SET007 Axioms: SET007+733.ax


%------------------------------------------------------------------------------
% File     : SET007+733 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Ordering of Points on a Curve.  Part III
% 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    : jordan17 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   28 (   0 unit)
%            Number of atoms       :  297 (  58 equality)
%            Maximal formula depth :   24 (  15 average)
%            Number of connectives :  336 (  67 ~  ;  18  |; 105  &)
%                                         (   1 <=>; 145 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   14 (   0 propositional; 1-5 arity)
%            Number of functors    :   15 (   6 constant; 0-2 arity)
%            Number of variables   :  132 (   0 singleton; 132 !;   0 ?)
%            Maximal term depth    :    4 (   1 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(t1_jordan17,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                     => ~ ( r2_hidden(B,E)
                          & r1_topreal1(k15_euclid(A),C,D,E)
                          & ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,u1_struct_0(k22_borsuk_1),u1_struct_0(k3_pre_topc(k15_euclid(A),E)))
                                & m2_relset_1(F,u1_struct_0(k22_borsuk_1),u1_struct_0(k3_pre_topc(k15_euclid(A),E))) )
                             => ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ~ ( v3_tops_2(F,k22_borsuk_1,k3_pre_topc(k15_euclid(A),E))
                                      & k1_funct_1(F,np__0) = C
                                      & k1_funct_1(F,np__1) = D
                                      & r1_xreal_0(np__0,G)
                                      & r1_xreal_0(G,np__1)
                                      & k1_funct_1(F,G) = B ) ) ) ) ) ) ) ) ) )).

fof(t2_jordan17,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_jordan6(A,k30_pscomp_1(A),k34_pscomp_1(A)) ) )).

fof(t3_jordan17,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r1_jordan6(A,B,k34_pscomp_1(A))
           => r2_hidden(B,k8_jordan6(A)) ) ) ) )).

fof(t4_jordan17,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r1_jordan6(A,k34_pscomp_1(A),B)
           => r2_hidden(B,k9_jordan6(A)) ) ) ) )).

fof(t5_jordan17,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r1_jordan6(A,B,k30_pscomp_1(A))
           => r2_hidden(B,k9_jordan6(A)) ) ) ) )).

fof(t6_jordan17,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] :
              ( 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,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                     => ~ ( A != B
                          & r1_topreal1(k15_euclid(np__2),C,D,E)
                          & r1_jordan5c(E,C,D,A,B)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                             => ~ ( A != F
                                  & B != F
                                  & r1_jordan5c(E,C,D,A,F)
                                  & r1_jordan5c(E,C,D,F,B) ) ) ) ) ) ) ) ) )).

fof(t7_jordan17,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)))
         => ~ ( r2_hidden(B,A)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( B != C
                      & r1_jordan6(A,B,C) ) ) ) ) ) )).

fof(t8_jordan17,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)))
             => ~ ( B != C
                  & r1_jordan6(A,B,C)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ~ ( D != B
                          & D != C
                          & r1_jordan6(A,B,D)
                          & r1_jordan6(A,D,C) ) ) ) ) ) ) )).

fof(d1_jordan17,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_jordan17(A,B,C,D,E)
                      <=> ~ ( ~ ( r1_jordan6(A,B,C)
                                & r1_jordan6(A,C,D)
                                & r1_jordan6(A,D,E) )
                            & ~ ( r1_jordan6(A,C,D)
                                & r1_jordan6(A,D,E)
                                & r1_jordan6(A,E,B) )
                            & ~ ( r1_jordan6(A,D,E)
                                & r1_jordan6(A,E,B)
                                & r1_jordan6(A,B,C) )
                            & ~ ( r1_jordan6(A,E,B)
                                & r1_jordan6(A,B,C)
                                & r1_jordan6(A,C,D) ) ) ) ) ) ) ) ) )).

fof(t9_jordan17,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)))
         => ( r2_hidden(B,A)
           => r1_jordan17(A,B,B,B,B) ) ) ) )).

fof(t10_jordan17,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)))
                     => ( r1_jordan17(A,B,C,D,E)
                       => r1_jordan17(A,C,D,E,B) ) ) ) ) ) ) )).

fof(t11_jordan17,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)))
                     => ( r1_jordan17(A,B,C,D,E)
                       => r1_jordan17(A,D,E,B,C) ) ) ) ) ) ) )).

fof(t12_jordan17,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)))
                     => ( r1_jordan17(A,B,C,D,E)
                       => r1_jordan17(A,E,B,C,D) ) ) ) ) ) ) )).

fof(t13_jordan17,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)))
                     => ~ ( B != C
                          & r1_jordan17(A,B,C,D,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                             => ~ ( F != B
                                  & F != C
                                  & r1_jordan17(A,B,F,C,D) ) ) ) ) ) ) ) ) )).

fof(t14_jordan17,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)))
                     => ~ ( B != C
                          & r1_jordan17(A,B,C,D,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                             => ~ ( F != B
                                  & F != C
                                  & r1_jordan17(A,B,F,C,E) ) ) ) ) ) ) ) ) )).

fof(t15_jordan17,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)))
                     => ~ ( B != C
                          & r1_jordan17(A,D,B,C,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                             => ~ ( F != B
                                  & F != C
                                  & r1_jordan17(A,D,B,F,C) ) ) ) ) ) ) ) ) )).

fof(t16_jordan17,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)))
                     => ~ ( B != C
                          & r1_jordan17(A,D,B,C,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                             => ~ ( F != B
                                  & F != C
                                  & r1_jordan17(A,B,F,C,E) ) ) ) ) ) ) ) ) )).

fof(t17_jordan17,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)))
                     => ~ ( B != C
                          & r1_jordan17(A,D,E,B,C)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                             => ~ ( F != B
                                  & F != C
                                  & r1_jordan17(A,D,B,F,C) ) ) ) ) ) ) ) ) )).

fof(t18_jordan17,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)))
                     => ~ ( B != C
                          & r1_jordan17(A,D,E,B,C)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                             => ~ ( F != B
                                  & F != C
                                  & r1_jordan17(A,E,B,F,C) ) ) ) ) ) ) ) ) )).

fof(t19_jordan17,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)))
                     => ~ ( B != C
                          & r1_jordan17(A,C,D,E,B)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                             => ~ ( F != B
                                  & F != C
                                  & r1_jordan17(A,C,D,B,F) ) ) ) ) ) ) ) ) )).

fof(t20_jordan17,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)))
                     => ~ ( B != C
                          & r1_jordan17(A,C,D,E,B)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                             => ~ ( F != B
                                  & F != C
                                  & r1_jordan17(A,C,E,B,F) ) ) ) ) ) ) ) ) )).

fof(t21_jordan17,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)))
                     => ( ( r1_jordan17(A,B,E,C,D)
                          & r1_jordan17(A,E,B,C,D) )
                       => ( B = C
                          | B = D
                          | E = D
                          | B = E ) ) ) ) ) ) ) )).

fof(t22_jordan17,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)))
                     => ( ( r1_jordan17(A,B,C,D,E)
                          & r1_jordan17(A,D,C,B,E) )
                       => ( B = C
                          | C = D
                          | D = E
                          | B = D ) ) ) ) ) ) ) )).

fof(t23_jordan17,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)))
                     => ( ( r1_jordan17(A,B,C,D,E)
                          & r1_jordan17(A,E,C,D,B) )
                       => ( B = C
                          | B = D
                          | C = E
                          | B = E ) ) ) ) ) ) ) )).

fof(t24_jordan17,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)))
                     => ( ( r1_jordan17(A,B,E,C,D)
                          & r1_jordan17(A,B,C,E,D) )
                       => ( B = C
                          | B = D
                          | E = D
                          | E = C ) ) ) ) ) ) ) )).

fof(t25_jordan17,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)))
                     => ( ( r1_jordan17(A,B,C,D,E)
                          & r1_jordan17(A,B,E,D,C) )
                       => ( B = C
                          | C = D
                          | D = E
                          | C = E ) ) ) ) ) ) ) )).

fof(t26_jordan17,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)))
                     => ( ( r1_jordan17(A,B,C,D,E)
                          & r1_jordan17(A,B,C,E,D) )
                       => ( B = C
                          | B = D
                          | C = E
                          | D = E ) ) ) ) ) ) ) )).

fof(t27_jordan17,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)
                          & r2_hidden(E,A)
                          & ~ r1_jordan17(A,B,C,D,E)
                          & ~ r1_jordan17(A,B,C,E,D)
                          & ~ r1_jordan17(A,B,D,C,E)
                          & ~ r1_jordan17(A,B,D,E,C)
                          & ~ r1_jordan17(A,B,E,C,D)
                          & ~ r1_jordan17(A,B,E,D,C) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------