         => ! [C] :
              ~ ( r2_hidden(C,B)
                & v1_xboole_0(C) ) ) ) )).

fof(t3_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( r2_hidden(C,k1_yellow19(A,B))
            <=> m1_connsp_2(C,A,B) ) ) ) )).

fof(t4_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v13_waybel_0(C,k3_yellow_1(k2_pre_topc(A)))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
             => ( r2_waybel_7(A,C,B)
              <=> r1_tarski(k1_yellow19(A,B),C) ) ) ) ) )).

fof(t5_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r2_waybel_7(A,k1_yellow19(A,B),B) ) ) )).

fof(t6_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                 => ! [D] :
                      ( ( ~ v1_xboole_0(D)
                        & v2_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
                        & v13_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
                     => ( r2_waybel_7(A,D,C)
                       => r2_hidden(B,D) ) ) ) ) ) ) ) )).

fof(d2_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( m1_yellow19(C,A,B)
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                    & C = k5_relset_1(u1_struct_0(k5_waybel_9(A,B,D)),u1_struct_0(A),u1_waybel_0(A,k5_waybel_9(A,B,D))) ) ) ) ) ) )).

fof(t7_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => m1_yellow19(k5_relset_1(u1_struct_0(k5_waybel_9(A,B,C)),u1_struct_0(A),u1_waybel_0(A,k5_waybel_9(A,B,C))),A,B) ) ) ) )).

fof(t8_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( r2_hidden(D,k5_relset_1(u1_struct_0(k6_waybel_9(A,B,C)),u1_struct_0(A),u1_waybel_0(A,k6_waybel_9(A,B,C))))
                <=> ? [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                      & r1_orders_2(B,C,E)
                      & D = k3_waybel_0(A,B,E) ) ) ) ) ) )).

fof(t9_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_yellow19(C,A,B)
             => r1_waybel_0(A,B,C) ) ) ) )).

fof(t10_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_finset_1(C) )
             => ~ ( ! [D] :
                      ( m1_subset_1(D,C)
                     => m1_yellow19(D,A,B) )
                  & ! [D] :
                      ( m1_yellow19(D,A,B)
                     => ~ r1_tarski(D,k1_setfam_1(C)) ) ) ) ) ) )).

fof(t11_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( r2_hidden(C,k2_yellow19(A,B))
            <=> ( r1_waybel_0(A,B,C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(t12_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_waybel_9(A,B,C)
              <=> r1_waybel_7(A,k2_yellow19(A,B),C) ) ) ) ) )).

fof(t13_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k11_yellow_6(A,B))
              <=> r2_waybel_7(A,k2_yellow19(A,B),C) ) ) ) ) )).

fof(t14_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
            & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
         => k4_xboole_0(B,k1_tarski(k1_xboole_0)) = k2_yellow19(A,k3_yellow19(A,k2_pre_topc(A),B)) ) ) )).

fof(t15_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
            & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
            & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
         => B = k2_yellow19(A,k3_yellow19(A,k2_pre_topc(A),B)) ) ) )).

fof(t16_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
            & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( r2_hidden(C,B)
              <=> r1_waybel_0(A,k3_yellow19(A,k2_pre_topc(A),B),C) ) ) ) ) )).

fof(t17_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
            & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
            & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_waybel_9(A,k3_yellow19(A,k2_pre_topc(A),B),C)
              <=> r1_waybel_7(A,B,C) ) ) ) ) )).

fof(t18_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
            & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
            & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k11_yellow_6(A,k3_yellow19(A,k2_pre_topc(A),B)))
              <=> r2_waybel_7(A,B,C) ) ) ) ) )).

fof(t19_yellow19,axiom,(
    $true )).

fof(t20_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k6_pre_topc(A,C))
               => ! [D] :
                    ( ( ~ v1_xboole_0(D)
                      & v2_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
                      & v13_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
                      & v1_tex_2(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
                   => ( D = k1_yellow19(A,B)
                     => r2_waybel_0(A,k3_yellow19(A,k2_pre_topc(A),D),C) ) ) ) ) ) ) )).

fof(t21_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B,C] :
          ( ( ~ v3_struct_0(C)
            & v3_orders_2(C)
            & v7_waybel_0(C)
            & l1_waybel_0(C,A) )
         => ( r1_waybel_0(A,C,B)
           => ! [D] :
                ( m2_yellow_6(D,A,C)
               => r1_waybel_0(A,D,B) ) ) ) ) )).

fof(t22_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B,C,D] :
          ( ( r1_tarski(B,C)
            & r2_waybel_7(A,B,D) )
         => r2_waybel_7(A,C,D) ) ) )).

fof(t23_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k6_pre_topc(A,B))
              <=> ? [D] :
                    ( ~ v3_struct_0(D)
                    & v3_orders_2(D)
                    & v7_waybel_0(D)
                    & l1_waybel_0(D,A)
                    & r1_waybel_0(A,D,B)
                    & r3_waybel_9(A,D,C) ) ) ) ) ) )).

fof(t24_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k6_pre_topc(A,B))
              <=> ? [D] :
                    ( ~ v3_struct_0(D)
                    & v3_orders_2(D)
                    & v7_waybel_0(D)
                    & v3_yellow_6(D,A)
                    & l1_waybel_0(D,A)
                    & r1_waybel_0(A,D,B)
                    & r2_hidden(C,k11_yellow_6(A,D)) ) ) ) ) ) )).

fof(t25_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
          <=> ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v3_orders_2(C)
                  & v7_waybel_0(C)
                  & l1_waybel_0(C,A) )
               => ( r1_waybel_0(A,C,B)
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r3_waybel_9(A,C,D)
                       => r2_hidden(D,B) ) ) ) ) ) ) ) )).

fof(t26_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
          <=> ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v3_orders_2(C)
                  & v7_waybel_0(C)
                  & v3_yellow_6(C,A)
                  & l1_waybel_0(C,A) )
               => ( r1_waybel_0(A,C,B)
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_hidden(D,k11_yellow_6(A,C))
                       => r2_hidden(D,B) ) ) ) ) ) ) ) )).

fof(t27_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k6_pre_topc(A,B))
              <=> ? [D] :
                    ( ~ v1_xboole_0(D)
                    & v2_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
                    & v13_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
                    & v1_tex_2(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
                    & r2_hidden(B,D)
                    & r1_waybel_7(A,D,C) ) ) ) ) ) )).

fof(t28_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k6_pre_topc(A,B))
              <=> ? [D] :
                    ( ~ v1_xboole_0(D)
                    & v2_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
                    & v13_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
                    & v3_waybel_7(D,k3_yellow_1(k2_pre_topc(A)))
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
                    & r2_hidden(B,D)
                    & r2_waybel_7(A,D,C) ) ) ) ) ) )).

fof(t29_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
          <=> ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v2_waybel_0(C,k3_yellow_1(k2_pre_topc(A)))
                  & v13_waybel_0(C,k3_yellow_1(k2_pre_topc(A)))
                  & v1_tex_2(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
               => ( r2_hidden(B,C)
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r1_waybel_7(A,C,D)
                       => r2_hidden(D,B) ) ) ) ) ) ) ) )).

fof(t30_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
          <=> ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v2_waybel_0(C,k3_yellow_1(k2_pre_topc(A)))
                  & v13_waybel_0(C,k3_yellow_1(k2_pre_topc(A)))
                  & v3_waybel_7(C,k3_yellow_1(k2_pre_topc(A)))
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
               => ( r2_hidden(B,C)
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_waybel_7(A,C,D)
                       => r2_hidden(D,B) ) ) ) ) ) ) ) )).

fof(t31_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_waybel_9(A,B,C)
              <=> ! [D] :
                    ( m1_yellow19(D,A,B)
                   => r2_hidden(C,k6_pre_topc(A,D)) ) ) ) ) ) )).

fof(t32_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v2_tops_2(B,A)
           => v2_tops_2(k2_cantor_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t33_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_compts_1(A)
      <=> ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
              & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
              & v3_waybel_7(B,k3_yellow_1(k2_pre_topc(A)))
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
           => ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & r2_waybel_7(A,B,C) ) ) ) ) )).

fof(t34_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_compts_1(A)
      <=> ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
              & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
              & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
           => ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & r1_waybel_7(A,B,C) ) ) ) ) )).

fof(t35_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_compts_1(A)
      <=> ! [B] :
            ( ( ~ v3_struct_0(B)
              & v3_orders_2(B)
              & v7_waybel_0(B)
              & l1_waybel_0(B,A) )
           => ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & r3_waybel_9(A,B,C) ) ) ) ) )).

fof(t36_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_compts_1(A)
      <=> ! [B] :
            ( ( ~ v3_struct_0(B)
              & v3_orders_2(B)
              & v7_waybel_0(B)
              & l1_waybel_0(B,A) )
           => ~ ( r2_hidden(B,k7_yellow_6(A))
                & ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => ~ r3_waybel_9(A,B,C) ) ) ) ) ) )).

fof(t37_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_compts_1(A)
      <=> ! [B] :
            ( ( ~ v3_struct_0(B)
              & v3_orders_2(B)
              & v7_waybel_0(B)
              & l1_waybel_0(B,A) )
           => ? [C] :
                ( m2_yellow_6(C,A,B)
                & v3_yellow_6(C,A) ) ) ) ) )).

fof(d5_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ( v1_yellow19(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r1_waybel_0(A,B,C)
                  | r1_waybel_0(A,B,k3_subset_1(u1_struct_0(A),C)) ) ) ) ) ) )).

fof(t38_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_compts_1(A)
      <=> ! [B] :
            ( ( ~ v3_struct_0(B)
              & v3_orders_2(B)
              & v7_waybel_0(B)
              & l1_waybel_0(B,A) )
           => ( v1_yellow19(B,A)
             => v3_yellow_6(B,A) ) ) ) ) )).

fof(dt_m1_yellow19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_waybel_0(B,A) )
     => ! [C] :
          ( m1_yellow19(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(existence_m1_yellow19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_waybel_0(B,A) )
     => ? [C] : m1_yellow19(C,A,B) ) )).

fof(dt_k1_yellow19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_yellow19(A,B),k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) )).

fof(dt_k2_yellow19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_waybel_0(B,A) )
     => m1_subset_1(k2_yellow19(A,B),k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) )).

fof(dt_k3_yellow19,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & ~ v1_xboole_0(C)
        & v2_waybel_0(C,k3_yellow_1(B))
        & v13_waybel_0(C,k3_yellow_1(B))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) )
     => ( ~ v3_struct_0(k3_yellow19(A,B,C))
        & v6_waybel_0(k3_yellow19(A,B,C),A)
        & l1_waybel_0(k3_yellow19(A,B,C),A) ) ) )).

fof(d1_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_yellow19(A,B) = a_2_0_yellow19(A,B) ) ) )).

fof(d3_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => k2_yellow19(A,B) = a_2_1_yellow19(A,B) ) ) )).

fof(d4_yellow19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v2_waybel_0(C,k3_yellow_1(B))
                & v13_waybel_0(C,k3_yellow_1(B))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_waybel_0(D,A)
                    & l1_waybel_0(D,A) )
                 => ( D = k3_yellow19(A,B,C)
                  <=> ( u1_struct_0(D) = a_3_0_yellow19(A,B,C)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(D))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(D))
                             => ( r1_orders_2(D,E,F)
                              <=> r1_tarski(k2_mcart_1(F),k2_mcart_1(E)) ) ) )
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(D))
                         => k3_waybel_0(A,D,E) = k1_mcart_1(E) ) ) ) ) ) ) ) )).

fof(fraenkel_a_2_0_yellow19,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_0_yellow19(B,C))
      <=> ? [D] :
            ( m1_connsp_2(D,B,C)
            & A = D ) ) ) )).

fof(fraenkel_a_2_1_yellow19,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(B)
        & ~ v3_struct_0(C)
        & l1_waybel_0(C,B) )
     => ( r2_hidden(A,a_2_1_yellow19(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & r1_waybel_0(B,C,D) ) ) ) )).

fof(fraenkel_a_3_0_yellow19,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & ~ v1_xboole_0(D)
        & v2_waybel_0(D,k3_yellow_1(C))
        & v13_waybel_0(D,k3_yellow_1(C))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(C)))) )
     => ( r2_hidden(A,a_3_0_yellow19(B,C,D))
      <=> ? [E,F] :
            ( m1_subset_1(E,u1_struct_0(B))
            & m1_struct_0(F,k3_yellow_1(C),D)
            & A = k4_tarski(E,F)
            & r2_hidden(E,F) ) ) ) )).
%------------------------------------------------------------------------------