SET007 Axioms: SET007+558.ax


%------------------------------------------------------------------------------
% File     : SET007+558 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Lawson Topology
% 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    : waybel19 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   66 (   0 unit)
%            Number of atoms       :  857 (  33 equality)
%            Maximal formula depth :   23 (  11 average)
%            Number of connectives :  859 (  68 ~  ;   1  |; 584  &)
%                                         (  12 <=>; 194 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   59 (   0 propositional; 1-4 arity)
%            Number of functors    :   41 (   1 constant; 0-4 arity)
%            Number of variables   :  175 (   0 singleton; 161 !;  14 ?)
%            Maximal term depth    :    6 (   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(cc1_waybel19,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v2_pre_topc(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v2_pre_topc(A)
          & ~ v1_yellow_3(A)
          & v1_waybel19(A) ) ) ) )).

fof(rc1_waybel19,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v16_waybel_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v2_pre_topc(A)
      & v2_waybel_3(A)
      & v3_waybel_3(A)
      & ~ v1_yellow_3(A)
      & v1_waybel_9(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v3_realset2(A)
      & v1_waybel19(A) ) )).

fof(rc2_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_yellow_9(B,A)
          & ~ v3_struct_0(B)
          & v2_pre_topc(B)
          & v1_waybel_9(B)
          & v1_waybel19(B) ) ) )).

fof(cc2_waybel19,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v2_pre_topc(A)
          & v1_waybel19(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v2_pre_topc(A)
          & v2_t_0topsp(A)
          & ~ v1_yellow_3(A) ) ) ) )).

fof(cc3_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_9(B,A)
         => ( ~ v3_struct_0(B)
            & v1_yellow_0(B) ) ) ) )).

fof(cc4_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_9(B,A)
         => ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & v2_waybel_3(B)
            & v3_waybel_3(B)
            & ~ v1_yellow_3(B) ) ) ) )).

fof(rc3_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_yellow_9(B,A)
          & ~ v3_struct_0(B)
          & v2_orders_2(B)
          & v3_orders_2(B)
          & v4_orders_2(B)
          & v1_yellow_0(B)
          & v2_yellow_0(B)
          & v3_yellow_0(B)
          & v24_waybel_0(B)
          & v25_waybel_0(B)
          & v2_pre_topc(B)
          & ~ v1_yellow_3(B)
          & v1_waybel_9(B)
          & v1_lattice3(B)
          & v2_lattice3(B)
          & v3_lattice3(B)
          & v2_waybel19(B) ) ) )).

fof(rc4_waybel19,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v2_pre_topc(A)
      & ~ v1_yellow_3(A)
      & v1_waybel_9(A)
      & v4_waybel11(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A) ) )).

fof(rc5_waybel19,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v2_pre_topc(A)
      & v2_waybel_3(A)
      & v3_waybel_3(A)
      & ~ v1_yellow_3(A)
      & v1_waybel_9(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v2_waybel19(A) ) )).

fof(cc5_waybel19,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v2_pre_topc(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A)
          & v2_waybel19(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_yellow_0(A)
          & v2_yellow_0(A)
          & v3_yellow_0(A)
          & v24_waybel_0(A)
          & v25_waybel_0(A)
          & v2_pre_topc(A)
          & ~ v1_yellow_3(A)
          & v2_compts_1(A)
          & v1_urysohn1(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A) ) ) ) )).

fof(cc6_waybel19,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v2_pre_topc(A)
          & v3_waybel_3(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A)
          & v2_waybel19(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_yellow_0(A)
          & v2_yellow_0(A)
          & v3_yellow_0(A)
          & v24_waybel_0(A)
          & v25_waybel_0(A)
          & v2_pre_topc(A)
          & v2_waybel_3(A)
          & v3_waybel_3(A)
          & ~ v1_yellow_3(A)
          & v3_compts_1(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A) ) ) ) )).

fof(t1_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( v2_pre_topc(B)
          & v1_waybel_9(B)
          & m1_yellow_9(B,A)
          & v1_waybel19(B) ) ) )).

fof(t2_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v1_waybel19(B)
            & l1_waybel_9(B) )
         => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
           => u1_pre_topc(A) = u1_pre_topc(B) ) ) ) )).

fof(d2_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( B = k1_waybel19(A)
          <=> ! [C] :
                ( ( v2_pre_topc(C)
                  & v1_waybel19(C)
                  & m1_yellow_9(C,A) )
               => B = u1_pre_topc(C) ) ) ) ) )).

fof(t3_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
           => k1_waybel19(A) = k1_waybel19(B) ) ) ) )).

fof(t4_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v3_pre_topc(k3_subset_1(u1_struct_0(A),k7_waybel_0(A,B)),A)
            & v4_pre_topc(k7_waybel_0(A,B),A) ) ) ) )).

fof(t5_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
           => v12_waybel_0(B,A) ) ) ) )).

fof(t6_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
           => v13_waybel_0(B,A) ) ) ) )).

fof(t8_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_pre_topc(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & v1_waybel19(B)
            & l1_waybel_9(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ! [D] :
                    ( ( ~ v1_xboole_0(D)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => r3_waybel_0(A,B,C,D) )
               => v5_pre_topc(C,A,B) ) ) ) ) )).

fof(t9_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_pre_topc(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & v1_waybel19(B)
            & l1_waybel_9(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v17_waybel_0(C,A,B)
               => v5_pre_topc(C,A,B) ) ) ) ) )).

fof(t10_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m2_cantor_1(B,A)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v2_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( r2_hidden(D,B)
                        & r2_hidden(k2_yellow_0(A,C),D)
                        & r1_xboole_0(C,D) ) )
               => r2_hidden(k2_yellow_0(A,C),k6_pre_topc(A,C)) ) ) ) ) )).

fof(t11_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_pre_topc(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & v1_waybel19(B)
            & l1_waybel_9(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v5_pre_topc(C,A,B)
               => v21_waybel_0(C,A,B) ) ) ) ) )).

fof(t12_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_pre_topc(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & v1_waybel19(B)
            & l1_waybel_9(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ( v5_pre_topc(C,A,B)
                  & ! [D] :
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                     => r3_waybel_0(A,B,C,D) ) )
               => v17_waybel_0(C,A,B) ) ) ) ) )).

fof(t13_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v2_pre_topc(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_pre_topc(A,k1_struct_0(A,B)) = k7_waybel_0(A,B) ) ) )).

fof(t14_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k3_subset_1(u1_struct_0(k3_yellow_3(A,B)),k7_waybel_0(k3_yellow_3(A,B),k7_yellow_3(A,B,C,D))) = k2_xboole_0(k2_zfmisc_1(k3_subset_1(u1_struct_0(A),k7_waybel_0(A,C)),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),k3_subset_1(u1_struct_0(B),k7_waybel_0(B,D)))) ) ) ) ) )).

fof(t15_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v2_pre_topc(C)
                & v1_waybel19(C)
                & m1_yellow_9(C,A) )
             => ! [D] :
                  ( ( v2_pre_topc(D)
                    & v1_waybel19(D)
                    & m1_yellow_9(D,B) )
                 => k1_waybel19(k3_yellow_3(A,B)) = u1_pre_topc(k6_borsuk_1(C,D)) ) ) ) ) )).

fof(t16_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_pre_topc(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v2_pre_topc(B)
            & v1_waybel19(B)
            & l1_waybel_9(B) )
         => k1_waybel19(k3_yellow_3(A,B)) = u1_pre_topc(k6_borsuk_1(A,B)) ) ) )).

fof(t17_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_pre_topc(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & v1_waybel19(B)
            & l1_waybel_9(B) )
         => ( m1_yellow_9(B,k3_yellow_3(A,A))
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                  & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
               => ( C = k4_waybel_2(A)
                 => v5_pre_topc(C,B,A) ) ) ) ) ) )).

fof(t18_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & l1_orders_2(B) )
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( v1_waybel_0(k1_waybel_3(A,C),A)
                    & ~ v1_xboole_0(k1_waybel_3(A,C)) ) )
              & v2_waybel_3(A) )
           => v2_waybel_3(B) ) ) ) )).

fof(t19_waybel19,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m3_yellow_9(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
                 => ( ( r2_hidden(D,u1_pre_topc(A))
                      | r2_hidden(D,u1_pre_topc(B)) )
                   => v3_pre_topc(D,C) ) ) ) ) ) )).

fof(t20_waybel19,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m3_yellow_9(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
                     => ( ( E = D
                          & v3_pre_topc(D,A) )
                       => v3_pre_topc(E,C) ) ) ) ) ) ) )).

fof(t21_waybel19,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( u1_struct_0(A) = u1_struct_0(B)
           => ! [C] :
                ( m3_yellow_9(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
                       => ( ( E = D
                            & v4_pre_topc(D,A) )
                         => v4_pre_topc(E,C) ) ) ) ) ) ) ) )).

fof(t22_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B,C] :
          ( ( r1_tarski(B,C)
            & r1_tarski(C,u1_pre_topc(A)) )
         => ( ( m1_cantor_1(B,A)
             => m1_cantor_1(C,A) )
            & ( m2_cantor_1(B,A)
             => m2_cantor_1(C,A) ) ) ) ) )).

fof(t23_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( u1_struct_0(A) = u1_struct_0(B)
           => ! [C] :
                ( m3_yellow_9(C,A,B)
               => ! [D] :
                    ( m2_cantor_1(D,A)
                   => ! [E] :
                        ( m2_cantor_1(E,B)
                       => m2_cantor_1(k2_xboole_0(D,E),C) ) ) ) ) ) ) )).

fof(t24_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_pre_topc(D)
                    & l1_pre_topc(D) )
                 => ! [E] :
                      ( m3_yellow_9(E,A,B)
                     => ! [F] :
                          ( m3_yellow_9(F,C,D)
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(A),u1_struct_0(C))
                                & m2_relset_1(G,u1_struct_0(A),u1_struct_0(C)) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,u1_struct_0(B),u1_struct_0(D))
                                    & m2_relset_1(H,u1_struct_0(B),u1_struct_0(D)) )
                                 => ! [I] :
                                      ( ( v1_funct_1(I)
                                        & v1_funct_2(I,u1_struct_0(E),u1_struct_0(F))
                                        & m2_relset_1(I,u1_struct_0(E),u1_struct_0(F)) )
                                     => ( ( I = G
                                          & I = H
                                          & v5_pre_topc(G,A,C)
                                          & v5_pre_topc(H,B,D) )
                                       => v5_pre_topc(I,E,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t25_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_cantor_1(B,A)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ( ( r2_hidden(D,E)
                            & r2_hidden(E,B) )
                         => r1_waybel_0(A,C,E) ) )
                   => r2_hidden(D,k11_yellow_6(A,C)) ) ) ) ) ) )).

fof(t26_waybel19,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,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_waybel_0(A,B,C)
               => r1_tarski(k11_yellow_6(A,B),k6_pre_topc(A,C)) ) ) ) ) )).

fof(t27_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( u1_waybel_0(A,k2_yellow_9(A,B)) = k6_relat_1(B)
            & u1_waybel_0(A,k3_yellow_9(A,B)) = k6_relat_1(B) ) ) ) )).

fof(t28_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k6_waybel_0(A,B)) = k1_struct_0(A,B) ) ) )).

fof(d3_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_waybel_9(A) )
     => ( v2_waybel19(A)
      <=> m2_cantor_1(k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),k1_waybel19(A),k5_waybel11(A)),A) ) ) )).

fof(t29_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & v1_waybel19(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( ( v4_waybel11(C)
                & m1_yellow_9(C,A) )
             => ! [D] :
                  ( ( v2_pre_topc(D)
                    & m1_yellow_9(D,A) )
                 => ( v2_waybel19(D)
                  <=> m3_yellow_9(D,C,B) ) ) ) ) ) )).

fof(d4_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( B = k2_waybel19(A)
          <=> ! [C] :
                ( ( v2_pre_topc(C)
                  & v2_waybel19(C)
                  & m1_yellow_9(C,A) )
               => B = u1_pre_topc(C) ) ) ) ) )).

fof(t33_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => k2_waybel19(A) = k1_cantor_1(u1_struct_0(A),k2_cantor_1(u1_struct_0(A),k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),k5_waybel11(A),k1_waybel19(A)))) ) )).

fof(t34_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & v1_waybel19(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( ( v2_pre_topc(C)
                & v4_waybel11(C)
                & m1_yellow_9(C,A) )
             => ! [D] :
                  ( m3_yellow_9(D,C,B)
                 => k2_waybel19(A) = u1_pre_topc(D) ) ) ) ) )).

fof(t35_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
           => v3_waybel11(B,A) ) ) ) )).

fof(t36_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
           => v3_waybel11(B,A) ) ) ) )).

fof(t37_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v4_waybel11(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & v2_waybel19(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( v3_pre_topc(C,A)
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => ( D = C
                     => v3_pre_topc(D,B) ) ) ) ) ) ) )).

fof(t38_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v4_pre_topc(k7_waybel_0(A,B),A)
            & v4_pre_topc(k6_waybel_0(A,B),A)
            & v4_pre_topc(k1_struct_0(A,B),A) ) ) ) )).

fof(t39_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v3_pre_topc(k3_subset_1(u1_struct_0(A),k7_waybel_0(A,B)),A)
            & v3_pre_topc(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),A)
            & v3_pre_topc(k3_subset_1(u1_struct_0(A),k1_struct_0(A,B)),A) ) ) ) )).

fof(t40_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v3_pre_topc(k2_waybel_3(A,B),A)
            & v4_pre_topc(k3_subset_1(u1_struct_0(A),k2_waybel_3(A,B)),A) ) ) ) )).

fof(t41_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v4_waybel11(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & v2_waybel19(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( ( v13_waybel_0(C,B)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
             => ( v3_pre_topc(C,B)
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( D = C
                     => v3_pre_topc(D,A) ) ) ) ) ) ) )).

fof(t42_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v4_pre_topc(B,A)
          <=> v2_waybel11(B,A) ) ) ) )).

fof(t43_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => k11_yellow_6(A,k3_yellow_9(A,B)) = k1_struct_0(A,k2_yellow_0(A,B)) ) ) )).

fof(s1_waybel19,axiom,
    ( ( ? [A] :
          ( m2_cantor_1(A,f1_s1_waybel19)
          & ! [B] :
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_waybel19)))
             => ( r2_hidden(B,A)
               => p1_s1_waybel19(B) ) ) )
      & ! [A] :
          ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(f1_s1_waybel19))))
         => ( ! [B] :
                ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_waybel19)))
               => ( r2_hidden(B,A)
                 => p1_s1_waybel19(B) ) )
           => p1_s1_waybel19(k5_setfam_1(u1_struct_0(f1_s1_waybel19),A)) ) )
      & ! [A] :
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f1_s1_waybel19)))
         => ! [B] :
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_waybel19)))
             => ( ( p1_s1_waybel19(A)
                  & p1_s1_waybel19(B) )
               => p1_s1_waybel19(k5_subset_1(u1_struct_0(f1_s1_waybel19),A,B)) ) ) )
      & p1_s1_waybel19(k2_pre_topc(f1_s1_waybel19)) )
   => ! [A] :
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f1_s1_waybel19)))
       => ( v3_pre_topc(A,f1_s1_waybel19)
         => p1_s1_waybel19(A) ) ) )).

fof(dt_k1_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => m1_subset_1(k1_waybel19(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k2_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => m1_subset_1(k2_waybel19(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(d1_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_waybel_9(A) )
     => ( v1_waybel19(A)
      <=> m2_cantor_1(a_1_0_waybel19(A),A) ) ) )).

fof(t7_waybel19,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_waybel_9(A) )
     => ( v1_waybel19(A)
      <=> m1_cantor_1(a_1_1_waybel19(A),A) ) ) )).

fof(t30_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => m2_cantor_1(k2_xboole_0(k5_waybel11(A),a_1_2_waybel19(A)),A) ) )).

fof(t31_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => m2_cantor_1(k2_xboole_0(k5_waybel11(A),a_1_3_waybel19(A)),A) ) )).

fof(t32_waybel19,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => m1_cantor_1(a_1_4_waybel19(A),A) ) )).

fof(fraenkel_a_1_0_waybel19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_waybel_9(B) )
     => ( r2_hidden(A,a_1_0_waybel19(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(B))
            & A = k3_subset_1(u1_struct_0(B),k7_waybel_0(B,C)) ) ) ) )).

fof(fraenkel_a_1_1_waybel19,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_waybel_9(B) )
     => ( r2_hidden(A,a_1_1_waybel19(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = k3_subset_1(u1_struct_0(B),k5_waybel_0(B,C))
            & v1_finset_1(C) ) ) ) )).

fof(fraenkel_a_1_2_waybel19,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v2_pre_topc(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v2_waybel19(B)
        & l1_waybel_9(B) )
     => ( r2_hidden(A,a_1_2_waybel19(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(B))
            & A = k3_subset_1(u1_struct_0(B),k7_waybel_0(B,C)) ) ) ) )).

fof(fraenkel_a_1_3_waybel19,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v2_pre_topc(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v2_waybel19(B)
        & l1_waybel_9(B) )
     => ( r2_hidden(A,a_1_3_waybel19(B))
      <=> ? [C,D] :
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & m1_subset_1(D,u1_struct_0(B))
            & A = k6_subset_1(u1_struct_0(B),C,k7_waybel_0(B,D))
            & r2_hidden(C,k5_waybel11(B)) ) ) ) )).

fof(fraenkel_a_1_4_waybel19,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v2_pre_topc(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v2_waybel19(B)
        & l1_waybel_9(B) )
     => ( r2_hidden(A,a_1_4_waybel19(B))
      <=> ? [C,D] :
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = k6_subset_1(u1_struct_0(B),C,k5_waybel_0(B,D))
            & r2_hidden(C,k5_waybel11(B))
            & v1_finset_1(D) ) ) ) )).
%------------------------------------------------------------------------------