% Mizar problem: t20_net_1,net_1,318,58 
fof(t20_net_1,conjecture,(
    ! [A,B] : 
      ( ( v2_net_1(B)
        & l1_net_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,k1_net_1(B))
         => ( r2_hidden(C,u2_net_1(B))
           => ( r2_hidden(A,k2_net_1(B,C))
            <=> r1_net_1(B,C,A) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relat_1,commutativity_k2_xboole_0,d2_net_1,d5_net_1,d7_net_1,dt_k1_net_1,dt_k1_xboole_0,dt_k2_net_1,dt_k2_xboole_0,dt_k4_tarski,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,fc2_relat_1,fc4_relat_1,idempotence_k2_xboole_0,rc1_relat_1,rc2_relat_1,rc3_relat_1,t13_net_1,t1_boole,t1_subset,t2_subset,t6_boole,t6_net_1,t7_boole,t8_boole]),
    [file(net_1,t20_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(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(d2_net_1,axiom,(
    ! [A] : 
      ( l1_net_1(A)
     => k1_net_1(A) = k2_xboole_0(u1_net_1(A),u2_net_1(A)) ) ),
    file(net_1,d2_net_1),
    []).

fof(d5_net_1,axiom,(
    ! [A] : 
      ( ( v2_net_1(A)
        & l1_net_1(A) )
     => ! [B,C] : 
          ( r1_net_1(A,B,C)
        <=> ( r2_hidden(k4_tarski(C,B),u3_net_1(A))
            & r2_hidden(B,u2_net_1(A)) ) ) ) ),
    file(net_1,d5_net_1),
    []).

fof(d7_net_1,axiom,(
    ! [A] : 
      ( l1_net_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_net_1(A))
         => ! [C] : 
              ( C = k2_net_1(A,B)
            <=> ! [D] : 
                  ( r2_hidden(D,C)
                <=> ( r2_hidden(D,k1_net_1(A))
                    & r2_hidden(k4_tarski(D,B),u3_net_1(A)) ) ) ) ) ) ),
    file(net_1,d7_net_1),
    []).

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

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

fof(dt_k2_net_1,axiom,(
    $true ),
    file(net_1,k2_net_1),
    []).

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

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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

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

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(t13_net_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_net_1(C)
        & l1_net_1(C) )
     => ( ( r2_hidden(k4_tarski(A,B),u3_net_1(C))
          & r2_hidden(B,u2_net_1(C)) )
       => r2_hidden(A,u1_net_1(C)) ) ) ),
    file(net_1,t13_net_1),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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(t6_net_1,axiom,(
    ! [A,B] : 
      ( l1_net_1(B)
     => ( r2_hidden(A,k1_net_1(B))
      <=> ( r2_hidden(A,u1_net_1(B))
          | r2_hidden(A,u2_net_1(B)) ) ) ) ),
    file(net_1,t6_net_1),
    []).

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),
    []).