% Mizar problem: t16_e_siec,e_siec,231,51 
fof(t16_e_siec,conjecture,(
    ! [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))) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d2_e_siec,dt_k1_relat_1,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,fc1_sysrel,fc3_relat_1,rc2_e_siec,rc3_e_siec,reflexivity_r1_tarski,t38_sysrel,t3_subset]),
    [file(e_siec,t16_e_siec)]).

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

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

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

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

fof(t38_sysrel,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(B,k2_zfmisc_1(A,A))
       => ( k4_xboole_0(B,k6_relat_1(k1_relat_1(B))) = k4_xboole_0(B,k6_relat_1(A))
          & k4_xboole_0(B,k6_relat_1(k2_relat_1(B))) = k4_xboole_0(B,k6_relat_1(A)) ) ) ) ),
    file(sysrel,t38_sysrel),
    []).

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