SET007 Axioms: SET007+555.ax


%------------------------------------------------------------------------------
% File     : SET007+555 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Dividing Function of the Simple Closed Curve into Segments
% 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    : jordan7 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   26 (   0 unit)
%            Number of atoms       :  304 (  54 equality)
%            Maximal formula depth :   31 (  12 average)
%            Number of connectives :  322 (  44 ~  ;  19  |; 150  &)
%                                         (   2 <=>; 107 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   0 propositional; 1-5 arity)
%            Number of functors    :   30 (   8 constant; 0-4 arity)
%            Number of variables   :   94 (   0 singleton;  92 !;   2 ?)
%            Maximal term depth    :    6 (   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(cc1_jordan7,axiom,(
    ! [A] :
      ( m1_finseq_1(A,k1_numbers)
     => ( v1_goboard1(A)
       => v2_funct_1(A) ) ) )).

fof(t1_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( v1_topreal2(A)
       => ( r2_hidden(k30_pscomp_1(A),k9_jordan6(A))
          & r2_hidden(k34_pscomp_1(A),k9_jordan6(A))
          & r2_hidden(k30_pscomp_1(A),k8_jordan6(A))
          & r2_hidden(k34_pscomp_1(A),k8_jordan6(A)) ) ) ) )).

fof(t2_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v1_topreal2(A)
              & r1_jordan6(A,B,k30_pscomp_1(A)) )
           => B = k30_pscomp_1(A) ) ) ) )).

fof(t3_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v1_topreal2(A)
              & r2_hidden(B,A) )
           => r1_jordan6(A,k30_pscomp_1(A),B) ) ) ) )).

fof(t4_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( v1_topreal2(A)
       => ( k1_jordan7(A,k30_pscomp_1(A),k34_pscomp_1(A)) = k8_jordan6(A)
          & k1_jordan7(A,k34_pscomp_1(A),k30_pscomp_1(A)) = k9_jordan6(A) ) ) ) )).

fof(t5_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( v1_topreal2(A)
                  & r1_jordan6(A,B,C) )
               => ( r2_hidden(B,A)
                  & r2_hidden(C,A) ) ) ) ) ) )).

fof(t6_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( v1_topreal2(A)
                  & r1_jordan6(A,B,C) )
               => ( r2_hidden(B,k1_jordan7(A,B,C))
                  & r2_hidden(C,k1_jordan7(A,B,C)) ) ) ) ) ) )).

fof(t7_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( r2_hidden(B,A)
              & v1_topreal2(A) )
           => r2_hidden(B,k1_jordan7(A,B,k30_pscomp_1(A))) ) ) ) )).

fof(t8_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v1_topreal2(A)
              & r2_hidden(B,A) )
           => ( B = k30_pscomp_1(A)
              | k1_jordan7(A,B,B) = k1_struct_0(k15_euclid(np__2),B) ) ) ) ) )).

fof(t9_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ~ ( v1_topreal2(A)
                  & B != k30_pscomp_1(A)
                  & C != k30_pscomp_1(A)
                  & r2_hidden(k30_pscomp_1(A),k1_jordan7(A,B,C)) ) ) ) ) )).

fof(t10_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( 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)))
                 => ( ( v1_topreal2(A)
                      & r1_jordan6(A,B,C)
                      & r1_jordan6(A,C,D) )
                   => ( ( B = C
                        & B = k30_pscomp_1(A) )
                      | B = D
                      | ( C = D
                        & C = k30_pscomp_1(A) )
                      | k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_jordan7(A,B,C),k1_jordan7(A,C,D)) = k1_struct_0(k15_euclid(np__2),C) ) ) ) ) ) ) )).

fof(t11_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( v1_topreal2(A)
                  & r1_jordan6(A,B,C) )
               => ( B = k30_pscomp_1(A)
                  | C = k30_pscomp_1(A)
                  | k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_jordan7(A,B,C),k1_jordan7(A,C,k30_pscomp_1(A))) = k1_struct_0(k15_euclid(np__2),C) ) ) ) ) ) )).

fof(t12_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( v1_topreal2(A)
                  & r1_jordan6(A,B,C) )
               => ( B = C
                  | B = k30_pscomp_1(A)
                  | k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_jordan7(A,C,k30_pscomp_1(A)),k1_jordan7(A,k30_pscomp_1(A),B)) = k1_struct_0(k15_euclid(np__2),k30_pscomp_1(A)) ) ) ) ) ) )).

fof(t13_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( 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)))
                     => ( ( v1_topreal2(A)
                          & r1_jordan6(A,B,C)
                          & r1_jordan6(A,C,D)
                          & r1_jordan6(A,D,E) )
                       => ( B = C
                          | C = D
                          | r1_xboole_0(k1_jordan7(A,B,C),k1_jordan7(A,D,E)) ) ) ) ) ) ) ) )).

fof(t14_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( 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)))
                 => ( ( v1_topreal2(A)
                      & r1_jordan6(A,B,C)
                      & r1_jordan6(A,C,D) )
                   => ( B = k30_pscomp_1(A)
                      | B = C
                      | C = D
                      | r1_xboole_0(k1_jordan7(A,B,C),k1_jordan7(A,D,k30_pscomp_1(A))) ) ) ) ) ) ) )).

fof(t15_jordan7,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B)))
                & m2_relset_1(C,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B))) )
             => ~ ( B != k1_xboole_0
                  & v3_tops_2(C,k5_topmetr,k3_pre_topc(k15_euclid(A),B))
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
                        & m2_relset_1(D,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
                     => ~ ( C = D
                          & v5_pre_topc(D,k5_topmetr,k15_euclid(A))
                          & v2_funct_1(D) ) ) ) ) ) ) )).

fof(t16_jordan7,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
                & m2_relset_1(C,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
             => ~ ( v5_pre_topc(C,k5_topmetr,k15_euclid(A))
                  & v2_funct_1(C)
                  & k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),C) = B
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B)))
                        & m2_relset_1(D,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B))) )
                     => ~ ( D = C
                          & v3_tops_2(D,k5_topmetr,k3_pre_topc(k15_euclid(A),B)) ) ) ) ) ) ) )).

fof(t17_jordan7,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => ( v1_goboard1(A)
       => v2_funct_1(A) ) ) )).

fof(t18_jordan7,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)))
             => ~ ( r1_topreal1(k15_euclid(np__2),B,C,A)
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
                        & m2_relset_1(D,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
                     => ~ ( v5_pre_topc(D,k5_topmetr,k15_euclid(np__2))
                          & v2_funct_1(D)
                          & k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),D) = A
                          & k1_funct_1(D,np__0) = B
                          & k1_funct_1(D,np__1) = C ) ) ) ) ) ) )).

fof(t19_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(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)))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
                            & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
                         => ! [G] :
                              ( m1_subset_1(G,k1_numbers)
                             => ! [H] :
                                  ( m1_subset_1(H,k1_numbers)
                                 => ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
                                      & v5_pre_topc(F,k5_topmetr,k15_euclid(np__2))
                                      & v2_funct_1(F)
                                      & k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F) = A
                                      & k1_funct_1(F,np__0) = B
                                      & k1_funct_1(F,np__1) = C
                                      & k1_funct_1(F,G) = D
                                      & r1_xreal_0(np__0,G)
                                      & r1_xreal_0(G,np__1)
                                      & k1_funct_1(F,H) = E
                                      & r1_xreal_0(np__0,H)
                                      & r1_xreal_0(H,np__1)
                                      & r1_xreal_0(G,H) )
                                   => r1_jordan5c(A,B,C,D,E) ) ) ) ) ) ) ) ) ) )).

fof(t20_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(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)))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
                            & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
                         => ! [G] :
                              ( m1_subset_1(G,k1_numbers)
                             => ! [H] :
                                  ( m1_subset_1(H,k1_numbers)
                                 => ( ( v5_pre_topc(F,k5_topmetr,k15_euclid(np__2))
                                      & v2_funct_1(F)
                                      & k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F) = A
                                      & k1_funct_1(F,np__0) = B
                                      & k1_funct_1(F,np__1) = C
                                      & k1_funct_1(F,G) = D
                                      & r1_xreal_0(np__0,G)
                                      & r1_xreal_0(G,np__1)
                                      & k1_funct_1(F,H) = E
                                      & r1_xreal_0(np__0,H)
                                      & r1_xreal_0(H,np__1)
                                      & r1_jordan5c(A,B,C,D,E) )
                                   => r1_xreal_0(G,H) ) ) ) ) ) ) ) ) ) )).

fof(t21_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ~ ( v1_topreal2(A)
              & ~ r1_xreal_0(B,np__0)
              & ! [C] :
                  ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( k1_funct_1(C,np__1) = k30_pscomp_1(A)
                      & v2_funct_1(C)
                      & r1_xreal_0(np__8,k3_finseq_1(C))
                      & r1_tarski(k2_relat_1(C),A)
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(np__1,D)
                           => ( r1_xreal_0(k3_finseq_1(C),D)
                              | r1_jordan6(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1))) ) ) )
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ! [E] :
                              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k14_euclid(np__2))))
                             => ~ ( r1_xreal_0(np__1,D)
                                  & ~ r1_xreal_0(k3_finseq_1(C),D)
                                  & E = k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1)))
                                  & r1_xreal_0(B,k2_tbsp_1(k14_euclid(np__2),E)) ) ) )
                      & ! [D] :
                          ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k14_euclid(np__2))))
                         => ~ ( D = k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1))
                              & r1_xreal_0(B,k2_tbsp_1(k14_euclid(np__2),D)) ) )
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(np__1,D)
                           => ( r1_xreal_0(k3_finseq_1(C),k1_nat_1(D,np__1))
                              | k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1))),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)))) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1))) ) ) )
                      & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1)),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2))) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1))
                      & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C))),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1))) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)))
                      & r1_xboole_0(k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C))),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2)))
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ! [E] :
                              ( m2_subset_1(E,k1_numbers,k5_numbers)
                             => ( r1_xreal_0(np__1,D)
                               => ( r1_xreal_0(E,D)
                                  | r1_xreal_0(k3_finseq_1(C),E)
                                  | r1_gobrd10(D,E)
                                  | r1_xboole_0(k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1))),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,E),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(E,np__1)))) ) ) ) )
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ~ ( ~ r1_xreal_0(D,np__1)
                              & ~ r1_xreal_0(k3_finseq_1(C),k1_nat_1(D,np__1))
                              & ~ r1_xboole_0(k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1)),k1_jordan7(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1)))) ) ) ) ) ) ) ) )).

fof(dt_k1_jordan7,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
     => m1_subset_1(k1_jordan7(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(d1_jordan7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( C != k30_pscomp_1(A)
                 => k1_jordan7(A,B,C) = a_3_0_jordan7(A,B,C) )
                & ( C = k30_pscomp_1(A)
                 => k1_jordan7(A,B,C) = a_2_0_jordan7(A,B) ) ) ) ) ) )).

fof(fraenkel_a_3_0_jordan7,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v6_compts_1(B,k15_euclid(np__2))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(D,u1_struct_0(k15_euclid(np__2))) )
     => ( r2_hidden(A,a_3_0_jordan7(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
            & A = E
            & r1_jordan6(B,C,E)
            & r1_jordan6(B,E,D) ) ) ) )).

fof(fraenkel_a_2_0_jordan7,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v6_compts_1(B,k15_euclid(np__2))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
     => ( r2_hidden(A,a_2_0_jordan7(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
            & A = D
            & ( r1_jordan6(B,C,D)
              | ( r2_hidden(C,B)
                & D = k30_pscomp_1(B) ) ) ) ) ) )).
%------------------------------------------------------------------------------