% Mizar problem: t10_funct_4,funct_4,182,32 
fof(t10_funct_4,conjecture,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( r1_tarski(C,D)
           => r1_tarski(k7_relat_1(k8_relat_1(A,C),B),k7_relat_1(k8_relat_1(A,D),B)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k1_zfmisc_1,dt_k7_relat_1,dt_k8_relat_1,dt_m1_subset_1,existence_m1_subset_1,fc4_funct_1,fc5_funct_1,rc1_funct_1,reflexivity_r1_tarski,t105_relat_1,t132_relat_1,t3_subset]),
    [file(funct_4,t10_funct_4)]).

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

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

fof(dt_k8_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => v1_relat_1(k8_relat_1(A,B)) ) ),
    file(relat_1,k8_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(fc4_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_1),
    []).

fof(fc5_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k8_relat_1(A,B))
        & v1_funct_1(k8_relat_1(A,B)) ) ) ),
    file(funct_1,fc5_funct_1),
    []).

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

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

fof(t105_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => ( r1_tarski(B,C)
           => r1_tarski(k7_relat_1(B,A),k7_relat_1(C,A)) ) ) ) ),
    file(relat_1,t105_relat_1),
    []).

fof(t132_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => ( r1_tarski(B,C)
           => r1_tarski(k8_relat_1(A,B),k8_relat_1(A,C)) ) ) ) ),
    file(relat_1,t132_relat_1),
    []).

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