SET007 Axioms: SET007+518.ax


%------------------------------------------------------------------------------
% File     : SET007+518 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Steinitz Theorem and the Dimension of a Real Linear Space
% 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    : rlvect_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   52 (   2 unit)
%            Number of atoms       :  605 (  47 equality)
%            Maximal formula depth :   16 (  10 average)
%            Number of connectives :  624 (  71 ~  ;   0  |; 389  &)
%                                         (  11 <=>; 153 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-3 arity)
%            Number of functors    :   40 (   6 constant; 0-4 arity)
%            Number of variables   :  146 (   0 singleton; 131 !;  15 ?)
%            Maximal term depth    :    5 (   1 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(rc1_rlvect_5,axiom,(
    ? [A] :
      ( l2_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v2_rlvect_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v7_rlvect_1(A)
      & v1_rlvect_5(A) ) )).

fof(rc2_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ? [B] :
          ( m1_rlsub_1(B,A)
          & ~ v3_struct_0(B)
          & v2_rlvect_1(B)
          & v3_rlvect_1(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & v7_rlvect_1(B)
          & v1_rlvect_5(B) ) ) )).

fof(cc1_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => v1_rlvect_5(B) ) ) )).

fof(rc3_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => ? [B] :
          ( m1_rlsub_1(B,A)
          & ~ v3_struct_0(B)
          & v2_rlvect_1(B)
          & v3_rlvect_1(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & v7_rlvect_1(B)
          & v1_rlvect_5(B) ) ) )).

fof(t1_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlvect_2(B,A)
         => ! [C] :
              ( m1_rlvect_2(C,A)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_rlvect_3(D,A)
                      & r1_tarski(k10_rlvect_2(A,B),D)
                      & r1_tarski(k10_rlvect_2(A,C),D)
                      & k13_rlvect_2(A,B) = k13_rlvect_2(A,C) )
                   => r1_rlvect_2(A,B,C) ) ) ) ) ) )).

fof(t2_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( v1_rlvect_3(B,A)
              & ! [C] :
                  ( m1_rlvect_3(C,A)
                 => ~ r1_tarski(B,C) ) ) ) ) )).

fof(t3_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlvect_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k10_rlvect_2(A,B))
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & C = D
                    & k8_funct_2(u1_struct_0(A),k1_numbers,B,D) != np__0 ) ) ) ) ) )).

fof(t4_rlvect_5,axiom,(
    $true )).

fof(t5_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlvect_2(B,A)
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k4_finseq_1(C),k4_finseq_1(C))
                        & v3_funct_2(E,k4_finseq_1(C),k4_finseq_1(C))
                        & m2_relset_1(E,k4_finseq_1(C),k4_finseq_1(C)) )
                     => ( D = k5_relat_1(E,C)
                       => k9_rlvect_1(A,k12_rlvect_2(A,C,B)) = k9_rlvect_1(A,k12_rlvect_2(A,D,B)) ) ) ) ) ) ) )).

fof(t6_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlvect_2(B,A)
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ( r1_xboole_0(k10_rlvect_2(A,B),k2_relat_1(C))
               => k9_rlvect_1(A,k12_rlvect_2(A,C,B)) = k1_rlvect_1(A) ) ) ) ) )).

fof(t7_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ( v2_funct_1(B)
           => ! [C] :
                ( m1_rlvect_2(C,A)
               => ( r1_tarski(k10_rlvect_2(A,C),k2_relat_1(B))
                 => k9_rlvect_1(A,k12_rlvect_2(A,B,C)) = k13_rlvect_2(A,C) ) ) ) ) ) )).

fof(t8_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlvect_2(B,A)
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ? [D] :
                  ( m1_rlvect_2(D,A)
                  & k10_rlvect_2(A,D) = k3_xboole_0(k2_relat_1(C),k10_rlvect_2(A,B))
                  & k12_rlvect_2(A,C,B) = k12_rlvect_2(A,C,D) ) ) ) ) )).

fof(t9_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlvect_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ~ ( r1_tarski(k2_relat_1(D),u1_struct_0(k1_rlvect_3(A,C)))
                      & ! [E] :
                          ( m2_rlvect_2(E,A,C)
                         => k9_rlvect_1(A,k12_rlvect_2(A,D,B)) != k13_rlvect_2(A,E) ) ) ) ) ) ) )).

fof(t10_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlvect_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( r1_tarski(k10_rlvect_2(A,B),u1_struct_0(k1_rlvect_3(A,C)))
                  & ! [D] :
                      ( m2_rlvect_2(D,A,C)
                     => k13_rlvect_2(A,B) != k13_rlvect_2(A,D) ) ) ) ) ) )).

fof(t11_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlvect_2(C,A)
             => ( r1_tarski(k10_rlvect_2(A,C),u1_struct_0(B))
               => ! [D] :
                    ( m1_rlvect_2(D,B)
                   => ( D = k7_relat_1(C,u1_struct_0(B))
                     => ( k10_rlvect_2(A,C) = k10_rlvect_2(B,D)
                        & k13_rlvect_2(A,C) = k13_rlvect_2(B,D) ) ) ) ) ) ) ) )).

fof(t12_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlvect_2(C,B)
             => ? [D] :
                  ( m1_rlvect_2(D,A)
                  & k10_rlvect_2(B,C) = k10_rlvect_2(A,D)
                  & k13_rlvect_2(B,C) = k13_rlvect_2(A,D) ) ) ) ) )).

fof(t13_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlvect_2(C,A)
             => ~ ( r1_tarski(k10_rlvect_2(A,C),u1_struct_0(B))
                  & ! [D] :
                      ( m1_rlvect_2(D,B)
                     => ~ ( k10_rlvect_2(B,D) = k10_rlvect_2(A,C)
                          & k13_rlvect_2(B,D) = k13_rlvect_2(A,C) ) ) ) ) ) ) )).

fof(t14_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlvect_3(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_rlvect_1(k1_rlvect_3(A,B),C) ) ) ) )).

fof(t15_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( v1_rlvect_3(C,B)
               => ( v1_rlvect_3(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) )).

fof(t16_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_rlvect_3(C,A)
                  & r1_tarski(C,u1_struct_0(B)) )
               => ( v1_rlvect_3(C,B)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) )).

fof(t17_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlvect_3(C,B)
             => ? [D] :
                  ( m1_rlvect_3(D,A)
                  & r1_tarski(C,D) ) ) ) ) )).

fof(t18_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_rlvect_3(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                 => ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( D = k6_subset_1(u1_struct_0(A),B,k7_rlvect_2(A,C))
                          & r1_rlvect_1(k1_rlvect_3(A,D),C) ) ) ) ) ) ) ) )).

fof(t19_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlvect_3(B,A)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( r1_xboole_0(C,B)
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( D = k4_subset_1(u1_struct_0(A),B,C)
                        & v1_rlvect_3(D,A) ) ) ) ) ) ) )).

fof(t20_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(C,u1_struct_0(B))
               => m1_rlsub_1(k1_rlvect_3(A,C),B) ) ) ) ) )).

fof(t21_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => k1_rlvect_3(A,C) = k1_rlvect_3(B,D) ) ) ) ) ) )).

fof(t22_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( r1_rlvect_1(k1_rlvect_3(A,k2_rlvect_2(A,B,C)),D)
                      & ~ r1_rlvect_1(k1_rlvect_3(A,C),D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(E,B)
                              & r1_rlvect_1(k1_rlvect_3(A,k2_rlvect_2(A,k4_rlvect_2(A,k2_rlvect_2(A,B,C),k7_rlvect_2(A,E)),k7_rlvect_2(A,D))),E) ) ) ) ) ) ) ) )).

fof(t23_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( ( g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) = k1_rlvect_3(A,B)
                  & v1_rlvect_3(C,A) )
               => ( r1_xreal_0(k4_card_1(C),k4_card_1(B))
                  & ? [D] :
                      ( v1_finset_1(D)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                      & r1_tarski(D,B)
                      & k4_card_1(D) = k5_real_1(k4_card_1(B),k4_card_1(C))
                      & g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) = k1_rlvect_3(A,k2_rlvect_2(A,C,D)) ) ) ) ) ) ) )).

fof(d1_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ( v1_rlvect_5(A)
      <=> ? [B] :
            ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
            & m1_rlvect_3(B,A) ) ) ) )).

fof(d2_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ( v1_rlvect_5(A)
      <=> ? [B] :
            ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
            & m1_rlvect_3(B,A) ) ) ) )).

fof(t24_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ( v1_rlvect_5(A)
       => ! [B] :
            ( m1_rlvect_3(B,A)
           => v1_finset_1(B) ) ) ) )).

fof(t25_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ( v1_rlvect_5(A)
       => ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v1_rlvect_3(B,A)
             => v1_finset_1(B) ) ) ) ) )).

fof(t26_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ( v1_rlvect_5(A)
       => ! [B] :
            ( m1_rlvect_3(B,A)
           => ! [C] :
                ( m1_rlvect_3(C,A)
               => k1_card_1(B) = k1_card_1(C) ) ) ) ) )).

fof(t27_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => v1_rlvect_5(k1_rlsub_1(A)) ) )).

fof(t28_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ( v1_rlvect_5(A)
           => v1_rlvect_5(B) ) ) ) )).

fof(d3_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ( v1_rlvect_5(A)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( B = k1_rlvect_5(A)
            <=> ! [C] :
                  ( m1_rlvect_3(C,A)
                 => B = k1_card_1(C) ) ) ) ) ) )).

fof(t29_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => r1_xreal_0(k1_rlvect_5(B),k1_rlvect_5(A)) ) ) )).

fof(t30_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_rlvect_3(B,A)
           => k1_card_1(B) = k1_rlvect_5(k1_rlvect_3(A,B)) ) ) ) )).

fof(t31_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => k1_rlvect_5(A) = k1_rlvect_5(k2_rlsub_1(A)) ) )).

fof(t32_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ( k1_rlvect_5(A) = k1_rlvect_5(B)
          <=> k2_rlsub_1(A) = k2_rlsub_1(B) ) ) ) )).

fof(t33_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => ( k1_rlvect_5(A) = np__0
      <=> k2_rlsub_1(A) = k1_rlsub_1(A) ) ) )).

fof(t34_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => ( k1_rlvect_5(A) = np__1
      <=> ? [B] :
            ( m1_subset_1(B,u1_struct_0(A))
            & B != k1_rlvect_1(A)
            & k2_rlsub_1(A) = k1_rlvect_3(A,k7_rlvect_2(A,B)) ) ) ) )).

fof(t35_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => ( k1_rlvect_5(A) = np__2
      <=> ? [B] :
            ( m1_subset_1(B,u1_struct_0(A))
            & ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & B != C
                & v1_rlvect_3(k8_rlvect_2(A,B,C),A)
                & k2_rlsub_1(A) = k1_rlvect_3(A,k8_rlvect_2(A,B,C)) ) ) ) ) )).

fof(t36_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => k1_nat_1(k1_rlvect_5(k1_rlsub_2(A,B,C)),k1_rlvect_5(k2_rlsub_2(A,B,C))) = k1_nat_1(k1_rlvect_5(B),k1_rlvect_5(C)) ) ) ) )).

fof(t37_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => r1_xreal_0(k5_real_1(k1_nat_1(k1_rlvect_5(B),k1_rlvect_5(C)),k1_rlvect_5(A)),k1_rlvect_5(k2_rlsub_2(A,B,C))) ) ) ) )).

fof(t38_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r1_rlsub_2(A,B,C)
               => k1_rlvect_5(A) = k1_nat_1(k1_rlvect_5(B),k1_rlvect_5(C)) ) ) ) ) )).

fof(t39_rlvect_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v1_rlvect_5(B)
            & l2_rlvect_1(B) )
         => ( r1_xreal_0(A,k1_rlvect_5(B))
          <=> ? [C] :
                ( v2_rlvect_1(C)
                & m1_rlsub_1(C,B)
                & k1_rlvect_5(C) = A ) ) ) ) )).

fof(d4_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v1_rlvect_5(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( C = k2_rlvect_5(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> ? [E] :
                      ( v2_rlvect_1(E)
                      & m1_rlsub_1(E,A)
                      & E = D
                      & k1_rlvect_5(E) = B ) ) ) ) ) )).

fof(t40_rlvect_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v1_rlvect_5(B)
            & l2_rlvect_1(B) )
         => ~ ( r1_xreal_0(A,k1_rlvect_5(B))
              & v1_xboole_0(k2_rlvect_5(B,A)) ) ) ) )).

fof(t41_rlvect_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v1_rlvect_5(B)
            & l2_rlvect_1(B) )
         => ( ~ r1_xreal_0(A,k1_rlvect_5(B))
           => k2_rlvect_5(B,A) = k1_xboole_0 ) ) ) )).

fof(t42_rlvect_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v1_rlvect_5(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_rlsub_1(C,B)
             => r1_tarski(k2_rlvect_5(C,A),k2_rlvect_5(B,A)) ) ) ) )).

fof(dt_k1_rlvect_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => m2_subset_1(k1_rlvect_5(A),k1_numbers,k5_numbers) ) )).

fof(dt_k2_rlvect_5,axiom,(
    $true )).
%------------------------------------------------------------------------------