% Mizar problem: t1_partfun3,partfun3,67,15 
fof(t1_partfun3,conjecture,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v2_funct_1(A)
            & r1_tarski(B,k1_relat_1(k2_funct_1(A))) )
         => k9_relat_1(A,k9_relat_1(k2_funct_1(A),B)) = B ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_funct_1,dt_k9_relat_1,dt_m1_subset_1,existence_m1_subset_1,rc1_funct_1,rc3_funct_1,reflexivity_r1_tarski,t22_jgraph_6,t3_subset,t62_funct_1,t65_funct_1]),
    [file(partfun3,t1_partfun3)]).

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_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_1(A))
        & v1_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,k2_funct_1),
    []).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    []).

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

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_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(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t22_jgraph_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v2_funct_1(A)
            & r1_tarski(B,k1_relat_1(A)) )
         => k9_relat_1(k2_funct_1(A),k9_relat_1(A,B)) = B ) ) ),
    file(jgraph_6,t22_jgraph_6),
    []).

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

fof(t62_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => v2_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,t62_funct_1),
    []).

fof(t65_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => k2_funct_1(k2_funct_1(A)) = A ) ) ),
    file(funct_1,t65_funct_1),
    []).