SET007 Axioms: SET007+723.ax


%------------------------------------------------------------------------------
% File     : SET007+723 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the General Position of Special Polygons
% 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    : jordan12 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   41 (   2 unit)
%            Number of atoms       :  506 (  45 equality)
%            Maximal formula depth :   33 (  12 average)
%            Number of connectives :  557 (  92 ~  ;  12  |; 297  &)
%                                         (   6 <=>; 150 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-3 arity)
%            Number of functors    :   39 (   5 constant; 0-4 arity)
%            Number of variables   :  148 (   0 singleton; 137 !;  11 ?)
%            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(cc1_jordan12,axiom,(
    ! [A] :
      ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v3_topreal1(A)
       => v1_goboard5(A) ) ) )).

fof(t1_jordan12,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( ~ r1_xreal_0(A,np__1)
          & r1_xreal_0(k5_binarith(A,np__1),np__0) ) ) )).

fof(t2_jordan12,axiom,(
    $true )).

fof(t3_jordan12,axiom,(
    ~ v1_abian(np__1) )).

fof(t4_jordan12,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(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)) )
               => ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(A)),B,C),k2_relat_1(B))
                  & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(A)),B,k1_nat_1(C,np__1)),k2_relat_1(B)) ) ) ) ) ) )).

fof(t5_jordan12,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v2_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
              & v1_goboard5(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
              & r1_xreal_0(np__2,k3_finseq_1(B)) )
           => ( v2_topreal1(A)
              & v3_topreal1(A) ) ) ) ) )).

fof(t6_jordan12,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => r1_tarski(k5_topreal1(np__2,A),k5_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) )).

fof(d1_jordan12,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(A)))
             => ( r1_jordan12(A,B,C)
              <=> ( r1_xboole_0(k5_topreal1(A,B),k2_relat_1(C))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(np__1,D)
                       => ( r1_xreal_0(k3_finseq_1(C),D)
                          | v1_realset1(k5_subset_1(u1_struct_0(k15_euclid(A)),k5_topreal1(A,B),k4_topreal1(A,C,D))) ) ) ) ) ) ) ) ) )).

fof(d2_jordan12,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(A)))
             => ( r2_jordan12(A,B,C)
              <=> ( r1_jordan12(A,B,C)
                  & r1_jordan12(A,C,B) ) ) ) ) ) )).

fof(t7_jordan12,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r2_jordan12(np__2,B,C)
               => ! [D] :
                    ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                   => ( D = k7_relat_1(C,k2_finseq_1(A))
                     => r2_jordan12(np__2,B,D) ) ) ) ) ) ) )).

fof(t8_jordan12,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,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)))
                 => ( r2_jordan12(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B),k4_graph_2(u1_struct_0(k15_euclid(np__2)),C,D))
                   => r2_jordan12(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B),C) ) ) ) ) ) )).

fof(t9_jordan12,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_finseq_1(C,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))
                  & r2_jordan12(np__2,B,C) )
               => ( r2_hidden(k1_funct_1(C,A),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,B)))
                  & r2_hidden(k1_funct_1(C,k1_nat_1(A,np__1)),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,B))) ) ) ) ) ) )).

fof(t10_jordan12,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_jordan12(np__2,A,B)
           => ! [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),k3_finseq_1(B)) )
                     => v1_realset1(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,C),k4_topreal1(np__2,B,D))) ) ) ) ) ) ) )).

fof(t12_jordan12,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_jordan12(np__2,A,B)
           => v1_finset_1(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B))) ) ) ) )).

fof(t13_jordan12,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_jordan12(np__2,A,B)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => v1_finset_1(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k4_topreal1(np__2,B,C))) ) ) ) ) )).

fof(t14_jordan12,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_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)))
             => ~ ( r1_xboole_0(k3_topreal1(np__2,B,C),k5_topreal1(np__2,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                     => ~ ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A)),D)
                          & r2_hidden(B,D)
                          & r2_hidden(C,D) ) ) ) ) ) ) )).

fof(t15_jordan12,axiom,(
    ! [A,B,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))) )
     => ( ~ ( ? [D] :
                ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                & r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,C)),D)
                & r2_hidden(A,D)
                & r2_hidden(B,D) )
            & ~ ( r2_hidden(A,k3_goboard9(C))
                & r2_hidden(B,k3_goboard9(C)) )
            & ~ ( r2_hidden(A,k2_goboard9(C))
                & r2_hidden(B,k2_goboard9(C)) ) )
        & ~ ( ( ( r2_hidden(A,k3_goboard9(C))
                & r2_hidden(B,k3_goboard9(C)) )
              | ( r2_hidden(A,k2_goboard9(C))
                & r2_hidden(B,k2_goboard9(C)) ) )
            & ! [D] :
                ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
               => ~ ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,C)),D)
                    & r2_hidden(A,D)
                    & r2_hidden(B,D) ) ) ) ) ) )).

fof(t16_jordan12,axiom,(
    ! [A,B,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))) )
     => ( ( r2_hidden(A,k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,C)))
          & r2_hidden(B,k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,C)))
          & ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ~ ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,C)),D)
                  & r2_hidden(A,D)
                  & r2_hidden(B,D) ) ) )
      <=> ( ( r2_hidden(A,k2_goboard9(C))
            & r2_hidden(B,k3_goboard9(C)) )
          | ( r2_hidden(A,k3_goboard9(C))
            & r2_hidden(B,k2_goboard9(C)) ) ) ) ) )).

fof(t17_jordan12,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B,C,D] :
          ~ ( ? [E] :
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                & r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A)),E)
                & r2_hidden(B,E)
                & r2_hidden(C,E) )
            & ? [E] :
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                & r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A)),E)
                & r2_hidden(C,E)
                & r2_hidden(D,E) )
            & ! [E] :
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
               => ~ ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A)),E)
                    & r2_hidden(B,E)
                    & r2_hidden(D,E) ) ) ) ) )).

fof(t18_jordan12,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B,C,D] :
          ~ ( r2_hidden(B,k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A)))
            & r2_hidden(C,k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A)))
            & r2_hidden(D,k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A)))
            & ! [E] :
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
               => ~ ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A)),E)
                    & r2_hidden(B,E)
                    & r2_hidden(C,E) ) )
            & ! [E] :
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
               => ~ ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A)),E)
                    & r2_hidden(C,E)
                    & r2_hidden(D,E) ) )
            & ! [E] :
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
               => ~ ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A)),E)
                    & r2_hidden(B,E)
                    & r2_hidden(D,E) ) ) ) ) )).

fof(t19_jordan12,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)))) )
         => ( r1_xreal_0(A,k3_finseq_1(B))
           => v1_jordan1(k1_goboard5(B,A),np__2) ) ) ) )).

fof(t20_jordan12,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)))) )
         => ( r1_xreal_0(A,k1_matrix_1(B))
           => v1_jordan1(k2_goboard5(B,A),np__2) ) ) ) )).

fof(t21_jordan12,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(A,k3_finseq_1(C))
                  & r1_xreal_0(B,k1_matrix_1(C)) )
               => v1_jordan1(k3_goboard5(C,A,B),np__2) ) ) ) ) )).

fof(t22_jordan12,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(np__1,B)
              & r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A)) )
           => v1_jordan1(k5_goboard5(A,B),np__2) ) ) ) )).

fof(t23_jordan12,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(np__1,B)
              & r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A)) )
           => ( v1_jordan1(k4_gobrd13(A,k3_goboard2(A),B),np__2)
              & v1_jordan1(k3_gobrd13(A,k3_goboard2(A),B),np__2) ) ) ) ) )).

fof(t24_jordan12,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] :
              ( ( ~ 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))) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r2_hidden(D,k3_topreal1(np__2,A,B))
                      & ? [E] : k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,C),k3_topreal1(np__2,A,B)) = k1_tarski(E)
                      & ~ r2_hidden(D,k5_topreal1(np__2,C))
                      & ~ r1_xboole_0(k5_topreal1(np__2,C),k3_topreal1(np__2,A,D))
                      & ~ r1_xboole_0(k5_topreal1(np__2,C),k3_topreal1(np__2,D,B)) ) ) ) ) ) )).

fof(t25_jordan12,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)))
                 => ( ( v2_sppol_1(k3_topreal1(np__2,A,B))
                      & v2_sppol_1(k3_topreal1(np__2,C,D)) )
                   => ( r2_subset_1(k3_topreal1(np__2,A,B),k3_topreal1(np__2,C,D))
                      | k21_euclid(A) = k21_euclid(C) ) ) ) ) ) ) )).

fof(t26_jordan12,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)))
             => ~ ( ~ r2_hidden(A,k3_topreal1(np__2,B,C))
                  & k22_euclid(B) = k22_euclid(C)
                  & k22_euclid(C) = k22_euclid(A)
                  & ~ r2_hidden(B,k3_topreal1(np__2,A,C))
                  & ~ r2_hidden(C,k3_topreal1(np__2,A,B)) ) ) ) ) )).

fof(t27_jordan12,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)))
             => ~ ( ~ r2_hidden(A,k3_topreal1(np__2,B,C))
                  & k21_euclid(B) = k21_euclid(C)
                  & k21_euclid(C) = k21_euclid(A)
                  & ~ r2_hidden(B,k3_topreal1(np__2,A,C))
                  & ~ r2_hidden(C,k3_topreal1(np__2,A,B)) ) ) ) ) )).

fof(t28_jordan12,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)))
             => ~ ( A != B
                  & A != C
                  & r2_hidden(A,k3_topreal1(np__2,B,C))
                  & r2_hidden(B,k3_topreal1(np__2,A,C)) ) ) ) ) )).

fof(t29_jordan12,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)))
                 => ~ ( ~ r2_hidden(D,k3_topreal1(np__2,B,C))
                      & r2_hidden(A,k3_topreal1(np__2,B,C))
                      & A != B
                      & A != C
                      & ( ( k21_euclid(B) = k21_euclid(C)
                          & k21_euclid(C) = k21_euclid(D) )
                        | ( k22_euclid(B) = k22_euclid(C)
                          & k22_euclid(C) = k22_euclid(D) ) )
                      & ~ r2_hidden(B,k3_topreal1(np__2,D,A))
                      & ~ r2_hidden(C,k3_topreal1(np__2,D,A)) ) ) ) ) ) )).

fof(t30_jordan12,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,u1_struct_0(k15_euclid(np__2)))
                     => ~ ( ( ( k21_euclid(A) = k21_euclid(B)
                              & k21_euclid(C) = k21_euclid(D) )
                            | ( k22_euclid(A) = k22_euclid(B)
                              & k22_euclid(C) = k22_euclid(D) ) )
                          & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,A,B),k3_topreal1(np__2,C,D)) = k1_tarski(E)
                          & E != A
                          & E != B
                          & E != C ) ) ) ) ) ) )).

fof(t31_jordan12,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] :
                  ( ( ~ v1_xboole_0(D)
                    & ~ v5_seqm_3(D)
                    & v1_topreal1(D)
                    & v2_topreal1(D)
                    & v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
                    & v1_goboard5(D)
                    & v2_goboard5(D)
                    & m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
                 => ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k3_topreal1(np__2,B,C)) = k1_tarski(A)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                       => ~ ( ~ r2_hidden(E,k3_topreal1(np__2,B,C))
                            & ~ r2_hidden(B,k5_topreal1(np__2,D))
                            & ~ r2_hidden(C,k5_topreal1(np__2,D))
                            & ( ( k21_euclid(B) = k21_euclid(C)
                                & k21_euclid(B) = k21_euclid(E) )
                              | ( k22_euclid(B) = k22_euclid(C)
                                & k22_euclid(B) = k22_euclid(E) ) )
                            & ? [F] :
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                                & r1_xreal_0(np__1,F)
                                & r1_xreal_0(k1_nat_1(F,np__1),k3_finseq_1(D))
                                & ( r2_hidden(E,k3_gobrd13(D,k3_goboard2(D),F))
                                  | r2_hidden(E,k4_gobrd13(D,k3_goboard2(D),F)) )
                                & r2_hidden(A,k4_topreal1(np__2,D,F)) )
                            & ~ r2_hidden(E,k5_topreal1(np__2,D))
                            & ! [F] :
                                ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                               => ~ ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D)),F)
                                    & r2_hidden(E,F)
                                    & r2_hidden(B,F) ) )
                            & ! [F] :
                                ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                               => ~ ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D)),F)
                                    & r2_hidden(E,F)
                                    & r2_hidden(C,F) ) ) ) ) ) ) ) ) ) )).

fof(t32_jordan12,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_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)))
                 => ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k3_topreal1(np__2,B,C)) = k1_tarski(D)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                           => ~ ( ~ r2_hidden(B,k5_topreal1(np__2,A))
                                & ~ r2_hidden(C,k5_topreal1(np__2,A))
                                & ( ( k21_euclid(B) = k21_euclid(C)
                                    & k21_euclid(B) = k21_euclid(E)
                                    & k21_euclid(E) = k21_euclid(F) )
                                  | ( k22_euclid(B) = k22_euclid(C)
                                    & k22_euclid(B) = k22_euclid(E)
                                    & k22_euclid(E) = k22_euclid(F) ) )
                                & ? [G] :
                                    ( m2_subset_1(G,k1_numbers,k5_numbers)
                                    & r1_xreal_0(np__1,G)
                                    & r1_xreal_0(k1_nat_1(G,np__1),k3_finseq_1(A))
                                    & r2_hidden(E,k4_gobrd13(A,k3_goboard2(A),G))
                                    & r2_hidden(F,k3_gobrd13(A,k3_goboard2(A),G))
                                    & r2_hidden(D,k4_topreal1(np__2,A,G)) )
                                & ~ r2_hidden(E,k5_topreal1(np__2,A))
                                & ~ r2_hidden(F,k5_topreal1(np__2,A))
                                & ? [G] :
                                    ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                                    & r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A)),G)
                                    & r2_hidden(B,G)
                                    & r2_hidden(C,G) ) ) ) ) ) ) ) ) ) )).

fof(t33_jordan12,axiom,(
    ! [A] :
      ( m1_subset_1(A,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))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,B),k3_topreal1(np__2,C,D)) = k1_tarski(A)
                      & r1_xboole_0(k2_relat_1(B),k3_topreal1(np__2,C,D)) )
                   => ( ( k21_euclid(C) != k21_euclid(D)
                        & k22_euclid(C) != k22_euclid(D) )
                      | r2_hidden(C,k5_topreal1(np__2,B))
                      | r2_hidden(D,k5_topreal1(np__2,B))
                      | ! [E] :
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                         => ~ ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,B)),E)
                              & r2_hidden(C,E)
                              & r2_hidden(D,E) ) ) ) ) ) ) ) ) )).

fof(t34_jordan12,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( v1_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( r2_jordan12(np__2,A,B)
           => ! [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)) )
                 => ( ( v1_abian(k1_card_1(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k4_topreal1(np__2,B,C))))
                      & m2_subset_1(k1_card_1(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k4_topreal1(np__2,B,C))),k1_numbers,k5_numbers) )
                  <=> ? [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                        & r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A)),D)
                        & r2_hidden(k1_funct_1(B,C),D)
                        & r2_hidden(k1_funct_1(B,k1_nat_1(C,np__1)),D) ) ) ) ) ) ) ) )).

fof(t35_jordan12,axiom,(
    ! [A] :
      ( ( v1_topreal1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( v1_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ! [C] :
              ( ( v1_topreal1(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => ( ( ~ v1_xboole_0(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
                  & ~ v5_seqm_3(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
                  & v1_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
                  & v2_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
                  & v1_finseq_6(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B),u1_struct_0(k15_euclid(np__2)))
                  & v1_goboard5(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
                  & v2_goboard5(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
                  & m2_finseq_1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B),u1_struct_0(k15_euclid(np__2)))
                  & r2_jordan12(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B),C)
                  & r1_xreal_0(np__2,k3_finseq_1(C))
                  & v2_topreal1(C)
                  & v3_topreal1(C) )
               => ( ( v1_abian(k1_card_1(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)),k5_topreal1(np__2,C))))
                    & m2_subset_1(k1_card_1(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)),k5_topreal1(np__2,C))),k1_numbers,k5_numbers) )
                <=> ? [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                      & r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))),D)
                      & r2_hidden(k1_funct_1(C,np__1),D)
                      & r2_hidden(k1_funct_1(C,k3_finseq_1(C)),D) ) ) ) ) ) ) )).

fof(t36_jordan12,axiom,(
    ! [A] :
      ( ( v1_topreal1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( v1_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ! [C] :
              ( ( v1_topreal1(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => ! [D] :
                  ( ( v1_topreal1(D)
                    & m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
                 => ( ( ~ v1_xboole_0(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
                      & ~ v5_seqm_3(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
                      & v1_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
                      & v2_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
                      & v1_finseq_6(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B),u1_struct_0(k15_euclid(np__2)))
                      & v1_goboard5(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
                      & v2_goboard5(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))
                      & m2_finseq_1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B),u1_struct_0(k15_euclid(np__2)))
                      & ~ v1_xboole_0(k4_graph_2(u1_struct_0(k15_euclid(np__2)),C,D))
                      & ~ v5_seqm_3(k4_graph_2(u1_struct_0(k15_euclid(np__2)),C,D))
                      & v1_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),C,D))
                      & v2_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),C,D))
                      & v1_finseq_6(k4_graph_2(u1_struct_0(k15_euclid(np__2)),C,D),u1_struct_0(k15_euclid(np__2)))
                      & v1_goboard5(k4_graph_2(u1_struct_0(k15_euclid(np__2)),C,D))
                      & v2_goboard5(k4_graph_2(u1_struct_0(k15_euclid(np__2)),C,D))
                      & m2_finseq_1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),C,D),u1_struct_0(k15_euclid(np__2)))
                      & r1_xboole_0(k5_topreal1(np__2,A),k5_topreal1(np__2,D))
                      & r1_xboole_0(k5_topreal1(np__2,B),k5_topreal1(np__2,C))
                      & r2_jordan12(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B),k4_graph_2(u1_struct_0(k15_euclid(np__2)),C,D)) )
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(k15_euclid(np__2)))
                                   => ~ ( k1_funct_1(A,np__1) = E
                                        & k1_funct_1(A,k3_finseq_1(A)) = F
                                        & k1_funct_1(C,np__1) = G
                                        & k1_funct_1(C,k3_finseq_1(C)) = H
                                        & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)
                                        & 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)),D,np__1)
                                        & r2_hidden(E,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)))
                                        & r2_hidden(G,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,C),k5_topreal1(np__2,D)))
                                        & ? [I] :
                                            ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                                            & r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B))),I)
                                            & r2_hidden(G,I)
                                            & r2_hidden(H,I) )
                                        & ! [I] :
                                            ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                                           => ~ ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),C,D))),I)
                                                & r2_hidden(E,I)
                                                & r2_hidden(F,I) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(symmetry_r2_jordan12,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_finseq_1(B,u1_struct_0(k15_euclid(A)))
        & m1_finseq_1(C,u1_struct_0(k15_euclid(A))) )
     => ( r2_jordan12(A,B,C)
       => r2_jordan12(A,C,B) ) ) )).

fof(t11_jordan12,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => v1_finset_1(k3_setfam_1(a_1_0_jordan12(A),a_1_0_jordan12(B))) ) ) )).

fof(fraenkel_a_1_0_jordan12,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
     => ( r2_hidden(A,a_1_0_jordan12(B))
      <=> ? [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = k4_topreal1(np__2,B,C)
            & r1_xreal_0(np__1,C)
            & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(B)) ) ) ) )).
%------------------------------------------------------------------------------