% Mizar problem: t4_e_siec,e_siec,128,35 
fof(t4_e_siec,conjecture,
    ( v2_e_siec(g1_e_siec(k1_xboole_0,k1_xboole_0,k1_xboole_0))
    & v3_e_siec(g1_e_siec(k1_xboole_0,k1_xboole_0,k1_xboole_0))
    & l1_e_siec(g1_e_siec(k1_xboole_0,k1_xboole_0,k1_xboole_0)) ),
    inference(mizar_bg_added,[status(thm)],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,dt_u1_e_siec,dt_u1_struct_0,dt_u2_e_siec,t1_subset,abstractness_v1_e_siec,existence_l1_struct_0,dt_l1_struct_0,rc1_e_siec,rc4_e_siec,rc1_relat_1,cc1_relat_1,rc2_relat_1,rc3_relat_1,t7_boole,t8_boole,free_g1_e_siec,existence_l1_e_siec,dt_g1_e_siec,dt_k1_xboole_0,dt_l1_e_siec,rc2_e_siec,rc3_e_siec,fc4_relat_1,fc12_relat_1,t6_boole,t2_e_siec]),
    [file(e_siec,t4_e_siec)]).

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

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

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

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

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

fof(abstractness_v1_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => ( v1_e_siec(A)
       => A = g1_e_siec(u1_struct_0(A),u1_e_siec(A),u2_e_siec(A)) ) ) ),
    file(e_siec,v1_e_siec),
    []).

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

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

fof(rc1_e_siec,axiom,(
    ? [A] : 
      ( l1_e_siec(A)
      & v1_e_siec(A) ) ),
    file(e_siec,rc1_e_siec),
    []).

fof(rc4_e_siec,axiom,(
    ? [A] : 
      ( l1_e_siec(A)
      & v1_e_siec(A)
      & v2_e_siec(A)
      & v3_e_siec(A) ) ),
    file(e_siec,rc4_e_siec),
    []).

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

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_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(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),
    []).

fof(free_g1_e_siec,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(B)
        & v1_relat_1(C) )
     => ! [D,E,F] : 
          ( g1_e_siec(A,B,C) = g1_e_siec(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(e_siec,g1_e_siec),
    []).

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

fof(dt_g1_e_siec,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(B)
        & v1_relat_1(C) )
     => ( v1_e_siec(g1_e_siec(A,B,C))
        & l1_e_siec(g1_e_siec(A,B,C)) ) ) ),
    file(e_siec,g1_e_siec),
    []).

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

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

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(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_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(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t2_e_siec,axiom,(
    ! [A] : 
      ( v2_e_siec(g1_e_siec(A,k1_xboole_0,k1_xboole_0))
      & v3_e_siec(g1_e_siec(A,k1_xboole_0,k1_xboole_0))
      & l1_e_siec(g1_e_siec(A,k1_xboole_0,k1_xboole_0)) ) ),
    file(e_siec,t2_e_siec),
    []).