% Mizar problem: t22_ff_siec,ff_siec,919,40 
fof(t22_ff_siec,conjecture,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => ( r1_tarski(k9_ff_siec(A),k2_zfmisc_1(k1_net_1(A),k1_net_1(A)))
        & r1_tarski(k8_ff_siec(A),k2_zfmisc_1(k1_net_1(A),k1_net_1(A))) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,d10_ff_siec,d11_ff_siec,dt_k1_net_1,dt_k1_zfmisc_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k4_relat_1,dt_k6_relat_1,dt_k7_relat_1,dt_k8_ff_siec,dt_k9_ff_siec,dt_l1_net_1,dt_m1_subset_1,dt_u1_net_1,dt_u2_net_1,dt_u3_net_1,existence_l1_net_1,existence_m1_subset_1,fc1_sysrel,fc2_relat_1,idempotence_k2_xboole_0,involutiveness_k4_relat_1,reflexivity_r1_tarski,t13_ff_siec,t1_xboole_1,t28_relset_1,t33_sysrel,t3_subset,t4_net_1,t88_relat_1,t8_xboole_1]),
    [file(ff_siec,t22_ff_siec)]).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(d10_ff_siec,axiom,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => k8_ff_siec(A) = k2_xboole_0(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A)),k6_relat_1(u1_net_1(A))) ) ),
    file(ff_siec,d10_ff_siec),
    []).

fof(d11_ff_siec,axiom,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => k9_ff_siec(A) = k2_xboole_0(k7_relat_1(u3_net_1(A),u2_net_1(A)),k6_relat_1(u1_net_1(A))) ) ),
    file(ff_siec,d11_ff_siec),
    []).

fof(dt_k1_net_1,axiom,(
    $true ),
    file(net_1,k1_net_1),
    []).

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

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(dt_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v1_relat_1(k4_relat_1(A)) ) ),
    file(relat_1,k4_relat_1),
    []).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_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_ff_siec,axiom,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => v1_relat_1(k8_ff_siec(A)) ) ),
    file(ff_siec,k8_ff_siec),
    []).

fof(dt_k9_ff_siec,axiom,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => v1_relat_1(k9_ff_siec(A)) ) ),
    file(ff_siec,k9_ff_siec),
    []).

fof(dt_l1_net_1,axiom,(
    $true ),
    file(net_1,l1_net_1),
    []).

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

fof(dt_u1_net_1,axiom,(
    $true ),
    file(net_1,u1_net_1),
    []).

fof(dt_u2_net_1,axiom,(
    $true ),
    file(net_1,u2_net_1),
    []).

fof(dt_u3_net_1,axiom,(
    ! [A] : 
      ( l1_net_1(A)
     => v1_relat_1(u3_net_1(A)) ) ),
    file(net_1,u3_net_1),
    []).

fof(existence_l1_net_1,axiom,(
    ? [A] : l1_net_1(A) ),
    file(net_1,l1_net_1),
    []).

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

fof(fc1_sysrel,axiom,(
    ! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)) ),
    file(sysrel,fc1_sysrel),
    []).

fof(fc2_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(involutiveness_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k4_relat_1(k4_relat_1(A)) = A ) ),
    file(relat_1,k4_relat_1),
    []).

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

fof(t13_ff_siec,axiom,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => ( r1_tarski(u3_net_1(A),k2_zfmisc_1(k1_net_1(A),k1_net_1(A)))
        & r1_tarski(k4_relat_1(u3_net_1(A)),k2_zfmisc_1(k1_net_1(A),k1_net_1(A))) ) ) ),
    file(ff_siec,t13_ff_siec),
    []).

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t28_relset_1,axiom,(
    ! [A] : r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A)) ),
    file(relset_1,t28_relset_1),
    []).

fof(t33_sysrel,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k6_relat_1(A),k6_relat_1(B)) ) ),
    file(sysrel,t33_sysrel),
    []).

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

fof(t4_net_1,axiom,(
    ! [A] : 
      ( l1_net_1(A)
     => r1_tarski(u1_net_1(A),k1_net_1(A)) ) ),
    file(net_1,t4_net_1),
    []).

fof(t88_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k7_relat_1(B,A),B) ) ),
    file(relat_1,t88_relat_1),
    []).

fof(t8_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    []).