SET007 Axioms: SET007+546.ax


%------------------------------------------------------------------------------
% File     : SET007+546 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Characterization of Hausdorff Spaces
% 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    : yellow12 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   65 (   5 unit)
%            Number of atoms       :  588 (  63 equality)
%            Maximal formula depth :   21 (   9 average)
%            Number of connectives :  599 (  76 ~  ;   0  |; 325  &)
%                                         (   6 <=>; 192 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   64 (   0 propositional; 1-4 arity)
%            Number of functors    :   50 (   0 constant; 1-5 arity)
%            Number of variables   :  207 (   0 singleton; 197 !;  10 ?)
%            Maximal term depth    :    4 (   2 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_yellow12,axiom,(
    ! [A] :
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k3_tarski(A))
        & v1_membered(k3_tarski(A))
        & v2_membered(k3_tarski(A))
        & v3_membered(k3_tarski(A))
        & v4_membered(k3_tarski(A))
        & v5_membered(k3_tarski(A)) ) ) )).

fof(fc2_yellow12,axiom,(
    ! [A,B] :
      ( v1_relat_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B)))
      & v1_funct_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B)))
      & v2_funct_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B))) ) )).

fof(fc3_yellow12,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(k4_waybel_2(A))
        & v1_relat_1(k4_waybel_2(A))
        & v1_funct_1(k4_waybel_2(A))
        & v1_funct_2(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
        & v1_partfun1(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
        & v17_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A)
        & v19_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A)
        & v21_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A)
        & v5_orders_3(k4_waybel_2(A),k3_yellow_3(A,A),A) ) ) )).

fof(fc4_yellow12,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(k5_waybel_2(A))
        & v1_relat_1(k5_waybel_2(A))
        & v1_funct_1(k5_waybel_2(A))
        & v1_funct_2(k5_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
        & v1_partfun1(k5_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
        & v18_waybel_0(k5_waybel_2(A),k3_yellow_3(A,A),A)
        & v20_waybel_0(k5_waybel_2(A),k3_yellow_3(A,A),A)
        & v22_waybel_0(k5_waybel_2(A),k3_yellow_3(A,A),A)
        & v5_orders_3(k5_waybel_2(A),k3_yellow_3(A,A),A) ) ) )).

fof(fc5_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
        & v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) )).

fof(fc6_yellow12,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
        & v2_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) )).

fof(cc1_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_cantor_1(B,A)
         => ~ v1_xboole_0(B) ) ) )).

fof(cc2_yellow12,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_yellow_8(C,A,B)
         => ~ v1_xboole_0(C) ) ) )).

fof(rc1_yellow12,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & l1_pre_topc(B) )
     => ? [C] :
          ( m3_yellow_9(C,A,B)
          & v1_pre_topc(C)
          & v2_pre_topc(C) ) ) )).

fof(rc2_yellow12,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & l1_pre_topc(B) )
     => ? [C] :
          ( m3_yellow_9(C,A,B)
          & ~ v3_struct_0(C)
          & v1_pre_topc(C)
          & v2_pre_topc(C) ) ) )).

fof(rc3_yellow12,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & l1_pre_topc(B) )
     => ? [C] :
          ( m3_yellow_9(C,B,A)
          & ~ v3_struct_0(C)
          & v1_pre_topc(C)
          & v2_pre_topc(C) ) ) )).

fof(t1_yellow12,axiom,(
    ! [A,B] : r1_tarski(k10_relset_1(A,k2_zfmisc_1(A,A),k12_funct_3(A),B),k2_zfmisc_1(B,B)) )).

fof(t2_yellow12,axiom,(
    ! [A,B] : r1_tarski(k11_relset_1(A,k2_zfmisc_1(A,A),k12_funct_3(A),k2_zfmisc_1(B,B)),B) )).

fof(t3_yellow12,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k11_relset_1(A,k2_zfmisc_1(A,A),k12_funct_3(A),k12_mcart_1(A,A,B,B)) = B ) )).

fof(t4_yellow12,axiom,(
    ! [A,B] :
      ( k1_relat_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B))) = k2_zfmisc_1(A,B)
      & k2_relat_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B))) = k2_zfmisc_1(B,A) ) )).

fof(t5_yellow12,axiom,(
    ! [A,B,C,D] : r1_tarski(k9_relat_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B)),k2_zfmisc_1(C,D)),k2_zfmisc_1(D,C)) )).

fof(t6_yellow12,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,k1_zfmisc_1(A))
     => ! [D] :
          ( m1_subset_1(D,k1_zfmisc_1(B))
         => k9_relat_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B)),k12_mcart_1(A,B,C,D)) = k12_mcart_1(B,A,D,C) ) ) )).

fof(t7_yellow12,axiom,(
    ! [A,B] : v2_funct_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B))) )).

fof(t8_yellow12,axiom,(
    ! [A,B] : k2_funct_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B))) = k13_funct_3(k10_funct_3(B,A),k9_funct_3(B,A)) )).

fof(t9_yellow12,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(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(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                              & C = E
                              & D = F )
                           => k12_lattice3(A,C,D) = k11_lattice3(B,E,F) ) ) ) ) ) ) ) )).

fof(t10_yellow12,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(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(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                              & C = E
                              & D = F )
                           => k13_lattice3(A,C,D) = k10_lattice3(B,E,F) ) ) ) ) ) ) ) )).

fof(t11_yellow12,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
                         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                              & C = E
                              & D = F )
                           => k4_yellow_4(A,C,D) = k3_yellow_4(B,E,F) ) ) ) ) ) ) ) )).

fof(t12_yellow12,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
                         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                              & C = E
                              & D = F )
                           => k2_yellow_4(A,C,D) = k1_yellow_4(B,E,F) ) ) ) ) ) ) ) )).

fof(t13_yellow12,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)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & C = D )
                   => ( k1_waybel_3(A,C) = k1_waybel_3(B,D)
                      & k2_waybel_3(A,C) = k2_waybel_3(B,D) ) ) ) ) ) ) )).

fof(t14_yellow12,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v2_waybel_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(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))
           => v2_waybel_2(B) ) ) ) )).

fof(t15_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(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))
           => v3_waybel_3(B) ) ) ) )).

fof(t16_yellow12,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & C = D )
                   => k5_yellow_0(A,C) = k5_yellow_0(B,D) ) ) ) ) ) )).

fof(t17_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_yellow_0(C,A)
             => ! [D] :
                  ( m1_yellow_0(D,B)
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
                      & v5_yellow_0(C,A) )
                   => v5_yellow_0(D,B) ) ) ) ) ) )).

fof(t18_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_yellow_0(C,A)
             => ! [D] :
                  ( m1_yellow_0(D,B)
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
                      & v6_yellow_0(C,A) )
                   => v6_yellow_0(D,B) ) ) ) ) ) )).

fof(t19_yellow12,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)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & C = D
                      & v3_waybel11(C,A) )
                   => v3_waybel11(D,B) ) ) ) ) ) )).

fof(t20_yellow12,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)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & C = D
                      & v2_waybel11(C,A) )
                   => v2_waybel11(D,B) ) ) ) ) ) )).

fof(t21_yellow12,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v2_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)))
             => ! [D] :
                  ( ( v13_waybel_0(D,A)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                 => ( r1_xboole_0(B,D)
                   => r1_xboole_0(k4_yellow_4(A,B,C),D) ) ) ) ) ) )).

fof(t22_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => r1_tarski(k6_partfun1(u1_struct_0(A)),k3_xboole_0(u1_orders_2(A),u1_orders_2(k7_lattice3(A)))) ) )).

fof(t23_yellow12,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => r1_tarski(k3_xboole_0(u1_orders_2(A),u1_orders_2(k7_lattice3(A))),k6_partfun1(u1_struct_0(A))) ) )).

fof(t24_yellow12,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
         => ( r2_yellow_0(A,k4_pre_topc(k3_yellow_3(A,A),A,k4_waybel_2(A),B))
           => r3_waybel_0(k3_yellow_3(A,A),A,k4_waybel_2(A),B) ) ) ) )).

fof(t25_yellow12,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
         => ( r1_yellow_0(A,k4_pre_topc(k3_yellow_3(A,A),A,k5_waybel_2(A),B))
           => r4_waybel_0(k3_yellow_3(A,A),A,k5_waybel_2(A),B) ) ) ) )).

fof(t26_yellow12,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_yellow_0(k5_yellow_0(A,B),A)
           => v2_waybel_0(B,A) ) ) ) )).

fof(t27_yellow12,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_yellow_0(k5_yellow_0(A,B),A)
           => v1_waybel_0(B,A) ) ) ) )).

fof(t28_yellow12,axiom,(
    ! [A] :
      ( ( v3_orders_2(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)))
             => ( r2_yellow_4(A,k5_waybel_0(A,C),B)
               => r1_tarski(k5_waybel_0(A,B),k5_waybel_0(A,C)) ) ) ) ) )).

fof(t29_yellow12,axiom,(
    ! [A] :
      ( ( v3_orders_2(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)))
             => ( r1_yellow_4(A,B,k4_waybel_0(A,C))
               => r1_tarski(k4_waybel_0(A,B),k4_waybel_0(A,C)) ) ) ) ) )).

fof(t30_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,C)
               => r1_tarski(k7_waybel_0(A,B),k5_waybel_0(A,C)) ) ) ) ) )).

fof(t31_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,C)
               => r1_tarski(k6_waybel_0(A,B),k4_waybel_0(A,C)) ) ) ) ) )).

fof(t32_yellow12,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ! [C] :
              ( m1_cantor_1(C,A)
             => ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
               => m1_cantor_1(C,B) ) ) ) ) )).

fof(t33_yellow12,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ! [C] :
              ( m2_cantor_1(C,A)
             => ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
               => m2_cantor_1(C,B) ) ) ) ) )).

fof(t34_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_cantor_1(B,A)
         => ~ v1_xboole_0(B) ) ) )).

fof(t35_yellow12,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)
             => ~ v1_xboole_0(C) ) ) ) )).

fof(t36_yellow12,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ! [D] :
                  ( ( v2_pre_topc(D)
                    & l1_pre_topc(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
                         => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                              & g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(D),u1_pre_topc(D))
                              & E = F
                              & v5_pre_topc(E,A,C) )
                           => v5_pre_topc(F,B,D) ) ) ) ) ) ) ) )).

fof(t38_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_funct_1(k12_funct_3(u1_struct_0(A)))
        & v1_funct_2(k12_funct_3(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(k6_borsuk_1(A,A)))
        & v5_pre_topc(k12_funct_3(u1_struct_0(A)),A,k6_borsuk_1(A,A))
        & m2_relset_1(k12_funct_3(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(k6_borsuk_1(A,A))) ) ) )).

fof(t39_yellow12,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) )
         => ( v1_funct_1(k9_funct_3(u1_struct_0(A),u1_struct_0(B)))
            & v1_funct_2(k9_funct_3(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A))
            & v5_pre_topc(k9_funct_3(u1_struct_0(A),u1_struct_0(B)),k6_borsuk_1(A,B),A)
            & m2_relset_1(k9_funct_3(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A)) ) ) ) )).

fof(t40_yellow12,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) )
         => ( v1_funct_1(k10_funct_3(u1_struct_0(A),u1_struct_0(B)))
            & v1_funct_2(k10_funct_3(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B))
            & v5_pre_topc(k10_funct_3(u1_struct_0(A),u1_struct_0(B)),k6_borsuk_1(A,B),B)
            & m2_relset_1(k10_funct_3(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B)) ) ) ) )).

fof(t41_yellow12,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] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v5_pre_topc(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & v5_pre_topc(E,A,C)
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ( v1_funct_1(k14_funct_3(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E))
                        & v1_funct_2(k14_funct_3(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C)))
                        & v5_pre_topc(k14_funct_3(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,k6_borsuk_1(B,C))
                        & m2_relset_1(k14_funct_3(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C))) ) ) ) ) ) ) )).

fof(t42_yellow12,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) )
         => ( v1_funct_1(k14_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),u1_struct_0(A),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),k9_funct_3(u1_struct_0(A),u1_struct_0(B))))
            & v1_funct_2(k14_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),u1_struct_0(A),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),k9_funct_3(u1_struct_0(A),u1_struct_0(B))),u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(k6_borsuk_1(B,A)))
            & v5_pre_topc(k14_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),u1_struct_0(A),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),k9_funct_3(u1_struct_0(A),u1_struct_0(B))),k6_borsuk_1(A,B),k6_borsuk_1(B,A))
            & m2_relset_1(k14_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),u1_struct_0(A),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),k9_funct_3(u1_struct_0(A),u1_struct_0(B))),u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(k6_borsuk_1(B,A))) ) ) ) )).

fof(t43_yellow12,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(k6_borsuk_1(B,A)))
                & m2_relset_1(C,u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(k6_borsuk_1(B,A))) )
             => ( C = k14_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),u1_struct_0(A),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),k9_funct_3(u1_struct_0(A),u1_struct_0(B)))
               => v3_tops_2(C,k6_borsuk_1(A,B),k6_borsuk_1(B,A)) ) ) ) ) )).

fof(t44_yellow12,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) )
         => r1_t_0topsp(k6_borsuk_1(A,B),k6_borsuk_1(B,A)) ) ) )).

fof(t46_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_compts_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,A))))
           => ( B = k6_partfun1(u1_struct_0(A))
             => v4_pre_topc(B,k6_borsuk_1(A,A)) ) ) ) ) )).

fof(t47_yellow12,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ! [C] :
              ( l1_pre_topc(C)
             => ( m3_yellow_9(A,B,C)
              <=> m3_yellow_9(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)),B,C) ) ) ) ) )).

fof(t49_yellow12,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,k6_borsuk_1(A,C),k6_borsuk_1(B,D))
                     => ! [F] :
                          ( m3_yellow_9(F,A,B)
                         => ! [G] :
                              ( m3_yellow_9(G,C,D)
                             => ( ( u1_struct_0(A) = u1_struct_0(B)
                                  & u1_struct_0(C) = u1_struct_0(D) )
                               => ( u1_struct_0(k6_borsuk_1(F,G)) = u1_struct_0(E)
                                  & u1_pre_topc(k6_borsuk_1(F,G)) = u1_pre_topc(E) ) ) ) ) ) ) ) ) ) )).

fof(t50_yellow12,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)
                         => ( ( u1_struct_0(A) = u1_struct_0(B)
                              & u1_struct_0(C) = u1_struct_0(D) )
                           => m3_yellow_9(k6_borsuk_1(E,F),k6_borsuk_1(A,C),k6_borsuk_1(B,D)) ) ) ) ) ) ) ) )).

fof(t37_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k6_partfun1(u1_struct_0(A)) = a_1_0_yellow12(A) ) )).

fof(t45_yellow12,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v3_compts_1(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_pre_topc(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v5_pre_topc(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ( ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ( E = a_4_0_yellow12(A,B,C,D)
                         => v3_pre_topc(E,A) ) )
                    & ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ( E = a_4_1_yellow12(A,B,C,D)
                         => v4_pre_topc(E,A) ) ) ) ) ) ) ) )).

fof(t48_yellow12,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,k6_borsuk_1(A,C),k6_borsuk_1(B,D))
                     => ( ( u1_struct_0(A) = u1_struct_0(B)
                          & u1_struct_0(C) = u1_struct_0(D) )
                       => m1_cantor_1(a_4_2_yellow12(A,B,C,D),E) ) ) ) ) ) ) )).

fof(fraenkel_a_1_0_yellow12,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ( r2_hidden(A,a_1_0_yellow12(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k6_borsuk_1(B,B)))
            & A = C
            & k1_funct_1(k9_funct_3(u1_struct_0(B),u1_struct_0(B)),C) = k1_funct_1(k10_funct_3(u1_struct_0(B),u1_struct_0(B)),C) ) ) ) )).

fof(fraenkel_a_4_0_yellow12,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & v3_compts_1(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
        & v5_pre_topc(D,B,C)
        & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
        & v5_pre_topc(E,B,C)
        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
     => ( r2_hidden(A,a_4_0_yellow12(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(B))
            & A = F
            & k1_waybel_0(B,C,D,F) != k1_waybel_0(B,C,E,F) ) ) ) )).

fof(fraenkel_a_4_1_yellow12,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & v3_compts_1(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
        & v5_pre_topc(D,B,C)
        & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
        & v5_pre_topc(E,B,C)
        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
     => ( r2_hidden(A,a_4_1_yellow12(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(B))
            & A = F
            & k1_waybel_0(B,C,D,F) = k1_waybel_0(B,C,E,F) ) ) ) )).

fof(fraenkel_a_4_2_yellow12,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & ~ v3_struct_0(D)
        & v2_pre_topc(D)
        & l1_pre_topc(D)
        & ~ v3_struct_0(E)
        & v2_pre_topc(E)
        & l1_pre_topc(E) )
     => ( r2_hidden(A,a_4_2_yellow12(B,C,D,E))
      <=> ? [F,G,H,I] :
            ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
            & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(C)))
            & m1_subset_1(H,k1_zfmisc_1(u1_struct_0(D)))
            & m1_subset_1(I,k1_zfmisc_1(u1_struct_0(E)))
            & A = k3_xboole_0(k7_borsuk_1(B,D,F,H),k7_borsuk_1(C,E,G,I))
            & v3_pre_topc(F,B)
            & v3_pre_topc(G,C)
            & v3_pre_topc(H,D)
            & v3_pre_topc(I,E) ) ) ) )).
%------------------------------------------------------------------------------