SET007 Axioms: SET007+720.ax


%------------------------------------------------------------------------------
% File     : SET007+720 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Upper and Lower Sequence on the Cage, Upper and Lower Arcs
% 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    : jordan1j [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   66 (   0 unit)
%            Number of atoms       :  651 (  63 equality)
%            Maximal formula depth :   20 (  10 average)
%            Number of connectives :  711 ( 126 ~  ;   5  |; 363  &)
%                                         (   0 <=>; 217 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   37 (   0 propositional; 1-3 arity)
%            Number of functors    :   63 (   6 constant; 0-4 arity)
%            Number of variables   :  179 (   0 singleton; 177 !;   2 ?)
%            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(fc1_jordan1j,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k3_graph_2(A,B))
        & v1_relat_1(k3_graph_2(A,B))
        & v1_funct_1(k3_graph_2(A,B))
        & v1_finset_1(k3_graph_2(A,B))
        & v1_finseq_1(k3_graph_2(A,B)) ) ) )).

fof(rc1_jordan1j,axiom,(
    ? [A] :
      ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
      & ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & ~ v1_realset1(A)
      & ~ v5_seqm_3(A)
      & v1_topreal1(A)
      & v2_topreal1(A)
      & v3_topreal1(A)
      & v4_topreal1(A)
      & v1_goboard5(A)
      & v2_goboard5(A) ) )).

fof(t1_jordan1j,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,D)
                          & r1_xreal_0(D,k1_matrix_1(A))
                          & r1_xreal_0(np__1,E)
                          & r1_xreal_0(E,k1_matrix_1(A))
                          & r1_xreal_0(np__1,B)
                          & ~ r1_xreal_0(C,B)
                          & r1_xreal_0(C,k3_finseq_1(A))
                          & r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,E)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,D))) ) ) ) ) ) ) )).

fof(t2_jordan1j,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,k3_finseq_1(A))
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(A))
                          & r1_xreal_0(np__1,D)
                          & ~ r1_xreal_0(E,D)
                          & r1_xreal_0(E,k1_matrix_1(A))
                          & r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,E)),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,D))) ) ) ) ) ) ) )).

fof(t3_jordan1j,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)
         => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_finseq_5(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))),k5_topreal1(np__2,k2_finseq_5(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))))) = k2_struct_0(k15_euclid(np__2),k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) )).

fof(t4_jordan1j,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)))) )
         => k1_jordan1e(B,A) = k2_finseq_5(u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) )).

fof(t5_jordan1j,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)))) )
         => ( r2_hidden(k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k1_jordan1e(B,A)))
            & r2_hidden(k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) )).

fof(t6_jordan1j,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)))) )
         => ( r2_hidden(k31_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k1_jordan1e(B,A)))
            & r2_hidden(k31_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) )).

fof(t7_jordan1j,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)))) )
         => ( r2_hidden(k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k1_jordan1e(B,A)))
            & r2_hidden(k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) )).

fof(t8_jordan1j,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)))) )
         => ( r2_hidden(k33_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k1_jordan1e(B,A)))
            & r2_hidden(k33_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) )).

fof(t9_jordan1j,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)))) )
         => ( r2_hidden(k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k1_jordan1e(B,A)))
            & r2_hidden(k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) )).

fof(t10_jordan1j,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)))) )
         => ( r2_hidden(k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k2_jordan1e(B,A)))
            & r2_hidden(k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) )).

fof(t11_jordan1j,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)))) )
         => ( r2_hidden(k35_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k2_jordan1e(B,A)))
            & r2_hidden(k35_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) )).

fof(t12_jordan1j,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)))) )
         => ( r2_hidden(k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k2_jordan1e(B,A)))
            & r2_hidden(k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) )).

fof(t13_jordan1j,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)))) )
         => ( r2_hidden(k37_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k2_jordan1e(B,A)))
            & r2_hidden(k37_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) )).

fof(t14_jordan1j,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)))) )
         => ( r2_hidden(k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k2_jordan1e(B,A)))
            & r2_hidden(k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) )).

fof(t15_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ( r1_tarski(A,B)
              & r2_hidden(k32_pscomp_1(B),A) )
           => k32_pscomp_1(A) = k32_pscomp_1(B) ) ) ) )).

fof(t16_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ( r1_tarski(A,B)
              & r2_hidden(k33_pscomp_1(B),A) )
           => k33_pscomp_1(A) = k33_pscomp_1(B) ) ) ) )).

fof(t17_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ( r1_tarski(A,B)
              & r2_hidden(k35_pscomp_1(B),A) )
           => k35_pscomp_1(A) = k35_pscomp_1(B) ) ) ) )).

fof(t18_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ( r1_tarski(A,B)
              & r2_hidden(k34_pscomp_1(B),A) )
           => k34_pscomp_1(A) = k34_pscomp_1(B) ) ) ) )).

fof(t19_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ( r1_tarski(A,B)
              & r2_hidden(k37_pscomp_1(B),A) )
           => k37_pscomp_1(A) = k37_pscomp_1(B) ) ) ) )).

fof(t20_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ( r1_tarski(A,B)
              & r2_hidden(k36_pscomp_1(B),A) )
           => k36_pscomp_1(A) = k36_pscomp_1(B) ) ) ) )).

fof(t21_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ( r1_tarski(A,B)
              & r2_hidden(k30_pscomp_1(B),A) )
           => k30_pscomp_1(A) = k30_pscomp_1(B) ) ) ) )).

fof(t22_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ( r1_tarski(A,B)
              & r2_hidden(k31_pscomp_1(B),A) )
           => k31_pscomp_1(A) = k31_pscomp_1(B) ) ) ) )).

fof(t23_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_xreal_0(k19_pscomp_1(A),k19_pscomp_1(B))
           => k19_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k19_pscomp_1(B) ) ) ) )).

fof(t24_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_xreal_0(k20_pscomp_1(A),k20_pscomp_1(B))
           => k20_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k20_pscomp_1(B) ) ) ) )).

fof(t25_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_xreal_0(k21_pscomp_1(A),k21_pscomp_1(B))
           => k21_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k21_pscomp_1(A) ) ) ) )).

fof(t26_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_xreal_0(k18_pscomp_1(A),k18_pscomp_1(B))
           => k18_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k18_pscomp_1(A) ) ) ) )).

fof(t27_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ~ r1_xreal_0(k19_pscomp_1(B),k19_pscomp_1(A))
           => k32_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k32_pscomp_1(B) ) ) ) )).

fof(t28_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ~ r1_xreal_0(k19_pscomp_1(B),k19_pscomp_1(A))
           => k33_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k33_pscomp_1(B) ) ) ) )).

fof(t29_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ~ r1_xreal_0(k20_pscomp_1(B),k20_pscomp_1(A))
           => k35_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k35_pscomp_1(B) ) ) ) )).

fof(t30_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ~ r1_xreal_0(k20_pscomp_1(B),k20_pscomp_1(A))
           => k34_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k34_pscomp_1(B) ) ) ) )).

fof(t31_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ~ r1_xreal_0(k21_pscomp_1(B),k21_pscomp_1(A))
           => k37_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k37_pscomp_1(A) ) ) ) )).

fof(t32_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ~ r1_xreal_0(k21_pscomp_1(B),k21_pscomp_1(A))
           => k36_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k36_pscomp_1(A) ) ) ) )).

fof(t33_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ~ r1_xreal_0(k18_pscomp_1(B),k18_pscomp_1(A))
           => k30_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k30_pscomp_1(A) ) ) ) )).

fof(t34_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ~ r1_xreal_0(k18_pscomp_1(B),k18_pscomp_1(A))
           => k31_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k31_pscomp_1(A) ) ) ) )).

fof(t35_jordan1j,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v4_topreal1(A)
              & r2_hidden(B,k5_topreal1(np__2,A)) )
           => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k3_jordan3(A,B),k3_finseq_1(k3_jordan3(A,B))) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) ) ) ) )).

fof(t36_jordan1j,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_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] :
                  ( ( v2_connsp_1(D,k15_euclid(np__2))
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                 => ~ ( r2_hidden(B,k3_goboard9(A))
                      & r2_hidden(C,k2_goboard9(A))
                      & r2_hidden(B,D)
                      & r2_hidden(C,D)
                      & r1_xboole_0(D,k5_topreal1(np__2,A)) ) ) ) ) ) )).

fof(t37_jordan1j,axiom,(
    ! [A] :
      ( ( v4_topreal1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,k2_relat_1(A))
           => k3_jordan3(A,B) = k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k5_finseq_4(A,B),k3_finseq_1(A)) ) ) ) )).

fof(t38_jordan1j,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] :
          ( ( v4_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
               => ( r2_hidden(C,k2_relat_1(B))
                 => r1_goboard1(u1_struct_0(k15_euclid(np__2)),k4_jordan3(B,C),A) ) ) ) ) ) )).

fof(t39_jordan1j,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] :
          ( ( v4_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
               => ( r2_hidden(C,k2_relat_1(B))
                 => r1_goboard1(u1_struct_0(k15_euclid(np__2)),k3_jordan3(B,C),A) ) ) ) ) ) )).

fof(t40_jordan1j,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_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ( r1_xreal_0(np__1,C)
                        & r1_xreal_0(C,k3_finseq_1(A))
                        & r1_xreal_0(np__1,D)
                        & r1_xreal_0(D,k1_matrix_1(A))
                        & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D),k5_topreal1(np__2,B)) )
                     => r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D),k2_relat_1(B)) ) ) ) ) ) ) )).

fof(t41_jordan1j,axiom,(
    ! [A] :
      ( ( v4_topreal1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v2_topreal1(B)
              & v3_topreal1(B)
              & v2_funct_1(B)
              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(A)) )
                   => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,C),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))) = k1_xboole_0 ) )
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__2,C)
                      & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(B)) )
                   => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,B,C),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))) = k1_xboole_0 ) ) )
           => v1_goboard5(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t42_jordan1j,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(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)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan8(B,A)))
              & r2_hidden(k30_pscomp_1(B),k3_goboard5(k1_jordan8(B,A),np__1,C))
              & k30_pscomp_1(B) != k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),np__2,C) ) ) ) )).

fof(t43_jordan1j,axiom,(
    ! [A] :
      ( ( v4_topreal1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( r2_hidden(B,k5_topreal1(np__2,A))
              & r2_hidden(k1_funct_1(A,k3_finseq_1(A)),k5_topreal1(np__2,k4_jordan3(A,B))) )
           => k1_funct_1(A,k3_finseq_1(A)) = B ) ) ) )).

fof(t44_jordan1j,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => k4_jordan3(A,B) != k1_xboole_0 ) ) )).

fof(t45_jordan1j,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,k5_topreal1(np__2,A))
           => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k4_jordan3(A,B),k3_finseq_1(k4_jordan3(A,B))) = B ) ) ) )).

fof(t46_jordan1j,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] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r2_hidden(C,k5_topreal1(np__2,k1_jordan1e(B,A)))
                  & k21_euclid(C) = k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) )
               => C = k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) )).

fof(t47_jordan1j,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] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r2_hidden(C,k5_topreal1(np__2,k2_jordan1e(B,A)))
                  & k21_euclid(C) = k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) )
               => C = k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) )).

fof(t48_jordan1j,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_finseq_1(B,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_goboard1(u1_struct_0(k15_euclid(np__2)),k8_finseq_1(u1_struct_0(k15_euclid(np__2)),B,C),A) )
                   => ( r1_xreal_0(k3_finseq_1(B),D)
                      | ( k4_gobrd13(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),B,C),A,D) = k4_gobrd13(B,A,D)
                        & k3_gobrd13(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),B,C),A,D) = k3_gobrd13(B,A,D) ) ) ) ) ) ) ) )).

fof(t49_jordan1j,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ! [C] :
          ( m2_finseq_1(C,A)
         => ! [D] :
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => ( r1_xreal_0(D,k3_finseq_1(B))
               => k16_finseq_1(A,k4_graph_2(A,B,C),D) = k16_finseq_1(A,B,D) ) ) ) ) )).

fof(t50_jordan1j,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ! [C] :
          ( m2_finseq_1(C,A)
         => k16_finseq_1(A,k4_graph_2(A,B,C),k3_finseq_1(B)) = B ) ) )).

fof(t51_jordan1j,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_finseq_1(B,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_goboard1(u1_struct_0(k15_euclid(np__2)),k4_graph_2(u1_struct_0(k15_euclid(np__2)),B,C),A) )
                   => ( r1_xreal_0(k3_finseq_1(B),D)
                      | ( k4_gobrd13(k4_graph_2(u1_struct_0(k15_euclid(np__2)),B,C),A,D) = k4_gobrd13(B,A,D)
                        & k3_gobrd13(k4_graph_2(u1_struct_0(k15_euclid(np__2)),B,C),A,D) = k3_gobrd13(B,A,D) ) ) ) ) ) ) ) )).

fof(t52_jordan1j,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] :
          ( ( v4_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ! [C] :
              ( m1_subset_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_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
                      & r2_hidden(C,k2_relat_1(B)) )
                   => ( r1_xreal_0(k5_finseq_4(B,C),D)
                      | ( k4_gobrd13(k4_jordan3(B,C),A,D) = k4_gobrd13(B,A,D)
                        & k3_gobrd13(k4_jordan3(B,C),A,D) = k3_gobrd13(B,A,D) ) ) ) ) ) ) ) )).

fof(t53_jordan1j,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_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_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_goboard1(u1_struct_0(k15_euclid(np__2)),B,A) )
                   => ( r1_xreal_0(k5_finseq_4(B,C),D)
                      | ( k4_gobrd13(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),B,C),A,D) = k4_gobrd13(B,A,D)
                        & k3_gobrd13(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),B,C),A,D) = k3_gobrd13(B,A,D) ) ) ) ) ) ) ) )).

fof(t54_jordan1j,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v2_topreal1(A)
              & v3_topreal1(A)
              & v2_funct_1(A)
              & v2_topreal1(B)
              & v3_topreal1(B)
              & v2_funct_1(B)
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)
              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) )
           => v3_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t55_jordan1j,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v2_funct_1(A)
              & v2_funct_1(B)
              & r1_tarski(k3_xboole_0(k2_relat_1(A),k2_relat_1(B)),k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))) )
           => v2_funct_1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t56_jordan1j,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v4_topreal1(A)
              & r2_hidden(B,k2_relat_1(A)) )
           => ( B = k1_funct_1(A,np__1)
              | k1_nat_1(k2_jordan3(A,B),np__1) = k5_finseq_4(A,B) ) ) ) ) )).

fof(t57_jordan1j,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(C,np__1)
                          & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
                          & r1_xreal_0(np__1,D)
                          & 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)))
                          & D = E ) ) ) ) ) ) )).

fof(t58_jordan1j,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)))
                          & 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)),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,D),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,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(t59_jordan1j,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)))
                          & 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)),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,D),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,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(t60_jordan1j,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)),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,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)),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,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(t61_jordan1j,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)),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,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)),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,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(t62_jordan1j,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),k8_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)),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)),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1))))) ) ) ) ) )).

fof(t63_jordan1j,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))))
                      & 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,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(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1))))) = k1_struct_0(k15_euclid(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))
                      & 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,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(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1))))) = k1_struct_0(k15_euclid(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))
                      & 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(t64_jordan1j,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))))
                      & 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,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(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1))))) = k1_struct_0(k15_euclid(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))
                      & 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,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(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1))))) = k1_struct_0(k15_euclid(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))
                      & 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)) ) ) ) ) ) )).
%------------------------------------------------------------------------------