% Mizar problem: t39_zfrefle1,zfrefle1,1219,59 
fof(t39_zfrefle1,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ~ ( r2_hidden(k5_ordinal2,A)
          & ! [B] : 
              ( m2_ordinal4(B,A)
             => ~ ( v2_ordinal2(B)
                  & v3_ordinal2(B)
                  & ! [C] : 
                      ( m1_ordinal4(C,A)
                     => ! [D] : 
                          ( ~ v1_xboole_0(D)
                         => ( ( k4_ordinal4(A,B,C) = C
                              & D = k4_classes1(C) )
                           => ( k1_xboole_0 = C
                              | r2_zfrefle1(D,A) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_classes2,cc1_ordinal1,cc2_classes2,cc2_ordinal1,cc3_classes2,cc3_ordinal1,dt_k1_funct_1,dt_k1_xboole_0,dt_k4_classes1,dt_k4_ordinal4,dt_k5_ordinal2,dt_m1_ordinal4,dt_m1_subset_1,dt_m2_ordinal4,existence_m1_ordinal4,existence_m1_subset_1,existence_m2_ordinal4,fc1_ordinal2,fc2_ordinal1,fc3_ordinal2,fc7_classes2,rc1_classes2,rc1_ordinal1,rc1_partfun1,rc2_classes2,rc2_ordinal1,rc2_ordinal2,rc3_ordinal1,rc4_ordinal1,redefinition_k4_ordinal4,reflexivity_r2_zfrefle1,reflexivity_r3_zfrefle1,symmetry_r2_zfrefle1,t1_subset,t2_subset,t35_zfrefle1,t6_boole,t7_boole,t8_boole,t9_zfrefle1]),
    [file(zfrefle1,t39_zfrefle1)]).

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

fof(cc1_classes2,axiom,(
    ! [A] : 
      ( v2_classes1(A)
     => v1_classes1(A) ) ),
    file(classes2,cc1_classes2),
    []).

fof(cc1_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

fof(cc2_classes2,axiom,(
    ! [A] : 
      ( v1_classes2(A)
     => ( v1_ordinal1(A)
        & v1_classes1(A)
        & v2_classes1(A) ) ) ),
    file(classes2,cc2_classes2),
    []).

fof(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(cc3_classes2,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_classes1(A) )
     => v1_classes2(A) ) ),
    file(classes2,cc3_classes2),
    []).

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

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

fof(dt_k4_classes1,axiom,(
    $true ),
    file(classes1,k4_classes1),
    []).

fof(dt_k4_ordinal4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m2_ordinal4(B,A)
        & m1_ordinal4(C,A) )
     => m1_ordinal4(k4_ordinal4(A,B,C),A) ) ),
    file(ordinal4,k4_ordinal4),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_m1_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_ordinal4(B,A)
         => v3_ordinal1(B) ) ) ),
    file(ordinal4,m1_ordinal4),
    []).

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

fof(dt_m2_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m2_ordinal4(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B)
            & v5_ordinal1(B)
            & v1_ordinal2(B) ) ) ) ),
    file(ordinal4,m2_ordinal4),
    []).

fof(existence_m1_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : m1_ordinal4(B,A) ) ),
    file(ordinal4,m1_ordinal4),
    []).

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

fof(existence_m2_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : m2_ordinal4(B,A) ) ),
    file(ordinal4,m2_ordinal4),
    []).

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

fof(fc2_ordinal1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

fof(fc3_ordinal2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A)
        & v3_ordinal1(B) )
     => ( v1_ordinal1(k1_funct_1(A,B))
        & v2_ordinal1(k1_funct_1(A,B))
        & v3_ordinal1(k1_funct_1(A,B)) ) ) ),
    file(ordinal2,fc3_ordinal2),
    []).

fof(fc7_classes2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => v1_ordinal1(k4_classes1(A)) ) ),
    file(classes2,fc7_classes2),
    []).

fof(rc1_classes2,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & ~ v1_xboole_0(A)
      & v1_classes1(A)
      & v2_classes1(A)
      & v1_classes2(A) ) ),
    file(classes2,rc1_classes2),
    []).

fof(rc1_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc2_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & ~ v1_xboole_0(B) ) ) ),
    file(classes2,rc2_classes2),
    []).

fof(rc2_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

fof(rc2_ordinal2,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A)
      & v1_ordinal2(A) ) ),
    file(ordinal2,rc2_ordinal2),
    []).

fof(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

fof(rc4_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A) ) ),
    file(ordinal1,rc4_ordinal1),
    []).

fof(redefinition_k4_ordinal4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m2_ordinal4(B,A)
        & m1_ordinal4(C,A) )
     => k4_ordinal4(A,B,C) = k1_funct_1(B,C) ) ),
    file(ordinal4,k4_ordinal4),
    []).

fof(reflexivity_r2_zfrefle1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => r2_zfrefle1(A,A) ) ),
    file(zfrefle1,r2_zfrefle1),
    []).

fof(reflexivity_r3_zfrefle1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => r3_zfrefle1(A,A) ) ),
    file(zfrefle1,r3_zfrefle1),
    []).

fof(symmetry_r2_zfrefle1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r2_zfrefle1(A,B)
       => r2_zfrefle1(B,A) ) ) ),
    file(zfrefle1,r2_zfrefle1),
    []).

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(t35_zfrefle1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ~ ( r2_hidden(k5_ordinal2,A)
          & ! [B] : 
              ( m2_ordinal4(B,A)
             => ~ ( v2_ordinal2(B)
                  & v3_ordinal2(B)
                  & ! [C] : 
                      ( m1_ordinal4(C,A)
                     => ! [D] : 
                          ( ~ v1_xboole_0(D)
                         => ( ( k4_ordinal4(A,B,C) = C
                              & D = k4_classes1(C) )
                           => ( k1_xboole_0 = C
                              | r3_zfrefle1(D,A) ) ) ) ) ) ) ) ) ),
    file(zfrefle1,t35_zfrefle1),
    []).

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),
    []).

fof(t9_zfrefle1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ( r3_zfrefle1(A,B)
           => r2_zfrefle1(A,B) ) ) ) ),
    file(zfrefle1,t9_zfrefle1),
    []).