% Mizar problem: t85_rlsub_1,rlsub_1,1419,29 
fof(t85_rlsub_1,conjecture,(
    ! [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 ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v2_rlvect_1,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_membered,cc1_realset1,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,commutativity_k2_tarski,commutativity_k4_rlvect_1,d10_xboole_0,d11_rlvect_1,d1_rlvect_1,d2_rlvect_1,d3_rlvect_1,d4_xboole_0,d5_rlsub_1,d5_tarski,d6_rlvect_1,dt_g2_rlvect_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_rlsub_1,dt_k4_rlvect_1,dt_k4_tarski,dt_k4_xboole_0,dt_k5_rlvect_1,dt_k6_rlvect_1,dt_k8_funct_2,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_m1_relset_1,dt_m1_rlsub_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_u2_rlvect_1,dt_u2_struct_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,existence_m1_relset_1,existence_m1_rlsub_1,existence_m1_subset_1,existence_m2_relset_1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc1_rlvect_1,fc1_struct_0,fc1_subset_1,fc2_membered,fc2_subset_1,fc37_membered,fc38_membered,fc39_membered,fc3_realset1,fc3_subset_1,fc40_membered,fc41_membered,fc4_subset_1,fc6_membered,fc7_membered,fc8_membered,fc9_membered,fraenkel_a_3_1_rlsub_1,fraenkel_a_3_3_rlsub_1,free_g2_rlvect_1,rc1_funct_1,rc1_membered,rc1_realset1,rc1_rlsub_1,rc1_subset_1,rc2_funct_1,rc2_realset1,rc2_rlvect_1,rc2_subset_1,rc3_funct_1,rc3_rlvect_1,rc3_struct_0,rc4_struct_0,rc5_struct_0,rc6_rlvect_1,redefinition_k1_domain_1,redefinition_k4_rlvect_1,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t10_rlvect_1,t17_rlsub_1,t1_subset,t28_rlvect_1,t2_subset,t2_tarski,t37_xboole_1,t38_rlsub_1,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,t68_rlsub_1,t6_boole,t7_boole,t84_rlsub_1,t8_boole]),
    [file(rlsub_1,t85_rlsub_1)]).

fof(abstractness_v2_rlvect_1,axiom,(
    ! [A] : 
      ( l2_rlvect_1(A)
     => ( v2_rlvect_1(A)
       => A = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) ) ) ),
    file(rlvect_1,v2_rlvect_1),
    []).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc6_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ),
    file(rlvect_1,k4_rlvect_1),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d11_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k6_rlvect_1(A,B,C) = k2_rlvect_1(A,B,k5_rlvect_1(A,C)) ) ) ) ),
    file(rlvect_1,d11_rlvect_1),
    []).

fof(d1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( r1_rlvect_1(A,B)
        <=> r2_hidden(B,u1_struct_0(A)) ) ) ),
    file(rlvect_1,d1_rlvect_1),
    []).

fof(d2_rlvect_1,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => k1_rlvect_1(A) = u2_struct_0(A) ) ),
    file(rlvect_1,d2_rlvect_1),
    []).

fof(d3_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ),
    file(rlvect_1,d3_rlvect_1),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

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) ) ) ) ),
    file(rlsub_1,d5_rlsub_1),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d6_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v4_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))
                   => k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) ) ) ) ),
    file(rlvect_1,d6_rlvect_1),
    []).

fof(dt_g2_rlvect_1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) )
     => ( v2_rlvect_1(g2_rlvect_1(A,B,C,D))
        & l2_rlvect_1(g2_rlvect_1(A,B,C,D)) ) ) ),
    file(rlvect_1,g2_rlvect_1),
    []).

fof(dt_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

fof(dt_k1_rlvect_1,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ),
    file(rlvect_1,k1_rlvect_1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k2_rlvect_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

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))) ) ),
    file(rlsub_1,k3_rlsub_1),
    []).

fof(dt_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k4_rlvect_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_rlvect_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)) ) ),
    file(rlvect_1,k5_rlvect_1),
    []).

fof(dt_k6_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k6_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k6_rlvect_1),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_rlvect_1,axiom,(
    ! [A] : 
      ( l2_rlvect_1(A)
     => l1_rlvect_1(A) ) ),
    file(rlvect_1,l2_rlvect_1),
    []).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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) ) ) ) ),
    file(rlsub_1,m1_rlsub_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_u1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( v1_funct_1(u1_rlvect_1(A))
        & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(rlvect_1,u1_rlvect_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u2_rlvect_1,axiom,(
    ! [A] : 
      ( l2_rlvect_1(A)
     => ( v1_funct_1(u2_rlvect_1(A))
        & v1_funct_2(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(rlvect_1,u2_rlvect_1),
    []).

fof(dt_u2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) ),
    file(struct_0,u2_struct_0),
    []).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_rlvect_1,axiom,(
    ? [A] : l2_rlvect_1(A) ),
    file(rlvect_1,l2_rlvect_1),
    []).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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) ) ),
    file(rlsub_1,m1_rlsub_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc10_membered,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    []).

fof(fc11_membered,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    []).

fof(fc12_membered,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_membered(k2_tarski(A,B)) ) ),
    file(membered,fc12_membered),
    []).

fof(fc13_membered,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc13_membered),
    []).

fof(fc14_membered,axiom,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc14_membered),
    []).

fof(fc15_membered,axiom,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc15_membered),
    []).

fof(fc16_membered,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B))
        & v5_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc16_membered),
    []).

fof(fc1_rlvect_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) )
     => ( ~ v3_struct_0(g2_rlvect_1(A,B,C,D))
        & v2_rlvect_1(g2_rlvect_1(A,B,C,D)) ) ) ),
    file(rlvect_1,fc1_rlvect_1),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc37_membered,axiom,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k4_xboole_0(A,B)) ) ),
    file(membered,fc37_membered),
    []).

fof(fc38_membered,axiom,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc38_membered),
    []).

fof(fc39_membered,axiom,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc39_membered),
    []).

fof(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc40_membered,axiom,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B))
        & v4_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc40_membered),
    []).

fof(fc41_membered,axiom,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B))
        & v4_membered(k4_xboole_0(A,B))
        & v5_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc41_membered),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc6_membered,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    []).

fof(fc7_membered,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    []).

fof(fc8_membered,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    []).

fof(fc9_membered,axiom,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    []).

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) ) ) ) ),
    file(rlsub_1,a_3_1_rlsub_1),
    []).

fof(fraenkel_a_3_3_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))
        & v2_rlvect_1(D)
        & m1_rlsub_1(D,B) )
     => ( r2_hidden(A,a_3_3_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) ) ) ) ),
    file(rlsub_1,a_3_3_rlsub_1),
    []).

fof(free_g2_rlvect_1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) )
     => ! [E,F,G,H] : 
          ( g2_rlvect_1(A,B,C,D) = g2_rlvect_1(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) ),
    file(rlvect_1,g2_rlvect_1),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

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) ) ) ),
    file(rlsub_1,rc1_rlsub_1),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

fof(rc2_rlvect_1,axiom,(
    ? [A] : 
      ( l2_rlvect_1(A)
      & v2_rlvect_1(A) ) ),
    file(rlvect_1,rc2_rlvect_1),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_rlvect_1,axiom,(
    ? [A] : 
      ( l2_rlvect_1(A)
      & ~ v3_struct_0(A) ) ),
    file(rlvect_1,rc3_rlvect_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc4_struct_0,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc6_rlvect_1,axiom,(
    ? [A] : 
      ( l2_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v2_rlvect_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v7_rlvect_1(A) ) ),
    file(rlvect_1,rc6_rlvect_1),
    []).

fof(redefinition_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(redefinition_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ),
    file(rlvect_1,k4_rlvect_1),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t10_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
            & k2_rlvect_1(A,k1_rlvect_1(A),B) = B ) ) ) ),
    file(rlvect_1,t10_rlvect_1),
    []).

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) ) ) ) ),
    file(rlsub_1,t17_rlsub_1),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t28_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_rlvect_1(A,B,B) = k1_rlvect_1(A) ) ) ),
    file(rlvect_1,t28_rlvect_1),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t37_xboole_1,axiom,(
    ! [A,B] : 
      ( k4_xboole_0(A,B) = k1_xboole_0
    <=> r1_tarski(A,B) ) ),
    file(xboole_1,t37_xboole_1),
    []).

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 ) ) ) ) ),
    file(rlsub_1,t38_rlsub_1),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

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) ) ) ) ) ) ),
    file(rlsub_1,t68_rlsub_1),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

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 ) ) ) ) ) ),
    file(rlsub_1,t84_rlsub_1),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).