SET007 Axioms: SET007+794.ax


%------------------------------------------------------------------------------
% File     : SET007+794 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Upper and Lower Approximations of the 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    : jordan19 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   36 (   0 unit)
%            Number of atoms       :  385 (  27 equality)
%            Maximal formula depth :   23 (  14 average)
%            Number of connectives :  437 (  88 ~  ;   1  |; 208  &)
%                                         (   3 <=>; 137 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   22 (   0 propositional; 1-3 arity)
%            Number of functors    :   46 (   5 constant; 0-4 arity)
%            Number of variables   :  132 (   0 singleton; 132 !;   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(d1_jordan19,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( B = k1_jordan19(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,C) = k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,C))) ) ) ) ) )).

fof(d2_jordan19,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( B = k2_jordan19(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,C) = k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,C))) ) ) ) ) )).

fof(d3_jordan19,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k3_jordan19(A) = k8_kurato_2(k15_euclid(np__2),k1_jordan19(A)) ) )).

fof(d4_jordan19,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k4_jordan19(A) = k8_kurato_2(k15_euclid(np__2),k2_jordan19(A)) ) )).

fof(t1_jordan19,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => ( A = np__0
              | r1_xreal_0(k6_real_1(k1_nat_1(B,np__1),B),k6_real_1(k1_nat_1(A,np__1),A)) ) ) ) ) )).

fof(t2_jordan19,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( 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)
                 => ( ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,A)
                      & r1_xreal_0(np__1,D)
                      & r1_xreal_0(D,k1_matrix_1(k1_jordan8(B,A))) )
                   => r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),k1_matrix_1(k1_jordan8(B,A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),D)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,C),k1_jordan1a(k1_jordan8(B,C)),k1_matrix_1(k1_jordan8(B,C))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),D))) ) ) ) ) ) )).

fof(t3_jordan19,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)
                 => ~ ( 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,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_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,k1_matrix_1(k1_jordan8(B,A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) ) ) )).

fof(t4_jordan19,axiom,(
    ! [A] :
      ( ( v2_connsp_1(A,k15_euclid(np__2))
        & v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(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)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ~ ( r1_xreal_0(np__1,C)
                        & r1_xreal_0(C,k3_finseq_1(k1_jordan8(A,B)))
                        & r1_xreal_0(np__1,D)
                        & r1_xreal_0(D,k1_matrix_1(k1_jordan8(A,B)))
                        & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),C,D),k5_topreal1(np__2,k1_jordan9(A,B)))
                        & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),C,k1_matrix_1(k1_jordan8(A,B))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),C,D)),k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ) ) ) ) )).

fof(t5_jordan19,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)
             => ~ ( 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)))))
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(C,k1_matrix_1(k1_jordan8(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,np__1),k1_jordan1a(k1_jordan8(B,np__1)),k1_matrix_1(k1_jordan8(B,np__1))),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)),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1))))) ) ) ) ) )).

fof(t6_jordan19,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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(np__1,D)
                      & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(C))
                      & r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(B,A))
                      & k1_gobrd14(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1))) != k6_real_1(k5_real_1(k19_pscomp_1(B),k21_pscomp_1(B)),k1_card_4(np__2,A))
                      & k1_gobrd14(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1))) != k6_real_1(k5_real_1(k20_pscomp_1(B),k18_pscomp_1(B)),k1_card_4(np__2,A)) ) ) ) ) ) )).

fof(t7_jordan19,axiom,(
    ! [A] :
      ( ( v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_hidden(C,k9_metric_1(A,E,B))
                          & r2_hidden(D,k9_metric_1(A,E,B))
                          & r1_xreal_0(k3_xcmplx_0(np__2,B),k4_metric_1(A,C,D)) ) ) ) ) ) ) )).

fof(t8_jordan19,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
                 => ( C = D
                   => ! [E] :
                        ( v1_xreal_0(E)
                       => ( ~ r1_xreal_0(E,np__0)
                         => ( r2_hidden(C,k6_pre_topc(k15_euclid(A),B))
                          <=> ! [F] :
                                ( v1_xreal_0(F)
                               => ~ ( ~ r1_xreal_0(F,np__0)
                                    & ~ r1_xreal_0(E,F)
                                    & r1_xboole_0(k9_metric_1(k14_euclid(A),D,F),B) ) ) ) ) ) ) ) ) ) ) )).

fof(t9_jordan19,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)))) )
         => ~ r1_xreal_0(k19_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k19_pscomp_1(B)) ) ) )).

fof(t10_jordan19,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)))) )
         => ~ r1_xreal_0(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k20_pscomp_1(B)) ) ) )).

fof(t11_jordan19,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)))) )
         => ~ r1_xreal_0(k21_pscomp_1(B),k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) )).

fof(t12_jordan19,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)))) )
         => ~ r1_xreal_0(k18_pscomp_1(B),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) )).

fof(t13_jordan19,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,E)
                          & r1_xreal_0(E,D)
                          & r1_xreal_0(D,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),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),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,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,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),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,D))
                          & r2_subset_1(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,D)),k8_jordan6(B)) ) ) ) ) ) ) )).

fof(t14_jordan19,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,E)
                          & r1_xreal_0(E,D)
                          & r1_xreal_0(D,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),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),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,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,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),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,D))
                          & r2_subset_1(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,D)),k9_jordan6(B)) ) ) ) ) ) ) )).

fof(t15_jordan19,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)
                          & 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,E)),k9_jordan6(k5_topreal1(np__2,k1_jordan9(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))
                          & 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,E)),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D))
                          & 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(t16_jordan19,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)
                          & 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,E)),k9_jordan6(k5_topreal1(np__2,k1_jordan9(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))
                          & 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,E)),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D))
                          & 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(t17_jordan19,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,k2_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,k1_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(t18_jordan19,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,k2_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,k1_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(t19_jordan19,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),k9_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),k8_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(t20_jordan19,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),k9_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),k8_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(t21_jordan19,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),C,E))
                              & 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),D,F))
                              & 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(t22_jordan19,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),C,E))
                              & 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),D,F))
                              & 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(t23_jordan19,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),C,E))
                              & 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),D,F))
                              & 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(t24_jordan19,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),C,E))
                              & 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),D,F))
                              & 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(t25_jordan19,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),k9_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),k8_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(t26_jordan19,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),k9_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),k8_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(t27_jordan19,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( ~ r1_xreal_0(k21_euclid(B),k18_pscomp_1(A))
              & ~ r1_xreal_0(k20_pscomp_1(A),k21_euclid(B))
              & r2_hidden(B,k3_jordan19(A))
              & r2_hidden(B,k4_jordan19(A)) ) ) ) )).

fof(t28_jordan19,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( k21_euclid(B) = k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)
              & r2_hidden(B,k3_jordan19(A))
              & r2_hidden(B,k4_jordan19(A)) ) ) ) )).

fof(dt_k1_jordan19,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( v1_funct_1(k1_jordan19(A))
        & v1_funct_2(k1_jordan19(A),k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(k1_jordan19(A),k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) )).

fof(dt_k2_jordan19,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( v1_funct_1(k2_jordan19(A))
        & v1_funct_2(k2_jordan19(A),k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(k2_jordan19(A),k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) )).

fof(dt_k3_jordan19,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => m1_subset_1(k3_jordan19(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k4_jordan19,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => m1_subset_1(k4_jordan19(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).
%------------------------------------------------------------------------------