% Mizar problem: t162_orders_2,orders_2,1676,30 
fof(t162_orders_2,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ~ ( ! [B] : 
              ( ( v5_orders_2(B,A)
                & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
             => ? [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_hidden(D,B)
                       => r3_orders_2(A,D,C) ) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ? [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                  & r2_orders_2(A,B,C) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k3_xboole_0,commutativity_k4_subset_1,commutativity_k5_subset_1,d10_orders_2,d10_xboole_0,d11_orders_2,d12_orders_2,d13_orders_2,d14_orders_2,d16_orders_2,d17_orders_2,d1_orders_1,d1_tarski,d1_wellord1,d2_orders_1,d2_xboole_0,d3_tarski,d3_wellord1,d3_xboole_0,d4_orders_2,d4_tarski,d4_xboole_0,d5_orders_2,d5_tarski,d5_wellord1,d6_orders_2,d6_relat_2,d7_xboole_0,d9_orders_2,dt_k1_funct_1,dt_k1_orders_1,dt_k1_orders_2,dt_k1_struct_0,dt_k1_tarski,dt_k1_wellord1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_orders_2,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_orders_2,dt_k3_tarski,dt_k3_xboole_0,dt_k4_orders_2,dt_k4_subset_1,dt_k4_tarski,dt_k4_xboole_0,dt_k5_subset_1,dt_l1_orders_2,dt_l1_struct_0,dt_m1_orders_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_orders_2,dt_m2_relset_1,dt_u1_orders_2,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_orders_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_orders_2,existence_m2_relset_1,fc1_orders_1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_orders_2,fc2_subset_1,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,fc4_subset_1,fc5_orders_2,fraenkel_a_2_0_orders_2,fraenkel_a_2_1_orders_2,fraenkel_a_2_3_orders_2,fraenkel_a_3_0_orders_2,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k4_subset_1,idempotence_k5_subset_1,irreflexivity_r2_orders_2,l183_orders_2,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_orders_2,rc3_struct_0,rc5_struct_0,redefinition_k1_struct_0,redefinition_k4_subset_1,redefinition_k5_subset_1,redefinition_m2_relset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,symmetry_r1_xboole_0,t1_boole,t1_subset,t23_xboole_1,t28_orders_2,t2_boole,t2_subset,t2_tarski,t32_orders_2,t36_xboole_1,t37_xboole_1,t37_zfmisc_1,t38_orders_2,t39_zfmisc_1,t3_boole,t3_subset,t3_xboole_0,t45_xboole_1,t4_boole,t4_orders_1,t4_subset,t50_orders_2,t52_orders_2,t56_zfmisc_1,t5_subset,t65_orders_2,t6_boole,t7_boole,t7_xboole_1,t83_xboole_1,t89_orders_2,t8_boole,t92_orders_1,t93_orders_1,t94_orders_1,t95_orders_1]),
    [file(orders_2,t162_orders_2)]).

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

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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(commutativity_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(commutativity_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(d10_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_orders_2(A,B,C)
              <=> ( r1_orders_2(A,B,C)
                  & B != C ) ) ) ) ) ),
    file(orders_2,d10_orders_2),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d11_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_orders_2(B,A)
          <=> r7_relat_2(u1_orders_2(A),B) ) ) ) ),
    file(orders_2,d11_orders_2),
    []).

fof(d12_orders_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_orders_2(A,B) = a_2_0_orders_2(A,B) ) ) ),
    file(orders_2,d12_orders_2),
    []).

fof(d13_orders_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k2_orders_2(A,B) = a_2_1_orders_2(A,B) ) ) ),
    file(orders_2,d13_orders_2),
    []).

fof(d14_orders_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k3_orders_2(A,B,C) = k5_subset_1(u1_struct_0(A),k2_orders_2(A,k1_struct_0(A,C)),B) ) ) ) ),
    file(orders_2,d14_orders_2),
    []).

fof(d16_orders_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_orders_1(B,k1_orders_1(u1_struct_0(A)))
         => ! [C] : 
              ( ( v5_orders_2(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( m2_orders_2(C,A,B)
              <=> ( C != k1_xboole_0
                  & r2_wellord1(u1_orders_2(A),C)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_hidden(D,C)
                       => k1_funct_1(B,k1_orders_2(A,k3_orders_2(A,C,D))) = D ) ) ) ) ) ) ) ),
    file(orders_2,d16_orders_2),
    []).

fof(d17_orders_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_orders_1(B,k1_orders_1(u1_struct_0(A)))
         => ! [C] : 
              ( C = k4_orders_2(A,B)
            <=> ! [D] : 
                  ( r2_hidden(D,C)
                <=> m2_orders_2(D,A,B) ) ) ) ) ),
    file(orders_2,d17_orders_2),
    []).

fof(d1_orders_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ r2_hidden(k1_xboole_0,A)
       => ! [B] : 
            ( ( v1_funct_1(B)
              & v1_funct_2(B,A,k3_tarski(A))
              & m2_relset_1(B,A,k3_tarski(A)) )
           => ( m1_orders_1(B,A)
            <=> ! [C] : 
                  ( r2_hidden(C,A)
                 => r2_hidden(k1_funct_1(B,C),C) ) ) ) ) ) ),
    file(orders_1,d1_orders_1),
    []).

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d1_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( C = k1_wellord1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ( D != B
                & r2_hidden(k4_tarski(D,B),A) ) ) ) ) ),
    file(wellord1,d1_wellord1),
    []).

fof(d2_orders_1,axiom,(
    ! [A] : k1_orders_1(A) = k4_xboole_0(k1_zfmisc_1(A),k1_tarski(k1_xboole_0)) ),
    file(orders_1,d2_orders_1),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d3_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_wellord1(A,B)
        <=> ! [C] : ~ ( r1_tarski(C,B)
              & C != k1_xboole_0
              & ! [D] : ~ ( r2_hidden(D,C)
                  & r1_xboole_0(k1_wellord1(A,D),C) ) ) ) ) ),
    file(wellord1,d3_wellord1),
    []).

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d4_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v2_orders_2(A)
      <=> r1_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) ),
    file(orders_2,d4_orders_2),
    []).

fof(d4_tarski,axiom,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(d5_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v3_orders_2(A)
      <=> r8_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) ),
    file(orders_2,d5_orders_2),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d5_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r2_wellord1(A,B)
        <=> ( r1_relat_2(A,B)
            & r8_relat_2(A,B)
            & r4_relat_2(A,B)
            & r6_relat_2(A,B)
            & r1_wellord1(A,B) ) ) ) ),
    file(wellord1,d5_wellord1),
    []).

fof(d6_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v4_orders_2(A)
      <=> r4_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) ),
    file(orders_2,d6_orders_2),
    []).

fof(d6_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r6_relat_2(A,B)
        <=> ! [C,D] : ~ ( r2_hidden(C,B)
              & r2_hidden(D,B)
              & C != D
              & ~ r2_hidden(k4_tarski(C,D),A)
              & ~ r2_hidden(k4_tarski(D,C),A) ) ) ) ),
    file(relat_2,d6_relat_2),
    []).

fof(d7_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    []).

fof(d9_orders_2,axiom,(
    ! [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)
              <=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ) ),
    file(orders_2,d9_orders_2),
    []).

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

fof(dt_k1_orders_1,axiom,(
    $true ),
    file(orders_1,k1_orders_1),
    []).

fof(dt_k1_orders_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k1_orders_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(orders_2,k1_orders_2),
    []).

fof(dt_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(struct_0,k1_struct_0),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_wellord1,axiom,(
    $true ),
    file(wellord1,k1_wellord1),
    []).

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_orders_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k2_orders_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(orders_2,k2_orders_2),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(dt_k3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k3_orders_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(orders_2,k3_orders_2),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_orders_2,axiom,(
    $true ),
    file(orders_2,k4_orders_2),
    []).

fof(dt_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_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_orders_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_orders_1(B,A)
         => ( v1_funct_1(B)
            & v1_funct_2(B,A,k3_tarski(A))
            & m2_relset_1(B,A,k3_tarski(A)) ) ) ) ),
    file(orders_1,m1_orders_1),
    []).

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_m2_orders_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & m1_orders_1(B,k1_orders_1(u1_struct_0(A))) )
     => ! [C] : 
          ( m2_orders_2(C,A,B)
         => ( v5_orders_2(C,A)
            & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ),
    file(orders_2,m2_orders_2),
    []).

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_orders_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m1_orders_1(B,A) ) ),
    file(orders_1,m1_orders_1),
    []).

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_m2_orders_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & m1_orders_1(B,k1_orders_1(u1_struct_0(A))) )
     => ? [C] : m2_orders_2(C,A,B) ) ),
    file(orders_2,m2_orders_2),
    []).

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

fof(fc1_orders_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k1_orders_1(A)) ) ),
    file(orders_1,fc1_orders_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_orders_2,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(u1_orders_2(A))
        & v1_relat_2(u1_orders_2(A))
        & v4_relat_2(u1_orders_2(A))
        & v8_relat_2(u1_orders_2(A))
        & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) ),
    file(orders_2,fc2_orders_2),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

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(fc5_orders_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & m1_orders_1(B,k1_orders_1(u1_struct_0(A))) )
     => ~ v1_xboole_0(k4_orders_2(A,B)) ) ),
    file(orders_2,fc5_orders_2),
    []).

fof(fraenkel_a_2_0_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_0_orders_2(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ! [E] : 
                ( m1_subset_1(E,u1_struct_0(B))
               => ( r2_hidden(E,C)
                 => r2_orders_2(B,E,D) ) ) ) ) ) ),
    file(orders_2,a_2_0_orders_2),
    []).

fof(fraenkel_a_2_1_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_1_orders_2(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ! [E] : 
                ( m1_subset_1(E,u1_struct_0(B))
               => ( r2_hidden(E,C)
                 => r2_orders_2(B,D,E) ) ) ) ) ) ),
    file(orders_2,a_2_1_orders_2),
    []).

fof(fraenkel_a_2_3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_3_orders_2(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ! [E] : 
                ( m1_subset_1(E,u1_struct_0(B))
               => ( r2_hidden(E,k1_struct_0(B,C))
                 => r2_orders_2(B,D,E) ) ) ) ) ) ),
    file(orders_2,a_2_3_orders_2),
    []).

fof(fraenkel_a_3_0_orders_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B)
        & m1_orders_1(C,k1_orders_1(u1_struct_0(B)))
        & m2_orders_2(D,B,C) )
     => ( r2_hidden(A,a_3_0_orders_2(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(B))
            & A = E
            & ! [F] : 
                ( m1_subset_1(F,u1_struct_0(B))
               => ( r2_hidden(F,D)
                 => r2_orders_2(B,F,E) ) ) ) ) ) ),
    file(orders_2,a_3_0_orders_2),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(idempotence_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    []).

fof(idempotence_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    []).

fof(irreflexivity_r2_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ~ r2_orders_2(A,B,B) ) ),
    file(orders_2,r2_orders_2),
    []).

fof(l183_orders_2,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r2_wellord1(C,A)
          & r1_tarski(B,A) )
       => r2_wellord1(C,B) ) ) ),
    file(orders_2,l183_orders_2),
    []).

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_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v5_orders_2(B,A) ) ) ),
    file(orders_2,rc3_orders_2),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_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(redefinition_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k1_struct_0(A,B) = k1_tarski(B) ) ),
    file(struct_0,k1_struct_0),
    []).

fof(redefinition_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(redefinition_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    []).

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(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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

fof(t23_xboole_1,axiom,(
    ! [A,B,C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ),
    file(xboole_1,t23_xboole_1),
    []).

fof(t28_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))
             => ~ ( r2_orders_2(A,B,C)
                  & r2_orders_2(A,C,B) ) ) ) ) ),
    file(orders_2,t28_orders_2),
    []).

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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(t32_orders_2,axiom,(
    ! [A] : 
      ( ( v3_orders_2(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))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( ( r2_orders_2(A,B,C)
                        & r1_orders_2(A,C,D) )
                      | ( r1_orders_2(A,B,C)
                        & r2_orders_2(A,C,D) ) )
                   => r2_orders_2(A,B,D) ) ) ) ) ) ),
    file(orders_2,t32_orders_2),
    []).

fof(t36_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    []).

fof(t37_xboole_1,axiom,(
    ! [A,B] : 
      ( k4_xboole_0(A,B) = k1_xboole_0
    <=> r1_tarski(A,B) ) ),
    file(xboole_1,t37_xboole_1),
    []).

fof(t37_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    []).

fof(t38_orders_2,axiom,(
    ! [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))
             => ( ~ ( ? [D] : 
                        ( v5_orders_2(D,A)
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                        & r2_hidden(B,D)
                        & r2_hidden(C,D) )
                    & ~ r1_orders_2(A,B,C)
                    & ~ r1_orders_2(A,C,B) )
                & ~ ( ( r1_orders_2(A,B,C)
                      | r1_orders_2(A,C,B) )
                    & ! [D] : 
                        ( ( v5_orders_2(D,A)
                          & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                       => ~ ( r2_hidden(B,D)
                            & r2_hidden(C,D) ) ) ) ) ) ) ) ),
    file(orders_2,t38_orders_2),
    []).

fof(t39_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,k1_tarski(B))
    <=> ( A = k1_xboole_0
        | A = k1_tarski(B) ) ) ),
    file(zfmisc_1,t39_zfmisc_1),
    []).

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(t3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    []).

fof(t45_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => B = k2_xboole_0(A,k4_xboole_0(B,A)) ) ),
    file(xboole_1,t45_xboole_1),
    []).

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

fof(t4_orders_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ~ r2_hidden(k1_xboole_0,k1_orders_1(A)) ) ),
    file(orders_1,t4_orders_1),
    []).

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_orders_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ r2_hidden(B,k2_orders_2(A,k1_struct_0(A,B))) ) ) ),
    file(orders_2,t50_orders_2),
    []).

fof(t52_orders_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(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))
             => ( r2_orders_2(A,B,C)
              <=> r2_hidden(B,k2_orders_2(A,k1_struct_0(A,C))) ) ) ) ) ),
    file(orders_2,t52_orders_2),
    []).

fof(t56_zfmisc_1,axiom,(
    ! [A,B] : 
      ( ~ r2_hidden(A,B)
     => r1_xboole_0(k1_tarski(A),B) ) ),
    file(zfmisc_1,t56_zfmisc_1),
    []).

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(t65_orders_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r1_tarski(C,D)
                   => r1_tarski(k3_orders_2(A,C,B),k3_orders_2(A,D,B)) ) ) ) ) ) ),
    file(orders_2,t65_orders_2),
    []).

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(t7_xboole_1,axiom,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    []).

fof(t83_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k4_xboole_0(A,B) = A ) ),
    file(xboole_1,t83_xboole_1),
    []).

fof(t89_orders_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_orders_1(B,k1_orders_1(u1_struct_0(A)))
         => m2_orders_2(k3_tarski(k4_orders_2(A,B)),A,B) ) ) ),
    file(orders_2,t89_orders_2),
    []).

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

fof(t92_orders_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r7_relat_2(B,A)
      <=> ( r1_relat_2(B,A)
          & r6_relat_2(B,A) ) ) ) ),
    file(orders_1,t92_orders_1),
    []).

fof(t93_orders_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_relat_2(C,A)
          & r1_tarski(B,A) )
       => r1_relat_2(C,B) ) ) ),
    file(orders_1,t93_orders_1),
    []).

fof(t94_orders_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r4_relat_2(C,A)
          & r1_tarski(B,A) )
       => r4_relat_2(C,B) ) ) ),
    file(orders_1,t94_orders_1),
    []).

fof(t95_orders_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r8_relat_2(C,A)
          & r1_tarski(B,A) )
       => r8_relat_2(C,B) ) ) ),
    file(orders_1,t95_orders_1),
    []).