SET007 Axioms: SET007+740.ax


%------------------------------------------------------------------------------
% File     : SET007+740 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Subspaces and Cosets of Subspace of Real Unitary 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    : rusub_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   90 (   0 unit)
%            Number of atoms       : 1182 (  77 equality)
%            Maximal formula depth :   20 (  11 average)
%            Number of connectives : 1202 ( 110 ~  ;   2  |; 749  &)
%                                         (  25 <=>; 316 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   0 propositional; 1-3 arity)
%            Number of functors    :   25 (   4 constant; 0-5 arity)
%            Number of variables   :  302 (   0 singleton; 293 !;   9 ?)
%            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_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ? [B] :
          ( m1_rusub_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)
          & v1_bhsp_1(B)
          & v2_bhsp_1(B) ) ) )).

fof(d1_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_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)
            & v2_bhsp_1(B)
            & l1_bhsp_1(B) )
         => ( m1_rusub_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)))
              & u1_bhsp_1(B) = k1_realset1(u1_bhsp_1(A),u1_struct_0(B)) ) ) ) ) )).

fof(t1_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_rusub_1(C,A)
             => ! [D] :
                  ( ( r1_rlvect_1(B,D)
                    & m1_rusub_1(B,C) )
                 => r1_rlvect_1(C,D) ) ) ) ) )).

fof(t2_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( r1_rlvect_1(B,C)
             => r1_rlvect_1(A,C) ) ) ) )).

fof(t3_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).

fof(t4_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => k1_rlvect_1(B) = k1_rlvect_1(A) ) ) )).

fof(t5_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_rusub_1(C,A)
             => k1_rlvect_1(B) = k1_rlvect_1(C) ) ) ) )).

fof(t6_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( E = D
                              & F = C )
                           => k4_rlvect_1(B,E,F) = k4_rlvect_1(A,D,C) ) ) ) ) ) ) ) )).

fof(t7_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ( D = C
                       => k3_rlvect_1(B,D,E) = k3_rlvect_1(A,C,E) ) ) ) ) ) ) )).

fof(t8_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( E = C
                              & F = D )
                           => k2_bhsp_1(B,E,F) = k2_bhsp_1(A,C,D) ) ) ) ) ) ) ) )).

fof(t9_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( D = C
                   => k5_rlvect_1(A,C) = k5_rlvect_1(B,D) ) ) ) ) ) )).

fof(t10_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( E = D
                              & F = C )
                           => k6_rlvect_1(B,E,F) = k6_rlvect_1(A,D,C) ) ) ) ) ) ) ) )).

fof(t11_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => r1_rlvect_1(B,k1_rlvect_1(A)) ) ) )).

fof(t12_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_rusub_1(C,A)
             => r1_rlvect_1(C,k1_rlvect_1(B)) ) ) ) )).

fof(t13_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => r1_rlvect_1(A,k1_rlvect_1(B)) ) ) )).

fof(t14_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_rlvect_1(B,C)
                      & r1_rlvect_1(B,D) )
                   => r1_rlvect_1(B,k4_rlvect_1(A,C,D)) ) ) ) ) ) )).

fof(t15_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( r1_rlvect_1(B,C)
                   => r1_rlvect_1(B,k3_rlvect_1(A,C,D)) ) ) ) ) ) )).

fof(t16_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_rlvect_1(B,C)
               => r1_rlvect_1(B,k5_rlvect_1(A,C)) ) ) ) ) )).

fof(t17_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_rlvect_1(B,C)
                      & r1_rlvect_1(B,D) )
                   => r1_rlvect_1(B,k6_rlvect_1(A,C,D)) ) ) ) ) ) )).

fof(t18_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_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) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(C,C),k1_numbers)
                                & m2_relset_1(G,k2_zfmisc_1(C,C),k1_numbers) )
                             => ( ( 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))
                                  & G = k1_realset1(u1_bhsp_1(A),B) )
                               => m1_rusub_1(g1_bhsp_1(C,D,E,F,G),A) ) ) ) ) ) ) ) ) )).

fof(t19_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => m1_rusub_1(A,A) ) )).

fof(t20_rusub_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)
        & v1_bhsp_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_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)
            & v1_bhsp_1(B)
            & v2_bhsp_1(B)
            & l1_bhsp_1(B) )
         => ( ( m1_rusub_1(A,B)
              & m1_rusub_1(B,A) )
           => A = B ) ) ) )).

fof(t21_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_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)
            & v2_bhsp_1(B)
            & l1_bhsp_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)
                & v2_bhsp_1(C)
                & l1_bhsp_1(C) )
             => ( ( m1_rusub_1(A,B)
                  & m1_rusub_1(B,C) )
               => m1_rusub_1(A,C) ) ) ) ) )).

fof(t22_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_rusub_1(C,A)
             => ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
               => m1_rusub_1(B,C) ) ) ) ) )).

fof(t23_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_rusub_1(C,A)
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_rlvect_1(B,D)
                     => r1_rlvect_1(C,D) ) )
               => m1_rusub_1(B,C) ) ) ) ) )).

fof(t24_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( ( v1_bhsp_1(B)
            & m1_rusub_1(B,A) )
         => ! [C] :
              ( ( v1_bhsp_1(C)
                & m1_rusub_1(C,A) )
             => ( u1_struct_0(B) = u1_struct_0(C)
               => B = C ) ) ) ) )).

fof(t25_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( ( v1_bhsp_1(B)
            & m1_rusub_1(B,A) )
         => ! [C] :
              ( ( v1_bhsp_1(C)
                & m1_rusub_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(t26_rusub_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)
        & v1_bhsp_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( ( v1_bhsp_1(B)
            & m1_rusub_1(B,A) )
         => ( u1_struct_0(B) = u1_struct_0(A)
           => B = A ) ) ) )).

fof(t27_rusub_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)
        & v1_bhsp_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( ( v1_bhsp_1(B)
            & m1_rusub_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(t28_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( u1_struct_0(B) = C
               => v1_rlsub_1(C,A) ) ) ) ) )).

fof(t29_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( B != k1_xboole_0
              & v1_rlsub_1(B,A)
              & ! [C] :
                  ( ( v1_bhsp_1(C)
                    & m1_rusub_1(C,A) )
                 => B != u1_struct_0(C) ) ) ) ) )).

fof(d2_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( ( v1_bhsp_1(B)
            & m1_rusub_1(B,A) )
         => ( B = k1_rusub_1(A)
          <=> u1_struct_0(B) = k6_domain_1(u1_struct_0(A),k1_rlvect_1(A)) ) ) ) )).

fof(d3_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => k2_rusub_1(A) = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A)) ) )).

fof(t30_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => k1_rusub_1(B) = k1_rusub_1(A) ) ) )).

fof(t31_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_rusub_1(C,A)
             => k1_rusub_1(B) = k1_rusub_1(C) ) ) ) )).

fof(t32_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => m1_rusub_1(k1_rusub_1(B),A) ) ) )).

fof(t33_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => m1_rusub_1(k1_rusub_1(A),B) ) ) )).

fof(t34_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_rusub_1(C,A)
             => m1_rusub_1(k1_rusub_1(B),C) ) ) ) )).

fof(t35_rusub_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)
        & v1_bhsp_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => m1_rusub_1(A,k2_rusub_1(A)) ) )).

fof(d5_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( m2_rusub_1(C,A,B)
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & C = k3_rusub_1(A,D,B) ) ) ) ) ) )).

fof(t36_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(k1_rlvect_1(A),k3_rusub_1(A,C,B))
              <=> r1_rlvect_1(B,C) ) ) ) ) )).

fof(t37_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_hidden(C,k3_rusub_1(A,C,B)) ) ) ) )).

fof(t38_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => k3_rusub_1(A,k1_rlvect_1(A),B) = u1_struct_0(B) ) ) )).

fof(t39_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_rusub_1(A,B,k1_rusub_1(A)) = k6_domain_1(u1_struct_0(A),B) ) ) )).

fof(t40_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_rusub_1(A,B,k2_rusub_1(A)) = u1_struct_0(A) ) ) )).

fof(t41_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(k1_rlvect_1(A),k3_rusub_1(A,C,B))
              <=> k3_rusub_1(A,C,B) = u1_struct_0(B) ) ) ) ) )).

fof(t42_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_rlvect_1(B,C)
              <=> k3_rusub_1(A,C,B) = u1_struct_0(B) ) ) ) ) )).

fof(t43_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( r1_rlvect_1(B,C)
                   => k3_rusub_1(A,k3_rlvect_1(A,C,D),B) = u1_struct_0(B) ) ) ) ) ) )).

fof(t44_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( k3_rusub_1(A,k3_rlvect_1(A,C,D),B) = u1_struct_0(B)
                   => ( D = np__0
                      | r1_rlvect_1(B,C) ) ) ) ) ) ) )).

fof(t45_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_rlvect_1(B,C)
              <=> k3_rusub_1(A,k5_rlvect_1(A,C),B) = u1_struct_0(B) ) ) ) ) )).

fof(t46_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_rlvect_1(B,C)
                  <=> k3_rusub_1(A,D,B) = k3_rusub_1(A,k4_rlvect_1(A,D,C),B) ) ) ) ) ) )).

fof(t47_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_rlvect_1(B,C)
                  <=> k3_rusub_1(A,D,B) = k3_rusub_1(A,k6_rlvect_1(A,D,C),B) ) ) ) ) ) )).

fof(t48_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_hidden(D,k3_rusub_1(A,C,B))
                  <=> k3_rusub_1(A,C,B) = k3_rusub_1(A,D,B) ) ) ) ) ) )).

fof(t49_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k3_rusub_1(A,C,B) = k3_rusub_1(A,k5_rlvect_1(A,C),B)
              <=> r1_rlvect_1(B,C) ) ) ) ) )).

fof(t50_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r2_hidden(C,k3_rusub_1(A,D,B))
                          & r2_hidden(C,k3_rusub_1(A,E,B)) )
                       => k3_rusub_1(A,D,B) = k3_rusub_1(A,E,B) ) ) ) ) ) ) )).

fof(t51_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r2_hidden(C,k3_rusub_1(A,D,B))
                      & r2_hidden(C,k3_rusub_1(A,k5_rlvect_1(A,D),B)) )
                   => r1_rlvect_1(B,D) ) ) ) ) ) )).

fof(t52_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( r2_hidden(k3_rlvect_1(A,C,D),k3_rusub_1(A,C,B))
                   => ( D = np__1
                      | r1_rlvect_1(B,C) ) ) ) ) ) ) )).

fof(t53_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( r1_rlvect_1(B,C)
                   => r2_hidden(k3_rlvect_1(A,C,D),k3_rusub_1(A,C,B)) ) ) ) ) ) )).

fof(t54_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(k5_rlvect_1(A,C),k3_rusub_1(A,C,B))
              <=> r1_rlvect_1(B,C) ) ) ) ) )).

fof(t55_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_hidden(k4_rlvect_1(A,C,D),k3_rusub_1(A,D,B))
                  <=> r1_rlvect_1(B,C) ) ) ) ) ) )).

fof(t56_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_hidden(k6_rlvect_1(A,D,C),k3_rusub_1(A,D,B))
                  <=> r1_rlvect_1(B,C) ) ) ) ) ) )).

fof(t57_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_hidden(C,k3_rusub_1(A,D,B))
                  <=> ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r1_rlvect_1(B,E)
                        & C = k4_rlvect_1(A,D,E) ) ) ) ) ) ) )).

fof(t58_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_hidden(C,k3_rusub_1(A,D,B))
                  <=> ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r1_rlvect_1(B,E)
                        & C = k6_rlvect_1(A,D,E) ) ) ) ) ) ) )).

fof(t59_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r2_hidden(C,k3_rusub_1(A,E,B))
                        & r2_hidden(D,k3_rusub_1(A,E,B)) )
                  <=> r1_rlvect_1(B,k6_rlvect_1(A,C,D)) ) ) ) ) ) )).

fof(t60_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( k3_rusub_1(A,D,B) = k3_rusub_1(A,C,B)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r1_rlvect_1(B,E)
                              & k4_rlvect_1(A,D,E) = C ) ) ) ) ) ) ) )).

fof(t61_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( k3_rusub_1(A,D,B) = k3_rusub_1(A,C,B)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r1_rlvect_1(B,E)
                              & k6_rlvect_1(A,D,E) = C ) ) ) ) ) ) ) )).

fof(t62_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( ( v1_bhsp_1(B)
            & m1_rusub_1(B,A) )
         => ! [C] :
              ( ( v1_bhsp_1(C)
                & m1_rusub_1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( k3_rusub_1(A,D,B) = k3_rusub_1(A,D,C)
                  <=> B = C ) ) ) ) ) )).

fof(t63_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( ( v1_bhsp_1(B)
            & m1_rusub_1(B,A) )
         => ! [C] :
              ( ( v1_bhsp_1(C)
                & m1_rusub_1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( k3_rusub_1(A,E,B) = k3_rusub_1(A,D,C)
                       => B = C ) ) ) ) ) ) )).

fof(t64_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m2_rusub_1(C,A,B)
             => ( v1_rlsub_1(C,A)
              <=> C = u1_struct_0(B) ) ) ) ) )).

fof(t65_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( ( v1_bhsp_1(B)
            & m1_rusub_1(B,A) )
         => ! [C] :
              ( ( v1_bhsp_1(C)
                & m1_rusub_1(C,A) )
             => ! [D] :
                  ( m2_rusub_1(D,A,B)
                 => ! [E] :
                      ( m2_rusub_1(E,A,C)
                     => ( D = E
                       => B = C ) ) ) ) ) ) )).

fof(t66_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => m2_rusub_1(k6_domain_1(u1_struct_0(A),B),A,k1_rusub_1(A)) ) ) )).

fof(t67_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( m2_rusub_1(B,A,k1_rusub_1(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => B != k6_domain_1(u1_struct_0(A),C) ) ) ) ) )).

fof(t68_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => m2_rusub_1(u1_struct_0(B),A,B) ) ) )).

fof(t69_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => m2_rusub_1(u1_struct_0(A),A,k2_rusub_1(A)) ) )).

fof(t70_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( m2_rusub_1(B,A,k2_rusub_1(A))
           => B = u1_struct_0(A) ) ) ) )).

fof(t71_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m2_rusub_1(C,A,B)
             => ( r2_hidden(k1_rlvect_1(A),C)
              <=> C = u1_struct_0(B) ) ) ) ) )).

fof(t72_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m2_rusub_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_hidden(D,C)
                  <=> C = k3_rusub_1(A,D,B) ) ) ) ) ) )).

fof(t73_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m2_rusub_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & r2_hidden(E,C)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_rlvect_1(B,F)
                                  & k4_rlvect_1(A,D,F) = E ) ) ) ) ) ) ) ) )).

fof(t74_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m2_rusub_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & r2_hidden(E,C)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_rlvect_1(B,F)
                                  & k6_rlvect_1(A,D,F) = E ) ) ) ) ) ) ) ) )).

fof(t75_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ? [E] :
                        ( m2_rusub_1(E,A,B)
                        & r2_hidden(C,E)
                        & r2_hidden(D,E) )
                  <=> r1_rlvect_1(B,k6_rlvect_1(A,C,D)) ) ) ) ) ) )).

fof(t76_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m2_rusub_1(D,A,B)
                 => ! [E] :
                      ( m2_rusub_1(E,A,B)
                     => ( ( r2_hidden(C,D)
                          & r2_hidden(C,E) )
                       => D = E ) ) ) ) ) ) )).

fof(dt_m1_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_rusub_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)
            & v2_bhsp_1(B)
            & l1_bhsp_1(B) ) ) ) )).

fof(existence_m1_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ? [B] : m1_rusub_1(B,A) ) )).

fof(dt_m2_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A)
        & m1_rusub_1(B,A) )
     => ! [C] :
          ( m2_rusub_1(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(existence_m2_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A)
        & m1_rusub_1(B,A) )
     => ? [C] : m2_rusub_1(C,A,B) ) )).

fof(dt_k1_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ( v1_bhsp_1(k1_rusub_1(A))
        & m1_rusub_1(k1_rusub_1(A),A) ) ) )).

fof(dt_k2_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ( v1_bhsp_1(k2_rusub_1(A))
        & m1_rusub_1(k2_rusub_1(A),A) ) ) )).

fof(dt_k3_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_rusub_1(C,A) )
     => m1_subset_1(k3_rusub_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(d4_rusub_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)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_rusub_1(C,A)
             => k3_rusub_1(A,B,C) = a_3_0_rusub_1(A,B,C) ) ) ) )).

fof(fraenkel_a_3_0_rusub_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)
        & v2_bhsp_1(B)
        & l1_bhsp_1(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_rusub_1(D,B) )
     => ( r2_hidden(A,a_3_0_rusub_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) ) ) ) )).
%------------------------------------------------------------------------------