% Mizar problem: t2_ff_siec,ff_siec,79,42 
fof(t2_ff_siec,conjecture,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => ( u1_net_1(k2_ff_siec(A,B)) = A
        & u2_net_1(k2_ff_siec(A,B)) = B
        & u3_net_1(k2_ff_siec(A,B)) = k1_xboole_0 ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_net_1,antisymmetry_r2_hidden,cc1_relat_1,d4_ff_siec,dt_g1_net_1,dt_k1_xboole_0,dt_k2_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,fc12_relat_1,fc1_net_1,fc4_relat_1,free_g1_net_1,rc1_net_1,rc1_relat_1,rc2_net_1,rc2_relat_1,rc3_relat_1,symmetry_r1_xboole_0,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole]),
    [file(ff_siec,t2_ff_siec)]).

fof(abstractness_v1_net_1,axiom,(
    ! [A] : 
      ( l1_net_1(A)
     => ( v1_net_1(A)
       => A = g1_net_1(u1_net_1(A),u2_net_1(A),u3_net_1(A)) ) ) ),
    file(net_1,v1_net_1),
    []).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

fof(d4_ff_siec,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => k2_ff_siec(A,B) = g1_net_1(A,B,k1_xboole_0) ) ),
    file(ff_siec,d4_ff_siec),
    []).

fof(dt_g1_net_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( v1_net_1(g1_net_1(A,B,C))
        & l1_net_1(g1_net_1(A,B,C)) ) ) ),
    file(net_1,g1_net_1),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k2_ff_siec,axiom,(
    ! [A,B] : 
      ( v1_net_1(k2_ff_siec(A,B))
      & v2_net_1(k2_ff_siec(A,B))
      & l1_net_1(k2_ff_siec(A,B)) ) ),
    file(ff_siec,k2_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(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc1_net_1,axiom,
    ( v1_net_1(g1_net_1(k1_xboole_0,k1_xboole_0,k1_xboole_0))
    & v2_net_1(g1_net_1(k1_xboole_0,k1_xboole_0,k1_xboole_0)) ),
    file(net_1,fc1_net_1),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

fof(free_g1_net_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ! [D,E,F] : 
          ( g1_net_1(A,B,C) = g1_net_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(net_1,g1_net_1),
    []).

fof(rc1_net_1,axiom,(
    ? [A] : 
      ( l1_net_1(A)
      & v1_net_1(A) ) ),
    file(net_1,rc1_net_1),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

fof(rc2_net_1,axiom,(
    ? [A] : 
      ( l1_net_1(A)
      & v1_net_1(A)
      & v2_net_1(A) ) ),
    file(net_1,rc2_net_1),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).