% Mizar problem: t28_anproj_2,anproj_2,1988,28 
fof(t28_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k6_anproj_1(A)))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k6_anproj_1(A)))
                                 => ~ ( r1_collsp(k6_anproj_1(A),B,C,D)
                                      & r1_collsp(k6_anproj_1(A),E,F,D)
                                      & r1_collsp(k6_anproj_1(A),B,E,G)
                                      & r1_collsp(k6_anproj_1(A),C,F,G)
                                      & r1_collsp(k6_anproj_1(A),B,F,H)
                                      & r1_collsp(k6_anproj_1(A),C,E,H)
                                      & r1_collsp(k6_anproj_1(A),G,D,H)
                                      & ~ r1_collsp(k6_anproj_1(A),B,C,F)
                                      & ~ r1_collsp(k6_anproj_1(A),B,C,E)
                                      & ~ r1_collsp(k6_anproj_1(A),B,E,F)
                                      & ~ r1_collsp(k6_anproj_1(A),C,E,F) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_collsp,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,d10_anproj_1,d6_anproj_1,dt_g1_collsp,dt_k1_anproj_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_anproj_1,dt_k2_zfmisc_1,dt_k3_anproj_1,dt_k4_anproj_1,dt_k5_anproj_1,dt_k6_anproj_1,dt_k6_eqrel_1,dt_l1_collsp,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_m1_collsp,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_collsp,dt_u1_struct_0,existence_l1_collsp,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,existence_m1_collsp,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_anproj_1,fc1_anproj_2,fc1_struct_0,fc1_subset_1,fc2_anproj_1,fc2_anproj_2,fc3_anproj_1,fc4_subset_1,fc6_membered,free_g1_collsp,rc1_collsp,rc1_membered,rc1_subset_1,rc2_collsp,rc2_subset_1,rc3_collsp,rc3_struct_0,rc4_struct_0,rc5_struct_0,redefinition_m2_relset_1,reflexivity_r1_anproj_1,reflexivity_r1_tarski,symmetry_r1_anproj_1,t1_subset,t23_anproj_1,t24_anproj_2,t2_subset,t35_anproj_1,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,t9_anproj_1]),
    [file(anproj_2,t28_anproj_2)]).

fof(abstractness_v1_collsp,axiom,(
    ! [A] : 
      ( l1_collsp(A)
     => ( v1_collsp(A)
       => A = g1_collsp(u1_struct_0(A),u1_collsp(A)) ) ) ),
    file(collsp,v1_collsp),
    []).

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

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_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(d10_anproj_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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => k6_anproj_1(A) = g1_collsp(k4_anproj_1(A),k5_anproj_1(A)) ) ),
    file(anproj_1,d10_anproj_1),
    []).

fof(d6_anproj_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_anproj_1(A,B) = k6_eqrel_1(k1_anproj_1(A),k2_anproj_1(A),B) ) ) ),
    file(anproj_1,d6_anproj_1),
    []).

fof(dt_g1_collsp,axiom,(
    ! [A,B] : 
      ( m1_collsp(B,A)
     => ( v1_collsp(g1_collsp(A,B))
        & l1_collsp(g1_collsp(A,B)) ) ) ),
    file(collsp,g1_collsp),
    []).

fof(dt_k1_anproj_1,axiom,(
    $true ),
    file(anproj_1,k1_anproj_1),
    []).

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_anproj_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) )
     => ( v3_relat_2(k2_anproj_1(A))
        & v8_relat_2(k2_anproj_1(A))
        & v1_partfun1(k2_anproj_1(A),k1_anproj_1(A),k1_anproj_1(A))
        & m2_relset_1(k2_anproj_1(A),k1_anproj_1(A),k1_anproj_1(A)) ) ) ),
    file(anproj_1,k2_anproj_1),
    []).

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

fof(dt_k3_anproj_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_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k3_anproj_1(A,B),k1_zfmisc_1(k1_anproj_1(A))) ) ),
    file(anproj_1,k3_anproj_1),
    []).

fof(dt_k4_anproj_1,axiom,(
    $true ),
    file(anproj_1,k4_anproj_1),
    []).

fof(dt_k5_anproj_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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => m1_collsp(k5_anproj_1(A),k4_anproj_1(A)) ) ),
    file(anproj_1,k5_anproj_1),
    []).

fof(dt_k6_anproj_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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ( v1_collsp(k6_anproj_1(A))
        & l1_collsp(k6_anproj_1(A)) ) ) ),
    file(anproj_1,k6_anproj_1),
    []).

fof(dt_k6_eqrel_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_2(B)
        & v3_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(eqrel_1,k6_eqrel_1),
    []).

fof(dt_l1_collsp,axiom,(
    ! [A] : 
      ( l1_collsp(A)
     => l1_struct_0(A) ) ),
    file(collsp,l1_collsp),
    []).

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_collsp,axiom,(
    $true ),
    file(collsp,m1_collsp),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_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_collsp,axiom,(
    ! [A] : 
      ( l1_collsp(A)
     => m1_collsp(u1_collsp(A),u1_struct_0(A)) ) ),
    file(collsp,u1_collsp),
    []).

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

fof(existence_l1_collsp,axiom,(
    ? [A] : l1_collsp(A) ),
    file(collsp,l1_collsp),
    []).

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_collsp,axiom,(
    ! [A] : 
    ? [B] : m1_collsp(B,A) ),
    file(collsp,m1_collsp),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_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(fc1_anproj_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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ~ v1_xboole_0(k1_anproj_1(A)) ) ),
    file(anproj_1,fc1_anproj_1),
    []).

fof(fc1_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ( ~ v3_struct_0(k6_anproj_1(A))
        & v1_collsp(k6_anproj_1(A))
        & v2_collsp(k6_anproj_1(A))
        & v3_collsp(k6_anproj_1(A)) ) ) ),
    file(anproj_2,fc1_anproj_2),
    []).

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_anproj_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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ~ v1_xboole_0(k4_anproj_1(A)) ) ),
    file(anproj_1,fc2_anproj_1),
    []).

fof(fc2_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ( ~ v3_struct_0(k6_anproj_1(A))
        & v1_collsp(k6_anproj_1(A))
        & v2_collsp(k6_anproj_1(A))
        & v3_collsp(k6_anproj_1(A))
        & v2_anproj_2(k6_anproj_1(A)) ) ) ),
    file(anproj_2,fc2_anproj_2),
    []).

fof(fc3_anproj_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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ( ~ v3_struct_0(k6_anproj_1(A))
        & v1_collsp(k6_anproj_1(A)) ) ) ),
    file(anproj_1,fc3_anproj_1),
    []).

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(free_g1_collsp,axiom,(
    ! [A,B] : 
      ( m1_collsp(B,A)
     => ! [C,D] : 
          ( g1_collsp(A,B) = g1_collsp(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(collsp,g1_collsp),
    []).

fof(rc1_collsp,axiom,(
    ? [A] : 
      ( l1_collsp(A)
      & v1_collsp(A) ) ),
    file(collsp,rc1_collsp),
    []).

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_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_collsp,axiom,(
    ? [A] : 
      ( l1_collsp(A)
      & ~ v3_struct_0(A)
      & v1_collsp(A) ) ),
    file(collsp,rc2_collsp),
    []).

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_collsp,axiom,(
    ? [A] : 
      ( l1_collsp(A)
      & ~ v3_struct_0(A)
      & v1_collsp(A)
      & v2_collsp(A)
      & v3_collsp(A) ) ),
    file(collsp,rc3_collsp),
    []).

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(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_anproj_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_subset_1(C,u1_struct_0(A)) )
     => r1_anproj_1(A,B,B) ) ),
    file(anproj_1,r1_anproj_1),
    []).

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

fof(symmetry_r1_anproj_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_subset_1(C,u1_struct_0(A)) )
     => ( r1_anproj_1(A,B,C)
       => r1_anproj_1(A,C,B) ) ) ),
    file(anproj_1,r1_anproj_1),
    []).

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

fof(t23_anproj_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_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ~ ( r2_anproj_1(A,B,C,D)
                                      & r2_anproj_1(A,E,F,D)
                                      & r2_anproj_1(A,B,E,G)
                                      & r2_anproj_1(A,C,F,G)
                                      & r2_anproj_1(A,B,F,H)
                                      & r2_anproj_1(A,C,E,H)
                                      & r2_anproj_1(A,G,D,H)
                                      & v8_rlvect_1(G,A)
                                      & v8_rlvect_1(D,A)
                                      & v8_rlvect_1(H,A)
                                      & ~ r2_anproj_1(A,B,C,F)
                                      & ~ r2_anproj_1(A,B,C,E)
                                      & ~ r2_anproj_1(A,B,E,F)
                                      & ~ r2_anproj_1(A,C,E,F) ) ) ) ) ) ) ) ) ) ),
    file(anproj_1,t23_anproj_1),
    []).

fof(t24_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
                 => ( r1_collsp(k6_anproj_1(A),B,C,D)
                  <=> ? [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                        & ? [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                            & ? [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                                & B = k3_anproj_1(A,E)
                                & C = k3_anproj_1(A,F)
                                & D = k3_anproj_1(A,G)
                                & v8_rlvect_1(E,A)
                                & v8_rlvect_1(F,A)
                                & v8_rlvect_1(G,A)
                                & r2_anproj_1(A,E,F,G) ) ) ) ) ) ) ) ) ),
    file(anproj_2,t24_anproj_2),
    []).

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

fof(t35_anproj_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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( v8_rlvect_1(B,A)
                  & v8_rlvect_1(C,A) )
               => ( k3_anproj_1(A,B) = k3_anproj_1(A,C)
                <=> r1_anproj_1(A,B,C) ) ) ) ) ) ),
    file(anproj_1,t35_anproj_1),
    []).

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

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

fof(t9_anproj_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_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_anproj_1(A,B,C)
                                  & r1_anproj_1(A,D,E)
                                  & r1_anproj_1(A,F,G)
                                  & r2_anproj_1(A,B,D,F) )
                               => r2_anproj_1(A,C,E,G) ) ) ) ) ) ) ) ) ),
    file(anproj_1,t9_anproj_1),
    []).