% Mizar problem: t9_jgraph_5,jgraph_5,170,24 
fof(t9_jgraph_5,conjecture,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( l1_pre_topc(B)
         => ! [C] : 
              ( l1_pre_topc(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( ( v3_tops_2(E,B,C)
                          & v2_funct_1(D) )
                       => v2_funct_1(k5_relat_1(D,E)) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_relset_1,d5_tops_2,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_pre_topc,dt_k2_relat_1,dt_k2_tops_2,dt_k2_zfmisc_1,dt_k5_relat_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_funct_1,rc1_funct_1,rc3_funct_1,redefinition_m2_relset_1,reflexivity_r1_tarski,t3_subset,t46_funct_1]),
    [file(jgraph_5,t9_jgraph_5)]).

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(d5_tops_2,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( l1_pre_topc(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_tops_2(C,A,B)
              <=> ( k1_relat_1(C) = k2_pre_topc(A)
                  & k2_relat_1(C) = k2_pre_topc(B)
                  & v2_funct_1(C)
                  & v5_pre_topc(C,A,B)
                  & v5_pre_topc(k2_tops_2(A,B,C),B,A) ) ) ) ) ) ),
    file(tops_2,d5_tops_2),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

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

fof(dt_k2_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k2_pre_topc),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_tops_2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( v1_funct_1(k2_tops_2(A,B,C))
        & v1_funct_2(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A))
        & m2_relset_1(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) ) ) ),
    file(tops_2,k2_tops_2),
    []).

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

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    []).

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

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_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_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_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_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_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(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(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t46_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v2_funct_1(A)
              & v2_funct_1(B) )
           => v2_funct_1(k5_relat_1(A,B)) ) ) ) ),
    file(funct_1,t46_funct_1),
    []).