SET007 Axioms: SET007+572.ax


%------------------------------------------------------------------------------
% File     : SET007+572 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Introduction to Meet-Continuous Topological Lattices
% 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    : yellow13 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   69 (   0 unit)
%            Number of atoms       :  461 (   6 equality)
%            Maximal formula depth :   34 (   8 average)
%            Number of connectives :  449 (  57 ~  ;   0  |; 252  &)
%                                         (  10 <=>; 130 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   68 (   0 propositional; 1-4 arity)
%            Number of functors    :   20 (   0 constant; 1-4 arity)
%            Number of variables   :  145 (   0 singleton; 130 !;  15 ?)
%            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(fc1_yellow13,axiom,(
    ! [A] :
      ( ( v6_group_1(A)
        & l1_struct_0(A) )
     => v1_finset_1(u1_struct_0(A)) ) )).

fof(fc2_yellow13,axiom,(
    ! [A] :
      ( ( v3_realset2(A)
        & l1_struct_0(A) )
     => v1_realset1(u1_struct_0(A)) ) )).

fof(cc1_yellow13,axiom,(
    ! [A] :
      ( v1_realset1(A)
     => v1_finset_1(A) ) )).

fof(cc2_yellow13,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ( v3_realset2(A)
       => v6_group_1(A) ) ) )).

fof(cc3_yellow13,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ( ~ v3_realset2(A)
       => ~ v3_struct_0(A) ) ) )).

fof(rc1_yellow13,axiom,(
    ? [A] :
      ( l1_struct_0(A)
      & v1_struct_0(A)
      & ~ v3_struct_0(A)
      & v6_group_1(A)
      & v3_realset2(A) ) )).

fof(rc2_yellow13,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v6_group_1(A)
      & v3_realset2(A) ) )).

fof(rc3_yellow13,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v1_waybel_9(A)
      & v6_group_1(A)
      & v3_realset2(A) ) )).

fof(cc4_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_urysohn1(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_finset_1(B)
           => v4_pre_topc(B,A) ) ) ) )).

fof(fc3_yellow13,axiom,(
    ! [A] :
      ( ( v2_compts_1(A)
        & l1_pre_topc(A) )
     => ( v1_tops_1(k2_pre_topc(A),A)
        & v6_compts_1(k2_pre_topc(A),A) ) ) )).

fof(rc4_yellow13,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v1_tdlat_3(A)
      & v2_tdlat_3(A)
      & v3_tdlat_3(A)
      & v4_tdlat_3(A)
      & v5_tdlat_3(A)
      & v6_group_1(A)
      & v3_realset2(A) ) )).

fof(cc5_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_urysohn1(A)
          & v6_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A)
          & v3_tdlat_3(A)
          & v4_tdlat_3(A)
          & v5_tdlat_3(A) ) ) ) )).

fof(cc6_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v6_group_1(A) )
       => ( v2_pre_topc(A)
          & v2_compts_1(A) ) ) ) )).

fof(cc7_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A) )
       => ( v2_pre_topc(A)
          & v1_urysohn1(A)
          & v3_compts_1(A)
          & v4_compts_1(A)
          & v5_compts_1(A) ) ) ) )).

fof(cc8_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_urysohn1(A)
          & v5_compts_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v4_compts_1(A) ) ) ) )).

fof(cc9_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v1_urysohn1(A)
          & v4_compts_1(A) )
       => ( v2_pre_topc(A)
          & v3_compts_1(A) ) ) ) )).

fof(cc10_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v3_compts_1(A) )
       => ( v2_pre_topc(A)
          & v1_urysohn1(A) ) ) ) )).

fof(cc11_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v1_urysohn1(A) )
       => ( v2_pre_topc(A)
          & v2_t_0topsp(A) ) ) ) )).

fof(fc4_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k4_yellow_2(A))
        & v1_funct_1(k4_yellow_2(A))
        & v2_funct_1(k4_yellow_2(A))
        & v1_funct_2(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
        & v5_orders_3(k4_yellow_2(A),A,k2_yellow_1(k8_waybel_0(A))) ) ) )).

fof(fc5_yellow13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v6_group_1(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k3_yellow_2(A))
        & v1_funct_1(k3_yellow_2(A))
        & v2_funct_1(k3_yellow_2(A))
        & v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A))
        & v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) )).

fof(fc6_yellow13,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k4_waybel_1(A,B))
        & v1_relat_1(k4_waybel_1(A,B))
        & v1_funct_1(k4_waybel_1(A,B))
        & v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
        & v1_partfun1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
        & v19_waybel_0(k4_waybel_1(A,B),A,A)
        & v5_orders_3(k4_waybel_1(A,B),A,A) ) ) )).

fof(cc12_yellow13,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ! [C] :
          ( m1_yellow13(C,A,B)
         => ~ v1_xboole_0(C) ) ) )).

fof(rc5_yellow13,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ? [C] :
          ( m1_yellow13(C,A,B)
          & ~ v1_xboole_0(C) ) ) )).

fof(rc6_yellow13,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ? [C] :
          ( m1_yellow13(C,A,B)
          & v1_yellow13(C,A,B) ) ) )).

fof(rc7_yellow13,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ? [C] :
          ( m1_yellow13(C,A,B)
          & ~ v1_xboole_0(C)
          & v1_yellow13(C,A,B) ) ) )).

fof(cc13_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_yellow13(B,A)
         => ~ v1_xboole_0(B) ) ) )).

fof(rc8_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ? [B] :
          ( m2_yellow13(B,A)
          & ~ v1_xboole_0(B) ) ) )).

fof(cc14_yellow13,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_orders_2(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_yellow13(A) ) ) ) )).

fof(rc9_yellow13,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v1_tdlat_3(A)
      & v2_tdlat_3(A)
      & v3_tdlat_3(A)
      & v4_tdlat_3(A)
      & v5_tdlat_3(A)
      & v2_t_0topsp(A)
      & v1_urysohn1(A)
      & v3_yellow_8(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_waybel_3(A)
      & v3_waybel_3(A)
      & v6_waybel_3(A)
      & v2_compts_1(A)
      & v3_compts_1(A)
      & v4_compts_1(A)
      & v5_compts_1(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v6_group_1(A)
      & v3_realset2(A)
      & v2_yellow13(A) ) )).

fof(fc7_yellow13,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_yellow13(A)
        & l1_waybel_9(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_relat_1(k4_waybel_1(A,B))
        & v1_funct_1(k4_waybel_1(A,B))
        & v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
        & v5_pre_topc(k4_waybel_1(A,B),A,A) ) ) )).

fof(t1_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_urysohn1(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v4_pre_topc(B,A) ) ) )).

fof(t2_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => v5_compts_1(A) ) )).

fof(t3_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => v4_compts_1(A) ) )).

fof(t4_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => v3_compts_1(A) ) )).

fof(t5_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => v1_urysohn1(A) ) )).

fof(t6_yellow13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & l1_orders_2(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] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => r1_tarski(k4_waybel_0(B,k4_pre_topc(A,B,C,D)),k4_waybel_0(B,k4_pre_topc(A,B,C,k4_waybel_0(A,D)))) ) ) ) ) )).

fof(t7_yellow13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & l1_orders_2(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] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( v5_orders_3(C,A,B)
                   => k4_waybel_0(B,k4_pre_topc(A,B,C,D)) = k4_waybel_0(B,k4_pre_topc(A,B,C,k4_waybel_0(A,D))) ) ) ) ) ) )).

fof(t8_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => v2_funct_1(k4_yellow_2(A)) ) )).

fof(t9_yellow13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v6_group_1(A)
        & l1_orders_2(A) )
     => v2_funct_1(k3_yellow_2(A)) ) )).

fof(t10_yellow13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v6_group_1(A)
        & l1_orders_2(A) )
     => r5_waybel_1(A,k2_yellow_1(k8_waybel_0(A))) ) )).

fof(t11_yellow13,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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => r3_waybel_0(A,A,k4_waybel_1(A,B),C) ) ) ) )).

fof(t12_yellow13,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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v19_waybel_0(k4_waybel_1(A,B),A,A) ) ) )).

fof(t13_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => m1_yellow_8(k1_tarski(u1_struct_0(A)),A,B) ) ) )).

fof(t14_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_yellow_8(C,A,B)
             => C = k1_tarski(u1_struct_0(A)) ) ) ) )).

fof(t16_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k6_pre_topc(A,B))
              <=> ! [D] :
                    ( m1_yellow_8(D,A,C)
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( r2_hidden(E,D)
                            & r1_xboole_0(B,E) ) ) ) ) ) ) ) )).

fof(t17_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k6_pre_topc(A,B))
              <=> ? [D] :
                    ( m1_yellow_8(D,A,C)
                    & ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( r2_hidden(E,D)
                            & r1_xboole_0(B,E) ) ) ) ) ) ) ) )).

fof(d1_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( m1_yellow13(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( r2_hidden(B,k1_tops_1(A,D))
                        & ! [E] :
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( r2_hidden(E,C)
                                & r2_hidden(B,k1_tops_1(A,E))
                                & r1_tarski(E,D) ) ) ) ) ) ) ) ) )).

fof(d2_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( m1_yellow13(C,A,B)
              <=> ! [D] :
                    ( m1_connsp_2(D,A,B)
                   => ? [E] :
                        ( m1_connsp_2(E,A,B)
                        & r2_hidden(E,C)
                        & r1_tarski(E,D) ) ) ) ) ) ) )).

fof(t18_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => m1_yellow13(k1_zfmisc_1(u1_struct_0(A)),A,B) ) ) )).

fof(t19_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_yellow13(C,A,B)
             => ~ v1_xboole_0(C) ) ) ) )).

fof(d3_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_yellow13(C,A,B)
             => ( v1_yellow13(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( r2_hidden(D,C)
                    <=> r2_hidden(B,k1_tops_1(A,D)) ) ) ) ) ) ) )).

fof(t21_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_yellow13(k1_tarski(u1_struct_0(A)),A,B)
            & m1_yellow13(k1_tarski(u1_struct_0(A)),A,B) ) ) ) )).

fof(t22_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_yellow13(C,A,B)
                & m1_yellow13(C,A,B) )
             => C = k1_tarski(u1_struct_0(A)) ) ) ) )).

fof(t23_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_yellow_8(C,A,B)
             => m1_yellow13(C,A,B) ) ) ) )).

fof(d4_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( m2_yellow13(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => m1_yellow13(B,A,C) ) ) ) ) )).

fof(t24_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => m2_yellow13(k1_zfmisc_1(u1_struct_0(A)),A) ) )).

fof(t25_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_yellow13(B,A)
         => ~ v1_xboole_0(B) ) ) )).

fof(t26_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_yellow13(B,A)
         => r1_tarski(u1_pre_topc(A),k1_cantor_1(u1_struct_0(A),k1_tdlat_2(A,B))) ) ) )).

fof(t27_yellow13,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_cantor_1(B,A)
         => m2_yellow13(B,A) ) ) )).

fof(d5_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_waybel_9(A) )
     => ( v2_yellow13(A)
      <=> ! [B] :
            ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(k6_borsuk_1(A,A)),u1_struct_0(A))
              & m2_relset_1(B,u1_struct_0(k6_borsuk_1(A,A)),u1_struct_0(A)) )
           => ( B = k4_waybel_2(A)
             => v5_pre_topc(B,k6_borsuk_1(A,A),A) ) ) ) ) )).

fof(t28_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_yellow13(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v5_pre_topc(k4_waybel_1(A,B),A,A) ) ) )).

fof(dt_m1_yellow13,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ! [C] :
          ( m1_yellow13(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).

fof(existence_m1_yellow13,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ? [C] : m1_yellow13(C,A,B) ) )).

fof(dt_m2_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m2_yellow13(B,A)
         => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).

fof(existence_m2_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ? [B] : m2_yellow13(B,A) ) )).

fof(t15_yellow13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_cantor_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => m1_yellow_8(a_3_0_yellow13(A,B,C),A,C) ) ) ) )).

fof(t20_yellow13,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_yellow13(a_2_0_yellow13(A,B),A,B)
            & m1_yellow13(a_2_0_yellow13(A,B),A,B) ) ) ) )).

fof(fraenkel_a_3_0_yellow13,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_cantor_1(C,B)
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_0_yellow13(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
            & A = E
            & r2_hidden(E,C)
            & r2_hidden(D,E) ) ) ) )).

fof(fraenkel_a_2_0_yellow13,axiom,(
    ! [A,B,C] :
      ( ( l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_0_yellow13(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & r2_hidden(C,k1_tops_1(B,D)) ) ) ) )).
%------------------------------------------------------------------------------