% Mizar problem: t18_e_siec,e_siec,260,46 
fof(t18_e_siec,conjecture,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k2_relat_1(u1_e_siec(A)) = k2_relat_1(k1_sysrel(u1_e_siec(A)))
        & k2_relat_1(u1_e_siec(A)) = k1_relat_1(k1_sysrel(u1_e_siec(A)))
        & k2_relat_1(u2_e_siec(A)) = k2_relat_1(k1_sysrel(u2_e_siec(A)))
        & k2_relat_1(u2_e_siec(A)) = k1_relat_1(k1_sysrel(u2_e_siec(A)))
        & k2_relat_1(u1_e_siec(A)) = k2_relat_1(u2_e_siec(A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relat_1,d2_e_siec,d3_e_siec,dt_k1_relat_1,dt_k1_sysrel,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k4_xboole_0,dt_k5_relat_1,dt_k6_relat_1,dt_l1_e_siec,dt_l1_struct_0,dt_m1_subset_1,dt_u1_e_siec,dt_u1_struct_0,dt_u2_e_siec,existence_l1_e_siec,existence_l1_struct_0,existence_m1_subset_1,fc10_relat_1,fc12_relat_1,fc1_sysrel,fc3_relat_1,fc4_relat_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,rc1_relat_1,rc2_e_siec,rc2_relat_1,rc3_e_siec,rc3_relat_1,reflexivity_r1_tarski,t16_e_siec,t17_e_siec,t1_subset,t2_subset,t3_boole,t3_subset,t4_boole,t4_subset,t50_sysrel,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(e_siec,t18_e_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(d2_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => ( v2_e_siec(A)
      <=> ( r1_tarski(u1_e_siec(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
          & r1_tarski(u2_e_siec(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
          & k5_relat_1(u1_e_siec(A),u1_e_siec(A)) = u1_e_siec(A)
          & k5_relat_1(u1_e_siec(A),u2_e_siec(A)) = u1_e_siec(A)
          & k5_relat_1(u2_e_siec(A),u2_e_siec(A)) = u2_e_siec(A)
          & k5_relat_1(u2_e_siec(A),u1_e_siec(A)) = u2_e_siec(A) ) ) ) ),
    file(e_siec,d2_e_siec),
    []).

fof(d3_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => ( v3_e_siec(A)
      <=> ( k5_relat_1(u1_e_siec(A),k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0
          & k5_relat_1(u2_e_siec(A),k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0 ) ) ) ),
    file(e_siec,d3_e_siec),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_sysrel,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v1_relat_1(k1_sysrel(A)) ) ),
    file(sysrel,k1_sysrel),
    []).

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_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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    []).

fof(dt_l1_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => l1_struct_0(A) ) ),
    file(e_siec,l1_e_siec),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

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

fof(dt_u1_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => v1_relat_1(u1_e_siec(A)) ) ),
    file(e_siec,u1_e_siec),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u2_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => v1_relat_1(u2_e_siec(A)) ) ),
    file(e_siec,u2_e_siec),
    []).

fof(existence_l1_e_siec,axiom,(
    ? [A] : l1_e_siec(A) ),
    file(e_siec,l1_e_siec),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

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

fof(fc10_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_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(fc1_sysrel,axiom,(
    ! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)) ),
    file(sysrel,fc1_sysrel),
    []).

fof(fc3_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k4_xboole_0(A,B)) ) ),
    file(relat_1,fc3_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(fc5_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    []).

fof(fc6_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    []).

fof(fc7_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    []).

fof(fc8_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    []).

fof(fc9_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    []).

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

fof(rc2_e_siec,axiom,(
    ? [A] : 
      ( l1_e_siec(A)
      & v2_e_siec(A) ) ),
    file(e_siec,rc2_e_siec),
    []).

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

fof(rc3_e_siec,axiom,(
    ? [A] : 
      ( l1_e_siec(A)
      & v3_e_siec(A) ) ),
    file(e_siec,rc3_e_siec),
    []).

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(t16_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k4_xboole_0(u1_e_siec(A),k6_relat_1(k1_relat_1(u1_e_siec(A)))) = k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))
        & k4_xboole_0(u2_e_siec(A),k6_relat_1(k1_relat_1(u2_e_siec(A)))) = k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))
        & k4_xboole_0(u1_e_siec(A),k6_relat_1(k2_relat_1(u1_e_siec(A)))) = k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))
        & k4_xboole_0(u2_e_siec(A),k6_relat_1(k2_relat_1(u2_e_siec(A)))) = k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))) ) ) ),
    file(e_siec,t16_e_siec),
    []).

fof(t17_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k1_sysrel(u1_e_siec(A)) = k1_sysrel(u2_e_siec(A)) ) ),
    file(e_siec,t17_e_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_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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(t50_sysrel,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( ( k5_relat_1(A,A) = A
            & k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) = k1_xboole_0 )
         => ( k1_relat_1(k1_sysrel(A)) = k2_relat_1(A)
            & k2_relat_1(k1_sysrel(A)) = k2_relat_1(A) ) )
        & ( ( k5_relat_1(A,A) = A
            & k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) = k1_xboole_0 )
         => ( k1_relat_1(k1_sysrel(A)) = k1_relat_1(A)
            & k2_relat_1(k1_sysrel(A)) = k1_relat_1(A) ) ) ) ) ),
    file(sysrel,t50_sysrel),
    []).

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),
    []).