SET007 Axioms: SET007+791.ax


%------------------------------------------------------------------------------
% File     : SET007+791 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Segmentation of a Simple Closed Curve
% 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    : jordan_a [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   61 (   0 unit)
%            Number of atoms       :  460 (  49 equality)
%            Maximal formula depth :   24 (   9 average)
%            Number of connectives :  450 (  51 ~  ;  15  |; 199  &)
%                                         (  12 <=>; 173 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   32 (   0 propositional; 1-4 arity)
%            Number of functors    :   52 (   6 constant; 0-5 arity)
%            Number of variables   :  190 (   0 singleton; 172 !;  18 ?)
%            Maximal term depth    :    6 (   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(rc1_jordan_a,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)))
          & ~ v1_xboole_0(B)
          & v6_compts_1(B,A) ) ) )).

fof(fc1_jordan_a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( v1_relat_1(k1_jordan_a(A))
        & v1_funct_1(k1_jordan_a(A))
        & v1_funct_2(k1_jordan_a(A),u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),k1_numbers)
        & v9_pscomp_1(k1_jordan_a(A),k6_borsuk_1(k15_euclid(A),k15_euclid(A))) ) ) )).

fof(cc1_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ( ~ v1_xboole_0(B)
            & v1_relat_1(B)
            & ~ v1_realset1(B) ) ) ) )).

fof(fc2_jordan_a,axiom,(
    ! [A,B,C] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_jordan_a(B,A)
        & m1_subset_1(C,k5_numbers) )
     => ( ~ v1_xboole_0(k2_jordan_a(A,C,B))
        & v6_compts_1(k2_jordan_a(A,C,B),k15_euclid(np__2)) ) ) )).

fof(t1_jordan_a,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => k3_seq_4(k4_subset_1(k1_numbers,A,B)) = k1_square_1(k3_seq_4(A),k3_seq_4(B)) ) ) )).

fof(t2_jordan_a,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & v9_pscomp_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ! [C] :
              ( ( v6_compts_1(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => v1_rcomp_1(k2_funct_2(u1_struct_0(A),k1_numbers,B,C)) ) ) ) )).

fof(t3_jordan_a,axiom,(
    ! [A] :
      ( ( v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ( r1_tarski(B,A)
           => r2_hidden(k4_pscomp_1(B),A) ) ) ) )).

fof(t6_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)))
         => ( r2_hidden(B,k9_jordan6(A))
           => ( B = k30_pscomp_1(A)
              | r1_jordan6(A,k34_pscomp_1(A),B) ) ) ) ) )).

fof(t7_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)))
         => ( r2_hidden(B,k8_jordan6(A))
           => r1_jordan6(A,B,k34_pscomp_1(A)) ) ) ) )).

fof(d1_jordan_a,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),k1_numbers)
            & m2_relset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),k1_numbers) )
         => ( B = k1_jordan_a(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                   => k1_binop_1(B,C,D) = k5_toprns_1(A,k20_euclid(A,C,D)) ) ) ) ) ) )).

fof(d2_jordan_a,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ( v9_pscomp_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_rcomp_1(D,k8_funct_2(u1_struct_0(A),k1_numbers,B,C))
                   => ? [E] :
                        ( m1_connsp_2(E,A,C)
                        & r1_tarski(k2_funct_2(u1_struct_0(A),k1_numbers,B,E),D) ) ) ) ) ) ) )).

fof(t8_jordan_a,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v6_compts_1(C,k15_euclid(A))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
             => ~ ( r1_subset_1(B,C)
                  & r1_xreal_0(k4_jordan1k(A,B,C),np__0) ) ) ) ) )).

fof(t9_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)
                  & r1_jordan6(A,C,k34_pscomp_1(A)) )
               => ( B = C
                  | k1_jordan7(A,B,C) = k5_jordan6(k8_jordan6(A),k30_pscomp_1(A),k34_pscomp_1(A),B,C) ) ) ) ) ) )).

fof(t10_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)))
         => ( r1_jordan6(A,k34_pscomp_1(A),B)
           => k1_jordan7(A,k34_pscomp_1(A),B) = k5_jordan6(k9_jordan6(A),k34_pscomp_1(A),k30_pscomp_1(A),k34_pscomp_1(A),B) ) ) ) )).

fof(t11_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)))
         => ( r1_jordan6(A,k34_pscomp_1(A),B)
           => k1_jordan7(A,B,k30_pscomp_1(A)) = k5_jordan6(k9_jordan6(A),k34_pscomp_1(A),k30_pscomp_1(A),B,k30_pscomp_1(A)) ) ) ) )).

fof(t12_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)
                  & r1_jordan6(A,k34_pscomp_1(A),B) )
               => k1_jordan7(A,B,C) = k5_jordan6(k9_jordan6(A),k34_pscomp_1(A),k30_pscomp_1(A),B,C) ) ) ) ) )).

fof(t13_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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,k34_pscomp_1(A))
                  & r1_jordan6(A,k34_pscomp_1(A),C) )
               => k1_jordan7(A,B,C) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k4_jordan6(k8_jordan6(A),k30_pscomp_1(A),k34_pscomp_1(A),B),k3_jordan6(k9_jordan6(A),k34_pscomp_1(A),k30_pscomp_1(A),C)) ) ) ) ) )).

fof(t14_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)))
         => ( r1_jordan6(A,B,k34_pscomp_1(A))
           => k1_jordan7(A,B,k30_pscomp_1(A)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k4_jordan6(k8_jordan6(A),k30_pscomp_1(A),k34_pscomp_1(A),B),k3_jordan6(k9_jordan6(A),k34_pscomp_1(A),k30_pscomp_1(A),k30_pscomp_1(A))) ) ) ) )).

fof(t15_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)))
         => k4_jordan6(k8_jordan6(A),k30_pscomp_1(A),k34_pscomp_1(A),B) = k5_jordan6(k8_jordan6(A),k30_pscomp_1(A),k34_pscomp_1(A),B,k34_pscomp_1(A)) ) ) )).

fof(t16_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)))
         => k3_jordan6(k9_jordan6(A),k34_pscomp_1(A),k30_pscomp_1(A),B) = k5_jordan6(k9_jordan6(A),k34_pscomp_1(A),k30_pscomp_1(A),k34_pscomp_1(A),B) ) ) )).

fof(t17_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)))
         => ( r2_hidden(B,A)
           => ( B = k30_pscomp_1(A)
              | r1_topreal1(k15_euclid(np__2),B,k30_pscomp_1(A),k1_jordan7(A,B,k30_pscomp_1(A))) ) ) ) ) )).

fof(t18_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)
               => ( B = C
                  | r1_topreal1(k15_euclid(np__2),B,C,k1_jordan7(A,B,C)) ) ) ) ) ) )).

fof(t19_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => A = k1_jordan7(A,k30_pscomp_1(A),k30_pscomp_1(A)) ) )).

fof(t20_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)))
         => ( r2_hidden(B,A)
           => v6_compts_1(k1_jordan7(A,B,k30_pscomp_1(A)),k15_euclid(np__2)) ) ) ) )).

fof(t21_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)
               => v6_compts_1(k1_jordan7(A,B,C),k15_euclid(np__2)) ) ) ) ) )).

fof(d3_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( m1_jordan_a(B,A)
          <=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1) = k30_pscomp_1(A)
              & v2_funct_1(B)
              & r1_xreal_0(np__8,k3_finseq_1(B))
              & r1_tarski(k2_relat_1(B),A)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(np__1,C)
                   => ( r1_xreal_0(k3_finseq_1(B),C)
                      | r1_jordan6(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1))) ) ) )
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(np__1,C)
                   => ( r1_xreal_0(k3_finseq_1(B),k1_nat_1(C,np__1))
                      | k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1))),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__2)))) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1))) ) ) )
              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__2))) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))
              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k5_binarith(k3_finseq_1(B),np__1)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)))
              & r1_xboole_0(k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k5_binarith(k3_finseq_1(B),np__1)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__2)))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(np__1,C)
                       => ( r1_xreal_0(D,C)
                          | r1_xreal_0(k3_finseq_1(B),D)
                          | r1_gobrd10(C,D)
                          | r1_xboole_0(k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1))),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(D,np__1)))) ) ) ) )
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( ~ r1_xreal_0(C,np__1)
                      & ~ r1_xreal_0(k3_finseq_1(B),k1_nat_1(C,np__1))
                      & ~ r1_xboole_0(k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1)))) ) ) ) ) ) ) )).

fof(t22_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(C,k3_finseq_1(B)) )
               => r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C),A) ) ) ) ) )).

fof(d4_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( v4_ordinal2(B)
         => ! [C] :
              ( m1_jordan_a(C,A)
             => ( ( r1_xreal_0(np__1,B)
                 => ( r1_xreal_0(k3_finseq_1(C),B)
                    | k2_jordan_a(A,B,C) = k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k2_xcmplx_0(B,np__1))) ) )
                & ( ~ ( r1_xreal_0(np__1,B)
                      & ~ r1_xreal_0(k3_finseq_1(C),B) )
                 => k2_jordan_a(A,B,C) = k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1)) ) ) ) ) ) )).

fof(t23_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_jordan_a(C,A)
             => ( r2_hidden(B,k4_finseq_1(C))
               => r1_tarski(k2_jordan_a(A,B,C),A) ) ) ) ) )).

fof(t24_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r2_hidden(C,A)
                  & ! [D] :
                      ( v4_ordinal2(D)
                     => ~ ( r2_hidden(D,k4_finseq_1(B))
                          & r2_hidden(C,k2_jordan_a(A,D,B)) ) ) ) ) ) ) )).

fof(t25_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(np__1,C)
                   => ( r1_xreal_0(D,C)
                      | r1_xreal_0(k3_finseq_1(B),D)
                      | r1_gobrd10(C,D)
                      | r1_subset_1(k2_jordan_a(A,C,B),k2_jordan_a(A,D,B)) ) ) ) ) ) ) )).

fof(t26_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( ~ r1_xreal_0(C,np__1)
                  & ~ r1_xreal_0(k5_binarith(k3_finseq_1(B),np__1),C)
                  & ~ r1_subset_1(k2_jordan_a(A,k3_finseq_1(B),B),k2_jordan_a(A,C,B)) ) ) ) ) )).

fof(t27_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,C)
                      & r1_gobrd10(C,D) )
                   => ( r1_xreal_0(D,C)
                      | r1_xreal_0(k3_finseq_1(B),D)
                      | k5_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jordan_a(A,C,B),k2_jordan_a(A,D,B)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1))) ) ) ) ) ) ) )).

fof(t28_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(np__1,C)
                      & ~ r1_xreal_0(D,C)
                      & ~ r1_xreal_0(k3_finseq_1(B),D)
                      & r1_gobrd10(C,D)
                      & r2_subset_1(k2_jordan_a(A,C,B),k2_jordan_a(A,D,B)) ) ) ) ) ) )).

fof(t29_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jordan_a(A,k3_finseq_1(B),B),k2_jordan_a(A,np__1,B)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) ) ) )).

fof(t30_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ~ r2_subset_1(k2_jordan_a(A,k3_finseq_1(B),B),k2_jordan_a(A,np__1,B)) ) ) )).

fof(t31_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jordan_a(A,k3_finseq_1(B),B),k2_jordan_a(A,k5_binarith(k3_finseq_1(B),np__1),B)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))) ) ) )).

fof(t32_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ~ r2_subset_1(k2_jordan_a(A,k3_finseq_1(B),B),k2_jordan_a(A,k5_binarith(k3_finseq_1(B),np__1),B)) ) ) )).

fof(d5_jordan_a,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_numbers)
             => ( C = k3_jordan_a(A,B)
              <=> ? [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
                    & D = B
                    & C = k2_tbsp_1(k14_euclid(A),D) ) ) ) ) ) )).

fof(t33_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => r1_xreal_0(k3_jordan_a(np__2,k2_jordan_a(A,C,B)),k4_jordan_a(A,B)) ) ) ) )).

fof(t34_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ~ ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ r1_xreal_0(C,k3_jordan_a(np__2,k2_jordan_a(A,D,B))) )
                  & r1_xreal_0(C,k4_jordan_a(A,B)) ) ) ) ) )).

fof(t35_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ~ ( ~ r1_xreal_0(B,np__0)
              & ! [C] :
                  ( m1_jordan_a(C,A)
                 => r1_xreal_0(B,k4_jordan_a(A,C)) ) ) ) ) )).

fof(t37_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ~ r1_xreal_0(k5_jordan_a(A,B),np__0) ) ) )).

fof(dt_m1_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) ) ) )).

fof(existence_m1_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ? [B] : m1_jordan_a(B,A) ) )).

fof(dt_k1_jordan_a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( v1_funct_1(k1_jordan_a(A))
        & v1_funct_2(k1_jordan_a(A),u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),k1_numbers)
        & m2_relset_1(k1_jordan_a(A),u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),k1_numbers) ) ) )).

fof(dt_k2_jordan_a,axiom,(
    ! [A,B,C] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & v4_ordinal2(B)
        & m1_jordan_a(C,A) )
     => m1_subset_1(k2_jordan_a(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k3_jordan_a,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
     => m1_subset_1(k3_jordan_a(A,B),k1_numbers) ) )).

fof(dt_k4_jordan_a,axiom,(
    ! [A,B] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_jordan_a(B,A) )
     => m1_subset_1(k4_jordan_a(A,B),k1_numbers) ) )).

fof(dt_k5_jordan_a,axiom,(
    ! [A,B] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_jordan_a(B,A) )
     => m1_subset_1(k5_jordan_a(A,B),k1_numbers) ) )).

fof(t4_jordan_a,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v6_compts_1(C,k15_euclid(A))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),k1_numbers)
                    & v9_pscomp_1(D,k6_borsuk_1(k15_euclid(A),k15_euclid(A)))
                    & m2_relset_1(D,u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),k1_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k15_euclid(A)),k1_numbers)
                        & m2_relset_1(E,u1_struct_0(k15_euclid(A)),k1_numbers) )
                     => ( ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                           => ? [G] :
                                ( m1_subset_1(G,k1_zfmisc_1(k1_numbers))
                                & G = a_4_0_jordan_a(A,C,D,F)
                                & k8_funct_2(u1_struct_0(k15_euclid(A)),k1_numbers,E,F) = k4_pscomp_1(G) ) )
                       => k4_pscomp_1(k2_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),k1_numbers,D,k7_borsuk_1(k15_euclid(A),k15_euclid(A),B,C))) = k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(A)),k1_numbers,E,B)) ) ) ) ) ) ) )).

fof(t5_jordan_a,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v6_compts_1(C,k15_euclid(A))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),k1_numbers)
                    & v9_pscomp_1(D,k6_borsuk_1(k15_euclid(A),k15_euclid(A)))
                    & m2_relset_1(D,u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),k1_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k15_euclid(A)),k1_numbers)
                        & m2_relset_1(E,u1_struct_0(k15_euclid(A)),k1_numbers) )
                     => ( ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                           => ? [G] :
                                ( m1_subset_1(G,k1_zfmisc_1(k1_numbers))
                                & G = a_4_1_jordan_a(A,B,D,F)
                                & k8_funct_2(u1_struct_0(k15_euclid(A)),k1_numbers,E,F) = k4_pscomp_1(G) ) )
                       => k4_pscomp_1(k2_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),k1_numbers,D,k7_borsuk_1(k15_euclid(A),k15_euclid(A),B,C))) = k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(A)),k1_numbers,E,C)) ) ) ) ) ) ) )).

fof(d6_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( C = k4_jordan_a(A,B)
              <=> ? [D] :
                    ( ~ v1_xboole_0(D)
                    & v1_finset_1(D)
                    & m1_subset_1(D,k1_zfmisc_1(k1_numbers))
                    & D = a_2_0_jordan_a(A,B)
                    & C = k1_pre_circ(D) ) ) ) ) ) )).

fof(d7_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( C = k5_jordan_a(A,B)
              <=> ? [D] :
                    ( ~ v1_xboole_0(D)
                    & v1_finset_1(D)
                    & m1_subset_1(D,k1_zfmisc_1(k1_numbers))
                    & ? [E] :
                        ( ~ v1_xboole_0(E)
                        & v1_finset_1(E)
                        & m1_subset_1(E,k1_zfmisc_1(k1_numbers))
                        & D = a_2_1_jordan_a(A,B)
                        & E = a_2_2_jordan_a(A,B)
                        & C = k1_square_1(k3_seq_4(D),k3_seq_4(E)) ) ) ) ) ) ) )).

fof(t36_jordan_a,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_jordan_a(B,A)
         => ? [C] :
              ( ~ v1_xboole_0(C)
              & v1_finset_1(C)
              & m1_subset_1(C,k1_zfmisc_1(k1_numbers))
              & C = a_2_3_jordan_a(A,B)
              & k5_jordan_a(A,B) = k3_seq_4(C) ) ) ) )).

fof(fraenkel_a_4_0_jordan_a,axiom,(
    ! [A,B,C,D,E] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & ~ v1_xboole_0(C)
        & v6_compts_1(C,k15_euclid(B))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B))))
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(k6_borsuk_1(k15_euclid(B),k15_euclid(B))),k1_numbers)
        & v9_pscomp_1(D,k6_borsuk_1(k15_euclid(B),k15_euclid(B)))
        & m2_relset_1(D,u1_struct_0(k6_borsuk_1(k15_euclid(B),k15_euclid(B))),k1_numbers)
        & m1_subset_1(E,u1_struct_0(k15_euclid(B))) )
     => ( r2_hidden(A,a_4_0_jordan_a(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(k15_euclid(B)))
            & A = k1_binop_1(D,E,F)
            & r2_hidden(F,C) ) ) ) )).

fof(fraenkel_a_4_1_jordan_a,axiom,(
    ! [A,B,C,D,E] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & ~ v1_xboole_0(C)
        & v6_compts_1(C,k15_euclid(B))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B))))
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(k6_borsuk_1(k15_euclid(B),k15_euclid(B))),k1_numbers)
        & v9_pscomp_1(D,k6_borsuk_1(k15_euclid(B),k15_euclid(B)))
        & m2_relset_1(D,u1_struct_0(k6_borsuk_1(k15_euclid(B),k15_euclid(B))),k1_numbers)
        & m1_subset_1(E,u1_struct_0(k15_euclid(B))) )
     => ( r2_hidden(A,a_4_1_jordan_a(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(k15_euclid(B)))
            & A = k1_binop_1(D,F,E)
            & r2_hidden(F,C) ) ) ) )).

fof(fraenkel_a_2_0_jordan_a,axiom,(
    ! [A,B,C] :
      ( ( v1_topreal2(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_jordan_a(C,B) )
     => ( r2_hidden(A,a_2_0_jordan_a(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k3_jordan_a(np__2,k2_jordan_a(B,D,C))
            & r2_hidden(D,k4_finseq_1(C)) ) ) ) )).

fof(fraenkel_a_2_1_jordan_a,axiom,(
    ! [A,B,C] :
      ( ( v1_topreal2(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_jordan_a(C,B) )
     => ( r2_hidden(A,a_2_1_jordan_a(B,C))
      <=> ? [D,E] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & m2_subset_1(E,k1_numbers,k5_numbers)
            & A = k4_jordan1k(np__2,k2_jordan_a(B,D,C),k2_jordan_a(B,E,C))
            & r1_xreal_0(np__1,D)
            & ~ r1_xreal_0(E,D)
            & ~ r1_xreal_0(k3_finseq_1(C),E)
            & ~ r1_gobrd10(D,E) ) ) ) )).

fof(fraenkel_a_2_2_jordan_a,axiom,(
    ! [A,B,C] :
      ( ( v1_topreal2(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_jordan_a(C,B) )
     => ( r2_hidden(A,a_2_2_jordan_a(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k4_jordan1k(np__2,k2_jordan_a(B,k3_finseq_1(C),C),k2_jordan_a(B,D,C))
            & ~ r1_xreal_0(D,np__1)
            & ~ r1_xreal_0(k5_binarith(k3_finseq_1(C),np__1),D) ) ) ) )).

fof(fraenkel_a_2_3_jordan_a,axiom,(
    ! [A,B,C] :
      ( ( v1_topreal2(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_jordan_a(C,B) )
     => ( r2_hidden(A,a_2_3_jordan_a(B,C))
      <=> ? [D,E] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & m2_subset_1(E,k1_numbers,k5_numbers)
            & A = k4_jordan1k(np__2,k2_jordan_a(B,D,C),k2_jordan_a(B,E,C))
            & r1_xreal_0(np__1,D)
            & ~ r1_xreal_0(E,D)
            & r1_xreal_0(E,k3_finseq_1(C))
            & r1_subset_1(k2_jordan_a(B,D,C),k2_jordan_a(B,E,C)) ) ) ) )).
%------------------------------------------------------------------------------