SET007 Axioms: SET007+707.ax


%------------------------------------------------------------------------------
% File     : SET007+707 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Upper and Lower Sequence on the Cage. Part II
% 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    : jordan1g [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   69 (   8 unit)
%            Number of atoms       :  542 (  62 equality)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :  650 ( 177 ~  ;  12  |; 309  &)
%                                         (   0 <=>; 152 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   35 (   1 propositional; 0-3 arity)
%            Number of functors    :   56 (   5 constant; 0-4 arity)
%            Number of variables   :  139 (   0 singleton; 138 !;   1 ?)
%            Maximal term depth    :   11 (   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(rc1_jordan1g,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_realset1(A)
      & v5_seqm_3(A) ) )).

fof(fc1_jordan1g,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_realset1(A) )
     => ( ~ v1_xboole_0(k3_finseq_5(A))
        & v1_relat_1(k3_finseq_5(A))
        & v1_funct_1(k3_finseq_5(A))
        & v1_finset_1(k3_finseq_5(A))
        & v1_finseq_1(k3_finseq_5(A))
        & ~ v1_realset1(k3_finseq_5(A)) ) ) )).

fof(fc2_jordan1g,axiom,(
    ! [A,B] :
      ( ( 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))))
        & 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))
        & v2_goboard5(k1_jordan1e(A,B)) ) ) )).

fof(fc3_jordan1g,axiom,(
    ! [A,B] :
      ( ( 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))))
        & 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))
        & v2_goboard5(k2_jordan1e(A,B)) ) ) )).

fof(t1_jordan1g,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_realset1(A) )
     => ~ ( ~ v1_xboole_0(A)
          & ! [B] : A != k9_finseq_1(B) ) ) )).

fof(t2_jordan1g,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(A)) )
             => ! [D] :
                  ( r1_goboard1(A,B,C)
                 => r1_goboard1(A,k1_finseq_5(A,B,D),C) ) ) ) ) )).

fof(t3_jordan1g,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(A)) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ( ( r2_hidden(D,k2_relat_1(B))
                      & r1_goboard1(A,B,C) )
                   => r1_goboard1(A,k2_finseq_5(A,B,D),C) ) ) ) ) ) )).

fof(t4_jordan1g,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_goboard1(u1_struct_0(k15_euclid(np__2)),k1_jordan1e(B,A),k1_jordan8(B,A)) ) ) )).

fof(t5_jordan1g,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_goboard1(u1_struct_0(k15_euclid(np__2)),k2_jordan1e(B,A),k1_jordan8(B,A)) ) ) )).

fof(t6_jordan1g,axiom,(
    ! [A] :
      ( ( v1_matrix_1(A)
        & v4_goboard1(A)
        & v5_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)
                     => ( ( r2_hidden(k4_tarski(B,D),k2_matrix_1(A))
                          & r2_hidden(k4_tarski(C,E),k2_matrix_1(A))
                          & k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,D)) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,E)) )
                       => D = E ) ) ) ) ) ) )).

fof(t7_jordan1g,axiom,(
    ! [A] :
      ( ( v1_matrix_1(A)
        & v3_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)
                     => ( ( r2_hidden(k4_tarski(B,D),k2_matrix_1(A))
                          & r2_hidden(k4_tarski(C,E),k2_matrix_1(A))
                          & k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,D)) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,E)) )
                       => B = C ) ) ) ) ) ) )).

fof(t8_jordan1g,axiom,(
    $true )).

fof(t9_jordan1g,axiom,(
    $true )).

fof(t10_jordan1g,axiom,(
    $true )).

fof(t11_jordan1g,axiom,(
    $true )).

fof(t12_jordan1g,axiom,(
    $true )).

fof(t13_jordan1g,axiom,(
    $true )).

fof(t14_jordan1g,axiom,(
    $true )).

fof(t15_jordan1g,axiom,(
    $true )).

fof(t16_jordan1g,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k32_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k32_pscomp_1(k5_topreal1(np__2,A)) )
            | ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k33_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k33_pscomp_1(k5_topreal1(np__2,A)) ) )
          & r1_xreal_0(k21_euclid(k33_pscomp_1(k5_topreal1(np__2,A))),k21_euclid(k32_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t17_jordan1g,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k32_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k32_pscomp_1(k5_topreal1(np__2,A)) )
            | ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k33_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k33_pscomp_1(k5_topreal1(np__2,A)) ) )
          & k32_pscomp_1(k5_topreal1(np__2,A)) = k33_pscomp_1(k5_topreal1(np__2,A)) ) ) )).

fof(t18_jordan1g,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k37_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k37_pscomp_1(k5_topreal1(np__2,A)) )
            | ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k36_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k36_pscomp_1(k5_topreal1(np__2,A)) ) )
          & r1_xreal_0(k21_euclid(k36_pscomp_1(k5_topreal1(np__2,A))),k21_euclid(k37_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t19_jordan1g,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k37_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k37_pscomp_1(k5_topreal1(np__2,A)) )
            | ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k36_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k36_pscomp_1(k5_topreal1(np__2,A)) ) )
          & k37_pscomp_1(k5_topreal1(np__2,A)) = k36_pscomp_1(k5_topreal1(np__2,A)) ) ) )).

fof(t20_jordan1g,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k30_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k30_pscomp_1(k5_topreal1(np__2,A)) )
            | ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k31_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k31_pscomp_1(k5_topreal1(np__2,A)) ) )
          & r1_xreal_0(k22_euclid(k31_pscomp_1(k5_topreal1(np__2,A))),k22_euclid(k30_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t21_jordan1g,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k30_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k30_pscomp_1(k5_topreal1(np__2,A)) )
            | ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k31_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k31_pscomp_1(k5_topreal1(np__2,A)) ) )
          & k30_pscomp_1(k5_topreal1(np__2,A)) = k31_pscomp_1(k5_topreal1(np__2,A)) ) ) )).

fof(t22_jordan1g,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k35_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k35_pscomp_1(k5_topreal1(np__2,A)) )
            | ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k34_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k34_pscomp_1(k5_topreal1(np__2,A)) ) )
          & r1_xreal_0(k22_euclid(k34_pscomp_1(k5_topreal1(np__2,A))),k22_euclid(k35_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t23_jordan1g,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k35_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k35_pscomp_1(k5_topreal1(np__2,A)) )
            | ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k34_pscomp_1(k5_topreal1(np__2,A))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k34_pscomp_1(k5_topreal1(np__2,A)) ) )
          & k35_pscomp_1(k5_topreal1(np__2,A)) = k34_pscomp_1(k5_topreal1(np__2,A)) ) ) )).

fof(t24_jordan1g,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ( ( r2_hidden(C,k2_relat_1(B))
                      & r2_hidden(D,k2_relat_1(B))
                      & r1_xreal_0(k5_finseq_4(B,D),k5_finseq_4(B,C)) )
                   => k2_finseq_5(A,k1_finseq_5(A,B,C),D) = k1_finseq_5(A,k2_finseq_5(A,B,D),C) ) ) ) ) ) )).

fof(t25_jordan1g,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),k30_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),k30_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))),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) )).

fof(t26_jordan1g,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)))) )
         => k2_jordan1e(B,A) = k1_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(t27_jordan1g,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)))) )
         => k5_finseq_4(k1_jordan1e(B,A),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) = np__1 ) ) )).

fof(t28_jordan1g,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_xreal_0(k5_finseq_4(k1_jordan1e(B,A),k31_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k1_jordan1e(B,A),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) )).

fof(t29_jordan1g,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_xreal_0(k5_finseq_4(k1_jordan1e(B,A),k31_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k1_jordan1e(B,A),k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) )).

fof(t30_jordan1g,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_xreal_0(k5_finseq_4(k1_jordan1e(B,A),k33_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k1_jordan1e(B,A),k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) )).

fof(t31_jordan1g,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_xreal_0(k5_finseq_4(k1_jordan1e(B,A),k33_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k1_jordan1e(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) )).

fof(t32_jordan1g,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)))) )
         => k5_finseq_4(k1_jordan1e(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) = k3_finseq_1(k1_jordan1e(B,A)) ) ) )).

fof(t33_jordan1g,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)))) )
         => k5_finseq_4(k2_jordan1e(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) = np__1 ) ) )).

fof(t34_jordan1g,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(k5_finseq_4(k2_jordan1e(B,A),k35_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k2_jordan1e(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) )).

fof(t35_jordan1g,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(k5_finseq_4(k2_jordan1e(B,A),k35_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k2_jordan1e(B,A),k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) )).

fof(t36_jordan1g,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(k5_finseq_4(k2_jordan1e(B,A),k37_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k2_jordan1e(B,A),k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) )).

fof(t37_jordan1g,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(k5_finseq_4(k2_jordan1e(B,A),k37_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k2_jordan1e(B,A),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) )).

fof(t38_jordan1g,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)))) )
         => k5_finseq_4(k2_jordan1e(B,A),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) = k3_finseq_1(k2_jordan1e(B,A)) ) ) )).

fof(t39_jordan1g,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)))) )
         => k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan1e(B,A),np__2)) = k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) )).

fof(t40_jordan1g,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)))) )
         => k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k2_jordan1e(B,A),np__2)) = k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) )).

fof(t41_jordan1g,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)))) )
         => k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) = k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)) ) ) )).

fof(t42_jordan1g,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)))) )
         => k3_real_1(k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k19_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) = k3_real_1(k21_pscomp_1(B),k19_pscomp_1(B)) ) ) )).

fof(t43_jordan1g,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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(C,k1_matrix_1(k1_jordan8(A,B))) )
               => ( r1_xreal_0(B,np__0)
                  | k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),C)) = k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2) ) ) ) ) ) )).

fof(t44_jordan1g,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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(C,k3_finseq_1(k1_jordan8(A,B))) )
               => ( r1_xreal_0(B,np__0)
                  | k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),C,k1_jordan1a(k1_jordan8(A,B)))) = k6_real_1(k3_real_1(k21_pscomp_1(A),k19_pscomp_1(A)),np__2) ) ) ) ) ) )).

fof(t45_jordan1g,axiom,(
    ! [A] :
      ( ( v4_topreal1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r1_xreal_0(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))
                  & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)))
                  & B != np__1
                  & C != np__1 ) ) ) ) )).

fof(t46_jordan1g,axiom,(
    ! [A] :
      ( ( v4_topreal1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r1_xreal_0(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))
                  & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)))
                  & B != k3_finseq_1(A)
                  & C != k3_finseq_1(A) ) ) ) ) )).

fof(t47_jordan1g,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_tarski(k2_relat_1(k1_jordan1e(A,B)),k2_relat_1(k1_jordan9(A,B)))
            & r1_tarski(k2_relat_1(k2_jordan1e(A,B)),k2_relat_1(k1_jordan9(A,B))) ) ) ) )).

fof(t48_jordan1g,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_sprect_2(k1_jordan9(B,A),k1_jordan1e(B,A)) ) ) )).

fof(t49_jordan1g,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_sprect_2(k1_jordan9(B,A),k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k2_jordan1e(B,A))) ) ) )).

fof(t50_jordan1g,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(C,np__1)
                  & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
                  & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1),k2_relat_1(k1_jordan1e(B,A))) ) ) ) ) )).

fof(t51_jordan1g,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(k3_finseq_1(k1_jordan8(B,A)),C)
                  & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k1_matrix_1(k1_jordan8(B,A))),k2_relat_1(k2_jordan1e(B,A))) ) ) ) ) )).

fof(t52_jordan1g,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(C,np__1)
                  & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
                  & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) ) )).

fof(t53_jordan1g,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(k3_finseq_1(k1_jordan8(B,A)),C)
                  & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k1_matrix_1(k1_jordan8(B,A))),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) ) )).

fof(t54_jordan1g,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,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) ) ) )).

fof(t55_jordan1g,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)
           => r2_hidden(k1_jordan5c(k5_topreal1(np__2,k1_jordan1e(A,B)),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),k2_relat_1(k1_jordan1e(A,B))) ) ) ) )).

fof(t56_jordan1g,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)
           => r2_hidden(k2_jordan5c(k5_topreal1(np__2,k2_jordan1e(A,B)),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),k2_relat_1(k2_jordan1e(A,B))) ) ) ) )).

fof(t57_jordan1g,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))
           => k4_jordan3(A,B) = k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,k5_finseq_4(A,B)) ) ) ) )).

fof(t58_jordan1g,axiom,(
    ! [A] :
      ( ( v4_topreal1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( v4_pre_topc(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r2_hidden(k1_jordan5c(k5_topreal1(np__2,A),B,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,k3_finseq_1(A))),k2_relat_1(A))
           => ( r1_xboole_0(k5_topreal1(np__2,A),B)
              | r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),B)
              | k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,k5_finseq_4(A,k1_jordan5c(k5_topreal1(np__2,A),B,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,k3_finseq_1(A)))))),B) = k1_struct_0(k15_euclid(np__2),k1_jordan5c(k5_topreal1(np__2,A),B,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,k3_finseq_1(A)))) ) ) ) ) )).

fof(t59_jordan1g,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)
               => ~ ( r1_xreal_0(np__1,C)
                    & ~ r1_xreal_0(k5_finseq_4(k1_jordan1e(A,B),k1_jordan5c(k5_topreal1(np__2,k1_jordan1e(A,B)),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))),C)
                    & r1_xreal_0(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan1e(A,B),C))) ) ) ) ) ) )).

fof(t60_jordan1g,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)
               => ~ ( r1_xreal_0(np__1,C)
                    & ~ r1_xreal_0(k5_finseq_4(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k2_jordan1e(A,B)),k1_jordan5c(k5_topreal1(np__2,k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k2_jordan1e(A,B))),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))),C)
                    & r1_xreal_0(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k2_jordan1e(A,B)),C))) ) ) ) ) ) )).

fof(t61_jordan1g,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] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
               => ( r2_hidden(C,k2_relat_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),k1_jordan1e(A,B),np__2,k5_finseq_4(k1_jordan1e(A,B),k1_jordan5c(k5_topreal1(np__2,k1_jordan1e(A,B)),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))))))
                 => r1_xreal_0(k21_euclid(C),k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)) ) ) ) ) ) )).

fof(t62_jordan1g,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)
              & r1_xreal_0(k22_euclid(k1_jordan5c(k5_topreal1(np__2,k1_jordan1e(A,B)),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))),k22_euclid(k2_jordan5c(k5_topreal1(np__2,k2_jordan1e(A,B)),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))))) ) ) ) )).

fof(t63_jordan1g,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)
           => k5_topreal1(np__2,k1_jordan1e(A,B)) = k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B))) ) ) ) )).

fof(t64_jordan1g,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)
           => k5_topreal1(np__2,k2_jordan1e(A,B)) = k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B))) ) ) ) )).

fof(t65_jordan1g,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,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),C,D)),k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------