SET007 Axioms: SET007+888.ax


%------------------------------------------------------------------------------
% File     : SET007+888 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Subsequences of Finite Sequences
% Version  : [Urb08] axioms.
% English  : Subsequences of Almost, Weakly and Poorly One-to-one Finite
%            Sequences

% 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    : jordan23 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   67 (   0 unit)
%            Number of atoms       :  566 (  59 equality)
%            Maximal formula depth :   40 (   9 average)
%            Number of connectives :  551 (  52 ~  ;  23  |; 295  &)
%                                         (   8 <=>; 173 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   34 (   0 propositional; 1-3 arity)
%            Number of functors    :   37 (   5 constant; 0-4 arity)
%            Number of variables   :  147 (   0 singleton; 140 !;   7 ?)
%            Maximal term depth    :   11 (   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(fc1_jordan23,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(k5_finseq_1(A))
      & v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v2_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A))
      & v5_seqm_3(k5_finseq_1(A))
      & v1_realset1(k5_finseq_1(A)) ) )).

fof(cc1_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_jordan23(A) ) ) )).

fof(cc2_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_jordan23(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v3_jordan23(A) ) ) )).

fof(fc2_jordan23,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v5_seqm_3(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_realset1(k1_xboole_0)
    & v1_jordan23(k1_xboole_0)
    & v2_jordan23(k1_xboole_0)
    & v3_jordan23(k1_xboole_0) )).

fof(fc3_jordan23,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(k5_finseq_1(A))
      & v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v2_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A))
      & v5_seqm_3(k5_finseq_1(A))
      & v1_realset1(k5_finseq_1(A))
      & v1_jordan23(k5_finseq_1(A))
      & v2_jordan23(k5_finseq_1(A))
      & v3_jordan23(k5_finseq_1(A)) ) )).

fof(fc4_jordan23,axiom,(
    ! [A,B] :
      ( v1_relat_1(k10_finseq_1(A,B))
      & v1_funct_1(k10_finseq_1(A,B))
      & v1_finset_1(k10_finseq_1(A,B))
      & v1_finseq_1(k10_finseq_1(A,B))
      & ~ v1_realset1(k10_finseq_1(A,B))
      & v3_jordan23(k10_finseq_1(A,B)) ) )).

fof(rc1_jordan23,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A)
      & v2_jordan23(A) ) )).

fof(rc2_jordan23,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_finseq_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B)
          & v1_finseq_6(B,A)
          & v2_jordan23(B) ) ) )).

fof(rc3_jordan23,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finseq_1(A)
      & v1_jordan23(A)
      & v3_jordan23(A) ) )).

fof(fc5_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_jordan23(A) )
     => ( v1_relat_1(k3_finseq_5(A))
        & v1_funct_1(k3_finseq_5(A))
        & v1_finseq_1(k3_finseq_5(A))
        & v1_jordan23(k3_finseq_5(A))
        & v3_jordan23(k3_finseq_5(A)) ) ) )).

fof(fc6_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v2_jordan23(A) )
     => ( v1_relat_1(k3_finseq_5(A))
        & v1_funct_1(k3_finseq_5(A))
        & v1_finseq_1(k3_finseq_5(A))
        & v2_jordan23(k3_finseq_5(A)) ) ) )).

fof(fc7_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v3_jordan23(A) )
     => ( v1_relat_1(k3_finseq_5(A))
        & v1_funct_1(k3_finseq_5(A))
        & v1_finseq_1(k3_finseq_5(A))
        & v3_jordan23(k3_finseq_5(A)) ) ) )).

fof(rc4_jordan23,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_finseq_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v2_funct_1(B)
          & v1_finseq_1(B)
          & v1_finseq_6(B,A)
          & v1_jordan23(B)
          & v3_jordan23(B) ) ) )).

fof(fc8_jordan23,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_jordan23(B)
        & m1_finseq_1(B,A)
        & m1_subset_1(C,A) )
     => ( v1_relat_1(k1_finseq_6(A,B,C))
        & v1_funct_1(k1_finseq_6(A,B,C))
        & v1_finseq_1(k1_finseq_6(A,B,C))
        & v1_jordan23(k1_finseq_6(A,B,C))
        & v3_jordan23(k1_finseq_6(A,B,C)) ) ) )).

fof(fc9_jordan23,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_finseq_6(B,A)
        & v2_jordan23(B)
        & m1_finseq_1(B,A)
        & m1_subset_1(C,A) )
     => ( v1_relat_1(k1_finseq_6(A,B,C))
        & v1_funct_1(k1_finseq_6(A,B,C))
        & v1_finseq_1(k1_finseq_6(A,B,C))
        & v2_jordan23(k1_finseq_6(A,B,C)) ) ) )).

fof(fc10_jordan23,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_finseq_6(B,A)
        & v3_jordan23(B)
        & m1_finseq_1(B,A)
        & m1_subset_1(C,A) )
     => ( v1_relat_1(k1_finseq_6(A,B,C))
        & v1_funct_1(k1_finseq_6(A,B,C))
        & v1_finseq_1(k1_finseq_6(A,B,C))
        & v3_jordan23(k1_finseq_6(A,B,C)) ) ) )).

fof(fc11_jordan23,axiom,(
    ! [A,B] :
      ( ( 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_relat_1(k1_jordan9(A,B))
        & v1_funct_1(k1_jordan9(A,B))
        & v1_finseq_1(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))
        & v1_sprect_2(k1_jordan9(A,B))
        & ~ v1_realset1(k1_jordan9(A,B))
        & v1_jordan23(k1_jordan9(A,B))
        & v3_jordan23(k1_jordan9(A,B)) ) ) )).

fof(fc12_jordan23,axiom,(
    ! [A,B] :
      ( ( 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_relat_1(k1_jordan9(A,B))
        & v1_funct_1(k1_jordan9(A,B))
        & v1_finseq_1(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))
        & v1_sprect_2(k1_jordan9(A,B))
        & ~ v1_realset1(k1_jordan9(A,B))
        & v1_jordan23(k1_jordan9(A,B))
        & v2_jordan23(k1_jordan9(A,B))
        & v3_jordan23(k1_jordan9(A,B)) ) ) )).

fof(cc3_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v2_jordan23(A) ) ) )).

fof(t1_jordan23,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)))
         => ( r2_hidden(B,k5_topreal1(np__2,A))
           => r1_xreal_0(np__1,k3_finseq_1(k3_jordan3(A,B))) ) ) ) )).

fof(t2_jordan23,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(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(k4_jordan3(A,B))) ) ) )).

fof(t3_jordan23,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)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => k5_jordan3(A,B,C) != k1_xboole_0 ) ) ) )).

fof(d1_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_jordan23(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( ( r2_hidden(B,k4_finseq_1(A))
                    & r2_hidden(C,k4_finseq_1(A))
                    & k1_funct_1(A,B) = k1_funct_1(A,C) )
                 => ( ( B = np__1
                      & C = k3_finseq_1(A) )
                    | ( B = k3_finseq_1(A)
                      & C = np__1 )
                    | B = C ) ) ) ) ) ) )).

fof(d2_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v2_jordan23(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ~ ( r1_xreal_0(np__1,B)
                & ~ r1_xreal_0(k3_finseq_1(A),B)
                & k1_funct_1(A,B) = k1_funct_1(A,k1_nat_1(B,np__1)) ) ) ) ) )).

fof(d3_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( ( k3_finseq_1(A) != np__2
         => ( v3_jordan23(A)
          <=> ! [B] :
                ( m2_subset_1(B,k1_numbers,k5_numbers)
               => ~ ( r1_xreal_0(np__1,B)
                    & ~ r1_xreal_0(k3_finseq_1(A),B)
                    & k1_funct_1(A,B) = k1_funct_1(A,k1_nat_1(B,np__1)) ) ) ) )
        & ( k3_finseq_1(A) = np__2
         => v3_jordan23(A) ) ) ) )).

fof(t4_jordan23,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ( v1_jordan23(B)
      <=> ! [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => ! [D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ( ( r2_hidden(C,k4_finseq_1(B))
                    & r2_hidden(D,k4_finseq_1(B))
                    & k4_finseq_4(k5_numbers,A,B,C) = k4_finseq_4(k5_numbers,A,B,D) )
                 => ( ( C = np__1
                      & D = k3_finseq_1(B) )
                    | ( C = k3_finseq_1(B)
                      & D = np__1 )
                    | C = D ) ) ) ) ) ) )).

fof(t5_jordan23,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ( v2_jordan23(B)
      <=> ! [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => ~ ( r1_xreal_0(np__1,C)
                & ~ r1_xreal_0(k3_finseq_1(B),C)
                & k4_finseq_4(k5_numbers,A,B,C) = k4_finseq_4(k5_numbers,A,B,k1_nat_1(C,np__1)) ) ) ) ) )).

fof(t6_jordan23,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ( v3_jordan23(B)
      <=> ( k3_finseq_1(B) != np__2
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r1_xreal_0(np__1,C)
                  & ~ r1_xreal_0(k3_finseq_1(B),C)
                  & k4_finseq_4(k5_numbers,A,B,C) = k4_finseq_4(k5_numbers,A,B,k1_nat_1(C,np__1)) ) ) ) ) ) )).

fof(t7_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k3_finseq_1(A) != np__2
       => ( v2_jordan23(A)
        <=> v3_jordan23(A) ) ) ) )).

fof(t8_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_jordan23(A)
       => v1_jordan23(k3_finseq_5(A)) ) ) )).

fof(t9_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v2_jordan23(A)
       => v2_jordan23(k3_finseq_5(A)) ) ) )).

fof(t10_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v3_jordan23(A)
       => v3_jordan23(k3_finseq_5(A)) ) ) )).

fof(t11_jordan23,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ( v1_jordan23(B)
           => ! [C] :
                ( m1_subset_1(C,A)
               => v1_jordan23(k1_finseq_6(A,B,C)) ) ) ) ) )).

fof(t12_jordan23,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ( ( v2_jordan23(B)
              & v1_finseq_6(B,A) )
           => ! [C] :
                ( m1_subset_1(C,A)
               => v2_jordan23(k1_finseq_6(A,B,C)) ) ) ) ) )).

fof(t13_jordan23,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ( ( v3_jordan23(B)
              & v1_finseq_6(B,A) )
           => ! [C] :
                ( m1_subset_1(C,A)
               => v3_jordan23(k1_finseq_6(A,B,C)) ) ) ) ) )).

fof(t14_jordan23,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ( v1_jordan23(B)
          <=> ( v2_funct_1(k1_rfinseq(A,B,np__1))
              & v2_funct_1(k16_finseq_1(A,B,k5_binarith(k3_finseq_1(B),np__1))) ) ) ) ) )).

fof(t15_jordan23,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)))
         => ( ( r2_hidden(B,k5_topreal1(np__2,A))
              & v2_jordan23(A) )
           => k5_jordan3(A,B,B) = k13_binarith(u1_struct_0(k15_euclid(np__2)),B) ) ) ) )).

fof(t16_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v2_funct_1(A)
       => v2_jordan23(A) ) ) )).

fof(t17_jordan23,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v2_jordan23(A)
       => ! [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(B,k5_topreal1(np__2,A))
                    & r2_hidden(C,k5_topreal1(np__2,A)) )
                 => k5_jordan3(A,B,C) = k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k5_jordan3(A,C,B)) ) ) ) ) ) )).

fof(t18_jordan23,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( v3_jordan23(A)
                  & v2_topreal1(A)
                  & v3_topreal1(A)
                  & r1_xreal_0(C,k3_finseq_1(A))
                  & B = k1_funct_1(A,C) )
               => ( r1_xreal_0(C,np__1)
                  | k1_nat_1(k2_jordan3(A,B),np__1) = C ) ) ) ) ) )).

fof(t19_jordan23,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v2_jordan23(A)
       => ! [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(B,k5_topreal1(np__2,A))
                    & r2_hidden(C,k5_topreal1(np__2,A)) )
                 => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k5_jordan3(A,B,C),np__1) = B ) ) ) ) ) )).

fof(t20_jordan23,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v2_jordan23(A)
       => ! [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(B,k5_topreal1(np__2,A))
                    & r2_hidden(C,k5_topreal1(np__2,A)) )
                 => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k5_jordan3(A,B,C),k3_finseq_1(k5_jordan3(A,B,C))) = C ) ) ) ) ) )).

fof(t21_jordan23,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)))
         => ( r2_hidden(B,k5_topreal1(np__2,A))
           => r1_tarski(k5_topreal1(np__2,k3_jordan3(A,B)),k5_topreal1(np__2,A)) ) ) ) )).

fof(t22_jordan23,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)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r2_hidden(B,k5_topreal1(np__2,A))
                  & r2_hidden(C,k5_topreal1(np__2,A))
                  & v2_jordan23(A) )
               => r1_tarski(k5_topreal1(np__2,k5_jordan3(A,B,C)),k5_topreal1(np__2,A)) ) ) ) ) )).

fof(t23_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_tarski(k4_finseq_1(A),k4_finseq_1(k3_graph_2(A,B))) ) ) )).

fof(t24_jordan23,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_tarski(k4_finseq_1(B),k4_finseq_1(k3_graph_2(A,B))) ) ) )).

fof(t25_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( v5_seqm_3(k3_graph_2(A,B))
           => v5_seqm_3(A) ) ) ) )).

fof(t26_jordan23,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( v5_seqm_3(k3_graph_2(A,B))
              & k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,np__1) )
           => ( A = k1_xboole_0
              | v5_seqm_3(B) ) ) ) ) )).

fof(t27_jordan23,axiom,(
    ! [A] :
      ( ( v1_topreal1(A)
        & m2_finseq_1(A,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)
             => v1_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) )).

fof(t28_jordan23,axiom,(
    ! [A] :
      ( ( v2_topreal1(A)
        & m2_finseq_1(A,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)
             => v2_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) )).

fof(t29_jordan23,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v1_topreal1(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
           => ( r2_hidden(B,k5_topreal1(np__2,A))
             => v1_topreal1(k3_jordan3(A,B)) ) ) ) ) )).

fof(t30_jordan23,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v1_topreal1(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
           => ( r2_hidden(B,k5_topreal1(np__2,A))
             => v1_topreal1(k4_jordan3(A,B)) ) ) ) ) )).

fof(t31_jordan23,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( v1_topreal1(A)
          & v2_jordan23(A) )
       => ! [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(B,k5_topreal1(np__2,A))
                    & r2_hidden(C,k5_topreal1(np__2,A)) )
                 => v1_topreal1(k5_jordan3(A,B,C)) ) ) ) ) ) )).

fof(t32_jordan23,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v2_topreal1(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
           => ( r2_hidden(B,k5_topreal1(np__2,A))
             => v2_topreal1(k3_jordan3(A,B)) ) ) ) ) )).

fof(t33_jordan23,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v2_topreal1(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
           => ( r2_hidden(B,k5_topreal1(np__2,A))
             => v2_topreal1(k4_jordan3(A,B)) ) ) ) ) )).

fof(t34_jordan23,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( v2_topreal1(A)
          & v2_jordan23(A) )
       => ! [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(B,k5_topreal1(np__2,A))
                    & r2_hidden(C,k5_topreal1(np__2,A)) )
                 => v2_topreal1(k5_jordan3(A,B,C)) ) ) ) ) ) )).

fof(t35_jordan23,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)))
             => ( ( v1_jordan23(A)
                  & v1_topreal1(A)
                  & v2_topreal1(A)
                  & v3_topreal1(A)
                  & r2_hidden(C,k5_topreal1(np__2,A))
                  & B = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,k2_jordan3(A,C)),k13_binarith(u1_struct_0(k15_euclid(np__2)),C)) )
               => ( C = k1_funct_1(A,np__1)
                  | r1_jordan3(B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),C) ) ) ) ) ) )).

fof(t36_jordan23,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)))
         => ( ( v3_jordan23(A)
              & v2_topreal1(A)
              & v3_topreal1(A)
              & r2_hidden(B,k5_topreal1(np__2,A))
              & B = k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),np__1)) )
           => ( B = k1_funct_1(A,k3_finseq_1(A))
              | k1_nat_1(k1_nat_1(k2_jordan3(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A),B),k2_jordan3(A,B)),np__1) = k3_finseq_1(A) ) ) ) ) )).

fof(t37_jordan23,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v2_jordan23(A)
              & r1_xreal_0(np__2,k3_finseq_1(A)) )
           => k3_jordan3(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) = A ) ) ) )).

fof(t38_jordan23,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v3_jordan23(A)
              & v2_topreal1(A)
              & v3_topreal1(A)
              & r2_hidden(B,k5_topreal1(np__2,A)) )
           => ( B = k1_funct_1(A,k3_finseq_1(A))
              | k3_jordan3(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A),B) = k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k4_jordan3(A,B)) ) ) ) ) )).

fof(t39_jordan23,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)))
         => ( ( v1_jordan23(A)
              & v1_topreal1(A)
              & v2_topreal1(A)
              & v3_topreal1(A)
              & r2_hidden(B,k5_topreal1(np__2,A)) )
           => ( B = k1_funct_1(A,np__1)
              | r1_jordan3(k4_jordan3(A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),B) ) ) ) ) )).

fof(t40_jordan23,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v1_jordan23(A)
              & v1_topreal1(A)
              & v2_topreal1(A)
              & v3_topreal1(A)
              & r2_hidden(B,k5_topreal1(np__2,A)) )
           => ( B = k1_funct_1(A,k3_finseq_1(A))
              | B = k1_funct_1(A,np__1)
              | r1_jordan3(k3_jordan3(A,B),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) ) ) ) ) )).

fof(t41_jordan23,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)))
         => ( ( v1_jordan23(A)
              & v1_topreal1(A)
              & v2_topreal1(A)
              & v3_topreal1(A)
              & r2_hidden(B,k5_topreal1(np__2,A)) )
           => ( B = k1_funct_1(A,np__1)
              | v4_topreal1(k4_jordan3(A,B)) ) ) ) ) )).

fof(t42_jordan23,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v1_jordan23(A)
              & v1_topreal1(A)
              & v2_topreal1(A)
              & v3_topreal1(A)
              & r2_hidden(B,k5_topreal1(np__2,A)) )
           => ( B = k1_funct_1(A,k3_finseq_1(A))
              | B = k1_funct_1(A,np__1)
              | v4_topreal1(k3_jordan3(A,B)) ) ) ) ) )).

fof(t43_jordan23,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(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)))
             => ( ( v1_jordan23(A)
                  & v1_topreal1(A)
                  & v2_topreal1(A)
                  & v3_topreal1(A)
                  & r2_hidden(B,k5_topreal1(np__2,A))
                  & r2_hidden(C,k5_topreal1(np__2,A)) )
               => ( k3_finseq_1(A) = np__2
                  | B = C
                  | B = k1_funct_1(A,np__1)
                  | C = k1_funct_1(A,np__1)
                  | r1_jordan3(k5_jordan3(A,B,C),B,C) ) ) ) ) ) )).

fof(t44_jordan23,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(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)))
             => ( ( v1_jordan23(A)
                  & v1_topreal1(A)
                  & v2_topreal1(A)
                  & v3_topreal1(A)
                  & r2_hidden(B,k5_topreal1(np__2,A))
                  & r2_hidden(C,k5_topreal1(np__2,A)) )
               => ( k3_finseq_1(A) = np__2
                  | B = C
                  | B = k1_funct_1(A,np__1)
                  | C = k1_funct_1(A,np__1)
                  | v4_topreal1(k5_jordan3(A,B,C)) ) ) ) ) ) )).

fof(t45_jordan23,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [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] :
              ( 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(C,k1_jordan2c(np__2,k5_topreal1(np__2,k1_jordan9(B,A))))
                      & ! [E] :
                          ( ( v4_topreal1(E)
                            & m2_finseq_1(E,u1_struct_0(k15_euclid(np__2))) )
                         => ~ ( E = k5_jordan3(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k2_jordan3(k1_jordan9(B,A),k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A)))))),k5_binarith(k3_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k2_jordan3(k1_jordan9(B,A),k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))))))),np__1)),k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))),k1_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))))
                              & ? [F] :
                                  ( v4_topreal1(F)
                                  & m2_finseq_1(F,u1_struct_0(k15_euclid(np__2)))
                                  & r1_goboard1(u1_struct_0(k15_euclid(np__2)),F,k3_goboard2(k4_graph_2(u1_struct_0(k15_euclid(np__2)),E,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),k1_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))),k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A)))))))
                                  & k5_topreal1(np__2,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),k1_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))),k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))))) = k5_topreal1(np__2,F)
                                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),F,np__1) = k1_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A)))
                                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),F,k3_finseq_1(F)) = k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A)))
                                  & r1_xreal_0(np__2,k3_finseq_1(F))
                                  & ? [G] :
                                      ( v4_topreal1(G)
                                      & m2_finseq_1(G,u1_struct_0(k15_euclid(np__2)))
                                      & r1_goboard1(u1_struct_0(k15_euclid(np__2)),G,k3_goboard2(k4_graph_2(u1_struct_0(k15_euclid(np__2)),E,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),k1_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))),k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A)))))))
                                      & k5_topreal1(np__2,E) = k5_topreal1(np__2,G)
                                      & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),G,np__1)
                                      & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,k3_finseq_1(E)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),G,k3_finseq_1(G))
                                      & r1_xreal_0(k3_finseq_1(E),k3_finseq_1(G))
                                      & ? [H] :
                                          ( ~ v1_xboole_0(H)
                                          & ~ v5_seqm_3(H)
                                          & v1_topreal1(H)
                                          & v2_topreal1(H)
                                          & v1_finseq_6(H,u1_struct_0(k15_euclid(np__2)))
                                          & v1_goboard5(H)
                                          & v2_goboard5(H)
                                          & m2_finseq_1(H,u1_struct_0(k15_euclid(np__2)))
                                          & H = k4_graph_2(u1_struct_0(k15_euclid(np__2)),G,F) ) ) ) ) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------