SET007 Axioms: SET007+211.ax


%------------------------------------------------------------------------------
% File     : SET007+211 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Subspaces and Cosets of Subspaces in 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    : rlsub_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  114 (  16 unit)
%            Number of atoms       : 1196 (  76 equality)
%            Maximal formula depth :   18 (   9 average)
%            Number of connectives : 1200 ( 118 ~  ;   3  |; 708  &)
%                                         (  27 <=>; 344 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   1 propositional; 0-3 arity)
%            Number of functors    :   25 (   4 constant; 0-4 arity)
%            Number of variables   :  326 (   0 singleton; 315 !;  11 ?)
%            Maximal term depth    :    4 (   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_rlsub_1,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) ) ) )).

fof(d1_rlsub_1,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_rlsub_1(B,A)
          <=> ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( ( r2_hidden(C,B)
                          & r2_hidden(D,B) )
                       => r2_hidden(k4_rlvect_1(A,C,D),B) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_hidden(D,B)
                       => r2_hidden(k3_rlvect_1(A,D,C),B) ) ) ) ) ) ) ) )).

fof(t1_rlsub_1,axiom,(
    $true )).

fof(t2_rlsub_1,axiom,(
    $true )).

fof(t3_rlsub_1,axiom,(
    $true )).

fof(t4_rlsub_1,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_rlsub_1(B,A)
           => ( B = k1_xboole_0
              | r2_hidden(k1_rlvect_1(A),B) ) ) ) ) )).

fof(t5_rlsub_1,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_rlsub_1(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                 => r2_hidden(k5_rlvect_1(A,C),B) ) ) ) ) ) )).

fof(t6_rlsub_1,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_rlsub_1(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => r2_hidden(k6_rlvect_1(A,C,D),B) ) ) ) ) ) ) )).

fof(t7_rlsub_1,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_rlsub_1(k1_struct_0(A,k1_rlvect_1(A)),A) ) )).

fof(t8_rlsub_1,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)))
         => ( u1_struct_0(A) = B
           => v1_rlsub_1(B,A) ) ) ) )).

fof(t10_rlsub_1,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)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_rlsub_1(B,A)
                  & v1_rlsub_1(C,A) )
               => v1_rlsub_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(d2_rlsub_1,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ( m1_rlsub_1(B,A)
          <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & u2_struct_0(B) = u2_struct_0(A)
              & u1_rlvect_1(B) = k1_realset1(u1_rlvect_1(A),u1_struct_0(B))
              & u2_rlvect_1(B) = k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(B))) ) ) ) ) )).

fof(t11_rlsub_1,axiom,(
    $true )).

fof(t12_rlsub_1,axiom,(
    $true )).

fof(t13_rlsub_1,axiom,(
    $true )).

fof(t14_rlsub_1,axiom,(
    $true )).

fof(t15_rlsub_1,axiom,(
    $true )).

fof(t16_rlsub_1,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,C] :
          ( m1_rlsub_1(C,A)
         => ! [D] :
              ( m1_rlsub_1(D,A)
             => ( ( r1_rlvect_1(C,B)
                  & m1_rlsub_1(C,D) )
               => r1_rlvect_1(D,B) ) ) ) ) )).

fof(t17_rlsub_1,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,C] :
          ( m1_rlsub_1(C,A)
         => ( r1_rlvect_1(C,B)
           => r1_rlvect_1(A,B) ) ) ) )).

fof(t18_rlsub_1,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,u1_struct_0(B))
             => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).

fof(t19_rlsub_1,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)
         => k1_rlvect_1(B) = k1_rlvect_1(A) ) ) )).

fof(t20_rlsub_1,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_rlsub_1(C,A)
             => k1_rlvect_1(B) = k1_rlvect_1(C) ) ) ) )).

fof(t21_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ( ( E = B
                              & F = C )
                           => k4_rlvect_1(D,E,F) = k4_rlvect_1(A,B,C) ) ) ) ) ) ) ) )).

fof(t22_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ( E = B
                       => k3_rlvect_1(D,E,C) = k3_rlvect_1(A,B,C) ) ) ) ) ) ) )).

fof(t23_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ( D = B
                   => k5_rlvect_1(A,B) = k5_rlvect_1(C,D) ) ) ) ) ) )).

fof(t24_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ( ( E = B
                              & F = C )
                           => k6_rlvect_1(D,E,F) = k6_rlvect_1(A,B,C) ) ) ) ) ) ) ) )).

fof(t25_rlsub_1,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)
         => r1_rlvect_1(B,k1_rlvect_1(A)) ) ) )).

fof(t26_rlsub_1,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_rlsub_1(C,A)
             => r1_rlvect_1(C,k1_rlvect_1(B)) ) ) ) )).

fof(t27_rlsub_1,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)
         => r1_rlvect_1(A,k1_rlvect_1(B)) ) ) )).

fof(t28_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( ( r1_rlvect_1(D,B)
                      & r1_rlvect_1(D,C) )
                   => r1_rlvect_1(D,k4_rlvect_1(A,B,C)) ) ) ) ) ) )).

fof(t29_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( r1_rlvect_1(D,B)
                   => r1_rlvect_1(D,k3_rlvect_1(A,B,C)) ) ) ) ) ) )).

fof(t30_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r1_rlvect_1(C,B)
               => r1_rlvect_1(C,k5_rlvect_1(A,B)) ) ) ) ) )).

fof(t31_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( ( r1_rlvect_1(D,B)
                      & r1_rlvect_1(D,C) )
                   => r1_rlvect_1(D,k6_rlvect_1(A,B,C)) ) ) ) ) ) )).

fof(t32_rlsub_1,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)))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,C)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(C,C),C)
                        & m2_relset_1(E,k2_zfmisc_1(C,C),C) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(k1_numbers,C),C)
                            & m2_relset_1(F,k2_zfmisc_1(k1_numbers,C),C) )
                         => ( ( B = C
                              & D = k1_rlvect_1(A)
                              & E = k1_realset1(u1_rlvect_1(A),B)
                              & F = k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,B)) )
                           => m1_rlsub_1(g2_rlvect_1(C,D,E,F),A) ) ) ) ) ) ) ) )).

fof(t33_rlsub_1,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) )
     => m1_rlsub_1(A,A) ) )).

fof(t34_rlsub_1,axiom,(
    ! [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)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( ~ 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)
            & l2_rlvect_1(B) )
         => ( ( m1_rlsub_1(A,B)
              & m1_rlsub_1(B,A) )
           => A = B ) ) ) )).

fof(t35_rlsub_1,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_rlvect_1(C)
                & l2_rlvect_1(C) )
             => ( ( m1_rlsub_1(A,B)
                  & m1_rlsub_1(B,C) )
               => m1_rlsub_1(A,C) ) ) ) ) )).

fof(t36_rlsub_1,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_rlsub_1(C,A)
             => ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
               => m1_rlsub_1(B,C) ) ) ) ) )).

fof(t37_rlsub_1,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_rlsub_1(C,A)
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_rlvect_1(B,D)
                     => r1_rlvect_1(C,D) ) )
               => m1_rlsub_1(B,C) ) ) ) ) )).

fof(t38_rlsub_1,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] :
          ( ( v2_rlvect_1(B)
            & m1_rlsub_1(B,A) )
         => ! [C] :
              ( ( v2_rlvect_1(C)
                & m1_rlsub_1(C,A) )
             => ( u1_struct_0(B) = u1_struct_0(C)
               => B = C ) ) ) ) )).

fof(t39_rlsub_1,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] :
          ( ( v2_rlvect_1(B)
            & m1_rlsub_1(B,A) )
         => ! [C] :
              ( ( v2_rlvect_1(C)
                & m1_rlsub_1(C,A) )
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_rlvect_1(B,D)
                    <=> r1_rlvect_1(C,D) ) )
               => B = C ) ) ) ) )).

fof(t40_rlsub_1,axiom,(
    ! [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)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( v2_rlvect_1(B)
            & m1_rlsub_1(B,A) )
         => ( u1_struct_0(B) = u1_struct_0(A)
           => B = A ) ) ) )).

fof(t41_rlsub_1,axiom,(
    ! [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)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( v2_rlvect_1(B)
            & m1_rlsub_1(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r1_rlvect_1(B,C)
                <=> r1_rlvect_1(A,C) ) )
           => B = A ) ) ) )).

fof(t42_rlsub_1,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)))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( u1_struct_0(C) = B
               => v1_rlsub_1(B,A) ) ) ) ) )).

fof(t43_rlsub_1,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)))
         => ~ ( B != k1_xboole_0
              & v1_rlsub_1(B,A)
              & ! [C] :
                  ( ( v2_rlvect_1(C)
                    & m1_rlsub_1(C,A) )
                 => B != u1_struct_0(C) ) ) ) ) )).

fof(d3_rlsub_1,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] :
          ( ( v2_rlvect_1(B)
            & m1_rlsub_1(B,A) )
         => ( B = k1_rlsub_1(A)
          <=> u1_struct_0(B) = k1_struct_0(A,k1_rlvect_1(A)) ) ) ) )).

fof(d4_rlsub_1,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) )
     => k2_rlsub_1(A) = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) ) )).

fof(t44_rlsub_1,axiom,(
    $true )).

fof(t45_rlsub_1,axiom,(
    $true )).

fof(t46_rlsub_1,axiom,(
    $true )).

fof(t47_rlsub_1,axiom,(
    $true )).

fof(t48_rlsub_1,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)
         => k1_rlsub_1(B) = k1_rlsub_1(A) ) ) )).

fof(t49_rlsub_1,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_rlsub_1(C,A)
             => k1_rlsub_1(B) = k1_rlsub_1(C) ) ) ) )).

fof(t50_rlsub_1,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)
         => m1_rlsub_1(k1_rlsub_1(B),A) ) ) )).

fof(t51_rlsub_1,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)
         => m1_rlsub_1(k1_rlsub_1(A),B) ) ) )).

fof(t52_rlsub_1,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_rlsub_1(C,A)
             => m1_rlsub_1(k1_rlsub_1(B),C) ) ) ) )).

fof(t53_rlsub_1,axiom,(
    $true )).

fof(t54_rlsub_1,axiom,(
    ! [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)
        & l2_rlvect_1(A) )
     => m1_rlsub_1(A,k2_rlsub_1(A)) ) )).

fof(d6_rlsub_1,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)))
             => ( m2_rlsub_1(C,A,B)
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & C = k3_rlsub_1(A,D,B) ) ) ) ) ) )).

fof(t55_rlsub_1,axiom,(
    $true )).

fof(t56_rlsub_1,axiom,(
    $true )).

fof(t57_rlsub_1,axiom,(
    $true )).

fof(t58_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r2_hidden(k1_rlvect_1(A),k3_rlsub_1(A,B,C))
              <=> r1_rlvect_1(C,B) ) ) ) ) )).

fof(t59_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => r2_hidden(B,k3_rlsub_1(A,B,C)) ) ) ) )).

fof(t60_rlsub_1,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)
         => k3_rlsub_1(A,k1_rlvect_1(A),B) = u1_struct_0(B) ) ) )).

fof(t61_rlsub_1,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,u1_struct_0(A))
         => k3_rlsub_1(A,B,k1_rlsub_1(A)) = k1_struct_0(A,B) ) ) )).

fof(t62_rlsub_1,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,u1_struct_0(A))
         => k3_rlsub_1(A,B,k2_rlsub_1(A)) = u1_struct_0(A) ) ) )).

fof(t63_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r2_hidden(k1_rlvect_1(A),k3_rlsub_1(A,B,C))
              <=> k3_rlsub_1(A,B,C) = u1_struct_0(C) ) ) ) ) )).

fof(t64_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r1_rlvect_1(C,B)
              <=> k3_rlsub_1(A,B,C) = u1_struct_0(C) ) ) ) ) )).

fof(t65_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( r1_rlvect_1(D,B)
                   => k3_rlsub_1(A,k3_rlvect_1(A,B,C),D) = u1_struct_0(D) ) ) ) ) ) )).

fof(t66_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( k3_rlsub_1(A,k3_rlvect_1(A,B,C),D) = u1_struct_0(D)
                   => ( C = np__0
                      | r1_rlvect_1(D,B) ) ) ) ) ) ) )).

fof(t67_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r1_rlvect_1(C,B)
              <=> k3_rlsub_1(A,k5_rlvect_1(A,B),C) = u1_struct_0(C) ) ) ) ) )).

fof(t68_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( r1_rlvect_1(D,B)
                  <=> k3_rlsub_1(A,C,D) = k3_rlsub_1(A,k4_rlvect_1(A,C,B),D) ) ) ) ) ) )).

fof(t69_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( r1_rlvect_1(D,B)
                  <=> k3_rlsub_1(A,C,D) = k3_rlsub_1(A,k6_rlvect_1(A,C,B),D) ) ) ) ) ) )).

fof(t70_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( r2_hidden(B,k3_rlsub_1(A,C,D))
                  <=> k3_rlsub_1(A,C,D) = k3_rlsub_1(A,B,D) ) ) ) ) ) )).

fof(t71_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( k3_rlsub_1(A,B,C) = k3_rlsub_1(A,k5_rlvect_1(A,B),C)
              <=> r1_rlvect_1(C,B) ) ) ) ) )).

fof(t72_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_rlsub_1(E,A)
                     => ( ( r2_hidden(B,k3_rlsub_1(A,C,E))
                          & r2_hidden(B,k3_rlsub_1(A,D,E)) )
                       => k3_rlsub_1(A,C,E) = k3_rlsub_1(A,D,E) ) ) ) ) ) ) )).

fof(t73_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( ( r2_hidden(B,k3_rlsub_1(A,C,D))
                      & r2_hidden(B,k3_rlsub_1(A,k5_rlvect_1(A,C),D)) )
                   => r1_rlvect_1(D,C) ) ) ) ) ) )).

fof(t74_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( r2_hidden(k3_rlvect_1(A,B,C),k3_rlsub_1(A,B,D))
                   => ( C = np__1
                      | r1_rlvect_1(D,B) ) ) ) ) ) ) )).

fof(t75_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( r1_rlvect_1(D,B)
                   => r2_hidden(k3_rlvect_1(A,B,C),k3_rlsub_1(A,B,D)) ) ) ) ) ) )).

fof(t76_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r2_hidden(k5_rlvect_1(A,B),k3_rlsub_1(A,B,C))
              <=> r1_rlvect_1(C,B) ) ) ) ) )).

fof(t77_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( r2_hidden(k4_rlvect_1(A,B,C),k3_rlsub_1(A,C,D))
                  <=> r1_rlvect_1(D,B) ) ) ) ) ) )).

fof(t78_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( r2_hidden(k6_rlvect_1(A,B,C),k3_rlsub_1(A,B,D))
                  <=> r1_rlvect_1(D,C) ) ) ) ) ) )).

fof(t79_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( r2_hidden(B,k3_rlsub_1(A,C,D))
                  <=> ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r1_rlvect_1(D,E)
                        & B = k4_rlvect_1(A,C,E) ) ) ) ) ) ) )).

fof(t80_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( r2_hidden(B,k3_rlsub_1(A,C,D))
                  <=> ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r1_rlvect_1(D,E)
                        & B = k6_rlvect_1(A,C,E) ) ) ) ) ) ) )).

fof(t81_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r2_hidden(B,k3_rlsub_1(A,E,D))
                        & r2_hidden(C,k3_rlsub_1(A,E,D)) )
                  <=> r1_rlvect_1(D,k6_rlvect_1(A,B,C)) ) ) ) ) ) )).

fof(t82_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ~ ( k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r1_rlvect_1(D,E)
                              & k4_rlvect_1(A,B,E) = C ) ) ) ) ) ) ) )).

fof(t83_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ~ ( k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r1_rlvect_1(D,E)
                              & k6_rlvect_1(A,B,E) = C ) ) ) ) ) ) ) )).

fof(t84_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( ( v2_rlvect_1(C)
                & m1_rlsub_1(C,A) )
             => ! [D] :
                  ( ( v2_rlvect_1(D)
                    & m1_rlsub_1(D,A) )
                 => ( k3_rlsub_1(A,B,C) = k3_rlsub_1(A,B,D)
                  <=> C = D ) ) ) ) ) )).

fof(t85_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v2_rlvect_1(D)
                    & m1_rlsub_1(D,A) )
                 => ! [E] :
                      ( ( v2_rlvect_1(E)
                        & m1_rlsub_1(E,A) )
                     => ( k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,E)
                       => D = E ) ) ) ) ) ) )).

fof(t86_rlsub_1,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] :
              ( m2_rlsub_1(C,A,B)
             => ( v1_rlsub_1(C,A)
              <=> C = u1_struct_0(B) ) ) ) ) )).

fof(t87_rlsub_1,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] :
          ( ( v2_rlvect_1(B)
            & m1_rlsub_1(B,A) )
         => ! [C] :
              ( ( v2_rlvect_1(C)
                & m1_rlsub_1(C,A) )
             => ! [D] :
                  ( m2_rlsub_1(D,A,B)
                 => ! [E] :
                      ( m2_rlsub_1(E,A,C)
                     => ( D = E
                       => B = C ) ) ) ) ) ) )).

fof(t88_rlsub_1,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,u1_struct_0(A))
         => m2_rlsub_1(k1_struct_0(A,B),A,k1_rlsub_1(A)) ) ) )).

fof(t89_rlsub_1,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)))
         => ~ ( m2_rlsub_1(B,A,k1_rlsub_1(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => B != k1_struct_0(A,C) ) ) ) ) )).

fof(t90_rlsub_1,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)
         => m2_rlsub_1(u1_struct_0(B),A,B) ) ) )).

fof(t91_rlsub_1,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_rlsub_1(u1_struct_0(A),A,k2_rlsub_1(A)) ) )).

fof(t92_rlsub_1,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)))
         => ( m2_rlsub_1(B,A,k2_rlsub_1(A))
           => B = u1_struct_0(A) ) ) ) )).

fof(t93_rlsub_1,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] :
              ( m2_rlsub_1(C,A,B)
             => ( r2_hidden(k1_rlvect_1(A),C)
              <=> C = u1_struct_0(B) ) ) ) ) )).

fof(t94_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ! [D] :
                  ( m2_rlsub_1(D,A,C)
                 => ( r2_hidden(B,D)
                  <=> D = k3_rlsub_1(A,B,C) ) ) ) ) ) )).

fof(t95_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ! [E] :
                      ( m2_rlsub_1(E,A,D)
                     => ~ ( r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_rlvect_1(D,F)
                                  & k4_rlvect_1(A,B,F) = C ) ) ) ) ) ) ) ) )).

fof(t96_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ! [E] :
                      ( m2_rlsub_1(E,A,D)
                     => ~ ( r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_rlvect_1(D,F)
                                  & k6_rlvect_1(A,B,F) = C ) ) ) ) ) ) ) ) )).

fof(t97_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( ? [E] :
                        ( m2_rlsub_1(E,A,D)
                        & r2_hidden(B,E)
                        & r2_hidden(C,E) )
                  <=> r1_rlvect_1(D,k6_rlvect_1(A,B,C)) ) ) ) ) ) )).

fof(t98_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ! [D] :
                  ( m2_rlsub_1(D,A,C)
                 => ! [E] :
                      ( m2_rlsub_1(E,A,C)
                     => ( ( r2_hidden(B,D)
                          & r2_hidden(B,E) )
                       => D = E ) ) ) ) ) ) )).

fof(dt_m1_rlsub_1,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)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) ) ) ) )).

fof(existence_m1_rlsub_1,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) ) )).

fof(dt_m2_rlsub_1,axiom,(
    ! [A,B] :
      ( ( ~ 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)
        & m1_rlsub_1(B,A) )
     => ! [C] :
          ( m2_rlsub_1(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(existence_m2_rlsub_1,axiom,(
    ! [A,B] :
      ( ( ~ 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)
        & m1_rlsub_1(B,A) )
     => ? [C] : m2_rlsub_1(C,A,B) ) )).

fof(dt_k1_rlsub_1,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) )
     => ( v2_rlvect_1(k1_rlsub_1(A))
        & m1_rlsub_1(k1_rlsub_1(A),A) ) ) )).

fof(dt_k2_rlsub_1,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) )
     => ( v2_rlvect_1(k2_rlsub_1(A))
        & m1_rlsub_1(k2_rlsub_1(A),A) ) ) )).

fof(dt_k3_rlsub_1,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_rlsub_1(C,A) )
     => m1_subset_1(k3_rlsub_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(t9_rlsub_1,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)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_rlsub_1(B,A)
                      & v1_rlsub_1(C,A)
                      & D = a_3_0_rlsub_1(A,B,C) )
                   => v1_rlsub_1(D,A) ) ) ) ) ) )).

fof(d5_rlsub_1,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,u1_struct_0(A))
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => k3_rlsub_1(A,B,C) = a_3_1_rlsub_1(A,B,C) ) ) ) )).

fof(fraenkel_a_3_0_rlsub_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & l2_rlvect_1(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_3_0_rlsub_1(B,C,D))
      <=> ? [E,F] :
            ( m1_subset_1(E,u1_struct_0(B))
            & m1_subset_1(F,u1_struct_0(B))
            & A = k4_rlvect_1(B,E,F)
            & r2_hidden(E,C)
            & r2_hidden(F,D) ) ) ) )).

fof(fraenkel_a_3_1_rlsub_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & l2_rlvect_1(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_rlsub_1(D,B) )
     => ( r2_hidden(A,a_3_1_rlsub_1(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k4_rlvect_1(B,C,E)
            & r1_rlvect_1(D,E) ) ) ) )).
%------------------------------------------------------------------------------