% Mizar problem: t27_ff_siec,ff_siec,1337,50 
fof(t27_ff_siec,conjecture,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => ( r1_tarski(k14_ff_siec(A),k2_zfmisc_1(k13_ff_siec(A),k12_ff_siec(A)))
        & r1_tarski(k15_ff_siec(A),k2_zfmisc_1(k13_ff_siec(A),k12_ff_siec(A))) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relat_1,d11_relat_1,d14_ff_siec,d15_ff_siec,d16_ff_siec,d17_ff_siec,d3_relat_1,d7_relat_1,dt_k12_ff_siec,dt_k13_ff_siec,dt_k14_ff_siec,dt_k15_ff_siec,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k4_relat_1,dt_k4_tarski,dt_k7_relat_1,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,fc11_relat_1,fc12_relat_1,fc13_relat_1,fc1_sysrel,fc4_relat_1,involutiveness_k4_relat_1,rc1_relat_1,rc2_relat_1,rc3_relat_1,reflexivity_r1_tarski,t106_zfmisc_1,t11_ff_siec,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(ff_siec,t27_ff_siec)]).

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(d11_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( v1_relat_1(C)
         => ( C = k7_relat_1(A,B)
          <=> ! [D,E] : 
                ( r2_hidden(k4_tarski(D,E),C)
              <=> ( r2_hidden(D,B)
                  & r2_hidden(k4_tarski(D,E),A) ) ) ) ) ) ),
    file(relat_1,d11_relat_1),
    []).

fof(d14_ff_siec,axiom,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => k12_ff_siec(A) = u1_net_1(A) ) ),
    file(ff_siec,d14_ff_siec),
    []).

fof(d15_ff_siec,axiom,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => k13_ff_siec(A) = u2_net_1(A) ) ),
    file(ff_siec,d15_ff_siec),
    []).

fof(d16_ff_siec,axiom,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => k14_ff_siec(A) = k7_relat_1(u3_net_1(A),u2_net_1(A)) ) ),
    file(ff_siec,d16_ff_siec),
    []).

fof(d17_ff_siec,axiom,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => k15_ff_siec(A) = k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A)) ) ),
    file(ff_siec,d17_ff_siec),
    []).

fof(d3_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
               => r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d3_relat_1),
    []).

fof(d7_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( B = k4_relat_1(A)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),B)
              <=> r2_hidden(k4_tarski(D,C),A) ) ) ) ) ),
    file(relat_1,d7_relat_1),
    []).

fof(dt_k12_ff_siec,axiom,(
    $true ),
    file(ff_siec,k12_ff_siec),
    []).

fof(dt_k13_ff_siec,axiom,(
    $true ),
    file(ff_siec,k13_ff_siec),
    []).

fof(dt_k14_ff_siec,axiom,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => v1_relat_1(k14_ff_siec(A)) ) ),
    file(ff_siec,k14_ff_siec),
    []).

fof(dt_k15_ff_siec,axiom,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => v1_relat_1(k15_ff_siec(A)) ) ),
    file(ff_siec,k15_ff_siec),
    []).

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

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

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_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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_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(fc11_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k4_relat_1(A))
        & v1_relat_1(k4_relat_1(A)) ) ) ),
    file(relat_1,fc11_relat_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(fc13_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v3_relat_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v3_relat_1(k7_relat_1(A,B)) ) ) ),
    file(relat_1,fc13_relat_1),
    []).

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

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

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(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_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(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t106_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    []).

fof(t11_ff_siec,axiom,(
    ! [A,B,C] : 
      ( ( v2_net_1(C)
        & l1_net_1(C) )
     => ( ( ( r2_hidden(k4_tarski(A,B),u3_net_1(C))
            & r2_hidden(A,u2_net_1(C)) )
         => ( ~ r2_hidden(A,u1_net_1(C))
            & ~ r2_hidden(B,u2_net_1(C))
            & r2_hidden(B,u1_net_1(C)) ) )
        & ( ( r2_hidden(k4_tarski(A,B),u3_net_1(C))
            & r2_hidden(B,u2_net_1(C)) )
         => ( ~ r2_hidden(B,u1_net_1(C))
            & ~ r2_hidden(A,u2_net_1(C))
            & r2_hidden(A,u1_net_1(C)) ) )
        & ( ( r2_hidden(k4_tarski(A,B),u3_net_1(C))
            & r2_hidden(A,u1_net_1(C)) )
         => ( ~ r2_hidden(B,u1_net_1(C))
            & ~ r2_hidden(A,u2_net_1(C))
            & r2_hidden(B,u2_net_1(C)) ) )
        & ( ( r2_hidden(k4_tarski(A,B),u3_net_1(C))
            & r2_hidden(B,u1_net_1(C)) )
         => ( ~ r2_hidden(A,u1_net_1(C))
            & ~ r2_hidden(B,u2_net_1(C))
            & r2_hidden(A,u2_net_1(C)) ) ) ) ) ),
    file(ff_siec,t11_ff_siec),
    []).

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

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_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),
    []).