SET007 Axioms: SET007+871.ax


%------------------------------------------------------------------------------
% File     : SET007+871 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On Some Points 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    : jordan21 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   95 (   0 unit)
%            Number of atoms       :  446 (  43 equality)
%            Maximal formula depth :   18 (   6 average)
%            Number of connectives :  437 (  86 ~  ;   8  |; 158  &)
%                                         (   5 <=>; 180 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   24 (   0 propositional; 1-4 arity)
%            Number of functors    :   54 (   6 constant; 0-5 arity)
%            Number of variables   :  170 (   0 singleton; 165 !;   5 ?)
%            Maximal term depth    :   10 (   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_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_jordan21(A)
       => ~ v1_xboole_0(A) ) ) )).

fof(cc2_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal2(A)
       => ( ~ v1_xboole_0(A)
          & v4_pre_topc(A,k15_euclid(np__2))
          & v2_connsp_1(A,k15_euclid(np__2))
          & v6_compts_1(A,k15_euclid(np__2))
          & ~ v1_sppol_1(A)
          & ~ v2_sppol_1(A)
          & ~ v1_realset1(A)
          & v1_topreal2(A)
          & v1_jordan21(A) ) ) ) )).

fof(rc1_jordan21,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
      & ~ v1_xboole_0(A)
      & v4_pre_topc(A,k15_euclid(np__2))
      & v2_connsp_1(A,k15_euclid(np__2))
      & v6_compts_1(A,k15_euclid(np__2))
      & ~ v1_sppol_1(A)
      & ~ v2_sppol_1(A)
      & ~ v1_realset1(A)
      & v1_topreal2(A)
      & v1_jordan21(A) ) )).

fof(fc1_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( ~ v1_xboole_0(k9_jordan6(A))
        & v4_pre_topc(k9_jordan6(A),k15_euclid(np__2))
        & v1_jordan2c(k9_jordan6(A),np__2)
        & v6_compts_1(k9_jordan6(A),k15_euclid(np__2))
        & v1_jordan21(k9_jordan6(A)) ) ) )).

fof(fc2_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( ~ v1_xboole_0(k8_jordan6(A))
        & v4_pre_topc(k8_jordan6(A),k15_euclid(np__2))
        & v1_jordan2c(k8_jordan6(A),np__2)
        & v6_compts_1(k8_jordan6(A),k15_euclid(np__2))
        & v1_jordan21(k8_jordan6(A)) ) ) )).

fof(t1_jordan21,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => v1_jordan2c(k1_struct_0(k15_euclid(A),B),A) ) ) )).

fof(t6_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => v1_jordan1(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jordan1a(A),k1_struct_0(k15_euclid(np__2),A)),np__2) ) )).

fof(t7_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => v1_jordan1(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k4_jordan1a(A),k1_struct_0(k15_euclid(np__2),A)),np__2) ) )).

fof(t8_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => v1_jordan1(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k5_jordan1a(A),k1_struct_0(k15_euclid(np__2),A)),np__2) ) )).

fof(t9_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => v1_jordan1(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_jordan1a(A),k1_struct_0(k15_euclid(np__2),A)),np__2) ) )).

fof(t10_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => r1_xboole_0(k2_jordan2c(np__2,A),A) ) )).

fof(t11_jordan21,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)
                       => ( B = D
                          | C = E
                          | ( ~ r2_hidden(B,k5_jordan6(A,B,C,D,E))
                            & ~ r2_hidden(C,k5_jordan6(A,B,C,D,E)) ) ) ) ) ) ) ) ) )).

fof(d1_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_jordan21(A)
      <=> ~ r1_xboole_0(A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))) ) ) )).

fof(t12_jordan21,axiom,(
    ! [A] :
      ( ( v1_jordan21(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ~ v1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))) ) )).

fof(t13_jordan21,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( v2_rcomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)))))
        & v2_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)))))
        & v1_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))) ) ) )).

fof(t14_jordan21,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r2_hidden(k4_tarski(np__1,np__1),k2_matrix_1(k1_jordan8(A,B))) ) ) )).

fof(t15_jordan21,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r2_hidden(k4_tarski(np__1,np__2),k2_matrix_1(k1_jordan8(A,B))) ) ) )).

fof(t16_jordan21,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r2_hidden(k4_tarski(np__2,np__1),k2_matrix_1(k1_jordan8(A,B))) ) ) )).

fof(t17_jordan21,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( v6_compts_1(E,k15_euclid(np__2))
                        & ~ v1_sppol_1(E)
                        & ~ v2_sppol_1(E)
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                     => ~ ( ~ r1_xreal_0(A,B)
                          & r2_hidden(k4_tarski(C,D),k2_matrix_1(k1_jordan8(E,B)))
                          & r2_hidden(k4_tarski(C,k1_nat_1(D,np__1)),k2_matrix_1(k1_jordan8(E,B)))
                          & r1_xreal_0(k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),C,k1_nat_1(D,np__1))),k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,A),C,k1_nat_1(D,np__1)))) ) ) ) ) ) ) )).

fof(t18_jordan21,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v6_compts_1(C,k15_euclid(np__2))
                & ~ v1_sppol_1(C)
                & ~ v2_sppol_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ~ ( ~ r1_xreal_0(A,B)
                  & r1_xreal_0(k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),np__1,np__2)),k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),np__1,np__2))) ) ) ) ) )).

fof(t19_jordan21,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( v6_compts_1(E,k15_euclid(np__2))
                        & ~ v1_sppol_1(E)
                        & ~ v2_sppol_1(E)
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                     => ~ ( ~ r1_xreal_0(A,B)
                          & r2_hidden(k4_tarski(C,D),k2_matrix_1(k1_jordan8(E,B)))
                          & r2_hidden(k4_tarski(k1_nat_1(C,np__1),D),k2_matrix_1(k1_jordan8(E,B)))
                          & r1_xreal_0(k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),k1_nat_1(C,np__1),D)),k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,A),k1_nat_1(C,np__1),D))) ) ) ) ) ) ) )).

fof(t20_jordan21,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v6_compts_1(C,k15_euclid(np__2))
                & ~ v1_sppol_1(C)
                & ~ v2_sppol_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ~ ( ~ r1_xreal_0(A,B)
                  & r1_xreal_0(k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),np__2,np__1)),k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),np__2,np__1))) ) ) ) ) )).

fof(t21_jordan21,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] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ~ r1_xreal_0(D,np__0)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( ~ r1_xreal_0(E,B)
                              & ~ r1_xreal_0(C,k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),np__1,np__2)))
                              & ~ r1_xreal_0(D,k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),np__2,np__1))) ) ) ) ) ) ) ) )).

fof(t22_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r2_hidden(k7_jordan1k(A),A) ) )).

fof(t23_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r2_hidden(k6_jordan1k(A),A) ) )).

fof(t24_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k22_euclid(k6_jordan1k(A)) != k22_euclid(k7_jordan1k(A)) ) )).

fof(t25_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k6_jordan1k(A) != k7_jordan1k(A) ) )).

fof(t26_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k18_pscomp_1(A) = k18_pscomp_1(k8_jordan6(A)) ) )).

fof(t27_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k20_pscomp_1(A) = k20_pscomp_1(k8_jordan6(A)) ) )).

fof(t28_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k18_pscomp_1(A) = k18_pscomp_1(k9_jordan6(A)) ) )).

fof(t29_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k20_pscomp_1(A) = k20_pscomp_1(k9_jordan6(A)) ) )).

fof(t30_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( ~ v1_xboole_0(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k8_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))
        & ~ v1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k8_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))) ) ) )).

fof(t31_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( ~ v1_xboole_0(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k9_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))
        & ~ v1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k9_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))) ) ) )).

fof(t32_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ~ ( r1_tarski(B,A)
              & r2_hidden(k30_pscomp_1(A),B)
              & r2_hidden(k34_pscomp_1(A),B)
              & ~ r1_tarski(k8_jordan6(A),B)
              & ~ r1_tarski(k9_jordan6(A),B) ) ) ) )).

fof(d2_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k1_jordan21(A) = k23_euclid(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),np__2),k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),np__2)))))) ) )).

fof(d3_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k2_jordan21(A) = k23_euclid(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),np__2),k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),np__2)))))) ) )).

fof(t33_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k21_euclid(k1_jordan21(A)) = k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2) ) )).

fof(t34_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k22_euclid(k1_jordan21(A)) = k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),np__2))))) ) )).

fof(t35_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k21_euclid(k2_jordan21(A)) = k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2) ) )).

fof(t36_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k22_euclid(k2_jordan21(A)) = k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),np__2))))) ) )).

fof(t37_jordan21,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k1_jordan21(A) != k30_pscomp_1(A) ) )).

fof(t38_jordan21,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k1_jordan21(A) != k34_pscomp_1(A) ) )).

fof(t39_jordan21,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k2_jordan21(A) != k30_pscomp_1(A) ) )).

fof(t40_jordan21,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k2_jordan21(A) != k34_pscomp_1(A) ) )).

fof(t41_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r2_hidden(A,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)),np__2))))
           => r1_xreal_0(k22_euclid(A),k22_euclid(k1_jordan21(B))) ) ) ) )).

fof(t42_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r2_hidden(A,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)),np__2))))
           => r1_xreal_0(k22_euclid(k2_jordan21(B)),k22_euclid(A)) ) ) ) )).

fof(t43_jordan21,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & v1_jordan21(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r2_hidden(k1_jordan21(A),A) ) )).

fof(t44_jordan21,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & v1_jordan21(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r2_hidden(k2_jordan21(A),A) ) )).

fof(t45_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => v2_sppol_1(k3_topreal1(np__2,k1_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k19_pscomp_1(A)))) ) )).

fof(t46_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => v2_sppol_1(k3_topreal1(np__2,k2_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k21_pscomp_1(A)))) ) )).

fof(t47_jordan21,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & v1_jordan21(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k1_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k19_pscomp_1(A))),A) = k1_struct_0(k15_euclid(np__2),k1_jordan21(A)) ) )).

fof(t48_jordan21,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & v1_jordan21(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k2_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k21_pscomp_1(A))),A) = k1_struct_0(k15_euclid(np__2),k2_jordan21(A)) ) )).

fof(t49_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ~ r1_xreal_0(k22_euclid(k1_jordan21(A)),k22_euclid(k2_jordan21(A))) ) )).

fof(t50_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k1_jordan21(A) != k2_jordan21(A) ) )).

fof(t51_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ~ r1_xreal_0(k22_euclid(k1_jordan21(A)),k21_pscomp_1(A)) ) )).

fof(t52_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_xreal_0(k22_euclid(k1_jordan21(A)),k19_pscomp_1(A)) ) )).

fof(t53_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_xreal_0(k21_pscomp_1(A),k22_euclid(k2_jordan21(A))) ) )).

fof(t54_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ~ r1_xreal_0(k19_pscomp_1(A),k22_euclid(k2_jordan21(A))) ) )).

fof(t55_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_subset_1(k3_topreal1(np__2,k1_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k19_pscomp_1(A))),k3_topreal1(np__2,k2_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k21_pscomp_1(A)))) ) )).

fof(t56_jordan21,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))))
         => ( ( r1_tarski(A,B)
              & k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)) = k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B))
              & v1_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))) )
           => ( v1_xboole_0(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))
              | r1_xreal_0(k22_euclid(k1_jordan21(A)),k22_euclid(k1_jordan21(B))) ) ) ) ) )).

fof(t57_jordan21,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))))
         => ( ( r1_tarski(A,B)
              & k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)) = k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B))
              & v2_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))) )
           => ( v1_xboole_0(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))
              | r1_xreal_0(k22_euclid(k2_jordan21(B)),k22_euclid(k2_jordan21(A))) ) ) ) ) )).

fof(t58_jordan21,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))))
         => ( ( r1_tarski(A,B)
              & r2_hidden(k1_jordan21(B),A)
              & v1_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)),np__2)))))
              & k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)) = k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)) )
           => ( v1_xboole_0(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))
              | k1_jordan21(A) = k1_jordan21(B) ) ) ) ) )).

fof(t59_jordan21,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))))
         => ( ( r1_tarski(A,B)
              & r2_hidden(k2_jordan21(B),A)
              & v2_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)),np__2)))))
              & k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)) = k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)) )
           => ( v1_xboole_0(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))
              | k2_jordan21(A) = k2_jordan21(B) ) ) ) ) )).

fof(t60_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_xreal_0(k22_euclid(k1_jordan21(k8_jordan6(A))),k19_pscomp_1(A)) ) )).

fof(t61_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_xreal_0(k21_pscomp_1(A),k22_euclid(k2_jordan21(k9_jordan6(A)))) ) )).

fof(t62_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ~ ( r2_hidden(k2_jordan21(A),k9_jordan6(A))
          & r2_hidden(k1_jordan21(A),k9_jordan6(A)) ) ) )).

fof(t63_jordan21,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ~ ( r2_hidden(k2_jordan21(A),k8_jordan6(A))
          & r2_hidden(k1_jordan21(A),k8_jordan6(A)) ) ) )).

fof(t64_jordan21,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)
         => ( ~ r1_xreal_0(B,np__0)
           => k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan9(A,B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),k3_finseq_1(k1_jordan8(A,B))))))) = k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan9(A,B)),k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2))))) ) ) ) )).

fof(t65_jordan21,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)
         => ( ~ r1_xreal_0(B,np__0)
           => k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan9(A,B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),k3_finseq_1(k1_jordan8(A,B))))))) = k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan9(A,B)),k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2))))) ) ) ) )).

fof(t66_jordan21,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)
         => ( ~ r1_xreal_0(B,np__0)
           => k1_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))) = k23_euclid(k6_real_1(k3_real_1(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2),k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan9(A,B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),k3_finseq_1(k1_jordan8(A,B)))))))) ) ) ) )).

fof(t67_jordan21,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)
         => ( ~ r1_xreal_0(B,np__0)
           => k2_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))) = k23_euclid(k6_real_1(k3_real_1(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2),k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan9(A,B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),k3_finseq_1(k1_jordan8(A,B)))))))) ) ) ) )).

fof(t68_jordan21,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)
         => ~ r1_xreal_0(k22_euclid(k1_jordan21(k5_topreal1(np__2,k1_jordan9(A,B)))),k22_euclid(k1_jordan21(A))) ) ) )).

fof(t69_jordan21,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)
         => ~ r1_xreal_0(k22_euclid(k2_jordan21(A)),k22_euclid(k2_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))))) ) ) )).

fof(t70_jordan21,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)
         => r2_hidden(k1_jordan21(k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))),k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) )).

fof(t71_jordan21,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)
         => r2_hidden(k2_jordan21(k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) )).

fof(t72_jordan21,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)
         => ~ ( ~ r1_xreal_0(B,np__0)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,k3_finseq_1(k1_jordan8(A,B)))
                      & k1_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),C) ) ) ) ) ) )).

fof(t73_jordan21,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)
         => ~ ( ~ r1_xreal_0(B,np__0)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,k3_finseq_1(k1_jordan8(A,B)))
                      & k2_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),C) ) ) ) ) ) )).

fof(t74_jordan21,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)
         => ( ~ r1_xreal_0(B,np__0)
           => k1_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))) = k1_jordan21(k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ) )).

fof(t75_jordan21,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)
         => ( ~ r1_xreal_0(B,np__0)
           => k2_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))) = k2_jordan21(k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ) )).

fof(t76_jordan21,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)
         => ~ ( ~ r1_xreal_0(B,np__0)
              & r1_xreal_0(k22_euclid(k1_jordan21(k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B))))),k22_euclid(k1_jordan21(A))) ) ) ) )).

fof(t77_jordan21,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)
         => ~ ( ~ r1_xreal_0(B,np__0)
              & r1_xreal_0(k22_euclid(k2_jordan21(A)),k22_euclid(k2_jordan21(k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))))) ) ) ) )).

fof(t78_jordan21,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] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(B,C)
               => r1_xreal_0(k22_euclid(k1_jordan21(k5_topreal1(np__2,k1_jordan9(A,C)))),k22_euclid(k1_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))))) ) ) ) ) )).

fof(t79_jordan21,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] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(B,C)
               => r1_xreal_0(k22_euclid(k2_jordan21(k5_topreal1(np__2,k1_jordan9(A,B)))),k22_euclid(k2_jordan21(k5_topreal1(np__2,k1_jordan9(A,C))))) ) ) ) ) )).

fof(t80_jordan21,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] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(B,C)
               => ( r1_xreal_0(B,np__0)
                  | r1_xreal_0(k22_euclid(k1_jordan21(k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,C))))),k22_euclid(k1_jordan21(k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))))) ) ) ) ) ) )).

fof(t81_jordan21,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] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(B,C)
               => ( r1_xreal_0(B,np__0)
                  | r1_xreal_0(k22_euclid(k2_jordan21(k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B))))),k22_euclid(k2_jordan21(k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,C)))))) ) ) ) ) ) )).

fof(dt_k1_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k1_jordan21(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k2_jordan21,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k2_jordan21(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(t2_jordan21,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ( C = a_2_0_jordan21(A,B)
               => v1_jordan1(C,np__2) ) ) ) ) )).

fof(t3_jordan21,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ( C = a_2_1_jordan21(A,B)
               => v1_jordan1(C,np__2) ) ) ) ) )).

fof(t4_jordan21,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ( C = a_2_2_jordan21(A,B)
               => v1_jordan1(C,np__2) ) ) ) ) )).

fof(t5_jordan21,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ( C = a_2_3_jordan21(A,B)
               => v1_jordan1(C,np__2) ) ) ) ) )).

fof(fraenkel_a_2_0_jordan21,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C) )
     => ( r2_hidden(A,a_2_0_jordan21(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_numbers)
            & A = k23_euclid(D,C)
            & ~ r1_xreal_0(D,B) ) ) ) )).

fof(fraenkel_a_2_1_jordan21,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C) )
     => ( r2_hidden(A,a_2_1_jordan21(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_numbers)
            & A = k23_euclid(D,C)
            & ~ r1_xreal_0(B,D) ) ) ) )).

fof(fraenkel_a_2_2_jordan21,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C) )
     => ( r2_hidden(A,a_2_2_jordan21(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_numbers)
            & A = k23_euclid(B,D)
            & ~ r1_xreal_0(D,C) ) ) ) )).

fof(fraenkel_a_2_3_jordan21,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C) )
     => ( r2_hidden(A,a_2_3_jordan21(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_numbers)
            & A = k23_euclid(B,D)
            & ~ r1_xreal_0(C,D) ) ) ) )).
%------------------------------------------------------------------------------