SET007 Axioms: SET007+701.ax


%------------------------------------------------------------------------------
% File     : SET007+701 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Upper and Lower Sequence of a 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    : jordan1e [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   36 (   0 unit)
%            Number of atoms       :  273 (  21 equality)
%            Maximal formula depth :   14 (   8 average)
%            Number of connectives :  301 (  64 ~  ;   0  |; 151  &)
%                                         (   0 <=>;  86 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   24 (   0 propositional; 1-3 arity)
%            Number of functors    :   42 (   6 constant; 0-4 arity)
%            Number of variables   :   78 (   0 singleton;  78 !;   0 ?)
%            Maximal term depth    :    8 (   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_jordan1e,axiom,(
    ! [A,B] :
      ( ( 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))))
        & m1_subset_1(B,k5_numbers) )
     => ( ~ v1_xboole_0(k1_jordan1e(A,B))
        & v1_relat_1(k1_jordan1e(A,B))
        & v1_funct_1(k1_jordan1e(A,B))
        & v1_finset_1(k1_jordan1e(A,B))
        & v1_finseq_1(k1_jordan1e(A,B)) ) ) )).

fof(fc2_jordan1e,axiom,(
    ! [A,B] :
      ( ( 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))))
        & m1_subset_1(B,k5_numbers) )
     => ( ~ v1_xboole_0(k2_jordan1e(A,B))
        & v1_relat_1(k2_jordan1e(A,B))
        & v1_funct_1(k2_jordan1e(A,B))
        & v1_finset_1(k2_jordan1e(A,B))
        & v1_finseq_1(k2_jordan1e(A,B)) ) ) )).

fof(fc3_jordan1e,axiom,(
    ! [A,B] :
      ( ( 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))))
        & m1_subset_1(B,k5_numbers) )
     => ( ~ v1_xboole_0(k1_jordan1e(A,B))
        & v1_relat_1(k1_jordan1e(A,B))
        & v1_funct_1(k1_jordan1e(A,B))
        & v2_funct_1(k1_jordan1e(A,B))
        & v1_finset_1(k1_jordan1e(A,B))
        & v1_finseq_1(k1_jordan1e(A,B))
        & v1_topreal1(k1_jordan1e(A,B))
        & v2_topreal1(k1_jordan1e(A,B))
        & v3_topreal1(k1_jordan1e(A,B)) ) ) )).

fof(fc4_jordan1e,axiom,(
    ! [A,B] :
      ( ( 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))))
        & m1_subset_1(B,k5_numbers) )
     => ( ~ v1_xboole_0(k2_jordan1e(A,B))
        & v1_relat_1(k2_jordan1e(A,B))
        & v1_funct_1(k2_jordan1e(A,B))
        & v2_funct_1(k2_jordan1e(A,B))
        & v1_finset_1(k2_jordan1e(A,B))
        & v1_finseq_1(k2_jordan1e(A,B))
        & v1_topreal1(k2_jordan1e(A,B))
        & v2_topreal1(k2_jordan1e(A,B))
        & v3_topreal1(k2_jordan1e(A,B)) ) ) )).

fof(fc5_jordan1e,axiom,(
    ! [A,B] :
      ( ( 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))))
        & m1_subset_1(B,k5_numbers) )
     => ( ~ v1_xboole_0(k1_jordan1e(A,B))
        & v1_relat_1(k1_jordan1e(A,B))
        & v1_funct_1(k1_jordan1e(A,B))
        & v2_funct_1(k1_jordan1e(A,B))
        & v1_finset_1(k1_jordan1e(A,B))
        & v1_finseq_1(k1_jordan1e(A,B))
        & ~ v1_realset1(k1_jordan1e(A,B))
        & v1_topreal1(k1_jordan1e(A,B))
        & v2_topreal1(k1_jordan1e(A,B))
        & v3_topreal1(k1_jordan1e(A,B))
        & v4_topreal1(k1_jordan1e(A,B)) ) ) )).

fof(fc6_jordan1e,axiom,(
    ! [A,B] :
      ( ( 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))))
        & m1_subset_1(B,k5_numbers) )
     => ( ~ v1_xboole_0(k2_jordan1e(A,B))
        & v1_relat_1(k2_jordan1e(A,B))
        & v1_funct_1(k2_jordan1e(A,B))
        & v2_funct_1(k2_jordan1e(A,B))
        & v1_finset_1(k2_jordan1e(A,B))
        & v1_finseq_1(k2_jordan1e(A,B))
        & ~ v1_realset1(k2_jordan1e(A,B))
        & v1_topreal1(k2_jordan1e(A,B))
        & v2_topreal1(k2_jordan1e(A,B))
        & v3_topreal1(k2_jordan1e(A,B))
        & v4_topreal1(k2_jordan1e(A,B)) ) ) )).

fof(t1_jordan1e,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_tarski(A,B)
           => r1_xreal_0(k19_pscomp_1(A),k19_pscomp_1(B)) ) ) ) )).

fof(t2_jordan1e,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_tarski(A,B)
           => r1_xreal_0(k20_pscomp_1(A),k20_pscomp_1(B)) ) ) ) )).

fof(t3_jordan1e,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_tarski(A,B)
           => r1_xreal_0(k21_pscomp_1(B),k21_pscomp_1(A)) ) ) ) )).

fof(t4_jordan1e,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_tarski(A,B)
           => r1_xreal_0(k18_pscomp_1(B),k18_pscomp_1(A)) ) ) ) )).

fof(t5_jordan1e,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)))
         => ( r1_sprect_2(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
               => ( r2_hidden(C,k2_relat_1(A))
                 => r1_sprect_2(B,k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,C)) ) ) ) ) ) )).

fof(t6_jordan1e,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)))
         => ( r1_sprect_2(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
               => ( r2_hidden(C,k2_relat_1(A))
                 => r1_sprect_2(B,k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,C)) ) ) ) ) ) )).

fof(t7_jordan1e,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))
              & k3_jordan3(A,B) = k1_xboole_0 ) ) ) )).

fof(t8_jordan1e,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))
              & r1_xreal_0(np__2,k3_finseq_1(k4_jordan3(A,B))) )
           => r2_hidden(k1_funct_1(A,np__1),k5_topreal1(np__2,k4_jordan3(A,B))) ) ) ) )).

fof(t9_jordan1e,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v4_topreal1(A)
       => ! [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,np__1),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,B),np__1),k3_finseq_1(A)))) ) ) ) ) )).

fof(t10_jordan1e,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( k1_nat_1(A,B) = k1_nat_1(C,D)
                      & r1_xreal_0(A,C)
                      & r1_xreal_0(B,D) )
                   => A = C ) ) ) ) ) )).

fof(t11_jordan1e,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v4_topreal1(A)
       => ! [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,np__1),k5_topreal1(np__2,k3_jordan3(A,B))) )
             => k1_funct_1(A,np__1) = B ) ) ) ) )).

fof(d1_jordan1e,axiom,(
    ! [A] :
      ( ( 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)
         => k1_jordan1e(A,B) = k1_finseq_5(u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) )).

fof(t12_jordan1e,axiom,(
    ! [A] :
      ( ( 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)
         => k3_finseq_1(k1_jordan1e(A,B)) = k5_finseq_4(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) )).

fof(d2_jordan1e,axiom,(
    ! [A] :
      ( ( 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)
         => k2_jordan1e(A,B) = k2_finseq_5(u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) )).

fof(t13_jordan1e,axiom,(
    ! [A] :
      ( ( 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)
         => k3_finseq_1(k2_jordan1e(A,B)) = k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))),k5_finseq_4(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))),np__1) ) ) )).

fof(t14_jordan1e,axiom,(
    ! [A] :
      ( ( 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)
         => k1_nat_1(k3_finseq_1(k1_jordan1e(A,B)),k3_finseq_1(k2_jordan1e(A,B))) = k1_nat_1(k3_finseq_1(k1_jordan9(A,B)),np__1) ) ) )).

fof(t15_jordan1e,axiom,(
    ! [A] :
      ( ( 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)
         => k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) = k4_graph_2(u1_struct_0(k15_euclid(np__2)),k1_jordan1e(A,B),k2_jordan1e(A,B)) ) ) )).

fof(t16_jordan1e,axiom,(
    ! [A] :
      ( ( 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_topreal1(np__2,k1_jordan9(A,B)) = k5_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),k1_jordan1e(A,B),k2_jordan1e(A,B))) ) ) )).

fof(t17_jordan1e,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & 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_topreal1(np__2,k1_jordan9(A,B)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan1e(A,B)),k5_topreal1(np__2,k2_jordan1e(A,B))) ) ) )).

fof(t18_jordan1e,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k30_pscomp_1(A) != k35_pscomp_1(A) ) )).

fof(t19_jordan1e,axiom,(
    ! [A] :
      ( ( 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(np__3,k3_finseq_1(k1_jordan1e(A,B)))
            & r1_xreal_0(np__3,k3_finseq_1(k2_jordan1e(A,B))) ) ) ) )).

fof(t20_jordan1e,axiom,(
    ! [A] :
      ( ( 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_jordan1e(A,B)),k5_topreal1(np__2,k2_jordan1e(A,B))) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) )).

fof(t21_jordan1e,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)))) )
         => r1_sprect_2(k1_jordan9(B,A),k1_jordan1e(B,A)) ) ) )).

fof(t22_jordan1e,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)))) )
         => r1_sprect_2(k1_jordan9(B,A),k2_jordan1e(B,A)) ) ) )).

fof(t23_jordan1e,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)))) )
         => k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),np__2)) = k19_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) )).

fof(t24_jordan1e,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)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan9(B,A)))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),C) = k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) )
               => k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k1_nat_1(C,np__1))) = k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) )).

fof(t25_jordan1e,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)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan9(B,A)))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),C) = k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) )
               => k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k1_nat_1(C,np__1))) = k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) )).

fof(t26_jordan1e,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)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan9(B,A)))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),C) = k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) )
               => k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k1_nat_1(C,np__1))) = k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) )).

fof(dt_k1_jordan1e,axiom,(
    ! [A,B] :
      ( ( 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))))
        & m1_subset_1(B,k5_numbers) )
     => m2_finseq_1(k1_jordan1e(A,B),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k2_jordan1e,axiom,(
    ! [A,B] :
      ( ( 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))))
        & m1_subset_1(B,k5_numbers) )
     => m2_finseq_1(k2_jordan1e(A,B),u1_struct_0(k15_euclid(np__2))) ) )).
%------------------------------------------------------------------------------