SET007 Axioms: SET007+734.ax


%------------------------------------------------------------------------------
% File     : SET007+734 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Ordering of Points on a Curve.  Part IV
% 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    : jordan18 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   51 (   0 unit)
%            Number of atoms       :  287 (  32 equality)
%            Maximal formula depth :   25 (   8 average)
%            Number of connectives :  282 (  46 ~  ;   2  |;  88  &)
%                                         (   1 <=>; 145 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   26 (   0 propositional; 1-6 arity)
%            Number of functors    :   32 (   5 constant; 0-4 arity)
%            Number of variables   :  138 (   0 singleton; 138 !;   0 ?)
%            Maximal term depth    :    7 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ~ v1_xboole_0(k9_relat_1(k17_pscomp_1,k2_jordan1a(A))) ) )).

fof(fc2_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ~ v1_xboole_0(k9_relat_1(k17_pscomp_1,k4_jordan1a(A))) ) )).

fof(fc3_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ~ v1_xboole_0(k9_relat_1(k16_pscomp_1,k5_jordan1a(A))) ) )).

fof(fc4_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ~ v1_xboole_0(k9_relat_1(k16_pscomp_1,k3_jordan1a(A))) ) )).

fof(fc5_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ~ v1_xboole_0(k2_jordan1a(A))
        & v4_pre_topc(k2_jordan1a(A),k15_euclid(np__2))
        & v2_connsp_1(k2_jordan1a(A),k15_euclid(np__2))
        & v1_jordan1(k2_jordan1a(A),np__2) ) ) )).

fof(fc6_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ~ v1_xboole_0(k4_jordan1a(A))
        & v4_pre_topc(k4_jordan1a(A),k15_euclid(np__2))
        & v2_connsp_1(k4_jordan1a(A),k15_euclid(np__2))
        & v1_jordan1(k4_jordan1a(A),np__2) ) ) )).

fof(fc7_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ~ v1_xboole_0(k3_jordan1a(A))
        & v4_pre_topc(k3_jordan1a(A),k15_euclid(np__2))
        & v2_connsp_1(k3_jordan1a(A),k15_euclid(np__2))
        & v1_jordan1(k3_jordan1a(A),np__2) ) ) )).

fof(fc8_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ~ v1_xboole_0(k5_jordan1a(A))
        & v4_pre_topc(k5_jordan1a(A),k15_euclid(np__2))
        & v2_connsp_1(k5_jordan1a(A),k15_euclid(np__2))
        & v1_jordan1(k5_jordan1a(A),np__2) ) ) )).

fof(t1_jordan18,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k5_square_1(k6_xcmplx_0(A,B)) = k5_square_1(k6_xcmplx_0(B,A)) ) ) )).

fof(t2_jordan18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( v3_tops_2(C,A,B)
                      & v2_connsp_1(D,B) )
                   => v2_connsp_1(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) )).

fof(t3_jordan18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( v3_tops_2(C,A,B)
                      & v6_compts_1(D,B) )
                   => v6_compts_1(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) )).

fof(t4_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => v2_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_jordan1a(A))) ) )).

fof(t5_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => v1_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k4_jordan1a(A))) ) )).

fof(t6_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => v1_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k5_jordan1a(A))) ) )).

fof(t7_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => v2_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k3_jordan1a(A))) ) )).

fof(t8_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_jordan1a(A))) = k22_euclid(A) ) )).

fof(t9_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k4_jordan1a(A))) = k22_euclid(A) ) )).

fof(t10_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k5_jordan1a(A))) = k21_euclid(A) ) )).

fof(t11_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k3_jordan1a(A))) = k21_euclid(A) ) )).

fof(t12_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( r2_hidden(B,k1_jordan2c(np__2,A))
              & r1_tarski(k2_jordan1a(B),k2_jordan2c(np__2,A)) ) ) ) )).

fof(t13_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( r2_hidden(B,k1_jordan2c(np__2,A))
              & r1_tarski(k4_jordan1a(B),k2_jordan2c(np__2,A)) ) ) ) )).

fof(t14_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( r2_hidden(B,k1_jordan2c(np__2,A))
              & r1_tarski(k3_jordan1a(B),k2_jordan2c(np__2,A)) ) ) ) )).

fof(t15_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( r2_hidden(B,k1_jordan2c(np__2,A))
              & r1_tarski(k5_jordan1a(B),k2_jordan2c(np__2,A)) ) ) ) )).

fof(t16_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r1_topreal1(k15_euclid(np__2),B,C,A)
                      & D != C
                      & r2_hidden(C,k3_jordan6(A,B,C,D)) ) ) ) ) ) )).

fof(t17_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r1_topreal1(k15_euclid(np__2),B,C,A)
                      & D != B
                      & r2_hidden(B,k4_jordan6(A,B,C,D)) ) ) ) ) ) )).

fof(t18_jordan18,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r1_topreal1(k15_euclid(np__2),C,D,B)
                      & r1_tarski(B,A)
                      & ! [E] :
                          ( ( ~ v1_xboole_0(E)
                            & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                         => ~ ( r1_topreal1(k15_euclid(np__2),C,D,E)
                              & k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,E) = A
                              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,E) = k2_struct_0(k15_euclid(np__2),C,D) ) ) ) ) ) ) ) )).

fof(t19_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ~ ( r1_topreal1(k15_euclid(np__2),B,C,A)
                          & r2_hidden(D,A)
                          & r2_hidden(E,A)
                          & D != B
                          & D != C
                          & E != B
                          & E != C
                          & D != E
                          & ! [F] :
                              ( ( ~ v1_xboole_0(F)
                                & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                             => ~ ( r1_topreal1(k15_euclid(np__2),D,E,F)
                                  & r1_tarski(F,A)
                                  & r1_xboole_0(F,k2_struct_0(k15_euclid(np__2),B,C)) ) ) ) ) ) ) ) ) )).

fof(d1_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => k1_jordan18(A,B) = k23_euclid(k21_euclid(A),k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k2_jordan1a(A))))) ) ) )).

fof(d2_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => k2_jordan18(A,B) = k23_euclid(k21_euclid(A),k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k4_jordan1a(A))))) ) ) )).

fof(t20_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( k21_euclid(k1_jordan18(B,A)) = k21_euclid(B)
            & k21_euclid(k2_jordan18(B,A)) = k21_euclid(B) ) ) ) )).

fof(t21_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( k22_euclid(k1_jordan18(B,A)) = k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k2_jordan1a(B))))
            & k22_euclid(k2_jordan18(B,A)) = k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k4_jordan1a(B)))) ) ) ) )).

fof(t22_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,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)))) )
         => ( r2_hidden(A,k1_jordan2c(np__2,B))
           => ( r2_hidden(k1_jordan18(A,B),B)
              & r2_hidden(k1_jordan18(A,B),k2_jordan1a(A))
              & r2_hidden(k2_jordan18(A,B),B)
              & r2_hidden(k2_jordan18(A,B),k4_jordan1a(A)) ) ) ) ) )).

fof(t23_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,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)))) )
         => ( r2_hidden(A,k1_jordan2c(np__2,B))
           => ( ~ r1_xreal_0(k22_euclid(A),k22_euclid(k2_jordan18(A,B)))
              & ~ r1_xreal_0(k22_euclid(k1_jordan18(A,B)),k22_euclid(A)) ) ) ) ) )).

fof(t24_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,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)))) )
         => ~ ( r2_hidden(A,k1_jordan2c(np__2,B))
              & r1_xreal_0(k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k2_jordan1a(A)))),k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k4_jordan1a(A))))) ) ) ) )).

fof(t25_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,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)))) )
         => ~ ( r2_hidden(A,k1_jordan2c(np__2,B))
              & k2_jordan18(A,B) = k1_jordan18(A,B) ) ) ) )).

fof(t26_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => v2_sppol_1(k3_topreal1(np__2,k1_jordan18(A,B),k2_jordan18(A,B))) ) ) )).

fof(t27_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,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)))) )
         => ( r2_hidden(A,k1_jordan2c(np__2,B))
           => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k1_jordan18(A,B),k2_jordan18(A,B)),B) = k2_struct_0(k15_euclid(np__2),k1_jordan18(A,B),k2_jordan18(A,B)) ) ) ) )).

fof(t28_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( ( v6_compts_1(C,k15_euclid(np__2))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ( ( r2_hidden(A,k1_jordan2c(np__2,C))
                  & r2_hidden(B,k1_jordan2c(np__2,C)) )
               => ( k21_euclid(A) = k21_euclid(B)
                  | r2_incproj(k1_jordan18(A,C),k2_jordan18(B,C),k1_jordan18(B,C),k2_jordan18(A,C)) ) ) ) ) ) )).

fof(d3_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                         => ( r1_jordan18(A,B,C,D,E,F)
                          <=> ! [G] :
                                ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                               => ~ ( r1_topreal1(k15_euclid(A),C,D,G)
                                    & r1_tarski(G,B)
                                    & r1_xboole_0(G,k2_struct_0(k15_euclid(A),E,F)) ) ) ) ) ) ) ) ) ) )).

fof(t29_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => r1_jordan18(A,B,C,C,D,E) ) ) ) ) ) )).

fof(t30_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                         => ( r1_jordan18(A,B,C,D,E,F)
                           => r1_jordan18(A,B,D,C,E,F) ) ) ) ) ) ) ) )).

fof(t31_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                         => ( r1_jordan18(A,B,C,D,E,F)
                           => r1_jordan18(A,B,C,D,F,E) ) ) ) ) ) ) ) )).

fof(t32_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => r1_jordan18(A,B,C,D,C,E) ) ) ) ) ) )).

fof(t33_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => r1_jordan18(A,B,C,D,E,D) ) ) ) ) ) )).

fof(t34_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => r1_jordan18(A,B,C,D,D,E) ) ) ) ) ) )).

fof(t35_jordan18,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => r1_jordan18(A,B,C,D,E,C) ) ) ) ) ) )).

fof(t36_jordan18,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r2_hidden(D,A)
                      & r2_hidden(B,A)
                      & r2_hidden(C,A)
                      & B != C
                      & B != D
                      & C != D
                      & r1_jordan18(np__2,A,B,C,D,D) ) ) ) ) ) )).

fof(t37_jordan18,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r2_hidden(B,A)
                          & r2_hidden(C,A)
                          & r1_jordan18(np__2,A,B,C,D,E) )
                       => ( B = C
                          | r1_jordan18(np__2,A,D,E,B,C) ) ) ) ) ) ) ) )).

fof(t38_jordan18,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ~ ( r2_hidden(B,A)
                          & r2_hidden(C,A)
                          & r2_hidden(D,A)
                          & B != C
                          & D != B
                          & D != C
                          & E != B
                          & E != C
                          & r1_jordan18(np__2,A,B,C,D,E)
                          & r1_jordan18(np__2,A,B,D,C,E) ) ) ) ) ) ) )).

fof(dt_k1_jordan18,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => m1_subset_1(k1_jordan18(A,B),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k2_jordan18,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => m1_subset_1(k2_jordan18(A,B),u1_struct_0(k15_euclid(np__2))) ) )).
%------------------------------------------------------------------------------