SET007 Axioms: SET007+613.ax


%------------------------------------------------------------------------------
% File     : SET007+613 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Cages - the External Approximation of Jordan's Curve
% 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    : jordan9 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   37 (   2 unit)
%            Number of atoms       :  536 (  40 equality)
%            Maximal formula depth :   22 (  13 average)
%            Number of connectives :  583 (  84 ~  ;   7  |; 333  &)
%                                         (   4 <=>; 155 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   36 (   1 propositional; 0-4 arity)
%            Number of functors    :   41 (   5 constant; 0-4 arity)
%            Number of variables   :  132 (   0 singleton; 128 !;   4 ?)
%            Maximal term depth    :    5 (   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(t1_jordan9,axiom,(
    $true )).

fof(t2_jordan9,axiom,(
    $true )).

fof(t3_jordan9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( v2_connsp_1(B,A)
                          & r4_connsp_1(A,E,C)
                          & r4_connsp_1(A,E,D)
                          & r1_tarski(B,E) )
                       => ( r1_xboole_0(B,C)
                          | r1_xboole_0(B,D)
                          | C = D ) ) ) ) ) ) ) )).

fof(t4_jordan9,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k16_finseq_1(A,B,D) = k16_finseq_1(A,C,D) )
               => B = C ) ) ) ) )).

fof(t5_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,B)
             => ~ ( r2_hidden(A,k4_finseq_1(C))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r2_hidden(D,k4_finseq_1(k4_finseq_5(B,C)))
                          & k1_nat_1(A,D) = k1_nat_1(k3_finseq_1(C),np__1)
                          & k4_finseq_4(k5_numbers,B,C,A) = k4_finseq_4(k5_numbers,B,k4_finseq_5(B,C),D) ) ) ) ) ) ) )).

fof(t6_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,B)
             => ~ ( r2_hidden(A,k4_finseq_1(k4_finseq_5(B,C)))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r2_hidden(D,k4_finseq_1(C))
                          & k1_nat_1(A,D) = k1_nat_1(k3_finseq_1(C),np__1)
                          & k4_finseq_4(k5_numbers,B,k4_finseq_5(B,C),A) = k4_finseq_4(k5_numbers,B,C,D) ) ) ) ) ) ) )).

fof(t7_jordan9,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(A)) )
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ( r1_goboard1(A,C,B)
              <=> r1_goboard1(A,k4_finseq_5(A,C),B) ) ) ) ) )).

fof(t8_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                  & r1_xreal_0(np__1,A)
                  & r1_xreal_0(A,k3_finseq_1(C)) )
               => r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,A),k2_gobrd13(B)) ) ) ) ) )).

fof(t9_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ~ ( r1_xreal_0(A,k3_finseq_1(B))
                & r2_hidden(C,k5_topreal1(np__2,k1_rfinseq(u1_struct_0(k15_euclid(np__2)),B,A)))
                & ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ~ ( r1_xreal_0(k1_nat_1(A,np__1),D)
                        & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(B))
                        & r2_hidden(C,k4_topreal1(np__2,B,D)) ) ) ) ) ) )).

fof(t10_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                  & r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C)) )
               => ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,A),k4_gobrd13(C,B,A))
                  & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,A),k3_gobrd13(C,B,A)) ) ) ) ) ) )).

fof(t11_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                  & r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C)) )
               => ( k1_tops_1(k15_euclid(np__2),k4_gobrd13(C,B,A)) != k1_xboole_0
                  & k1_tops_1(k15_euclid(np__2),k3_gobrd13(C,B,A)) != k1_xboole_0 ) ) ) ) ) )).

fof(t12_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                  & r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C)) )
               => ( v2_connsp_1(k1_tops_1(k15_euclid(np__2),k4_gobrd13(C,B,A)),k15_euclid(np__2))
                  & v2_connsp_1(k1_tops_1(k15_euclid(np__2),k3_gobrd13(C,B,A)),k15_euclid(np__2)) ) ) ) ) ) )).

fof(t13_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                  & r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C)) )
               => ( k6_pre_topc(k15_euclid(np__2),k1_tops_1(k15_euclid(np__2),k4_gobrd13(C,B,A))) = k4_gobrd13(C,B,A)
                  & k6_pre_topc(k15_euclid(np__2),k1_tops_1(k15_euclid(np__2),k3_gobrd13(C,B,A))) = k3_gobrd13(C,B,A) ) ) ) ) ) )).

fof(t14_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                  & v1_sppol_1(k4_topreal1(np__2,C,A))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k1_matrix_1(B))
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                             => ( r2_hidden(E,k4_topreal1(np__2,C,A))
                               => k22_euclid(E) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,np__1,D)) ) ) ) ) ) ) ) ) )).

fof(t15_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                  & v2_sppol_1(k4_topreal1(np__2,C,A))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k3_finseq_1(B))
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                             => ( r2_hidden(E,k4_topreal1(np__2,C,A))
                               => k21_euclid(E) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,np__1)) ) ) ) ) ) ) ) ) )).

fof(t16_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_relat_1(C)
                & v1_matrix_1(C)
                & v3_goboard1(C)
                & v4_goboard1(C)
                & v5_goboard1(C)
                & v6_goboard1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
                      & v1_topreal1(D)
                      & r1_xreal_0(A,k3_finseq_1(C))
                      & r1_xreal_0(B,k1_matrix_1(C)) )
                   => r1_xboole_0(k1_tops_1(k15_euclid(np__2),k3_goboard5(C,A,B)),k5_topreal1(np__2,D)) ) ) ) ) ) )).

fof(t17_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                  & v1_topreal1(C)
                  & r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C)) )
               => ( r1_xboole_0(k1_tops_1(k15_euclid(np__2),k4_gobrd13(C,B,A)),k5_topreal1(np__2,C))
                  & r1_xboole_0(k1_tops_1(k15_euclid(np__2),k3_gobrd13(C,B,A)),k5_topreal1(np__2,C)) ) ) ) ) ) )).

fof(t18_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_relat_1(C)
                & v1_matrix_1(C)
                & v3_goboard1(C)
                & v4_goboard1(C)
                & v5_goboard1(C)
                & v6_goboard1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
             => ( ( r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                  & r1_xreal_0(np__1,B)
                  & r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(C)) )
               => ( k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B)) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1)))
                  & k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B)) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B))
                  & k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B))
                  & k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1))) ) ) ) ) ) )).

fof(t19_jordan9,axiom,(
    ! [A] :
      ( ( ~ v3_relat_1(A)
        & v1_matrix_1(A)
        & v3_goboard1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & v6_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,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(k1_nat_1(C,np__1),k3_finseq_1(A))
                      & r1_xreal_0(np__1,D)
                      & r1_xreal_0(k1_nat_1(D,np__1),k1_matrix_1(A)) )
                   => ( r2_hidden(B,k3_goboard5(A,C,D))
                    <=> ( r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D)),k21_euclid(B))
                        & r1_xreal_0(k21_euclid(B),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1),D)))
                        & r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D)),k22_euclid(B))
                        & r1_xreal_0(k22_euclid(B),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,k1_nat_1(D,np__1)))) ) ) ) ) ) ) ) )).

fof(t21_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_relat_1(C)
                & v1_matrix_1(C)
                & v3_goboard1(C)
                & v4_goboard1(C)
                & v5_goboard1(C)
                & v6_goboard1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                      & r1_xreal_0(np__1,B)
                      & r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(C))
                      & r2_hidden(D,k2_gobrd13(C))
                      & r2_hidden(D,k3_goboard5(C,A,B))
                      & D != k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B)
                      & D != k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1))
                      & D != k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1))
                      & D != k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B) ) ) ) ) ) )).

fof(t22_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_relat_1(C)
                & v1_matrix_1(C)
                & v3_goboard1(C)
                & v4_goboard1(C)
                & v5_goboard1(C)
                & v6_goboard1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
             => ( ( r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                  & r1_xreal_0(np__1,B)
                  & r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(C)) )
               => ( r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_goboard5(C,A,B))
                  & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1)),k3_goboard5(C,A,B))
                  & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1)),k3_goboard5(C,A,B))
                  & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B),k3_goboard5(C,A,B)) ) ) ) ) ) )).

fof(t23_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_relat_1(C)
                & v1_matrix_1(C)
                & v3_goboard1(C)
                & v4_goboard1(C)
                & v5_goboard1(C)
                & v6_goboard1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                      & r1_xreal_0(np__1,B)
                      & r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(C))
                      & r2_hidden(D,k2_gobrd13(C))
                      & r2_hidden(D,k3_goboard5(C,A,B)) )
                   => r1_sppol_1(np__2,D,k3_goboard5(C,A,B)) ) ) ) ) ) )).

fof(t24_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r1_xreal_0(np__2,k3_finseq_1(B))
                  & r1_xreal_0(np__2,k1_matrix_1(B))
                  & r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                  & r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                  & ! [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(k1_nat_1(D,np__1),k3_finseq_1(B))
                              & r1_xreal_0(np__1,E)
                              & r1_xreal_0(k1_nat_1(E,np__1),k1_matrix_1(B))
                              & r1_tarski(k4_topreal1(np__2,C,A),k3_goboard5(B,D,E)) ) ) ) ) ) ) ) )).

fof(t25_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r1_xreal_0(np__2,k3_finseq_1(B))
                      & r1_xreal_0(np__2,k1_matrix_1(B))
                      & r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                      & r1_xreal_0(np__1,A)
                      & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                      & r2_hidden(D,k2_gobrd13(B))
                      & r2_hidden(D,k4_topreal1(np__2,C,A))
                      & D != k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,A)
                      & D != k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1)) ) ) ) ) ) )).

fof(t26_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v3_relat_1(D)
                    & v1_matrix_1(D)
                    & v3_goboard1(D)
                    & v4_goboard1(D)
                    & v5_goboard1(D)
                    & v6_goboard1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                 => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(D))
                      & r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,k1_matrix_1(D)) )
                   => r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,k3_finseq_1(D),C))) ) ) ) ) ) )).

fof(t27_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v3_relat_1(D)
                    & v1_matrix_1(D)
                    & v3_goboard1(D)
                    & v4_goboard1(D)
                    & v5_goboard1(D)
                    & v6_goboard1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                 => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(D))
                      & r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,k3_finseq_1(D)) )
                   => r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B)),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,k1_matrix_1(D)))) ) ) ) ) ) )).

fof(t28_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                      & v1_topreal1(C)
                      & r1_tarski(k5_topreal1(np__2,D),k5_topreal1(np__2,C))
                      & r1_xreal_0(np__1,A)
                      & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C)) )
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                       => ( ( E = k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_gobrd13(C,B,A),k5_topreal1(np__2,D))
                            | E = k6_subset_1(u1_struct_0(k15_euclid(np__2)),k4_gobrd13(C,B,A),k5_topreal1(np__2,D)) )
                         => v2_connsp_1(E,k15_euclid(np__2)) ) ) ) ) ) ) ) )).

fof(t29_jordan9,axiom,(
    ! [A] :
      ( ( ~ v3_relat_1(A)
        & v1_matrix_1(A)
        & v3_goboard1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & v6_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & ~ v5_seqm_3(B)
            & v1_topreal1(B)
            & v2_topreal1(B)
            & v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
            & v1_goboard5(B)
            & v2_goboard5(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( ( r1_xreal_0(np__1,C)
                    & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(B)) )
                 => ( r1_tarski(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_gobrd13(B,A,C),k5_topreal1(np__2,B)),k3_goboard9(B))
                    & r1_tarski(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k4_gobrd13(B,A,C),k5_topreal1(np__2,B)),k2_goboard9(B)) ) ) ) ) ) ) )).

fof(t30_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan8(B,A)))
              & r2_hidden(k32_pscomp_1(B),k3_goboard5(k1_jordan8(B,A),C,k5_binarith(k1_matrix_1(k1_jordan8(B,A)),np__1)))
              & k32_pscomp_1(B) != k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k5_binarith(k1_matrix_1(k1_jordan8(B,A)),np__1)) ) ) ) )).

fof(t31_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(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)))) )
         => ! [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(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan8(B,A)))
                      & r2_hidden(k32_pscomp_1(B),k3_goboard5(k1_jordan8(B,A),C,k5_binarith(k1_matrix_1(k1_jordan8(B,A)),np__1)))
                      & r1_xreal_0(np__1,D)
                      & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(k1_jordan8(B,A)))
                      & r2_hidden(k32_pscomp_1(B),k3_goboard5(k1_jordan8(B,A),D,k5_binarith(k1_matrix_1(k1_jordan8(B,A)),np__1))) )
                   => ( k32_pscomp_1(B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k5_binarith(k1_matrix_1(k1_jordan8(B,A)),np__1))
                      | k32_pscomp_1(B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,k5_binarith(k1_matrix_1(k1_jordan8(B,A)),np__1))
                      | C = D ) ) ) ) ) ) )).

fof(t32_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(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)))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & ~ v5_seqm_3(C)
                & v1_topreal1(C)
                & v2_topreal1(C)
                & v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
                & v1_goboard5(C)
                & v2_goboard5(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(B,A))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(C)) )
                       => ( r1_xboole_0(k4_gobrd13(C,k1_jordan8(B,A),D),B)
                          & ~ r1_xboole_0(k3_gobrd13(C,k1_jordan8(B,A),D),B) ) ) ) )
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(k1_jordan8(B,A)))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,k1_matrix_1(k1_jordan8(B,A)))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_nat_1(D,np__1),k1_matrix_1(k1_jordan8(B,A)))
                          & r2_hidden(k32_pscomp_1(B),k3_goboard5(k1_jordan8(B,A),D,k5_binarith(k1_matrix_1(k1_jordan8(B,A)),np__1)))
                          & k32_pscomp_1(B) != k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,k5_binarith(k1_matrix_1(k1_jordan8(B,A)),np__1)) ) )
                  | k32_pscomp_1(k5_topreal1(np__2,C)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1) ) ) ) ) ) )).

fof(d1_jordan9,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( v2_connsp_1(A,k15_euclid(np__2))
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_sprect_2(C)
                  & ~ v5_seqm_3(C)
                  & v1_topreal1(C)
                  & v2_topreal1(C)
                  & v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
                  & v1_goboard5(C)
                  & v2_goboard5(C)
                  & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
               => ( C = k1_jordan9(A,B)
                <=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
                    & ? [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & r1_xreal_0(np__1,D)
                        & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(k1_jordan8(A,B)))
                        & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,k1_matrix_1(k1_jordan8(A,B)))
                        & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_nat_1(D,np__1),k1_matrix_1(k1_jordan8(A,B)))
                        & r2_hidden(k32_pscomp_1(A),k3_goboard5(k1_jordan8(A,B),D,k5_binarith(k1_matrix_1(k1_jordan8(A,B)),np__1)))
                        & k32_pscomp_1(A) != k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,k5_binarith(k1_matrix_1(k1_jordan8(A,B)),np__1)) )
                    & ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ( ( r1_xreal_0(np__1,D)
                            & r1_xreal_0(k1_nat_1(D,np__2),k3_finseq_1(C)) )
                         => ( ( ( r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),D),A)
                                & r1_xboole_0(k5_gobrd13(C,k1_jordan8(A,B),D),A) )
                             => r1_gobrd13(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B),D) )
                            & ( r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),D),A)
                             => ( r1_xboole_0(k5_gobrd13(C,k1_jordan8(A,B),D),A)
                                | r3_gobrd13(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B),D) ) )
                            & ( ~ r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),D),A)
                             => r2_gobrd13(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B),D) ) ) ) ) ) ) ) ) ) ) )).

fof(t33_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v6_compts_1(C,k15_euclid(np__2))
                & ~ v1_sppol_1(C)
                & ~ v2_sppol_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ( ( v2_connsp_1(C,k15_euclid(np__2))
                  & r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k1_jordan9(C,B))) )
               => ( r1_xboole_0(k4_gobrd13(k1_jordan9(C,B),k1_jordan8(C,B),A),C)
                  & ~ r1_xboole_0(k3_gobrd13(k1_jordan9(C,B),k1_jordan8(C,B),A),C) ) ) ) ) ) )).

fof(t34_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(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)))) )
         => ( v2_connsp_1(B,k15_euclid(np__2))
           => k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),np__1) ) ) ) )).

fof(dt_k1_jordan9,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(B,k5_numbers) )
     => ( ~ v1_xboole_0(k1_jordan9(A,B))
        & v1_sprect_2(k1_jordan9(A,B))
        & ~ v5_seqm_3(k1_jordan9(A,B))
        & v1_topreal1(k1_jordan9(A,B))
        & v2_topreal1(k1_jordan9(A,B))
        & v1_finseq_6(k1_jordan9(A,B),u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(k1_jordan9(A,B))
        & v2_goboard5(k1_jordan9(A,B))
        & m2_finseq_1(k1_jordan9(A,B),u1_struct_0(k15_euclid(np__2))) ) ) )).

fof(t20_jordan9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_relat_1(C)
                & v1_matrix_1(C)
                & v3_goboard1(C)
                & v4_goboard1(C)
                & v5_goboard1(C)
                & v6_goboard1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
             => ( ( r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                  & r1_xreal_0(np__1,B)
                  & r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(C)) )
               => k3_goboard5(C,A,B) = a_3_0_jordan9(A,B,C) ) ) ) ) )).

fof(fraenkel_a_3_0_jordan9,axiom,(
    ! [A,B,C,D] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m2_subset_1(C,k1_numbers,k5_numbers)
        & ~ v3_relat_1(D)
        & v1_matrix_1(D)
        & v3_goboard1(D)
        & v4_goboard1(D)
        & v5_goboard1(D)
        & v6_goboard1(D)
        & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ( r2_hidden(A,a_3_0_jordan9(B,C,D))
      <=> ? [E,F] :
            ( m1_subset_1(E,k1_numbers)
            & m1_subset_1(F,k1_numbers)
            & A = k23_euclid(E,F)
            & r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,B,C)),E)
            & r1_xreal_0(E,k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(B,np__1),C)))
            & r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,B,C)),F)
            & r1_xreal_0(F,k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,B,k1_nat_1(C,np__1)))) ) ) ) )).
%------------------------------------------------------------------------------