SET007 Axioms: SET007+728.ax


%------------------------------------------------------------------------------
% File     : SET007+728 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Properties of the Upper and Lower Sequence on the Cage
% 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    : jordan15 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   53 (   0 unit)
%            Number of atoms       :  797 (  36 equality)
%            Maximal formula depth :   28 (  19 average)
%            Number of connectives :  899 ( 155 ~  ;   0  |; 467  &)
%                                         (   0 <=>; 277 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   25 (   0 propositional; 1-3 arity)
%            Number of functors    :   30 (   6 constant; 0-4 arity)
%            Number of variables   :  268 (   0 singleton; 268 !;   0 ?)
%            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(t1_jordan15,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_xboole_0(A,B)
              & r1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A),k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,B)) ) ) ) )).

fof(t2_jordan15,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] :
              ( v1_xreal_0(C)
             => ( ( r1_xboole_0(A,B)
                  & r1_tarski(A,k7_jordan6(C))
                  & r1_tarski(B,k7_jordan6(C)) )
               => r1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A),k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,B)) ) ) ) ) )).

fof(t3_jordan15,axiom,(
    ! [A] :
      ( ( v4_pre_topc(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( v1_jordan2c(A,np__2)
       => v2_rcomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A)) ) ) )).

fof(t4_jordan15,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => v1_rcomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A)) ) )).

fof(t5_jordan15,axiom,(
    ! [A] :
      ( m1_subset_1(A,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)))
                 => ( ( v2_sppol_1(k3_topreal1(np__2,A,B))
                      & v2_sppol_1(k3_topreal1(np__2,C,D))
                      & k21_euclid(A) = k21_euclid(C)
                      & r1_xreal_0(k22_euclid(A),k22_euclid(C))
                      & r1_xreal_0(k22_euclid(C),k22_euclid(D))
                      & r1_xreal_0(k22_euclid(D),k22_euclid(B)) )
                   => r1_tarski(k3_topreal1(np__2,C,D),k3_topreal1(np__2,A,B)) ) ) ) ) ) )).

fof(t6_jordan15,axiom,(
    ! [A] :
      ( m1_subset_1(A,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_sppol_1(k3_topreal1(np__2,A,B))
                      & v1_sppol_1(k3_topreal1(np__2,C,D))
                      & k22_euclid(A) = k22_euclid(C)
                      & r1_xreal_0(k21_euclid(A),k21_euclid(C))
                      & r1_xreal_0(k21_euclid(C),k21_euclid(D))
                      & r1_xreal_0(k21_euclid(D),k21_euclid(B)) )
                   => r1_tarski(k3_topreal1(np__2,C,D),k3_topreal1(np__2,A,B)) ) ) ) ) ) )).

fof(t7_jordan15,axiom,(
    ! [A] :
      ( ( ~ v3_relat_1(A)
        & v1_matrix_1(A)
        & v3_goboard1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & v6_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(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)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( ( r1_xreal_0(np__1,B)
                              & r1_xreal_0(B,k3_finseq_1(A))
                              & r1_xreal_0(np__1,C)
                              & r1_xreal_0(C,E)
                              & r1_xreal_0(E,F)
                              & r1_xreal_0(F,D)
                              & r1_xreal_0(D,k1_matrix_1(A)) )
                           => r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,D))) ) ) ) ) ) ) ) )).

fof(t8_jordan15,axiom,(
    ! [A] :
      ( ( ~ v3_relat_1(A)
        & v1_matrix_1(A)
        & v3_goboard1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & v6_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(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)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( ( r1_xreal_0(np__1,B)
                              & r1_xreal_0(B,k1_matrix_1(A))
                              & r1_xreal_0(np__1,C)
                              & r1_xreal_0(C,E)
                              & r1_xreal_0(E,F)
                              & r1_xreal_0(F,D)
                              & r1_xreal_0(D,k3_finseq_1(A)) )
                           => r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,E,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,F,B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,B))) ) ) ) ) ) ) ) )).

fof(t9_jordan15,axiom,(
    ! [A] :
      ( ( ~ v3_relat_1(A)
        & v1_matrix_1(A)
        & v3_goboard1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & v6_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(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)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__1,B)
                          & r1_xreal_0(B,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,C)
                          & r1_xreal_0(C,k1_matrix_1(A)) )
                       => r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_jordan1a(A),D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_jordan1a(A),E)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_jordan1a(A),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_jordan1a(A),C))) ) ) ) ) ) ) )).

fof(t10_jordan15,axiom,(
    ! [A] :
      ( ( ~ v3_relat_1(A)
        & v1_matrix_1(A)
        & v3_goboard1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & v6_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ( k3_finseq_1(A) = k1_matrix_1(A)
       => ! [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] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( ( r1_xreal_0(np__1,B)
                            & r1_xreal_0(B,D)
                            & r1_xreal_0(D,E)
                            & r1_xreal_0(E,C)
                            & r1_xreal_0(C,k3_finseq_1(A)) )
                         => r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,k1_jordan1a(A)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,E,k1_jordan1a(A))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,k1_jordan1a(A)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,k1_jordan1a(A)))) ) ) ) ) ) ) ) )).

fof(t11_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r1_xreal_0(D,F)
                                  & r1_xreal_0(F,E)
                                  & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)) ) ) ) ) ) ) ) ) )).

fof(t12_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r1_xreal_0(D,F)
                                  & r1_xreal_0(F,E)
                                  & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)) ) ) ) ) ) ) ) ) )).

fof(t13_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ~ ( r1_xreal_0(D,F)
                                      & r1_xreal_0(F,G)
                                      & r1_xreal_0(G,E)
                                      & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,G)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F))
                                      & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,G)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,G)) ) ) ) ) ) ) ) ) ) )).

fof(t14_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k3_finseq_1(k1_jordan8(B,A)))
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r1_xreal_0(D,F)
                                  & r1_xreal_0(F,E)
                                  & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C)) ) ) ) ) ) ) ) ) )).

fof(t15_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k3_finseq_1(k1_jordan8(B,A)))
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r1_xreal_0(D,F)
                                  & r1_xreal_0(F,E)
                                  & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C)) ) ) ) ) ) ) ) ) )).

fof(t16_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k3_finseq_1(k1_jordan8(B,A)))
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ~ ( r1_xreal_0(D,F)
                                      & r1_xreal_0(F,G)
                                      & r1_xreal_0(G,E)
                                      & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),G,C)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C))
                                      & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),G,C)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),G,C)) ) ) ) ) ) ) ) ) ) )).

fof(t17_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r1_xreal_0(D,F)
                                  & r1_xreal_0(F,E)
                                  & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)) ) ) ) ) ) ) ) ) )).

fof(t18_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r1_xreal_0(D,F)
                                  & r1_xreal_0(F,E)
                                  & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)) ) ) ) ) ) ) ) ) )).

fof(t19_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ~ ( r1_xreal_0(D,F)
                                      & r1_xreal_0(F,G)
                                      & r1_xreal_0(G,E)
                                      & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,G)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F))
                                      & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,G)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,G)) ) ) ) ) ) ) ) ) ) )).

fof(t20_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k3_finseq_1(k1_jordan8(B,A)))
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r1_xreal_0(D,F)
                                  & r1_xreal_0(F,E)
                                  & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C)) ) ) ) ) ) ) ) ) )).

fof(t21_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k3_finseq_1(k1_jordan8(B,A)))
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r1_xreal_0(D,F)
                                  & r1_xreal_0(F,E)
                                  & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C)) ) ) ) ) ) ) ) ) )).

fof(t22_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k3_finseq_1(k1_jordan8(B,A)))
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ~ ( r1_xreal_0(D,F)
                                      & r1_xreal_0(F,G)
                                      & r1_xreal_0(G,E)
                                      & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),G,C)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C))
                                      & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),G,C)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),G,C)) ) ) ) ) ) ) ) ) ) )).

fof(t23_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(C,np__1)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) )).

fof(t24_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(C,np__1)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) )).

fof(t25_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(C,np__1)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
                          & ~ r1_xreal_0(A,np__0)
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) )).

fof(t26_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(C,np__1)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
                          & ~ r1_xreal_0(A,np__0)
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) )).

fof(t27_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(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(C,D)
                      & r1_xreal_0(D,k1_matrix_1(k1_jordan8(B,k1_nat_1(A,np__1))))
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),C),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                      & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D)),k9_jordan6(B)) ) ) ) ) ) )).

fof(t28_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(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(C,D)
                      & r1_xreal_0(D,k1_matrix_1(k1_jordan8(B,k1_nat_1(A,np__1))))
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),C),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                      & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D)),k8_jordan6(B)) ) ) ) ) ) )).

fof(t29_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & D = E ) ) ) ) ) ) )).

fof(t30_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C))
                          & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) )).

fof(t31_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C))
                          & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) )).

fof(t32_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) )).

fof(t33_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) )).

fof(t34_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & ~ r1_xreal_0(A,np__0)
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) )).

fof(t35_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & ~ r1_xreal_0(A,np__0)
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) )).

fof(t36_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( ~ r1_xreal_0(C,np__1)
                      & r1_xreal_0(C,D)
                      & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),D)
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                      & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))))),k9_jordan6(B)) ) ) ) ) ) )).

fof(t37_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( ~ r1_xreal_0(C,np__1)
                      & r1_xreal_0(C,D)
                      & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),D)
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                      & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))))),k8_jordan6(B)) ) ) ) ) ) )).

fof(t38_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C))
                          & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) )).

fof(t39_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C))
                          & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) )).

fof(t40_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) )).

fof(t41_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) )).

fof(t42_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & ~ r1_xreal_0(A,np__0)
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) )).

fof(t43_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
                          & ~ r1_xreal_0(A,np__0)
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
                          & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) )).

fof(t44_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( ~ r1_xreal_0(C,np__1)
                      & r1_xreal_0(C,D)
                      & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),D)
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                      & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))))),k9_jordan6(B)) ) ) ) ) ) )).

fof(t45_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( ~ r1_xreal_0(C,np__1)
                      & r1_xreal_0(C,D)
                      & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),D)
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                      & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))))),k8_jordan6(B)) ) ) ) ) ) )).

fof(t46_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ~ ( ~ r1_xreal_0(C,np__1)
                              & r1_xreal_0(C,D)
                              & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),D)
                              & r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,F)
                              & r1_xreal_0(F,k1_matrix_1(k1_jordan8(B,A)))
                              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))
                              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
                              & r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k8_jordan6(B)) ) ) ) ) ) ) ) )).

fof(t47_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ~ ( ~ r1_xreal_0(C,np__1)
                              & r1_xreal_0(C,D)
                              & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),D)
                              & r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,F)
                              & r1_xreal_0(F,k1_matrix_1(k1_jordan8(B,A)))
                              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))
                              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
                              & r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k9_jordan6(B)) ) ) ) ) ) ) ) )).

fof(t48_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ~ ( ~ r1_xreal_0(D,np__1)
                              & r1_xreal_0(D,C)
                              & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
                              & r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,F)
                              & r1_xreal_0(F,k1_matrix_1(k1_jordan8(B,A)))
                              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))
                              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
                              & r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k8_jordan6(B)) ) ) ) ) ) ) ) )).

fof(t49_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ~ ( ~ r1_xreal_0(D,np__1)
                              & r1_xreal_0(D,C)
                              & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
                              & r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,F)
                              & r1_xreal_0(F,k1_matrix_1(k1_jordan8(B,A)))
                              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))
                              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
                              & r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k9_jordan6(B)) ) ) ) ) ) ) ) )).

fof(t50_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ~ ( ~ r1_xreal_0(C,np__1)
                              & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),C)
                              & ~ r1_xreal_0(D,np__1)
                              & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),D)
                              & r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,F)
                              & r1_xreal_0(F,k1_matrix_1(k1_jordan8(B,k1_nat_1(A,np__1))))
                              & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,F),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                              & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,E),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                              & r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,F))),k8_jordan6(B)) ) ) ) ) ) ) ) )).

fof(t51_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ~ ( ~ r1_xreal_0(C,np__1)
                              & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),C)
                              & ~ r1_xreal_0(D,np__1)
                              & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),D)
                              & r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,F)
                              & r1_xreal_0(F,k1_matrix_1(k1_jordan8(B,k1_nat_1(A,np__1))))
                              & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,F),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                              & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,E),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                              & r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,F))),k9_jordan6(B)) ) ) ) ) ) ) ) )).

fof(t52_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(C,np__1)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),C)
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,k1_nat_1(A,np__1))))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,E),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                          & r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),E)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,E))),k8_jordan6(B)) ) ) ) ) ) ) )).

fof(t53_jordan15,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(C,np__1)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),C)
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,k1_nat_1(A,np__1))))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,E),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                          & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
                          & r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),E)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,E))),k9_jordan6(B)) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------