SET007 Axioms: SET007+505.ax


%------------------------------------------------------------------------------
% File     : SET007+505 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Scott 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    : waybel11 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  102 (   0 unit)
%            Number of atoms       : 1028 (  41 equality)
%            Maximal formula depth :   23 (  10 average)
%            Number of connectives : 1031 ( 105 ~  ;   0  |; 677  &)
%                                         (  33 <=>; 216 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   81 (   0 propositional; 1-3 arity)
%            Number of functors    :   52 (   4 constant; 0-3 arity)
%            Number of variables   :  247 (   0 singleton; 227 !;  20 ?)
%            Maximal term depth    :    4 (   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(rc1_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B)
          & v1_waybel_0(B,A) ) ) )).

fof(rc2_waybel11,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(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)
      & v2_waybel_3(A)
      & v3_waybel_3(A)
      & v1_waybel_5(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v16_waybel_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v9_waybel_1(A)
      & v6_group_1(A)
      & v3_realset2(A) ) )).

fof(rc3_waybel11,axiom,(
    ? [A] :
      ( l1_struct_0(A)
      & v1_struct_0(A)
      & ~ v3_struct_0(A)
      & v6_group_1(A) ) )).

fof(cc1_waybel11,axiom,(
    ! [A] :
      ( ( v6_group_1(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => v1_finset_1(B) ) ) )).

fof(fc1_waybel11,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_xboole_0(k1_pre_topc(A))
        & v1_finset_1(k1_pre_topc(A))
        & v5_orders_2(k1_pre_topc(A),A)
        & v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A))
        & v1_waybel_0(k1_pre_topc(A),A)
        & v2_waybel_0(k1_pre_topc(A),A)
        & v12_waybel_0(k1_pre_topc(A),A)
        & v13_waybel_0(k1_pre_topc(A),A) ) ) )).

fof(cc2_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => v13_waybel_0(B,A) ) ) )).

fof(fc2_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_xboole_0(k1_pre_topc(A))
        & v1_finset_1(k1_pre_topc(A))
        & v5_orders_2(k1_pre_topc(A),A)
        & v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A))
        & v1_waybel_0(k1_pre_topc(A),A)
        & v2_waybel_0(k1_pre_topc(A),A)
        & v12_waybel_0(k1_pre_topc(A),A)
        & v13_waybel_0(k1_pre_topc(A),A)
        & v2_waybel11(k1_pre_topc(A),A)
        & v3_waybel11(k1_pre_topc(A),A) ) ) )).

fof(rc4_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v2_waybel11(B,A)
          & v3_waybel11(B,A) ) ) )).

fof(fc3_waybel11,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & v3_waybel11(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v2_waybel11(k3_subset_1(u1_struct_0(A),B),A) ) )).

fof(cc3_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v6_group_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_finset_1(B)
            & v1_waybel11(B,A) ) ) ) )).

fof(rc5_waybel11,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(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)
      & v2_waybel_3(A)
      & v3_waybel_3(A)
      & v1_waybel_5(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v16_waybel_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v1_waybel_9(A)
      & v9_waybel_1(A)
      & v3_realset2(A)
      & v4_waybel11(A) ) )).

fof(fc4_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(k2_pre_topc(A))
        & v12_waybel_0(k2_pre_topc(A),A)
        & v13_waybel_0(k2_pre_topc(A),A)
        & v1_waybel11(k2_pre_topc(A),A)
        & v2_waybel11(k2_pre_topc(A),A) ) ) )).

fof(rc6_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v12_waybel_0(B,A)
          & v13_waybel_0(B,A)
          & v1_waybel11(B,A)
          & v2_waybel11(B,A) ) ) )).

fof(fc5_waybel11,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & v1_waybel11(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v2_waybel11(k3_subset_1(u1_struct_0(A),B),A) ) )).

fof(fc6_waybel11,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & v2_waybel11(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_waybel11(k3_subset_1(u1_struct_0(A),B),A) ) )).

fof(cc4_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v12_waybel_0(B,A)
           => v3_waybel11(B,A) ) ) ) )).

fof(fc7_waybel11,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u1_struct_0(A))
        & m1_relset_1(C,B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k3_waybel11(A,B,C))
        & v6_waybel_0(k3_waybel11(A,B,C),A)
        & v8_waybel_0(k3_waybel11(A,B,C),A) ) ) )).

fof(fc8_waybel11,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u1_struct_0(A))
        & m1_relset_1(C,B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k3_waybel11(A,B,C))
        & v3_orders_2(k3_waybel11(A,B,C))
        & v6_waybel_0(k3_waybel11(A,B,C),A)
        & v8_waybel_0(k3_waybel11(A,B,C),A) ) ) )).

fof(fc9_waybel11,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u1_struct_0(A))
        & m1_relset_1(C,B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k3_waybel11(A,B,C))
        & v2_orders_2(k3_waybel11(A,B,C))
        & v6_waybel_0(k3_waybel11(A,B,C),A)
        & v8_waybel_0(k3_waybel11(A,B,C),A) ) ) )).

fof(rc7_waybel11,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( l1_waybel_0(B,A)
          & ~ v3_struct_0(B)
          & v2_orders_2(B)
          & v3_orders_2(B)
          & v6_waybel_0(B,A)
          & v7_waybel_0(B)
          & v8_waybel_0(B,A)
          & v10_waybel_0(B,A) ) ) )).

fof(fc10_waybel11,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k4_waybel11(A,B))
        & v6_waybel_0(k4_waybel11(A,B),A) ) ) )).

fof(fc11_waybel11,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k4_waybel11(A,B))
        & v2_orders_2(k4_waybel11(A,B))
        & v3_orders_2(k4_waybel11(A,B))
        & v4_orders_2(k4_waybel11(A,B))
        & v6_waybel_0(k4_waybel11(A,B),A)
        & v7_waybel_0(k4_waybel11(A,B)) ) ) )).

fof(fc12_waybel11,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) )
     => ( v1_relat_1(k2_waybel11(A))
        & v4_yellow_6(k2_waybel11(A),A) ) ) )).

fof(fc13_waybel11,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) )
     => ( v1_relat_1(k2_waybel11(A))
        & v4_yellow_6(k2_waybel11(A),A)
        & v5_yellow_6(k2_waybel11(A),A) ) ) )).

fof(fc14_waybel11,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k2_waybel11(A))
        & v4_yellow_6(k2_waybel11(A),A)
        & v5_yellow_6(k2_waybel11(A),A)
        & v6_yellow_6(k2_waybel11(A),A)
        & v7_yellow_6(k2_waybel11(A),A)
        & v8_yellow_6(k2_waybel11(A),A) ) ) )).

fof(t1_waybel11,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(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r4_yellow_4(A,B,C)
               => r3_orders_2(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) ) ) ) ) )).

fof(t2_waybel11,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(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r3_yellow_4(A,B,C)
               => r3_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ) ) )).

fof(t3_waybel11,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => v1_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) )).

fof(t4_waybel11,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_finset_1(B)
            & v1_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => r2_hidden(k1_yellow_0(A,B),B) ) ) )).

fof(t5_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v13_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( ~ r2_hidden(B,C)
               => r1_xboole_0(C,k6_waybel_0(A,B)) ) ) ) ) )).

fof(t6_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v12_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( r2_hidden(B,C)
               => r1_tarski(k6_waybel_0(A,B),C) ) ) ) ) )).

fof(d1_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_waybel11(B,A)
          <=> ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ~ ( r2_hidden(k1_yellow_0(A,C),B)
                    & r1_xboole_0(C,B) ) ) ) ) ) )).

fof(d2_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_waybel11(B,A)
          <=> ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ( r1_tarski(C,B)
                 => r2_hidden(k1_yellow_0(A,C),B) ) ) ) ) ) )).

fof(d3_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_waybel11(B,A)
          <=> ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ~ ( r2_hidden(k1_yellow_0(A,C),B)
                    & ! [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                       => ~ ( r2_hidden(D,C)
                            & ! [E] :
                                ( m1_subset_1(E,u1_struct_0(A))
                               => ( ( r2_hidden(E,C)
                                    & r1_orders_2(A,D,E) )
                                 => r2_hidden(E,B) ) ) ) ) ) ) ) ) ) )).

fof(d4_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_waybel_9(A) )
     => ( v4_waybel11(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v3_pre_topc(B,A)
            <=> ( v1_waybel11(B,A)
                & v13_waybel_0(B,A) ) ) ) ) ) )).

fof(d5_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v6_group_1(A)
        & l1_waybel_9(A) )
     => ( v4_waybel11(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v3_pre_topc(B,A)
            <=> v13_waybel_0(B,A) ) ) ) ) )).

fof(t7_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v24_waybel_0(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
          <=> ( v2_waybel11(B,A)
              & v12_waybel_0(B,A) ) ) ) ) )).

fof(t8_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v2_waybel11(k6_waybel_0(A,B),A) ) ) )).

fof(t9_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_pre_topc(A,k1_struct_0(A,B)) = k6_waybel_0(A,B) ) ) )).

fof(t10_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & l1_pre_topc(A) ) ) )).

fof(t11_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v4_pre_topc(k6_waybel_0(A,B),A) ) ) )).

fof(t12_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v24_waybel_0(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v3_pre_topc(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),A) ) ) )).

fof(t13_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v24_waybel_0(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v13_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( ~ r2_hidden(B,C)
               => m2_connsp_2(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),A,C) ) ) ) ) )).

fof(t14_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ? [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
              & B = k6_setfam_1(u1_struct_0(A),C)
              & ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_hidden(D,C)
                   => m2_connsp_2(D,A,B) ) ) ) ) ) )).

fof(t15_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
          <=> ( v13_waybel_0(B,A)
              & v3_waybel11(B,A) ) ) ) ) )).

fof(d7_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(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))
             => ( r1_waybel11(A,B,C)
              <=> r3_orders_2(A,C,k1_waybel11(A,B)) ) ) ) ) )).

fof(d8_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m4_yellow_6(B,A)
         => ( B = k2_waybel11(A)
          <=> ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v3_orders_2(C)
                  & v6_waybel_0(C,A)
                  & v7_waybel_0(C)
                  & l1_waybel_0(C,A) )
               => ( r2_hidden(C,k7_yellow_6(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_hidden(k4_tarski(C,D),B)
                      <=> r1_waybel11(A,C,D) ) ) ) ) ) ) ) )).

fof(t17_waybel11,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] :
          ( ( ~ 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))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_waybel11(A,B,C)
                      & r1_waybel_0(A,B,k6_waybel_0(A,D)) )
                   => r3_orders_2(A,C,D) ) ) ) ) ) )).

fof(t18_waybel11,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] :
          ( ( ~ 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))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_waybel_0(A,B,k7_waybel_0(A,D))
                   => r1_orders_2(A,D,k1_waybel11(A,B)) ) ) ) ) ) )).

fof(d9_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ( v8_waybel_0(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(B))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ( r1_orders_2(B,C,D)
                     => r3_orders_2(A,k3_waybel_0(A,B,C),k3_waybel_0(A,B,D)) ) ) ) ) ) ) )).

fof(d10_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,u1_struct_0(A))
                & m2_relset_1(C,B,u1_struct_0(A)) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_waybel_0(D,A)
                    & l1_waybel_0(D,A) )
                 => ( D = k3_waybel11(A,B,C)
                  <=> ( u1_struct_0(D) = B
                      & u1_waybel_0(A,D) = 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_orders_2(A,k3_waybel_0(A,D,E),k3_waybel_0(A,D,F)) ) ) ) ) ) ) ) ) ) )).

fof(t20_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,u1_struct_0(A))
                & m2_relset_1(C,B,u1_struct_0(A)) )
             => ( v1_waybel_0(k8_yellow_2(B,A,C),A)
               => v7_waybel_0(k3_waybel11(A,B,C)) ) ) ) ) )).

fof(t21_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,u1_struct_0(A))
                & m2_relset_1(C,B,u1_struct_0(A)) )
             => ( ( r1_tarski(B,u1_struct_0(A))
                  & v7_waybel_0(k3_waybel11(A,B,C)) )
               => r2_hidden(k3_waybel11(A,B,C),k7_yellow_6(A)) ) ) ) ) )).

fof(t22_waybel11,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] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v8_waybel_0(B,A)
            & l1_waybel_0(B,A) )
         => k1_waybel11(A,B) = k1_waybel_2(A,B) ) ) )).

fof(t23_waybel11,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] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v1_yellow_6(B,A)
            & l1_waybel_0(B,A) )
         => k5_yellow_6(A,B) = k1_waybel11(A,B) ) ) )).

fof(t24_waybel11,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] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v1_yellow_6(B,A)
            & l1_waybel_0(B,A) )
         => r1_waybel11(A,B,k5_yellow_6(A,B)) ) ) )).

fof(d11_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v6_waybel_0(C,A)
                & l1_waybel_0(C,A) )
             => ( C = k4_waybel11(A,B)
              <=> ( u1_struct_0(C) = k1_struct_0(A,B)
                  & u1_orders_2(C) = k1_tarski(k4_tarski(B,B))
                  & u1_waybel_0(A,C) = k6_partfun1(k1_struct_0(A,B)) ) ) ) ) ) )).

fof(t25_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k4_waybel11(A,B)))
             => C = B ) ) ) )).

fof(t26_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k4_waybel11(A,B)))
             => k3_waybel_0(A,k4_waybel11(A,B),C) = B ) ) ) )).

fof(t27_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( r1_waybel_0(A,k4_waybel11(A,B),C)
            <=> r2_hidden(B,C) ) ) ) )).

fof(t28_waybel11,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))
         => B = k1_waybel11(A,k4_waybel11(A,B)) ) ) )).

fof(t29_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r2_hidden(k4_waybel11(A,B),k7_yellow_6(A)) ) ) )).

fof(t31_waybel11,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(u1_struct_0(A)))
         => ( r2_hidden(B,u1_pre_topc(k14_yellow_6(A,k2_waybel11(A))))
          <=> ( v1_waybel11(B,A)
              & v13_waybel_0(B,A) ) ) ) ) )).

fof(t32_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k14_yellow_6(A,k2_waybel11(A)) ) )).

fof(t33_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_waybel_9(A) )
     => ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k14_yellow_6(A,k2_waybel11(A))
       => ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v3_pre_topc(B,A)
            <=> ( v1_waybel11(B,A)
                & v13_waybel_0(B,A) ) ) ) ) ) )).

fof(t34_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_waybel_9(A) )
     => ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k14_yellow_6(A,k2_waybel11(A))
       => v4_waybel11(A) ) ) )).

fof(t35_waybel11,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,D] :
              ( m2_yellow_6(D,A,B)
             => ( D = k6_yellow_6(A,B,C)
               => ! [E] :
                    ( m1_subset_1(E,u1_struct_0(D))
                   => r2_hidden(k3_waybel_0(A,D,E),C) ) ) ) ) ) )).

fof(d12_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => k5_waybel11(A) = u1_pre_topc(k14_yellow_6(A,k2_waybel11(A))) ) )).

fof(t36_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v3_pre_topc(k2_waybel_3(A,B),A) ) ) )).

fof(t37_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_waybel_9(A) )
     => ( u1_pre_topc(A) = k5_waybel11(A)
       => v4_waybel11(A) ) ) )).

fof(t38_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,A) )
             => ( r2_hidden(C,k7_yellow_6(A))
               => ( r1_waybel11(A,C,B)
                <=> r2_hidden(B,k11_yellow_6(A,C)) ) ) ) ) ) )).

fof(t39_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( v7_yellow_6(k2_waybel11(A),A)
       => v3_waybel_3(A) ) ) )).

fof(t40_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ( v3_waybel_3(A)
      <=> k13_yellow_6(A) = k2_waybel11(A) ) ) )).

fof(t41_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v1_waybel_6(B,A)
           => v3_pre_topc(B,A) ) ) ) )).

fof(t42_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,B)
               => r1_tarski(k7_waybel_0(A,C),B) ) ) ) ) )).

fof(t43_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v3_pre_topc(C,A)
                  & r2_hidden(B,C)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r1_waybel_3(A,D,B)
                          & r2_hidden(D,C) ) ) ) ) ) ) )).

fof(t46_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v3_pre_topc(B,A)
          <=> v1_waybel_6(B,A) ) ) ) )).

fof(t47_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_tops_1(A,k7_waybel_0(A,B)) = k2_waybel_3(A,B) ) ) )).

fof(dt_k1_waybel11,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A) )
     => m1_subset_1(k1_waybel11(A,B),u1_struct_0(A)) ) )).

fof(dt_k2_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => m4_yellow_6(k2_waybel11(A),A) ) )).

fof(dt_k3_waybel11,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u1_struct_0(A))
        & m1_relset_1(C,B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k3_waybel11(A,B,C))
        & v6_waybel_0(k3_waybel11(A,B,C),A)
        & l1_waybel_0(k3_waybel11(A,B,C),A) ) ) )).

fof(dt_k4_waybel11,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v6_waybel_0(k4_waybel11(A,B),A)
        & l1_waybel_0(k4_waybel11(A,B),A) ) ) )).

fof(dt_k5_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => m1_subset_1(k5_waybel11(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(t16_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_waybel_9(A) )
     => ( u1_pre_topc(A) = a_1_0_waybel11(A)
       => v2_pre_topc(A) ) ) )).

fof(d6_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => k1_waybel11(A,B) = k1_yellow_0(A,a_2_0_waybel11(A,B)) ) ) )).

fof(t19_waybel11,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B)) = a_2_1_waybel11(A,B) ) ) )).

fof(t30_waybel11,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] :
          ( ( ~ 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)))
             => ( C = a_2_2_waybel11(A,B)
               => ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A) ) ) ) ) ) )).

fof(t44_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => m1_yellow_8(a_2_3_waybel11(A,B),A,B) ) ) )).

fof(t45_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => m1_cantor_1(a_1_1_waybel11(A),A) ) )).

fof(t48_waybel11,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_tops_1(A,B) = k3_tarski(a_2_4_waybel11(A,B)) ) ) )).

fof(s1_waybel11,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f2_s1_waybel11)
       => ! [B] :
            ( m1_subset_1(B,f1_s1_waybel11)
           => f3_s1_waybel11(B) = f4_s1_waybel11(A,B) ) )
   => a_0_0_waybel11 = a_0_1_waybel11 )).

fof(fraenkel_a_1_0_waybel11,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & l1_waybel_9(B) )
     => ( r2_hidden(A,a_1_0_waybel11(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = C
            & v3_waybel11(C,B) ) ) ) )).

fof(fraenkel_a_2_0_waybel11,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,B) )
     => ( r2_hidden(A,a_2_0_waybel11(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(C))
            & A = k2_yellow_0(B,a_3_0_waybel11(B,C,D)) ) ) ) )).

fof(fraenkel_a_3_0_waybel11,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,B)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_0_waybel11(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = k3_waybel_0(B,C,E)
            & r1_orders_2(C,D,E) ) ) ) )).

fof(fraenkel_a_2_1_waybel11,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_waybel11(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(C))
            & A = k3_waybel_0(B,C,D) ) ) ) )).

fof(fraenkel_a_2_2_waybel11,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,B) )
     => ( r2_hidden(A,a_2_2_waybel11(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(C))
            & A = k2_yellow_0(B,a_3_1_waybel11(B,C,D)) ) ) ) )).

fof(fraenkel_a_3_1_waybel11,axiom,(
    ! [A,B,C,D] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,B)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_1_waybel11(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = k3_waybel_0(B,C,E)
            & r1_orders_2(C,D,E) ) ) ) )).

fof(fraenkel_a_2_3_waybel11,axiom,(
    ! [A,B,C] :
      ( ( v2_pre_topc(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v3_waybel_3(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v4_waybel11(B)
        & l1_waybel_9(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_3_waybel11(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = k2_waybel_3(B,D)
            & r1_waybel_3(B,D,C) ) ) ) )).

fof(fraenkel_a_1_1_waybel11,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v3_waybel_3(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v4_waybel11(B)
        & l1_waybel_9(B) )
     => ( r2_hidden(A,a_1_1_waybel11(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(B))
            & A = k2_waybel_3(B,C) ) ) ) )).

fof(fraenkel_a_2_4_waybel11,axiom,(
    ! [A,B,C] :
      ( ( v2_pre_topc(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v3_waybel_3(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v4_waybel11(B)
        & l1_waybel_9(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_4_waybel11(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = k2_waybel_3(B,D)
            & r1_tarski(k2_waybel_3(B,D),C) ) ) ) )).

fof(fraenkel_a_0_0_waybel11,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_waybel11)
    <=> ? [B] :
          ( m1_subset_1(B,f1_s1_waybel11)
          & A = f3_s1_waybel11(B)
          & p1_s1_waybel11(B) ) ) )).

fof(fraenkel_a_0_1_waybel11,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_1_waybel11)
    <=> ? [B,C] :
          ( m1_subset_1(B,f2_s1_waybel11)
          & m1_subset_1(C,f1_s1_waybel11)
          & A = f4_s1_waybel11(B,C)
          & p1_s1_waybel11(C) ) ) )).
%------------------------------------------------------------------------------