% Mizar problem: t69_grfunc_1,grfunc_1,430,39 
fof(t69_grfunc_1,conjecture,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( r1_tarski(k5_relat_1(C,k8_relat_1(A,B)),k5_relat_1(C,B))
                & r1_tarski(k5_relat_1(k8_relat_1(A,B),D),k5_relat_1(B,D)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,reflexivity_r1_tarski,dt_k5_relat_1,dt_k8_relat_1,rc1_funct_1,fc1_funct_1,fc5_funct_1,t3_subset,t121_relat_1,t122_relat_1]),
    [file(grfunc_1,t69_grfunc_1)]).

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

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

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

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

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

fof(t121_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => r1_tarski(k5_relat_1(k8_relat_1(A,B),C),k5_relat_1(B,C)) ) ) ),
    file(relat_1,t121_relat_1),
    []).

fof(t122_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => r1_tarski(k5_relat_1(B,k8_relat_1(A,C)),k5_relat_1(B,C)) ) ) ),
    file(relat_1,t122_relat_1),
    []).