% Mizar problem: t39_relset_1,relset_1,542,38 
fof(t39_relset_1,conjecture,(
    ! [A,B,C] : 
      ( m2_relset_1(C,B,A)
     => ( k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)) = k5_relset_1(B,A,C)
        & k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)) = k4_relset_1(B,A,C) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_relset_1,dt_k10_relat_1,dt_k10_relset_1,dt_k11_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_relset_1,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_k10_relset_1,redefinition_k11_relset_1,redefinition_k4_relset_1,redefinition_k5_relset_1,redefinition_m2_relset_1,reflexivity_r1_tarski,t146_relat_1,t169_relat_1,t38_relset_1,t3_subset]),
    [file(relset_1,t39_relset_1)]).

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(dt_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_1),
    []).

fof(dt_k10_relset_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k10_relset_1(A,B,C,D),k1_zfmisc_1(B)) ) ),
    file(relset_1,k10_relset_1),
    []).

fof(dt_k11_relset_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k11_relset_1(A,B,C,D),k1_zfmisc_1(A)) ) ),
    file(relset_1,k11_relset_1),
    []).

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_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

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

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(relset_1,k5_relset_1),
    []).

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

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(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(redefinition_k10_relset_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_relset_1(C,A,B)
     => k10_relset_1(A,B,C,D) = k9_relat_1(C,D) ) ),
    file(relset_1,k10_relset_1),
    []).

fof(redefinition_k11_relset_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_relset_1(C,A,B)
     => k11_relset_1(A,B,C,D) = k10_relat_1(C,D) ) ),
    file(relset_1,k11_relset_1),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(redefinition_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k5_relset_1(A,B,C) = k2_relat_1(C) ) ),
    file(relset_1,k5_relset_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(t146_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A) ) ),
    file(relat_1,t146_relat_1),
    []).

fof(t169_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k10_relat_1(A,k2_relat_1(A)) = k1_relat_1(A) ) ),
    file(relat_1,t169_relat_1),
    []).

fof(t38_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( k10_relset_1(A,B,C,A) = k5_relset_1(A,B,C)
        & k11_relset_1(A,B,C,B) = k4_relset_1(A,B,C) ) ) ),
    file(relset_1,t38_relset_1),
    []).

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