SET007 Axioms: SET007+535.ax


%------------------------------------------------------------------------------
% File     : SET007+535 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Decomposition of Simple Closed Curves and the Order of Their Points
% 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    : jordan6 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  104 (  14 unit)
%            Number of atoms       :  620 ( 101 equality)
%            Maximal formula depth :   26 (   9 average)
%            Number of connectives :  562 (  46 ~  ;   0  |; 185  &)
%                                         (  21 <=>; 310 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   25 (   1 propositional; 0-5 arity)
%            Number of functors    :   55 (   8 constant; 0-5 arity)
%            Number of variables   :  310 (   0 singleton; 298 !;  12 ?)
%            Maximal term depth    :    7 (   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(cc1_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_topmetr))
     => ( v1_xreal_0(A)
        & v1_xcmplx_0(A) ) ) )).

fof(t1_jordan6,axiom,(
    $true )).

fof(t2_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( r1_xreal_0(A,k7_xcmplx_0(k2_xcmplx_0(A,B),np__2))
              & r1_xreal_0(k7_xcmplx_0(k2_xcmplx_0(A,B),np__2),B) ) ) ) ) )).

fof(t3_jordan6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v4_pre_topc(D,A)
                      & C = k5_subset_1(u1_struct_0(A),D,B) )
                   => v4_pre_topc(C,k3_pre_topc(A,B)) ) ) ) ) ) )).

fof(t4_jordan6,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_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,C)))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,C))) )
                 => ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(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(B))
                          & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                       => ( ( E = D
                            & v5_pre_topc(D,A,k3_pre_topc(B,C)) )
                         => v5_pre_topc(E,A,B) ) ) ) ) ) ) ) )).

fof(t11_jordan6,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ( r1_topreal1(k15_euclid(A),C,D,B)
                   => v2_connsp_1(B,k15_euclid(A)) ) ) ) ) ) )).

fof(t12_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_topreal1(k15_euclid(np__2),B,C,A)
               => v4_pre_topc(A,k15_euclid(np__2)) ) ) ) ) )).

fof(t13_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r1_topreal1(k15_euclid(np__2),B,C,A)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ~ ( r2_hidden(D,A)
                          & k21_euclid(D) = k6_real_1(k3_real_1(k21_euclid(B),k21_euclid(C)),np__2) ) ) ) ) ) ) )).

fof(t16_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_topreal1(k15_euclid(np__2),B,C,A)
               => ( r2_hidden(k1_jordan6(A,B,C),A)
                  & r2_hidden(k2_jordan6(A,B,C),A) ) ) ) ) ) )).

fof(t17_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_topreal1(k15_euclid(np__2),B,C,A)
               => ( B = k1_jordan6(A,B,C)
                <=> k21_euclid(B) = k21_euclid(C) ) ) ) ) ) )).

fof(t18_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_topreal1(k15_euclid(np__2),B,C,A)
               => ( B = k2_jordan6(A,B,C)
                <=> k22_euclid(B) = k22_euclid(C) ) ) ) ) ) )).

fof(t19_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
                          & r1_jordan5c(A,B,C,D,E) )
                       => r1_jordan5c(A,C,B,E,D) ) ) ) ) ) ) )).

fof(t20_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => r1_tarski(k3_jordan6(A,B,C,D),A) ) ) ) ) )).

fof(t21_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => r1_tarski(k4_jordan6(A,B,C,D),A) ) ) ) ) )).

fof(t22_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_topreal1(k15_euclid(np__2),B,C,A)
               => k3_jordan6(A,B,C,B) = k1_struct_0(k15_euclid(np__2),B) ) ) ) ) )).

fof(t23_jordan6,axiom,(
    $true )).

fof(t24_jordan6,axiom,(
    $true )).

fof(t25_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_topreal1(k15_euclid(np__2),B,C,A)
               => k3_jordan6(A,B,C,C) = A ) ) ) ) )).

fof(t26_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_topreal1(k15_euclid(np__2),B,C,A)
               => k4_jordan6(A,B,C,C) = k1_struct_0(k15_euclid(np__2),C) ) ) ) ) )).

fof(t27_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_topreal1(k15_euclid(np__2),B,C,A)
               => k4_jordan6(A,B,C,B) = A ) ) ) ) )).

fof(t28_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
                      & r2_hidden(D,A) )
                   => k4_jordan6(A,B,C,D) = k3_jordan6(A,C,B,D) ) ) ) ) ) )).

fof(d5_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => k5_jordan6(A,B,C,D,E) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_jordan6(A,B,C,D),k3_jordan6(A,B,C,E)) ) ) ) ) ) )).

fof(t30_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( r1_topreal1(k15_euclid(np__2),B,C,A)
                       => ( r1_jordan5c(A,B,C,D,E)
                        <=> r1_jordan5c(A,C,B,E,D) ) ) ) ) ) ) ) )).

fof(t31_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
                      & r2_hidden(D,A) )
                   => k3_jordan6(A,B,C,D) = k4_jordan6(A,C,B,D) ) ) ) ) ) )).

fof(t32_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
                          & r2_hidden(D,A)
                          & r2_hidden(E,A) )
                       => k5_jordan6(A,B,C,D,E) = k5_jordan6(A,C,B,E,D) ) ) ) ) ) ) )).

fof(t33_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( v4_pre_topc(k6_jordan6(A),k15_euclid(np__2))
        & v4_pre_topc(k7_jordan6(A),k15_euclid(np__2)) ) ) )).

fof(t34_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,k6_jordan6(A))
          <=> k21_euclid(B) = A ) ) ) )).

fof(t35_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,k7_jordan6(A))
          <=> k22_euclid(B) = A ) ) ) )).

fof(t36_jordan6,axiom,(
    $true )).

fof(t37_jordan6,axiom,(
    $true )).

fof(t38_jordan6,axiom,(
    $true )).

fof(t39_jordan6,axiom,(
    $true )).

fof(t40_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ~ ( v1_topreal2(A)
          & ! [B] :
              ( ( ~ v1_xboole_0(B)
                & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ! [C] :
                  ( ( ~ v1_xboole_0(C)
                    & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                 => ~ ( r1_topreal1(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A),B)
                      & r1_topreal1(k15_euclid(np__2),k34_pscomp_1(A),k30_pscomp_1(A),C)
                      & k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,C) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))
                      & k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C) = A
                      & ~ r1_xreal_0(k22_euclid(k1_jordan5c(B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k30_pscomp_1(A),k34_pscomp_1(A))),k22_euclid(k2_jordan5c(C,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k34_pscomp_1(A),k30_pscomp_1(A)))) ) ) ) ) ) )).

fof(t41_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k22_borsuk_1)))
     => ( A = k4_xboole_0(u1_struct_0(k22_borsuk_1),k2_tarski(np__0,np__1))
       => v3_pre_topc(A,k22_borsuk_1) ) ) )).

fof(t42_jordan6,axiom,(
    $true )).

fof(t43_jordan6,axiom,(
    $true )).

fof(t44_jordan6,axiom,(
    $true )).

fof(t45_jordan6,axiom,(
    $true )).

fof(t46_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k2_rcomp_1(B,C)
               => v3_pre_topc(A,k3_topmetr) ) ) ) ) )).

fof(t47_jordan6,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(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] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,C))))
                 => ( ( B = D
                      & r1_tarski(B,C) )
                   => k3_pre_topc(A,B) = k3_pre_topc(k3_pre_topc(A,C),D) ) ) ) ) ) )).

fof(t48_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k22_borsuk_1)))
     => ( A = k4_xboole_0(u1_struct_0(k22_borsuk_1),k2_tarski(np__0,np__1))
       => ( A != k1_xboole_0
          & v2_connsp_1(A,k22_borsuk_1) ) ) ) )).

fof(t49_jordan6,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ~ ( r1_topreal1(k15_euclid(A),C,D,B)
                      & C = D ) ) ) ) ) )).

fof(t50_jordan6,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),B))))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ( ( r1_topreal1(k15_euclid(A),D,E,B)
                          & C = k6_subset_1(u1_struct_0(k15_euclid(A)),B,k2_struct_0(k15_euclid(A),D,E)) )
                       => v3_pre_topc(C,k3_pre_topc(k15_euclid(A),B)) ) ) ) ) ) ) )).

fof(t51_jordan6,axiom,(
    $true )).

fof(t52_jordan6,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),B))))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
                             => ( ( r2_hidden(F,B)
                                  & r2_hidden(G,B)
                                  & r1_topreal1(k15_euclid(A),F,G,C)
                                  & r1_topreal1(k15_euclid(A),F,G,D)
                                  & k4_subset_1(u1_struct_0(k15_euclid(A)),C,D) = B
                                  & k5_subset_1(u1_struct_0(k15_euclid(A)),C,D) = k2_struct_0(k15_euclid(A),F,G)
                                  & E = k6_subset_1(u1_struct_0(k15_euclid(A)),C,k2_struct_0(k15_euclid(A),F,G)) )
                               => v3_pre_topc(E,k3_pre_topc(k15_euclid(A),B)) ) ) ) ) ) ) ) ) )).

fof(t53_jordan6,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),B))))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ( ( r1_topreal1(k15_euclid(A),D,E,B)
                          & C = k6_subset_1(u1_struct_0(k15_euclid(A)),B,k2_struct_0(k15_euclid(A),D,E)) )
                       => v2_connsp_1(C,k3_pre_topc(k15_euclid(A),B)) ) ) ) ) ) ) )).

fof(t54_jordan6,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(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] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,C))))
                     => ( ( r1_tarski(B,C)
                          & E = D
                          & v2_connsp_1(D,k3_pre_topc(A,B)) )
                       => v2_connsp_1(E,k3_pre_topc(A,C)) ) ) ) ) ) ) )).

fof(t55_jordan6,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ~ ( r1_topreal1(k15_euclid(A),C,D,B)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                         => ~ ( r2_hidden(E,B)
                              & E != C
                              & E != D ) ) ) ) ) ) ) )).

fof(t56_jordan6,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ~ ( r1_topreal1(k15_euclid(A),C,D,B)
                      & k6_subset_1(u1_struct_0(k15_euclid(A)),B,k2_struct_0(k15_euclid(A),C,D)) = k1_xboole_0 ) ) ) ) ) )).

fof(t57_jordan6,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),C))))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                         => ( ( r1_topreal1(k15_euclid(A),E,F,B)
                              & r1_tarski(B,C)
                              & D = k6_subset_1(u1_struct_0(k15_euclid(A)),B,k2_struct_0(k15_euclid(A),E,F)) )
                           => v2_connsp_1(D,k3_pre_topc(k15_euclid(A),C)) ) ) ) ) ) ) ) )).

fof(t58_jordan6,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_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D)))
                            & m2_relset_1(F,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D))) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(k3_pre_topc(B,E)),u1_struct_0(C))
                                & m2_relset_1(G,u1_struct_0(k3_pre_topc(B,E)),u1_struct_0(C)) )
                             => ~ ( r1_tarski(D,E)
                                  & v5_pre_topc(F,A,k3_pre_topc(B,D))
                                  & v5_pre_topc(G,k3_pre_topc(B,E),C)
                                  & ! [H] :
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,u1_struct_0(A),u1_struct_0(C))
                                        & m2_relset_1(H,u1_struct_0(A),u1_struct_0(C)) )
                                     => ~ ( H = k5_relat_1(F,G)
                                          & v5_pre_topc(H,A,C) ) ) ) ) ) ) ) ) ) ) )).

fof(t59_jordan6,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ( ( r1_topreal1(k15_euclid(A),D,E,B)
                          & r1_topreal1(k15_euclid(A),D,E,C)
                          & r1_tarski(B,C) )
                       => B = C ) ) ) ) ) ) )).

fof(t60_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( v1_topreal2(A)
                      & r2_hidden(C,A)
                      & r2_hidden(D,A)
                      & C != D
                      & B = k6_subset_1(u1_struct_0(k15_euclid(np__2)),A,k2_struct_0(k15_euclid(np__2),C,D))
                      & v2_connsp_1(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ) )).

fof(t61_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
                             => ~ ( v1_topreal2(A)
                                  & r1_topreal1(k15_euclid(np__2),F,G,B)
                                  & r1_topreal1(k15_euclid(np__2),F,G,C)
                                  & k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C) = A
                                  & r1_topreal1(k15_euclid(np__2),F,G,D)
                                  & r1_topreal1(k15_euclid(np__2),F,G,E)
                                  & k4_subset_1(u1_struct_0(k15_euclid(np__2)),D,E) = A
                                  & ~ ( B = D
                                      & C = E )
                                  & ~ ( B = E
                                      & C = D ) ) ) ) ) ) ) ) ) )).

fof(t62_jordan6,axiom,(
    $true )).

fof(t63_jordan6,axiom,(
    $true )).

fof(t64_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_xreal_0(k21_euclid(C),B)
                      & r1_xreal_0(B,k21_euclid(D))
                      & r1_topreal1(k15_euclid(np__2),C,D,A) )
                   => ( ~ r1_xboole_0(A,k6_jordan6(B))
                      & v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(B)),k15_euclid(np__2)) ) ) ) ) ) ) )).

fof(d8_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal2(A)
       => ! [B] :
            ( ( ~ v1_xboole_0(B)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
           => ( B = k8_jordan6(A)
            <=> ( r1_topreal1(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A),B)
                & ? [C] :
                    ( ~ v1_xboole_0(C)
                    & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                    & r1_topreal1(k15_euclid(np__2),k34_pscomp_1(A),k30_pscomp_1(A),C)
                    & k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,C) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))
                    & k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C) = A
                    & ~ r1_xreal_0(k22_euclid(k1_jordan5c(B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k30_pscomp_1(A),k34_pscomp_1(A))),k22_euclid(k2_jordan5c(C,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k34_pscomp_1(A),k30_pscomp_1(A)))) ) ) ) ) ) ) )).

fof(d9_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal2(A)
       => ! [B] :
            ( ( ~ v1_xboole_0(B)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
           => ( B = k9_jordan6(A)
            <=> ( r1_topreal1(k15_euclid(np__2),k34_pscomp_1(A),k30_pscomp_1(A),B)
                & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k8_jordan6(A),B) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))
                & k4_subset_1(u1_struct_0(k15_euclid(np__2)),k8_jordan6(A),B) = A
                & ~ r1_xreal_0(k22_euclid(k1_jordan5c(k8_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k30_pscomp_1(A),k34_pscomp_1(A))),k22_euclid(k2_jordan5c(B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k34_pscomp_1(A),k30_pscomp_1(A)))) ) ) ) ) ) )).

fof(t65_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal2(A)
       => ( r1_topreal1(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A),k8_jordan6(A))
          & r1_topreal1(k15_euclid(np__2),k34_pscomp_1(A),k30_pscomp_1(A),k8_jordan6(A))
          & r1_topreal1(k15_euclid(np__2),k34_pscomp_1(A),k30_pscomp_1(A),k9_jordan6(A))
          & r1_topreal1(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A),k9_jordan6(A))
          & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k8_jordan6(A),k9_jordan6(A)) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))
          & k4_subset_1(u1_struct_0(k15_euclid(np__2)),k8_jordan6(A),k9_jordan6(A)) = A
          & ~ r1_xreal_0(k22_euclid(k1_jordan5c(k8_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k30_pscomp_1(A),k34_pscomp_1(A))),k22_euclid(k2_jordan5c(k9_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k34_pscomp_1(A),k30_pscomp_1(A)))) ) ) ) )).

fof(t66_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal2(A)
       => ( k9_jordan6(A) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k6_subset_1(u1_struct_0(k15_euclid(np__2)),A,k8_jordan6(A)),k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A)))
          & k8_jordan6(A) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k6_subset_1(u1_struct_0(k15_euclid(np__2)),A,k9_jordan6(A)),k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))) ) ) ) )).

fof(t67_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))))
         => ( ( v1_topreal2(A)
              & k3_xboole_0(k8_jordan6(A),B) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))
              & k2_xboole_0(k8_jordan6(A),B) = A )
           => B = k9_jordan6(A) ) ) ) )).

fof(t68_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))))
         => ( ( v1_topreal2(A)
              & k3_xboole_0(B,k9_jordan6(A)) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))
              & k2_xboole_0(B,k9_jordan6(A)) = A )
           => B = k8_jordan6(A) ) ) ) )).

fof(t69_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
                      & r1_jordan5c(A,B,C,D,B) )
                   => D = B ) ) ) ) ) )).

fof(t70_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
                      & r1_jordan5c(A,B,C,C,D) )
                   => D = C ) ) ) ) ) )).

fof(d10_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_jordan6(A,B,C)
              <=> ~ ( ~ ( r2_hidden(B,k8_jordan6(A))
                        & r2_hidden(C,k9_jordan6(A))
                        & C != k30_pscomp_1(A) )
                    & ~ ( r2_hidden(B,k8_jordan6(A))
                        & r2_hidden(C,k8_jordan6(A))
                        & r1_jordan5c(k8_jordan6(A),k30_pscomp_1(A),k34_pscomp_1(A),B,C) )
                    & ~ ( r2_hidden(B,k9_jordan6(A))
                        & r2_hidden(C,k9_jordan6(A))
                        & C != k30_pscomp_1(A)
                        & r1_jordan5c(k9_jordan6(A),k34_pscomp_1(A),k30_pscomp_1(A),B,C) ) ) ) ) ) ) )).

fof(t71_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v1_topreal2(A)
              & r2_hidden(B,A) )
           => r1_jordan6(A,B,B) ) ) ) )).

fof(t72_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( v1_topreal2(A)
                  & r1_jordan6(A,B,C)
                  & r1_jordan6(A,C,B) )
               => B = C ) ) ) ) )).

fof(t73_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( v1_topreal2(A)
                      & r1_jordan6(A,B,C)
                      & r1_jordan6(A,C,D) )
                   => r1_jordan6(A,B,D) ) ) ) ) ) )).

fof(dt_k1_jordan6,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
     => m1_subset_1(k1_jordan6(A,B,C),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k2_jordan6,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
     => m1_subset_1(k2_jordan6(A,B,C),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k3_jordan6,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(D,u1_struct_0(k15_euclid(np__2))) )
     => m1_subset_1(k3_jordan6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k4_jordan6,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(D,u1_struct_0(k15_euclid(np__2))) )
     => m1_subset_1(k4_jordan6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k5_jordan6,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(E,u1_struct_0(k15_euclid(np__2))) )
     => m1_subset_1(k5_jordan6(A,B,C,D,E),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k6_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => m1_subset_1(k6_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k7_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => m1_subset_1(k7_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k8_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( ~ v1_xboole_0(k8_jordan6(A))
        & m1_subset_1(k8_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) )).

fof(dt_k9_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( ~ v1_xboole_0(k9_jordan6(A))
        & m1_subset_1(k9_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) )).

fof(t5_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( B = a_1_0_jordan6(A)
           => v4_pre_topc(B,k15_euclid(np__2)) ) ) ) )).

fof(t6_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( B = a_1_1_jordan6(A)
           => v4_pre_topc(B,k15_euclid(np__2)) ) ) ) )).

fof(t7_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( B = a_1_2_jordan6(A)
           => v4_pre_topc(B,k15_euclid(np__2)) ) ) ) )).

fof(t8_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( B = a_1_3_jordan6(A)
           => v4_pre_topc(B,k15_euclid(np__2)) ) ) ) )).

fof(t9_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( B = a_1_4_jordan6(A)
           => v4_pre_topc(B,k15_euclid(np__2)) ) ) ) )).

fof(t10_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( B = a_1_5_jordan6(A)
           => v4_pre_topc(B,k15_euclid(np__2)) ) ) ) )).

fof(t14_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_topreal1(k15_euclid(np__2),C,D,A)
                      & B = a_2_0_jordan6(C,D) )
                   => ( ~ r1_xboole_0(A,B)
                      & v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2)) ) ) ) ) ) ) )).

fof(t15_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_topreal1(k15_euclid(np__2),C,D,A)
                      & B = a_2_1_jordan6(C,D) )
                   => ( ~ r1_xboole_0(A,B)
                      & v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2)) ) ) ) ) ) ) )).

fof(d1_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( D = k1_jordan6(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                       => ( E = a_2_0_jordan6(B,C)
                         => D = k1_jordan5c(A,E,B,C) ) ) ) ) ) ) ) )).

fof(d2_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( D = k2_jordan6(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                       => ( E = a_2_1_jordan6(B,C)
                         => D = k1_jordan5c(A,E,B,C) ) ) ) ) ) ) ) )).

fof(d3_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => k3_jordan6(A,B,C,D) = a_4_0_jordan6(A,B,C,D) ) ) ) ) )).

fof(d4_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => k4_jordan6(A,B,C,D) = a_4_1_jordan6(A,B,C,D) ) ) ) ) )).

fof(t29_jordan6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => k5_jordan6(A,B,C,D,E) = a_5_0_jordan6(A,B,C,D,E) ) ) ) ) ) )).

fof(d6_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k6_jordan6(A) = a_1_2_jordan6(A) ) )).

fof(d7_jordan6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k7_jordan6(A) = a_1_5_jordan6(A) ) )).

fof(fraenkel_a_1_0_jordan6,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_0_jordan6(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & r1_xreal_0(B,k21_euclid(C)) ) ) ) )).

fof(fraenkel_a_1_1_jordan6,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_1_jordan6(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & r1_xreal_0(k21_euclid(C),B) ) ) ) )).

fof(fraenkel_a_1_2_jordan6,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_2_jordan6(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & k21_euclid(C) = B ) ) ) )).

fof(fraenkel_a_1_3_jordan6,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_3_jordan6(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & r1_xreal_0(B,k22_euclid(C)) ) ) ) )).

fof(fraenkel_a_1_4_jordan6,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_4_jordan6(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & r1_xreal_0(k22_euclid(C),B) ) ) ) )).

fof(fraenkel_a_1_5_jordan6,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_5_jordan6(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & k22_euclid(C) = B ) ) ) )).

fof(fraenkel_a_2_0_jordan6,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
     => ( r2_hidden(A,a_2_0_jordan6(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
            & A = D
            & k21_euclid(D) = k6_real_1(k3_real_1(k21_euclid(B),k21_euclid(C)),np__2) ) ) ) )).

fof(fraenkel_a_2_1_jordan6,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
     => ( r2_hidden(A,a_2_1_jordan6(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
            & A = D
            & k22_euclid(D) = k6_real_1(k3_real_1(k22_euclid(B),k22_euclid(C)),np__2) ) ) ) )).

fof(fraenkel_a_4_0_jordan6,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(E,u1_struct_0(k15_euclid(np__2))) )
     => ( r2_hidden(A,a_4_0_jordan6(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
            & A = F
            & r1_jordan5c(B,C,D,F,E) ) ) ) )).

fof(fraenkel_a_4_1_jordan6,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(E,u1_struct_0(k15_euclid(np__2))) )
     => ( r2_hidden(A,a_4_1_jordan6(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
            & A = F
            & r1_jordan5c(B,C,D,E,F) ) ) ) )).

fof(fraenkel_a_5_0_jordan6,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(F,u1_struct_0(k15_euclid(np__2))) )
     => ( r2_hidden(A,a_5_0_jordan6(B,C,D,E,F))
      <=> ? [G] :
            ( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
            & A = G
            & r1_jordan5c(B,C,D,E,G)
            & r1_jordan5c(B,C,D,G,F) ) ) ) )).
%------------------------------------------------------------------------------