% Mizar problem: t7_waybel_8,waybel_8,304,22 
fof(t7_waybel_8,conjecture,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_8(A)
      <=> ( v3_waybel_3(A)
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ~ ( r1_waybel_3(A,B,C)
                      & ! [D] : 
                          ( m1_subset_1(D,u1_struct_0(A))
                         => ~ ( r2_hidden(D,u1_struct_0(k1_waybel_8(A)))
                              & r3_orders_2(A,B,D)
                              & r3_orders_2(A,D,C) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,antisymmetry_r2_hidden,cc1_finset_1,cc1_lattice3,cc1_relset_1,cc2_finset_1,cc2_lattice3,cc4_waybel_3,cc6_yellow_0,cc7_yellow_0,cc8_yellow_0,cc9_waybel_0,d1_waybel_3,d1_waybel_8,d1_xboole_0,d2_waybel_3,d2_waybel_8,d3_waybel_8,d4_waybel_8,d5_waybel_3,d6_waybel_3,d9_lattice3,d9_yellow_0,dt_g1_orders_2,dt_k1_waybel_3,dt_k1_waybel_8,dt_k1_xboole_0,dt_k1_yellow_0,dt_k1_zfmisc_1,dt_k2_waybel_8,dt_k2_zfmisc_1,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m1_yellow_0,dt_m2_relset_1,dt_u1_orders_2,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m1_yellow_0,existence_m2_relset_1,fc14_finset_1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_waybel_3,fc4_subset_1,fc4_waybel_3,fc6_waybel_3,fraenkel_a_2_0_waybel_8,free_g1_orders_2,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc3_struct_0,rc3_yellow_0,rc4_finset_1,rc4_yellow_0,rc5_struct_0,rc9_waybel_0,redefinition_m2_relset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,t1_subset,t1_waybel_0,t1_xboole_1,t25_orders_2,t26_orders_2,t2_subset,t2_tarski,t2_waybel_3,t34_yellow_0,t3_subset,t47_yellow_0,t4_subset,t4_waybel_8,t4_yellow_0,t5_subset,t6_boole,t6_waybel_8,t75_waybel_0,t7_boole,t7_waybel_3,t8_boole,t9_waybel_3]),
    [file(waybel_8,t7_waybel_8)]).

fof(abstractness_v1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_orders_2(A)
       => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ),
    file(orders_2,v1_orders_2),
    []).

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

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_lattice3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_lattice3(A)
       => ~ v3_struct_0(A) ) ) ),
    file(lattice3,cc1_lattice3),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_lattice3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v2_lattice3(A)
       => ~ v3_struct_0(A) ) ) ),
    file(lattice3,cc2_lattice3),
    []).

fof(cc4_waybel_3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_waybel_3(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v24_waybel_0(A)
          & v2_waybel_3(A) ) ) ) ),
    file(waybel_3,cc4_waybel_3),
    []).

fof(cc6_yellow_0,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_yellow_0(B,A)
         => ( v4_yellow_0(B,A)
           => ( v2_orders_2(B)
              & v4_yellow_0(B,A) ) ) ) ) ),
    file(yellow_0,cc6_yellow_0),
    []).

fof(cc7_yellow_0,axiom,(
    ! [A] : 
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_yellow_0(B,A)
         => ( v4_yellow_0(B,A)
           => ( v3_orders_2(B)
              & v4_yellow_0(B,A) ) ) ) ) ),
    file(yellow_0,cc7_yellow_0),
    []).

fof(cc8_yellow_0,axiom,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_yellow_0(B,A)
         => ( v4_yellow_0(B,A)
           => ( v4_orders_2(B)
              & v4_yellow_0(B,A) ) ) ) ) ),
    file(yellow_0,cc8_yellow_0),
    []).

fof(cc9_waybel_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v1_lattice3(A)
          & v24_waybel_0(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v1_lattice3(A)
          & v2_yellow_0(A) ) ) ) ),
    file(waybel_0,cc9_waybel_0),
    []).

fof(d1_waybel_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_waybel_3(A,B,C)
              <=> ! [D] : 
                    ( ( ~ v1_xboole_0(D)
                      & v1_waybel_0(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => ~ ( r3_orders_2(A,C,k1_yellow_0(A,D))
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,D)
                                & r3_orders_2(A,B,E) ) ) ) ) ) ) ) ) ),
    file(waybel_3,d1_waybel_3),
    []).

fof(d1_waybel_8,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_orders_2(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( B = k1_waybel_8(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,u1_struct_0(B))
                <=> v1_waybel_3(C,A) ) ) ) ) ) ),
    file(waybel_8,d1_waybel_8),
    []).

fof(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

fof(d2_waybel_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_waybel_3(B,A)
          <=> r1_waybel_3(A,B,B) ) ) ) ),
    file(waybel_3,d2_waybel_3),
    []).

fof(d2_waybel_8,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_waybel_8(A,B) = a_2_0_waybel_8(A,B) ) ) ),
    file(waybel_8,d2_waybel_8),
    []).

fof(d3_waybel_8,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_waybel_8(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => B = k1_yellow_0(A,k2_waybel_8(A,B)) ) ) ) ),
    file(waybel_8,d3_waybel_8),
    []).

fof(d4_waybel_8,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_waybel_8(A)
      <=> ( ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ( ~ v1_xboole_0(k2_waybel_8(A,B))
                & v1_waybel_0(k2_waybel_8(A,B),A) ) )
          & v24_waybel_0(A)
          & v1_waybel_8(A) ) ) ) ),
    file(waybel_8,d4_waybel_8),
    []).

fof(d5_waybel_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_waybel_3(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => B = k1_yellow_0(A,k1_waybel_3(A,B)) ) ) ) ),
    file(waybel_3,d5_waybel_3),
    []).

fof(d6_waybel_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v3_waybel_3(A)
      <=> ( ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ( ~ v1_xboole_0(k1_waybel_3(A,B))
                & v1_waybel_0(k1_waybel_3(A,B),A) ) )
          & v24_waybel_0(A)
          & v2_waybel_3(A) ) ) ) ),
    file(waybel_3,d6_waybel_3),
    []).

fof(d9_lattice3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r2_lattice3(A,B,C)
          <=> ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_hidden(D,B)
                 => r1_orders_2(A,D,C) ) ) ) ) ) ),
    file(lattice3,d9_lattice3),
    []).

fof(d9_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r1_yellow_0(A,B)
           => ( C = k1_yellow_0(A,B)
            <=> ( r2_lattice3(A,B,C)
                & ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_lattice3(A,B,D)
                     => r1_orders_2(A,C,D) ) ) ) ) ) ) ) ),
    file(yellow_0,d9_yellow_0),
    []).

fof(dt_g1_orders_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ( v1_orders_2(g1_orders_2(A,B))
        & l1_orders_2(g1_orders_2(A,B)) ) ) ),
    file(orders_2,g1_orders_2),
    []).

fof(dt_k1_waybel_3,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_waybel_3(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(waybel_3,k1_waybel_3),
    []).

fof(dt_k1_waybel_8,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(k1_waybel_8(A))
        & v4_yellow_0(k1_waybel_8(A),A)
        & m1_yellow_0(k1_waybel_8(A),A) ) ) ),
    file(waybel_8,k1_waybel_8),
    []).

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

fof(dt_k1_yellow_0,axiom,(
    ! [A,B] : 
      ( l1_orders_2(A)
     => m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)) ) ),
    file(yellow_0,k1_yellow_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_waybel_8,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k2_waybel_8(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(waybel_8,k2_waybel_8),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_l1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => l1_struct_0(A) ) ),
    file(orders_2,l1_orders_2),
    []).

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

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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

fof(dt_m1_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_yellow_0(B,A)
         => l1_orders_2(B) ) ) ),
    file(yellow_0,m1_yellow_0),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_u1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ),
    file(orders_2,u1_orders_2),
    []).

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

fof(existence_l1_orders_2,axiom,(
    ? [A] : l1_orders_2(A) ),
    file(orders_2,l1_orders_2),
    []).

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

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

fof(existence_m1_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ? [B] : m1_yellow_0(B,A) ) ),
    file(yellow_0,m1_yellow_0),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_waybel_3,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => v12_waybel_0(k1_waybel_3(A,B),A) ) ),
    file(waybel_3,fc2_waybel_3),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc4_waybel_3,axiom,(
    ! [A,B] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_waybel_0(k1_waybel_3(A,B),A)
        & v12_waybel_0(k1_waybel_3(A,B),A) ) ) ),
    file(waybel_3,fc4_waybel_3),
    []).

fof(fc6_waybel_3,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_waybel_3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k1_waybel_3(A,B))
        & v1_waybel_0(k1_waybel_3(A,B),A) ) ) ),
    file(waybel_3,fc6_waybel_3),
    []).

fof(fraenkel_a_2_0_waybel_8,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_0_waybel_8(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r1_orders_2(B,D,C)
            & v1_waybel_3(D,B) ) ) ) ),
    file(waybel_8,a_2_0_waybel_8),
    []).

fof(free_g1_orders_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ! [C,D] : 
          ( g1_orders_2(A,B) = g1_orders_2(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(orders_2,g1_orders_2),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc3_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ? [B] : 
          ( m1_yellow_0(B,A)
          & v1_orders_2(B)
          & v4_yellow_0(B,A) ) ) ),
    file(yellow_0,rc3_yellow_0),
    []).

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

fof(rc4_yellow_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_yellow_0(B,A)
          & ~ v3_struct_0(B)
          & v1_orders_2(B)
          & v4_yellow_0(B,A) ) ) ),
    file(yellow_0,rc4_yellow_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc9_waybel_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_waybel_0(B,A)
          & v12_waybel_0(B,A) ) ) ),
    file(waybel_0,rc9_waybel_0),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_r3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r3_orders_2(A,B,C)
      <=> r1_orders_2(A,B,C) ) ) ),
    file(orders_2,r3_orders_2),
    []).

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

fof(reflexivity_r3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r3_orders_2(A,B,B) ) ),
    file(orders_2,r3_orders_2),
    []).

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

fof(t1_waybel_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A) )
          <=> ! [C] : 
                ( ( v1_finset_1(C)
                  & m1_subset_1(C,k1_zfmisc_1(B)) )
               => ? [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                    & r2_hidden(D,B)
                    & r2_lattice3(A,C,D) ) ) ) ) ) ),
    file(waybel_0,t1_waybel_0),
    []).

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t25_orders_2,axiom,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( r1_orders_2(A,B,C)
                  & r1_orders_2(A,C,B) )
               => B = C ) ) ) ) ),
    file(orders_2,t25_orders_2),
    []).

fof(t26_orders_2,axiom,(
    ! [A] : 
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_orders_2(A,B,C)
                      & r1_orders_2(A,C,D) )
                   => r1_orders_2(A,B,D) ) ) ) ) ) ),
    file(orders_2,t26_orders_2),
    []).

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

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t2_waybel_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r3_orders_2(A,B,C)
                          & r1_waybel_3(A,C,D)
                          & r3_orders_2(A,D,E) )
                       => r1_waybel_3(A,B,E) ) ) ) ) ) ) ),
    file(waybel_3,t2_waybel_3),
    []).

fof(t34_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( ( r1_tarski(B,C)
            & r1_yellow_0(A,B)
            & r1_yellow_0(A,C) )
         => r1_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ),
    file(yellow_0,t34_yellow_0),
    []).

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

fof(t47_yellow_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] : 
          ( ( r1_yellow_0(A,B)
            & ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_lattice3(A,B,D)
                <=> r2_lattice3(A,C,D) ) ) )
         => k1_yellow_0(A,B) = k1_yellow_0(A,C) ) ) ),
    file(yellow_0,t47_yellow_0),
    []).

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(t4_waybel_8,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k2_waybel_8(A,B))
              <=> ( r1_orders_2(A,C,B)
                  & v1_waybel_3(C,A) ) ) ) ) ) ),
    file(waybel_8,t4_waybel_8),
    []).

fof(t4_yellow_0,axiom,(
    ! [A] : 
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_orders_2(A,B,C)
               => ! [D] : 
                    ( ( r1_lattice3(A,D,C)
                     => r1_lattice3(A,D,B) )
                    & ( r2_lattice3(A,D,B)
                     => r2_lattice3(A,D,C) ) ) ) ) ) ) ),
    file(yellow_0,t4_yellow_0),
    []).

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(t6_waybel_8,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_tarski(k2_waybel_8(A,B),k1_waybel_3(A,B)) ) ) ),
    file(waybel_8,t6_waybel_8),
    []).

fof(t75_waybel_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v24_waybel_0(A)
      <=> ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => r1_yellow_0(A,B) ) ) ) ),
    file(waybel_0,t75_waybel_0),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t7_waybel_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(B,k1_waybel_3(A,C))
              <=> r1_waybel_3(A,B,C) ) ) ) ) ),
    file(waybel_3,t7_waybel_3),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

fof(t9_waybel_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r2_lattice3(A,k1_waybel_3(A,B),B) ) ) ),
    file(waybel_3,t9_waybel_3),
    []).