SET007 Axioms: SET007+218.ax


%------------------------------------------------------------------------------
% File     : SET007+218 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Kuratowski - Zorn Lemma
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : orders_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  207 ( 112 unit)
%            Number of atoms       :  882 (  40 equality)
%            Maximal formula depth :   18 (   5 average)
%            Number of connectives :  784 ( 109 ~  ;   4  |; 387  &)
%                                         (  27 <=>; 257 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   45 (   1 propositional; 0-3 arity)
%            Number of functors    :   23 (   1 constant; 0-3 arity)
%            Number of variables   :  271 (   0 singleton; 256 !;  15 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_orders_2,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & v1_orders_2(A) ) )).

fof(fc1_orders_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_relset_1(B,A,A) )
     => ( ~ v3_struct_0(g1_orders_2(A,B))
        & v1_orders_2(g1_orders_2(A,B)) ) ) )).

fof(rc2_orders_2,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A) ) )).

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)) ) ) )).

fof(fc3_orders_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => ( v1_orders_2(g1_orders_2(A,B))
        & v2_orders_2(g1_orders_2(A,B))
        & v3_orders_2(g1_orders_2(A,B))
        & v4_orders_2(g1_orders_2(A,B)) ) ) )).

fof(fc4_orders_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_xboole_0(k1_pre_topc(A))
        & v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A))
        & v5_orders_2(k1_pre_topc(A),A) ) ) )).

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) ) ) )).

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)) ) )).

fof(d1_orders_2,axiom,(
    $true )).

fof(d2_orders_2,axiom,(
    $true )).

fof(d3_orders_2,axiom,(
    $true )).

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)) ) ) )).

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)) ) ) )).

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)) ) ) )).

fof(d7_orders_2,axiom,(
    $true )).

fof(d8_orders_2,axiom,(
    $true )).

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)) ) ) ) ) )).

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 ) ) ) ) ) )).

fof(t1_orders_2,axiom,(
    $true )).

fof(t2_orders_2,axiom,(
    $true )).

fof(t3_orders_2,axiom,(
    $true )).

fof(t4_orders_2,axiom,(
    $true )).

fof(t5_orders_2,axiom,(
    $true )).

fof(t6_orders_2,axiom,(
    $true )).

fof(t7_orders_2,axiom,(
    $true )).

fof(t8_orders_2,axiom,(
    $true )).

fof(t9_orders_2,axiom,(
    $true )).

fof(t10_orders_2,axiom,(
    $true )).

fof(t11_orders_2,axiom,(
    $true )).

fof(t12_orders_2,axiom,(
    $true )).

fof(t13_orders_2,axiom,(
    $true )).

fof(t14_orders_2,axiom,(
    $true )).

fof(t15_orders_2,axiom,(
    $true )).

fof(t16_orders_2,axiom,(
    $true )).

fof(t17_orders_2,axiom,(
    $true )).

fof(t18_orders_2,axiom,(
    $true )).

fof(t19_orders_2,axiom,(
    $true )).

fof(t20_orders_2,axiom,(
    $true )).

fof(t21_orders_2,axiom,(
    $true )).

fof(t22_orders_2,axiom,(
    $true )).

fof(t23_orders_2,axiom,(
    $true )).

fof(t24_orders_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_orders_2(A,B,B) ) ) )).

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 ) ) ) ) )).

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) ) ) ) ) ) )).

fof(t27_orders_2,axiom,(
    $true )).

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) ) ) ) ) )).

fof(t29_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)
                      & r2_orders_2(A,C,D) )
                   => r2_orders_2(A,B,D) ) ) ) ) ) )).

fof(t30_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)
                  & r2_orders_2(A,C,B) ) ) ) ) )).

fof(t31_orders_2,axiom,(
    $true )).

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) ) ) ) ) ) )).

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) ) ) ) )).

fof(t33_orders_2,axiom,(
    $true )).

fof(t34_orders_2,axiom,(
    $true )).

fof(t35_orders_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v5_orders_2(k1_struct_0(A,B),A)
            & m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t36_orders_2,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))
             => ( ( v5_orders_2(k2_struct_0(A,B,C),A)
                  & m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))) )
              <=> ( r3_orders_2(A,B,C)
                  | r3_orders_2(A,C,B) ) ) ) ) ) )).

fof(t37_orders_2,axiom,(
    ! [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,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(C,B)
               => ( v5_orders_2(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) )).

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) ) ) ) ) ) ) ) )).

fof(t39_orders_2,axiom,(
    ! [A] :
      ( ( v2_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] :
                    ( v5_orders_2(D,A)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                    & r2_hidden(B,D)
                    & r2_hidden(C,D) )
              <=> ( r2_orders_2(A,B,C)
                <=> ~ r1_orders_2(A,C,B) ) ) ) ) ) )).

fof(t40_orders_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_wellord1(u1_orders_2(A),B)
           => ( v5_orders_2(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(t41_orders_2,axiom,(
    $true )).

fof(t42_orders_2,axiom,(
    $true )).

fof(t43_orders_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => k1_orders_2(A,k1_pre_topc(A)) = u1_struct_0(A) ) )).

fof(t44_orders_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => k1_orders_2(A,k2_pre_topc(A)) = k1_xboole_0 ) )).

fof(t45_orders_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => k2_orders_2(A,k1_pre_topc(A)) = u1_struct_0(A) ) )).

fof(t46_orders_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => k2_orders_2(A,k2_pre_topc(A)) = k1_xboole_0 ) )).

fof(t47_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)))
             => ~ ( r2_hidden(B,C)
                  & r2_hidden(B,k1_orders_2(A,C)) ) ) ) ) )).

fof(t48_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,k1_orders_2(A,k1_struct_0(A,B))) ) ) )).

fof(t49_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)))
             => ~ ( r2_hidden(B,C)
                  & r2_hidden(B,k2_orders_2(A,C)) ) ) ) ) )).

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))) ) ) )).

fof(t51_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(C,k1_orders_2(A,k1_struct_0(A,B))) ) ) ) ) )).

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))) ) ) ) ) )).

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) ) ) ) )).

fof(d15_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,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( B != k1_xboole_0
                 => ( m1_orders_2(C,A,B)
                  <=> ? [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                        & r2_hidden(D,B)
                        & C = k3_orders_2(A,B,D) ) ) )
                & ( B = k1_xboole_0
                 => ( m1_orders_2(C,A,B)
                  <=> C = k1_xboole_0 ) ) ) ) ) ) )).

fof(t53_orders_2,axiom,(
    $true )).

fof(t54_orders_2,axiom,(
    $true )).

fof(t55_orders_2,axiom,(
    $true )).

fof(t56_orders_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
             => ( r2_hidden(A,k3_orders_2(B,D,C))
              <=> ( r2_hidden(A,k2_orders_2(B,k1_struct_0(B,C)))
                  & r2_hidden(A,D) ) ) ) ) ) )).

fof(t57_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))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_hidden(B,k3_orders_2(A,D,C))
                  <=> ( r2_orders_2(A,B,C)
                      & r2_hidden(B,D) ) ) ) ) ) ) )).

fof(t58_orders_2,axiom,(
    $true )).

fof(t59_orders_2,axiom,(
    $true )).

fof(t60_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))
         => k3_orders_2(A,k1_pre_topc(A),B) = k1_xboole_0 ) ) )).

fof(t61_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)))
             => r1_tarski(k3_orders_2(A,C,B),C) ) ) ) )).

fof(t62_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)))
             => ~ r2_hidden(B,k3_orders_2(A,C,B)) ) ) ) )).

fof(t63_orders_2,axiom,(
    $true )).

fof(t64_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))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_orders_2(A,B,C)
                   => r1_tarski(k3_orders_2(A,D,B),k3_orders_2(A,D,C)) ) ) ) ) ) )).

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)) ) ) ) ) ) )).

fof(t66_orders_2,axiom,(
    $true )).

fof(t67_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_orders_2(C,A,B)
             => r1_tarski(C,B) ) ) ) )).

fof(t68_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)))
         => ( ~ ( B != k1_xboole_0
                & m1_orders_2(B,A,B) )
            & ~ ( ~ m1_orders_2(B,A,B)
                & B = k1_xboole_0 ) ) ) ) )).

fof(t69_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,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( ~ ( B = k1_xboole_0
                      & C = k1_xboole_0 )
                  & m1_orders_2(B,A,C)
                  & m1_orders_2(C,A,B) ) ) ) ) )).

fof(t70_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))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_orders_2(A,B,C)
                          & r2_hidden(B,D)
                          & r2_hidden(C,E)
                          & m1_orders_2(E,A,D) )
                       => r2_hidden(B,E) ) ) ) ) ) ) )).

fof(t71_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)))
                 => ( ( r2_hidden(B,C)
                      & m1_orders_2(C,A,D) )
                   => k3_orders_2(A,C,B) = k3_orders_2(A,D,B) ) ) ) ) ) )).

fof(t72_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,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( r1_tarski(B,C)
                  & r2_wellord1(u1_orders_2(A),C)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r2_hidden(E,B)
                              & r2_orders_2(A,D,E) )
                           => r2_hidden(D,B) ) ) )
                  & B != C
                  & ~ m1_orders_2(B,A,C) ) ) ) ) )).

fof(t73_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,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( r1_tarski(B,C)
                  & r2_wellord1(u1_orders_2(A),C)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r2_hidden(E,B)
                              & r2_hidden(D,C)
                              & r2_orders_2(A,D,E) )
                           => r2_hidden(D,B) ) ) )
                  & B != C
                  & ~ m1_orders_2(B,A,C) ) ) ) ) )).

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 ) ) ) ) ) ) ) )).

fof(t74_orders_2,axiom,(
    $true )).

fof(t75_orders_2,axiom,(
    $true )).

fof(t76_orders_2,axiom,(
    $true )).

fof(t77_orders_2,axiom,(
    $true )).

fof(t78_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(k1_tarski(k1_funct_1(B,u1_struct_0(A))),A,B) ) ) )).

fof(t79_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] :
              ( m2_orders_2(C,A,B)
             => r2_hidden(k1_funct_1(B,u1_struct_0(A)),C) ) ) ) )).

fof(t80_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))
             => ! [D] :
                  ( m1_orders_1(D,k1_orders_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m2_orders_2(E,A,D)
                     => ( ( r2_hidden(B,E)
                          & C = k1_funct_1(D,u1_struct_0(A)) )
                       => r3_orders_2(A,C,B) ) ) ) ) ) ) )).

fof(t81_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_orders_1(C,k1_orders_1(u1_struct_0(A)))
             => ! [D] :
                  ( m2_orders_2(D,A,C)
                 => ( B = k1_funct_1(C,u1_struct_0(A))
                   => k3_orders_2(A,D,B) = k1_xboole_0 ) ) ) ) ) )).

fof(t82_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] :
              ( m2_orders_2(C,A,B)
             => ! [D] :
                  ( m2_orders_2(D,A,B)
                 => ~ r1_xboole_0(C,D) ) ) ) ) )).

fof(t83_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] :
              ( m2_orders_2(C,A,B)
             => ! [D] :
                  ( m2_orders_2(D,A,B)
                 => ( C != D
                   => ( m1_orders_2(C,A,D)
                    <=> ~ m1_orders_2(D,A,C) ) ) ) ) ) ) )).

fof(t84_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] :
              ( m2_orders_2(C,A,B)
             => ! [D] :
                  ( m2_orders_2(D,A,B)
                 => ( r2_xboole_0(C,D)
                  <=> m1_orders_2(C,A,D) ) ) ) ) ) )).

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) ) ) ) ) )).

fof(t85_orders_2,axiom,(
    $true )).

fof(t86_orders_2,axiom,(
    $true )).

fof(t87_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)))
         => k3_tarski(k4_orders_2(A,B)) != k1_xboole_0 ) ) )).

fof(t88_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_orders_1(C,k1_orders_1(u1_struct_0(A)))
             => ! [D] :
                  ( m2_orders_2(D,A,C)
                 => ( B = k3_tarski(k4_orders_2(A,C))
                   => ( D = k3_tarski(k4_orders_2(A,C))
                      | m1_orders_2(D,A,B) ) ) ) ) ) ) )).

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) ) ) )).

fof(t90_orders_2,axiom,(
    $true )).

fof(t91_orders_2,axiom,(
    $true )).

fof(t92_orders_2,axiom,(
    $true )).

fof(t93_orders_2,axiom,(
    $true )).

fof(t94_orders_2,axiom,(
    $true )).

fof(t95_orders_2,axiom,(
    $true )).

fof(t96_orders_2,axiom,(
    $true )).

fof(t97_orders_2,axiom,(
    $true )).

fof(t98_orders_2,axiom,(
    $true )).

fof(t99_orders_2,axiom,(
    $true )).

fof(t100_orders_2,axiom,(
    $true )).

fof(t101_orders_2,axiom,(
    $true )).

fof(t102_orders_2,axiom,(
    $true )).

fof(t103_orders_2,axiom,(
    $true )).

fof(t104_orders_2,axiom,(
    $true )).

fof(t105_orders_2,axiom,(
    $true )).

fof(t106_orders_2,axiom,(
    $true )).

fof(t107_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)))
         => k3_relat_1(k2_wellord1(u1_orders_2(A),B)) = B ) ) )).

fof(t108_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)))
         => ( v3_orders_1(k2_wellord1(u1_orders_2(A),B))
           => ( v5_orders_2(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(t109_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] :
          ( ( v5_orders_2(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v3_orders_1(k2_wellord1(u1_orders_2(A),B)) ) ) )).

fof(t110_orders_2,axiom,(
    $true )).

fof(t111_orders_2,axiom,(
    $true )).

fof(t112_orders_2,axiom,(
    $true )).

fof(t113_orders_2,axiom,(
    $true )).

fof(t114_orders_2,axiom,(
    $true )).

fof(t115_orders_2,axiom,(
    $true )).

fof(t116_orders_2,axiom,(
    $true )).

fof(t117_orders_2,axiom,(
    $true )).

fof(t118_orders_2,axiom,(
    $true )).

fof(t119_orders_2,axiom,(
    $true )).

fof(t120_orders_2,axiom,(
    $true )).

fof(t121_orders_2,axiom,(
    $true )).

fof(t122_orders_2,axiom,(
    $true )).

fof(t123_orders_2,axiom,(
    $true )).

fof(t124_orders_2,axiom,(
    $true )).

fof(t125_orders_2,axiom,(
    $true )).

fof(t126_orders_2,axiom,(
    $true )).

fof(t127_orders_2,axiom,(
    $true )).

fof(t128_orders_2,axiom,(
    $true )).

fof(t129_orders_2,axiom,(
    $true )).

fof(t130_orders_2,axiom,(
    $true )).

fof(t131_orders_2,axiom,(
    $true )).

fof(t132_orders_2,axiom,(
    $true )).

fof(t133_orders_2,axiom,(
    $true )).

fof(t134_orders_2,axiom,(
    $true )).

fof(t135_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)))
         => ( r3_orders_1(u1_orders_2(A),B)
           => ( v5_orders_2(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(t136_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] :
          ( ( v5_orders_2(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => r3_orders_1(u1_orders_2(A),B) ) ) )).

fof(t137_orders_2,axiom,(
    $true )).

fof(t138_orders_2,axiom,(
    $true )).

fof(t139_orders_2,axiom,(
    $true )).

fof(t140_orders_2,axiom,(
    $true )).

fof(t141_orders_2,axiom,(
    $true )).

fof(t142_orders_2,axiom,(
    $true )).

fof(t143_orders_2,axiom,(
    $true )).

fof(t144_orders_2,axiom,(
    $true )).

fof(t145_orders_2,axiom,(
    $true )).

fof(t146_orders_2,axiom,(
    $true )).

fof(t147_orders_2,axiom,(
    $true )).

fof(t148_orders_2,axiom,(
    $true )).

fof(t149_orders_2,axiom,(
    $true )).

fof(t150_orders_2,axiom,(
    $true )).

fof(t151_orders_2,axiom,(
    $true )).

fof(t152_orders_2,axiom,(
    $true )).

fof(t153_orders_2,axiom,(
    $true )).

fof(t154_orders_2,axiom,(
    $true )).

fof(t155_orders_2,axiom,(
    $true )).

fof(t156_orders_2,axiom,(
    $true )).

fof(t157_orders_2,axiom,(
    $true )).

fof(t158_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))
         => ( r7_orders_1(u1_orders_2(A),B)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ r2_orders_2(A,C,B) ) ) ) ) )).

fof(t159_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))
         => ( r6_orders_1(u1_orders_2(A),B)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ r2_orders_2(A,B,C) ) ) ) ) )).

fof(t160_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))
         => ( r8_orders_1(u1_orders_2(A),B)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( B != C
                 => r2_orders_2(A,C,B) ) ) ) ) ) )).

fof(t161_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))
         => ( r9_orders_1(u1_orders_2(A),B)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( B != C
                 => r2_orders_2(A,B,C) ) ) ) ) ) )).

fof(t162_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] :
              ( ( 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) ) ) ) ) )).

fof(t163_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] :
              ( ( 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,C,D) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ? [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                  & r2_orders_2(A,C,B) ) ) ) ) )).

fof(dt_m1_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))) )
     => ! [C] :
          ( m1_orders_2(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(existence_m1_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))) )
     => ? [C] : m1_orders_2(C,A,B) ) )).

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))) ) ) ) )).

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) ) )).

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

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

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)) ) ) )).

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) ) )).

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) ) )).

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) ) ) )).

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))) ) )).

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))) ) )).

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))) ) )).

fof(dt_k4_orders_2,axiom,(
    $true )).

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)) ) )).

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)) ) ) )).

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 ) ) ) )).

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) ) ) )).

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) ) ) )).

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) ) ) ) ) ) )).

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) ) ) ) ) ) )).
%------------------------------------------------------------------------------