SET007 Axioms: SET007+696.ax


%------------------------------------------------------------------------------
% File     : SET007+696 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Compactness of Lim-inf 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    : waybel33 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   41 (   0 unit)
%            Number of atoms       :  559 (  38 equality)
%            Maximal formula depth :   18 (  11 average)
%            Number of connectives :  581 (  63 ~  ;   0  |; 396  &)
%                                         (   5 <=>; 117 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   54 (   0 propositional; 1-3 arity)
%            Number of functors    :   29 (   0 constant; 1-3 arity)
%            Number of variables   :  111 (   0 singleton; 105 !;   6 ?)
%            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(cc1_waybel33,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( ~ v3_struct_0(A)
          & v1_waybel33(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A) ) ) ) )).

fof(cc2_waybel33,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( v2_pre_topc(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v1_waybel33(A) ) ) ) )).

fof(rc1_waybel33,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)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_waybel33(A) ) )).

fof(cc3_waybel33,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v25_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_9(B,A)
         => ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v1_yellow_0(B)
            & v25_waybel_0(B) ) ) ) )).

fof(cc4_waybel33,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_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)
            & v2_lattice3(B) ) ) ) )).

fof(rc2_waybel33,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_yellow_9(B,A)
          & ~ v3_struct_0(B)
          & v2_pre_topc(B)
          & v2_orders_2(B)
          & v3_orders_2(B)
          & v4_orders_2(B)
          & v1_yellow_0(B)
          & v24_waybel_0(B)
          & v25_waybel_0(B)
          & v2_lattice3(B)
          & ~ v1_yellow_3(B)
          & v1_waybel_9(B)
          & v1_waybel33(B) ) ) )).

fof(fc1_waybel33,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_waybel33(A))
        & v2_pre_topc(k2_waybel33(A))
        & v2_orders_2(k2_waybel33(A))
        & v3_orders_2(k2_waybel33(A))
        & v4_orders_2(k2_waybel33(A))
        & v1_yellow_0(k2_waybel33(A))
        & v24_waybel_0(k2_waybel33(A))
        & v25_waybel_0(k2_waybel33(A))
        & v2_lattice3(k2_waybel33(A))
        & ~ v1_yellow_3(k2_waybel33(A))
        & v1_waybel_9(k2_waybel33(A))
        & v1_waybel33(k2_waybel33(A)) ) ) )).

fof(t1_waybel33,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_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(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] :
                ( ( ~ v1_xboole_0(C)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ! [D] :
                    ( ( ~ v1_xboole_0(D)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                   => ! [E] :
                        ( ( ~ v1_xboole_0(E)
                          & v2_waybel_0(E,k3_yellow_1(C))
                          & v13_waybel_0(E,k3_yellow_1(C))
                          & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_yellow_1(C)))) )
                       => ! [F] :
                            ( ( ~ v1_xboole_0(F)
                              & v2_waybel_0(F,k3_yellow_1(D))
                              & v13_waybel_0(F,k3_yellow_1(D))
                              & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k3_yellow_1(D)))) )
                           => ( E = F
                             => k1_waybel33(A,C,E) = k1_waybel33(B,D,F) ) ) ) ) ) ) ) ) )).

fof(d2_waybel33,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_waybel_9(A) )
     => ( v1_waybel33(A)
      <=> u1_pre_topc(A) = k4_waybel28(A) ) ) )).

fof(t2_waybel33,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_struct_0(B) )
         => ( u1_struct_0(A) = u1_struct_0(B)
           => ! [C] :
                ( l1_waybel_0(C,A)
               => ? [D] :
                    ( v6_waybel_0(D,B)
                    & l1_waybel_0(D,B)
                    & g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
                    & u1_waybel_0(A,C) = u1_waybel_0(B,D) ) ) ) ) ) )).

fof(t3_waybel33,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_struct_0(B) )
         => ( u1_struct_0(A) = u1_struct_0(B)
           => ! [C] :
                ( l1_waybel_0(C,A)
               => ~ ( r2_hidden(C,k7_yellow_6(A))
                    & ! [D] :
                        ( ( ~ v3_struct_0(D)
                          & v3_orders_2(D)
                          & v6_waybel_0(D,B)
                          & v7_waybel_0(D)
                          & l1_waybel_0(D,B) )
                       => ~ ( r2_hidden(D,k7_yellow_6(B))
                            & g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
                            & u1_waybel_0(A,C) = u1_waybel_0(B,D) ) ) ) ) ) ) ) )).

fof(t4_waybel33,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & v25_waybel_0(B)
            & v2_lattice3(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] :
                ( ( ~ v3_struct_0(C)
                  & v3_orders_2(C)
                  & v7_waybel_0(C)
                  & l1_waybel_0(C,A) )
               => ! [D] :
                    ( ( ~ v3_struct_0(D)
                      & v3_orders_2(D)
                      & v7_waybel_0(D)
                      & l1_waybel_0(D,B) )
                   => ( ( g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
                        & u1_waybel_0(A,C) = u1_waybel_0(B,D) )
                     => k1_waybel11(A,C) = k1_waybel11(B,D) ) ) ) ) ) ) )).

fof(t5_waybel33,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_struct_0(B) )
         => ( u1_struct_0(A) = u1_struct_0(B)
           => ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v3_orders_2(C)
                  & v7_waybel_0(C)
                  & l1_waybel_0(C,A) )
               => ! [D] :
                    ( ( ~ v3_struct_0(D)
                      & v3_orders_2(D)
                      & v7_waybel_0(D)
                      & l1_waybel_0(D,B) )
                   => ( ( g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
                        & u1_waybel_0(A,C) = u1_waybel_0(B,D) )
                     => ! [E] :
                          ( m2_yellow_6(E,A,C)
                         => ? [F] :
                              ( v6_waybel_0(F,B)
                              & m2_yellow_6(F,B,D)
                              & g1_orders_2(u1_struct_0(E),u1_orders_2(E)) = g1_orders_2(u1_struct_0(F),u1_orders_2(F))
                              & u1_waybel_0(A,E) = u1_waybel_0(B,F) ) ) ) ) ) ) ) ) )).

fof(t6_waybel33,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & v25_waybel_0(B)
            & v2_lattice3(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] :
                ( l1_waybel_0(C,A)
               => ! [D] :
                    ~ ( r2_hidden(k4_tarski(C,D),k3_waybel28(A))
                      & ! [E] :
                          ( ( ~ v3_struct_0(E)
                            & v3_orders_2(E)
                            & v6_waybel_0(E,B)
                            & v7_waybel_0(E)
                            & l1_waybel_0(E,B) )
                         => ~ ( r2_hidden(k4_tarski(E,D),k3_waybel28(B))
                              & g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(E),u1_orders_2(E))
                              & u1_waybel_0(A,C) = u1_waybel_0(B,E) ) ) ) ) ) ) ) )).

fof(t7_waybel33,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_struct_0(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_waybel_0(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_waybel_0(D,B) )
                 => ( ( g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
                      & u1_waybel_0(A,C) = u1_waybel_0(B,D) )
                   => ! [E] :
                        ( r1_waybel_0(A,C,E)
                       => r1_waybel_0(B,D,E) ) ) ) ) ) ) )).

fof(t8_waybel33,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & v25_waybel_0(B)
            & v2_lattice3(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))
           => k14_yellow_6(A,k3_waybel28(A)) = k14_yellow_6(B,k3_waybel28(B)) ) ) ) )).

fof(t9_waybel33,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & v25_waybel_0(B)
            & v2_lattice3(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))
           => k4_waybel28(A) = k4_waybel28(B) ) ) ) )).

fof(t10_waybel33,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel33(B)
            & m1_yellow_9(B,A) )
         => k4_waybel28(A) = u1_pre_topc(B) ) ) )).

fof(d3_waybel33,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_9(B)
            & m1_yellow_9(B,A) )
         => ( B = k2_waybel33(A)
          <=> v1_waybel33(B) ) ) ) )).

fof(t12_waybel33,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] :
          ( ( ~ 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,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(C,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k3_yellow19(A,k2_pre_topc(A),B)))
                   => ( k2_mcart_1(D) = C
                     => k2_yellow_0(A,C) = k2_waybel_9(A,k6_waybel_9(A,k3_yellow19(A,k2_pre_topc(A),B),D)) ) ) ) ) ) ) )).

fof(t13_waybel33,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] :
          ( ( ~ 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))))) )
         => k1_waybel33(A,k2_pre_topc(A),B) = k1_waybel11(A,k3_yellow19(A,k2_pre_topc(A),B)) ) ) )).

fof(t14_waybel33,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] :
          ( ( ~ 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))))) )
         => r2_hidden(k3_yellow19(A,k2_pre_topc(A),B),k7_yellow_6(A)) ) ) )).

fof(t15_waybel33,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] :
          ( ( ~ 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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k3_yellow19(A,k2_pre_topc(A),B)),u1_struct_0(k3_yellow19(A,k2_pre_topc(A),B)))
                & v1_waybel28(C,k3_yellow19(A,k2_pre_topc(A),B))
                & m2_relset_1(C,u1_struct_0(k3_yellow19(A,k2_pre_topc(A),B)),u1_struct_0(k3_yellow19(A,k2_pre_topc(A),B))) )
             => r1_orders_2(A,k2_waybel_9(A,k2_waybel28(A,k3_yellow19(A,k2_pre_topc(A),B),C)),k1_waybel33(A,k2_pre_topc(A),B)) ) ) ) )).

fof(t16_waybel33,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] :
          ( ( ~ 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] :
              ( m2_yellow_6(C,A,k3_yellow19(A,k2_pre_topc(A),B))
             => k1_waybel33(A,k2_pre_topc(A),B) = k1_waybel11(A,C) ) ) ) )).

fof(t17_waybel33,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] :
              ~ ( r2_waybel_0(A,B,C)
                & ! [D] :
                    ( ( v6_waybel_0(D,A)
                      & m2_yellow_6(D,A,B) )
                   => ~ ( r1_tarski(k8_yellow_2(u1_struct_0(D),A,u1_waybel_0(A,D)),C)
                        & m1_yellow_6(D,A,B) ) ) ) ) ) )).

fof(t18_waybel33,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)
        & v1_waybel33(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(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)
                 => r2_hidden(k1_waybel33(A,k2_pre_topc(A),C),B) ) ) ) ) ) )).

fof(t19_waybel33,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => r1_tarski(k5_waybel11(A),k4_waybel28(A)) ) )).

fof(t20_waybel33,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] :
              ( m2_cantor_1(C,A)
             => ( ( r1_tarski(C,u1_pre_topc(B))
                  & r2_hidden(u1_struct_0(A),u1_pre_topc(B)) )
               => r1_tarski(u1_pre_topc(A),u1_pre_topc(B)) ) ) ) ) )).

fof(t21_waybel33,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) )
     => r1_tarski(k1_waybel19(A),k4_waybel28(A)) ) )).

fof(t22_waybel33,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ( ( m2_yellow_9(C,A)
                  & m2_yellow_9(C,B) )
               => ! [D] :
                    ( m3_yellow_9(D,A,B)
                   => m2_yellow_9(C,D) ) ) ) ) ) )).

fof(t23_waybel33,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_yellow_9(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v3_pre_topc(C,A)
                 => ( v3_pre_topc(C,B)
                    & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) )
                & ( v4_pre_topc(C,A)
                 => ( v4_pre_topc(C,B)
                    & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) ) )).

fof(t24_waybel33,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) )
     => r1_tarski(k2_waybel19(A),k4_waybel28(A)) ) )).

fof(t25_waybel33,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] :
          ( ( v1_waybel33(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( ( v2_pre_topc(C)
                & v2_waybel19(C)
                & m1_yellow_9(C,A) )
             => m2_yellow_9(B,C) ) ) ) )).

fof(t26_waybel33,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)
        & v1_waybel33(A)
        & l1_waybel_9(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))))) )
         => r2_waybel_7(A,B,k1_waybel33(A,k2_pre_topc(A),B)) ) ) )).

fof(t27_waybel33,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)
        & v1_waybel33(A)
        & l1_waybel_9(A) )
     => ( v2_compts_1(A)
        & v1_urysohn1(A) ) ) )).

fof(dt_k1_waybel33,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(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)))) )
     => m1_subset_1(k1_waybel33(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k2_waybel33,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_waybel_9(k2_waybel33(A))
        & m1_yellow_9(k2_waybel33(A),A) ) ) )).

fof(d1_waybel33,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(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)))) )
             => k1_waybel33(A,B,C) = k1_yellow_0(A,a_3_0_waybel33(A,B,C)) ) ) ) )).

fof(t11_waybel33,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) )
         => k1_waybel11(A,B) = k1_yellow_0(A,a_2_0_waybel33(A,B)) ) ) )).

fof(fraenkel_a_3_0_waybel33,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(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_waybel33(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
            & A = k2_yellow_0(B,E)
            & r2_hidden(E,D) ) ) ) )).

fof(fraenkel_a_2_0_waybel33,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_0_waybel33(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(C))
            & A = k2_waybel_9(B,k6_waybel_9(B,C,D)) ) ) ) )).
%------------------------------------------------------------------------------