SET007 Axioms: SET007+672.ax


%------------------------------------------------------------------------------
% File     : SET007+672 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Properties of Cells and Arcs
% 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    : jordan1b [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   46 (   0 unit)
%            Number of atoms       :  380 (  19 equality)
%            Maximal formula depth :   26 (  10 average)
%            Number of connectives :  416 (  82 ~  ;   5  |; 203  &)
%                                         (   1 <=>; 125 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   0 propositional; 1-3 arity)
%            Number of functors    :   47 (   6 constant; 0-4 arity)
%            Number of variables   :  114 (   0 singleton; 111 !;   3 ?)
%            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(cc1_jordan1b,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal2(A)
       => ( ~ v1_xboole_0(A)
          & v2_connsp_1(A,k15_euclid(np__2))
          & v6_compts_1(A,k15_euclid(np__2))
          & ~ v1_sppol_1(A)
          & ~ v2_sppol_1(A)
          & v1_topreal2(A) ) ) ) )).

fof(rc1_jordan1b,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_connsp_3(B,A)
          & ~ v1_xboole_0(B) ) ) )).

fof(t1_jordan1b,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_connsp_3(B,A) )
         => ( v2_connsp_1(B,A)
           => r3_connsp_1(A,B) ) ) ) )).

fof(t2_jordan1b,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_xboole_0(A)
      <=> v1_xboole_0(k3_finseq_5(A)) ) ) )).

fof(t3_jordan1b,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [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(C,k3_finseq_1(B))
                      & r1_xreal_0(np__1,D)
                      & r1_xreal_0(D,k3_finseq_1(B))
                      & v1_xboole_0(k1_jordan3(A,B,C,D)) ) ) ) ) ) )).

fof(t4_jordan1b,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( r1_xreal_0(np__1,k3_finseq_1(A))
              & r2_hidden(B,k5_topreal1(np__2,A)) )
           => k1_funct_1(k4_jordan3(A,B),np__1) = k1_funct_1(A,np__1) ) ) ) )).

fof(t5_jordan1b,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v4_topreal1(A)
              & r2_hidden(B,k5_topreal1(np__2,A)) )
           => k1_funct_1(k3_jordan3(A,B),k3_finseq_1(k3_jordan3(A,B))) = k1_funct_1(A,k3_finseq_1(A)) ) ) ) )).

fof(t6_jordan1b,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => k31_pscomp_1(A) != k34_pscomp_1(A) ) )).

fof(t7_jordan1b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,B)
             => ( r1_xreal_0(np__1,A)
               => ( r1_xreal_0(k3_finseq_1(C),A)
                  | k8_finseq_1(B,k1_jordan3(B,C,A,k5_binarith(k3_finseq_1(C),np__1)),k13_binarith(B,k4_finseq_4(k5_numbers,B,C,k3_finseq_1(C)))) = k1_jordan3(B,C,A,k3_finseq_1(C)) ) ) ) ) ) )).

fof(t8_jordan1b,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)))
         => ( v2_sppol_1(k3_topreal1(np__2,A,B))
           => ( A = B
              | v4_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) )).

fof(t9_jordan1b,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)))
         => ( v1_sppol_1(k3_topreal1(np__2,A,B))
           => ( A = B
              | v4_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) )).

fof(t10_jordan1b,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] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_sprect_2(B,A)
               => r1_sprect_2(B,k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,C)) ) ) ) ) )).

fof(t11_jordan1b,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => r1_sprect_2(A,k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) )).

fof(t12_jordan1b,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => r1_xreal_0(np__1,k1_jordan1a(A)) ) )).

fof(t13_jordan1b,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( r1_xreal_0(np__1,k3_finseq_1(A))
       => r1_xreal_0(k1_jordan1a(A),k3_finseq_1(A)) ) ) )).

fof(t14_jordan1b,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)))) )
     => r1_xreal_0(k1_jordan1a(A),k3_finseq_1(A)) ) )).

fof(t15_jordan1b,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ~ ( r1_xreal_0(np__2,k3_finseq_1(A))
          & r1_xreal_0(k1_jordan1a(A),np__1) ) ) )).

fof(t16_jordan1b,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ~ ( r1_xreal_0(np__3,k3_finseq_1(A))
          & r1_xreal_0(k3_finseq_1(A),k1_jordan1a(A)) ) ) )).

fof(t17_jordan1b,axiom,(
    ! [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)
         => k1_jordan1a(k1_jordan8(A,B)) = k1_nat_1(k1_card_4(np__2,k5_binarith(B,np__1)),np__2) ) ) )).

fof(t18_jordan1b,axiom,(
    ! [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)))) )
     => r1_tarski(A,k3_goboard5(k1_jordan8(A,np__0),np__2,np__2)) ) )).

fof(t19_jordan1b,axiom,(
    ! [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)))) )
     => ~ r1_tarski(k3_goboard5(k1_jordan8(A,np__0),np__2,np__2),k1_jordan2c(np__2,A)) ) )).

fof(t20_jordan1b,axiom,(
    ! [A] :
      ( ( v2_connsp_1(A,k15_euclid(np__2))
        & 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)))) )
     => k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,np__1),k1_jordan1a(k1_jordan8(A,np__1)),np__1) = k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,np__1)))) ) )).

fof(t21_jordan1b,axiom,(
    ! [A] :
      ( ( v2_connsp_1(A,k15_euclid(np__2))
        & 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)))) )
     => k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,np__1),k1_jordan1a(k1_jordan8(A,np__1)),k3_finseq_1(k1_jordan8(A,np__1))) = k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k19_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,np__1)))) ) )).

fof(t22_jordan1b,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r1_xreal_0(np__1,B)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(A))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k1_matrix_1(A))
                          & r2_hidden(E,k3_goboard5(A,k3_finseq_1(A),B))
                          & k21_euclid(E) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D)) )
                       => ( r1_xreal_0(k1_matrix_1(A),B)
                          | k3_finseq_1(A) = C ) ) ) ) ) ) ) )).

fof(t23_jordan1b,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ~ ( r1_xreal_0(np__1,B)
                              & r1_xreal_0(B,k3_finseq_1(A))
                              & r1_xreal_0(np__1,C)
                              & ~ r1_xreal_0(k1_matrix_1(A),C)
                              & r1_xreal_0(np__1,D)
                              & r1_xreal_0(D,k3_finseq_1(A))
                              & r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,k1_matrix_1(A))
                              & r2_hidden(F,k3_goboard5(A,B,C))
                              & k21_euclid(F) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E))
                              & B != D
                              & B != k5_binarith(D,np__1) ) ) ) ) ) ) ) )).

fof(t24_jordan1b,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r1_xreal_0(np__1,B)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(A))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k1_matrix_1(A))
                          & r2_hidden(E,k3_goboard5(A,B,k1_matrix_1(A)))
                          & k22_euclid(E) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D)) )
                       => ( r1_xreal_0(k3_finseq_1(A),B)
                          | k1_matrix_1(A) = D ) ) ) ) ) ) ) )).

fof(t25_jordan1b,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ~ ( r1_xreal_0(np__1,B)
                              & ~ r1_xreal_0(k3_finseq_1(A),B)
                              & r1_xreal_0(np__1,C)
                              & r1_xreal_0(C,k1_matrix_1(A))
                              & r1_xreal_0(np__1,D)
                              & r1_xreal_0(D,k3_finseq_1(A))
                              & r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,k1_matrix_1(A))
                              & r2_hidden(F,k3_goboard5(A,B,C))
                              & k22_euclid(F) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E))
                              & C != E
                              & C != k5_binarith(E,np__1) ) ) ) ) ) ) ) )).

fof(t26_jordan1b,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(k18_pscomp_1(A),B)
              & r1_xreal_0(B,k20_pscomp_1(A))
              & r2_subset_1(k3_topreal1(np__2,k23_euclid(B,k21_pscomp_1(A)),k23_euclid(B,k19_pscomp_1(A))),k8_jordan6(A)) ) ) ) )).

fof(t27_jordan1b,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(k18_pscomp_1(A),B)
              & r1_xreal_0(B,k20_pscomp_1(A))
              & r2_subset_1(k3_topreal1(np__2,k23_euclid(B,k21_pscomp_1(A)),k23_euclid(B,k19_pscomp_1(A))),k9_jordan6(A)) ) ) ) )).

fof(t28_jordan1b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(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(C,np__1)
                  & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
                  & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k3_finseq_1(k1_jordan8(B,A)))),k8_jordan6(B)) ) ) ) ) )).

fof(t29_jordan1b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(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(C,np__1)
                  & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
                  & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k3_finseq_1(k1_jordan8(B,A)))),k9_jordan6(B)) ) ) ) ) )).

fof(t30_jordan1b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ~ r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),k3_finseq_1(k1_jordan8(B,A)))),k8_jordan6(B)) ) ) )).

fof(t31_jordan1b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_topreal2(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ~ r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),k3_finseq_1(k1_jordan8(B,A)))),k9_jordan6(B)) ) ) )).

fof(t32_jordan1b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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(C,k3_finseq_1(k1_jordan8(B,A)))
                  & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k3_finseq_1(k1_jordan8(B,A)))),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) ) ) )).

fof(t33_jordan1b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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(C,k3_finseq_1(k1_jordan8(B,A)))
                  & r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k3_finseq_1(k1_jordan8(B,A)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) ) ) )).

fof(t34_jordan1b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ~ r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),k3_finseq_1(k1_jordan8(B,A)))),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) )).

fof(t35_jordan1b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ~ r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),k3_finseq_1(k1_jordan8(B,A)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) )).

fof(t36_jordan1b,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r1_xreal_0(B,k1_matrix_1(A))
              & v1_jordan2c(k3_goboard5(A,np__0,B),np__2) ) ) ) )).

fof(t37_jordan1b,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r1_xreal_0(B,k1_matrix_1(A))
              & v1_jordan2c(k3_goboard5(A,k3_finseq_1(A),B),np__2) ) ) ) )).

fof(t38_jordan1b,axiom,(
    ! [A] :
      ( ( v2_connsp_1(A,k15_euclid(np__2))
        & 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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(B,k1_matrix_1(k1_jordan8(A,C)))
               => r1_tarski(k3_goboard5(k1_jordan8(A,C),np__0,B),k2_jordan2c(np__2,A)) ) ) ) ) )).

fof(t39_jordan1b,axiom,(
    ! [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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(B,k3_finseq_1(k1_jordan8(A,C)))
               => r1_tarski(k3_goboard5(k1_jordan8(A,C),k3_finseq_1(k1_jordan8(A,C)),B),k2_jordan2c(np__2,A)) ) ) ) ) )).

fof(t40_jordan1b,axiom,(
    ! [A] :
      ( ( v2_connsp_1(A,k15_euclid(np__2))
        & 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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(B,k3_finseq_1(k1_jordan8(A,C)))
                      & r1_xreal_0(D,k1_matrix_1(k1_jordan8(A,C)))
                      & r1_tarski(k3_goboard5(k1_jordan8(A,C),B,D),k1_jordan2c(np__2,A))
                      & r1_xreal_0(D,np__1) ) ) ) ) ) )).

fof(t41_jordan1b,axiom,(
    ! [A] :
      ( ( v2_connsp_1(A,k15_euclid(np__2))
        & 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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(B,k3_finseq_1(k1_jordan8(A,C)))
                      & r1_xreal_0(D,k1_matrix_1(k1_jordan8(A,C)))
                      & r1_tarski(k3_goboard5(k1_jordan8(A,C),B,D),k1_jordan2c(np__2,A))
                      & r1_xreal_0(B,np__1) ) ) ) ) ) )).

fof(t42_jordan1b,axiom,(
    ! [A] :
      ( ( v2_connsp_1(A,k15_euclid(np__2))
        & 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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(B,k3_finseq_1(k1_jordan8(A,C)))
                      & r1_xreal_0(D,k1_matrix_1(k1_jordan8(A,C)))
                      & r1_tarski(k3_goboard5(k1_jordan8(A,C),B,D),k1_jordan2c(np__2,A))
                      & r1_xreal_0(k1_matrix_1(k1_jordan8(A,C)),k1_nat_1(D,np__1)) ) ) ) ) ) )).

fof(t43_jordan1b,axiom,(
    ! [A] :
      ( ( v2_connsp_1(A,k15_euclid(np__2))
        & 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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(B,k3_finseq_1(k1_jordan8(A,C)))
                      & r1_xreal_0(D,k1_matrix_1(k1_jordan8(A,C)))
                      & r1_tarski(k3_goboard5(k1_jordan8(A,C),B,D),k1_jordan2c(np__2,A))
                      & r1_xreal_0(k3_finseq_1(k1_jordan8(A,C)),k1_nat_1(B,np__1)) ) ) ) ) ) )).

fof(t44_jordan1b,axiom,(
    ! [A] :
      ( ( v2_connsp_1(A,k15_euclid(np__2))
        & 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)
         => ( ? [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & ? [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & r1_xreal_0(C,k3_finseq_1(k1_jordan8(A,B)))
                    & r1_xreal_0(D,k1_matrix_1(k1_jordan8(A,B)))
                    & r1_tarski(k3_goboard5(k1_jordan8(A,B),C,D),k1_jordan2c(np__2,A)) ) )
           => r1_xreal_0(np__1,B) ) ) ) )).
%------------------------------------------------------------------------------